./PaxHeaders.21776/elk-7.2.420000644000000000000000000000013214061636525012214 xustar0030 mtime=1623670101.157096698 30 atime=1623670090.110106952 30 ctime=1623670101.157096698 elk-7.2.42/0000755002504400250440000000000014061636525014171 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/PaxHeaders.21776/src0000644000000000000000000000013114061636517012646 xustar0030 mtime=1623670095.997101488 29 atime=1623670092.98910428 30 ctime=1623670095.997101488 elk-7.2.42/src/0000755002504400250440000000000014061636517014761 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/src/PaxHeaders.21776/BLAS0000644000000000000000000000013214061636515013366 xustar0030 mtime=1623670093.105104172 30 atime=1623670092.996104273 30 ctime=1623670093.105104172 elk-7.2.42/src/BLAS/0000755002504400250440000000000014061636515015500 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/src/BLAS/PaxHeaders.21776/zdotc.f0000644000000000000000000000012714061636514014740 xustar0029 mtime=1623670092.99910427 29 atime=1623670092.99910427 29 ctime=1623670092.99910427 elk-7.2.42/src/BLAS/zdotc.f0000644002504400250440000000564414061636514017002 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZDOTC * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) * * .. Scalar Arguments .. * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*),ZY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZDOTC forms the dot product of two complex vectors *> ZDOTC = X^H * Y *> *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] ZX *> \verbatim *> ZX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim *> *> \param[in] ZY *> \verbatim *> ZY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of ZY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== COMPLEX*16 FUNCTION ZDOTC(N,ZX,INCX,ZY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,INCY,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*),ZY(*) * .. * * ===================================================================== * * .. Local Scalars .. COMPLEX*16 ZTEMP INTEGER I,IX,IY * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. ZTEMP = (0.0d0,0.0d0) ZDOTC = (0.0d0,0.0d0) IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * DO I = 1,N ZTEMP = ZTEMP + DCONJG(ZX(I))*ZY(I) END DO ELSE * * code for unequal increments or equal increments * not equal to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N ZTEMP = ZTEMP + DCONJG(ZX(IX))*ZY(IY) IX = IX + INCX IY = IY + INCY END DO END IF ZDOTC = ZTEMP RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zgerc.f0000644000000000000000000000013214061636515014724 xustar0030 mtime=1623670093.001104268 30 atime=1623670093.001104268 30 ctime=1623670093.001104268 elk-7.2.42/src/BLAS/zgerc.f0000644002504400250440000001304714061636515016766 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGERC * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA * INTEGER INCX,INCY,LDA,M,N * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGERC performs the rank 1 operation *> *> A := alpha*x*y**H + A, *> *> where alpha is a scalar, x is an m element vector, y is an n element *> vector and A is an m by n matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix A. *> M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( m - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the m *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, N ) *> Before entry, the leading m by n part of the array A must *> contain the matrix of coefficients. On exit, A is *> overwritten by the updated matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX,INCY,LDA,M,N * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,J,JY,KX * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX * .. * * Test the input parameters. * INFO = 0 IF (M.LT.0) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 5 ELSE IF (INCY.EQ.0) THEN INFO = 7 ELSE IF (LDA.LT.MAX(1,M)) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZGERC ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (INCY.GT.0) THEN JY = 1 ELSE JY = 1 - (N-1)*INCY END IF IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (Y(JY).NE.ZERO) THEN TEMP = ALPHA*DCONJG(Y(JY)) DO 10 I = 1,M A(I,J) = A(I,J) + X(I)*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (M-1)*INCX END IF DO 40 J = 1,N IF (Y(JY).NE.ZERO) THEN TEMP = ALPHA*DCONJG(Y(JY)) IX = KX DO 30 I = 1,M A(I,J) = A(I,J) + X(IX)*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of ZGERC . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dzasum.f0000644000000000000000000000013214061636515015115 xustar0030 mtime=1623670093.004104266 30 atime=1623670093.004104266 30 ctime=1623670093.004104266 elk-7.2.42/src/BLAS/dzasum.f0000644002504400250440000000507314061636515017157 0ustar00dewhurstdewhurst00000000000000*> \brief \b DZASUM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DZASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and *> returns a single precision result. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in,out] ZX *> \verbatim *> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, 3/11/78. *> modified 3/93 to return if incx .le. 0. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*) * .. * * ===================================================================== * * .. Local Scalars .. DOUBLE PRECISION STEMP INTEGER I,NINCX * .. * .. External Functions .. DOUBLE PRECISION DCABS1 EXTERNAL DCABS1 * .. DZASUM = 0.0d0 STEMP = 0.0d0 IF (N.LE.0 .OR. INCX.LE.0) RETURN IF (INCX.EQ.1) THEN * * code for increment equal to 1 * DO I = 1,N STEMP = STEMP + DCABS1(ZX(I)) END DO ELSE * * code for increment not equal to 1 * NINCX = N*INCX DO I = 1,NINCX,INCX STEMP = STEMP + DCABS1(ZX(I)) END DO END IF DZASUM = STEMP RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zherk.f0000644000000000000000000000013214061636515014735 xustar0030 mtime=1623670093.007104263 30 atime=1623670093.006104264 30 ctime=1623670093.007104263 elk-7.2.42/src/BLAS/zherk.f0000644002504400250440000002770214061636515017002 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHERK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA,BETA * INTEGER K,LDA,LDC,N * CHARACTER TRANS,UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHERK performs one of the hermitian rank k operations *> *> C := alpha*A*A**H + beta*C, *> *> or *> *> C := alpha*A**H*A + beta*C, *> *> where alpha and beta are real scalars, C is an n by n hermitian *> matrix and A is an n by k matrix in the first case and a k by n *> matrix in the second case. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array C is to be referenced as *> follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of C *> is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of C *> is to be referenced. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. *> *> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix C. N must be *> at least zero. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> On entry with TRANS = 'N' or 'n', K specifies the number *> of columns of the matrix A, and on entry with *> TRANS = 'C' or 'c', K specifies the number of rows of the *> matrix A. K must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION . *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is *> k when TRANS = 'N' or 'n', and is n otherwise. *> Before entry with TRANS = 'N' or 'n', the leading n by k *> part of the array A must contain the matrix A, otherwise *> the leading k by n part of the array A must contain the *> matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When TRANS = 'N' or 'n' *> then LDA must be at least max( 1, n ), otherwise LDA must *> be at least max( 1, k ). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION. *> On entry, BETA specifies the scalar beta. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension ( LDC, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array C must contain the upper *> triangular part of the hermitian matrix and the strictly *> lower triangular part of C is not referenced. On exit, the *> upper triangular part of the array C is overwritten by the *> upper triangular part of the updated matrix. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array C must contain the lower *> triangular part of the hermitian matrix and the strictly *> upper triangular part of C is not referenced. On exit, the *> lower triangular part of the array C is overwritten by the *> lower triangular part of the updated matrix. *> Note that the imaginary parts of the diagonal elements need *> not be set, they are assumed to be zero, and on exit they *> are set to zero. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> On entry, LDC specifies the first dimension of C as declared *> in the calling (sub) program. LDC must be at least *> max( 1, n ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> *> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. *> Ed Anderson, Cray Research Inc. *> \endverbatim *> * ===================================================================== SUBROUTINE ZHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER K,LDA,LDC,N CHARACTER TRANS,UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE,DCMPLX,DCONJG,MAX * .. * .. Local Scalars .. COMPLEX*16 TEMP DOUBLE PRECISION RTEMP INTEGER I,INFO,J,L,NROWA LOGICAL UPPER * .. * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * * Test the input parameters. * IF (LSAME(TRANS,'N')) THEN NROWA = N ELSE NROWA = K END IF UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 1 ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. + (.NOT.LSAME(TRANS,'C'))) THEN INFO = 2 ELSE IF (N.LT.0) THEN INFO = 3 ELSE IF (K.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 7 ELSE IF (LDC.LT.MAX(1,N)) THEN INFO = 10 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHERK ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (UPPER) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,J C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,J - 1 C(I,J) = BETA*C(I,J) 30 CONTINUE C(J,J) = BETA*DBLE(C(J,J)) 40 CONTINUE END IF ELSE IF (BETA.EQ.ZERO) THEN DO 60 J = 1,N DO 50 I = J,N C(I,J) = ZERO 50 CONTINUE 60 CONTINUE ELSE DO 80 J = 1,N C(J,J) = BETA*DBLE(C(J,J)) DO 70 I = J + 1,N C(I,J) = BETA*C(I,J) 70 CONTINUE 80 CONTINUE END IF END IF RETURN END IF * * Start the operations. * IF (LSAME(TRANS,'N')) THEN * * Form C := alpha*A*A**H + beta*C. * IF (UPPER) THEN DO 130 J = 1,N IF (BETA.EQ.ZERO) THEN DO 90 I = 1,J C(I,J) = ZERO 90 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 100 I = 1,J - 1 C(I,J) = BETA*C(I,J) 100 CONTINUE C(J,J) = BETA*DBLE(C(J,J)) ELSE C(J,J) = DBLE(C(J,J)) END IF DO 120 L = 1,K IF (A(J,L).NE.DCMPLX(ZERO)) THEN TEMP = ALPHA*DCONJG(A(J,L)) DO 110 I = 1,J - 1 C(I,J) = C(I,J) + TEMP*A(I,L) 110 CONTINUE C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(I,L)) END IF 120 CONTINUE 130 CONTINUE ELSE DO 180 J = 1,N IF (BETA.EQ.ZERO) THEN DO 140 I = J,N C(I,J) = ZERO 140 CONTINUE ELSE IF (BETA.NE.ONE) THEN C(J,J) = BETA*DBLE(C(J,J)) DO 150 I = J + 1,N C(I,J) = BETA*C(I,J) 150 CONTINUE ELSE C(J,J) = DBLE(C(J,J)) END IF DO 170 L = 1,K IF (A(J,L).NE.DCMPLX(ZERO)) THEN TEMP = ALPHA*DCONJG(A(J,L)) C(J,J) = DBLE(C(J,J)) + DBLE(TEMP*A(J,L)) DO 160 I = J + 1,N C(I,J) = C(I,J) + TEMP*A(I,L) 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE END IF ELSE * * Form C := alpha*A**H*A + beta*C. * IF (UPPER) THEN DO 220 J = 1,N DO 200 I = 1,J - 1 TEMP = ZERO DO 190 L = 1,K TEMP = TEMP + DCONJG(A(L,I))*A(L,J) 190 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 200 CONTINUE RTEMP = ZERO DO 210 L = 1,K RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J) 210 CONTINUE IF (BETA.EQ.ZERO) THEN C(J,J) = ALPHA*RTEMP ELSE C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J)) END IF 220 CONTINUE ELSE DO 260 J = 1,N RTEMP = ZERO DO 230 L = 1,K RTEMP = RTEMP + DCONJG(A(L,J))*A(L,J) 230 CONTINUE IF (BETA.EQ.ZERO) THEN C(J,J) = ALPHA*RTEMP ELSE C(J,J) = ALPHA*RTEMP + BETA*DBLE(C(J,J)) END IF DO 250 I = J + 1,N TEMP = ZERO DO 240 L = 1,K TEMP = TEMP + DCONJG(A(L,I))*A(L,J) 240 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 250 CONTINUE 260 CONTINUE END IF END IF * RETURN * * End of ZHERK . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zhpr.f0000644000000000000000000000013014061636515014573 xustar0029 mtime=1623670093.01010426 30 atime=1623670093.009104261 29 ctime=1623670093.01010426 elk-7.2.42/src/BLAS/zhpr.f0000644002504400250440000001767214061636515016647 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHPR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA * INTEGER INCX,N * CHARACTER UPLO * .. * .. Array Arguments .. * COMPLEX*16 AP(*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHPR performs the hermitian rank 1 operation *> *> A := alpha*x*x**H + A, *> *> where alpha is a real scalar, x is an n element vector and A is an *> n by n hermitian matrix, supplied in packed form. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: *> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. *> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is COMPLEX*16 array, dimension at least *> ( ( n*( n + 1 ) )/2 ). *> Before entry with UPLO = 'U' or 'u', the array AP must *> contain the upper triangular part of the hermitian matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) *> and a( 2, 2 ) respectively, and so on. On exit, the array *> AP is overwritten by the upper triangular part of the *> updated matrix. *> Before entry with UPLO = 'L' or 'l', the array AP must *> contain the lower triangular part of the hermitian matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) *> and a( 3, 1 ) respectively, and so on. On exit, the array *> AP is overwritten by the lower triangular part of the *> updated matrix. *> Note that the imaginary parts of the diagonal elements need *> not be set, they are assumed to be zero, and on exit they *> are set to zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX*16 AP(*),X(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,J,JX,K,KK,KX * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE,DCONJG * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 5 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHPR ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(ZERO))) RETURN * * Set the start point in X if the increment is not unity. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF (LSAME(UPLO,'U')) THEN * * Form A when upper triangle is stored in AP. * IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = ALPHA*DCONJG(X(J)) K = KK DO 10 I = 1,J - 1 AP(K) = AP(K) + X(I)*TEMP K = K + 1 10 CONTINUE AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP) ELSE AP(KK+J-1) = DBLE(AP(KK+J-1)) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = ALPHA*DCONJG(X(JX)) IX = KX DO 30 K = KK,KK + J - 2 AP(K) = AP(K) + X(IX)*TEMP IX = IX + INCX 30 CONTINUE AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP) ELSE AP(KK+J-1) = DBLE(AP(KK+J-1)) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF (INCX.EQ.1) THEN DO 60 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = ALPHA*DCONJG(X(J)) AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J)) K = KK + 1 DO 50 I = J + 1,N AP(K) = AP(K) + X(I)*TEMP K = K + 1 50 CONTINUE ELSE AP(KK) = DBLE(AP(KK)) END IF KK = KK + N - J + 1 60 CONTINUE ELSE JX = KX DO 80 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = ALPHA*DCONJG(X(JX)) AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX)) IX = JX DO 70 K = KK + 1,KK + N - J IX = IX + INCX AP(K) = AP(K) + X(IX)*TEMP 70 CONTINUE ELSE AP(KK) = DBLE(AP(KK)) END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of ZHPR . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dcabs1.f0000644000000000000000000000013214061636515014747 xustar0030 mtime=1623670093.012104258 30 atime=1623670093.012104258 30 ctime=1623670093.012104258 elk-7.2.42/src/BLAS/dcabs1.f0000644002504400250440000000256514061636515017014 0ustar00dewhurstdewhurst00000000000000*> \brief \b DCABS1 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DCABS1(Z) * * .. Scalar Arguments .. * COMPLEX*16 Z * .. * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DCABS1 computes |Re(.)| + |Im(.)| of a double complex number *> \endverbatim * * Arguments: * ========== * *> \param[in] Z *> \verbatim *> Z is COMPLEX*16 *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * * ===================================================================== DOUBLE PRECISION FUNCTION DCABS1(Z) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. COMPLEX*16 Z * .. * .. * ===================================================================== * * .. Intrinsic Functions .. INTRINSIC ABS,DBLE,DIMAG * DCABS1 = ABS(DBLE(Z)) + ABS(DIMAG(Z)) RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/xerbla.f0000644000000000000000000000013214061636515015067 xustar0030 mtime=1623670093.015104255 30 atime=1623670093.014104256 30 ctime=1623670093.015104255 elk-7.2.42/src/BLAS/xerbla.f0000644002504400250440000000415014061636515017124 0ustar00dewhurstdewhurst00000000000000*> \brief \b XERBLA * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE XERBLA( SRNAME, INFO ) * * .. Scalar Arguments .. * CHARACTER*(*) SRNAME * INTEGER INFO * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> XERBLA is an error handler for the LAPACK routines. *> It is called by an LAPACK routine if an input parameter has an *> invalid value. A message is printed and execution stops. *> *> Installers may consider modifying the STOP statement in order to *> call system-specific exception-handling facilities. *> \endverbatim * * Arguments: * ========== * *> \param[in] SRNAME *> \verbatim *> SRNAME is CHARACTER*(*) *> The name of the routine which called XERBLA. *> \endverbatim *> *> \param[in] INFO *> \verbatim *> INFO is INTEGER *> The position of the invalid parameter in the parameter list *> of the calling routine. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup aux_blas * * ===================================================================== SUBROUTINE XERBLA( SRNAME, INFO ) * * -- Reference BLAS level1 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER*(*) SRNAME INTEGER INFO * .. * * ===================================================================== * * .. Intrinsic Functions .. INTRINSIC LEN_TRIM * .. * .. Executable Statements .. * WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO * STOP * 9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ', $ 'an illegal value' ) * * End of XERBLA * END elk-7.2.42/src/BLAS/PaxHeaders.21776/Makefile0000644000000000000000000000013214061636515015103 xustar0030 mtime=1623670093.017104254 30 atime=1623670093.017104254 30 ctime=1623670093.017104254 elk-7.2.42/src/BLAS/Makefile0000644002504400250440000000215214061636515017140 0ustar00dewhurstdewhurst00000000000000 AR = ar include ../../make.inc #------------------------------------------------------------------------------- # Suffix Rules #------------------------------------------------------------------------------- .SUFFIXES: .o .f .f.o: $(F77) $(F77_OPTS) -c $< #------------------------------------------------------------------------------- # File dependencies #------------------------------------------------------------------------------- SRC = \ cdotc.f daxpy.f dcabs1.f dcopy.f ddot.f dgemm.f dgemv.f dger.f \ dnrm2.f drot.f dscal.f dspmv.f dspr2.f dswap.f dsymm.f dsymv.f \ dsyr2.f dsyr2k.f dsyrk.f dtrmm.f dtrmv.f dtrsm.f dtrsv.f dzasum.f \ dznrm2.f idamax.f izamax.f lsame.f zaxpy.f zcopy.f zdotc.f zdotu.f \ zdrot.f zdscal.f zgemm.f zgemv.f zgerc.f zgeru.f zhemm.f zhemv.f \ zher2.f zher2k.f zherk.f zhpmv.f zhpr2.f zhpr.f zscal.f zswap.f \ ztbsv.f ztpmv.f ztpsv.f ztrmm.f ztrmv.f ztrsm.f ztrsv.f OBJ = $(SRC:.f=.o) blas: $(OBJ) $(AR) -rc blas.a $(OBJ) clean: rm -f *.o *.mod *~ *.a ifc* *.gcno gmon.out ls: ls -x --tabsize=0 --width=80 *.f elk-7.2.42/src/BLAS/PaxHeaders.21776/zgemm.f0000644000000000000000000000013214061636515014731 xustar0030 mtime=1623670093.020104251 30 atime=1623670093.019104252 30 ctime=1623670093.020104251 elk-7.2.42/src/BLAS/zgemm.f0000644002504400250440000003377514061636515017005 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEMM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA,BETA * INTEGER K,LDA,LDB,LDC,M,N * CHARACTER TRANSA,TRANSB * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEMM performs one of the matrix-matrix operations *> *> C := alpha*op( A )*op( B ) + beta*C, *> *> where op( X ) is one of *> *> op( X ) = X or op( X ) = X**T or op( X ) = X**H, *> *> alpha and beta are scalars, and A, B and C are matrices, with op( A ) *> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANSA *> \verbatim *> TRANSA is CHARACTER*1 *> On entry, TRANSA specifies the form of op( A ) to be used in *> the matrix multiplication as follows: *> *> TRANSA = 'N' or 'n', op( A ) = A. *> *> TRANSA = 'T' or 't', op( A ) = A**T. *> *> TRANSA = 'C' or 'c', op( A ) = A**H. *> \endverbatim *> *> \param[in] TRANSB *> \verbatim *> TRANSB is CHARACTER*1 *> On entry, TRANSB specifies the form of op( B ) to be used in *> the matrix multiplication as follows: *> *> TRANSB = 'N' or 'n', op( B ) = B. *> *> TRANSB = 'T' or 't', op( B ) = B**T. *> *> TRANSB = 'C' or 'c', op( B ) = B**H. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix *> op( A ) and of the matrix C. M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix *> op( B ) and the number of columns of the matrix C. N must be *> at least zero. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> On entry, K specifies the number of columns of the matrix *> op( A ) and the number of rows of the matrix op( B ). K must *> be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is *> k when TRANSA = 'N' or 'n', and is m otherwise. *> Before entry with TRANSA = 'N' or 'n', the leading m by k *> part of the array A must contain the matrix A, otherwise *> the leading k by m part of the array A must contain the *> matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When TRANSA = 'N' or 'n' then *> LDA must be at least max( 1, m ), otherwise LDA must be at *> least max( 1, k ). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is *> n when TRANSB = 'N' or 'n', and is k otherwise. *> Before entry with TRANSB = 'N' or 'n', the leading k by n *> part of the array B must contain the matrix B, otherwise *> the leading n by k part of the array B must contain the *> matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. When TRANSB = 'N' or 'n' then *> LDB must be at least max( 1, k ), otherwise LDB must be at *> least max( 1, n ). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is COMPLEX*16 *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then C need not be set on input. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension ( LDC, N ) *> Before entry, the leading m by n part of the array C must *> contain the matrix C, except when beta is zero, in which *> case C need not be set on entry. *> On exit, the array C is overwritten by the m by n matrix *> ( alpha*op( A )*op( B ) + beta*C ). *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> On entry, LDC specifies the first dimension of C as declared *> in the calling (sub) program. LDC must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA,BETA INTEGER K,LDA,LDB,LDC,M,N CHARACTER TRANSA,TRANSB * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB LOGICAL CONJA,CONJB,NOTA,NOTB * .. * .. Parameters .. COMPLEX*16 ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * * Set NOTA and NOTB as true if A and B respectively are not * conjugated or transposed, set CONJA and CONJB as true if A and * B respectively are to be transposed but not conjugated and set * NROWA, NCOLA and NROWB as the number of rows and columns of A * and the number of rows of B respectively. * NOTA = LSAME(TRANSA,'N') NOTB = LSAME(TRANSB,'N') CONJA = LSAME(TRANSA,'C') CONJB = LSAME(TRANSB,'C') IF (NOTA) THEN NROWA = M NCOLA = K ELSE NROWA = K NCOLA = M END IF IF (NOTB) THEN NROWB = K ELSE NROWB = N END IF * * Test the input parameters. * INFO = 0 IF ((.NOT.NOTA) .AND. (.NOT.CONJA) .AND. + (.NOT.LSAME(TRANSA,'T'))) THEN INFO = 1 ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND. + (.NOT.LSAME(TRANSB,'T'))) THEN INFO = 2 ELSE IF (M.LT.0) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (K.LT.0) THEN INFO = 5 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 8 ELSE IF (LDB.LT.MAX(1,NROWB)) THEN INFO = 10 ELSE IF (LDC.LT.MAX(1,M)) THEN INFO = 13 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZGEMM ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,M C(I,J) = BETA*C(I,J) 30 CONTINUE 40 CONTINUE END IF RETURN END IF * * Start the operations. * IF (NOTB) THEN IF (NOTA) THEN * * Form C := alpha*A*B + beta*C. * DO 90 J = 1,N IF (BETA.EQ.ZERO) THEN DO 50 I = 1,M C(I,J) = ZERO 50 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 60 I = 1,M C(I,J) = BETA*C(I,J) 60 CONTINUE END IF DO 80 L = 1,K TEMP = ALPHA*B(L,J) DO 70 I = 1,M C(I,J) = C(I,J) + TEMP*A(I,L) 70 CONTINUE 80 CONTINUE 90 CONTINUE ELSE IF (CONJA) THEN * * Form C := alpha*A**H*B + beta*C. * DO 120 J = 1,N DO 110 I = 1,M TEMP = ZERO DO 100 L = 1,K TEMP = TEMP + DCONJG(A(L,I))*B(L,J) 100 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 110 CONTINUE 120 CONTINUE ELSE * * Form C := alpha*A**T*B + beta*C * DO 150 J = 1,N DO 140 I = 1,M TEMP = ZERO DO 130 L = 1,K TEMP = TEMP + A(L,I)*B(L,J) 130 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 140 CONTINUE 150 CONTINUE END IF ELSE IF (NOTA) THEN IF (CONJB) THEN * * Form C := alpha*A*B**H + beta*C. * DO 200 J = 1,N IF (BETA.EQ.ZERO) THEN DO 160 I = 1,M C(I,J) = ZERO 160 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 170 I = 1,M C(I,J) = BETA*C(I,J) 170 CONTINUE END IF DO 190 L = 1,K TEMP = ALPHA*DCONJG(B(J,L)) DO 180 I = 1,M C(I,J) = C(I,J) + TEMP*A(I,L) 180 CONTINUE 190 CONTINUE 200 CONTINUE ELSE * * Form C := alpha*A*B**T + beta*C * DO 250 J = 1,N IF (BETA.EQ.ZERO) THEN DO 210 I = 1,M C(I,J) = ZERO 210 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 220 I = 1,M C(I,J) = BETA*C(I,J) 220 CONTINUE END IF DO 240 L = 1,K TEMP = ALPHA*B(J,L) DO 230 I = 1,M C(I,J) = C(I,J) + TEMP*A(I,L) 230 CONTINUE 240 CONTINUE 250 CONTINUE END IF ELSE IF (CONJA) THEN IF (CONJB) THEN * * Form C := alpha*A**H*B**H + beta*C. * DO 280 J = 1,N DO 270 I = 1,M TEMP = ZERO DO 260 L = 1,K TEMP = TEMP + DCONJG(A(L,I))*DCONJG(B(J,L)) 260 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 270 CONTINUE 280 CONTINUE ELSE * * Form C := alpha*A**H*B**T + beta*C * DO 310 J = 1,N DO 300 I = 1,M TEMP = ZERO DO 290 L = 1,K TEMP = TEMP + DCONJG(A(L,I))*B(J,L) 290 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 300 CONTINUE 310 CONTINUE END IF ELSE IF (CONJB) THEN * * Form C := alpha*A**T*B**H + beta*C * DO 340 J = 1,N DO 330 I = 1,M TEMP = ZERO DO 320 L = 1,K TEMP = TEMP + A(L,I)*DCONJG(B(J,L)) 320 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 330 CONTINUE 340 CONTINUE ELSE * * Form C := alpha*A**T*B**T + beta*C * DO 370 J = 1,N DO 360 I = 1,M TEMP = ZERO DO 350 L = 1,K TEMP = TEMP + A(L,I)*B(J,L) 350 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 360 CONTINUE 370 CONTINUE END IF END IF * RETURN * * End of ZGEMM . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/ddot.f0000644000000000000000000000013214061636515014544 xustar0030 mtime=1623670093.022104249 30 atime=1623670093.022104249 30 ctime=1623670093.022104249 elk-7.2.42/src/BLAS/ddot.f0000644002504400250440000000652314061636515016607 0ustar00dewhurstdewhurst00000000000000*> \brief \b DDOT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) * * .. Scalar Arguments .. * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * DOUBLE PRECISION DX(*),DY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DDOT forms the dot product of two vectors. *> uses unrolled loops for increments equal to one. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] DX *> \verbatim *> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim *> *> \param[in] DY *> \verbatim *> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of DY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,INCY,N * .. * .. Array Arguments .. DOUBLE PRECISION DX(*),DY(*) * .. * * ===================================================================== * * .. Local Scalars .. DOUBLE PRECISION DTEMP INTEGER I,IX,IY,M,MP1 * .. * .. Intrinsic Functions .. INTRINSIC MOD * .. DDOT = 0.0d0 DTEMP = 0.0d0 IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * * * clean-up loop * M = MOD(N,5) IF (M.NE.0) THEN DO I = 1,M DTEMP = DTEMP + DX(I)*DY(I) END DO IF (N.LT.5) THEN DDOT=DTEMP RETURN END IF END IF MP1 = M + 1 DO I = MP1,N,5 DTEMP = DTEMP + DX(I)*DY(I) + DX(I+1)*DY(I+1) + $ DX(I+2)*DY(I+2) + DX(I+3)*DY(I+3) + DX(I+4)*DY(I+4) END DO ELSE * * code for unequal increments or equal increments * not equal to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N DTEMP = DTEMP + DX(IX)*DY(IY) IX = IX + INCX IY = IY + INCY END DO END IF DDOT = DTEMP RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zgemv.f0000644000000000000000000000013214061636515014742 xustar0030 mtime=1623670093.025104246 30 atime=1623670093.025104246 30 ctime=1623670093.025104246 elk-7.2.42/src/BLAS/zgemv.f0000644002504400250440000002224014061636515016777 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA,BETA * INTEGER INCX,INCY,LDA,M,N * CHARACTER TRANS * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEMV performs one of the matrix-vector operations *> *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or *> *> y := alpha*A**H*x + beta*y, *> *> where alpha and beta are scalars, x and y are vectors and A is an *> m by n matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. *> *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. *> *> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix A. *> M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, N ) *> Before entry, the leading m by n part of the array A must *> contain the matrix of coefficients. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, m ). *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' *> and at least *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. *> Before entry, the incremented array X must contain the *> vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is COMPLEX*16 *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then Y need not be set on input. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is COMPLEX*16 array, dimension at least *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' *> and at least *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. *> Before entry with BETA non-zero, the incremented array Y *> must contain the vector y. On exit, Y is overwritten by the *> updated vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA,BETA INTEGER INCX,INCY,LDA,M,N CHARACTER TRANS * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY LOGICAL NOCONJ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 1 ELSE IF (M.LT.0) THEN INFO = 2 ELSE IF (N.LT.0) THEN INFO = 3 ELSE IF (LDA.LT.MAX(1,M)) THEN INFO = 6 ELSE IF (INCX.EQ.0) THEN INFO = 8 ELSE IF (INCY.EQ.0) THEN INFO = 11 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZGEMV ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * NOCONJ = LSAME(TRANS,'T') * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF (LSAME(TRANS,'N')) THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (LENX-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (LENY-1)*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := beta*y. * IF (BETA.NE.ONE) THEN IF (INCY.EQ.1) THEN IF (BETA.EQ.ZERO) THEN DO 10 I = 1,LENY Y(I) = ZERO 10 CONTINUE ELSE DO 20 I = 1,LENY Y(I) = BETA*Y(I) 20 CONTINUE END IF ELSE IY = KY IF (BETA.EQ.ZERO) THEN DO 30 I = 1,LENY Y(IY) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40 I = 1,LENY Y(IY) = BETA*Y(IY) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF (ALPHA.EQ.ZERO) RETURN IF (LSAME(TRANS,'N')) THEN * * Form y := alpha*A*x + y. * JX = KX IF (INCY.EQ.1) THEN DO 60 J = 1,N TEMP = ALPHA*X(JX) DO 50 I = 1,M Y(I) = Y(I) + TEMP*A(I,J) 50 CONTINUE JX = JX + INCX 60 CONTINUE ELSE DO 80 J = 1,N TEMP = ALPHA*X(JX) IY = KY DO 70 I = 1,M Y(IY) = Y(IY) + TEMP*A(I,J) IY = IY + INCY 70 CONTINUE JX = JX + INCX 80 CONTINUE END IF ELSE * * Form y := alpha*A**T*x + y or y := alpha*A**H*x + y. * JY = KY IF (INCX.EQ.1) THEN DO 110 J = 1,N TEMP = ZERO IF (NOCONJ) THEN DO 90 I = 1,M TEMP = TEMP + A(I,J)*X(I) 90 CONTINUE ELSE DO 100 I = 1,M TEMP = TEMP + DCONJG(A(I,J))*X(I) 100 CONTINUE END IF Y(JY) = Y(JY) + ALPHA*TEMP JY = JY + INCY 110 CONTINUE ELSE DO 140 J = 1,N TEMP = ZERO IX = KX IF (NOCONJ) THEN DO 120 I = 1,M TEMP = TEMP + A(I,J)*X(IX) IX = IX + INCX 120 CONTINUE ELSE DO 130 I = 1,M TEMP = TEMP + DCONJG(A(I,J))*X(IX) IX = IX + INCX 130 CONTINUE END IF Y(JY) = Y(JY) + ALPHA*TEMP JY = JY + INCY 140 CONTINUE END IF END IF * RETURN * * End of ZGEMV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zhemv.f0000644000000000000000000000013214061636515014743 xustar0030 mtime=1623670093.028104243 30 atime=1623670093.028104243 30 ctime=1623670093.028104243 elk-7.2.42/src/BLAS/zhemv.f0000644002504400250440000002255414061636515017010 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHEMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA,BETA * INTEGER INCX,INCY,LDA,N * CHARACTER UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEMV performs the matrix-vector operation *> *> y := alpha*A*x + beta*y, *> *> where alpha and beta are scalars, x and y are n element vectors and *> A is an n by n hermitian matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of A *> is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of A *> is to be referenced. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular part of the hermitian matrix and the strictly *> lower triangular part of A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular part of the hermitian matrix and the strictly *> upper triangular part of A is not referenced. *> Note that the imaginary parts of the diagonal elements need *> not be set and are assumed to be zero. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is COMPLEX*16 *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then Y need not be set on input. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. On exit, Y is overwritten by the updated *> vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA,BETA INTEGER INCX,INCY,LDA,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE,DCONJG,MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 5 ELSE IF (INCX.EQ.0) THEN INFO = 7 ELSE IF (INCY.EQ.0) THEN INFO = 10 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHEMV ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * * Set up the start points in X and Y. * IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * * First form y := beta*y. * IF (BETA.NE.ONE) THEN IF (INCY.EQ.1) THEN IF (BETA.EQ.ZERO) THEN DO 10 I = 1,N Y(I) = ZERO 10 CONTINUE ELSE DO 20 I = 1,N Y(I) = BETA*Y(I) 20 CONTINUE END IF ELSE IY = KY IF (BETA.EQ.ZERO) THEN DO 30 I = 1,N Y(IY) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40 I = 1,N Y(IY) = BETA*Y(IY) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF (ALPHA.EQ.ZERO) RETURN IF (LSAME(UPLO,'U')) THEN * * Form y when A is stored in upper triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO DO 50 I = 1,J - 1 Y(I) = Y(I) + TEMP1*A(I,J) TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I) 50 CONTINUE Y(J) = Y(J) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO IX = KX IY = KY DO 70 I = 1,J - 1 Y(IY) = Y(IY) + TEMP1*A(I,J) TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE * * Form y when A is stored in lower triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 100 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO Y(J) = Y(J) + TEMP1*DBLE(A(J,J)) DO 90 I = J + 1,N Y(I) = Y(I) + TEMP1*A(I,J) TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I) 90 CONTINUE Y(J) = Y(J) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J)) IX = JX IY = JY DO 110 I = J + 1,N IX = IX + INCX IY = IY + INCY Y(IY) = Y(IY) + TEMP1*A(I,J) TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX) 110 CONTINUE Y(JY) = Y(JY) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of ZHEMV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zaxpy.f0000644000000000000000000000013214061636515014765 xustar0030 mtime=1623670093.031104241 30 atime=1623670093.031104241 30 ctime=1623670093.031104241 elk-7.2.42/src/BLAS/zaxpy.f0000644002504400250440000000600414061636515017022 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZAXPY * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) * * .. Scalar Arguments .. * COMPLEX*16 ZA * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*),ZY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZAXPY constant times a vector plus a vector. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] ZA *> \verbatim *> ZA is COMPLEX*16 *> On entry, ZA specifies the scalar alpha. *> \endverbatim *> *> \param[in] ZX *> \verbatim *> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim *> *> \param[in,out] ZY *> \verbatim *> ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of ZY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE ZAXPY(N,ZA,ZX,INCX,ZY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. COMPLEX*16 ZA INTEGER INCX,INCY,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*),ZY(*) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I,IX,IY * .. * .. External Functions .. DOUBLE PRECISION DCABS1 EXTERNAL DCABS1 * .. IF (N.LE.0) RETURN IF (DCABS1(ZA).EQ.0.0d0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * DO I = 1,N ZY(I) = ZY(I) + ZA*ZX(I) END DO ELSE * * code for unequal increments or equal increments * not equal to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N ZY(IY) = ZY(IY) + ZA*ZX(IX) IX = IX + INCX IY = IY + INCY END DO END IF * RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/daxpy.f0000644000000000000000000000013214061636515014737 xustar0030 mtime=1623670093.033104239 30 atime=1623670093.033104239 30 ctime=1623670093.033104239 elk-7.2.42/src/BLAS/daxpy.f0000644002504400250440000000664514061636515017007 0ustar00dewhurstdewhurst00000000000000*> \brief \b DAXPY * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) * * .. Scalar Arguments .. * DOUBLE PRECISION DA * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * DOUBLE PRECISION DX(*),DY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DAXPY constant times a vector plus a vector. *> uses unrolled loops for increments equal to one. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] DA *> \verbatim *> DA is DOUBLE PRECISION *> On entry, DA specifies the scalar alpha. *> \endverbatim *> *> \param[in] DX *> \verbatim *> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim *> *> \param[in,out] DY *> \verbatim *> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of DY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. DOUBLE PRECISION DA INTEGER INCX,INCY,N * .. * .. Array Arguments .. DOUBLE PRECISION DX(*),DY(*) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I,IX,IY,M,MP1 * .. * .. Intrinsic Functions .. INTRINSIC MOD * .. IF (N.LE.0) RETURN IF (DA.EQ.0.0d0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * * * clean-up loop * M = MOD(N,4) IF (M.NE.0) THEN DO I = 1,M DY(I) = DY(I) + DA*DX(I) END DO END IF IF (N.LT.4) RETURN MP1 = M + 1 DO I = MP1,N,4 DY(I) = DY(I) + DA*DX(I) DY(I+1) = DY(I+1) + DA*DX(I+1) DY(I+2) = DY(I+2) + DA*DX(I+2) DY(I+3) = DY(I+3) + DA*DX(I+3) END DO ELSE * * code for unequal increments or equal increments * not equal to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N DY(IY) = DY(IY) + DA*DX(IX) IX = IX + INCX IY = IY + INCY END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zdotu.f0000644000000000000000000000013214061636515014757 xustar0030 mtime=1623670093.035104237 30 atime=1623670093.035104237 30 ctime=1623670093.035104237 elk-7.2.42/src/BLAS/zdotu.f0000644002504400250440000000552414061636515017022 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZDOTU * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * COMPLEX*16 FUNCTION ZDOTU(N,ZX,INCX,ZY,INCY) * * .. Scalar Arguments .. * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*),ZY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZDOTU forms the dot product of two complex vectors *> ZDOTU = X^T * Y *> *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] ZX *> \verbatim *> ZX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim *> *> \param[in] ZY *> \verbatim *> ZY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of ZY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== COMPLEX*16 FUNCTION ZDOTU(N,ZX,INCX,ZY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,INCY,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*),ZY(*) * .. * * ===================================================================== * * .. Local Scalars .. COMPLEX*16 ZTEMP INTEGER I,IX,IY * .. ZTEMP = (0.0d0,0.0d0) ZDOTU = (0.0d0,0.0d0) IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * DO I = 1,N ZTEMP = ZTEMP + ZX(I)*ZY(I) END DO ELSE * * code for unequal increments or equal increments * not equal to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N ZTEMP = ZTEMP + ZX(IX)*ZY(IY) IX = IX + INCX IY = IY + INCY END DO END IF ZDOTU = ZTEMP RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zcopy.f0000644000000000000000000000013214061636515014756 xustar0030 mtime=1623670093.036104236 30 atime=1623670093.036104236 30 ctime=1623670093.036104236 elk-7.2.42/src/BLAS/zcopy.f0000644002504400250440000000526614061636515017024 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZCOPY * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) * * .. Scalar Arguments .. * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*),ZY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZCOPY copies a vector, x, to a vector, y. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] ZX *> \verbatim *> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim *> *> \param[out] ZY *> \verbatim *> ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of ZY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 4/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE ZCOPY(N,ZX,INCX,ZY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,INCY,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*),ZY(*) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I,IX,IY * .. IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * DO I = 1,N ZY(I) = ZX(I) END DO ELSE * * code for unequal increments or equal increments * not equal to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N ZY(IY) = ZX(IX) IX = IX + INCX IY = IY + INCY END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/dscal.f0000644000000000000000000000013214061636515014700 xustar0030 mtime=1623670093.038104234 30 atime=1623670093.038104234 30 ctime=1623670093.038104234 elk-7.2.42/src/BLAS/dscal.f0000644002504400250440000000566414061636515016750 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSCAL * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSCAL(N,DA,DX,INCX) * * .. Scalar Arguments .. * DOUBLE PRECISION DA * INTEGER INCX,N * .. * .. Array Arguments .. * DOUBLE PRECISION DX(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSCAL scales a vector by a constant. *> uses unrolled loops for increment equal to 1. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] DA *> \verbatim *> DA is DOUBLE PRECISION *> On entry, DA specifies the scalar alpha. *> \endverbatim *> *> \param[in,out] DX *> \verbatim *> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 3/11/78. *> modified 3/93 to return if incx .le. 0. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE DSCAL(N,DA,DX,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. DOUBLE PRECISION DA INTEGER INCX,N * .. * .. Array Arguments .. DOUBLE PRECISION DX(*) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I,M,MP1,NINCX * .. * .. Intrinsic Functions .. INTRINSIC MOD * .. IF (N.LE.0 .OR. INCX.LE.0) RETURN IF (INCX.EQ.1) THEN * * code for increment equal to 1 * * * clean-up loop * M = MOD(N,5) IF (M.NE.0) THEN DO I = 1,M DX(I) = DA*DX(I) END DO IF (N.LT.5) RETURN END IF MP1 = M + 1 DO I = MP1,N,5 DX(I) = DA*DX(I) DX(I+1) = DA*DX(I+1) DX(I+2) = DA*DX(I+2) DX(I+3) = DA*DX(I+3) DX(I+4) = DA*DX(I+4) END DO ELSE * * code for increment not equal to 1 * NINCX = N*INCX DO I = 1,NINCX,INCX DX(I) = DA*DX(I) END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/cdotc.f0000644000000000000000000000013214061636515014706 xustar0030 mtime=1623670093.040104232 30 atime=1623670093.039104233 30 ctime=1623670093.040104232 elk-7.2.42/src/BLAS/cdotc.f0000644002504400250440000000562214061636515016750 0ustar00dewhurstdewhurst00000000000000*> \brief \b CDOTC * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY) * * .. Scalar Arguments .. * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * COMPLEX CX(*),CY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CDOTC forms the dot product of two complex vectors *> CDOTC = X^H * Y *> *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] CX *> \verbatim *> CX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of CX *> \endverbatim *> *> \param[in] CY *> \verbatim *> CY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of CY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,INCY,N * .. * .. Array Arguments .. COMPLEX CX(*),CY(*) * .. * * ===================================================================== * * .. Local Scalars .. COMPLEX CTEMP INTEGER I,IX,IY * .. * .. Intrinsic Functions .. INTRINSIC CONJG * .. CTEMP = (0.0,0.0) CDOTC = (0.0,0.0) IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * DO I = 1,N CTEMP = CTEMP + CONJG(CX(I))*CY(I) END DO ELSE * * code for unequal increments or equal increments * not equal to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N CTEMP = CTEMP + CONJG(CX(IX))*CY(IY) IX = IX + INCX IY = IY + INCY END DO END IF CDOTC = CTEMP RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/dznrm2.f0000644000000000000000000000013214061636515015026 xustar0030 mtime=1623670093.041104231 30 atime=1623670093.041104231 30 ctime=1623670093.041104231 elk-7.2.42/src/BLAS/dznrm2.f0000644002504400250440000000646414061636515017075 0ustar00dewhurstdewhurst00000000000000*> \brief \b DZNRM2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * .. * .. Array Arguments .. * COMPLEX*16 X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DZNRM2 returns the euclidean norm of a vector via the function *> name, so that *> *> DZNRM2 := sqrt( x**H*x ) *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension (N) *> complex vector with N elements *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of X *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> -- This version written on 25-October-1982. *> Modified on 14-October-1993 to inline the call to ZLASSQ. *> Sven Hammarling, Nag Ltd. *> \endverbatim *> * ===================================================================== DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,N * .. * .. Array Arguments .. COMPLEX*16 X(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION NORM,SCALE,SSQ,TEMP INTEGER IX * .. * .. Intrinsic Functions .. INTRINSIC ABS,DBLE,DIMAG,SQRT * .. IF (N.LT.1 .OR. INCX.LT.1) THEN NORM = ZERO ELSE SCALE = ZERO SSQ = ONE * The following loop is equivalent to this call to the LAPACK * auxiliary routine: * CALL ZLASSQ( N, X, INCX, SCALE, SSQ ) * DO 10 IX = 1,1 + (N-1)*INCX,INCX IF (DBLE(X(IX)).NE.ZERO) THEN TEMP = ABS(DBLE(X(IX))) IF (SCALE.LT.TEMP) THEN SSQ = ONE + SSQ* (SCALE/TEMP)**2 SCALE = TEMP ELSE SSQ = SSQ + (TEMP/SCALE)**2 END IF END IF IF (DIMAG(X(IX)).NE.ZERO) THEN TEMP = ABS(DIMAG(X(IX))) IF (SCALE.LT.TEMP) THEN SSQ = ONE + SSQ* (SCALE/TEMP)**2 SCALE = TEMP ELSE SSQ = SSQ + (TEMP/SCALE)**2 END IF END IF 10 CONTINUE NORM = SCALE*SQRT(SSQ) END IF * DZNRM2 = NORM RETURN * * End of DZNRM2. * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dnrm2.f0000644000000000000000000000012714061636515014640 xustar0029 mtime=1623670093.04310423 29 atime=1623670093.04210423 29 ctime=1623670093.04310423 elk-7.2.42/src/BLAS/dnrm2.f0000644002504400250440000000600114061636515016666 0ustar00dewhurstdewhurst00000000000000*> \brief \b DNRM2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * .. * .. Array Arguments .. * DOUBLE PRECISION X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DNRM2 returns the euclidean norm of a vector via the function *> name, so that *> *> DNRM2 := sqrt( x'*x ) *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> -- This version written on 25-October-1982. *> Modified on 14-October-1993 to inline the call to DLASSQ. *> Sven Hammarling, Nag Ltd. *> \endverbatim *> * ===================================================================== DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,N * .. * .. Array Arguments .. DOUBLE PRECISION X(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION ABSXI,NORM,SCALE,SSQ INTEGER IX * .. * .. Intrinsic Functions .. INTRINSIC ABS,SQRT * .. IF (N.LT.1 .OR. INCX.LT.1) THEN NORM = ZERO ELSE IF (N.EQ.1) THEN NORM = ABS(X(1)) ELSE SCALE = ZERO SSQ = ONE * The following loop is equivalent to this call to the LAPACK * auxiliary routine: * CALL DLASSQ( N, X, INCX, SCALE, SSQ ) * DO 10 IX = 1,1 + (N-1)*INCX,INCX IF (X(IX).NE.ZERO) THEN ABSXI = ABS(X(IX)) IF (SCALE.LT.ABSXI) THEN SSQ = ONE + SSQ* (SCALE/ABSXI)**2 SCALE = ABSXI ELSE SSQ = SSQ + (ABSXI/SCALE)**2 END IF END IF 10 CONTINUE NORM = SCALE*SQRT(SSQ) END IF * DNRM2 = NORM RETURN * * End of DNRM2. * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dcopy.f0000644000000000000000000000013214061636515014730 xustar0030 mtime=1623670093.044104228 30 atime=1623670093.044104228 30 ctime=1623670093.044104228 elk-7.2.42/src/BLAS/dcopy.f0000644002504400250440000000632314061636515016771 0ustar00dewhurstdewhurst00000000000000*> \brief \b DCOPY * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) * * .. Scalar Arguments .. * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * DOUBLE PRECISION DX(*),DY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DCOPY copies a vector, x, to a vector, y. *> uses unrolled loops for increments equal to 1. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] DX *> \verbatim *> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim *> *> \param[out] DY *> \verbatim *> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of DY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,INCY,N * .. * .. Array Arguments .. DOUBLE PRECISION DX(*),DY(*) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I,IX,IY,M,MP1 * .. * .. Intrinsic Functions .. INTRINSIC MOD * .. IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * * * clean-up loop * M = MOD(N,7) IF (M.NE.0) THEN DO I = 1,M DY(I) = DX(I) END DO IF (N.LT.7) RETURN END IF MP1 = M + 1 DO I = MP1,N,7 DY(I) = DX(I) DY(I+1) = DX(I+1) DY(I+2) = DX(I+2) DY(I+3) = DX(I+3) DY(I+4) = DX(I+4) DY(I+5) = DX(I+5) DY(I+6) = DX(I+6) END DO ELSE * * code for unequal increments or equal increments * not equal to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N DY(IY) = DX(IX) IX = IX + INCX IY = IY + INCY END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/dgemm.f0000644000000000000000000000013214061636515014703 xustar0030 mtime=1623670093.046104227 30 atime=1623670093.045104228 30 ctime=1623670093.046104227 elk-7.2.42/src/BLAS/dgemm.f0000644002504400250440000002555714061636515016756 0ustar00dewhurstdewhurst00000000000000*> \brief \b DGEMM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA,BETA * INTEGER K,LDA,LDB,LDC,M,N * CHARACTER TRANSA,TRANSB * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGEMM performs one of the matrix-matrix operations *> *> C := alpha*op( A )*op( B ) + beta*C, *> *> where op( X ) is one of *> *> op( X ) = X or op( X ) = X**T, *> *> alpha and beta are scalars, and A, B and C are matrices, with op( A ) *> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANSA *> \verbatim *> TRANSA is CHARACTER*1 *> On entry, TRANSA specifies the form of op( A ) to be used in *> the matrix multiplication as follows: *> *> TRANSA = 'N' or 'n', op( A ) = A. *> *> TRANSA = 'T' or 't', op( A ) = A**T. *> *> TRANSA = 'C' or 'c', op( A ) = A**T. *> \endverbatim *> *> \param[in] TRANSB *> \verbatim *> TRANSB is CHARACTER*1 *> On entry, TRANSB specifies the form of op( B ) to be used in *> the matrix multiplication as follows: *> *> TRANSB = 'N' or 'n', op( B ) = B. *> *> TRANSB = 'T' or 't', op( B ) = B**T. *> *> TRANSB = 'C' or 'c', op( B ) = B**T. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix *> op( A ) and of the matrix C. M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix *> op( B ) and the number of columns of the matrix C. N must be *> at least zero. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> On entry, K specifies the number of columns of the matrix *> op( A ) and the number of rows of the matrix op( B ). K must *> be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is *> k when TRANSA = 'N' or 'n', and is m otherwise. *> Before entry with TRANSA = 'N' or 'n', the leading m by k *> part of the array A must contain the matrix A, otherwise *> the leading k by m part of the array A must contain the *> matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When TRANSA = 'N' or 'n' then *> LDA must be at least max( 1, m ), otherwise LDA must be at *> least max( 1, k ). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is *> n when TRANSB = 'N' or 'n', and is k otherwise. *> Before entry with TRANSB = 'N' or 'n', the leading k by n *> part of the array B must contain the matrix B, otherwise *> the leading n by k part of the array B must contain the *> matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. When TRANSB = 'N' or 'n' then *> LDB must be at least max( 1, k ), otherwise LDB must be at *> least max( 1, n ). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION. *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then C need not be set on input. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension ( LDC, N ) *> Before entry, the leading m by n part of the array C must *> contain the matrix C, except when beta is zero, in which *> case C need not be set on entry. *> On exit, the array C is overwritten by the m by n matrix *> ( alpha*op( A )*op( B ) + beta*C ). *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> On entry, LDC specifies the first dimension of C as declared *> in the calling (sub) program. LDC must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER K,LDA,LDB,LDC,M,N CHARACTER TRANSA,TRANSB * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB LOGICAL NOTA,NOTB * .. * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * * Set NOTA and NOTB as true if A and B respectively are not * transposed and set NROWA, NCOLA and NROWB as the number of rows * and columns of A and the number of rows of B respectively. * NOTA = LSAME(TRANSA,'N') NOTB = LSAME(TRANSB,'N') IF (NOTA) THEN NROWA = M NCOLA = K ELSE NROWA = K NCOLA = M END IF IF (NOTB) THEN NROWB = K ELSE NROWB = N END IF * * Test the input parameters. * INFO = 0 IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND. + (.NOT.LSAME(TRANSA,'T'))) THEN INFO = 1 ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND. + (.NOT.LSAME(TRANSB,'T'))) THEN INFO = 2 ELSE IF (M.LT.0) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (K.LT.0) THEN INFO = 5 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 8 ELSE IF (LDB.LT.MAX(1,NROWB)) THEN INFO = 10 ELSE IF (LDC.LT.MAX(1,M)) THEN INFO = 13 END IF IF (INFO.NE.0) THEN CALL XERBLA('DGEMM ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN * * And if alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,M C(I,J) = BETA*C(I,J) 30 CONTINUE 40 CONTINUE END IF RETURN END IF * * Start the operations. * IF (NOTB) THEN IF (NOTA) THEN * * Form C := alpha*A*B + beta*C. * DO 90 J = 1,N IF (BETA.EQ.ZERO) THEN DO 50 I = 1,M C(I,J) = ZERO 50 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 60 I = 1,M C(I,J) = BETA*C(I,J) 60 CONTINUE END IF DO 80 L = 1,K TEMP = ALPHA*B(L,J) DO 70 I = 1,M C(I,J) = C(I,J) + TEMP*A(I,L) 70 CONTINUE 80 CONTINUE 90 CONTINUE ELSE * * Form C := alpha*A**T*B + beta*C * DO 120 J = 1,N DO 110 I = 1,M TEMP = ZERO DO 100 L = 1,K TEMP = TEMP + A(L,I)*B(L,J) 100 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 110 CONTINUE 120 CONTINUE END IF ELSE IF (NOTA) THEN * * Form C := alpha*A*B**T + beta*C * DO 170 J = 1,N IF (BETA.EQ.ZERO) THEN DO 130 I = 1,M C(I,J) = ZERO 130 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 140 I = 1,M C(I,J) = BETA*C(I,J) 140 CONTINUE END IF DO 160 L = 1,K TEMP = ALPHA*B(J,L) DO 150 I = 1,M C(I,J) = C(I,J) + TEMP*A(I,L) 150 CONTINUE 160 CONTINUE 170 CONTINUE ELSE * * Form C := alpha*A**T*B**T + beta*C * DO 200 J = 1,N DO 190 I = 1,M TEMP = ZERO DO 180 L = 1,K TEMP = TEMP + A(L,I)*B(J,L) 180 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 190 CONTINUE 200 CONTINUE END IF END IF * RETURN * * End of DGEMM . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/lsame.f0000644000000000000000000000013214061636515014713 xustar0030 mtime=1623670093.047104226 30 atime=1623670093.047104226 30 ctime=1623670093.047104226 elk-7.2.42/src/BLAS/lsame.f0000644002504400250440000000610114061636515016746 0ustar00dewhurstdewhurst00000000000000*> \brief \b LSAME * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * LOGICAL FUNCTION LSAME(CA,CB) * * .. Scalar Arguments .. * CHARACTER CA,CB * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> LSAME returns .TRUE. if CA is the same letter as CB regardless of *> case. *> \endverbatim * * Arguments: * ========== * *> \param[in] CA *> \verbatim *> CA is CHARACTER*1 *> \endverbatim *> *> \param[in] CB *> \verbatim *> CB is CHARACTER*1 *> CA and CB specify the single characters to be compared. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup aux_blas * * ===================================================================== LOGICAL FUNCTION LSAME(CA,CB) * * -- Reference BLAS level1 routine (version 3.1) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER CA,CB * .. * * ===================================================================== * * .. Intrinsic Functions .. INTRINSIC ICHAR * .. * .. Local Scalars .. INTEGER INTA,INTB,ZCODE * .. * * Test if the characters are equal * LSAME = CA .EQ. CB IF (LSAME) RETURN * * Now test for equivalence if both characters are alphabetic. * ZCODE = ICHAR('Z') * * Use 'Z' rather than 'A' so that ASCII can be detected on Prime * machines, on which ICHAR returns a value with bit 8 set. * ICHAR('A') on Prime machines returns 193 which is the same as * ICHAR('A') on an EBCDIC machine. * INTA = ICHAR(CA) INTB = ICHAR(CB) * IF (ZCODE.EQ.90 .OR. ZCODE.EQ.122) THEN * * ASCII is assumed - ZCODE is the ASCII code of either lower or * upper case 'Z'. * IF (INTA.GE.97 .AND. INTA.LE.122) INTA = INTA - 32 IF (INTB.GE.97 .AND. INTB.LE.122) INTB = INTB - 32 * ELSE IF (ZCODE.EQ.233 .OR. ZCODE.EQ.169) THEN * * EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or * upper case 'Z'. * IF (INTA.GE.129 .AND. INTA.LE.137 .OR. + INTA.GE.145 .AND. INTA.LE.153 .OR. + INTA.GE.162 .AND. INTA.LE.169) INTA = INTA + 64 IF (INTB.GE.129 .AND. INTB.LE.137 .OR. + INTB.GE.145 .AND. INTB.LE.153 .OR. + INTB.GE.162 .AND. INTB.LE.169) INTB = INTB + 64 * ELSE IF (ZCODE.EQ.218 .OR. ZCODE.EQ.250) THEN * * ASCII is assumed, on Prime machines - ZCODE is the ASCII code * plus 128 of either lower or upper case 'Z'. * IF (INTA.GE.225 .AND. INTA.LE.250) INTA = INTA - 32 IF (INTB.GE.225 .AND. INTB.LE.250) INTB = INTB - 32 END IF LSAME = INTA .EQ. INTB * * RETURN * * End of LSAME * END elk-7.2.42/src/BLAS/PaxHeaders.21776/drot.f0000644000000000000000000000013214061636515014562 xustar0030 mtime=1623670093.049104224 30 atime=1623670093.049104224 30 ctime=1623670093.049104224 elk-7.2.42/src/BLAS/drot.f0000644002504400250440000000614014061636515016620 0ustar00dewhurstdewhurst00000000000000*> \brief \b DROT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) * * .. Scalar Arguments .. * DOUBLE PRECISION C,S * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * DOUBLE PRECISION DX(*),DY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DROT applies a plane rotation. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in,out] DX *> \verbatim *> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim *> *> \param[in,out] DY *> \verbatim *> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of DY *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION *> \endverbatim *> *> \param[in] S *> \verbatim *> S is DOUBLE PRECISION *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. DOUBLE PRECISION C,S INTEGER INCX,INCY,N * .. * .. Array Arguments .. DOUBLE PRECISION DX(*),DY(*) * .. * * ===================================================================== * * .. Local Scalars .. DOUBLE PRECISION DTEMP INTEGER I,IX,IY * .. IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * DO I = 1,N DTEMP = C*DX(I) + S*DY(I) DY(I) = C*DY(I) - S*DX(I) DX(I) = DTEMP END DO ELSE * * code for unequal increments or equal increments not equal * to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N DTEMP = C*DX(IX) + S*DY(IY) DY(IY) = C*DY(IY) - S*DX(IX) DX(IX) = DTEMP IX = IX + INCX IY = IY + INCY END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/dswap.f0000644000000000000000000000013214061636515014730 xustar0030 mtime=1623670093.050104223 30 atime=1623670093.050104223 30 ctime=1623670093.050104223 elk-7.2.42/src/BLAS/dswap.f0000644002504400250440000000660514061636515016774 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSWAP * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) * * .. Scalar Arguments .. * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * DOUBLE PRECISION DX(*),DY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSWAP interchanges two vectors. *> uses unrolled loops for increments equal to 1. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in,out] DX *> \verbatim *> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim *> *> \param[in,out] DY *> \verbatim *> DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of DY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup double_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,INCY,N * .. * .. Array Arguments .. DOUBLE PRECISION DX(*),DY(*) * .. * * ===================================================================== * * .. Local Scalars .. DOUBLE PRECISION DTEMP INTEGER I,IX,IY,M,MP1 * .. * .. Intrinsic Functions .. INTRINSIC MOD * .. IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 * * * clean-up loop * M = MOD(N,3) IF (M.NE.0) THEN DO I = 1,M DTEMP = DX(I) DX(I) = DY(I) DY(I) = DTEMP END DO IF (N.LT.3) RETURN END IF MP1 = M + 1 DO I = MP1,N,3 DTEMP = DX(I) DX(I) = DY(I) DY(I) = DTEMP DTEMP = DX(I+1) DX(I+1) = DY(I+1) DY(I+1) = DTEMP DTEMP = DX(I+2) DX(I+2) = DY(I+2) DY(I+2) = DTEMP END DO ELSE * * code for unequal increments or equal increments not equal * to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N DTEMP = DX(IX) DX(IX) = DY(IY) DY(IY) = DTEMP IX = IX + INCX IY = IY + INCY END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/idamax.f0000644000000000000000000000013214061636515015055 xustar0030 mtime=1623670093.052104221 30 atime=1623670093.052104221 30 ctime=1623670093.052104221 elk-7.2.42/src/BLAS/idamax.f0000644002504400250440000000534314061636515017117 0ustar00dewhurstdewhurst00000000000000*> \brief \b IDAMAX * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * INTEGER FUNCTION IDAMAX(N,DX,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * .. * .. Array Arguments .. * DOUBLE PRECISION DX(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> IDAMAX finds the index of the first element having maximum absolute value. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] DX *> \verbatim *> DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of DX *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup aux_blas * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, linpack, 3/11/78. *> modified 3/93 to return if incx .le. 0. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== INTEGER FUNCTION IDAMAX(N,DX,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,N * .. * .. Array Arguments .. DOUBLE PRECISION DX(*) * .. * * ===================================================================== * * .. Local Scalars .. DOUBLE PRECISION DMAX INTEGER I,IX * .. * .. Intrinsic Functions .. INTRINSIC DABS * .. IDAMAX = 0 IF (N.LT.1 .OR. INCX.LE.0) RETURN IDAMAX = 1 IF (N.EQ.1) RETURN IF (INCX.EQ.1) THEN * * code for increment equal to 1 * DMAX = DABS(DX(1)) DO I = 2,N IF (DABS(DX(I)).GT.DMAX) THEN IDAMAX = I DMAX = DABS(DX(I)) END IF END DO ELSE * * code for increment not equal to 1 * IX = 1 DMAX = DABS(DX(1)) IX = IX + INCX DO I = 2,N IF (DABS(DX(IX)).GT.DMAX) THEN IDAMAX = I DMAX = DABS(DX(IX)) END IF IX = IX + INCX END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/dtrsm.f0000644000000000000000000000012714061636515014747 xustar0029 mtime=1623670093.05310422 29 atime=1623670093.05310422 29 ctime=1623670093.05310422 elk-7.2.42/src/BLAS/dtrsm.f0000644002504400250440000003273414061636515017011 0ustar00dewhurstdewhurst00000000000000*> \brief \b DTRSM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA * INTEGER LDA,LDB,M,N * CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),B(LDB,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTRSM solves one of the matrix equations *> *> op( A )*X = alpha*B, or X*op( A ) = alpha*B, *> *> where alpha is a scalar, X and B are m by n matrices, A is a unit, or *> non-unit, upper or lower triangular matrix and op( A ) is one of *> *> op( A ) = A or op( A ) = A**T. *> *> The matrix X is overwritten on B. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether op( A ) appears on the left *> or right of X as follows: *> *> SIDE = 'L' or 'l' op( A )*X = alpha*B. *> *> SIDE = 'R' or 'r' X*op( A ) = alpha*B. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix A is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANSA *> \verbatim *> TRANSA is CHARACTER*1 *> On entry, TRANSA specifies the form of op( A ) to be used in *> the matrix multiplication as follows: *> *> TRANSA = 'N' or 'n' op( A ) = A. *> *> TRANSA = 'T' or 't' op( A ) = A**T. *> *> TRANSA = 'C' or 'c' op( A ) = A**T. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit triangular *> as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of B. M must be at *> least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of B. N must be *> at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. When alpha is *> zero then A is not referenced and B need not be set before *> entry. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, k ), *> where k is m when SIDE = 'L' or 'l' *> and k is n when SIDE = 'R' or 'r'. *> Before entry with UPLO = 'U' or 'u', the leading k by k *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading k by k *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When SIDE = 'L' or 'l' then *> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' *> then LDA must be at least max( 1, n ). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension ( LDB, N ) *> Before entry, the leading m by n part of the array B must *> contain the right-hand side matrix B, and on exit is *> overwritten by the solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. LDB must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER LDA,LDB,M,N CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),B(LDB,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,J,K,NROWA LOGICAL LSIDE,NOUNIT,UPPER * .. * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * * Test the input parameters. * LSIDE = LSAME(SIDE,'L') IF (LSIDE) THEN NROWA = M ELSE NROWA = N END IF NOUNIT = LSAME(DIAG,'N') UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN INFO = 1 ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 2 ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. + (.NOT.LSAME(TRANSA,'T')) .AND. + (.NOT.LSAME(TRANSA,'C'))) THEN INFO = 3 ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN INFO = 4 ELSE IF (M.LT.0) THEN INFO = 5 ELSE IF (N.LT.0) THEN INFO = 6 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 9 ELSE IF (LDB.LT.MAX(1,M)) THEN INFO = 11 END IF IF (INFO.NE.0) THEN CALL XERBLA('DTRSM ',INFO) RETURN END IF * * Quick return if possible. * IF (M.EQ.0 .OR. N.EQ.0) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M B(I,J) = ZERO 10 CONTINUE 20 CONTINUE RETURN END IF * * Start the operations. * IF (LSIDE) THEN IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*inv( A )*B. * IF (UPPER) THEN DO 60 J = 1,N IF (ALPHA.NE.ONE) THEN DO 30 I = 1,M B(I,J) = ALPHA*B(I,J) 30 CONTINUE END IF DO 50 K = M,1,-1 IF (B(K,J).NE.ZERO) THEN IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) DO 40 I = 1,K - 1 B(I,J) = B(I,J) - B(K,J)*A(I,K) 40 CONTINUE END IF 50 CONTINUE 60 CONTINUE ELSE DO 100 J = 1,N IF (ALPHA.NE.ONE) THEN DO 70 I = 1,M B(I,J) = ALPHA*B(I,J) 70 CONTINUE END IF DO 90 K = 1,M IF (B(K,J).NE.ZERO) THEN IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) DO 80 I = K + 1,M B(I,J) = B(I,J) - B(K,J)*A(I,K) 80 CONTINUE END IF 90 CONTINUE 100 CONTINUE END IF ELSE * * Form B := alpha*inv( A**T )*B. * IF (UPPER) THEN DO 130 J = 1,N DO 120 I = 1,M TEMP = ALPHA*B(I,J) DO 110 K = 1,I - 1 TEMP = TEMP - A(K,I)*B(K,J) 110 CONTINUE IF (NOUNIT) TEMP = TEMP/A(I,I) B(I,J) = TEMP 120 CONTINUE 130 CONTINUE ELSE DO 160 J = 1,N DO 150 I = M,1,-1 TEMP = ALPHA*B(I,J) DO 140 K = I + 1,M TEMP = TEMP - A(K,I)*B(K,J) 140 CONTINUE IF (NOUNIT) TEMP = TEMP/A(I,I) B(I,J) = TEMP 150 CONTINUE 160 CONTINUE END IF END IF ELSE IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*B*inv( A ). * IF (UPPER) THEN DO 210 J = 1,N IF (ALPHA.NE.ONE) THEN DO 170 I = 1,M B(I,J) = ALPHA*B(I,J) 170 CONTINUE END IF DO 190 K = 1,J - 1 IF (A(K,J).NE.ZERO) THEN DO 180 I = 1,M B(I,J) = B(I,J) - A(K,J)*B(I,K) 180 CONTINUE END IF 190 CONTINUE IF (NOUNIT) THEN TEMP = ONE/A(J,J) DO 200 I = 1,M B(I,J) = TEMP*B(I,J) 200 CONTINUE END IF 210 CONTINUE ELSE DO 260 J = N,1,-1 IF (ALPHA.NE.ONE) THEN DO 220 I = 1,M B(I,J) = ALPHA*B(I,J) 220 CONTINUE END IF DO 240 K = J + 1,N IF (A(K,J).NE.ZERO) THEN DO 230 I = 1,M B(I,J) = B(I,J) - A(K,J)*B(I,K) 230 CONTINUE END IF 240 CONTINUE IF (NOUNIT) THEN TEMP = ONE/A(J,J) DO 250 I = 1,M B(I,J) = TEMP*B(I,J) 250 CONTINUE END IF 260 CONTINUE END IF ELSE * * Form B := alpha*B*inv( A**T ). * IF (UPPER) THEN DO 310 K = N,1,-1 IF (NOUNIT) THEN TEMP = ONE/A(K,K) DO 270 I = 1,M B(I,K) = TEMP*B(I,K) 270 CONTINUE END IF DO 290 J = 1,K - 1 IF (A(J,K).NE.ZERO) THEN TEMP = A(J,K) DO 280 I = 1,M B(I,J) = B(I,J) - TEMP*B(I,K) 280 CONTINUE END IF 290 CONTINUE IF (ALPHA.NE.ONE) THEN DO 300 I = 1,M B(I,K) = ALPHA*B(I,K) 300 CONTINUE END IF 310 CONTINUE ELSE DO 360 K = 1,N IF (NOUNIT) THEN TEMP = ONE/A(K,K) DO 320 I = 1,M B(I,K) = TEMP*B(I,K) 320 CONTINUE END IF DO 340 J = K + 1,N IF (A(J,K).NE.ZERO) THEN TEMP = A(J,K) DO 330 I = 1,M B(I,J) = B(I,J) - TEMP*B(I,K) 330 CONTINUE END IF 340 CONTINUE IF (ALPHA.NE.ONE) THEN DO 350 I = 1,M B(I,K) = ALPHA*B(I,K) 350 CONTINUE END IF 360 CONTINUE END IF END IF END IF * RETURN * * End of DTRSM . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dgemv.f0000644000000000000000000000013214061636515014714 xustar0030 mtime=1623670093.055104218 30 atime=1623670093.055104218 30 ctime=1623670093.055104218 elk-7.2.42/src/BLAS/dgemv.f0000644002504400250440000002107314061636515016754 0ustar00dewhurstdewhurst00000000000000*> \brief \b DGEMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA,BETA * INTEGER INCX,INCY,LDA,M,N * CHARACTER TRANS * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGEMV performs one of the matrix-vector operations *> *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, *> *> where alpha and beta are scalars, x and y are vectors and A is an *> m by n matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. *> *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. *> *> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix A. *> M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, N ) *> Before entry, the leading m by n part of the array A must *> contain the matrix of coefficients. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, m ). *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' *> and at least *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. *> Before entry, the incremented array X must contain the *> vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION. *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then Y need not be set on input. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is DOUBLE PRECISION array, dimension at least *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' *> and at least *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. *> Before entry with BETA non-zero, the incremented array Y *> must contain the vector y. On exit, Y is overwritten by the *> updated vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER INCX,INCY,LDA,M,N CHARACTER TRANS * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 1 ELSE IF (M.LT.0) THEN INFO = 2 ELSE IF (N.LT.0) THEN INFO = 3 ELSE IF (LDA.LT.MAX(1,M)) THEN INFO = 6 ELSE IF (INCX.EQ.0) THEN INFO = 8 ELSE IF (INCY.EQ.0) THEN INFO = 11 END IF IF (INFO.NE.0) THEN CALL XERBLA('DGEMV ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF (LSAME(TRANS,'N')) THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (LENX-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (LENY-1)*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := beta*y. * IF (BETA.NE.ONE) THEN IF (INCY.EQ.1) THEN IF (BETA.EQ.ZERO) THEN DO 10 I = 1,LENY Y(I) = ZERO 10 CONTINUE ELSE DO 20 I = 1,LENY Y(I) = BETA*Y(I) 20 CONTINUE END IF ELSE IY = KY IF (BETA.EQ.ZERO) THEN DO 30 I = 1,LENY Y(IY) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40 I = 1,LENY Y(IY) = BETA*Y(IY) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF (ALPHA.EQ.ZERO) RETURN IF (LSAME(TRANS,'N')) THEN * * Form y := alpha*A*x + y. * JX = KX IF (INCY.EQ.1) THEN DO 60 J = 1,N TEMP = ALPHA*X(JX) DO 50 I = 1,M Y(I) = Y(I) + TEMP*A(I,J) 50 CONTINUE JX = JX + INCX 60 CONTINUE ELSE DO 80 J = 1,N TEMP = ALPHA*X(JX) IY = KY DO 70 I = 1,M Y(IY) = Y(IY) + TEMP*A(I,J) IY = IY + INCY 70 CONTINUE JX = JX + INCX 80 CONTINUE END IF ELSE * * Form y := alpha*A**T*x + y. * JY = KY IF (INCX.EQ.1) THEN DO 100 J = 1,N TEMP = ZERO DO 90 I = 1,M TEMP = TEMP + A(I,J)*X(I) 90 CONTINUE Y(JY) = Y(JY) + ALPHA*TEMP JY = JY + INCY 100 CONTINUE ELSE DO 120 J = 1,N TEMP = ZERO IX = KX DO 110 I = 1,M TEMP = TEMP + A(I,J)*X(IX) IX = IX + INCX 110 CONTINUE Y(JY) = Y(JY) + ALPHA*TEMP JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of DGEMV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dtrmm.f0000644000000000000000000000013214061636515014735 xustar0030 mtime=1623670093.057104216 30 atime=1623670093.057104216 30 ctime=1623670093.057104216 elk-7.2.42/src/BLAS/dtrmm.f0000644002504400250440000003100714061636515016773 0ustar00dewhurstdewhurst00000000000000*> \brief \b DTRMM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA * INTEGER LDA,LDB,M,N * CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),B(LDB,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTRMM performs one of the matrix-matrix operations *> *> B := alpha*op( A )*B, or B := alpha*B*op( A ), *> *> where alpha is a scalar, B is an m by n matrix, A is a unit, or *> non-unit, upper or lower triangular matrix and op( A ) is one of *> *> op( A ) = A or op( A ) = A**T. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether op( A ) multiplies B from *> the left or right as follows: *> *> SIDE = 'L' or 'l' B := alpha*op( A )*B. *> *> SIDE = 'R' or 'r' B := alpha*B*op( A ). *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix A is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANSA *> \verbatim *> TRANSA is CHARACTER*1 *> On entry, TRANSA specifies the form of op( A ) to be used in *> the matrix multiplication as follows: *> *> TRANSA = 'N' or 'n' op( A ) = A. *> *> TRANSA = 'T' or 't' op( A ) = A**T. *> *> TRANSA = 'C' or 'c' op( A ) = A**T. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit triangular *> as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of B. M must be at *> least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of B. N must be *> at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. When alpha is *> zero then A is not referenced and B need not be set before *> entry. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m *> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. *> Before entry with UPLO = 'U' or 'u', the leading k by k *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading k by k *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When SIDE = 'L' or 'l' then *> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' *> then LDA must be at least max( 1, n ). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension ( LDB, N ) *> Before entry, the leading m by n part of the array B must *> contain the matrix B, and on exit is overwritten by the *> transformed matrix. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. LDB must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER LDA,LDB,M,N CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),B(LDB,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,J,K,NROWA LOGICAL LSIDE,NOUNIT,UPPER * .. * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * * Test the input parameters. * LSIDE = LSAME(SIDE,'L') IF (LSIDE) THEN NROWA = M ELSE NROWA = N END IF NOUNIT = LSAME(DIAG,'N') UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN INFO = 1 ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 2 ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. + (.NOT.LSAME(TRANSA,'T')) .AND. + (.NOT.LSAME(TRANSA,'C'))) THEN INFO = 3 ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN INFO = 4 ELSE IF (M.LT.0) THEN INFO = 5 ELSE IF (N.LT.0) THEN INFO = 6 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 9 ELSE IF (LDB.LT.MAX(1,M)) THEN INFO = 11 END IF IF (INFO.NE.0) THEN CALL XERBLA('DTRMM ',INFO) RETURN END IF * * Quick return if possible. * IF (M.EQ.0 .OR. N.EQ.0) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M B(I,J) = ZERO 10 CONTINUE 20 CONTINUE RETURN END IF * * Start the operations. * IF (LSIDE) THEN IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*A*B. * IF (UPPER) THEN DO 50 J = 1,N DO 40 K = 1,M IF (B(K,J).NE.ZERO) THEN TEMP = ALPHA*B(K,J) DO 30 I = 1,K - 1 B(I,J) = B(I,J) + TEMP*A(I,K) 30 CONTINUE IF (NOUNIT) TEMP = TEMP*A(K,K) B(K,J) = TEMP END IF 40 CONTINUE 50 CONTINUE ELSE DO 80 J = 1,N DO 70 K = M,1,-1 IF (B(K,J).NE.ZERO) THEN TEMP = ALPHA*B(K,J) B(K,J) = TEMP IF (NOUNIT) B(K,J) = B(K,J)*A(K,K) DO 60 I = K + 1,M B(I,J) = B(I,J) + TEMP*A(I,K) 60 CONTINUE END IF 70 CONTINUE 80 CONTINUE END IF ELSE * * Form B := alpha*A**T*B. * IF (UPPER) THEN DO 110 J = 1,N DO 100 I = M,1,-1 TEMP = B(I,J) IF (NOUNIT) TEMP = TEMP*A(I,I) DO 90 K = 1,I - 1 TEMP = TEMP + A(K,I)*B(K,J) 90 CONTINUE B(I,J) = ALPHA*TEMP 100 CONTINUE 110 CONTINUE ELSE DO 140 J = 1,N DO 130 I = 1,M TEMP = B(I,J) IF (NOUNIT) TEMP = TEMP*A(I,I) DO 120 K = I + 1,M TEMP = TEMP + A(K,I)*B(K,J) 120 CONTINUE B(I,J) = ALPHA*TEMP 130 CONTINUE 140 CONTINUE END IF END IF ELSE IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*B*A. * IF (UPPER) THEN DO 180 J = N,1,-1 TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(J,J) DO 150 I = 1,M B(I,J) = TEMP*B(I,J) 150 CONTINUE DO 170 K = 1,J - 1 IF (A(K,J).NE.ZERO) THEN TEMP = ALPHA*A(K,J) DO 160 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE ELSE DO 220 J = 1,N TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(J,J) DO 190 I = 1,M B(I,J) = TEMP*B(I,J) 190 CONTINUE DO 210 K = J + 1,N IF (A(K,J).NE.ZERO) THEN TEMP = ALPHA*A(K,J) DO 200 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 200 CONTINUE END IF 210 CONTINUE 220 CONTINUE END IF ELSE * * Form B := alpha*B*A**T. * IF (UPPER) THEN DO 260 K = 1,N DO 240 J = 1,K - 1 IF (A(J,K).NE.ZERO) THEN TEMP = ALPHA*A(J,K) DO 230 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 230 CONTINUE END IF 240 CONTINUE TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(K,K) IF (TEMP.NE.ONE) THEN DO 250 I = 1,M B(I,K) = TEMP*B(I,K) 250 CONTINUE END IF 260 CONTINUE ELSE DO 300 K = N,1,-1 DO 280 J = K + 1,N IF (A(J,K).NE.ZERO) THEN TEMP = ALPHA*A(J,K) DO 270 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 270 CONTINUE END IF 280 CONTINUE TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(K,K) IF (TEMP.NE.ONE) THEN DO 290 I = 1,M B(I,K) = TEMP*B(I,K) 290 CONTINUE END IF 300 CONTINUE END IF END IF END IF * RETURN * * End of DTRMM . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dger.f0000644000000000000000000000013214061636515014533 xustar0030 mtime=1623670093.059104215 30 atime=1623670093.058104216 30 ctime=1623670093.059104215 elk-7.2.42/src/BLAS/dger.f0000644002504400250440000001307514061636515016576 0ustar00dewhurstdewhurst00000000000000*> \brief \b DGER * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA * INTEGER INCX,INCY,LDA,M,N * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGER performs the rank 1 operation *> *> A := alpha*x*y**T + A, *> *> where alpha is a scalar, x is an m element vector, y is an n element *> vector and A is an m by n matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix A. *> M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension at least *> ( 1 + ( m - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the m *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, N ) *> Before entry, the leading m by n part of the array A must *> contain the matrix of coefficients. On exit, A is *> overwritten by the updated matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX,INCY,LDA,M,N * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER (ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,IX,J,JY,KX * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * * Test the input parameters. * INFO = 0 IF (M.LT.0) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 5 ELSE IF (INCY.EQ.0) THEN INFO = 7 ELSE IF (LDA.LT.MAX(1,M)) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('DGER ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (INCY.GT.0) THEN JY = 1 ELSE JY = 1 - (N-1)*INCY END IF IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (Y(JY).NE.ZERO) THEN TEMP = ALPHA*Y(JY) DO 10 I = 1,M A(I,J) = A(I,J) + X(I)*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (M-1)*INCX END IF DO 40 J = 1,N IF (Y(JY).NE.ZERO) THEN TEMP = ALPHA*Y(JY) IX = KX DO 30 I = 1,M A(I,J) = A(I,J) + X(IX)*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of DGER . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dtrmv.f0000644000000000000000000000013214061636515014746 xustar0030 mtime=1623670093.060104214 30 atime=1623670093.060104214 30 ctime=1623670093.060104214 elk-7.2.42/src/BLAS/dtrmv.f0000644002504400250440000002362014061636515017006 0ustar00dewhurstdewhurst00000000000000*> \brief \b DTRMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,LDA,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTRMV performs one of the matrix-vector operations *> *> x := A*x, or x := A**T*x, *> *> where x is an n element vector and A is an n by n unit, or non-unit, *> upper or lower triangular matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' x := A*x. *> *> TRANS = 'T' or 't' x := A**T*x. *> *> TRANS = 'C' or 'c' x := A**T*x. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit *> triangular as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. On exit, X is overwritten with the *> transformed vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX,LDA,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),X(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER (ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,IX,J,JX,KX LOGICAL NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 6 ELSE IF (INCX.EQ.0) THEN INFO = 8 END IF IF (INFO.NE.0) THEN CALL XERBLA('DTRMV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (LSAME(TRANS,'N')) THEN * * Form x := A*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = X(J) DO 10 I = 1,J - 1 X(I) = X(I) + TEMP*A(I,J) 10 CONTINUE IF (NOUNIT) X(J) = X(J)*A(J,J) END IF 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 30 I = 1,J - 1 X(IX) = X(IX) + TEMP*A(I,J) IX = IX + INCX 30 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(J,J) END IF JX = JX + INCX 40 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 60 J = N,1,-1 IF (X(J).NE.ZERO) THEN TEMP = X(J) DO 50 I = N,J + 1,-1 X(I) = X(I) + TEMP*A(I,J) 50 CONTINUE IF (NOUNIT) X(J) = X(J)*A(J,J) END IF 60 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 80 J = N,1,-1 IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 70 I = N,J + 1,-1 X(IX) = X(IX) + TEMP*A(I,J) IX = IX - INCX 70 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(J,J) END IF JX = JX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A**T*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 100 J = N,1,-1 TEMP = X(J) IF (NOUNIT) TEMP = TEMP*A(J,J) DO 90 I = J - 1,1,-1 TEMP = TEMP + A(I,J)*X(I) 90 CONTINUE X(J) = TEMP 100 CONTINUE ELSE JX = KX + (N-1)*INCX DO 120 J = N,1,-1 TEMP = X(JX) IX = JX IF (NOUNIT) TEMP = TEMP*A(J,J) DO 110 I = J - 1,1,-1 IX = IX - INCX TEMP = TEMP + A(I,J)*X(IX) 110 CONTINUE X(JX) = TEMP JX = JX - INCX 120 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 140 J = 1,N TEMP = X(J) IF (NOUNIT) TEMP = TEMP*A(J,J) DO 130 I = J + 1,N TEMP = TEMP + A(I,J)*X(I) 130 CONTINUE X(J) = TEMP 140 CONTINUE ELSE JX = KX DO 160 J = 1,N TEMP = X(JX) IX = JX IF (NOUNIT) TEMP = TEMP*A(J,J) DO 150 I = J + 1,N IX = IX + INCX TEMP = TEMP + A(I,J)*X(IX) 150 CONTINUE X(JX) = TEMP JX = JX + INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of DTRMV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dsymv.f0000644000000000000000000000013214061636515014754 xustar0030 mtime=1623670093.062104212 30 atime=1623670093.062104212 30 ctime=1623670093.062104212 elk-7.2.42/src/BLAS/dsymv.f0000644002504400250440000002226514061636515017020 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA,BETA * INTEGER INCX,INCY,LDA,N * CHARACTER UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYMV performs the matrix-vector operation *> *> y := alpha*A*x + beta*y, *> *> where alpha and beta are scalars, x and y are n element vectors and *> A is an n by n symmetric matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of A *> is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of A *> is to be referenced. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular part of the symmetric matrix and the strictly *> lower triangular part of A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular part of the symmetric matrix and the strictly *> upper triangular part of A is not referenced. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION. *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then Y need not be set on input. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. On exit, Y is overwritten by the updated *> vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER INCX,INCY,LDA,N CHARACTER UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 5 ELSE IF (INCX.EQ.0) THEN INFO = 7 ELSE IF (INCY.EQ.0) THEN INFO = 10 END IF IF (INFO.NE.0) THEN CALL XERBLA('DSYMV ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * * Set up the start points in X and Y. * IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * * First form y := beta*y. * IF (BETA.NE.ONE) THEN IF (INCY.EQ.1) THEN IF (BETA.EQ.ZERO) THEN DO 10 I = 1,N Y(I) = ZERO 10 CONTINUE ELSE DO 20 I = 1,N Y(I) = BETA*Y(I) 20 CONTINUE END IF ELSE IY = KY IF (BETA.EQ.ZERO) THEN DO 30 I = 1,N Y(IY) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40 I = 1,N Y(IY) = BETA*Y(IY) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF (ALPHA.EQ.ZERO) RETURN IF (LSAME(UPLO,'U')) THEN * * Form y when A is stored in upper triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO DO 50 I = 1,J - 1 Y(I) = Y(I) + TEMP1*A(I,J) TEMP2 = TEMP2 + A(I,J)*X(I) 50 CONTINUE Y(J) = Y(J) + TEMP1*A(J,J) + ALPHA*TEMP2 60 CONTINUE ELSE JX = KX JY = KY DO 80 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO IX = KX IY = KY DO 70 I = 1,J - 1 Y(IY) = Y(IY) + TEMP1*A(I,J) TEMP2 = TEMP2 + A(I,J)*X(IX) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y(JY) = Y(JY) + TEMP1*A(J,J) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF ELSE * * Form y when A is stored in lower triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 100 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO Y(J) = Y(J) + TEMP1*A(J,J) DO 90 I = J + 1,N Y(I) = Y(I) + TEMP1*A(I,J) TEMP2 = TEMP2 + A(I,J)*X(I) 90 CONTINUE Y(J) = Y(J) + ALPHA*TEMP2 100 CONTINUE ELSE JX = KX JY = KY DO 120 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO Y(JY) = Y(JY) + TEMP1*A(J,J) IX = JX IY = JY DO 110 I = J + 1,N IX = IX + INCX IY = IY + INCY Y(IY) = Y(IY) + TEMP1*A(I,J) TEMP2 = TEMP2 + A(I,J)*X(IX) 110 CONTINUE Y(JY) = Y(JY) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * End of DSYMV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dsyrk.f0000644000000000000000000000013014061636515014744 xustar0029 mtime=1623670093.06410421 30 atime=1623670093.063104211 29 ctime=1623670093.06410421 elk-7.2.42/src/BLAS/dsyrk.f0000644002504400250440000002505614061636515017013 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYRK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA,BETA * INTEGER K,LDA,LDC,N * CHARACTER TRANS,UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYRK performs one of the symmetric rank k operations *> *> C := alpha*A*A**T + beta*C, *> *> or *> *> C := alpha*A**T*A + beta*C, *> *> where alpha and beta are scalars, C is an n by n symmetric matrix *> and A is an n by k matrix in the first case and a k by n matrix *> in the second case. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array C is to be referenced as *> follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of C *> is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of C *> is to be referenced. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. *> *> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. *> *> TRANS = 'C' or 'c' C := alpha*A**T*A + beta*C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix C. N must be *> at least zero. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> On entry with TRANS = 'N' or 'n', K specifies the number *> of columns of the matrix A, and on entry with *> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number *> of rows of the matrix A. K must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is *> k when TRANS = 'N' or 'n', and is n otherwise. *> Before entry with TRANS = 'N' or 'n', the leading n by k *> part of the array A must contain the matrix A, otherwise *> the leading k by n part of the array A must contain the *> matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When TRANS = 'N' or 'n' *> then LDA must be at least max( 1, n ), otherwise LDA must *> be at least max( 1, k ). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION. *> On entry, BETA specifies the scalar beta. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension ( LDC, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array C must contain the upper *> triangular part of the symmetric matrix and the strictly *> lower triangular part of C is not referenced. On exit, the *> upper triangular part of the array C is overwritten by the *> upper triangular part of the updated matrix. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array C must contain the lower *> triangular part of the symmetric matrix and the strictly *> upper triangular part of C is not referenced. On exit, the *> lower triangular part of the array C is overwritten by the *> lower triangular part of the updated matrix. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> On entry, LDC specifies the first dimension of C as declared *> in the calling (sub) program. LDC must be at least *> max( 1, n ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER K,LDA,LDC,N CHARACTER TRANS,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,J,L,NROWA LOGICAL UPPER * .. * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * * Test the input parameters. * IF (LSAME(TRANS,'N')) THEN NROWA = N ELSE NROWA = K END IF UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 1 ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. + (.NOT.LSAME(TRANS,'T')) .AND. + (.NOT.LSAME(TRANS,'C'))) THEN INFO = 2 ELSE IF (N.LT.0) THEN INFO = 3 ELSE IF (K.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 7 ELSE IF (LDC.LT.MAX(1,N)) THEN INFO = 10 END IF IF (INFO.NE.0) THEN CALL XERBLA('DSYRK ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (UPPER) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,J C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,J C(I,J) = BETA*C(I,J) 30 CONTINUE 40 CONTINUE END IF ELSE IF (BETA.EQ.ZERO) THEN DO 60 J = 1,N DO 50 I = J,N C(I,J) = ZERO 50 CONTINUE 60 CONTINUE ELSE DO 80 J = 1,N DO 70 I = J,N C(I,J) = BETA*C(I,J) 70 CONTINUE 80 CONTINUE END IF END IF RETURN END IF * * Start the operations. * IF (LSAME(TRANS,'N')) THEN * * Form C := alpha*A*A**T + beta*C. * IF (UPPER) THEN DO 130 J = 1,N IF (BETA.EQ.ZERO) THEN DO 90 I = 1,J C(I,J) = ZERO 90 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 100 I = 1,J C(I,J) = BETA*C(I,J) 100 CONTINUE END IF DO 120 L = 1,K IF (A(J,L).NE.ZERO) THEN TEMP = ALPHA*A(J,L) DO 110 I = 1,J C(I,J) = C(I,J) + TEMP*A(I,L) 110 CONTINUE END IF 120 CONTINUE 130 CONTINUE ELSE DO 180 J = 1,N IF (BETA.EQ.ZERO) THEN DO 140 I = J,N C(I,J) = ZERO 140 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 150 I = J,N C(I,J) = BETA*C(I,J) 150 CONTINUE END IF DO 170 L = 1,K IF (A(J,L).NE.ZERO) THEN TEMP = ALPHA*A(J,L) DO 160 I = J,N C(I,J) = C(I,J) + TEMP*A(I,L) 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE END IF ELSE * * Form C := alpha*A**T*A + beta*C. * IF (UPPER) THEN DO 210 J = 1,N DO 200 I = 1,J TEMP = ZERO DO 190 L = 1,K TEMP = TEMP + A(L,I)*A(L,J) 190 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 200 CONTINUE 210 CONTINUE ELSE DO 240 J = 1,N DO 230 I = J,N TEMP = ZERO DO 220 L = 1,K TEMP = TEMP + A(L,I)*A(L,J) 220 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP ELSE C(I,J) = ALPHA*TEMP + BETA*C(I,J) END IF 230 CONTINUE 240 CONTINUE END IF END IF * RETURN * * End of DSYRK . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dspmv.f0000644000000000000000000000013214061636515014743 xustar0030 mtime=1623670093.066104208 30 atime=1623670093.065104209 30 ctime=1623670093.066104208 elk-7.2.42/src/BLAS/dspmv.f0000644002504400250440000002237214061636515017006 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSPMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA,BETA * INTEGER INCX,INCY,N * CHARACTER UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION AP(*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSPMV performs the matrix-vector operation *> *> y := alpha*A*x + beta*y, *> *> where alpha and beta are scalars, x and y are n element vectors and *> A is an n by n symmetric matrix, supplied in packed form. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: *> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. *> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is DOUBLE PRECISION array, dimension at least *> ( ( n*( n + 1 ) )/2 ). *> Before entry with UPLO = 'U' or 'u', the array AP must *> contain the upper triangular part of the symmetric matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) *> and a( 2, 2 ) respectively, and so on. *> Before entry with UPLO = 'L' or 'l', the array AP must *> contain the lower triangular part of the symmetric matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) *> and a( 3, 1 ) respectively, and so on. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION. *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then Y need not be set on input. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. On exit, Y is overwritten by the updated *> vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER INCX,INCY,N CHARACTER UPLO * .. * .. Array Arguments .. DOUBLE PRECISION AP(*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 6 ELSE IF (INCY.EQ.0) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('DSPMV ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * * Set up the start points in X and Y. * IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * * First form y := beta*y. * IF (BETA.NE.ONE) THEN IF (INCY.EQ.1) THEN IF (BETA.EQ.ZERO) THEN DO 10 I = 1,N Y(I) = ZERO 10 CONTINUE ELSE DO 20 I = 1,N Y(I) = BETA*Y(I) 20 CONTINUE END IF ELSE IY = KY IF (BETA.EQ.ZERO) THEN DO 30 I = 1,N Y(IY) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40 I = 1,N Y(IY) = BETA*Y(IY) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF (ALPHA.EQ.ZERO) RETURN KK = 1 IF (LSAME(UPLO,'U')) THEN * * Form y when AP contains the upper triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO K = KK DO 50 I = 1,J - 1 Y(I) = Y(I) + TEMP1*AP(K) TEMP2 = TEMP2 + AP(K)*X(I) K = K + 1 50 CONTINUE Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 KK = KK + J 60 CONTINUE ELSE JX = KX JY = KY DO 80 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO IX = KX IY = KY DO 70 K = KK,KK + J - 2 Y(IY) = Y(IY) + TEMP1*AP(K) TEMP2 = TEMP2 + AP(K)*X(IX) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + J 80 CONTINUE END IF ELSE * * Form y when AP contains the lower triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 100 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO Y(J) = Y(J) + TEMP1*AP(KK) K = KK + 1 DO 90 I = J + 1,N Y(I) = Y(I) + TEMP1*AP(K) TEMP2 = TEMP2 + AP(K)*X(I) K = K + 1 90 CONTINUE Y(J) = Y(J) + ALPHA*TEMP2 KK = KK + (N-J+1) 100 CONTINUE ELSE JX = KX JY = KY DO 120 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO Y(JY) = Y(JY) + TEMP1*AP(KK) IX = JX IY = JY DO 110 K = KK + 1,KK + N - J IX = IX + INCX IY = IY + INCY Y(IY) = Y(IY) + TEMP1*AP(K) TEMP2 = TEMP2 + AP(K)*X(IX) 110 CONTINUE Y(JY) = Y(JY) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + (N-J+1) 120 CONTINUE END IF END IF * RETURN * * End of DSPMV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dspr2.f0000644000000000000000000000013214061636515014644 xustar0030 mtime=1623670093.067104207 30 atime=1623670093.067104207 30 ctime=1623670093.067104207 elk-7.2.42/src/BLAS/dspr2.f0000644002504400250440000002064614061636515016711 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSPR2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA * INTEGER INCX,INCY,N * CHARACTER UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION AP(*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSPR2 performs the symmetric rank 2 operation *> *> A := alpha*x*y**T + alpha*y*x**T + A, *> *> where alpha is a scalar, x and y are n element vectors and A is an *> n by n symmetric matrix, supplied in packed form. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: *> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. *> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is DOUBLE PRECISION array, dimension at least *> ( ( n*( n + 1 ) )/2 ). *> Before entry with UPLO = 'U' or 'u', the array AP must *> contain the upper triangular part of the symmetric matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) *> and a( 2, 2 ) respectively, and so on. On exit, the array *> AP is overwritten by the upper triangular part of the *> updated matrix. *> Before entry with UPLO = 'L' or 'l', the array AP must *> contain the lower triangular part of the symmetric matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) *> and a( 3, 1 ) respectively, and so on. On exit, the array *> AP is overwritten by the lower triangular part of the *> updated matrix. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX,INCY,N CHARACTER UPLO * .. * .. Array Arguments .. DOUBLE PRECISION AP(*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER (ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 5 ELSE IF (INCY.EQ.0) THEN INFO = 7 END IF IF (INFO.NE.0) THEN CALL XERBLA('DSPR2 ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF (LSAME(UPLO,'U')) THEN * * Form A when upper triangle is stored in AP. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 20 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*Y(J) TEMP2 = ALPHA*X(J) K = KK DO 10 I = 1,J AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 K = K + 1 10 CONTINUE END IF KK = KK + J 20 CONTINUE ELSE DO 40 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*Y(JY) TEMP2 = ALPHA*X(JX) IX = KX IY = KY DO 30 K = KK,KK + J - 1 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*Y(J) TEMP2 = ALPHA*X(J) K = KK DO 50 I = J,N AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 K = K + 1 50 CONTINUE END IF KK = KK + N - J + 1 60 CONTINUE ELSE DO 80 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*Y(JY) TEMP2 = ALPHA*X(JX) IX = JX IY = JY DO 70 K = KK,KK + N - J AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of DSPR2 . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dsyr2.f0000644000000000000000000000013214061636515014655 xustar0030 mtime=1623670093.069104205 30 atime=1623670093.069104205 30 ctime=1623670093.069104205 elk-7.2.42/src/BLAS/dsyr2.f0000644002504400250440000002062214061636515016714 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYR2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA * INTEGER INCX,INCY,LDA,N * CHARACTER UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYR2 performs the symmetric rank 2 operation *> *> A := alpha*x*y**T + alpha*y*x**T + A, *> *> where alpha is a scalar, x and y are n element vectors and A is an n *> by n symmetric matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of A *> is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of A *> is to be referenced. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular part of the symmetric matrix and the strictly *> lower triangular part of A is not referenced. On exit, the *> upper triangular part of the array A is overwritten by the *> upper triangular part of the updated matrix. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular part of the symmetric matrix and the strictly *> upper triangular part of A is not referenced. On exit, the *> lower triangular part of the array A is overwritten by the *> lower triangular part of the updated matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX,INCY,LDA,N CHARACTER UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER (ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 5 ELSE IF (INCY.EQ.0) THEN INFO = 7 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('DSYR2 ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF (LSAME(UPLO,'U')) THEN * * Form A when A is stored in the upper triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 20 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*Y(J) TEMP2 = ALPHA*X(J) DO 10 I = 1,J A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 10 CONTINUE END IF 20 CONTINUE ELSE DO 40 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*Y(JY) TEMP2 = ALPHA*X(JX) IX = KX IY = KY DO 30 I = 1,J A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE * * Form A when A is stored in the lower triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*Y(J) TEMP2 = ALPHA*X(J) DO 50 I = J,N A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 50 CONTINUE END IF 60 CONTINUE ELSE DO 80 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*Y(JY) TEMP2 = ALPHA*X(JX) IX = JX IY = JY DO 70 I = J,N A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF * RETURN * * End of DSYR2 . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dtrsv.f0000644000000000000000000000013214061636515014754 xustar0030 mtime=1623670093.071104203 30 atime=1623670093.071104203 30 ctime=1623670093.071104203 elk-7.2.42/src/BLAS/dtrsv.f0000644002504400250440000002361414061636515017017 0ustar00dewhurstdewhurst00000000000000*> \brief \b DTRSV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,LDA,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTRSV solves one of the systems of equations *> *> A*x = b, or A**T*x = b, *> *> where b and x are n element vectors and A is an n by n unit, or *> non-unit, upper or lower triangular matrix. *> *> No test for singularity or near-singularity is included in this *> routine. Such tests must be performed before calling this routine. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the equations to be solved as *> follows: *> *> TRANS = 'N' or 'n' A*x = b. *> *> TRANS = 'T' or 't' A**T*x = b. *> *> TRANS = 'C' or 'c' A**T*x = b. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit *> triangular as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element right-hand side vector b. On exit, X is overwritten *> with the solution vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level1 * * ===================================================================== SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * -- Reference BLAS level1 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX,LDA,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),X(*) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER (ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I,INFO,IX,J,JX,KX LOGICAL NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 6 ELSE IF (INCX.EQ.0) THEN INFO = 8 END IF IF (INFO.NE.0) THEN CALL XERBLA('DTRSV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (LSAME(TRANS,'N')) THEN * * Form x := inv( A )*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 20 J = N,1,-1 IF (X(J).NE.ZERO) THEN IF (NOUNIT) X(J) = X(J)/A(J,J) TEMP = X(J) DO 10 I = J - 1,1,-1 X(I) = X(I) - TEMP*A(I,J) 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX + (N-1)*INCX DO 40 J = N,1,-1 IF (X(JX).NE.ZERO) THEN IF (NOUNIT) X(JX) = X(JX)/A(J,J) TEMP = X(JX) IX = JX DO 30 I = J - 1,1,-1 IX = IX - INCX X(IX) = X(IX) - TEMP*A(I,J) 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 60 J = 1,N IF (X(J).NE.ZERO) THEN IF (NOUNIT) X(J) = X(J)/A(J,J) TEMP = X(J) DO 50 I = J + 1,N X(I) = X(I) - TEMP*A(I,J) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80 J = 1,N IF (X(JX).NE.ZERO) THEN IF (NOUNIT) X(JX) = X(JX)/A(J,J) TEMP = X(JX) IX = JX DO 70 I = J + 1,N IX = IX + INCX X(IX) = X(IX) - TEMP*A(I,J) 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A**T )*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 100 J = 1,N TEMP = X(J) DO 90 I = 1,J - 1 TEMP = TEMP - A(I,J)*X(I) 90 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) X(J) = TEMP 100 CONTINUE ELSE JX = KX DO 120 J = 1,N TEMP = X(JX) IX = KX DO 110 I = 1,J - 1 TEMP = TEMP - A(I,J)*X(IX) IX = IX + INCX 110 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) X(JX) = TEMP JX = JX + INCX 120 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 140 J = N,1,-1 TEMP = X(J) DO 130 I = N,J + 1,-1 TEMP = TEMP - A(I,J)*X(I) 130 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) X(J) = TEMP 140 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 160 J = N,1,-1 TEMP = X(JX) IX = KX DO 150 I = N,J + 1,-1 TEMP = TEMP - A(I,J)*X(IX) IX = IX - INCX 150 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) X(JX) = TEMP JX = JX - INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of DTRSV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dsymm.f0000644000000000000000000000013214061636515014743 xustar0030 mtime=1623670093.073104202 30 atime=1623670093.072104203 30 ctime=1623670093.073104202 elk-7.2.42/src/BLAS/dsymm.f0000644002504400250440000002565514061636515017015 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYMM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA,BETA * INTEGER LDA,LDB,LDC,M,N * CHARACTER SIDE,UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYMM performs one of the matrix-matrix operations *> *> C := alpha*A*B + beta*C, *> *> or *> *> C := alpha*B*A + beta*C, *> *> where alpha and beta are scalars, A is a symmetric matrix and B and *> C are m by n matrices. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether the symmetric matrix A *> appears on the left or right in the operation as follows: *> *> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, *> *> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the symmetric matrix A is to be *> referenced as follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of the *> symmetric matrix is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of the *> symmetric matrix is to be referenced. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix C. *> M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix C. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is *> m when SIDE = 'L' or 'l' and is n otherwise. *> Before entry with SIDE = 'L' or 'l', the m by m part of *> the array A must contain the symmetric matrix, such that *> when UPLO = 'U' or 'u', the leading m by m upper triangular *> part of the array A must contain the upper triangular part *> of the symmetric matrix and the strictly lower triangular *> part of A is not referenced, and when UPLO = 'L' or 'l', *> the leading m by m lower triangular part of the array A *> must contain the lower triangular part of the symmetric *> matrix and the strictly upper triangular part of A is not *> referenced. *> Before entry with SIDE = 'R' or 'r', the n by n part of *> the array A must contain the symmetric matrix, such that *> when UPLO = 'U' or 'u', the leading n by n upper triangular *> part of the array A must contain the upper triangular part *> of the symmetric matrix and the strictly lower triangular *> part of A is not referenced, and when UPLO = 'L' or 'l', *> the leading n by n lower triangular part of the array A *> must contain the lower triangular part of the symmetric *> matrix and the strictly upper triangular part of A is not *> referenced. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When SIDE = 'L' or 'l' then *> LDA must be at least max( 1, m ), otherwise LDA must be at *> least max( 1, n ). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension ( LDB, N ) *> Before entry, the leading m by n part of the array B must *> contain the matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. LDB must be at least *> max( 1, m ). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION. *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then C need not be set on input. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension ( LDC, N ) *> Before entry, the leading m by n part of the array C must *> contain the matrix C, except when beta is zero, in which *> case C need not be set on entry. *> On exit, the array C is overwritten by the m by n updated *> matrix. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> On entry, LDC specifies the first dimension of C as declared *> in the calling (sub) program. LDC must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER LDA,LDB,LDC,M,N CHARACTER SIDE,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Local Scalars .. DOUBLE PRECISION TEMP1,TEMP2 INTEGER I,INFO,J,K,NROWA LOGICAL UPPER * .. * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * * Set NROWA as the number of rows of A. * IF (LSAME(SIDE,'L')) THEN NROWA = M ELSE NROWA = N END IF UPPER = LSAME(UPLO,'U') * * Test the input parameters. * INFO = 0 IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN INFO = 1 ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 2 ELSE IF (M.LT.0) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 7 ELSE IF (LDB.LT.MAX(1,M)) THEN INFO = 9 ELSE IF (LDC.LT.MAX(1,M)) THEN INFO = 12 END IF IF (INFO.NE.0) THEN CALL XERBLA('DSYMM ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,M C(I,J) = BETA*C(I,J) 30 CONTINUE 40 CONTINUE END IF RETURN END IF * * Start the operations. * IF (LSAME(SIDE,'L')) THEN * * Form C := alpha*A*B + beta*C. * IF (UPPER) THEN DO 70 J = 1,N DO 60 I = 1,M TEMP1 = ALPHA*B(I,J) TEMP2 = ZERO DO 50 K = 1,I - 1 C(K,J) = C(K,J) + TEMP1*A(K,I) TEMP2 = TEMP2 + B(K,J)*A(K,I) 50 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) + + ALPHA*TEMP2 END IF 60 CONTINUE 70 CONTINUE ELSE DO 100 J = 1,N DO 90 I = M,1,-1 TEMP1 = ALPHA*B(I,J) TEMP2 = ZERO DO 80 K = I + 1,M C(K,J) = C(K,J) + TEMP1*A(K,I) TEMP2 = TEMP2 + B(K,J)*A(K,I) 80 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) + + ALPHA*TEMP2 END IF 90 CONTINUE 100 CONTINUE END IF ELSE * * Form C := alpha*B*A + beta*C. * DO 170 J = 1,N TEMP1 = ALPHA*A(J,J) IF (BETA.EQ.ZERO) THEN DO 110 I = 1,M C(I,J) = TEMP1*B(I,J) 110 CONTINUE ELSE DO 120 I = 1,M C(I,J) = BETA*C(I,J) + TEMP1*B(I,J) 120 CONTINUE END IF DO 140 K = 1,J - 1 IF (UPPER) THEN TEMP1 = ALPHA*A(K,J) ELSE TEMP1 = ALPHA*A(J,K) END IF DO 130 I = 1,M C(I,J) = C(I,J) + TEMP1*B(I,K) 130 CONTINUE 140 CONTINUE DO 160 K = J + 1,N IF (UPPER) THEN TEMP1 = ALPHA*A(J,K) ELSE TEMP1 = ALPHA*A(K,J) END IF DO 150 I = 1,M C(I,J) = C(I,J) + TEMP1*B(I,K) 150 CONTINUE 160 CONTINUE 170 CONTINUE END IF * RETURN * * End of DSYMM . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/dsyr2k.f0000644000000000000000000000012614061636515015033 xustar0028 mtime=1623670093.0751042 30 atime=1623670093.074104201 28 ctime=1623670093.0751042 elk-7.2.42/src/BLAS/dsyr2k.f0000644002504400250440000003031614061636515017070 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYR2K * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * .. Scalar Arguments .. * DOUBLE PRECISION ALPHA,BETA * INTEGER K,LDA,LDB,LDC,N * CHARACTER TRANS,UPLO * .. * .. Array Arguments .. * DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYR2K performs one of the symmetric rank 2k operations *> *> C := alpha*A*B**T + alpha*B*A**T + beta*C, *> *> or *> *> C := alpha*A**T*B + alpha*B**T*A + beta*C, *> *> where alpha and beta are scalars, C is an n by n symmetric matrix *> and A and B are n by k matrices in the first case and k by n *> matrices in the second case. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array C is to be referenced as *> follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of C *> is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of C *> is to be referenced. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' C := alpha*A*B**T + alpha*B*A**T + *> beta*C. *> *> TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**T*A + *> beta*C. *> *> TRANS = 'C' or 'c' C := alpha*A**T*B + alpha*B**T*A + *> beta*C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix C. N must be *> at least zero. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> On entry with TRANS = 'N' or 'n', K specifies the number *> of columns of the matrices A and B, and on entry with *> TRANS = 'T' or 't' or 'C' or 'c', K specifies the number *> of rows of the matrices A and B. K must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION. *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is *> k when TRANS = 'N' or 'n', and is n otherwise. *> Before entry with TRANS = 'N' or 'n', the leading n by k *> part of the array A must contain the matrix A, otherwise *> the leading k by n part of the array A must contain the *> matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When TRANS = 'N' or 'n' *> then LDA must be at least max( 1, n ), otherwise LDA must *> be at least max( 1, k ). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is *> k when TRANS = 'N' or 'n', and is n otherwise. *> Before entry with TRANS = 'N' or 'n', the leading n by k *> part of the array B must contain the matrix B, otherwise *> the leading k by n part of the array B must contain the *> matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. When TRANS = 'N' or 'n' *> then LDB must be at least max( 1, n ), otherwise LDB must *> be at least max( 1, k ). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION. *> On entry, BETA specifies the scalar beta. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension ( LDC, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array C must contain the upper *> triangular part of the symmetric matrix and the strictly *> lower triangular part of C is not referenced. On exit, the *> upper triangular part of the array C is overwritten by the *> upper triangular part of the updated matrix. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array C must contain the lower *> triangular part of the symmetric matrix and the strictly *> upper triangular part of C is not referenced. On exit, the *> lower triangular part of the array C is overwritten by the *> lower triangular part of the updated matrix. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> On entry, LDC specifies the first dimension of C as declared *> in the calling (sub) program. LDC must be at least *> max( 1, n ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup double_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION ALPHA,BETA INTEGER K,LDA,LDB,LDC,N CHARACTER TRANS,UPLO * .. * .. Array Arguments .. DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Local Scalars .. DOUBLE PRECISION TEMP1,TEMP2 INTEGER I,INFO,J,L,NROWA LOGICAL UPPER * .. * .. Parameters .. DOUBLE PRECISION ONE,ZERO PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) * .. * * Test the input parameters. * IF (LSAME(TRANS,'N')) THEN NROWA = N ELSE NROWA = K END IF UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 1 ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. + (.NOT.LSAME(TRANS,'T')) .AND. + (.NOT.LSAME(TRANS,'C'))) THEN INFO = 2 ELSE IF (N.LT.0) THEN INFO = 3 ELSE IF (K.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 7 ELSE IF (LDB.LT.MAX(1,NROWA)) THEN INFO = 9 ELSE IF (LDC.LT.MAX(1,N)) THEN INFO = 12 END IF IF (INFO.NE.0) THEN CALL XERBLA('DSYR2K',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (UPPER) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,J C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,J C(I,J) = BETA*C(I,J) 30 CONTINUE 40 CONTINUE END IF ELSE IF (BETA.EQ.ZERO) THEN DO 60 J = 1,N DO 50 I = J,N C(I,J) = ZERO 50 CONTINUE 60 CONTINUE ELSE DO 80 J = 1,N DO 70 I = J,N C(I,J) = BETA*C(I,J) 70 CONTINUE 80 CONTINUE END IF END IF RETURN END IF * * Start the operations. * IF (LSAME(TRANS,'N')) THEN * * Form C := alpha*A*B**T + alpha*B*A**T + C. * IF (UPPER) THEN DO 130 J = 1,N IF (BETA.EQ.ZERO) THEN DO 90 I = 1,J C(I,J) = ZERO 90 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 100 I = 1,J C(I,J) = BETA*C(I,J) 100 CONTINUE END IF DO 120 L = 1,K IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN TEMP1 = ALPHA*B(J,L) TEMP2 = ALPHA*A(J,L) DO 110 I = 1,J C(I,J) = C(I,J) + A(I,L)*TEMP1 + + B(I,L)*TEMP2 110 CONTINUE END IF 120 CONTINUE 130 CONTINUE ELSE DO 180 J = 1,N IF (BETA.EQ.ZERO) THEN DO 140 I = J,N C(I,J) = ZERO 140 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 150 I = J,N C(I,J) = BETA*C(I,J) 150 CONTINUE END IF DO 170 L = 1,K IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN TEMP1 = ALPHA*B(J,L) TEMP2 = ALPHA*A(J,L) DO 160 I = J,N C(I,J) = C(I,J) + A(I,L)*TEMP1 + + B(I,L)*TEMP2 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE END IF ELSE * * Form C := alpha*A**T*B + alpha*B**T*A + C. * IF (UPPER) THEN DO 210 J = 1,N DO 200 I = 1,J TEMP1 = ZERO TEMP2 = ZERO DO 190 L = 1,K TEMP1 = TEMP1 + A(L,I)*B(L,J) TEMP2 = TEMP2 + B(L,I)*A(L,J) 190 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + + ALPHA*TEMP2 END IF 200 CONTINUE 210 CONTINUE ELSE DO 240 J = 1,N DO 230 I = J,N TEMP1 = ZERO TEMP2 = ZERO DO 220 L = 1,K TEMP1 = TEMP1 + A(L,I)*B(L,J) TEMP2 = TEMP2 + B(L,I)*A(L,J) 220 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = ALPHA*TEMP1 + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + + ALPHA*TEMP2 END IF 230 CONTINUE 240 CONTINUE END IF END IF * RETURN * * End of DSYR2K. * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zdrot.f0000644000000000000000000000013214061636515014754 xustar0030 mtime=1623670093.076104199 30 atime=1623670093.076104199 30 ctime=1623670093.076104199 elk-7.2.42/src/BLAS/zdrot.f0000644002504400250440000000753214061636515017020 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZDROT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZDROT( N, CX, INCX, CY, INCY, C, S ) * * .. Scalar Arguments .. * INTEGER INCX, INCY, N * DOUBLE PRECISION C, S * .. * .. Array Arguments .. * COMPLEX*16 CX( * ), CY( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Applies a plane rotation, where the cos and sin (c and s) are real *> and the vectors cx and cy are complex. *> jack dongarra, linpack, 3/11/78. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the vectors cx and cy. *> N must be at least zero. *> \endverbatim *> *> \param[in,out] CX *> \verbatim *> CX is COMPLEX*16 array, dimension at least *> ( 1 + ( N - 1 )*abs( INCX ) ). *> Before entry, the incremented array CX must contain the n *> element vector cx. On exit, CX is overwritten by the updated *> vector cx. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> CX. INCX must not be zero. *> \endverbatim *> *> \param[in,out] CY *> \verbatim *> CY is COMPLEX*16 array, dimension at least *> ( 1 + ( N - 1 )*abs( INCY ) ). *> Before entry, the incremented array CY must contain the n *> element vector cy. On exit, CY is overwritten by the updated *> vector cy. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> CY. INCY must not be zero. *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION *> On entry, C specifies the cosine, cos. *> \endverbatim *> *> \param[in] S *> \verbatim *> S is DOUBLE PRECISION *> On entry, S specifies the sine, sin. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level1 * * ===================================================================== SUBROUTINE ZDROT( N, CX, INCX, CY, INCY, C, S ) * * -- Reference BLAS level1 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX, INCY, N DOUBLE PRECISION C, S * .. * .. Array Arguments .. COMPLEX*16 CX( * ), CY( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, IX, IY COMPLEX*16 CTEMP * .. * .. Executable Statements .. * IF( N.LE.0 ) $ RETURN IF( INCX.EQ.1 .AND. INCY.EQ.1 ) THEN * * code for both increments equal to 1 * DO I = 1, N CTEMP = C*CX( I ) + S*CY( I ) CY( I ) = C*CY( I ) - S*CX( I ) CX( I ) = CTEMP END DO ELSE * * code for unequal increments or equal increments not equal * to 1 * IX = 1 IY = 1 IF( INCX.LT.0 ) $ IX = ( -N+1 )*INCX + 1 IF( INCY.LT.0 ) $ IY = ( -N+1 )*INCY + 1 DO I = 1, N CTEMP = C*CX( IX ) + S*CY( IY ) CY( IY ) = C*CY( IY ) - S*CX( IX ) CX( IX ) = CTEMP IX = IX + INCX IY = IY + INCY END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zdscal.f0000644000000000000000000000013214061636515015072 xustar0030 mtime=1623670093.078104197 30 atime=1623670093.078104197 30 ctime=1623670093.078104197 elk-7.2.42/src/BLAS/zdscal.f0000644002504400250440000000504414061636515017132 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZDSCAL * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZDSCAL(N,DA,ZX,INCX) * * .. Scalar Arguments .. * DOUBLE PRECISION DA * INTEGER INCX,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZDSCAL scales a vector by a constant. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] DA *> \verbatim *> DA is DOUBLE PRECISION *> On entry, DA specifies the scalar alpha. *> \endverbatim *> *> \param[in,out] ZX *> \verbatim *> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, 3/11/78. *> modified 3/93 to return if incx .le. 0. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE ZDSCAL(N,DA,ZX,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. DOUBLE PRECISION DA INTEGER INCX,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I,NINCX * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX * .. IF (N.LE.0 .OR. INCX.LE.0) RETURN IF (INCX.EQ.1) THEN * * code for increment equal to 1 * DO I = 1,N ZX(I) = DCMPLX(DA,0.0d0)*ZX(I) END DO ELSE * * code for increment not equal to 1 * NINCX = N*INCX DO I = 1,NINCX,INCX ZX(I) = DCMPLX(DA,0.0d0)*ZX(I) END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zswap.f0000644000000000000000000000013214061636515014756 xustar0030 mtime=1623670093.079104196 30 atime=1623670093.079104196 30 ctime=1623670093.079104196 elk-7.2.42/src/BLAS/zswap.f0000644002504400250440000000545014061636515017017 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZSWAP * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) * * .. Scalar Arguments .. * INTEGER INCX,INCY,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*),ZY(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSWAP interchanges two vectors. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in,out] ZX *> \verbatim *> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim *> *> \param[in,out] ZY *> \verbatim *> ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) ) *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> storage spacing between elements of ZY *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, 3/11/78. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE ZSWAP(N,ZX,INCX,ZY,INCY) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,INCY,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*),ZY(*) * .. * * ===================================================================== * * .. Local Scalars .. COMPLEX*16 ZTEMP INTEGER I,IX,IY * .. IF (N.LE.0) RETURN IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN * * code for both increments equal to 1 DO I = 1,N ZTEMP = ZX(I) ZX(I) = ZY(I) ZY(I) = ZTEMP END DO ELSE * * code for unequal increments or equal increments not equal * to 1 * IX = 1 IY = 1 IF (INCX.LT.0) IX = (-N+1)*INCX + 1 IF (INCY.LT.0) IY = (-N+1)*INCY + 1 DO I = 1,N ZTEMP = ZX(IX) ZX(IX) = ZY(IY) ZY(IY) = ZTEMP IX = IX + INCX IY = IY + INCY END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/izamax.f0000644000000000000000000000013214061636515015103 xustar0030 mtime=1623670093.081104194 30 atime=1623670093.081104194 30 ctime=1623670093.081104194 elk-7.2.42/src/BLAS/izamax.f0000644002504400250440000000536414061636515017150 0ustar00dewhurstdewhurst00000000000000*> \brief \b IZAMAX * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * INTEGER FUNCTION IZAMAX(N,ZX,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> IZAMAX finds the index of the first element having maximum |Re(.)| + |Im(.)| *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] ZX *> \verbatim *> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup aux_blas * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, 1/15/85. *> modified 3/93 to return if incx .le. 0. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== INTEGER FUNCTION IZAMAX(N,ZX,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*) * .. * * ===================================================================== * * .. Local Scalars .. DOUBLE PRECISION DMAX INTEGER I,IX * .. * .. External Functions .. DOUBLE PRECISION DCABS1 EXTERNAL DCABS1 * .. IZAMAX = 0 IF (N.LT.1 .OR. INCX.LE.0) RETURN IZAMAX = 1 IF (N.EQ.1) RETURN IF (INCX.EQ.1) THEN * * code for increment equal to 1 * DMAX = DCABS1(ZX(1)) DO I = 2,N IF (DCABS1(ZX(I)).GT.DMAX) THEN IZAMAX = I DMAX = DCABS1(ZX(I)) END IF END DO ELSE * * code for increment not equal to 1 * IX = 1 DMAX = DCABS1(ZX(1)) IX = IX + INCX DO I = 2,N IF (DCABS1(ZX(IX)).GT.DMAX) THEN IZAMAX = I DMAX = DCABS1(ZX(IX)) END IF IX = IX + INCX END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zscal.f0000644000000000000000000000013214061636515014726 xustar0030 mtime=1623670093.082104193 30 atime=1623670093.082104193 30 ctime=1623670093.082104193 elk-7.2.42/src/BLAS/zscal.f0000644002504400250440000000466214061636515016773 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZSCAL * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZSCAL(N,ZA,ZX,INCX) * * .. Scalar Arguments .. * COMPLEX*16 ZA * INTEGER INCX,N * .. * .. Array Arguments .. * COMPLEX*16 ZX(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSCAL scales a vector by a constant. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> number of elements in input vector(s) *> \endverbatim *> *> \param[in] ZA *> \verbatim *> ZA is COMPLEX*16 *> On entry, ZA specifies the scalar alpha. *> \endverbatim *> *> \param[in,out] ZX *> \verbatim *> ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) ) *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> storage spacing between elements of ZX *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16_blas_level1 * *> \par Further Details: * ===================== *> *> \verbatim *> *> jack dongarra, 3/11/78. *> modified 3/93 to return if incx .le. 0. *> modified 12/3/93, array(1) declarations changed to array(*) *> \endverbatim *> * ===================================================================== SUBROUTINE ZSCAL(N,ZA,ZX,INCX) * * -- Reference BLAS level1 routine (version 3.8.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. COMPLEX*16 ZA INTEGER INCX,N * .. * .. Array Arguments .. COMPLEX*16 ZX(*) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I,NINCX * .. IF (N.LE.0 .OR. INCX.LE.0) RETURN IF (INCX.EQ.1) THEN * * code for increment equal to 1 * DO I = 1,N ZX(I) = ZA*ZX(I) END DO ELSE * * code for increment not equal to 1 * NINCX = N*INCX DO I = 1,NINCX,INCX ZX(I) = ZA*ZX(I) END DO END IF RETURN END elk-7.2.42/src/BLAS/PaxHeaders.21776/zgeru.f0000644000000000000000000000013214061636515014746 xustar0030 mtime=1623670093.084104191 30 atime=1623670093.084104191 30 ctime=1623670093.084104191 elk-7.2.42/src/BLAS/zgeru.f0000644002504400250440000001302014061636515016777 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGERU * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA * INTEGER INCX,INCY,LDA,M,N * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGERU performs the rank 1 operation *> *> A := alpha*x*y**T + A, *> *> where alpha is a scalar, x is an m element vector, y is an n element *> vector and A is an m by n matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix A. *> M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( m - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the m *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, N ) *> Before entry, the leading m by n part of the array A must *> contain the matrix of coefficients. On exit, A is *> overwritten by the updated matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX,INCY,LDA,M,N * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,J,JY,KX * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * * Test the input parameters. * INFO = 0 IF (M.LT.0) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 5 ELSE IF (INCY.EQ.0) THEN INFO = 7 ELSE IF (LDA.LT.MAX(1,M)) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZGERU ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (INCY.GT.0) THEN JY = 1 ELSE JY = 1 - (N-1)*INCY END IF IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (Y(JY).NE.ZERO) THEN TEMP = ALPHA*Y(JY) DO 10 I = 1,M A(I,J) = A(I,J) + X(I)*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (M-1)*INCX END IF DO 40 J = 1,N IF (Y(JY).NE.ZERO) THEN TEMP = ALPHA*Y(JY) IX = KX DO 30 I = 1,M A(I,J) = A(I,J) + X(IX)*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of ZGERU . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/ztrsm.f0000644000000000000000000000013214061636515014771 xustar0030 mtime=1623670093.085104191 30 atime=1623670093.085104191 30 ctime=1623670093.085104191 elk-7.2.42/src/BLAS/ztrsm.f0000644002504400250440000003574714061636515017046 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTRSM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA * INTEGER LDA,LDB,M,N * CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),B(LDB,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTRSM solves one of the matrix equations *> *> op( A )*X = alpha*B, or X*op( A ) = alpha*B, *> *> where alpha is a scalar, X and B are m by n matrices, A is a unit, or *> non-unit, upper or lower triangular matrix and op( A ) is one of *> *> op( A ) = A or op( A ) = A**T or op( A ) = A**H. *> *> The matrix X is overwritten on B. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether op( A ) appears on the left *> or right of X as follows: *> *> SIDE = 'L' or 'l' op( A )*X = alpha*B. *> *> SIDE = 'R' or 'r' X*op( A ) = alpha*B. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix A is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANSA *> \verbatim *> TRANSA is CHARACTER*1 *> On entry, TRANSA specifies the form of op( A ) to be used in *> the matrix multiplication as follows: *> *> TRANSA = 'N' or 'n' op( A ) = A. *> *> TRANSA = 'T' or 't' op( A ) = A**T. *> *> TRANSA = 'C' or 'c' op( A ) = A**H. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit triangular *> as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of B. M must be at *> least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of B. N must be *> at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. When alpha is *> zero then A is not referenced and B need not be set before *> entry. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, k ), *> where k is m when SIDE = 'L' or 'l' *> and k is n when SIDE = 'R' or 'r'. *> Before entry with UPLO = 'U' or 'u', the leading k by k *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading k by k *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When SIDE = 'L' or 'l' then *> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' *> then LDA must be at least max( 1, n ). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension ( LDB, N ) *> Before entry, the leading m by n part of the array B must *> contain the right-hand side matrix B, and on exit is *> overwritten by the solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. LDB must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER LDA,LDB,M,N CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),B(LDB,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,J,K,NROWA LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER * .. * .. Parameters .. COMPLEX*16 ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * * Test the input parameters. * LSIDE = LSAME(SIDE,'L') IF (LSIDE) THEN NROWA = M ELSE NROWA = N END IF NOCONJ = LSAME(TRANSA,'T') NOUNIT = LSAME(DIAG,'N') UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN INFO = 1 ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 2 ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. + (.NOT.LSAME(TRANSA,'T')) .AND. + (.NOT.LSAME(TRANSA,'C'))) THEN INFO = 3 ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN INFO = 4 ELSE IF (M.LT.0) THEN INFO = 5 ELSE IF (N.LT.0) THEN INFO = 6 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 9 ELSE IF (LDB.LT.MAX(1,M)) THEN INFO = 11 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZTRSM ',INFO) RETURN END IF * * Quick return if possible. * IF (M.EQ.0 .OR. N.EQ.0) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M B(I,J) = ZERO 10 CONTINUE 20 CONTINUE RETURN END IF * * Start the operations. * IF (LSIDE) THEN IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*inv( A )*B. * IF (UPPER) THEN DO 60 J = 1,N IF (ALPHA.NE.ONE) THEN DO 30 I = 1,M B(I,J) = ALPHA*B(I,J) 30 CONTINUE END IF DO 50 K = M,1,-1 IF (B(K,J).NE.ZERO) THEN IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) DO 40 I = 1,K - 1 B(I,J) = B(I,J) - B(K,J)*A(I,K) 40 CONTINUE END IF 50 CONTINUE 60 CONTINUE ELSE DO 100 J = 1,N IF (ALPHA.NE.ONE) THEN DO 70 I = 1,M B(I,J) = ALPHA*B(I,J) 70 CONTINUE END IF DO 90 K = 1,M IF (B(K,J).NE.ZERO) THEN IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) DO 80 I = K + 1,M B(I,J) = B(I,J) - B(K,J)*A(I,K) 80 CONTINUE END IF 90 CONTINUE 100 CONTINUE END IF ELSE * * Form B := alpha*inv( A**T )*B * or B := alpha*inv( A**H )*B. * IF (UPPER) THEN DO 140 J = 1,N DO 130 I = 1,M TEMP = ALPHA*B(I,J) IF (NOCONJ) THEN DO 110 K = 1,I - 1 TEMP = TEMP - A(K,I)*B(K,J) 110 CONTINUE IF (NOUNIT) TEMP = TEMP/A(I,I) ELSE DO 120 K = 1,I - 1 TEMP = TEMP - DCONJG(A(K,I))*B(K,J) 120 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(I,I)) END IF B(I,J) = TEMP 130 CONTINUE 140 CONTINUE ELSE DO 180 J = 1,N DO 170 I = M,1,-1 TEMP = ALPHA*B(I,J) IF (NOCONJ) THEN DO 150 K = I + 1,M TEMP = TEMP - A(K,I)*B(K,J) 150 CONTINUE IF (NOUNIT) TEMP = TEMP/A(I,I) ELSE DO 160 K = I + 1,M TEMP = TEMP - DCONJG(A(K,I))*B(K,J) 160 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(I,I)) END IF B(I,J) = TEMP 170 CONTINUE 180 CONTINUE END IF END IF ELSE IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*B*inv( A ). * IF (UPPER) THEN DO 230 J = 1,N IF (ALPHA.NE.ONE) THEN DO 190 I = 1,M B(I,J) = ALPHA*B(I,J) 190 CONTINUE END IF DO 210 K = 1,J - 1 IF (A(K,J).NE.ZERO) THEN DO 200 I = 1,M B(I,J) = B(I,J) - A(K,J)*B(I,K) 200 CONTINUE END IF 210 CONTINUE IF (NOUNIT) THEN TEMP = ONE/A(J,J) DO 220 I = 1,M B(I,J) = TEMP*B(I,J) 220 CONTINUE END IF 230 CONTINUE ELSE DO 280 J = N,1,-1 IF (ALPHA.NE.ONE) THEN DO 240 I = 1,M B(I,J) = ALPHA*B(I,J) 240 CONTINUE END IF DO 260 K = J + 1,N IF (A(K,J).NE.ZERO) THEN DO 250 I = 1,M B(I,J) = B(I,J) - A(K,J)*B(I,K) 250 CONTINUE END IF 260 CONTINUE IF (NOUNIT) THEN TEMP = ONE/A(J,J) DO 270 I = 1,M B(I,J) = TEMP*B(I,J) 270 CONTINUE END IF 280 CONTINUE END IF ELSE * * Form B := alpha*B*inv( A**T ) * or B := alpha*B*inv( A**H ). * IF (UPPER) THEN DO 330 K = N,1,-1 IF (NOUNIT) THEN IF (NOCONJ) THEN TEMP = ONE/A(K,K) ELSE TEMP = ONE/DCONJG(A(K,K)) END IF DO 290 I = 1,M B(I,K) = TEMP*B(I,K) 290 CONTINUE END IF DO 310 J = 1,K - 1 IF (A(J,K).NE.ZERO) THEN IF (NOCONJ) THEN TEMP = A(J,K) ELSE TEMP = DCONJG(A(J,K)) END IF DO 300 I = 1,M B(I,J) = B(I,J) - TEMP*B(I,K) 300 CONTINUE END IF 310 CONTINUE IF (ALPHA.NE.ONE) THEN DO 320 I = 1,M B(I,K) = ALPHA*B(I,K) 320 CONTINUE END IF 330 CONTINUE ELSE DO 380 K = 1,N IF (NOUNIT) THEN IF (NOCONJ) THEN TEMP = ONE/A(K,K) ELSE TEMP = ONE/DCONJG(A(K,K)) END IF DO 340 I = 1,M B(I,K) = TEMP*B(I,K) 340 CONTINUE END IF DO 360 J = K + 1,N IF (A(J,K).NE.ZERO) THEN IF (NOCONJ) THEN TEMP = A(J,K) ELSE TEMP = DCONJG(A(J,K)) END IF DO 350 I = 1,M B(I,J) = B(I,J) - TEMP*B(I,K) 350 CONTINUE END IF 360 CONTINUE IF (ALPHA.NE.ONE) THEN DO 370 I = 1,M B(I,K) = ALPHA*B(I,K) 370 CONTINUE END IF 380 CONTINUE END IF END IF END IF * RETURN * * End of ZTRSM . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/ztbsv.f0000644000000000000000000000013214061636515014762 xustar0030 mtime=1623670093.087104189 30 atime=1623670093.087104189 30 ctime=1623670093.087104189 elk-7.2.42/src/BLAS/ztbsv.f0000644002504400250440000003351614061636515017027 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTBSV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,K,LDA,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTBSV solves one of the systems of equations *> *> A*x = b, or A**T*x = b, or A**H*x = b, *> *> where b and x are n element vectors and A is an n by n unit, or *> non-unit, upper or lower triangular band matrix, with ( k + 1 ) *> diagonals. *> *> No test for singularity or near-singularity is included in this *> routine. Such tests must be performed before calling this routine. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the equations to be solved as *> follows: *> *> TRANS = 'N' or 'n' A*x = b. *> *> TRANS = 'T' or 't' A**T*x = b. *> *> TRANS = 'C' or 'c' A**H*x = b. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit *> triangular as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> On entry with UPLO = 'U' or 'u', K specifies the number of *> super-diagonals of the matrix A. *> On entry with UPLO = 'L' or 'l', K specifies the number of *> sub-diagonals of the matrix A. *> K must satisfy 0 .le. K. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) *> by n part of the array A must contain the upper triangular *> band part of the matrix of coefficients, supplied column by *> column, with the leading diagonal of the matrix in row *> ( k + 1 ) of the array, the first super-diagonal starting at *> position 2 in row k, and so on. The top left k by k triangle *> of the array A is not referenced. *> The following program segment will transfer an upper *> triangular band matrix from conventional full matrix storage *> to band storage: *> *> DO 20, J = 1, N *> M = K + 1 - J *> DO 10, I = MAX( 1, J - K ), J *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE *> *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) *> by n part of the array A must contain the lower triangular *> band part of the matrix of coefficients, supplied column by *> column, with the leading diagonal of the matrix in row 1 of *> the array, the first sub-diagonal starting at position 1 in *> row 2, and so on. The bottom right k by k triangle of the *> array A is not referenced. *> The following program segment will transfer a lower *> triangular band matrix from conventional full matrix storage *> to band storage: *> *> DO 20, J = 1, N *> M = 1 - J *> DO 10, I = J, MIN( N, J + K ) *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE *> *> Note that when DIAG = 'U' or 'u' the elements of the array A *> corresponding to the diagonal elements of the matrix are not *> referenced, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> ( k + 1 ). *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element right-hand side vector b. On exit, X is overwritten *> with the solution vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX,K,LDA,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),X(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L LOGICAL NOCONJ,NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX,MIN * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (K.LT.0) THEN INFO = 5 ELSE IF (LDA.LT. (K+1)) THEN INFO = 7 ELSE IF (INCX.EQ.0) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZTBSV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOCONJ = LSAME(TRANS,'T') NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed by sequentially with one pass through A. * IF (LSAME(TRANS,'N')) THEN * * Form x := inv( A )*x. * IF (LSAME(UPLO,'U')) THEN KPLUS1 = K + 1 IF (INCX.EQ.1) THEN DO 20 J = N,1,-1 IF (X(J).NE.ZERO) THEN L = KPLUS1 - J IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J) TEMP = X(J) DO 10 I = J - 1,MAX(1,J-K),-1 X(I) = X(I) - TEMP*A(L+I,J) 10 CONTINUE END IF 20 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 40 J = N,1,-1 KX = KX - INCX IF (X(JX).NE.ZERO) THEN IX = KX L = KPLUS1 - J IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J) TEMP = X(JX) DO 30 I = J - 1,MAX(1,J-K),-1 X(IX) = X(IX) - TEMP*A(L+I,J) IX = IX - INCX 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 60 J = 1,N IF (X(J).NE.ZERO) THEN L = 1 - J IF (NOUNIT) X(J) = X(J)/A(1,J) TEMP = X(J) DO 50 I = J + 1,MIN(N,J+K) X(I) = X(I) - TEMP*A(L+I,J) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80 J = 1,N KX = KX + INCX IF (X(JX).NE.ZERO) THEN IX = KX L = 1 - J IF (NOUNIT) X(JX) = X(JX)/A(1,J) TEMP = X(JX) DO 70 I = J + 1,MIN(N,J+K) X(IX) = X(IX) - TEMP*A(L+I,J) IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A**T )*x or x := inv( A**H )*x. * IF (LSAME(UPLO,'U')) THEN KPLUS1 = K + 1 IF (INCX.EQ.1) THEN DO 110 J = 1,N TEMP = X(J) L = KPLUS1 - J IF (NOCONJ) THEN DO 90 I = MAX(1,J-K),J - 1 TEMP = TEMP - A(L+I,J)*X(I) 90 CONTINUE IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) ELSE DO 100 I = MAX(1,J-K),J - 1 TEMP = TEMP - DCONJG(A(L+I,J))*X(I) 100 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J)) END IF X(J) = TEMP 110 CONTINUE ELSE JX = KX DO 140 J = 1,N TEMP = X(JX) IX = KX L = KPLUS1 - J IF (NOCONJ) THEN DO 120 I = MAX(1,J-K),J - 1 TEMP = TEMP - A(L+I,J)*X(IX) IX = IX + INCX 120 CONTINUE IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) ELSE DO 130 I = MAX(1,J-K),J - 1 TEMP = TEMP - DCONJG(A(L+I,J))*X(IX) IX = IX + INCX 130 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J)) END IF X(JX) = TEMP JX = JX + INCX IF (J.GT.K) KX = KX + INCX 140 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 170 J = N,1,-1 TEMP = X(J) L = 1 - J IF (NOCONJ) THEN DO 150 I = MIN(N,J+K),J + 1,-1 TEMP = TEMP - A(L+I,J)*X(I) 150 CONTINUE IF (NOUNIT) TEMP = TEMP/A(1,J) ELSE DO 160 I = MIN(N,J+K),J + 1,-1 TEMP = TEMP - DCONJG(A(L+I,J))*X(I) 160 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(1,J)) END IF X(J) = TEMP 170 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 200 J = N,1,-1 TEMP = X(JX) IX = KX L = 1 - J IF (NOCONJ) THEN DO 180 I = MIN(N,J+K),J + 1,-1 TEMP = TEMP - A(L+I,J)*X(IX) IX = IX - INCX 180 CONTINUE IF (NOUNIT) TEMP = TEMP/A(1,J) ELSE DO 190 I = MIN(N,J+K),J + 1,-1 TEMP = TEMP - DCONJG(A(L+I,J))*X(IX) IX = IX - INCX 190 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(1,J)) END IF X(JX) = TEMP JX = JX - INCX IF ((N-J).GE.K) KX = KX - INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTBSV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/ztrmm.f0000644000000000000000000000013214061636515014763 xustar0030 mtime=1623670093.089104187 30 atime=1623670093.089104187 30 ctime=1623670093.089104187 elk-7.2.42/src/BLAS/ztrmm.f0000644002504400250440000003416614061636515017032 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTRMM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA * INTEGER LDA,LDB,M,N * CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),B(LDB,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTRMM performs one of the matrix-matrix operations *> *> B := alpha*op( A )*B, or B := alpha*B*op( A ) *> *> where alpha is a scalar, B is an m by n matrix, A is a unit, or *> non-unit, upper or lower triangular matrix and op( A ) is one of *> *> op( A ) = A or op( A ) = A**T or op( A ) = A**H. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether op( A ) multiplies B from *> the left or right as follows: *> *> SIDE = 'L' or 'l' B := alpha*op( A )*B. *> *> SIDE = 'R' or 'r' B := alpha*B*op( A ). *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix A is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANSA *> \verbatim *> TRANSA is CHARACTER*1 *> On entry, TRANSA specifies the form of op( A ) to be used in *> the matrix multiplication as follows: *> *> TRANSA = 'N' or 'n' op( A ) = A. *> *> TRANSA = 'T' or 't' op( A ) = A**T. *> *> TRANSA = 'C' or 'c' op( A ) = A**H. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit triangular *> as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of B. M must be at *> least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of B. N must be *> at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. When alpha is *> zero then A is not referenced and B need not be set before *> entry. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, k ), where k is m *> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. *> Before entry with UPLO = 'U' or 'u', the leading k by k *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading k by k *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When SIDE = 'L' or 'l' then *> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' *> then LDA must be at least max( 1, n ). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension ( LDB, N ). *> Before entry, the leading m by n part of the array B must *> contain the matrix B, and on exit is overwritten by the *> transformed matrix. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. LDB must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE ZTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER LDA,LDB,M,N CHARACTER DIAG,SIDE,TRANSA,UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),B(LDB,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,J,K,NROWA LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER * .. * .. Parameters .. COMPLEX*16 ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * * Test the input parameters. * LSIDE = LSAME(SIDE,'L') IF (LSIDE) THEN NROWA = M ELSE NROWA = N END IF NOCONJ = LSAME(TRANSA,'T') NOUNIT = LSAME(DIAG,'N') UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN INFO = 1 ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 2 ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. + (.NOT.LSAME(TRANSA,'T')) .AND. + (.NOT.LSAME(TRANSA,'C'))) THEN INFO = 3 ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN INFO = 4 ELSE IF (M.LT.0) THEN INFO = 5 ELSE IF (N.LT.0) THEN INFO = 6 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 9 ELSE IF (LDB.LT.MAX(1,M)) THEN INFO = 11 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZTRMM ',INFO) RETURN END IF * * Quick return if possible. * IF (M.EQ.0 .OR. N.EQ.0) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M B(I,J) = ZERO 10 CONTINUE 20 CONTINUE RETURN END IF * * Start the operations. * IF (LSIDE) THEN IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*A*B. * IF (UPPER) THEN DO 50 J = 1,N DO 40 K = 1,M IF (B(K,J).NE.ZERO) THEN TEMP = ALPHA*B(K,J) DO 30 I = 1,K - 1 B(I,J) = B(I,J) + TEMP*A(I,K) 30 CONTINUE IF (NOUNIT) TEMP = TEMP*A(K,K) B(K,J) = TEMP END IF 40 CONTINUE 50 CONTINUE ELSE DO 80 J = 1,N DO 70 K = M,1,-1 IF (B(K,J).NE.ZERO) THEN TEMP = ALPHA*B(K,J) B(K,J) = TEMP IF (NOUNIT) B(K,J) = B(K,J)*A(K,K) DO 60 I = K + 1,M B(I,J) = B(I,J) + TEMP*A(I,K) 60 CONTINUE END IF 70 CONTINUE 80 CONTINUE END IF ELSE * * Form B := alpha*A**T*B or B := alpha*A**H*B. * IF (UPPER) THEN DO 120 J = 1,N DO 110 I = M,1,-1 TEMP = B(I,J) IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(I,I) DO 90 K = 1,I - 1 TEMP = TEMP + A(K,I)*B(K,J) 90 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(I,I)) DO 100 K = 1,I - 1 TEMP = TEMP + DCONJG(A(K,I))*B(K,J) 100 CONTINUE END IF B(I,J) = ALPHA*TEMP 110 CONTINUE 120 CONTINUE ELSE DO 160 J = 1,N DO 150 I = 1,M TEMP = B(I,J) IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(I,I) DO 130 K = I + 1,M TEMP = TEMP + A(K,I)*B(K,J) 130 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(I,I)) DO 140 K = I + 1,M TEMP = TEMP + DCONJG(A(K,I))*B(K,J) 140 CONTINUE END IF B(I,J) = ALPHA*TEMP 150 CONTINUE 160 CONTINUE END IF END IF ELSE IF (LSAME(TRANSA,'N')) THEN * * Form B := alpha*B*A. * IF (UPPER) THEN DO 200 J = N,1,-1 TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(J,J) DO 170 I = 1,M B(I,J) = TEMP*B(I,J) 170 CONTINUE DO 190 K = 1,J - 1 IF (A(K,J).NE.ZERO) THEN TEMP = ALPHA*A(K,J) DO 180 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 180 CONTINUE END IF 190 CONTINUE 200 CONTINUE ELSE DO 240 J = 1,N TEMP = ALPHA IF (NOUNIT) TEMP = TEMP*A(J,J) DO 210 I = 1,M B(I,J) = TEMP*B(I,J) 210 CONTINUE DO 230 K = J + 1,N IF (A(K,J).NE.ZERO) THEN TEMP = ALPHA*A(K,J) DO 220 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 220 CONTINUE END IF 230 CONTINUE 240 CONTINUE END IF ELSE * * Form B := alpha*B*A**T or B := alpha*B*A**H. * IF (UPPER) THEN DO 280 K = 1,N DO 260 J = 1,K - 1 IF (A(J,K).NE.ZERO) THEN IF (NOCONJ) THEN TEMP = ALPHA*A(J,K) ELSE TEMP = ALPHA*DCONJG(A(J,K)) END IF DO 250 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 250 CONTINUE END IF 260 CONTINUE TEMP = ALPHA IF (NOUNIT) THEN IF (NOCONJ) THEN TEMP = TEMP*A(K,K) ELSE TEMP = TEMP*DCONJG(A(K,K)) END IF END IF IF (TEMP.NE.ONE) THEN DO 270 I = 1,M B(I,K) = TEMP*B(I,K) 270 CONTINUE END IF 280 CONTINUE ELSE DO 320 K = N,1,-1 DO 300 J = K + 1,N IF (A(J,K).NE.ZERO) THEN IF (NOCONJ) THEN TEMP = ALPHA*A(J,K) ELSE TEMP = ALPHA*DCONJG(A(J,K)) END IF DO 290 I = 1,M B(I,J) = B(I,J) + TEMP*B(I,K) 290 CONTINUE END IF 300 CONTINUE TEMP = ALPHA IF (NOUNIT) THEN IF (NOCONJ) THEN TEMP = TEMP*A(K,K) ELSE TEMP = TEMP*DCONJG(A(K,K)) END IF END IF IF (TEMP.NE.ONE) THEN DO 310 I = 1,M B(I,K) = TEMP*B(I,K) 310 CONTINUE END IF 320 CONTINUE END IF END IF END IF * RETURN * * End of ZTRMM . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zher2.f0000644000000000000000000000013214061636515014644 xustar0030 mtime=1623670093.091104185 30 atime=1623670093.091104185 30 ctime=1623670093.091104185 elk-7.2.42/src/BLAS/zher2.f0000644002504400250440000002245114061636515016705 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHER2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA * INTEGER INCX,INCY,LDA,N * CHARACTER UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHER2 performs the hermitian rank 2 operation *> *> A := alpha*x*y**H + conjg( alpha )*y*x**H + A, *> *> where alpha is a scalar, x and y are n element vectors and A is an n *> by n hermitian matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of A *> is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of A *> is to be referenced. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular part of the hermitian matrix and the strictly *> lower triangular part of A is not referenced. On exit, the *> upper triangular part of the array A is overwritten by the *> upper triangular part of the updated matrix. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular part of the hermitian matrix and the strictly *> upper triangular part of A is not referenced. On exit, the *> lower triangular part of the array A is overwritten by the *> lower triangular part of the updated matrix. *> Note that the imaginary parts of the diagonal elements need *> not be set, they are assumed to be zero, and on exit they *> are set to zero. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX,INCY,LDA,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE,DCONJG,MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 5 ELSE IF (INCY.EQ.0) THEN INFO = 7 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHER2 ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through the triangular part * of A. * IF (LSAME(UPLO,'U')) THEN * * Form A when A is stored in the upper triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 20 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(Y(J)) TEMP2 = DCONJG(ALPHA*X(J)) DO 10 I = 1,J - 1 A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 10 CONTINUE A(J,J) = DBLE(A(J,J)) + + DBLE(X(J)*TEMP1+Y(J)*TEMP2) ELSE A(J,J) = DBLE(A(J,J)) END IF 20 CONTINUE ELSE DO 40 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(Y(JY)) TEMP2 = DCONJG(ALPHA*X(JX)) IX = KX IY = KY DO 30 I = 1,J - 1 A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE A(J,J) = DBLE(A(J,J)) + + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) ELSE A(J,J) = DBLE(A(J,J)) END IF JX = JX + INCX JY = JY + INCY 40 CONTINUE END IF ELSE * * Form A when A is stored in the lower triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(Y(J)) TEMP2 = DCONJG(ALPHA*X(J)) A(J,J) = DBLE(A(J,J)) + + DBLE(X(J)*TEMP1+Y(J)*TEMP2) DO 50 I = J + 1,N A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2 50 CONTINUE ELSE A(J,J) = DBLE(A(J,J)) END IF 60 CONTINUE ELSE DO 80 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(Y(JY)) TEMP2 = DCONJG(ALPHA*X(JX)) A(J,J) = DBLE(A(J,J)) + + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) IX = JX IY = JY DO 70 I = J + 1,N IX = IX + INCX IY = IY + INCY A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2 70 CONTINUE ELSE A(J,J) = DBLE(A(J,J)) END IF JX = JX + INCX JY = JY + INCY 80 CONTINUE END IF END IF * RETURN * * End of ZHER2 . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/ztrsv.f0000644000000000000000000000013214061636515015002 xustar0030 mtime=1623670093.093104183 30 atime=1623670093.093104183 30 ctime=1623670093.093104183 elk-7.2.42/src/BLAS/ztrsv.f0000644002504400250440000002661514061636515017051 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTRSV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,LDA,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTRSV solves one of the systems of equations *> *> A*x = b, or A**T*x = b, or A**H*x = b, *> *> where b and x are n element vectors and A is an n by n unit, or *> non-unit, upper or lower triangular matrix. *> *> No test for singularity or near-singularity is included in this *> routine. Such tests must be performed before calling this routine. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the equations to be solved as *> follows: *> *> TRANS = 'N' or 'n' A*x = b. *> *> TRANS = 'T' or 't' A**T*x = b. *> *> TRANS = 'C' or 'c' A**H*x = b. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit *> triangular as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element right-hand side vector b. On exit, X is overwritten *> with the solution vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX,LDA,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),X(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,J,JX,KX LOGICAL NOCONJ,NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 6 ELSE IF (INCX.EQ.0) THEN INFO = 8 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZTRSV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOCONJ = LSAME(TRANS,'T') NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (LSAME(TRANS,'N')) THEN * * Form x := inv( A )*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 20 J = N,1,-1 IF (X(J).NE.ZERO) THEN IF (NOUNIT) X(J) = X(J)/A(J,J) TEMP = X(J) DO 10 I = J - 1,1,-1 X(I) = X(I) - TEMP*A(I,J) 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX + (N-1)*INCX DO 40 J = N,1,-1 IF (X(JX).NE.ZERO) THEN IF (NOUNIT) X(JX) = X(JX)/A(J,J) TEMP = X(JX) IX = JX DO 30 I = J - 1,1,-1 IX = IX - INCX X(IX) = X(IX) - TEMP*A(I,J) 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 60 J = 1,N IF (X(J).NE.ZERO) THEN IF (NOUNIT) X(J) = X(J)/A(J,J) TEMP = X(J) DO 50 I = J + 1,N X(I) = X(I) - TEMP*A(I,J) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80 J = 1,N IF (X(JX).NE.ZERO) THEN IF (NOUNIT) X(JX) = X(JX)/A(J,J) TEMP = X(JX) IX = JX DO 70 I = J + 1,N IX = IX + INCX X(IX) = X(IX) - TEMP*A(I,J) 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A**T )*x or x := inv( A**H )*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 110 J = 1,N TEMP = X(J) IF (NOCONJ) THEN DO 90 I = 1,J - 1 TEMP = TEMP - A(I,J)*X(I) 90 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) ELSE DO 100 I = 1,J - 1 TEMP = TEMP - DCONJG(A(I,J))*X(I) 100 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) END IF X(J) = TEMP 110 CONTINUE ELSE JX = KX DO 140 J = 1,N IX = KX TEMP = X(JX) IF (NOCONJ) THEN DO 120 I = 1,J - 1 TEMP = TEMP - A(I,J)*X(IX) IX = IX + INCX 120 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) ELSE DO 130 I = 1,J - 1 TEMP = TEMP - DCONJG(A(I,J))*X(IX) IX = IX + INCX 130 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) END IF X(JX) = TEMP JX = JX + INCX 140 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 170 J = N,1,-1 TEMP = X(J) IF (NOCONJ) THEN DO 150 I = N,J + 1,-1 TEMP = TEMP - A(I,J)*X(I) 150 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) ELSE DO 160 I = N,J + 1,-1 TEMP = TEMP - DCONJG(A(I,J))*X(I) 160 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) END IF X(J) = TEMP 170 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 200 J = N,1,-1 IX = KX TEMP = X(JX) IF (NOCONJ) THEN DO 180 I = N,J + 1,-1 TEMP = TEMP - A(I,J)*X(IX) IX = IX - INCX 180 CONTINUE IF (NOUNIT) TEMP = TEMP/A(J,J) ELSE DO 190 I = N,J + 1,-1 TEMP = TEMP - DCONJG(A(I,J))*X(IX) IX = IX - INCX 190 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) END IF X(JX) = TEMP JX = JX - INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTRSV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/ztrmv.f0000644000000000000000000000013214061636515014774 xustar0030 mtime=1623670093.095104181 30 atime=1623670093.094104182 30 ctime=1623670093.095104181 elk-7.2.42/src/BLAS/ztrmv.f0000644002504400250440000002646714061636515017050 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTRMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,LDA,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTRMV performs one of the matrix-vector operations *> *> x := A*x, or x := A**T*x, or x := A**H*x, *> *> where x is an n element vector and A is an n by n unit, or non-unit, *> upper or lower triangular matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' x := A*x. *> *> TRANS = 'T' or 't' x := A**T*x. *> *> TRANS = 'C' or 'c' x := A**H*x. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit *> triangular as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, N ). *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array A must contain the upper *> triangular matrix and the strictly lower triangular part of *> A is not referenced. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array A must contain the lower *> triangular matrix and the strictly upper triangular part of *> A is not referenced. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced either, but are assumed to be unity. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> max( 1, n ). *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. On exit, X is overwritten with the *> transformed vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX,LDA,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),X(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,J,JX,KX LOGICAL NOCONJ,NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG,MAX * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,N)) THEN INFO = 6 ELSE IF (INCX.EQ.0) THEN INFO = 8 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZTRMV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOCONJ = LSAME(TRANS,'T') NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF (LSAME(TRANS,'N')) THEN * * Form x := A*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = X(J) DO 10 I = 1,J - 1 X(I) = X(I) + TEMP*A(I,J) 10 CONTINUE IF (NOUNIT) X(J) = X(J)*A(J,J) END IF 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 30 I = 1,J - 1 X(IX) = X(IX) + TEMP*A(I,J) IX = IX + INCX 30 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(J,J) END IF JX = JX + INCX 40 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 60 J = N,1,-1 IF (X(J).NE.ZERO) THEN TEMP = X(J) DO 50 I = N,J + 1,-1 X(I) = X(I) + TEMP*A(I,J) 50 CONTINUE IF (NOUNIT) X(J) = X(J)*A(J,J) END IF 60 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 80 J = N,1,-1 IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 70 I = N,J + 1,-1 X(IX) = X(IX) + TEMP*A(I,J) IX = IX - INCX 70 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(J,J) END IF JX = JX - INCX 80 CONTINUE END IF END IF ELSE * * Form x := A**T*x or x := A**H*x. * IF (LSAME(UPLO,'U')) THEN IF (INCX.EQ.1) THEN DO 110 J = N,1,-1 TEMP = X(J) IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(J,J) DO 90 I = J - 1,1,-1 TEMP = TEMP + A(I,J)*X(I) 90 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J)) DO 100 I = J - 1,1,-1 TEMP = TEMP + DCONJG(A(I,J))*X(I) 100 CONTINUE END IF X(J) = TEMP 110 CONTINUE ELSE JX = KX + (N-1)*INCX DO 140 J = N,1,-1 TEMP = X(JX) IX = JX IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(J,J) DO 120 I = J - 1,1,-1 IX = IX - INCX TEMP = TEMP + A(I,J)*X(IX) 120 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J)) DO 130 I = J - 1,1,-1 IX = IX - INCX TEMP = TEMP + DCONJG(A(I,J))*X(IX) 130 CONTINUE END IF X(JX) = TEMP JX = JX - INCX 140 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 170 J = 1,N TEMP = X(J) IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(J,J) DO 150 I = J + 1,N TEMP = TEMP + A(I,J)*X(I) 150 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J)) DO 160 I = J + 1,N TEMP = TEMP + DCONJG(A(I,J))*X(I) 160 CONTINUE END IF X(J) = TEMP 170 CONTINUE ELSE JX = KX DO 200 J = 1,N TEMP = X(JX) IX = JX IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(J,J) DO 180 I = J + 1,N IX = IX + INCX TEMP = TEMP + A(I,J)*X(IX) 180 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J)) DO 190 I = J + 1,N IX = IX + INCX TEMP = TEMP + DCONJG(A(I,J))*X(IX) 190 CONTINUE END IF X(JX) = TEMP JX = JX + INCX 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTRMV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zhemm.f0000644000000000000000000000013114061636515014731 xustar0030 mtime=1623670093.097104179 29 atime=1623670093.09610418 30 ctime=1623670093.097104179 elk-7.2.42/src/BLAS/zhemm.f0000644002504400250440000002615314061636515016776 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHEMM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA,BETA * INTEGER LDA,LDB,LDC,M,N * CHARACTER SIDE,UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEMM performs one of the matrix-matrix operations *> *> C := alpha*A*B + beta*C, *> *> or *> *> C := alpha*B*A + beta*C, *> *> where alpha and beta are scalars, A is an hermitian matrix and B and *> C are m by n matrices. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether the hermitian matrix A *> appears on the left or right in the operation as follows: *> *> SIDE = 'L' or 'l' C := alpha*A*B + beta*C, *> *> SIDE = 'R' or 'r' C := alpha*B*A + beta*C, *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the hermitian matrix A is to be *> referenced as follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of the *> hermitian matrix is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of the *> hermitian matrix is to be referenced. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of the matrix C. *> M must be at least zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of the matrix C. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is *> m when SIDE = 'L' or 'l' and is n otherwise. *> Before entry with SIDE = 'L' or 'l', the m by m part of *> the array A must contain the hermitian matrix, such that *> when UPLO = 'U' or 'u', the leading m by m upper triangular *> part of the array A must contain the upper triangular part *> of the hermitian matrix and the strictly lower triangular *> part of A is not referenced, and when UPLO = 'L' or 'l', *> the leading m by m lower triangular part of the array A *> must contain the lower triangular part of the hermitian *> matrix and the strictly upper triangular part of A is not *> referenced. *> Before entry with SIDE = 'R' or 'r', the n by n part of *> the array A must contain the hermitian matrix, such that *> when UPLO = 'U' or 'u', the leading n by n upper triangular *> part of the array A must contain the upper triangular part *> of the hermitian matrix and the strictly lower triangular *> part of A is not referenced, and when UPLO = 'L' or 'l', *> the leading n by n lower triangular part of the array A *> must contain the lower triangular part of the hermitian *> matrix and the strictly upper triangular part of A is not *> referenced. *> Note that the imaginary parts of the diagonal elements need *> not be set, they are assumed to be zero. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When SIDE = 'L' or 'l' then *> LDA must be at least max( 1, m ), otherwise LDA must be at *> least max( 1, n ). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is COMPLEX*16 array, dimension ( LDB, N ) *> Before entry, the leading m by n part of the array B must *> contain the matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. LDB must be at least *> max( 1, m ). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is COMPLEX*16 *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then C need not be set on input. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension ( LDC, N ) *> Before entry, the leading m by n part of the array C must *> contain the matrix C, except when beta is zero, in which *> case C need not be set on entry. *> On exit, the array C is overwritten by the m by n updated *> matrix. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> On entry, LDC specifies the first dimension of C as declared *> in the calling (sub) program. LDC must be at least *> max( 1, m ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> \endverbatim *> * ===================================================================== SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA,BETA INTEGER LDA,LDB,LDC,M,N CHARACTER SIDE,UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE,DCONJG,MAX * .. * .. Local Scalars .. COMPLEX*16 TEMP1,TEMP2 INTEGER I,INFO,J,K,NROWA LOGICAL UPPER * .. * .. Parameters .. COMPLEX*16 ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * * Set NROWA as the number of rows of A. * IF (LSAME(SIDE,'L')) THEN NROWA = M ELSE NROWA = N END IF UPPER = LSAME(UPLO,'U') * * Test the input parameters. * INFO = 0 IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN INFO = 1 ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 2 ELSE IF (M.LT.0) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 7 ELSE IF (LDB.LT.MAX(1,M)) THEN INFO = 9 ELSE IF (LDC.LT.MAX(1,M)) THEN INFO = 12 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHEMM ',INFO) RETURN END IF * * Quick return if possible. * IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (BETA.EQ.ZERO) THEN DO 20 J = 1,N DO 10 I = 1,M C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,M C(I,J) = BETA*C(I,J) 30 CONTINUE 40 CONTINUE END IF RETURN END IF * * Start the operations. * IF (LSAME(SIDE,'L')) THEN * * Form C := alpha*A*B + beta*C. * IF (UPPER) THEN DO 70 J = 1,N DO 60 I = 1,M TEMP1 = ALPHA*B(I,J) TEMP2 = ZERO DO 50 K = 1,I - 1 C(K,J) = C(K,J) + TEMP1*A(K,I) TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I)) 50 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) + + ALPHA*TEMP2 END IF 60 CONTINUE 70 CONTINUE ELSE DO 100 J = 1,N DO 90 I = M,1,-1 TEMP1 = ALPHA*B(I,J) TEMP2 = ZERO DO 80 K = I + 1,M C(K,J) = C(K,J) + TEMP1*A(K,I) TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I)) 80 CONTINUE IF (BETA.EQ.ZERO) THEN C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2 ELSE C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) + + ALPHA*TEMP2 END IF 90 CONTINUE 100 CONTINUE END IF ELSE * * Form C := alpha*B*A + beta*C. * DO 170 J = 1,N TEMP1 = ALPHA*DBLE(A(J,J)) IF (BETA.EQ.ZERO) THEN DO 110 I = 1,M C(I,J) = TEMP1*B(I,J) 110 CONTINUE ELSE DO 120 I = 1,M C(I,J) = BETA*C(I,J) + TEMP1*B(I,J) 120 CONTINUE END IF DO 140 K = 1,J - 1 IF (UPPER) THEN TEMP1 = ALPHA*A(K,J) ELSE TEMP1 = ALPHA*DCONJG(A(J,K)) END IF DO 130 I = 1,M C(I,J) = C(I,J) + TEMP1*B(I,K) 130 CONTINUE 140 CONTINUE DO 160 K = J + 1,N IF (UPPER) THEN TEMP1 = ALPHA*DCONJG(A(J,K)) ELSE TEMP1 = ALPHA*A(K,J) END IF DO 150 I = 1,M C(I,J) = C(I,J) + TEMP1*B(I,K) 150 CONTINUE 160 CONTINUE 170 CONTINUE END IF * RETURN * * End of ZHEMM . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zher2k.f0000644000000000000000000000013214061636515015017 xustar0030 mtime=1623670093.098104178 30 atime=1623670093.098104178 30 ctime=1623670093.098104178 elk-7.2.42/src/BLAS/zher2k.f0000644002504400250440000003453014061636515017061 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHER2K * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA * DOUBLE PRECISION BETA * INTEGER K,LDA,LDB,LDC,N * CHARACTER TRANS,UPLO * .. * .. Array Arguments .. * COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHER2K performs one of the hermitian rank 2k operations *> *> C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, *> *> or *> *> C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, *> *> where alpha and beta are scalars with beta real, C is an n by n *> hermitian matrix and A and B are n by k matrices in the first case *> and k by n matrices in the second case. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array C is to be referenced as *> follows: *> *> UPLO = 'U' or 'u' Only the upper triangular part of C *> is to be referenced. *> *> UPLO = 'L' or 'l' Only the lower triangular part of C *> is to be referenced. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' C := alpha*A*B**H + *> conjg( alpha )*B*A**H + *> beta*C. *> *> TRANS = 'C' or 'c' C := alpha*A**H*B + *> conjg( alpha )*B**H*A + *> beta*C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix C. N must be *> at least zero. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> On entry with TRANS = 'N' or 'n', K specifies the number *> of columns of the matrices A and B, and on entry with *> TRANS = 'C' or 'c', K specifies the number of rows of the *> matrices A and B. K must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 . *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is *> k when TRANS = 'N' or 'n', and is n otherwise. *> Before entry with TRANS = 'N' or 'n', the leading n by k *> part of the array A must contain the matrix A, otherwise *> the leading k by n part of the array A must contain the *> matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. When TRANS = 'N' or 'n' *> then LDA must be at least max( 1, n ), otherwise LDA must *> be at least max( 1, k ). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is *> k when TRANS = 'N' or 'n', and is n otherwise. *> Before entry with TRANS = 'N' or 'n', the leading n by k *> part of the array B must contain the matrix B, otherwise *> the leading k by n part of the array B must contain the *> matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> On entry, LDB specifies the first dimension of B as declared *> in the calling (sub) program. When TRANS = 'N' or 'n' *> then LDB must be at least max( 1, n ), otherwise LDB must *> be at least max( 1, k ). *> Unchanged on exit. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION . *> On entry, BETA specifies the scalar beta. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension ( LDC, N ) *> Before entry with UPLO = 'U' or 'u', the leading n by n *> upper triangular part of the array C must contain the upper *> triangular part of the hermitian matrix and the strictly *> lower triangular part of C is not referenced. On exit, the *> upper triangular part of the array C is overwritten by the *> upper triangular part of the updated matrix. *> Before entry with UPLO = 'L' or 'l', the leading n by n *> lower triangular part of the array C must contain the lower *> triangular part of the hermitian matrix and the strictly *> upper triangular part of C is not referenced. On exit, the *> lower triangular part of the array C is overwritten by the *> lower triangular part of the updated matrix. *> Note that the imaginary parts of the diagonal elements need *> not be set, they are assumed to be zero, and on exit they *> are set to zero. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> On entry, LDC specifies the first dimension of C as declared *> in the calling (sub) program. LDC must be at least *> max( 1, n ). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level3 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 3 Blas routine. *> *> -- Written on 8-February-1989. *> Jack Dongarra, Argonne National Laboratory. *> Iain Duff, AERE Harwell. *> Jeremy Du Croz, Numerical Algorithms Group Ltd. *> Sven Hammarling, Numerical Algorithms Group Ltd. *> *> -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. *> Ed Anderson, Cray Research Inc. *> \endverbatim *> * ===================================================================== SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) * * -- Reference BLAS level3 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA DOUBLE PRECISION BETA INTEGER K,LDA,LDB,LDC,N CHARACTER TRANS,UPLO * .. * .. Array Arguments .. COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) * .. * * ===================================================================== * * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE,DCONJG,MAX * .. * .. Local Scalars .. COMPLEX*16 TEMP1,TEMP2 INTEGER I,INFO,J,L,NROWA LOGICAL UPPER * .. * .. Parameters .. DOUBLE PRECISION ONE PARAMETER (ONE=1.0D+0) COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * * Test the input parameters. * IF (LSAME(TRANS,'N')) THEN NROWA = N ELSE NROWA = K END IF UPPER = LSAME(UPLO,'U') * INFO = 0 IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN INFO = 1 ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. + (.NOT.LSAME(TRANS,'C'))) THEN INFO = 2 ELSE IF (N.LT.0) THEN INFO = 3 ELSE IF (K.LT.0) THEN INFO = 4 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN INFO = 7 ELSE IF (LDB.LT.MAX(1,NROWA)) THEN INFO = 9 ELSE IF (LDC.LT.MAX(1,N)) THEN INFO = 12 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHER2K',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. + (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN * * And when alpha.eq.zero. * IF (ALPHA.EQ.ZERO) THEN IF (UPPER) THEN IF (BETA.EQ.DBLE(ZERO)) THEN DO 20 J = 1,N DO 10 I = 1,J C(I,J) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1,N DO 30 I = 1,J - 1 C(I,J) = BETA*C(I,J) 30 CONTINUE C(J,J) = BETA*DBLE(C(J,J)) 40 CONTINUE END IF ELSE IF (BETA.EQ.DBLE(ZERO)) THEN DO 60 J = 1,N DO 50 I = J,N C(I,J) = ZERO 50 CONTINUE 60 CONTINUE ELSE DO 80 J = 1,N C(J,J) = BETA*DBLE(C(J,J)) DO 70 I = J + 1,N C(I,J) = BETA*C(I,J) 70 CONTINUE 80 CONTINUE END IF END IF RETURN END IF * * Start the operations. * IF (LSAME(TRANS,'N')) THEN * * Form C := alpha*A*B**H + conjg( alpha )*B*A**H + * C. * IF (UPPER) THEN DO 130 J = 1,N IF (BETA.EQ.DBLE(ZERO)) THEN DO 90 I = 1,J C(I,J) = ZERO 90 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 100 I = 1,J - 1 C(I,J) = BETA*C(I,J) 100 CONTINUE C(J,J) = BETA*DBLE(C(J,J)) ELSE C(J,J) = DBLE(C(J,J)) END IF DO 120 L = 1,K IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(B(J,L)) TEMP2 = DCONJG(ALPHA*A(J,L)) DO 110 I = 1,J - 1 C(I,J) = C(I,J) + A(I,L)*TEMP1 + + B(I,L)*TEMP2 110 CONTINUE C(J,J) = DBLE(C(J,J)) + + DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2) END IF 120 CONTINUE 130 CONTINUE ELSE DO 180 J = 1,N IF (BETA.EQ.DBLE(ZERO)) THEN DO 140 I = J,N C(I,J) = ZERO 140 CONTINUE ELSE IF (BETA.NE.ONE) THEN DO 150 I = J + 1,N C(I,J) = BETA*C(I,J) 150 CONTINUE C(J,J) = BETA*DBLE(C(J,J)) ELSE C(J,J) = DBLE(C(J,J)) END IF DO 170 L = 1,K IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(B(J,L)) TEMP2 = DCONJG(ALPHA*A(J,L)) DO 160 I = J + 1,N C(I,J) = C(I,J) + A(I,L)*TEMP1 + + B(I,L)*TEMP2 160 CONTINUE C(J,J) = DBLE(C(J,J)) + + DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2) END IF 170 CONTINUE 180 CONTINUE END IF ELSE * * Form C := alpha*A**H*B + conjg( alpha )*B**H*A + * C. * IF (UPPER) THEN DO 210 J = 1,N DO 200 I = 1,J TEMP1 = ZERO TEMP2 = ZERO DO 190 L = 1,K TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J) TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J) 190 CONTINUE IF (I.EQ.J) THEN IF (BETA.EQ.DBLE(ZERO)) THEN C(J,J) = DBLE(ALPHA*TEMP1+ + DCONJG(ALPHA)*TEMP2) ELSE C(J,J) = BETA*DBLE(C(J,J)) + + DBLE(ALPHA*TEMP1+ + DCONJG(ALPHA)*TEMP2) END IF ELSE IF (BETA.EQ.DBLE(ZERO)) THEN C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2 ELSE C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + + DCONJG(ALPHA)*TEMP2 END IF END IF 200 CONTINUE 210 CONTINUE ELSE DO 240 J = 1,N DO 230 I = J,N TEMP1 = ZERO TEMP2 = ZERO DO 220 L = 1,K TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J) TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J) 220 CONTINUE IF (I.EQ.J) THEN IF (BETA.EQ.DBLE(ZERO)) THEN C(J,J) = DBLE(ALPHA*TEMP1+ + DCONJG(ALPHA)*TEMP2) ELSE C(J,J) = BETA*DBLE(C(J,J)) + + DBLE(ALPHA*TEMP1+ + DCONJG(ALPHA)*TEMP2) END IF ELSE IF (BETA.EQ.DBLE(ZERO)) THEN C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2 ELSE C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + + DCONJG(ALPHA)*TEMP2 END IF END IF 230 CONTINUE 240 CONTINUE END IF END IF * RETURN * * End of ZHER2K. * END elk-7.2.42/src/BLAS/PaxHeaders.21776/ztpsv.f0000644000000000000000000000013214061636515015000 xustar0030 mtime=1623670093.100104177 30 atime=1623670093.100104177 30 ctime=1623670093.100104177 elk-7.2.42/src/BLAS/ztpsv.f0000644002504400250440000003011714061636515017037 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTPSV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * COMPLEX*16 AP(*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTPSV solves one of the systems of equations *> *> A*x = b, or A**T*x = b, or A**H*x = b, *> *> where b and x are n element vectors and A is an n by n unit, or *> non-unit, upper or lower triangular matrix, supplied in packed form. *> *> No test for singularity or near-singularity is included in this *> routine. Such tests must be performed before calling this routine. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the equations to be solved as *> follows: *> *> TRANS = 'N' or 'n' A*x = b. *> *> TRANS = 'T' or 't' A**T*x = b. *> *> TRANS = 'C' or 'c' A**H*x = b. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit *> triangular as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX*16 array, dimension at least *> ( ( n*( n + 1 ) )/2 ). *> Before entry with UPLO = 'U' or 'u', the array AP must *> contain the upper triangular matrix packed sequentially, *> column by column, so that AP( 1 ) contains a( 1, 1 ), *> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) *> respectively, and so on. *> Before entry with UPLO = 'L' or 'l', the array AP must *> contain the lower triangular matrix packed sequentially, *> column by column, so that AP( 1 ) contains a( 1, 1 ), *> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) *> respectively, and so on. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced, but are assumed to be unity. *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element right-hand side vector b. On exit, X is overwritten *> with the solution vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. COMPLEX*16 AP(*),X(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,J,JX,K,KK,KX LOGICAL NOCONJ,NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (INCX.EQ.0) THEN INFO = 7 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZTPSV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOCONJ = LSAME(TRANS,'T') NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF (LSAME(TRANS,'N')) THEN * * Form x := inv( A )*x. * IF (LSAME(UPLO,'U')) THEN KK = (N* (N+1))/2 IF (INCX.EQ.1) THEN DO 20 J = N,1,-1 IF (X(J).NE.ZERO) THEN IF (NOUNIT) X(J) = X(J)/AP(KK) TEMP = X(J) K = KK - 1 DO 10 I = J - 1,1,-1 X(I) = X(I) - TEMP*AP(K) K = K - 1 10 CONTINUE END IF KK = KK - J 20 CONTINUE ELSE JX = KX + (N-1)*INCX DO 40 J = N,1,-1 IF (X(JX).NE.ZERO) THEN IF (NOUNIT) X(JX) = X(JX)/AP(KK) TEMP = X(JX) IX = JX DO 30 K = KK - 1,KK - J + 1,-1 IX = IX - INCX X(IX) = X(IX) - TEMP*AP(K) 30 CONTINUE END IF JX = JX - INCX KK = KK - J 40 CONTINUE END IF ELSE KK = 1 IF (INCX.EQ.1) THEN DO 60 J = 1,N IF (X(J).NE.ZERO) THEN IF (NOUNIT) X(J) = X(J)/AP(KK) TEMP = X(J) K = KK + 1 DO 50 I = J + 1,N X(I) = X(I) - TEMP*AP(K) K = K + 1 50 CONTINUE END IF KK = KK + (N-J+1) 60 CONTINUE ELSE JX = KX DO 80 J = 1,N IF (X(JX).NE.ZERO) THEN IF (NOUNIT) X(JX) = X(JX)/AP(KK) TEMP = X(JX) IX = JX DO 70 K = KK + 1,KK + N - J IX = IX + INCX X(IX) = X(IX) - TEMP*AP(K) 70 CONTINUE END IF JX = JX + INCX KK = KK + (N-J+1) 80 CONTINUE END IF END IF ELSE * * Form x := inv( A**T )*x or x := inv( A**H )*x. * IF (LSAME(UPLO,'U')) THEN KK = 1 IF (INCX.EQ.1) THEN DO 110 J = 1,N TEMP = X(J) K = KK IF (NOCONJ) THEN DO 90 I = 1,J - 1 TEMP = TEMP - AP(K)*X(I) K = K + 1 90 CONTINUE IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) ELSE DO 100 I = 1,J - 1 TEMP = TEMP - DCONJG(AP(K))*X(I) K = K + 1 100 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1)) END IF X(J) = TEMP KK = KK + J 110 CONTINUE ELSE JX = KX DO 140 J = 1,N TEMP = X(JX) IX = KX IF (NOCONJ) THEN DO 120 K = KK,KK + J - 2 TEMP = TEMP - AP(K)*X(IX) IX = IX + INCX 120 CONTINUE IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) ELSE DO 130 K = KK,KK + J - 2 TEMP = TEMP - DCONJG(AP(K))*X(IX) IX = IX + INCX 130 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1)) END IF X(JX) = TEMP JX = JX + INCX KK = KK + J 140 CONTINUE END IF ELSE KK = (N* (N+1))/2 IF (INCX.EQ.1) THEN DO 170 J = N,1,-1 TEMP = X(J) K = KK IF (NOCONJ) THEN DO 150 I = N,J + 1,-1 TEMP = TEMP - AP(K)*X(I) K = K - 1 150 CONTINUE IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) ELSE DO 160 I = N,J + 1,-1 TEMP = TEMP - DCONJG(AP(K))*X(I) K = K - 1 160 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J)) END IF X(J) = TEMP KK = KK - (N-J+1) 170 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 200 J = N,1,-1 TEMP = X(JX) IX = KX IF (NOCONJ) THEN DO 180 K = KK,KK - (N- (J+1)),-1 TEMP = TEMP - AP(K)*X(IX) IX = IX - INCX 180 CONTINUE IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) ELSE DO 190 K = KK,KK - (N- (J+1)),-1 TEMP = TEMP - DCONJG(AP(K))*X(IX) IX = IX - INCX 190 CONTINUE IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J)) END IF X(JX) = TEMP JX = JX - INCX KK = KK - (N-J+1) 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTPSV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zhpmv.f0000644000000000000000000000013214061636515014756 xustar0030 mtime=1623670093.102104175 30 atime=1623670093.102104175 30 ctime=1623670093.102104175 elk-7.2.42/src/BLAS/zhpmv.f0000644002504400250440000002275214061636515017023 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHPMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA,BETA * INTEGER INCX,INCY,N * CHARACTER UPLO * .. * .. Array Arguments .. * COMPLEX*16 AP(*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHPMV performs the matrix-vector operation *> *> y := alpha*A*x + beta*y, *> *> where alpha and beta are scalars, x and y are n element vectors and *> A is an n by n hermitian matrix, supplied in packed form. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: *> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. *> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX*16 array, dimension at least *> ( ( n*( n + 1 ) )/2 ). *> Before entry with UPLO = 'U' or 'u', the array AP must *> contain the upper triangular part of the hermitian matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) *> and a( 2, 2 ) respectively, and so on. *> Before entry with UPLO = 'L' or 'l', the array AP must *> contain the lower triangular part of the hermitian matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) *> and a( 3, 1 ) respectively, and so on. *> Note that the imaginary parts of the diagonal elements need *> not be set and are assumed to be zero. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is COMPLEX*16 *> On entry, BETA specifies the scalar beta. When BETA is *> supplied as zero then Y need not be set on input. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. On exit, Y is overwritten by the updated *> vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA,BETA INTEGER INCX,INCY,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX*16 AP(*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER (ONE= (1.0D+0,0.0D+0)) COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE,DCONJG * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 6 ELSE IF (INCY.EQ.0) THEN INFO = 9 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHPMV ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN * * Set up the start points in X and Y. * IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * * First form y := beta*y. * IF (BETA.NE.ONE) THEN IF (INCY.EQ.1) THEN IF (BETA.EQ.ZERO) THEN DO 10 I = 1,N Y(I) = ZERO 10 CONTINUE ELSE DO 20 I = 1,N Y(I) = BETA*Y(I) 20 CONTINUE END IF ELSE IY = KY IF (BETA.EQ.ZERO) THEN DO 30 I = 1,N Y(IY) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40 I = 1,N Y(IY) = BETA*Y(IY) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF (ALPHA.EQ.ZERO) RETURN KK = 1 IF (LSAME(UPLO,'U')) THEN * * Form y when AP contains the upper triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO K = KK DO 50 I = 1,J - 1 Y(I) = Y(I) + TEMP1*AP(K) TEMP2 = TEMP2 + DCONJG(AP(K))*X(I) K = K + 1 50 CONTINUE Y(J) = Y(J) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2 KK = KK + J 60 CONTINUE ELSE JX = KX JY = KY DO 80 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO IX = KX IY = KY DO 70 K = KK,KK + J - 2 Y(IY) = Y(IY) + TEMP1*AP(K) TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + J 80 CONTINUE END IF ELSE * * Form y when AP contains the lower triangle. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 100 J = 1,N TEMP1 = ALPHA*X(J) TEMP2 = ZERO Y(J) = Y(J) + TEMP1*DBLE(AP(KK)) K = KK + 1 DO 90 I = J + 1,N Y(I) = Y(I) + TEMP1*AP(K) TEMP2 = TEMP2 + DCONJG(AP(K))*X(I) K = K + 1 90 CONTINUE Y(J) = Y(J) + ALPHA*TEMP2 KK = KK + (N-J+1) 100 CONTINUE ELSE JX = KX JY = KY DO 120 J = 1,N TEMP1 = ALPHA*X(JX) TEMP2 = ZERO Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK)) IX = JX IY = JY DO 110 K = KK + 1,KK + N - J IX = IX + INCX IY = IY + INCY Y(IY) = Y(IY) + TEMP1*AP(K) TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX) 110 CONTINUE Y(JY) = Y(JY) + ALPHA*TEMP2 JX = JX + INCX JY = JY + INCY KK = KK + (N-J+1) 120 CONTINUE END IF END IF * RETURN * * End of ZHPMV . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/zhpr2.f0000644000000000000000000000013214061636515014657 xustar0030 mtime=1623670093.104104173 30 atime=1623670093.103104174 30 ctime=1623670093.104104173 elk-7.2.42/src/BLAS/zhpr2.f0000644002504400250440000002263614061636515016725 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHPR2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * * .. Scalar Arguments .. * COMPLEX*16 ALPHA * INTEGER INCX,INCY,N * CHARACTER UPLO * .. * .. Array Arguments .. * COMPLEX*16 AP(*),X(*),Y(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHPR2 performs the hermitian rank 2 operation *> *> A := alpha*x*y**H + conjg( alpha )*y*x**H + A, *> *> where alpha is a scalar, x and y are n element vectors and A is an *> n by n hermitian matrix, supplied in packed form. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: *> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. *> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the n *> element vector y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is COMPLEX*16 array, dimension at least *> ( ( n*( n + 1 ) )/2 ). *> Before entry with UPLO = 'U' or 'u', the array AP must *> contain the upper triangular part of the hermitian matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) *> and a( 2, 2 ) respectively, and so on. On exit, the array *> AP is overwritten by the upper triangular part of the *> updated matrix. *> Before entry with UPLO = 'L' or 'l', the array AP must *> contain the lower triangular part of the hermitian matrix *> packed sequentially, column by column, so that AP( 1 ) *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) *> and a( 3, 1 ) respectively, and so on. On exit, the array *> AP is overwritten by the lower triangular part of the *> updated matrix. *> Note that the imaginary parts of the diagonal elements need *> not be set, they are assumed to be zero, and on exit they *> are set to zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX,INCY,N CHARACTER UPLO * .. * .. Array Arguments .. COMPLEX*16 AP(*),X(*),Y(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE,DCONJG * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (N.LT.0) THEN INFO = 2 ELSE IF (INCX.EQ.0) THEN INFO = 5 ELSE IF (INCY.EQ.0) THEN INFO = 7 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZHPR2 ',INFO) RETURN END IF * * Quick return if possible. * IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN IF (INCX.GT.0) THEN KX = 1 ELSE KX = 1 - (N-1)*INCX END IF IF (INCY.GT.0) THEN KY = 1 ELSE KY = 1 - (N-1)*INCY END IF JX = KX JY = KY END IF * * Start the operations. In this version the elements of the array AP * are accessed sequentially with one pass through AP. * KK = 1 IF (LSAME(UPLO,'U')) THEN * * Form A when upper triangle is stored in AP. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 20 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(Y(J)) TEMP2 = DCONJG(ALPHA*X(J)) K = KK DO 10 I = 1,J - 1 AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 K = K + 1 10 CONTINUE AP(KK+J-1) = DBLE(AP(KK+J-1)) + + DBLE(X(J)*TEMP1+Y(J)*TEMP2) ELSE AP(KK+J-1) = DBLE(AP(KK+J-1)) END IF KK = KK + J 20 CONTINUE ELSE DO 40 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(Y(JY)) TEMP2 = DCONJG(ALPHA*X(JX)) IX = KX IY = KY DO 30 K = KK,KK + J - 2 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE AP(KK+J-1) = DBLE(AP(KK+J-1)) + + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) ELSE AP(KK+J-1) = DBLE(AP(KK+J-1)) END IF JX = JX + INCX JY = JY + INCY KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN DO 60 J = 1,N IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(Y(J)) TEMP2 = DCONJG(ALPHA*X(J)) AP(KK) = DBLE(AP(KK)) + + DBLE(X(J)*TEMP1+Y(J)*TEMP2) K = KK + 1 DO 50 I = J + 1,N AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 K = K + 1 50 CONTINUE ELSE AP(KK) = DBLE(AP(KK)) END IF KK = KK + N - J + 1 60 CONTINUE ELSE DO 80 J = 1,N IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN TEMP1 = ALPHA*DCONJG(Y(JY)) TEMP2 = DCONJG(ALPHA*X(JX)) AP(KK) = DBLE(AP(KK)) + + DBLE(X(JX)*TEMP1+Y(JY)*TEMP2) IX = JX IY = JY DO 70 K = KK + 1,KK + N - J IX = IX + INCX IY = IY + INCY AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 70 CONTINUE ELSE AP(KK) = DBLE(AP(KK)) END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of ZHPR2 . * END elk-7.2.42/src/BLAS/PaxHeaders.21776/ztpmv.f0000644000000000000000000000013214061636515014772 xustar0030 mtime=1623670093.106104171 30 atime=1623670093.105104172 30 ctime=1623670093.106104171 elk-7.2.42/src/BLAS/ztpmv.f0000644002504400250440000002775214061636515017044 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTPMV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) * * .. Scalar Arguments .. * INTEGER INCX,N * CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. * COMPLEX*16 AP(*),X(*) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTPMV performs one of the matrix-vector operations *> *> x := A*x, or x := A**T*x, or x := A**H*x, *> *> where x is an n element vector and A is an n by n unit, or non-unit, *> upper or lower triangular matrix, supplied in packed form. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> On entry, UPLO specifies whether the matrix is an upper or *> lower triangular matrix as follows: *> *> UPLO = 'U' or 'u' A is an upper triangular matrix. *> *> UPLO = 'L' or 'l' A is a lower triangular matrix. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> *> TRANS = 'N' or 'n' x := A*x. *> *> TRANS = 'T' or 't' x := A**T*x. *> *> TRANS = 'C' or 'c' x := A**H*x. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not A is unit *> triangular as follows: *> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. *> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX*16 array, dimension at least *> ( ( n*( n + 1 ) )/2 ). *> Before entry with UPLO = 'U' or 'u', the array AP must *> contain the upper triangular matrix packed sequentially, *> column by column, so that AP( 1 ) contains a( 1, 1 ), *> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) *> respectively, and so on. *> Before entry with UPLO = 'L' or 'l', the array AP must *> contain the lower triangular matrix packed sequentially, *> column by column, so that AP( 1 ) contains a( 1, 1 ), *> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) *> respectively, and so on. *> Note that when DIAG = 'U' or 'u', the diagonal elements of *> A are not referenced, but are assumed to be unity. *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension at least *> ( 1 + ( n - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the n *> element vector x. On exit, X is overwritten with the *> transformed vector x. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16_blas_level2 * *> \par Further Details: * ===================== *> *> \verbatim *> *> Level 2 Blas routine. *> The vector and matrix arguments are not referenced when N = 0, or M = 0 *> *> -- Written on 22-October-1986. *> Jack Dongarra, Argonne National Lab. *> Jeremy Du Croz, Nag Central Office. *> Sven Hammarling, Nag Central Office. *> Richard Hanson, Sandia National Labs. *> \endverbatim *> * ===================================================================== SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) * * -- Reference BLAS level2 routine (version 3.7.0) -- * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX,N CHARACTER DIAG,TRANS,UPLO * .. * .. Array Arguments .. COMPLEX*16 AP(*),X(*) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0)) * .. * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I,INFO,IX,J,JX,K,KK,KX LOGICAL NOCONJ,NOUNIT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * * Test the input parameters. * INFO = 0 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN INFO = 1 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. + .NOT.LSAME(TRANS,'C')) THEN INFO = 2 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN INFO = 3 ELSE IF (N.LT.0) THEN INFO = 4 ELSE IF (INCX.EQ.0) THEN INFO = 7 END IF IF (INFO.NE.0) THEN CALL XERBLA('ZTPMV ',INFO) RETURN END IF * * Quick return if possible. * IF (N.EQ.0) RETURN * NOCONJ = LSAME(TRANS,'T') NOUNIT = LSAME(DIAG,'N') * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * IF (INCX.LE.0) THEN KX = 1 - (N-1)*INCX ELSE IF (INCX.NE.1) THEN KX = 1 END IF * * Start the operations. In this version the elements of AP are * accessed sequentially with one pass through AP. * IF (LSAME(TRANS,'N')) THEN * * Form x:= A*x. * IF (LSAME(UPLO,'U')) THEN KK = 1 IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = X(J) K = KK DO 10 I = 1,J - 1 X(I) = X(I) + TEMP*AP(K) K = K + 1 10 CONTINUE IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) END IF KK = KK + J 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 30 K = KK,KK + J - 2 X(IX) = X(IX) + TEMP*AP(K) IX = IX + INCX 30 CONTINUE IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) END IF JX = JX + INCX KK = KK + J 40 CONTINUE END IF ELSE KK = (N* (N+1))/2 IF (INCX.EQ.1) THEN DO 60 J = N,1,-1 IF (X(J).NE.ZERO) THEN TEMP = X(J) K = KK DO 50 I = N,J + 1,-1 X(I) = X(I) + TEMP*AP(K) K = K - 1 50 CONTINUE IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) END IF KK = KK - (N-J+1) 60 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 80 J = N,1,-1 IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX DO 70 K = KK,KK - (N- (J+1)),-1 X(IX) = X(IX) + TEMP*AP(K) IX = IX - INCX 70 CONTINUE IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) END IF JX = JX - INCX KK = KK - (N-J+1) 80 CONTINUE END IF END IF ELSE * * Form x := A**T*x or x := A**H*x. * IF (LSAME(UPLO,'U')) THEN KK = (N* (N+1))/2 IF (INCX.EQ.1) THEN DO 110 J = N,1,-1 TEMP = X(J) K = KK - 1 IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*AP(KK) DO 90 I = J - 1,1,-1 TEMP = TEMP + AP(K)*X(I) K = K - 1 90 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) DO 100 I = J - 1,1,-1 TEMP = TEMP + DCONJG(AP(K))*X(I) K = K - 1 100 CONTINUE END IF X(J) = TEMP KK = KK - J 110 CONTINUE ELSE JX = KX + (N-1)*INCX DO 140 J = N,1,-1 TEMP = X(JX) IX = JX IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*AP(KK) DO 120 K = KK - 1,KK - J + 1,-1 IX = IX - INCX TEMP = TEMP + AP(K)*X(IX) 120 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) DO 130 K = KK - 1,KK - J + 1,-1 IX = IX - INCX TEMP = TEMP + DCONJG(AP(K))*X(IX) 130 CONTINUE END IF X(JX) = TEMP JX = JX - INCX KK = KK - J 140 CONTINUE END IF ELSE KK = 1 IF (INCX.EQ.1) THEN DO 170 J = 1,N TEMP = X(J) K = KK + 1 IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*AP(KK) DO 150 I = J + 1,N TEMP = TEMP + AP(K)*X(I) K = K + 1 150 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) DO 160 I = J + 1,N TEMP = TEMP + DCONJG(AP(K))*X(I) K = K + 1 160 CONTINUE END IF X(J) = TEMP KK = KK + (N-J+1) 170 CONTINUE ELSE JX = KX DO 200 J = 1,N TEMP = X(JX) IX = JX IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*AP(KK) DO 180 K = KK + 1,KK + N - J IX = IX + INCX TEMP = TEMP + AP(K)*X(IX) 180 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) DO 190 K = KK + 1,KK + N - J IX = IX + INCX TEMP = TEMP + DCONJG(AP(K))*X(IX) 190 CONTINUE END IF X(JX) = TEMP JX = JX + INCX KK = KK + (N-J+1) 200 CONTINUE END IF END IF END IF * RETURN * * End of ZTPMV . * END elk-7.2.42/src/PaxHeaders.21776/LAPACK0000644000000000000000000000013214061636515013600 xustar0030 mtime=1623670093.464103839 30 atime=1623670093.112104166 30 ctime=1623670093.464103839 elk-7.2.42/src/LAPACK/0000755002504400250440000000000014061636515015712 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaisnan.f0000644000000000000000000000013214061636515015615 xustar0030 mtime=1623670093.113104164 30 atime=1623670093.113104164 30 ctime=1623670093.113104164 elk-7.2.42/src/LAPACK/dlaisnan.f0000644002504400250440000000506014061636515017653 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAISNAN tests input for NaN by comparing two arguments for inequality. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAISNAN + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 ) * * .. Scalar Arguments .. * DOUBLE PRECISION, INTENT(IN) :: DIN1, DIN2 * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> This routine is not for general use. It exists solely to avoid *> over-optimization in DISNAN. *> *> DLAISNAN checks for NaNs by comparing its two arguments for *> inequality. NaN is the only floating-point value where NaN != NaN *> returns .TRUE. To check for NaNs, pass the same variable as both *> arguments. *> *> A compiler must assume that the two arguments are *> not the same variable, and the test will not be optimized away. *> Interprocedural or whole-program optimization may delete this *> test. The ISNAN functions will be replaced by the correct *> Fortran 03 intrinsic once the intrinsic is widely available. *> \endverbatim * * Arguments: * ========== * *> \param[in] DIN1 *> \verbatim *> DIN1 is DOUBLE PRECISION *> \endverbatim *> *> \param[in] DIN2 *> \verbatim *> DIN2 is DOUBLE PRECISION *> Two numbers to compare for inequality. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup OTHERauxiliary * * ===================================================================== LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. DOUBLE PRECISION, INTENT(IN) :: DIN1, DIN2 * .. * * ===================================================================== * * .. Executable Statements .. DLAISNAN = (DIN1.NE.DIN2) RETURN END elk-7.2.42/src/LAPACK/PaxHeaders.21776/disnan.f0000644000000000000000000000013214061636515015300 xustar0030 mtime=1623670093.115104163 30 atime=1623670093.115104163 30 ctime=1623670093.115104163 elk-7.2.42/src/LAPACK/disnan.f0000644002504400250440000000372714061636515017346 0ustar00dewhurstdewhurst00000000000000*> \brief \b DISNAN tests input for NaN. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DISNAN + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * LOGICAL FUNCTION DISNAN( DIN ) * * .. Scalar Arguments .. * DOUBLE PRECISION, INTENT(IN) :: DIN * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DISNAN returns .TRUE. if its argument is NaN, and .FALSE. *> otherwise. To be replaced by the Fortran 2003 intrinsic in the *> future. *> \endverbatim * * Arguments: * ========== * *> \param[in] DIN *> \verbatim *> DIN is DOUBLE PRECISION *> Input to test for NaN. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup OTHERauxiliary * * ===================================================================== LOGICAL FUNCTION DISNAN( DIN ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. DOUBLE PRECISION, INTENT(IN) :: DIN * .. * * ===================================================================== * * .. External Functions .. LOGICAL DLAISNAN EXTERNAL DLAISNAN * .. * .. Executable Statements .. DISNAN = DLAISNAN(DIN,DIN) RETURN END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsyev.f0000644000000000000000000000013214061636515015156 xustar0030 mtime=1623670093.117104161 30 atime=1623670093.116104162 30 ctime=1623670093.117104161 elk-7.2.42/src/LAPACK/dsyev.f0000644002504400250440000002036414061636515017220 0ustar00dewhurstdewhurst00000000000000*> \brief DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYEV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, UPLO * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYEV computes all eigenvalues and, optionally, eigenvectors of a *> real symmetric matrix A. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA, N) *> On entry, the symmetric matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> orthonormal eigenvectors of the matrix A. *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') *> or the upper triangle (if UPLO='U') of A, including the *> diagonal, is destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> If INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(1,3*N-1). *> For optimal efficiency, LWORK >= (NB+2)*N, *> where NB is the blocksize for DSYTRD returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the algorithm failed to converge; i *> off-diagonal elements of an intermediate tridiagonal *> form did not converge to zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleSYeigen * * ===================================================================== SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. LOGICAL LOWER, LQUERY, WANTZ INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE, $ LLWORK, LWKOPT, NB DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, $ SMLNUM * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLANSY EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY * .. * .. External Subroutines .. EXTERNAL DLASCL, DORGTR, DSCAL, DSTEQR, DSTERF, DSYTRD, $ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LOWER = LSAME( UPLO, 'L' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF * IF( INFO.EQ.0 ) THEN NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) LWKOPT = MAX( 1, ( NB+2 )*N ) WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, 3*N-1 ) .AND. .NOT.LQUERY ) $ INFO = -8 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYEV ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN RETURN END IF * IF( N.EQ.1 ) THEN W( 1 ) = A( 1, 1 ) WORK( 1 ) = 2 IF( WANTZ ) $ A( 1, 1 ) = ONE RETURN END IF * * Get machine constants. * SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) ISCALE = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) * * Call DSYTRD to reduce symmetric matrix to tridiagonal form. * INDE = 1 INDTAU = INDE + N INDWRK = INDTAU + N LLWORK = LWORK - INDWRK + 1 CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), $ WORK( INDWRK ), LLWORK, IINFO ) * * For eigenvalues only, call DSTERF. For eigenvectors, first call * DORGTR to generate the orthogonal matrix, then call DSTEQR. * IF( .NOT.WANTZ ) THEN CALL DSTERF( N, W, WORK( INDE ), INFO ) ELSE CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), $ LLWORK, IINFO ) CALL DSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ), $ INFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = N ELSE IMAX = INFO - 1 END IF CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * * Set WORK(1) to optimal workspace size. * WORK( 1 ) = LWKOPT * RETURN * * End of DSYEV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsygvx.f0000644000000000000000000000013114061636515015347 xustar0030 mtime=1623670093.119104159 29 atime=1623670093.11810416 30 ctime=1623670093.119104159 elk-7.2.42/src/LAPACK/dsygvx.f0000644002504400250440000003556114061636515017417 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYGVX * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYGVX + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, * VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, * LWORK, IWORK, IFAIL, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, RANGE, UPLO * INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N * DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER IFAIL( * ), IWORK( * ) * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ), * $ Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYGVX computes selected eigenvalues, and optionally, eigenvectors *> of a real generalized symmetric-definite eigenproblem, of the form *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A *> and B are assumed to be symmetric and B is also positive definite. *> Eigenvalues and eigenvectors can be selected by specifying either a *> range of values or a range of indices for the desired eigenvalues. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> Specifies the problem type to be solved: *> = 1: A*x = (lambda)*B*x *> = 2: A*B*x = (lambda)*x *> = 3: B*A*x = (lambda)*x *> \endverbatim *> *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] RANGE *> \verbatim *> RANGE is CHARACTER*1 *> = 'A': all eigenvalues will be found. *> = 'V': all eigenvalues in the half-open interval (VL,VU] *> will be found. *> = 'I': the IL-th through IU-th eigenvalues will be found. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A and B are stored; *> = 'L': Lower triangle of A and B are stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix pencil (A,B). N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA, N) *> On entry, the symmetric matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> *> On exit, the lower triangle (if UPLO='L') or the upper *> triangle (if UPLO='U') of A, including the diagonal, is *> destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB, N) *> On entry, the symmetric matrix B. If UPLO = 'U', the *> leading N-by-N upper triangular part of B contains the *> upper triangular part of the matrix B. If UPLO = 'L', *> the leading N-by-N lower triangular part of B contains *> the lower triangular part of the matrix B. *> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[in] VL *> \verbatim *> VL is DOUBLE PRECISION *> If RANGE='V', the lower bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION *> If RANGE='V', the upper bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] IL *> \verbatim *> IL is INTEGER *> If RANGE='I', the index of the *> smallest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] IU *> \verbatim *> IU is INTEGER *> If RANGE='I', the index of the *> largest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] ABSTOL *> \verbatim *> ABSTOL is DOUBLE PRECISION *> The absolute error tolerance for the eigenvalues. *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to *> *> ABSTOL + EPS * max( |a|,|b| ) , *> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing C to tridiagonal form, where C is the symmetric *> matrix of the standard symmetric problem to which the *> generalized problem is transformed. *> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). *> \endverbatim *> *> \param[out] M *> \verbatim *> M is INTEGER *> The total number of eigenvalues found. 0 <= M <= N. *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> On normal exit, the first M elements contain the selected *> eigenvalues in ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M)) *> If JOBZ = 'N', then Z is not referenced. *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z *> contain the orthonormal eigenvectors of the matrix A *> corresponding to the selected eigenvalues, with the i-th *> column of Z holding the eigenvector associated with W(i). *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**T*B*Z = I; *> if ITYPE = 3, Z**T*inv(B)*Z = I. *> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. *> Note: the user must ensure that at least max(1,M) columns are *> supplied in the array Z; if RANGE = 'V', the exact value of M *> is not known in advance and an upper bound must be used. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> JOBZ = 'V', LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(1,8*N). *> For optimal efficiency, LWORK >= (NB+3)*N, *> where NB is the blocksize for DSYTRD returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (5*N) *> \endverbatim *> *> \param[out] IFAIL *> \verbatim *> IFAIL is INTEGER array, dimension (N) *> If JOBZ = 'V', then if INFO = 0, the first M elements of *> IFAIL are zero. If INFO > 0, then IFAIL contains the *> indices of the eigenvectors that failed to converge. *> If JOBZ = 'N', then IFAIL is not referenced. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: DPOTRF or DSYEVX returned an error code: *> <= N: if INFO = i, DSYEVX failed to converge; *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= N, then the leading *> minor of order i of B is not positive definite. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup doubleSYeigen * *> \par Contributors: * ================== *> *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA * * ===================================================================== SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, $ LWORK, IWORK, IFAIL, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, RANGE, UPLO INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER IFAIL( * ), IWORK( * ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ), $ Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ CHARACTER TRANS INTEGER LWKMIN, LWKOPT, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DPOTRF, DSYEVX, DSYGST, DTRMM, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * UPPER = LSAME( UPLO, 'U' ) WANTZ = LSAME( JOBZ, 'V' ) ALLEIG = LSAME( RANGE, 'A' ) VALEIG = LSAME( RANGE, 'V' ) INDEIG = LSAME( RANGE, 'I' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -2 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN INFO = -3 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -9 ELSE IF( VALEIG ) THEN IF( N.GT.0 .AND. VU.LE.VL ) $ INFO = -11 ELSE IF( INDEIG ) THEN IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN INFO = -12 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN INFO = -13 END IF END IF END IF IF (INFO.EQ.0) THEN IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN INFO = -18 END IF END IF * IF( INFO.EQ.0 ) THEN LWKMIN = MAX( 1, 8*N ) NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) LWKOPT = MAX( LWKMIN, ( NB + 3 )*N ) WORK( 1 ) = LWKOPT * IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN INFO = -20 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYGVX', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * M = 0 IF( N.EQ.0 ) THEN RETURN END IF * * Form a Cholesky factorization of B. * CALL DPOTRF( UPLO, N, B, LDB, INFO ) IF( INFO.NE.0 ) THEN INFO = N + INFO RETURN END IF * * Transform problem to standard eigenvalue problem and solve. * CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) CALL DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, $ M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO ) * IF( WANTZ ) THEN * * Backtransform eigenvectors to the original problem. * IF( INFO.GT.0 ) $ M = INFO - 1 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN * * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y * IF( UPPER ) THEN TRANS = 'N' ELSE TRANS = 'T' END IF * CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, ONE, B, $ LDB, Z, LDZ ) * ELSE IF( ITYPE.EQ.3 ) THEN * * For B*A*x=(lambda)*x; * backtransform eigenvectors: x = L*y or U**T*y * IF( UPPER ) THEN TRANS = 'T' ELSE TRANS = 'N' END IF * CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, ONE, B, $ LDB, Z, LDZ ) END IF END IF * * Set WORK(1) to optimal workspace size. * WORK( 1 ) = LWKOPT * RETURN * * End of DSYGVX * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlamch.f0000644000000000000000000000013214061636515015254 xustar0030 mtime=1623670093.120104158 30 atime=1623670093.120104158 30 ctime=1623670093.120104158 elk-7.2.42/src/LAPACK/dlamch.f0000644002504400250440000000672314061636515017321 0ustar00dewhurstdewhurst00000000000000 FUNCTION DLAMCH ( CMACH ) RESULT(RMACH) ! ! -- LAPACK auxiliary routine Replacement for DLAMCH.f ! use Fortran 90 Machine Parameter built-in functions. ! character(len=1) :: CMACH real(kind(1.d0)) :: xdbl, ydbl, RMACH ! ! Purpose ! ======= ! ! ! DLAMCH determines double precision machine parameters. ! ! Arguments ! ========= ! ! CMACH (input) CHARACTER*1 ! Specifies the value to be returned by DLAMCH: ! = 'E' or 'e', DLAMCH := eps ! = 'S' or 's , DLAMCH := sfmin ! = 'B' or 'b', DLAMCH := base ! = 'P' or 'p', DLAMCH := eps*base ! = 'N' or 'n', DLAMCH := t ! = 'R' or 'r', DLAMCH := rnd ! = 'M' or 'm', DLAMCH := emin ! = 'U' or 'u', DLAMCH := rmin ! = 'L' or 'l', DLAMCH := emax ! = 'O' or 'o', DLAMCH := rmax ! ! where ! ! ! ===================================================================== xdbl=1.d0 IF( CMACH == 'E' .or. CMACH == 'e' ) THEN ! eps = relative machine precision RMACH = Epsilon(xdbl) ELSE IF( CMACH == 'S' .or. CMACH == 's' ) THEN ! sfmin = safe minimum, such that 1/sfmin does not overflow RMACH = Tiny(xdbl) ELSE IF( CMACH == 'B' .or. CMACH == 'b' ) THEN ! base = base of the machine RMACH = Radix(xdbl) ELSE IF( CMACH == 'P' .or. CMACH == 'p' ) THEN ! prec = eps*base RMACH = Radix(xdbl)*Epsilon(xdbl) ELSE IF( CMACH == 'N' .or. CMACH == 'n' ) THEN ! t = number of (base) digits in the mantissa RMACH = Digits(xdbl) ELSE IF( CMACH == 'R' .or. CMACH == 'r' ) THEN ! rnd = 1.0 when rounding occurs in addition, 0.0 otherwise ! Assume rounding (IEEE). RMACH = 1.0 ELSE IF( CMACH == 'M' .or. CMACH == 'm' ) THEN ! emin = minimum exponent before (gradual) underflow RMACH = Minexponent(xdbl) ELSE IF( CMACH == 'U' .or. CMACH == 'u' ) THEN ! rmin = underflow threshold - base**(emin-1) RMACH = Tiny(xdbl) ELSE IF( CMACH == 'L' .or. CMACH == 'l' ) THEN ! emax = largest exponent before overflow RMACH = Maxexponent(xdbl) ELSE IF( CMACH == 'O' .or. CMACH == 'o' ) THEN ! rmax = overflow threshold - (base**emax)*(1-eps) RMACH = Huge(xdbl) END IF ! END * ************************************************************************ * DOUBLE PRECISION FUNCTION DLAMC3( A, B ) * * -- LAPACK auxiliary routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. DOUBLE PRECISION A, B * * .. Local variables .. INTEGER I DOUBLE PRECISION X(10),Y(10) * .. * * Purpose * ======= * * DLAMC3 is intended to force A and B to be stored prior to doing * the addition of A and B , for use in situations where optimizers * might hold one of these in a register. * * Arguments * ========= * * A (input) DOUBLE PRECISION * B (input) DOUBLE PRECISION * The values A and B. * * ===================================================================== * * .. Executable Statements .. * * DLAMC3 = A + B * Modification by JKD to ensure variables are flushed to memory DO I=1,10 X(I)=A END DO DO I=1,10 Y(I)=X(I)+B END DO DLAMC3=Y(10) * RETURN * * End of DLAMC3 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhpgvx.f0000644000000000000000000000013214061636515015352 xustar0030 mtime=1623670093.122104156 30 atime=1623670093.122104156 30 ctime=1623670093.122104156 elk-7.2.42/src/LAPACK/zhpgvx.f0000644002504400250440000003221414061636515017411 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHPGVX * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHPGVX + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, * IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, * IWORK, IFAIL, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, RANGE, UPLO * INTEGER IL, INFO, ITYPE, IU, LDZ, M, N * DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER IFAIL( * ), IWORK( * ) * DOUBLE PRECISION RWORK( * ), W( * ) * COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHPGVX computes selected eigenvalues and, optionally, eigenvectors *> of a complex generalized Hermitian-definite eigenproblem, of the form *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and *> B are assumed to be Hermitian, stored in packed format, and B is also *> positive definite. Eigenvalues and eigenvectors can be selected by *> specifying either a range of values or a range of indices for the *> desired eigenvalues. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> Specifies the problem type to be solved: *> = 1: A*x = (lambda)*B*x *> = 2: A*B*x = (lambda)*x *> = 3: B*A*x = (lambda)*x *> \endverbatim *> *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] RANGE *> \verbatim *> RANGE is CHARACTER*1 *> = 'A': all eigenvalues will be found; *> = 'V': all eigenvalues in the half-open interval (VL,VU] *> will be found; *> = 'I': the IL-th through IU-th eigenvalues will be found. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangles of A and B are stored; *> = 'L': Lower triangles of A and B are stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the Hermitian matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. *> *> On exit, the contents of AP are destroyed. *> \endverbatim *> *> \param[in,out] BP *> \verbatim *> BP is COMPLEX*16 array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the Hermitian matrix *> B, packed columnwise in a linear array. The j-th column of B *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. *> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H, in the same storage *> format as B. *> \endverbatim *> *> \param[in] VL *> \verbatim *> VL is DOUBLE PRECISION *> *> If RANGE='V', the lower bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION *> *> If RANGE='V', the upper bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] IL *> \verbatim *> IL is INTEGER *> *> If RANGE='I', the index of the *> smallest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] IU *> \verbatim *> IU is INTEGER *> *> If RANGE='I', the index of the *> largest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] ABSTOL *> \verbatim *> ABSTOL is DOUBLE PRECISION *> The absolute error tolerance for the eigenvalues. *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to *> *> ABSTOL + EPS * max( |a|,|b| ) , *> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. *> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). *> \endverbatim *> *> \param[out] M *> \verbatim *> M is INTEGER *> The total number of eigenvalues found. 0 <= M <= N. *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> On normal exit, the first M elements contain the selected *> eigenvalues in ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ, N) *> If JOBZ = 'N', then Z is not referenced. *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z *> contain the orthonormal eigenvectors of the matrix A *> corresponding to the selected eigenvalues, with the i-th *> column of Z holding the eigenvector associated with W(i). *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**H*B*Z = I; *> if ITYPE = 3, Z**H*inv(B)*Z = I. *> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. *> Note: the user must ensure that at least max(1,M) columns are *> supplied in the array Z; if RANGE = 'V', the exact value of M *> is not known in advance and an upper bound must be used. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> JOBZ = 'V', LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (2*N) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (7*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (5*N) *> \endverbatim *> *> \param[out] IFAIL *> \verbatim *> IFAIL is INTEGER array, dimension (N) *> If JOBZ = 'V', then if INFO = 0, the first M elements of *> IFAIL are zero. If INFO > 0, then IFAIL contains the *> indices of the eigenvectors that failed to converge. *> If JOBZ = 'N', then IFAIL is not referenced. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: ZPPTRF or ZHPEVX returned an error code: *> <= N: if INFO = i, ZHPEVX failed to converge; *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= n, then the leading *> minor of order i of B is not positive definite. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16OTHEReigen * *> \par Contributors: * ================== *> *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA * * ===================================================================== SUBROUTINE ZHPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, $ IWORK, IFAIL, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, RANGE, UPLO INTEGER IL, INFO, ITYPE, IU, LDZ, M, N DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER IFAIL( * ), IWORK( * ) DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL ALLEIG, INDEIG, UPPER, VALEIG, WANTZ CHARACTER TRANS INTEGER J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZHPEVX, ZHPGST, ZPPTRF, ZTPMV, ZTPSV * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) UPPER = LSAME( UPLO, 'U' ) ALLEIG = LSAME( RANGE, 'A' ) VALEIG = LSAME( RANGE, 'V' ) INDEIG = LSAME( RANGE, 'I' ) * INFO = 0 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -2 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN INFO = -3 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( VALEIG ) THEN IF( N.GT.0 .AND. VU.LE.VL ) THEN INFO = -9 END IF ELSE IF( INDEIG ) THEN IF( IL.LT.1 ) THEN INFO = -10 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN INFO = -11 END IF END IF END IF IF( INFO.EQ.0 ) THEN IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -16 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHPGVX', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Form a Cholesky factorization of B. * CALL ZPPTRF( UPLO, N, BP, INFO ) IF( INFO.NE.0 ) THEN INFO = N + INFO RETURN END IF * * Transform problem to standard eigenvalue problem and solve. * CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) CALL ZHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M, $ W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO ) * IF( WANTZ ) THEN * * Backtransform eigenvectors to the original problem. * IF( INFO.GT.0 ) $ M = INFO - 1 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN * * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y * IF( UPPER ) THEN TRANS = 'N' ELSE TRANS = 'C' END IF * DO 10 J = 1, M CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), $ 1 ) 10 CONTINUE * ELSE IF( ITYPE.EQ.3 ) THEN * * For B*A*x=(lambda)*x; * backtransform eigenvectors: x = L*y or U**H *y * IF( UPPER ) THEN TRANS = 'C' ELSE TRANS = 'N' END IF * DO 20 J = 1, M CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ), $ 1 ) 20 CONTINUE END IF END IF * RETURN * * End of ZHPGVX * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/iparam2stage.f0000644000000000000000000000013214061636515016403 xustar0030 mtime=1623670093.124104154 30 atime=1623670093.124104154 30 ctime=1623670093.124104154 elk-7.2.42/src/LAPACK/iparam2stage.f0000644002504400250440000003000414061636515020435 0ustar00dewhurstdewhurst00000000000000*> \brief \b IPARAM2STAGE * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download IPARAM2STAGE + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * INTEGER FUNCTION IPARAM2STAGE( ISPEC, NAME, OPTS, * NI, NBI, IBI, NXI ) * #if defined(_OPENMP) * use omp_lib * #endif * IMPLICIT NONE * * .. Scalar Arguments .. * CHARACTER*( * ) NAME, OPTS * INTEGER ISPEC, NI, NBI, IBI, NXI * *> \par Purpose: * ============= *> *> \verbatim *> *> This program sets problem and machine dependent parameters *> useful for xHETRD_2STAGE, xHETRD_HE2HB, xHETRD_HB2ST, *> xGEBRD_2STAGE, xGEBRD_GE2GB, xGEBRD_GB2BD *> and related subroutines for eigenvalue problems. *> It is called whenever ILAENV is called with 17 <= ISPEC <= 21. *> It is called whenever ILAENV2STAGE is called with 1 <= ISPEC <= 5 *> with a direct conversion ISPEC + 16. *> \endverbatim * * Arguments: * ========== * *> \param[in] ISPEC *> \verbatim *> ISPEC is integer scalar *> ISPEC specifies which tunable parameter IPARAM2STAGE should *> return. *> *> ISPEC=17: the optimal blocksize nb for the reduction to *> BAND *> *> ISPEC=18: the optimal blocksize ib for the eigenvectors *> singular vectors update routine *> *> ISPEC=19: The length of the array that store the Housholder *> representation for the second stage *> Band to Tridiagonal or Bidiagonal *> *> ISPEC=20: The workspace needed for the routine in input. *> *> ISPEC=21: For future release. *> \endverbatim *> *> \param[in] NAME *> \verbatim *> NAME is character string *> Name of the calling subroutine *> \endverbatim *> *> \param[in] OPTS *> \verbatim *> OPTS is CHARACTER*(*) *> The character options to the subroutine NAME, concatenated *> into a single character string. For example, UPLO = 'U', *> TRANS = 'T', and DIAG = 'N' for a triangular routine would *> be specified as OPTS = 'UTN'. *> \endverbatim *> *> \param[in] NI *> \verbatim *> NI is INTEGER which is the size of the matrix *> \endverbatim *> *> \param[in] NBI *> \verbatim *> NBI is INTEGER which is the used in the reduciton, *> (e.g., the size of the band), needed to compute workspace *> and LHOUS2. *> \endverbatim *> *> \param[in] IBI *> \verbatim *> IBI is INTEGER which represent the IB of the reduciton, *> needed to compute workspace and LHOUS2. *> \endverbatim *> *> \param[in] NXI *> \verbatim *> NXI is INTEGER needed in the future release. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup auxOTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> Implemented by Azzam Haidar. *> *> All detail are available on technical report, SC11, SC13 papers. *> *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra. *> Parallel reduction to condensed forms for symmetric eigenvalue problems *> using aggregated fine-grained and memory-aware kernels. In Proceedings *> of 2011 International Conference for High Performance Computing, *> Networking, Storage and Analysis (SC '11), New York, NY, USA, *> Article 8 , 11 pages. *> http://doi.acm.org/10.1145/2063384.2063394 *> *> A. Haidar, J. Kurzak, P. Luszczek, 2013. *> An improved parallel singular value algorithm and its implementation *> for multicore hardware, In Proceedings of 2013 International Conference *> for High Performance Computing, Networking, Storage and Analysis (SC '13). *> Denver, Colorado, USA, 2013. *> Article 90, 12 pages. *> http://doi.acm.org/10.1145/2503210.2503292 *> *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure *> calculations based on fine-grained memory aware tasks. *> International Journal of High Performance Computing Applications. *> Volume 28 Issue 2, Pages 196-209, May 2014. *> http://hpc.sagepub.com/content/28/2/196 *> *> \endverbatim *> * ===================================================================== INTEGER FUNCTION IPARAM2STAGE( ISPEC, NAME, OPTS, $ NI, NBI, IBI, NXI ) #if defined(_OPENMP) use omp_lib #endif IMPLICIT NONE * * -- LAPACK auxiliary routine (version 3.8.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER*( * ) NAME, OPTS INTEGER ISPEC, NI, NBI, IBI, NXI * * ================================================================ * .. * .. Local Scalars .. INTEGER I, IC, IZ, KD, IB, LHOUS, LWORK, NTHREADS, $ FACTOPTNB, QROPTNB, LQOPTNB LOGICAL RPREC, CPREC CHARACTER PREC*1, ALGO*3, STAG*5, SUBNAM*12, VECT*1 * .. * .. Intrinsic Functions .. INTRINSIC CHAR, ICHAR, MAX * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Invalid value for ISPEC * IF( (ISPEC.LT.17).OR.(ISPEC.GT.21) ) THEN IPARAM2STAGE = -1 RETURN ENDIF * * Get the number of threads * NTHREADS = 1 #if defined(_OPENMP) !$OMP PARALLEL NTHREADS = OMP_GET_NUM_THREADS() !$OMP END PARALLEL #endif * WRITE(*,*) 'IPARAM VOICI NTHREADS ISPEC ',NTHREADS, ISPEC * IF( ISPEC .NE. 19 ) THEN * * Convert NAME to upper case if the first character is lower case. * IPARAM2STAGE = -1 SUBNAM = NAME IC = ICHAR( SUBNAM( 1: 1 ) ) IZ = ICHAR( 'Z' ) IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN * * ASCII character set * IF( IC.GE.97 .AND. IC.LE.122 ) THEN SUBNAM( 1: 1 ) = CHAR( IC-32 ) DO 100 I = 2, 12 IC = ICHAR( SUBNAM( I: I ) ) IF( IC.GE.97 .AND. IC.LE.122 ) $ SUBNAM( I: I ) = CHAR( IC-32 ) 100 CONTINUE END IF * ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN * * EBCDIC character set * IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. $ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN SUBNAM( 1: 1 ) = CHAR( IC+64 ) DO 110 I = 2, 12 IC = ICHAR( SUBNAM( I: I ) ) IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. $ ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I: $ I ) = CHAR( IC+64 ) 110 CONTINUE END IF * ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN * * Prime machines: ASCII+128 * IF( IC.GE.225 .AND. IC.LE.250 ) THEN SUBNAM( 1: 1 ) = CHAR( IC-32 ) DO 120 I = 2, 12 IC = ICHAR( SUBNAM( I: I ) ) IF( IC.GE.225 .AND. IC.LE.250 ) $ SUBNAM( I: I ) = CHAR( IC-32 ) 120 CONTINUE END IF END IF * PREC = SUBNAM( 1: 1 ) ALGO = SUBNAM( 4: 6 ) STAG = SUBNAM( 8:12 ) RPREC = PREC.EQ.'S' .OR. PREC.EQ.'D' CPREC = PREC.EQ.'C' .OR. PREC.EQ.'Z' * * Invalid value for PRECISION * IF( .NOT.( RPREC .OR. CPREC ) ) THEN IPARAM2STAGE = -1 RETURN ENDIF ENDIF * WRITE(*,*),'RPREC,CPREC ',RPREC,CPREC, * $ ' ALGO ',ALGO,' STAGE ',STAG * * IF (( ISPEC .EQ. 17 ) .OR. ( ISPEC .EQ. 18 )) THEN * * ISPEC = 17, 18: block size KD, IB * Could be also dependent from N but for now it * depend only on sequential or parallel * IF( NTHREADS.GT.4 ) THEN IF( CPREC ) THEN KD = 128 IB = 32 ELSE KD = 160 IB = 40 ENDIF ELSE IF( NTHREADS.GT.1 ) THEN IF( CPREC ) THEN KD = 64 IB = 32 ELSE KD = 64 IB = 32 ENDIF ELSE IF( CPREC ) THEN KD = 16 IB = 16 ELSE KD = 32 IB = 16 ENDIF ENDIF IF( ISPEC.EQ.17 ) IPARAM2STAGE = KD IF( ISPEC.EQ.18 ) IPARAM2STAGE = IB * ELSE IF ( ISPEC .EQ. 19 ) THEN * * ISPEC = 19: * LHOUS length of the Houselholder representation * matrix (V,T) of the second stage. should be >= 1. * * Will add the VECT OPTION HERE next release VECT = OPTS(1:1) IF( VECT.EQ.'N' ) THEN LHOUS = MAX( 1, 4*NI ) ELSE * This is not correct, it need to call the ALGO and the stage2 LHOUS = MAX( 1, 4*NI ) + IBI ENDIF IF( LHOUS.GE.0 ) THEN IPARAM2STAGE = LHOUS ELSE IPARAM2STAGE = -1 ENDIF * ELSE IF ( ISPEC .EQ. 20 ) THEN * * ISPEC = 20: (21 for future use) * LWORK length of the workspace for * either or both stages for TRD and BRD. should be >= 1. * TRD: * TRD_stage 1: = LT + LW + LS1 + LS2 * = LDT*KD + N*KD + N*MAX(KD,FACTOPTNB) + LDS2*KD * where LDT=LDS2=KD * = N*KD + N*max(KD,FACTOPTNB) + 2*KD*KD * TRD_stage 2: = (2NB+1)*N + KD*NTHREADS * TRD_both : = max(stage1,stage2) + AB ( AB=(KD+1)*N ) * = N*KD + N*max(KD+1,FACTOPTNB) * + max(2*KD*KD, KD*NTHREADS) * + (KD+1)*N LWORK = -1 SUBNAM(1:1) = PREC SUBNAM(2:6) = 'GEQRF' QROPTNB = ILAENV( 1, SUBNAM, ' ', NI, NBI, -1, -1 ) SUBNAM(2:6) = 'GELQF' LQOPTNB = ILAENV( 1, SUBNAM, ' ', NBI, NI, -1, -1 ) * Could be QR or LQ for TRD and the max for BRD FACTOPTNB = MAX(QROPTNB, LQOPTNB) IF( ALGO.EQ.'TRD' ) THEN IF( STAG.EQ.'2STAG' ) THEN LWORK = NI*NBI + NI*MAX(NBI+1,FACTOPTNB) $ + MAX(2*NBI*NBI, NBI*NTHREADS) $ + (NBI+1)*NI ELSE IF( (STAG.EQ.'HE2HB').OR.(STAG.EQ.'SY2SB') ) THEN LWORK = NI*NBI + NI*MAX(NBI,FACTOPTNB) + 2*NBI*NBI ELSE IF( (STAG.EQ.'HB2ST').OR.(STAG.EQ.'SB2ST') ) THEN LWORK = (2*NBI+1)*NI + NBI*NTHREADS ENDIF ELSE IF( ALGO.EQ.'BRD' ) THEN IF( STAG.EQ.'2STAG' ) THEN LWORK = 2*NI*NBI + NI*MAX(NBI+1,FACTOPTNB) $ + MAX(2*NBI*NBI, NBI*NTHREADS) $ + (NBI+1)*NI ELSE IF( STAG.EQ.'GE2GB' ) THEN LWORK = NI*NBI + NI*MAX(NBI,FACTOPTNB) + 2*NBI*NBI ELSE IF( STAG.EQ.'GB2BD' ) THEN LWORK = (3*NBI+1)*NI + NBI*NTHREADS ENDIF ENDIF LWORK = MAX ( 1, LWORK ) IF( LWORK.GT.0 ) THEN IPARAM2STAGE = LWORK ELSE IPARAM2STAGE = -1 ENDIF * ELSE IF ( ISPEC .EQ. 21 ) THEN * * ISPEC = 21 for future use IPARAM2STAGE = NXI ENDIF * * ==== End of IPARAM2STAGE ==== * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhegv.f0000644000000000000000000000013214061636515015147 xustar0030 mtime=1623670093.126104152 30 atime=1623670093.126104152 30 ctime=1623670093.126104152 elk-7.2.42/src/LAPACK/zhegv.f0000644002504400250440000002306714061636515017214 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHEGV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHEGV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, * LWORK, RWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, UPLO * INTEGER INFO, ITYPE, LDA, LDB, LWORK, N * .. * .. Array Arguments .. * DOUBLE PRECISION RWORK( * ), W( * ) * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEGV computes all the eigenvalues, and optionally, the eigenvectors *> of a complex generalized Hermitian-definite eigenproblem, of the form *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. *> Here A and B are assumed to be Hermitian and B is also *> positive definite. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> Specifies the problem type to be solved: *> = 1: A*x = (lambda)*B*x *> = 2: A*B*x = (lambda)*x *> = 3: B*A*x = (lambda)*x *> \endverbatim *> *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangles of A and B are stored; *> = 'L': Lower triangles of A and B are stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA, N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: *> if ITYPE = 1 or 2, Z**H*B*Z = I; *> if ITYPE = 3, Z**H*inv(B)*Z = I. *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') *> or the lower triangle (if UPLO='L') of A, including the *> diagonal, is destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB, N) *> On entry, the Hermitian positive definite matrix B. *> If UPLO = 'U', the leading N-by-N upper triangular part of B *> contains the upper triangular part of the matrix B. *> If UPLO = 'L', the leading N-by-N lower triangular part of B *> contains the lower triangular part of the matrix B. *> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> If INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(1,2*N-1). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for ZHETRD returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: ZPOTRF or ZHEEV returned an error code: *> <= N: if INFO = i, ZHEEV failed to converge; *> i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> > N: if INFO = N + i, for 1 <= i <= N, then the leading *> minor of order i of B is not positive definite. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16HEeigen * * ===================================================================== SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, $ LWORK, RWORK, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, ITYPE, LDA, LDB, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER, WANTZ CHARACTER TRANS INTEGER LWKOPT, NB, NEIG * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZHEEV, ZHEGST, ZPOTRF, ZTRMM, ZTRSM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -2 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 END IF * IF( INFO.EQ.0 ) THEN NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) LWKOPT = MAX( 1, ( NB + 1 )*N ) WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, 2*N - 1 ) .AND. .NOT.LQUERY ) THEN INFO = -11 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHEGV ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Form a Cholesky factorization of B. * CALL ZPOTRF( UPLO, N, B, LDB, INFO ) IF( INFO.NE.0 ) THEN INFO = N + INFO RETURN END IF * * Transform problem to standard eigenvalue problem and solve. * CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) CALL ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO ) * IF( WANTZ ) THEN * * Backtransform eigenvectors to the original problem. * NEIG = N IF( INFO.GT.0 ) $ NEIG = INFO - 1 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN * * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y * IF( UPPER ) THEN TRANS = 'N' ELSE TRANS = 'C' END IF * CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, $ B, LDB, A, LDA ) * ELSE IF( ITYPE.EQ.3 ) THEN * * For B*A*x=(lambda)*x; * backtransform eigenvectors: x = L*y or U**H *y * IF( UPPER ) THEN TRANS = 'C' ELSE TRANS = 'N' END IF * CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, $ B, LDB, A, LDA ) END IF END IF * WORK( 1 ) = LWKOPT * RETURN * * End of ZHEGV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dgesv.f0000644000000000000000000000013214061636515015134 xustar0030 mtime=1623670093.128104151 30 atime=1623670093.127104151 30 ctime=1623670093.128104151 elk-7.2.42/src/LAPACK/dgesv.f0000644002504400250440000001202714061636515017173 0ustar00dewhurstdewhurst00000000000000*> \brief DGESV computes the solution to system of linear equations A * X = B for GE matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DGESV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGESV computes the solution to a real system of linear equations *> A * X = B, *> where A is an N-by-N matrix and X and B are N-by-NRHS matrices. *> *> The LU decomposition with partial pivoting and row interchanges is *> used to factor A as *> A = P * L * U, *> where P is a permutation matrix, L is unit lower triangular, and U is *> upper triangular. The factored form of A is then used to solve the *> system of equations A * X = B. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of linear equations, i.e., the order of the *> matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the N-by-N coefficient matrix A. *> On exit, the factors L and U from the factorization *> A = P*L*U; the unit diagonal elements of L are not stored. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices that define the permutation matrix P; *> row i of the matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> On entry, the N-by-NRHS matrix of right hand side matrix B. *> On exit, if INFO = 0, the N-by-NRHS solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization *> has been completed, but the factor U is exactly *> singular, so the solution could not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleGEsolve * * ===================================================================== SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. External Subroutines .. EXTERNAL DGETRF, DGETRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 ELSE IF( NRHS.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGESV ', -INFO ) RETURN END IF * * Compute the LU factorization of A. * CALL DGETRF( N, N, A, LDA, IPIV, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * CALL DGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, B, LDB, $ INFO ) END IF RETURN * * End of DGESV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhegvx.f0000644000000000000000000000012714061636515015343 xustar0029 mtime=1623670093.12910415 29 atime=1623670093.12910415 29 ctime=1623670093.12910415 elk-7.2.42/src/LAPACK/zhegvx.f0000644002504400250440000003606414061636515017405 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHEGVX * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHEGVX + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, * VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, * LWORK, RWORK, IWORK, IFAIL, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, RANGE, UPLO * INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N * DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER IFAIL( * ), IWORK( * ) * DOUBLE PRECISION RWORK( * ), W( * ) * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ), * $ Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEGVX computes selected eigenvalues, and optionally, eigenvectors *> of a complex generalized Hermitian-definite eigenproblem, of the form *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and *> B are assumed to be Hermitian and B is also positive definite. *> Eigenvalues and eigenvectors can be selected by specifying either a *> range of values or a range of indices for the desired eigenvalues. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> Specifies the problem type to be solved: *> = 1: A*x = (lambda)*B*x *> = 2: A*B*x = (lambda)*x *> = 3: B*A*x = (lambda)*x *> \endverbatim *> *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] RANGE *> \verbatim *> RANGE is CHARACTER*1 *> = 'A': all eigenvalues will be found. *> = 'V': all eigenvalues in the half-open interval (VL,VU] *> will be found. *> = 'I': the IL-th through IU-th eigenvalues will be found. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangles of A and B are stored; *> = 'L': Lower triangles of A and B are stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA, N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> *> On exit, the lower triangle (if UPLO='L') or the upper *> triangle (if UPLO='U') of A, including the diagonal, is *> destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB, N) *> On entry, the Hermitian matrix B. If UPLO = 'U', the *> leading N-by-N upper triangular part of B contains the *> upper triangular part of the matrix B. If UPLO = 'L', *> the leading N-by-N lower triangular part of B contains *> the lower triangular part of the matrix B. *> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[in] VL *> \verbatim *> VL is DOUBLE PRECISION *> *> If RANGE='V', the lower bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION *> *> If RANGE='V', the upper bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] IL *> \verbatim *> IL is INTEGER *> *> If RANGE='I', the index of the *> smallest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] IU *> \verbatim *> IU is INTEGER *> *> If RANGE='I', the index of the *> largest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] ABSTOL *> \verbatim *> ABSTOL is DOUBLE PRECISION *> The absolute error tolerance for the eigenvalues. *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to *> *> ABSTOL + EPS * max( |a|,|b| ) , *> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing C to tridiagonal form, where C is the symmetric *> matrix of the standard symmetric problem to which the *> generalized problem is transformed. *> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). *> \endverbatim *> *> \param[out] M *> \verbatim *> M is INTEGER *> The total number of eigenvalues found. 0 <= M <= N. *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> The first M elements contain the selected *> eigenvalues in ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ, max(1,M)) *> If JOBZ = 'N', then Z is not referenced. *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z *> contain the orthonormal eigenvectors of the matrix A *> corresponding to the selected eigenvalues, with the i-th *> column of Z holding the eigenvector associated with W(i). *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**T*B*Z = I; *> if ITYPE = 3, Z**T*inv(B)*Z = I. *> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. *> Note: the user must ensure that at least max(1,M) columns are *> supplied in the array Z; if RANGE = 'V', the exact value of M *> is not known in advance and an upper bound must be used. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> JOBZ = 'V', LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(1,2*N). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for ZHETRD returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (7*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (5*N) *> \endverbatim *> *> \param[out] IFAIL *> \verbatim *> IFAIL is INTEGER array, dimension (N) *> If JOBZ = 'V', then if INFO = 0, the first M elements of *> IFAIL are zero. If INFO > 0, then IFAIL contains the *> indices of the eigenvectors that failed to converge. *> If JOBZ = 'N', then IFAIL is not referenced. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: ZPOTRF or ZHEEVX returned an error code: *> <= N: if INFO = i, ZHEEVX failed to converge; *> i eigenvectors failed to converge. Their indices *> are stored in array IFAIL. *> > N: if INFO = N + i, for 1 <= i <= N, then the leading *> minor of order i of B is not positive definite. *> The factorization of B could not be completed and *> no eigenvalues or eigenvectors were computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16HEeigen * *> \par Contributors: * ================== *> *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA * * ===================================================================== SUBROUTINE ZHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, $ LWORK, RWORK, IWORK, IFAIL, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, RANGE, UPLO INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER IFAIL( * ), IWORK( * ) DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ), $ Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ CHARACTER TRANS INTEGER LWKOPT, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZHEEVX, ZHEGST, ZPOTRF, ZTRMM, ZTRSM * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) UPPER = LSAME( UPLO, 'U' ) ALLEIG = LSAME( RANGE, 'A' ) VALEIG = LSAME( RANGE, 'V' ) INDEIG = LSAME( RANGE, 'I' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -2 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN INFO = -3 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -9 ELSE IF( VALEIG ) THEN IF( N.GT.0 .AND. VU.LE.VL ) $ INFO = -11 ELSE IF( INDEIG ) THEN IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN INFO = -12 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN INFO = -13 END IF END IF END IF IF (INFO.EQ.0) THEN IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN INFO = -18 END IF END IF * IF( INFO.EQ.0 ) THEN NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) LWKOPT = MAX( 1, ( NB + 1 )*N ) WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN INFO = -20 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHEGVX', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * M = 0 IF( N.EQ.0 ) THEN RETURN END IF * * Form a Cholesky factorization of B. * CALL ZPOTRF( UPLO, N, B, LDB, INFO ) IF( INFO.NE.0 ) THEN INFO = N + INFO RETURN END IF * * Transform problem to standard eigenvalue problem and solve. * CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) CALL ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, $ M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, $ INFO ) * IF( WANTZ ) THEN * * Backtransform eigenvectors to the original problem. * IF( INFO.GT.0 ) $ M = INFO - 1 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN * * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y * IF( UPPER ) THEN TRANS = 'N' ELSE TRANS = 'C' END IF * CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B, $ LDB, Z, LDZ ) * ELSE IF( ITYPE.EQ.3 ) THEN * * For B*A*x=(lambda)*x; * backtransform eigenvectors: x = L*y or U**H *y * IF( UPPER ) THEN TRANS = 'C' ELSE TRANS = 'N' END IF * CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B, $ LDB, Z, LDZ ) END IF END IF * * Set WORK(1) to optimal complex workspace size. * WORK( 1 ) = LWKOPT * RETURN * * End of ZHEGVX * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgeev.f0000644000000000000000000000013214061636515015144 xustar0030 mtime=1623670093.131104148 30 atime=1623670093.131104148 30 ctime=1623670093.131104148 elk-7.2.42/src/LAPACK/zgeev.f0000644002504400250440000003727614061636515017220 0ustar00dewhurstdewhurst00000000000000*> \brief ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEEV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, * WORK, LWORK, RWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBVL, JOBVR * INTEGER INFO, LDA, LDVL, LDVR, LWORK, N * .. * .. Array Arguments .. * DOUBLE PRECISION RWORK( * ) * COMPLEX*16 A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), * $ W( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the *> eigenvalues and, optionally, the left and/or right eigenvectors. *> *> The right eigenvector v(j) of A satisfies *> A * v(j) = lambda(j) * v(j) *> where lambda(j) is its eigenvalue. *> The left eigenvector u(j) of A satisfies *> u(j)**H * A = lambda(j) * u(j)**H *> where u(j)**H denotes the conjugate transpose of u(j). *> *> The computed eigenvectors are normalized to have Euclidean norm *> equal to 1 and largest component real. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBVL *> \verbatim *> JOBVL is CHARACTER*1 *> = 'N': left eigenvectors of A are not computed; *> = 'V': left eigenvectors of are computed. *> \endverbatim *> *> \param[in] JOBVR *> \verbatim *> JOBVR is CHARACTER*1 *> = 'N': right eigenvectors of A are not computed; *> = 'V': right eigenvectors of A are computed. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the N-by-N matrix A. *> On exit, A has been overwritten. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is COMPLEX*16 array, dimension (N) *> W contains the computed eigenvalues. *> \endverbatim *> *> \param[out] VL *> \verbatim *> VL is COMPLEX*16 array, dimension (LDVL,N) *> If JOBVL = 'V', the left eigenvectors u(j) are stored one *> after another in the columns of VL, in the same order *> as their eigenvalues. *> If JOBVL = 'N', VL is not referenced. *> u(j) = VL(:,j), the j-th column of VL. *> \endverbatim *> *> \param[in] LDVL *> \verbatim *> LDVL is INTEGER *> The leading dimension of the array VL. LDVL >= 1; if *> JOBVL = 'V', LDVL >= N. *> \endverbatim *> *> \param[out] VR *> \verbatim *> VR is COMPLEX*16 array, dimension (LDVR,N) *> If JOBVR = 'V', the right eigenvectors v(j) are stored one *> after another in the columns of VR, in the same order *> as their eigenvalues. *> If JOBVR = 'N', VR is not referenced. *> v(j) = VR(:,j), the j-th column of VR. *> \endverbatim *> *> \param[in] LDVR *> \verbatim *> LDVR is INTEGER *> The leading dimension of the array VR. LDVR >= 1; if *> JOBVR = 'V', LDVR >= N. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (2*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = i, the QR algorithm failed to compute all the *> eigenvalues, and no eigenvectors have been computed; *> elements i+1:N of W contain eigenvalues which have *> converged. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * * @precisions fortran z -> c * *> \ingroup complex16GEeigen * * ===================================================================== SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, $ WORK, LWORK, RWORK, INFO ) implicit none * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER JOBVL, JOBVR INTEGER INFO, LDA, LDVL, LDVR, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), $ W( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, SCALEA, WANTVL, WANTVR CHARACTER SIDE INTEGER HSWORK, I, IBAL, IERR, IHI, ILO, IRWORK, ITAU, $ IWRK, K, LWORK_TREVC, MAXWRK, MINWRK, NOUT DOUBLE PRECISION ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM COMPLEX*16 TMP * .. * .. Local Arrays .. LOGICAL SELECT( 1 ) DOUBLE PRECISION DUM( 1 ) * .. * .. External Subroutines .. EXTERNAL DLABAD, XERBLA, ZDSCAL, ZGEBAK, ZGEBAL, ZGEHRD, $ ZHSEQR, ZLACPY, ZLASCL, ZSCAL, ZTREVC3, ZUNGHR * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX, ILAENV DOUBLE PRECISION DLAMCH, DZNRM2, ZLANGE EXTERNAL LSAME, IDAMAX, ILAENV, DLAMCH, DZNRM2, ZLANGE * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, CONJG, AIMAG, MAX, SQRT * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) WANTVL = LSAME( JOBVL, 'V' ) WANTVR = LSAME( JOBVR, 'V' ) IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN INFO = -1 ELSE IF( ( .NOT.WANTVR ) .AND. ( .NOT.LSAME( JOBVR, 'N' ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDVL.LT.1 .OR. ( WANTVL .AND. LDVL.LT.N ) ) THEN INFO = -8 ELSE IF( LDVR.LT.1 .OR. ( WANTVR .AND. LDVR.LT.N ) ) THEN INFO = -10 END IF * * Compute workspace * (Note: Comments in the code beginning "Workspace:" describe the * minimal amount of workspace needed at that point in the code, * as well as the preferred amount for good performance. * CWorkspace refers to complex workspace, and RWorkspace to real * workspace. NB refers to the optimal block size for the * immediately following subroutine, as returned by ILAENV. * HSWORK refers to the workspace preferred by ZHSEQR, as * calculated below. HSWORK is computed assuming ILO=1 and IHI=N, * the worst case.) * IF( INFO.EQ.0 ) THEN IF( N.EQ.0 ) THEN MINWRK = 1 MAXWRK = 1 ELSE MAXWRK = N + N*ILAENV( 1, 'ZGEHRD', ' ', N, 1, N, 0 ) MINWRK = 2*N IF( WANTVL ) THEN MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR', $ ' ', N, 1, N, -1 ) ) CALL ZTREVC3( 'L', 'B', SELECT, N, A, LDA, $ VL, LDVL, VR, LDVR, $ N, NOUT, WORK, -1, RWORK, -1, IERR ) LWORK_TREVC = INT( WORK(1) ) MAXWRK = MAX( MAXWRK, N + LWORK_TREVC ) CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL, $ WORK, -1, INFO ) ELSE IF( WANTVR ) THEN MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR', $ ' ', N, 1, N, -1 ) ) CALL ZTREVC3( 'R', 'B', SELECT, N, A, LDA, $ VL, LDVL, VR, LDVR, $ N, NOUT, WORK, -1, RWORK, -1, IERR ) LWORK_TREVC = INT( WORK(1) ) MAXWRK = MAX( MAXWRK, N + LWORK_TREVC ) CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR, $ WORK, -1, INFO ) ELSE CALL ZHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR, $ WORK, -1, INFO ) END IF HSWORK = INT( WORK(1) ) MAXWRK = MAX( MAXWRK, HSWORK, MINWRK ) END IF WORK( 1 ) = MAXWRK * IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN INFO = -12 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGEEV ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Get machine constants * EPS = DLAMCH( 'P' ) SMLNUM = DLAMCH( 'S' ) BIGNUM = ONE / SMLNUM CALL DLABAD( SMLNUM, BIGNUM ) SMLNUM = SQRT( SMLNUM ) / EPS BIGNUM = ONE / SMLNUM * * Scale A if max element outside range [SMLNUM,BIGNUM] * ANRM = ZLANGE( 'M', N, N, A, LDA, DUM ) SCALEA = .FALSE. IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN SCALEA = .TRUE. CSCALE = SMLNUM ELSE IF( ANRM.GT.BIGNUM ) THEN SCALEA = .TRUE. CSCALE = BIGNUM END IF IF( SCALEA ) $ CALL ZLASCL( 'G', 0, 0, ANRM, CSCALE, N, N, A, LDA, IERR ) * * Balance the matrix * (CWorkspace: none) * (RWorkspace: need N) * IBAL = 1 CALL ZGEBAL( 'B', N, A, LDA, ILO, IHI, RWORK( IBAL ), IERR ) * * Reduce to upper Hessenberg form * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: none) * ITAU = 1 IWRK = ITAU + N CALL ZGEHRD( N, ILO, IHI, A, LDA, WORK( ITAU ), WORK( IWRK ), $ LWORK-IWRK+1, IERR ) * IF( WANTVL ) THEN * * Want left eigenvectors * Copy Householder vectors to VL * SIDE = 'L' CALL ZLACPY( 'L', N, N, A, LDA, VL, LDVL ) * * Generate unitary matrix in VL * (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) * (RWorkspace: none) * CALL ZUNGHR( N, ILO, IHI, VL, LDVL, WORK( ITAU ), WORK( IWRK ), $ LWORK-IWRK+1, IERR ) * * Perform QR iteration, accumulating Schur vectors in VL * (CWorkspace: need 1, prefer HSWORK (see comments) ) * (RWorkspace: none) * IWRK = ITAU CALL ZHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VL, LDVL, $ WORK( IWRK ), LWORK-IWRK+1, INFO ) * IF( WANTVR ) THEN * * Want left and right eigenvectors * Copy Schur vectors to VR * SIDE = 'B' CALL ZLACPY( 'F', N, N, VL, LDVL, VR, LDVR ) END IF * ELSE IF( WANTVR ) THEN * * Want right eigenvectors * Copy Householder vectors to VR * SIDE = 'R' CALL ZLACPY( 'L', N, N, A, LDA, VR, LDVR ) * * Generate unitary matrix in VR * (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) * (RWorkspace: none) * CALL ZUNGHR( N, ILO, IHI, VR, LDVR, WORK( ITAU ), WORK( IWRK ), $ LWORK-IWRK+1, IERR ) * * Perform QR iteration, accumulating Schur vectors in VR * (CWorkspace: need 1, prefer HSWORK (see comments) ) * (RWorkspace: none) * IWRK = ITAU CALL ZHSEQR( 'S', 'V', N, ILO, IHI, A, LDA, W, VR, LDVR, $ WORK( IWRK ), LWORK-IWRK+1, INFO ) * ELSE * * Compute eigenvalues only * (CWorkspace: need 1, prefer HSWORK (see comments) ) * (RWorkspace: none) * IWRK = ITAU CALL ZHSEQR( 'E', 'N', N, ILO, IHI, A, LDA, W, VR, LDVR, $ WORK( IWRK ), LWORK-IWRK+1, INFO ) END IF * * If INFO .NE. 0 from ZHSEQR, then quit * IF( INFO.NE.0 ) $ GO TO 50 * IF( WANTVL .OR. WANTVR ) THEN * * Compute left and/or right eigenvectors * (CWorkspace: need 2*N, prefer N + 2*N*NB) * (RWorkspace: need 2*N) * IRWORK = IBAL + N CALL ZTREVC3( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, $ N, NOUT, WORK( IWRK ), LWORK-IWRK+1, $ RWORK( IRWORK ), N, IERR ) END IF * IF( WANTVL ) THEN * * Undo balancing of left eigenvectors * (CWorkspace: none) * (RWorkspace: need N) * CALL ZGEBAK( 'B', 'L', N, ILO, IHI, RWORK( IBAL ), N, VL, LDVL, $ IERR ) * * Normalize left eigenvectors and make largest component real * DO 20 I = 1, N SCL = ONE / DZNRM2( N, VL( 1, I ), 1 ) CALL ZDSCAL( N, SCL, VL( 1, I ), 1 ) DO 10 K = 1, N RWORK( IRWORK+K-1 ) = DBLE( VL( K, I ) )**2 + $ AIMAG( VL( K, I ) )**2 10 CONTINUE K = IDAMAX( N, RWORK( IRWORK ), 1 ) TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) ) CALL ZSCAL( N, TMP, VL( 1, I ), 1 ) VL( K, I ) = DCMPLX( DBLE( VL( K, I ) ), ZERO ) 20 CONTINUE END IF * IF( WANTVR ) THEN * * Undo balancing of right eigenvectors * (CWorkspace: none) * (RWorkspace: need N) * CALL ZGEBAK( 'B', 'R', N, ILO, IHI, RWORK( IBAL ), N, VR, LDVR, $ IERR ) * * Normalize right eigenvectors and make largest component real * DO 40 I = 1, N SCL = ONE / DZNRM2( N, VR( 1, I ), 1 ) CALL ZDSCAL( N, SCL, VR( 1, I ), 1 ) DO 30 K = 1, N RWORK( IRWORK+K-1 ) = DBLE( VR( K, I ) )**2 + $ AIMAG( VR( K, I ) )**2 30 CONTINUE K = IDAMAX( N, RWORK( IRWORK ), 1 ) TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) ) CALL ZSCAL( N, TMP, VR( 1, I ), 1 ) VR( K, I ) = DCMPLX( DBLE( VR( K, I ) ), ZERO ) 40 CONTINUE END IF * * Undo scaling if necessary * 50 CONTINUE IF( SCALEA ) THEN CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, N-INFO, 1, W( INFO+1 ), $ MAX( N-INFO, 1 ), IERR ) IF( INFO.GT.0 ) THEN CALL ZLASCL( 'G', 0, 0, CSCALE, ANRM, ILO-1, 1, W, N, IERR ) END IF END IF * WORK( 1 ) = MAXWRK RETURN * * End of ZGEEV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zheevd.f0000644000000000000000000000013214061636515015311 xustar0030 mtime=1623670093.133104146 30 atime=1623670093.133104146 30 ctime=1623670093.133104146 elk-7.2.42/src/LAPACK/zheevd.f0000644002504400250440000003133714061636515017355 0ustar00dewhurstdewhurst00000000000000*> \brief ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHEEVD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, * LRWORK, IWORK, LIWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, UPLO * INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N * .. * .. Array Arguments .. * INTEGER IWORK( * ) * DOUBLE PRECISION RWORK( * ), W( * ) * COMPLEX*16 A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a *> complex Hermitian matrix A. If eigenvectors are desired, it uses a *> divide and conquer algorithm. *> *> The divide and conquer algorithm makes very mild assumptions about *> floating point arithmetic. It will work on machines with a guard *> digit in add/subtract, or on those binary machines without guard *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or *> Cray-2. It could conceivably fail on hexadecimal or decimal machines *> without guard digits, but we know of none. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA, N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> orthonormal eigenvectors of the matrix A. *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') *> or the upper triangle (if UPLO='U') of A, including the *> diagonal, is destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> If INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. *> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. *> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of *> the WORK, RWORK and IWORK arrays, and no error message *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, *> dimension (LRWORK) *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. *> \endverbatim *> *> \param[in] LRWORK *> \verbatim *> LRWORK is INTEGER *> The dimension of the array RWORK. *> If N <= 1, LRWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LRWORK must be at least N. *> If JOBZ = 'V' and N > 1, LRWORK must be at least *> 1 + 5*N + 2*N**2. *> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries *> of the WORK, RWORK and IWORK arrays, and no error message *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. *> \endverbatim *> *> \param[in] LIWORK *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. *> If N <= 1, LIWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. *> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries *> of the WORK, RWORK and IWORK arrays, and no error message *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed *> to converge; i off-diagonal elements of an intermediate *> tridiagonal form did not converge to zero; *> if INFO = i and JOBZ = 'V', then the algorithm failed *> to compute an eigenvalue while working on the submatrix *> lying in rows and columns INFO/(N+1) through *> mod(INFO,N+1). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16HEeigen * *> \par Further Details: * ===================== *> *> Modified description of INFO. Sven, 16 Feb 05. * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA *> * ===================================================================== SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, $ LRWORK, IWORK, LIWORK, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) ) * .. * .. Local Scalars .. LOGICAL LOWER, LQUERY, WANTZ INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2, $ INDWRK, ISCALE, LIOPT, LIWMIN, LLRWK, LLWORK, $ LLWRK2, LOPT, LROPT, LRWMIN, LWMIN DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, $ SMLNUM * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, ZLANHE EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE * .. * .. External Subroutines .. EXTERNAL DSCAL, DSTERF, XERBLA, ZHETRD, ZLACPY, ZLASCL, $ ZSTEDC, ZUNMTR * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LOWER = LSAME( UPLO, 'L' ) LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF * IF( INFO.EQ.0 ) THEN IF( N.LE.1 ) THEN LWMIN = 1 LRWMIN = 1 LIWMIN = 1 LOPT = LWMIN LROPT = LRWMIN LIOPT = LIWMIN ELSE IF( WANTZ ) THEN LWMIN = 2*N + N*N LRWMIN = 1 + 5*N + 2*N**2 LIWMIN = 3 + 5*N ELSE LWMIN = N + 1 LRWMIN = N LIWMIN = 1 END IF LOPT = MAX( LWMIN, N + $ ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) ) LROPT = LRWMIN LIOPT = LIWMIN END IF WORK( 1 ) = LOPT RWORK( 1 ) = LROPT IWORK( 1 ) = LIOPT * IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -8 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN INFO = -10 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -12 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHEEVD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( N.EQ.1 ) THEN W( 1 ) = A( 1, 1 ) IF( WANTZ ) $ A( 1, 1 ) = CONE RETURN END IF * * Get machine constants. * SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK ) ISCALE = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) $ CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) * * Call ZHETRD to reduce Hermitian matrix to tridiagonal form. * INDE = 1 INDTAU = 1 INDWRK = INDTAU + N INDRWK = INDE + N INDWK2 = INDWRK + N*N LLWORK = LWORK - INDWRK + 1 LLWRK2 = LWORK - INDWK2 + 1 LLRWK = LRWORK - INDRWK + 1 CALL ZHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ), $ WORK( INDWRK ), LLWORK, IINFO ) * * For eigenvalues only, call DSTERF. For eigenvectors, first call * ZSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the * tridiagonal matrix, then call ZUNMTR to multiply it to the * Householder transformations represented as Householder vectors in * A. * IF( .NOT.WANTZ ) THEN CALL DSTERF( N, W, RWORK( INDE ), INFO ) ELSE CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK( INDWRK ), N, $ WORK( INDWK2 ), LLWRK2, RWORK( INDRWK ), LLRWK, $ IWORK, LIWORK, INFO ) CALL ZUNMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) CALL ZLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = N ELSE IMAX = INFO - 1 END IF CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * WORK( 1 ) = LOPT RWORK( 1 ) = LROPT IWORK( 1 ) = LIOPT * RETURN * * End of ZHEEVD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zheev.f0000644000000000000000000000013214061636515015145 xustar0030 mtime=1623670093.135104144 30 atime=1623670093.135104144 30 ctime=1623670093.135104144 elk-7.2.42/src/LAPACK/zheev.f0000644002504400250440000002114614061636515017206 0ustar00dewhurstdewhurst00000000000000*> \brief ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHEEV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, * INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, UPLO * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * DOUBLE PRECISION RWORK( * ), W( * ) * COMPLEX*16 A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a *> complex Hermitian matrix A. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA, N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> orthonormal eigenvectors of the matrix A. *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') *> or the upper triangle (if UPLO='U') of A, including the *> diagonal, is destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> If INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(1,2*N-1). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for ZHETRD returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2)) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the algorithm failed to converge; i *> off-diagonal elements of an intermediate tridiagonal *> form did not converge to zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16HEeigen * * ===================================================================== SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, $ INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) ) * .. * .. Local Scalars .. LOGICAL LOWER, LQUERY, WANTZ INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE, $ LLWORK, LWKOPT, NB DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, $ SMLNUM * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, ZLANHE EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE * .. * .. External Subroutines .. EXTERNAL DSCAL, DSTERF, XERBLA, ZHETRD, ZLASCL, ZSTEQR, $ ZUNGTR * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LOWER = LSAME( UPLO, 'L' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF * IF( INFO.EQ.0 ) THEN NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) LWKOPT = MAX( 1, ( NB+1 )*N ) WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY ) $ INFO = -8 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHEEV ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN RETURN END IF * IF( N.EQ.1 ) THEN W( 1 ) = A( 1, 1 ) WORK( 1 ) = 1 IF( WANTZ ) $ A( 1, 1 ) = CONE RETURN END IF * * Get machine constants. * SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK ) ISCALE = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) $ CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) * * Call ZHETRD to reduce Hermitian matrix to tridiagonal form. * INDE = 1 INDTAU = 1 INDWRK = INDTAU + N LLWORK = LWORK - INDWRK + 1 CALL ZHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ), $ WORK( INDWRK ), LLWORK, IINFO ) * * For eigenvalues only, call DSTERF. For eigenvectors, first call * ZUNGTR to generate the unitary matrix, then call ZSTEQR. * IF( .NOT.WANTZ ) THEN CALL DSTERF( N, W, RWORK( INDE ), INFO ) ELSE CALL ZUNGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ), $ LLWORK, IINFO ) INDWRK = INDE + N CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), A, LDA, $ RWORK( INDWRK ), INFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = N ELSE IMAX = INFO - 1 END IF CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * * Set WORK(1) to optimal complex workspace size. * WORK( 1 ) = LWKOPT * RETURN * * End of ZHEEV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgesv.f0000644000000000000000000000013214061636515015162 xustar0030 mtime=1623670093.137104142 30 atime=1623670093.136104143 30 ctime=1623670093.137104142 elk-7.2.42/src/LAPACK/zgesv.f0000644002504400250440000001203214061636515017215 0ustar00dewhurstdewhurst00000000000000*> \brief ZGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver) * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGESV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGESV computes the solution to a complex system of linear equations *> A * X = B, *> where A is an N-by-N matrix and X and B are N-by-NRHS matrices. *> *> The LU decomposition with partial pivoting and row interchanges is *> used to factor A as *> A = P * L * U, *> where P is a permutation matrix, L is unit lower triangular, and U is *> upper triangular. The factored form of A is then used to solve the *> system of equations A * X = B. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of linear equations, i.e., the order of the *> matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the N-by-N coefficient matrix A. *> On exit, the factors L and U from the factorization *> A = P*L*U; the unit diagonal elements of L are not stored. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices that define the permutation matrix P; *> row i of the matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,NRHS) *> On entry, the N-by-NRHS matrix of right hand side matrix B. *> On exit, if INFO = 0, the N-by-NRHS solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization *> has been completed, but the factor U is exactly *> singular, so the solution could not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complex16GEsolve * * ===================================================================== SUBROUTINE ZGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * -- LAPACK driver routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. External Subroutines .. EXTERNAL XERBLA, ZGETRF, ZGETRS * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 ELSE IF( NRHS.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGESV ', -INFO ) RETURN END IF * * Compute the LU factorization of A. * CALL ZGETRF( N, N, A, LDA, IPIV, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * CALL ZGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, B, LDB, $ INFO ) END IF RETURN * * End of ZGESV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dgetrf.f0000644000000000000000000000013214061636515015277 xustar0030 mtime=1623670093.138104141 30 atime=1623670093.138104141 30 ctime=1623670093.138104141 elk-7.2.42/src/LAPACK/dgetrf.f0000644002504400250440000001422614061636515017341 0ustar00dewhurstdewhurst00000000000000*> \brief \b DGETRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DGETRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGETRF computes an LU factorization of a general M-by-N matrix A *> using partial pivoting with row interchanges. *> *> The factorization has the form *> A = P * L * U *> where P is a permutation matrix, L is lower triangular with unit *> diagonal elements (lower trapezoidal if m > n), and U is upper *> triangular (upper trapezoidal if m < n). *> *> This is the right-looking Level 3 BLAS version of the algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the M-by-N matrix to be factored. *> On exit, the factors L and U from the factorization *> A = P*L*U; the unit diagonal elements of L are not stored. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (min(M,N)) *> The pivot indices; for 1 <= i <= min(M,N), row i of the *> matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization *> has been completed, but the factor U is exactly *> singular, and division by zero will occur if it is used *> to solve a system of equations. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleGEcomputational * * ===================================================================== SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, IINFO, J, JB, NB * .. * .. External Subroutines .. EXTERNAL DGEMM, DGETRF2, DLASWP, DTRSM, XERBLA * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGETRF', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN * * Use unblocked code. * CALL DGETRF2( M, N, A, LDA, IPIV, INFO ) ELSE * * Use blocked code. * DO 20 J = 1, MIN( M, N ), NB JB = MIN( MIN( M, N )-J+1, NB ) * * Factor diagonal and subdiagonal blocks and test for exact * singularity. * CALL DGETRF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO ) * * Adjust INFO and the pivot indices. * IF( INFO.EQ.0 .AND. IINFO.GT.0 ) $ INFO = IINFO + J - 1 DO 10 I = J, MIN( M, J+JB-1 ) IPIV( I ) = J - 1 + IPIV( I ) 10 CONTINUE * * Apply interchanges to columns 1:J-1. * CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) * IF( J+JB.LE.N ) THEN * * Apply interchanges to columns J+JB:N. * CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, $ IPIV, 1 ) * * Compute block row of U. * CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ), $ LDA ) IF( J+JB.LE.M ) THEN * * Update trailing submatrix. * CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1, $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA, $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ), $ LDA ) END IF END IF 20 CONTINUE END IF RETURN * * End of DGETRF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dgetri.f0000644000000000000000000000013214061636515015302 xustar0030 mtime=1623670093.140104139 30 atime=1623670093.140104139 30 ctime=1623670093.140104139 elk-7.2.42/src/LAPACK/dgetri.f0000644002504400250440000001631514061636515017345 0ustar00dewhurstdewhurst00000000000000*> \brief \b DGETRI * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DGETRI + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGETRI computes the inverse of a matrix using the LU factorization *> computed by DGETRF. *> *> This method inverts U and then computes inv(A) by solving the system *> inv(A)*L = inv(U) for inv(A). *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the factors L and U from the factorization *> A = P*L*U as computed by DGETRF. *> On exit, if INFO = 0, the inverse of the original matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices from DGETRF; for 1<=i<=N, row i of the *> matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO=0, then WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimal performance LWORK >= N*NB, where NB is *> the optimal blocksize returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is *> singular and its inverse could not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleGEcomputational * * ===================================================================== SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, $ NBMIN, NN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. External Subroutines .. EXTERNAL DGEMM, DGEMV, DSWAP, DTRSM, DTRTRI, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 ) LWKOPT = N*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( N.LT.0 ) THEN INFO = -1 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -3 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGETRI', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Form inv(U). If INFO > 0 from DTRTRI, then U is singular, * and the inverse is not computed. * CALL DTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) IF( INFO.GT.0 ) $ RETURN * NBMIN = 2 LDWORK = N IF( NB.GT.1 .AND. NB.LT.N ) THEN IWS = MAX( LDWORK*NB, 1 ) IF( LWORK.LT.IWS ) THEN NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DGETRI', ' ', N, -1, -1, -1 ) ) END IF ELSE IWS = N END IF * * Solve the equation inv(A)*L = inv(U) for inv(A). * IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN * * Use unblocked code. * DO 20 J = N, 1, -1 * * Copy current column of L to WORK and replace with zeros. * DO 10 I = J + 1, N WORK( I ) = A( I, J ) A( I, J ) = ZERO 10 CONTINUE * * Compute current column of inv(A). * IF( J.LT.N ) $ CALL DGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) 20 CONTINUE ELSE * * Use blocked code. * NN = ( ( N-1 ) / NB )*NB + 1 DO 50 J = NN, 1, -NB JB = MIN( NB, N-J+1 ) * * Copy current block column of L to WORK and replace with * zeros. * DO 40 JJ = J, J + JB - 1 DO 30 I = JJ + 1, N WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) A( I, JJ ) = ZERO 30 CONTINUE 40 CONTINUE * * Compute current block column of inv(A). * IF( J+JB.LE.N ) $ CALL DGEMM( 'No transpose', 'No transpose', N, JB, $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) 50 CONTINUE END IF * * Apply column interchanges. * DO 60 J = N - 1, 1, -1 JP = IPIV( J ) IF( JP.NE.J ) $ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) 60 CONTINUE * WORK( 1 ) = IWS RETURN * * End of DGETRI * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgesvd.f0000644000000000000000000000013214061636515015326 xustar0030 mtime=1623670093.143104137 30 atime=1623670093.141104139 30 ctime=1623670093.143104137 elk-7.2.42/src/LAPACK/zgesvd.f0000644002504400250440000042645314061636515017401 0ustar00dewhurstdewhurst00000000000000*> \brief ZGESVD computes the singular value decomposition (SVD) for GE matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGESVD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, * WORK, LWORK, RWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBU, JOBVT * INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION RWORK( * ), S( * ) * COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), * $ WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGESVD computes the singular value decomposition (SVD) of a complex *> M-by-N matrix A, optionally computing the left and/or right singular *> vectors. The SVD is written *> *> A = U * SIGMA * conjugate-transpose(V) *> *> where SIGMA is an M-by-N matrix which is zero except for its *> min(m,n) diagonal elements, U is an M-by-M unitary matrix, and *> V is an N-by-N unitary matrix. The diagonal elements of SIGMA *> are the singular values of A; they are real and non-negative, and *> are returned in descending order. The first min(m,n) columns of *> U and V are the left and right singular vectors of A. *> *> Note that the routine returns V**H, not V. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBU *> \verbatim *> JOBU is CHARACTER*1 *> Specifies options for computing all or part of the matrix U: *> = 'A': all M columns of U are returned in array U: *> = 'S': the first min(m,n) columns of U (the left singular *> vectors) are returned in the array U; *> = 'O': the first min(m,n) columns of U (the left singular *> vectors) are overwritten on the array A; *> = 'N': no columns of U (no left singular vectors) are *> computed. *> \endverbatim *> *> \param[in] JOBVT *> \verbatim *> JOBVT is CHARACTER*1 *> Specifies options for computing all or part of the matrix *> V**H: *> = 'A': all N rows of V**H are returned in the array VT; *> = 'S': the first min(m,n) rows of V**H (the right singular *> vectors) are returned in the array VT; *> = 'O': the first min(m,n) rows of V**H (the right singular *> vectors) are overwritten on the array A; *> = 'N': no rows of V**H (no right singular vectors) are *> computed. *> *> JOBVT and JOBU cannot both be 'O'. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the input matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the input matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the M-by-N matrix A. *> On exit, *> if JOBU = 'O', A is overwritten with the first min(m,n) *> columns of U (the left singular vectors, *> stored columnwise); *> if JOBVT = 'O', A is overwritten with the first min(m,n) *> rows of V**H (the right singular vectors, *> stored rowwise); *> if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A *> are destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] S *> \verbatim *> S is DOUBLE PRECISION array, dimension (min(M,N)) *> The singular values of A, sorted so that S(i) >= S(i+1). *> \endverbatim *> *> \param[out] U *> \verbatim *> U is COMPLEX*16 array, dimension (LDU,UCOL) *> (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. *> If JOBU = 'A', U contains the M-by-M unitary matrix U; *> if JOBU = 'S', U contains the first min(m,n) columns of U *> (the left singular vectors, stored columnwise); *> if JOBU = 'N' or 'O', U is not referenced. *> \endverbatim *> *> \param[in] LDU *> \verbatim *> LDU is INTEGER *> The leading dimension of the array U. LDU >= 1; if *> JOBU = 'S' or 'A', LDU >= M. *> \endverbatim *> *> \param[out] VT *> \verbatim *> VT is COMPLEX*16 array, dimension (LDVT,N) *> If JOBVT = 'A', VT contains the N-by-N unitary matrix *> V**H; *> if JOBVT = 'S', VT contains the first min(m,n) rows of *> V**H (the right singular vectors, stored rowwise); *> if JOBVT = 'N' or 'O', VT is not referenced. *> \endverbatim *> *> \param[in] LDVT *> \verbatim *> LDVT is INTEGER *> The leading dimension of the array VT. LDVT >= 1; if *> JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)). *> For good performance, LWORK should generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (5*min(M,N)) *> On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the *> unconverged superdiagonal elements of an upper bidiagonal *> matrix B whose diagonal is in S (not necessarily sorted). *> B satisfies A = U * B * VT, so it has the same singular *> values as A, and singular vectors related by U and VT. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if ZBDSQR did not converge, INFO specifies how many *> superdiagonals of an intermediate bidiagonal form B *> did not converge to zero. See the description of RWORK *> above for details. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date April 2012 * *> \ingroup complex16GEsing * * ===================================================================== SUBROUTINE ZGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, $ VT, LDVT, WORK, LWORK, RWORK, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * April 2012 * * .. Scalar Arguments .. CHARACTER JOBU, JOBVT INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ), S( * ) COMPLEX*16 A( LDA, * ), U( LDU, * ), VT( LDVT, * ), $ WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), $ CONE = ( 1.0D0, 0.0D0 ) ) DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS, $ WNTVA, WNTVAS, WNTVN, WNTVO, WNTVS INTEGER BLK, CHUNK, I, IE, IERR, IR, IRWORK, ISCL, $ ITAU, ITAUP, ITAUQ, IU, IWORK, LDWRKR, LDWRKU, $ MAXWRK, MINMN, MINWRK, MNTHR, NCU, NCVT, NRU, $ NRVT, WRKBL INTEGER LWORK_ZGEQRF, LWORK_ZUNGQR_N, LWORK_ZUNGQR_M, $ LWORK_ZGEBRD, LWORK_ZUNGBR_P, LWORK_ZUNGBR_Q, $ LWORK_ZGELQF, LWORK_ZUNGLQ_N, LWORK_ZUNGLQ_M DOUBLE PRECISION ANRM, BIGNUM, EPS, SMLNUM * .. * .. Local Arrays .. DOUBLE PRECISION DUM( 1 ) COMPLEX*16 CDUM( 1 ) * .. * .. External Subroutines .. EXTERNAL DLASCL, XERBLA, ZBDSQR, ZGEBRD, ZGELQF, ZGEMM, $ ZGEQRF, ZLACPY, ZLASCL, ZLASET, ZUNGBR, ZUNGLQ, $ ZUNGQR, ZUNMBR * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, ZLANGE EXTERNAL LSAME, ILAENV, DLAMCH, ZLANGE * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 MINMN = MIN( M, N ) WNTUA = LSAME( JOBU, 'A' ) WNTUS = LSAME( JOBU, 'S' ) WNTUAS = WNTUA .OR. WNTUS WNTUO = LSAME( JOBU, 'O' ) WNTUN = LSAME( JOBU, 'N' ) WNTVA = LSAME( JOBVT, 'A' ) WNTVS = LSAME( JOBVT, 'S' ) WNTVAS = WNTVA .OR. WNTVS WNTVO = LSAME( JOBVT, 'O' ) WNTVN = LSAME( JOBVT, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * IF( .NOT.( WNTUA .OR. WNTUS .OR. WNTUO .OR. WNTUN ) ) THEN INFO = -1 ELSE IF( .NOT.( WNTVA .OR. WNTVS .OR. WNTVO .OR. WNTVN ) .OR. $ ( WNTVO .AND. WNTUO ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -6 ELSE IF( LDU.LT.1 .OR. ( WNTUAS .AND. LDU.LT.M ) ) THEN INFO = -9 ELSE IF( LDVT.LT.1 .OR. ( WNTVA .AND. LDVT.LT.N ) .OR. $ ( WNTVS .AND. LDVT.LT.MINMN ) ) THEN INFO = -11 END IF * * Compute workspace * (Note: Comments in the code beginning "Workspace:" describe the * minimal amount of workspace needed at that point in the code, * as well as the preferred amount for good performance. * CWorkspace refers to complex workspace, and RWorkspace to * real workspace. NB refers to the optimal block size for the * immediately following subroutine, as returned by ILAENV.) * IF( INFO.EQ.0 ) THEN MINWRK = 1 MAXWRK = 1 IF( M.GE.N .AND. MINMN.GT.0 ) THEN * * Space needed for ZBDSQR is BDSPAC = 5*N * MNTHR = ILAENV( 6, 'ZGESVD', JOBU // JOBVT, M, N, 0, 0 ) * Compute space needed for ZGEQRF CALL ZGEQRF( M, N, A, LDA, CDUM(1), CDUM(1), -1, IERR ) LWORK_ZGEQRF = INT( CDUM(1) ) * Compute space needed for ZUNGQR CALL ZUNGQR( M, N, N, A, LDA, CDUM(1), CDUM(1), -1, IERR ) LWORK_ZUNGQR_N = INT( CDUM(1) ) CALL ZUNGQR( M, M, N, A, LDA, CDUM(1), CDUM(1), -1, IERR ) LWORK_ZUNGQR_M = INT( CDUM(1) ) * Compute space needed for ZGEBRD CALL ZGEBRD( N, N, A, LDA, S, DUM(1), CDUM(1), $ CDUM(1), CDUM(1), -1, IERR ) LWORK_ZGEBRD = INT( CDUM(1) ) * Compute space needed for ZUNGBR CALL ZUNGBR( 'P', N, N, N, A, LDA, CDUM(1), $ CDUM(1), -1, IERR ) LWORK_ZUNGBR_P = INT( CDUM(1) ) CALL ZUNGBR( 'Q', N, N, N, A, LDA, CDUM(1), $ CDUM(1), -1, IERR ) LWORK_ZUNGBR_Q = INT( CDUM(1) ) * IF( M.GE.MNTHR ) THEN IF( WNTUN ) THEN * * Path 1 (M much larger than N, JOBU='N') * MAXWRK = N + LWORK_ZGEQRF MAXWRK = MAX( MAXWRK, 2*N+LWORK_ZGEBRD ) IF( WNTVO .OR. WNTVAS ) $ MAXWRK = MAX( MAXWRK, 2*N+LWORK_ZUNGBR_P ) MINWRK = 3*N ELSE IF( WNTUO .AND. WNTVN ) THEN * * Path 2 (M much larger than N, JOBU='O', JOBVT='N') * WRKBL = N + LWORK_ZGEQRF WRKBL = MAX( WRKBL, N+LWORK_ZUNGQR_N ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_Q ) MAXWRK = MAX( N*N+WRKBL, N*N+M*N ) MINWRK = 2*N + M ELSE IF( WNTUO .AND. WNTVAS ) THEN * * Path 3 (M much larger than N, JOBU='O', JOBVT='S' or * 'A') * WRKBL = N + LWORK_ZGEQRF WRKBL = MAX( WRKBL, N+LWORK_ZUNGQR_N ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_Q ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_P ) MAXWRK = MAX( N*N+WRKBL, N*N+M*N ) MINWRK = 2*N + M ELSE IF( WNTUS .AND. WNTVN ) THEN * * Path 4 (M much larger than N, JOBU='S', JOBVT='N') * WRKBL = N + LWORK_ZGEQRF WRKBL = MAX( WRKBL, N+LWORK_ZUNGQR_N ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_Q ) MAXWRK = N*N + WRKBL MINWRK = 2*N + M ELSE IF( WNTUS .AND. WNTVO ) THEN * * Path 5 (M much larger than N, JOBU='S', JOBVT='O') * WRKBL = N + LWORK_ZGEQRF WRKBL = MAX( WRKBL, N+LWORK_ZUNGQR_N ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_Q ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_P ) MAXWRK = 2*N*N + WRKBL MINWRK = 2*N + M ELSE IF( WNTUS .AND. WNTVAS ) THEN * * Path 6 (M much larger than N, JOBU='S', JOBVT='S' or * 'A') * WRKBL = N + LWORK_ZGEQRF WRKBL = MAX( WRKBL, N+LWORK_ZUNGQR_N ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_Q ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_P ) MAXWRK = N*N + WRKBL MINWRK = 2*N + M ELSE IF( WNTUA .AND. WNTVN ) THEN * * Path 7 (M much larger than N, JOBU='A', JOBVT='N') * WRKBL = N + LWORK_ZGEQRF WRKBL = MAX( WRKBL, N+LWORK_ZUNGQR_M ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_Q ) MAXWRK = N*N + WRKBL MINWRK = 2*N + M ELSE IF( WNTUA .AND. WNTVO ) THEN * * Path 8 (M much larger than N, JOBU='A', JOBVT='O') * WRKBL = N + LWORK_ZGEQRF WRKBL = MAX( WRKBL, N+LWORK_ZUNGQR_M ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_Q ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_P ) MAXWRK = 2*N*N + WRKBL MINWRK = 2*N + M ELSE IF( WNTUA .AND. WNTVAS ) THEN * * Path 9 (M much larger than N, JOBU='A', JOBVT='S' or * 'A') * WRKBL = N + LWORK_ZGEQRF WRKBL = MAX( WRKBL, N+LWORK_ZUNGQR_M ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_Q ) WRKBL = MAX( WRKBL, 2*N+LWORK_ZUNGBR_P ) MAXWRK = N*N + WRKBL MINWRK = 2*N + M END IF ELSE * * Path 10 (M at least N, but not much larger) * CALL ZGEBRD( M, N, A, LDA, S, DUM(1), CDUM(1), $ CDUM(1), CDUM(1), -1, IERR ) LWORK_ZGEBRD = INT( CDUM(1) ) MAXWRK = 2*N + LWORK_ZGEBRD IF( WNTUS .OR. WNTUO ) THEN CALL ZUNGBR( 'Q', M, N, N, A, LDA, CDUM(1), $ CDUM(1), -1, IERR ) LWORK_ZUNGBR_Q = INT( CDUM(1) ) MAXWRK = MAX( MAXWRK, 2*N+LWORK_ZUNGBR_Q ) END IF IF( WNTUA ) THEN CALL ZUNGBR( 'Q', M, M, N, A, LDA, CDUM(1), $ CDUM(1), -1, IERR ) LWORK_ZUNGBR_Q = INT( CDUM(1) ) MAXWRK = MAX( MAXWRK, 2*N+LWORK_ZUNGBR_Q ) END IF IF( .NOT.WNTVN ) THEN MAXWRK = MAX( MAXWRK, 2*N+LWORK_ZUNGBR_P ) END IF MINWRK = 2*N + M END IF ELSE IF( MINMN.GT.0 ) THEN * * Space needed for ZBDSQR is BDSPAC = 5*M * MNTHR = ILAENV( 6, 'ZGESVD', JOBU // JOBVT, M, N, 0, 0 ) * Compute space needed for ZGELQF CALL ZGELQF( M, N, A, LDA, CDUM(1), CDUM(1), -1, IERR ) LWORK_ZGELQF = INT( CDUM(1) ) * Compute space needed for ZUNGLQ CALL ZUNGLQ( N, N, M, CDUM(1), N, CDUM(1), CDUM(1), -1, $ IERR ) LWORK_ZUNGLQ_N = INT( CDUM(1) ) CALL ZUNGLQ( M, N, M, A, LDA, CDUM(1), CDUM(1), -1, IERR ) LWORK_ZUNGLQ_M = INT( CDUM(1) ) * Compute space needed for ZGEBRD CALL ZGEBRD( M, M, A, LDA, S, DUM(1), CDUM(1), $ CDUM(1), CDUM(1), -1, IERR ) LWORK_ZGEBRD = INT( CDUM(1) ) * Compute space needed for ZUNGBR P CALL ZUNGBR( 'P', M, M, M, A, N, CDUM(1), $ CDUM(1), -1, IERR ) LWORK_ZUNGBR_P = INT( CDUM(1) ) * Compute space needed for ZUNGBR Q CALL ZUNGBR( 'Q', M, M, M, A, N, CDUM(1), $ CDUM(1), -1, IERR ) LWORK_ZUNGBR_Q = INT( CDUM(1) ) IF( N.GE.MNTHR ) THEN IF( WNTVN ) THEN * * Path 1t(N much larger than M, JOBVT='N') * MAXWRK = M + LWORK_ZGELQF MAXWRK = MAX( MAXWRK, 2*M+LWORK_ZGEBRD ) IF( WNTUO .OR. WNTUAS ) $ MAXWRK = MAX( MAXWRK, 2*M+LWORK_ZUNGBR_Q ) MINWRK = 3*M ELSE IF( WNTVO .AND. WNTUN ) THEN * * Path 2t(N much larger than M, JOBU='N', JOBVT='O') * WRKBL = M + LWORK_ZGELQF WRKBL = MAX( WRKBL, M+LWORK_ZUNGLQ_M ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_P ) MAXWRK = MAX( M*M+WRKBL, M*M+M*N ) MINWRK = 2*M + N ELSE IF( WNTVO .AND. WNTUAS ) THEN * * Path 3t(N much larger than M, JOBU='S' or 'A', * JOBVT='O') * WRKBL = M + LWORK_ZGELQF WRKBL = MAX( WRKBL, M+LWORK_ZUNGLQ_M ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_P ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_Q ) MAXWRK = MAX( M*M+WRKBL, M*M+M*N ) MINWRK = 2*M + N ELSE IF( WNTVS .AND. WNTUN ) THEN * * Path 4t(N much larger than M, JOBU='N', JOBVT='S') * WRKBL = M + LWORK_ZGELQF WRKBL = MAX( WRKBL, M+LWORK_ZUNGLQ_M ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_P ) MAXWRK = M*M + WRKBL MINWRK = 2*M + N ELSE IF( WNTVS .AND. WNTUO ) THEN * * Path 5t(N much larger than M, JOBU='O', JOBVT='S') * WRKBL = M + LWORK_ZGELQF WRKBL = MAX( WRKBL, M+LWORK_ZUNGLQ_M ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_P ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_Q ) MAXWRK = 2*M*M + WRKBL MINWRK = 2*M + N ELSE IF( WNTVS .AND. WNTUAS ) THEN * * Path 6t(N much larger than M, JOBU='S' or 'A', * JOBVT='S') * WRKBL = M + LWORK_ZGELQF WRKBL = MAX( WRKBL, M+LWORK_ZUNGLQ_M ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_P ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_Q ) MAXWRK = M*M + WRKBL MINWRK = 2*M + N ELSE IF( WNTVA .AND. WNTUN ) THEN * * Path 7t(N much larger than M, JOBU='N', JOBVT='A') * WRKBL = M + LWORK_ZGELQF WRKBL = MAX( WRKBL, M+LWORK_ZUNGLQ_N ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_P ) MAXWRK = M*M + WRKBL MINWRK = 2*M + N ELSE IF( WNTVA .AND. WNTUO ) THEN * * Path 8t(N much larger than M, JOBU='O', JOBVT='A') * WRKBL = M + LWORK_ZGELQF WRKBL = MAX( WRKBL, M+LWORK_ZUNGLQ_N ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_P ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_Q ) MAXWRK = 2*M*M + WRKBL MINWRK = 2*M + N ELSE IF( WNTVA .AND. WNTUAS ) THEN * * Path 9t(N much larger than M, JOBU='S' or 'A', * JOBVT='A') * WRKBL = M + LWORK_ZGELQF WRKBL = MAX( WRKBL, M+LWORK_ZUNGLQ_N ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZGEBRD ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_P ) WRKBL = MAX( WRKBL, 2*M+LWORK_ZUNGBR_Q ) MAXWRK = M*M + WRKBL MINWRK = 2*M + N END IF ELSE * * Path 10t(N greater than M, but not much larger) * CALL ZGEBRD( M, N, A, LDA, S, DUM(1), CDUM(1), $ CDUM(1), CDUM(1), -1, IERR ) LWORK_ZGEBRD = INT( CDUM(1) ) MAXWRK = 2*M + LWORK_ZGEBRD IF( WNTVS .OR. WNTVO ) THEN * Compute space needed for ZUNGBR P CALL ZUNGBR( 'P', M, N, M, A, N, CDUM(1), $ CDUM(1), -1, IERR ) LWORK_ZUNGBR_P = INT( CDUM(1) ) MAXWRK = MAX( MAXWRK, 2*M+LWORK_ZUNGBR_P ) END IF IF( WNTVA ) THEN CALL ZUNGBR( 'P', N, N, M, A, N, CDUM(1), $ CDUM(1), -1, IERR ) LWORK_ZUNGBR_P = INT( CDUM(1) ) MAXWRK = MAX( MAXWRK, 2*M+LWORK_ZUNGBR_P ) END IF IF( .NOT.WNTUN ) THEN MAXWRK = MAX( MAXWRK, 2*M+LWORK_ZUNGBR_Q ) END IF MINWRK = 2*M + N END IF END IF MAXWRK = MAX( MAXWRK, MINWRK ) WORK( 1 ) = MAXWRK * IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN INFO = -13 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGESVD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) THEN RETURN END IF * * Get machine constants * EPS = DLAMCH( 'P' ) SMLNUM = SQRT( DLAMCH( 'S' ) ) / EPS BIGNUM = ONE / SMLNUM * * Scale A if max element outside range [SMLNUM,BIGNUM] * ANRM = ZLANGE( 'M', M, N, A, LDA, DUM ) ISCL = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN ISCL = 1 CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, IERR ) ELSE IF( ANRM.GT.BIGNUM ) THEN ISCL = 1 CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, IERR ) END IF * IF( M.GE.N ) THEN * * A has at least as many rows as columns. If A has sufficiently * more rows than columns, first reduce using the QR * decomposition (if sufficient workspace available) * IF( M.GE.MNTHR ) THEN * IF( WNTUN ) THEN * * Path 1 (M much larger than N, JOBU='N') * No left singular vectors to be computed * ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: need 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Zero out below R * IF( N .GT. 1 ) THEN CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, A( 2, 1 ), $ LDA ) END IF IE = 1 ITAUQ = 1 ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in A * (CWorkspace: need 3*N, prefer 2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, $ IERR ) NCVT = 0 IF( WNTVO .OR. WNTVAS ) THEN * * If right singular vectors desired, generate P'. * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) NCVT = N END IF IRWORK = IE + N * * Perform bidiagonal QR iteration, computing right * singular vectors of A in A if desired * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, NCVT, 0, 0, S, RWORK( IE ), A, LDA, $ CDUM, 1, CDUM, 1, RWORK( IRWORK ), INFO ) * * If right singular vectors desired in VT, copy them there * IF( WNTVAS ) $ CALL ZLACPY( 'F', N, N, A, LDA, VT, LDVT ) * ELSE IF( WNTUO .AND. WNTVN ) THEN * * Path 2 (M much larger than N, JOBU='O', JOBVT='N') * N left singular vectors to be overwritten on A and * no right singular vectors to be computed * IF( LWORK.GE.N*N+3*N ) THEN * * Sufficient workspace for a fast algorithm * IR = 1 IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*N ) THEN * * WORK(IU) is LDA by N, WORK(IR) is LDA by N * LDWRKU = LDA LDWRKR = LDA ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N )+N*N ) THEN * * WORK(IU) is LDA by N, WORK(IR) is N by N * LDWRKU = LDA LDWRKR = N ELSE * * WORK(IU) is LDWRKU by N, WORK(IR) is N by N * LDWRKU = ( LWORK-N*N ) / N LDWRKR = N END IF ITAU = IR + LDWRKR*N IWORK = ITAU + N * * Compute A=Q*R * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to WORK(IR) and zero out below it * CALL ZLACPY( 'U', N, N, A, LDA, WORK( IR ), LDWRKR ) CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ WORK( IR+1 ), LDWRKR ) * * Generate Q in A * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in WORK(IR) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, WORK( IR ), LDWRKR, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Generate left vectors bidiagonalizing R * (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) * (RWorkspace: need 0) * CALL ZUNGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of R in WORK(IR) * (CWorkspace: need N*N) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, 0, N, 0, S, RWORK( IE ), CDUM, 1, $ WORK( IR ), LDWRKR, CDUM, 1, $ RWORK( IRWORK ), INFO ) IU = ITAUQ * * Multiply Q in A by left singular vectors of R in * WORK(IR), storing result in WORK(IU) and copying to A * (CWorkspace: need N*N+N, prefer N*N+M*N) * (RWorkspace: 0) * DO 10 I = 1, M, LDWRKU CHUNK = MIN( M-I+1, LDWRKU ) CALL ZGEMM( 'N', 'N', CHUNK, N, N, CONE, A( I, 1 ), $ LDA, WORK( IR ), LDWRKR, CZERO, $ WORK( IU ), LDWRKU ) CALL ZLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU, $ A( I, 1 ), LDA ) 10 CONTINUE * ELSE * * Insufficient workspace for a fast algorithm * IE = 1 ITAUQ = 1 ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize A * (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) * (RWorkspace: N) * CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Generate left vectors bidiagonalizing A * (CWorkspace: need 3*N, prefer 2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of A in A * (CWorkspace: need 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, 0, M, 0, S, RWORK( IE ), CDUM, 1, $ A, LDA, CDUM, 1, RWORK( IRWORK ), INFO ) * END IF * ELSE IF( WNTUO .AND. WNTVAS ) THEN * * Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A') * N left singular vectors to be overwritten on A and * N right singular vectors to be computed in VT * IF( LWORK.GE.N*N+3*N ) THEN * * Sufficient workspace for a fast algorithm * IR = 1 IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*N ) THEN * * WORK(IU) is LDA by N and WORK(IR) is LDA by N * LDWRKU = LDA LDWRKR = LDA ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N )+N*N ) THEN * * WORK(IU) is LDA by N and WORK(IR) is N by N * LDWRKU = LDA LDWRKR = N ELSE * * WORK(IU) is LDWRKU by N and WORK(IR) is N by N * LDWRKU = ( LWORK-N*N ) / N LDWRKR = N END IF ITAU = IR + LDWRKR*N IWORK = ITAU + N * * Compute A=Q*R * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to VT, zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) IF( N.GT.1 ) $ CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ VT( 2, 1 ), LDVT ) * * Generate Q in A * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in VT, copying result to WORK(IR) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, VT, LDVT, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', N, N, VT, LDVT, WORK( IR ), LDWRKR ) * * Generate left vectors bidiagonalizing R in WORK(IR) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right vectors bidiagonalizing R in VT * (CWorkspace: need N*N+3*N-1, prefer N*N+2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of R in WORK(IR) and computing right * singular vectors of R in VT * (CWorkspace: need N*N) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), VT, $ LDVT, WORK( IR ), LDWRKR, CDUM, 1, $ RWORK( IRWORK ), INFO ) IU = ITAUQ * * Multiply Q in A by left singular vectors of R in * WORK(IR), storing result in WORK(IU) and copying to A * (CWorkspace: need N*N+N, prefer N*N+M*N) * (RWorkspace: 0) * DO 20 I = 1, M, LDWRKU CHUNK = MIN( M-I+1, LDWRKU ) CALL ZGEMM( 'N', 'N', CHUNK, N, N, CONE, A( I, 1 ), $ LDA, WORK( IR ), LDWRKR, CZERO, $ WORK( IU ), LDWRKU ) CALL ZLACPY( 'F', CHUNK, N, WORK( IU ), LDWRKU, $ A( I, 1 ), LDA ) 20 CONTINUE * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to VT, zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) IF( N.GT.1 ) $ CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ VT( 2, 1 ), LDVT ) * * Generate Q in A * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in VT * (CWorkspace: need 3*N, prefer 2*N+2*N*NB) * (RWorkspace: N) * CALL ZGEBRD( N, N, VT, LDVT, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply Q in A by left vectors bidiagonalizing R * (CWorkspace: need 2*N+M, prefer 2*N+M*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, $ WORK( ITAUQ ), A, LDA, WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right vectors bidiagonalizing R in VT * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of A in A and computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), VT, $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ), $ INFO ) * END IF * ELSE IF( WNTUS ) THEN * IF( WNTVN ) THEN * * Path 4 (M much larger than N, JOBU='S', JOBVT='N') * N left singular vectors to be computed in U and * no right singular vectors to be computed * IF( LWORK.GE.N*N+3*N ) THEN * * Sufficient workspace for a fast algorithm * IR = 1 IF( LWORK.GE.WRKBL+LDA*N ) THEN * * WORK(IR) is LDA by N * LDWRKR = LDA ELSE * * WORK(IR) is N by N * LDWRKR = N END IF ITAU = IR + LDWRKR*N IWORK = ITAU + N * * Compute A=Q*R * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to WORK(IR), zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, WORK( IR ), $ LDWRKR ) CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ WORK( IR+1 ), LDWRKR ) * * Generate Q in A * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in WORK(IR) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, WORK( IR ), LDWRKR, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate left vectors bidiagonalizing R in WORK(IR) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of R in WORK(IR) * (CWorkspace: need N*N) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, 0, N, 0, S, RWORK( IE ), CDUM, $ 1, WORK( IR ), LDWRKR, CDUM, 1, $ RWORK( IRWORK ), INFO ) * * Multiply Q in A by left singular vectors of R in * WORK(IR), storing result in U * (CWorkspace: need N*N) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, N, CONE, A, LDA, $ WORK( IR ), LDWRKR, CZERO, U, LDU ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Generate Q in U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Zero out below R in A * IF( N .GT. 1 ) THEN CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ A( 2, 1 ), LDA ) END IF * * Bidiagonalize R in A * (CWorkspace: need 3*N, prefer 2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply Q in U by left vectors bidiagonalizing R * (CWorkspace: need 2*N+M, prefer 2*N+M*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, A, LDA, $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, 0, M, 0, S, RWORK( IE ), CDUM, $ 1, U, LDU, CDUM, 1, RWORK( IRWORK ), $ INFO ) * END IF * ELSE IF( WNTVO ) THEN * * Path 5 (M much larger than N, JOBU='S', JOBVT='O') * N left singular vectors to be computed in U and * N right singular vectors to be overwritten on A * IF( LWORK.GE.2*N*N+3*N ) THEN * * Sufficient workspace for a fast algorithm * IU = 1 IF( LWORK.GE.WRKBL+2*LDA*N ) THEN * * WORK(IU) is LDA by N and WORK(IR) is LDA by N * LDWRKU = LDA IR = IU + LDWRKU*N LDWRKR = LDA ELSE IF( LWORK.GE.WRKBL+( LDA+N )*N ) THEN * * WORK(IU) is LDA by N and WORK(IR) is N by N * LDWRKU = LDA IR = IU + LDWRKU*N LDWRKR = N ELSE * * WORK(IU) is N by N and WORK(IR) is N by N * LDWRKU = N IR = IU + LDWRKU*N LDWRKR = N END IF ITAU = IR + LDWRKR*N IWORK = ITAU + N * * Compute A=Q*R * (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to WORK(IU), zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, WORK( IU ), $ LDWRKU ) CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ WORK( IU+1 ), LDWRKU ) * * Generate Q in A * (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in WORK(IU), copying result to * WORK(IR) * (CWorkspace: need 2*N*N+3*N, * prefer 2*N*N+2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, WORK( IU ), LDWRKU, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', N, N, WORK( IU ), LDWRKU, $ WORK( IR ), LDWRKR ) * * Generate left bidiagonalizing vectors in WORK(IU) * (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right bidiagonalizing vectors in WORK(IR) * (CWorkspace: need 2*N*N+3*N-1, * prefer 2*N*N+2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, WORK( IR ), LDWRKR, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of R in WORK(IU) and computing * right singular vectors of R in WORK(IR) * (CWorkspace: need 2*N*N) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), $ WORK( IR ), LDWRKR, WORK( IU ), $ LDWRKU, CDUM, 1, RWORK( IRWORK ), $ INFO ) * * Multiply Q in A by left singular vectors of R in * WORK(IU), storing result in U * (CWorkspace: need N*N) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, N, CONE, A, LDA, $ WORK( IU ), LDWRKU, CZERO, U, LDU ) * * Copy right singular vectors of R to A * (CWorkspace: need N*N) * (RWorkspace: 0) * CALL ZLACPY( 'F', N, N, WORK( IR ), LDWRKR, A, $ LDA ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Generate Q in U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Zero out below R in A * IF( N .GT. 1 ) THEN CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ A( 2, 1 ), LDA ) END IF * * Bidiagonalize R in A * (CWorkspace: need 3*N, prefer 2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply Q in U by left vectors bidiagonalizing R * (CWorkspace: need 2*N+M, prefer 2*N+M*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, A, LDA, $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right vectors bidiagonalizing R in A * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U and computing right * singular vectors of A in A * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), A, $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ), $ INFO ) * END IF * ELSE IF( WNTVAS ) THEN * * Path 6 (M much larger than N, JOBU='S', JOBVT='S' * or 'A') * N left singular vectors to be computed in U and * N right singular vectors to be computed in VT * IF( LWORK.GE.N*N+3*N ) THEN * * Sufficient workspace for a fast algorithm * IU = 1 IF( LWORK.GE.WRKBL+LDA*N ) THEN * * WORK(IU) is LDA by N * LDWRKU = LDA ELSE * * WORK(IU) is N by N * LDWRKU = N END IF ITAU = IU + LDWRKU*N IWORK = ITAU + N * * Compute A=Q*R * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to WORK(IU), zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, WORK( IU ), $ LDWRKU ) CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ WORK( IU+1 ), LDWRKU ) * * Generate Q in A * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in WORK(IU), copying result to VT * (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, WORK( IU ), LDWRKU, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', N, N, WORK( IU ), LDWRKU, VT, $ LDVT ) * * Generate left bidiagonalizing vectors in WORK(IU) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right bidiagonalizing vectors in VT * (CWorkspace: need N*N+3*N-1, * prefer N*N+2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of R in WORK(IU) and computing * right singular vectors of R in VT * (CWorkspace: need N*N) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), VT, $ LDVT, WORK( IU ), LDWRKU, CDUM, 1, $ RWORK( IRWORK ), INFO ) * * Multiply Q in A by left singular vectors of R in * WORK(IU), storing result in U * (CWorkspace: need N*N) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, N, CONE, A, LDA, $ WORK( IU ), LDWRKU, CZERO, U, LDU ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Generate Q in U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, N, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to VT, zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) IF( N.GT.1 ) $ CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ VT( 2, 1 ), LDVT ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in VT * (CWorkspace: need 3*N, prefer 2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, VT, LDVT, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply Q in U by left bidiagonalizing vectors * in VT * (CWorkspace: need 2*N+M, prefer 2*N+M*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right bidiagonalizing vectors in VT * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U and computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), VT, $ LDVT, U, LDU, CDUM, 1, $ RWORK( IRWORK ), INFO ) * END IF * END IF * ELSE IF( WNTUA ) THEN * IF( WNTVN ) THEN * * Path 7 (M much larger than N, JOBU='A', JOBVT='N') * M left singular vectors to be computed in U and * no right singular vectors to be computed * IF( LWORK.GE.N*N+MAX( N+M, 3*N ) ) THEN * * Sufficient workspace for a fast algorithm * IR = 1 IF( LWORK.GE.WRKBL+LDA*N ) THEN * * WORK(IR) is LDA by N * LDWRKR = LDA ELSE * * WORK(IR) is N by N * LDWRKR = N END IF ITAU = IR + LDWRKR*N IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Copy R to WORK(IR), zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, WORK( IR ), $ LDWRKR ) CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ WORK( IR+1 ), LDWRKR ) * * Generate Q in U * (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in WORK(IR) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, WORK( IR ), LDWRKR, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors in WORK(IR) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', N, N, N, WORK( IR ), LDWRKR, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of R in WORK(IR) * (CWorkspace: need N*N) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, 0, N, 0, S, RWORK( IE ), CDUM, $ 1, WORK( IR ), LDWRKR, CDUM, 1, $ RWORK( IRWORK ), INFO ) * * Multiply Q in U by left singular vectors of R in * WORK(IR), storing result in A * (CWorkspace: need N*N) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, N, CONE, U, LDU, $ WORK( IR ), LDWRKR, CZERO, A, LDA ) * * Copy left singular vectors of A from A to U * CALL ZLACPY( 'F', M, N, A, LDA, U, LDU ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Generate Q in U * (CWorkspace: need N+M, prefer N+M*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Zero out below R in A * IF( N .GT. 1 ) THEN CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ A( 2, 1 ), LDA ) END IF * * Bidiagonalize R in A * (CWorkspace: need 3*N, prefer 2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply Q in U by left bidiagonalizing vectors * in A * (CWorkspace: need 2*N+M, prefer 2*N+M*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, A, LDA, $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, 0, M, 0, S, RWORK( IE ), CDUM, $ 1, U, LDU, CDUM, 1, RWORK( IRWORK ), $ INFO ) * END IF * ELSE IF( WNTVO ) THEN * * Path 8 (M much larger than N, JOBU='A', JOBVT='O') * M left singular vectors to be computed in U and * N right singular vectors to be overwritten on A * IF( LWORK.GE.2*N*N+MAX( N+M, 3*N ) ) THEN * * Sufficient workspace for a fast algorithm * IU = 1 IF( LWORK.GE.WRKBL+2*LDA*N ) THEN * * WORK(IU) is LDA by N and WORK(IR) is LDA by N * LDWRKU = LDA IR = IU + LDWRKU*N LDWRKR = LDA ELSE IF( LWORK.GE.WRKBL+( LDA+N )*N ) THEN * * WORK(IU) is LDA by N and WORK(IR) is N by N * LDWRKU = LDA IR = IU + LDWRKU*N LDWRKR = N ELSE * * WORK(IU) is N by N and WORK(IR) is N by N * LDWRKU = N IR = IU + LDWRKU*N LDWRKR = N END IF ITAU = IR + LDWRKR*N IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Generate Q in U * (CWorkspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to WORK(IU), zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, WORK( IU ), $ LDWRKU ) CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ WORK( IU+1 ), LDWRKU ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in WORK(IU), copying result to * WORK(IR) * (CWorkspace: need 2*N*N+3*N, * prefer 2*N*N+2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, WORK( IU ), LDWRKU, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', N, N, WORK( IU ), LDWRKU, $ WORK( IR ), LDWRKR ) * * Generate left bidiagonalizing vectors in WORK(IU) * (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right bidiagonalizing vectors in WORK(IR) * (CWorkspace: need 2*N*N+3*N-1, * prefer 2*N*N+2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, WORK( IR ), LDWRKR, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of R in WORK(IU) and computing * right singular vectors of R in WORK(IR) * (CWorkspace: need 2*N*N) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), $ WORK( IR ), LDWRKR, WORK( IU ), $ LDWRKU, CDUM, 1, RWORK( IRWORK ), $ INFO ) * * Multiply Q in U by left singular vectors of R in * WORK(IU), storing result in A * (CWorkspace: need N*N) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, N, CONE, U, LDU, $ WORK( IU ), LDWRKU, CZERO, A, LDA ) * * Copy left singular vectors of A from A to U * CALL ZLACPY( 'F', M, N, A, LDA, U, LDU ) * * Copy right singular vectors of R from WORK(IR) to A * CALL ZLACPY( 'F', N, N, WORK( IR ), LDWRKR, A, $ LDA ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Generate Q in U * (CWorkspace: need N+M, prefer N+M*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Zero out below R in A * IF( N .GT. 1 ) THEN CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ A( 2, 1 ), LDA ) END IF * * Bidiagonalize R in A * (CWorkspace: need 3*N, prefer 2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply Q in U by left bidiagonalizing vectors * in A * (CWorkspace: need 2*N+M, prefer 2*N+M*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, A, LDA, $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right bidiagonalizing vectors in A * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U and computing right * singular vectors of A in A * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), A, $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ), $ INFO ) * END IF * ELSE IF( WNTVAS ) THEN * * Path 9 (M much larger than N, JOBU='A', JOBVT='S' * or 'A') * M left singular vectors to be computed in U and * N right singular vectors to be computed in VT * IF( LWORK.GE.N*N+MAX( N+M, 3*N ) ) THEN * * Sufficient workspace for a fast algorithm * IU = 1 IF( LWORK.GE.WRKBL+LDA*N ) THEN * * WORK(IU) is LDA by N * LDWRKU = LDA ELSE * * WORK(IU) is N by N * LDWRKU = N END IF ITAU = IU + LDWRKU*N IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Generate Q in U * (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R to WORK(IU), zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, WORK( IU ), $ LDWRKU ) CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ WORK( IU+1 ), LDWRKU ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in WORK(IU), copying result to VT * (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, WORK( IU ), LDWRKU, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', N, N, WORK( IU ), LDWRKU, VT, $ LDVT ) * * Generate left bidiagonalizing vectors in WORK(IU) * (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', N, N, N, WORK( IU ), LDWRKU, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right bidiagonalizing vectors in VT * (CWorkspace: need N*N+3*N-1, * prefer N*N+2*N+(N-1)*NB) * (RWorkspace: need 0) * CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of R in WORK(IU) and computing * right singular vectors of R in VT * (CWorkspace: need N*N) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, N, 0, S, RWORK( IE ), VT, $ LDVT, WORK( IU ), LDWRKU, CDUM, 1, $ RWORK( IRWORK ), INFO ) * * Multiply Q in U by left singular vectors of R in * WORK(IU), storing result in A * (CWorkspace: need N*N) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, N, CONE, U, LDU, $ WORK( IU ), LDWRKU, CZERO, A, LDA ) * * Copy left singular vectors of A from A to U * CALL ZLACPY( 'F', M, N, A, LDA, U, LDU ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + N * * Compute A=Q*R, copying result to U * (CWorkspace: need 2*N, prefer N+N*NB) * (RWorkspace: 0) * CALL ZGEQRF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) * * Generate Q in U * (CWorkspace: need N+M, prefer N+M*NB) * (RWorkspace: 0) * CALL ZUNGQR( M, M, N, U, LDU, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy R from A to VT, zeroing out below it * CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) IF( N.GT.1 ) $ CALL ZLASET( 'L', N-1, N-1, CZERO, CZERO, $ VT( 2, 1 ), LDVT ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize R in VT * (CWorkspace: need 3*N, prefer 2*N+2*N*NB) * (RWorkspace: need N) * CALL ZGEBRD( N, N, VT, LDVT, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply Q in U by left bidiagonalizing vectors * in VT * (CWorkspace: need 2*N+M, prefer 2*N+M*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'Q', 'R', 'N', M, N, N, VT, LDVT, $ WORK( ITAUQ ), U, LDU, WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right bidiagonalizing vectors in VT * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + N * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U and computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, N, M, 0, S, RWORK( IE ), VT, $ LDVT, U, LDU, CDUM, 1, $ RWORK( IRWORK ), INFO ) * END IF * END IF * END IF * ELSE * * M .LT. MNTHR * * Path 10 (M at least N, but not much larger) * Reduce to bidiagonal form without QR decomposition * IE = 1 ITAUQ = 1 ITAUP = ITAUQ + N IWORK = ITAUP + N * * Bidiagonalize A * (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB) * (RWorkspace: need N) * CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, $ IERR ) IF( WNTUAS ) THEN * * If left singular vectors desired in U, copy result to U * and generate left bidiagonalizing vectors in U * (CWorkspace: need 2*N+NCU, prefer 2*N+NCU*NB) * (RWorkspace: 0) * CALL ZLACPY( 'L', M, N, A, LDA, U, LDU ) IF( WNTUS ) $ NCU = N IF( WNTUA ) $ NCU = M CALL ZUNGBR( 'Q', M, NCU, N, U, LDU, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IF( WNTVAS ) THEN * * If right singular vectors desired in VT, copy result to * VT and generate right bidiagonalizing vectors in VT * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZLACPY( 'U', N, N, A, LDA, VT, LDVT ) CALL ZUNGBR( 'P', N, N, N, VT, LDVT, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IF( WNTUO ) THEN * * If left singular vectors desired in A, generate left * bidiagonalizing vectors in A * (CWorkspace: need 3*N, prefer 2*N+N*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, N, N, A, LDA, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IF( WNTVO ) THEN * * If right singular vectors desired in A, generate right * bidiagonalizing vectors in A * (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', N, N, N, A, LDA, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IRWORK = IE + N IF( WNTUAS .OR. WNTUO ) $ NRU = M IF( WNTUN ) $ NRU = 0 IF( WNTVAS .OR. WNTVO ) $ NCVT = N IF( WNTVN ) $ NCVT = 0 IF( ( .NOT.WNTUO ) .AND. ( .NOT.WNTVO ) ) THEN * * Perform bidiagonal QR iteration, if desired, computing * left singular vectors in U and computing right singular * vectors in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, NCVT, NRU, 0, S, RWORK( IE ), VT, $ LDVT, U, LDU, CDUM, 1, RWORK( IRWORK ), $ INFO ) ELSE IF( ( .NOT.WNTUO ) .AND. WNTVO ) THEN * * Perform bidiagonal QR iteration, if desired, computing * left singular vectors in U and computing right singular * vectors in A * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, NCVT, NRU, 0, S, RWORK( IE ), A, $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ), $ INFO ) ELSE * * Perform bidiagonal QR iteration, if desired, computing * left singular vectors in A and computing right singular * vectors in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', N, NCVT, NRU, 0, S, RWORK( IE ), VT, $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ), $ INFO ) END IF * END IF * ELSE * * A has more columns than rows. If A has sufficiently more * columns than rows, first reduce using the LQ decomposition (if * sufficient workspace available) * IF( N.GE.MNTHR ) THEN * IF( WNTVN ) THEN * * Path 1t(N much larger than M, JOBVT='N') * No right singular vectors to be computed * ITAU = 1 IWORK = ITAU + M * * Compute A=L*Q * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Zero out above L * CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, A( 1, 2 ), $ LDA ) IE = 1 ITAUQ = 1 ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in A * (CWorkspace: need 3*M, prefer 2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, $ IERR ) IF( WNTUO .OR. WNTUAS ) THEN * * If left singular vectors desired, generate Q * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IRWORK = IE + M NRU = 0 IF( WNTUO .OR. WNTUAS ) $ NRU = M * * Perform bidiagonal QR iteration, computing left singular * vectors of A in A if desired * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, 0, NRU, 0, S, RWORK( IE ), CDUM, 1, $ A, LDA, CDUM, 1, RWORK( IRWORK ), INFO ) * * If left singular vectors desired in U, copy them there * IF( WNTUAS ) $ CALL ZLACPY( 'F', M, M, A, LDA, U, LDU ) * ELSE IF( WNTVO .AND. WNTUN ) THEN * * Path 2t(N much larger than M, JOBU='N', JOBVT='O') * M right singular vectors to be overwritten on A and * no left singular vectors to be computed * IF( LWORK.GE.M*M+3*M ) THEN * * Sufficient workspace for a fast algorithm * IR = 1 IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*M ) THEN * * WORK(IU) is LDA by N and WORK(IR) is LDA by M * LDWRKU = LDA CHUNK = N LDWRKR = LDA ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N )+M*M ) THEN * * WORK(IU) is LDA by N and WORK(IR) is M by M * LDWRKU = LDA CHUNK = N LDWRKR = M ELSE * * WORK(IU) is M by CHUNK and WORK(IR) is M by M * LDWRKU = M CHUNK = ( LWORK-M*M ) / M LDWRKR = M END IF ITAU = IR + LDWRKR*M IWORK = ITAU + M * * Compute A=L*Q * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to WORK(IR) and zero out above it * CALL ZLACPY( 'L', M, M, A, LDA, WORK( IR ), LDWRKR ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ WORK( IR+LDWRKR ), LDWRKR ) * * Generate Q in A * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in WORK(IR) * (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, WORK( IR ), LDWRKR, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Generate right vectors bidiagonalizing L * (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, M, M, WORK( IR ), LDWRKR, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing right * singular vectors of L in WORK(IR) * (CWorkspace: need M*M) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, M, 0, 0, S, RWORK( IE ), $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1, $ RWORK( IRWORK ), INFO ) IU = ITAUQ * * Multiply right singular vectors of L in WORK(IR) by Q * in A, storing result in WORK(IU) and copying to A * (CWorkspace: need M*M+M, prefer M*M+M*N) * (RWorkspace: 0) * DO 30 I = 1, N, CHUNK BLK = MIN( N-I+1, CHUNK ) CALL ZGEMM( 'N', 'N', M, BLK, M, CONE, WORK( IR ), $ LDWRKR, A( 1, I ), LDA, CZERO, $ WORK( IU ), LDWRKU ) CALL ZLACPY( 'F', M, BLK, WORK( IU ), LDWRKU, $ A( 1, I ), LDA ) 30 CONTINUE * ELSE * * Insufficient workspace for a fast algorithm * IE = 1 ITAUQ = 1 ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize A * (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Generate right vectors bidiagonalizing A * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing right * singular vectors of A in A * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'L', M, N, 0, 0, S, RWORK( IE ), A, LDA, $ CDUM, 1, CDUM, 1, RWORK( IRWORK ), INFO ) * END IF * ELSE IF( WNTVO .AND. WNTUAS ) THEN * * Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O') * M right singular vectors to be overwritten on A and * M left singular vectors to be computed in U * IF( LWORK.GE.M*M+3*M ) THEN * * Sufficient workspace for a fast algorithm * IR = 1 IF( LWORK.GE.MAX( WRKBL, LDA*N )+LDA*M ) THEN * * WORK(IU) is LDA by N and WORK(IR) is LDA by M * LDWRKU = LDA CHUNK = N LDWRKR = LDA ELSE IF( LWORK.GE.MAX( WRKBL, LDA*N )+M*M ) THEN * * WORK(IU) is LDA by N and WORK(IR) is M by M * LDWRKU = LDA CHUNK = N LDWRKR = M ELSE * * WORK(IU) is M by CHUNK and WORK(IR) is M by M * LDWRKU = M CHUNK = ( LWORK-M*M ) / M LDWRKR = M END IF ITAU = IR + LDWRKR*M IWORK = ITAU + M * * Compute A=L*Q * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to U, zeroing about above it * CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, U( 1, 2 ), $ LDU ) * * Generate Q in A * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in U, copying result to WORK(IR) * (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, U, LDU, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, M, U, LDU, WORK( IR ), LDWRKR ) * * Generate right vectors bidiagonalizing L in WORK(IR) * (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, M, M, WORK( IR ), LDWRKR, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate left vectors bidiagonalizing L in U * (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of L in U, and computing right * singular vectors of L in WORK(IR) * (CWorkspace: need M*M) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), $ WORK( IR ), LDWRKR, U, LDU, CDUM, 1, $ RWORK( IRWORK ), INFO ) IU = ITAUQ * * Multiply right singular vectors of L in WORK(IR) by Q * in A, storing result in WORK(IU) and copying to A * (CWorkspace: need M*M+M, prefer M*M+M*N)) * (RWorkspace: 0) * DO 40 I = 1, N, CHUNK BLK = MIN( N-I+1, CHUNK ) CALL ZGEMM( 'N', 'N', M, BLK, M, CONE, WORK( IR ), $ LDWRKR, A( 1, I ), LDA, CZERO, $ WORK( IU ), LDWRKU ) CALL ZLACPY( 'F', M, BLK, WORK( IU ), LDWRKU, $ A( 1, I ), LDA ) 40 CONTINUE * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + M * * Compute A=L*Q * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to U, zeroing out above it * CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, U( 1, 2 ), $ LDU ) * * Generate Q in A * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in U * (CWorkspace: need 3*M, prefer 2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, U, LDU, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply right vectors bidiagonalizing L by Q in A * (CWorkspace: need 2*M+N, prefer 2*M+N*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'P', 'L', 'C', M, N, M, U, LDU, $ WORK( ITAUP ), A, LDA, WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate left vectors bidiagonalizing L in U * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U and computing right * singular vectors of A in A * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), A, LDA, $ U, LDU, CDUM, 1, RWORK( IRWORK ), INFO ) * END IF * ELSE IF( WNTVS ) THEN * IF( WNTUN ) THEN * * Path 4t(N much larger than M, JOBU='N', JOBVT='S') * M right singular vectors to be computed in VT and * no left singular vectors to be computed * IF( LWORK.GE.M*M+3*M ) THEN * * Sufficient workspace for a fast algorithm * IR = 1 IF( LWORK.GE.WRKBL+LDA*M ) THEN * * WORK(IR) is LDA by M * LDWRKR = LDA ELSE * * WORK(IR) is M by M * LDWRKR = M END IF ITAU = IR + LDWRKR*M IWORK = ITAU + M * * Compute A=L*Q * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to WORK(IR), zeroing out above it * CALL ZLACPY( 'L', M, M, A, LDA, WORK( IR ), $ LDWRKR ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ WORK( IR+LDWRKR ), LDWRKR ) * * Generate Q in A * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in WORK(IR) * (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, WORK( IR ), LDWRKR, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right vectors bidiagonalizing L in * WORK(IR) * (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, M, M, WORK( IR ), LDWRKR, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing right * singular vectors of L in WORK(IR) * (CWorkspace: need M*M) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, M, 0, 0, S, RWORK( IE ), $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1, $ RWORK( IRWORK ), INFO ) * * Multiply right singular vectors of L in WORK(IR) by * Q in A, storing result in VT * (CWorkspace: need M*M) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IR ), $ LDWRKR, A, LDA, CZERO, VT, LDVT ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + M * * Compute A=L*Q * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy result to VT * CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Generate Q in VT * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Zero out above L in A * CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ A( 1, 2 ), LDA ) * * Bidiagonalize L in A * (CWorkspace: need 3*M, prefer 2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply right vectors bidiagonalizing L by Q in VT * (CWorkspace: need 2*M+N, prefer 2*M+N*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'P', 'L', 'C', M, N, M, A, LDA, $ WORK( ITAUP ), VT, LDVT, $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, N, 0, 0, S, RWORK( IE ), VT, $ LDVT, CDUM, 1, CDUM, 1, $ RWORK( IRWORK ), INFO ) * END IF * ELSE IF( WNTUO ) THEN * * Path 5t(N much larger than M, JOBU='O', JOBVT='S') * M right singular vectors to be computed in VT and * M left singular vectors to be overwritten on A * IF( LWORK.GE.2*M*M+3*M ) THEN * * Sufficient workspace for a fast algorithm * IU = 1 IF( LWORK.GE.WRKBL+2*LDA*M ) THEN * * WORK(IU) is LDA by M and WORK(IR) is LDA by M * LDWRKU = LDA IR = IU + LDWRKU*M LDWRKR = LDA ELSE IF( LWORK.GE.WRKBL+( LDA+M )*M ) THEN * * WORK(IU) is LDA by M and WORK(IR) is M by M * LDWRKU = LDA IR = IU + LDWRKU*M LDWRKR = M ELSE * * WORK(IU) is M by M and WORK(IR) is M by M * LDWRKU = M IR = IU + LDWRKU*M LDWRKR = M END IF ITAU = IR + LDWRKR*M IWORK = ITAU + M * * Compute A=L*Q * (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to WORK(IU), zeroing out below it * CALL ZLACPY( 'L', M, M, A, LDA, WORK( IU ), $ LDWRKU ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ WORK( IU+LDWRKU ), LDWRKU ) * * Generate Q in A * (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in WORK(IU), copying result to * WORK(IR) * (CWorkspace: need 2*M*M+3*M, * prefer 2*M*M+2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, WORK( IU ), LDWRKU, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, M, WORK( IU ), LDWRKU, $ WORK( IR ), LDWRKR ) * * Generate right bidiagonalizing vectors in WORK(IU) * (CWorkspace: need 2*M*M+3*M-1, * prefer 2*M*M+2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, M, M, WORK( IU ), LDWRKU, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors in WORK(IR) * (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, WORK( IR ), LDWRKR, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of L in WORK(IR) and computing * right singular vectors of L in WORK(IU) * (CWorkspace: need 2*M*M) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), $ WORK( IU ), LDWRKU, WORK( IR ), $ LDWRKR, CDUM, 1, RWORK( IRWORK ), $ INFO ) * * Multiply right singular vectors of L in WORK(IU) by * Q in A, storing result in VT * (CWorkspace: need M*M) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IU ), $ LDWRKU, A, LDA, CZERO, VT, LDVT ) * * Copy left singular vectors of L to A * (CWorkspace: need M*M) * (RWorkspace: 0) * CALL ZLACPY( 'F', M, M, WORK( IR ), LDWRKR, A, $ LDA ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + M * * Compute A=L*Q, copying result to VT * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Generate Q in VT * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Zero out above L in A * CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ A( 1, 2 ), LDA ) * * Bidiagonalize L in A * (CWorkspace: need 3*M, prefer 2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply right vectors bidiagonalizing L by Q in VT * (CWorkspace: need 2*M+N, prefer 2*M+N*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'P', 'L', 'C', M, N, M, A, LDA, $ WORK( ITAUP ), VT, LDVT, $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors of L in A * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of A in A and computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), VT, $ LDVT, A, LDA, CDUM, 1, $ RWORK( IRWORK ), INFO ) * END IF * ELSE IF( WNTUAS ) THEN * * Path 6t(N much larger than M, JOBU='S' or 'A', * JOBVT='S') * M right singular vectors to be computed in VT and * M left singular vectors to be computed in U * IF( LWORK.GE.M*M+3*M ) THEN * * Sufficient workspace for a fast algorithm * IU = 1 IF( LWORK.GE.WRKBL+LDA*M ) THEN * * WORK(IU) is LDA by N * LDWRKU = LDA ELSE * * WORK(IU) is LDA by M * LDWRKU = M END IF ITAU = IU + LDWRKU*M IWORK = ITAU + M * * Compute A=L*Q * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to WORK(IU), zeroing out above it * CALL ZLACPY( 'L', M, M, A, LDA, WORK( IU ), $ LDWRKU ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ WORK( IU+LDWRKU ), LDWRKU ) * * Generate Q in A * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in WORK(IU), copying result to U * (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, WORK( IU ), LDWRKU, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, M, WORK( IU ), LDWRKU, U, $ LDU ) * * Generate right bidiagonalizing vectors in WORK(IU) * (CWorkspace: need M*M+3*M-1, * prefer M*M+2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, M, M, WORK( IU ), LDWRKU, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors in U * (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of L in U and computing right * singular vectors of L in WORK(IU) * (CWorkspace: need M*M) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), $ WORK( IU ), LDWRKU, U, LDU, CDUM, 1, $ RWORK( IRWORK ), INFO ) * * Multiply right singular vectors of L in WORK(IU) by * Q in A, storing result in VT * (CWorkspace: need M*M) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IU ), $ LDWRKU, A, LDA, CZERO, VT, LDVT ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + M * * Compute A=L*Q, copying result to VT * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Generate Q in VT * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZUNGLQ( M, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to U, zeroing out above it * CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ U( 1, 2 ), LDU ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in U * (CWorkspace: need 3*M, prefer 2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, U, LDU, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply right bidiagonalizing vectors in U by Q * in VT * (CWorkspace: need 2*M+N, prefer 2*M+N*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'P', 'L', 'C', M, N, M, U, LDU, $ WORK( ITAUP ), VT, LDVT, $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors in U * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U and computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), VT, $ LDVT, U, LDU, CDUM, 1, $ RWORK( IRWORK ), INFO ) * END IF * END IF * ELSE IF( WNTVA ) THEN * IF( WNTUN ) THEN * * Path 7t(N much larger than M, JOBU='N', JOBVT='A') * N right singular vectors to be computed in VT and * no left singular vectors to be computed * IF( LWORK.GE.M*M+MAX( N+M, 3*M ) ) THEN * * Sufficient workspace for a fast algorithm * IR = 1 IF( LWORK.GE.WRKBL+LDA*M ) THEN * * WORK(IR) is LDA by M * LDWRKR = LDA ELSE * * WORK(IR) is M by M * LDWRKR = M END IF ITAU = IR + LDWRKR*M IWORK = ITAU + M * * Compute A=L*Q, copying result to VT * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Copy L to WORK(IR), zeroing out above it * CALL ZLACPY( 'L', M, M, A, LDA, WORK( IR ), $ LDWRKR ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ WORK( IR+LDWRKR ), LDWRKR ) * * Generate Q in VT * (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) * (RWorkspace: 0) * CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in WORK(IR) * (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, WORK( IR ), LDWRKR, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate right bidiagonalizing vectors in WORK(IR) * (CWorkspace: need M*M+3*M-1, * prefer M*M+2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, M, M, WORK( IR ), LDWRKR, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing right * singular vectors of L in WORK(IR) * (CWorkspace: need M*M) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, M, 0, 0, S, RWORK( IE ), $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1, $ RWORK( IRWORK ), INFO ) * * Multiply right singular vectors of L in WORK(IR) by * Q in VT, storing result in A * (CWorkspace: need M*M) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IR ), $ LDWRKR, VT, LDVT, CZERO, A, LDA ) * * Copy right singular vectors of A from A to VT * CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + M * * Compute A=L*Q, copying result to VT * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Generate Q in VT * (CWorkspace: need M+N, prefer M+N*NB) * (RWorkspace: 0) * CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Zero out above L in A * CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ A( 1, 2 ), LDA ) * * Bidiagonalize L in A * (CWorkspace: need 3*M, prefer 2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply right bidiagonalizing vectors in A by Q * in VT * (CWorkspace: need 2*M+N, prefer 2*M+N*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'P', 'L', 'C', M, N, M, A, LDA, $ WORK( ITAUP ), VT, LDVT, $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, N, 0, 0, S, RWORK( IE ), VT, $ LDVT, CDUM, 1, CDUM, 1, $ RWORK( IRWORK ), INFO ) * END IF * ELSE IF( WNTUO ) THEN * * Path 8t(N much larger than M, JOBU='O', JOBVT='A') * N right singular vectors to be computed in VT and * M left singular vectors to be overwritten on A * IF( LWORK.GE.2*M*M+MAX( N+M, 3*M ) ) THEN * * Sufficient workspace for a fast algorithm * IU = 1 IF( LWORK.GE.WRKBL+2*LDA*M ) THEN * * WORK(IU) is LDA by M and WORK(IR) is LDA by M * LDWRKU = LDA IR = IU + LDWRKU*M LDWRKR = LDA ELSE IF( LWORK.GE.WRKBL+( LDA+M )*M ) THEN * * WORK(IU) is LDA by M and WORK(IR) is M by M * LDWRKU = LDA IR = IU + LDWRKU*M LDWRKR = M ELSE * * WORK(IU) is M by M and WORK(IR) is M by M * LDWRKU = M IR = IU + LDWRKU*M LDWRKR = M END IF ITAU = IR + LDWRKR*M IWORK = ITAU + M * * Compute A=L*Q, copying result to VT * (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Generate Q in VT * (CWorkspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB) * (RWorkspace: 0) * CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to WORK(IU), zeroing out above it * CALL ZLACPY( 'L', M, M, A, LDA, WORK( IU ), $ LDWRKU ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ WORK( IU+LDWRKU ), LDWRKU ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in WORK(IU), copying result to * WORK(IR) * (CWorkspace: need 2*M*M+3*M, * prefer 2*M*M+2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, WORK( IU ), LDWRKU, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, M, WORK( IU ), LDWRKU, $ WORK( IR ), LDWRKR ) * * Generate right bidiagonalizing vectors in WORK(IU) * (CWorkspace: need 2*M*M+3*M-1, * prefer 2*M*M+2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, M, M, WORK( IU ), LDWRKU, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors in WORK(IR) * (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, WORK( IR ), LDWRKR, $ WORK( ITAUQ ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of L in WORK(IR) and computing * right singular vectors of L in WORK(IU) * (CWorkspace: need 2*M*M) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), $ WORK( IU ), LDWRKU, WORK( IR ), $ LDWRKR, CDUM, 1, RWORK( IRWORK ), $ INFO ) * * Multiply right singular vectors of L in WORK(IU) by * Q in VT, storing result in A * (CWorkspace: need M*M) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IU ), $ LDWRKU, VT, LDVT, CZERO, A, LDA ) * * Copy right singular vectors of A from A to VT * CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT ) * * Copy left singular vectors of A from WORK(IR) to A * CALL ZLACPY( 'F', M, M, WORK( IR ), LDWRKR, A, $ LDA ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + M * * Compute A=L*Q, copying result to VT * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Generate Q in VT * (CWorkspace: need M+N, prefer M+N*NB) * (RWorkspace: 0) * CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Zero out above L in A * CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ A( 1, 2 ), LDA ) * * Bidiagonalize L in A * (CWorkspace: need 3*M, prefer 2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, A, LDA, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply right bidiagonalizing vectors in A by Q * in VT * (CWorkspace: need 2*M+N, prefer 2*M+N*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'P', 'L', 'C', M, N, M, A, LDA, $ WORK( ITAUP ), VT, LDVT, $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors in A * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, A, LDA, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of A in A and computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), VT, $ LDVT, A, LDA, CDUM, 1, $ RWORK( IRWORK ), INFO ) * END IF * ELSE IF( WNTUAS ) THEN * * Path 9t(N much larger than M, JOBU='S' or 'A', * JOBVT='A') * N right singular vectors to be computed in VT and * M left singular vectors to be computed in U * IF( LWORK.GE.M*M+MAX( N+M, 3*M ) ) THEN * * Sufficient workspace for a fast algorithm * IU = 1 IF( LWORK.GE.WRKBL+LDA*M ) THEN * * WORK(IU) is LDA by M * LDWRKU = LDA ELSE * * WORK(IU) is M by M * LDWRKU = M END IF ITAU = IU + LDWRKU*M IWORK = ITAU + M * * Compute A=L*Q, copying result to VT * (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Generate Q in VT * (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB) * (RWorkspace: 0) * CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to WORK(IU), zeroing out above it * CALL ZLACPY( 'L', M, M, A, LDA, WORK( IU ), $ LDWRKU ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ WORK( IU+LDWRKU ), LDWRKU ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in WORK(IU), copying result to U * (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, WORK( IU ), LDWRKU, S, $ RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) CALL ZLACPY( 'L', M, M, WORK( IU ), LDWRKU, U, $ LDU ) * * Generate right bidiagonalizing vectors in WORK(IU) * (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, M, M, WORK( IU ), LDWRKU, $ WORK( ITAUP ), WORK( IWORK ), $ LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors in U * (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of L in U and computing right * singular vectors of L in WORK(IU) * (CWorkspace: need M*M) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, M, M, 0, S, RWORK( IE ), $ WORK( IU ), LDWRKU, U, LDU, CDUM, 1, $ RWORK( IRWORK ), INFO ) * * Multiply right singular vectors of L in WORK(IU) by * Q in VT, storing result in A * (CWorkspace: need M*M) * (RWorkspace: 0) * CALL ZGEMM( 'N', 'N', M, N, M, CONE, WORK( IU ), $ LDWRKU, VT, LDVT, CZERO, A, LDA ) * * Copy right singular vectors of A from A to VT * CALL ZLACPY( 'F', M, N, A, LDA, VT, LDVT ) * ELSE * * Insufficient workspace for a fast algorithm * ITAU = 1 IWORK = ITAU + M * * Compute A=L*Q, copying result to VT * (CWorkspace: need 2*M, prefer M+M*NB) * (RWorkspace: 0) * CALL ZGELQF( M, N, A, LDA, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) * * Generate Q in VT * (CWorkspace: need M+N, prefer M+N*NB) * (RWorkspace: 0) * CALL ZUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Copy L to U, zeroing out above it * CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) CALL ZLASET( 'U', M-1, M-1, CZERO, CZERO, $ U( 1, 2 ), LDU ) IE = 1 ITAUQ = ITAU ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize L in U * (CWorkspace: need 3*M, prefer 2*M+2*M*NB) * (RWorkspace: need M) * CALL ZGEBRD( M, M, U, LDU, S, RWORK( IE ), $ WORK( ITAUQ ), WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Multiply right bidiagonalizing vectors in U by Q * in VT * (CWorkspace: need 2*M+N, prefer 2*M+N*NB) * (RWorkspace: 0) * CALL ZUNMBR( 'P', 'L', 'C', M, N, M, U, LDU, $ WORK( ITAUP ), VT, LDVT, $ WORK( IWORK ), LWORK-IWORK+1, IERR ) * * Generate left bidiagonalizing vectors in U * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, M, U, LDU, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) IRWORK = IE + M * * Perform bidiagonal QR iteration, computing left * singular vectors of A in U and computing right * singular vectors of A in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'U', M, N, M, 0, S, RWORK( IE ), VT, $ LDVT, U, LDU, CDUM, 1, $ RWORK( IRWORK ), INFO ) * END IF * END IF * END IF * ELSE * * N .LT. MNTHR * * Path 10t(N greater than M, but not much larger) * Reduce to bidiagonal form without LQ decomposition * IE = 1 ITAUQ = 1 ITAUP = ITAUQ + M IWORK = ITAUP + M * * Bidiagonalize A * (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB) * (RWorkspace: M) * CALL ZGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ), $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1, $ IERR ) IF( WNTUAS ) THEN * * If left singular vectors desired in U, copy result to U * and generate left bidiagonalizing vectors in U * (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZLACPY( 'L', M, M, A, LDA, U, LDU ) CALL ZUNGBR( 'Q', M, M, N, U, LDU, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IF( WNTVAS ) THEN * * If right singular vectors desired in VT, copy result to * VT and generate right bidiagonalizing vectors in VT * (CWorkspace: need 2*M+NRVT, prefer 2*M+NRVT*NB) * (RWorkspace: 0) * CALL ZLACPY( 'U', M, N, A, LDA, VT, LDVT ) IF( WNTVA ) $ NRVT = N IF( WNTVS ) $ NRVT = M CALL ZUNGBR( 'P', NRVT, N, M, VT, LDVT, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IF( WNTUO ) THEN * * If left singular vectors desired in A, generate left * bidiagonalizing vectors in A * (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'Q', M, M, N, A, LDA, WORK( ITAUQ ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IF( WNTVO ) THEN * * If right singular vectors desired in A, generate right * bidiagonalizing vectors in A * (CWorkspace: need 3*M, prefer 2*M+M*NB) * (RWorkspace: 0) * CALL ZUNGBR( 'P', M, N, M, A, LDA, WORK( ITAUP ), $ WORK( IWORK ), LWORK-IWORK+1, IERR ) END IF IRWORK = IE + M IF( WNTUAS .OR. WNTUO ) $ NRU = M IF( WNTUN ) $ NRU = 0 IF( WNTVAS .OR. WNTVO ) $ NCVT = N IF( WNTVN ) $ NCVT = 0 IF( ( .NOT.WNTUO ) .AND. ( .NOT.WNTVO ) ) THEN * * Perform bidiagonal QR iteration, if desired, computing * left singular vectors in U and computing right singular * vectors in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'L', M, NCVT, NRU, 0, S, RWORK( IE ), VT, $ LDVT, U, LDU, CDUM, 1, RWORK( IRWORK ), $ INFO ) ELSE IF( ( .NOT.WNTUO ) .AND. WNTVO ) THEN * * Perform bidiagonal QR iteration, if desired, computing * left singular vectors in U and computing right singular * vectors in A * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'L', M, NCVT, NRU, 0, S, RWORK( IE ), A, $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ), $ INFO ) ELSE * * Perform bidiagonal QR iteration, if desired, computing * left singular vectors in A and computing right singular * vectors in VT * (CWorkspace: 0) * (RWorkspace: need BDSPAC) * CALL ZBDSQR( 'L', M, NCVT, NRU, 0, S, RWORK( IE ), VT, $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ), $ INFO ) END IF * END IF * END IF * * Undo scaling if necessary * IF( ISCL.EQ.1 ) THEN IF( ANRM.GT.BIGNUM ) $ CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN, $ IERR ) IF( INFO.NE.0 .AND. ANRM.GT.BIGNUM ) $ CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MINMN-1, 1, $ RWORK( IE ), MINMN, IERR ) IF( ANRM.LT.SMLNUM ) $ CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN, $ IERR ) IF( INFO.NE.0 .AND. ANRM.LT.SMLNUM ) $ CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MINMN-1, 1, $ RWORK( IE ), MINMN, IERR ) END IF * * Return optimal workspace in WORK(1) * WORK( 1 ) = MAXWRK * RETURN * * End of ZGESVD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgetrf.f0000644000000000000000000000013214061636515015325 xustar0030 mtime=1623670093.145104135 30 atime=1623670093.144104136 30 ctime=1623670093.145104135 elk-7.2.42/src/LAPACK/zgetrf.f0000644002504400250440000001423714061636515017371 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGETRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGETRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGETRF computes an LU factorization of a general M-by-N matrix A *> using partial pivoting with row interchanges. *> *> The factorization has the form *> A = P * L * U *> where P is a permutation matrix, L is lower triangular with unit *> diagonal elements (lower trapezoidal if m > n), and U is upper *> triangular (upper trapezoidal if m < n). *> *> This is the right-looking Level 3 BLAS version of the algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the M-by-N matrix to be factored. *> On exit, the factors L and U from the factorization *> A = P*L*U; the unit diagonal elements of L are not stored. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (min(M,N)) *> The pivot indices; for 1 <= i <= min(M,N), row i of the *> matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization *> has been completed, but the factor U is exactly *> singular, and division by zero will occur if it is used *> to solve a system of equations. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GEcomputational * * ===================================================================== SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, IINFO, J, JB, NB * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMM, ZGETRF2, ZLASWP, ZTRSM * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGETRF', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'ZGETRF', ' ', M, N, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN * * Use unblocked code. * CALL ZGETRF2( M, N, A, LDA, IPIV, INFO ) ELSE * * Use blocked code. * DO 20 J = 1, MIN( M, N ), NB JB = MIN( MIN( M, N )-J+1, NB ) * * Factor diagonal and subdiagonal blocks and test for exact * singularity. * CALL ZGETRF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO ) * * Adjust INFO and the pivot indices. * IF( INFO.EQ.0 .AND. IINFO.GT.0 ) $ INFO = IINFO + J - 1 DO 10 I = J, MIN( M, J+JB-1 ) IPIV( I ) = J - 1 + IPIV( I ) 10 CONTINUE * * Apply interchanges to columns 1:J-1. * CALL ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) * IF( J+JB.LE.N ) THEN * * Apply interchanges to columns J+JB:N. * CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, $ IPIV, 1 ) * * Compute block row of U. * CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ), $ LDA ) IF( J+JB.LE.M ) THEN * * Update trailing submatrix. * CALL ZGEMM( 'No transpose', 'No transpose', M-J-JB+1, $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA, $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ), $ LDA ) END IF END IF 20 CONTINUE END IF RETURN * * End of ZGETRF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgetri.f0000644000000000000000000000013214061636515015330 xustar0030 mtime=1623670093.146104134 30 atime=1623670093.146104134 30 ctime=1623670093.146104134 elk-7.2.42/src/LAPACK/zgetri.f0000644002504400250440000001636514061636515017400 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGETRI * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGETRI + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGETRI computes the inverse of a matrix using the LU factorization *> computed by ZGETRF. *> *> This method inverts U and then computes inv(A) by solving the system *> inv(A)*L = inv(U) for inv(A). *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the factors L and U from the factorization *> A = P*L*U as computed by ZGETRF. *> On exit, if INFO = 0, the inverse of the original matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices from ZGETRF; for 1<=i<=N, row i of the *> matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO=0, then WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimal performance LWORK >= N*NB, where NB is *> the optimal blocksize returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is *> singular and its inverse could not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GEcomputational * * ===================================================================== SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB, $ NBMIN, NN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMM, ZGEMV, ZSWAP, ZTRSM, ZTRTRI * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 NB = ILAENV( 1, 'ZGETRI', ' ', N, -1, -1, -1 ) LWKOPT = N*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( N.LT.0 ) THEN INFO = -1 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -3 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGETRI', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Form inv(U). If INFO > 0 from ZTRTRI, then U is singular, * and the inverse is not computed. * CALL ZTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO ) IF( INFO.GT.0 ) $ RETURN * NBMIN = 2 LDWORK = N IF( NB.GT.1 .AND. NB.LT.N ) THEN IWS = MAX( LDWORK*NB, 1 ) IF( LWORK.LT.IWS ) THEN NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZGETRI', ' ', N, -1, -1, -1 ) ) END IF ELSE IWS = N END IF * * Solve the equation inv(A)*L = inv(U) for inv(A). * IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN * * Use unblocked code. * DO 20 J = N, 1, -1 * * Copy current column of L to WORK and replace with zeros. * DO 10 I = J + 1, N WORK( I ) = A( I, J ) A( I, J ) = ZERO 10 CONTINUE * * Compute current column of inv(A). * IF( J.LT.N ) $ CALL ZGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ), $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 ) 20 CONTINUE ELSE * * Use blocked code. * NN = ( ( N-1 ) / NB )*NB + 1 DO 50 J = NN, 1, -NB JB = MIN( NB, N-J+1 ) * * Copy current block column of L to WORK and replace with * zeros. * DO 40 JJ = J, J + JB - 1 DO 30 I = JJ + 1, N WORK( I+( JJ-J )*LDWORK ) = A( I, JJ ) A( I, JJ ) = ZERO 30 CONTINUE 40 CONTINUE * * Compute current block column of inv(A). * IF( J+JB.LE.N ) $ CALL ZGEMM( 'No transpose', 'No transpose', N, JB, $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA ) CALL ZTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB, $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA ) 50 CONTINUE END IF * * Apply column interchanges. * DO 60 J = N - 1, 1, -1 JP = IPIV( J ) IF( JP.NE.J ) $ CALL ZSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 ) 60 CONTINUE * WORK( 1 ) = IWS RETURN * * End of ZGETRI * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/ilaenv.f0000644000000000000000000000013214061636515015302 xustar0030 mtime=1623670093.148104132 30 atime=1623670093.148104132 30 ctime=1623670093.148104132 elk-7.2.42/src/LAPACK/ilaenv.f0000644002504400250440000005051714061636515017347 0ustar00dewhurstdewhurst00000000000000*> \brief \b ILAENV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ILAENV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) * * .. Scalar Arguments .. * CHARACTER*( * ) NAME, OPTS * INTEGER ISPEC, N1, N2, N3, N4 * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ILAENV is called from the LAPACK routines to choose problem-dependent *> parameters for the local environment. See ISPEC for a description of *> the parameters. *> *> ILAENV returns an INTEGER *> if ILAENV >= 0: ILAENV returns the value of the parameter specified by ISPEC *> if ILAENV < 0: if ILAENV = -k, the k-th argument had an illegal value. *> *> This version provides a set of parameters which should give good, *> but not optimal, performance on many of the currently available *> computers. Users are encouraged to modify this subroutine to set *> the tuning parameters for their particular machine using the option *> and problem size information in the arguments. *> *> This routine will not function correctly if it is converted to all *> lower case. Converting it to all upper case is allowed. *> \endverbatim * * Arguments: * ========== * *> \param[in] ISPEC *> \verbatim *> ISPEC is INTEGER *> Specifies the parameter to be returned as the value of *> ILAENV. *> = 1: the optimal blocksize; if this value is 1, an unblocked *> algorithm will give the best performance. *> = 2: the minimum block size for which the block routine *> should be used; if the usable block size is less than *> this value, an unblocked routine should be used. *> = 3: the crossover point (in a block routine, for N less *> than this value, an unblocked routine should be used) *> = 4: the number of shifts, used in the nonsymmetric *> eigenvalue routines (DEPRECATED) *> = 5: the minimum column dimension for blocking to be used; *> rectangular blocks must have dimension at least k by m, *> where k is given by ILAENV(2,...) and m by ILAENV(5,...) *> = 6: the crossover point for the SVD (when reducing an m by n *> matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds *> this value, a QR factorization is used first to reduce *> the matrix to a triangular form.) *> = 7: the number of processors *> = 8: the crossover point for the multishift QR method *> for nonsymmetric eigenvalue problems (DEPRECATED) *> = 9: maximum size of the subproblems at the bottom of the *> computation tree in the divide-and-conquer algorithm *> (used by xGELSD and xGESDD) *> =10: ieee NaN arithmetic can be trusted not to trap *> =11: infinity arithmetic can be trusted not to trap *> 12 <= ISPEC <= 16: *> xHSEQR or related subroutines, *> see IPARMQ for detailed explanation *> \endverbatim *> *> \param[in] NAME *> \verbatim *> NAME is CHARACTER*(*) *> The name of the calling subroutine, in either upper case or *> lower case. *> \endverbatim *> *> \param[in] OPTS *> \verbatim *> OPTS is CHARACTER*(*) *> The character options to the subroutine NAME, concatenated *> into a single character string. For example, UPLO = 'U', *> TRANS = 'T', and DIAG = 'N' for a triangular routine would *> be specified as OPTS = 'UTN'. *> \endverbatim *> *> \param[in] N1 *> \verbatim *> N1 is INTEGER *> \endverbatim *> *> \param[in] N2 *> \verbatim *> N2 is INTEGER *> \endverbatim *> *> \param[in] N3 *> \verbatim *> N3 is INTEGER *> \endverbatim *> *> \param[in] N4 *> \verbatim *> N4 is INTEGER *> Problem dimensions for the subroutine NAME; these may not all *> be required. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2019 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> The following conventions have been used when calling ILAENV from the *> LAPACK routines: *> 1) OPTS is a concatenation of all of the character options to *> subroutine NAME, in the same order that they appear in the *> argument list for NAME, even if they are not used in determining *> the value of the parameter specified by ISPEC. *> 2) The problem dimensions N1, N2, N3, N4 are specified in the order *> that they appear in the argument list for NAME. N1 is used *> first, N2 second, and so on, and unused problem dimensions are *> passed a value of -1. *> 3) The parameter value returned by ILAENV is checked for validity in *> the calling subroutine. For example, ILAENV is used to retrieve *> the optimal blocksize for STRTRI as follows: *> *> NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) *> IF( NB.LE.1 ) NB = MAX( 1, N ) *> \endverbatim *> * ===================================================================== INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) * * -- LAPACK auxiliary routine (version 3.9.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2019 * * .. Scalar Arguments .. CHARACTER*( * ) NAME, OPTS INTEGER ISPEC, N1, N2, N3, N4 * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, IC, IZ, NB, NBMIN, NX LOGICAL CNAME, SNAME, TWOSTAGE CHARACTER C1*1, C2*2, C4*2, C3*3, SUBNAM*16 * .. * .. Intrinsic Functions .. INTRINSIC CHAR, ICHAR, INT, MIN, REAL * .. * .. External Functions .. INTEGER IEEECK, IPARMQ, IPARAM2STAGE EXTERNAL IEEECK, IPARMQ, IPARAM2STAGE * .. * .. Executable Statements .. * GO TO ( 10, 10, 10, 80, 90, 100, 110, 120, $ 130, 140, 150, 160, 160, 160, 160, 160)ISPEC * * Invalid value for ISPEC * ILAENV = -1 RETURN * 10 CONTINUE * * Convert NAME to upper case if the first character is lower case. * ILAENV = 1 SUBNAM = NAME IC = ICHAR( SUBNAM( 1: 1 ) ) IZ = ICHAR( 'Z' ) IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN * * ASCII character set * IF( IC.GE.97 .AND. IC.LE.122 ) THEN SUBNAM( 1: 1 ) = CHAR( IC-32 ) DO 20 I = 2, 6 IC = ICHAR( SUBNAM( I: I ) ) IF( IC.GE.97 .AND. IC.LE.122 ) $ SUBNAM( I: I ) = CHAR( IC-32 ) 20 CONTINUE END IF * ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN * * EBCDIC character set * IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. $ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN SUBNAM( 1: 1 ) = CHAR( IC+64 ) DO 30 I = 2, 6 IC = ICHAR( SUBNAM( I: I ) ) IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. $ ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I: $ I ) = CHAR( IC+64 ) 30 CONTINUE END IF * ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN * * Prime machines: ASCII+128 * IF( IC.GE.225 .AND. IC.LE.250 ) THEN SUBNAM( 1: 1 ) = CHAR( IC-32 ) DO 40 I = 2, 6 IC = ICHAR( SUBNAM( I: I ) ) IF( IC.GE.225 .AND. IC.LE.250 ) $ SUBNAM( I: I ) = CHAR( IC-32 ) 40 CONTINUE END IF END IF * C1 = SUBNAM( 1: 1 ) SNAME = C1.EQ.'S' .OR. C1.EQ.'D' CNAME = C1.EQ.'C' .OR. C1.EQ.'Z' IF( .NOT.( CNAME .OR. SNAME ) ) $ RETURN C2 = SUBNAM( 2: 3 ) C3 = SUBNAM( 4: 6 ) C4 = C3( 2: 3 ) TWOSTAGE = LEN( SUBNAM ).GE.11 $ .AND. SUBNAM( 11: 11 ).EQ.'2' * GO TO ( 50, 60, 70 )ISPEC * 50 CONTINUE * * ISPEC = 1: block size * * In these examples, separate code is provided for setting NB for * real and complex. We assume that NB will take the same value in * single or double precision. * NB = 1 * IF( SUBNAM(2:6).EQ.'LAORH' ) THEN * * This is for *LAORHR_GETRFNP routine * IF( SNAME ) THEN NB = 32 ELSE NB = 32 END IF ELSE IF( C2.EQ.'GE' ) THEN IF( C3.EQ.'TRF' ) THEN IF( SNAME ) THEN NB = 64 ELSE NB = 64 END IF ELSE IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. $ C3.EQ.'QLF' ) THEN IF( SNAME ) THEN NB = 32 ELSE NB = 32 END IF ELSE IF( C3.EQ.'QR ') THEN IF( N3 .EQ. 1) THEN IF( SNAME ) THEN * M*N IF ((N1*N2.LE.131072).OR.(N1.LE.8192)) THEN NB = N1 ELSE NB = 32768/N2 END IF ELSE IF ((N1*N2.LE.131072).OR.(N1.LE.8192)) THEN NB = N1 ELSE NB = 32768/N2 END IF END IF ELSE IF( SNAME ) THEN NB = 1 ELSE NB = 1 END IF END IF ELSE IF( C3.EQ.'LQ ') THEN IF( N3 .EQ. 2) THEN IF( SNAME ) THEN * M*N IF ((N1*N2.LE.131072).OR.(N1.LE.8192)) THEN NB = N1 ELSE NB = 32768/N2 END IF ELSE IF ((N1*N2.LE.131072).OR.(N1.LE.8192)) THEN NB = N1 ELSE NB = 32768/N2 END IF END IF ELSE IF( SNAME ) THEN NB = 1 ELSE NB = 1 END IF END IF ELSE IF( C3.EQ.'HRD' ) THEN IF( SNAME ) THEN NB = 32 ELSE NB = 32 END IF ELSE IF( C3.EQ.'BRD' ) THEN IF( SNAME ) THEN NB = 32 ELSE NB = 32 END IF ELSE IF( C3.EQ.'TRI' ) THEN IF( SNAME ) THEN NB = 64 ELSE NB = 64 END IF END IF ELSE IF( C2.EQ.'PO' ) THEN IF( C3.EQ.'TRF' ) THEN IF( SNAME ) THEN NB = 64 ELSE NB = 64 END IF END IF ELSE IF( C2.EQ.'SY' ) THEN IF( C3.EQ.'TRF' ) THEN IF( SNAME ) THEN IF( TWOSTAGE ) THEN NB = 192 ELSE NB = 64 END IF ELSE IF( TWOSTAGE ) THEN NB = 192 ELSE NB = 64 END IF END IF ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN NB = 32 ELSE IF( SNAME .AND. C3.EQ.'GST' ) THEN NB = 64 END IF ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN IF( C3.EQ.'TRF' ) THEN IF( TWOSTAGE ) THEN NB = 192 ELSE NB = 64 END IF ELSE IF( C3.EQ.'TRD' ) THEN NB = 32 ELSE IF( C3.EQ.'GST' ) THEN NB = 64 END IF ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN IF( C3( 1: 1 ).EQ.'G' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NB = 32 END IF ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NB = 32 END IF END IF ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN IF( C3( 1: 1 ).EQ.'G' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NB = 32 END IF ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NB = 32 END IF END IF ELSE IF( C2.EQ.'GB' ) THEN IF( C3.EQ.'TRF' ) THEN IF( SNAME ) THEN IF( N4.LE.64 ) THEN NB = 1 ELSE NB = 32 END IF ELSE IF( N4.LE.64 ) THEN NB = 1 ELSE NB = 32 END IF END IF END IF ELSE IF( C2.EQ.'PB' ) THEN IF( C3.EQ.'TRF' ) THEN IF( SNAME ) THEN IF( N2.LE.64 ) THEN NB = 1 ELSE NB = 32 END IF ELSE IF( N2.LE.64 ) THEN NB = 1 ELSE NB = 32 END IF END IF END IF ELSE IF( C2.EQ.'TR' ) THEN IF( C3.EQ.'TRI' ) THEN IF( SNAME ) THEN NB = 64 ELSE NB = 64 END IF ELSE IF ( C3.EQ.'EVC' ) THEN IF( SNAME ) THEN NB = 64 ELSE NB = 64 END IF END IF ELSE IF( C2.EQ.'LA' ) THEN IF( C3.EQ.'UUM' ) THEN IF( SNAME ) THEN NB = 64 ELSE NB = 64 END IF END IF ELSE IF( SNAME .AND. C2.EQ.'ST' ) THEN IF( C3.EQ.'EBZ' ) THEN NB = 1 END IF ELSE IF( C2.EQ.'GG' ) THEN NB = 32 IF( C3.EQ.'HD3' ) THEN IF( SNAME ) THEN NB = 32 ELSE NB = 32 END IF END IF END IF ILAENV = NB RETURN * 60 CONTINUE * * ISPEC = 2: minimum block size * NBMIN = 2 IF( C2.EQ.'GE' ) THEN IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ. $ 'QLF' ) THEN IF( SNAME ) THEN NBMIN = 2 ELSE NBMIN = 2 END IF ELSE IF( C3.EQ.'HRD' ) THEN IF( SNAME ) THEN NBMIN = 2 ELSE NBMIN = 2 END IF ELSE IF( C3.EQ.'BRD' ) THEN IF( SNAME ) THEN NBMIN = 2 ELSE NBMIN = 2 END IF ELSE IF( C3.EQ.'TRI' ) THEN IF( SNAME ) THEN NBMIN = 2 ELSE NBMIN = 2 END IF END IF ELSE IF( C2.EQ.'SY' ) THEN IF( C3.EQ.'TRF' ) THEN IF( SNAME ) THEN NBMIN = 8 ELSE NBMIN = 8 END IF ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN NBMIN = 2 END IF ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN IF( C3.EQ.'TRD' ) THEN NBMIN = 2 END IF ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN IF( C3( 1: 1 ).EQ.'G' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NBMIN = 2 END IF ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NBMIN = 2 END IF END IF ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN IF( C3( 1: 1 ).EQ.'G' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NBMIN = 2 END IF ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NBMIN = 2 END IF END IF ELSE IF( C2.EQ.'GG' ) THEN NBMIN = 2 IF( C3.EQ.'HD3' ) THEN NBMIN = 2 END IF END IF ILAENV = NBMIN RETURN * 70 CONTINUE * * ISPEC = 3: crossover point * NX = 0 IF( C2.EQ.'GE' ) THEN IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ. $ 'QLF' ) THEN IF( SNAME ) THEN NX = 128 ELSE NX = 128 END IF ELSE IF( C3.EQ.'HRD' ) THEN IF( SNAME ) THEN NX = 128 ELSE NX = 128 END IF ELSE IF( C3.EQ.'BRD' ) THEN IF( SNAME ) THEN NX = 128 ELSE NX = 128 END IF END IF ELSE IF( C2.EQ.'SY' ) THEN IF( SNAME .AND. C3.EQ.'TRD' ) THEN NX = 32 END IF ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN IF( C3.EQ.'TRD' ) THEN NX = 32 END IF ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN IF( C3( 1: 1 ).EQ.'G' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NX = 128 END IF END IF ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN IF( C3( 1: 1 ).EQ.'G' ) THEN IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) $ THEN NX = 128 END IF END IF ELSE IF( C2.EQ.'GG' ) THEN NX = 128 IF( C3.EQ.'HD3' ) THEN NX = 128 END IF END IF ILAENV = NX RETURN * 80 CONTINUE * * ISPEC = 4: number of shifts (used by xHSEQR) * ILAENV = 6 RETURN * 90 CONTINUE * * ISPEC = 5: minimum column dimension (not used) * ILAENV = 2 RETURN * 100 CONTINUE * * ISPEC = 6: crossover point for SVD (used by xGELSS and xGESVD) * ILAENV = INT( REAL( MIN( N1, N2 ) )*1.6E0 ) RETURN * 110 CONTINUE * * ISPEC = 7: number of processors (not used) * ILAENV = 1 RETURN * 120 CONTINUE * * ISPEC = 8: crossover point for multishift (used by xHSEQR) * ILAENV = 50 RETURN * 130 CONTINUE * * ISPEC = 9: maximum size of the subproblems at the bottom of the * computation tree in the divide-and-conquer algorithm * (used by xGELSD and xGESDD) * ILAENV = 25 RETURN * 140 CONTINUE * * ISPEC = 10: ieee NaN arithmetic can be trusted not to trap * * ILAENV = 0 ILAENV = 1 IF( ILAENV.EQ.1 ) THEN ILAENV = IEEECK( 1, 0.0, 1.0 ) END IF RETURN * 150 CONTINUE * * ISPEC = 11: infinity arithmetic can be trusted not to trap * * ILAENV = 0 ILAENV = 1 IF( ILAENV.EQ.1 ) THEN ILAENV = IEEECK( 0, 0.0, 1.0 ) END IF RETURN * 160 CONTINUE * * 12 <= ISPEC <= 16: xHSEQR or related subroutines. * ILAENV = IPARMQ( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) RETURN * * End of ILAENV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/xerbla.f0000644000000000000000000000012714061636515015305 xustar0029 mtime=1623670093.15010413 29 atime=1623670093.15010413 29 ctime=1623670093.15010413 elk-7.2.42/src/LAPACK/xerbla.f0000644002504400250440000000503114061636515017335 0ustar00dewhurstdewhurst00000000000000*> \brief \b XERBLA * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download XERBLA + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE XERBLA( SRNAME, INFO ) * * .. Scalar Arguments .. * CHARACTER*(*) SRNAME * INTEGER INFO * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> XERBLA is an error handler for the LAPACK routines. *> It is called by an LAPACK routine if an input parameter has an *> invalid value. A message is printed and execution stops. *> *> Installers may consider modifying the STOP statement in order to *> call system-specific exception-handling facilities. *> \endverbatim * * Arguments: * ========== * *> \param[in] SRNAME *> \verbatim *> SRNAME is CHARACTER*(*) *> The name of the routine which called XERBLA. *> \endverbatim *> *> \param[in] INFO *> \verbatim *> INFO is INTEGER *> The position of the invalid parameter in the parameter list *> of the calling routine. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE XERBLA( SRNAME, INFO ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER*(*) SRNAME INTEGER INFO * .. * * ===================================================================== * * .. Intrinsic Functions .. INTRINSIC LEN_TRIM * .. * .. Executable Statements .. * WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO * STOP * 9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ', $ 'an illegal value' ) * * End of XERBLA * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zpptrf.f0000644000000000000000000000013214061636515015351 xustar0030 mtime=1623670093.152104128 30 atime=1623670093.152104128 30 ctime=1623670093.152104128 elk-7.2.42/src/LAPACK/zpptrf.f0000644002504400250440000001447614061636515017422 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZPPTRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZPPTRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZPPTRF( UPLO, N, AP, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, N * .. * .. Array Arguments .. * COMPLEX*16 AP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZPPTRF computes the Cholesky factorization of a complex Hermitian *> positive definite matrix A stored in packed format. *> *> The factorization has the form *> A = U**H * U, if UPLO = 'U', or *> A = L * L**H, if UPLO = 'L', *> where U is an upper triangular matrix and L is lower triangular. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the Hermitian matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. *> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H*U or A = L*L**H, in the same *> storage format as A. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The packed storage scheme is illustrated by the following example *> when N = 4, UPLO = 'U': *> *> Two-dimensional storage of the Hermitian matrix A: *> *> a11 a12 a13 a14 *> a22 a23 a24 *> a33 a34 (aij = conjg(aji)) *> a44 *> *> Packed storage of the upper triangle of A: *> *> AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] *> \endverbatim *> * ===================================================================== SUBROUTINE ZPPTRF( UPLO, N, AP, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N * .. * .. Array Arguments .. COMPLEX*16 AP( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, JC, JJ DOUBLE PRECISION AJJ * .. * .. External Functions .. LOGICAL LSAME COMPLEX*16 ZDOTC EXTERNAL LSAME, ZDOTC * .. * .. External Subroutines .. EXTERNAL XERBLA, ZDSCAL, ZHPR, ZTPSV * .. * .. Intrinsic Functions .. INTRINSIC DBLE, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZPPTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( UPPER ) THEN * * Compute the Cholesky factorization A = U**H * U. * JJ = 0 DO 10 J = 1, N JC = JJ + 1 JJ = JJ + J * * Compute elements 1:J-1 of column J. * IF( J.GT.1 ) $ CALL ZTPSV( 'Upper', 'Conjugate transpose', 'Non-unit', $ J-1, AP, AP( JC ), 1 ) * * Compute U(J,J) and test for non-positive-definiteness. * AJJ = DBLE( AP( JJ ) ) - ZDOTC( J-1, AP( JC ), 1, AP( JC ), $ 1 ) IF( AJJ.LE.ZERO ) THEN AP( JJ ) = AJJ GO TO 30 END IF AP( JJ ) = SQRT( AJJ ) 10 CONTINUE ELSE * * Compute the Cholesky factorization A = L * L**H. * JJ = 1 DO 20 J = 1, N * * Compute L(J,J) and test for non-positive-definiteness. * AJJ = DBLE( AP( JJ ) ) IF( AJJ.LE.ZERO ) THEN AP( JJ ) = AJJ GO TO 30 END IF AJJ = SQRT( AJJ ) AP( JJ ) = AJJ * * Compute elements J+1:N of column J and update the trailing * submatrix. * IF( J.LT.N ) THEN CALL ZDSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 ) CALL ZHPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1, $ AP( JJ+N-J+1 ) ) JJ = JJ + N - J + 1 END IF 20 CONTINUE END IF GO TO 40 * 30 CONTINUE INFO = J * 40 CONTINUE RETURN * * End of ZPPTRF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhpgst.f0000644000000000000000000000013214061636515015343 xustar0030 mtime=1623670093.154104127 30 atime=1623670093.153104127 30 ctime=1623670093.154104127 elk-7.2.42/src/LAPACK/zhpgst.f0000644002504400250440000002054214061636515017403 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHPGST * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHPGST + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, ITYPE, N * .. * .. Array Arguments .. * COMPLEX*16 AP( * ), BP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHPGST reduces a complex Hermitian-definite generalized *> eigenproblem to standard form, using packed storage. *> *> If ITYPE = 1, the problem is A*x = lambda*B*x, *> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) *> *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or *> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. *> *> B must have been previously factorized as U**H*U or L*L**H by ZPPTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); *> = 2 or 3: compute U*A*U**H or L**H*A*L. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored and B is factored as *> U**H*U; *> = 'L': Lower triangle of A is stored and B is factored as *> L*L**H. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the Hermitian matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim *> *> \param[in] BP *> \verbatim *> BP is COMPLEX*16 array, dimension (N*(N+1)/2) *> The triangular factor from the Cholesky factorization of B, *> stored in the same format as A, as returned by ZPPTRF. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, ITYPE, N * .. * .. Array Arguments .. COMPLEX*16 AP( * ), BP( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, HALF PARAMETER ( ONE = 1.0D+0, HALF = 0.5D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, J1, J1J1, JJ, K, K1, K1K1, KK DOUBLE PRECISION AJJ, AKK, BJJ, BKK COMPLEX*16 CT * .. * .. External Subroutines .. EXTERNAL XERBLA, ZAXPY, ZDSCAL, ZHPMV, ZHPR2, ZTPMV, $ ZTPSV * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. External Functions .. LOGICAL LSAME COMPLEX*16 ZDOTC EXTERNAL LSAME, ZDOTC * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHPGST', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**H)*A*inv(U) * * J1 and JJ are the indices of A(1,j) and A(j,j) * JJ = 0 DO 10 J = 1, N J1 = JJ + 1 JJ = JJ + J * * Compute the j-th column of the upper triangle of A * AP( JJ ) = DBLE( AP( JJ ) ) BJJ = BP( JJ ) CALL ZTPSV( UPLO, 'Conjugate transpose', 'Non-unit', J, $ BP, AP( J1 ), 1 ) CALL ZHPMV( UPLO, J-1, -CONE, AP, BP( J1 ), 1, CONE, $ AP( J1 ), 1 ) CALL ZDSCAL( J-1, ONE / BJJ, AP( J1 ), 1 ) AP( JJ ) = ( AP( JJ )-ZDOTC( J-1, AP( J1 ), 1, BP( J1 ), $ 1 ) ) / BJJ 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**H) * * KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) * KK = 1 DO 20 K = 1, N K1K1 = KK + N - K + 1 * * Update the lower triangle of A(k:n,k:n) * AKK = AP( KK ) BKK = BP( KK ) AKK = AKK / BKK**2 AP( KK ) = AKK IF( K.LT.N ) THEN CALL ZDSCAL( N-K, ONE / BKK, AP( KK+1 ), 1 ) CT = -HALF*AKK CALL ZAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 ) CALL ZHPR2( UPLO, N-K, -CONE, AP( KK+1 ), 1, $ BP( KK+1 ), 1, AP( K1K1 ) ) CALL ZAXPY( N-K, CT, BP( KK+1 ), 1, AP( KK+1 ), 1 ) CALL ZTPSV( UPLO, 'No transpose', 'Non-unit', N-K, $ BP( K1K1 ), AP( KK+1 ), 1 ) END IF KK = K1K1 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**H * * K1 and KK are the indices of A(1,k) and A(k,k) * KK = 0 DO 30 K = 1, N K1 = KK + 1 KK = KK + K * * Update the upper triangle of A(1:k,1:k) * AKK = AP( KK ) BKK = BP( KK ) CALL ZTPMV( UPLO, 'No transpose', 'Non-unit', K-1, BP, $ AP( K1 ), 1 ) CT = HALF*AKK CALL ZAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 ) CALL ZHPR2( UPLO, K-1, CONE, AP( K1 ), 1, BP( K1 ), 1, $ AP ) CALL ZAXPY( K-1, CT, BP( K1 ), 1, AP( K1 ), 1 ) CALL ZDSCAL( K-1, BKK, AP( K1 ), 1 ) AP( KK ) = AKK*BKK**2 30 CONTINUE ELSE * * Compute L**H *A*L * * JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) * JJ = 1 DO 40 J = 1, N J1J1 = JJ + N - J + 1 * * Compute the j-th column of the lower triangle of A * AJJ = AP( JJ ) BJJ = BP( JJ ) AP( JJ ) = AJJ*BJJ + ZDOTC( N-J, AP( JJ+1 ), 1, $ BP( JJ+1 ), 1 ) CALL ZDSCAL( N-J, BJJ, AP( JJ+1 ), 1 ) CALL ZHPMV( UPLO, N-J, CONE, AP( J1J1 ), BP( JJ+1 ), 1, $ CONE, AP( JJ+1 ), 1 ) CALL ZTPMV( UPLO, 'Conjugate transpose', 'Non-unit', $ N-J+1, BP( JJ ), AP( JJ ), 1 ) JJ = J1J1 40 CONTINUE END IF END IF RETURN * * End of ZHPGST * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhpevx.f0000644000000000000000000000013214061636515015350 xustar0030 mtime=1623670093.156104125 30 atime=1623670093.155104125 30 ctime=1623670093.156104125 elk-7.2.42/src/LAPACK/zhpevx.f0000644002504400250440000003762714061636515017424 0ustar00dewhurstdewhurst00000000000000*> \brief ZHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHPEVX + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, * ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, * IFAIL, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, RANGE, UPLO * INTEGER IL, INFO, IU, LDZ, M, N * DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER IFAIL( * ), IWORK( * ) * DOUBLE PRECISION RWORK( * ), W( * ) * COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHPEVX computes selected eigenvalues and, optionally, eigenvectors *> of a complex Hermitian matrix A in packed storage. *> Eigenvalues/vectors can be selected by specifying either a range of *> values or a range of indices for the desired eigenvalues. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] RANGE *> \verbatim *> RANGE is CHARACTER*1 *> = 'A': all eigenvalues will be found; *> = 'V': all eigenvalues in the half-open interval (VL,VU] *> will be found; *> = 'I': the IL-th through IU-th eigenvalues will be found. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the Hermitian matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. *> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite *> the corresponding elements of A, and if UPLO = 'L', the *> diagonal and first subdiagonal of T overwrite the *> corresponding elements of A. *> \endverbatim *> *> \param[in] VL *> \verbatim *> VL is DOUBLE PRECISION *> If RANGE='V', the lower bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION *> If RANGE='V', the upper bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] IL *> \verbatim *> IL is INTEGER *> If RANGE='I', the index of the *> smallest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] IU *> \verbatim *> IU is INTEGER *> If RANGE='I', the index of the *> largest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] ABSTOL *> \verbatim *> ABSTOL is DOUBLE PRECISION *> The absolute error tolerance for the eigenvalues. *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to *> *> ABSTOL + EPS * max( |a|,|b| ) , *> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. *> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). *> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. *> \endverbatim *> *> \param[out] M *> \verbatim *> M is INTEGER *> The total number of eigenvalues found. 0 <= M <= N. *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> If INFO = 0, the selected eigenvalues in ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ, max(1,M)) *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z *> contain the orthonormal eigenvectors of the matrix A *> corresponding to the selected eigenvalues, with the i-th *> column of Z holding the eigenvector associated with W(i). *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and *> the index of the eigenvector is returned in IFAIL. *> If JOBZ = 'N', then Z is not referenced. *> Note: the user must ensure that at least max(1,M) columns are *> supplied in the array Z; if RANGE = 'V', the exact value of M *> is not known in advance and an upper bound must be used. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> JOBZ = 'V', LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (2*N) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (7*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (5*N) *> \endverbatim *> *> \param[out] IFAIL *> \verbatim *> IFAIL is INTEGER array, dimension (N) *> If JOBZ = 'V', then if INFO = 0, the first M elements of *> IFAIL are zero. If INFO > 0, then IFAIL contains the *> indices of the eigenvectors that failed to converge. *> If JOBZ = 'N', then IFAIL is not referenced. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, then i eigenvectors failed to converge. *> Their indices are stored in array IFAIL. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16OTHEReigen * * ===================================================================== SUBROUTINE ZHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, $ ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, $ IFAIL, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, RANGE, UPLO INTEGER IL, INFO, IU, LDZ, M, N DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER IFAIL( * ), IWORK( * ) DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) ) * .. * .. Local Scalars .. LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ CHARACTER ORDER INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL, $ INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE, $ ITMP1, J, JJ, NSPLIT DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, $ SIGMA, SMLNUM, TMP1, VLL, VUU * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANHP EXTERNAL LSAME, DLAMCH, ZLANHP * .. * .. External Subroutines .. EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTERF, XERBLA, ZDSCAL, $ ZHPTRD, ZSTEIN, ZSTEQR, ZSWAP, ZUPGTR, ZUPMTR * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) ALLEIG = LSAME( RANGE, 'A' ) VALEIG = LSAME( RANGE, 'V' ) INDEIG = LSAME( RANGE, 'I' ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN INFO = -2 ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) ) $ THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( VALEIG ) THEN IF( N.GT.0 .AND. VU.LE.VL ) $ INFO = -7 ELSE IF( INDEIG ) THEN IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN INFO = -8 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN INFO = -9 END IF END IF END IF IF( INFO.EQ.0 ) THEN IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) $ INFO = -14 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHPEVX', -INFO ) RETURN END IF * * Quick return if possible * M = 0 IF( N.EQ.0 ) $ RETURN * IF( N.EQ.1 ) THEN IF( ALLEIG .OR. INDEIG ) THEN M = 1 W( 1 ) = AP( 1 ) ELSE IF( VL.LT.DBLE( AP( 1 ) ) .AND. VU.GE.DBLE( AP( 1 ) ) ) THEN M = 1 W( 1 ) = AP( 1 ) END IF END IF IF( WANTZ ) $ Z( 1, 1 ) = CONE RETURN END IF * * Get machine constants. * SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) * * Scale matrix to allowable range, if necessary. * ISCALE = 0 ABSTLL = ABSTOL IF( VALEIG ) THEN VLL = VL VUU = VU ELSE VLL = ZERO VUU = ZERO END IF ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK ) IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) THEN CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 ) IF( ABSTOL.GT.0 ) $ ABSTLL = ABSTOL*SIGMA IF( VALEIG ) THEN VLL = VL*SIGMA VUU = VU*SIGMA END IF END IF * * Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. * INDD = 1 INDE = INDD + N INDRWK = INDE + N INDTAU = 1 INDWRK = INDTAU + N CALL ZHPTRD( UPLO, N, AP, RWORK( INDD ), RWORK( INDE ), $ WORK( INDTAU ), IINFO ) * * If all eigenvalues are desired and ABSTOL is less than or equal * to zero, then call DSTERF or ZUPGTR and ZSTEQR. If this fails * for some eigenvalue, then try DSTEBZ. * TEST = .FALSE. IF (INDEIG) THEN IF (IL.EQ.1 .AND. IU.EQ.N) THEN TEST = .TRUE. END IF END IF IF ((ALLEIG .OR. TEST) .AND. (ABSTOL.LE.ZERO)) THEN CALL DCOPY( N, RWORK( INDD ), 1, W, 1 ) INDEE = INDRWK + 2*N IF( .NOT.WANTZ ) THEN CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 ) CALL DSTERF( N, W, RWORK( INDEE ), INFO ) ELSE CALL ZUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ, $ WORK( INDWRK ), IINFO ) CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 ) CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ, $ RWORK( INDRWK ), INFO ) IF( INFO.EQ.0 ) THEN DO 10 I = 1, N IFAIL( I ) = 0 10 CONTINUE END IF END IF IF( INFO.EQ.0 ) THEN M = N GO TO 20 END IF INFO = 0 END IF * * Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. * IF( WANTZ ) THEN ORDER = 'B' ELSE ORDER = 'E' END IF INDIBL = 1 INDISP = INDIBL + N INDIWK = INDISP + N CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, $ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W, $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ), $ IWORK( INDIWK ), INFO ) * IF( WANTZ ) THEN CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W, $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, $ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO ) * * Apply unitary matrix used in reduction to tridiagonal * form to eigenvectors returned by ZSTEIN. * INDWRK = INDTAU + N CALL ZUPMTR( 'L', UPLO, 'N', N, M, AP, WORK( INDTAU ), Z, LDZ, $ WORK( INDWRK ), IINFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * 20 CONTINUE IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = M ELSE IMAX = INFO - 1 END IF CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * * If eigenvalues are not in order, then sort them, along with * eigenvectors. * IF( WANTZ ) THEN DO 40 J = 1, M - 1 I = 0 TMP1 = W( J ) DO 30 JJ = J + 1, M IF( W( JJ ).LT.TMP1 ) THEN I = JJ TMP1 = W( JJ ) END IF 30 CONTINUE * IF( I.NE.0 ) THEN ITMP1 = IWORK( INDIBL+I-1 ) W( I ) = W( J ) IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 ) W( J ) = TMP1 IWORK( INDIBL+J-1 ) = ITMP1 CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) IF( INFO.NE.0 ) THEN ITMP1 = IFAIL( I ) IFAIL( I ) = IFAIL( J ) IFAIL( J ) = ITMP1 END IF END IF 40 CONTINUE END IF * RETURN * * End of ZHPEVX * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dgetrs.f0000644000000000000000000000013214061636515015314 xustar0030 mtime=1623670093.157104124 30 atime=1623670093.157104124 30 ctime=1623670093.157104124 elk-7.2.42/src/LAPACK/dgetrs.f0000644002504400250440000001356414061636515017362 0ustar00dewhurstdewhurst00000000000000*> \brief \b DGETRS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DGETRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER TRANS * INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGETRS solves a system of linear equations *> A * X = B or A**T * X = B *> with a general N-by-N matrix A using the LU factorization computed *> by DGETRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the form of the system of equations: *> = 'N': A * X = B (No transpose) *> = 'T': A**T* X = B (Transpose) *> = 'C': A**T* X = B (Conjugate transpose = Transpose) *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The factors L and U from the factorization A = P*L*U *> as computed by DGETRF. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices from DGETRF; for 1<=i<=N, row i of the *> matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> On entry, the right hand side matrix B. *> On exit, the solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleGEcomputational * * ===================================================================== SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL NOTRAN * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DLASWP, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 NOTRAN = LSAME( TRANS, 'N' ) IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. $ LSAME( TRANS, 'C' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( NRHS.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGETRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * IF( NOTRAN ) THEN * * Solve A * X = B. * * Apply row interchanges to the right hand sides. * CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, 1 ) * * Solve L*X = B, overwriting B with X. * CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS, $ ONE, A, LDA, B, LDB ) * * Solve U*X = B, overwriting B with X. * CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, $ NRHS, ONE, A, LDA, B, LDB ) ELSE * * Solve A**T * X = B. * * Solve U**T *X = B, overwriting B with X. * CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS, $ ONE, A, LDA, B, LDB ) * * Solve L**T *X = B, overwriting B with X. * CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE, $ A, LDA, B, LDB ) * * Apply row interchanges to the solution vectors. * CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, -1 ) END IF * RETURN * * End of DGETRS * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dgetrf2.f0000644000000000000000000000013214061636515015361 xustar0030 mtime=1623670093.159104122 30 atime=1623670093.159104122 30 ctime=1623670093.159104122 elk-7.2.42/src/LAPACK/dgetrf2.f0000644002504400250440000001560214061636515017422 0ustar00dewhurstdewhurst00000000000000*> \brief \b DGETRF2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DGETRF2 computes an LU factorization of a general M-by-N matrix A *> using partial pivoting with row interchanges. *> *> The factorization has the form *> A = P * L * U *> where P is a permutation matrix, L is lower triangular with unit *> diagonal elements (lower trapezoidal if m > n), and U is upper *> triangular (upper trapezoidal if m < n). *> *> This is the recursive version of the algorithm. It divides *> the matrix into four submatrices: *> *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 *> A = [ -----|----- ] with n1 = min(m,n)/2 *> [ A21 | A22 ] n2 = n-n1 *> *> [ A11 ] *> The subroutine calls itself to factor [ --- ], *> [ A12 ] *> [ A12 ] *> do the swaps on [ --- ], solve A12, update A22, *> [ A22 ] *> *> then calls itself to factor A22 and do the swaps on A21. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the M-by-N matrix to be factored. *> On exit, the factors L and U from the factorization *> A = P*L*U; the unit diagonal elements of L are not stored. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (min(M,N)) *> The pivot indices; for 1 <= i <= min(M,N), row i of the *> matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization *> has been completed, but the factor U is exactly *> singular, and division by zero will occur if it is used *> to solve a system of equations. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup doubleGEcomputational * * ===================================================================== RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. DOUBLE PRECISION SFMIN, TEMP INTEGER I, IINFO, N1, N2 * .. * .. External Functions .. DOUBLE PRECISION DLAMCH INTEGER IDAMAX EXTERNAL DLAMCH, IDAMAX * .. * .. External Subroutines .. EXTERNAL DGEMM, DSCAL, DLASWP, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGETRF2', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN IF ( M.EQ.1 ) THEN * * Use unblocked code for one row case * Just need to handle IPIV and INFO * IPIV( 1 ) = 1 IF ( A(1,1).EQ.ZERO ) $ INFO = 1 * ELSE IF( N.EQ.1 ) THEN * * Use unblocked code for one column case * * * Compute machine safe minimum * SFMIN = DLAMCH('S') * * Find pivot and test for singularity * I = IDAMAX( M, A( 1, 1 ), 1 ) IPIV( 1 ) = I IF( A( I, 1 ).NE.ZERO ) THEN * * Apply the interchange * IF( I.NE.1 ) THEN TEMP = A( 1, 1 ) A( 1, 1 ) = A( I, 1 ) A( I, 1 ) = TEMP END IF * * Compute elements 2:M of the column * IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN CALL DSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 ) ELSE DO 10 I = 1, M-1 A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 ) 10 CONTINUE END IF * ELSE INFO = 1 END IF * ELSE * * Use recursive code * N1 = MIN( M, N ) / 2 N2 = N-N1 * * [ A11 ] * Factor [ --- ] * [ A21 ] * CALL DGETRF2( M, N1, A, LDA, IPIV, IINFO ) IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) $ INFO = IINFO * * [ A12 ] * Apply interchanges to [ --- ] * [ A22 ] * CALL DLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 ) * * Solve A12 * CALL DTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA, $ A( 1, N1+1 ), LDA ) * * Update A22 * CALL DGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA, $ A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA ) * * Factor A22 * CALL DGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ), $ IINFO ) * * Adjust INFO and the pivot indices * IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) $ INFO = IINFO + N1 DO 20 I = N1+1, MIN( M, N ) IPIV( I ) = IPIV( I ) + N1 20 CONTINUE * * Apply interchanges to A21 * CALL DLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 ) * END IF RETURN * * End of DGETRF2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaswp.f0000644000000000000000000000013214061636515015316 xustar0030 mtime=1623670093.160104121 30 atime=1623670093.160104121 30 ctime=1623670093.160104121 elk-7.2.42/src/LAPACK/dlaswp.f0000644002504400250440000001201014061636515017345 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASWP performs a series of row interchanges on a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASWP + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX ) * * .. Scalar Arguments .. * INTEGER INCX, K1, K2, LDA, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASWP performs a series of row interchanges on the matrix A. *> One row interchange is initiated for each of rows K1 through K2 of A. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the matrix of column dimension N to which the row *> interchanges will be applied. *> On exit, the permuted matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> \endverbatim *> *> \param[in] K1 *> \verbatim *> K1 is INTEGER *> The first element of IPIV for which a row interchange will *> be done. *> \endverbatim *> *> \param[in] K2 *> \verbatim *> K2 is INTEGER *> (K2-K1+1) is the number of elements of IPIV for which a row *> interchange will be done. *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (K1+(K2-K1)*abs(INCX)) *> The vector of pivot indices. Only the elements in positions *> K1 through K1+(K2-K1)*abs(INCX) of IPIV are accessed. *> IPIV(K1+(K-K1)*abs(INCX)) = L implies rows K and L are to be *> interchanged. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between successive values of IPIV. If INCX *> is negative, the pivots are applied in reverse order. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup doubleOTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> Modified by *> R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA *> \endverbatim *> * ===================================================================== SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER INCX, K1, K2, LDA, N * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, I1, I2, INC, IP, IX, IX0, J, K, N32 DOUBLE PRECISION TEMP * .. * .. Executable Statements .. * * Interchange row I with row IPIV(K1+(I-K1)*abs(INCX)) for each of rows * K1 through K2. * IF( INCX.GT.0 ) THEN IX0 = K1 I1 = K1 I2 = K2 INC = 1 ELSE IF( INCX.LT.0 ) THEN IX0 = K1 + ( K1-K2 )*INCX I1 = K2 I2 = K1 INC = -1 ELSE RETURN END IF * N32 = ( N / 32 )*32 IF( N32.NE.0 ) THEN DO 30 J = 1, N32, 32 IX = IX0 DO 20 I = I1, I2, INC IP = IPIV( IX ) IF( IP.NE.I ) THEN DO 10 K = J, J + 31 TEMP = A( I, K ) A( I, K ) = A( IP, K ) A( IP, K ) = TEMP 10 CONTINUE END IF IX = IX + INCX 20 CONTINUE 30 CONTINUE END IF IF( N32.NE.N ) THEN N32 = N32 + 1 IX = IX0 DO 50 I = I1, I2, INC IP = IPIV( IX ) IF( IP.NE.I ) THEN DO 40 K = N32, N TEMP = A( I, K ) A( I, K ) = A( IP, K ) A( IP, K ) = TEMP 40 CONTINUE END IF IX = IX + INCX 50 CONTINUE END IF * RETURN * * End of DLASWP * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dtrtri.f0000644000000000000000000000013214061636515015334 xustar0030 mtime=1623670093.162104119 30 atime=1623670093.162104119 30 ctime=1623670093.162104119 elk-7.2.42/src/LAPACK/dtrtri.f0000644002504400250440000001536714061636515017405 0ustar00dewhurstdewhurst00000000000000*> \brief \b DTRTRI * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DTRTRI + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTRTRI computes the inverse of a real upper or lower triangular *> matrix A. *> *> This is the Level 3 BLAS version of the algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': A is upper triangular; *> = 'L': A is lower triangular. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> = 'N': A is non-unit triangular; *> = 'U': A is unit triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the triangular matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of the array A contains *> the upper triangular matrix, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of the array A contains *> the lower triangular matrix, and the strictly upper *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, A(i,i) is exactly zero. The triangular *> matrix is singular and its inverse can not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DTRTRI( UPLO, DIAG, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER J, JB, NB, NN * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DTRMM, DTRSM, DTRTI2, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) NOUNIT = LSAME( DIAG, 'N' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DTRTRI', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Check for singularity if non-unit. * IF( NOUNIT ) THEN DO 10 INFO = 1, N IF( A( INFO, INFO ).EQ.ZERO ) $ RETURN 10 CONTINUE INFO = 0 END IF * * Determine the block size for this environment. * NB = ILAENV( 1, 'DTRTRI', UPLO // DIAG, N, -1, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) ELSE * * Use blocked code * IF( UPPER ) THEN * * Compute inverse of upper triangular matrix * DO 20 J = 1, N, NB JB = MIN( NB, N-J+1 ) * * Compute rows 1:j-1 of current block column * CALL DTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1, $ JB, ONE, A, LDA, A( 1, J ), LDA ) CALL DTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1, $ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA ) * * Compute inverse of current diagonal block * CALL DTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO ) 20 CONTINUE ELSE * * Compute inverse of lower triangular matrix * NN = ( ( N-1 ) / NB )*NB + 1 DO 30 J = NN, 1, -NB JB = MIN( NB, N-J+1 ) IF( J+JB.LE.N ) THEN * * Compute rows j+jb:n of current block column * CALL DTRMM( 'Left', 'Lower', 'No transpose', DIAG, $ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA, $ A( J+JB, J ), LDA ) CALL DTRSM( 'Right', 'Lower', 'No transpose', DIAG, $ N-J-JB+1, JB, -ONE, A( J, J ), LDA, $ A( J+JB, J ), LDA ) END IF * * Compute inverse of current diagonal block * CALL DTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO ) 30 CONTINUE END IF END IF * RETURN * * End of DTRTRI * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlansy.f0000644000000000000000000000013214061636515015316 xustar0030 mtime=1623670093.164104117 30 atime=1623670093.163104118 30 ctime=1623670093.164104117 elk-7.2.42/src/LAPACK/dlansy.f0000644002504400250440000001753414061636515017365 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLANSY + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) * * .. Scalar Arguments .. * CHARACTER NORM, UPLO * INTEGER LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLANSY returns the value of the one norm, or the Frobenius norm, or *> the infinity norm, or the element of largest absolute value of a *> real symmetric matrix A. *> \endverbatim *> *> \return DLANSY *> \verbatim *> *> DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm' *> ( *> ( norm1(A), NORM = '1', 'O' or 'o' *> ( *> ( normI(A), NORM = 'I' or 'i' *> ( *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' *> *> where norm1 denotes the one norm of a matrix (maximum column sum), *> normI denotes the infinity norm of a matrix (maximum row sum) and *> normF denotes the Frobenius norm of a matrix (square root of sum of *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] NORM *> \verbatim *> NORM is CHARACTER*1 *> Specifies the value to be returned in DLANSY as described *> above. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> symmetric matrix A is to be referenced. *> = 'U': Upper triangular part of A is referenced *> = 'L': Lower triangular part of A is referenced *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, DLANSY is *> set to zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The symmetric matrix A. If UPLO = 'U', the leading n by n *> upper triangular part of A contains the upper triangular part *> of the matrix A, and the strictly lower triangular part of A *> is not referenced. If UPLO = 'L', the leading n by n lower *> triangular part of A contains the lower triangular part of *> the matrix A, and the strictly upper triangular part of A is *> not referenced. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(N,1). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, *> WORK is not referenced. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleSYauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * IMPLICIT NONE * .. Scalar Arguments .. CHARACTER NORM, UPLO INTEGER LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION ABSA, SUM, VALUE * .. * .. Local Arrays .. DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL DLASSQ, DCOMBSSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * IF( N.EQ.0 ) THEN VALUE = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * VALUE = ZERO IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, J SUM = ABS( A( I, J ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J, N SUM = ABS( A( I, J ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE 40 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. $ ( NORM.EQ.'1' ) ) THEN * * Find normI(A) ( = norm1(A), since A is symmetric). * VALUE = ZERO IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N SUM = ZERO DO 50 I = 1, J - 1 ABSA = ABS( A( I, J ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA 50 CONTINUE WORK( J ) = SUM + ABS( A( J, J ) ) 60 CONTINUE DO 70 I = 1, N SUM = WORK( I ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE ELSE DO 80 I = 1, N WORK( I ) = ZERO 80 CONTINUE DO 100 J = 1, N SUM = WORK( J ) + ABS( A( J, J ) ) DO 90 I = J + 1, N ABSA = ABS( A( I, J ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA 90 CONTINUE IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 100 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SSQ(1) is scale * SSQ(2) is sum-of-squares * For better accuracy, sum each column separately. * SSQ( 1 ) = ZERO SSQ( 2 ) = ONE * * Sum off-diagonals * IF( LSAME( UPLO, 'U' ) ) THEN DO 110 J = 2, N COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL DLASSQ( J-1, A( 1, J ), 1, COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) 110 CONTINUE ELSE DO 120 J = 1, N - 1 COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL DLASSQ( N-J, A( J+1, J ), 1, COLSSQ(1), COLSSQ(2) ) CALL DCOMBSSQ( SSQ, COLSSQ ) 120 CONTINUE END IF SSQ( 2 ) = 2*SSQ( 2 ) * * Sum diagonal * COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL DLASSQ( N, A, LDA+1, COLSSQ( 1 ), COLSSQ( 2 ) ) CALL DCOMBSSQ( SSQ, COLSSQ ) VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) END IF * DLANSY = VALUE RETURN * * End of DLANSY * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlascl.f0000644000000000000000000000013214061636515015266 xustar0030 mtime=1623670093.165104116 30 atime=1623670093.165104116 30 ctime=1623670093.165104116 elk-7.2.42/src/LAPACK/dlascl.f0000644002504400250440000002342714061636515017333 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASCL + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER TYPE * INTEGER INFO, KL, KU, LDA, M, N * DOUBLE PRECISION CFROM, CTO * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASCL multiplies the M by N real matrix A by the real scalar *> CTO/CFROM. This is done without over/underflow as long as the final *> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that *> A may be full, upper triangular, lower triangular, upper Hessenberg, *> or banded. *> \endverbatim * * Arguments: * ========== * *> \param[in] TYPE *> \verbatim *> TYPE is CHARACTER*1 *> TYPE indices the storage type of the input matrix. *> = 'G': A is a full matrix. *> = 'L': A is a lower triangular matrix. *> = 'U': A is an upper triangular matrix. *> = 'H': A is an upper Hessenberg matrix. *> = 'B': A is a symmetric band matrix with lower bandwidth KL *> and upper bandwidth KU and with the only the lower *> half stored. *> = 'Q': A is a symmetric band matrix with lower bandwidth KL *> and upper bandwidth KU and with the only the upper *> half stored. *> = 'Z': A is a band matrix with lower bandwidth KL and upper *> bandwidth KU. See DGBTRF for storage details. *> \endverbatim *> *> \param[in] KL *> \verbatim *> KL is INTEGER *> The lower bandwidth of A. Referenced only if TYPE = 'B', *> 'Q' or 'Z'. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is INTEGER *> The upper bandwidth of A. Referenced only if TYPE = 'B', *> 'Q' or 'Z'. *> \endverbatim *> *> \param[in] CFROM *> \verbatim *> CFROM is DOUBLE PRECISION *> \endverbatim *> *> \param[in] CTO *> \verbatim *> CTO is DOUBLE PRECISION *> *> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed *> without over/underflow if the final result CTO*A(I,J)/CFROM *> can be represented without over/underflow. CFROM must be *> nonzero. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The matrix to be multiplied by CTO/CFROM. See TYPE for the *> storage type. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M); *> TYPE = 'B', LDA >= KL+1; *> TYPE = 'Q', LDA >= KU+1; *> TYPE = 'Z', LDA >= 2*KL+KU+1. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> 0 - successful exit *> <0 - if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER TYPE INTEGER INFO, KL, KU, LDA, M, N DOUBLE PRECISION CFROM, CTO * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. LOGICAL DONE INTEGER I, ITYPE, J, K1, K2, K3, K4 DOUBLE PRECISION BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM * .. * .. External Functions .. LOGICAL LSAME, DISNAN DOUBLE PRECISION DLAMCH EXTERNAL LSAME, DLAMCH, DISNAN * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 * IF( LSAME( TYPE, 'G' ) ) THEN ITYPE = 0 ELSE IF( LSAME( TYPE, 'L' ) ) THEN ITYPE = 1 ELSE IF( LSAME( TYPE, 'U' ) ) THEN ITYPE = 2 ELSE IF( LSAME( TYPE, 'H' ) ) THEN ITYPE = 3 ELSE IF( LSAME( TYPE, 'B' ) ) THEN ITYPE = 4 ELSE IF( LSAME( TYPE, 'Q' ) ) THEN ITYPE = 5 ELSE IF( LSAME( TYPE, 'Z' ) ) THEN ITYPE = 6 ELSE ITYPE = -1 END IF * IF( ITYPE.EQ.-1 ) THEN INFO = -1 ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN INFO = -4 ELSE IF( DISNAN(CTO) ) THEN INFO = -5 ELSE IF( M.LT.0 ) THEN INFO = -6 ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR. $ ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN INFO = -7 ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN INFO = -9 ELSE IF( ITYPE.GE.4 ) THEN IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN INFO = -2 ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR. $ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) ) $ THEN INFO = -3 ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR. $ ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR. $ ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN INFO = -9 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLASCL', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. M.EQ.0 ) $ RETURN * * Get machine parameters * SMLNUM = DLAMCH( 'S' ) BIGNUM = ONE / SMLNUM * CFROMC = CFROM CTOC = CTO * 10 CONTINUE CFROM1 = CFROMC*SMLNUM IF( CFROM1.EQ.CFROMC ) THEN ! CFROMC is an inf. Multiply by a correctly signed zero for ! finite CTOC, or a NaN if CTOC is infinite. MUL = CTOC / CFROMC DONE = .TRUE. CTO1 = CTOC ELSE CTO1 = CTOC / BIGNUM IF( CTO1.EQ.CTOC ) THEN ! CTOC is either 0 or an inf. In both cases, CTOC itself ! serves as the correct multiplication factor. MUL = CTOC DONE = .TRUE. CFROMC = ONE ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN MUL = SMLNUM DONE = .FALSE. CFROMC = CFROM1 ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN MUL = BIGNUM DONE = .FALSE. CTOC = CTO1 ELSE MUL = CTOC / CFROMC DONE = .TRUE. END IF END IF * IF( ITYPE.EQ.0 ) THEN * * Full matrix * DO 30 J = 1, N DO 20 I = 1, M A( I, J ) = A( I, J )*MUL 20 CONTINUE 30 CONTINUE * ELSE IF( ITYPE.EQ.1 ) THEN * * Lower triangular matrix * DO 50 J = 1, N DO 40 I = J, M A( I, J ) = A( I, J )*MUL 40 CONTINUE 50 CONTINUE * ELSE IF( ITYPE.EQ.2 ) THEN * * Upper triangular matrix * DO 70 J = 1, N DO 60 I = 1, MIN( J, M ) A( I, J ) = A( I, J )*MUL 60 CONTINUE 70 CONTINUE * ELSE IF( ITYPE.EQ.3 ) THEN * * Upper Hessenberg matrix * DO 90 J = 1, N DO 80 I = 1, MIN( J+1, M ) A( I, J ) = A( I, J )*MUL 80 CONTINUE 90 CONTINUE * ELSE IF( ITYPE.EQ.4 ) THEN * * Lower half of a symmetric band matrix * K3 = KL + 1 K4 = N + 1 DO 110 J = 1, N DO 100 I = 1, MIN( K3, K4-J ) A( I, J ) = A( I, J )*MUL 100 CONTINUE 110 CONTINUE * ELSE IF( ITYPE.EQ.5 ) THEN * * Upper half of a symmetric band matrix * K1 = KU + 2 K3 = KU + 1 DO 130 J = 1, N DO 120 I = MAX( K1-J, 1 ), K3 A( I, J ) = A( I, J )*MUL 120 CONTINUE 130 CONTINUE * ELSE IF( ITYPE.EQ.6 ) THEN * * Band matrix * K1 = KL + KU + 2 K2 = KL + 1 K3 = 2*KL + KU + 1 K4 = KL + KU + 1 + M DO 150 J = 1, N DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J ) A( I, J ) = A( I, J )*MUL 140 CONTINUE 150 CONTINUE * END IF * IF( .NOT.DONE ) $ GO TO 10 * RETURN * * End of DLASCL * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsytrd.f0000644000000000000000000000013214061636515015335 xustar0030 mtime=1623670093.167104114 30 atime=1623670093.167104114 30 ctime=1623670093.167104114 elk-7.2.42/src/LAPACK/dsytrd.f0000644002504400250440000002634614061636515017405 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYTRD * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYTRD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), * $ WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYTRD reduces a real symmetric matrix A to real symmetric *> tridiagonal form T by an orthogonal similarity transformation: *> Q**T * A * Q = T. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> On exit, if UPLO = 'U', the diagonal and first superdiagonal *> of A are overwritten by the corresponding elements of the *> tridiagonal matrix T, and the elements above the first *> superdiagonal, with the array TAU, represent the orthogonal *> matrix Q as a product of elementary reflectors; if UPLO *> = 'L', the diagonal and first subdiagonal of A are over- *> written by the corresponding elements of the tridiagonal *> matrix T, and the elements below the first subdiagonal, with *> the array TAU, represent the orthogonal matrix Q as a product *> of elementary reflectors. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of the tridiagonal matrix T: *> D(i) = A(i,i). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The off-diagonal elements of the tridiagonal matrix T: *> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (N-1) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= 1. *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleSYcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> If UPLO = 'U', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(n-1) . . . H(2) H(1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**T *> *> where tau is a real scalar, and v is a real vector with *> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in *> A(1:i-1,i+1), and tau in TAU(i). *> *> If UPLO = 'L', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(1) H(2) . . . H(n-1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**T *> *> where tau is a real scalar, and v is a real vector with *> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), *> and tau in TAU(i). *> *> The contents of A on exit are illustrated by the following examples *> with n = 5: *> *> if UPLO = 'U': if UPLO = 'L': *> *> ( d e v2 v3 v4 ) ( d ) *> ( d e v3 v4 ) ( e d ) *> ( d e v4 ) ( v1 e d ) *> ( d e ) ( v1 v2 e d ) *> ( d ) ( v1 v2 v3 e d ) *> *> where d and e denote diagonal and off-diagonal elements of T, and vi *> denotes an element of the vector defining H(i). *> \endverbatim *> * ===================================================================== SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), $ WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER INTEGER I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB, $ NBMIN, NX * .. * .. External Subroutines .. EXTERNAL DLATRD, DSYR2K, DSYTD2, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN INFO = -9 END IF * IF( INFO.EQ.0 ) THEN * * Determine the block size. * NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) LWKOPT = N*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYTRD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NX = N IWS = 1 IF( NB.GT.1 .AND. NB.LT.N ) THEN * * Determine when to cross over from blocked to unblocked code * (last block is always handled by unblocked code). * NX = MAX( NB, ILAENV( 3, 'DSYTRD', UPLO, N, -1, -1, -1 ) ) IF( NX.LT.N ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = N IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: determine the * minimum value of NB, and reduce NB or force use of * unblocked code by setting NX = N. * NB = MAX( LWORK / LDWORK, 1 ) NBMIN = ILAENV( 2, 'DSYTRD', UPLO, N, -1, -1, -1 ) IF( NB.LT.NBMIN ) $ NX = N END IF ELSE NX = N END IF ELSE NB = 1 END IF * IF( UPPER ) THEN * * Reduce the upper triangle of A. * Columns 1:kk are handled by the unblocked method. * KK = N - ( ( N-NX+NB-1 ) / NB )*NB DO 20 I = N - NB + 1, KK + 1, -NB * * Reduce columns i:i+nb-1 to tridiagonal form and form the * matrix W which is needed to update the unreduced part of * the matrix * CALL DLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK, $ LDWORK ) * * Update the unreduced submatrix A(1:i-1,1:i-1), using an * update of the form: A := A - V*W**T - W*V**T * CALL DSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ), $ LDA, WORK, LDWORK, ONE, A, LDA ) * * Copy superdiagonal elements back into A, and diagonal * elements into D * DO 10 J = I, I + NB - 1 A( J-1, J ) = E( J-1 ) D( J ) = A( J, J ) 10 CONTINUE 20 CONTINUE * * Use unblocked code to reduce the last or only block * CALL DSYTD2( UPLO, KK, A, LDA, D, E, TAU, IINFO ) ELSE * * Reduce the lower triangle of A * DO 40 I = 1, N - NX, NB * * Reduce columns i:i+nb-1 to tridiagonal form and form the * matrix W which is needed to update the unreduced part of * the matrix * CALL DLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ), $ TAU( I ), WORK, LDWORK ) * * Update the unreduced submatrix A(i+ib:n,i+ib:n), using * an update of the form: A := A - V*W**T - W*V**T * CALL DSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE, $ A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE, $ A( I+NB, I+NB ), LDA ) * * Copy subdiagonal elements back into A, and diagonal * elements into D * DO 30 J = I, I + NB - 1 A( J+1, J ) = E( J ) D( J ) = A( J, J ) 30 CONTINUE 40 CONTINUE * * Use unblocked code to reduce the last or only block * CALL DSYTD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ), $ TAU( I ), IINFO ) END IF * WORK( 1 ) = LWKOPT RETURN * * End of DSYTRD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsterf.f0000644000000000000000000000013214061636515015313 xustar0030 mtime=1623670093.169104112 30 atime=1623670093.168104113 30 ctime=1623670093.169104112 elk-7.2.42/src/LAPACK/dsterf.f0000644002504400250440000002463114061636515017356 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSTERF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSTERF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSTERF( N, D, E, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSTERF computes all eigenvalues of a symmetric tridiagonal matrix *> using the Pal-Walker-Kahan variant of the QL or QR algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the n diagonal elements of the tridiagonal matrix. *> On exit, if INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> On entry, the (n-1) subdiagonal elements of the tridiagonal *> matrix. *> On exit, E has been destroyed. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: the algorithm failed to find all of the eigenvalues in *> a total of 30*N iterations; if INFO = i, then i *> elements of E have not converged to zero. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DSTERF( N, D, E, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO, THREE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ THREE = 3.0D0 ) INTEGER MAXIT PARAMETER ( MAXIT = 30 ) * .. * .. Local Scalars .. INTEGER I, ISCALE, JTOT, L, L1, LEND, LENDSV, LSV, M, $ NMAXIT DOUBLE PRECISION ALPHA, ANORM, BB, C, EPS, EPS2, GAMMA, OLDC, $ OLDGAM, P, R, RT1, RT2, RTE, S, SAFMAX, SAFMIN, $ SIGMA, SSFMAX, SSFMIN, RMAX * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANST, DLAPY2 EXTERNAL DLAMCH, DLANST, DLAPY2 * .. * .. External Subroutines .. EXTERNAL DLAE2, DLASCL, DLASRT, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, SIGN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * * Quick return if possible * IF( N.LT.0 ) THEN INFO = -1 CALL XERBLA( 'DSTERF', -INFO ) RETURN END IF IF( N.LE.1 ) $ RETURN * * Determine the unit roundoff for this environment. * EPS = DLAMCH( 'E' ) EPS2 = EPS**2 SAFMIN = DLAMCH( 'S' ) SAFMAX = ONE / SAFMIN SSFMAX = SQRT( SAFMAX ) / THREE SSFMIN = SQRT( SAFMIN ) / EPS2 RMAX = DLAMCH( 'O' ) * * Compute the eigenvalues of the tridiagonal matrix. * NMAXIT = N*MAXIT SIGMA = ZERO JTOT = 0 * * Determine where the matrix splits and choose QL or QR iteration * for each block, according to whether top or bottom diagonal * element is smaller. * L1 = 1 * 10 CONTINUE IF( L1.GT.N ) $ GO TO 170 IF( L1.GT.1 ) $ E( L1-1 ) = ZERO DO 20 M = L1, N - 1 IF( ABS( E( M ) ).LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+ $ 1 ) ) ) )*EPS ) THEN E( M ) = ZERO GO TO 30 END IF 20 CONTINUE M = N * 30 CONTINUE L = L1 LSV = L LEND = M LENDSV = LEND L1 = M + 1 IF( LEND.EQ.L ) $ GO TO 10 * * Scale submatrix in rows and columns L to LEND * ANORM = DLANST( 'M', LEND-L+1, D( L ), E( L ) ) ISCALE = 0 IF( ANORM.EQ.ZERO ) $ GO TO 10 IF( (ANORM.GT.SSFMAX) ) THEN ISCALE = 1 CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N, $ INFO ) CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N, $ INFO ) ELSE IF( ANORM.LT.SSFMIN ) THEN ISCALE = 2 CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N, $ INFO ) CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N, $ INFO ) END IF * DO 40 I = L, LEND - 1 E( I ) = E( I )**2 40 CONTINUE * * Choose between QL and QR iteration * IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN LEND = LSV L = LENDSV END IF * IF( LEND.GE.L ) THEN * * QL Iteration * * Look for small subdiagonal element. * 50 CONTINUE IF( L.NE.LEND ) THEN DO 60 M = L, LEND - 1 IF( ABS( E( M ) ).LE.EPS2*ABS( D( M )*D( M+1 ) ) ) $ GO TO 70 60 CONTINUE END IF M = LEND * 70 CONTINUE IF( M.LT.LEND ) $ E( M ) = ZERO P = D( L ) IF( M.EQ.L ) $ GO TO 90 * * If remaining matrix is 2 by 2, use DLAE2 to compute its * eigenvalues. * IF( M.EQ.L+1 ) THEN RTE = SQRT( E( L ) ) CALL DLAE2( D( L ), RTE, D( L+1 ), RT1, RT2 ) D( L ) = RT1 D( L+1 ) = RT2 E( L ) = ZERO L = L + 2 IF( L.LE.LEND ) $ GO TO 50 GO TO 150 END IF * IF( JTOT.EQ.NMAXIT ) $ GO TO 150 JTOT = JTOT + 1 * * Form shift. * RTE = SQRT( E( L ) ) SIGMA = ( D( L+1 )-P ) / ( TWO*RTE ) R = DLAPY2( SIGMA, ONE ) SIGMA = P - ( RTE / ( SIGMA+SIGN( R, SIGMA ) ) ) * C = ONE S = ZERO GAMMA = D( M ) - SIGMA P = GAMMA*GAMMA * * Inner loop * DO 80 I = M - 1, L, -1 BB = E( I ) R = P + BB IF( I.NE.M-1 ) $ E( I+1 ) = S*R OLDC = C C = P / R S = BB / R OLDGAM = GAMMA ALPHA = D( I ) GAMMA = C*( ALPHA-SIGMA ) - S*OLDGAM D( I+1 ) = OLDGAM + ( ALPHA-GAMMA ) IF( C.NE.ZERO ) THEN P = ( GAMMA*GAMMA ) / C ELSE P = OLDC*BB END IF 80 CONTINUE * E( L ) = S*P D( L ) = SIGMA + GAMMA GO TO 50 * * Eigenvalue found. * 90 CONTINUE D( L ) = P * L = L + 1 IF( L.LE.LEND ) $ GO TO 50 GO TO 150 * ELSE * * QR Iteration * * Look for small superdiagonal element. * 100 CONTINUE DO 110 M = L, LEND + 1, -1 IF( ABS( E( M-1 ) ).LE.EPS2*ABS( D( M )*D( M-1 ) ) ) $ GO TO 120 110 CONTINUE M = LEND * 120 CONTINUE IF( M.GT.LEND ) $ E( M-1 ) = ZERO P = D( L ) IF( M.EQ.L ) $ GO TO 140 * * If remaining matrix is 2 by 2, use DLAE2 to compute its * eigenvalues. * IF( M.EQ.L-1 ) THEN RTE = SQRT( E( L-1 ) ) CALL DLAE2( D( L ), RTE, D( L-1 ), RT1, RT2 ) D( L ) = RT1 D( L-1 ) = RT2 E( L-1 ) = ZERO L = L - 2 IF( L.GE.LEND ) $ GO TO 100 GO TO 150 END IF * IF( JTOT.EQ.NMAXIT ) $ GO TO 150 JTOT = JTOT + 1 * * Form shift. * RTE = SQRT( E( L-1 ) ) SIGMA = ( D( L-1 )-P ) / ( TWO*RTE ) R = DLAPY2( SIGMA, ONE ) SIGMA = P - ( RTE / ( SIGMA+SIGN( R, SIGMA ) ) ) * C = ONE S = ZERO GAMMA = D( M ) - SIGMA P = GAMMA*GAMMA * * Inner loop * DO 130 I = M, L - 1 BB = E( I ) R = P + BB IF( I.NE.M ) $ E( I-1 ) = S*R OLDC = C C = P / R S = BB / R OLDGAM = GAMMA ALPHA = D( I+1 ) GAMMA = C*( ALPHA-SIGMA ) - S*OLDGAM D( I ) = OLDGAM + ( ALPHA-GAMMA ) IF( C.NE.ZERO ) THEN P = ( GAMMA*GAMMA ) / C ELSE P = OLDC*BB END IF 130 CONTINUE * E( L-1 ) = S*P D( L ) = SIGMA + GAMMA GO TO 100 * * Eigenvalue found. * 140 CONTINUE D( L ) = P * L = L - 1 IF( L.GE.LEND ) $ GO TO 100 GO TO 150 * END IF * * Undo scaling if necessary * 150 CONTINUE IF( ISCALE.EQ.1 ) $ CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1, $ D( LSV ), N, INFO ) IF( ISCALE.EQ.2 ) $ CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1, $ D( LSV ), N, INFO ) * * Check for no convergence to an eigenvalue after a total * of N*MAXIT iterations. * IF( JTOT.LT.NMAXIT ) $ GO TO 10 DO 160 I = 1, N - 1 IF( E( I ).NE.ZERO ) $ INFO = INFO + 1 160 CONTINUE GO TO 180 * * Sort eigenvalues in increasing order. * 170 CONTINUE CALL DLASRT( 'I', N, D, INFO ) * 180 CONTINUE RETURN * * End of DSTERF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dorgtr.f0000644000000000000000000000013214061636515015325 xustar0030 mtime=1623670093.170104112 30 atime=1623670093.170104112 30 ctime=1623670093.170104112 elk-7.2.42/src/LAPACK/dorgtr.f0000644002504400250440000001562014061636515017366 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORGTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORGTR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORGTR generates a real orthogonal matrix Q which is defined as the *> product of n-1 elementary reflectors of order N, as returned by *> DSYTRD: *> *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), *> *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A contains elementary reflectors *> from DSYTRD; *> = 'L': Lower triangle of A contains elementary reflectors *> from DSYTRD. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix Q. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the vectors which define the elementary reflectors, *> as returned by DSYTRD. *> On exit, the N-by-N orthogonal matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (N-1) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DSYTRD. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N-1). *> For optimum performance LWORK >= (N-1)*NB, where NB is *> the optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER INTEGER I, IINFO, J, LWKOPT, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DORGQL, DORGQR, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN INFO = -7 END IF * IF( INFO.EQ.0 ) THEN IF( UPPER ) THEN NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 ) ELSE NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 ) END IF LWKOPT = MAX( 1, N-1 )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORGTR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * IF( UPPER ) THEN * * Q was determined by a call to DSYTRD with UPLO = 'U' * * Shift the vectors which define the elementary reflectors one * column to the left, and set the last row and column of Q to * those of the unit matrix * DO 20 J = 1, N - 1 DO 10 I = 1, J - 1 A( I, J ) = A( I, J+1 ) 10 CONTINUE A( N, J ) = ZERO 20 CONTINUE DO 30 I = 1, N - 1 A( I, N ) = ZERO 30 CONTINUE A( N, N ) = ONE * * Generate Q(1:n-1,1:n-1) * CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO ) * ELSE * * Q was determined by a call to DSYTRD with UPLO = 'L'. * * Shift the vectors which define the elementary reflectors one * column to the right, and set the first row and column of Q to * those of the unit matrix * DO 50 J = N, 2, -1 A( 1, J ) = ZERO DO 40 I = J + 1, N A( I, J ) = A( I, J-1 ) 40 CONTINUE 50 CONTINUE A( 1, 1 ) = ONE DO 60 I = 2, N A( I, 1 ) = ZERO 60 CONTINUE IF( N.GT.1 ) THEN * * Generate Q(2:n,2:n) * CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, $ LWORK, IINFO ) END IF END IF WORK( 1 ) = LWKOPT RETURN * * End of DORGTR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsteqr.f0000644000000000000000000000012714061636515015332 xustar0029 mtime=1623670093.17210411 29 atime=1623670093.17210411 29 ctime=1623670093.17210411 elk-7.2.42/src/LAPACK/dsteqr.f0000644002504400250440000003627614061636515017401 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSTEQR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSTEQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER COMPZ * INTEGER INFO, LDZ, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSTEQR computes all eigenvalues and, optionally, eigenvectors of a *> symmetric tridiagonal matrix using the implicit QL or QR method. *> The eigenvectors of a full or band symmetric matrix can also be found *> if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to *> tridiagonal form. *> \endverbatim * * Arguments: * ========== * *> \param[in] COMPZ *> \verbatim *> COMPZ is CHARACTER*1 *> = 'N': Compute eigenvalues only. *> = 'V': Compute eigenvalues and eigenvectors of the original *> symmetric matrix. On entry, Z must contain the *> orthogonal matrix used to reduce the original matrix *> to tridiagonal form. *> = 'I': Compute eigenvalues and eigenvectors of the *> tridiagonal matrix. Z is initialized to the identity *> matrix. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the diagonal elements of the tridiagonal matrix. *> On exit, if INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> On entry, the (n-1) subdiagonal elements of the tridiagonal *> matrix. *> On exit, E has been destroyed. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (LDZ, N) *> On entry, if COMPZ = 'V', then Z contains the orthogonal *> matrix used in the reduction to tridiagonal form. *> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the *> orthonormal eigenvectors of the original symmetric matrix, *> and if COMPZ = 'I', Z contains the orthonormal eigenvectors *> of the symmetric tridiagonal matrix. *> If COMPZ = 'N', then Z is not referenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> eigenvectors are desired, then LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) *> If COMPZ = 'N', then WORK is not referenced. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: the algorithm has failed to find all the eigenvalues in *> a total of 30*N iterations; if INFO = i, then i *> elements of E have not converged to zero; on exit, D *> and E contain the elements of a symmetric tridiagonal *> matrix which is orthogonally similar to the original *> matrix. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER COMPZ INTEGER INFO, LDZ, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO, THREE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ THREE = 3.0D0 ) INTEGER MAXIT PARAMETER ( MAXIT = 30 ) * .. * .. Local Scalars .. INTEGER I, ICOMPZ, II, ISCALE, J, JTOT, K, L, L1, LEND, $ LENDM1, LENDP1, LENDSV, LM1, LSV, M, MM, MM1, $ NM1, NMAXIT DOUBLE PRECISION ANORM, B, C, EPS, EPS2, F, G, P, R, RT1, RT2, $ S, SAFMAX, SAFMIN, SSFMAX, SSFMIN, TST * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANST, DLAPY2 EXTERNAL LSAME, DLAMCH, DLANST, DLAPY2 * .. * .. External Subroutines .. EXTERNAL DLAE2, DLAEV2, DLARTG, DLASCL, DLASET, DLASR, $ DLASRT, DSWAP, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SIGN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( LSAME( COMPZ, 'N' ) ) THEN ICOMPZ = 0 ELSE IF( LSAME( COMPZ, 'V' ) ) THEN ICOMPZ = 1 ELSE IF( LSAME( COMPZ, 'I' ) ) THEN ICOMPZ = 2 ELSE ICOMPZ = -1 END IF IF( ICOMPZ.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, $ N ) ) ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSTEQR', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( N.EQ.1 ) THEN IF( ICOMPZ.EQ.2 ) $ Z( 1, 1 ) = ONE RETURN END IF * * Determine the unit roundoff and over/underflow thresholds. * EPS = DLAMCH( 'E' ) EPS2 = EPS**2 SAFMIN = DLAMCH( 'S' ) SAFMAX = ONE / SAFMIN SSFMAX = SQRT( SAFMAX ) / THREE SSFMIN = SQRT( SAFMIN ) / EPS2 * * Compute the eigenvalues and eigenvectors of the tridiagonal * matrix. * IF( ICOMPZ.EQ.2 ) $ CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ ) * NMAXIT = N*MAXIT JTOT = 0 * * Determine where the matrix splits and choose QL or QR iteration * for each block, according to whether top or bottom diagonal * element is smaller. * L1 = 1 NM1 = N - 1 * 10 CONTINUE IF( L1.GT.N ) $ GO TO 160 IF( L1.GT.1 ) $ E( L1-1 ) = ZERO IF( L1.LE.NM1 ) THEN DO 20 M = L1, NM1 TST = ABS( E( M ) ) IF( TST.EQ.ZERO ) $ GO TO 30 IF( TST.LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+ $ 1 ) ) ) )*EPS ) THEN E( M ) = ZERO GO TO 30 END IF 20 CONTINUE END IF M = N * 30 CONTINUE L = L1 LSV = L LEND = M LENDSV = LEND L1 = M + 1 IF( LEND.EQ.L ) $ GO TO 10 * * Scale submatrix in rows and columns L to LEND * ANORM = DLANST( 'M', LEND-L+1, D( L ), E( L ) ) ISCALE = 0 IF( ANORM.EQ.ZERO ) $ GO TO 10 IF( ANORM.GT.SSFMAX ) THEN ISCALE = 1 CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N, $ INFO ) CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N, $ INFO ) ELSE IF( ANORM.LT.SSFMIN ) THEN ISCALE = 2 CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N, $ INFO ) CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N, $ INFO ) END IF * * Choose between QL and QR iteration * IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN LEND = LSV L = LENDSV END IF * IF( LEND.GT.L ) THEN * * QL Iteration * * Look for small subdiagonal element. * 40 CONTINUE IF( L.NE.LEND ) THEN LENDM1 = LEND - 1 DO 50 M = L, LENDM1 TST = ABS( E( M ) )**2 IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M+1 ) )+ $ SAFMIN )GO TO 60 50 CONTINUE END IF * M = LEND * 60 CONTINUE IF( M.LT.LEND ) $ E( M ) = ZERO P = D( L ) IF( M.EQ.L ) $ GO TO 80 * * If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 * to compute its eigensystem. * IF( M.EQ.L+1 ) THEN IF( ICOMPZ.GT.0 ) THEN CALL DLAEV2( D( L ), E( L ), D( L+1 ), RT1, RT2, C, S ) WORK( L ) = C WORK( N-1+L ) = S CALL DLASR( 'R', 'V', 'B', N, 2, WORK( L ), $ WORK( N-1+L ), Z( 1, L ), LDZ ) ELSE CALL DLAE2( D( L ), E( L ), D( L+1 ), RT1, RT2 ) END IF D( L ) = RT1 D( L+1 ) = RT2 E( L ) = ZERO L = L + 2 IF( L.LE.LEND ) $ GO TO 40 GO TO 140 END IF * IF( JTOT.EQ.NMAXIT ) $ GO TO 140 JTOT = JTOT + 1 * * Form shift. * G = ( D( L+1 )-P ) / ( TWO*E( L ) ) R = DLAPY2( G, ONE ) G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) ) * S = ONE C = ONE P = ZERO * * Inner loop * MM1 = M - 1 DO 70 I = MM1, L, -1 F = S*E( I ) B = C*E( I ) CALL DLARTG( G, F, C, S, R ) IF( I.NE.M-1 ) $ E( I+1 ) = R G = D( I+1 ) - P R = ( D( I )-G )*S + TWO*C*B P = S*R D( I+1 ) = G + P G = C*R - B * * If eigenvectors are desired, then save rotations. * IF( ICOMPZ.GT.0 ) THEN WORK( I ) = C WORK( N-1+I ) = -S END IF * 70 CONTINUE * * If eigenvectors are desired, then apply saved rotations. * IF( ICOMPZ.GT.0 ) THEN MM = M - L + 1 CALL DLASR( 'R', 'V', 'B', N, MM, WORK( L ), WORK( N-1+L ), $ Z( 1, L ), LDZ ) END IF * D( L ) = D( L ) - P E( L ) = G GO TO 40 * * Eigenvalue found. * 80 CONTINUE D( L ) = P * L = L + 1 IF( L.LE.LEND ) $ GO TO 40 GO TO 140 * ELSE * * QR Iteration * * Look for small superdiagonal element. * 90 CONTINUE IF( L.NE.LEND ) THEN LENDP1 = LEND + 1 DO 100 M = L, LENDP1, -1 TST = ABS( E( M-1 ) )**2 IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M-1 ) )+ $ SAFMIN )GO TO 110 100 CONTINUE END IF * M = LEND * 110 CONTINUE IF( M.GT.LEND ) $ E( M-1 ) = ZERO P = D( L ) IF( M.EQ.L ) $ GO TO 130 * * If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 * to compute its eigensystem. * IF( M.EQ.L-1 ) THEN IF( ICOMPZ.GT.0 ) THEN CALL DLAEV2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2, C, S ) WORK( M ) = C WORK( N-1+M ) = S CALL DLASR( 'R', 'V', 'F', N, 2, WORK( M ), $ WORK( N-1+M ), Z( 1, L-1 ), LDZ ) ELSE CALL DLAE2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2 ) END IF D( L-1 ) = RT1 D( L ) = RT2 E( L-1 ) = ZERO L = L - 2 IF( L.GE.LEND ) $ GO TO 90 GO TO 140 END IF * IF( JTOT.EQ.NMAXIT ) $ GO TO 140 JTOT = JTOT + 1 * * Form shift. * G = ( D( L-1 )-P ) / ( TWO*E( L-1 ) ) R = DLAPY2( G, ONE ) G = D( M ) - P + ( E( L-1 ) / ( G+SIGN( R, G ) ) ) * S = ONE C = ONE P = ZERO * * Inner loop * LM1 = L - 1 DO 120 I = M, LM1 F = S*E( I ) B = C*E( I ) CALL DLARTG( G, F, C, S, R ) IF( I.NE.M ) $ E( I-1 ) = R G = D( I ) - P R = ( D( I+1 )-G )*S + TWO*C*B P = S*R D( I ) = G + P G = C*R - B * * If eigenvectors are desired, then save rotations. * IF( ICOMPZ.GT.0 ) THEN WORK( I ) = C WORK( N-1+I ) = S END IF * 120 CONTINUE * * If eigenvectors are desired, then apply saved rotations. * IF( ICOMPZ.GT.0 ) THEN MM = L - M + 1 CALL DLASR( 'R', 'V', 'F', N, MM, WORK( M ), WORK( N-1+M ), $ Z( 1, M ), LDZ ) END IF * D( L ) = D( L ) - P E( LM1 ) = G GO TO 90 * * Eigenvalue found. * 130 CONTINUE D( L ) = P * L = L - 1 IF( L.GE.LEND ) $ GO TO 90 GO TO 140 * END IF * * Undo scaling if necessary * 140 CONTINUE IF( ISCALE.EQ.1 ) THEN CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1, $ D( LSV ), N, INFO ) CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV, 1, E( LSV ), $ N, INFO ) ELSE IF( ISCALE.EQ.2 ) THEN CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1, $ D( LSV ), N, INFO ) CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV, 1, E( LSV ), $ N, INFO ) END IF * * Check for no convergence to an eigenvalue after a total * of N*MAXIT iterations. * IF( JTOT.LT.NMAXIT ) $ GO TO 10 DO 150 I = 1, N - 1 IF( E( I ).NE.ZERO ) $ INFO = INFO + 1 150 CONTINUE GO TO 190 * * Order eigenvalues and eigenvectors. * 160 CONTINUE IF( ICOMPZ.EQ.0 ) THEN * * Use Quick Sort * CALL DLASRT( 'I', N, D, INFO ) * ELSE * * Use Selection Sort to minimize swaps of eigenvectors * DO 180 II = 2, N I = II - 1 K = I P = D( I ) DO 170 J = II, N IF( D( J ).LT.P ) THEN K = J P = D( J ) END IF 170 CONTINUE IF( K.NE.I ) THEN D( K ) = D( I ) D( I ) = P CALL DSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) END IF 180 CONTINUE END IF * 190 CONTINUE RETURN * * End of DSTEQR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dpotrf.f0000644000000000000000000000013214061636515015322 xustar0030 mtime=1623670093.174104108 30 atime=1623670093.174104108 30 ctime=1623670093.174104108 elk-7.2.42/src/LAPACK/dpotrf.f0000644002504400250440000001604614061636515017366 0ustar00dewhurstdewhurst00000000000000*> \brief \b DPOTRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DPOTRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DPOTRF computes the Cholesky factorization of a real symmetric *> positive definite matrix A. *> *> The factorization has the form *> A = U**T * U, if UPLO = 'U', or *> A = L * L**T, if UPLO = 'L', *> where U is an upper triangular matrix and L is lower triangular. *> *> This is the block version of the algorithm, calling Level 3 BLAS. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doublePOcomputational * * ===================================================================== SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, JB, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DGEMM, DPOTRF2, DSYRK, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DPOTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'DPOTRF', UPLO, N, -1, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code. * CALL DPOTRF2( UPLO, N, A, LDA, INFO ) ELSE * * Use blocked code. * IF( UPPER ) THEN * * Compute the Cholesky factorization A = U**T*U. * DO 10 J = 1, N, NB * * Update and factorize the current diagonal block and test * for non-positive-definiteness. * JB = MIN( NB, N-J+1 ) CALL DSYRK( 'Upper', 'Transpose', JB, J-1, -ONE, $ A( 1, J ), LDA, ONE, A( J, J ), LDA ) CALL DPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) $ GO TO 30 IF( J+JB.LE.N ) THEN * * Compute the current block row. * CALL DGEMM( 'Transpose', 'No transpose', JB, N-J-JB+1, $ J-1, -ONE, A( 1, J ), LDA, A( 1, J+JB ), $ LDA, ONE, A( J, J+JB ), LDA ) CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', $ JB, N-J-JB+1, ONE, A( J, J ), LDA, $ A( J, J+JB ), LDA ) END IF 10 CONTINUE * ELSE * * Compute the Cholesky factorization A = L*L**T. * DO 20 J = 1, N, NB * * Update and factorize the current diagonal block and test * for non-positive-definiteness. * JB = MIN( NB, N-J+1 ) CALL DSYRK( 'Lower', 'No transpose', JB, J-1, -ONE, $ A( J, 1 ), LDA, ONE, A( J, J ), LDA ) CALL DPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) $ GO TO 30 IF( J+JB.LE.N ) THEN * * Compute the current block column. * CALL DGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, $ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), $ LDA, ONE, A( J+JB, J ), LDA ) CALL DTRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', $ N-J-JB+1, JB, ONE, A( J, J ), LDA, $ A( J+JB, J ), LDA ) END IF 20 CONTINUE END IF END IF GO TO 40 * 30 CONTINUE INFO = INFO + J - 1 * 40 CONTINUE RETURN * * End of DPOTRF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsygst.f0000644000000000000000000000013214061636515015341 xustar0030 mtime=1623670093.176104106 30 atime=1623670093.176104106 30 ctime=1623670093.176104106 elk-7.2.42/src/LAPACK/dsygst.f0000644002504400250440000002536014061636515017404 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYGST * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYGST + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYGST reduces a real symmetric-definite generalized eigenproblem *> to standard form. *> *> If ITYPE = 1, the problem is A*x = lambda*B*x, *> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) *> *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or *> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L. *> *> B must have been previously factorized as U**T*U or L*L**T by DPOTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); *> = 2 or 3: compute U*A*U**T or L**T*A*L. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored and B is factored as *> U**T*U; *> = 'L': Lower triangle of A is stored and B is factored as *> L*L**T. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,N) *> The triangular factor from the Cholesky factorization of B, *> as returned by DPOTRF. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleSYcomputational * * ===================================================================== SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, HALF PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER K, KB, NB * .. * .. External Subroutines .. EXTERNAL DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYGST', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 ) * IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) ELSE * * Use blocked code * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**T)*A*inv(U) * DO 10 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the upper triangle of A(k:n,k:n) * CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, $ B( K, K ), LDB, INFO ) IF( K+KB.LE.N ) THEN CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit', $ KB, N-K-KB+1, ONE, B( K, K ), LDB, $ A( K, K+KB ), LDA ) CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, $ A( K, K+KB ), LDA ) CALL DSYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE, $ A( K, K+KB ), LDA, B( K, K+KB ), LDB, $ ONE, A( K+KB, K+KB ), LDA ) CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE, $ A( K, K+KB ), LDA ) CALL DTRSM( 'Right', UPLO, 'No transpose', $ 'Non-unit', KB, N-K-KB+1, ONE, $ B( K+KB, K+KB ), LDB, A( K, K+KB ), $ LDA ) END IF 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**T) * DO 20 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the lower triangle of A(k:n,k:n) * CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, $ B( K, K ), LDB, INFO ) IF( K+KB.LE.N ) THEN CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit', $ N-K-KB+1, KB, ONE, B( K, K ), LDB, $ A( K+KB, K ), LDA ) CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, $ A( K+KB, K ), LDA ) CALL DSYR2K( UPLO, 'No transpose', N-K-KB+1, KB, $ -ONE, A( K+KB, K ), LDA, B( K+KB, K ), $ LDB, ONE, A( K+KB, K+KB ), LDA ) CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE, $ A( K+KB, K ), LDA ) CALL DTRSM( 'Left', UPLO, 'No transpose', $ 'Non-unit', N-K-KB+1, KB, ONE, $ B( K+KB, K+KB ), LDB, A( K+KB, K ), $ LDA ) END IF 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**T * DO 30 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the upper triangle of A(1:k+kb-1,1:k+kb-1) * CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit', $ K-1, KB, ONE, B, LDB, A( 1, K ), LDA ) CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE, $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, $ LDA ) CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA ) CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit', $ K-1, KB, ONE, B( K, K ), LDB, A( 1, K ), $ LDA ) CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, $ B( K, K ), LDB, INFO ) 30 CONTINUE ELSE * * Compute L**T*A*L * DO 40 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the lower triangle of A(1:k+kb-1,1:k+kb-1) * CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit', $ KB, K-1, ONE, B, LDB, A( K, 1 ), LDA ) CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE, $ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A, $ LDA ) CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA ) CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB, $ K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA ) CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA, $ B( K, K ), LDB, INFO ) 40 CONTINUE END IF END IF END IF RETURN * * End of DSYGST * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsyevx.f0000644000000000000000000000013214061636515015346 xustar0030 mtime=1623670093.178104104 30 atime=1623670093.178104104 30 ctime=1623670093.178104104 elk-7.2.42/src/LAPACK/dsyevx.f0000644002504400250440000004261614061636515017414 0ustar00dewhurstdewhurst00000000000000*> \brief DSYEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYEVX + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, * ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, * IFAIL, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, RANGE, UPLO * INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N * DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER IFAIL( * ), IWORK( * ) * DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYEVX computes selected eigenvalues and, optionally, eigenvectors *> of a real symmetric matrix A. Eigenvalues and eigenvectors can be *> selected by specifying either a range of values or a range of indices *> for the desired eigenvalues. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] RANGE *> \verbatim *> RANGE is CHARACTER*1 *> = 'A': all eigenvalues will be found. *> = 'V': all eigenvalues in the half-open interval (VL,VU] *> will be found. *> = 'I': the IL-th through IU-th eigenvalues will be found. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA, N) *> On entry, the symmetric matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> On exit, the lower triangle (if UPLO='L') or the upper *> triangle (if UPLO='U') of A, including the diagonal, is *> destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] VL *> \verbatim *> VL is DOUBLE PRECISION *> If RANGE='V', the lower bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION *> If RANGE='V', the upper bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] IL *> \verbatim *> IL is INTEGER *> If RANGE='I', the index of the *> smallest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] IU *> \verbatim *> IU is INTEGER *> If RANGE='I', the index of the *> largest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] ABSTOL *> \verbatim *> ABSTOL is DOUBLE PRECISION *> The absolute error tolerance for the eigenvalues. *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to *> *> ABSTOL + EPS * max( |a|,|b| ) , *> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. *> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). *> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. *> \endverbatim *> *> \param[out] M *> \verbatim *> M is INTEGER *> The total number of eigenvalues found. 0 <= M <= N. *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> On normal exit, the first M elements contain the selected *> eigenvalues in ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M)) *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z *> contain the orthonormal eigenvectors of the matrix A *> corresponding to the selected eigenvalues, with the i-th *> column of Z holding the eigenvector associated with W(i). *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. *> If JOBZ = 'N', then Z is not referenced. *> Note: the user must ensure that at least max(1,M) columns are *> supplied in the array Z; if RANGE = 'V', the exact value of M *> is not known in advance and an upper bound must be used. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> JOBZ = 'V', LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= 1, when N <= 1; *> otherwise 8*N. *> For optimal efficiency, LWORK >= (NB+3)*N, *> where NB is the max of the blocksize for DSYTRD and DORMTR *> returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (5*N) *> \endverbatim *> *> \param[out] IFAIL *> \verbatim *> IFAIL is INTEGER array, dimension (N) *> If JOBZ = 'V', then if INFO = 0, the first M elements of *> IFAIL are zero. If INFO > 0, then IFAIL contains the *> indices of the eigenvectors that failed to converge. *> If JOBZ = 'N', then IFAIL is not referenced. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, then i eigenvectors failed to converge. *> Their indices are stored in array IFAIL. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup doubleSYeigen * * ===================================================================== SUBROUTINE DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, $ ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, $ IFAIL, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, RANGE, UPLO INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER IFAIL( * ), IWORK( * ) DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG, $ WANTZ CHARACTER ORDER INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL, $ INDISP, INDIWO, INDTAU, INDWKN, INDWRK, ISCALE, $ ITMP1, J, JJ, LLWORK, LLWRKN, LWKMIN, $ LWKOPT, NB, NSPLIT DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, $ SIGMA, SMLNUM, TMP1, VLL, VUU * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLANSY EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY * .. * .. External Subroutines .. EXTERNAL DCOPY, DLACPY, DORGTR, DORMTR, DSCAL, DSTEBZ, $ DSTEIN, DSTEQR, DSTERF, DSWAP, DSYTRD, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * LOWER = LSAME( UPLO, 'L' ) WANTZ = LSAME( JOBZ, 'V' ) ALLEIG = LSAME( RANGE, 'A' ) VALEIG = LSAME( RANGE, 'V' ) INDEIG = LSAME( RANGE, 'I' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN INFO = -2 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( VALEIG ) THEN IF( N.GT.0 .AND. VU.LE.VL ) $ INFO = -8 ELSE IF( INDEIG ) THEN IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN INFO = -9 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN INFO = -10 END IF END IF END IF IF( INFO.EQ.0 ) THEN IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -15 END IF END IF * IF( INFO.EQ.0 ) THEN IF( N.LE.1 ) THEN LWKMIN = 1 WORK( 1 ) = LWKMIN ELSE LWKMIN = 8*N NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) NB = MAX( NB, ILAENV( 1, 'DORMTR', UPLO, N, -1, -1, -1 ) ) LWKOPT = MAX( LWKMIN, ( NB + 3 )*N ) WORK( 1 ) = LWKOPT END IF * IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) $ INFO = -17 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYEVX', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * M = 0 IF( N.EQ.0 ) THEN RETURN END IF * IF( N.EQ.1 ) THEN IF( ALLEIG .OR. INDEIG ) THEN M = 1 W( 1 ) = A( 1, 1 ) ELSE IF( VL.LT.A( 1, 1 ) .AND. VU.GE.A( 1, 1 ) ) THEN M = 1 W( 1 ) = A( 1, 1 ) END IF END IF IF( WANTZ ) $ Z( 1, 1 ) = ONE RETURN END IF * * Get machine constants. * SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) * * Scale matrix to allowable range, if necessary. * ISCALE = 0 ABSTLL = ABSTOL IF( VALEIG ) THEN VLL = VL VUU = VU END IF ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) THEN IF( LOWER ) THEN DO 10 J = 1, N CALL DSCAL( N-J+1, SIGMA, A( J, J ), 1 ) 10 CONTINUE ELSE DO 20 J = 1, N CALL DSCAL( J, SIGMA, A( 1, J ), 1 ) 20 CONTINUE END IF IF( ABSTOL.GT.0 ) $ ABSTLL = ABSTOL*SIGMA IF( VALEIG ) THEN VLL = VL*SIGMA VUU = VU*SIGMA END IF END IF * * Call DSYTRD to reduce symmetric matrix to tridiagonal form. * INDTAU = 1 INDE = INDTAU + N INDD = INDE + N INDWRK = INDD + N LLWORK = LWORK - INDWRK + 1 CALL DSYTRD( UPLO, N, A, LDA, WORK( INDD ), WORK( INDE ), $ WORK( INDTAU ), WORK( INDWRK ), LLWORK, IINFO ) * * If all eigenvalues are desired and ABSTOL is less than or equal to * zero, then call DSTERF or DORGTR and SSTEQR. If this fails for * some eigenvalue, then try DSTEBZ. * TEST = .FALSE. IF( INDEIG ) THEN IF( IL.EQ.1 .AND. IU.EQ.N ) THEN TEST = .TRUE. END IF END IF IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN CALL DCOPY( N, WORK( INDD ), 1, W, 1 ) INDEE = INDWRK + 2*N IF( .NOT.WANTZ ) THEN CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 ) CALL DSTERF( N, W, WORK( INDEE ), INFO ) ELSE CALL DLACPY( 'A', N, N, A, LDA, Z, LDZ ) CALL DORGTR( UPLO, N, Z, LDZ, WORK( INDTAU ), $ WORK( INDWRK ), LLWORK, IINFO ) CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 ) CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ, $ WORK( INDWRK ), INFO ) IF( INFO.EQ.0 ) THEN DO 30 I = 1, N IFAIL( I ) = 0 30 CONTINUE END IF END IF IF( INFO.EQ.0 ) THEN M = N GO TO 40 END IF INFO = 0 END IF * * Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN. * IF( WANTZ ) THEN ORDER = 'B' ELSE ORDER = 'E' END IF INDIBL = 1 INDISP = INDIBL + N INDIWO = INDISP + N CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W, $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ), $ IWORK( INDIWO ), INFO ) * IF( WANTZ ) THEN CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W, $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, $ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO ) * * Apply orthogonal matrix used in reduction to tridiagonal * form to eigenvectors returned by DSTEIN. * INDWKN = INDE LLWRKN = LWORK - INDWKN + 1 CALL DORMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z, $ LDZ, WORK( INDWKN ), LLWRKN, IINFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * 40 CONTINUE IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = M ELSE IMAX = INFO - 1 END IF CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * * If eigenvalues are not in order, then sort them, along with * eigenvectors. * IF( WANTZ ) THEN DO 60 J = 1, M - 1 I = 0 TMP1 = W( J ) DO 50 JJ = J + 1, M IF( W( JJ ).LT.TMP1 ) THEN I = JJ TMP1 = W( JJ ) END IF 50 CONTINUE * IF( I.NE.0 ) THEN ITMP1 = IWORK( INDIBL+I-1 ) W( I ) = W( J ) IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 ) W( J ) = TMP1 IWORK( INDIBL+J-1 ) = ITMP1 CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) IF( INFO.NE.0 ) THEN ITMP1 = IFAIL( I ) IFAIL( I ) = IFAIL( J ) IFAIL( J ) = ITMP1 END IF END IF 60 CONTINUE END IF * * Set WORK(1) to optimal workspace size. * WORK( 1 ) = LWKOPT * RETURN * * End of DSYEVX * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/ieeeck.f0000644000000000000000000000013214061636515015251 xustar0030 mtime=1623670093.180104102 30 atime=1623670093.180104102 30 ctime=1623670093.180104102 elk-7.2.42/src/LAPACK/ieeeck.f0000644002504400250440000001072414061636515017312 0ustar00dewhurstdewhurst00000000000000*> \brief \b IEEECK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download IEEECK + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE ) * * .. Scalar Arguments .. * INTEGER ISPEC * REAL ONE, ZERO * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> IEEECK is called from the ILAENV to verify that Infinity and *> possibly NaN arithmetic is safe (i.e. will not trap). *> \endverbatim * * Arguments: * ========== * *> \param[in] ISPEC *> \verbatim *> ISPEC is INTEGER *> Specifies whether to test just for inifinity arithmetic *> or whether to test for infinity and NaN arithmetic. *> = 0: Verify infinity arithmetic only. *> = 1: Verify infinity and NaN arithmetic. *> \endverbatim *> *> \param[in] ZERO *> \verbatim *> ZERO is REAL *> Must contain the value 0.0 *> This is passed to prevent the compiler from optimizing *> away this code. *> \endverbatim *> *> \param[in] ONE *> \verbatim *> ONE is REAL *> Must contain the value 1.0 *> This is passed to prevent the compiler from optimizing *> away this code. *> *> RETURN VALUE: INTEGER *> = 0: Arithmetic failed to produce the correct answers *> = 1: Arithmetic produced the correct answers *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER ISPEC REAL ONE, ZERO * .. * * ===================================================================== * * .. Local Scalars .. REAL NAN1, NAN2, NAN3, NAN4, NAN5, NAN6, NEGINF, $ NEGZRO, NEWZRO, POSINF * .. * .. Executable Statements .. IEEECK = 1 * POSINF = ONE / ZERO IF( POSINF.LE.ONE ) THEN IEEECK = 0 RETURN END IF * NEGINF = -ONE / ZERO IF( NEGINF.GE.ZERO ) THEN IEEECK = 0 RETURN END IF * NEGZRO = ONE / ( NEGINF+ONE ) IF( NEGZRO.NE.ZERO ) THEN IEEECK = 0 RETURN END IF * NEGINF = ONE / NEGZRO IF( NEGINF.GE.ZERO ) THEN IEEECK = 0 RETURN END IF * NEWZRO = NEGZRO + ZERO IF( NEWZRO.NE.ZERO ) THEN IEEECK = 0 RETURN END IF * POSINF = ONE / NEWZRO IF( POSINF.LE.ONE ) THEN IEEECK = 0 RETURN END IF * NEGINF = NEGINF*POSINF IF( NEGINF.GE.ZERO ) THEN IEEECK = 0 RETURN END IF * POSINF = POSINF*POSINF IF( POSINF.LE.ONE ) THEN IEEECK = 0 RETURN END IF * * * * * Return if we were only asked to check infinity arithmetic * IF( ISPEC.EQ.0 ) $ RETURN * NAN1 = POSINF + NEGINF * NAN2 = POSINF / NEGINF * NAN3 = POSINF / POSINF * NAN4 = POSINF*ZERO * NAN5 = NEGINF*NEGZRO * NAN6 = NAN5*ZERO * IF( NAN1.EQ.NAN1 ) THEN IEEECK = 0 RETURN END IF * IF( NAN2.EQ.NAN2 ) THEN IEEECK = 0 RETURN END IF * IF( NAN3.EQ.NAN3 ) THEN IEEECK = 0 RETURN END IF * IF( NAN4.EQ.NAN4 ) THEN IEEECK = 0 RETURN END IF * IF( NAN5.EQ.NAN5 ) THEN IEEECK = 0 RETURN END IF * IF( NAN6.EQ.NAN6 ) THEN IEEECK = 0 RETURN END IF * RETURN END elk-7.2.42/src/LAPACK/PaxHeaders.21776/iparmq.f0000644000000000000000000000012614061636515015320 xustar0028 mtime=1623670093.1821041 30 atime=1623670093.181104101 28 ctime=1623670093.1821041 elk-7.2.42/src/LAPACK/iparmq.f0000644002504400250440000003342614061636515017362 0ustar00dewhurstdewhurst00000000000000*> \brief \b IPARMQ * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download IPARMQ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) * * .. Scalar Arguments .. * INTEGER IHI, ILO, ISPEC, LWORK, N * CHARACTER NAME*( * ), OPTS*( * ) * * *> \par Purpose: * ============= *> *> \verbatim *> *> This program sets problem and machine dependent parameters *> useful for xHSEQR and related subroutines for eigenvalue *> problems. It is called whenever *> IPARMQ is called with 12 <= ISPEC <= 16 *> \endverbatim * * Arguments: * ========== * *> \param[in] ISPEC *> \verbatim *> ISPEC is INTEGER *> ISPEC specifies which tunable parameter IPARMQ should *> return. *> *> ISPEC=12: (INMIN) Matrices of order nmin or less *> are sent directly to xLAHQR, the implicit *> double shift QR algorithm. NMIN must be *> at least 11. *> *> ISPEC=13: (INWIN) Size of the deflation window. *> This is best set greater than or equal to *> the number of simultaneous shifts NS. *> Larger matrices benefit from larger deflation *> windows. *> *> ISPEC=14: (INIBL) Determines when to stop nibbling and *> invest in an (expensive) multi-shift QR sweep. *> If the aggressive early deflation subroutine *> finds LD converged eigenvalues from an order *> NW deflation window and LD > (NW*NIBBLE)/100, *> then the next QR sweep is skipped and early *> deflation is applied immediately to the *> remaining active diagonal block. Setting *> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a *> multi-shift QR sweep whenever early deflation *> finds a converged eigenvalue. Setting *> IPARMQ(ISPEC=14) greater than or equal to 100 *> prevents TTQRE from skipping a multi-shift *> QR sweep. *> *> ISPEC=15: (NSHFTS) The number of simultaneous shifts in *> a multi-shift QR iteration. *> *> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the *> following meanings. *> 0: During the multi-shift QR/QZ sweep, *> blocked eigenvalue reordering, blocked *> Hessenberg-triangular reduction, *> reflections and/or rotations are not *> accumulated when updating the *> far-from-diagonal matrix entries. *> 1: During the multi-shift QR/QZ sweep, *> blocked eigenvalue reordering, blocked *> Hessenberg-triangular reduction, *> reflections and/or rotations are *> accumulated, and matrix-matrix *> multiplication is used to update the *> far-from-diagonal matrix entries. *> 2: During the multi-shift QR/QZ sweep, *> blocked eigenvalue reordering, blocked *> Hessenberg-triangular reduction, *> reflections and/or rotations are *> accumulated, and 2-by-2 block structure *> is exploited during matrix-matrix *> multiplies. *> (If xTRMM is slower than xGEMM, then *> IPARMQ(ISPEC=16)=1 may be more efficient than *> IPARMQ(ISPEC=16)=2 despite the greater level of *> arithmetic work implied by the latter choice.) *> \endverbatim *> *> \param[in] NAME *> \verbatim *> NAME is CHARACTER string *> Name of the calling subroutine *> \endverbatim *> *> \param[in] OPTS *> \verbatim *> OPTS is CHARACTER string *> This is a concatenation of the string arguments to *> TTQRE. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> N is the order of the Hessenberg matrix H. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> It is assumed that H is already upper triangular *> in rows and columns 1:ILO-1 and IHI+1:N. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The amount of workspace available. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> Little is known about how best to choose these parameters. *> It is possible to use different values of the parameters *> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. *> *> It is probably best to choose different parameters for *> different matrices and different parameters at different *> times during the iteration, but this has not been *> implemented --- yet. *> *> *> The best choices of most of the parameters depend *> in an ill-understood way on the relative execution *> rate of xLAQR3 and xLAQR5 and on the nature of each *> particular eigenvalue problem. Experiment may be the *> only practical way to determine which choices are most *> effective. *> *> Following is a list of default values supplied by IPARMQ. *> These defaults may be adjusted in order to attain better *> performance in any particular computational environment. *> *> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. *> Default: 75. (Must be at least 11.) *> *> IPARMQ(ISPEC=13) Recommended deflation window size. *> This depends on ILO, IHI and NS, the *> number of simultaneous shifts returned *> by IPARMQ(ISPEC=15). The default for *> (IHI-ILO+1) <= 500 is NS. The default *> for (IHI-ILO+1) > 500 is 3*NS/2. *> *> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14. *> *> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. *> a multi-shift QR iteration. *> *> If IHI-ILO+1 is ... *> *> greater than ...but less ... the *> or equal to ... than default is *> *> 0 30 NS = 2+ *> 30 60 NS = 4+ *> 60 150 NS = 10 *> 150 590 NS = ** *> 590 3000 NS = 64 *> 3000 6000 NS = 128 *> 6000 infinity NS = 256 *> *> (+) By default matrices of this order are *> passed to the implicit double shift routine *> xLAHQR. See IPARMQ(ISPEC=12) above. These *> values of NS are used only in case of a rare *> xLAHQR failure. *> *> (**) The asterisks (**) indicate an ad-hoc *> function increasing from 10 to 64. *> *> IPARMQ(ISPEC=16) Select structured matrix multiply. *> (See ISPEC=16 above for details.) *> Default: 3. *> \endverbatim *> * ===================================================================== INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER IHI, ILO, ISPEC, LWORK, N CHARACTER NAME*( * ), OPTS*( * ) * * ================================================================ * .. Parameters .. INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22 PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14, $ ISHFTS = 15, IACC22 = 16 ) INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14, $ NIBBLE = 14, KNWSWP = 500 ) REAL TWO PARAMETER ( TWO = 2.0 ) * .. * .. Local Scalars .. INTEGER NH, NS INTEGER I, IC, IZ CHARACTER SUBNAM*6 * .. * .. Intrinsic Functions .. INTRINSIC LOG, MAX, MOD, NINT, REAL * .. * .. Executable Statements .. IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR. $ ( ISPEC.EQ.IACC22 ) ) THEN * * ==== Set the number simultaneous shifts ==== * NH = IHI - ILO + 1 NS = 2 IF( NH.GE.30 ) $ NS = 4 IF( NH.GE.60 ) $ NS = 10 IF( NH.GE.150 ) $ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) ) IF( NH.GE.590 ) $ NS = 64 IF( NH.GE.3000 ) $ NS = 128 IF( NH.GE.6000 ) $ NS = 256 NS = MAX( 2, NS-MOD( NS, 2 ) ) END IF * IF( ISPEC.EQ.INMIN ) THEN * * * ===== Matrices of order smaller than NMIN get sent * . to xLAHQR, the classic double shift algorithm. * . This must be at least 11. ==== * IPARMQ = NMIN * ELSE IF( ISPEC.EQ.INIBL ) THEN * * ==== INIBL: skip a multi-shift qr iteration and * . whenever aggressive early deflation finds * . at least (NIBBLE*(window size)/100) deflations. ==== * IPARMQ = NIBBLE * ELSE IF( ISPEC.EQ.ISHFTS ) THEN * * ==== NSHFTS: The number of simultaneous shifts ===== * IPARMQ = NS * ELSE IF( ISPEC.EQ.INWIN ) THEN * * ==== NW: deflation window size. ==== * IF( NH.LE.KNWSWP ) THEN IPARMQ = NS ELSE IPARMQ = 3*NS / 2 END IF * ELSE IF( ISPEC.EQ.IACC22 ) THEN * * ==== IACC22: Whether to accumulate reflections * . before updating the far-from-diagonal elements * . and whether to use 2-by-2 block structure while * . doing it. A small amount of work could be saved * . by making this choice dependent also upon the * . NH=IHI-ILO+1. * * * Convert NAME to upper case if the first character is lower case. * IPARMQ = 0 SUBNAM = NAME IC = ICHAR( SUBNAM( 1: 1 ) ) IZ = ICHAR( 'Z' ) IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN * * ASCII character set * IF( IC.GE.97 .AND. IC.LE.122 ) THEN SUBNAM( 1: 1 ) = CHAR( IC-32 ) DO I = 2, 6 IC = ICHAR( SUBNAM( I: I ) ) IF( IC.GE.97 .AND. IC.LE.122 ) $ SUBNAM( I: I ) = CHAR( IC-32 ) END DO END IF * ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN * * EBCDIC character set * IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. $ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN SUBNAM( 1: 1 ) = CHAR( IC+64 ) DO I = 2, 6 IC = ICHAR( SUBNAM( I: I ) ) IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. $ ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I: $ I ) = CHAR( IC+64 ) END DO END IF * ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN * * Prime machines: ASCII+128 * IF( IC.GE.225 .AND. IC.LE.250 ) THEN SUBNAM( 1: 1 ) = CHAR( IC-32 ) DO I = 2, 6 IC = ICHAR( SUBNAM( I: I ) ) IF( IC.GE.225 .AND. IC.LE.250 ) $ SUBNAM( I: I ) = CHAR( IC-32 ) END DO END IF END IF * IF( SUBNAM( 2:6 ).EQ.'GGHRD' .OR. $ SUBNAM( 2:6 ).EQ.'GGHD3' ) THEN IPARMQ = 1 IF( NH.GE.K22MIN ) $ IPARMQ = 2 ELSE IF ( SUBNAM( 4:6 ).EQ.'EXC' ) THEN IF( NH.GE.KACMIN ) $ IPARMQ = 1 IF( NH.GE.K22MIN ) $ IPARMQ = 2 ELSE IF ( SUBNAM( 2:6 ).EQ.'HSEQR' .OR. $ SUBNAM( 2:5 ).EQ.'LAQR' ) THEN IF( NS.GE.KACMIN ) $ IPARMQ = 1 IF( NS.GE.K22MIN ) $ IPARMQ = 2 END IF * ELSE * ===== invalid value of ispec ===== IPARMQ = -1 * END IF * * ==== End of IPARMQ ==== * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/ztrevc3.f0000644000000000000000000000013014061636515015422 xustar0030 mtime=1623670093.184104099 28 atime=1623670093.1831041 30 ctime=1623670093.184104099 elk-7.2.42/src/LAPACK/ztrevc3.f0000644002504400250440000005123714061636515017471 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTREVC3 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZTREVC3 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZTREVC3( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, * $ LDVR, MM, M, WORK, LWORK, RWORK, LRWORK, INFO) * * .. Scalar Arguments .. * CHARACTER HOWMNY, SIDE * INTEGER INFO, LDT, LDVL, LDVR, LWORK, M, MM, N * .. * .. Array Arguments .. * LOGICAL SELECT( * ) * DOUBLE PRECISION RWORK( * ) * COMPLEX*16 T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), * $ WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTREVC3 computes some or all of the right and/or left eigenvectors of *> a complex upper triangular matrix T. *> Matrices of this type are produced by the Schur factorization of *> a complex general matrix: A = Q*T*Q**H, as computed by ZHSEQR. *> *> The right eigenvector x and the left eigenvector y of T corresponding *> to an eigenvalue w are defined by: *> *> T*x = w*x, (y**H)*T = w*(y**H) *> *> where y**H denotes the conjugate transpose of the vector y. *> The eigenvalues are not input to this routine, but are read directly *> from the diagonal of T. *> *> This routine returns the matrices X and/or Y of right and left *> eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an *> input matrix. If Q is the unitary factor that reduces a matrix A to *> Schur form T, then Q*X and Q*Y are the matrices of right and left *> eigenvectors of A. *> *> This uses a Level 3 BLAS version of the back transformation. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'R': compute right eigenvectors only; *> = 'L': compute left eigenvectors only; *> = 'B': compute both right and left eigenvectors. *> \endverbatim *> *> \param[in] HOWMNY *> \verbatim *> HOWMNY is CHARACTER*1 *> = 'A': compute all right and/or left eigenvectors; *> = 'B': compute all right and/or left eigenvectors, *> backtransformed using the matrices supplied in *> VR and/or VL; *> = 'S': compute selected right and/or left eigenvectors, *> as indicated by the logical array SELECT. *> \endverbatim *> *> \param[in] SELECT *> \verbatim *> SELECT is LOGICAL array, dimension (N) *> If HOWMNY = 'S', SELECT specifies the eigenvectors to be *> computed. *> The eigenvector corresponding to the j-th eigenvalue is *> computed if SELECT(j) = .TRUE.. *> Not referenced if HOWMNY = 'A' or 'B'. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix T. N >= 0. *> \endverbatim *> *> \param[in,out] T *> \verbatim *> T is COMPLEX*16 array, dimension (LDT,N) *> The upper triangular matrix T. T is modified, but restored *> on exit. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= max(1,N). *> \endverbatim *> *> \param[in,out] VL *> \verbatim *> VL is COMPLEX*16 array, dimension (LDVL,MM) *> On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must *> contain an N-by-N matrix Q (usually the unitary matrix Q of *> Schur vectors returned by ZHSEQR). *> On exit, if SIDE = 'L' or 'B', VL contains: *> if HOWMNY = 'A', the matrix Y of left eigenvectors of T; *> if HOWMNY = 'B', the matrix Q*Y; *> if HOWMNY = 'S', the left eigenvectors of T specified by *> SELECT, stored consecutively in the columns *> of VL, in the same order as their *> eigenvalues. *> Not referenced if SIDE = 'R'. *> \endverbatim *> *> \param[in] LDVL *> \verbatim *> LDVL is INTEGER *> The leading dimension of the array VL. *> LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N. *> \endverbatim *> *> \param[in,out] VR *> \verbatim *> VR is COMPLEX*16 array, dimension (LDVR,MM) *> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must *> contain an N-by-N matrix Q (usually the unitary matrix Q of *> Schur vectors returned by ZHSEQR). *> On exit, if SIDE = 'R' or 'B', VR contains: *> if HOWMNY = 'A', the matrix X of right eigenvectors of T; *> if HOWMNY = 'B', the matrix Q*X; *> if HOWMNY = 'S', the right eigenvectors of T specified by *> SELECT, stored consecutively in the columns *> of VR, in the same order as their *> eigenvalues. *> Not referenced if SIDE = 'L'. *> \endverbatim *> *> \param[in] LDVR *> \verbatim *> LDVR is INTEGER *> The leading dimension of the array VR. *> LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N. *> \endverbatim *> *> \param[in] MM *> \verbatim *> MM is INTEGER *> The number of columns in the arrays VL and/or VR. MM >= M. *> \endverbatim *> *> \param[out] M *> \verbatim *> M is INTEGER *> The number of columns in the arrays VL and/or VR actually *> used to store the eigenvectors. *> If HOWMNY = 'A' or 'B', M is set to N. *> Each selected eigenvector occupies one column. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of array WORK. LWORK >= max(1,2*N). *> For optimum performance, LWORK >= N + 2*N*NB, where NB is *> the optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (LRWORK) *> \endverbatim *> *> \param[in] LRWORK *> \verbatim *> LRWORK is INTEGER *> The dimension of array RWORK. LRWORK >= max(1,N). *> *> If LRWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the RWORK array, returns *> this value as the first entry of the RWORK array, and no error *> message related to LRWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * * @precisions fortran z -> c * *> \ingroup complex16OTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The algorithm used in this program is basically backward (forward) *> substitution, with scaling to make the the code robust against *> possible overflow. *> *> Each eigenvector is normalized so that the element of largest *> magnitude has magnitude 1; here the magnitude of a complex number *> (x,y) is taken to be |x| + |y|. *> \endverbatim *> * ===================================================================== SUBROUTINE ZTREVC3( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, $ LDVR, MM, M, WORK, LWORK, RWORK, LRWORK, INFO) IMPLICIT NONE * * -- LAPACK computational routine (version 3.8.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. CHARACTER HOWMNY, SIDE INTEGER INFO, LDT, LDVL, LDVR, LWORK, LRWORK, M, MM, N * .. * .. Array Arguments .. LOGICAL SELECT( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), $ WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) INTEGER NBMIN, NBMAX PARAMETER ( NBMIN = 8, NBMAX = 128 ) * .. * .. Local Scalars .. LOGICAL ALLV, BOTHV, LEFTV, LQUERY, OVER, RIGHTV, SOMEV INTEGER I, II, IS, J, K, KI, IV, MAXWRK, NB DOUBLE PRECISION OVFL, REMAX, SCALE, SMIN, SMLNUM, ULP, UNFL COMPLEX*16 CDUM * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV, IZAMAX DOUBLE PRECISION DLAMCH, DZASUM EXTERNAL LSAME, ILAENV, IZAMAX, DLAMCH, DZASUM * .. * .. External Subroutines .. EXTERNAL XERBLA, ZCOPY, ZDSCAL, ZGEMV, ZLATRS, $ ZGEMM, DLABAD, ZLASET, ZLACPY * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, CONJG, AIMAG, MAX * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( AIMAG( CDUM ) ) * .. * .. Executable Statements .. * * Decode and test the input parameters * BOTHV = LSAME( SIDE, 'B' ) RIGHTV = LSAME( SIDE, 'R' ) .OR. BOTHV LEFTV = LSAME( SIDE, 'L' ) .OR. BOTHV * ALLV = LSAME( HOWMNY, 'A' ) OVER = LSAME( HOWMNY, 'B' ) SOMEV = LSAME( HOWMNY, 'S' ) * * Set M to the number of columns required to store the selected * eigenvectors. * IF( SOMEV ) THEN M = 0 DO 10 J = 1, N IF( SELECT( J ) ) $ M = M + 1 10 CONTINUE ELSE M = N END IF * INFO = 0 NB = ILAENV( 1, 'ZTREVC', SIDE // HOWMNY, N, -1, -1, -1 ) MAXWRK = N + 2*N*NB WORK(1) = MAXWRK RWORK(1) = N LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 ) IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN INFO = -1 ELSE IF( .NOT.ALLV .AND. .NOT.OVER .AND. .NOT.SOMEV ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDT.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( LDVL.LT.1 .OR. ( LEFTV .AND. LDVL.LT.N ) ) THEN INFO = -8 ELSE IF( LDVR.LT.1 .OR. ( RIGHTV .AND. LDVR.LT.N ) ) THEN INFO = -10 ELSE IF( MM.LT.M ) THEN INFO = -11 ELSE IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN INFO = -14 ELSE IF ( LRWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -16 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZTREVC3', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * * Use blocked version of back-transformation if sufficient workspace. * Zero-out the workspace to avoid potential NaN propagation. * IF( OVER .AND. LWORK .GE. N + 2*N*NBMIN ) THEN NB = (LWORK - N) / (2*N) NB = MIN( NB, NBMAX ) CALL ZLASET( 'F', N, 1+2*NB, CZERO, CZERO, WORK, N ) ELSE NB = 1 END IF * * Set the constants to control overflow. * UNFL = DLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL CALL DLABAD( UNFL, OVFL ) ULP = DLAMCH( 'Precision' ) SMLNUM = UNFL*( N / ULP ) * * Store the diagonal elements of T in working array WORK. * DO 20 I = 1, N WORK( I ) = T( I, I ) 20 CONTINUE * * Compute 1-norm of each column of strictly upper triangular * part of T to control overflow in triangular solver. * RWORK( 1 ) = ZERO DO 30 J = 2, N RWORK( J ) = DZASUM( J-1, T( 1, J ), 1 ) 30 CONTINUE * IF( RIGHTV ) THEN * * ============================================================ * Compute right eigenvectors. * * IV is index of column in current block. * Non-blocked version always uses IV=NB=1; * blocked version starts with IV=NB, goes down to 1. * (Note the "0-th" column is used to store the original diagonal.) IV = NB IS = M DO 80 KI = N, 1, -1 IF( SOMEV ) THEN IF( .NOT.SELECT( KI ) ) $ GO TO 80 END IF SMIN = MAX( ULP*( CABS1( T( KI, KI ) ) ), SMLNUM ) * * -------------------------------------------------------- * Complex right eigenvector * WORK( KI + IV*N ) = CONE * * Form right-hand side. * DO 40 K = 1, KI - 1 WORK( K + IV*N ) = -T( K, KI ) 40 CONTINUE * * Solve upper triangular system: * [ T(1:KI-1,1:KI-1) - T(KI,KI) ]*X = SCALE*WORK. * DO 50 K = 1, KI - 1 T( K, K ) = T( K, K ) - T( KI, KI ) IF( CABS1( T( K, K ) ).LT.SMIN ) $ T( K, K ) = SMIN 50 CONTINUE * IF( KI.GT.1 ) THEN CALL ZLATRS( 'Upper', 'No transpose', 'Non-unit', 'Y', $ KI-1, T, LDT, WORK( 1 + IV*N ), SCALE, $ RWORK, INFO ) WORK( KI + IV*N ) = SCALE END IF * * Copy the vector x or Q*x to VR and normalize. * IF( .NOT.OVER ) THEN * ------------------------------ * no back-transform: copy x to VR and normalize. CALL ZCOPY( KI, WORK( 1 + IV*N ), 1, VR( 1, IS ), 1 ) * II = IZAMAX( KI, VR( 1, IS ), 1 ) REMAX = ONE / CABS1( VR( II, IS ) ) CALL ZDSCAL( KI, REMAX, VR( 1, IS ), 1 ) * DO 60 K = KI + 1, N VR( K, IS ) = CZERO 60 CONTINUE * ELSE IF( NB.EQ.1 ) THEN * ------------------------------ * version 1: back-transform each vector with GEMV, Q*x. IF( KI.GT.1 ) $ CALL ZGEMV( 'N', N, KI-1, CONE, VR, LDVR, $ WORK( 1 + IV*N ), 1, DCMPLX( SCALE ), $ VR( 1, KI ), 1 ) * II = IZAMAX( N, VR( 1, KI ), 1 ) REMAX = ONE / CABS1( VR( II, KI ) ) CALL ZDSCAL( N, REMAX, VR( 1, KI ), 1 ) * ELSE * ------------------------------ * version 2: back-transform block of vectors with GEMM * zero out below vector DO K = KI + 1, N WORK( K + IV*N ) = CZERO END DO * * Columns IV:NB of work are valid vectors. * When the number of vectors stored reaches NB, * or if this was last vector, do the GEMM IF( (IV.EQ.1) .OR. (KI.EQ.1) ) THEN CALL ZGEMM( 'N', 'N', N, NB-IV+1, KI+NB-IV, CONE, $ VR, LDVR, $ WORK( 1 + (IV)*N ), N, $ CZERO, $ WORK( 1 + (NB+IV)*N ), N ) * normalize vectors DO K = IV, NB II = IZAMAX( N, WORK( 1 + (NB+K)*N ), 1 ) REMAX = ONE / CABS1( WORK( II + (NB+K)*N ) ) CALL ZDSCAL( N, REMAX, WORK( 1 + (NB+K)*N ), 1 ) END DO CALL ZLACPY( 'F', N, NB-IV+1, $ WORK( 1 + (NB+IV)*N ), N, $ VR( 1, KI ), LDVR ) IV = NB ELSE IV = IV - 1 END IF END IF * * Restore the original diagonal elements of T. * DO 70 K = 1, KI - 1 T( K, K ) = WORK( K ) 70 CONTINUE * IS = IS - 1 80 CONTINUE END IF * IF( LEFTV ) THEN * * ============================================================ * Compute left eigenvectors. * * IV is index of column in current block. * Non-blocked version always uses IV=1; * blocked version starts with IV=1, goes up to NB. * (Note the "0-th" column is used to store the original diagonal.) IV = 1 IS = 1 DO 130 KI = 1, N * IF( SOMEV ) THEN IF( .NOT.SELECT( KI ) ) $ GO TO 130 END IF SMIN = MAX( ULP*( CABS1( T( KI, KI ) ) ), SMLNUM ) * * -------------------------------------------------------- * Complex left eigenvector * WORK( KI + IV*N ) = CONE * * Form right-hand side. * DO 90 K = KI + 1, N WORK( K + IV*N ) = -CONJG( T( KI, K ) ) 90 CONTINUE * * Solve conjugate-transposed triangular system: * [ T(KI+1:N,KI+1:N) - T(KI,KI) ]**H * X = SCALE*WORK. * DO 100 K = KI + 1, N T( K, K ) = T( K, K ) - T( KI, KI ) IF( CABS1( T( K, K ) ).LT.SMIN ) $ T( K, K ) = SMIN 100 CONTINUE * IF( KI.LT.N ) THEN CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit', $ 'Y', N-KI, T( KI+1, KI+1 ), LDT, $ WORK( KI+1 + IV*N ), SCALE, RWORK, INFO ) WORK( KI + IV*N ) = SCALE END IF * * Copy the vector x or Q*x to VL and normalize. * IF( .NOT.OVER ) THEN * ------------------------------ * no back-transform: copy x to VL and normalize. CALL ZCOPY( N-KI+1, WORK( KI + IV*N ), 1, VL(KI,IS), 1 ) * II = IZAMAX( N-KI+1, VL( KI, IS ), 1 ) + KI - 1 REMAX = ONE / CABS1( VL( II, IS ) ) CALL ZDSCAL( N-KI+1, REMAX, VL( KI, IS ), 1 ) * DO 110 K = 1, KI - 1 VL( K, IS ) = CZERO 110 CONTINUE * ELSE IF( NB.EQ.1 ) THEN * ------------------------------ * version 1: back-transform each vector with GEMV, Q*x. IF( KI.LT.N ) $ CALL ZGEMV( 'N', N, N-KI, CONE, VL( 1, KI+1 ), LDVL, $ WORK( KI+1 + IV*N ), 1, DCMPLX( SCALE ), $ VL( 1, KI ), 1 ) * II = IZAMAX( N, VL( 1, KI ), 1 ) REMAX = ONE / CABS1( VL( II, KI ) ) CALL ZDSCAL( N, REMAX, VL( 1, KI ), 1 ) * ELSE * ------------------------------ * version 2: back-transform block of vectors with GEMM * zero out above vector * could go from KI-NV+1 to KI-1 DO K = 1, KI - 1 WORK( K + IV*N ) = CZERO END DO * * Columns 1:IV of work are valid vectors. * When the number of vectors stored reaches NB, * or if this was last vector, do the GEMM IF( (IV.EQ.NB) .OR. (KI.EQ.N) ) THEN CALL ZGEMM( 'N', 'N', N, IV, N-KI+IV, CONE, $ VL( 1, KI-IV+1 ), LDVL, $ WORK( KI-IV+1 + (1)*N ), N, $ CZERO, $ WORK( 1 + (NB+1)*N ), N ) * normalize vectors DO K = 1, IV II = IZAMAX( N, WORK( 1 + (NB+K)*N ), 1 ) REMAX = ONE / CABS1( WORK( II + (NB+K)*N ) ) CALL ZDSCAL( N, REMAX, WORK( 1 + (NB+K)*N ), 1 ) END DO CALL ZLACPY( 'F', N, IV, $ WORK( 1 + (NB+1)*N ), N, $ VL( 1, KI-IV+1 ), LDVL ) IV = 1 ELSE IV = IV + 1 END IF END IF * * Restore the original diagonal elements of T. * DO 120 K = KI + 1, N T( K, K ) = WORK( K ) 120 CONTINUE * IS = IS + 1 130 CONTINUE END IF * RETURN * * End of ZTREVC3 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhseqr.f0000644000000000000000000000013214061636515015340 xustar0030 mtime=1623670093.186104097 30 atime=1623670093.185104098 30 ctime=1623670093.186104097 elk-7.2.42/src/LAPACK/zhseqr.f0000644002504400250440000004275714061636515017414 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHSEQR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHSEQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N * CHARACTER COMPZ, JOB * .. * .. Array Arguments .. * COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHSEQR computes the eigenvalues of a Hessenberg matrix H *> and, optionally, the matrices T and Z from the Schur decomposition *> H = Z T Z**H, where T is an upper triangular matrix (the *> Schur form), and Z is the unitary matrix of Schur vectors. *> *> Optionally Z may be postmultiplied into an input unitary *> matrix Q so that this routine can give the Schur factorization *> of a matrix A which has been reduced to the Hessenberg form H *> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*T*(QZ)**H. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOB *> \verbatim *> JOB is CHARACTER*1 *> = 'E': compute eigenvalues only; *> = 'S': compute eigenvalues and the Schur form T. *> \endverbatim *> *> \param[in] COMPZ *> \verbatim *> COMPZ is CHARACTER*1 *> = 'N': no Schur vectors are computed; *> = 'I': Z is initialized to the unit matrix and the matrix Z *> of Schur vectors of H is returned; *> = 'V': Z must contain an unitary matrix Q on entry, and *> the product Q*Z is returned. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix H. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> It is assumed that H is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to ZGEBAL, and then passed to ZGEHRD *> when the matrix output by ZGEBAL is reduced to Hessenberg *> form. Otherwise ILO and IHI should be set to 1 and N *> respectively. If N > 0, then 1 <= ILO <= IHI <= N. *> If N = 0, then ILO = 1 and IHI = 0. *> \endverbatim *> *> \param[in,out] H *> \verbatim *> H is COMPLEX*16 array, dimension (LDH,N) *> On entry, the upper Hessenberg matrix H. *> On exit, if INFO = 0 and JOB = 'S', H contains the upper *> triangular matrix T from the Schur decomposition (the *> Schur form). If INFO = 0 and JOB = 'E', the contents of *> H are unspecified on exit. (The output value of H when *> INFO > 0 is given under the description of INFO below.) *> *> Unlike earlier versions of ZHSEQR, this subroutine may *> explicitly H(i,j) = 0 for i > j and j = 1, 2, ... ILO-1 *> or j = IHI+1, IHI+2, ... N. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> The leading dimension of the array H. LDH >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is COMPLEX*16 array, dimension (N) *> The computed eigenvalues. If JOB = 'S', the eigenvalues are *> stored in the same order as on the diagonal of the Schur *> form returned in H, with W(i) = H(i,i). *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ,N) *> If COMPZ = 'N', Z is not referenced. *> If COMPZ = 'I', on entry Z need not be set and on exit, *> if INFO = 0, Z contains the unitary matrix Z of the Schur *> vectors of H. If COMPZ = 'V', on entry Z must contain an *> N-by-N matrix Q, which is assumed to be equal to the unit *> matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, *> if INFO = 0, Z contains Q*Z. *> Normally Q is the unitary matrix generated by ZUNGHR *> after the call to ZGEHRD which formed the Hessenberg matrix *> H. (The output value of Z when INFO > 0 is given under *> the description of INFO below.) *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. if COMPZ = 'I' or *> COMPZ = 'V', then LDZ >= MAX(1,N). Otherwise, LDZ >= 1. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (LWORK) *> On exit, if INFO = 0, WORK(1) returns an estimate of *> the optimal value for LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N) *> is sufficient and delivers very good and sometimes *> optimal performance. However, LWORK as large as 11*N *> may be required for optimal performance. A workspace *> query is recommended to determine the optimal workspace *> size. *> *> If LWORK = -1, then ZHSEQR does a workspace query. *> In this case, ZHSEQR checks the input parameters and *> estimates the optimal workspace size for the given *> values of N, ILO and IHI. The estimate is returned *> in WORK(1). No error message related to LWORK is *> issued by XERBLA. Neither H nor Z are accessed. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal *> value *> > 0: if INFO = i, ZHSEQR failed to compute all of *> the eigenvalues. Elements 1:ilo-1 and i+1:n of W *> contain those eigenvalues which have been *> successfully computed. (Failures are rare.) *> *> If INFO > 0 and JOB = 'E', then on exit, the *> remaining unconverged eigenvalues are the eigen- *> values of the upper Hessenberg matrix rows and *> columns ILO through INFO of the final, output *> value of H. *> *> If INFO > 0 and JOB = 'S', then on exit *> *> (*) (initial value of H)*U = U*(final value of H) *> *> where U is a unitary matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. *> *> If INFO > 0 and COMPZ = 'V', then on exit *> *> (final value of Z) = (initial value of Z)*U *> *> where U is the unitary matrix in (*) (regard- *> less of the value of JOB.) *> *> If INFO > 0 and COMPZ = 'I', then on exit *> (final value of Z) = U *> where U is the unitary matrix in (*) (regard- *> less of the value of JOB.) *> *> If INFO > 0 and COMPZ = 'N', then Z is not *> accessed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * *> \par Contributors: * ================== *> *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA * *> \par Further Details: * ===================== *> *> \verbatim *> *> Default values supplied by *> ILAENV(ISPEC,'ZHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK). *> It is suggested that these defaults be adjusted in order *> to attain best performance in each particular *> computational environment. *> *> ISPEC=12: The ZLAHQR vs ZLAQR0 crossover point. *> Default: 75. (Must be at least 11.) *> *> ISPEC=13: Recommended deflation window size. *> This depends on ILO, IHI and NS. NS is the *> number of simultaneous shifts returned *> by ILAENV(ISPEC=15). (See ISPEC=15 below.) *> The default for (IHI-ILO+1) <= 500 is NS. *> The default for (IHI-ILO+1) > 500 is 3*NS/2. *> *> ISPEC=14: Nibble crossover point. (See IPARMQ for *> details.) Default: 14% of deflation window *> size. *> *> ISPEC=15: Number of simultaneous shifts in a multishift *> QR iteration. *> *> If IHI-ILO+1 is ... *> *> greater than ...but less ... the *> or equal to ... than default is *> *> 1 30 NS = 2(+) *> 30 60 NS = 4(+) *> 60 150 NS = 10(+) *> 150 590 NS = ** *> 590 3000 NS = 64 *> 3000 6000 NS = 128 *> 6000 infinity NS = 256 *> *> (+) By default some or all matrices of this order *> are passed to the implicit double shift routine *> ZLAHQR and this parameter is ignored. See *> ISPEC=12 above and comments in IPARMQ for *> details. *> *> (**) The asterisks (**) indicate an ad-hoc *> function of N increasing from 10 to 64. *> *> ISPEC=16: Select structured matrix multiply. *> If the number of simultaneous shifts (specified *> by ISPEC=15) is less than 14, then the default *> for ISPEC=16 is 0. Otherwise the default for *> ISPEC=16 is 2. *> \endverbatim * *> \par References: * ================ *> *> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR *> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 *> Performance, SIAM Journal of Matrix Analysis, volume 23, pages *> 929--947, 2002. *> \n *> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR *> Algorithm Part II: Aggressive Early Deflation, SIAM Journal *> of Matrix Analysis, volume 23, pages 948--973, 2002. * * ===================================================================== SUBROUTINE ZHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IHI, ILO, INFO, LDH, LDZ, LWORK, N CHARACTER COMPZ, JOB * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. * * ==== Matrices of order NTINY or smaller must be processed by * . ZLAHQR because of insufficient subdiagonal scratch space. * . (This is a hard limit.) ==== INTEGER NTINY PARAMETER ( NTINY = 11 ) * * ==== NL allocates some local workspace to help small matrices * . through a rare ZLAHQR failure. NL > NTINY = 11 is * . required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom- * . mended. (The default value of NMIN is 75.) Using NL = 49 * . allows up to six simultaneous shifts and a 16-by-16 * . deflation window. ==== INTEGER NL PARAMETER ( NL = 49 ) COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), $ ONE = ( 1.0d0, 0.0d0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0d0 ) * .. * .. Local Arrays .. COMPLEX*16 HL( NL, NL ), WORKL( NL ) * .. * .. Local Scalars .. INTEGER KBOT, NMIN LOGICAL INITZ, LQUERY, WANTT, WANTZ * .. * .. External Functions .. INTEGER ILAENV LOGICAL LSAME EXTERNAL ILAENV, LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZCOPY, ZLACPY, ZLAHQR, ZLAQR0, ZLASET * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, MAX, MIN * .. * .. Executable Statements .. * * ==== Decode and check the input parameters. ==== * WANTT = LSAME( JOB, 'S' ) INITZ = LSAME( COMPZ, 'I' ) WANTZ = INITZ .OR. LSAME( COMPZ, 'V' ) WORK( 1 ) = DCMPLX( DBLE( MAX( 1, N ) ), RZERO ) LQUERY = LWORK.EQ.-1 * INFO = 0 IF( .NOT.LSAME( JOB, 'E' ) .AND. .NOT.WANTT ) THEN INFO = -1 ELSE IF( .NOT.LSAME( COMPZ, 'N' ) .AND. .NOT.WANTZ ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN INFO = -5 ELSE IF( LDH.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.MAX( 1, N ) ) ) THEN INFO = -10 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -12 END IF * IF( INFO.NE.0 ) THEN * * ==== Quick return in case of invalid argument. ==== * CALL XERBLA( 'ZHSEQR', -INFO ) RETURN * ELSE IF( N.EQ.0 ) THEN * * ==== Quick return in case N = 0; nothing to do. ==== * RETURN * ELSE IF( LQUERY ) THEN * * ==== Quick return in case of a workspace query ==== * CALL ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILO, IHI, Z, $ LDZ, WORK, LWORK, INFO ) * ==== Ensure reported workspace size is backward-compatible with * . previous LAPACK versions. ==== WORK( 1 ) = DCMPLX( MAX( DBLE( WORK( 1 ) ), DBLE( MAX( 1, $ N ) ) ), RZERO ) RETURN * ELSE * * ==== copy eigenvalues isolated by ZGEBAL ==== * IF( ILO.GT.1 ) $ CALL ZCOPY( ILO-1, H, LDH+1, W, 1 ) IF( IHI.LT.N ) $ CALL ZCOPY( N-IHI, H( IHI+1, IHI+1 ), LDH+1, W( IHI+1 ), 1 ) * * ==== Initialize Z, if requested ==== * IF( INITZ ) $ CALL ZLASET( 'A', N, N, ZERO, ONE, Z, LDZ ) * * ==== Quick return if possible ==== * IF( ILO.EQ.IHI ) THEN W( ILO ) = H( ILO, ILO ) RETURN END IF * * ==== ZLAHQR/ZLAQR0 crossover point ==== * NMIN = ILAENV( 12, 'ZHSEQR', JOB( : 1 ) // COMPZ( : 1 ), N, $ ILO, IHI, LWORK ) NMIN = MAX( NTINY, NMIN ) * * ==== ZLAQR0 for big matrices; ZLAHQR for small ones ==== * IF( N.GT.NMIN ) THEN CALL ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILO, IHI, $ Z, LDZ, WORK, LWORK, INFO ) ELSE * * ==== Small matrix ==== * CALL ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILO, IHI, $ Z, LDZ, INFO ) * IF( INFO.GT.0 ) THEN * * ==== A rare ZLAHQR failure! ZLAQR0 sometimes succeeds * . when ZLAHQR fails. ==== * KBOT = INFO * IF( N.GE.NL ) THEN * * ==== Larger matrices have enough subdiagonal scratch * . space to call ZLAQR0 directly. ==== * CALL ZLAQR0( WANTT, WANTZ, N, ILO, KBOT, H, LDH, W, $ ILO, IHI, Z, LDZ, WORK, LWORK, INFO ) * ELSE * * ==== Tiny matrices don't have enough subdiagonal * . scratch space to benefit from ZLAQR0. Hence, * . tiny matrices must be copied into a larger * . array before calling ZLAQR0. ==== * CALL ZLACPY( 'A', N, N, H, LDH, HL, NL ) HL( N+1, N ) = ZERO CALL ZLASET( 'A', NL, NL-N, ZERO, ZERO, HL( 1, N+1 ), $ NL ) CALL ZLAQR0( WANTT, WANTZ, NL, ILO, KBOT, HL, NL, W, $ ILO, IHI, Z, LDZ, WORKL, NL, INFO ) IF( WANTT .OR. INFO.NE.0 ) $ CALL ZLACPY( 'A', N, N, HL, NL, H, LDH ) END IF END IF END IF * * ==== Clear out the trash, if necessary. ==== * IF( ( WANTT .OR. INFO.NE.0 ) .AND. N.GT.2 ) $ CALL ZLASET( 'L', N-2, N-2, ZERO, ZERO, H( 3, 1 ), LDH ) * * ==== Ensure reported workspace size is backward-compatible with * . previous LAPACK versions. ==== * WORK( 1 ) = DCMPLX( MAX( DBLE( MAX( 1, N ) ), $ DBLE( WORK( 1 ) ) ), RZERO ) END IF * * ==== End of ZHSEQR ==== * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlabad.f0000644000000000000000000000013214061636515015233 xustar0030 mtime=1623670093.188104095 30 atime=1623670093.187104096 30 ctime=1623670093.188104095 elk-7.2.42/src/LAPACK/dlabad.f0000644002504400250440000000601514061636515017272 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLABAD * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLABAD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLABAD( SMALL, LARGE ) * * .. Scalar Arguments .. * DOUBLE PRECISION LARGE, SMALL * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLABAD takes as input the values computed by DLAMCH for underflow and *> overflow, and returns the square root of each of these values if the *> log of LARGE is sufficiently large. This subroutine is intended to *> identify machines with a large exponent range, such as the Crays, and *> redefine the underflow and overflow limits to be the square roots of *> the values computed by DLAMCH. This subroutine is needed because *> DLAMCH does not compensate for poor arithmetic in the upper half of *> the exponent range, as is found on a Cray. *> \endverbatim * * Arguments: * ========== * *> \param[in,out] SMALL *> \verbatim *> SMALL is DOUBLE PRECISION *> On entry, the underflow threshold as computed by DLAMCH. *> On exit, if LOG10(LARGE) is sufficiently large, the square *> root of SMALL, otherwise unchanged. *> \endverbatim *> *> \param[in,out] LARGE *> \verbatim *> LARGE is DOUBLE PRECISION *> On entry, the overflow threshold as computed by DLAMCH. *> On exit, if LOG10(LARGE) is sufficiently large, the square *> root of LARGE, otherwise unchanged. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLABAD( SMALL, LARGE ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION LARGE, SMALL * .. * * ===================================================================== * * .. Intrinsic Functions .. INTRINSIC LOG10, SQRT * .. * .. Executable Statements .. * * If it looks like we're on a Cray, take the square root of * SMALL and LARGE to avoid overflow and underflow problems. * IF( LOG10( LARGE ).GT.2000.D0 ) THEN SMALL = SQRT( SMALL ) LARGE = SQRT( LARGE ) END IF * RETURN * * End of DLABAD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlange.f0000644000000000000000000000013214061636515015304 xustar0030 mtime=1623670093.189104094 30 atime=1623670093.189104094 30 ctime=1623670093.189104094 elk-7.2.42/src/LAPACK/zlange.f0000644002504400250440000001416014061636515017343 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLANGE + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION ZLANGE( NORM, M, N, A, LDA, WORK ) * * .. Scalar Arguments .. * CHARACTER NORM * INTEGER LDA, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION WORK( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLANGE returns the value of the one norm, or the Frobenius norm, or *> the infinity norm, or the element of largest absolute value of a *> complex matrix A. *> \endverbatim *> *> \return ZLANGE *> \verbatim *> *> ZLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm' *> ( *> ( norm1(A), NORM = '1', 'O' or 'o' *> ( *> ( normI(A), NORM = 'I' or 'i' *> ( *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' *> *> where norm1 denotes the one norm of a matrix (maximum column sum), *> normI denotes the infinity norm of a matrix (maximum row sum) and *> normF denotes the Frobenius norm of a matrix (square root of sum of *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] NORM *> \verbatim *> NORM is CHARACTER*1 *> Specifies the value to be returned in ZLANGE as described *> above. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. When M = 0, *> ZLANGE is set to zero. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. When N = 0, *> ZLANGE is set to zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The m by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(M,1). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), *> where LWORK >= M when NORM = 'I'; otherwise, WORK is not *> referenced. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GEauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION ZLANGE( NORM, M, N, A, LDA, WORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * IMPLICIT NONE * .. Scalar Arguments .. CHARACTER NORM INTEGER LDA, M, N * .. * .. Array Arguments .. DOUBLE PRECISION WORK( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION SUM, VALUE, TEMP * .. * .. Local Arrays .. DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZLASSQ, DCOMBSSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, MIN, SQRT * .. * .. Executable Statements .. * IF( MIN( M, N ).EQ.0 ) THEN VALUE = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * VALUE = ZERO DO 20 J = 1, N DO 10 I = 1, M TEMP = ABS( A( I, J ) ) IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP 10 CONTINUE 20 CONTINUE ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN * * Find norm1(A). * VALUE = ZERO DO 40 J = 1, N SUM = ZERO DO 30 I = 1, M SUM = SUM + ABS( A( I, J ) ) 30 CONTINUE IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM 40 CONTINUE ELSE IF( LSAME( NORM, 'I' ) ) THEN * * Find normI(A). * DO 50 I = 1, M WORK( I ) = ZERO 50 CONTINUE DO 70 J = 1, N DO 60 I = 1, M WORK( I ) = WORK( I ) + ABS( A( I, J ) ) 60 CONTINUE 70 CONTINUE VALUE = ZERO DO 80 I = 1, M TEMP = WORK( I ) IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP 80 CONTINUE ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SSQ(1) is scale * SSQ(2) is sum-of-squares * For better accuracy, sum each column separately. * SSQ( 1 ) = ZERO SSQ( 2 ) = ONE DO 90 J = 1, N COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL ZLASSQ( M, A( 1, J ), 1, COLSSQ( 1 ), COLSSQ( 2 ) ) CALL DCOMBSSQ( SSQ, COLSSQ ) 90 CONTINUE VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) END IF * ZLANGE = VALUE RETURN * * End of ZLANGE * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlascl.f0000644000000000000000000000013214061636515015314 xustar0030 mtime=1623670093.191104092 30 atime=1623670093.191104092 30 ctime=1623670093.191104092 elk-7.2.42/src/LAPACK/zlascl.f0000644002504400250440000002343514061636515017360 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLASCL + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER TYPE * INTEGER INFO, KL, KU, LDA, M, N * DOUBLE PRECISION CFROM, CTO * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLASCL multiplies the M by N complex matrix A by the real scalar *> CTO/CFROM. This is done without over/underflow as long as the final *> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that *> A may be full, upper triangular, lower triangular, upper Hessenberg, *> or banded. *> \endverbatim * * Arguments: * ========== * *> \param[in] TYPE *> \verbatim *> TYPE is CHARACTER*1 *> TYPE indices the storage type of the input matrix. *> = 'G': A is a full matrix. *> = 'L': A is a lower triangular matrix. *> = 'U': A is an upper triangular matrix. *> = 'H': A is an upper Hessenberg matrix. *> = 'B': A is a symmetric band matrix with lower bandwidth KL *> and upper bandwidth KU and with the only the lower *> half stored. *> = 'Q': A is a symmetric band matrix with lower bandwidth KL *> and upper bandwidth KU and with the only the upper *> half stored. *> = 'Z': A is a band matrix with lower bandwidth KL and upper *> bandwidth KU. See ZGBTRF for storage details. *> \endverbatim *> *> \param[in] KL *> \verbatim *> KL is INTEGER *> The lower bandwidth of A. Referenced only if TYPE = 'B', *> 'Q' or 'Z'. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is INTEGER *> The upper bandwidth of A. Referenced only if TYPE = 'B', *> 'Q' or 'Z'. *> \endverbatim *> *> \param[in] CFROM *> \verbatim *> CFROM is DOUBLE PRECISION *> \endverbatim *> *> \param[in] CTO *> \verbatim *> CTO is DOUBLE PRECISION *> *> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed *> without over/underflow if the final result CTO*A(I,J)/CFROM *> can be represented without over/underflow. CFROM must be *> nonzero. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The matrix to be multiplied by CTO/CFROM. See TYPE for the *> storage type. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M); *> TYPE = 'B', LDA >= KL+1; *> TYPE = 'Q', LDA >= KU+1; *> TYPE = 'Z', LDA >= 2*KL+KU+1. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> 0 - successful exit *> <0 - if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER TYPE INTEGER INFO, KL, KU, LDA, M, N DOUBLE PRECISION CFROM, CTO * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. LOGICAL DONE INTEGER I, ITYPE, J, K1, K2, K3, K4 DOUBLE PRECISION BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM * .. * .. External Functions .. LOGICAL LSAME, DISNAN DOUBLE PRECISION DLAMCH EXTERNAL LSAME, DLAMCH, DISNAN * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 * IF( LSAME( TYPE, 'G' ) ) THEN ITYPE = 0 ELSE IF( LSAME( TYPE, 'L' ) ) THEN ITYPE = 1 ELSE IF( LSAME( TYPE, 'U' ) ) THEN ITYPE = 2 ELSE IF( LSAME( TYPE, 'H' ) ) THEN ITYPE = 3 ELSE IF( LSAME( TYPE, 'B' ) ) THEN ITYPE = 4 ELSE IF( LSAME( TYPE, 'Q' ) ) THEN ITYPE = 5 ELSE IF( LSAME( TYPE, 'Z' ) ) THEN ITYPE = 6 ELSE ITYPE = -1 END IF * IF( ITYPE.EQ.-1 ) THEN INFO = -1 ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN INFO = -4 ELSE IF( DISNAN(CTO) ) THEN INFO = -5 ELSE IF( M.LT.0 ) THEN INFO = -6 ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR. $ ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN INFO = -7 ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN INFO = -9 ELSE IF( ITYPE.GE.4 ) THEN IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN INFO = -2 ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR. $ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) ) $ THEN INFO = -3 ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR. $ ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR. $ ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN INFO = -9 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLASCL', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. M.EQ.0 ) $ RETURN * * Get machine parameters * SMLNUM = DLAMCH( 'S' ) BIGNUM = ONE / SMLNUM * CFROMC = CFROM CTOC = CTO * 10 CONTINUE CFROM1 = CFROMC*SMLNUM IF( CFROM1.EQ.CFROMC ) THEN ! CFROMC is an inf. Multiply by a correctly signed zero for ! finite CTOC, or a NaN if CTOC is infinite. MUL = CTOC / CFROMC DONE = .TRUE. CTO1 = CTOC ELSE CTO1 = CTOC / BIGNUM IF( CTO1.EQ.CTOC ) THEN ! CTOC is either 0 or an inf. In both cases, CTOC itself ! serves as the correct multiplication factor. MUL = CTOC DONE = .TRUE. CFROMC = ONE ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN MUL = SMLNUM DONE = .FALSE. CFROMC = CFROM1 ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN MUL = BIGNUM DONE = .FALSE. CTOC = CTO1 ELSE MUL = CTOC / CFROMC DONE = .TRUE. END IF END IF * IF( ITYPE.EQ.0 ) THEN * * Full matrix * DO 30 J = 1, N DO 20 I = 1, M A( I, J ) = A( I, J )*MUL 20 CONTINUE 30 CONTINUE * ELSE IF( ITYPE.EQ.1 ) THEN * * Lower triangular matrix * DO 50 J = 1, N DO 40 I = J, M A( I, J ) = A( I, J )*MUL 40 CONTINUE 50 CONTINUE * ELSE IF( ITYPE.EQ.2 ) THEN * * Upper triangular matrix * DO 70 J = 1, N DO 60 I = 1, MIN( J, M ) A( I, J ) = A( I, J )*MUL 60 CONTINUE 70 CONTINUE * ELSE IF( ITYPE.EQ.3 ) THEN * * Upper Hessenberg matrix * DO 90 J = 1, N DO 80 I = 1, MIN( J+1, M ) A( I, J ) = A( I, J )*MUL 80 CONTINUE 90 CONTINUE * ELSE IF( ITYPE.EQ.4 ) THEN * * Lower half of a symmetric band matrix * K3 = KL + 1 K4 = N + 1 DO 110 J = 1, N DO 100 I = 1, MIN( K3, K4-J ) A( I, J ) = A( I, J )*MUL 100 CONTINUE 110 CONTINUE * ELSE IF( ITYPE.EQ.5 ) THEN * * Upper half of a symmetric band matrix * K1 = KU + 2 K3 = KU + 1 DO 130 J = 1, N DO 120 I = MAX( K1-J, 1 ), K3 A( I, J ) = A( I, J )*MUL 120 CONTINUE 130 CONTINUE * ELSE IF( ITYPE.EQ.6 ) THEN * * Band matrix * K1 = KL + KU + 2 K2 = KL + 1 K3 = 2*KL + KU + 1 K4 = KL + KU + 1 + M DO 150 J = 1, N DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J ) A( I, J ) = A( I, J )*MUL 140 CONTINUE 150 CONTINUE * END IF * IF( .NOT.DONE ) $ GO TO 10 * RETURN * * End of ZLASCL * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgebal.f0000644000000000000000000000012714061636515015274 xustar0029 mtime=1623670093.19310409 29 atime=1623670093.19310409 29 ctime=1623670093.19310409 elk-7.2.42/src/LAPACK/zgebal.f0000644002504400250440000002471614061636515017337 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEBAL * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEBAL + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO ) * * .. Scalar Arguments .. * CHARACTER JOB * INTEGER IHI, ILO, INFO, LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION SCALE( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEBAL balances a general complex matrix A. This involves, first, *> permuting A by a similarity transformation to isolate eigenvalues *> in the first 1 to ILO-1 and last IHI+1 to N elements on the *> diagonal; and second, applying a diagonal similarity transformation *> to rows and columns ILO to IHI to make the rows and columns as *> close in norm as possible. Both steps are optional. *> *> Balancing may reduce the 1-norm of the matrix, and improve the *> accuracy of the computed eigenvalues and/or eigenvectors. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOB *> \verbatim *> JOB is CHARACTER*1 *> Specifies the operations to be performed on A: *> = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0 *> for i = 1,...,N; *> = 'P': permute only; *> = 'S': scale only; *> = 'B': both permute and scale. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the input matrix A. *> On exit, A is overwritten by the balanced matrix. *> If JOB = 'N', A is not referenced. *> See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[out] IHI *> \verbatim *> IHI is INTEGER *> ILO and IHI are set to INTEGER such that on exit *> A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N. *> If JOB = 'N' or 'S', ILO = 1 and IHI = N. *> \endverbatim *> *> \param[out] SCALE *> \verbatim *> SCALE is DOUBLE PRECISION array, dimension (N) *> Details of the permutations and scaling factors applied to *> A. If P(j) is the index of the row and column interchanged *> with row and column j and D(j) is the scaling factor *> applied to row and column j, then *> SCALE(j) = P(j) for j = 1,...,ILO-1 *> = D(j) for j = ILO,...,IHI *> = P(j) for j = IHI+1,...,N. *> The order in which the interchanges are made is N to IHI+1, *> then 1 to ILO-1. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The permutations consist of row and column interchanges which put *> the matrix in the form *> *> ( T1 X Y ) *> P A P = ( 0 B Z ) *> ( 0 0 T2 ) *> *> where T1 and T2 are upper triangular matrices whose eigenvalues lie *> along the diagonal. The column indices ILO and IHI mark the starting *> and ending columns of the submatrix B. Balancing consists of applying *> a diagonal similarity transformation inv(D) * B * D to make the *> 1-norms of each row of B and its corresponding column nearly equal. *> The output matrix is *> *> ( T1 X*D Y ) *> ( 0 inv(D)*B*D inv(D)*Z ). *> ( 0 0 T2 ) *> *> Information about the permutations P and the diagonal matrix D is *> returned in the vector SCALE. *> *> This subroutine is based on the EISPACK routine CBAL. *> *> Modified by Tzu-Yi Chen, Computer Science Division, University of *> California at Berkeley, USA *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO ) * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. CHARACTER JOB INTEGER IHI, ILO, INFO, LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION SCALE( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) DOUBLE PRECISION SCLFAC PARAMETER ( SCLFAC = 2.0D+0 ) DOUBLE PRECISION FACTOR PARAMETER ( FACTOR = 0.95D+0 ) * .. * .. Local Scalars .. LOGICAL NOCONV INTEGER I, ICA, IEXC, IRA, J, K, L, M DOUBLE PRECISION C, CA, F, G, R, RA, S, SFMAX1, SFMAX2, SFMIN1, $ SFMIN2 * .. * .. External Functions .. LOGICAL DISNAN, LSAME INTEGER IZAMAX DOUBLE PRECISION DLAMCH, DZNRM2 EXTERNAL DISNAN, LSAME, IZAMAX, DLAMCH, DZNRM2 * .. * .. External Subroutines .. EXTERNAL XERBLA, ZDSCAL, ZSWAP * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DIMAG, MAX, MIN * * Test the input parameters * INFO = 0 IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND. $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGEBAL', -INFO ) RETURN END IF * K = 1 L = N * IF( N.EQ.0 ) $ GO TO 210 * IF( LSAME( JOB, 'N' ) ) THEN DO 10 I = 1, N SCALE( I ) = ONE 10 CONTINUE GO TO 210 END IF * IF( LSAME( JOB, 'S' ) ) $ GO TO 120 * * Permutation to isolate eigenvalues if possible * GO TO 50 * * Row and column exchange. * 20 CONTINUE SCALE( M ) = J IF( J.EQ.M ) $ GO TO 30 * CALL ZSWAP( L, A( 1, J ), 1, A( 1, M ), 1 ) CALL ZSWAP( N-K+1, A( J, K ), LDA, A( M, K ), LDA ) * 30 CONTINUE GO TO ( 40, 80 )IEXC * * Search for rows isolating an eigenvalue and push them down. * 40 CONTINUE IF( L.EQ.1 ) $ GO TO 210 L = L - 1 * 50 CONTINUE DO 70 J = L, 1, -1 * DO 60 I = 1, L IF( I.EQ.J ) $ GO TO 60 IF( DBLE( A( J, I ) ).NE.ZERO .OR. DIMAG( A( J, I ) ).NE. $ ZERO )GO TO 70 60 CONTINUE * M = L IEXC = 1 GO TO 20 70 CONTINUE * GO TO 90 * * Search for columns isolating an eigenvalue and push them left. * 80 CONTINUE K = K + 1 * 90 CONTINUE DO 110 J = K, L * DO 100 I = K, L IF( I.EQ.J ) $ GO TO 100 IF( DBLE( A( I, J ) ).NE.ZERO .OR. DIMAG( A( I, J ) ).NE. $ ZERO )GO TO 110 100 CONTINUE * M = K IEXC = 2 GO TO 20 110 CONTINUE * 120 CONTINUE DO 130 I = K, L SCALE( I ) = ONE 130 CONTINUE * IF( LSAME( JOB, 'P' ) ) $ GO TO 210 * * Balance the submatrix in rows K to L. * * Iterative loop for norm reduction * SFMIN1 = DLAMCH( 'S' ) / DLAMCH( 'P' ) SFMAX1 = ONE / SFMIN1 SFMIN2 = SFMIN1*SCLFAC SFMAX2 = ONE / SFMIN2 140 CONTINUE NOCONV = .FALSE. * DO 200 I = K, L * C = DZNRM2( L-K+1, A( K, I ), 1 ) R = DZNRM2( L-K+1, A( I, K ), LDA ) ICA = IZAMAX( L, A( 1, I ), 1 ) CA = ABS( A( ICA, I ) ) IRA = IZAMAX( N-K+1, A( I, K ), LDA ) RA = ABS( A( I, IRA+K-1 ) ) * * Guard against zero C or R due to underflow. * IF( C.EQ.ZERO .OR. R.EQ.ZERO ) $ GO TO 200 G = R / SCLFAC F = ONE S = C + R 160 CONTINUE IF( C.GE.G .OR. MAX( F, C, CA ).GE.SFMAX2 .OR. $ MIN( R, G, RA ).LE.SFMIN2 )GO TO 170 IF( DISNAN( C+F+CA+R+G+RA ) ) THEN * * Exit if NaN to avoid infinite loop * INFO = -3 CALL XERBLA( 'ZGEBAL', -INFO ) RETURN END IF F = F*SCLFAC C = C*SCLFAC CA = CA*SCLFAC R = R / SCLFAC G = G / SCLFAC RA = RA / SCLFAC GO TO 160 * 170 CONTINUE G = C / SCLFAC 180 CONTINUE IF( G.LT.R .OR. MAX( R, RA ).GE.SFMAX2 .OR. $ MIN( F, C, G, CA ).LE.SFMIN2 )GO TO 190 F = F / SCLFAC C = C / SCLFAC G = G / SCLFAC CA = CA / SCLFAC R = R*SCLFAC RA = RA*SCLFAC GO TO 180 * * Now balance. * 190 CONTINUE IF( ( C+R ).GE.FACTOR*S ) $ GO TO 200 IF( F.LT.ONE .AND. SCALE( I ).LT.ONE ) THEN IF( F*SCALE( I ).LE.SFMIN1 ) $ GO TO 200 END IF IF( F.GT.ONE .AND. SCALE( I ).GT.ONE ) THEN IF( SCALE( I ).GE.SFMAX1 / F ) $ GO TO 200 END IF G = ONE / F SCALE( I ) = SCALE( I )*F NOCONV = .TRUE. * CALL ZDSCAL( N-K+1, G, A( I, K ), LDA ) CALL ZDSCAL( L, F, A( 1, I ), 1 ) * 200 CONTINUE * IF( NOCONV ) $ GO TO 140 * 210 CONTINUE ILO = K IHI = L * RETURN * * End of ZGEBAL * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgehrd.f0000644000000000000000000000013214061636515015307 xustar0030 mtime=1623670093.195104088 30 atime=1623670093.195104088 30 ctime=1623670093.195104088 elk-7.2.42/src/LAPACK/zgehrd.f0000644002504400250440000002525514061636515017355 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEHRD * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEHRD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER IHI, ILO, INFO, LDA, LWORK, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by *> an unitary similarity transformation: Q**H * A * Q = H . *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> It is assumed that A is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to ZGEBAL; otherwise they should be *> set to 1 and N respectively. See Further Details. *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the N-by-N general matrix to be reduced. *> On exit, the upper triangle and the first subdiagonal of A *> are overwritten with the upper Hessenberg matrix H, and the *> elements below the first subdiagonal, with the array TAU, *> represent the unitary matrix Q as a product of elementary *> reflectors. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> The scalar factors of the elementary reflectors (see Further *> Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to *> zero. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (LWORK) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(1,N). *> For good performance, LWORK should generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of (ihi-ilo) elementary *> reflectors *> *> Q = H(ilo) H(ilo+1) . . . H(ihi-1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on *> exit in A(i+2:ihi,i), and tau in TAU(i). *> *> The contents of A are illustrated by the following example, with *> n = 7, ilo = 2 and ihi = 6: *> *> on entry, on exit, *> *> ( a a a a a a a ) ( a a h h h h a ) *> ( a a a a a a ) ( a h h h h a ) *> ( a a a a a a ) ( h h h h h h ) *> ( a a a a a a ) ( v2 h h h h h ) *> ( a a a a a a ) ( v2 v3 h h h h ) *> ( a a a a a a ) ( v2 v3 v4 h h h ) *> ( a ) ( a ) *> *> where a denotes an element of the original matrix A, h denotes a *> modified element of the upper Hessenberg matrix H, and vi denotes an *> element of the vector defining H(i). *> *> This file is a slight modification of LAPACK-3.0's DGEHRD *> subroutine incorporating improvements proposed by Quintana-Orti and *> Van de Geijn (2006). (See DLAHR2.) *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEHRD( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IHI, ILO, INFO, LDA, LWORK, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NBMAX, LDT, TSIZE PARAMETER ( NBMAX = 64, LDT = NBMAX+1, $ TSIZE = LDT*NBMAX ) COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWT, J, LDWORK, LWKOPT, NB, $ NBMIN, NH, NX COMPLEX*16 EI * .. * .. External Subroutines .. EXTERNAL ZAXPY, ZGEHD2, ZGEMM, ZLAHR2, ZLARFB, ZTRMM, $ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( N.LT.0 ) THEN INFO = -1 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN INFO = -2 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF * IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) LWKOPT = N*NB + TSIZE WORK( 1 ) = LWKOPT ENDIF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGEHRD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Set elements 1:ILO-1 and IHI:N-1 of TAU to zero * DO 10 I = 1, ILO - 1 TAU( I ) = ZERO 10 CONTINUE DO 20 I = MAX( 1, IHI ), N - 1 TAU( I ) = ZERO 20 CONTINUE * * Quick return if possible * NH = IHI - ILO + 1 IF( NH.LE.1 ) THEN WORK( 1 ) = 1 RETURN END IF * * Determine the block size * NB = MIN( NBMAX, ILAENV( 1, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) NBMIN = 2 IF( NB.GT.1 .AND. NB.LT.NH ) THEN * * Determine when to cross over from blocked to unblocked code * (last block is always handled by unblocked code) * NX = MAX( NB, ILAENV( 3, 'ZGEHRD', ' ', N, ILO, IHI, -1 ) ) IF( NX.LT.NH ) THEN * * Determine if workspace is large enough for blocked code * IF( LWORK.LT.N*NB+TSIZE ) THEN * * Not enough workspace to use optimal NB: determine the * minimum value of NB, and reduce NB or force use of * unblocked code * NBMIN = MAX( 2, ILAENV( 2, 'ZGEHRD', ' ', N, ILO, IHI, $ -1 ) ) IF( LWORK.GE.(N*NBMIN + TSIZE) ) THEN NB = (LWORK-TSIZE) / N ELSE NB = 1 END IF END IF END IF END IF LDWORK = N * IF( NB.LT.NBMIN .OR. NB.GE.NH ) THEN * * Use unblocked code below * I = ILO * ELSE * * Use blocked code * IWT = 1 + N*NB DO 40 I = ILO, IHI - 1 - NX, NB IB = MIN( NB, IHI-I ) * * Reduce columns i:i+ib-1 to Hessenberg form, returning the * matrices V and T of the block reflector H = I - V*T*V**H * which performs the reduction, and also the matrix Y = A*V*T * CALL ZLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), $ WORK( IWT ), LDT, WORK, LDWORK ) * * Apply the block reflector H to A(1:ihi,i+ib:ihi) from the * right, computing A := A - Y * V**H. V(i+ib,ib-1) must be set * to 1 * EI = A( I+IB, I+IB-1 ) A( I+IB, I+IB-1 ) = ONE CALL ZGEMM( 'No transpose', 'Conjugate transpose', $ IHI, IHI-I-IB+1, $ IB, -ONE, WORK, LDWORK, A( I+IB, I ), LDA, ONE, $ A( 1, I+IB ), LDA ) A( I+IB, I+IB-1 ) = EI * * Apply the block reflector H to A(1:i,i+1:i+ib-1) from the * right * CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', $ 'Unit', I, IB-1, $ ONE, A( I+1, I ), LDA, WORK, LDWORK ) DO 30 J = 0, IB-2 CALL ZAXPY( I, -ONE, WORK( LDWORK*J+1 ), 1, $ A( 1, I+J+1 ), 1 ) 30 CONTINUE * * Apply the block reflector H to A(i+1:ihi,i+ib:n) from the * left * CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward', $ 'Columnwise', $ IHI-I, N-I-IB+1, IB, A( I+1, I ), LDA, $ WORK( IWT ), LDT, A( I+1, I+IB ), LDA, $ WORK, LDWORK ) 40 CONTINUE END IF * * Use unblocked code to reduce the rest of the matrix * CALL ZGEHD2( N, I, IHI, A, LDA, TAU, WORK, IINFO ) WORK( 1 ) = LWKOPT * RETURN * * End of ZGEHRD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlacpy.f0000644000000000000000000000013214061636515015326 xustar0030 mtime=1623670093.197104087 30 atime=1623670093.197104087 30 ctime=1623670093.197104087 elk-7.2.42/src/LAPACK/zlacpy.f0000644002504400250440000000775414061636515017400 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLACPY copies all or part of one two-dimensional array to another. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLACPY + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLACPY( UPLO, M, N, A, LDA, B, LDB ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDB, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLACPY copies all or part of a two-dimensional matrix A to another *> matrix B. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies the part of the matrix A to be copied to B. *> = 'U': Upper triangular part *> = 'L': Lower triangular part *> Otherwise: All of the matrix A *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The m by n matrix A. If UPLO = 'U', only the upper trapezium *> is accessed; if UPLO = 'L', only the lower trapezium is *> accessed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,N) *> On exit, B = A in the locations specified by UPLO. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLACPY( UPLO, M, N, A, LDA, B, LDB ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDB, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, MIN( J, M ) B( I, J ) = A( I, J ) 10 CONTINUE 20 CONTINUE * ELSE IF( LSAME( UPLO, 'L' ) ) THEN DO 40 J = 1, N DO 30 I = J, M B( I, J ) = A( I, J ) 30 CONTINUE 40 CONTINUE * ELSE DO 60 J = 1, N DO 50 I = 1, M B( I, J ) = A( I, J ) 50 CONTINUE 60 CONTINUE END IF * RETURN * * End of ZLACPY * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunghr.f0000644000000000000000000000013214061636515015341 xustar0030 mtime=1623670093.199104085 30 atime=1623670093.198104086 30 ctime=1623670093.199104085 elk-7.2.42/src/LAPACK/zunghr.f0000644002504400250440000001470714061636515017407 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNGHR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNGHR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER IHI, ILO, INFO, LDA, LWORK, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNGHR generates a complex unitary matrix Q which is defined as the *> product of IHI-ILO elementary reflectors of order N, as returned by *> ZGEHRD: *> *> Q = H(ilo) H(ilo+1) . . . H(ihi-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix Q. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> ILO and IHI must have the same values as in the previous call *> of ZGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the vectors which define the elementary reflectors, *> as returned by ZGEHRD. *> On exit, the N-by-N unitary matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEHRD. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= IHI-ILO. *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is *> the optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IHI, ILO, INFO, LDA, LWORK, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IINFO, J, LWKOPT, NB, NH * .. * .. External Subroutines .. EXTERNAL XERBLA, ZUNGQR * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 NH = IHI - ILO LQUERY = ( LWORK.EQ.-1 ) IF( N.LT.0 ) THEN INFO = -1 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN INFO = -2 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF * IF( INFO.EQ.0 ) THEN NB = ILAENV( 1, 'ZUNGQR', ' ', NH, NH, NH, -1 ) LWKOPT = MAX( 1, NH )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNGHR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * * Shift the vectors which define the elementary reflectors one * column to the right, and set the first ilo and the last n-ihi * rows and columns to those of the unit matrix * DO 40 J = IHI, ILO + 1, -1 DO 10 I = 1, J - 1 A( I, J ) = ZERO 10 CONTINUE DO 20 I = J + 1, IHI A( I, J ) = A( I, J-1 ) 20 CONTINUE DO 30 I = IHI + 1, N A( I, J ) = ZERO 30 CONTINUE 40 CONTINUE DO 60 J = 1, ILO DO 50 I = 1, N A( I, J ) = ZERO 50 CONTINUE A( J, J ) = ONE 60 CONTINUE DO 80 J = IHI + 1, N DO 70 I = 1, N A( I, J ) = ZERO 70 CONTINUE A( J, J ) = ONE 80 CONTINUE * IF( NH.GT.0 ) THEN * * Generate Q(ilo+1:ihi,ilo+1:ihi) * CALL ZUNGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ), $ WORK, LWORK, IINFO ) END IF WORK( 1 ) = LWKOPT RETURN * * End of ZUNGHR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgebak.f0000644000000000000000000000013214061636515015267 xustar0030 mtime=1623670093.200104084 30 atime=1623670093.200104084 30 ctime=1623670093.200104084 elk-7.2.42/src/LAPACK/zgebak.f0000644002504400250440000001615714061636515017336 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEBAK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEBAK + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, * INFO ) * * .. Scalar Arguments .. * CHARACTER JOB, SIDE * INTEGER IHI, ILO, INFO, LDV, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION SCALE( * ) * COMPLEX*16 V( LDV, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEBAK forms the right or left eigenvectors of a complex general *> matrix by backward transformation on the computed eigenvectors of the *> balanced matrix output by ZGEBAL. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOB *> \verbatim *> JOB is CHARACTER*1 *> Specifies the type of backward transformation required: *> = 'N': do nothing, return immediately; *> = 'P': do backward transformation for permutation only; *> = 'S': do backward transformation for scaling only; *> = 'B': do backward transformations for both permutation and *> scaling. *> JOB must be the same as the argument JOB supplied to ZGEBAL. *> \endverbatim *> *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'R': V contains right eigenvectors; *> = 'L': V contains left eigenvectors. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows of the matrix V. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> The integers ILO and IHI determined by ZGEBAL. *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0. *> \endverbatim *> *> \param[in] SCALE *> \verbatim *> SCALE is DOUBLE PRECISION array, dimension (N) *> Details of the permutation and scaling factors, as returned *> by ZGEBAL. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of columns of the matrix V. M >= 0. *> \endverbatim *> *> \param[in,out] V *> \verbatim *> V is COMPLEX*16 array, dimension (LDV,M) *> On entry, the matrix of right or left eigenvectors to be *> transformed, as returned by ZHSEIN or ZTREVC. *> On exit, V is overwritten by the transformed eigenvectors. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V. LDV >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GEcomputational * * ===================================================================== SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, $ INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER JOB, SIDE INTEGER IHI, ILO, INFO, LDV, M, N * .. * .. Array Arguments .. DOUBLE PRECISION SCALE( * ) COMPLEX*16 V( LDV, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LEFTV, RIGHTV INTEGER I, II, K DOUBLE PRECISION S * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZDSCAL, ZSWAP * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Decode and Test the input parameters * RIGHTV = LSAME( SIDE, 'R' ) LEFTV = LSAME( SIDE, 'L' ) * INFO = 0 IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND. $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN INFO = -1 ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN INFO = -5 ELSE IF( M.LT.0 ) THEN INFO = -7 ELSE IF( LDV.LT.MAX( 1, N ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGEBAK', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN IF( M.EQ.0 ) $ RETURN IF( LSAME( JOB, 'N' ) ) $ RETURN * IF( ILO.EQ.IHI ) $ GO TO 30 * * Backward balance * IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN * IF( RIGHTV ) THEN DO 10 I = ILO, IHI S = SCALE( I ) CALL ZDSCAL( M, S, V( I, 1 ), LDV ) 10 CONTINUE END IF * IF( LEFTV ) THEN DO 20 I = ILO, IHI S = ONE / SCALE( I ) CALL ZDSCAL( M, S, V( I, 1 ), LDV ) 20 CONTINUE END IF * END IF * * Backward permutation * * For I = ILO-1 step -1 until 1, * IHI+1 step 1 until N do -- * 30 CONTINUE IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN IF( RIGHTV ) THEN DO 40 II = 1, N I = II IF( I.GE.ILO .AND. I.LE.IHI ) $ GO TO 40 IF( I.LT.ILO ) $ I = ILO - II K = SCALE( I ) IF( K.EQ.I ) $ GO TO 40 CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) 40 CONTINUE END IF * IF( LEFTV ) THEN DO 50 II = 1, N I = II IF( I.GE.ILO .AND. I.LE.IHI ) $ GO TO 50 IF( I.LT.ILO ) $ I = ILO - II K = SCALE( I ) IF( K.EQ.I ) $ GO TO 50 CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV ) 50 CONTINUE END IF END IF * RETURN * * End of ZGEBAK * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgeqrf.f0000644000000000000000000000013214061636515015322 xustar0030 mtime=1623670093.202104082 30 atime=1623670093.202104082 30 ctime=1623670093.202104082 elk-7.2.42/src/LAPACK/zgeqrf.f0000644002504400250440000001712214061636515017362 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEQRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEQRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEQRF computes a QR factorization of a complex M-by-N matrix A: *> *> A = Q * ( R ), *> ( 0 ) *> *> where: *> *> Q is a M-by-M orthogonal matrix; *> R is an upper-triangular N-by-N matrix; *> 0 is a (M-N)-by-N zero matrix, if M > N. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the M-by-N matrix A. *> On exit, the elements on and above the diagonal of the array *> contain the min(M,N)-by-N upper trapezoidal matrix R (R is *> upper triangular if m >= n); the elements below the diagonal, *> with the array TAU, represent the unitary matrix Q as a *> product of min(m,n) elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2019 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of elementary reflectors *> *> Q = H(1) H(2) . . . H(k), where k = min(m,n). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), *> and tau in TAU(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.9.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2019 * * .. Scalar Arguments .. INTEGER INFO, LDA, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, $ NBMIN, NX * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEQR2, ZLARFB, ZLARFT * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 NB = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) LWKOPT = N*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGEQRF', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * K = MIN( M, N ) IF( K.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NBMIN = 2 NX = 0 IWS = N IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. * NX = MAX( 0, ILAENV( 3, 'ZGEQRF', ' ', M, N, -1, -1 ) ) IF( NX.LT.K ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = N IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: reduce NB and * determine the minimum value of NB. * NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZGEQRF', ' ', M, N, -1, $ -1 ) ) END IF END IF END IF * IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN * * Use blocked code initially * DO 10 I = 1, K - NX, NB IB = MIN( K-I+1, NB ) * * Compute the QR factorization of the current block * A(i:m,i:i+ib-1) * CALL ZGEQR2( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK, $ IINFO ) IF( I+IB.LE.N ) THEN * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL ZLARFT( 'Forward', 'Columnwise', M-I+1, IB, $ A( I, I ), LDA, TAU( I ), WORK, LDWORK ) * * Apply H**H to A(i:m,i+ib:n) from the left * CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward', $ 'Columnwise', M-I+1, N-I-IB+1, IB, $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), $ LDA, WORK( IB+1 ), LDWORK ) END IF 10 CONTINUE ELSE I = 1 END IF * * Use unblocked code to factor the last or only block. * IF( I.LE.K ) $ CALL ZGEQR2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, $ IINFO ) * WORK( 1 ) = IWS RETURN * * End of ZGEQRF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zungqr.f0000644000000000000000000000012714061636515015356 xustar0029 mtime=1623670093.20410408 29 atime=1623670093.20410408 29 ctime=1623670093.20410408 elk-7.2.42/src/LAPACK/zungqr.f0000644002504400250440000001761014061636515017414 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNGQR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNGQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns, *> which is defined as the first N columns of a product of K elementary *> reflectors of order M *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by ZGEQRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. M >= N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the i-th column must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by ZGEQRF in the first k columns of its array *> argument A. *> On exit, the M-by-N matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEQRF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, $ LWKOPT, NB, NBMIN, NX * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2R * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 NB = ILAENV( 1, 'ZUNGQR', ' ', M, N, K, -1 ) LWKOPT = MAX( 1, N )*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNGQR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.LE.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NBMIN = 2 NX = 0 IWS = N IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. * NX = MAX( 0, ILAENV( 3, 'ZUNGQR', ' ', M, N, K, -1 ) ) IF( NX.LT.K ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = N IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: reduce NB and * determine the minimum value of NB. * NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQR', ' ', M, N, K, -1 ) ) END IF END IF END IF * IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN * * Use blocked code after the last block. * The first kk columns are handled by the block method. * KI = ( ( K-NX-1 ) / NB )*NB KK = MIN( K, KI+NB ) * * Set A(1:kk,kk+1:n) to zero. * DO 20 J = KK + 1, N DO 10 I = 1, KK A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE KK = 0 END IF * * Use unblocked code for the last or only block. * IF( KK.LT.N ) $ CALL ZUNG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, $ TAU( KK+1 ), WORK, IINFO ) * IF( KK.GT.0 ) THEN * * Use blocked code * DO 50 I = KI + 1, 1, -NB IB = MIN( NB, K-I+1 ) IF( I+IB.LE.N ) THEN * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL ZLARFT( 'Forward', 'Columnwise', M-I+1, IB, $ A( I, I ), LDA, TAU( I ), WORK, LDWORK ) * * Apply H to A(i:m,i+ib:n) from the left * CALL ZLARFB( 'Left', 'No transpose', 'Forward', $ 'Columnwise', M-I+1, N-I-IB+1, IB, $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), $ LDA, WORK( IB+1 ), LDWORK ) END IF * * Apply H to rows i:m of current block * CALL ZUNG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK, $ IINFO ) * * Set rows 1:i-1 of current block to zero * DO 40 J = I, I + IB - 1 DO 30 L = 1, I - 1 A( L, J ) = ZERO 30 CONTINUE 40 CONTINUE 50 CONTINUE END IF * WORK( 1 ) = IWS RETURN * * End of ZUNGQR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgebrd.f0000644000000000000000000000013214061636515015301 xustar0030 mtime=1623670093.206104078 30 atime=1623670093.205104079 30 ctime=1623670093.206104078 elk-7.2.42/src/LAPACK/zgebrd.f0000644002504400250440000002574014061636515017346 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEBRD * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEBRD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, * INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ) * COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEBRD reduces a general complex M-by-N matrix A to upper or lower *> bidiagonal form B by a unitary transformation: Q**H * A * P = B. *> *> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows in the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns in the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the M-by-N general matrix to be reduced. *> On exit, *> if m >= n, the diagonal and the first superdiagonal are *> overwritten with the upper bidiagonal matrix B; the *> elements below the diagonal, with the array TAUQ, represent *> the unitary matrix Q as a product of elementary *> reflectors, and the elements above the first superdiagonal, *> with the array TAUP, represent the unitary matrix P as *> a product of elementary reflectors; *> if m < n, the diagonal and the first subdiagonal are *> overwritten with the lower bidiagonal matrix B; the *> elements below the first subdiagonal, with the array TAUQ, *> represent the unitary matrix Q as a product of *> elementary reflectors, and the elements above the diagonal, *> with the array TAUP, represent the unitary matrix P as *> a product of elementary reflectors. *> See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (min(M,N)) *> The diagonal elements of the bidiagonal matrix B: *> D(i) = A(i,i). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (min(M,N)-1) *> The off-diagonal elements of the bidiagonal matrix B: *> if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; *> if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. *> \endverbatim *> *> \param[out] TAUQ *> \verbatim *> TAUQ is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors which *> represent the unitary matrix Q. See Further Details. *> \endverbatim *> *> \param[out] TAUP *> \verbatim *> TAUP is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors which *> represent the unitary matrix P. See Further Details. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= max(1,M,N). *> For optimum performance LWORK >= (M+N)*NB, where NB *> is the optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrices Q and P are represented as products of elementary *> reflectors: *> *> If m >= n, *> *> Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) *> *> Each H(i) and G(i) has the form: *> *> H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H *> *> where tauq and taup are complex scalars, and v and u are complex *> vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in *> A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in *> A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). *> *> If m < n, *> *> Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) *> *> Each H(i) and G(i) has the form: *> *> H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H *> *> where tauq and taup are complex scalars, and v and u are complex *> vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in *> A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in *> A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). *> *> The contents of A on exit are illustrated by the following examples: *> *> m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): *> *> ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) *> ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) *> ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) *> ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) *> ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) *> ( v1 v2 v3 v4 v5 ) *> *> where d and e denote diagonal and off-diagonal elements of B, vi *> denotes an element of the vector defining H(i), and ui an element of *> the vector defining G(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEBRD( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, $ INFO ) * * -- LAPACK computational routine (version 3.8.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INFO, LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ) COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IINFO, J, LDWRKX, LDWRKY, LWKOPT, MINMN, NB, $ NBMIN, NX, WS * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEBD2, ZGEMM, ZLABRD * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 NB = MAX( 1, ILAENV( 1, 'ZGEBRD', ' ', M, N, -1, -1 ) ) LWKOPT = ( M+N )*NB WORK( 1 ) = DBLE( LWKOPT ) LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 ELSE IF( LWORK.LT.MAX( 1, M, N ) .AND. .NOT.LQUERY ) THEN INFO = -10 END IF IF( INFO.LT.0 ) THEN CALL XERBLA( 'ZGEBRD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * MINMN = MIN( M, N ) IF( MINMN.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * WS = MAX( M, N ) LDWRKX = M LDWRKY = N * IF( NB.GT.1 .AND. NB.LT.MINMN ) THEN * * Set the crossover point NX. * NX = MAX( NB, ILAENV( 3, 'ZGEBRD', ' ', M, N, -1, -1 ) ) * * Determine when to switch from blocked to unblocked code. * IF( NX.LT.MINMN ) THEN WS = ( M+N )*NB IF( LWORK.LT.WS ) THEN * * Not enough work space for the optimal NB, consider using * a smaller block size. * NBMIN = ILAENV( 2, 'ZGEBRD', ' ', M, N, -1, -1 ) IF( LWORK.GE.( M+N )*NBMIN ) THEN NB = LWORK / ( M+N ) ELSE NB = 1 NX = MINMN END IF END IF END IF ELSE NX = MINMN END IF * DO 30 I = 1, MINMN - NX, NB * * Reduce rows and columns i:i+ib-1 to bidiagonal form and return * the matrices X and Y which are needed to update the unreduced * part of the matrix * CALL ZLABRD( M-I+1, N-I+1, NB, A( I, I ), LDA, D( I ), E( I ), $ TAUQ( I ), TAUP( I ), WORK, LDWRKX, $ WORK( LDWRKX*NB+1 ), LDWRKY ) * * Update the trailing submatrix A(i+ib:m,i+ib:n), using * an update of the form A := A - V*Y**H - X*U**H * CALL ZGEMM( 'No transpose', 'Conjugate transpose', M-I-NB+1, $ N-I-NB+1, NB, -ONE, A( I+NB, I ), LDA, $ WORK( LDWRKX*NB+NB+1 ), LDWRKY, ONE, $ A( I+NB, I+NB ), LDA ) CALL ZGEMM( 'No transpose', 'No transpose', M-I-NB+1, N-I-NB+1, $ NB, -ONE, WORK( NB+1 ), LDWRKX, A( I, I+NB ), LDA, $ ONE, A( I+NB, I+NB ), LDA ) * * Copy diagonal and off-diagonal elements of B back into A * IF( M.GE.N ) THEN DO 10 J = I, I + NB - 1 A( J, J ) = D( J ) A( J, J+1 ) = E( J ) 10 CONTINUE ELSE DO 20 J = I, I + NB - 1 A( J, J ) = D( J ) A( J+1, J ) = E( J ) 20 CONTINUE END IF 30 CONTINUE * * Use unblocked code to reduce the remainder of the matrix * CALL ZGEBD2( M-I+1, N-I+1, A( I, I ), LDA, D( I ), E( I ), $ TAUQ( I ), TAUP( I ), WORK, IINFO ) WORK( 1 ) = WS RETURN * * End of ZGEBRD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zungbr.f0000644000000000000000000000013214061636515015333 xustar0030 mtime=1623670093.208104076 30 atime=1623670093.207104077 30 ctime=1623670093.208104076 elk-7.2.42/src/LAPACK/zungbr.f0000644002504400250440000002326614061636515017401 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNGBR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNGBR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER VECT * INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNGBR generates one of the complex unitary matrices Q or P**H *> determined by ZGEBRD when reducing a complex matrix A to bidiagonal *> form: A = Q * B * P**H. Q and P**H are defined as products of *> elementary reflectors H(i) or G(i) respectively. *> *> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q *> is of order M: *> if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n *> columns of Q, where m >= n >= k; *> if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an *> M-by-M matrix. *> *> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H *> is of order N: *> if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m *> rows of P**H, where n >= m >= k; *> if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as *> an N-by-N matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] VECT *> \verbatim *> VECT is CHARACTER*1 *> Specifies whether the matrix Q or the matrix P**H is *> required, as defined in the transformation applied by ZGEBRD: *> = 'Q': generate Q; *> = 'P': generate P**H. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q or P**H to be returned. *> M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q or P**H to be returned. *> N >= 0. *> If VECT = 'Q', M >= N >= min(M,K); *> if VECT = 'P', N >= M >= min(N,K). *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> If VECT = 'Q', the number of columns in the original M-by-K *> matrix reduced by ZGEBRD. *> If VECT = 'P', the number of rows in the original K-by-N *> matrix reduced by ZGEBRD. *> K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the vectors which define the elementary reflectors, *> as returned by ZGEBRD. *> On exit, the M-by-N matrix Q or P**H. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= M. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension *> (min(M,K)) if VECT = 'Q' *> (min(N,K)) if VECT = 'P' *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i) or G(i), which determines Q or P**H, as *> returned by ZGEBRD in its array argument TAUQ or TAUP. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,min(M,N)). *> For optimum performance LWORK >= min(M,N)*NB, where NB *> is the optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date April 2012 * *> \ingroup complex16GBcomputational * * ===================================================================== SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * April 2012 * * .. Scalar Arguments .. CHARACTER VECT INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY, WANTQ INTEGER I, IINFO, J, LWKOPT, MN * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZUNGLQ, ZUNGQR * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 WANTQ = LSAME( VECT, 'Q' ) MN = MIN( M, N ) LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN INFO = -1 ELSE IF( M.LT.0 ) THEN INFO = -2 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M, $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT. $ MIN( N, K ) ) ) ) THEN INFO = -3 ELSE IF( K.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -6 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN INFO = -9 END IF * IF( INFO.EQ.0 ) THEN WORK( 1 ) = 1 IF( WANTQ ) THEN IF( M.GE.K ) THEN CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) ELSE IF( M.GT.1 ) THEN CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, $ -1, IINFO ) END IF END IF ELSE IF( K.LT.N ) THEN CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) ELSE IF( N.GT.1 ) THEN CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, $ -1, IINFO ) END IF END IF END IF LWKOPT = WORK( 1 ) LWKOPT = MAX (LWKOPT, MN) END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNGBR', -INFO ) RETURN ELSE IF( LQUERY ) THEN WORK( 1 ) = LWKOPT RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * IF( WANTQ ) THEN * * Form Q, determined by a call to ZGEBRD to reduce an m-by-k * matrix * IF( M.GE.K ) THEN * * If m >= k, assume m >= n >= k * CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) * ELSE * * If m < k, assume m = n * * Shift the vectors which define the elementary reflectors one * column to the right, and set the first row and column of Q * to those of the unit matrix * DO 20 J = M, 2, -1 A( 1, J ) = ZERO DO 10 I = J + 1, M A( I, J ) = A( I, J-1 ) 10 CONTINUE 20 CONTINUE A( 1, 1 ) = ONE DO 30 I = 2, M A( I, 1 ) = ZERO 30 CONTINUE IF( M.GT.1 ) THEN * * Form Q(2:m,2:m) * CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, $ LWORK, IINFO ) END IF END IF ELSE * * Form P**H, determined by a call to ZGEBRD to reduce a k-by-n * matrix * IF( K.LT.N ) THEN * * If k < n, assume k <= m <= n * CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) * ELSE * * If k >= n, assume m = n * * Shift the vectors which define the elementary reflectors one * row downward, and set the first row and column of P**H to * those of the unit matrix * A( 1, 1 ) = ONE DO 40 I = 2, N A( I, 1 ) = ZERO 40 CONTINUE DO 60 J = 2, N DO 50 I = J - 1, 2, -1 A( I, J ) = A( I-1, J ) 50 CONTINUE A( 1, J ) = ZERO 60 CONTINUE IF( N.GT.1 ) THEN * * Form P**H(2:n,2:n) * CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, $ LWORK, IINFO ) END IF END IF END IF WORK( 1 ) = LWKOPT RETURN * * End of ZUNGBR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgelqf.f0000644000000000000000000000013214061636515015314 xustar0030 mtime=1623670093.210104075 30 atime=1623670093.210104075 30 ctime=1623670093.210104075 elk-7.2.42/src/LAPACK/zgelqf.f0000644002504400250440000001705614061636515017362 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGELQF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGELQF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGELQF computes an LQ factorization of a complex M-by-N matrix A: *> *> A = ( L 0 ) * Q *> *> where: *> *> Q is a N-by-N orthogonal matrix; *> L is an lower-triangular M-by-M matrix; *> 0 is a M-by-(N-M) zero matrix, if M < N. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the M-by-N matrix A. *> On exit, the elements on and below the diagonal of the array *> contain the m-by-min(m,n) lower trapezoidal matrix L (L is *> lower triangular if m <= n); the elements above the diagonal, *> with the array TAU, represent the unitary matrix Q as a *> product of elementary reflectors (see Further Details). *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2019 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of elementary reflectors *> *> Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in *> A(i,i+1:n), and tau in TAU(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.9.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2019 * * .. Scalar Arguments .. INTEGER INFO, LDA, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB, $ NBMIN, NX * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGELQ2, ZLARFB, ZLARFT * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 NB = ILAENV( 1, 'ZGELQF', ' ', M, N, -1, -1 ) LWKOPT = M*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGELQF', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * K = MIN( M, N ) IF( K.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NBMIN = 2 NX = 0 IWS = M IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. * NX = MAX( 0, ILAENV( 3, 'ZGELQF', ' ', M, N, -1, -1 ) ) IF( NX.LT.K ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = M IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: reduce NB and * determine the minimum value of NB. * NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZGELQF', ' ', M, N, -1, $ -1 ) ) END IF END IF END IF * IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN * * Use blocked code initially * DO 10 I = 1, K - NX, NB IB = MIN( K-I+1, NB ) * * Compute the LQ factorization of the current block * A(i:i+ib-1,i:n) * CALL ZGELQ2( IB, N-I+1, A( I, I ), LDA, TAU( I ), WORK, $ IINFO ) IF( I+IB.LE.M ) THEN * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), $ LDA, TAU( I ), WORK, LDWORK ) * * Apply H to A(i+ib:m,i:n) from the right * CALL ZLARFB( 'Right', 'No transpose', 'Forward', $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ), $ LDA, WORK, LDWORK, A( I+IB, I ), LDA, $ WORK( IB+1 ), LDWORK ) END IF 10 CONTINUE ELSE I = 1 END IF * * Use unblocked code to factor the last or only block. * IF( I.LE.K ) $ CALL ZGELQ2( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK, $ IINFO ) * WORK( 1 ) = IWS RETURN * * End of ZGELQF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunglq.f0000644000000000000000000000013214061636515015344 xustar0030 mtime=1623670093.212104073 30 atime=1623670093.211104073 30 ctime=1623670093.212104073 elk-7.2.42/src/LAPACK/zunglq.f0000644002504400250440000001756514061636515017417 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNGLQ * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNGLQ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows, *> which is defined as the first M rows of a product of K elementary *> reflectors of order N *> *> Q = H(k)**H . . . H(2)**H H(1)**H *> *> as returned by ZGELQF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. N >= M. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. M >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the i-th row must contain the vector which defines *> the elementary reflector H(i), for i = 1,2,...,k, as returned *> by ZGELQF in the first k rows of its array argument A. *> On exit, the M-by-N matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGELQF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit; *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, $ LWKOPT, NB, NBMIN, NX * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNGL2 * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 ) LWKOPT = MAX( 1, M )*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNGLQ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.LE.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NBMIN = 2 NX = 0 IWS = M IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. * NX = MAX( 0, ILAENV( 3, 'ZUNGLQ', ' ', M, N, K, -1 ) ) IF( NX.LT.K ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = M IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: reduce NB and * determine the minimum value of NB. * NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZUNGLQ', ' ', M, N, K, -1 ) ) END IF END IF END IF * IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN * * Use blocked code after the last block. * The first kk rows are handled by the block method. * KI = ( ( K-NX-1 ) / NB )*NB KK = MIN( K, KI+NB ) * * Set A(kk+1:m,1:kk) to zero. * DO 20 J = 1, KK DO 10 I = KK + 1, M A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE KK = 0 END IF * * Use unblocked code for the last or only block. * IF( KK.LT.M ) $ CALL ZUNGL2( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, $ TAU( KK+1 ), WORK, IINFO ) * IF( KK.GT.0 ) THEN * * Use blocked code * DO 50 I = KI + 1, 1, -NB IB = MIN( NB, K-I+1 ) IF( I+IB.LE.M ) THEN * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ), $ LDA, TAU( I ), WORK, LDWORK ) * * Apply H**H to A(i+ib:m,i:n) from the right * CALL ZLARFB( 'Right', 'Conjugate transpose', 'Forward', $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ), $ LDA, WORK, LDWORK, A( I+IB, I ), LDA, $ WORK( IB+1 ), LDWORK ) END IF * * Apply H**H to columns i:n of current block * CALL ZUNGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK, $ IINFO ) * * Set columns 1:i-1 of current block to zero * DO 40 J = 1, I - 1 DO 30 L = I, I + IB - 1 A( L, J ) = ZERO 30 CONTINUE 40 CONTINUE 50 CONTINUE END IF * WORK( 1 ) = IWS RETURN * * End of ZUNGLQ * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaset.f0000644000000000000000000000013214061636515015326 xustar0030 mtime=1623670093.213104072 30 atime=1623670093.213104072 30 ctime=1623670093.213104072 elk-7.2.42/src/LAPACK/zlaset.f0000644002504400250440000001136014061636515017364 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLASET + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, M, N * COMPLEX*16 ALPHA, BETA * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLASET initializes a 2-D array A to BETA on the diagonal and *> ALPHA on the offdiagonals. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies the part of the matrix A to be set. *> = 'U': Upper triangular part is set. The lower triangle *> is unchanged. *> = 'L': Lower triangular part is set. The upper triangle *> is unchanged. *> Otherwise: All of the matrix A is set. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> On entry, M specifies the number of rows of A. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> On entry, N specifies the number of columns of A. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> All the offdiagonal array elements are set to ALPHA. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is COMPLEX*16 *> All the diagonal array elements are set to BETA. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the m by n matrix A. *> On exit, A(i,j) = ALPHA, 1 <= i <= m, 1 <= j <= n, i.ne.j; *> A(i,i) = BETA , 1 <= i <= min(m,n) *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, M, N COMPLEX*16 ALPHA, BETA * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( LSAME( UPLO, 'U' ) ) THEN * * Set the diagonal to BETA and the strictly upper triangular * part of the array to ALPHA. * DO 20 J = 2, N DO 10 I = 1, MIN( J-1, M ) A( I, J ) = ALPHA 10 CONTINUE 20 CONTINUE DO 30 I = 1, MIN( N, M ) A( I, I ) = BETA 30 CONTINUE * ELSE IF( LSAME( UPLO, 'L' ) ) THEN * * Set the diagonal to BETA and the strictly lower triangular * part of the array to ALPHA. * DO 50 J = 1, MIN( M, N ) DO 40 I = J + 1, M A( I, J ) = ALPHA 40 CONTINUE 50 CONTINUE DO 60 I = 1, MIN( N, M ) A( I, I ) = BETA 60 CONTINUE * ELSE * * Set the array to BETA on the diagonal and ALPHA on the * offdiagonal. * DO 80 J = 1, N DO 70 I = 1, M A( I, J ) = ALPHA 70 CONTINUE 80 CONTINUE DO 90 I = 1, MIN( M, N ) A( I, I ) = BETA 90 CONTINUE END IF * RETURN * * End of ZLASET * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zbdsqr.f0000644000000000000000000000012714061636515015335 xustar0029 mtime=1623670093.21510407 29 atime=1623670093.21510407 29 ctime=1623670093.21510407 elk-7.2.42/src/LAPACK/zbdsqr.f0000644002504400250440000006251714061636515017401 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZBDSQR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZBDSQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, * LDU, C, LDC, RWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ), RWORK( * ) * COMPLEX*16 C( LDC, * ), U( LDU, * ), VT( LDVT, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZBDSQR computes the singular values and, optionally, the right and/or *> left singular vectors from the singular value decomposition (SVD) of *> a real N-by-N (upper or lower) bidiagonal matrix B using the implicit *> zero-shift QR algorithm. The SVD of B has the form *> *> B = Q * S * P**H *> *> where S is the diagonal matrix of singular values, Q is an orthogonal *> matrix of left singular vectors, and P is an orthogonal matrix of *> right singular vectors. If left singular vectors are requested, this *> subroutine actually returns U*Q instead of Q, and, if right singular *> vectors are requested, this subroutine returns P**H*VT instead of *> P**H, for given complex input matrices U and VT. When U and VT are *> the unitary matrices that reduce a general matrix A to bidiagonal *> form: A = U*B*VT, as computed by ZGEBRD, then *> *> A = (U*Q) * S * (P**H*VT) *> *> is the SVD of A. Optionally, the subroutine may also compute Q**H*C *> for a given complex input matrix C. *> *> See "Computing Small Singular Values of Bidiagonal Matrices With *> Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, *> LAPACK Working Note #3 (or SIAM J. Sci. Statist. Comput. vol. 11, *> no. 5, pp. 873-912, Sept 1990) and *> "Accurate singular values and differential qd algorithms," by *> B. Parlett and V. Fernando, Technical Report CPAM-554, Mathematics *> Department, University of California at Berkeley, July 1992 *> for a detailed description of the algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': B is upper bidiagonal; *> = 'L': B is lower bidiagonal. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix B. N >= 0. *> \endverbatim *> *> \param[in] NCVT *> \verbatim *> NCVT is INTEGER *> The number of columns of the matrix VT. NCVT >= 0. *> \endverbatim *> *> \param[in] NRU *> \verbatim *> NRU is INTEGER *> The number of rows of the matrix U. NRU >= 0. *> \endverbatim *> *> \param[in] NCC *> \verbatim *> NCC is INTEGER *> The number of columns of the matrix C. NCC >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the n diagonal elements of the bidiagonal matrix B. *> On exit, if INFO=0, the singular values of B in decreasing *> order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> On entry, the N-1 offdiagonal elements of the bidiagonal *> matrix B. *> On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E *> will contain the diagonal and superdiagonal elements of a *> bidiagonal matrix orthogonally equivalent to the one given *> as input. *> \endverbatim *> *> \param[in,out] VT *> \verbatim *> VT is COMPLEX*16 array, dimension (LDVT, NCVT) *> On entry, an N-by-NCVT matrix VT. *> On exit, VT is overwritten by P**H * VT. *> Not referenced if NCVT = 0. *> \endverbatim *> *> \param[in] LDVT *> \verbatim *> LDVT is INTEGER *> The leading dimension of the array VT. *> LDVT >= max(1,N) if NCVT > 0; LDVT >= 1 if NCVT = 0. *> \endverbatim *> *> \param[in,out] U *> \verbatim *> U is COMPLEX*16 array, dimension (LDU, N) *> On entry, an NRU-by-N matrix U. *> On exit, U is overwritten by U * Q. *> Not referenced if NRU = 0. *> \endverbatim *> *> \param[in] LDU *> \verbatim *> LDU is INTEGER *> The leading dimension of the array U. LDU >= max(1,NRU). *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC, NCC) *> On entry, an N-by-NCC matrix C. *> On exit, C is overwritten by Q**H * C. *> Not referenced if NCC = 0. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. *> LDC >= max(1,N) if NCC > 0; LDC >=1 if NCC = 0. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (4*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: If INFO = -i, the i-th argument had an illegal value *> > 0: the algorithm did not converge; D and E contain the *> elements of a bidiagonal matrix which is orthogonally *> similar to the input matrix B; if INFO = i, i *> elements of E have not converged to zero. *> \endverbatim * *> \par Internal Parameters: * ========================= *> *> \verbatim *> TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> If it is positive, TOLMUL*EPS is the desired relative *> precision in the computed singular values. *> If it is negative, abs(TOLMUL*EPS*sigma_max) is the *> desired absolute accuracy in the computed singular *> values (corresponds to relative accuracy *> abs(TOLMUL*EPS) in the largest singular value. *> abs(TOLMUL) should be between 1 and 1/EPS, and preferably *> between 10 (for fast convergence) and .1/EPS *> (for there to be some accuracy in the results). *> Default is to lose at either one eighth or 2 of the *> available decimal digits in each computed singular value *> (whichever is smaller). *> *> MAXITR INTEGER, default = 6 *> MAXITR controls the maximum number of passes of the *> algorithm through its inner loop. The algorithms stops *> (and so fails to converge) if the number of passes *> through the inner loop exceeds MAXITR*N**2. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, $ LDU, C, LDC, RWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ), RWORK( * ) COMPLEX*16 C( LDC, * ), U( LDU, * ), VT( LDVT, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION NEGONE PARAMETER ( NEGONE = -1.0D0 ) DOUBLE PRECISION HNDRTH PARAMETER ( HNDRTH = 0.01D0 ) DOUBLE PRECISION TEN PARAMETER ( TEN = 10.0D0 ) DOUBLE PRECISION HNDRD PARAMETER ( HNDRD = 100.0D0 ) DOUBLE PRECISION MEIGTH PARAMETER ( MEIGTH = -0.125D0 ) INTEGER MAXITR PARAMETER ( MAXITR = 6 ) * .. * .. Local Scalars .. LOGICAL LOWER, ROTATE INTEGER I, IDIR, ISUB, ITER, J, LL, LLL, M, MAXIT, NM1, $ NM12, NM13, OLDLL, OLDM DOUBLE PRECISION ABSE, ABSS, COSL, COSR, CS, EPS, F, G, H, MU, $ OLDCS, OLDSN, R, SHIFT, SIGMN, SIGMX, SINL, $ SINR, SLL, SMAX, SMIN, SMINL, SMINOA, $ SN, THRESH, TOL, TOLMUL, UNFL * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH EXTERNAL LSAME, DLAMCH * .. * .. External Subroutines .. EXTERNAL DLARTG, DLAS2, DLASQ1, DLASV2, XERBLA, ZDROT, $ ZDSCAL, ZLASR, ZSWAP * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, SIGN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 LOWER = LSAME( UPLO, 'L' ) IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LOWER ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( NCVT.LT.0 ) THEN INFO = -3 ELSE IF( NRU.LT.0 ) THEN INFO = -4 ELSE IF( NCC.LT.0 ) THEN INFO = -5 ELSE IF( ( NCVT.EQ.0 .AND. LDVT.LT.1 ) .OR. $ ( NCVT.GT.0 .AND. LDVT.LT.MAX( 1, N ) ) ) THEN INFO = -9 ELSE IF( LDU.LT.MAX( 1, NRU ) ) THEN INFO = -11 ELSE IF( ( NCC.EQ.0 .AND. LDC.LT.1 ) .OR. $ ( NCC.GT.0 .AND. LDC.LT.MAX( 1, N ) ) ) THEN INFO = -13 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZBDSQR', -INFO ) RETURN END IF IF( N.EQ.0 ) $ RETURN IF( N.EQ.1 ) $ GO TO 160 * * ROTATE is true if any singular vectors desired, false otherwise * ROTATE = ( NCVT.GT.0 ) .OR. ( NRU.GT.0 ) .OR. ( NCC.GT.0 ) * * If no singular vectors desired, use qd algorithm * IF( .NOT.ROTATE ) THEN CALL DLASQ1( N, D, E, RWORK, INFO ) * * If INFO equals 2, dqds didn't finish, try to finish * IF( INFO .NE. 2 ) RETURN INFO = 0 END IF * NM1 = N - 1 NM12 = NM1 + NM1 NM13 = NM12 + NM1 IDIR = 0 * * Get machine constants * EPS = DLAMCH( 'Epsilon' ) UNFL = DLAMCH( 'Safe minimum' ) * * If matrix lower bidiagonal, rotate to be upper bidiagonal * by applying Givens rotations on the left * IF( LOWER ) THEN DO 10 I = 1, N - 1 CALL DLARTG( D( I ), E( I ), CS, SN, R ) D( I ) = R E( I ) = SN*D( I+1 ) D( I+1 ) = CS*D( I+1 ) RWORK( I ) = CS RWORK( NM1+I ) = SN 10 CONTINUE * * Update singular vectors if desired * IF( NRU.GT.0 ) $ CALL ZLASR( 'R', 'V', 'F', NRU, N, RWORK( 1 ), RWORK( N ), $ U, LDU ) IF( NCC.GT.0 ) $ CALL ZLASR( 'L', 'V', 'F', N, NCC, RWORK( 1 ), RWORK( N ), $ C, LDC ) END IF * * Compute singular values to relative accuracy TOL * (By setting TOL to be negative, algorithm will compute * singular values to absolute accuracy ABS(TOL)*norm(input matrix)) * TOLMUL = MAX( TEN, MIN( HNDRD, EPS**MEIGTH ) ) TOL = TOLMUL*EPS * * Compute approximate maximum, minimum singular values * SMAX = ZERO DO 20 I = 1, N SMAX = MAX( SMAX, ABS( D( I ) ) ) 20 CONTINUE DO 30 I = 1, N - 1 SMAX = MAX( SMAX, ABS( E( I ) ) ) 30 CONTINUE SMINL = ZERO IF( TOL.GE.ZERO ) THEN * * Relative accuracy desired * SMINOA = ABS( D( 1 ) ) IF( SMINOA.EQ.ZERO ) $ GO TO 50 MU = SMINOA DO 40 I = 2, N MU = ABS( D( I ) )*( MU / ( MU+ABS( E( I-1 ) ) ) ) SMINOA = MIN( SMINOA, MU ) IF( SMINOA.EQ.ZERO ) $ GO TO 50 40 CONTINUE 50 CONTINUE SMINOA = SMINOA / SQRT( DBLE( N ) ) THRESH = MAX( TOL*SMINOA, MAXITR*N*N*UNFL ) ELSE * * Absolute accuracy desired * THRESH = MAX( ABS( TOL )*SMAX, MAXITR*N*N*UNFL ) END IF * * Prepare for main iteration loop for the singular values * (MAXIT is the maximum number of passes through the inner * loop permitted before nonconvergence signalled.) * MAXIT = MAXITR*N*N ITER = 0 OLDLL = -1 OLDM = -1 * * M points to last element of unconverged part of matrix * M = N * * Begin main iteration loop * 60 CONTINUE * * Check for convergence or exceeding iteration count * IF( M.LE.1 ) $ GO TO 160 IF( ITER.GT.MAXIT ) $ GO TO 200 * * Find diagonal block of matrix to work on * IF( TOL.LT.ZERO .AND. ABS( D( M ) ).LE.THRESH ) $ D( M ) = ZERO SMAX = ABS( D( M ) ) SMIN = SMAX DO 70 LLL = 1, M - 1 LL = M - LLL ABSS = ABS( D( LL ) ) ABSE = ABS( E( LL ) ) IF( TOL.LT.ZERO .AND. ABSS.LE.THRESH ) $ D( LL ) = ZERO IF( ABSE.LE.THRESH ) $ GO TO 80 SMIN = MIN( SMIN, ABSS ) SMAX = MAX( SMAX, ABSS, ABSE ) 70 CONTINUE LL = 0 GO TO 90 80 CONTINUE E( LL ) = ZERO * * Matrix splits since E(LL) = 0 * IF( LL.EQ.M-1 ) THEN * * Convergence of bottom singular value, return to top of loop * M = M - 1 GO TO 60 END IF 90 CONTINUE LL = LL + 1 * * E(LL) through E(M-1) are nonzero, E(LL-1) is zero * IF( LL.EQ.M-1 ) THEN * * 2 by 2 block, handle separately * CALL DLASV2( D( M-1 ), E( M-1 ), D( M ), SIGMN, SIGMX, SINR, $ COSR, SINL, COSL ) D( M-1 ) = SIGMX E( M-1 ) = ZERO D( M ) = SIGMN * * Compute singular vectors, if desired * IF( NCVT.GT.0 ) $ CALL ZDROT( NCVT, VT( M-1, 1 ), LDVT, VT( M, 1 ), LDVT, $ COSR, SINR ) IF( NRU.GT.0 ) $ CALL ZDROT( NRU, U( 1, M-1 ), 1, U( 1, M ), 1, COSL, SINL ) IF( NCC.GT.0 ) $ CALL ZDROT( NCC, C( M-1, 1 ), LDC, C( M, 1 ), LDC, COSL, $ SINL ) M = M - 2 GO TO 60 END IF * * If working on new submatrix, choose shift direction * (from larger end diagonal element towards smaller) * IF( LL.GT.OLDM .OR. M.LT.OLDLL ) THEN IF( ABS( D( LL ) ).GE.ABS( D( M ) ) ) THEN * * Chase bulge from top (big end) to bottom (small end) * IDIR = 1 ELSE * * Chase bulge from bottom (big end) to top (small end) * IDIR = 2 END IF END IF * * Apply convergence tests * IF( IDIR.EQ.1 ) THEN * * Run convergence test in forward direction * First apply standard test to bottom of matrix * IF( ABS( E( M-1 ) ).LE.ABS( TOL )*ABS( D( M ) ) .OR. $ ( TOL.LT.ZERO .AND. ABS( E( M-1 ) ).LE.THRESH ) ) THEN E( M-1 ) = ZERO GO TO 60 END IF * IF( TOL.GE.ZERO ) THEN * * If relative accuracy desired, * apply convergence criterion forward * MU = ABS( D( LL ) ) SMINL = MU DO 100 LLL = LL, M - 1 IF( ABS( E( LLL ) ).LE.TOL*MU ) THEN E( LLL ) = ZERO GO TO 60 END IF MU = ABS( D( LLL+1 ) )*( MU / ( MU+ABS( E( LLL ) ) ) ) SMINL = MIN( SMINL, MU ) 100 CONTINUE END IF * ELSE * * Run convergence test in backward direction * First apply standard test to top of matrix * IF( ABS( E( LL ) ).LE.ABS( TOL )*ABS( D( LL ) ) .OR. $ ( TOL.LT.ZERO .AND. ABS( E( LL ) ).LE.THRESH ) ) THEN E( LL ) = ZERO GO TO 60 END IF * IF( TOL.GE.ZERO ) THEN * * If relative accuracy desired, * apply convergence criterion backward * MU = ABS( D( M ) ) SMINL = MU DO 110 LLL = M - 1, LL, -1 IF( ABS( E( LLL ) ).LE.TOL*MU ) THEN E( LLL ) = ZERO GO TO 60 END IF MU = ABS( D( LLL ) )*( MU / ( MU+ABS( E( LLL ) ) ) ) SMINL = MIN( SMINL, MU ) 110 CONTINUE END IF END IF OLDLL = LL OLDM = M * * Compute shift. First, test if shifting would ruin relative * accuracy, and if so set the shift to zero. * IF( TOL.GE.ZERO .AND. N*TOL*( SMINL / SMAX ).LE. $ MAX( EPS, HNDRTH*TOL ) ) THEN * * Use a zero shift to avoid loss of relative accuracy * SHIFT = ZERO ELSE * * Compute the shift from 2-by-2 block at end of matrix * IF( IDIR.EQ.1 ) THEN SLL = ABS( D( LL ) ) CALL DLAS2( D( M-1 ), E( M-1 ), D( M ), SHIFT, R ) ELSE SLL = ABS( D( M ) ) CALL DLAS2( D( LL ), E( LL ), D( LL+1 ), SHIFT, R ) END IF * * Test if shift negligible, and if so set to zero * IF( SLL.GT.ZERO ) THEN IF( ( SHIFT / SLL )**2.LT.EPS ) $ SHIFT = ZERO END IF END IF * * Increment iteration count * ITER = ITER + M - LL * * If SHIFT = 0, do simplified QR iteration * IF( SHIFT.EQ.ZERO ) THEN IF( IDIR.EQ.1 ) THEN * * Chase bulge from top to bottom * Save cosines and sines for later singular vector updates * CS = ONE OLDCS = ONE DO 120 I = LL, M - 1 CALL DLARTG( D( I )*CS, E( I ), CS, SN, R ) IF( I.GT.LL ) $ E( I-1 ) = OLDSN*R CALL DLARTG( OLDCS*R, D( I+1 )*SN, OLDCS, OLDSN, D( I ) ) RWORK( I-LL+1 ) = CS RWORK( I-LL+1+NM1 ) = SN RWORK( I-LL+1+NM12 ) = OLDCS RWORK( I-LL+1+NM13 ) = OLDSN 120 CONTINUE H = D( M )*CS D( M ) = H*OLDCS E( M-1 ) = H*OLDSN * * Update singular vectors * IF( NCVT.GT.0 ) $ CALL ZLASR( 'L', 'V', 'F', M-LL+1, NCVT, RWORK( 1 ), $ RWORK( N ), VT( LL, 1 ), LDVT ) IF( NRU.GT.0 ) $ CALL ZLASR( 'R', 'V', 'F', NRU, M-LL+1, RWORK( NM12+1 ), $ RWORK( NM13+1 ), U( 1, LL ), LDU ) IF( NCC.GT.0 ) $ CALL ZLASR( 'L', 'V', 'F', M-LL+1, NCC, RWORK( NM12+1 ), $ RWORK( NM13+1 ), C( LL, 1 ), LDC ) * * Test convergence * IF( ABS( E( M-1 ) ).LE.THRESH ) $ E( M-1 ) = ZERO * ELSE * * Chase bulge from bottom to top * Save cosines and sines for later singular vector updates * CS = ONE OLDCS = ONE DO 130 I = M, LL + 1, -1 CALL DLARTG( D( I )*CS, E( I-1 ), CS, SN, R ) IF( I.LT.M ) $ E( I ) = OLDSN*R CALL DLARTG( OLDCS*R, D( I-1 )*SN, OLDCS, OLDSN, D( I ) ) RWORK( I-LL ) = CS RWORK( I-LL+NM1 ) = -SN RWORK( I-LL+NM12 ) = OLDCS RWORK( I-LL+NM13 ) = -OLDSN 130 CONTINUE H = D( LL )*CS D( LL ) = H*OLDCS E( LL ) = H*OLDSN * * Update singular vectors * IF( NCVT.GT.0 ) $ CALL ZLASR( 'L', 'V', 'B', M-LL+1, NCVT, RWORK( NM12+1 ), $ RWORK( NM13+1 ), VT( LL, 1 ), LDVT ) IF( NRU.GT.0 ) $ CALL ZLASR( 'R', 'V', 'B', NRU, M-LL+1, RWORK( 1 ), $ RWORK( N ), U( 1, LL ), LDU ) IF( NCC.GT.0 ) $ CALL ZLASR( 'L', 'V', 'B', M-LL+1, NCC, RWORK( 1 ), $ RWORK( N ), C( LL, 1 ), LDC ) * * Test convergence * IF( ABS( E( LL ) ).LE.THRESH ) $ E( LL ) = ZERO END IF ELSE * * Use nonzero shift * IF( IDIR.EQ.1 ) THEN * * Chase bulge from top to bottom * Save cosines and sines for later singular vector updates * F = ( ABS( D( LL ) )-SHIFT )* $ ( SIGN( ONE, D( LL ) )+SHIFT / D( LL ) ) G = E( LL ) DO 140 I = LL, M - 1 CALL DLARTG( F, G, COSR, SINR, R ) IF( I.GT.LL ) $ E( I-1 ) = R F = COSR*D( I ) + SINR*E( I ) E( I ) = COSR*E( I ) - SINR*D( I ) G = SINR*D( I+1 ) D( I+1 ) = COSR*D( I+1 ) CALL DLARTG( F, G, COSL, SINL, R ) D( I ) = R F = COSL*E( I ) + SINL*D( I+1 ) D( I+1 ) = COSL*D( I+1 ) - SINL*E( I ) IF( I.LT.M-1 ) THEN G = SINL*E( I+1 ) E( I+1 ) = COSL*E( I+1 ) END IF RWORK( I-LL+1 ) = COSR RWORK( I-LL+1+NM1 ) = SINR RWORK( I-LL+1+NM12 ) = COSL RWORK( I-LL+1+NM13 ) = SINL 140 CONTINUE E( M-1 ) = F * * Update singular vectors * IF( NCVT.GT.0 ) $ CALL ZLASR( 'L', 'V', 'F', M-LL+1, NCVT, RWORK( 1 ), $ RWORK( N ), VT( LL, 1 ), LDVT ) IF( NRU.GT.0 ) $ CALL ZLASR( 'R', 'V', 'F', NRU, M-LL+1, RWORK( NM12+1 ), $ RWORK( NM13+1 ), U( 1, LL ), LDU ) IF( NCC.GT.0 ) $ CALL ZLASR( 'L', 'V', 'F', M-LL+1, NCC, RWORK( NM12+1 ), $ RWORK( NM13+1 ), C( LL, 1 ), LDC ) * * Test convergence * IF( ABS( E( M-1 ) ).LE.THRESH ) $ E( M-1 ) = ZERO * ELSE * * Chase bulge from bottom to top * Save cosines and sines for later singular vector updates * F = ( ABS( D( M ) )-SHIFT )*( SIGN( ONE, D( M ) )+SHIFT / $ D( M ) ) G = E( M-1 ) DO 150 I = M, LL + 1, -1 CALL DLARTG( F, G, COSR, SINR, R ) IF( I.LT.M ) $ E( I ) = R F = COSR*D( I ) + SINR*E( I-1 ) E( I-1 ) = COSR*E( I-1 ) - SINR*D( I ) G = SINR*D( I-1 ) D( I-1 ) = COSR*D( I-1 ) CALL DLARTG( F, G, COSL, SINL, R ) D( I ) = R F = COSL*E( I-1 ) + SINL*D( I-1 ) D( I-1 ) = COSL*D( I-1 ) - SINL*E( I-1 ) IF( I.GT.LL+1 ) THEN G = SINL*E( I-2 ) E( I-2 ) = COSL*E( I-2 ) END IF RWORK( I-LL ) = COSR RWORK( I-LL+NM1 ) = -SINR RWORK( I-LL+NM12 ) = COSL RWORK( I-LL+NM13 ) = -SINL 150 CONTINUE E( LL ) = F * * Test convergence * IF( ABS( E( LL ) ).LE.THRESH ) $ E( LL ) = ZERO * * Update singular vectors if desired * IF( NCVT.GT.0 ) $ CALL ZLASR( 'L', 'V', 'B', M-LL+1, NCVT, RWORK( NM12+1 ), $ RWORK( NM13+1 ), VT( LL, 1 ), LDVT ) IF( NRU.GT.0 ) $ CALL ZLASR( 'R', 'V', 'B', NRU, M-LL+1, RWORK( 1 ), $ RWORK( N ), U( 1, LL ), LDU ) IF( NCC.GT.0 ) $ CALL ZLASR( 'L', 'V', 'B', M-LL+1, NCC, RWORK( 1 ), $ RWORK( N ), C( LL, 1 ), LDC ) END IF END IF * * QR iteration finished, go back and check convergence * GO TO 60 * * All singular values converged, so make them positive * 160 CONTINUE DO 170 I = 1, N IF( D( I ).LT.ZERO ) THEN D( I ) = -D( I ) * * Change sign of singular vectors, if desired * IF( NCVT.GT.0 ) $ CALL ZDSCAL( NCVT, NEGONE, VT( I, 1 ), LDVT ) END IF 170 CONTINUE * * Sort the singular values into decreasing order (insertion sort on * singular values, but only one transposition per singular vector) * DO 190 I = 1, N - 1 * * Scan for smallest D(I) * ISUB = 1 SMIN = D( 1 ) DO 180 J = 2, N + 1 - I IF( D( J ).LE.SMIN ) THEN ISUB = J SMIN = D( J ) END IF 180 CONTINUE IF( ISUB.NE.N+1-I ) THEN * * Swap singular values and vectors * D( ISUB ) = D( N+1-I ) D( N+1-I ) = SMIN IF( NCVT.GT.0 ) $ CALL ZSWAP( NCVT, VT( ISUB, 1 ), LDVT, VT( N+1-I, 1 ), $ LDVT ) IF( NRU.GT.0 ) $ CALL ZSWAP( NRU, U( 1, ISUB ), 1, U( 1, N+1-I ), 1 ) IF( NCC.GT.0 ) $ CALL ZSWAP( NCC, C( ISUB, 1 ), LDC, C( N+1-I, 1 ), LDC ) END IF 190 CONTINUE GO TO 220 * * Maximum number of iterations exceeded, failure to converge * 200 CONTINUE INFO = 0 DO 210 I = 1, N - 1 IF( E( I ).NE.ZERO ) $ INFO = INFO + 1 210 CONTINUE 220 CONTINUE RETURN * * End of ZBDSQR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunmbr.f0000644000000000000000000000013214061636515015341 xustar0030 mtime=1623670093.217104068 30 atime=1623670093.217104068 30 ctime=1623670093.217104068 elk-7.2.42/src/LAPACK/zunmbr.f0000644002504400250440000002555314061636515017410 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNMBR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNMBR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, * LDC, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS, VECT * INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C *> with *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'C': Q**H * C C * Q**H *> *> If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C *> with *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': P * C C * P *> TRANS = 'C': P**H * C C * P**H *> *> Here Q and P**H are the unitary matrices determined by ZGEBRD when *> reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q *> and P**H are defined as products of elementary reflectors H(i) and *> G(i) respectively. *> *> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the *> order of the unitary matrix Q or P**H that is applied. *> *> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: *> if nq >= k, Q = H(1) H(2) . . . H(k); *> if nq < k, Q = H(1) H(2) . . . H(nq-1). *> *> If VECT = 'P', A is assumed to have been a K-by-NQ matrix: *> if k < nq, P = G(1) G(2) . . . G(k); *> if k >= nq, P = G(1) G(2) . . . G(nq-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] VECT *> \verbatim *> VECT is CHARACTER*1 *> = 'Q': apply Q or Q**H; *> = 'P': apply P or P**H. *> \endverbatim *> *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q, Q**H, P or P**H from the Left; *> = 'R': apply Q, Q**H, P or P**H from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q or P; *> = 'C': Conjugate transpose, apply Q**H or P**H. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> If VECT = 'Q', the number of columns in the original *> matrix reduced by ZGEBRD. *> If VECT = 'P', the number of rows in the original *> matrix reduced by ZGEBRD. *> K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension *> (LDA,min(nq,K)) if VECT = 'Q' *> (LDA,nq) if VECT = 'P' *> The vectors which define the elementary reflectors H(i) and *> G(i), whose products determine the matrices Q and P, as *> returned by ZGEBRD. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If VECT = 'Q', LDA >= max(1,nq); *> if VECT = 'P', LDA >= max(1,min(nq,K)). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (min(nq,K)) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i) or G(i) which determines Q or P, as returned *> by ZGEBRD in the array argument TAUQ or TAUP. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q *> or P*C or P**H*C or C*P or C*P**H. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M); *> if N = 0 or M = 0, LWORK >= 1. *> For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', *> and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the *> optimal blocksize. (NB = 0 if M = 0 or N = 0.) *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, $ LDC, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, VECT INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN CHARACTER TRANST INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZUNMLQ, ZUNMQR * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 APPLYQ = LSAME( VECT, 'Q' ) LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q or P and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( M.EQ.0 .OR. N.EQ.0 ) THEN NW = 0 END IF IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN INFO = -1 ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -2 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -3 ELSE IF( M.LT.0 ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( K.LT.0 ) THEN INFO = -6 ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) $ THEN INFO = -8 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN IF( NW.GT.0 ) THEN IF( APPLYQ ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1, $ -1 ) ELSE NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1, $ -1 ) END IF ELSE IF( LEFT ) THEN NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M-1, N, M-1, $ -1 ) ELSE NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N-1, N-1, $ -1 ) END IF END IF LWKOPT = MAX( 1, NW*NB ) ELSE LWKOPT = 1 END IF WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNMBR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * IF( APPLYQ ) THEN * * Apply Q * IF( NQ.GE.K ) THEN * * Q was determined by a call to ZGEBRD with nq >= k * CALL ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN * * Q was determined by a call to ZGEBRD with nq < k * IF( LEFT ) THEN MI = M - 1 NI = N I1 = 2 I2 = 1 ELSE MI = M NI = N - 1 I1 = 1 I2 = 2 END IF CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF ELSE * * Apply P * IF( NOTRAN ) THEN TRANST = 'C' ELSE TRANST = 'N' END IF IF( NQ.GT.K ) THEN * * P was determined by a call to ZGEBRD with nq > k * CALL ZUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, IINFO ) ELSE IF( NQ.GT.1 ) THEN * * P was determined by a call to ZGEBRD with nq <= k * IF( LEFT ) THEN MI = M - 1 NI = N I1 = 2 I2 = 1 ELSE MI = M NI = N - 1 I1 = 1 I2 = 2 END IF CALL ZUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF END IF WORK( 1 ) = LWKOPT RETURN * * End of ZUNMBR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgetrs.f0000644000000000000000000000013214061636515015342 xustar0030 mtime=1623670093.219104066 30 atime=1623670093.219104066 30 ctime=1623670093.219104066 elk-7.2.42/src/LAPACK/zgetrs.f0000644002504400250440000001364314061636515017406 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGETRS * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGETRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER TRANS * INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGETRS solves a system of linear equations *> A * X = B, A**T * X = B, or A**H * X = B *> with a general N-by-N matrix A using the LU factorization computed *> by ZGETRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the form of the system of equations: *> = 'N': A * X = B (No transpose) *> = 'T': A**T * X = B (Transpose) *> = 'C': A**H * X = B (Conjugate transpose) *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The factors L and U from the factorization A = P*L*U *> as computed by ZGETRF. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices from ZGETRF; for 1<=i<=N, row i of the *> matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,NRHS) *> On entry, the right hand side matrix B. *> On exit, the solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GEcomputational * * ===================================================================== SUBROUTINE ZGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER INFO, LDA, LDB, N, NRHS * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL NOTRAN * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLASWP, ZTRSM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 NOTRAN = LSAME( TRANS, 'N' ) IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. $ LSAME( TRANS, 'C' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( NRHS.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGETRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * IF( NOTRAN ) THEN * * Solve A * X = B. * * Apply row interchanges to the right hand sides. * CALL ZLASWP( NRHS, B, LDB, 1, N, IPIV, 1 ) * * Solve L*X = B, overwriting B with X. * CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS, $ ONE, A, LDA, B, LDB ) * * Solve U*X = B, overwriting B with X. * CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, $ NRHS, ONE, A, LDA, B, LDB ) ELSE * * Solve A**T * X = B or A**H * X = B. * * Solve U**T *X = B or U**H *X = B, overwriting B with X. * CALL ZTRSM( 'Left', 'Upper', TRANS, 'Non-unit', N, NRHS, ONE, $ A, LDA, B, LDB ) * * Solve L**T *X = B, or L**H *X = B overwriting B with X. * CALL ZTRSM( 'Left', 'Lower', TRANS, 'Unit', N, NRHS, ONE, A, $ LDA, B, LDB ) * * Apply row interchanges to the solution vectors. * CALL ZLASWP( NRHS, B, LDB, 1, N, IPIV, -1 ) END IF * RETURN * * End of ZGETRS * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgetrf2.f0000644000000000000000000000013214061636515015407 xustar0030 mtime=1623670093.221104064 30 atime=1623670093.221104064 30 ctime=1623670093.221104064 elk-7.2.42/src/LAPACK/zgetrf2.f0000644002504400250440000001571114061636515017451 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGETRF2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * RECURSIVE SUBROUTINE ZGETRF2( M, N, A, LDA, IPIV, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGETRF2 computes an LU factorization of a general M-by-N matrix A *> using partial pivoting with row interchanges. *> *> The factorization has the form *> A = P * L * U *> where P is a permutation matrix, L is lower triangular with unit *> diagonal elements (lower trapezoidal if m > n), and U is upper *> triangular (upper trapezoidal if m < n). *> *> This is the recursive version of the algorithm. It divides *> the matrix into four submatrices: *> *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 *> A = [ -----|----- ] with n1 = min(m,n)/2 *> [ A21 | A22 ] n2 = n-n1 *> *> [ A11 ] *> The subroutine calls itself to factor [ --- ], *> [ A12 ] *> [ A12 ] *> do the swaps on [ --- ], solve A12, update A22, *> [ A22 ] *> *> then calls itself to factor A22 and do the swaps on A21. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the M-by-N matrix to be factored. *> On exit, the factors L and U from the factorization *> A = P*L*U; the unit diagonal elements of L are not stored. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (min(M,N)) *> The pivot indices; for 1 <= i <= min(M,N), row i of the *> matrix was interchanged with row IPIV(i). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, U(i,i) is exactly zero. The factorization *> has been completed, but the factor U is exactly *> singular, and division by zero will occur if it is used *> to solve a system of equations. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16GEcomputational * * ===================================================================== RECURSIVE SUBROUTINE ZGETRF2( M, N, A, LDA, IPIV, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. DOUBLE PRECISION SFMIN COMPLEX*16 TEMP INTEGER I, IINFO, N1, N2 * .. * .. External Functions .. DOUBLE PRECISION DLAMCH INTEGER IZAMAX EXTERNAL DLAMCH, IZAMAX * .. * .. External Subroutines .. EXTERNAL ZGEMM, ZSCAL, ZLASWP, ZTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGETRF2', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN IF ( M.EQ.1 ) THEN * * Use unblocked code for one row case * Just need to handle IPIV and INFO * IPIV( 1 ) = 1 IF ( A(1,1).EQ.ZERO ) $ INFO = 1 * ELSE IF( N.EQ.1 ) THEN * * Use unblocked code for one column case * * * Compute machine safe minimum * SFMIN = DLAMCH('S') * * Find pivot and test for singularity * I = IZAMAX( M, A( 1, 1 ), 1 ) IPIV( 1 ) = I IF( A( I, 1 ).NE.ZERO ) THEN * * Apply the interchange * IF( I.NE.1 ) THEN TEMP = A( 1, 1 ) A( 1, 1 ) = A( I, 1 ) A( I, 1 ) = TEMP END IF * * Compute elements 2:M of the column * IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN CALL ZSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 ) ELSE DO 10 I = 1, M-1 A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 ) 10 CONTINUE END IF * ELSE INFO = 1 END IF ELSE * * Use recursive code * N1 = MIN( M, N ) / 2 N2 = N-N1 * * [ A11 ] * Factor [ --- ] * [ A21 ] * CALL ZGETRF2( M, N1, A, LDA, IPIV, IINFO ) IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) $ INFO = IINFO * * [ A12 ] * Apply interchanges to [ --- ] * [ A22 ] * CALL ZLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 ) * * Solve A12 * CALL ZTRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA, $ A( 1, N1+1 ), LDA ) * * Update A22 * CALL ZGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA, $ A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA ) * * Factor A22 * CALL ZGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ), $ IINFO ) * * Adjust INFO and the pivot indices * IF ( INFO.EQ.0 .AND. IINFO.GT.0 ) $ INFO = IINFO + N1 DO 20 I = N1+1, MIN( M, N ) IPIV( I ) = IPIV( I ) + N1 20 CONTINUE * * Apply interchanges to A21 * CALL ZLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 ) * END IF RETURN * * End of ZGETRF2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaswp.f0000644000000000000000000000013214061636515015344 xustar0030 mtime=1623670093.223104062 30 atime=1623670093.222104063 30 ctime=1623670093.223104062 elk-7.2.42/src/LAPACK/zlaswp.f0000644002504400250440000001200514061636515017377 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLASWP performs a series of row interchanges on a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLASWP + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLASWP( N, A, LDA, K1, K2, IPIV, INCX ) * * .. Scalar Arguments .. * INTEGER INCX, K1, K2, LDA, N * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLASWP performs a series of row interchanges on the matrix A. *> One row interchange is initiated for each of rows K1 through K2 of A. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the matrix of column dimension N to which the row *> interchanges will be applied. *> On exit, the permuted matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> \endverbatim *> *> \param[in] K1 *> \verbatim *> K1 is INTEGER *> The first element of IPIV for which a row interchange will *> be done. *> \endverbatim *> *> \param[in] K2 *> \verbatim *> K2 is INTEGER *> (K2-K1+1) is the number of elements of IPIV for which a row *> interchange will be done. *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (K1+(K2-K1)*abs(INCX)) *> The vector of pivot indices. Only the elements in positions *> K1 through K1+(K2-K1)*abs(INCX) of IPIV are accessed. *> IPIV(K1+(K-K1)*abs(INCX)) = L implies rows K and L are to be *> interchanged. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between successive values of IPIV. If INCX *> is negative, the pivots are applied in reverse order. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complex16OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> Modified by *> R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA *> \endverbatim *> * ===================================================================== SUBROUTINE ZLASWP( N, A, LDA, K1, K2, IPIV, INCX ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER INCX, K1, K2, LDA, N * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, I1, I2, INC, IP, IX, IX0, J, K, N32 COMPLEX*16 TEMP * .. * .. Executable Statements .. * * Interchange row I with row IPIV(K1+(I-K1)*abs(INCX)) for each of rows * K1 through K2. * IF( INCX.GT.0 ) THEN IX0 = K1 I1 = K1 I2 = K2 INC = 1 ELSE IF( INCX.LT.0 ) THEN IX0 = K1 + ( K1-K2 )*INCX I1 = K2 I2 = K1 INC = -1 ELSE RETURN END IF * N32 = ( N / 32 )*32 IF( N32.NE.0 ) THEN DO 30 J = 1, N32, 32 IX = IX0 DO 20 I = I1, I2, INC IP = IPIV( IX ) IF( IP.NE.I ) THEN DO 10 K = J, J + 31 TEMP = A( I, K ) A( I, K ) = A( IP, K ) A( IP, K ) = TEMP 10 CONTINUE END IF IX = IX + INCX 20 CONTINUE 30 CONTINUE END IF IF( N32.NE.N ) THEN N32 = N32 + 1 IX = IX0 DO 50 I = I1, I2, INC IP = IPIV( IX ) IF( IP.NE.I ) THEN DO 40 K = N32, N TEMP = A( I, K ) A( I, K ) = A( IP, K ) A( IP, K ) = TEMP 40 CONTINUE END IF IX = IX + INCX 50 CONTINUE END IF * RETURN * * End of ZLASWP * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/ztrtri.f0000644000000000000000000000013214061636515015362 xustar0030 mtime=1623670093.225104061 30 atime=1623670093.224104061 30 ctime=1623670093.225104061 elk-7.2.42/src/LAPACK/ztrtri.f0000644002504400250440000001545014061636515017424 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTRTRI * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZTRTRI + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZTRTRI( UPLO, DIAG, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTRTRI computes the inverse of a complex upper or lower triangular *> matrix A. *> *> This is the Level 3 BLAS version of the algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': A is upper triangular; *> = 'L': A is lower triangular. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> = 'N': A is non-unit triangular; *> = 'U': A is unit triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the triangular matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of the array A contains *> the upper triangular matrix, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of the array A contains *> the lower triangular matrix, and the strictly upper *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, A(i,i) is exactly zero. The triangular *> matrix is singular and its inverse can not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZTRTRI( UPLO, DIAG, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER J, JB, NB, NN * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZTRMM, ZTRSM, ZTRTI2 * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) NOUNIT = LSAME( DIAG, 'N' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZTRTRI', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Check for singularity if non-unit. * IF( NOUNIT ) THEN DO 10 INFO = 1, N IF( A( INFO, INFO ).EQ.ZERO ) $ RETURN 10 CONTINUE INFO = 0 END IF * * Determine the block size for this environment. * NB = ILAENV( 1, 'ZTRTRI', UPLO // DIAG, N, -1, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL ZTRTI2( UPLO, DIAG, N, A, LDA, INFO ) ELSE * * Use blocked code * IF( UPPER ) THEN * * Compute inverse of upper triangular matrix * DO 20 J = 1, N, NB JB = MIN( NB, N-J+1 ) * * Compute rows 1:j-1 of current block column * CALL ZTRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1, $ JB, ONE, A, LDA, A( 1, J ), LDA ) CALL ZTRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1, $ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA ) * * Compute inverse of current diagonal block * CALL ZTRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO ) 20 CONTINUE ELSE * * Compute inverse of lower triangular matrix * NN = ( ( N-1 ) / NB )*NB + 1 DO 30 J = NN, 1, -NB JB = MIN( NB, N-J+1 ) IF( J+JB.LE.N ) THEN * * Compute rows j+jb:n of current block column * CALL ZTRMM( 'Left', 'Lower', 'No transpose', DIAG, $ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA, $ A( J+JB, J ), LDA ) CALL ZTRSM( 'Right', 'Lower', 'No transpose', DIAG, $ N-J-JB+1, JB, -ONE, A( J, J ), LDA, $ A( J+JB, J ), LDA ) END IF * * Compute inverse of current diagonal block * CALL ZTRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO ) 30 CONTINUE END IF END IF * RETURN * * End of ZTRTRI * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlanhe.f0000644000000000000000000000012714061636515015311 xustar0029 mtime=1623670093.22610406 29 atime=1623670093.22610406 29 ctime=1623670093.22610406 elk-7.2.42/src/LAPACK/zlanhe.f0000644002504400250440000002107414061636515017346 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLANHE + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) * * .. Scalar Arguments .. * CHARACTER NORM, UPLO * INTEGER LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION WORK( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLANHE returns the value of the one norm, or the Frobenius norm, or *> the infinity norm, or the element of largest absolute value of a *> complex hermitian matrix A. *> \endverbatim *> *> \return ZLANHE *> \verbatim *> *> ZLANHE = ( max(abs(A(i,j))), NORM = 'M' or 'm' *> ( *> ( norm1(A), NORM = '1', 'O' or 'o' *> ( *> ( normI(A), NORM = 'I' or 'i' *> ( *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' *> *> where norm1 denotes the one norm of a matrix (maximum column sum), *> normI denotes the infinity norm of a matrix (maximum row sum) and *> normF denotes the Frobenius norm of a matrix (square root of sum of *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] NORM *> \verbatim *> NORM is CHARACTER*1 *> Specifies the value to be returned in ZLANHE as described *> above. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> hermitian matrix A is to be referenced. *> = 'U': Upper triangular part of A is referenced *> = 'L': Lower triangular part of A is referenced *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, ZLANHE is *> set to zero. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The hermitian matrix A. If UPLO = 'U', the leading n by n *> upper triangular part of A contains the upper triangular part *> of the matrix A, and the strictly lower triangular part of A *> is not referenced. If UPLO = 'L', the leading n by n lower *> triangular part of A contains the lower triangular part of *> the matrix A, and the strictly upper triangular part of A is *> not referenced. Note that the imaginary parts of the diagonal *> elements need not be set and are assumed to be zero. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(N,1). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, *> WORK is not referenced. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16HEauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * IMPLICIT NONE * .. Scalar Arguments .. CHARACTER NORM, UPLO INTEGER LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION WORK( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION ABSA, SUM, VALUE * .. * .. Local Arrays .. DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZLASSQ, DCOMBSSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, SQRT * .. * .. Executable Statements .. * IF( N.EQ.0 ) THEN VALUE = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * VALUE = ZERO IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, J - 1 SUM = ABS( A( I, J ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE SUM = ABS( DBLE( A( J, J ) ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 20 CONTINUE ELSE DO 40 J = 1, N SUM = ABS( DBLE( A( J, J ) ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM DO 30 I = J + 1, N SUM = ABS( A( I, J ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE 40 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. $ ( NORM.EQ.'1' ) ) THEN * * Find normI(A) ( = norm1(A), since A is hermitian). * VALUE = ZERO IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N SUM = ZERO DO 50 I = 1, J - 1 ABSA = ABS( A( I, J ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA 50 CONTINUE WORK( J ) = SUM + ABS( DBLE( A( J, J ) ) ) 60 CONTINUE DO 70 I = 1, N SUM = WORK( I ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE ELSE DO 80 I = 1, N WORK( I ) = ZERO 80 CONTINUE DO 100 J = 1, N SUM = WORK( J ) + ABS( DBLE( A( J, J ) ) ) DO 90 I = J + 1, N ABSA = ABS( A( I, J ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA 90 CONTINUE IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 100 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SSQ(1) is scale * SSQ(2) is sum-of-squares * For better accuracy, sum each column separately. * SSQ( 1 ) = ZERO SSQ( 2 ) = ONE * * Sum off-diagonals * IF( LSAME( UPLO, 'U' ) ) THEN DO 110 J = 2, N COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL ZLASSQ( J-1, A( 1, J ), 1, $ COLSSQ( 1 ), COLSSQ( 2 ) ) CALL DCOMBSSQ( SSQ, COLSSQ ) 110 CONTINUE ELSE DO 120 J = 1, N - 1 COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL ZLASSQ( N-J, A( J+1, J ), 1, $ COLSSQ( 1 ), COLSSQ( 2 ) ) CALL DCOMBSSQ( SSQ, COLSSQ ) 120 CONTINUE END IF SSQ( 2 ) = 2*SSQ( 2 ) * * Sum diagonal * DO 130 I = 1, N IF( DBLE( A( I, I ) ).NE.ZERO ) THEN ABSA = ABS( DBLE( A( I, I ) ) ) IF( SSQ( 1 ).LT.ABSA ) THEN SSQ( 2 ) = ONE + SSQ( 2 )*( SSQ( 1 ) / ABSA )**2 SSQ( 1 ) = ABSA ELSE SSQ( 2 ) = SSQ( 2 ) + ( ABSA / SSQ( 1 ) )**2 END IF END IF 130 CONTINUE VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) END IF * ZLANHE = VALUE RETURN * * End of ZLANHE * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhetrd.f0000644000000000000000000000013214061636515015324 xustar0030 mtime=1623670093.228104058 30 atime=1623670093.228104058 30 ctime=1623670093.228104058 elk-7.2.42/src/LAPACK/zhetrd.f0000644002504400250440000002646114061636515017372 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHETRD * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHETRD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ) * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHETRD reduces a complex Hermitian matrix A to real symmetric *> tridiagonal form T by a unitary similarity transformation: *> Q**H * A * Q = T. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> On exit, if UPLO = 'U', the diagonal and first superdiagonal *> of A are overwritten by the corresponding elements of the *> tridiagonal matrix T, and the elements above the first *> superdiagonal, with the array TAU, represent the unitary *> matrix Q as a product of elementary reflectors; if UPLO *> = 'L', the diagonal and first subdiagonal of A are over- *> written by the corresponding elements of the tridiagonal *> matrix T, and the elements below the first subdiagonal, with *> the array TAU, represent the unitary matrix Q as a product *> of elementary reflectors. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of the tridiagonal matrix T: *> D(i) = A(i,i). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The off-diagonal elements of the tridiagonal matrix T: *> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= 1. *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16HEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> If UPLO = 'U', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(n-1) . . . H(2) H(1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in *> A(1:i-1,i+1), and tau in TAU(i). *> *> If UPLO = 'L', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(1) H(2) . . . H(n-1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), *> and tau in TAU(i). *> *> The contents of A on exit are illustrated by the following examples *> with n = 5: *> *> if UPLO = 'U': if UPLO = 'L': *> *> ( d e v2 v3 v4 ) ( d ) *> ( d e v3 v4 ) ( e d ) *> ( d e v4 ) ( v1 e d ) *> ( d e ) ( v1 v2 e d ) *> ( d ) ( v1 v2 v3 e d ) *> *> where d and e denote diagonal and off-diagonal elements of T, and vi *> denotes an element of the vector defining H(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ) COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER INTEGER I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB, $ NBMIN, NX * .. * .. External Subroutines .. EXTERNAL XERBLA, ZHER2K, ZHETD2, ZLATRD * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN INFO = -9 END IF * IF( INFO.EQ.0 ) THEN * * Determine the block size. * NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) LWKOPT = N*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHETRD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NX = N IWS = 1 IF( NB.GT.1 .AND. NB.LT.N ) THEN * * Determine when to cross over from blocked to unblocked code * (last block is always handled by unblocked code). * NX = MAX( NB, ILAENV( 3, 'ZHETRD', UPLO, N, -1, -1, -1 ) ) IF( NX.LT.N ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = N IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: determine the * minimum value of NB, and reduce NB or force use of * unblocked code by setting NX = N. * NB = MAX( LWORK / LDWORK, 1 ) NBMIN = ILAENV( 2, 'ZHETRD', UPLO, N, -1, -1, -1 ) IF( NB.LT.NBMIN ) $ NX = N END IF ELSE NX = N END IF ELSE NB = 1 END IF * IF( UPPER ) THEN * * Reduce the upper triangle of A. * Columns 1:kk are handled by the unblocked method. * KK = N - ( ( N-NX+NB-1 ) / NB )*NB DO 20 I = N - NB + 1, KK + 1, -NB * * Reduce columns i:i+nb-1 to tridiagonal form and form the * matrix W which is needed to update the unreduced part of * the matrix * CALL ZLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK, $ LDWORK ) * * Update the unreduced submatrix A(1:i-1,1:i-1), using an * update of the form: A := A - V*W**H - W*V**H * CALL ZHER2K( UPLO, 'No transpose', I-1, NB, -CONE, $ A( 1, I ), LDA, WORK, LDWORK, ONE, A, LDA ) * * Copy superdiagonal elements back into A, and diagonal * elements into D * DO 10 J = I, I + NB - 1 A( J-1, J ) = E( J-1 ) D( J ) = A( J, J ) 10 CONTINUE 20 CONTINUE * * Use unblocked code to reduce the last or only block * CALL ZHETD2( UPLO, KK, A, LDA, D, E, TAU, IINFO ) ELSE * * Reduce the lower triangle of A * DO 40 I = 1, N - NX, NB * * Reduce columns i:i+nb-1 to tridiagonal form and form the * matrix W which is needed to update the unreduced part of * the matrix * CALL ZLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ), $ TAU( I ), WORK, LDWORK ) * * Update the unreduced submatrix A(i+nb:n,i+nb:n), using * an update of the form: A := A - V*W**H - W*V**H * CALL ZHER2K( UPLO, 'No transpose', N-I-NB+1, NB, -CONE, $ A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE, $ A( I+NB, I+NB ), LDA ) * * Copy subdiagonal elements back into A, and diagonal * elements into D * DO 30 J = I, I + NB - 1 A( J+1, J ) = E( J ) D( J ) = A( J, J ) 30 CONTINUE 40 CONTINUE * * Use unblocked code to reduce the last or only block * CALL ZHETD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ), $ TAU( I ), IINFO ) END IF * WORK( 1 ) = LWKOPT RETURN * * End of ZHETRD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zstedc.f0000644000000000000000000000013214061636515015320 xustar0030 mtime=1623670093.231104055 30 atime=1623670093.230104056 30 ctime=1623670093.231104055 elk-7.2.42/src/LAPACK/zstedc.f0000644002504400250440000003732414061636515017366 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZSTEDC * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZSTEDC + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, * LRWORK, IWORK, LIWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER COMPZ * INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N * .. * .. Array Arguments .. * INTEGER IWORK( * ) * DOUBLE PRECISION D( * ), E( * ), RWORK( * ) * COMPLEX*16 WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a *> symmetric tridiagonal matrix using the divide and conquer method. *> The eigenvectors of a full or band complex Hermitian matrix can also *> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this *> matrix to tridiagonal form. *> *> This code makes very mild assumptions about floating point *> arithmetic. It will work on machines with a guard digit in *> add/subtract, or on those binary machines without guard digits *> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. *> It could conceivably fail on hexadecimal or decimal machines *> without guard digits, but we know of none. See DLAED3 for details. *> \endverbatim * * Arguments: * ========== * *> \param[in] COMPZ *> \verbatim *> COMPZ is CHARACTER*1 *> = 'N': Compute eigenvalues only. *> = 'I': Compute eigenvectors of tridiagonal matrix also. *> = 'V': Compute eigenvectors of original Hermitian matrix *> also. On entry, Z contains the unitary matrix used *> to reduce the original matrix to tridiagonal form. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the diagonal elements of the tridiagonal matrix. *> On exit, if INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> On entry, the subdiagonal elements of the tridiagonal matrix. *> On exit, E has been destroyed. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ,N) *> On entry, if COMPZ = 'V', then Z contains the unitary *> matrix used in the reduction to tridiagonal form. *> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the *> orthonormal eigenvectors of the original Hermitian matrix, *> and if COMPZ = 'I', Z contains the orthonormal eigenvectors *> of the symmetric tridiagonal matrix. *> If COMPZ = 'N', then Z is not referenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1. *> If eigenvectors are desired, then LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1. *> If COMPZ = 'V' and N > 1, LWORK must be at least N*N. *> Note that for COMPZ = 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LWORK need *> only be 1. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of *> the WORK, RWORK and IWORK arrays, and no error message *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. *> \endverbatim *> *> \param[in] LRWORK *> \verbatim *> LRWORK is INTEGER *> The dimension of the array RWORK. *> If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. *> If COMPZ = 'V' and N > 1, LRWORK must be at least *> 1 + 3*N + 2*N*lg N + 4*N**2 , *> where lg( N ) = smallest integer k such *> that 2**k >= N. *> If COMPZ = 'I' and N > 1, LRWORK must be at least *> 1 + 4*N + 2*N**2 . *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LRWORK *> need only be max(1,2*(N-1)). *> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries *> of the WORK, RWORK and IWORK arrays, and no error message *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. *> \endverbatim *> *> \param[in] LIWORK *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. *> If COMPZ = 'N' or N <= 1, LIWORK must be at least 1. *> If COMPZ = 'V' or N > 1, LIWORK must be at least *> 6 + 6*N + 5*N*lg N. *> If COMPZ = 'I' or N > 1, LIWORK must be at least *> 3 + 5*N . *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LIWORK *> need only be 1. *> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries *> of the WORK, RWORK and IWORK arrays, and no error message *> related to LWORK or LRWORK or LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: The algorithm failed to compute an eigenvalue while *> working on the submatrix lying in rows and columns *> INFO/(N+1) through mod(INFO,N+1). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complex16OTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA * * ===================================================================== SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, $ LRWORK, IWORK, LIWORK, INFO ) * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. CHARACTER COMPZ INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION D( * ), E( * ), RWORK( * ) COMPLEX*16 WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER FINISH, I, ICOMPZ, II, J, K, LGN, LIWMIN, LL, $ LRWMIN, LWMIN, M, SMLSIZ, START DOUBLE PRECISION EPS, ORGNRM, P, TINY * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLANST EXTERNAL LSAME, ILAENV, DLAMCH, DLANST * .. * .. External Subroutines .. EXTERNAL DLASCL, DLASET, DSTEDC, DSTEQR, DSTERF, XERBLA, $ ZLACPY, ZLACRM, ZLAED0, ZSTEQR, ZSWAP * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, INT, LOG, MAX, MOD, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * IF( LSAME( COMPZ, 'N' ) ) THEN ICOMPZ = 0 ELSE IF( LSAME( COMPZ, 'V' ) ) THEN ICOMPZ = 1 ELSE IF( LSAME( COMPZ, 'I' ) ) THEN ICOMPZ = 2 ELSE ICOMPZ = -1 END IF IF( ICOMPZ.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ( LDZ.LT.1 ) .OR. $ ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, N ) ) ) THEN INFO = -6 END IF * IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * SMLSIZ = ILAENV( 9, 'ZSTEDC', ' ', 0, 0, 0, 0 ) IF( N.LE.1 .OR. ICOMPZ.EQ.0 ) THEN LWMIN = 1 LIWMIN = 1 LRWMIN = 1 ELSE IF( N.LE.SMLSIZ ) THEN LWMIN = 1 LIWMIN = 1 LRWMIN = 2*( N - 1 ) ELSE IF( ICOMPZ.EQ.1 ) THEN LGN = INT( LOG( DBLE( N ) ) / LOG( TWO ) ) IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IF( 2**LGN.LT.N ) $ LGN = LGN + 1 LWMIN = N*N LRWMIN = 1 + 3*N + 2*N*LGN + 4*N**2 LIWMIN = 6 + 6*N + 5*N*LGN ELSE IF( ICOMPZ.EQ.2 ) THEN LWMIN = 1 LRWMIN = 1 + 4*N + 2*N**2 LIWMIN = 3 + 5*N END IF WORK( 1 ) = LWMIN RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN * IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -8 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN INFO = -10 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -12 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZSTEDC', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN IF( N.EQ.1 ) THEN IF( ICOMPZ.NE.0 ) $ Z( 1, 1 ) = ONE RETURN END IF * * If the following conditional clause is removed, then the routine * will use the Divide and Conquer routine to compute only the * eigenvalues, which requires (3N + 3N**2) real workspace and * (2 + 5N + 2N lg(N)) integer workspace. * Since on many architectures DSTERF is much faster than any other * algorithm for finding eigenvalues only, it is used here * as the default. If the conditional clause is removed, then * information on the size of workspace needs to be changed. * * If COMPZ = 'N', use DSTERF to compute the eigenvalues. * IF( ICOMPZ.EQ.0 ) THEN CALL DSTERF( N, D, E, INFO ) GO TO 70 END IF * * If N is smaller than the minimum divide size (SMLSIZ+1), then * solve the problem with another solver. * IF( N.LE.SMLSIZ ) THEN * CALL ZSTEQR( COMPZ, N, D, E, Z, LDZ, RWORK, INFO ) * ELSE * * If COMPZ = 'I', we simply call DSTEDC instead. * IF( ICOMPZ.EQ.2 ) THEN CALL DLASET( 'Full', N, N, ZERO, ONE, RWORK, N ) LL = N*N + 1 CALL DSTEDC( 'I', N, D, E, RWORK, N, $ RWORK( LL ), LRWORK-LL+1, IWORK, LIWORK, INFO ) DO 20 J = 1, N DO 10 I = 1, N Z( I, J ) = RWORK( ( J-1 )*N+I ) 10 CONTINUE 20 CONTINUE GO TO 70 END IF * * From now on, only option left to be handled is COMPZ = 'V', * i.e. ICOMPZ = 1. * * Scale. * ORGNRM = DLANST( 'M', N, D, E ) IF( ORGNRM.EQ.ZERO ) $ GO TO 70 * EPS = DLAMCH( 'Epsilon' ) * START = 1 * * while ( START <= N ) * 30 CONTINUE IF( START.LE.N ) THEN * * Let FINISH be the position of the next subdiagonal entry * such that E( FINISH ) <= TINY or FINISH = N if no such * subdiagonal exists. The matrix identified by the elements * between START and FINISH constitutes an independent * sub-problem. * FINISH = START 40 CONTINUE IF( FINISH.LT.N ) THEN TINY = EPS*SQRT( ABS( D( FINISH ) ) )* $ SQRT( ABS( D( FINISH+1 ) ) ) IF( ABS( E( FINISH ) ).GT.TINY ) THEN FINISH = FINISH + 1 GO TO 40 END IF END IF * * (Sub) Problem determined. Compute its size and solve it. * M = FINISH - START + 1 IF( M.GT.SMLSIZ ) THEN * * Scale. * ORGNRM = DLANST( 'M', M, D( START ), E( START ) ) CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M, 1, D( START ), M, $ INFO ) CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M-1, 1, E( START ), $ M-1, INFO ) * CALL ZLAED0( N, M, D( START ), E( START ), Z( 1, START ), $ LDZ, WORK, N, RWORK, IWORK, INFO ) IF( INFO.GT.0 ) THEN INFO = ( INFO / ( M+1 )+START-1 )*( N+1 ) + $ MOD( INFO, ( M+1 ) ) + START - 1 GO TO 70 END IF * * Scale back. * CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, M, 1, D( START ), M, $ INFO ) * ELSE CALL DSTEQR( 'I', M, D( START ), E( START ), RWORK, M, $ RWORK( M*M+1 ), INFO ) CALL ZLACRM( N, M, Z( 1, START ), LDZ, RWORK, M, WORK, N, $ RWORK( M*M+1 ) ) CALL ZLACPY( 'A', N, M, WORK, N, Z( 1, START ), LDZ ) IF( INFO.GT.0 ) THEN INFO = START*( N+1 ) + FINISH GO TO 70 END IF END IF * START = FINISH + 1 GO TO 30 END IF * * endwhile * * * Use Selection Sort to minimize swaps of eigenvectors * DO 60 II = 2, N I = II - 1 K = I P = D( I ) DO 50 J = II, N IF( D( J ).LT.P ) THEN K = J P = D( J ) END IF 50 CONTINUE IF( K.NE.I ) THEN D( K ) = D( I ) D( I ) = P CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) END IF 60 CONTINUE END IF * 70 CONTINUE WORK( 1 ) = LWMIN RWORK( 1 ) = LRWMIN IWORK( 1 ) = LIWMIN * RETURN * * End of ZSTEDC * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunmtr.f0000644000000000000000000000013214061636515015363 xustar0030 mtime=1623670093.233104053 30 atime=1623670093.232104054 30 ctime=1623670093.233104053 elk-7.2.42/src/LAPACK/zunmtr.f0000644002504400250440000002112314061636515017417 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNMTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNMTR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS, UPLO * INTEGER INFO, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNMTR overwrites the general complex M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'C': Q**H * C C * Q**H *> *> where Q is a complex unitary matrix of order nq, with nq = m if *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of *> nq-1 elementary reflectors, as returned by ZHETRD: *> *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); *> *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left; *> = 'R': apply Q or Q**H from the Right. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A contains elementary reflectors *> from ZHETRD; *> = 'L': Lower triangle of A contains elementary reflectors *> from ZHETRD. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'C': Conjugate transpose, apply Q**H. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension *> (LDA,M) if SIDE = 'L' *> (LDA,N) if SIDE = 'R' *> The vectors which define the elementary reflectors, as *> returned by ZHETRD. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension *> (M-1) if SIDE = 'L' *> (N-1) if SIDE = 'R' *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZHETRD. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >=M*NB if SIDE = 'R', where NB is the optimal *> blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, UPLO INTEGER INFO, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL LEFT, LQUERY, UPPER INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZUNMQL, ZUNMQR * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) $ THEN INFO = -3 ELSE IF( M.LT.0 ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -12 END IF * IF( INFO.EQ.0 ) THEN IF( UPPER ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'ZUNMQL', SIDE // TRANS, M-1, N, M-1, $ -1 ) ELSE NB = ILAENV( 1, 'ZUNMQL', SIDE // TRANS, M, N-1, N-1, $ -1 ) END IF ELSE IF( LEFT ) THEN NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1, $ -1 ) ELSE NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1, $ -1 ) END IF END IF LWKOPT = MAX( 1, NW )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNMTR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) THEN WORK( 1 ) = 1 RETURN END IF * IF( LEFT ) THEN MI = M - 1 NI = N ELSE MI = M NI = N - 1 END IF * IF( UPPER ) THEN * * Q was determined by a call to ZHETRD with UPLO = 'U' * CALL ZUNMQL( SIDE, TRANS, MI, NI, NQ-1, A( 1, 2 ), LDA, TAU, C, $ LDC, WORK, LWORK, IINFO ) ELSE * * Q was determined by a call to ZHETRD with UPLO = 'L' * IF( LEFT ) THEN I1 = 2 I2 = 1 ELSE I1 = 1 I2 = 2 END IF CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF WORK( 1 ) = LWKOPT RETURN * * End of ZUNMTR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zungtr.f0000644000000000000000000000013214061636515015355 xustar0030 mtime=1623670093.235104051 30 atime=1623670093.234104052 30 ctime=1623670093.235104051 elk-7.2.42/src/LAPACK/zungtr.f0000644002504400250440000001564114061636515017421 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNGTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNGTR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNGTR generates a complex unitary matrix Q which is defined as the *> product of n-1 elementary reflectors of order N, as returned by *> ZHETRD: *> *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), *> *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A contains elementary reflectors *> from ZHETRD; *> = 'L': Lower triangle of A contains elementary reflectors *> from ZHETRD. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix Q. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the vectors which define the elementary reflectors, *> as returned by ZHETRD. *> On exit, the N-by-N unitary matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= N. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZHETRD. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= N-1. *> For optimum performance LWORK >= (N-1)*NB, where NB is *> the optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, LWORK, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER INTEGER I, IINFO, J, LWKOPT, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZUNGQL, ZUNGQR * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN INFO = -7 END IF * IF( INFO.EQ.0 ) THEN IF( UPPER ) THEN NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 ) ELSE NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 ) END IF LWKOPT = MAX( 1, N-1 )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNGTR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * IF( UPPER ) THEN * * Q was determined by a call to ZHETRD with UPLO = 'U' * * Shift the vectors which define the elementary reflectors one * column to the left, and set the last row and column of Q to * those of the unit matrix * DO 20 J = 1, N - 1 DO 10 I = 1, J - 1 A( I, J ) = A( I, J+1 ) 10 CONTINUE A( N, J ) = ZERO 20 CONTINUE DO 30 I = 1, N - 1 A( I, N ) = ZERO 30 CONTINUE A( N, N ) = ONE * * Generate Q(1:n-1,1:n-1) * CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO ) * ELSE * * Q was determined by a call to ZHETRD with UPLO = 'L'. * * Shift the vectors which define the elementary reflectors one * column to the right, and set the first row and column of Q to * those of the unit matrix * DO 50 J = N, 2, -1 A( 1, J ) = ZERO DO 40 I = J + 1, N A( I, J ) = A( I, J-1 ) 40 CONTINUE 50 CONTINUE A( 1, 1 ) = ONE DO 60 I = 2, N A( I, 1 ) = ZERO 60 CONTINUE IF( N.GT.1 ) THEN * * Generate Q(2:n,2:n) * CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, $ LWORK, IINFO ) END IF END IF WORK( 1 ) = LWKOPT RETURN * * End of ZUNGTR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zsteqr.f0000644000000000000000000000013114061636515015353 xustar0030 mtime=1623670093.237104049 29 atime=1623670093.23610405 30 ctime=1623670093.237104049 elk-7.2.42/src/LAPACK/zsteqr.f0000644002504400250440000003661014061636515017417 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZSTEQR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZSTEQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER COMPZ * INTEGER INFO, LDZ, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ), WORK( * ) * COMPLEX*16 Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a *> symmetric tridiagonal matrix using the implicit QL or QR method. *> The eigenvectors of a full or band complex Hermitian matrix can also *> be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this *> matrix to tridiagonal form. *> \endverbatim * * Arguments: * ========== * *> \param[in] COMPZ *> \verbatim *> COMPZ is CHARACTER*1 *> = 'N': Compute eigenvalues only. *> = 'V': Compute eigenvalues and eigenvectors of the original *> Hermitian matrix. On entry, Z must contain the *> unitary matrix used to reduce the original matrix *> to tridiagonal form. *> = 'I': Compute eigenvalues and eigenvectors of the *> tridiagonal matrix. Z is initialized to the identity *> matrix. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the diagonal elements of the tridiagonal matrix. *> On exit, if INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> On entry, the (n-1) subdiagonal elements of the tridiagonal *> matrix. *> On exit, E has been destroyed. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ, N) *> On entry, if COMPZ = 'V', then Z contains the unitary *> matrix used in the reduction to tridiagonal form. *> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the *> orthonormal eigenvectors of the original Hermitian matrix, *> and if COMPZ = 'I', Z contains the orthonormal eigenvectors *> of the symmetric tridiagonal matrix. *> If COMPZ = 'N', then Z is not referenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> eigenvectors are desired, then LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) *> If COMPZ = 'N', then WORK is not referenced. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: the algorithm has failed to find all the eigenvalues in *> a total of 30*N iterations; if INFO = i, then i *> elements of E have not converged to zero; on exit, D *> and E contain the elements of a symmetric tridiagonal *> matrix which is unitarily similar to the original *> matrix. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER COMPZ INTEGER INFO, LDZ, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ), WORK( * ) COMPLEX*16 Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO, THREE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ THREE = 3.0D0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ), $ CONE = ( 1.0D0, 0.0D0 ) ) INTEGER MAXIT PARAMETER ( MAXIT = 30 ) * .. * .. Local Scalars .. INTEGER I, ICOMPZ, II, ISCALE, J, JTOT, K, L, L1, LEND, $ LENDM1, LENDP1, LENDSV, LM1, LSV, M, MM, MM1, $ NM1, NMAXIT DOUBLE PRECISION ANORM, B, C, EPS, EPS2, F, G, P, R, RT1, RT2, $ S, SAFMAX, SAFMIN, SSFMAX, SSFMIN, TST * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANST, DLAPY2 EXTERNAL LSAME, DLAMCH, DLANST, DLAPY2 * .. * .. External Subroutines .. EXTERNAL DLAE2, DLAEV2, DLARTG, DLASCL, DLASRT, XERBLA, $ ZLASET, ZLASR, ZSWAP * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SIGN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( LSAME( COMPZ, 'N' ) ) THEN ICOMPZ = 0 ELSE IF( LSAME( COMPZ, 'V' ) ) THEN ICOMPZ = 1 ELSE IF( LSAME( COMPZ, 'I' ) ) THEN ICOMPZ = 2 ELSE ICOMPZ = -1 END IF IF( ICOMPZ.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, $ N ) ) ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZSTEQR', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( N.EQ.1 ) THEN IF( ICOMPZ.EQ.2 ) $ Z( 1, 1 ) = CONE RETURN END IF * * Determine the unit roundoff and over/underflow thresholds. * EPS = DLAMCH( 'E' ) EPS2 = EPS**2 SAFMIN = DLAMCH( 'S' ) SAFMAX = ONE / SAFMIN SSFMAX = SQRT( SAFMAX ) / THREE SSFMIN = SQRT( SAFMIN ) / EPS2 * * Compute the eigenvalues and eigenvectors of the tridiagonal * matrix. * IF( ICOMPZ.EQ.2 ) $ CALL ZLASET( 'Full', N, N, CZERO, CONE, Z, LDZ ) * NMAXIT = N*MAXIT JTOT = 0 * * Determine where the matrix splits and choose QL or QR iteration * for each block, according to whether top or bottom diagonal * element is smaller. * L1 = 1 NM1 = N - 1 * 10 CONTINUE IF( L1.GT.N ) $ GO TO 160 IF( L1.GT.1 ) $ E( L1-1 ) = ZERO IF( L1.LE.NM1 ) THEN DO 20 M = L1, NM1 TST = ABS( E( M ) ) IF( TST.EQ.ZERO ) $ GO TO 30 IF( TST.LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+ $ 1 ) ) ) )*EPS ) THEN E( M ) = ZERO GO TO 30 END IF 20 CONTINUE END IF M = N * 30 CONTINUE L = L1 LSV = L LEND = M LENDSV = LEND L1 = M + 1 IF( LEND.EQ.L ) $ GO TO 10 * * Scale submatrix in rows and columns L to LEND * ANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) ) ISCALE = 0 IF( ANORM.EQ.ZERO ) $ GO TO 10 IF( ANORM.GT.SSFMAX ) THEN ISCALE = 1 CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N, $ INFO ) CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N, $ INFO ) ELSE IF( ANORM.LT.SSFMIN ) THEN ISCALE = 2 CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N, $ INFO ) CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N, $ INFO ) END IF * * Choose between QL and QR iteration * IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN LEND = LSV L = LENDSV END IF * IF( LEND.GT.L ) THEN * * QL Iteration * * Look for small subdiagonal element. * 40 CONTINUE IF( L.NE.LEND ) THEN LENDM1 = LEND - 1 DO 50 M = L, LENDM1 TST = ABS( E( M ) )**2 IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M+1 ) )+ $ SAFMIN )GO TO 60 50 CONTINUE END IF * M = LEND * 60 CONTINUE IF( M.LT.LEND ) $ E( M ) = ZERO P = D( L ) IF( M.EQ.L ) $ GO TO 80 * * If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 * to compute its eigensystem. * IF( M.EQ.L+1 ) THEN IF( ICOMPZ.GT.0 ) THEN CALL DLAEV2( D( L ), E( L ), D( L+1 ), RT1, RT2, C, S ) WORK( L ) = C WORK( N-1+L ) = S CALL ZLASR( 'R', 'V', 'B', N, 2, WORK( L ), $ WORK( N-1+L ), Z( 1, L ), LDZ ) ELSE CALL DLAE2( D( L ), E( L ), D( L+1 ), RT1, RT2 ) END IF D( L ) = RT1 D( L+1 ) = RT2 E( L ) = ZERO L = L + 2 IF( L.LE.LEND ) $ GO TO 40 GO TO 140 END IF * IF( JTOT.EQ.NMAXIT ) $ GO TO 140 JTOT = JTOT + 1 * * Form shift. * G = ( D( L+1 )-P ) / ( TWO*E( L ) ) R = DLAPY2( G, ONE ) G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) ) * S = ONE C = ONE P = ZERO * * Inner loop * MM1 = M - 1 DO 70 I = MM1, L, -1 F = S*E( I ) B = C*E( I ) CALL DLARTG( G, F, C, S, R ) IF( I.NE.M-1 ) $ E( I+1 ) = R G = D( I+1 ) - P R = ( D( I )-G )*S + TWO*C*B P = S*R D( I+1 ) = G + P G = C*R - B * * If eigenvectors are desired, then save rotations. * IF( ICOMPZ.GT.0 ) THEN WORK( I ) = C WORK( N-1+I ) = -S END IF * 70 CONTINUE * * If eigenvectors are desired, then apply saved rotations. * IF( ICOMPZ.GT.0 ) THEN MM = M - L + 1 CALL ZLASR( 'R', 'V', 'B', N, MM, WORK( L ), WORK( N-1+L ), $ Z( 1, L ), LDZ ) END IF * D( L ) = D( L ) - P E( L ) = G GO TO 40 * * Eigenvalue found. * 80 CONTINUE D( L ) = P * L = L + 1 IF( L.LE.LEND ) $ GO TO 40 GO TO 140 * ELSE * * QR Iteration * * Look for small superdiagonal element. * 90 CONTINUE IF( L.NE.LEND ) THEN LENDP1 = LEND + 1 DO 100 M = L, LENDP1, -1 TST = ABS( E( M-1 ) )**2 IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M-1 ) )+ $ SAFMIN )GO TO 110 100 CONTINUE END IF * M = LEND * 110 CONTINUE IF( M.GT.LEND ) $ E( M-1 ) = ZERO P = D( L ) IF( M.EQ.L ) $ GO TO 130 * * If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 * to compute its eigensystem. * IF( M.EQ.L-1 ) THEN IF( ICOMPZ.GT.0 ) THEN CALL DLAEV2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2, C, S ) WORK( M ) = C WORK( N-1+M ) = S CALL ZLASR( 'R', 'V', 'F', N, 2, WORK( M ), $ WORK( N-1+M ), Z( 1, L-1 ), LDZ ) ELSE CALL DLAE2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2 ) END IF D( L-1 ) = RT1 D( L ) = RT2 E( L-1 ) = ZERO L = L - 2 IF( L.GE.LEND ) $ GO TO 90 GO TO 140 END IF * IF( JTOT.EQ.NMAXIT ) $ GO TO 140 JTOT = JTOT + 1 * * Form shift. * G = ( D( L-1 )-P ) / ( TWO*E( L-1 ) ) R = DLAPY2( G, ONE ) G = D( M ) - P + ( E( L-1 ) / ( G+SIGN( R, G ) ) ) * S = ONE C = ONE P = ZERO * * Inner loop * LM1 = L - 1 DO 120 I = M, LM1 F = S*E( I ) B = C*E( I ) CALL DLARTG( G, F, C, S, R ) IF( I.NE.M ) $ E( I-1 ) = R G = D( I ) - P R = ( D( I+1 )-G )*S + TWO*C*B P = S*R D( I ) = G + P G = C*R - B * * If eigenvectors are desired, then save rotations. * IF( ICOMPZ.GT.0 ) THEN WORK( I ) = C WORK( N-1+I ) = S END IF * 120 CONTINUE * * If eigenvectors are desired, then apply saved rotations. * IF( ICOMPZ.GT.0 ) THEN MM = L - M + 1 CALL ZLASR( 'R', 'V', 'F', N, MM, WORK( M ), WORK( N-1+M ), $ Z( 1, M ), LDZ ) END IF * D( L ) = D( L ) - P E( LM1 ) = G GO TO 90 * * Eigenvalue found. * 130 CONTINUE D( L ) = P * L = L - 1 IF( L.GE.LEND ) $ GO TO 90 GO TO 140 * END IF * * Undo scaling if necessary * 140 CONTINUE IF( ISCALE.EQ.1 ) THEN CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1, $ D( LSV ), N, INFO ) CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV, 1, E( LSV ), $ N, INFO ) ELSE IF( ISCALE.EQ.2 ) THEN CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1, $ D( LSV ), N, INFO ) CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV, 1, E( LSV ), $ N, INFO ) END IF * * Check for no convergence to an eigenvalue after a total * of N*MAXIT iterations. * IF( JTOT.EQ.NMAXIT ) THEN DO 150 I = 1, N - 1 IF( E( I ).NE.ZERO ) $ INFO = INFO + 1 150 CONTINUE RETURN END IF GO TO 10 * * Order eigenvalues and eigenvectors. * 160 CONTINUE IF( ICOMPZ.EQ.0 ) THEN * * Use Quick Sort * CALL DLASRT( 'I', N, D, INFO ) * ELSE * * Use Selection Sort to minimize swaps of eigenvectors * DO 180 II = 2, N I = II - 1 K = I P = D( I ) DO 170 J = II, N IF( D( J ).LT.P ) THEN K = J P = D( J ) END IF 170 CONTINUE IF( K.NE.I ) THEN D( K ) = D( I ) D( I ) = P CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) END IF 180 CONTINUE END IF RETURN * * End of ZSTEQR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zpotrf.f0000644000000000000000000000013214061636515015350 xustar0030 mtime=1623670093.239104048 30 atime=1623670093.238104048 30 ctime=1623670093.239104048 elk-7.2.42/src/LAPACK/zpotrf.f0000644002504400250440000001632514061636515017414 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZPOTRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZPOTRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZPOTRF( UPLO, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZPOTRF computes the Cholesky factorization of a complex Hermitian *> positive definite matrix A. *> *> The factorization has the form *> A = U**H * U, if UPLO = 'U', or *> A = L * L**H, if UPLO = 'L', *> where U is an upper triangular matrix and L is lower triangular. *> *> This is the block version of the algorithm, calling Level 3 BLAS. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16POcomputational * * ===================================================================== SUBROUTINE ZPOTRF( UPLO, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE COMPLEX*16 CONE PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER J, JB, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMM, ZHERK, ZPOTRF2, ZTRSM * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZPOTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'ZPOTRF', UPLO, N, -1, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code. * CALL ZPOTRF2( UPLO, N, A, LDA, INFO ) ELSE * * Use blocked code. * IF( UPPER ) THEN * * Compute the Cholesky factorization A = U**H *U. * DO 10 J = 1, N, NB * * Update and factorize the current diagonal block and test * for non-positive-definiteness. * JB = MIN( NB, N-J+1 ) CALL ZHERK( 'Upper', 'Conjugate transpose', JB, J-1, $ -ONE, A( 1, J ), LDA, ONE, A( J, J ), LDA ) CALL ZPOTRF2( 'Upper', JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) $ GO TO 30 IF( J+JB.LE.N ) THEN * * Compute the current block row. * CALL ZGEMM( 'Conjugate transpose', 'No transpose', JB, $ N-J-JB+1, J-1, -CONE, A( 1, J ), LDA, $ A( 1, J+JB ), LDA, CONE, A( J, J+JB ), $ LDA ) CALL ZTRSM( 'Left', 'Upper', 'Conjugate transpose', $ 'Non-unit', JB, N-J-JB+1, CONE, A( J, J ), $ LDA, A( J, J+JB ), LDA ) END IF 10 CONTINUE * ELSE * * Compute the Cholesky factorization A = L*L**H. * DO 20 J = 1, N, NB * * Update and factorize the current diagonal block and test * for non-positive-definiteness. * JB = MIN( NB, N-J+1 ) CALL ZHERK( 'Lower', 'No transpose', JB, J-1, -ONE, $ A( J, 1 ), LDA, ONE, A( J, J ), LDA ) CALL ZPOTRF2( 'Lower', JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) $ GO TO 30 IF( J+JB.LE.N ) THEN * * Compute the current block column. * CALL ZGEMM( 'No transpose', 'Conjugate transpose', $ N-J-JB+1, JB, J-1, -CONE, A( J+JB, 1 ), $ LDA, A( J, 1 ), LDA, CONE, A( J+JB, J ), $ LDA ) CALL ZTRSM( 'Right', 'Lower', 'Conjugate transpose', $ 'Non-unit', N-J-JB+1, JB, CONE, A( J, J ), $ LDA, A( J+JB, J ), LDA ) END IF 20 CONTINUE END IF END IF GO TO 40 * 30 CONTINUE INFO = INFO + J - 1 * 40 CONTINUE RETURN * * End of ZPOTRF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhegst.f0000644000000000000000000000013214061636515015330 xustar0030 mtime=1623670093.241104046 30 atime=1623670093.240104047 30 ctime=1623670093.241104046 elk-7.2.42/src/LAPACK/zhegst.f0000644002504400250440000002632314061636515017373 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHEGST * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHEGST + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEGST reduces a complex Hermitian-definite generalized *> eigenproblem to standard form. *> *> If ITYPE = 1, the problem is A*x = lambda*B*x, *> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) *> *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or *> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. *> *> B must have been previously factorized as U**H*U or L*L**H by ZPOTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); *> = 2 or 3: compute U*A*U**H or L**H*A*L. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored and B is factored as *> U**H*U; *> = 'L': Lower triangle of A is stored and B is factored as *> L*L**H. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,N) *> The triangular factor from the Cholesky factorization of B, *> as returned by ZPOTRF. *> B is modified by the routine but restored on exit. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16HEcomputational * * ===================================================================== SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) COMPLEX*16 CONE, HALF PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ), $ HALF = ( 0.5D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER K, KB, NB * .. * .. External Subroutines .. EXTERNAL XERBLA, ZHEGS2, ZHEMM, ZHER2K, ZTRMM, ZTRSM * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHEGST', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'ZHEGST', UPLO, N, -1, -1, -1 ) * IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) ELSE * * Use blocked code * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**H)*A*inv(U) * DO 10 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the upper triangle of A(k:n,k:n) * CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, $ B( K, K ), LDB, INFO ) IF( K+KB.LE.N ) THEN CALL ZTRSM( 'Left', UPLO, 'Conjugate transpose', $ 'Non-unit', KB, N-K-KB+1, CONE, $ B( K, K ), LDB, A( K, K+KB ), LDA ) CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, $ A( K, K ), LDA, B( K, K+KB ), LDB, $ CONE, A( K, K+KB ), LDA ) CALL ZHER2K( UPLO, 'Conjugate transpose', N-K-KB+1, $ KB, -CONE, A( K, K+KB ), LDA, $ B( K, K+KB ), LDB, ONE, $ A( K+KB, K+KB ), LDA ) CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF, $ A( K, K ), LDA, B( K, K+KB ), LDB, $ CONE, A( K, K+KB ), LDA ) CALL ZTRSM( 'Right', UPLO, 'No transpose', $ 'Non-unit', KB, N-K-KB+1, CONE, $ B( K+KB, K+KB ), LDB, A( K, K+KB ), $ LDA ) END IF 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**H) * DO 20 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the lower triangle of A(k:n,k:n) * CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, $ B( K, K ), LDB, INFO ) IF( K+KB.LE.N ) THEN CALL ZTRSM( 'Right', UPLO, 'Conjugate transpose', $ 'Non-unit', N-K-KB+1, KB, CONE, $ B( K, K ), LDB, A( K+KB, K ), LDA ) CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, $ A( K, K ), LDA, B( K+KB, K ), LDB, $ CONE, A( K+KB, K ), LDA ) CALL ZHER2K( UPLO, 'No transpose', N-K-KB+1, KB, $ -CONE, A( K+KB, K ), LDA, $ B( K+KB, K ), LDB, ONE, $ A( K+KB, K+KB ), LDA ) CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF, $ A( K, K ), LDA, B( K+KB, K ), LDB, $ CONE, A( K+KB, K ), LDA ) CALL ZTRSM( 'Left', UPLO, 'No transpose', $ 'Non-unit', N-K-KB+1, KB, CONE, $ B( K+KB, K+KB ), LDB, A( K+KB, K ), $ LDA ) END IF 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**H * DO 30 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the upper triangle of A(1:k+kb-1,1:k+kb-1) * CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Non-unit', $ K-1, KB, CONE, B, LDB, A( 1, K ), LDA ) CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), $ LDA, B( 1, K ), LDB, CONE, A( 1, K ), $ LDA ) CALL ZHER2K( UPLO, 'No transpose', K-1, KB, CONE, $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A, $ LDA ) CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ), $ LDA, B( 1, K ), LDB, CONE, A( 1, K ), $ LDA ) CALL ZTRMM( 'Right', UPLO, 'Conjugate transpose', $ 'Non-unit', K-1, KB, CONE, B( K, K ), LDB, $ A( 1, K ), LDA ) CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, $ B( K, K ), LDB, INFO ) 30 CONTINUE ELSE * * Compute L**H*A*L * DO 40 K = 1, N, NB KB = MIN( N-K+1, NB ) * * Update the lower triangle of A(1:k+kb-1,1:k+kb-1) * CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Non-unit', $ KB, K-1, CONE, B, LDB, A( K, 1 ), LDA ) CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ), $ LDA ) CALL ZHER2K( UPLO, 'Conjugate transpose', K-1, KB, $ CONE, A( K, 1 ), LDA, B( K, 1 ), LDB, $ ONE, A, LDA ) CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ), $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ), $ LDA ) CALL ZTRMM( 'Left', UPLO, 'Conjugate transpose', $ 'Non-unit', KB, K-1, CONE, B( K, K ), LDB, $ A( K, 1 ), LDA ) CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA, $ B( K, K ), LDB, INFO ) 40 CONTINUE END IF END IF END IF RETURN * * End of ZHEGST * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zheevx.f0000644000000000000000000000013214061636515015335 xustar0030 mtime=1623670093.243104044 30 atime=1623670093.242104045 30 ctime=1623670093.243104044 elk-7.2.42/src/LAPACK/zheevx.f0000644002504400250440000004334414061636515017402 0ustar00dewhurstdewhurst00000000000000*> \brief ZHEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHEEVX + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, * ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, * IWORK, IFAIL, INFO ) * * .. Scalar Arguments .. * CHARACTER JOBZ, RANGE, UPLO * INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N * DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER IFAIL( * ), IWORK( * ) * DOUBLE PRECISION RWORK( * ), W( * ) * COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEEVX computes selected eigenvalues and, optionally, eigenvectors *> of a complex Hermitian matrix A. Eigenvalues and eigenvectors can *> be selected by specifying either a range of values or a range of *> indices for the desired eigenvalues. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBZ *> \verbatim *> JOBZ is CHARACTER*1 *> = 'N': Compute eigenvalues only; *> = 'V': Compute eigenvalues and eigenvectors. *> \endverbatim *> *> \param[in] RANGE *> \verbatim *> RANGE is CHARACTER*1 *> = 'A': all eigenvalues will be found. *> = 'V': all eigenvalues in the half-open interval (VL,VU] *> will be found. *> = 'I': the IL-th through IU-th eigenvalues will be found. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA, N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the *> leading N-by-N upper triangular part of A contains the *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. *> On exit, the lower triangle (if UPLO='L') or the upper *> triangle (if UPLO='U') of A, including the diagonal, is *> destroyed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] VL *> \verbatim *> VL is DOUBLE PRECISION *> If RANGE='V', the lower bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION *> If RANGE='V', the upper bound of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] IL *> \verbatim *> IL is INTEGER *> If RANGE='I', the index of the *> smallest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] IU *> \verbatim *> IU is INTEGER *> If RANGE='I', the index of the *> largest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] ABSTOL *> \verbatim *> ABSTOL is DOUBLE PRECISION *> The absolute error tolerance for the eigenvalues. *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to *> *> ABSTOL + EPS * max( |a|,|b| ) , *> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. *> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). *> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. *> \endverbatim *> *> \param[out] M *> \verbatim *> M is INTEGER *> The total number of eigenvalues found. 0 <= M <= N. *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> On normal exit, the first M elements contain the selected *> eigenvalues in ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ, max(1,M)) *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z *> contain the orthonormal eigenvectors of the matrix A *> corresponding to the selected eigenvalues, with the i-th *> column of Z holding the eigenvector associated with W(i). *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. *> If JOBZ = 'N', then Z is not referenced. *> Note: the user must ensure that at least max(1,M) columns are *> supplied in the array Z; if RANGE = 'V', the exact value of M *> is not known in advance and an upper bound must be used. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1, and if *> JOBZ = 'V', LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= 1, when N <= 1; *> otherwise 2*N. *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the max of the blocksize for ZHETRD and for *> ZUNMTR as returned by ILAENV. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (7*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (5*N) *> \endverbatim *> *> \param[out] IFAIL *> \verbatim *> IFAIL is INTEGER array, dimension (N) *> If JOBZ = 'V', then if INFO = 0, the first M elements of *> IFAIL are zero. If INFO > 0, then IFAIL contains the *> indices of the eigenvectors that failed to converge. *> If JOBZ = 'N', then IFAIL is not referenced. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, then i eigenvectors failed to converge. *> Their indices are stored in array IFAIL. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16HEeigen * * ===================================================================== SUBROUTINE ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, $ ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, $ IWORK, IFAIL, INFO ) * * -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER JOBZ, RANGE, UPLO INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER IFAIL( * ), IWORK( * ) DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 A( LDA, * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG, $ WANTZ CHARACTER ORDER INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL, $ INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE, $ ITMP1, J, JJ, LLWORK, LWKMIN, LWKOPT, NB, $ NSPLIT DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, $ SIGMA, SMLNUM, TMP1, VLL, VUU * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, ZLANHE EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE * .. * .. External Subroutines .. EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTERF, XERBLA, ZDSCAL, $ ZHETRD, ZLACPY, ZSTEIN, ZSTEQR, ZSWAP, ZUNGTR, $ ZUNMTR * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * LOWER = LSAME( UPLO, 'L' ) WANTZ = LSAME( JOBZ, 'V' ) ALLEIG = LSAME( RANGE, 'A' ) VALEIG = LSAME( RANGE, 'V' ) INDEIG = LSAME( RANGE, 'I' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN INFO = -2 ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( VALEIG ) THEN IF( N.GT.0 .AND. VU.LE.VL ) $ INFO = -8 ELSE IF( INDEIG ) THEN IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN INFO = -9 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN INFO = -10 END IF END IF END IF IF( INFO.EQ.0 ) THEN IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -15 END IF END IF * IF( INFO.EQ.0 ) THEN IF( N.LE.1 ) THEN LWKMIN = 1 WORK( 1 ) = LWKMIN ELSE LWKMIN = 2*N NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) NB = MAX( NB, ILAENV( 1, 'ZUNMTR', UPLO, N, -1, -1, -1 ) ) LWKOPT = MAX( 1, ( NB + 1 )*N ) WORK( 1 ) = LWKOPT END IF * IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) $ INFO = -17 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHEEVX', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * M = 0 IF( N.EQ.0 ) THEN RETURN END IF * IF( N.EQ.1 ) THEN IF( ALLEIG .OR. INDEIG ) THEN M = 1 W( 1 ) = A( 1, 1 ) ELSE IF( VALEIG ) THEN IF( VL.LT.DBLE( A( 1, 1 ) ) .AND. VU.GE.DBLE( A( 1, 1 ) ) ) $ THEN M = 1 W( 1 ) = A( 1, 1 ) END IF END IF IF( WANTZ ) $ Z( 1, 1 ) = CONE RETURN END IF * * Get machine constants. * SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) * * Scale matrix to allowable range, if necessary. * ISCALE = 0 ABSTLL = ABSTOL IF( VALEIG ) THEN VLL = VL VUU = VU END IF ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK ) IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) THEN IF( LOWER ) THEN DO 10 J = 1, N CALL ZDSCAL( N-J+1, SIGMA, A( J, J ), 1 ) 10 CONTINUE ELSE DO 20 J = 1, N CALL ZDSCAL( J, SIGMA, A( 1, J ), 1 ) 20 CONTINUE END IF IF( ABSTOL.GT.0 ) $ ABSTLL = ABSTOL*SIGMA IF( VALEIG ) THEN VLL = VL*SIGMA VUU = VU*SIGMA END IF END IF * * Call ZHETRD to reduce Hermitian matrix to tridiagonal form. * INDD = 1 INDE = INDD + N INDRWK = INDE + N INDTAU = 1 INDWRK = INDTAU + N LLWORK = LWORK - INDWRK + 1 CALL ZHETRD( UPLO, N, A, LDA, RWORK( INDD ), RWORK( INDE ), $ WORK( INDTAU ), WORK( INDWRK ), LLWORK, IINFO ) * * If all eigenvalues are desired and ABSTOL is less than or equal to * zero, then call DSTERF or ZUNGTR and ZSTEQR. If this fails for * some eigenvalue, then try DSTEBZ. * TEST = .FALSE. IF( INDEIG ) THEN IF( IL.EQ.1 .AND. IU.EQ.N ) THEN TEST = .TRUE. END IF END IF IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN CALL DCOPY( N, RWORK( INDD ), 1, W, 1 ) INDEE = INDRWK + 2*N IF( .NOT.WANTZ ) THEN CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 ) CALL DSTERF( N, W, RWORK( INDEE ), INFO ) ELSE CALL ZLACPY( 'A', N, N, A, LDA, Z, LDZ ) CALL ZUNGTR( UPLO, N, Z, LDZ, WORK( INDTAU ), $ WORK( INDWRK ), LLWORK, IINFO ) CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 ) CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ, $ RWORK( INDRWK ), INFO ) IF( INFO.EQ.0 ) THEN DO 30 I = 1, N IFAIL( I ) = 0 30 CONTINUE END IF END IF IF( INFO.EQ.0 ) THEN M = N GO TO 40 END IF INFO = 0 END IF * * Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN. * IF( WANTZ ) THEN ORDER = 'B' ELSE ORDER = 'E' END IF INDIBL = 1 INDISP = INDIBL + N INDIWK = INDISP + N CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL, $ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W, $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ), $ IWORK( INDIWK ), INFO ) * IF( WANTZ ) THEN CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W, $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ, $ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO ) * * Apply unitary matrix used in reduction to tridiagonal * form to eigenvectors returned by ZSTEIN. * CALL ZUNMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z, $ LDZ, WORK( INDWRK ), LLWORK, IINFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * 40 CONTINUE IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = M ELSE IMAX = INFO - 1 END IF CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * * If eigenvalues are not in order, then sort them, along with * eigenvectors. * IF( WANTZ ) THEN DO 60 J = 1, M - 1 I = 0 TMP1 = W( J ) DO 50 JJ = J + 1, M IF( W( JJ ).LT.TMP1 ) THEN I = JJ TMP1 = W( JJ ) END IF 50 CONTINUE * IF( I.NE.0 ) THEN ITMP1 = IWORK( INDIBL+I-1 ) W( I ) = W( J ) IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 ) W( J ) = TMP1 IWORK( INDIBL+J-1 ) = ITMP1 CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) IF( INFO.NE.0 ) THEN ITMP1 = IFAIL( I ) IFAIL( I ) = IFAIL( J ) IFAIL( J ) = ITMP1 END IF END IF 60 CONTINUE END IF * * Set WORK(1) to optimal complex workspace size. * WORK( 1 ) = LWKOPT * RETURN * * End of ZHEEVX * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlanhp.f0000644000000000000000000000013214061636515015320 xustar0030 mtime=1623670093.245104042 30 atime=1623670093.245104042 30 ctime=1623670093.245104042 elk-7.2.42/src/LAPACK/zlanhp.f0000644002504400250440000002146314061636515017363 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLANHP + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK ) * * .. Scalar Arguments .. * CHARACTER NORM, UPLO * INTEGER N * .. * .. Array Arguments .. * DOUBLE PRECISION WORK( * ) * COMPLEX*16 AP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLANHP returns the value of the one norm, or the Frobenius norm, or *> the infinity norm, or the element of largest absolute value of a *> complex hermitian matrix A, supplied in packed form. *> \endverbatim *> *> \return ZLANHP *> \verbatim *> *> ZLANHP = ( max(abs(A(i,j))), NORM = 'M' or 'm' *> ( *> ( norm1(A), NORM = '1', 'O' or 'o' *> ( *> ( normI(A), NORM = 'I' or 'i' *> ( *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' *> *> where norm1 denotes the one norm of a matrix (maximum column sum), *> normI denotes the infinity norm of a matrix (maximum row sum) and *> normF denotes the Frobenius norm of a matrix (square root of sum of *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] NORM *> \verbatim *> NORM is CHARACTER*1 *> Specifies the value to be returned in ZLANHP as described *> above. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> hermitian matrix A is supplied. *> = 'U': Upper triangular part of A is supplied *> = 'L': Lower triangular part of A is supplied *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, ZLANHP is *> set to zero. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> The upper or lower triangle of the hermitian matrix A, packed *> columnwise in a linear array. The j-th column of A is stored *> in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> Note that the imaginary parts of the diagonal elements need *> not be set and are assumed to be zero. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, *> WORK is not referenced. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * IMPLICIT NONE * .. Scalar Arguments .. CHARACTER NORM, UPLO INTEGER N * .. * .. Array Arguments .. DOUBLE PRECISION WORK( * ) COMPLEX*16 AP( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, K DOUBLE PRECISION ABSA, SUM, VALUE * .. * .. Local Arrays .. DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 ) * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZLASSQ, DCOMBSSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, SQRT * .. * .. Executable Statements .. * IF( N.EQ.0 ) THEN VALUE = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * VALUE = ZERO IF( LSAME( UPLO, 'U' ) ) THEN K = 0 DO 20 J = 1, N DO 10 I = K + 1, K + J - 1 SUM = ABS( AP( I ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 10 CONTINUE K = K + J SUM = ABS( DBLE( AP( K ) ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 20 CONTINUE ELSE K = 1 DO 40 J = 1, N SUM = ABS( DBLE( AP( K ) ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM DO 30 I = K + 1, K + N - J SUM = ABS( AP( I ) ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 30 CONTINUE K = K + N - J + 1 40 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. $ ( NORM.EQ.'1' ) ) THEN * * Find normI(A) ( = norm1(A), since A is hermitian). * VALUE = ZERO K = 1 IF( LSAME( UPLO, 'U' ) ) THEN DO 60 J = 1, N SUM = ZERO DO 50 I = 1, J - 1 ABSA = ABS( AP( K ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA K = K + 1 50 CONTINUE WORK( J ) = SUM + ABS( DBLE( AP( K ) ) ) K = K + 1 60 CONTINUE DO 70 I = 1, N SUM = WORK( I ) IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 70 CONTINUE ELSE DO 80 I = 1, N WORK( I ) = ZERO 80 CONTINUE DO 100 J = 1, N SUM = WORK( J ) + ABS( DBLE( AP( K ) ) ) K = K + 1 DO 90 I = J + 1, N ABSA = ABS( AP( K ) ) SUM = SUM + ABSA WORK( I ) = WORK( I ) + ABSA K = K + 1 90 CONTINUE IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM 100 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SSQ(1) is scale * SSQ(2) is sum-of-squares * For better accuracy, sum each column separately. * SSQ( 1 ) = ZERO SSQ( 2 ) = ONE * * Sum off-diagonals * K = 2 IF( LSAME( UPLO, 'U' ) ) THEN DO 110 J = 2, N COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL ZLASSQ( J-1, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) ) CALL DCOMBSSQ( SSQ, COLSSQ ) K = K + J 110 CONTINUE ELSE DO 120 J = 1, N - 1 COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE CALL ZLASSQ( N-J, AP( K ), 1, COLSSQ( 1 ), COLSSQ( 2 ) ) CALL DCOMBSSQ( SSQ, COLSSQ ) K = K + N - J + 1 120 CONTINUE END IF SSQ( 2 ) = 2*SSQ( 2 ) * * Sum diagonal * K = 1 COLSSQ( 1 ) = ZERO COLSSQ( 2 ) = ONE DO 130 I = 1, N IF( DBLE( AP( K ) ).NE.ZERO ) THEN ABSA = ABS( DBLE( AP( K ) ) ) IF( COLSSQ( 1 ).LT.ABSA ) THEN COLSSQ( 2 ) = ONE + COLSSQ(2)*( COLSSQ(1) / ABSA )**2 COLSSQ( 1 ) = ABSA ELSE COLSSQ( 2 ) = COLSSQ( 2 ) + ( ABSA / COLSSQ( 1 ) )**2 END IF END IF IF( LSAME( UPLO, 'U' ) ) THEN K = K + I + 1 ELSE K = K + N - I + 1 END IF 130 CONTINUE CALL DCOMBSSQ( SSQ, COLSSQ ) VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) ) END IF * ZLANHP = VALUE RETURN * * End of ZLANHP * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhptrd.f0000644000000000000000000000012714061636515015343 xustar0029 mtime=1623670093.24710404 29 atime=1623670093.24710404 29 ctime=1623670093.24710404 elk-7.2.42/src/LAPACK/zhptrd.f0000644002504400250440000002163014061636515017376 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHPTRD * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHPTRD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHPTRD( UPLO, N, AP, D, E, TAU, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ) * COMPLEX*16 AP( * ), TAU( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHPTRD reduces a complex Hermitian matrix A stored in packed form to *> real symmetric tridiagonal form T by a unitary similarity *> transformation: Q**H * A * Q = T. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangle of the Hermitian matrix *> A, packed columnwise in a linear array. The j-th column of A *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. *> On exit, if UPLO = 'U', the diagonal and first superdiagonal *> of A are overwritten by the corresponding elements of the *> tridiagonal matrix T, and the elements above the first *> superdiagonal, with the array TAU, represent the unitary *> matrix Q as a product of elementary reflectors; if UPLO *> = 'L', the diagonal and first subdiagonal of A are over- *> written by the corresponding elements of the tridiagonal *> matrix T, and the elements below the first subdiagonal, with *> the array TAU, represent the unitary matrix Q as a product *> of elementary reflectors. See Further Details. *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of the tridiagonal matrix T: *> D(i) = A(i,i). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The off-diagonal elements of the tridiagonal matrix T: *> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> If UPLO = 'U', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(n-1) . . . H(2) H(1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP, *> overwriting A(1:i-1,i+1), and tau is stored in TAU(i). *> *> If UPLO = 'L', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(1) H(2) . . . H(n-1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP, *> overwriting A(i+2:n,i), and tau is stored in TAU(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZHPTRD( UPLO, N, AP, D, E, TAU, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ) COMPLEX*16 AP( * ), TAU( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO, HALF PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ), $ HALF = ( 0.5D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, I1, I1I1, II COMPLEX*16 ALPHA, TAUI * .. * .. External Subroutines .. EXTERNAL XERBLA, ZAXPY, ZHPMV, ZHPR2, ZLARFG * .. * .. External Functions .. LOGICAL LSAME COMPLEX*16 ZDOTC EXTERNAL LSAME, ZDOTC * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHPTRD', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.0 ) $ RETURN * IF( UPPER ) THEN * * Reduce the upper triangle of A. * I1 is the index in AP of A(1,I+1). * I1 = N*( N-1 ) / 2 + 1 AP( I1+N-1 ) = DBLE( AP( I1+N-1 ) ) DO 10 I = N - 1, 1, -1 * * Generate elementary reflector H(i) = I - tau * v * v**H * to annihilate A(1:i-1,i+1) * ALPHA = AP( I1+I-1 ) CALL ZLARFG( I, ALPHA, AP( I1 ), 1, TAUI ) E( I ) = ALPHA * IF( TAUI.NE.ZERO ) THEN * * Apply H(i) from both sides to A(1:i,1:i) * AP( I1+I-1 ) = ONE * * Compute y := tau * A * v storing y in TAU(1:i) * CALL ZHPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU, $ 1 ) * * Compute w := y - 1/2 * tau * (y**H *v) * v * ALPHA = -HALF*TAUI*ZDOTC( I, TAU, 1, AP( I1 ), 1 ) CALL ZAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 ) * * Apply the transformation as a rank-2 update: * A := A - v * w**H - w * v**H * CALL ZHPR2( UPLO, I, -ONE, AP( I1 ), 1, TAU, 1, AP ) * END IF AP( I1+I-1 ) = E( I ) D( I+1 ) = AP( I1+I ) TAU( I ) = TAUI I1 = I1 - I 10 CONTINUE D( 1 ) = AP( 1 ) ELSE * * Reduce the lower triangle of A. II is the index in AP of * A(i,i) and I1I1 is the index of A(i+1,i+1). * II = 1 AP( 1 ) = DBLE( AP( 1 ) ) DO 20 I = 1, N - 1 I1I1 = II + N - I + 1 * * Generate elementary reflector H(i) = I - tau * v * v**H * to annihilate A(i+2:n,i) * ALPHA = AP( II+1 ) CALL ZLARFG( N-I, ALPHA, AP( II+2 ), 1, TAUI ) E( I ) = ALPHA * IF( TAUI.NE.ZERO ) THEN * * Apply H(i) from both sides to A(i+1:n,i+1:n) * AP( II+1 ) = ONE * * Compute y := tau * A * v storing y in TAU(i:n-1) * CALL ZHPMV( UPLO, N-I, TAUI, AP( I1I1 ), AP( II+1 ), 1, $ ZERO, TAU( I ), 1 ) * * Compute w := y - 1/2 * tau * (y**H *v) * v * ALPHA = -HALF*TAUI*ZDOTC( N-I, TAU( I ), 1, AP( II+1 ), $ 1 ) CALL ZAXPY( N-I, ALPHA, AP( II+1 ), 1, TAU( I ), 1 ) * * Apply the transformation as a rank-2 update: * A := A - v * w**H - w * v**H * CALL ZHPR2( UPLO, N-I, -ONE, AP( II+1 ), 1, TAU( I ), 1, $ AP( I1I1 ) ) * END IF AP( II+1 ) = E( I ) D( I ) = AP( II ) TAU( I ) = TAUI II = I1I1 20 CONTINUE D( N ) = AP( II ) END IF * RETURN * * End of ZHPTRD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zupgtr.f0000644000000000000000000000013214061636515015357 xustar0030 mtime=1623670093.249104038 30 atime=1623670093.249104038 30 ctime=1623670093.249104038 elk-7.2.42/src/LAPACK/zupgtr.f0000644002504400250440000001373214061636515017422 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUPGTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUPGTR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDQ, N * .. * .. Array Arguments .. * COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUPGTR generates a complex unitary matrix Q which is defined as the *> product of n-1 elementary reflectors H(i) of order n, as returned by *> ZHPTRD using packed storage: *> *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), *> *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangular packed storage used in previous *> call to ZHPTRD; *> = 'L': Lower triangular packed storage used in previous *> call to ZHPTRD. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix Q. N >= 0. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) *> The vectors which define the elementary reflectors, as *> returned by ZHPTRD. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZHPTRD. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDQ,N) *> The N-by-N unitary matrix Q. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N-1) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDQ, N * .. * .. Array Arguments .. COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, IINFO, IJ, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZUNG2L, ZUNG2R * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUPGTR', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( UPPER ) THEN * * Q was determined by a call to ZHPTRD with UPLO = 'U' * * Unpack the vectors which define the elementary reflectors and * set the last row and column of Q equal to those of the unit * matrix * IJ = 2 DO 20 J = 1, N - 1 DO 10 I = 1, J - 1 Q( I, J ) = AP( IJ ) IJ = IJ + 1 10 CONTINUE IJ = IJ + 2 Q( N, J ) = CZERO 20 CONTINUE DO 30 I = 1, N - 1 Q( I, N ) = CZERO 30 CONTINUE Q( N, N ) = CONE * * Generate Q(1:n-1,1:n-1) * CALL ZUNG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO ) * ELSE * * Q was determined by a call to ZHPTRD with UPLO = 'L'. * * Unpack the vectors which define the elementary reflectors and * set the first row and column of Q equal to those of the unit * matrix * Q( 1, 1 ) = CONE DO 40 I = 2, N Q( I, 1 ) = CZERO 40 CONTINUE IJ = 3 DO 60 J = 2, N Q( 1, J ) = CZERO DO 50 I = J + 1, N Q( I, J ) = AP( IJ ) IJ = IJ + 1 50 CONTINUE IJ = IJ + 2 60 CONTINUE IF( N.GT.1 ) THEN * * Generate Q(2:n,2:n) * CALL ZUNG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK, $ IINFO ) END IF END IF RETURN * * End of ZUPGTR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dstebz.f0000644000000000000000000000013214061636515015317 xustar0030 mtime=1623670093.251104036 30 atime=1623670093.251104036 30 ctime=1623670093.251104036 elk-7.2.42/src/LAPACK/dstebz.f0000644002504400250440000005716214061636515017367 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSTEBZ * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSTEBZ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, * M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, * INFO ) * * .. Scalar Arguments .. * CHARACTER ORDER, RANGE * INTEGER IL, INFO, IU, M, N, NSPLIT * DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ) * DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSTEBZ computes the eigenvalues of a symmetric tridiagonal *> matrix T. The user may ask for all eigenvalues, all eigenvalues *> in the half-open interval (VL, VU], or the IL-th through IU-th *> eigenvalues. *> *> To avoid overflow, the matrix must be scaled so that its *> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest *> accuracy, it should not be much smaller than that. *> *> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal *> Matrix", Report CS41, Computer Science Dept., Stanford *> University, July 21, 1966. *> \endverbatim * * Arguments: * ========== * *> \param[in] RANGE *> \verbatim *> RANGE is CHARACTER*1 *> = 'A': ("All") all eigenvalues will be found. *> = 'V': ("Value") all eigenvalues in the half-open interval *> (VL, VU] will be found. *> = 'I': ("Index") the IL-th through IU-th eigenvalues (of the *> entire matrix) will be found. *> \endverbatim *> *> \param[in] ORDER *> \verbatim *> ORDER is CHARACTER*1 *> = 'B': ("By Block") the eigenvalues will be grouped by *> split-off block (see IBLOCK, ISPLIT) and *> ordered from smallest to largest within *> the block. *> = 'E': ("Entire matrix") *> the eigenvalues for the entire matrix *> will be ordered from smallest to *> largest. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the tridiagonal matrix T. N >= 0. *> \endverbatim *> *> \param[in] VL *> \verbatim *> VL is DOUBLE PRECISION *> *> If RANGE='V', the lower bound of the interval to *> be searched for eigenvalues. Eigenvalues less than or equal *> to VL, or greater than VU, will not be returned. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION *> *> If RANGE='V', the upper bound of the interval to *> be searched for eigenvalues. Eigenvalues less than or equal *> to VL, or greater than VU, will not be returned. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. *> \endverbatim *> *> \param[in] IL *> \verbatim *> IL is INTEGER *> *> If RANGE='I', the index of the *> smallest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] IU *> \verbatim *> IU is INTEGER *> *> If RANGE='I', the index of the *> largest eigenvalue to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. *> Not referenced if RANGE = 'A' or 'V'. *> \endverbatim *> *> \param[in] ABSTOL *> \verbatim *> ABSTOL is DOUBLE PRECISION *> The absolute tolerance for the eigenvalues. An eigenvalue *> (or cluster) is considered to be located if it has been *> determined to lie in an interval whose width is ABSTOL or *> less. If ABSTOL is less than or equal to zero, then ULP*|T| *> will be used, where |T| means the 1-norm of T. *> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The n diagonal elements of the tridiagonal matrix T. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The (n-1) off-diagonal elements of the tridiagonal matrix T. *> \endverbatim *> *> \param[out] M *> \verbatim *> M is INTEGER *> The actual number of eigenvalues found. 0 <= M <= N. *> (See also the description of INFO=2,3.) *> \endverbatim *> *> \param[out] NSPLIT *> \verbatim *> NSPLIT is INTEGER *> The number of diagonal blocks in the matrix T. *> 1 <= NSPLIT <= N. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> On exit, the first M elements of W will contain the *> eigenvalues. (DSTEBZ may use the remaining N-M elements as *> workspace.) *> \endverbatim *> *> \param[out] IBLOCK *> \verbatim *> IBLOCK is INTEGER array, dimension (N) *> At each row/column j where E(j) is zero or small, the *> matrix T is considered to split into a block diagonal *> matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which *> block (from 1 to the number of blocks) the eigenvalue W(i) *> belongs. (DSTEBZ may use the remaining N-M elements as *> workspace.) *> \endverbatim *> *> \param[out] ISPLIT *> \verbatim *> ISPLIT is INTEGER array, dimension (N) *> The splitting points, at which T breaks up into submatrices. *> The first submatrix consists of rows/columns 1 to ISPLIT(1), *> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), *> etc., and the NSPLIT-th consists of rows/columns *> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. *> (Only the first NSPLIT elements will actually be used, but *> since the user cannot know a priori what value NSPLIT will *> have, N words must be reserved for ISPLIT.) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (4*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (3*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: some or all of the eigenvalues failed to converge or *> were not computed: *> =1 or 3: Bisection failed to converge for some *> eigenvalues; these eigenvalues are flagged by a *> negative block number. The effect is that the *> eigenvalues may not be as accurate as the *> absolute and relative tolerances. This is *> generally caused by unexpectedly inaccurate *> arithmetic. *> =2 or 3: RANGE='I' only: Not all of the eigenvalues *> IL:IU were found. *> Effect: M < IU+1-IL *> Cause: non-monotonic arithmetic, causing the *> Sturm sequence to be non-monotonic. *> Cure: recalculate, using RANGE='A', and pick *> out eigenvalues IL:IU. In some cases, *> increasing the PARAMETER "FUDGE" may *> make things work. *> = 4: RANGE='I', and the Gershgorin interval *> initially used was too small. No eigenvalues *> were computed. *> Probable cause: your machine has sloppy *> floating-point arithmetic. *> Cure: Increase the PARAMETER "FUDGE", *> recompile, and try again. *> \endverbatim * *> \par Internal Parameters: * ========================= *> *> \verbatim *> RELFAC DOUBLE PRECISION, default = 2.0e0 *> The relative tolerance. An interval (a,b] lies within *> "relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|), *> where "ulp" is the machine precision (distance from 1 to *> the next larger floating point number.) *> *> FUDGE DOUBLE PRECISION, default = 2 *> A "fudge factor" to widen the Gershgorin intervals. Ideally, *> a value of 1 should work, but on machines with sloppy *> arithmetic, this needs to be larger. The default for *> publicly released versions should be large enough to handle *> the worst machine around. Note that this has no effect *> on accuracy of the solution. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, $ M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, $ INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER ORDER, RANGE INTEGER IL, INFO, IU, M, N, NSPLIT DOUBLE PRECISION ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ) DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO, HALF PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ HALF = 1.0D0 / TWO ) DOUBLE PRECISION FUDGE, RELFAC PARAMETER ( FUDGE = 2.1D0, RELFAC = 2.0D0 ) * .. * .. Local Scalars .. LOGICAL NCNVRG, TOOFEW INTEGER IB, IBEGIN, IDISCL, IDISCU, IE, IEND, IINFO, $ IM, IN, IOFF, IORDER, IOUT, IRANGE, ITMAX, $ ITMP1, IW, IWOFF, J, JB, JDISC, JE, NB, NWL, $ NWU DOUBLE PRECISION ATOLI, BNORM, GL, GU, PIVMIN, RTOLI, SAFEMN, $ TMP1, TMP2, TNORM, ULP, WKILL, WL, WLU, WU, WUL * .. * .. Local Arrays .. INTEGER IDUMMA( 1 ) * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH EXTERNAL LSAME, ILAENV, DLAMCH * .. * .. External Subroutines .. EXTERNAL DLAEBZ, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, INT, LOG, MAX, MIN, SQRT * .. * .. Executable Statements .. * INFO = 0 * * Decode RANGE * IF( LSAME( RANGE, 'A' ) ) THEN IRANGE = 1 ELSE IF( LSAME( RANGE, 'V' ) ) THEN IRANGE = 2 ELSE IF( LSAME( RANGE, 'I' ) ) THEN IRANGE = 3 ELSE IRANGE = 0 END IF * * Decode ORDER * IF( LSAME( ORDER, 'B' ) ) THEN IORDER = 2 ELSE IF( LSAME( ORDER, 'E' ) ) THEN IORDER = 1 ELSE IORDER = 0 END IF * * Check for Errors * IF( IRANGE.LE.0 ) THEN INFO = -1 ELSE IF( IORDER.LE.0 ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( IRANGE.EQ.2 ) THEN IF( VL.GE.VU ) $ INFO = -5 ELSE IF( IRANGE.EQ.3 .AND. ( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) ) $ THEN INFO = -6 ELSE IF( IRANGE.EQ.3 .AND. ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) ) $ THEN INFO = -7 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSTEBZ', -INFO ) RETURN END IF * * Initialize error flags * INFO = 0 NCNVRG = .FALSE. TOOFEW = .FALSE. * * Quick return if possible * M = 0 IF( N.EQ.0 ) $ RETURN * * Simplifications: * IF( IRANGE.EQ.3 .AND. IL.EQ.1 .AND. IU.EQ.N ) $ IRANGE = 1 * * Get machine constants * NB is the minimum vector length for vector bisection, or 0 * if only scalar is to be done. * SAFEMN = DLAMCH( 'S' ) ULP = DLAMCH( 'P' ) RTOLI = ULP*RELFAC NB = ILAENV( 1, 'DSTEBZ', ' ', N, -1, -1, -1 ) IF( NB.LE.1 ) $ NB = 0 * * Special Case when N=1 * IF( N.EQ.1 ) THEN NSPLIT = 1 ISPLIT( 1 ) = 1 IF( IRANGE.EQ.2 .AND. ( VL.GE.D( 1 ) .OR. VU.LT.D( 1 ) ) ) THEN M = 0 ELSE W( 1 ) = D( 1 ) IBLOCK( 1 ) = 1 M = 1 END IF RETURN END IF * * Compute Splitting Points * NSPLIT = 1 WORK( N ) = ZERO PIVMIN = ONE * DO 10 J = 2, N TMP1 = E( J-1 )**2 IF( ABS( D( J )*D( J-1 ) )*ULP**2+SAFEMN.GT.TMP1 ) THEN ISPLIT( NSPLIT ) = J - 1 NSPLIT = NSPLIT + 1 WORK( J-1 ) = ZERO ELSE WORK( J-1 ) = TMP1 PIVMIN = MAX( PIVMIN, TMP1 ) END IF 10 CONTINUE ISPLIT( NSPLIT ) = N PIVMIN = PIVMIN*SAFEMN * * Compute Interval and ATOLI * IF( IRANGE.EQ.3 ) THEN * * RANGE='I': Compute the interval containing eigenvalues * IL through IU. * * Compute Gershgorin interval for entire (split) matrix * and use it as the initial interval * GU = D( 1 ) GL = D( 1 ) TMP1 = ZERO * DO 20 J = 1, N - 1 TMP2 = SQRT( WORK( J ) ) GU = MAX( GU, D( J )+TMP1+TMP2 ) GL = MIN( GL, D( J )-TMP1-TMP2 ) TMP1 = TMP2 20 CONTINUE * GU = MAX( GU, D( N )+TMP1 ) GL = MIN( GL, D( N )-TMP1 ) TNORM = MAX( ABS( GL ), ABS( GU ) ) GL = GL - FUDGE*TNORM*ULP*N - FUDGE*TWO*PIVMIN GU = GU + FUDGE*TNORM*ULP*N + FUDGE*PIVMIN * * Compute Iteration parameters * ITMAX = INT( ( LOG( TNORM+PIVMIN )-LOG( PIVMIN ) ) / $ LOG( TWO ) ) + 2 IF( ABSTOL.LE.ZERO ) THEN ATOLI = ULP*TNORM ELSE ATOLI = ABSTOL END IF * WORK( N+1 ) = GL WORK( N+2 ) = GL WORK( N+3 ) = GU WORK( N+4 ) = GU WORK( N+5 ) = GL WORK( N+6 ) = GU IWORK( 1 ) = -1 IWORK( 2 ) = -1 IWORK( 3 ) = N + 1 IWORK( 4 ) = N + 1 IWORK( 5 ) = IL - 1 IWORK( 6 ) = IU * CALL DLAEBZ( 3, ITMAX, N, 2, 2, NB, ATOLI, RTOLI, PIVMIN, D, E, $ WORK, IWORK( 5 ), WORK( N+1 ), WORK( N+5 ), IOUT, $ IWORK, W, IBLOCK, IINFO ) * IF( IWORK( 6 ).EQ.IU ) THEN WL = WORK( N+1 ) WLU = WORK( N+3 ) NWL = IWORK( 1 ) WU = WORK( N+4 ) WUL = WORK( N+2 ) NWU = IWORK( 4 ) ELSE WL = WORK( N+2 ) WLU = WORK( N+4 ) NWL = IWORK( 2 ) WU = WORK( N+3 ) WUL = WORK( N+1 ) NWU = IWORK( 3 ) END IF * IF( NWL.LT.0 .OR. NWL.GE.N .OR. NWU.LT.1 .OR. NWU.GT.N ) THEN INFO = 4 RETURN END IF ELSE * * RANGE='A' or 'V' -- Set ATOLI * TNORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ), $ ABS( D( N ) )+ABS( E( N-1 ) ) ) * DO 30 J = 2, N - 1 TNORM = MAX( TNORM, ABS( D( J ) )+ABS( E( J-1 ) )+ $ ABS( E( J ) ) ) 30 CONTINUE * IF( ABSTOL.LE.ZERO ) THEN ATOLI = ULP*TNORM ELSE ATOLI = ABSTOL END IF * IF( IRANGE.EQ.2 ) THEN WL = VL WU = VU ELSE WL = ZERO WU = ZERO END IF END IF * * Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU. * NWL accumulates the number of eigenvalues .le. WL, * NWU accumulates the number of eigenvalues .le. WU * M = 0 IEND = 0 INFO = 0 NWL = 0 NWU = 0 * DO 70 JB = 1, NSPLIT IOFF = IEND IBEGIN = IOFF + 1 IEND = ISPLIT( JB ) IN = IEND - IOFF * IF( IN.EQ.1 ) THEN * * Special Case -- IN=1 * IF( IRANGE.EQ.1 .OR. WL.GE.D( IBEGIN )-PIVMIN ) $ NWL = NWL + 1 IF( IRANGE.EQ.1 .OR. WU.GE.D( IBEGIN )-PIVMIN ) $ NWU = NWU + 1 IF( IRANGE.EQ.1 .OR. ( WL.LT.D( IBEGIN )-PIVMIN .AND. WU.GE. $ D( IBEGIN )-PIVMIN ) ) THEN M = M + 1 W( M ) = D( IBEGIN ) IBLOCK( M ) = JB END IF ELSE * * General Case -- IN > 1 * * Compute Gershgorin Interval * and use it as the initial interval * GU = D( IBEGIN ) GL = D( IBEGIN ) TMP1 = ZERO * DO 40 J = IBEGIN, IEND - 1 TMP2 = ABS( E( J ) ) GU = MAX( GU, D( J )+TMP1+TMP2 ) GL = MIN( GL, D( J )-TMP1-TMP2 ) TMP1 = TMP2 40 CONTINUE * GU = MAX( GU, D( IEND )+TMP1 ) GL = MIN( GL, D( IEND )-TMP1 ) BNORM = MAX( ABS( GL ), ABS( GU ) ) GL = GL - FUDGE*BNORM*ULP*IN - FUDGE*PIVMIN GU = GU + FUDGE*BNORM*ULP*IN + FUDGE*PIVMIN * * Compute ATOLI for the current submatrix * IF( ABSTOL.LE.ZERO ) THEN ATOLI = ULP*MAX( ABS( GL ), ABS( GU ) ) ELSE ATOLI = ABSTOL END IF * IF( IRANGE.GT.1 ) THEN IF( GU.LT.WL ) THEN NWL = NWL + IN NWU = NWU + IN GO TO 70 END IF GL = MAX( GL, WL ) GU = MIN( GU, WU ) IF( GL.GE.GU ) $ GO TO 70 END IF * * Set Up Initial Interval * WORK( N+1 ) = GL WORK( N+IN+1 ) = GU CALL DLAEBZ( 1, 0, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN, $ D( IBEGIN ), E( IBEGIN ), WORK( IBEGIN ), $ IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IM, $ IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO ) * NWL = NWL + IWORK( 1 ) NWU = NWU + IWORK( IN+1 ) IWOFF = M - IWORK( 1 ) * * Compute Eigenvalues * ITMAX = INT( ( LOG( GU-GL+PIVMIN )-LOG( PIVMIN ) ) / $ LOG( TWO ) ) + 2 CALL DLAEBZ( 2, ITMAX, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN, $ D( IBEGIN ), E( IBEGIN ), WORK( IBEGIN ), $ IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IOUT, $ IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO ) * * Copy Eigenvalues Into W and IBLOCK * Use -JB for block number for unconverged eigenvalues. * DO 60 J = 1, IOUT TMP1 = HALF*( WORK( J+N )+WORK( J+IN+N ) ) * * Flag non-convergence. * IF( J.GT.IOUT-IINFO ) THEN NCNVRG = .TRUE. IB = -JB ELSE IB = JB END IF DO 50 JE = IWORK( J ) + 1 + IWOFF, $ IWORK( J+IN ) + IWOFF W( JE ) = TMP1 IBLOCK( JE ) = IB 50 CONTINUE 60 CONTINUE * M = M + IM END IF 70 CONTINUE * * If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU * If NWL+1 < IL or NWU > IU, discard extra eigenvalues. * IF( IRANGE.EQ.3 ) THEN IM = 0 IDISCL = IL - 1 - NWL IDISCU = NWU - IU * IF( IDISCL.GT.0 .OR. IDISCU.GT.0 ) THEN DO 80 JE = 1, M IF( W( JE ).LE.WLU .AND. IDISCL.GT.0 ) THEN IDISCL = IDISCL - 1 ELSE IF( W( JE ).GE.WUL .AND. IDISCU.GT.0 ) THEN IDISCU = IDISCU - 1 ELSE IM = IM + 1 W( IM ) = W( JE ) IBLOCK( IM ) = IBLOCK( JE ) END IF 80 CONTINUE M = IM END IF IF( IDISCL.GT.0 .OR. IDISCU.GT.0 ) THEN * * Code to deal with effects of bad arithmetic: * Some low eigenvalues to be discarded are not in (WL,WLU], * or high eigenvalues to be discarded are not in (WUL,WU] * so just kill off the smallest IDISCL/largest IDISCU * eigenvalues, by simply finding the smallest/largest * eigenvalue(s). * * (If N(w) is monotone non-decreasing, this should never * happen.) * IF( IDISCL.GT.0 ) THEN WKILL = WU DO 100 JDISC = 1, IDISCL IW = 0 DO 90 JE = 1, M IF( IBLOCK( JE ).NE.0 .AND. $ ( W( JE ).LT.WKILL .OR. IW.EQ.0 ) ) THEN IW = JE WKILL = W( JE ) END IF 90 CONTINUE IBLOCK( IW ) = 0 100 CONTINUE END IF IF( IDISCU.GT.0 ) THEN * WKILL = WL DO 120 JDISC = 1, IDISCU IW = 0 DO 110 JE = 1, M IF( IBLOCK( JE ).NE.0 .AND. $ ( W( JE ).GT.WKILL .OR. IW.EQ.0 ) ) THEN IW = JE WKILL = W( JE ) END IF 110 CONTINUE IBLOCK( IW ) = 0 120 CONTINUE END IF IM = 0 DO 130 JE = 1, M IF( IBLOCK( JE ).NE.0 ) THEN IM = IM + 1 W( IM ) = W( JE ) IBLOCK( IM ) = IBLOCK( JE ) END IF 130 CONTINUE M = IM END IF IF( IDISCL.LT.0 .OR. IDISCU.LT.0 ) THEN TOOFEW = .TRUE. END IF END IF * * If ORDER='B', do nothing -- the eigenvalues are already sorted * by block. * If ORDER='E', sort the eigenvalues from smallest to largest * IF( IORDER.EQ.1 .AND. NSPLIT.GT.1 ) THEN DO 150 JE = 1, M - 1 IE = 0 TMP1 = W( JE ) DO 140 J = JE + 1, M IF( W( J ).LT.TMP1 ) THEN IE = J TMP1 = W( J ) END IF 140 CONTINUE * IF( IE.NE.0 ) THEN ITMP1 = IBLOCK( IE ) W( IE ) = W( JE ) IBLOCK( IE ) = IBLOCK( JE ) W( JE ) = TMP1 IBLOCK( JE ) = ITMP1 END IF 150 CONTINUE END IF * INFO = 0 IF( NCNVRG ) $ INFO = INFO + 1 IF( TOOFEW ) $ INFO = INFO + 2 RETURN * * End of DSTEBZ * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zstein.f0000644000000000000000000000013214061636515015340 xustar0030 mtime=1623670093.253104035 30 atime=1623670093.253104035 30 ctime=1623670093.253104035 elk-7.2.42/src/LAPACK/zstein.f0000644002504400250440000003342014061636515017377 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZSTEIN * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZSTEIN + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, * IWORK, IFAIL, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDZ, M, N * .. * .. Array Arguments .. * INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), * $ IWORK( * ) * DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) * COMPLEX*16 Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZSTEIN computes the eigenvectors of a real symmetric tridiagonal *> matrix T corresponding to specified eigenvalues, using inverse *> iteration. *> *> The maximum number of iterations allowed for each eigenvector is *> specified by an internal parameter MAXITS (currently set to 5). *> *> Although the eigenvectors are real, they are stored in a complex *> array, which may be passed to ZUNMTR or ZUPMTR for back *> transformation to the eigenvectors of a complex Hermitian matrix *> which was reduced to tridiagonal form. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix. N >= 0. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The n diagonal elements of the tridiagonal matrix T. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The (n-1) subdiagonal elements of the tridiagonal matrix *> T, stored in elements 1 to N-1. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of eigenvectors to be found. 0 <= M <= N. *> \endverbatim *> *> \param[in] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> The first M elements of W contain the eigenvalues for *> which eigenvectors are to be computed. The eigenvalues *> should be grouped by split-off block and ordered from *> smallest to largest within the block. ( The output array *> W from DSTEBZ with ORDER = 'B' is expected here. ) *> \endverbatim *> *> \param[in] IBLOCK *> \verbatim *> IBLOCK is INTEGER array, dimension (N) *> The submatrix indices associated with the corresponding *> eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to *> the first submatrix from the top, =2 if W(i) belongs to *> the second submatrix, etc. ( The output array IBLOCK *> from DSTEBZ is expected here. ) *> \endverbatim *> *> \param[in] ISPLIT *> \verbatim *> ISPLIT is INTEGER array, dimension (N) *> The splitting points, at which T breaks up into submatrices. *> The first submatrix consists of rows/columns 1 to *> ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 *> through ISPLIT( 2 ), etc. *> ( The output array ISPLIT from DSTEBZ is expected here. ) *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ, M) *> The computed eigenvectors. The eigenvector associated *> with the eigenvalue W(i) is stored in the i-th column of *> Z. Any vector which fails to converge is set to its current *> iterate after MAXITS iterations. *> The imaginary parts of the eigenvectors are set to zero. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (5*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (N) *> \endverbatim *> *> \param[out] IFAIL *> \verbatim *> IFAIL is INTEGER array, dimension (M) *> On normal exit, all elements of IFAIL are zero. *> If one or more eigenvectors fail to converge after *> MAXITS iterations, then their indices are stored in *> array IFAIL. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, then i eigenvectors failed to converge *> in MAXITS iterations. Their indices are stored in *> array IFAIL. *> \endverbatim * *> \par Internal Parameters: * ========================= *> *> \verbatim *> MAXITS INTEGER, default = 5 *> The maximum number of iterations performed. *> *> EXTRA INTEGER, default = 2 *> The number of iterations performed after norm growth *> criterion is satisfied, should be at least 1. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, $ IWORK, IFAIL, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDZ, M, N * .. * .. Array Arguments .. INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), $ IWORK( * ) DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) COMPLEX*16 Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) DOUBLE PRECISION ZERO, ONE, TEN, ODM3, ODM1 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TEN = 1.0D+1, $ ODM3 = 1.0D-3, ODM1 = 1.0D-1 ) INTEGER MAXITS, EXTRA PARAMETER ( MAXITS = 5, EXTRA = 2 ) * .. * .. Local Scalars .. INTEGER B1, BLKSIZ, BN, GPIND, I, IINFO, INDRV1, $ INDRV2, INDRV3, INDRV4, INDRV5, ITS, J, J1, $ JBLK, JMAX, JR, NBLK, NRMCHK DOUBLE PRECISION DTPCRT, EPS, EPS1, NRM, ONENRM, ORTOL, PERTOL, $ SCL, SEP, TOL, XJ, XJM, ZTR * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DLAMCH, DNRM2 EXTERNAL IDAMAX, DLAMCH, DNRM2 * .. * .. External Subroutines .. EXTERNAL DCOPY, DLAGTF, DLAGTS, DLARNV, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 DO 10 I = 1, M IFAIL( I ) = 0 10 CONTINUE * IF( N.LT.0 ) THEN INFO = -1 ELSE IF( M.LT.0 .OR. M.GT.N ) THEN INFO = -4 ELSE IF( LDZ.LT.MAX( 1, N ) ) THEN INFO = -9 ELSE DO 20 J = 2, M IF( IBLOCK( J ).LT.IBLOCK( J-1 ) ) THEN INFO = -6 GO TO 30 END IF IF( IBLOCK( J ).EQ.IBLOCK( J-1 ) .AND. W( J ).LT.W( J-1 ) ) $ THEN INFO = -5 GO TO 30 END IF 20 CONTINUE 30 CONTINUE END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZSTEIN', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. M.EQ.0 ) THEN RETURN ELSE IF( N.EQ.1 ) THEN Z( 1, 1 ) = CONE RETURN END IF * * Get machine constants. * EPS = DLAMCH( 'Precision' ) * * Initialize seed for random number generator DLARNV. * DO 40 I = 1, 4 ISEED( I ) = 1 40 CONTINUE * * Initialize pointers. * INDRV1 = 0 INDRV2 = INDRV1 + N INDRV3 = INDRV2 + N INDRV4 = INDRV3 + N INDRV5 = INDRV4 + N * * Compute eigenvectors of matrix blocks. * J1 = 1 DO 180 NBLK = 1, IBLOCK( M ) * * Find starting and ending indices of block nblk. * IF( NBLK.EQ.1 ) THEN B1 = 1 ELSE B1 = ISPLIT( NBLK-1 ) + 1 END IF BN = ISPLIT( NBLK ) BLKSIZ = BN - B1 + 1 IF( BLKSIZ.EQ.1 ) $ GO TO 60 GPIND = J1 * * Compute reorthogonalization criterion and stopping criterion. * ONENRM = ABS( D( B1 ) ) + ABS( E( B1 ) ) ONENRM = MAX( ONENRM, ABS( D( BN ) )+ABS( E( BN-1 ) ) ) DO 50 I = B1 + 1, BN - 1 ONENRM = MAX( ONENRM, ABS( D( I ) )+ABS( E( I-1 ) )+ $ ABS( E( I ) ) ) 50 CONTINUE ORTOL = ODM3*ONENRM * DTPCRT = SQRT( ODM1 / BLKSIZ ) * * Loop through eigenvalues of block nblk. * 60 CONTINUE JBLK = 0 DO 170 J = J1, M IF( IBLOCK( J ).NE.NBLK ) THEN J1 = J GO TO 180 END IF JBLK = JBLK + 1 XJ = W( J ) * * Skip all the work if the block size is one. * IF( BLKSIZ.EQ.1 ) THEN WORK( INDRV1+1 ) = ONE GO TO 140 END IF * * If eigenvalues j and j-1 are too close, add a relatively * small perturbation. * IF( JBLK.GT.1 ) THEN EPS1 = ABS( EPS*XJ ) PERTOL = TEN*EPS1 SEP = XJ - XJM IF( SEP.LT.PERTOL ) $ XJ = XJM + PERTOL END IF * ITS = 0 NRMCHK = 0 * * Get random starting vector. * CALL DLARNV( 2, ISEED, BLKSIZ, WORK( INDRV1+1 ) ) * * Copy the matrix T so it won't be destroyed in factorization. * CALL DCOPY( BLKSIZ, D( B1 ), 1, WORK( INDRV4+1 ), 1 ) CALL DCOPY( BLKSIZ-1, E( B1 ), 1, WORK( INDRV2+2 ), 1 ) CALL DCOPY( BLKSIZ-1, E( B1 ), 1, WORK( INDRV3+1 ), 1 ) * * Compute LU factors with partial pivoting ( PT = LU ) * TOL = ZERO CALL DLAGTF( BLKSIZ, WORK( INDRV4+1 ), XJ, WORK( INDRV2+2 ), $ WORK( INDRV3+1 ), TOL, WORK( INDRV5+1 ), IWORK, $ IINFO ) * * Update iteration count. * 70 CONTINUE ITS = ITS + 1 IF( ITS.GT.MAXITS ) $ GO TO 120 * * Normalize and scale the righthand side vector Pb. * JMAX = IDAMAX( BLKSIZ, WORK( INDRV1+1 ), 1 ) SCL = BLKSIZ*ONENRM*MAX( EPS, $ ABS( WORK( INDRV4+BLKSIZ ) ) ) / $ ABS( WORK( INDRV1+JMAX ) ) CALL DSCAL( BLKSIZ, SCL, WORK( INDRV1+1 ), 1 ) * * Solve the system LU = Pb. * CALL DLAGTS( -1, BLKSIZ, WORK( INDRV4+1 ), WORK( INDRV2+2 ), $ WORK( INDRV3+1 ), WORK( INDRV5+1 ), IWORK, $ WORK( INDRV1+1 ), TOL, IINFO ) * * Reorthogonalize by modified Gram-Schmidt if eigenvalues are * close enough. * IF( JBLK.EQ.1 ) $ GO TO 110 IF( ABS( XJ-XJM ).GT.ORTOL ) $ GPIND = J IF( GPIND.NE.J ) THEN DO 100 I = GPIND, J - 1 ZTR = ZERO DO 80 JR = 1, BLKSIZ ZTR = ZTR + WORK( INDRV1+JR )* $ DBLE( Z( B1-1+JR, I ) ) 80 CONTINUE DO 90 JR = 1, BLKSIZ WORK( INDRV1+JR ) = WORK( INDRV1+JR ) - $ ZTR*DBLE( Z( B1-1+JR, I ) ) 90 CONTINUE 100 CONTINUE END IF * * Check the infinity norm of the iterate. * 110 CONTINUE JMAX = IDAMAX( BLKSIZ, WORK( INDRV1+1 ), 1 ) NRM = ABS( WORK( INDRV1+JMAX ) ) * * Continue for additional iterations after norm reaches * stopping criterion. * IF( NRM.LT.DTPCRT ) $ GO TO 70 NRMCHK = NRMCHK + 1 IF( NRMCHK.LT.EXTRA+1 ) $ GO TO 70 * GO TO 130 * * If stopping criterion was not satisfied, update info and * store eigenvector number in array ifail. * 120 CONTINUE INFO = INFO + 1 IFAIL( INFO ) = J * * Accept iterate as jth eigenvector. * 130 CONTINUE SCL = ONE / DNRM2( BLKSIZ, WORK( INDRV1+1 ), 1 ) JMAX = IDAMAX( BLKSIZ, WORK( INDRV1+1 ), 1 ) IF( WORK( INDRV1+JMAX ).LT.ZERO ) $ SCL = -SCL CALL DSCAL( BLKSIZ, SCL, WORK( INDRV1+1 ), 1 ) 140 CONTINUE DO 150 I = 1, N Z( I, J ) = CZERO 150 CONTINUE DO 160 I = 1, BLKSIZ Z( B1+I-1, J ) = DCMPLX( WORK( INDRV1+I ), ZERO ) 160 CONTINUE * * Save the shift to check eigenvalue spacing at next * iteration. * XJM = XJ * 170 CONTINUE 180 CONTINUE * RETURN * * End of ZSTEIN * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zupmtr.f0000644000000000000000000000013214061636515015365 xustar0030 mtime=1623670093.255104033 30 atime=1623670093.255104033 30 ctime=1623670093.255104033 elk-7.2.42/src/LAPACK/zupmtr.f0000644002504400250440000002155414061636515017431 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUPMTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUPMTR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, * INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS, UPLO * INTEGER INFO, LDC, M, N * .. * .. Array Arguments .. * COMPLEX*16 AP( * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUPMTR overwrites the general complex M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'C': Q**H * C C * Q**H *> *> where Q is a complex unitary matrix of order nq, with nq = m if *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of *> nq-1 elementary reflectors, as returned by ZHPTRD using packed *> storage: *> *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); *> *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left; *> = 'R': apply Q or Q**H from the Right. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangular packed storage used in previous *> call to ZHPTRD; *> = 'L': Lower triangular packed storage used in previous *> call to ZHPTRD. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'C': Conjugate transpose, apply Q**H. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] AP *> \verbatim *> AP is COMPLEX*16 array, dimension *> (M*(M+1)/2) if SIDE = 'L' *> (N*(N+1)/2) if SIDE = 'R' *> The vectors which define the elementary reflectors, as *> returned by ZHPTRD. AP is modified by the routine but *> restored on exit. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (M-1) if SIDE = 'L' *> or (N-1) if SIDE = 'R' *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZHPTRD. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension *> (N) if SIDE = 'L' *> (M) if SIDE = 'R' *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, $ INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, UPLO INTEGER INFO, LDC, M, N * .. * .. Array Arguments .. COMPLEX*16 AP( * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL FORWRD, LEFT, NOTRAN, UPPER INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ COMPLEX*16 AII, TAUI * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) UPPER = LSAME( UPLO, 'U' ) * * NQ is the order of Q * IF( LEFT ) THEN NQ = M ELSE NQ = N END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -3 ELSE IF( M.LT.0 ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUPMTR', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) $ RETURN * IF( UPPER ) THEN * * Q was determined by a call to ZHPTRD with UPLO = 'U' * FORWRD = ( LEFT .AND. NOTRAN ) .OR. $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) * IF( FORWRD ) THEN I1 = 1 I2 = NQ - 1 I3 = 1 II = 2 ELSE I1 = NQ - 1 I2 = 1 I3 = -1 II = NQ*( NQ+1 ) / 2 - 1 END IF * IF( LEFT ) THEN NI = N ELSE MI = M END IF * DO 10 I = I1, I2, I3 IF( LEFT ) THEN * * H(i) or H(i)**H is applied to C(1:i,1:n) * MI = I ELSE * * H(i) or H(i)**H is applied to C(1:m,1:i) * NI = I END IF * * Apply H(i) or H(i)**H * IF( NOTRAN ) THEN TAUI = TAU( I ) ELSE TAUI = DCONJG( TAU( I ) ) END IF AII = AP( II ) AP( II ) = ONE CALL ZLARF( SIDE, MI, NI, AP( II-I+1 ), 1, TAUI, C, LDC, $ WORK ) AP( II ) = AII * IF( FORWRD ) THEN II = II + I + 2 ELSE II = II - I - 1 END IF 10 CONTINUE ELSE * * Q was determined by a call to ZHPTRD with UPLO = 'L'. * FORWRD = ( LEFT .AND. .NOT.NOTRAN ) .OR. $ ( .NOT.LEFT .AND. NOTRAN ) * IF( FORWRD ) THEN I1 = 1 I2 = NQ - 1 I3 = 1 II = 2 ELSE I1 = NQ - 1 I2 = 1 I3 = -1 II = NQ*( NQ+1 ) / 2 - 1 END IF * IF( LEFT ) THEN NI = N JC = 1 ELSE MI = M IC = 1 END IF * DO 20 I = I1, I2, I3 AII = AP( II ) AP( II ) = ONE IF( LEFT ) THEN * * H(i) or H(i)**H is applied to C(i+1:m,1:n) * MI = M - I IC = I + 1 ELSE * * H(i) or H(i)**H is applied to C(1:m,i+1:n) * NI = N - I JC = I + 1 END IF * * Apply H(i) or H(i)**H * IF( NOTRAN ) THEN TAUI = TAU( I ) ELSE TAUI = DCONJG( TAU( I ) ) END IF CALL ZLARF( SIDE, MI, NI, AP( II ), 1, TAUI, C( IC, JC ), $ LDC, WORK ) AP( II ) = AII * IF( FORWRD ) THEN II = II + NQ - I + 1 ELSE II = II - NQ + I - 2 END IF 20 CONTINUE END IF RETURN * * End of ZUPMTR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed1.f0000644000000000000000000000013214061636515015156 xustar0030 mtime=1623670093.257104031 30 atime=1623670093.257104031 30 ctime=1623670093.257104031 elk-7.2.42/src/LAPACK/dlaed1.f0000644002504400250440000002043514061636515017217 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED1 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED1 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, * INFO ) * * .. Scalar Arguments .. * INTEGER CUTPNT, INFO, LDQ, N * DOUBLE PRECISION RHO * .. * .. Array Arguments .. * INTEGER INDXQ( * ), IWORK( * ) * DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAED1 computes the updated eigensystem of a diagonal *> matrix after modification by a rank-one symmetric matrix. This *> routine is used only for the eigenproblem which requires all *> eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles *> the case in which eigenvalues only or eigenvalues and eigenvectors *> of a full symmetric matrix (which was reduced to tridiagonal form) *> are desired. *> *> T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) *> *> where Z = Q**T*u, u is a vector of length N with ones in the *> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. *> *> The eigenvectors of the original matrix are stored in Q, and the *> eigenvalues are in D. The algorithm consists of three stages: *> *> The first stage consists of deflating the size of the problem *> when there are multiple eigenvalues or if there is a zero in *> the Z vector. For each such occurrence the dimension of the *> secular equation problem is reduced by one. This stage is *> performed by the routine DLAED2. *> *> The second stage consists of calculating the updated *> eigenvalues. This is done by finding the roots of the secular *> equation via the routine DLAED4 (as called by DLAED3). *> This routine also calculates the eigenvectors of the current *> problem. *> *> The final stage consists of computing the updated eigenvectors *> directly using the updated eigenvalues. The eigenvectors for *> the current problem are multiplied with the eigenvectors from *> the overall problem. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the eigenvalues of the rank-1-perturbed matrix. *> On exit, the eigenvalues of the repaired matrix. *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDQ,N) *> On entry, the eigenvectors of the rank-1-perturbed matrix. *> On exit, the eigenvectors of the repaired tridiagonal matrix. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[in,out] INDXQ *> \verbatim *> INDXQ is INTEGER array, dimension (N) *> On entry, the permutation which separately sorts the two *> subproblems in D into ascending order. *> On exit, the permutation which will reintegrate the *> subproblems back into sorted order, *> i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. *> \endverbatim *> *> \param[in] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> The subdiagonal entry used to create the rank-1 modification. *> \endverbatim *> *> \param[in] CUTPNT *> \verbatim *> CUTPNT is INTEGER *> The location of the last eigenvalue in the leading sub-matrix. *> min(1,N) <= CUTPNT <= N/2. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (4*N + N**2) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (4*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, an eigenvalue did not converge *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA \n *> Modified by Francoise Tisseur, University of Tennessee *> * ===================================================================== SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, $ INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER CUTPNT, INFO, LDQ, N DOUBLE PRECISION RHO * .. * .. Array Arguments .. INTEGER INDXQ( * ), IWORK( * ) DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER COLTYP, I, IDLMDA, INDX, INDXC, INDXP, IQ2, IS, $ IW, IZ, K, N1, N2, ZPP1 * .. * .. External Subroutines .. EXTERNAL DCOPY, DLAED2, DLAED3, DLAMRG, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( N.LT.0 ) THEN INFO = -1 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( MIN( 1, N / 2 ).GT.CUTPNT .OR. ( N / 2 ).LT.CUTPNT ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAED1', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * The following values are integer pointers which indicate * the portion of the workspace * used by a particular array in DLAED2 and DLAED3. * IZ = 1 IDLMDA = IZ + N IW = IDLMDA + N IQ2 = IW + N * INDX = 1 INDXC = INDX + N COLTYP = INDXC + N INDXP = COLTYP + N * * * Form the z-vector which consists of the last row of Q_1 and the * first row of Q_2. * CALL DCOPY( CUTPNT, Q( CUTPNT, 1 ), LDQ, WORK( IZ ), 1 ) ZPP1 = CUTPNT + 1 CALL DCOPY( N-CUTPNT, Q( ZPP1, ZPP1 ), LDQ, WORK( IZ+CUTPNT ), 1 ) * * Deflate eigenvalues. * CALL DLAED2( K, N, CUTPNT, D, Q, LDQ, INDXQ, RHO, WORK( IZ ), $ WORK( IDLMDA ), WORK( IW ), WORK( IQ2 ), $ IWORK( INDX ), IWORK( INDXC ), IWORK( INDXP ), $ IWORK( COLTYP ), INFO ) * IF( INFO.NE.0 ) $ GO TO 20 * * Solve Secular Equation. * IF( K.NE.0 ) THEN IS = ( IWORK( COLTYP )+IWORK( COLTYP+1 ) )*CUTPNT + $ ( IWORK( COLTYP+1 )+IWORK( COLTYP+2 ) )*( N-CUTPNT ) + IQ2 CALL DLAED3( K, N, CUTPNT, D, Q, LDQ, RHO, WORK( IDLMDA ), $ WORK( IQ2 ), IWORK( INDXC ), IWORK( COLTYP ), $ WORK( IW ), WORK( IS ), INFO ) IF( INFO.NE.0 ) $ GO TO 20 * * Prepare the INDXQ sorting permutation. * N1 = K N2 = N - K CALL DLAMRG( N1, N2, D, 1, -1, INDXQ ) ELSE DO 10 I = 1, N INDXQ( I ) = I 10 CONTINUE END IF * 20 CONTINUE RETURN * * End of DLAED1 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlassq.f0000644000000000000000000000013214061636515015313 xustar0030 mtime=1623670093.259104029 30 atime=1623670093.259104029 30 ctime=1623670093.259104029 elk-7.2.42/src/LAPACK/dlassq.f0000644002504400250440000001037414061636515017355 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASSQ updates a sum of squares represented in scaled form. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASSQ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) * * .. Scalar Arguments .. * INTEGER INCX, N * DOUBLE PRECISION SCALE, SUMSQ * .. * .. Array Arguments .. * DOUBLE PRECISION X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASSQ returns the values scl and smsq such that *> *> ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, *> *> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is *> assumed to be non-negative and scl returns the value *> *> scl = max( scale, abs( x( i ) ) ). *> *> scale and sumsq must be supplied in SCALE and SUMSQ and *> scl and smsq are overwritten on SCALE and SUMSQ respectively. *> *> The routine makes only one pass through the vector x. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of elements to be used from the vector X. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (1+(N-1)*INCX) *> The vector for which a scaled sum of squares is computed. *> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between successive values of the vector X. *> INCX > 0. *> \endverbatim *> *> \param[in,out] SCALE *> \verbatim *> SCALE is DOUBLE PRECISION *> On entry, the value scale in the equation above. *> On exit, SCALE is overwritten with scl , the scaling factor *> for the sum of squares. *> \endverbatim *> *> \param[in,out] SUMSQ *> \verbatim *> SUMSQ is DOUBLE PRECISION *> On entry, the value sumsq in the equation above. *> On exit, SUMSQ is overwritten with smsq , the basic sum of *> squares from which scl has been factored out. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX, N DOUBLE PRECISION SCALE, SUMSQ * .. * .. Array Arguments .. DOUBLE PRECISION X( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER IX DOUBLE PRECISION ABSXI * .. * .. External Functions .. LOGICAL DISNAN EXTERNAL DISNAN * .. * .. Intrinsic Functions .. INTRINSIC ABS * .. * .. Executable Statements .. * IF( N.GT.0 ) THEN DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX ABSXI = ABS( X( IX ) ) IF( ABSXI.GT.ZERO.OR.DISNAN( ABSXI ) ) THEN IF( SCALE.LT.ABSXI ) THEN SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2 SCALE = ABSXI ELSE SUMSQ = SUMSQ + ( ABSXI / SCALE )**2 END IF END IF 10 CONTINUE END IF RETURN * * End of DLASSQ * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dcombssq.f0000644000000000000000000000013214061636515015637 xustar0030 mtime=1623670093.261104027 30 atime=1623670093.261104027 30 ctime=1623670093.261104027 elk-7.2.42/src/LAPACK/dcombssq.f0000644002504400250440000000423414061636515017677 0ustar00dewhurstdewhurst00000000000000*> \brief \b DCOMBSSQ adds two scaled sum of squares quantities. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * * Definition: * =========== * * SUBROUTINE DCOMBSSQ( V1, V2 ) * * .. Array Arguments .. * DOUBLE PRECISION V1( 2 ), V2( 2 ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DCOMBSSQ adds two scaled sum of squares quantities, V1 := V1 + V2. *> That is, *> *> V1_scale**2 * V1_sumsq := V1_scale**2 * V1_sumsq *> + V2_scale**2 * V2_sumsq *> \endverbatim * * Arguments: * ========== * *> \param[in,out] V1 *> \verbatim *> V1 is DOUBLE PRECISION array, dimension (2). *> The first scaled sum. *> V1(1) = V1_scale, V1(2) = V1_sumsq. *> \endverbatim *> *> \param[in] V2 *> \verbatim *> V2 is DOUBLE PRECISION array, dimension (2). *> The second scaled sum. *> V2(1) = V2_scale, V2(2) = V2_sumsq. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2018 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DCOMBSSQ( V1, V2 ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2018 * * .. Array Arguments .. DOUBLE PRECISION V1( 2 ), V2( 2 ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Executable Statements .. * IF( V1( 1 ).GE.V2( 1 ) ) THEN IF( V1( 1 ).NE.ZERO ) THEN V1( 2 ) = V1( 2 ) + ( V2( 1 ) / V1( 1 ) )**2 * V2( 2 ) END IF ELSE V1( 2 ) = V2( 2 ) + ( V1( 1 ) / V2( 1 ) )**2 * V1( 2 ) V1( 1 ) = V2( 1 ) END IF RETURN * * End of DCOMBSSQ * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dorgql.f0000644000000000000000000000013214061636515015314 xustar0030 mtime=1623670093.263104025 30 atime=1623670093.262104026 30 ctime=1623670093.263104025 elk-7.2.42/src/LAPACK/dorgql.f0000644002504400250440000002000614061636515017347 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORGQL * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORGQL + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORGQL generates an M-by-N real matrix Q with orthonormal columns, *> which is defined as the last N columns of a product of K elementary *> reflectors of order M *> *> Q = H(k) . . . H(2) H(1) *> *> as returned by DGEQLF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. M >= N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the (n-k+i)-th column must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by DGEQLF in the last k columns of its array *> argument A. *> On exit, the M-by-N matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEQLF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT, $ NB, NBMIN, NX * .. * .. External Subroutines .. EXTERNAL DLARFB, DLARFT, DORG2L, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF * IF( INFO.EQ.0 ) THEN IF( N.EQ.0 ) THEN LWKOPT = 1 ELSE NB = ILAENV( 1, 'DORGQL', ' ', M, N, K, -1 ) LWKOPT = N*NB END IF WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORGQL', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.LE.0 ) THEN RETURN END IF * NBMIN = 2 NX = 0 IWS = N IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. * NX = MAX( 0, ILAENV( 3, 'DORGQL', ' ', M, N, K, -1 ) ) IF( NX.LT.K ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = N IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: reduce NB and * determine the minimum value of NB. * NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DORGQL', ' ', M, N, K, -1 ) ) END IF END IF END IF * IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN * * Use blocked code after the first block. * The last kk columns are handled by the block method. * KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB ) * * Set A(m-kk+1:m,1:n-kk) to zero. * DO 20 J = 1, N - KK DO 10 I = M - KK + 1, M A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE KK = 0 END IF * * Use unblocked code for the first or only block. * CALL DORG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO ) * IF( KK.GT.0 ) THEN * * Use blocked code * DO 50 I = K - KK + 1, K, NB IB = MIN( NB, K-I+1 ) IF( N-K+I.GT.1 ) THEN * * Form the triangular factor of the block reflector * H = H(i+ib-1) . . . H(i+1) H(i) * CALL DLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB, $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK ) * * Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left * CALL DLARFB( 'Left', 'No transpose', 'Backward', $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB, $ A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA, $ WORK( IB+1 ), LDWORK ) END IF * * Apply H to rows 1:m-k+i+ib-1 of current block * CALL DORG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA, $ TAU( I ), WORK, IINFO ) * * Set rows m-k+i+ib:m of current block to zero * DO 40 J = N - K + I, N - K + I + IB - 1 DO 30 L = M - K + I + IB, M A( L, J ) = ZERO 30 CONTINUE 40 CONTINUE 50 CONTINUE END IF * WORK( 1 ) = IWS RETURN * * End of DORGQL * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dorgqr.f0000644000000000000000000000013214061636515015322 xustar0030 mtime=1623670093.264104024 30 atime=1623670093.264104024 30 ctime=1623670093.264104024 elk-7.2.42/src/LAPACK/dorgqr.f0000644002504400250440000001761014061636515017364 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORGQR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORGQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORGQR generates an M-by-N real matrix Q with orthonormal columns, *> which is defined as the first N columns of a product of K elementary *> reflectors of order M *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by DGEQRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. M >= N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the i-th column must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by DGEQRF in the first k columns of its array *> argument A. *> On exit, the M-by-N matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEQRF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, $ LWKOPT, NB, NBMIN, NX * .. * .. External Subroutines .. EXTERNAL DLARFB, DLARFT, DORG2R, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 ) LWKOPT = MAX( 1, N )*NB WORK( 1 ) = LWKOPT LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORGQR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.LE.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NBMIN = 2 NX = 0 IWS = N IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. * NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) ) IF( NX.LT.K ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = N IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: reduce NB and * determine the minimum value of NB. * NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) ) END IF END IF END IF * IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN * * Use blocked code after the last block. * The first kk columns are handled by the block method. * KI = ( ( K-NX-1 ) / NB )*NB KK = MIN( K, KI+NB ) * * Set A(1:kk,kk+1:n) to zero. * DO 20 J = KK + 1, N DO 10 I = 1, KK A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE KK = 0 END IF * * Use unblocked code for the last or only block. * IF( KK.LT.N ) $ CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA, $ TAU( KK+1 ), WORK, IINFO ) * IF( KK.GT.0 ) THEN * * Use blocked code * DO 50 I = KI + 1, 1, -NB IB = MIN( NB, K-I+1 ) IF( I+IB.LE.N ) THEN * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB, $ A( I, I ), LDA, TAU( I ), WORK, LDWORK ) * * Apply H to A(i:m,i+ib:n) from the left * CALL DLARFB( 'Left', 'No transpose', 'Forward', $ 'Columnwise', M-I+1, N-I-IB+1, IB, $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ), $ LDA, WORK( IB+1 ), LDWORK ) END IF * * Apply H to rows i:m of current block * CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK, $ IINFO ) * * Set rows 1:i-1 of current block to zero * DO 40 J = I, I + IB - 1 DO 30 L = 1, I - 1 A( L, J ) = ZERO 30 CONTINUE 40 CONTINUE 50 CONTINUE END IF * WORK( 1 ) = IWS RETURN * * End of DORGQR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dpotrf2.f0000644000000000000000000000013214061636515015404 xustar0030 mtime=1623670093.266104023 30 atime=1623670093.266104023 30 ctime=1623670093.266104023 elk-7.2.42/src/LAPACK/dpotrf2.f0000644002504400250440000001425614061636515017451 0ustar00dewhurstdewhurst00000000000000*> \brief \b DPOTRF2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * REAL A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DPOTRF2 computes the Cholesky factorization of a real symmetric *> positive definite matrix A using the recursive algorithm. *> *> The factorization has the form *> A = U**T * U, if UPLO = 'U', or *> A = L * L**T, if UPLO = 'L', *> where U is an upper triangular matrix and L is lower triangular. *> *> This is the recursive version of the algorithm. It divides *> the matrix into four submatrices: *> *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 *> A = [ -----|----- ] with n1 = n/2 *> [ A21 | A22 ] n2 = n-n1 *> *> The subroutine calls itself to factor A11. Update and scale A21 *> or A12, update A22 then calls itself to factor A22. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doublePOcomputational * * ===================================================================== RECURSIVE SUBROUTINE DPOTRF2( UPLO, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER N1, N2, IINFO * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL DSYRK, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DPOTRF2', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * N=1 case * IF( N.EQ.1 ) THEN * * Test for non-positive-definiteness * IF( A( 1, 1 ).LE.ZERO.OR.DISNAN( A( 1, 1 ) ) ) THEN INFO = 1 RETURN END IF * * Factor * A( 1, 1 ) = SQRT( A( 1, 1 ) ) * * Use recursive code * ELSE N1 = N/2 N2 = N-N1 * * Factor A11 * CALL DPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO ) IF ( IINFO.NE.0 ) THEN INFO = IINFO RETURN END IF * * Compute the Cholesky factorization A = U**T*U * IF( UPPER ) THEN * * Update and scale A12 * CALL DTRSM( 'L', 'U', 'T', 'N', N1, N2, ONE, $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA ) * * Update and factor A22 * CALL DSYRK( UPLO, 'T', N2, N1, -ONE, A( 1, N1+1 ), LDA, $ ONE, A( N1+1, N1+1 ), LDA ) CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) IF ( IINFO.NE.0 ) THEN INFO = IINFO + N1 RETURN END IF * * Compute the Cholesky factorization A = L*L**T * ELSE * * Update and scale A21 * CALL DTRSM( 'R', 'L', 'T', 'N', N2, N1, ONE, $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA ) * * Update and factor A22 * CALL DSYRK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA, $ ONE, A( N1+1, N1+1 ), LDA ) CALL DPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) IF ( IINFO.NE.0 ) THEN INFO = IINFO + N1 RETURN END IF END IF END IF RETURN * * End of DPOTRF2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaebz.f0000644000000000000000000000013214061636515015265 xustar0030 mtime=1623670093.268104021 30 atime=1623670093.268104021 30 ctime=1623670093.268104021 elk-7.2.42/src/LAPACK/dlaebz.f0000644002504400250440000005402014061636515017323 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAEBZ computes the number of eigenvalues of a real symmetric tridiagonal matrix which are less than or equal to a given value, and performs other tasks required by the routine sstebz. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAEBZ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, * RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, * NAB, WORK, IWORK, INFO ) * * .. Scalar Arguments .. * INTEGER IJOB, INFO, MINP, MMAX, MOUT, N, NBMIN, NITMAX * DOUBLE PRECISION ABSTOL, PIVMIN, RELTOL * .. * .. Array Arguments .. * INTEGER IWORK( * ), NAB( MMAX, * ), NVAL( * ) * DOUBLE PRECISION AB( MMAX, * ), C( * ), D( * ), E( * ), E2( * ), * $ WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAEBZ contains the iteration loops which compute and use the *> function N(w), which is the count of eigenvalues of a symmetric *> tridiagonal matrix T less than or equal to its argument w. It *> performs a choice of two types of loops: *> *> IJOB=1, followed by *> IJOB=2: It takes as input a list of intervals and returns a list of *> sufficiently small intervals whose union contains the same *> eigenvalues as the union of the original intervals. *> The input intervals are (AB(j,1),AB(j,2)], j=1,...,MINP. *> The output interval (AB(j,1),AB(j,2)] will contain *> eigenvalues NAB(j,1)+1,...,NAB(j,2), where 1 <= j <= MOUT. *> *> IJOB=3: It performs a binary search in each input interval *> (AB(j,1),AB(j,2)] for a point w(j) such that *> N(w(j))=NVAL(j), and uses C(j) as the starting point of *> the search. If such a w(j) is found, then on output *> AB(j,1)=AB(j,2)=w. If no such w(j) is found, then on output *> (AB(j,1),AB(j,2)] will be a small interval containing the *> point where N(w) jumps through NVAL(j), unless that point *> lies outside the initial interval. *> *> Note that the intervals are in all cases half-open intervals, *> i.e., of the form (a,b] , which includes b but not a . *> *> To avoid underflow, the matrix should be scaled so that its largest *> element is no greater than overflow**(1/2) * underflow**(1/4) *> in absolute value. To assure the most accurate computation *> of small eigenvalues, the matrix should be scaled to be *> not much smaller than that, either. *> *> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal *> Matrix", Report CS41, Computer Science Dept., Stanford *> University, July 21, 1966 *> *> Note: the arguments are, in general, *not* checked for unreasonable *> values. *> \endverbatim * * Arguments: * ========== * *> \param[in] IJOB *> \verbatim *> IJOB is INTEGER *> Specifies what is to be done: *> = 1: Compute NAB for the initial intervals. *> = 2: Perform bisection iteration to find eigenvalues of T. *> = 3: Perform bisection iteration to invert N(w), i.e., *> to find a point which has a specified number of *> eigenvalues of T to its left. *> Other values will cause DLAEBZ to return with INFO=-1. *> \endverbatim *> *> \param[in] NITMAX *> \verbatim *> NITMAX is INTEGER *> The maximum number of "levels" of bisection to be *> performed, i.e., an interval of width W will not be made *> smaller than 2^(-NITMAX) * W. If not all intervals *> have converged after NITMAX iterations, then INFO is set *> to the number of non-converged intervals. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension n of the tridiagonal matrix T. It must be at *> least 1. *> \endverbatim *> *> \param[in] MMAX *> \verbatim *> MMAX is INTEGER *> The maximum number of intervals. If more than MMAX intervals *> are generated, then DLAEBZ will quit with INFO=MMAX+1. *> \endverbatim *> *> \param[in] MINP *> \verbatim *> MINP is INTEGER *> The initial number of intervals. It may not be greater than *> MMAX. *> \endverbatim *> *> \param[in] NBMIN *> \verbatim *> NBMIN is INTEGER *> The smallest number of intervals that should be processed *> using a vector loop. If zero, then only the scalar loop *> will be used. *> \endverbatim *> *> \param[in] ABSTOL *> \verbatim *> ABSTOL is DOUBLE PRECISION *> The minimum (absolute) width of an interval. When an *> interval is narrower than ABSTOL, or than RELTOL times the *> larger (in magnitude) endpoint, then it is considered to be *> sufficiently small, i.e., converged. This must be at least *> zero. *> \endverbatim *> *> \param[in] RELTOL *> \verbatim *> RELTOL is DOUBLE PRECISION *> The minimum relative width of an interval. When an interval *> is narrower than ABSTOL, or than RELTOL times the larger (in *> magnitude) endpoint, then it is considered to be *> sufficiently small, i.e., converged. Note: this should *> always be at least radix*machine epsilon. *> \endverbatim *> *> \param[in] PIVMIN *> \verbatim *> PIVMIN is DOUBLE PRECISION *> The minimum absolute value of a "pivot" in the Sturm *> sequence loop. *> This must be at least max |e(j)**2|*safe_min and at *> least safe_min, where safe_min is at least *> the smallest number that can divide one without overflow. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of the tridiagonal matrix T. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N) *> The offdiagonal elements of the tridiagonal matrix T in *> positions 1 through N-1. E(N) is arbitrary. *> \endverbatim *> *> \param[in] E2 *> \verbatim *> E2 is DOUBLE PRECISION array, dimension (N) *> The squares of the offdiagonal elements of the tridiagonal *> matrix T. E2(N) is ignored. *> \endverbatim *> *> \param[in,out] NVAL *> \verbatim *> NVAL is INTEGER array, dimension (MINP) *> If IJOB=1 or 2, not referenced. *> If IJOB=3, the desired values of N(w). The elements of NVAL *> will be reordered to correspond with the intervals in AB. *> Thus, NVAL(j) on output will not, in general be the same as *> NVAL(j) on input, but it will correspond with the interval *> (AB(j,1),AB(j,2)] on output. *> \endverbatim *> *> \param[in,out] AB *> \verbatim *> AB is DOUBLE PRECISION array, dimension (MMAX,2) *> The endpoints of the intervals. AB(j,1) is a(j), the left *> endpoint of the j-th interval, and AB(j,2) is b(j), the *> right endpoint of the j-th interval. The input intervals *> will, in general, be modified, split, and reordered by the *> calculation. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (MMAX) *> If IJOB=1, ignored. *> If IJOB=2, workspace. *> If IJOB=3, then on input C(j) should be initialized to the *> first search point in the binary search. *> \endverbatim *> *> \param[out] MOUT *> \verbatim *> MOUT is INTEGER *> If IJOB=1, the number of eigenvalues in the intervals. *> If IJOB=2 or 3, the number of intervals output. *> If IJOB=3, MOUT will equal MINP. *> \endverbatim *> *> \param[in,out] NAB *> \verbatim *> NAB is INTEGER array, dimension (MMAX,2) *> If IJOB=1, then on output NAB(i,j) will be set to N(AB(i,j)). *> If IJOB=2, then on input, NAB(i,j) should be set. It must *> satisfy the condition: *> N(AB(i,1)) <= NAB(i,1) <= NAB(i,2) <= N(AB(i,2)), *> which means that in interval i only eigenvalues *> NAB(i,1)+1,...,NAB(i,2) will be considered. Usually, *> NAB(i,j)=N(AB(i,j)), from a previous call to DLAEBZ with *> IJOB=1. *> On output, NAB(i,j) will contain *> max(na(k),min(nb(k),N(AB(i,j)))), where k is the index of *> the input interval that the output interval *> (AB(j,1),AB(j,2)] came from, and na(k) and nb(k) are the *> the input values of NAB(k,1) and NAB(k,2). *> If IJOB=3, then on output, NAB(i,j) contains N(AB(i,j)), *> unless N(w) > NVAL(i) for all search points w , in which *> case NAB(i,1) will not be modified, i.e., the output *> value will be the same as the input value (modulo *> reorderings -- see NVAL and AB), or unless N(w) < NVAL(i) *> for all search points w , in which case NAB(i,2) will *> not be modified. Normally, NAB should be set to some *> distinctive value(s) before DLAEBZ is called. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MMAX) *> Workspace. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (MMAX) *> Workspace. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: All intervals converged. *> = 1--MMAX: The last INFO intervals did not converge. *> = MMAX+1: More than MMAX intervals were generated. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> This routine is intended to be called only by other LAPACK *> routines, thus the interface is less user-friendly. It is intended *> for two purposes: *> *> (a) finding eigenvalues. In this case, DLAEBZ should have one or *> more initial intervals set up in AB, and DLAEBZ should be called *> with IJOB=1. This sets up NAB, and also counts the eigenvalues. *> Intervals with no eigenvalues would usually be thrown out at *> this point. Also, if not all the eigenvalues in an interval i *> are desired, NAB(i,1) can be increased or NAB(i,2) decreased. *> For example, set NAB(i,1)=NAB(i,2)-1 to get the largest *> eigenvalue. DLAEBZ is then called with IJOB=2 and MMAX *> no smaller than the value of MOUT returned by the call with *> IJOB=1. After this (IJOB=2) call, eigenvalues NAB(i,1)+1 *> through NAB(i,2) are approximately AB(i,1) (or AB(i,2)) to the *> tolerance specified by ABSTOL and RELTOL. *> *> (b) finding an interval (a',b'] containing eigenvalues w(f),...,w(l). *> In this case, start with a Gershgorin interval (a,b). Set up *> AB to contain 2 search intervals, both initially (a,b). One *> NVAL element should contain f-1 and the other should contain l *> , while C should contain a and b, resp. NAB(i,1) should be -1 *> and NAB(i,2) should be N+1, to flag an error if the desired *> interval does not lie in (a,b). DLAEBZ is then called with *> IJOB=3. On exit, if w(f-1) < w(f), then one of the intervals -- *> j -- will have AB(j,1)=AB(j,2) and NAB(j,1)=NAB(j,2)=f-1, while *> if, to the specified tolerance, w(f-k)=...=w(f+r), k > 0 and r *> >= 0, then the interval will have N(AB(j,1))=NAB(j,1)=f-k and *> N(AB(j,2))=NAB(j,2)=f+r. The cases w(l) < w(l+1) and *> w(l-r)=...=w(l+k) are handled similarly. *> \endverbatim *> * ===================================================================== SUBROUTINE DLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, $ RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, $ NAB, WORK, IWORK, INFO ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IJOB, INFO, MINP, MMAX, MOUT, N, NBMIN, NITMAX DOUBLE PRECISION ABSTOL, PIVMIN, RELTOL * .. * .. Array Arguments .. INTEGER IWORK( * ), NAB( MMAX, * ), NVAL( * ) DOUBLE PRECISION AB( MMAX, * ), C( * ), D( * ), E( * ), E2( * ), $ WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, TWO, HALF PARAMETER ( ZERO = 0.0D0, TWO = 2.0D0, $ HALF = 1.0D0 / TWO ) * .. * .. Local Scalars .. INTEGER ITMP1, ITMP2, J, JI, JIT, JP, KF, KFNEW, KL, $ KLNEW DOUBLE PRECISION TMP1, TMP2 * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. Executable Statements .. * * Check for Errors * INFO = 0 IF( IJOB.LT.1 .OR. IJOB.GT.3 ) THEN INFO = -1 RETURN END IF * * Initialize NAB * IF( IJOB.EQ.1 ) THEN * * Compute the number of eigenvalues in the initial intervals. * MOUT = 0 DO 30 JI = 1, MINP DO 20 JP = 1, 2 TMP1 = D( 1 ) - AB( JI, JP ) IF( ABS( TMP1 ).LT.PIVMIN ) $ TMP1 = -PIVMIN NAB( JI, JP ) = 0 IF( TMP1.LE.ZERO ) $ NAB( JI, JP ) = 1 * DO 10 J = 2, N TMP1 = D( J ) - E2( J-1 ) / TMP1 - AB( JI, JP ) IF( ABS( TMP1 ).LT.PIVMIN ) $ TMP1 = -PIVMIN IF( TMP1.LE.ZERO ) $ NAB( JI, JP ) = NAB( JI, JP ) + 1 10 CONTINUE 20 CONTINUE MOUT = MOUT + NAB( JI, 2 ) - NAB( JI, 1 ) 30 CONTINUE RETURN END IF * * Initialize for loop * * KF and KL have the following meaning: * Intervals 1,...,KF-1 have converged. * Intervals KF,...,KL still need to be refined. * KF = 1 KL = MINP * * If IJOB=2, initialize C. * If IJOB=3, use the user-supplied starting point. * IF( IJOB.EQ.2 ) THEN DO 40 JI = 1, MINP C( JI ) = HALF*( AB( JI, 1 )+AB( JI, 2 ) ) 40 CONTINUE END IF * * Iteration loop * DO 130 JIT = 1, NITMAX * * Loop over intervals * IF( KL-KF+1.GE.NBMIN .AND. NBMIN.GT.0 ) THEN * * Begin of Parallel Version of the loop * DO 60 JI = KF, KL * * Compute N(c), the number of eigenvalues less than c * WORK( JI ) = D( 1 ) - C( JI ) IWORK( JI ) = 0 IF( WORK( JI ).LE.PIVMIN ) THEN IWORK( JI ) = 1 WORK( JI ) = MIN( WORK( JI ), -PIVMIN ) END IF * DO 50 J = 2, N WORK( JI ) = D( J ) - E2( J-1 ) / WORK( JI ) - C( JI ) IF( WORK( JI ).LE.PIVMIN ) THEN IWORK( JI ) = IWORK( JI ) + 1 WORK( JI ) = MIN( WORK( JI ), -PIVMIN ) END IF 50 CONTINUE 60 CONTINUE * IF( IJOB.LE.2 ) THEN * * IJOB=2: Choose all intervals containing eigenvalues. * KLNEW = KL DO 70 JI = KF, KL * * Insure that N(w) is monotone * IWORK( JI ) = MIN( NAB( JI, 2 ), $ MAX( NAB( JI, 1 ), IWORK( JI ) ) ) * * Update the Queue -- add intervals if both halves * contain eigenvalues. * IF( IWORK( JI ).EQ.NAB( JI, 2 ) ) THEN * * No eigenvalue in the upper interval: * just use the lower interval. * AB( JI, 2 ) = C( JI ) * ELSE IF( IWORK( JI ).EQ.NAB( JI, 1 ) ) THEN * * No eigenvalue in the lower interval: * just use the upper interval. * AB( JI, 1 ) = C( JI ) ELSE KLNEW = KLNEW + 1 IF( KLNEW.LE.MMAX ) THEN * * Eigenvalue in both intervals -- add upper to * queue. * AB( KLNEW, 2 ) = AB( JI, 2 ) NAB( KLNEW, 2 ) = NAB( JI, 2 ) AB( KLNEW, 1 ) = C( JI ) NAB( KLNEW, 1 ) = IWORK( JI ) AB( JI, 2 ) = C( JI ) NAB( JI, 2 ) = IWORK( JI ) ELSE INFO = MMAX + 1 END IF END IF 70 CONTINUE IF( INFO.NE.0 ) $ RETURN KL = KLNEW ELSE * * IJOB=3: Binary search. Keep only the interval containing * w s.t. N(w) = NVAL * DO 80 JI = KF, KL IF( IWORK( JI ).LE.NVAL( JI ) ) THEN AB( JI, 1 ) = C( JI ) NAB( JI, 1 ) = IWORK( JI ) END IF IF( IWORK( JI ).GE.NVAL( JI ) ) THEN AB( JI, 2 ) = C( JI ) NAB( JI, 2 ) = IWORK( JI ) END IF 80 CONTINUE END IF * ELSE * * End of Parallel Version of the loop * * Begin of Serial Version of the loop * KLNEW = KL DO 100 JI = KF, KL * * Compute N(w), the number of eigenvalues less than w * TMP1 = C( JI ) TMP2 = D( 1 ) - TMP1 ITMP1 = 0 IF( TMP2.LE.PIVMIN ) THEN ITMP1 = 1 TMP2 = MIN( TMP2, -PIVMIN ) END IF * DO 90 J = 2, N TMP2 = D( J ) - E2( J-1 ) / TMP2 - TMP1 IF( TMP2.LE.PIVMIN ) THEN ITMP1 = ITMP1 + 1 TMP2 = MIN( TMP2, -PIVMIN ) END IF 90 CONTINUE * IF( IJOB.LE.2 ) THEN * * IJOB=2: Choose all intervals containing eigenvalues. * * Insure that N(w) is monotone * ITMP1 = MIN( NAB( JI, 2 ), $ MAX( NAB( JI, 1 ), ITMP1 ) ) * * Update the Queue -- add intervals if both halves * contain eigenvalues. * IF( ITMP1.EQ.NAB( JI, 2 ) ) THEN * * No eigenvalue in the upper interval: * just use the lower interval. * AB( JI, 2 ) = TMP1 * ELSE IF( ITMP1.EQ.NAB( JI, 1 ) ) THEN * * No eigenvalue in the lower interval: * just use the upper interval. * AB( JI, 1 ) = TMP1 ELSE IF( KLNEW.LT.MMAX ) THEN * * Eigenvalue in both intervals -- add upper to queue. * KLNEW = KLNEW + 1 AB( KLNEW, 2 ) = AB( JI, 2 ) NAB( KLNEW, 2 ) = NAB( JI, 2 ) AB( KLNEW, 1 ) = TMP1 NAB( KLNEW, 1 ) = ITMP1 AB( JI, 2 ) = TMP1 NAB( JI, 2 ) = ITMP1 ELSE INFO = MMAX + 1 RETURN END IF ELSE * * IJOB=3: Binary search. Keep only the interval * containing w s.t. N(w) = NVAL * IF( ITMP1.LE.NVAL( JI ) ) THEN AB( JI, 1 ) = TMP1 NAB( JI, 1 ) = ITMP1 END IF IF( ITMP1.GE.NVAL( JI ) ) THEN AB( JI, 2 ) = TMP1 NAB( JI, 2 ) = ITMP1 END IF END IF 100 CONTINUE KL = KLNEW * END IF * * Check for convergence * KFNEW = KF DO 110 JI = KF, KL TMP1 = ABS( AB( JI, 2 )-AB( JI, 1 ) ) TMP2 = MAX( ABS( AB( JI, 2 ) ), ABS( AB( JI, 1 ) ) ) IF( TMP1.LT.MAX( ABSTOL, PIVMIN, RELTOL*TMP2 ) .OR. $ NAB( JI, 1 ).GE.NAB( JI, 2 ) ) THEN * * Converged -- Swap with position KFNEW, * then increment KFNEW * IF( JI.GT.KFNEW ) THEN TMP1 = AB( JI, 1 ) TMP2 = AB( JI, 2 ) ITMP1 = NAB( JI, 1 ) ITMP2 = NAB( JI, 2 ) AB( JI, 1 ) = AB( KFNEW, 1 ) AB( JI, 2 ) = AB( KFNEW, 2 ) NAB( JI, 1 ) = NAB( KFNEW, 1 ) NAB( JI, 2 ) = NAB( KFNEW, 2 ) AB( KFNEW, 1 ) = TMP1 AB( KFNEW, 2 ) = TMP2 NAB( KFNEW, 1 ) = ITMP1 NAB( KFNEW, 2 ) = ITMP2 IF( IJOB.EQ.3 ) THEN ITMP1 = NVAL( JI ) NVAL( JI ) = NVAL( KFNEW ) NVAL( KFNEW ) = ITMP1 END IF END IF KFNEW = KFNEW + 1 END IF 110 CONTINUE KF = KFNEW * * Choose Midpoints * DO 120 JI = KF, KL C( JI ) = HALF*( AB( JI, 1 )+AB( JI, 2 ) ) 120 CONTINUE * * If no more intervals to refine, quit. * IF( KF.GT.KL ) $ GO TO 140 130 CONTINUE * * Converged * 140 CONTINUE INFO = MAX( KL+1-KF, 0 ) MOUT = KL * RETURN * * End of DLAEBZ * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaset.f0000644000000000000000000000013214061636515015300 xustar0030 mtime=1623670093.270104019 30 atime=1623670093.270104019 30 ctime=1623670093.270104019 elk-7.2.42/src/LAPACK/dlaset.f0000644002504400250440000001147414061636515017344 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASET + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, M, N * DOUBLE PRECISION ALPHA, BETA * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASET initializes an m-by-n matrix A to BETA on the diagonal and *> ALPHA on the offdiagonals. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies the part of the matrix A to be set. *> = 'U': Upper triangular part is set; the strictly lower *> triangular part of A is not changed. *> = 'L': Lower triangular part is set; the strictly upper *> triangular part of A is not changed. *> Otherwise: All of the matrix A is set. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION *> The constant to which the offdiagonal elements are to be set. *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION *> The constant to which the diagonal elements are to be set. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On exit, the leading m-by-n submatrix of A is set as follows: *> *> if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n, *> if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n, *> otherwise, A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j, *> *> and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n). *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, M, N DOUBLE PRECISION ALPHA, BETA * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( LSAME( UPLO, 'U' ) ) THEN * * Set the strictly upper triangular or trapezoidal part of the * array to ALPHA. * DO 20 J = 2, N DO 10 I = 1, MIN( J-1, M ) A( I, J ) = ALPHA 10 CONTINUE 20 CONTINUE * ELSE IF( LSAME( UPLO, 'L' ) ) THEN * * Set the strictly lower triangular or trapezoidal part of the * array to ALPHA. * DO 40 J = 1, MIN( M, N ) DO 30 I = J + 1, M A( I, J ) = ALPHA 30 CONTINUE 40 CONTINUE * ELSE * * Set the leading m-by-n submatrix to ALPHA. * DO 60 J = 1, N DO 50 I = 1, M A( I, J ) = ALPHA 50 CONTINUE 60 CONTINUE END IF * * Set the first min(M,N) diagonal elements to BETA. * DO 70 I = 1, MIN( M, N ) A( I, I ) = BETA 70 CONTINUE * RETURN * * End of DLASET * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlanst.f0000644000000000000000000000013214061636515015311 xustar0030 mtime=1623670093.272104017 30 atime=1623670093.272104017 30 ctime=1623670093.272104017 elk-7.2.42/src/LAPACK/dlanst.f0000644002504400250440000001232414061636515017350 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLANST + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) * * .. Scalar Arguments .. * CHARACTER NORM * INTEGER N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLANST returns the value of the one norm, or the Frobenius norm, or *> the infinity norm, or the element of largest absolute value of a *> real symmetric tridiagonal matrix A. *> \endverbatim *> *> \return DLANST *> \verbatim *> *> DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' *> ( *> ( norm1(A), NORM = '1', 'O' or 'o' *> ( *> ( normI(A), NORM = 'I' or 'i' *> ( *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' *> *> where norm1 denotes the one norm of a matrix (maximum column sum), *> normI denotes the infinity norm of a matrix (maximum row sum) and *> normF denotes the Frobenius norm of a matrix (square root of sum of *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. *> \endverbatim * * Arguments: * ========== * *> \param[in] NORM *> \verbatim *> NORM is CHARACTER*1 *> Specifies the value to be returned in DLANST as described *> above. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. When N = 0, DLANST is *> set to zero. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of A. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The (n-1) sub-diagonal or super-diagonal elements of A. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER NORM INTEGER N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I DOUBLE PRECISION ANORM, SCALE, SUM * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL DLASSQ * .. * .. Intrinsic Functions .. INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * IF( N.LE.0 ) THEN ANORM = ZERO ELSE IF( LSAME( NORM, 'M' ) ) THEN * * Find max(abs(A(i,j))). * ANORM = ABS( D( N ) ) DO 10 I = 1, N - 1 SUM = ABS( D( I ) ) IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM SUM = ABS( E( I ) ) IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 10 CONTINUE ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. $ LSAME( NORM, 'I' ) ) THEN * * Find norm1(A). * IF( N.EQ.1 ) THEN ANORM = ABS( D( 1 ) ) ELSE ANORM = ABS( D( 1 ) )+ABS( E( 1 ) ) SUM = ABS( E( N-1 ) )+ABS( D( N ) ) IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM DO 20 I = 2, N - 1 SUM = ABS( D( I ) )+ABS( E( I ) )+ABS( E( I-1 ) ) IF( ANORM .LT. SUM .OR. DISNAN( SUM ) ) ANORM = SUM 20 CONTINUE END IF ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN * * Find normF(A). * SCALE = ZERO SUM = ONE IF( N.GT.1 ) THEN CALL DLASSQ( N-1, E, 1, SCALE, SUM ) SUM = 2*SUM END IF CALL DLASSQ( N, D, 1, SCALE, SUM ) ANORM = SCALE*SQRT( SUM ) END IF * DLANST = ANORM RETURN * * End of DLANST * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaev2.f0000644000000000000000000000013214061636515015201 xustar0030 mtime=1623670093.274104015 30 atime=1623670093.273104016 30 ctime=1623670093.274104015 elk-7.2.42/src/LAPACK/dlaev2.f0000644002504400250440000001407214061636515017242 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAEV2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) * * .. Scalar Arguments .. * DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix *> [ A B ] *> [ B C ]. *> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the *> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right *> eigenvector for RT1, giving the decomposition *> *> [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] *> [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. *> \endverbatim * * Arguments: * ========== * *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION *> The (1,1) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION *> The (1,2) element and the conjugate of the (2,1) element of *> the 2-by-2 matrix. *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION *> The (2,2) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[out] RT1 *> \verbatim *> RT1 is DOUBLE PRECISION *> The eigenvalue of larger absolute value. *> \endverbatim *> *> \param[out] RT2 *> \verbatim *> RT2 is DOUBLE PRECISION *> The eigenvalue of smaller absolute value. *> \endverbatim *> *> \param[out] CS1 *> \verbatim *> CS1 is DOUBLE PRECISION *> \endverbatim *> *> \param[out] SN1 *> \verbatim *> SN1 is DOUBLE PRECISION *> The vector (CS1, SN1) is a unit right eigenvector for RT1. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> RT1 is accurate to a few ulps barring over/underflow. *> *> RT2 may be inaccurate if there is massive cancellation in the *> determinant A*C-B*B; higher precision or correctly rounded or *> correctly truncated arithmetic would be needed to compute RT2 *> accurately in all cases. *> *> CS1 and SN1 are accurate to a few ulps barring over/underflow. *> *> Overflow is possible only if RT1 is within a factor of 5 of overflow. *> Underflow is harmless if the input data is 0 or exceeds *> underflow_threshold / macheps. *> \endverbatim *> * ===================================================================== SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0D0 ) DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION HALF PARAMETER ( HALF = 0.5D0 ) * .. * .. Local Scalars .. INTEGER SGN1, SGN2 DOUBLE PRECISION AB, ACMN, ACMX, ACS, ADF, CS, CT, DF, RT, SM, $ TB, TN * .. * .. Intrinsic Functions .. INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * * Compute the eigenvalues * SM = A + C DF = A - C ADF = ABS( DF ) TB = B + B AB = ABS( TB ) IF( ABS( A ).GT.ABS( C ) ) THEN ACMX = A ACMN = C ELSE ACMX = C ACMN = A END IF IF( ADF.GT.AB ) THEN RT = ADF*SQRT( ONE+( AB / ADF )**2 ) ELSE IF( ADF.LT.AB ) THEN RT = AB*SQRT( ONE+( ADF / AB )**2 ) ELSE * * Includes case AB=ADF=0 * RT = AB*SQRT( TWO ) END IF IF( SM.LT.ZERO ) THEN RT1 = HALF*( SM-RT ) SGN1 = -1 * * Order of execution important. * To get fully accurate smaller eigenvalue, * next line needs to be executed in higher precision. * RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B ELSE IF( SM.GT.ZERO ) THEN RT1 = HALF*( SM+RT ) SGN1 = 1 * * Order of execution important. * To get fully accurate smaller eigenvalue, * next line needs to be executed in higher precision. * RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B ELSE * * Includes case RT1 = RT2 = 0 * RT1 = HALF*RT RT2 = -HALF*RT SGN1 = 1 END IF * * Compute the eigenvector * IF( DF.GE.ZERO ) THEN CS = DF + RT SGN2 = 1 ELSE CS = DF - RT SGN2 = -1 END IF ACS = ABS( CS ) IF( ACS.GT.AB ) THEN CT = -TB / CS SN1 = ONE / SQRT( ONE+CT*CT ) CS1 = CT*SN1 ELSE IF( AB.EQ.ZERO ) THEN CS1 = ONE SN1 = ZERO ELSE TN = -CS / TB CS1 = ONE / SQRT( ONE+TN*TN ) SN1 = TN*CS1 END IF END IF IF( SGN1.EQ.SGN2 ) THEN TN = CS1 CS1 = -SN1 SN1 = TN END IF RETURN * * End of DLAEV2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasr.f0000644000000000000000000000013214061636515015131 xustar0030 mtime=1623670093.276104013 30 atime=1623670093.275104014 30 ctime=1623670093.276104013 elk-7.2.42/src/LAPACK/dlasr.f0000644002504400250440000003530614061636515017175 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) * * .. Scalar Arguments .. * CHARACTER DIRECT, PIVOT, SIDE * INTEGER LDA, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASR applies a sequence of plane rotations to a real matrix A, *> from either the left or the right. *> *> When SIDE = 'L', the transformation takes the form *> *> A := P*A *> *> and when SIDE = 'R', the transformation takes the form *> *> A := A*P**T *> *> where P is an orthogonal matrix consisting of a sequence of z plane *> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', *> and P**T is the transpose of P. *> *> When DIRECT = 'F' (Forward sequence), then *> *> P = P(z-1) * ... * P(2) * P(1) *> *> and when DIRECT = 'B' (Backward sequence), then *> *> P = P(1) * P(2) * ... * P(z-1) *> *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation *> *> R(k) = ( c(k) s(k) ) *> = ( -s(k) c(k) ). *> *> When PIVOT = 'V' (Variable pivot), the rotation is performed *> for the plane (k,k+1), i.e., P(k) has the form *> *> P(k) = ( 1 ) *> ( ... ) *> ( 1 ) *> ( c(k) s(k) ) *> ( -s(k) c(k) ) *> ( 1 ) *> ( ... ) *> ( 1 ) *> *> where R(k) appears as a rank-2 modification to the identity matrix in *> rows and columns k and k+1. *> *> When PIVOT = 'T' (Top pivot), the rotation is performed for the *> plane (1,k+1), so P(k) has the form *> *> P(k) = ( c(k) s(k) ) *> ( 1 ) *> ( ... ) *> ( 1 ) *> ( -s(k) c(k) ) *> ( 1 ) *> ( ... ) *> ( 1 ) *> *> where R(k) appears in rows and columns 1 and k+1. *> *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is *> performed for the plane (k,z), giving P(k) the form *> *> P(k) = ( 1 ) *> ( ... ) *> ( 1 ) *> ( c(k) s(k) ) *> ( 1 ) *> ( ... ) *> ( 1 ) *> ( -s(k) c(k) ) *> *> where R(k) appears in rows and columns k and z. The rotations are *> performed without ever forming P(k) explicitly. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> Specifies whether the plane rotation matrix P is applied to *> A on the left or the right. *> = 'L': Left, compute A := P*A *> = 'R': Right, compute A:= A*P**T *> \endverbatim *> *> \param[in] PIVOT *> \verbatim *> PIVOT is CHARACTER*1 *> Specifies the plane for which P(k) is a plane rotation *> matrix. *> = 'V': Variable pivot, the plane (k,k+1) *> = 'T': Top pivot, the plane (1,k+1) *> = 'B': Bottom pivot, the plane (k,z) *> \endverbatim *> *> \param[in] DIRECT *> \verbatim *> DIRECT is CHARACTER*1 *> Specifies whether P is a forward or backward sequence of *> plane rotations. *> = 'F': Forward, P = P(z-1)*...*P(2)*P(1) *> = 'B': Backward, P = P(1)*P(2)*...*P(z-1) *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. If m <= 1, an immediate *> return is effected. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. If n <= 1, an *> immediate return is effected. *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION array, dimension *> (M-1) if SIDE = 'L' *> (N-1) if SIDE = 'R' *> The cosines c(k) of the plane rotations. *> \endverbatim *> *> \param[in] S *> \verbatim *> S is DOUBLE PRECISION array, dimension *> (M-1) if SIDE = 'L' *> (N-1) if SIDE = 'R' *> The sines s(k) of the plane rotations. The 2-by-2 plane *> rotation part of the matrix P(k), R(k), has the form *> R(k) = ( c(k) s(k) ) *> ( -s(k) c(k) ). *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The M-by-N matrix A. On exit, A is overwritten by P*A if *> SIDE = 'L' or by A*P**T if SIDE = 'R'. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIRECT, PIVOT, SIDE INTEGER LDA, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J DOUBLE PRECISION CTEMP, STEMP, TEMP * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN INFO = 1 ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN INFO = 2 ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) $ THEN INFO = 3 ELSE IF( M.LT.0 ) THEN INFO = 4 ELSE IF( N.LT.0 ) THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = 9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLASR ', INFO ) RETURN END IF * * Quick return if possible * IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) $ RETURN IF( LSAME( SIDE, 'L' ) ) THEN * * Form P * A * IF( LSAME( PIVOT, 'V' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 20 J = 1, M - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 10 I = 1, N TEMP = A( J+1, I ) A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 10 CONTINUE END IF 20 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 40 J = M - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 30 I = 1, N TEMP = A( J+1, I ) A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 30 CONTINUE END IF 40 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'T' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 60 J = 2, M CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 50 I = 1, N TEMP = A( J, I ) A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 50 CONTINUE END IF 60 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 80 J = M, 2, -1 CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 70 I = 1, N TEMP = A( J, I ) A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 70 CONTINUE END IF 80 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'B' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 100 J = 1, M - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 90 I = 1, N TEMP = A( J, I ) A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 90 CONTINUE END IF 100 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 120 J = M - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 110 I = 1, N TEMP = A( J, I ) A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 110 CONTINUE END IF 120 CONTINUE END IF END IF ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form A * P**T * IF( LSAME( PIVOT, 'V' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 140 J = 1, N - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 130 I = 1, M TEMP = A( I, J+1 ) A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 130 CONTINUE END IF 140 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 160 J = N - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 150 I = 1, M TEMP = A( I, J+1 ) A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 150 CONTINUE END IF 160 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'T' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 180 J = 2, N CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 170 I = 1, M TEMP = A( I, J ) A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 170 CONTINUE END IF 180 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 200 J = N, 2, -1 CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 190 I = 1, M TEMP = A( I, J ) A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 190 CONTINUE END IF 200 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'B' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 220 J = 1, N - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 210 I = 1, M TEMP = A( I, J ) A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 210 CONTINUE END IF 220 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 240 J = N - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 230 I = 1, M TEMP = A( I, J ) A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 230 CONTINUE END IF 240 CONTINUE END IF END IF END IF * RETURN * * End of DLASR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlae2.f0000644000000000000000000000013214061636515015013 xustar0030 mtime=1623670093.277104012 30 atime=1623670093.277104012 30 ctime=1623670093.277104012 elk-7.2.42/src/LAPACK/dlae2.f0000644002504400250440000001131114061636515017045 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAE2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) * * .. Scalar Arguments .. * DOUBLE PRECISION A, B, C, RT1, RT2 * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix *> [ A B ] *> [ B C ]. *> On return, RT1 is the eigenvalue of larger absolute value, and RT2 *> is the eigenvalue of smaller absolute value. *> \endverbatim * * Arguments: * ========== * *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION *> The (1,1) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION *> The (1,2) and (2,1) elements of the 2-by-2 matrix. *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION *> The (2,2) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[out] RT1 *> \verbatim *> RT1 is DOUBLE PRECISION *> The eigenvalue of larger absolute value. *> \endverbatim *> *> \param[out] RT2 *> \verbatim *> RT2 is DOUBLE PRECISION *> The eigenvalue of smaller absolute value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> RT1 is accurate to a few ulps barring over/underflow. *> *> RT2 may be inaccurate if there is massive cancellation in the *> determinant A*C-B*B; higher precision or correctly rounded or *> correctly truncated arithmetic would be needed to compute RT2 *> accurately in all cases. *> *> Overflow is possible only if RT1 is within a factor of 5 of overflow. *> Underflow is harmless if the input data is 0 or exceeds *> underflow_threshold / macheps. *> \endverbatim *> * ===================================================================== SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION A, B, C, RT1, RT2 * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0D0 ) DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION HALF PARAMETER ( HALF = 0.5D0 ) * .. * .. Local Scalars .. DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB * .. * .. Intrinsic Functions .. INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * * Compute the eigenvalues * SM = A + C DF = A - C ADF = ABS( DF ) TB = B + B AB = ABS( TB ) IF( ABS( A ).GT.ABS( C ) ) THEN ACMX = A ACMN = C ELSE ACMX = C ACMN = A END IF IF( ADF.GT.AB ) THEN RT = ADF*SQRT( ONE+( AB / ADF )**2 ) ELSE IF( ADF.LT.AB ) THEN RT = AB*SQRT( ONE+( ADF / AB )**2 ) ELSE * * Includes case AB=ADF=0 * RT = AB*SQRT( TWO ) END IF IF( SM.LT.ZERO ) THEN RT1 = HALF*( SM-RT ) * * Order of execution important. * To get fully accurate smaller eigenvalue, * next line needs to be executed in higher precision. * RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B ELSE IF( SM.GT.ZERO ) THEN RT1 = HALF*( SM+RT ) * * Order of execution important. * To get fully accurate smaller eigenvalue, * next line needs to be executed in higher precision. * RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B ELSE * * Includes case RT1 = RT2 = 0 * RT1 = HALF*RT RT2 = -HALF*RT END IF RETURN * * End of DLAE2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlapy2.f0000644000000000000000000000013214061636515015217 xustar0030 mtime=1623670093.279104011 30 atime=1623670093.279104011 30 ctime=1623670093.279104011 elk-7.2.42/src/LAPACK/dlapy2.f0000644002504400250440000000546614061636515017267 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAPY2 returns sqrt(x2+y2). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAPY2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) * * .. Scalar Arguments .. * DOUBLE PRECISION X, Y * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary *> overflow. *> \endverbatim * * Arguments: * ========== * *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is DOUBLE PRECISION *> X and Y specify the values x and y. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup OTHERauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. DOUBLE PRECISION X, Y * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) * .. * .. Local Scalars .. DOUBLE PRECISION W, XABS, YABS, Z LOGICAL X_IS_NAN, Y_IS_NAN * .. * .. External Functions .. LOGICAL DISNAN EXTERNAL DISNAN * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Executable Statements .. * X_IS_NAN = DISNAN( X ) Y_IS_NAN = DISNAN( Y ) IF ( X_IS_NAN ) DLAPY2 = X IF ( Y_IS_NAN ) DLAPY2 = Y * IF ( .NOT.( X_IS_NAN.OR.Y_IS_NAN ) ) THEN XABS = ABS( X ) YABS = ABS( Y ) W = MAX( XABS, YABS ) Z = MIN( XABS, YABS ) IF( Z.EQ.ZERO ) THEN DLAPY2 = W ELSE DLAPY2 = W*SQRT( ONE+( Z / W )**2 ) END IF END IF RETURN * * End of DLAPY2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlartg.f0000644000000000000000000000013214061636515015301 xustar0030 mtime=1623670093.281104009 30 atime=1623670093.281104009 30 ctime=1623670093.281104009 elk-7.2.42/src/LAPACK/dlartg.f0000644002504400250440000001261314061636515017341 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLARTG generates a plane rotation with real cosine and real sine. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARTG + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARTG( F, G, CS, SN, R ) * * .. Scalar Arguments .. * DOUBLE PRECISION CS, F, G, R, SN * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARTG generate a plane rotation so that *> *> [ CS SN ] . [ F ] = [ R ] where CS**2 + SN**2 = 1. *> [ -SN CS ] [ G ] [ 0 ] *> *> This is a slower, more accurate version of the BLAS1 routine DROTG, *> with the following other differences: *> F and G are unchanged on return. *> If G=0, then CS=1 and SN=0. *> If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any *> floating point operations (saves work in DBDSQR when *> there are zeros on the diagonal). *> *> If F exceeds G in magnitude, CS will be positive. *> \endverbatim * * Arguments: * ========== * *> \param[in] F *> \verbatim *> F is DOUBLE PRECISION *> The first component of vector to be rotated. *> \endverbatim *> *> \param[in] G *> \verbatim *> G is DOUBLE PRECISION *> The second component of vector to be rotated. *> \endverbatim *> *> \param[out] CS *> \verbatim *> CS is DOUBLE PRECISION *> The cosine of the rotation. *> \endverbatim *> *> \param[out] SN *> \verbatim *> SN is DOUBLE PRECISION *> The sine of the rotation. *> \endverbatim *> *> \param[out] R *> \verbatim *> R is DOUBLE PRECISION *> The nonzero component of the rotated vector. *> *> This version has a few statements commented out for thread safety *> (machine parameters are computed on each entry). 10 feb 03, SJH. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLARTG( F, G, CS, SN, R ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION CS, F, G, R, SN * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0D0 ) * .. * .. Local Scalars .. * LOGICAL FIRST INTEGER COUNT, I DOUBLE PRECISION EPS, F1, G1, SAFMIN, SAFMN2, SAFMX2, SCALE * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, INT, LOG, MAX, SQRT * .. * .. Save statement .. * SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 * .. * .. Data statements .. * DATA FIRST / .TRUE. / * .. * .. Executable Statements .. * * IF( FIRST ) THEN SAFMIN = DLAMCH( 'S' ) EPS = DLAMCH( 'E' ) SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / $ LOG( DLAMCH( 'B' ) ) / TWO ) SAFMX2 = ONE / SAFMN2 * FIRST = .FALSE. * END IF IF( G.EQ.ZERO ) THEN CS = ONE SN = ZERO R = F ELSE IF( F.EQ.ZERO ) THEN CS = ZERO SN = ONE R = G ELSE F1 = F G1 = G SCALE = MAX( ABS( F1 ), ABS( G1 ) ) IF( SCALE.GE.SAFMX2 ) THEN COUNT = 0 10 CONTINUE COUNT = COUNT + 1 F1 = F1*SAFMN2 G1 = G1*SAFMN2 SCALE = MAX( ABS( F1 ), ABS( G1 ) ) IF( SCALE.GE.SAFMX2 ) $ GO TO 10 R = SQRT( F1**2+G1**2 ) CS = F1 / R SN = G1 / R DO 20 I = 1, COUNT R = R*SAFMX2 20 CONTINUE ELSE IF( SCALE.LE.SAFMN2 ) THEN COUNT = 0 30 CONTINUE COUNT = COUNT + 1 F1 = F1*SAFMX2 G1 = G1*SAFMX2 SCALE = MAX( ABS( F1 ), ABS( G1 ) ) IF( SCALE.LE.SAFMN2 ) $ GO TO 30 R = SQRT( F1**2+G1**2 ) CS = F1 / R SN = G1 / R DO 40 I = 1, COUNT R = R*SAFMN2 40 CONTINUE ELSE R = SQRT( F1**2+G1**2 ) CS = F1 / R SN = G1 / R END IF IF( ABS( F ).GT.ABS( G ) .AND. CS.LT.ZERO ) THEN CS = -CS SN = -SN R = -R END IF END IF RETURN * * End of DLARTG * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasrt.f0000644000000000000000000000013214061636515015315 xustar0030 mtime=1623670093.283104007 30 atime=1623670093.282104008 30 ctime=1623670093.283104007 elk-7.2.42/src/LAPACK/dlasrt.f0000644002504400250440000001731414061636515017360 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASRT sorts numbers in increasing or decreasing order. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASRT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASRT( ID, N, D, INFO ) * * .. Scalar Arguments .. * CHARACTER ID * INTEGER INFO, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Sort the numbers in D in increasing order (if ID = 'I') or *> in decreasing order (if ID = 'D' ). *> *> Use Quick Sort, reverting to Insertion sort on arrays of *> size <= 20. Dimension of STACK limits N to about 2**32. *> \endverbatim * * Arguments: * ========== * *> \param[in] ID *> \verbatim *> ID is CHARACTER*1 *> = 'I': sort D in increasing order; *> = 'D': sort D in decreasing order. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The length of the array D. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the array to be sorted. *> On exit, D has been sorted into increasing order *> (D(1) <= ... <= D(N) ) or into decreasing order *> (D(1) >= ... >= D(N) ), depending on ID. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DLASRT( ID, N, D, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER ID INTEGER INFO, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER SELECT PARAMETER ( SELECT = 20 ) * .. * .. Local Scalars .. INTEGER DIR, ENDD, I, J, START, STKPNT DOUBLE PRECISION D1, D2, D3, DMNMX, TMP * .. * .. Local Arrays .. INTEGER STACK( 2, 32 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 DIR = -1 IF( LSAME( ID, 'D' ) ) THEN DIR = 0 ELSE IF( LSAME( ID, 'I' ) ) THEN DIR = 1 END IF IF( DIR.EQ.-1 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLASRT', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.1 ) $ RETURN * STKPNT = 1 STACK( 1, 1 ) = 1 STACK( 2, 1 ) = N 10 CONTINUE START = STACK( 1, STKPNT ) ENDD = STACK( 2, STKPNT ) STKPNT = STKPNT - 1 IF( ENDD-START.LE.SELECT .AND. ENDD-START.GT.0 ) THEN * * Do Insertion sort on D( START:ENDD ) * IF( DIR.EQ.0 ) THEN * * Sort into decreasing order * DO 30 I = START + 1, ENDD DO 20 J = I, START + 1, -1 IF( D( J ).GT.D( J-1 ) ) THEN DMNMX = D( J ) D( J ) = D( J-1 ) D( J-1 ) = DMNMX ELSE GO TO 30 END IF 20 CONTINUE 30 CONTINUE * ELSE * * Sort into increasing order * DO 50 I = START + 1, ENDD DO 40 J = I, START + 1, -1 IF( D( J ).LT.D( J-1 ) ) THEN DMNMX = D( J ) D( J ) = D( J-1 ) D( J-1 ) = DMNMX ELSE GO TO 50 END IF 40 CONTINUE 50 CONTINUE * END IF * ELSE IF( ENDD-START.GT.SELECT ) THEN * * Partition D( START:ENDD ) and stack parts, largest one first * * Choose partition entry as median of 3 * D1 = D( START ) D2 = D( ENDD ) I = ( START+ENDD ) / 2 D3 = D( I ) IF( D1.LT.D2 ) THEN IF( D3.LT.D1 ) THEN DMNMX = D1 ELSE IF( D3.LT.D2 ) THEN DMNMX = D3 ELSE DMNMX = D2 END IF ELSE IF( D3.LT.D2 ) THEN DMNMX = D2 ELSE IF( D3.LT.D1 ) THEN DMNMX = D3 ELSE DMNMX = D1 END IF END IF * IF( DIR.EQ.0 ) THEN * * Sort into decreasing order * I = START - 1 J = ENDD + 1 60 CONTINUE 70 CONTINUE J = J - 1 IF( D( J ).LT.DMNMX ) $ GO TO 70 80 CONTINUE I = I + 1 IF( D( I ).GT.DMNMX ) $ GO TO 80 IF( I.LT.J ) THEN TMP = D( I ) D( I ) = D( J ) D( J ) = TMP GO TO 60 END IF IF( J-START.GT.ENDD-J-1 ) THEN STKPNT = STKPNT + 1 STACK( 1, STKPNT ) = START STACK( 2, STKPNT ) = J STKPNT = STKPNT + 1 STACK( 1, STKPNT ) = J + 1 STACK( 2, STKPNT ) = ENDD ELSE STKPNT = STKPNT + 1 STACK( 1, STKPNT ) = J + 1 STACK( 2, STKPNT ) = ENDD STKPNT = STKPNT + 1 STACK( 1, STKPNT ) = START STACK( 2, STKPNT ) = J END IF ELSE * * Sort into increasing order * I = START - 1 J = ENDD + 1 90 CONTINUE 100 CONTINUE J = J - 1 IF( D( J ).GT.DMNMX ) $ GO TO 100 110 CONTINUE I = I + 1 IF( D( I ).LT.DMNMX ) $ GO TO 110 IF( I.LT.J ) THEN TMP = D( I ) D( I ) = D( J ) D( J ) = TMP GO TO 90 END IF IF( J-START.GT.ENDD-J-1 ) THEN STKPNT = STKPNT + 1 STACK( 1, STKPNT ) = START STACK( 2, STKPNT ) = J STKPNT = STKPNT + 1 STACK( 1, STKPNT ) = J + 1 STACK( 2, STKPNT ) = ENDD ELSE STKPNT = STKPNT + 1 STACK( 1, STKPNT ) = J + 1 STACK( 2, STKPNT ) = ENDD STKPNT = STKPNT + 1 STACK( 1, STKPNT ) = START STACK( 2, STKPNT ) = J END IF END IF END IF IF( STKPNT.GT.0 ) $ GO TO 10 RETURN * * End of DLASRT * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlacpy.f0000644000000000000000000000013214061636515015300 xustar0030 mtime=1623670093.285104005 30 atime=1623670093.284104006 30 ctime=1623670093.285104005 elk-7.2.42/src/LAPACK/dlacpy.f0000644002504400250440000001000114061636515017325 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLACPY copies all or part of one two-dimensional array to another. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLACPY + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDB, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLACPY copies all or part of a two-dimensional matrix A to another *> matrix B. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies the part of the matrix A to be copied to B. *> = 'U': Upper triangular part *> = 'L': Lower triangular part *> Otherwise: All of the matrix A *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The m by n matrix A. If UPLO = 'U', only the upper triangle *> or trapezoid is accessed; if UPLO = 'L', only the lower *> triangle or trapezoid is accessed. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,N) *> On exit, B = A in the locations specified by UPLO. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLACPY( UPLO, M, N, A, LDA, B, LDB ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDB, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, MIN( J, M ) B( I, J ) = A( I, J ) 10 CONTINUE 20 CONTINUE ELSE IF( LSAME( UPLO, 'L' ) ) THEN DO 40 J = 1, N DO 30 I = J, M B( I, J ) = A( I, J ) 30 CONTINUE 40 CONTINUE ELSE DO 60 J = 1, N DO 50 I = 1, M B( I, J ) = A( I, J ) 50 CONTINUE 60 CONTINUE END IF RETURN * * End of DLACPY * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dstein.f0000644000000000000000000000013214061636515015312 xustar0030 mtime=1623670093.286104004 30 atime=1623670093.286104004 30 ctime=1623670093.286104004 elk-7.2.42/src/LAPACK/dstein.f0000644002504400250440000003214114061636515017350 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSTEIN * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSTEIN + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, * IWORK, IFAIL, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDZ, M, N * .. * .. Array Arguments .. * INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), * $ IWORK( * ) * DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSTEIN computes the eigenvectors of a real symmetric tridiagonal *> matrix T corresponding to specified eigenvalues, using inverse *> iteration. *> *> The maximum number of iterations allowed for each eigenvector is *> specified by an internal parameter MAXITS (currently set to 5). *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix. N >= 0. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The n diagonal elements of the tridiagonal matrix T. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The (n-1) subdiagonal elements of the tridiagonal matrix *> T, in elements 1 to N-1. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of eigenvectors to be found. 0 <= M <= N. *> \endverbatim *> *> \param[in] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> The first M elements of W contain the eigenvalues for *> which eigenvectors are to be computed. The eigenvalues *> should be grouped by split-off block and ordered from *> smallest to largest within the block. ( The output array *> W from DSTEBZ with ORDER = 'B' is expected here. ) *> \endverbatim *> *> \param[in] IBLOCK *> \verbatim *> IBLOCK is INTEGER array, dimension (N) *> The submatrix indices associated with the corresponding *> eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to *> the first submatrix from the top, =2 if W(i) belongs to *> the second submatrix, etc. ( The output array IBLOCK *> from DSTEBZ is expected here. ) *> \endverbatim *> *> \param[in] ISPLIT *> \verbatim *> ISPLIT is INTEGER array, dimension (N) *> The splitting points, at which T breaks up into submatrices. *> The first submatrix consists of rows/columns 1 to *> ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 *> through ISPLIT( 2 ), etc. *> ( The output array ISPLIT from DSTEBZ is expected here. ) *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (LDZ, M) *> The computed eigenvectors. The eigenvector associated *> with the eigenvalue W(i) is stored in the i-th column of *> Z. Any vector which fails to converge is set to its current *> iterate after MAXITS iterations. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (5*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (N) *> \endverbatim *> *> \param[out] IFAIL *> \verbatim *> IFAIL is INTEGER array, dimension (M) *> On normal exit, all elements of IFAIL are zero. *> If one or more eigenvectors fail to converge after *> MAXITS iterations, then their indices are stored in *> array IFAIL. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, then i eigenvectors failed to converge *> in MAXITS iterations. Their indices are stored in *> array IFAIL. *> \endverbatim * *> \par Internal Parameters: * ========================= *> *> \verbatim *> MAXITS INTEGER, default = 5 *> The maximum number of iterations performed. *> *> EXTRA INTEGER, default = 2 *> The number of iterations performed after norm growth *> criterion is satisfied, should be at least 1. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, $ IWORK, IFAIL, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDZ, M, N * .. * .. Array Arguments .. INTEGER IBLOCK( * ), IFAIL( * ), ISPLIT( * ), $ IWORK( * ) DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TEN, ODM3, ODM1 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TEN = 1.0D+1, $ ODM3 = 1.0D-3, ODM1 = 1.0D-1 ) INTEGER MAXITS, EXTRA PARAMETER ( MAXITS = 5, EXTRA = 2 ) * .. * .. Local Scalars .. INTEGER B1, BLKSIZ, BN, GPIND, I, IINFO, INDRV1, $ INDRV2, INDRV3, INDRV4, INDRV5, ITS, J, J1, $ JBLK, JMAX, NBLK, NRMCHK DOUBLE PRECISION DTPCRT, EPS, EPS1, NRM, ONENRM, ORTOL, PERTOL, $ SCL, SEP, TOL, XJ, XJM, ZTR * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DDOT, DLAMCH, DNRM2 EXTERNAL IDAMAX, DDOT, DLAMCH, DNRM2 * .. * .. External Subroutines .. EXTERNAL DAXPY, DCOPY, DLAGTF, DLAGTS, DLARNV, DSCAL, $ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 DO 10 I = 1, M IFAIL( I ) = 0 10 CONTINUE * IF( N.LT.0 ) THEN INFO = -1 ELSE IF( M.LT.0 .OR. M.GT.N ) THEN INFO = -4 ELSE IF( LDZ.LT.MAX( 1, N ) ) THEN INFO = -9 ELSE DO 20 J = 2, M IF( IBLOCK( J ).LT.IBLOCK( J-1 ) ) THEN INFO = -6 GO TO 30 END IF IF( IBLOCK( J ).EQ.IBLOCK( J-1 ) .AND. W( J ).LT.W( J-1 ) ) $ THEN INFO = -5 GO TO 30 END IF 20 CONTINUE 30 CONTINUE END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSTEIN', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. M.EQ.0 ) THEN RETURN ELSE IF( N.EQ.1 ) THEN Z( 1, 1 ) = ONE RETURN END IF * * Get machine constants. * EPS = DLAMCH( 'Precision' ) * * Initialize seed for random number generator DLARNV. * DO 40 I = 1, 4 ISEED( I ) = 1 40 CONTINUE * * Initialize pointers. * INDRV1 = 0 INDRV2 = INDRV1 + N INDRV3 = INDRV2 + N INDRV4 = INDRV3 + N INDRV5 = INDRV4 + N * * Compute eigenvectors of matrix blocks. * J1 = 1 DO 160 NBLK = 1, IBLOCK( M ) * * Find starting and ending indices of block nblk. * IF( NBLK.EQ.1 ) THEN B1 = 1 ELSE B1 = ISPLIT( NBLK-1 ) + 1 END IF BN = ISPLIT( NBLK ) BLKSIZ = BN - B1 + 1 IF( BLKSIZ.EQ.1 ) $ GO TO 60 GPIND = J1 * * Compute reorthogonalization criterion and stopping criterion. * ONENRM = ABS( D( B1 ) ) + ABS( E( B1 ) ) ONENRM = MAX( ONENRM, ABS( D( BN ) )+ABS( E( BN-1 ) ) ) DO 50 I = B1 + 1, BN - 1 ONENRM = MAX( ONENRM, ABS( D( I ) )+ABS( E( I-1 ) )+ $ ABS( E( I ) ) ) 50 CONTINUE ORTOL = ODM3*ONENRM * DTPCRT = SQRT( ODM1 / BLKSIZ ) * * Loop through eigenvalues of block nblk. * 60 CONTINUE JBLK = 0 DO 150 J = J1, M IF( IBLOCK( J ).NE.NBLK ) THEN J1 = J GO TO 160 END IF JBLK = JBLK + 1 XJ = W( J ) * * Skip all the work if the block size is one. * IF( BLKSIZ.EQ.1 ) THEN WORK( INDRV1+1 ) = ONE GO TO 120 END IF * * If eigenvalues j and j-1 are too close, add a relatively * small perturbation. * IF( JBLK.GT.1 ) THEN EPS1 = ABS( EPS*XJ ) PERTOL = TEN*EPS1 SEP = XJ - XJM IF( SEP.LT.PERTOL ) $ XJ = XJM + PERTOL END IF * ITS = 0 NRMCHK = 0 * * Get random starting vector. * CALL DLARNV( 2, ISEED, BLKSIZ, WORK( INDRV1+1 ) ) * * Copy the matrix T so it won't be destroyed in factorization. * CALL DCOPY( BLKSIZ, D( B1 ), 1, WORK( INDRV4+1 ), 1 ) CALL DCOPY( BLKSIZ-1, E( B1 ), 1, WORK( INDRV2+2 ), 1 ) CALL DCOPY( BLKSIZ-1, E( B1 ), 1, WORK( INDRV3+1 ), 1 ) * * Compute LU factors with partial pivoting ( PT = LU ) * TOL = ZERO CALL DLAGTF( BLKSIZ, WORK( INDRV4+1 ), XJ, WORK( INDRV2+2 ), $ WORK( INDRV3+1 ), TOL, WORK( INDRV5+1 ), IWORK, $ IINFO ) * * Update iteration count. * 70 CONTINUE ITS = ITS + 1 IF( ITS.GT.MAXITS ) $ GO TO 100 * * Normalize and scale the righthand side vector Pb. * JMAX = IDAMAX( BLKSIZ, WORK( INDRV1+1 ), 1 ) SCL = BLKSIZ*ONENRM*MAX( EPS, $ ABS( WORK( INDRV4+BLKSIZ ) ) ) / $ ABS( WORK( INDRV1+JMAX ) ) CALL DSCAL( BLKSIZ, SCL, WORK( INDRV1+1 ), 1 ) * * Solve the system LU = Pb. * CALL DLAGTS( -1, BLKSIZ, WORK( INDRV4+1 ), WORK( INDRV2+2 ), $ WORK( INDRV3+1 ), WORK( INDRV5+1 ), IWORK, $ WORK( INDRV1+1 ), TOL, IINFO ) * * Reorthogonalize by modified Gram-Schmidt if eigenvalues are * close enough. * IF( JBLK.EQ.1 ) $ GO TO 90 IF( ABS( XJ-XJM ).GT.ORTOL ) $ GPIND = J IF( GPIND.NE.J ) THEN DO 80 I = GPIND, J - 1 ZTR = -DDOT( BLKSIZ, WORK( INDRV1+1 ), 1, Z( B1, I ), $ 1 ) CALL DAXPY( BLKSIZ, ZTR, Z( B1, I ), 1, $ WORK( INDRV1+1 ), 1 ) 80 CONTINUE END IF * * Check the infinity norm of the iterate. * 90 CONTINUE JMAX = IDAMAX( BLKSIZ, WORK( INDRV1+1 ), 1 ) NRM = ABS( WORK( INDRV1+JMAX ) ) * * Continue for additional iterations after norm reaches * stopping criterion. * IF( NRM.LT.DTPCRT ) $ GO TO 70 NRMCHK = NRMCHK + 1 IF( NRMCHK.LT.EXTRA+1 ) $ GO TO 70 * GO TO 110 * * If stopping criterion was not satisfied, update info and * store eigenvector number in array ifail. * 100 CONTINUE INFO = INFO + 1 IFAIL( INFO ) = J * * Accept iterate as jth eigenvector. * 110 CONTINUE SCL = ONE / DNRM2( BLKSIZ, WORK( INDRV1+1 ), 1 ) JMAX = IDAMAX( BLKSIZ, WORK( INDRV1+1 ), 1 ) IF( WORK( INDRV1+JMAX ).LT.ZERO ) $ SCL = -SCL CALL DSCAL( BLKSIZ, SCL, WORK( INDRV1+1 ), 1 ) 120 CONTINUE DO 130 I = 1, N Z( I, J ) = ZERO 130 CONTINUE DO 140 I = 1, BLKSIZ Z( B1+I-1, J ) = WORK( INDRV1+I ) 140 CONTINUE * * Save the shift to check eigenvalue spacing at next * iteration. * XJM = XJ * 150 CONTINUE 160 CONTINUE * RETURN * * End of DSTEIN * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dormtr.f0000644000000000000000000000013214061636515015333 xustar0030 mtime=1623670093.288104002 30 atime=1623670093.288104002 30 ctime=1623670093.288104002 elk-7.2.42/src/LAPACK/dormtr.f0000644002504400250440000002113414061636515017371 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORMTR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORMTR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS, UPLO * INTEGER INFO, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORMTR overwrites the general real M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'T': Q**T * C C * Q**T *> *> where Q is a real orthogonal matrix of order nq, with nq = m if *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of *> nq-1 elementary reflectors, as returned by DSYTRD: *> *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); *> *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**T from the Left; *> = 'R': apply Q or Q**T from the Right. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A contains elementary reflectors *> from DSYTRD; *> = 'L': Lower triangle of A contains elementary reflectors *> from DSYTRD. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'T': Transpose, apply Q**T. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension *> (LDA,M) if SIDE = 'L' *> (LDA,N) if SIDE = 'R' *> The vectors which define the elementary reflectors, as *> returned by DSYTRD. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension *> (M-1) if SIDE = 'L' *> (N-1) if SIDE = 'R' *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DSYTRD. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS, UPLO INTEGER INFO, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL LEFT, LQUERY, UPPER INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DORMQL, DORMQR, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) $ THEN INFO = -3 ELSE IF( M.LT.0 ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -12 END IF * IF( INFO.EQ.0 ) THEN IF( UPPER ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M-1, N, M-1, $ -1 ) ELSE NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N-1, N-1, $ -1 ) END IF ELSE IF( LEFT ) THEN NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1, $ -1 ) ELSE NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1, $ -1 ) END IF END IF LWKOPT = MAX( 1, NW )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMTR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) THEN WORK( 1 ) = 1 RETURN END IF * IF( LEFT ) THEN MI = M - 1 NI = N ELSE MI = M NI = N - 1 END IF * IF( UPPER ) THEN * * Q was determined by a call to DSYTRD with UPLO = 'U' * CALL DORMQL( SIDE, TRANS, MI, NI, NQ-1, A( 1, 2 ), LDA, TAU, C, $ LDC, WORK, LWORK, IINFO ) ELSE * * Q was determined by a call to DSYTRD with UPLO = 'L' * IF( LEFT ) THEN I1 = 2 I2 = 1 ELSE I1 = 1 I2 = 2 END IF CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) END IF WORK( 1 ) = LWKOPT RETURN * * End of DORMTR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsygs2.f0000644000000000000000000000012114061636515015235 xustar0027 mtime=1623670093.290104 27 atime=1623670093.290104 27 ctime=1623670093.290104 elk-7.2.42/src/LAPACK/dsygs2.f0000644002504400250440000002123714061636515017301 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYGS2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYGS2 reduces a real symmetric-definite generalized eigenproblem *> to standard form. *> *> If ITYPE = 1, the problem is A*x = lambda*B*x, *> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T) *> *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or *> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L. *> *> B must have been previously factorized as U**T *U or L*L**T by DPOTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); *> = 2 or 3: compute U*A*U**T or L**T *A*L. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> symmetric matrix A is stored, and how B has been factorized. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> n by n upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,N) *> The triangular factor from the Cholesky factorization of B, *> as returned by DPOTRF. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleSYcomputational * * ===================================================================== SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, HALF PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER K DOUBLE PRECISION AKK, BKK, CT * .. * .. External Subroutines .. EXTERNAL DAXPY, DSCAL, DSYR2, DTRMV, DTRSV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYGS2', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**T)*A*inv(U) * DO 10 K = 1, N * * Update the upper triangle of A(k:n,k:n) * AKK = A( K, K ) BKK = B( K, K ) AKK = AKK / BKK**2 A( K, K ) = AKK IF( K.LT.N ) THEN CALL DSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) CT = -HALF*AKK CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), $ LDA ) CALL DSYR2( UPLO, N-K, -ONE, A( K, K+1 ), LDA, $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), $ LDA ) CALL DTRSV( UPLO, 'Transpose', 'Non-unit', N-K, $ B( K+1, K+1 ), LDB, A( K, K+1 ), LDA ) END IF 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**T) * DO 20 K = 1, N * * Update the lower triangle of A(k:n,k:n) * AKK = A( K, K ) BKK = B( K, K ) AKK = AKK / BKK**2 A( K, K ) = AKK IF( K.LT.N ) THEN CALL DSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) CT = -HALF*AKK CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) CALL DSYR2( UPLO, N-K, -ONE, A( K+1, K ), 1, $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) CALL DTRSV( UPLO, 'No transpose', 'Non-unit', N-K, $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) END IF 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**T * DO 30 K = 1, N * * Update the upper triangle of A(1:k,1:k) * AKK = A( K, K ) BKK = B( K, K ) CALL DTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, $ LDB, A( 1, K ), 1 ) CT = HALF*AKK CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) CALL DSYR2( UPLO, K-1, ONE, A( 1, K ), 1, B( 1, K ), 1, $ A, LDA ) CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) CALL DSCAL( K-1, BKK, A( 1, K ), 1 ) A( K, K ) = AKK*BKK**2 30 CONTINUE ELSE * * Compute L**T *A*L * DO 40 K = 1, N * * Update the lower triangle of A(1:k,1:k) * AKK = A( K, K ) BKK = B( K, K ) CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB, $ A( K, 1 ), LDA ) CT = HALF*AKK CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) CALL DSYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ), $ LDB, A, LDA ) CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) CALL DSCAL( K-1, BKK, A( K, 1 ), LDA ) A( K, K ) = AKK*BKK**2 40 CONTINUE END IF END IF RETURN * * End of DSYGS2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlatrd.f0000644000000000000000000000013214061636515015276 xustar0030 mtime=1623670093.292103998 30 atime=1623670093.292103998 30 ctime=1623670093.292103998 elk-7.2.42/src/LAPACK/dlatrd.f0000644002504400250440000002656014061636515017344 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an orthogonal similarity transformation. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLATRD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDW, N, NB * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLATRD reduces NB rows and columns of a real symmetric matrix A to *> symmetric tridiagonal form by an orthogonal similarity *> transformation Q**T * A * Q, and returns the matrices V and W which are *> needed to apply the transformation to the unreduced part of A. *> *> If UPLO = 'U', DLATRD reduces the last NB rows and columns of a *> matrix, of which the upper triangle is supplied; *> if UPLO = 'L', DLATRD reduces the first NB rows and columns of a *> matrix, of which the lower triangle is supplied. *> *> This is an auxiliary routine called by DSYTRD. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> symmetric matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> The number of rows and columns to be reduced. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> n-by-n upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> On exit: *> if UPLO = 'U', the last NB columns have been reduced to *> tridiagonal form, with the diagonal elements overwriting *> the diagonal elements of A; the elements above the diagonal *> with the array TAU, represent the orthogonal matrix Q as a *> product of elementary reflectors; *> if UPLO = 'L', the first NB columns have been reduced to *> tridiagonal form, with the diagonal elements overwriting *> the diagonal elements of A; the elements below the diagonal *> with the array TAU, represent the orthogonal matrix Q as a *> product of elementary reflectors. *> See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= (1,N). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal *> elements of the last NB columns of the reduced matrix; *> if UPLO = 'L', E(1:nb) contains the subdiagonal elements of *> the first NB columns of the reduced matrix. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (N-1) *> The scalar factors of the elementary reflectors, stored in *> TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. *> See Further Details. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (LDW,NB) *> The n-by-nb matrix W required to update the unreduced part *> of A. *> \endverbatim *> *> \param[in] LDW *> \verbatim *> LDW is INTEGER *> The leading dimension of the array W. LDW >= max(1,N). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> If UPLO = 'U', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(n) H(n-1) . . . H(n-nb+1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**T *> *> where tau is a real scalar, and v is a real vector with *> v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), *> and tau in TAU(i-1). *> *> If UPLO = 'L', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(1) H(2) . . . H(nb). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**T *> *> where tau is a real scalar, and v is a real vector with *> v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), *> and tau in TAU(i). *> *> The elements of the vectors v together form the n-by-nb matrix V *> which is needed, with W, to apply the transformation to the unreduced *> part of the matrix, using a symmetric rank-2k update of the form: *> A := A - V*W**T - W*V**T. *> *> The contents of A on exit are illustrated by the following examples *> with n = 5 and nb = 2: *> *> if UPLO = 'U': if UPLO = 'L': *> *> ( a a a v4 v5 ) ( d ) *> ( a a v4 v5 ) ( 1 d ) *> ( a 1 v5 ) ( v1 1 a ) *> ( d 1 ) ( v1 v2 a a ) *> ( d ) ( v1 v2 a a a ) *> *> where d denotes a diagonal element of the reduced matrix, a denotes *> an element of the original matrix that is unchanged, and vi denotes *> an element of the vector defining H(i). *> \endverbatim *> * ===================================================================== SUBROUTINE DLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDW, N, NB * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), E( * ), TAU( * ), W( LDW, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, HALF PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, HALF = 0.5D+0 ) * .. * .. Local Scalars .. INTEGER I, IW DOUBLE PRECISION ALPHA * .. * .. External Subroutines .. EXTERNAL DAXPY, DGEMV, DLARFG, DSCAL, DSYMV * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DDOT EXTERNAL LSAME, DDOT * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) $ RETURN * IF( LSAME( UPLO, 'U' ) ) THEN * * Reduce last NB columns of upper triangle * DO 10 I = N, N - NB + 1, -1 IW = I - N + NB IF( I.LT.N ) THEN * * Update A(1:i,i) * CALL DGEMV( 'No transpose', I, N-I, -ONE, A( 1, I+1 ), $ LDA, W( I, IW+1 ), LDW, ONE, A( 1, I ), 1 ) CALL DGEMV( 'No transpose', I, N-I, -ONE, W( 1, IW+1 ), $ LDW, A( I, I+1 ), LDA, ONE, A( 1, I ), 1 ) END IF IF( I.GT.1 ) THEN * * Generate elementary reflector H(i) to annihilate * A(1:i-2,i) * CALL DLARFG( I-1, A( I-1, I ), A( 1, I ), 1, TAU( I-1 ) ) E( I-1 ) = A( I-1, I ) A( I-1, I ) = ONE * * Compute W(1:i-1,i) * CALL DSYMV( 'Upper', I-1, ONE, A, LDA, A( 1, I ), 1, $ ZERO, W( 1, IW ), 1 ) IF( I.LT.N ) THEN CALL DGEMV( 'Transpose', I-1, N-I, ONE, W( 1, IW+1 ), $ LDW, A( 1, I ), 1, ZERO, W( I+1, IW ), 1 ) CALL DGEMV( 'No transpose', I-1, N-I, -ONE, $ A( 1, I+1 ), LDA, W( I+1, IW ), 1, ONE, $ W( 1, IW ), 1 ) CALL DGEMV( 'Transpose', I-1, N-I, ONE, A( 1, I+1 ), $ LDA, A( 1, I ), 1, ZERO, W( I+1, IW ), 1 ) CALL DGEMV( 'No transpose', I-1, N-I, -ONE, $ W( 1, IW+1 ), LDW, W( I+1, IW ), 1, ONE, $ W( 1, IW ), 1 ) END IF CALL DSCAL( I-1, TAU( I-1 ), W( 1, IW ), 1 ) ALPHA = -HALF*TAU( I-1 )*DDOT( I-1, W( 1, IW ), 1, $ A( 1, I ), 1 ) CALL DAXPY( I-1, ALPHA, A( 1, I ), 1, W( 1, IW ), 1 ) END IF * 10 CONTINUE ELSE * * Reduce first NB columns of lower triangle * DO 20 I = 1, NB * * Update A(i:n,i) * CALL DGEMV( 'No transpose', N-I+1, I-1, -ONE, A( I, 1 ), $ LDA, W( I, 1 ), LDW, ONE, A( I, I ), 1 ) CALL DGEMV( 'No transpose', N-I+1, I-1, -ONE, W( I, 1 ), $ LDW, A( I, 1 ), LDA, ONE, A( I, I ), 1 ) IF( I.LT.N ) THEN * * Generate elementary reflector H(i) to annihilate * A(i+2:n,i) * CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1, $ TAU( I ) ) E( I ) = A( I+1, I ) A( I+1, I ) = ONE * * Compute W(i+1:n,i) * CALL DSYMV( 'Lower', N-I, ONE, A( I+1, I+1 ), LDA, $ A( I+1, I ), 1, ZERO, W( I+1, I ), 1 ) CALL DGEMV( 'Transpose', N-I, I-1, ONE, W( I+1, 1 ), LDW, $ A( I+1, I ), 1, ZERO, W( 1, I ), 1 ) CALL DGEMV( 'No transpose', N-I, I-1, -ONE, A( I+1, 1 ), $ LDA, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) CALL DGEMV( 'Transpose', N-I, I-1, ONE, A( I+1, 1 ), LDA, $ A( I+1, I ), 1, ZERO, W( 1, I ), 1 ) CALL DGEMV( 'No transpose', N-I, I-1, -ONE, W( I+1, 1 ), $ LDW, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) CALL DSCAL( N-I, TAU( I ), W( I+1, I ), 1 ) ALPHA = -HALF*TAU( I )*DDOT( N-I, W( I+1, I ), 1, $ A( I+1, I ), 1 ) CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, W( I+1, I ), 1 ) END IF * 20 CONTINUE END IF * RETURN * * End of DLATRD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dsytd2.f0000644000000000000000000000013214061636515015235 xustar0030 mtime=1623670093.294103996 30 atime=1623670093.294103996 30 ctime=1623670093.294103996 elk-7.2.42/src/LAPACK/dsytd2.f0000644002504400250440000002317214061636515017277 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSYTD2 reduces a symmetric matrix to real symmetric tridiagonal form by an orthogonal similarity transformation (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYTD2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal *> form T by an orthogonal similarity transformation: Q**T * A * Q = T. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> symmetric matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the symmetric matrix A. If UPLO = 'U', the leading *> n-by-n upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> On exit, if UPLO = 'U', the diagonal and first superdiagonal *> of A are overwritten by the corresponding elements of the *> tridiagonal matrix T, and the elements above the first *> superdiagonal, with the array TAU, represent the orthogonal *> matrix Q as a product of elementary reflectors; if UPLO *> = 'L', the diagonal and first subdiagonal of A are over- *> written by the corresponding elements of the tridiagonal *> matrix T, and the elements below the first subdiagonal, with *> the array TAU, represent the orthogonal matrix Q as a product *> of elementary reflectors. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of the tridiagonal matrix T: *> D(i) = A(i,i). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The off-diagonal elements of the tridiagonal matrix T: *> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (N-1) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleSYcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> If UPLO = 'U', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(n-1) . . . H(2) H(1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**T *> *> where tau is a real scalar, and v is a real vector with *> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in *> A(1:i-1,i+1), and tau in TAU(i). *> *> If UPLO = 'L', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(1) H(2) . . . H(n-1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**T *> *> where tau is a real scalar, and v is a real vector with *> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), *> and tau in TAU(i). *> *> The contents of A on exit are illustrated by the following examples *> with n = 5: *> *> if UPLO = 'U': if UPLO = 'L': *> *> ( d e v2 v3 v4 ) ( d ) *> ( d e v3 v4 ) ( e d ) *> ( d e v4 ) ( v1 e d ) *> ( d e ) ( v1 v2 e d ) *> ( d ) ( v1 v2 v3 e d ) *> *> where d and e denote diagonal and off-diagonal elements of T, and vi *> denotes an element of the vector defining H(i). *> \endverbatim *> * ===================================================================== SUBROUTINE DSYTD2( UPLO, N, A, LDA, D, E, TAU, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO, HALF PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0, $ HALF = 1.0D0 / 2.0D0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I DOUBLE PRECISION ALPHA, TAUI * .. * .. External Subroutines .. EXTERNAL DAXPY, DLARFG, DSYMV, DSYR2, XERBLA * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DDOT EXTERNAL LSAME, DDOT * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYTD2', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.0 ) $ RETURN * IF( UPPER ) THEN * * Reduce the upper triangle of A * DO 10 I = N - 1, 1, -1 * * Generate elementary reflector H(i) = I - tau * v * v**T * to annihilate A(1:i-1,i+1) * CALL DLARFG( I, A( I, I+1 ), A( 1, I+1 ), 1, TAUI ) E( I ) = A( I, I+1 ) * IF( TAUI.NE.ZERO ) THEN * * Apply H(i) from both sides to A(1:i,1:i) * A( I, I+1 ) = ONE * * Compute x := tau * A * v storing x in TAU(1:i) * CALL DSYMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO, $ TAU, 1 ) * * Compute w := x - 1/2 * tau * (x**T * v) * v * ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, A( 1, I+1 ), 1 ) CALL DAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 ) * * Apply the transformation as a rank-2 update: * A := A - v * w**T - w * v**T * CALL DSYR2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A, $ LDA ) * A( I, I+1 ) = E( I ) END IF D( I+1 ) = A( I+1, I+1 ) TAU( I ) = TAUI 10 CONTINUE D( 1 ) = A( 1, 1 ) ELSE * * Reduce the lower triangle of A * DO 20 I = 1, N - 1 * * Generate elementary reflector H(i) = I - tau * v * v**T * to annihilate A(i+2:n,i) * CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1, $ TAUI ) E( I ) = A( I+1, I ) * IF( TAUI.NE.ZERO ) THEN * * Apply H(i) from both sides to A(i+1:n,i+1:n) * A( I+1, I ) = ONE * * Compute x := tau * A * v storing y in TAU(i:n-1) * CALL DSYMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA, $ A( I+1, I ), 1, ZERO, TAU( I ), 1 ) * * Compute w := x - 1/2 * tau * (x**T * v) * v * ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, A( I+1, I ), $ 1 ) CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 ) * * Apply the transformation as a rank-2 update: * A := A - v * w**T - w * v**T * CALL DSYR2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1, $ A( I+1, I+1 ), LDA ) * A( I+1, I ) = E( I ) END IF D( I ) = A( I, I ) TAU( I ) = TAUI 20 CONTINUE D( N ) = A( N, N ) END IF * RETURN * * End of DSYTD2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dtrti2.f0000644000000000000000000000013214061636515015234 xustar0030 mtime=1623670093.296103995 30 atime=1623670093.296103995 30 ctime=1623670093.296103995 elk-7.2.42/src/LAPACK/dtrti2.f0000644002504400250440000001342314061636515017274 0ustar00dewhurstdewhurst00000000000000*> \brief \b DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DTRTI2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTRTI2 computes the inverse of a real upper or lower triangular *> matrix. *> *> This is the Level 2 BLAS version of the algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the matrix A is upper or lower triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> Specifies whether or not the matrix A is unit triangular. *> = 'N': Non-unit triangular *> = 'U': Unit triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the triangular matrix A. If UPLO = 'U', the *> leading n by n upper triangular part of the array A contains *> the upper triangular matrix, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n by n lower triangular part of the array A contains *> the lower triangular matrix, and the strictly upper *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. *> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER J DOUBLE PRECISION AJJ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DSCAL, DTRMV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) NOUNIT = LSAME( DIAG, 'N' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DTRTI2', -INFO ) RETURN END IF * IF( UPPER ) THEN * * Compute inverse of upper triangular matrix. * DO 10 J = 1, N IF( NOUNIT ) THEN A( J, J ) = ONE / A( J, J ) AJJ = -A( J, J ) ELSE AJJ = -ONE END IF * * Compute elements 1:j-1 of j-th column. * CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA, $ A( 1, J ), 1 ) CALL DSCAL( J-1, AJJ, A( 1, J ), 1 ) 10 CONTINUE ELSE * * Compute inverse of lower triangular matrix. * DO 20 J = N, 1, -1 IF( NOUNIT ) THEN A( J, J ) = ONE / A( J, J ) AJJ = -A( J, J ) ELSE AJJ = -ONE END IF IF( J.LT.N ) THEN * * Compute elements j+1:n of j-th column. * CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J, $ A( J+1, J+1 ), LDA, A( J+1, J ), 1 ) CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 ) END IF 20 CONTINUE END IF * RETURN * * End of DTRTI2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasq1.f0000644000000000000000000000013214061636515015211 xustar0030 mtime=1623670093.298103993 30 atime=1623670093.298103993 30 ctime=1623670093.298103993 elk-7.2.42/src/LAPACK/dlasq1.f0000644002504400250440000001502314061636515017247 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASQ1 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASQ1 computes the singular values of a real N-by-N bidiagonal *> matrix with diagonal D and off-diagonal E. The singular values *> are computed to high relative accuracy, in the absence of *> denormalization, underflow and overflow. The algorithm was first *> presented in *> *> "Accurate singular values and differential qd algorithms" by K. V. *> Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, *> 1994, *> *> and the present implementation is described in "An implementation of *> the dqds Algorithm (Positive Case)", LAPACK Working Note. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns in the matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, D contains the diagonal elements of the *> bidiagonal matrix whose SVD is desired. On normal exit, *> D contains the singular values in decreasing order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N) *> On entry, elements E(1:N-1) contain the off-diagonal elements *> of the bidiagonal matrix whose SVD is desired. *> On exit, E is overwritten. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (4*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: the algorithm failed *> = 1, a split was marked by a positive value in E *> = 2, current block of Z not diagonalized after 100*N *> iterations (in inner while loop) On exit D and E *> represent a matrix with the same singular values *> which the calling subroutine could use to finish the *> computation, or even feed back into DLASQ1 *> = 3, termination criterion of outer while loop not met *> (program created more than N unreduced blocks) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DLASQ1( N, D, E, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) * .. * .. Local Scalars .. INTEGER I, IINFO DOUBLE PRECISION EPS, SCALE, SAFMIN, SIGMN, SIGMX * .. * .. External Subroutines .. EXTERNAL DCOPY, DLAS2, DLASCL, DLASQ2, DLASRT, XERBLA * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 CALL XERBLA( 'DLASQ1', -INFO ) RETURN ELSE IF( N.EQ.0 ) THEN RETURN ELSE IF( N.EQ.1 ) THEN D( 1 ) = ABS( D( 1 ) ) RETURN ELSE IF( N.EQ.2 ) THEN CALL DLAS2( D( 1 ), E( 1 ), D( 2 ), SIGMN, SIGMX ) D( 1 ) = SIGMX D( 2 ) = SIGMN RETURN END IF * * Estimate the largest singular value. * SIGMX = ZERO DO 10 I = 1, N - 1 D( I ) = ABS( D( I ) ) SIGMX = MAX( SIGMX, ABS( E( I ) ) ) 10 CONTINUE D( N ) = ABS( D( N ) ) * * Early return if SIGMX is zero (matrix is already diagonal). * IF( SIGMX.EQ.ZERO ) THEN CALL DLASRT( 'D', N, D, IINFO ) RETURN END IF * DO 20 I = 1, N SIGMX = MAX( SIGMX, D( I ) ) 20 CONTINUE * * Copy D and E into WORK (in the Z format) and scale (squaring the * input data makes scaling by a power of the radix pointless). * EPS = DLAMCH( 'Precision' ) SAFMIN = DLAMCH( 'Safe minimum' ) SCALE = SQRT( EPS / SAFMIN ) CALL DCOPY( N, D, 1, WORK( 1 ), 2 ) CALL DCOPY( N-1, E, 1, WORK( 2 ), 2 ) CALL DLASCL( 'G', 0, 0, SIGMX, SCALE, 2*N-1, 1, WORK, 2*N-1, $ IINFO ) * * Compute the q's and e's. * DO 30 I = 1, 2*N - 1 WORK( I ) = WORK( I )**2 30 CONTINUE WORK( 2*N ) = ZERO * CALL DLASQ2( N, WORK, INFO ) * IF( INFO.EQ.0 ) THEN DO 40 I = 1, N D( I ) = SQRT( WORK( I ) ) 40 CONTINUE CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO ) ELSE IF( INFO.EQ.2 ) THEN * * Maximum number of iterations exceeded. Move data from WORK * into D and E so the calling subroutine can try to finish * DO I = 1, N D( I ) = SQRT( WORK( 2*I-1 ) ) E( I ) = SQRT( WORK( 2*I ) ) END DO CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, D, N, IINFO ) CALL DLASCL( 'G', 0, 0, SCALE, SIGMX, N, 1, E, N, IINFO ) END IF * RETURN * * End of DLASQ1 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlasr.f0000644000000000000000000000013214061636515015157 xustar0030 mtime=1623670093.300103991 30 atime=1623670093.300103991 30 ctime=1623670093.300103991 elk-7.2.42/src/LAPACK/zlasr.f0000644002504400250440000003543314061636515017224 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLASR applies a sequence of plane rotations to a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLASR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) * * .. Scalar Arguments .. * CHARACTER DIRECT, PIVOT, SIDE * INTEGER LDA, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION C( * ), S( * ) * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLASR applies a sequence of real plane rotations to a complex matrix *> A, from either the left or the right. *> *> When SIDE = 'L', the transformation takes the form *> *> A := P*A *> *> and when SIDE = 'R', the transformation takes the form *> *> A := A*P**T *> *> where P is an orthogonal matrix consisting of a sequence of z plane *> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', *> and P**T is the transpose of P. *> *> When DIRECT = 'F' (Forward sequence), then *> *> P = P(z-1) * ... * P(2) * P(1) *> *> and when DIRECT = 'B' (Backward sequence), then *> *> P = P(1) * P(2) * ... * P(z-1) *> *> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation *> *> R(k) = ( c(k) s(k) ) *> = ( -s(k) c(k) ). *> *> When PIVOT = 'V' (Variable pivot), the rotation is performed *> for the plane (k,k+1), i.e., P(k) has the form *> *> P(k) = ( 1 ) *> ( ... ) *> ( 1 ) *> ( c(k) s(k) ) *> ( -s(k) c(k) ) *> ( 1 ) *> ( ... ) *> ( 1 ) *> *> where R(k) appears as a rank-2 modification to the identity matrix in *> rows and columns k and k+1. *> *> When PIVOT = 'T' (Top pivot), the rotation is performed for the *> plane (1,k+1), so P(k) has the form *> *> P(k) = ( c(k) s(k) ) *> ( 1 ) *> ( ... ) *> ( 1 ) *> ( -s(k) c(k) ) *> ( 1 ) *> ( ... ) *> ( 1 ) *> *> where R(k) appears in rows and columns 1 and k+1. *> *> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is *> performed for the plane (k,z), giving P(k) the form *> *> P(k) = ( 1 ) *> ( ... ) *> ( 1 ) *> ( c(k) s(k) ) *> ( 1 ) *> ( ... ) *> ( 1 ) *> ( -s(k) c(k) ) *> *> where R(k) appears in rows and columns k and z. The rotations are *> performed without ever forming P(k) explicitly. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> Specifies whether the plane rotation matrix P is applied to *> A on the left or the right. *> = 'L': Left, compute A := P*A *> = 'R': Right, compute A:= A*P**T *> \endverbatim *> *> \param[in] PIVOT *> \verbatim *> PIVOT is CHARACTER*1 *> Specifies the plane for which P(k) is a plane rotation *> matrix. *> = 'V': Variable pivot, the plane (k,k+1) *> = 'T': Top pivot, the plane (1,k+1) *> = 'B': Bottom pivot, the plane (k,z) *> \endverbatim *> *> \param[in] DIRECT *> \verbatim *> DIRECT is CHARACTER*1 *> Specifies whether P is a forward or backward sequence of *> plane rotations. *> = 'F': Forward, P = P(z-1)*...*P(2)*P(1) *> = 'B': Backward, P = P(1)*P(2)*...*P(z-1) *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. If m <= 1, an immediate *> return is effected. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. If n <= 1, an *> immediate return is effected. *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION array, dimension *> (M-1) if SIDE = 'L' *> (N-1) if SIDE = 'R' *> The cosines c(k) of the plane rotations. *> \endverbatim *> *> \param[in] S *> \verbatim *> S is DOUBLE PRECISION array, dimension *> (M-1) if SIDE = 'L' *> (N-1) if SIDE = 'R' *> The sines s(k) of the plane rotations. The 2-by-2 plane *> rotation part of the matrix P(k), R(k), has the form *> R(k) = ( c(k) s(k) ) *> ( -s(k) c(k) ). *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The M-by-N matrix A. On exit, A is overwritten by P*A if *> SIDE = 'R' or by A*P**T if SIDE = 'L'. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIRECT, PIVOT, SIDE INTEGER LDA, M, N * .. * .. Array Arguments .. DOUBLE PRECISION C( * ), S( * ) COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J DOUBLE PRECISION CTEMP, STEMP COMPLEX*16 TEMP * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN INFO = 1 ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN INFO = 2 ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) $ THEN INFO = 3 ELSE IF( M.LT.0 ) THEN INFO = 4 ELSE IF( N.LT.0 ) THEN INFO = 5 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = 9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLASR ', INFO ) RETURN END IF * * Quick return if possible * IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) $ RETURN IF( LSAME( SIDE, 'L' ) ) THEN * * Form P * A * IF( LSAME( PIVOT, 'V' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 20 J = 1, M - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 10 I = 1, N TEMP = A( J+1, I ) A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 10 CONTINUE END IF 20 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 40 J = M - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 30 I = 1, N TEMP = A( J+1, I ) A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) 30 CONTINUE END IF 40 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'T' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 60 J = 2, M CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 50 I = 1, N TEMP = A( J, I ) A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 50 CONTINUE END IF 60 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 80 J = M, 2, -1 CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 70 I = 1, N TEMP = A( J, I ) A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) 70 CONTINUE END IF 80 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'B' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 100 J = 1, M - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 90 I = 1, N TEMP = A( J, I ) A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 90 CONTINUE END IF 100 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 120 J = M - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 110 I = 1, N TEMP = A( J, I ) A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP 110 CONTINUE END IF 120 CONTINUE END IF END IF ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form A * P**T * IF( LSAME( PIVOT, 'V' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 140 J = 1, N - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 130 I = 1, M TEMP = A( I, J+1 ) A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 130 CONTINUE END IF 140 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 160 J = N - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 150 I = 1, M TEMP = A( I, J+1 ) A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) 150 CONTINUE END IF 160 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'T' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 180 J = 2, N CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 170 I = 1, M TEMP = A( I, J ) A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 170 CONTINUE END IF 180 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 200 J = N, 2, -1 CTEMP = C( J-1 ) STEMP = S( J-1 ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 190 I = 1, M TEMP = A( I, J ) A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) 190 CONTINUE END IF 200 CONTINUE END IF ELSE IF( LSAME( PIVOT, 'B' ) ) THEN IF( LSAME( DIRECT, 'F' ) ) THEN DO 220 J = 1, N - 1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 210 I = 1, M TEMP = A( I, J ) A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 210 CONTINUE END IF 220 CONTINUE ELSE IF( LSAME( DIRECT, 'B' ) ) THEN DO 240 J = N - 1, 1, -1 CTEMP = C( J ) STEMP = S( J ) IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN DO 230 I = 1, M TEMP = A( I, J ) A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP 230 CONTINUE END IF 240 CONTINUE END IF END IF END IF * RETURN * * End of ZLASR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasv2.f0000644000000000000000000000013214061636515015217 xustar0030 mtime=1623670093.302103989 30 atime=1623670093.302103989 30 ctime=1623670093.302103989 elk-7.2.42/src/LAPACK/dlasv2.f0000644002504400250440000002045114061636515017256 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASV2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) * * .. Scalar Arguments .. * DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASV2 computes the singular value decomposition of a 2-by-2 *> triangular matrix *> [ F G ] *> [ 0 H ]. *> On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the *> smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and *> right singular vectors for abs(SSMAX), giving the decomposition *> *> [ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ] *> [-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ]. *> \endverbatim * * Arguments: * ========== * *> \param[in] F *> \verbatim *> F is DOUBLE PRECISION *> The (1,1) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[in] G *> \verbatim *> G is DOUBLE PRECISION *> The (1,2) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[in] H *> \verbatim *> H is DOUBLE PRECISION *> The (2,2) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[out] SSMIN *> \verbatim *> SSMIN is DOUBLE PRECISION *> abs(SSMIN) is the smaller singular value. *> \endverbatim *> *> \param[out] SSMAX *> \verbatim *> SSMAX is DOUBLE PRECISION *> abs(SSMAX) is the larger singular value. *> \endverbatim *> *> \param[out] SNL *> \verbatim *> SNL is DOUBLE PRECISION *> \endverbatim *> *> \param[out] CSL *> \verbatim *> CSL is DOUBLE PRECISION *> The vector (CSL, SNL) is a unit left singular vector for the *> singular value abs(SSMAX). *> \endverbatim *> *> \param[out] SNR *> \verbatim *> SNR is DOUBLE PRECISION *> \endverbatim *> *> \param[out] CSR *> \verbatim *> CSR is DOUBLE PRECISION *> The vector (CSR, SNR) is a unit right singular vector for the *> singular value abs(SSMAX). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> Any input parameter may be aliased with any output parameter. *> *> Barring over/underflow and assuming a guard digit in subtraction, all *> output quantities are correct to within a few units in the last *> place (ulps). *> *> In IEEE arithmetic, the code works correctly if one matrix element is *> infinite. *> *> Overflow will not occur unless the largest singular value itself *> overflows or is within a few ulps of overflow. (On machines with *> partial overflow, like the Cray, overflow may occur if the largest *> singular value is within a factor of 2 of overflow.) *> *> Underflow is harmless if underflow is gradual. Otherwise, results *> may correspond to a matrix modified by perturbations of size near *> the underflow threshold. *> \endverbatim *> * ===================================================================== SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION HALF PARAMETER ( HALF = 0.5D0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0D0 ) DOUBLE PRECISION FOUR PARAMETER ( FOUR = 4.0D0 ) * .. * .. Local Scalars .. LOGICAL GASMAL, SWAP INTEGER PMAX DOUBLE PRECISION A, CLT, CRT, D, FA, FT, GA, GT, HA, HT, L, M, $ MM, R, S, SLT, SRT, T, TEMP, TSIGN, TT * .. * .. Intrinsic Functions .. INTRINSIC ABS, SIGN, SQRT * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. Executable Statements .. * FT = F FA = ABS( FT ) HT = H HA = ABS( H ) * * PMAX points to the maximum absolute element of matrix * PMAX = 1 if F largest in absolute values * PMAX = 2 if G largest in absolute values * PMAX = 3 if H largest in absolute values * PMAX = 1 SWAP = ( HA.GT.FA ) IF( SWAP ) THEN PMAX = 3 TEMP = FT FT = HT HT = TEMP TEMP = FA FA = HA HA = TEMP * * Now FA .ge. HA * END IF GT = G GA = ABS( GT ) IF( GA.EQ.ZERO ) THEN * * Diagonal matrix * SSMIN = HA SSMAX = FA CLT = ONE CRT = ONE SLT = ZERO SRT = ZERO ELSE GASMAL = .TRUE. IF( GA.GT.FA ) THEN PMAX = 2 IF( ( FA / GA ).LT.DLAMCH( 'EPS' ) ) THEN * * Case of very large GA * GASMAL = .FALSE. SSMAX = GA IF( HA.GT.ONE ) THEN SSMIN = FA / ( GA / HA ) ELSE SSMIN = ( FA / GA )*HA END IF CLT = ONE SLT = HT / GT SRT = ONE CRT = FT / GT END IF END IF IF( GASMAL ) THEN * * Normal case * D = FA - HA IF( D.EQ.FA ) THEN * * Copes with infinite F or H * L = ONE ELSE L = D / FA END IF * * Note that 0 .le. L .le. 1 * M = GT / FT * * Note that abs(M) .le. 1/macheps * T = TWO - L * * Note that T .ge. 1 * MM = M*M TT = T*T S = SQRT( TT+MM ) * * Note that 1 .le. S .le. 1 + 1/macheps * IF( L.EQ.ZERO ) THEN R = ABS( M ) ELSE R = SQRT( L*L+MM ) END IF * * Note that 0 .le. R .le. 1 + 1/macheps * A = HALF*( S+R ) * * Note that 1 .le. A .le. 1 + abs(M) * SSMIN = HA / A SSMAX = FA*A IF( MM.EQ.ZERO ) THEN * * Note that M is very tiny * IF( L.EQ.ZERO ) THEN T = SIGN( TWO, FT )*SIGN( ONE, GT ) ELSE T = GT / SIGN( D, FT ) + M / T END IF ELSE T = ( M / ( S+T )+M / ( R+L ) )*( ONE+A ) END IF L = SQRT( T*T+FOUR ) CRT = TWO / L SRT = T / L CLT = ( CRT+SRT*M ) / A SLT = ( HT / FT )*SRT / A END IF END IF IF( SWAP ) THEN CSL = SRT SNL = CRT CSR = SLT SNR = CLT ELSE CSL = CLT SNL = SLT CSR = CRT SNR = SRT END IF * * Correct signs of SSMAX and SSMIN * IF( PMAX.EQ.1 ) $ TSIGN = SIGN( ONE, CSR )*SIGN( ONE, CSL )*SIGN( ONE, F ) IF( PMAX.EQ.2 ) $ TSIGN = SIGN( ONE, SNR )*SIGN( ONE, CSL )*SIGN( ONE, G ) IF( PMAX.EQ.3 ) $ TSIGN = SIGN( ONE, SNR )*SIGN( ONE, SNL )*SIGN( ONE, H ) SSMAX = SIGN( SSMAX, TSIGN ) SSMIN = SIGN( SSMIN, TSIGN*SIGN( ONE, F )*SIGN( ONE, H ) ) RETURN * * End of DLASV2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlas2.f0000644000000000000000000000013214061636515015031 xustar0030 mtime=1623670093.304103987 30 atime=1623670093.303103988 30 ctime=1623670093.304103987 elk-7.2.42/src/LAPACK/dlas2.f0000644002504400250440000001175314061636515017075 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAS2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) * * .. Scalar Arguments .. * DOUBLE PRECISION F, G, H, SSMAX, SSMIN * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAS2 computes the singular values of the 2-by-2 matrix *> [ F G ] *> [ 0 H ]. *> On return, SSMIN is the smaller singular value and SSMAX is the *> larger singular value. *> \endverbatim * * Arguments: * ========== * *> \param[in] F *> \verbatim *> F is DOUBLE PRECISION *> The (1,1) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[in] G *> \verbatim *> G is DOUBLE PRECISION *> The (1,2) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[in] H *> \verbatim *> H is DOUBLE PRECISION *> The (2,2) element of the 2-by-2 matrix. *> \endverbatim *> *> \param[out] SSMIN *> \verbatim *> SSMIN is DOUBLE PRECISION *> The smaller singular value. *> \endverbatim *> *> \param[out] SSMAX *> \verbatim *> SSMAX is DOUBLE PRECISION *> The larger singular value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> Barring over/underflow, all output quantities are correct to within *> a few units in the last place (ulps), even in the absence of a guard *> digit in addition/subtraction. *> *> In IEEE arithmetic, the code works correctly if one matrix element is *> infinite. *> *> Overflow will not occur unless the largest singular value itself *> overflows, or is within a few ulps of overflow. (On machines with *> partial overflow, like the Cray, overflow may occur if the largest *> singular value is within a factor of 2 of overflow.) *> *> Underflow is harmless if underflow is gradual. Otherwise, results *> may correspond to a matrix modified by perturbations of size near *> the underflow threshold. *> \endverbatim *> * ===================================================================== SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION F, G, H, SSMAX, SSMIN * .. * * ==================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0D0 ) * .. * .. Local Scalars .. DOUBLE PRECISION AS, AT, AU, C, FA, FHMN, FHMX, GA, HA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Executable Statements .. * FA = ABS( F ) GA = ABS( G ) HA = ABS( H ) FHMN = MIN( FA, HA ) FHMX = MAX( FA, HA ) IF( FHMN.EQ.ZERO ) THEN SSMIN = ZERO IF( FHMX.EQ.ZERO ) THEN SSMAX = GA ELSE SSMAX = MAX( FHMX, GA )*SQRT( ONE+ $ ( MIN( FHMX, GA ) / MAX( FHMX, GA ) )**2 ) END IF ELSE IF( GA.LT.FHMX ) THEN AS = ONE + FHMN / FHMX AT = ( FHMX-FHMN ) / FHMX AU = ( GA / FHMX )**2 C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) ) SSMIN = FHMN*C SSMAX = FHMX / C ELSE AU = FHMX / GA IF( AU.EQ.ZERO ) THEN * * Avoid possible harmful underflow if exponent range * asymmetric (true SSMIN may not underflow even if * AU underflows) * SSMIN = ( FHMN*FHMX ) / GA SSMAX = GA ELSE AS = ONE + FHMN / FHMX AT = ( FHMX-FHMN ) / FHMX C = ONE / ( SQRT( ONE+( AS*AU )**2 )+ $ SQRT( ONE+( AT*AU )**2 ) ) SSMIN = ( FHMN*C )*AU SSMIN = SSMIN + SSMIN SSMAX = GA / ( C+C ) END IF END IF END IF RETURN * * End of DLAS2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlabrd.f0000644000000000000000000000013214061636515015302 xustar0030 mtime=1623670093.306103985 30 atime=1623670093.305103986 30 ctime=1623670093.306103985 elk-7.2.42/src/LAPACK/zlabrd.f0000644002504400250440000003576714061636515017361 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLABRD reduces the first nb rows and columns of a general matrix to a bidiagonal form. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLABRD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, * LDY ) * * .. Scalar Arguments .. * INTEGER LDA, LDX, LDY, M, N, NB * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ) * COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), X( LDX, * ), * $ Y( LDY, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLABRD reduces the first NB rows and columns of a complex general *> m by n matrix A to upper or lower real bidiagonal form by a unitary *> transformation Q**H * A * P, and returns the matrices X and Y which *> are needed to apply the transformation to the unreduced part of A. *> *> If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower *> bidiagonal form. *> *> This is an auxiliary routine called by ZGEBRD *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows in the matrix A. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns in the matrix A. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> The number of leading rows and columns of A to be reduced. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the m by n general matrix to be reduced. *> On exit, the first NB rows and columns of the matrix are *> overwritten; the rest of the array is unchanged. *> If m >= n, elements on and below the diagonal in the first NB *> columns, with the array TAUQ, represent the unitary *> matrix Q as a product of elementary reflectors; and *> elements above the diagonal in the first NB rows, with the *> array TAUP, represent the unitary matrix P as a product *> of elementary reflectors. *> If m < n, elements below the diagonal in the first NB *> columns, with the array TAUQ, represent the unitary *> matrix Q as a product of elementary reflectors, and *> elements on and above the diagonal in the first NB rows, *> with the array TAUP, represent the unitary matrix P as *> a product of elementary reflectors. *> See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (NB) *> The diagonal elements of the first NB rows and columns of *> the reduced matrix. D(i) = A(i,i). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (NB) *> The off-diagonal elements of the first NB rows and columns of *> the reduced matrix. *> \endverbatim *> *> \param[out] TAUQ *> \verbatim *> TAUQ is COMPLEX*16 array, dimension (NB) *> The scalar factors of the elementary reflectors which *> represent the unitary matrix Q. See Further Details. *> \endverbatim *> *> \param[out] TAUP *> \verbatim *> TAUP is COMPLEX*16 array, dimension (NB) *> The scalar factors of the elementary reflectors which *> represent the unitary matrix P. See Further Details. *> \endverbatim *> *> \param[out] X *> \verbatim *> X is COMPLEX*16 array, dimension (LDX,NB) *> The m-by-nb matrix X required to update the unreduced part *> of A. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= max(1,M). *> \endverbatim *> *> \param[out] Y *> \verbatim *> Y is COMPLEX*16 array, dimension (LDY,NB) *> The n-by-nb matrix Y required to update the unreduced part *> of A. *> \endverbatim *> *> \param[in] LDY *> \verbatim *> LDY is INTEGER *> The leading dimension of the array Y. LDY >= max(1,N). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complex16OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrices Q and P are represented as products of elementary *> reflectors: *> *> Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb) *> *> Each H(i) and G(i) has the form: *> *> H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H *> *> where tauq and taup are complex scalars, and v and u are complex *> vectors. *> *> If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in *> A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in *> A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). *> *> If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in *> A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in *> A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i). *> *> The elements of the vectors v and u together form the m-by-nb matrix *> V and the nb-by-n matrix U**H which are needed, with X and Y, to apply *> the transformation to the unreduced part of the matrix, using a block *> update of the form: A := A - V*Y**H - X*U**H. *> *> The contents of A on exit are illustrated by the following examples *> with nb = 2: *> *> m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): *> *> ( 1 1 u1 u1 u1 ) ( 1 u1 u1 u1 u1 u1 ) *> ( v1 1 1 u2 u2 ) ( 1 1 u2 u2 u2 u2 ) *> ( v1 v2 a a a ) ( v1 1 a a a a ) *> ( v1 v2 a a a ) ( v1 v2 a a a a ) *> ( v1 v2 a a a ) ( v1 v2 a a a a ) *> ( v1 v2 a a a ) *> *> where a denotes an element of the original matrix which is unchanged, *> vi denotes an element of the vector defining H(i), and ui an element *> of the vector defining G(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y, $ LDY ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER LDA, LDX, LDY, M, N, NB * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ) COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), X( LDX, * ), $ Y( LDY, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I COMPLEX*16 ALPHA * .. * .. External Subroutines .. EXTERNAL ZGEMV, ZLACGV, ZLARFG, ZSCAL * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * IF( M.GE.N ) THEN * * Reduce to upper bidiagonal form * DO 10 I = 1, NB * * Update A(i:m,i) * CALL ZLACGV( I-1, Y( I, 1 ), LDY ) CALL ZGEMV( 'No transpose', M-I+1, I-1, -ONE, A( I, 1 ), $ LDA, Y( I, 1 ), LDY, ONE, A( I, I ), 1 ) CALL ZLACGV( I-1, Y( I, 1 ), LDY ) CALL ZGEMV( 'No transpose', M-I+1, I-1, -ONE, X( I, 1 ), $ LDX, A( 1, I ), 1, ONE, A( I, I ), 1 ) * * Generate reflection Q(i) to annihilate A(i+1:m,i) * ALPHA = A( I, I ) CALL ZLARFG( M-I+1, ALPHA, A( MIN( I+1, M ), I ), 1, $ TAUQ( I ) ) D( I ) = ALPHA IF( I.LT.N ) THEN A( I, I ) = ONE * * Compute Y(i+1:n,i) * CALL ZGEMV( 'Conjugate transpose', M-I+1, N-I, ONE, $ A( I, I+1 ), LDA, A( I, I ), 1, ZERO, $ Y( I+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', M-I+1, I-1, ONE, $ A( I, 1 ), LDA, A( I, I ), 1, ZERO, $ Y( 1, I ), 1 ) CALL ZGEMV( 'No transpose', N-I, I-1, -ONE, Y( I+1, 1 ), $ LDY, Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', M-I+1, I-1, ONE, $ X( I, 1 ), LDX, A( I, I ), 1, ZERO, $ Y( 1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', I-1, N-I, -ONE, $ A( 1, I+1 ), LDA, Y( 1, I ), 1, ONE, $ Y( I+1, I ), 1 ) CALL ZSCAL( N-I, TAUQ( I ), Y( I+1, I ), 1 ) * * Update A(i,i+1:n) * CALL ZLACGV( N-I, A( I, I+1 ), LDA ) CALL ZLACGV( I, A( I, 1 ), LDA ) CALL ZGEMV( 'No transpose', N-I, I, -ONE, Y( I+1, 1 ), $ LDY, A( I, 1 ), LDA, ONE, A( I, I+1 ), LDA ) CALL ZLACGV( I, A( I, 1 ), LDA ) CALL ZLACGV( I-1, X( I, 1 ), LDX ) CALL ZGEMV( 'Conjugate transpose', I-1, N-I, -ONE, $ A( 1, I+1 ), LDA, X( I, 1 ), LDX, ONE, $ A( I, I+1 ), LDA ) CALL ZLACGV( I-1, X( I, 1 ), LDX ) * * Generate reflection P(i) to annihilate A(i,i+2:n) * ALPHA = A( I, I+1 ) CALL ZLARFG( N-I, ALPHA, A( I, MIN( I+2, N ) ), LDA, $ TAUP( I ) ) E( I ) = ALPHA A( I, I+1 ) = ONE * * Compute X(i+1:m,i) * CALL ZGEMV( 'No transpose', M-I, N-I, ONE, A( I+1, I+1 ), $ LDA, A( I, I+1 ), LDA, ZERO, X( I+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', N-I, I, ONE, $ Y( I+1, 1 ), LDY, A( I, I+1 ), LDA, ZERO, $ X( 1, I ), 1 ) CALL ZGEMV( 'No transpose', M-I, I, -ONE, A( I+1, 1 ), $ LDA, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) CALL ZGEMV( 'No transpose', I-1, N-I, ONE, A( 1, I+1 ), $ LDA, A( I, I+1 ), LDA, ZERO, X( 1, I ), 1 ) CALL ZGEMV( 'No transpose', M-I, I-1, -ONE, X( I+1, 1 ), $ LDX, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) CALL ZSCAL( M-I, TAUP( I ), X( I+1, I ), 1 ) CALL ZLACGV( N-I, A( I, I+1 ), LDA ) END IF 10 CONTINUE ELSE * * Reduce to lower bidiagonal form * DO 20 I = 1, NB * * Update A(i,i:n) * CALL ZLACGV( N-I+1, A( I, I ), LDA ) CALL ZLACGV( I-1, A( I, 1 ), LDA ) CALL ZGEMV( 'No transpose', N-I+1, I-1, -ONE, Y( I, 1 ), $ LDY, A( I, 1 ), LDA, ONE, A( I, I ), LDA ) CALL ZLACGV( I-1, A( I, 1 ), LDA ) CALL ZLACGV( I-1, X( I, 1 ), LDX ) CALL ZGEMV( 'Conjugate transpose', I-1, N-I+1, -ONE, $ A( 1, I ), LDA, X( I, 1 ), LDX, ONE, A( I, I ), $ LDA ) CALL ZLACGV( I-1, X( I, 1 ), LDX ) * * Generate reflection P(i) to annihilate A(i,i+1:n) * ALPHA = A( I, I ) CALL ZLARFG( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA, $ TAUP( I ) ) D( I ) = ALPHA IF( I.LT.M ) THEN A( I, I ) = ONE * * Compute X(i+1:m,i) * CALL ZGEMV( 'No transpose', M-I, N-I+1, ONE, A( I+1, I ), $ LDA, A( I, I ), LDA, ZERO, X( I+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', N-I+1, I-1, ONE, $ Y( I, 1 ), LDY, A( I, I ), LDA, ZERO, $ X( 1, I ), 1 ) CALL ZGEMV( 'No transpose', M-I, I-1, -ONE, A( I+1, 1 ), $ LDA, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) CALL ZGEMV( 'No transpose', I-1, N-I+1, ONE, A( 1, I ), $ LDA, A( I, I ), LDA, ZERO, X( 1, I ), 1 ) CALL ZGEMV( 'No transpose', M-I, I-1, -ONE, X( I+1, 1 ), $ LDX, X( 1, I ), 1, ONE, X( I+1, I ), 1 ) CALL ZSCAL( M-I, TAUP( I ), X( I+1, I ), 1 ) CALL ZLACGV( N-I+1, A( I, I ), LDA ) * * Update A(i+1:m,i) * CALL ZLACGV( I-1, Y( I, 1 ), LDY ) CALL ZGEMV( 'No transpose', M-I, I-1, -ONE, A( I+1, 1 ), $ LDA, Y( I, 1 ), LDY, ONE, A( I+1, I ), 1 ) CALL ZLACGV( I-1, Y( I, 1 ), LDY ) CALL ZGEMV( 'No transpose', M-I, I, -ONE, X( I+1, 1 ), $ LDX, A( 1, I ), 1, ONE, A( I+1, I ), 1 ) * * Generate reflection Q(i) to annihilate A(i+2:m,i) * ALPHA = A( I+1, I ) CALL ZLARFG( M-I, ALPHA, A( MIN( I+2, M ), I ), 1, $ TAUQ( I ) ) E( I ) = ALPHA A( I+1, I ) = ONE * * Compute Y(i+1:n,i) * CALL ZGEMV( 'Conjugate transpose', M-I, N-I, ONE, $ A( I+1, I+1 ), LDA, A( I+1, I ), 1, ZERO, $ Y( I+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', M-I, I-1, ONE, $ A( I+1, 1 ), LDA, A( I+1, I ), 1, ZERO, $ Y( 1, I ), 1 ) CALL ZGEMV( 'No transpose', N-I, I-1, -ONE, Y( I+1, 1 ), $ LDY, Y( 1, I ), 1, ONE, Y( I+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', M-I, I, ONE, $ X( I+1, 1 ), LDX, A( I+1, I ), 1, ZERO, $ Y( 1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', I, N-I, -ONE, $ A( 1, I+1 ), LDA, Y( 1, I ), 1, ONE, $ Y( I+1, I ), 1 ) CALL ZSCAL( N-I, TAUQ( I ), Y( I+1, I ), 1 ) ELSE CALL ZLACGV( N-I+1, A( I, I ), LDA ) END IF 20 CONTINUE END IF RETURN * * End of ZLABRD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgebd2.f0000644000000000000000000000013214061636515015201 xustar0030 mtime=1623670093.308103984 30 atime=1623670093.307103984 30 ctime=1623670093.308103984 elk-7.2.42/src/LAPACK/zgebd2.f0000644002504400250440000002430314061636515017240 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEBD2 reduces a general matrix to bidiagonal form using an unblocked algorithm. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEBD2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ) * COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEBD2 reduces a complex general m by n matrix A to upper or lower *> real bidiagonal form B by a unitary transformation: Q**H * A * P = B. *> *> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows in the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns in the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the m by n general matrix to be reduced. *> On exit, *> if m >= n, the diagonal and the first superdiagonal are *> overwritten with the upper bidiagonal matrix B; the *> elements below the diagonal, with the array TAUQ, represent *> the unitary matrix Q as a product of elementary *> reflectors, and the elements above the first superdiagonal, *> with the array TAUP, represent the unitary matrix P as *> a product of elementary reflectors; *> if m < n, the diagonal and the first subdiagonal are *> overwritten with the lower bidiagonal matrix B; the *> elements below the first subdiagonal, with the array TAUQ, *> represent the unitary matrix Q as a product of *> elementary reflectors, and the elements above the diagonal, *> with the array TAUP, represent the unitary matrix P as *> a product of elementary reflectors. *> See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (min(M,N)) *> The diagonal elements of the bidiagonal matrix B: *> D(i) = A(i,i). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (min(M,N)-1) *> The off-diagonal elements of the bidiagonal matrix B: *> if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1; *> if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1. *> \endverbatim *> *> \param[out] TAUQ *> \verbatim *> TAUQ is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors which *> represent the unitary matrix Q. See Further Details. *> \endverbatim *> *> \param[out] TAUP *> \verbatim *> TAUP is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors which *> represent the unitary matrix P. See Further Details. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (max(M,N)) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrices Q and P are represented as products of elementary *> reflectors: *> *> If m >= n, *> *> Q = H(1) H(2) . . . H(n) and P = G(1) G(2) . . . G(n-1) *> *> Each H(i) and G(i) has the form: *> *> H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H *> *> where tauq and taup are complex scalars, and v and u are complex *> vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in *> A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in *> A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i). *> *> If m < n, *> *> Q = H(1) H(2) . . . H(m-1) and P = G(1) G(2) . . . G(m) *> *> Each H(i) and G(i) has the form: *> *> H(i) = I - tauq * v * v**H and G(i) = I - taup * u * u**H *> *> where tauq and taup are complex scalars, v and u are complex vectors; *> v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i); *> u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); *> tauq is stored in TAUQ(i) and taup in TAUP(i). *> *> The contents of A on exit are illustrated by the following examples: *> *> m = 6 and n = 5 (m > n): m = 5 and n = 6 (m < n): *> *> ( d e u1 u1 u1 ) ( d u1 u1 u1 u1 u1 ) *> ( v1 d e u2 u2 ) ( e d u2 u2 u2 u2 ) *> ( v1 v2 d e u3 ) ( v1 e d u3 u3 u3 ) *> ( v1 v2 v3 d e ) ( v1 v2 e d u4 u4 ) *> ( v1 v2 v3 v4 d ) ( v1 v2 v3 e d u5 ) *> ( v1 v2 v3 v4 v5 ) *> *> where d and e denote diagonal and off-diagonal elements of B, vi *> denotes an element of the vector defining H(i), and ui an element of *> the vector defining G(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEBD2( M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ) COMPLEX*16 A( LDA, * ), TAUP( * ), TAUQ( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I COMPLEX*16 ALPHA * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLACGV, ZLARF, ZLARFG * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF IF( INFO.LT.0 ) THEN CALL XERBLA( 'ZGEBD2', -INFO ) RETURN END IF * IF( M.GE.N ) THEN * * Reduce to upper bidiagonal form * DO 10 I = 1, N * * Generate elementary reflector H(i) to annihilate A(i+1:m,i) * ALPHA = A( I, I ) CALL ZLARFG( M-I+1, ALPHA, A( MIN( I+1, M ), I ), 1, $ TAUQ( I ) ) D( I ) = ALPHA A( I, I ) = ONE * * Apply H(i)**H to A(i:m,i+1:n) from the left * IF( I.LT.N ) $ CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, $ DCONJG( TAUQ( I ) ), A( I, I+1 ), LDA, WORK ) A( I, I ) = D( I ) * IF( I.LT.N ) THEN * * Generate elementary reflector G(i) to annihilate * A(i,i+2:n) * CALL ZLACGV( N-I, A( I, I+1 ), LDA ) ALPHA = A( I, I+1 ) CALL ZLARFG( N-I, ALPHA, A( I, MIN( I+2, N ) ), LDA, $ TAUP( I ) ) E( I ) = ALPHA A( I, I+1 ) = ONE * * Apply G(i) to A(i+1:m,i+1:n) from the right * CALL ZLARF( 'Right', M-I, N-I, A( I, I+1 ), LDA, $ TAUP( I ), A( I+1, I+1 ), LDA, WORK ) CALL ZLACGV( N-I, A( I, I+1 ), LDA ) A( I, I+1 ) = E( I ) ELSE TAUP( I ) = ZERO END IF 10 CONTINUE ELSE * * Reduce to lower bidiagonal form * DO 20 I = 1, M * * Generate elementary reflector G(i) to annihilate A(i,i+1:n) * CALL ZLACGV( N-I+1, A( I, I ), LDA ) ALPHA = A( I, I ) CALL ZLARFG( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA, $ TAUP( I ) ) D( I ) = ALPHA A( I, I ) = ONE * * Apply G(i) to A(i+1:m,i:n) from the right * IF( I.LT.M ) $ CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, $ TAUP( I ), A( I+1, I ), LDA, WORK ) CALL ZLACGV( N-I+1, A( I, I ), LDA ) A( I, I ) = D( I ) * IF( I.LT.M ) THEN * * Generate elementary reflector H(i) to annihilate * A(i+2:m,i) * ALPHA = A( I+1, I ) CALL ZLARFG( M-I, ALPHA, A( MIN( I+2, M ), I ), 1, $ TAUQ( I ) ) E( I ) = ALPHA A( I+1, I ) = ONE * * Apply H(i)**H to A(i+1:m,i+1:n) from the left * CALL ZLARF( 'Left', M-I, N-I, A( I+1, I ), 1, $ DCONJG( TAUQ( I ) ), A( I+1, I+1 ), LDA, $ WORK ) A( I+1, I ) = E( I ) ELSE TAUQ( I ) = ZERO END IF 20 CONTINUE END IF RETURN * * End of ZGEBD2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlahr2.f0000644000000000000000000000013214061636515015226 xustar0030 mtime=1623670093.310103982 30 atime=1623670093.310103982 30 ctime=1623670093.310103982 elk-7.2.42/src/LAPACK/zlahr2.f0000644002504400250440000002415714061636515017274 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAHR2 reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAHR2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) * * .. Scalar Arguments .. * INTEGER K, LDA, LDT, LDY, N, NB * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), T( LDT, NB ), TAU( NB ), * $ Y( LDY, NB ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1) *> matrix A so that elements below the k-th subdiagonal are zero. The *> reduction is performed by an unitary similarity transformation *> Q**H * A * Q. The routine returns the matrices V and T which determine *> Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T. *> *> This is an auxiliary routine called by ZGEHRD. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The offset for the reduction. Elements below the k-th *> subdiagonal in the first NB columns are reduced to zero. *> K < N. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> The number of columns to be reduced. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N-K+1) *> On entry, the n-by-(n-k+1) general matrix A. *> On exit, the elements on and above the k-th subdiagonal in *> the first NB columns are overwritten with the corresponding *> elements of the reduced matrix; the elements below the k-th *> subdiagonal, with the array TAU, represent the matrix Q as a *> product of elementary reflectors. The other columns of A are *> unchanged. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (NB) *> The scalar factors of the elementary reflectors. See Further *> Details. *> \endverbatim *> *> \param[out] T *> \verbatim *> T is COMPLEX*16 array, dimension (LDT,NB) *> The upper triangular matrix T. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= NB. *> \endverbatim *> *> \param[out] Y *> \verbatim *> Y is COMPLEX*16 array, dimension (LDY,NB) *> The n-by-nb matrix Y. *> \endverbatim *> *> \param[in] LDY *> \verbatim *> LDY is INTEGER *> The leading dimension of the array Y. LDY >= N. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of nb elementary reflectors *> *> Q = H(1) H(2) . . . H(nb). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in *> A(i+k+1:n,i), and tau in TAU(i). *> *> The elements of the vectors v together form the (n-k+1)-by-nb matrix *> V which is needed, with T and Y, to apply the transformation to the *> unreduced part of the matrix, using an update of the form: *> A := (I - V*T*V**H) * (A - Y*V**H). *> *> The contents of A on exit are illustrated by the following example *> with n = 7, k = 3 and nb = 2: *> *> ( a a a a a ) *> ( a a a a a ) *> ( a a a a a ) *> ( h h a a a ) *> ( v1 h a a a ) *> ( v1 v2 a a a ) *> ( v1 v2 a a a ) *> *> where a denotes an element of the original matrix A, h denotes a *> modified element of the upper Hessenberg matrix H, and vi denotes an *> element of the vector defining H(i). *> *> This subroutine is a slight modification of LAPACK-3.0's DLAHRD *> incorporating improvements proposed by Quintana-Orti and Van de *> Gejin. Note that the entries of A(1:K,2:NB) differ from those *> returned by the original LAPACK-3.0's DLAHRD routine. (This *> subroutine is not backward compatible with LAPACK-3.0's DLAHRD.) *> \endverbatim * *> \par References: * ================ *> *> Gregorio Quintana-Orti and Robert van de Geijn, "Improving the *> performance of reduction to Hessenberg form," ACM Transactions on *> Mathematical Software, 32(2):180-194, June 2006. *> * ===================================================================== SUBROUTINE ZLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER K, LDA, LDT, LDY, N, NB * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), T( LDT, NB ), TAU( NB ), $ Y( LDY, NB ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I COMPLEX*16 EI * .. * .. External Subroutines .. EXTERNAL ZAXPY, ZCOPY, ZGEMM, ZGEMV, ZLACPY, $ ZLARFG, ZSCAL, ZTRMM, ZTRMV, ZLACGV * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.1 ) $ RETURN * DO 10 I = 1, NB IF( I.GT.1 ) THEN * * Update A(K+1:N,I) * * Update I-th column of A - Y * V**H * CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY, $ A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 ) CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) * * Apply I - V * T**H * V**H to this column (call it b) from the * left, using the last column of T as workspace * * Let V = ( V1 ) and b = ( b1 ) (first I-1 rows) * ( V2 ) ( b2 ) * * where V1 is unit lower triangular * * w := V1**H * b1 * CALL ZCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 ) CALL ZTRMV( 'Lower', 'Conjugate transpose', 'UNIT', $ I-1, A( K+1, 1 ), $ LDA, T( 1, NB ), 1 ) * * w := w + V2**H * b2 * CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, $ ONE, A( K+I, 1 ), $ LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 ) * * w := T**H * w * CALL ZTRMV( 'Upper', 'Conjugate transpose', 'NON-UNIT', $ I-1, T, LDT, $ T( 1, NB ), 1 ) * * b2 := b2 - V2*w * CALL ZGEMV( 'NO TRANSPOSE', N-K-I+1, I-1, -ONE, $ A( K+I, 1 ), $ LDA, T( 1, NB ), 1, ONE, A( K+I, I ), 1 ) * * b1 := b1 - V1*w * CALL ZTRMV( 'Lower', 'NO TRANSPOSE', $ 'UNIT', I-1, $ A( K+1, 1 ), LDA, T( 1, NB ), 1 ) CALL ZAXPY( I-1, -ONE, T( 1, NB ), 1, A( K+1, I ), 1 ) * A( K+I-1, I-1 ) = EI END IF * * Generate the elementary reflector H(I) to annihilate * A(K+I+1:N,I) * CALL ZLARFG( N-K-I+1, A( K+I, I ), A( MIN( K+I+1, N ), I ), 1, $ TAU( I ) ) EI = A( K+I, I ) A( K+I, I ) = ONE * * Compute Y(K+1:N,I) * CALL ZGEMV( 'NO TRANSPOSE', N-K, N-K-I+1, $ ONE, A( K+1, I+1 ), $ LDA, A( K+I, I ), 1, ZERO, Y( K+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, $ ONE, A( K+I, 1 ), LDA, $ A( K+I, I ), 1, ZERO, T( 1, I ), 1 ) CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, $ Y( K+1, 1 ), LDY, $ T( 1, I ), 1, ONE, Y( K+1, I ), 1 ) CALL ZSCAL( N-K, TAU( I ), Y( K+1, I ), 1 ) * * Compute T(1:I,I) * CALL ZSCAL( I-1, -TAU( I ), T( 1, I ), 1 ) CALL ZTRMV( 'Upper', 'No Transpose', 'NON-UNIT', $ I-1, T, LDT, $ T( 1, I ), 1 ) T( I, I ) = TAU( I ) * 10 CONTINUE A( K+NB, NB ) = EI * * Compute Y(1:K,1:NB) * CALL ZLACPY( 'ALL', K, NB, A( 1, 2 ), LDA, Y, LDY ) CALL ZTRMM( 'RIGHT', 'Lower', 'NO TRANSPOSE', $ 'UNIT', K, NB, $ ONE, A( K+1, 1 ), LDA, Y, LDY ) IF( N.GT.K+NB ) $ CALL ZGEMM( 'NO TRANSPOSE', 'NO TRANSPOSE', K, $ NB, N-K-NB, ONE, $ A( 1, 2+NB ), LDA, A( K+1+NB, 1 ), LDA, ONE, Y, $ LDY ) CALL ZTRMM( 'RIGHT', 'Upper', 'NO TRANSPOSE', $ 'NON-UNIT', K, NB, $ ONE, T, LDT, Y, LDY ) * RETURN * * End of ZLAHR2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlarfb.f0000644000000000000000000000012714061636515015310 xustar0029 mtime=1623670093.31210398 29 atime=1623670093.31210398 29 ctime=1623670093.31210398 elk-7.2.42/src/LAPACK/zlarfb.f0000644002504400250440000005337114061636515017352 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLARFB + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, * T, LDT, C, LDC, WORK, LDWORK ) * * .. Scalar Arguments .. * CHARACTER DIRECT, SIDE, STOREV, TRANS * INTEGER K, LDC, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), * $ WORK( LDWORK, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLARFB applies a complex block reflector H or its transpose H**H to a *> complex M-by-N matrix C, from either the left or the right. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply H or H**H from the Left *> = 'R': apply H or H**H from the Right *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply H (No transpose) *> = 'C': apply H**H (Conjugate transpose) *> \endverbatim *> *> \param[in] DIRECT *> \verbatim *> DIRECT is CHARACTER*1 *> Indicates how H is formed from a product of elementary *> reflectors *> = 'F': H = H(1) H(2) . . . H(k) (Forward) *> = 'B': H = H(k) . . . H(2) H(1) (Backward) *> \endverbatim *> *> \param[in] STOREV *> \verbatim *> STOREV is CHARACTER*1 *> Indicates how the vectors which define the elementary *> reflectors are stored: *> = 'C': Columnwise *> = 'R': Rowwise *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The order of the matrix T (= the number of elementary *> reflectors whose product defines the block reflector). *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is COMPLEX*16 array, dimension *> (LDV,K) if STOREV = 'C' *> (LDV,M) if STOREV = 'R' and SIDE = 'L' *> (LDV,N) if STOREV = 'R' and SIDE = 'R' *> See Further Details. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V. *> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); *> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); *> if STOREV = 'R', LDV >= K. *> \endverbatim *> *> \param[in] T *> \verbatim *> T is COMPLEX*16 array, dimension (LDT,K) *> The triangular K-by-K matrix T in the representation of the *> block reflector. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= K. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (LDWORK,K) *> \endverbatim *> *> \param[in] LDWORK *> \verbatim *> LDWORK is INTEGER *> The leading dimension of the array WORK. *> If SIDE = 'L', LDWORK >= max(1,N); *> if SIDE = 'R', LDWORK >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2013 * *> \ingroup complex16OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> The shape of the matrix V and the storage of the vectors which define *> the H(i) is best illustrated by the following example with n = 5 and *> k = 3. The elements equal to 1 are not stored; the corresponding *> array elements are modified but restored on exit. The rest of the *> array is not used. *> *> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': *> *> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) *> ( v1 1 ) ( 1 v2 v2 v2 ) *> ( v1 v2 1 ) ( 1 v3 v3 ) *> ( v1 v2 v3 ) *> ( v1 v2 v3 ) *> *> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': *> *> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) *> ( v1 v2 v3 ) ( v2 v2 v2 1 ) *> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) *> ( 1 v3 ) *> ( 1 ) *> \endverbatim *> * ===================================================================== SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, $ T, LDT, C, LDC, WORK, LDWORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2013 * * .. Scalar Arguments .. CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, LDC, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), $ WORK( LDWORK, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. CHARACTER TRANST INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL ZCOPY, ZGEMM, ZLACGV, ZTRMM * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * IF( LSAME( TRANS, 'N' ) ) THEN TRANST = 'C' ELSE TRANST = 'N' END IF * IF( LSAME( STOREV, 'C' ) ) THEN * IF( LSAME( DIRECT, 'F' ) ) THEN * * Let V = ( V1 ) (first K rows) * ( V2 ) * where V1 is unit lower triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**H * C where C = ( C1 ) * ( C2 ) * * W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) * * W := C1**H * DO 10 J = 1, K CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) CALL ZLACGV( N, WORK( 1, J ), 1 ) 10 CONTINUE * * W := W * V1 * CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, $ K, ONE, V, LDV, WORK, LDWORK ) IF( M.GT.K ) THEN * * W := W + C2**H * V2 * CALL ZGEMM( 'Conjugate transpose', 'No transpose', N, $ K, M-K, ONE, C( K+1, 1 ), LDC, $ V( K+1, 1 ), LDV, ONE, WORK, LDWORK ) END IF * * W := W * T**H or W * T * CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - V * W**H * IF( M.GT.K ) THEN * * C2 := C2 - V2 * W**H * CALL ZGEMM( 'No transpose', 'Conjugate transpose', $ M-K, N, K, -ONE, V( K+1, 1 ), LDV, WORK, $ LDWORK, ONE, C( K+1, 1 ), LDC ) END IF * * W := W * V1**H * CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', $ 'Unit', N, K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W**H * DO 30 J = 1, K DO 20 I = 1, N C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) 20 CONTINUE 30 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**H where C = ( C1 C2 ) * * W := C * V = (C1*V1 + C2*V2) (stored in WORK) * * W := C1 * DO 40 J = 1, K CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE * * W := W * V1 * CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, $ K, ONE, V, LDV, WORK, LDWORK ) IF( N.GT.K ) THEN * * W := W + C2 * V2 * CALL ZGEMM( 'No transpose', 'No transpose', M, K, N-K, $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, $ ONE, WORK, LDWORK ) END IF * * W := W * T or W * T**H * CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V**H * IF( N.GT.K ) THEN * * C2 := C2 - W * V2**H * CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, $ N-K, K, -ONE, WORK, LDWORK, V( K+1, 1 ), $ LDV, ONE, C( 1, K+1 ), LDC ) END IF * * W := W * V1**H * CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', $ 'Unit', M, K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W * DO 60 J = 1, K DO 50 I = 1, M C( I, J ) = C( I, J ) - WORK( I, J ) 50 CONTINUE 60 CONTINUE END IF * ELSE * * Let V = ( V1 ) * ( V2 ) (last K rows) * where V2 is unit upper triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**H * C where C = ( C1 ) * ( C2 ) * * W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) * * W := C2**H * DO 70 J = 1, K CALL ZCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) CALL ZLACGV( N, WORK( 1, J ), 1 ) 70 CONTINUE * * W := W * V2 * CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, $ K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) IF( M.GT.K ) THEN * * W := W + C1**H * V1 * CALL ZGEMM( 'Conjugate transpose', 'No transpose', N, $ K, M-K, ONE, C, LDC, V, LDV, ONE, WORK, $ LDWORK ) END IF * * W := W * T**H or W * T * CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - V * W**H * IF( M.GT.K ) THEN * * C1 := C1 - V1 * W**H * CALL ZGEMM( 'No transpose', 'Conjugate transpose', $ M-K, N, K, -ONE, V, LDV, WORK, LDWORK, $ ONE, C, LDC ) END IF * * W := W * V2**H * CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', $ 'Unit', N, K, ONE, V( M-K+1, 1 ), LDV, WORK, $ LDWORK ) * * C2 := C2 - W**H * DO 90 J = 1, K DO 80 I = 1, N C( M-K+J, I ) = C( M-K+J, I ) - $ DCONJG( WORK( I, J ) ) 80 CONTINUE 90 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**H where C = ( C1 C2 ) * * W := C * V = (C1*V1 + C2*V2) (stored in WORK) * * W := C2 * DO 100 J = 1, K CALL ZCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 100 CONTINUE * * W := W * V2 * CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, $ K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) IF( N.GT.K ) THEN * * W := W + C1 * V1 * CALL ZGEMM( 'No transpose', 'No transpose', M, K, N-K, $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF * * W := W * T or W * T**H * CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V**H * IF( N.GT.K ) THEN * * C1 := C1 - W * V1**H * CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, $ N-K, K, -ONE, WORK, LDWORK, V, LDV, ONE, $ C, LDC ) END IF * * W := W * V2**H * CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', $ 'Unit', M, K, ONE, V( N-K+1, 1 ), LDV, WORK, $ LDWORK ) * * C2 := C2 - W * DO 120 J = 1, K DO 110 I = 1, M C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) 110 CONTINUE 120 CONTINUE END IF END IF * ELSE IF( LSAME( STOREV, 'R' ) ) THEN * IF( LSAME( DIRECT, 'F' ) ) THEN * * Let V = ( V1 V2 ) (V1: first K columns) * where V1 is unit upper triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**H * C where C = ( C1 ) * ( C2 ) * * W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) * * W := C1**H * DO 130 J = 1, K CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) CALL ZLACGV( N, WORK( 1, J ), 1 ) 130 CONTINUE * * W := W * V1**H * CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', $ 'Unit', N, K, ONE, V, LDV, WORK, LDWORK ) IF( M.GT.K ) THEN * * W := W + C2**H * V2**H * CALL ZGEMM( 'Conjugate transpose', $ 'Conjugate transpose', N, K, M-K, ONE, $ C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE, $ WORK, LDWORK ) END IF * * W := W * T**H or W * T * CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - V**H * W**H * IF( M.GT.K ) THEN * * C2 := C2 - V2**H * W**H * CALL ZGEMM( 'Conjugate transpose', $ 'Conjugate transpose', M-K, N, K, -ONE, $ V( 1, K+1 ), LDV, WORK, LDWORK, ONE, $ C( K+1, 1 ), LDC ) END IF * * W := W * V1 * CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, $ K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W**H * DO 150 J = 1, K DO 140 I = 1, N C( J, I ) = C( J, I ) - DCONJG( WORK( I, J ) ) 140 CONTINUE 150 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**H where C = ( C1 C2 ) * * W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) * * W := C1 * DO 160 J = 1, K CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 160 CONTINUE * * W := W * V1**H * CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose', $ 'Unit', M, K, ONE, V, LDV, WORK, LDWORK ) IF( N.GT.K ) THEN * * W := W + C2 * V2**H * CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, $ K, N-K, ONE, C( 1, K+1 ), LDC, $ V( 1, K+1 ), LDV, ONE, WORK, LDWORK ) END IF * * W := W * T or W * T**H * CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V * IF( N.GT.K ) THEN * * C2 := C2 - W * V2 * CALL ZGEMM( 'No transpose', 'No transpose', M, N-K, K, $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE, $ C( 1, K+1 ), LDC ) END IF * * W := W * V1 * CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, $ K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W * DO 180 J = 1, K DO 170 I = 1, M C( I, J ) = C( I, J ) - WORK( I, J ) 170 CONTINUE 180 CONTINUE * END IF * ELSE * * Let V = ( V1 V2 ) (V2: last K columns) * where V2 is unit lower triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**H * C where C = ( C1 ) * ( C2 ) * * W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) * * W := C2**H * DO 190 J = 1, K CALL ZCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) CALL ZLACGV( N, WORK( 1, J ), 1 ) 190 CONTINUE * * W := W * V2**H * CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', $ 'Unit', N, K, ONE, V( 1, M-K+1 ), LDV, WORK, $ LDWORK ) IF( M.GT.K ) THEN * * W := W + C1**H * V1**H * CALL ZGEMM( 'Conjugate transpose', $ 'Conjugate transpose', N, K, M-K, ONE, C, $ LDC, V, LDV, ONE, WORK, LDWORK ) END IF * * W := W * T**H or W * T * CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - V**H * W**H * IF( M.GT.K ) THEN * * C1 := C1 - V1**H * W**H * CALL ZGEMM( 'Conjugate transpose', $ 'Conjugate transpose', M-K, N, K, -ONE, V, $ LDV, WORK, LDWORK, ONE, C, LDC ) END IF * * W := W * V2 * CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, $ K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) * * C2 := C2 - W**H * DO 210 J = 1, K DO 200 I = 1, N C( M-K+J, I ) = C( M-K+J, I ) - $ DCONJG( WORK( I, J ) ) 200 CONTINUE 210 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**H where C = ( C1 C2 ) * * W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) * * W := C2 * DO 220 J = 1, K CALL ZCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 220 CONTINUE * * W := W * V2**H * CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose', $ 'Unit', M, K, ONE, V( 1, N-K+1 ), LDV, WORK, $ LDWORK ) IF( N.GT.K ) THEN * * W := W + C1 * V1**H * CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, $ K, N-K, ONE, C, LDC, V, LDV, ONE, WORK, $ LDWORK ) END IF * * W := W * T or W * T**H * CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V * IF( N.GT.K ) THEN * * C1 := C1 - W * V1 * CALL ZGEMM( 'No transpose', 'No transpose', M, N-K, K, $ -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) END IF * * W := W * V2 * CALL ZTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, $ K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) * * C1 := C1 - W * DO 240 J = 1, K DO 230 I = 1, M C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) 230 CONTINUE 240 CONTINUE * END IF * END IF END IF * RETURN * * End of ZLARFB * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgehd2.f0000644000000000000000000000013214061636515015207 xustar0030 mtime=1623670093.314103978 30 atime=1623670093.314103978 30 ctime=1623670093.314103978 elk-7.2.42/src/LAPACK/zgehd2.f0000644002504400250440000001467314061636515017257 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEHD2 reduces a general square matrix to upper Hessenberg form using an unblocked algorithm. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEHD2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER IHI, ILO, INFO, LDA, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H *> by a unitary similarity transformation: Q**H * A * Q = H . *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> It is assumed that A is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to ZGEBAL; otherwise they should be *> set to 1 and N respectively. See Further Details. *> 1 <= ILO <= IHI <= max(1,N). *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the n by n general matrix to be reduced. *> On exit, the upper triangle and the first subdiagonal of A *> are overwritten with the upper Hessenberg matrix H, and the *> elements below the first subdiagonal, with the array TAU, *> represent the unitary matrix Q as a product of elementary *> reflectors. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of (ihi-ilo) elementary *> reflectors *> *> Q = H(ilo) H(ilo+1) . . . H(ihi-1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on *> exit in A(i+2:ihi,i), and tau in TAU(i). *> *> The contents of A are illustrated by the following example, with *> n = 7, ilo = 2 and ihi = 6: *> *> on entry, on exit, *> *> ( a a a a a a a ) ( a a h h h h a ) *> ( a a a a a a ) ( a h h h h a ) *> ( a a a a a a ) ( h h h h h h ) *> ( a a a a a a ) ( v2 h h h h h ) *> ( a a a a a a ) ( v2 v3 h h h h ) *> ( a a a a a a ) ( v2 v3 v4 h h h ) *> ( a ) ( a ) *> *> where a denotes an element of the original matrix A, h denotes a *> modified element of the upper Hessenberg matrix H, and vi denotes an *> element of the vector defining H(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEHD2( N, ILO, IHI, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IHI, ILO, INFO, LDA, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I COMPLEX*16 ALPHA * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF, ZLARFG * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN INFO = -2 ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGEHD2', -INFO ) RETURN END IF * DO 10 I = ILO, IHI - 1 * * Compute elementary reflector H(i) to annihilate A(i+2:ihi,i) * ALPHA = A( I+1, I ) CALL ZLARFG( IHI-I, ALPHA, A( MIN( I+2, N ), I ), 1, TAU( I ) ) A( I+1, I ) = ONE * * Apply H(i) to A(1:ihi,i+1:ihi) from the right * CALL ZLARF( 'Right', IHI, IHI-I, A( I+1, I ), 1, TAU( I ), $ A( 1, I+1 ), LDA, WORK ) * * Apply H(i)**H to A(i+1:ihi,i+1:n) from the left * CALL ZLARF( 'Left', IHI-I, N-I, A( I+1, I ), 1, $ DCONJG( TAU( I ) ), A( I+1, I+1 ), LDA, WORK ) * A( I+1, I ) = ALPHA 10 CONTINUE * RETURN * * End of ZGEHD2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgelq2.f0000644000000000000000000000013214061636515015230 xustar0030 mtime=1623670093.316103976 30 atime=1623670093.316103976 30 ctime=1623670093.316103976 elk-7.2.42/src/LAPACK/zgelq2.f0000644002504400250440000001244714061636515017275 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGELQ2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGELQ2 computes an LQ factorization of a complex m-by-n matrix A: *> *> A = ( L 0 ) * Q *> *> where: *> *> Q is a n-by-n orthogonal matrix; *> L is an lower-triangular m-by-m matrix; *> 0 is a m-by-(n-m) zero matrix, if m < n. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the m by n matrix A. *> On exit, the elements on and below the diagonal of the array *> contain the m by min(m,n) lower trapezoidal matrix L (L is *> lower triangular if m <= n); the elements above the diagonal, *> with the array TAU, represent the unitary matrix Q as a *> product of elementary reflectors (see Further Details). *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (M) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2019 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of elementary reflectors *> *> Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in *> A(i,i+1:n), and tau in TAU(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGELQ2( M, N, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.9.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2019 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, K COMPLEX*16 ALPHA * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLACGV, ZLARF, ZLARFG * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGELQ2', -INFO ) RETURN END IF * K = MIN( M, N ) * DO 10 I = 1, K * * Generate elementary reflector H(i) to annihilate A(i,i+1:n) * CALL ZLACGV( N-I+1, A( I, I ), LDA ) ALPHA = A( I, I ) CALL ZLARFG( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA, $ TAU( I ) ) IF( I.LT.M ) THEN * * Apply H(i) to A(i+1:m,i:n) from the right * A( I, I ) = ONE CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ), $ A( I+1, I ), LDA, WORK ) END IF A( I, I ) = ALPHA CALL ZLACGV( N-I+1, A( I, I ), LDA ) 10 CONTINUE RETURN * * End of ZGELQ2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlarft.f0000644000000000000000000000013214061636515015326 xustar0030 mtime=1623670093.318103974 30 atime=1623670093.318103974 30 ctime=1623670093.318103974 elk-7.2.42/src/LAPACK/zlarft.f0000644002504400250440000002415514061636515017372 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLARFT forms the triangular factor T of a block reflector H = I - vtvH * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLARFT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) * * .. Scalar Arguments .. * CHARACTER DIRECT, STOREV * INTEGER K, LDT, LDV, N * .. * .. Array Arguments .. * COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLARFT forms the triangular factor T of a complex block reflector H *> of order n, which is defined as a product of k elementary reflectors. *> *> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; *> *> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. *> *> If STOREV = 'C', the vector which defines the elementary reflector *> H(i) is stored in the i-th column of the array V, and *> *> H = I - V * T * V**H *> *> If STOREV = 'R', the vector which defines the elementary reflector *> H(i) is stored in the i-th row of the array V, and *> *> H = I - V**H * T * V *> \endverbatim * * Arguments: * ========== * *> \param[in] DIRECT *> \verbatim *> DIRECT is CHARACTER*1 *> Specifies the order in which the elementary reflectors are *> multiplied to form the block reflector: *> = 'F': H = H(1) H(2) . . . H(k) (Forward) *> = 'B': H = H(k) . . . H(2) H(1) (Backward) *> \endverbatim *> *> \param[in] STOREV *> \verbatim *> STOREV is CHARACTER*1 *> Specifies how the vectors which define the elementary *> reflectors are stored (see also Further Details): *> = 'C': columnwise *> = 'R': rowwise *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the block reflector H. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The order of the triangular factor T (= the number of *> elementary reflectors). K >= 1. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is COMPLEX*16 array, dimension *> (LDV,K) if STOREV = 'C' *> (LDV,N) if STOREV = 'R' *> The matrix V. See further details. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V. *> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i). *> \endverbatim *> *> \param[out] T *> \verbatim *> T is COMPLEX*16 array, dimension (LDT,K) *> The k by k triangular factor T of the block reflector. *> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is *> lower triangular. The rest of the array is not used. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= K. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> The shape of the matrix V and the storage of the vectors which define *> the H(i) is best illustrated by the following example with n = 5 and *> k = 3. The elements equal to 1 are not stored. *> *> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': *> *> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) *> ( v1 1 ) ( 1 v2 v2 v2 ) *> ( v1 v2 1 ) ( 1 v3 v3 ) *> ( v1 v2 v3 ) *> ( v1 v2 v3 ) *> *> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': *> *> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) *> ( v1 v2 v3 ) ( v2 v2 v2 1 ) *> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) *> ( 1 v3 ) *> ( 1 ) *> \endverbatim *> * ===================================================================== SUBROUTINE ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. CHARACTER DIRECT, STOREV INTEGER K, LDT, LDV, N * .. * .. Array Arguments .. COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, J, PREVLASTV, LASTV * .. * .. External Subroutines .. EXTERNAL ZGEMV, ZTRMV, ZGEMM * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Executable Statements .. * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( LSAME( DIRECT, 'F' ) ) THEN PREVLASTV = N DO I = 1, K PREVLASTV = MAX( PREVLASTV, I ) IF( TAU( I ).EQ.ZERO ) THEN * * H(i) = I * DO J = 1, I T( J, I ) = ZERO END DO ELSE * * general case * IF( LSAME( STOREV, 'C' ) ) THEN * Skip any trailing zeros. DO LASTV = N, I+1, -1 IF( V( LASTV, I ).NE.ZERO ) EXIT END DO DO J = 1, I-1 T( J, I ) = -TAU( I ) * CONJG( V( I , J ) ) END DO J = MIN( LASTV, PREVLASTV ) * * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) * CALL ZGEMV( 'Conjugate transpose', J-I, I-1, $ -TAU( I ), V( I+1, 1 ), LDV, $ V( I+1, I ), 1, ONE, T( 1, I ), 1 ) ELSE * Skip any trailing zeros. DO LASTV = N, I+1, -1 IF( V( I, LASTV ).NE.ZERO ) EXIT END DO DO J = 1, I-1 T( J, I ) = -TAU( I ) * V( J , I ) END DO J = MIN( LASTV, PREVLASTV ) * * T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H * CALL ZGEMM( 'N', 'C', I-1, 1, J-I, -TAU( I ), $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, $ ONE, T( 1, I ), LDT ) END IF * * T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) * CALL ZTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, $ LDT, T( 1, I ), 1 ) T( I, I ) = TAU( I ) IF( I.GT.1 ) THEN PREVLASTV = MAX( PREVLASTV, LASTV ) ELSE PREVLASTV = LASTV END IF END IF END DO ELSE PREVLASTV = 1 DO I = K, 1, -1 IF( TAU( I ).EQ.ZERO ) THEN * * H(i) = I * DO J = I, K T( J, I ) = ZERO END DO ELSE * * general case * IF( I.LT.K ) THEN IF( LSAME( STOREV, 'C' ) ) THEN * Skip any leading zeros. DO LASTV = 1, I-1 IF( V( LASTV, I ).NE.ZERO ) EXIT END DO DO J = I+1, K T( J, I ) = -TAU( I ) * CONJG( V( N-K+I , J ) ) END DO J = MAX( LASTV, PREVLASTV ) * * T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) * CALL ZGEMV( 'Conjugate transpose', N-K+I-J, K-I, $ -TAU( I ), V( J, I+1 ), LDV, V( J, I ), $ 1, ONE, T( I+1, I ), 1 ) ELSE * Skip any leading zeros. DO LASTV = 1, I-1 IF( V( I, LASTV ).NE.ZERO ) EXIT END DO DO J = I+1, K T( J, I ) = -TAU( I ) * V( J, N-K+I ) END DO J = MAX( LASTV, PREVLASTV ) * * T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H * CALL ZGEMM( 'N', 'C', K-I, 1, N-K+I-J, -TAU( I ), $ V( I+1, J ), LDV, V( I, J ), LDV, $ ONE, T( I+1, I ), LDT ) END IF * * T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) * CALL ZTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) IF( I.GT.1 ) THEN PREVLASTV = MIN( PREVLASTV, LASTV ) ELSE PREVLASTV = LASTV END IF END IF T( I, I ) = TAU( I ) END IF END DO END IF RETURN * * End of ZLARFT * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zgeqr2.f0000644000000000000000000000013214061636515015236 xustar0030 mtime=1623670093.320103972 30 atime=1623670093.320103972 30 ctime=1623670093.320103972 elk-7.2.42/src/LAPACK/zgeqr2.f0000644002504400250440000001233514061636515017277 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGEQR2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEQR2 computes a QR factorization of a complex m-by-n matrix A: *> *> A = Q * ( R ), *> ( 0 ) *> *> where: *> *> Q is a m-by-m orthogonal matrix; *> R is an upper-triangular n-by-n matrix; *> 0 is a (m-n)-by-n zero matrix, if m > n. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the m by n matrix A. *> On exit, the elements on and above the diagonal of the array *> contain the min(m,n) by n upper trapezoidal matrix R (R is *> upper triangular if m >= n); the elements below the diagonal, *> with the array TAU, represent the unitary matrix Q as a *> product of elementary reflectors (see Further Details). *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2019 * *> \ingroup complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of elementary reflectors *> *> Q = H(1) H(2) . . . H(k), where k = min(m,n). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), *> and tau in TAU(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEQR2( M, N, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.9.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2019 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, K COMPLEX*16 ALPHA * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF, ZLARFG * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGEQR2', -INFO ) RETURN END IF * K = MIN( M, N ) * DO 10 I = 1, K * * Generate elementary reflector H(i) to annihilate A(i+1:m,i) * CALL ZLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, $ TAU( I ) ) IF( I.LT.N ) THEN * * Apply H(i)**H to A(i:m,i+1:n) from the left * ALPHA = A( I, I ) A( I, I ) = ONE CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK ) A( I, I ) = ALPHA END IF 10 CONTINUE RETURN * * End of ZGEQR2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhegs2.f0000644000000000000000000000013014061636515015224 xustar0029 mtime=1623670093.32210397 30 atime=1623670093.321103971 29 ctime=1623670093.32210397 elk-7.2.42/src/LAPACK/zhegs2.f0000644002504400250440000002251314061636515017266 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHEGS2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHEGS2 reduces a complex Hermitian-definite generalized *> eigenproblem to standard form. *> *> If ITYPE = 1, the problem is A*x = lambda*B*x, *> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) *> *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or *> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L. *> *> B must have been previously factorized as U**H *U or L*L**H by ZPOTRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] ITYPE *> \verbatim *> ITYPE is INTEGER *> = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); *> = 2 or 3: compute U*A*U**H or L**H *A*L. *> \endverbatim *> *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> Hermitian matrix A is stored, and how B has been factorized. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrices A and B. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading *> n by n upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,N) *> The triangular factor from the Cholesky factorization of B, *> as returned by ZPOTRF. *> B is modified by the routine but restored on exit. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16HEcomputational * * ===================================================================== SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, ITYPE, LDA, LDB, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), B( LDB, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, HALF PARAMETER ( ONE = 1.0D+0, HALF = 0.5D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER K DOUBLE PRECISION AKK, BKK COMPLEX*16 CT * .. * .. External Subroutines .. EXTERNAL XERBLA, ZAXPY, ZDSCAL, ZHER2, ZLACGV, ZTRMV, $ ZTRSV * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHEGS2', -INFO ) RETURN END IF * IF( ITYPE.EQ.1 ) THEN IF( UPPER ) THEN * * Compute inv(U**H)*A*inv(U) * DO 10 K = 1, N * * Update the upper triangle of A(k:n,k:n) * AKK = A( K, K ) BKK = B( K, K ) AKK = AKK / BKK**2 A( K, K ) = AKK IF( K.LT.N ) THEN CALL ZDSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA ) CT = -HALF*AKK CALL ZLACGV( N-K, A( K, K+1 ), LDA ) CALL ZLACGV( N-K, B( K, K+1 ), LDB ) CALL ZAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), $ LDA ) CALL ZHER2( UPLO, N-K, -CONE, A( K, K+1 ), LDA, $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA ) CALL ZAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ), $ LDA ) CALL ZLACGV( N-K, B( K, K+1 ), LDB ) CALL ZTRSV( UPLO, 'Conjugate transpose', 'Non-unit', $ N-K, B( K+1, K+1 ), LDB, A( K, K+1 ), $ LDA ) CALL ZLACGV( N-K, A( K, K+1 ), LDA ) END IF 10 CONTINUE ELSE * * Compute inv(L)*A*inv(L**H) * DO 20 K = 1, N * * Update the lower triangle of A(k:n,k:n) * AKK = A( K, K ) BKK = B( K, K ) AKK = AKK / BKK**2 A( K, K ) = AKK IF( K.LT.N ) THEN CALL ZDSCAL( N-K, ONE / BKK, A( K+1, K ), 1 ) CT = -HALF*AKK CALL ZAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) CALL ZHER2( UPLO, N-K, -CONE, A( K+1, K ), 1, $ B( K+1, K ), 1, A( K+1, K+1 ), LDA ) CALL ZAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 ) CALL ZTRSV( UPLO, 'No transpose', 'Non-unit', N-K, $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 ) END IF 20 CONTINUE END IF ELSE IF( UPPER ) THEN * * Compute U*A*U**H * DO 30 K = 1, N * * Update the upper triangle of A(1:k,1:k) * AKK = A( K, K ) BKK = B( K, K ) CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B, $ LDB, A( 1, K ), 1 ) CT = HALF*AKK CALL ZAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) CALL ZHER2( UPLO, K-1, CONE, A( 1, K ), 1, B( 1, K ), 1, $ A, LDA ) CALL ZAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 ) CALL ZDSCAL( K-1, BKK, A( 1, K ), 1 ) A( K, K ) = AKK*BKK**2 30 CONTINUE ELSE * * Compute L**H *A*L * DO 40 K = 1, N * * Update the lower triangle of A(1:k,1:k) * AKK = A( K, K ) BKK = B( K, K ) CALL ZLACGV( K-1, A( K, 1 ), LDA ) CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1, $ B, LDB, A( K, 1 ), LDA ) CT = HALF*AKK CALL ZLACGV( K-1, B( K, 1 ), LDB ) CALL ZAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) CALL ZHER2( UPLO, K-1, CONE, A( K, 1 ), LDA, B( K, 1 ), $ LDB, A, LDA ) CALL ZAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA ) CALL ZLACGV( K-1, B( K, 1 ), LDB ) CALL ZDSCAL( K-1, BKK, A( K, 1 ), LDA ) CALL ZLACGV( K-1, A( K, 1 ), LDA ) A( K, K ) = AKK*BKK**2 40 CONTINUE END IF END IF RETURN * * End of ZHEGS2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlatrd.f0000644000000000000000000000013114061636515015323 xustar0030 mtime=1623670093.324103969 29 atime=1623670093.32310397 30 ctime=1623670093.324103969 elk-7.2.42/src/LAPACK/zlatrd.f0000644002504400250440000003040414061636515017362 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLATRD reduces the first nb rows and columns of a symmetric/Hermitian matrix A to real tridiagonal form by an unitary similarity transformation. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLATRD + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDW, N, NB * .. * .. Array Arguments .. * DOUBLE PRECISION E( * ) * COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to *> Hermitian tridiagonal form by a unitary similarity *> transformation Q**H * A * Q, and returns the matrices V and W which are *> needed to apply the transformation to the unreduced part of A. *> *> If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a *> matrix, of which the upper triangle is supplied; *> if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a *> matrix, of which the lower triangle is supplied. *> *> This is an auxiliary routine called by ZHETRD. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> Hermitian matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> The number of rows and columns to be reduced. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading *> n-by-n upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> On exit: *> if UPLO = 'U', the last NB columns have been reduced to *> tridiagonal form, with the diagonal elements overwriting *> the diagonal elements of A; the elements above the diagonal *> with the array TAU, represent the unitary matrix Q as a *> product of elementary reflectors; *> if UPLO = 'L', the first NB columns have been reduced to *> tridiagonal form, with the diagonal elements overwriting *> the diagonal elements of A; the elements below the diagonal *> with the array TAU, represent the unitary matrix Q as a *> product of elementary reflectors. *> See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal *> elements of the last NB columns of the reduced matrix; *> if UPLO = 'L', E(1:nb) contains the subdiagonal elements of *> the first NB columns of the reduced matrix. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> The scalar factors of the elementary reflectors, stored in *> TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'. *> See Further Details. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is COMPLEX*16 array, dimension (LDW,NB) *> The n-by-nb matrix W required to update the unreduced part *> of A. *> \endverbatim *> *> \param[in] LDW *> \verbatim *> LDW is INTEGER *> The leading dimension of the array W. LDW >= max(1,N). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> If UPLO = 'U', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(n) H(n-1) . . . H(n-nb+1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i), *> and tau in TAU(i-1). *> *> If UPLO = 'L', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(1) H(2) . . . H(nb). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), *> and tau in TAU(i). *> *> The elements of the vectors v together form the n-by-nb matrix V *> which is needed, with W, to apply the transformation to the unreduced *> part of the matrix, using a Hermitian rank-2k update of the form: *> A := A - V*W**H - W*V**H. *> *> The contents of A on exit are illustrated by the following examples *> with n = 5 and nb = 2: *> *> if UPLO = 'U': if UPLO = 'L': *> *> ( a a a v4 v5 ) ( d ) *> ( a a v4 v5 ) ( 1 d ) *> ( a 1 v5 ) ( v1 1 a ) *> ( d 1 ) ( v1 v2 a a ) *> ( d ) ( v1 v2 a a a ) *> *> where d denotes a diagonal element of the reduced matrix, a denotes *> an element of the original matrix that is unchanged, and vi denotes *> an element of the vector defining H(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDW, N, NB * .. * .. Array Arguments .. DOUBLE PRECISION E( * ) COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE, HALF PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ), $ HALF = ( 0.5D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, IW COMPLEX*16 ALPHA * .. * .. External Subroutines .. EXTERNAL ZAXPY, ZGEMV, ZHEMV, ZLACGV, ZLARFG, ZSCAL * .. * .. External Functions .. LOGICAL LSAME COMPLEX*16 ZDOTC EXTERNAL LSAME, ZDOTC * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MIN * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.0 ) $ RETURN * IF( LSAME( UPLO, 'U' ) ) THEN * * Reduce last NB columns of upper triangle * DO 10 I = N, N - NB + 1, -1 IW = I - N + NB IF( I.LT.N ) THEN * * Update A(1:i,i) * A( I, I ) = DBLE( A( I, I ) ) CALL ZLACGV( N-I, W( I, IW+1 ), LDW ) CALL ZGEMV( 'No transpose', I, N-I, -ONE, A( 1, I+1 ), $ LDA, W( I, IW+1 ), LDW, ONE, A( 1, I ), 1 ) CALL ZLACGV( N-I, W( I, IW+1 ), LDW ) CALL ZLACGV( N-I, A( I, I+1 ), LDA ) CALL ZGEMV( 'No transpose', I, N-I, -ONE, W( 1, IW+1 ), $ LDW, A( I, I+1 ), LDA, ONE, A( 1, I ), 1 ) CALL ZLACGV( N-I, A( I, I+1 ), LDA ) A( I, I ) = DBLE( A( I, I ) ) END IF IF( I.GT.1 ) THEN * * Generate elementary reflector H(i) to annihilate * A(1:i-2,i) * ALPHA = A( I-1, I ) CALL ZLARFG( I-1, ALPHA, A( 1, I ), 1, TAU( I-1 ) ) E( I-1 ) = ALPHA A( I-1, I ) = ONE * * Compute W(1:i-1,i) * CALL ZHEMV( 'Upper', I-1, ONE, A, LDA, A( 1, I ), 1, $ ZERO, W( 1, IW ), 1 ) IF( I.LT.N ) THEN CALL ZGEMV( 'Conjugate transpose', I-1, N-I, ONE, $ W( 1, IW+1 ), LDW, A( 1, I ), 1, ZERO, $ W( I+1, IW ), 1 ) CALL ZGEMV( 'No transpose', I-1, N-I, -ONE, $ A( 1, I+1 ), LDA, W( I+1, IW ), 1, ONE, $ W( 1, IW ), 1 ) CALL ZGEMV( 'Conjugate transpose', I-1, N-I, ONE, $ A( 1, I+1 ), LDA, A( 1, I ), 1, ZERO, $ W( I+1, IW ), 1 ) CALL ZGEMV( 'No transpose', I-1, N-I, -ONE, $ W( 1, IW+1 ), LDW, W( I+1, IW ), 1, ONE, $ W( 1, IW ), 1 ) END IF CALL ZSCAL( I-1, TAU( I-1 ), W( 1, IW ), 1 ) ALPHA = -HALF*TAU( I-1 )*ZDOTC( I-1, W( 1, IW ), 1, $ A( 1, I ), 1 ) CALL ZAXPY( I-1, ALPHA, A( 1, I ), 1, W( 1, IW ), 1 ) END IF * 10 CONTINUE ELSE * * Reduce first NB columns of lower triangle * DO 20 I = 1, NB * * Update A(i:n,i) * A( I, I ) = DBLE( A( I, I ) ) CALL ZLACGV( I-1, W( I, 1 ), LDW ) CALL ZGEMV( 'No transpose', N-I+1, I-1, -ONE, A( I, 1 ), $ LDA, W( I, 1 ), LDW, ONE, A( I, I ), 1 ) CALL ZLACGV( I-1, W( I, 1 ), LDW ) CALL ZLACGV( I-1, A( I, 1 ), LDA ) CALL ZGEMV( 'No transpose', N-I+1, I-1, -ONE, W( I, 1 ), $ LDW, A( I, 1 ), LDA, ONE, A( I, I ), 1 ) CALL ZLACGV( I-1, A( I, 1 ), LDA ) A( I, I ) = DBLE( A( I, I ) ) IF( I.LT.N ) THEN * * Generate elementary reflector H(i) to annihilate * A(i+2:n,i) * ALPHA = A( I+1, I ) CALL ZLARFG( N-I, ALPHA, A( MIN( I+2, N ), I ), 1, $ TAU( I ) ) E( I ) = ALPHA A( I+1, I ) = ONE * * Compute W(i+1:n,i) * CALL ZHEMV( 'Lower', N-I, ONE, A( I+1, I+1 ), LDA, $ A( I+1, I ), 1, ZERO, W( I+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', N-I, I-1, ONE, $ W( I+1, 1 ), LDW, A( I+1, I ), 1, ZERO, $ W( 1, I ), 1 ) CALL ZGEMV( 'No transpose', N-I, I-1, -ONE, A( I+1, 1 ), $ LDA, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) CALL ZGEMV( 'Conjugate transpose', N-I, I-1, ONE, $ A( I+1, 1 ), LDA, A( I+1, I ), 1, ZERO, $ W( 1, I ), 1 ) CALL ZGEMV( 'No transpose', N-I, I-1, -ONE, W( I+1, 1 ), $ LDW, W( 1, I ), 1, ONE, W( I+1, I ), 1 ) CALL ZSCAL( N-I, TAU( I ), W( I+1, I ), 1 ) ALPHA = -HALF*TAU( I )*ZDOTC( N-I, W( I+1, I ), 1, $ A( I+1, I ), 1 ) CALL ZAXPY( N-I, ALPHA, A( I+1, I ), 1, W( I+1, I ), 1 ) END IF * 20 CONTINUE END IF * RETURN * * End of ZLATRD * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zhetd2.f0000644000000000000000000000013214061636515015224 xustar0030 mtime=1623670093.326103967 30 atime=1623670093.326103967 30 ctime=1623670093.326103967 elk-7.2.42/src/LAPACK/zhetd2.f0000644002504400250440000002371114061636515017265 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZHETD2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZHETD2( UPLO, N, A, LDA, D, E, TAU, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), E( * ) * COMPLEX*16 A( LDA, * ), TAU( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZHETD2 reduces a complex Hermitian matrix A to real symmetric *> tridiagonal form T by a unitary similarity transformation: *> Q**H * A * Q = T. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> Hermitian matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading *> n-by-n upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> On exit, if UPLO = 'U', the diagonal and first superdiagonal *> of A are overwritten by the corresponding elements of the *> tridiagonal matrix T, and the elements above the first *> superdiagonal, with the array TAU, represent the unitary *> matrix Q as a product of elementary reflectors; if UPLO *> = 'L', the diagonal and first subdiagonal of A are over- *> written by the corresponding elements of the tridiagonal *> matrix T, and the elements below the first subdiagonal, with *> the array TAU, represent the unitary matrix Q as a product *> of elementary reflectors. See Further Details. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The diagonal elements of the tridiagonal matrix T: *> D(i) = A(i,i). *> \endverbatim *> *> \param[out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The off-diagonal elements of the tridiagonal matrix T: *> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (N-1) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16HEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> If UPLO = 'U', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(n-1) . . . H(2) H(1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in *> A(1:i-1,i+1), and tau in TAU(i). *> *> If UPLO = 'L', the matrix Q is represented as a product of elementary *> reflectors *> *> Q = H(1) H(2) . . . H(n-1). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), *> and tau in TAU(i). *> *> The contents of A on exit are illustrated by the following examples *> with n = 5: *> *> if UPLO = 'U': if UPLO = 'L': *> *> ( d e v2 v3 v4 ) ( d ) *> ( d e v3 v4 ) ( e d ) *> ( d e v4 ) ( v1 e d ) *> ( d e ) ( v1 v2 e d ) *> ( d ) ( v1 v2 v3 e d ) *> *> where d and e denote diagonal and off-diagonal elements of T, and vi *> denotes an element of the vector defining H(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZHETD2( UPLO, N, A, LDA, D, E, TAU, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), E( * ) COMPLEX*16 A( LDA, * ), TAU( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO, HALF PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ), $ HALF = ( 0.5D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I COMPLEX*16 ALPHA, TAUI * .. * .. External Subroutines .. EXTERNAL XERBLA, ZAXPY, ZHEMV, ZHER2, ZLARFG * .. * .. External Functions .. LOGICAL LSAME COMPLEX*16 ZDOTC EXTERNAL LSAME, ZDOTC * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 UPPER = LSAME( UPLO, 'U') IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHETD2', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.0 ) $ RETURN * IF( UPPER ) THEN * * Reduce the upper triangle of A * A( N, N ) = DBLE( A( N, N ) ) DO 10 I = N - 1, 1, -1 * * Generate elementary reflector H(i) = I - tau * v * v**H * to annihilate A(1:i-1,i+1) * ALPHA = A( I, I+1 ) CALL ZLARFG( I, ALPHA, A( 1, I+1 ), 1, TAUI ) E( I ) = ALPHA * IF( TAUI.NE.ZERO ) THEN * * Apply H(i) from both sides to A(1:i,1:i) * A( I, I+1 ) = ONE * * Compute x := tau * A * v storing x in TAU(1:i) * CALL ZHEMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO, $ TAU, 1 ) * * Compute w := x - 1/2 * tau * (x**H * v) * v * ALPHA = -HALF*TAUI*ZDOTC( I, TAU, 1, A( 1, I+1 ), 1 ) CALL ZAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 ) * * Apply the transformation as a rank-2 update: * A := A - v * w**H - w * v**H * CALL ZHER2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A, $ LDA ) * ELSE A( I, I ) = DBLE( A( I, I ) ) END IF A( I, I+1 ) = E( I ) D( I+1 ) = A( I+1, I+1 ) TAU( I ) = TAUI 10 CONTINUE D( 1 ) = A( 1, 1 ) ELSE * * Reduce the lower triangle of A * A( 1, 1 ) = DBLE( A( 1, 1 ) ) DO 20 I = 1, N - 1 * * Generate elementary reflector H(i) = I - tau * v * v**H * to annihilate A(i+2:n,i) * ALPHA = A( I+1, I ) CALL ZLARFG( N-I, ALPHA, A( MIN( I+2, N ), I ), 1, TAUI ) E( I ) = ALPHA * IF( TAUI.NE.ZERO ) THEN * * Apply H(i) from both sides to A(i+1:n,i+1:n) * A( I+1, I ) = ONE * * Compute x := tau * A * v storing y in TAU(i:n-1) * CALL ZHEMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA, $ A( I+1, I ), 1, ZERO, TAU( I ), 1 ) * * Compute w := x - 1/2 * tau * (x**H * v) * v * ALPHA = -HALF*TAUI*ZDOTC( N-I, TAU( I ), 1, A( I+1, I ), $ 1 ) CALL ZAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 ) * * Apply the transformation as a rank-2 update: * A := A - v * w**H - w * v**H * CALL ZHER2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1, $ A( I+1, I+1 ), LDA ) * ELSE A( I+1, I+1 ) = DBLE( A( I+1, I+1 ) ) END IF A( I+1, I ) = E( I ) D( I ) = A( I, I ) TAU( I ) = TAUI 20 CONTINUE D( N ) = A( N, N ) END IF * RETURN * * End of ZHETD2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlarfg.f0000644000000000000000000000013214061636515015311 xustar0030 mtime=1623670093.328103965 30 atime=1623670093.328103965 30 ctime=1623670093.328103965 elk-7.2.42/src/LAPACK/zlarfg.f0000644002504400250440000001245514061636515017355 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLARFG generates an elementary reflector (Householder matrix). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLARFG + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) * * .. Scalar Arguments .. * INTEGER INCX, N * COMPLEX*16 ALPHA, TAU * .. * .. Array Arguments .. * COMPLEX*16 X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLARFG generates a complex elementary reflector H of order n, such *> that *> *> H**H * ( alpha ) = ( beta ), H**H * H = I. *> ( x ) ( 0 ) *> *> where alpha and beta are scalars, with beta real, and x is an *> (n-1)-element complex vector. H is represented in the form *> *> H = I - tau * ( 1 ) * ( 1 v**H ) , *> ( v ) *> *> where tau is a complex scalar and v is a complex (n-1)-element *> vector. Note that H is not hermitian. *> *> If the elements of x are all zero and alpha is real, then tau = 0 *> and H is taken to be the unit matrix. *> *> Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the elementary reflector. *> \endverbatim *> *> \param[in,out] ALPHA *> \verbatim *> ALPHA is COMPLEX*16 *> On entry, the value alpha. *> On exit, it is overwritten with the value beta. *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension *> (1+(N-2)*abs(INCX)) *> On entry, the vector x. *> On exit, it is overwritten with the vector v. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between elements of X. INCX > 0. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 *> The value tau. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) * * -- LAPACK auxiliary routine (version 3.8.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX, N COMPLEX*16 ALPHA, TAU * .. * .. Array Arguments .. COMPLEX*16 X( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER J, KNT DOUBLE PRECISION ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLAPY3, DZNRM2 COMPLEX*16 ZLADIV EXTERNAL DLAMCH, DLAPY3, DZNRM2, ZLADIV * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DIMAG, SIGN * .. * .. External Subroutines .. EXTERNAL ZDSCAL, ZSCAL * .. * .. Executable Statements .. * IF( N.LE.0 ) THEN TAU = ZERO RETURN END IF * XNORM = DZNRM2( N-1, X, INCX ) ALPHR = DBLE( ALPHA ) ALPHI = DIMAG( ALPHA ) * IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN * * H = I * TAU = ZERO ELSE * * general case * BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) RSAFMN = ONE / SAFMIN * KNT = 0 IF( ABS( BETA ).LT.SAFMIN ) THEN * * XNORM, BETA may be inaccurate; scale X and recompute them * 10 CONTINUE KNT = KNT + 1 CALL ZDSCAL( N-1, RSAFMN, X, INCX ) BETA = BETA*RSAFMN ALPHI = ALPHI*RSAFMN ALPHR = ALPHR*RSAFMN IF( (ABS( BETA ).LT.SAFMIN) .AND. (KNT .LT. 20) ) $ GO TO 10 * * New BETA is at most 1, at least SAFMIN * XNORM = DZNRM2( N-1, X, INCX ) ALPHA = DCMPLX( ALPHR, ALPHI ) BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) END IF TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA ) CALL ZSCAL( N-1, ALPHA, X, INCX ) * * If ALPHA is subnormal, it may lose relative accuracy * DO 20 J = 1, KNT BETA = BETA*SAFMIN 20 CONTINUE ALPHA = BETA END IF * RETURN * * End of ZLARFG * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaqr0.f0000644000000000000000000000013214061636515015235 xustar0030 mtime=1623670093.330103963 30 atime=1623670093.329103964 30 ctime=1623670093.330103963 elk-7.2.42/src/LAPACK/zlaqr0.f0000644002504400250440000006072614061636515017305 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAQR0 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAQR0 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, * IHIZ, Z, LDZ, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N * LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. * COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAQR0 computes the eigenvalues of a Hessenberg matrix H *> and, optionally, the matrices T and Z from the Schur decomposition *> H = Z T Z**H, where T is an upper triangular matrix (the *> Schur form), and Z is the unitary matrix of Schur vectors. *> *> Optionally Z may be postmultiplied into an input unitary *> matrix Q so that this routine can give the Schur factorization *> of a matrix A which has been reduced to the Hessenberg form H *> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H. *> \endverbatim * * Arguments: * ========== * *> \param[in] WANTT *> \verbatim *> WANTT is LOGICAL *> = .TRUE. : the full Schur form T is required; *> = .FALSE.: only eigenvalues are required. *> \endverbatim *> *> \param[in] WANTZ *> \verbatim *> WANTZ is LOGICAL *> = .TRUE. : the matrix of Schur vectors Z is required; *> = .FALSE.: Schur vectors are not required. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix H. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> It is assumed that H is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N and, if ILO > 1, *> H(ILO,ILO-1) is zero. ILO and IHI are normally set by a *> previous call to ZGEBAL, and then passed to ZGEHRD when the *> matrix output by ZGEBAL is reduced to Hessenberg form. *> Otherwise, ILO and IHI should be set to 1 and N, *> respectively. If N > 0, then 1 <= ILO <= IHI <= N. *> If N = 0, then ILO = 1 and IHI = 0. *> \endverbatim *> *> \param[in,out] H *> \verbatim *> H is COMPLEX*16 array, dimension (LDH,N) *> On entry, the upper Hessenberg matrix H. *> On exit, if INFO = 0 and WANTT is .TRUE., then H *> contains the upper triangular matrix T from the Schur *> decomposition (the Schur form). If INFO = 0 and WANT is *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO > 0 is given under the *> description of INFO below.) *> *> This subroutine may explicitly set H(i,j) = 0 for i > j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> The leading dimension of the array H. LDH >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is COMPLEX*16 array, dimension (N) *> The computed eigenvalues of H(ILO:IHI,ILO:IHI) are stored *> in W(ILO:IHI). If WANTT is .TRUE., then the eigenvalues are *> stored in the same order as on the diagonal of the Schur *> form returned in H, with W(i) = H(i,i). *> \endverbatim *> *> \param[in] ILOZ *> \verbatim *> ILOZ is INTEGER *> \endverbatim *> *> \param[in] IHIZ *> \verbatim *> IHIZ is INTEGER *> Specify the rows of Z to which transformations must be *> applied if WANTZ is .TRUE.. *> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ,IHI) *> If WANTZ is .FALSE., then Z is not referenced. *> If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is *> replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the *> orthogonal Schur factor of H(ILO:IHI,ILO:IHI). *> (The output value of Z when INFO > 0 is given under *> the description of INFO below.) *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. if WANTZ is .TRUE. *> then LDZ >= MAX(1,IHIZ). Otherwise, LDZ >= 1. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension LWORK *> On exit, if LWORK = -1, WORK(1) returns an estimate of *> the optimal value for LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N) *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. *> *> If LWORK = -1, then ZLAQR0 does a workspace query. *> In this case, ZLAQR0 checks the input parameters and *> estimates the optimal workspace size for the given *> values of N, ILO and IHI. The estimate is returned *> in WORK(1). No error message related to LWORK is *> issued by XERBLA. Neither H nor Z are accessed. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = i, ZLAQR0 failed to compute all of *> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR *> and WI contain those eigenvalues which have been *> successfully computed. (Failures are rare.) *> *> If INFO > 0 and WANT is .FALSE., then on exit, *> the remaining unconverged eigenvalues are the eigen- *> values of the upper Hessenberg matrix rows and *> columns ILO through INFO of the final, output *> value of H. *> *> If INFO > 0 and WANTT is .TRUE., then on exit *> *> (*) (initial value of H)*U = U*(final value of H) *> *> where U is a unitary matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. *> *> If INFO > 0 and WANTZ is .TRUE., then on exit *> *> (final value of Z(ILO:IHI,ILOZ:IHIZ) *> = (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U *> *> where U is the unitary matrix in (*) (regard- *> less of the value of WANTT.) *> *> If INFO > 0 and WANTZ is .FALSE., then Z is not *> accessed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Contributors: * ================== *> *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA * *> \par References: * ================ *> *> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR *> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 *> Performance, SIAM Journal of Matrix Analysis, volume 23, pages *> 929--947, 2002. *> \n *> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR *> Algorithm Part II: Aggressive Early Deflation, SIAM Journal *> of Matrix Analysis, volume 23, pages 948--973, 2002. *> * ===================================================================== SUBROUTINE ZLAQR0( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, $ IHIZ, Z, LDZ, WORK, LWORK, INFO ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * ================================================================ * * .. Parameters .. * * ==== Matrices of order NTINY or smaller must be processed by * . ZLAHQR because of insufficient subdiagonal scratch space. * . (This is a hard limit.) ==== INTEGER NTINY PARAMETER ( NTINY = 11 ) * * ==== Exceptional deflation windows: try to cure rare * . slow convergence by varying the size of the * . deflation window after KEXNW iterations. ==== INTEGER KEXNW PARAMETER ( KEXNW = 5 ) * * ==== Exceptional shifts: try to cure rare slow convergence * . with ad-hoc exceptional shifts every KEXSH iterations. * . ==== INTEGER KEXSH PARAMETER ( KEXSH = 6 ) * * ==== The constant WILK1 is used to form the exceptional * . shifts. ==== DOUBLE PRECISION WILK1 PARAMETER ( WILK1 = 0.75d0 ) COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), $ ONE = ( 1.0d0, 0.0d0 ) ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0d0 ) * .. * .. Local Scalars .. COMPLEX*16 AA, BB, CC, CDUM, DD, DET, RTDISC, SWAP, TR2 DOUBLE PRECISION S INTEGER I, INF, IT, ITMAX, K, KACC22, KBOT, KDU, KS, $ KT, KTOP, KU, KV, KWH, KWTOP, KWV, LD, LS, $ LWKOPT, NDEC, NDFL, NH, NHO, NIBBLE, NMIN, NS, $ NSMAX, NSR, NVE, NW, NWMAX, NWR, NWUPBD LOGICAL SORTED CHARACTER JBCMPZ*2 * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Local Arrays .. COMPLEX*16 ZDUM( 1, 1 ) * .. * .. External Subroutines .. EXTERNAL ZLACPY, ZLAHQR, ZLAQR3, ZLAQR4, ZLAQR5 * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DIMAG, INT, MAX, MIN, MOD, $ SQRT * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. Executable Statements .. INFO = 0 * * ==== Quick return for N = 0: nothing to do. ==== * IF( N.EQ.0 ) THEN WORK( 1 ) = ONE RETURN END IF * IF( N.LE.NTINY ) THEN * * ==== Tiny matrices must use ZLAHQR. ==== * LWKOPT = 1 IF( LWORK.NE.-1 ) $ CALL ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, $ IHIZ, Z, LDZ, INFO ) ELSE * * ==== Use small bulge multi-shift QR with aggressive early * . deflation on larger-than-tiny matrices. ==== * * ==== Hope for the best. ==== * INFO = 0 * * ==== Set up job flags for ILAENV. ==== * IF( WANTT ) THEN JBCMPZ( 1: 1 ) = 'S' ELSE JBCMPZ( 1: 1 ) = 'E' END IF IF( WANTZ ) THEN JBCMPZ( 2: 2 ) = 'V' ELSE JBCMPZ( 2: 2 ) = 'N' END IF * * ==== NWR = recommended deflation window size. At this * . point, N .GT. NTINY = 11, so there is enough * . subdiagonal workspace for NWR.GE.2 as required. * . (In fact, there is enough subdiagonal space for * . NWR.GE.3.) ==== * NWR = ILAENV( 13, 'ZLAQR0', JBCMPZ, N, ILO, IHI, LWORK ) NWR = MAX( 2, NWR ) NWR = MIN( IHI-ILO+1, ( N-1 ) / 3, NWR ) * * ==== NSR = recommended number of simultaneous shifts. * . At this point N .GT. NTINY = 11, so there is at * . enough subdiagonal workspace for NSR to be even * . and greater than or equal to two as required. ==== * NSR = ILAENV( 15, 'ZLAQR0', JBCMPZ, N, ILO, IHI, LWORK ) NSR = MIN( NSR, ( N+6 ) / 9, IHI-ILO ) NSR = MAX( 2, NSR-MOD( NSR, 2 ) ) * * ==== Estimate optimal workspace ==== * * ==== Workspace query call to ZLAQR3 ==== * CALL ZLAQR3( WANTT, WANTZ, N, ILO, IHI, NWR+1, H, LDH, ILOZ, $ IHIZ, Z, LDZ, LS, LD, W, H, LDH, N, H, LDH, N, H, $ LDH, WORK, -1 ) * * ==== Optimal workspace = MAX(ZLAQR5, ZLAQR3) ==== * LWKOPT = MAX( 3*NSR / 2, INT( WORK( 1 ) ) ) * * ==== Quick return in case of workspace query. ==== * IF( LWORK.EQ.-1 ) THEN WORK( 1 ) = DCMPLX( LWKOPT, 0 ) RETURN END IF * * ==== ZLAHQR/ZLAQR0 crossover point ==== * NMIN = ILAENV( 12, 'ZLAQR0', JBCMPZ, N, ILO, IHI, LWORK ) NMIN = MAX( NTINY, NMIN ) * * ==== Nibble crossover point ==== * NIBBLE = ILAENV( 14, 'ZLAQR0', JBCMPZ, N, ILO, IHI, LWORK ) NIBBLE = MAX( 0, NIBBLE ) * * ==== Accumulate reflections during ttswp? Use block * . 2-by-2 structure during matrix-matrix multiply? ==== * KACC22 = ILAENV( 16, 'ZLAQR0', JBCMPZ, N, ILO, IHI, LWORK ) KACC22 = MAX( 0, KACC22 ) KACC22 = MIN( 2, KACC22 ) * * ==== NWMAX = the largest possible deflation window for * . which there is sufficient workspace. ==== * NWMAX = MIN( ( N-1 ) / 3, LWORK / 2 ) NW = NWMAX * * ==== NSMAX = the Largest number of simultaneous shifts * . for which there is sufficient workspace. ==== * NSMAX = MIN( ( N+6 ) / 9, 2*LWORK / 3 ) NSMAX = NSMAX - MOD( NSMAX, 2 ) * * ==== NDFL: an iteration count restarted at deflation. ==== * NDFL = 1 * * ==== ITMAX = iteration limit ==== * ITMAX = MAX( 30, 2*KEXSH )*MAX( 10, ( IHI-ILO+1 ) ) * * ==== Last row and column in the active block ==== * KBOT = IHI * * ==== Main Loop ==== * DO 70 IT = 1, ITMAX * * ==== Done when KBOT falls below ILO ==== * IF( KBOT.LT.ILO ) $ GO TO 80 * * ==== Locate active block ==== * DO 10 K = KBOT, ILO + 1, -1 IF( H( K, K-1 ).EQ.ZERO ) $ GO TO 20 10 CONTINUE K = ILO 20 CONTINUE KTOP = K * * ==== Select deflation window size: * . Typical Case: * . If possible and advisable, nibble the entire * . active block. If not, use size MIN(NWR,NWMAX) * . or MIN(NWR+1,NWMAX) depending upon which has * . the smaller corresponding subdiagonal entry * . (a heuristic). * . * . Exceptional Case: * . If there have been no deflations in KEXNW or * . more iterations, then vary the deflation window * . size. At first, because, larger windows are, * . in general, more powerful than smaller ones, * . rapidly increase the window to the maximum possible. * . Then, gradually reduce the window size. ==== * NH = KBOT - KTOP + 1 NWUPBD = MIN( NH, NWMAX ) IF( NDFL.LT.KEXNW ) THEN NW = MIN( NWUPBD, NWR ) ELSE NW = MIN( NWUPBD, 2*NW ) END IF IF( NW.LT.NWMAX ) THEN IF( NW.GE.NH-1 ) THEN NW = NH ELSE KWTOP = KBOT - NW + 1 IF( CABS1( H( KWTOP, KWTOP-1 ) ).GT. $ CABS1( H( KWTOP-1, KWTOP-2 ) ) )NW = NW + 1 END IF END IF IF( NDFL.LT.KEXNW ) THEN NDEC = -1 ELSE IF( NDEC.GE.0 .OR. NW.GE.NWUPBD ) THEN NDEC = NDEC + 1 IF( NW-NDEC.LT.2 ) $ NDEC = 0 NW = NW - NDEC END IF * * ==== Aggressive early deflation: * . split workspace under the subdiagonal into * . - an nw-by-nw work array V in the lower * . left-hand-corner, * . - an NW-by-at-least-NW-but-more-is-better * . (NW-by-NHO) horizontal work array along * . the bottom edge, * . - an at-least-NW-but-more-is-better (NHV-by-NW) * . vertical work array along the left-hand-edge. * . ==== * KV = N - NW + 1 KT = NW + 1 NHO = ( N-NW-1 ) - KT + 1 KWV = NW + 2 NVE = ( N-NW ) - KWV + 1 * * ==== Aggressive early deflation ==== * CALL ZLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, $ IHIZ, Z, LDZ, LS, LD, W, H( KV, 1 ), LDH, NHO, $ H( KV, KT ), LDH, NVE, H( KWV, 1 ), LDH, WORK, $ LWORK ) * * ==== Adjust KBOT accounting for new deflations. ==== * KBOT = KBOT - LD * * ==== KS points to the shifts. ==== * KS = KBOT - LS + 1 * * ==== Skip an expensive QR sweep if there is a (partly * . heuristic) reason to expect that many eigenvalues * . will deflate without it. Here, the QR sweep is * . skipped if many eigenvalues have just been deflated * . or if the remaining active block is small. * IF( ( LD.EQ.0 ) .OR. ( ( 100*LD.LE.NW*NIBBLE ) .AND. ( KBOT- $ KTOP+1.GT.MIN( NMIN, NWMAX ) ) ) ) THEN * * ==== NS = nominal number of simultaneous shifts. * . This may be lowered (slightly) if ZLAQR3 * . did not provide that many shifts. ==== * NS = MIN( NSMAX, NSR, MAX( 2, KBOT-KTOP ) ) NS = NS - MOD( NS, 2 ) * * ==== If there have been no deflations * . in a multiple of KEXSH iterations, * . then try exceptional shifts. * . Otherwise use shifts provided by * . ZLAQR3 above or from the eigenvalues * . of a trailing principal submatrix. ==== * IF( MOD( NDFL, KEXSH ).EQ.0 ) THEN KS = KBOT - NS + 1 DO 30 I = KBOT, KS + 1, -2 W( I ) = H( I, I ) + WILK1*CABS1( H( I, I-1 ) ) W( I-1 ) = W( I ) 30 CONTINUE ELSE * * ==== Got NS/2 or fewer shifts? Use ZLAQR4 or * . ZLAHQR on a trailing principal submatrix to * . get more. (Since NS.LE.NSMAX.LE.(N+6)/9, * . there is enough space below the subdiagonal * . to fit an NS-by-NS scratch array.) ==== * IF( KBOT-KS+1.LE.NS / 2 ) THEN KS = KBOT - NS + 1 KT = N - NS + 1 CALL ZLACPY( 'A', NS, NS, H( KS, KS ), LDH, $ H( KT, 1 ), LDH ) IF( NS.GT.NMIN ) THEN CALL ZLAQR4( .false., .false., NS, 1, NS, $ H( KT, 1 ), LDH, W( KS ), 1, 1, $ ZDUM, 1, WORK, LWORK, INF ) ELSE CALL ZLAHQR( .false., .false., NS, 1, NS, $ H( KT, 1 ), LDH, W( KS ), 1, 1, $ ZDUM, 1, INF ) END IF KS = KS + INF * * ==== In case of a rare QR failure use * . eigenvalues of the trailing 2-by-2 * . principal submatrix. Scale to avoid * . overflows, underflows and subnormals. * . (The scale factor S can not be zero, * . because H(KBOT,KBOT-1) is nonzero.) ==== * IF( KS.GE.KBOT ) THEN S = CABS1( H( KBOT-1, KBOT-1 ) ) + $ CABS1( H( KBOT, KBOT-1 ) ) + $ CABS1( H( KBOT-1, KBOT ) ) + $ CABS1( H( KBOT, KBOT ) ) AA = H( KBOT-1, KBOT-1 ) / S CC = H( KBOT, KBOT-1 ) / S BB = H( KBOT-1, KBOT ) / S DD = H( KBOT, KBOT ) / S TR2 = ( AA+DD ) / TWO DET = ( AA-TR2 )*( DD-TR2 ) - BB*CC RTDISC = SQRT( -DET ) W( KBOT-1 ) = ( TR2+RTDISC )*S W( KBOT ) = ( TR2-RTDISC )*S * KS = KBOT - 1 END IF END IF * IF( KBOT-KS+1.GT.NS ) THEN * * ==== Sort the shifts (Helps a little) ==== * SORTED = .false. DO 50 K = KBOT, KS + 1, -1 IF( SORTED ) $ GO TO 60 SORTED = .true. DO 40 I = KS, K - 1 IF( CABS1( W( I ) ).LT.CABS1( W( I+1 ) ) ) $ THEN SORTED = .false. SWAP = W( I ) W( I ) = W( I+1 ) W( I+1 ) = SWAP END IF 40 CONTINUE 50 CONTINUE 60 CONTINUE END IF END IF * * ==== If there are only two shifts, then use * . only one. ==== * IF( KBOT-KS+1.EQ.2 ) THEN IF( CABS1( W( KBOT )-H( KBOT, KBOT ) ).LT. $ CABS1( W( KBOT-1 )-H( KBOT, KBOT ) ) ) THEN W( KBOT-1 ) = W( KBOT ) ELSE W( KBOT ) = W( KBOT-1 ) END IF END IF * * ==== Use up to NS of the the smallest magnitude * . shifts. If there aren't NS shifts available, * . then use them all, possibly dropping one to * . make the number of shifts even. ==== * NS = MIN( NS, KBOT-KS+1 ) NS = NS - MOD( NS, 2 ) KS = KBOT - NS + 1 * * ==== Small-bulge multi-shift QR sweep: * . split workspace under the subdiagonal into * . - a KDU-by-KDU work array U in the lower * . left-hand-corner, * . - a KDU-by-at-least-KDU-but-more-is-better * . (KDU-by-NHo) horizontal work array WH along * . the bottom edge, * . - and an at-least-KDU-but-more-is-better-by-KDU * . (NVE-by-KDU) vertical work WV arrow along * . the left-hand-edge. ==== * KDU = 3*NS - 3 KU = N - KDU + 1 KWH = KDU + 1 NHO = ( N-KDU+1-4 ) - ( KDU+1 ) + 1 KWV = KDU + 4 NVE = N - KDU - KWV + 1 * * ==== Small-bulge multi-shift QR sweep ==== * CALL ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NS, $ W( KS ), H, LDH, ILOZ, IHIZ, Z, LDZ, WORK, $ 3, H( KU, 1 ), LDH, NVE, H( KWV, 1 ), LDH, $ NHO, H( KU, KWH ), LDH ) END IF * * ==== Note progress (or the lack of it). ==== * IF( LD.GT.0 ) THEN NDFL = 1 ELSE NDFL = NDFL + 1 END IF * * ==== End of main loop ==== 70 CONTINUE * * ==== Iteration limit exceeded. Set INFO to show where * . the problem occurred and exit. ==== * INFO = KBOT 80 CONTINUE END IF * * ==== Return the optimal value of LWORK. ==== * WORK( 1 ) = DCMPLX( LWKOPT, 0 ) * * ==== End of ZLAQR0 ==== * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlahqr.f0000644000000000000000000000013214061636515015325 xustar0030 mtime=1623670093.332103961 30 atime=1623670093.332103961 30 ctime=1623670093.332103961 elk-7.2.42/src/LAPACK/zlahqr.f0000644002504400250440000004405414061636515017371 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAHQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, * IHIZ, Z, LDZ, INFO ) * * .. Scalar Arguments .. * INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N * LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. * COMPLEX*16 H( LDH, * ), W( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAHQR is an auxiliary routine called by CHSEQR to update the *> eigenvalues and Schur decomposition already computed by CHSEQR, by *> dealing with the Hessenberg submatrix in rows and columns ILO to *> IHI. *> \endverbatim * * Arguments: * ========== * *> \param[in] WANTT *> \verbatim *> WANTT is LOGICAL *> = .TRUE. : the full Schur form T is required; *> = .FALSE.: only eigenvalues are required. *> \endverbatim *> *> \param[in] WANTZ *> \verbatim *> WANTZ is LOGICAL *> = .TRUE. : the matrix of Schur vectors Z is required; *> = .FALSE.: Schur vectors are not required. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix H. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> It is assumed that H is already upper triangular in rows and *> columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1). *> ZLAHQR works primarily with the Hessenberg submatrix in rows *> and columns ILO to IHI, but applies transformations to all of *> H if WANTT is .TRUE.. *> 1 <= ILO <= max(1,IHI); IHI <= N. *> \endverbatim *> *> \param[in,out] H *> \verbatim *> H is COMPLEX*16 array, dimension (LDH,N) *> On entry, the upper Hessenberg matrix H. *> On exit, if INFO is zero and if WANTT is .TRUE., then H *> is upper triangular in rows and columns ILO:IHI. If INFO *> is zero and if WANTT is .FALSE., then the contents of H *> are unspecified on exit. The output state of H in case *> INF is positive is below under the description of INFO. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> The leading dimension of the array H. LDH >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is COMPLEX*16 array, dimension (N) *> The computed eigenvalues ILO to IHI are stored in the *> corresponding elements of W. If WANTT is .TRUE., the *> eigenvalues are stored in the same order as on the diagonal *> of the Schur form returned in H, with W(i) = H(i,i). *> \endverbatim *> *> \param[in] ILOZ *> \verbatim *> ILOZ is INTEGER *> \endverbatim *> *> \param[in] IHIZ *> \verbatim *> IHIZ is INTEGER *> Specify the rows of Z to which transformations must be *> applied if WANTZ is .TRUE.. *> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ,N) *> If WANTZ is .TRUE., on entry Z must contain the current *> matrix Z of transformations accumulated by CHSEQR, and on *> exit Z has been updated; transformations are applied only to *> the submatrix Z(ILOZ:IHIZ,ILO:IHI). *> If WANTZ is .FALSE., Z is not referenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = i, ZLAHQR failed to compute all the *> eigenvalues ILO to IHI in a total of 30 iterations *> per eigenvalue; elements i+1:ihi of W contain *> those eigenvalues which have been successfully *> computed. *> *> If INFO > 0 and WANTT is .FALSE., then on exit, *> the remaining unconverged eigenvalues are the *> eigenvalues of the upper Hessenberg matrix *> rows and columns ILO through INFO of the final, *> output value of H. *> *> If INFO > 0 and WANTT is .TRUE., then on exit *> (*) (initial value of H)*U = U*(final value of H) *> where U is an orthogonal matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. *> *> If INFO > 0 and WANTZ is .TRUE., then on exit *> (final value of Z) = (initial value of Z)*U *> where U is the orthogonal matrix in (*) *> (regardless of the value of WANTT.) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Contributors: * ================== *> *> \verbatim *> *> 02-96 Based on modifications by *> David Day, Sandia National Laboratory, USA *> *> 12-04 Further modifications by *> Ralph Byers, University of Kansas, USA *> This is a modified version of ZLAHQR from LAPACK version 3.0. *> It is (1) more robust against overflow and underflow and *> (2) adopts the more conservative Ahues & Tisseur stopping *> criterion (LAWN 122, 1997). *> \endverbatim *> * ===================================================================== SUBROUTINE ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, $ IHIZ, Z, LDZ, INFO ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), W( * ), Z( LDZ, * ) * .. * * ========================================================= * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), $ ONE = ( 1.0d0, 0.0d0 ) ) DOUBLE PRECISION RZERO, RONE, HALF PARAMETER ( RZERO = 0.0d0, RONE = 1.0d0, HALF = 0.5d0 ) DOUBLE PRECISION DAT1 PARAMETER ( DAT1 = 3.0d0 / 4.0d0 ) * .. * .. Local Scalars .. COMPLEX*16 CDUM, H11, H11S, H22, SC, SUM, T, T1, TEMP, U, $ V2, X, Y DOUBLE PRECISION AA, AB, BA, BB, H10, H21, RTEMP, S, SAFMAX, $ SAFMIN, SMLNUM, SX, T2, TST, ULP INTEGER I, I1, I2, ITS, ITMAX, J, JHI, JLO, K, L, M, $ NH, NZ * .. * .. Local Arrays .. COMPLEX*16 V( 2 ) * .. * .. External Functions .. COMPLEX*16 ZLADIV DOUBLE PRECISION DLAMCH EXTERNAL ZLADIV, DLAMCH * .. * .. External Subroutines .. EXTERNAL DLABAD, ZCOPY, ZLARFG, ZSCAL * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, MIN, SQRT * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. Executable Statements .. * INFO = 0 * * Quick return if possible * IF( N.EQ.0 ) $ RETURN IF( ILO.EQ.IHI ) THEN W( ILO ) = H( ILO, ILO ) RETURN END IF * * ==== clear out the trash ==== DO 10 J = ILO, IHI - 3 H( J+2, J ) = ZERO H( J+3, J ) = ZERO 10 CONTINUE IF( ILO.LE.IHI-2 ) $ H( IHI, IHI-2 ) = ZERO * ==== ensure that subdiagonal entries are real ==== IF( WANTT ) THEN JLO = 1 JHI = N ELSE JLO = ILO JHI = IHI END IF DO 20 I = ILO + 1, IHI IF( DIMAG( H( I, I-1 ) ).NE.RZERO ) THEN * ==== The following redundant normalization * . avoids problems with both gradual and * . sudden underflow in ABS(H(I,I-1)) ==== SC = H( I, I-1 ) / CABS1( H( I, I-1 ) ) SC = DCONJG( SC ) / ABS( SC ) H( I, I-1 ) = ABS( H( I, I-1 ) ) CALL ZSCAL( JHI-I+1, SC, H( I, I ), LDH ) CALL ZSCAL( MIN( JHI, I+1 )-JLO+1, DCONJG( SC ), $ H( JLO, I ), 1 ) IF( WANTZ ) $ CALL ZSCAL( IHIZ-ILOZ+1, DCONJG( SC ), Z( ILOZ, I ), 1 ) END IF 20 CONTINUE * NH = IHI - ILO + 1 NZ = IHIZ - ILOZ + 1 * * Set machine-dependent constants for the stopping criterion. * SAFMIN = DLAMCH( 'SAFE MINIMUM' ) SAFMAX = RONE / SAFMIN CALL DLABAD( SAFMIN, SAFMAX ) ULP = DLAMCH( 'PRECISION' ) SMLNUM = SAFMIN*( DBLE( NH ) / ULP ) * * I1 and I2 are the indices of the first row and last column of H * to which transformations must be applied. If eigenvalues only are * being computed, I1 and I2 are set inside the main loop. * IF( WANTT ) THEN I1 = 1 I2 = N END IF * * ITMAX is the total number of QR iterations allowed. * ITMAX = 30 * MAX( 10, NH ) * * The main loop begins here. I is the loop index and decreases from * IHI to ILO in steps of 1. Each iteration of the loop works * with the active submatrix in rows and columns L to I. * Eigenvalues I+1 to IHI have already converged. Either L = ILO, or * H(L,L-1) is negligible so that the matrix splits. * I = IHI 30 CONTINUE IF( I.LT.ILO ) $ GO TO 150 * * Perform QR iterations on rows and columns ILO to I until a * submatrix of order 1 splits off at the bottom because a * subdiagonal element has become negligible. * L = ILO DO 130 ITS = 0, ITMAX * * Look for a single small subdiagonal element. * DO 40 K = I, L + 1, -1 IF( CABS1( H( K, K-1 ) ).LE.SMLNUM ) $ GO TO 50 TST = CABS1( H( K-1, K-1 ) ) + CABS1( H( K, K ) ) IF( TST.EQ.ZERO ) THEN IF( K-2.GE.ILO ) $ TST = TST + ABS( DBLE( H( K-1, K-2 ) ) ) IF( K+1.LE.IHI ) $ TST = TST + ABS( DBLE( H( K+1, K ) ) ) END IF * ==== The following is a conservative small subdiagonal * . deflation criterion due to Ahues & Tisseur (LAWN 122, * . 1997). It has better mathematical foundation and * . improves accuracy in some examples. ==== IF( ABS( DBLE( H( K, K-1 ) ) ).LE.ULP*TST ) THEN AB = MAX( CABS1( H( K, K-1 ) ), CABS1( H( K-1, K ) ) ) BA = MIN( CABS1( H( K, K-1 ) ), CABS1( H( K-1, K ) ) ) AA = MAX( CABS1( H( K, K ) ), $ CABS1( H( K-1, K-1 )-H( K, K ) ) ) BB = MIN( CABS1( H( K, K ) ), $ CABS1( H( K-1, K-1 )-H( K, K ) ) ) S = AA + AB IF( BA*( AB / S ).LE.MAX( SMLNUM, $ ULP*( BB*( AA / S ) ) ) )GO TO 50 END IF 40 CONTINUE 50 CONTINUE L = K IF( L.GT.ILO ) THEN * * H(L,L-1) is negligible * H( L, L-1 ) = ZERO END IF * * Exit from loop if a submatrix of order 1 has split off. * IF( L.GE.I ) $ GO TO 140 * * Now the active submatrix is in rows and columns L to I. If * eigenvalues only are being computed, only the active submatrix * need be transformed. * IF( .NOT.WANTT ) THEN I1 = L I2 = I END IF * IF( ITS.EQ.10 ) THEN * * Exceptional shift. * S = DAT1*ABS( DBLE( H( L+1, L ) ) ) T = S + H( L, L ) ELSE IF( ITS.EQ.20 ) THEN * * Exceptional shift. * S = DAT1*ABS( DBLE( H( I, I-1 ) ) ) T = S + H( I, I ) ELSE * * Wilkinson's shift. * T = H( I, I ) U = SQRT( H( I-1, I ) )*SQRT( H( I, I-1 ) ) S = CABS1( U ) IF( S.NE.RZERO ) THEN X = HALF*( H( I-1, I-1 )-T ) SX = CABS1( X ) S = MAX( S, CABS1( X ) ) Y = S*SQRT( ( X / S )**2+( U / S )**2 ) IF( SX.GT.RZERO ) THEN IF( DBLE( X / SX )*DBLE( Y )+DIMAG( X / SX )* $ DIMAG( Y ).LT.RZERO )Y = -Y END IF T = T - U*ZLADIV( U, ( X+Y ) ) END IF END IF * * Look for two consecutive small subdiagonal elements. * DO 60 M = I - 1, L + 1, -1 * * Determine the effect of starting the single-shift QR * iteration at row M, and see if this would make H(M,M-1) * negligible. * H11 = H( M, M ) H22 = H( M+1, M+1 ) H11S = H11 - T H21 = DBLE( H( M+1, M ) ) S = CABS1( H11S ) + ABS( H21 ) H11S = H11S / S H21 = H21 / S V( 1 ) = H11S V( 2 ) = H21 H10 = DBLE( H( M, M-1 ) ) IF( ABS( H10 )*ABS( H21 ).LE.ULP* $ ( CABS1( H11S )*( CABS1( H11 )+CABS1( H22 ) ) ) ) $ GO TO 70 60 CONTINUE H11 = H( L, L ) H22 = H( L+1, L+1 ) H11S = H11 - T H21 = DBLE( H( L+1, L ) ) S = CABS1( H11S ) + ABS( H21 ) H11S = H11S / S H21 = H21 / S V( 1 ) = H11S V( 2 ) = H21 70 CONTINUE * * Single-shift QR step * DO 120 K = M, I - 1 * * The first iteration of this loop determines a reflection G * from the vector V and applies it from left and right to H, * thus creating a nonzero bulge below the subdiagonal. * * Each subsequent iteration determines a reflection G to * restore the Hessenberg form in the (K-1)th column, and thus * chases the bulge one step toward the bottom of the active * submatrix. * * V(2) is always real before the call to ZLARFG, and hence * after the call T2 ( = T1*V(2) ) is also real. * IF( K.GT.M ) $ CALL ZCOPY( 2, H( K, K-1 ), 1, V, 1 ) CALL ZLARFG( 2, V( 1 ), V( 2 ), 1, T1 ) IF( K.GT.M ) THEN H( K, K-1 ) = V( 1 ) H( K+1, K-1 ) = ZERO END IF V2 = V( 2 ) T2 = DBLE( T1*V2 ) * * Apply G from the left to transform the rows of the matrix * in columns K to I2. * DO 80 J = K, I2 SUM = DCONJG( T1 )*H( K, J ) + T2*H( K+1, J ) H( K, J ) = H( K, J ) - SUM H( K+1, J ) = H( K+1, J ) - SUM*V2 80 CONTINUE * * Apply G from the right to transform the columns of the * matrix in rows I1 to min(K+2,I). * DO 90 J = I1, MIN( K+2, I ) SUM = T1*H( J, K ) + T2*H( J, K+1 ) H( J, K ) = H( J, K ) - SUM H( J, K+1 ) = H( J, K+1 ) - SUM*DCONJG( V2 ) 90 CONTINUE * IF( WANTZ ) THEN * * Accumulate transformations in the matrix Z * DO 100 J = ILOZ, IHIZ SUM = T1*Z( J, K ) + T2*Z( J, K+1 ) Z( J, K ) = Z( J, K ) - SUM Z( J, K+1 ) = Z( J, K+1 ) - SUM*DCONJG( V2 ) 100 CONTINUE END IF * IF( K.EQ.M .AND. M.GT.L ) THEN * * If the QR step was started at row M > L because two * consecutive small subdiagonals were found, then extra * scaling must be performed to ensure that H(M,M-1) remains * real. * TEMP = ONE - T1 TEMP = TEMP / ABS( TEMP ) H( M+1, M ) = H( M+1, M )*DCONJG( TEMP ) IF( M+2.LE.I ) $ H( M+2, M+1 ) = H( M+2, M+1 )*TEMP DO 110 J = M, I IF( J.NE.M+1 ) THEN IF( I2.GT.J ) $ CALL ZSCAL( I2-J, TEMP, H( J, J+1 ), LDH ) CALL ZSCAL( J-I1, DCONJG( TEMP ), H( I1, J ), 1 ) IF( WANTZ ) THEN CALL ZSCAL( NZ, DCONJG( TEMP ), Z( ILOZ, J ), $ 1 ) END IF END IF 110 CONTINUE END IF 120 CONTINUE * * Ensure that H(I,I-1) is real. * TEMP = H( I, I-1 ) IF( DIMAG( TEMP ).NE.RZERO ) THEN RTEMP = ABS( TEMP ) H( I, I-1 ) = RTEMP TEMP = TEMP / RTEMP IF( I2.GT.I ) $ CALL ZSCAL( I2-I, DCONJG( TEMP ), H( I, I+1 ), LDH ) CALL ZSCAL( I-I1, TEMP, H( I1, I ), 1 ) IF( WANTZ ) THEN CALL ZSCAL( NZ, TEMP, Z( ILOZ, I ), 1 ) END IF END IF * 130 CONTINUE * * Failure to converge in remaining number of iterations * INFO = I RETURN * 140 CONTINUE * * H(I,I-1) is negligible: one eigenvalue has converged. * W( I ) = H( I, I ) * * return to start of the main loop with new value of I. * I = L - 1 GO TO 30 * 150 CONTINUE RETURN * * End of ZLAHQR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlassq.f0000644000000000000000000000013214061636515015341 xustar0030 mtime=1623670093.334103959 30 atime=1623670093.334103959 30 ctime=1623670093.334103959 elk-7.2.42/src/LAPACK/zlassq.f0000644002504400250440000001122414061636515017376 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLASSQ updates a sum of squares represented in scaled form. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLASSQ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ ) * * .. Scalar Arguments .. * INTEGER INCX, N * DOUBLE PRECISION SCALE, SUMSQ * .. * .. Array Arguments .. * COMPLEX*16 X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLASSQ returns the values scl and ssq such that *> *> ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, *> *> where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is *> assumed to be at least unity and the value of ssq will then satisfy *> *> 1.0 <= ssq <= ( sumsq + 2*n ). *> *> scale is assumed to be non-negative and scl returns the value *> *> scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ), *> i *> *> scale and sumsq must be supplied in SCALE and SUMSQ respectively. *> SCALE and SUMSQ are overwritten by scl and ssq respectively. *> *> The routine makes only one pass through the vector X. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of elements to be used from the vector X. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension (1+(N-1)*INCX) *> The vector x as described above. *> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between successive values of the vector X. *> INCX > 0. *> \endverbatim *> *> \param[in,out] SCALE *> \verbatim *> SCALE is DOUBLE PRECISION *> On entry, the value scale in the equation above. *> On exit, SCALE is overwritten with the value scl . *> \endverbatim *> *> \param[in,out] SUMSQ *> \verbatim *> SUMSQ is DOUBLE PRECISION *> On entry, the value sumsq in the equation above. *> On exit, SUMSQ is overwritten with the value ssq . *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLASSQ( N, X, INCX, SCALE, SUMSQ ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX, N DOUBLE PRECISION SCALE, SUMSQ * .. * .. Array Arguments .. COMPLEX*16 X( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER IX DOUBLE PRECISION TEMP1 * .. * .. External Functions .. LOGICAL DISNAN EXTERNAL DISNAN * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DIMAG * .. * .. Executable Statements .. * IF( N.GT.0 ) THEN DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX TEMP1 = ABS( DBLE( X( IX ) ) ) IF( TEMP1.GT.ZERO.OR.DISNAN( TEMP1 ) ) THEN IF( SCALE.LT.TEMP1 ) THEN SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 SCALE = TEMP1 ELSE SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 END IF END IF TEMP1 = ABS( DIMAG( X( IX ) ) ) IF( TEMP1.GT.ZERO.OR.DISNAN( TEMP1 ) ) THEN IF( SCALE.LT.TEMP1 ) THEN SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2 SCALE = TEMP1 ELSE SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2 END IF END IF 10 CONTINUE END IF * RETURN * * End of ZLASSQ * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zpotrf2.f0000644000000000000000000000013214061636515015432 xustar0030 mtime=1623670093.336103957 30 atime=1623670093.336103957 30 ctime=1623670093.336103957 elk-7.2.42/src/LAPACK/zpotrf2.f0000644002504400250440000001445414061636515017477 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZPOTRF2 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZPOTRF2 computes the Cholesky factorization of a Hermitian *> positive definite matrix A using the recursive algorithm. *> *> The factorization has the form *> A = U**H * U, if UPLO = 'U', or *> A = L * L**H, if UPLO = 'L', *> where U is an upper triangular matrix and L is lower triangular. *> *> This is the recursive version of the algorithm. It divides *> the matrix into four submatrices: *> *> [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 *> A = [ -----|----- ] with n1 = n/2 *> [ A21 | A22 ] n2 = n-n1 *> *> The subroutine calls itself to factor A11. Update and scale A21 *> or A12, update A22 then call itself to factor A22. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of A is stored; *> = 'L': Lower triangle of A is stored. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading *> N-by-N upper triangular part of A contains the upper *> triangular part of the matrix A, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. *> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16POcomputational * * ===================================================================== RECURSIVE SUBROUTINE ZPOTRF2( UPLO, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) COMPLEX*16 CONE PARAMETER ( CONE = (1.0D+0, 0.0D+0) ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER N1, N2, IINFO DOUBLE PRECISION AJJ * .. * .. External Functions .. LOGICAL LSAME, DISNAN EXTERNAL LSAME, DISNAN * .. * .. External Subroutines .. EXTERNAL ZHERK, ZTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, DBLE, SQRT * .. * .. Executable Statements .. * * Test the input parameters * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZPOTRF2', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * N=1 case * IF( N.EQ.1 ) THEN * * Test for non-positive-definiteness * AJJ = DBLE( A( 1, 1 ) ) IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN INFO = 1 RETURN END IF * * Factor * A( 1, 1 ) = SQRT( AJJ ) * * Use recursive code * ELSE N1 = N/2 N2 = N-N1 * * Factor A11 * CALL ZPOTRF2( UPLO, N1, A( 1, 1 ), LDA, IINFO ) IF ( IINFO.NE.0 ) THEN INFO = IINFO RETURN END IF * * Compute the Cholesky factorization A = U**H*U * IF( UPPER ) THEN * * Update and scale A12 * CALL ZTRSM( 'L', 'U', 'C', 'N', N1, N2, CONE, $ A( 1, 1 ), LDA, A( 1, N1+1 ), LDA ) * * Update and factor A22 * CALL ZHERK( UPLO, 'C', N2, N1, -ONE, A( 1, N1+1 ), LDA, $ ONE, A( N1+1, N1+1 ), LDA ) CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) IF ( IINFO.NE.0 ) THEN INFO = IINFO + N1 RETURN END IF * * Compute the Cholesky factorization A = L*L**H * ELSE * * Update and scale A21 * CALL ZTRSM( 'R', 'L', 'C', 'N', N2, N1, CONE, $ A( 1, 1 ), LDA, A( N1+1, 1 ), LDA ) * * Update and factor A22 * CALL ZHERK( UPLO, 'N', N2, N1, -ONE, A( N1+1, 1 ), LDA, $ ONE, A( N1+1, N1+1 ), LDA ) CALL ZPOTRF2( UPLO, N2, A( N1+1, N1+1 ), LDA, IINFO ) IF ( IINFO.NE.0 ) THEN INFO = IINFO + N1 RETURN END IF END IF END IF RETURN * * End of ZPOTRF2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dstedc.f0000644000000000000000000000013214061636515015272 xustar0030 mtime=1623670093.338103956 30 atime=1623670093.338103956 30 ctime=1623670093.338103956 elk-7.2.42/src/LAPACK/dstedc.f0000644002504400250440000003632614061636515017341 0ustar00dewhurstdewhurst00000000000000*> \brief \b DSTEDC * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSTEDC + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, * LIWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER COMPZ * INTEGER INFO, LDZ, LIWORK, LWORK, N * .. * .. Array Arguments .. * INTEGER IWORK( * ) * DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSTEDC computes all eigenvalues and, optionally, eigenvectors of a *> symmetric tridiagonal matrix using the divide and conquer method. *> The eigenvectors of a full or band real symmetric matrix can also be *> found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this *> matrix to tridiagonal form. *> *> This code makes very mild assumptions about floating point *> arithmetic. It will work on machines with a guard digit in *> add/subtract, or on those binary machines without guard digits *> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. *> It could conceivably fail on hexadecimal or decimal machines *> without guard digits, but we know of none. See DLAED3 for details. *> \endverbatim * * Arguments: * ========== * *> \param[in] COMPZ *> \verbatim *> COMPZ is CHARACTER*1 *> = 'N': Compute eigenvalues only. *> = 'I': Compute eigenvectors of tridiagonal matrix also. *> = 'V': Compute eigenvectors of original dense symmetric *> matrix also. On entry, Z contains the orthogonal *> matrix used to reduce the original matrix to *> tridiagonal form. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the diagonal elements of the tridiagonal matrix. *> On exit, if INFO = 0, the eigenvalues in ascending order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> On entry, the subdiagonal elements of the tridiagonal matrix. *> On exit, E has been destroyed. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (LDZ,N) *> On entry, if COMPZ = 'V', then Z contains the orthogonal *> matrix used in the reduction to tridiagonal form. *> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the *> orthonormal eigenvectors of the original symmetric matrix, *> and if COMPZ = 'I', Z contains the orthonormal eigenvectors *> of the symmetric tridiagonal matrix. *> If COMPZ = 'N', then Z is not referenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. LDZ >= 1. *> If eigenvectors are desired, then LDZ >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. *> If COMPZ = 'V' and N > 1 then LWORK must be at least *> ( 1 + 3*N + 2*N*lg N + 4*N**2 ), *> where lg( N ) = smallest integer k such *> that 2**k >= N. *> If COMPZ = 'I' and N > 1 then LWORK must be at least *> ( 1 + 4*N + N**2 ). *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LWORK need *> only be max(1,2*(N-1)). *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. *> \endverbatim *> *> \param[in] LIWORK *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. *> If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. *> If COMPZ = 'V' and N > 1 then LIWORK must be at least *> ( 6 + 6*N + 5*N*lg N ). *> If COMPZ = 'I' and N > 1 then LIWORK must be at least *> ( 3 + 5*N ). *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LIWORK *> need only be 1. *> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and *> no error message related to LIWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: The algorithm failed to compute an eigenvalue while *> working on the submatrix lying in rows and columns *> INFO/(N+1) through mod(INFO,N+1). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA \n *> Modified by Francoise Tisseur, University of Tennessee *> * ===================================================================== SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, $ LIWORK, INFO ) * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. CHARACTER COMPZ INTEGER INFO, LDZ, LIWORK, LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0 ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER FINISH, I, ICOMPZ, II, J, K, LGN, LIWMIN, $ LWMIN, M, SMLSIZ, START, STOREZ, STRTRW DOUBLE PRECISION EPS, ORGNRM, P, TINY * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLANST EXTERNAL LSAME, ILAENV, DLAMCH, DLANST * .. * .. External Subroutines .. EXTERNAL DGEMM, DLACPY, DLAED0, DLASCL, DLASET, DLASRT, $ DSTEQR, DSTERF, DSWAP, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, INT, LOG, MAX, MOD, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * IF( LSAME( COMPZ, 'N' ) ) THEN ICOMPZ = 0 ELSE IF( LSAME( COMPZ, 'V' ) ) THEN ICOMPZ = 1 ELSE IF( LSAME( COMPZ, 'I' ) ) THEN ICOMPZ = 2 ELSE ICOMPZ = -1 END IF IF( ICOMPZ.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ( LDZ.LT.1 ) .OR. $ ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, N ) ) ) THEN INFO = -6 END IF * IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * SMLSIZ = ILAENV( 9, 'DSTEDC', ' ', 0, 0, 0, 0 ) IF( N.LE.1 .OR. ICOMPZ.EQ.0 ) THEN LIWMIN = 1 LWMIN = 1 ELSE IF( N.LE.SMLSIZ ) THEN LIWMIN = 1 LWMIN = 2*( N - 1 ) ELSE LGN = INT( LOG( DBLE( N ) )/LOG( TWO ) ) IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IF( ICOMPZ.EQ.1 ) THEN LWMIN = 1 + 3*N + 2*N*LGN + 4*N**2 LIWMIN = 6 + 6*N + 5*N*LGN ELSE IF( ICOMPZ.EQ.2 ) THEN LWMIN = 1 + 4*N + N**2 LIWMIN = 3 + 5*N END IF END IF WORK( 1 ) = LWMIN IWORK( 1 ) = LIWMIN * IF( LWORK.LT.LWMIN .AND. .NOT. LQUERY ) THEN INFO = -8 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT. LQUERY ) THEN INFO = -10 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSTEDC', -INFO ) RETURN ELSE IF (LQUERY) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN IF( N.EQ.1 ) THEN IF( ICOMPZ.NE.0 ) $ Z( 1, 1 ) = ONE RETURN END IF * * If the following conditional clause is removed, then the routine * will use the Divide and Conquer routine to compute only the * eigenvalues, which requires (3N + 3N**2) real workspace and * (2 + 5N + 2N lg(N)) integer workspace. * Since on many architectures DSTERF is much faster than any other * algorithm for finding eigenvalues only, it is used here * as the default. If the conditional clause is removed, then * information on the size of workspace needs to be changed. * * If COMPZ = 'N', use DSTERF to compute the eigenvalues. * IF( ICOMPZ.EQ.0 ) THEN CALL DSTERF( N, D, E, INFO ) GO TO 50 END IF * * If N is smaller than the minimum divide size (SMLSIZ+1), then * solve the problem with another solver. * IF( N.LE.SMLSIZ ) THEN * CALL DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) * ELSE * * If COMPZ = 'V', the Z matrix must be stored elsewhere for later * use. * IF( ICOMPZ.EQ.1 ) THEN STOREZ = 1 + N*N ELSE STOREZ = 1 END IF * IF( ICOMPZ.EQ.2 ) THEN CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ ) END IF * * Scale. * ORGNRM = DLANST( 'M', N, D, E ) IF( ORGNRM.EQ.ZERO ) $ GO TO 50 * EPS = DLAMCH( 'Epsilon' ) * START = 1 * * while ( START <= N ) * 10 CONTINUE IF( START.LE.N ) THEN * * Let FINISH be the position of the next subdiagonal entry * such that E( FINISH ) <= TINY or FINISH = N if no such * subdiagonal exists. The matrix identified by the elements * between START and FINISH constitutes an independent * sub-problem. * FINISH = START 20 CONTINUE IF( FINISH.LT.N ) THEN TINY = EPS*SQRT( ABS( D( FINISH ) ) )* $ SQRT( ABS( D( FINISH+1 ) ) ) IF( ABS( E( FINISH ) ).GT.TINY ) THEN FINISH = FINISH + 1 GO TO 20 END IF END IF * * (Sub) Problem determined. Compute its size and solve it. * M = FINISH - START + 1 IF( M.EQ.1 ) THEN START = FINISH + 1 GO TO 10 END IF IF( M.GT.SMLSIZ ) THEN * * Scale. * ORGNRM = DLANST( 'M', M, D( START ), E( START ) ) CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M, 1, D( START ), M, $ INFO ) CALL DLASCL( 'G', 0, 0, ORGNRM, ONE, M-1, 1, E( START ), $ M-1, INFO ) * IF( ICOMPZ.EQ.1 ) THEN STRTRW = 1 ELSE STRTRW = START END IF CALL DLAED0( ICOMPZ, N, M, D( START ), E( START ), $ Z( STRTRW, START ), LDZ, WORK( 1 ), N, $ WORK( STOREZ ), IWORK, INFO ) IF( INFO.NE.0 ) THEN INFO = ( INFO / ( M+1 )+START-1 )*( N+1 ) + $ MOD( INFO, ( M+1 ) ) + START - 1 GO TO 50 END IF * * Scale back. * CALL DLASCL( 'G', 0, 0, ONE, ORGNRM, M, 1, D( START ), M, $ INFO ) * ELSE IF( ICOMPZ.EQ.1 ) THEN * * Since QR won't update a Z matrix which is larger than * the length of D, we must solve the sub-problem in a * workspace and then multiply back into Z. * CALL DSTEQR( 'I', M, D( START ), E( START ), WORK, M, $ WORK( M*M+1 ), INFO ) CALL DLACPY( 'A', N, M, Z( 1, START ), LDZ, $ WORK( STOREZ ), N ) CALL DGEMM( 'N', 'N', N, M, M, ONE, $ WORK( STOREZ ), N, WORK, M, ZERO, $ Z( 1, START ), LDZ ) ELSE IF( ICOMPZ.EQ.2 ) THEN CALL DSTEQR( 'I', M, D( START ), E( START ), $ Z( START, START ), LDZ, WORK, INFO ) ELSE CALL DSTERF( M, D( START ), E( START ), INFO ) END IF IF( INFO.NE.0 ) THEN INFO = START*( N+1 ) + FINISH GO TO 50 END IF END IF * START = FINISH + 1 GO TO 10 END IF * * endwhile * IF( ICOMPZ.EQ.0 ) THEN * * Use Quick Sort * CALL DLASRT( 'I', N, D, INFO ) * ELSE * * Use Selection Sort to minimize swaps of eigenvectors * DO 40 II = 2, N I = II - 1 K = I P = D( I ) DO 30 J = II, N IF( D( J ).LT.P ) THEN K = J P = D( J ) END IF 30 CONTINUE IF( K.NE.I ) THEN D( K ) = D( I ) D( I ) = P CALL DSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) END IF 40 CONTINUE END IF END IF * 50 CONTINUE WORK( 1 ) = LWMIN IWORK( 1 ) = LIWMIN * RETURN * * End of DSTEDC * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaed0.f0000644000000000000000000000013214061636515015203 xustar0030 mtime=1623670093.340103954 30 atime=1623670093.340103954 30 ctime=1623670093.340103954 elk-7.2.42/src/LAPACK/zlaed0.f0000644002504400250440000002607714061636515017254 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAED0 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, * IWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDQ, LDQS, N, QSIZ * .. * .. Array Arguments .. * INTEGER IWORK( * ) * DOUBLE PRECISION D( * ), E( * ), RWORK( * ) * COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Using the divide and conquer method, ZLAED0 computes all eigenvalues *> of a symmetric tridiagonal matrix which is one diagonal block of *> those from reducing a dense or band Hermitian matrix and *> corresponding eigenvectors of the dense or band matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] QSIZ *> \verbatim *> QSIZ is INTEGER *> The dimension of the unitary matrix used to reduce *> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the diagonal elements of the tridiagonal matrix. *> On exit, the eigenvalues in ascending order. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> On entry, the off-diagonal elements of the tridiagonal matrix. *> On exit, E has been destroyed. *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDQ,N) *> On entry, Q must contain an QSIZ x N matrix whose columns *> unitarily orthonormal. It is a part of the unitary matrix *> that reduces the full dense Hermitian matrix to a *> (reducible) symmetric tridiagonal matrix. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, *> the dimension of IWORK must be at least *> 6 + 6*N + 5*N*lg N *> ( lg( N ) = smallest integer k *> such that 2^k >= N ) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, *> dimension (1 + 3*N + 2*N*lg N + 3*N**2) *> ( lg( N ) = smallest integer k *> such that 2^k >= N ) *> \endverbatim *> *> \param[out] QSTORE *> \verbatim *> QSTORE is COMPLEX*16 array, dimension (LDQS, N) *> Used to store parts of *> the eigenvector matrix when the updating matrix multiplies *> take place. *> \endverbatim *> *> \param[in] LDQS *> \verbatim *> LDQS is INTEGER *> The leading dimension of the array QSTORE. *> LDQS >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: The algorithm failed to compute an eigenvalue while *> working on the submatrix lying in rows and columns *> INFO/(N+1) through mod(INFO,N+1). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, $ IWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, LDQ, LDQS, N, QSIZ * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION D( * ), E( * ), RWORK( * ) COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) * .. * * ===================================================================== * * Warning: N could be as big as QSIZ! * * .. Parameters .. DOUBLE PRECISION TWO PARAMETER ( TWO = 2.D+0 ) * .. * .. Local Scalars .. INTEGER CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM, $ IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM, $ J, K, LGN, LL, MATSIZ, MSD2, SMLSIZ, SMM1, $ SPM1, SPM2, SUBMAT, SUBPBS, TLVLS DOUBLE PRECISION TEMP * .. * .. External Subroutines .. EXTERNAL DCOPY, DSTEQR, XERBLA, ZCOPY, ZLACRM, ZLAED7 * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, INT, LOG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * * IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN * INFO = -1 * ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) ) * $ THEN IF( QSIZ.LT.MAX( 0, N ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLAED0', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * SMLSIZ = ILAENV( 9, 'ZLAED0', ' ', 0, 0, 0, 0 ) * * Determine the size and placement of the submatrices, and save in * the leading elements of IWORK. * IWORK( 1 ) = N SUBPBS = 1 TLVLS = 0 10 CONTINUE IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN DO 20 J = SUBPBS, 1, -1 IWORK( 2*J ) = ( IWORK( J )+1 ) / 2 IWORK( 2*J-1 ) = IWORK( J ) / 2 20 CONTINUE TLVLS = TLVLS + 1 SUBPBS = 2*SUBPBS GO TO 10 END IF DO 30 J = 2, SUBPBS IWORK( J ) = IWORK( J ) + IWORK( J-1 ) 30 CONTINUE * * Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 * using rank-1 modifications (cuts). * SPM1 = SUBPBS - 1 DO 40 I = 1, SPM1 SUBMAT = IWORK( I ) + 1 SMM1 = SUBMAT - 1 D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) ) D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) ) 40 CONTINUE * INDXQ = 4*N + 3 * * Set up workspaces for eigenvalues only/accumulate new vectors * routine * TEMP = LOG( DBLE( N ) ) / LOG( TWO ) LGN = INT( TEMP ) IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IPRMPT = INDXQ + N + 1 IPERM = IPRMPT + N*LGN IQPTR = IPERM + N*LGN IGIVPT = IQPTR + N + 2 IGIVCL = IGIVPT + N*LGN * IGIVNM = 1 IQ = IGIVNM + 2*N*LGN IWREM = IQ + N**2 + 1 * Initialize pointers DO 50 I = 0, SUBPBS IWORK( IPRMPT+I ) = 1 IWORK( IGIVPT+I ) = 1 50 CONTINUE IWORK( IQPTR ) = 1 * * Solve each submatrix eigenproblem at the bottom of the divide and * conquer tree. * CURR = 0 DO 70 I = 0, SPM1 IF( I.EQ.0 ) THEN SUBMAT = 1 MATSIZ = IWORK( 1 ) ELSE SUBMAT = IWORK( I ) + 1 MATSIZ = IWORK( I+1 ) - IWORK( I ) END IF LL = IQ - 1 + IWORK( IQPTR+CURR ) CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ), $ RWORK( LL ), MATSIZ, RWORK, INFO ) CALL ZLACRM( QSIZ, MATSIZ, Q( 1, SUBMAT ), LDQ, RWORK( LL ), $ MATSIZ, QSTORE( 1, SUBMAT ), LDQS, $ RWORK( IWREM ) ) IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2 CURR = CURR + 1 IF( INFO.GT.0 ) THEN INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1 RETURN END IF K = 1 DO 60 J = SUBMAT, IWORK( I+1 ) IWORK( INDXQ+J ) = K K = K + 1 60 CONTINUE 70 CONTINUE * * Successively merge eigensystems of adjacent submatrices * into eigensystem for the corresponding larger matrix. * * while ( SUBPBS > 1 ) * CURLVL = 1 80 CONTINUE IF( SUBPBS.GT.1 ) THEN SPM2 = SUBPBS - 2 DO 90 I = 0, SPM2, 2 IF( I.EQ.0 ) THEN SUBMAT = 1 MATSIZ = IWORK( 2 ) MSD2 = IWORK( 1 ) CURPRB = 0 ELSE SUBMAT = IWORK( I ) + 1 MATSIZ = IWORK( I+2 ) - IWORK( I ) MSD2 = MATSIZ / 2 CURPRB = CURPRB + 1 END IF * * Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) * into an eigensystem of size MATSIZ. ZLAED7 handles the case * when the eigenvectors of a full or band Hermitian matrix (which * was reduced to tridiagonal form) are desired. * * I am free to use Q as a valuable working space until Loop 150. * CALL ZLAED7( MATSIZ, MSD2, QSIZ, TLVLS, CURLVL, CURPRB, $ D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS, $ E( SUBMAT+MSD2-1 ), IWORK( INDXQ+SUBMAT ), $ RWORK( IQ ), IWORK( IQPTR ), IWORK( IPRMPT ), $ IWORK( IPERM ), IWORK( IGIVPT ), $ IWORK( IGIVCL ), RWORK( IGIVNM ), $ Q( 1, SUBMAT ), RWORK( IWREM ), $ IWORK( SUBPBS+1 ), INFO ) IF( INFO.GT.0 ) THEN INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1 RETURN END IF IWORK( I / 2+1 ) = IWORK( I+2 ) 90 CONTINUE SUBPBS = SUBPBS / 2 CURLVL = CURLVL + 1 GO TO 80 END IF * * end while * * Re-merge the eigenvalues/vectors which were deflated at the final * merge step. * DO 100 I = 1, N J = IWORK( INDXQ+I ) RWORK( I ) = D( J ) CALL ZCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 ) 100 CONTINUE CALL DCOPY( N, RWORK, 1, D, 1 ) * RETURN * * End of ZLAED0 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlacrm.f0000644000000000000000000000013214061636515015314 xustar0030 mtime=1623670093.342103952 30 atime=1623670093.342103952 30 ctime=1623670093.342103952 elk-7.2.42/src/LAPACK/zlacrm.f0000644002504400250440000001135114061636515017352 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLACRM multiplies a complex matrix by a square real matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLACRM + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLACRM( M, N, A, LDA, B, LDB, C, LDC, RWORK ) * * .. Scalar Arguments .. * INTEGER LDA, LDB, LDC, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION B( LDB, * ), RWORK( * ) * COMPLEX*16 A( LDA, * ), C( LDC, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLACRM performs a very simple matrix-matrix multiplication: *> C := A * B, *> where A is M by N and complex; B is N by N and real; *> C is M by N and complex. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A and of the matrix C. *> M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns and rows of the matrix B and *> the number of columns of the matrix C. *> N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA, N) *> On entry, A contains the M by N matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >=max(1,M). *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB, N) *> On entry, B contains the N by N matrix B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >=max(1,N). *> \endverbatim *> *> \param[out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC, N) *> On exit, C contains the M by N matrix C. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >=max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (2*M*N) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLACRM( M, N, A, LDA, B, LDB, C, LDC, RWORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER LDA, LDB, LDC, M, N * .. * .. Array Arguments .. DOUBLE PRECISION B( LDB, * ), RWORK( * ) COMPLEX*16 A( LDA, * ), C( LDC, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) * .. * .. Local Scalars .. INTEGER I, J, L * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, DIMAG * .. * .. External Subroutines .. EXTERNAL DGEMM * .. * .. Executable Statements .. * * Quick return if possible. * IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) $ RETURN * DO 20 J = 1, N DO 10 I = 1, M RWORK( ( J-1 )*M+I ) = DBLE( A( I, J ) ) 10 CONTINUE 20 CONTINUE * L = M*N + 1 CALL DGEMM( 'N', 'N', M, N, N, ONE, RWORK, M, B, LDB, ZERO, $ RWORK( L ), M ) DO 40 J = 1, N DO 30 I = 1, M C( I, J ) = RWORK( L+( J-1 )*M+I-1 ) 30 CONTINUE 40 CONTINUE * DO 60 J = 1, N DO 50 I = 1, M RWORK( ( J-1 )*M+I ) = DIMAG( A( I, J ) ) 50 CONTINUE 60 CONTINUE CALL DGEMM( 'N', 'N', M, N, N, ONE, RWORK, M, B, LDB, ZERO, $ RWORK( L ), M ) DO 80 J = 1, N DO 70 I = 1, M C( I, J ) = DCMPLX( DBLE( C( I, J ) ), $ RWORK( L+( J-1 )*M+I-1 ) ) 70 CONTINUE 80 CONTINUE * RETURN * * End of ZLACRM * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlarnv.f0000644000000000000000000000012714061636515015316 xustar0029 mtime=1623670093.34410395 29 atime=1623670093.34410395 29 ctime=1623670093.34410395 elk-7.2.42/src/LAPACK/dlarnv.f0000644002504400250440000001126214061636515017351 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLARNV returns a vector of random numbers from a uniform or normal distribution. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARNV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARNV( IDIST, ISEED, N, X ) * * .. Scalar Arguments .. * INTEGER IDIST, N * .. * .. Array Arguments .. * INTEGER ISEED( 4 ) * DOUBLE PRECISION X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARNV returns a vector of n random real numbers from a uniform or *> normal distribution. *> \endverbatim * * Arguments: * ========== * *> \param[in] IDIST *> \verbatim *> IDIST is INTEGER *> Specifies the distribution of the random numbers: *> = 1: uniform (0,1) *> = 2: uniform (-1,1) *> = 3: normal (0,1) *> \endverbatim *> *> \param[in,out] ISEED *> \verbatim *> ISEED is INTEGER array, dimension (4) *> On entry, the seed of the random number generator; the array *> elements must be between 0 and 4095, and ISEED(4) must be *> odd. *> On exit, the seed is updated. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of random numbers to be generated. *> \endverbatim *> *> \param[out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (N) *> The generated random numbers. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> This routine calls the auxiliary routine DLARUV to generate random *> real numbers from a uniform (0,1) distribution, in batches of up to *> 128 using vectorisable code. The Box-Muller method is used to *> transform numbers from a uniform to a normal distribution. *> \endverbatim *> * ===================================================================== SUBROUTINE DLARNV( IDIST, ISEED, N, X ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IDIST, N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION X( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, TWO PARAMETER ( ONE = 1.0D+0, TWO = 2.0D+0 ) INTEGER LV PARAMETER ( LV = 128 ) DOUBLE PRECISION TWOPI PARAMETER ( TWOPI = 6.2831853071795864769252867663D+0 ) * .. * .. Local Scalars .. INTEGER I, IL, IL2, IV * .. * .. Local Arrays .. DOUBLE PRECISION U( LV ) * .. * .. Intrinsic Functions .. INTRINSIC COS, LOG, MIN, SQRT * .. * .. External Subroutines .. EXTERNAL DLARUV * .. * .. Executable Statements .. * DO 40 IV = 1, N, LV / 2 IL = MIN( LV / 2, N-IV+1 ) IF( IDIST.EQ.3 ) THEN IL2 = 2*IL ELSE IL2 = IL END IF * * Call DLARUV to generate IL2 numbers from a uniform (0,1) * distribution (IL2 <= LV) * CALL DLARUV( ISEED, IL2, U ) * IF( IDIST.EQ.1 ) THEN * * Copy generated numbers * DO 10 I = 1, IL X( IV+I-1 ) = U( I ) 10 CONTINUE ELSE IF( IDIST.EQ.2 ) THEN * * Convert generated numbers to uniform (-1,1) distribution * DO 20 I = 1, IL X( IV+I-1 ) = TWO*U( I ) - ONE 20 CONTINUE ELSE IF( IDIST.EQ.3 ) THEN * * Convert generated numbers to normal (0,1) distribution * DO 30 I = 1, IL X( IV+I-1 ) = SQRT( -TWO*LOG( U( 2*I-1 ) ) )* $ COS( TWOPI*U( 2*I ) ) 30 CONTINUE END IF 40 CONTINUE RETURN * * End of DLARNV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlagtf.f0000644000000000000000000000013214061636515015265 xustar0030 mtime=1623670093.346103948 30 atime=1623670093.345103949 30 ctime=1623670093.346103948 elk-7.2.42/src/LAPACK/dlagtf.f0000644002504400250440000002005514061636515017324 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal matrix, and λ a scalar, using partial pivoting with row interchanges. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAGTF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, N * DOUBLE PRECISION LAMBDA, TOL * .. * .. Array Arguments .. * INTEGER IN( * ) * DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAGTF factorizes the matrix (T - lambda*I), where T is an n by n *> tridiagonal matrix and lambda is a scalar, as *> *> T - lambda*I = PLU, *> *> where P is a permutation matrix, L is a unit lower tridiagonal matrix *> with at most one non-zero sub-diagonal elements per column and U is *> an upper triangular matrix with at most two non-zero super-diagonal *> elements per column. *> *> The factorization is obtained by Gaussian elimination with partial *> pivoting and implicit row scaling. *> *> The parameter LAMBDA is included in the routine so that DLAGTF may *> be used, in conjunction with DLAGTS, to obtain eigenvectors of T by *> inverse iteration. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix T. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (N) *> On entry, A must contain the diagonal elements of T. *> *> On exit, A is overwritten by the n diagonal elements of the *> upper triangular matrix U of the factorization of T. *> \endverbatim *> *> \param[in] LAMBDA *> \verbatim *> LAMBDA is DOUBLE PRECISION *> On entry, the scalar lambda. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (N-1) *> On entry, B must contain the (n-1) super-diagonal elements of *> T. *> *> On exit, B is overwritten by the (n-1) super-diagonal *> elements of the matrix U of the factorization of T. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (N-1) *> On entry, C must contain the (n-1) sub-diagonal elements of *> T. *> *> On exit, C is overwritten by the (n-1) sub-diagonal elements *> of the matrix L of the factorization of T. *> \endverbatim *> *> \param[in] TOL *> \verbatim *> TOL is DOUBLE PRECISION *> On entry, a relative tolerance used to indicate whether or *> not the matrix (T - lambda*I) is nearly singular. TOL should *> normally be chose as approximately the largest relative error *> in the elements of T. For example, if the elements of T are *> correct to about 4 significant figures, then TOL should be *> set to about 5*10**(-4). If TOL is supplied as less than eps, *> where eps is the relative machine precision, then the value *> eps is used in place of TOL. *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N-2) *> On exit, D is overwritten by the (n-2) second super-diagonal *> elements of the matrix U of the factorization of T. *> \endverbatim *> *> \param[out] IN *> \verbatim *> IN is INTEGER array, dimension (N) *> On exit, IN contains details of the permutation matrix P. If *> an interchange occurred at the kth step of the elimination, *> then IN(k) = 1, otherwise IN(k) = 0. The element IN(n) *> returns the smallest positive integer j such that *> *> abs( u(j,j) ) <= norm( (T - lambda*I)(j) )*TOL, *> *> where norm( A(j) ) denotes the sum of the absolute values of *> the jth row of the matrix A. If no such j exists then IN(n) *> is returned as zero. If IN(n) is returned as positive, then a *> diagonal element of U is small, indicating that *> (T - lambda*I) is singular or nearly singular, *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the kth argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, N DOUBLE PRECISION LAMBDA, TOL * .. * .. Array Arguments .. INTEGER IN( * ) DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER K DOUBLE PRECISION EPS, MULT, PIV1, PIV2, SCALE1, SCALE2, TEMP, TL * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 CALL XERBLA( 'DLAGTF', -INFO ) RETURN END IF * IF( N.EQ.0 ) $ RETURN * A( 1 ) = A( 1 ) - LAMBDA IN( N ) = 0 IF( N.EQ.1 ) THEN IF( A( 1 ).EQ.ZERO ) $ IN( 1 ) = 1 RETURN END IF * EPS = DLAMCH( 'Epsilon' ) * TL = MAX( TOL, EPS ) SCALE1 = ABS( A( 1 ) ) + ABS( B( 1 ) ) DO 10 K = 1, N - 1 A( K+1 ) = A( K+1 ) - LAMBDA SCALE2 = ABS( C( K ) ) + ABS( A( K+1 ) ) IF( K.LT.( N-1 ) ) $ SCALE2 = SCALE2 + ABS( B( K+1 ) ) IF( A( K ).EQ.ZERO ) THEN PIV1 = ZERO ELSE PIV1 = ABS( A( K ) ) / SCALE1 END IF IF( C( K ).EQ.ZERO ) THEN IN( K ) = 0 PIV2 = ZERO SCALE1 = SCALE2 IF( K.LT.( N-1 ) ) $ D( K ) = ZERO ELSE PIV2 = ABS( C( K ) ) / SCALE2 IF( PIV2.LE.PIV1 ) THEN IN( K ) = 0 SCALE1 = SCALE2 C( K ) = C( K ) / A( K ) A( K+1 ) = A( K+1 ) - C( K )*B( K ) IF( K.LT.( N-1 ) ) $ D( K ) = ZERO ELSE IN( K ) = 1 MULT = A( K ) / C( K ) A( K ) = C( K ) TEMP = A( K+1 ) A( K+1 ) = B( K ) - MULT*TEMP IF( K.LT.( N-1 ) ) THEN D( K ) = B( K+1 ) B( K+1 ) = -MULT*D( K ) END IF B( K ) = TEMP C( K ) = MULT END IF END IF IF( ( MAX( PIV1, PIV2 ).LE.TL ) .AND. ( IN( N ).EQ.0 ) ) $ IN( N ) = K 10 CONTINUE IF( ( ABS( A( N ) ).LE.SCALE1*TL ) .AND. ( IN( N ).EQ.0 ) ) $ IN( N ) = N * RETURN * * End of DLAGTF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlagts.f0000644000000000000000000000013214061636515015302 xustar0030 mtime=1623670093.348103946 30 atime=1623670093.347103947 30 ctime=1623670093.348103946 elk-7.2.42/src/LAPACK/dlagts.f0000644002504400250440000003031314061636515017337 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAGTS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, JOB, N * DOUBLE PRECISION TOL * .. * .. Array Arguments .. * INTEGER IN( * ) * DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAGTS may be used to solve one of the systems of equations *> *> (T - lambda*I)*x = y or (T - lambda*I)**T*x = y, *> *> where T is an n by n tridiagonal matrix, for x, following the *> factorization of (T - lambda*I) as *> *> (T - lambda*I) = P*L*U , *> *> by routine DLAGTF. The choice of equation to be solved is *> controlled by the argument JOB, and in each case there is an option *> to perturb zero or very small diagonal elements of U, this option *> being intended for use in applications such as inverse iteration. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOB *> \verbatim *> JOB is INTEGER *> Specifies the job to be performed by DLAGTS as follows: *> = 1: The equations (T - lambda*I)x = y are to be solved, *> but diagonal elements of U are not to be perturbed. *> = -1: The equations (T - lambda*I)x = y are to be solved *> and, if overflow would otherwise occur, the diagonal *> elements of U are to be perturbed. See argument TOL *> below. *> = 2: The equations (T - lambda*I)**Tx = y are to be solved, *> but diagonal elements of U are not to be perturbed. *> = -2: The equations (T - lambda*I)**Tx = y are to be solved *> and, if overflow would otherwise occur, the diagonal *> elements of U are to be perturbed. See argument TOL *> below. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix T. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (N) *> On entry, A must contain the diagonal elements of U as *> returned from DLAGTF. *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (N-1) *> On entry, B must contain the first super-diagonal elements of *> U as returned from DLAGTF. *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (N-1) *> On entry, C must contain the sub-diagonal elements of L as *> returned from DLAGTF. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N-2) *> On entry, D must contain the second super-diagonal elements *> of U as returned from DLAGTF. *> \endverbatim *> *> \param[in] IN *> \verbatim *> IN is INTEGER array, dimension (N) *> On entry, IN must contain details of the matrix P as returned *> from DLAGTF. *> \endverbatim *> *> \param[in,out] Y *> \verbatim *> Y is DOUBLE PRECISION array, dimension (N) *> On entry, the right hand side vector y. *> On exit, Y is overwritten by the solution vector x. *> \endverbatim *> *> \param[in,out] TOL *> \verbatim *> TOL is DOUBLE PRECISION *> On entry, with JOB < 0, TOL should be the minimum *> perturbation to be made to very small diagonal elements of U. *> TOL should normally be chosen as about eps*norm(U), where eps *> is the relative machine precision, but if TOL is supplied as *> non-positive, then it is reset to eps*max( abs( u(i,j) ) ). *> If JOB > 0 then TOL is not referenced. *> *> On exit, TOL is changed as described above, only if TOL is *> non-positive on entry. Otherwise TOL is unchanged. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: overflow would occur when computing the INFO(th) *> element of the solution vector x. This can only occur *> when JOB is supplied as positive and either means *> that a diagonal element of U is very small, or that *> the elements of the right-hand side vector y are very *> large. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, JOB, N DOUBLE PRECISION TOL * .. * .. Array Arguments .. INTEGER IN( * ) DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER K DOUBLE PRECISION ABSAK, AK, BIGNUM, EPS, PERT, SFMIN, TEMP * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SIGN * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * .. Executable Statements .. * INFO = 0 IF( ( ABS( JOB ).GT.2 ) .OR. ( JOB.EQ.0 ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAGTS', -INFO ) RETURN END IF * IF( N.EQ.0 ) $ RETURN * EPS = DLAMCH( 'Epsilon' ) SFMIN = DLAMCH( 'Safe minimum' ) BIGNUM = ONE / SFMIN * IF( JOB.LT.0 ) THEN IF( TOL.LE.ZERO ) THEN TOL = ABS( A( 1 ) ) IF( N.GT.1 ) $ TOL = MAX( TOL, ABS( A( 2 ) ), ABS( B( 1 ) ) ) DO 10 K = 3, N TOL = MAX( TOL, ABS( A( K ) ), ABS( B( K-1 ) ), $ ABS( D( K-2 ) ) ) 10 CONTINUE TOL = TOL*EPS IF( TOL.EQ.ZERO ) $ TOL = EPS END IF END IF * IF( ABS( JOB ).EQ.1 ) THEN DO 20 K = 2, N IF( IN( K-1 ).EQ.0 ) THEN Y( K ) = Y( K ) - C( K-1 )*Y( K-1 ) ELSE TEMP = Y( K-1 ) Y( K-1 ) = Y( K ) Y( K ) = TEMP - C( K-1 )*Y( K ) END IF 20 CONTINUE IF( JOB.EQ.1 ) THEN DO 30 K = N, 1, -1 IF( K.LE.N-2 ) THEN TEMP = Y( K ) - B( K )*Y( K+1 ) - D( K )*Y( K+2 ) ELSE IF( K.EQ.N-1 ) THEN TEMP = Y( K ) - B( K )*Y( K+1 ) ELSE TEMP = Y( K ) END IF AK = A( K ) ABSAK = ABS( AK ) IF( ABSAK.LT.ONE ) THEN IF( ABSAK.LT.SFMIN ) THEN IF( ABSAK.EQ.ZERO .OR. ABS( TEMP )*SFMIN.GT.ABSAK ) $ THEN INFO = K RETURN ELSE TEMP = TEMP*BIGNUM AK = AK*BIGNUM END IF ELSE IF( ABS( TEMP ).GT.ABSAK*BIGNUM ) THEN INFO = K RETURN END IF END IF Y( K ) = TEMP / AK 30 CONTINUE ELSE DO 50 K = N, 1, -1 IF( K.LE.N-2 ) THEN TEMP = Y( K ) - B( K )*Y( K+1 ) - D( K )*Y( K+2 ) ELSE IF( K.EQ.N-1 ) THEN TEMP = Y( K ) - B( K )*Y( K+1 ) ELSE TEMP = Y( K ) END IF AK = A( K ) PERT = SIGN( TOL, AK ) 40 CONTINUE ABSAK = ABS( AK ) IF( ABSAK.LT.ONE ) THEN IF( ABSAK.LT.SFMIN ) THEN IF( ABSAK.EQ.ZERO .OR. ABS( TEMP )*SFMIN.GT.ABSAK ) $ THEN AK = AK + PERT PERT = 2*PERT GO TO 40 ELSE TEMP = TEMP*BIGNUM AK = AK*BIGNUM END IF ELSE IF( ABS( TEMP ).GT.ABSAK*BIGNUM ) THEN AK = AK + PERT PERT = 2*PERT GO TO 40 END IF END IF Y( K ) = TEMP / AK 50 CONTINUE END IF ELSE * * Come to here if JOB = 2 or -2 * IF( JOB.EQ.2 ) THEN DO 60 K = 1, N IF( K.GE.3 ) THEN TEMP = Y( K ) - B( K-1 )*Y( K-1 ) - D( K-2 )*Y( K-2 ) ELSE IF( K.EQ.2 ) THEN TEMP = Y( K ) - B( K-1 )*Y( K-1 ) ELSE TEMP = Y( K ) END IF AK = A( K ) ABSAK = ABS( AK ) IF( ABSAK.LT.ONE ) THEN IF( ABSAK.LT.SFMIN ) THEN IF( ABSAK.EQ.ZERO .OR. ABS( TEMP )*SFMIN.GT.ABSAK ) $ THEN INFO = K RETURN ELSE TEMP = TEMP*BIGNUM AK = AK*BIGNUM END IF ELSE IF( ABS( TEMP ).GT.ABSAK*BIGNUM ) THEN INFO = K RETURN END IF END IF Y( K ) = TEMP / AK 60 CONTINUE ELSE DO 80 K = 1, N IF( K.GE.3 ) THEN TEMP = Y( K ) - B( K-1 )*Y( K-1 ) - D( K-2 )*Y( K-2 ) ELSE IF( K.EQ.2 ) THEN TEMP = Y( K ) - B( K-1 )*Y( K-1 ) ELSE TEMP = Y( K ) END IF AK = A( K ) PERT = SIGN( TOL, AK ) 70 CONTINUE ABSAK = ABS( AK ) IF( ABSAK.LT.ONE ) THEN IF( ABSAK.LT.SFMIN ) THEN IF( ABSAK.EQ.ZERO .OR. ABS( TEMP )*SFMIN.GT.ABSAK ) $ THEN AK = AK + PERT PERT = 2*PERT GO TO 70 ELSE TEMP = TEMP*BIGNUM AK = AK*BIGNUM END IF ELSE IF( ABS( TEMP ).GT.ABSAK*BIGNUM ) THEN AK = AK + PERT PERT = 2*PERT GO TO 70 END IF END IF Y( K ) = TEMP / AK 80 CONTINUE END IF * DO 90 K = N, 2, -1 IF( IN( K-1 ).EQ.0 ) THEN Y( K-1 ) = Y( K-1 ) - C( K-1 )*Y( K ) ELSE TEMP = Y( K-1 ) Y( K-1 ) = Y( K ) Y( K ) = TEMP - C( K-1 )*Y( K ) END IF 90 CONTINUE END IF * * End of DLAGTS * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlatrs.f0000644000000000000000000000013214061636515015343 xustar0030 mtime=1623670093.350103945 30 atime=1623670093.350103945 30 ctime=1623670093.350103945 elk-7.2.42/src/LAPACK/zlatrs.f0000644002504400250440000007253514061636515017414 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLATRS solves a triangular system of equations with the scale factor set to prevent overflow. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLATRS + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, * CNORM, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, NORMIN, TRANS, UPLO * INTEGER INFO, LDA, N * DOUBLE PRECISION SCALE * .. * .. Array Arguments .. * DOUBLE PRECISION CNORM( * ) * COMPLEX*16 A( LDA, * ), X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLATRS solves one of the triangular systems *> *> A * x = s*b, A**T * x = s*b, or A**H * x = s*b, *> *> with scaling to prevent overflow. Here A is an upper or lower *> triangular matrix, A**T denotes the transpose of A, A**H denotes the *> conjugate transpose of A, x and b are n-element vectors, and s is a *> scaling factor, usually less than or equal to 1, chosen so that the *> components of x will be less than the overflow threshold. If the *> unscaled problem will not cause overflow, the Level 2 BLAS routine *> ZTRSV is called. If the matrix A is singular (A(j,j) = 0 for some j), *> then s is set to 0 and a non-trivial solution to A*x = 0 is returned. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the matrix A is upper or lower triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the operation applied to A. *> = 'N': Solve A * x = s*b (No transpose) *> = 'T': Solve A**T * x = s*b (Transpose) *> = 'C': Solve A**H * x = s*b (Conjugate transpose) *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> Specifies whether or not the matrix A is unit triangular. *> = 'N': Non-unit triangular *> = 'U': Unit triangular *> \endverbatim *> *> \param[in] NORMIN *> \verbatim *> NORMIN is CHARACTER*1 *> Specifies whether CNORM has been set or not. *> = 'Y': CNORM contains the column norms on entry *> = 'N': CNORM is not set on entry. On exit, the norms will *> be computed and stored in CNORM. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The triangular matrix A. If UPLO = 'U', the leading n by n *> upper triangular part of the array A contains the upper *> triangular matrix, and the strictly lower triangular part of *> A is not referenced. If UPLO = 'L', the leading n by n lower *> triangular part of the array A contains the lower triangular *> matrix, and the strictly upper triangular part of A is not *> referenced. If DIAG = 'U', the diagonal elements of A are *> also not referenced and are assumed to be 1. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max (1,N). *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension (N) *> On entry, the right hand side b of the triangular system. *> On exit, X is overwritten by the solution vector x. *> \endverbatim *> *> \param[out] SCALE *> \verbatim *> SCALE is DOUBLE PRECISION *> The scaling factor s for the triangular system *> A * x = s*b, A**T * x = s*b, or A**H * x = s*b. *> If SCALE = 0, the matrix A is singular or badly scaled, and *> the vector x is an exact or approximate solution to A*x = 0. *> \endverbatim *> *> \param[in,out] CNORM *> \verbatim *> CNORM is DOUBLE PRECISION array, dimension (N) *> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. *> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup complex16OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> A rough bound on x is computed; if that is less than overflow, ZTRSV *> is called, otherwise, specific code is used which checks for possible *> overflow or divide-by-zero at every operation. *> *> A columnwise scheme is used for solving A*x = b. The basic algorithm *> if A is lower triangular is *> *> x[1:n] := b[1:n] *> for j = 1, ..., n *> x(j) := x(j) / A(j,j) *> x[j+1:n] := x[j+1:n] - x(j) * A[j+1:n,j] *> end *> *> Define bounds on the components of x after j iterations of the loop: *> M(j) = bound on x[1:j] *> G(j) = bound on x[j+1:n] *> Initially, let M(0) = 0 and G(0) = max{x(i), i=1,...,n}. *> *> Then for iteration j+1 we have *> M(j+1) <= G(j) / | A(j+1,j+1) | *> G(j+1) <= G(j) + M(j+1) * | A[j+2:n,j+1] | *> <= G(j) ( 1 + CNORM(j+1) / | A(j+1,j+1) | ) *> *> where CNORM(j+1) is greater than or equal to the infinity-norm of *> column j+1 of A, not counting the diagonal. Hence *> *> G(j) <= G(0) product ( 1 + CNORM(i) / | A(i,i) | ) *> 1<=i<=j *> and *> *> |x(j)| <= ( G(0) / |A(j,j)| ) product ( 1 + CNORM(i) / |A(i,i)| ) *> 1<=i< j *> *> Since |x(j)| <= M(j), we use the Level 2 BLAS routine ZTRSV if the *> reciprocal of the largest M(j), j=1,..,n, is larger than *> max(underflow, 1/overflow). *> *> The bound on x(j) is also used to determine when a step in the *> columnwise method can be performed without fear of overflow. If *> the computed bound is greater than a large constant, x is scaled to *> prevent overflow, but if the bound overflows, x is set to 0, x(j) to *> 1, and scale to 0, and a non-trivial solution to A*x = 0 is found. *> *> Similarly, a row-wise scheme is used to solve A**T *x = b or *> A**H *x = b. The basic algorithm for A upper triangular is *> *> for j = 1, ..., n *> x(j) := ( b(j) - A[1:j-1,j]' * x[1:j-1] ) / A(j,j) *> end *> *> We simultaneously compute two bounds *> G(j) = bound on ( b(i) - A[1:i-1,i]' * x[1:i-1] ), 1<=i<=j *> M(j) = bound on x(i), 1<=i<=j *> *> The initial values are G(0) = 0, M(0) = max{b(i), i=1,..,n}, and we *> add the constraint G(j) >= G(j-1) and M(j) >= M(j-1) for j >= 1. *> Then the bound on x(j) is *> *> M(j) <= M(j-1) * ( 1 + CNORM(j) ) / | A(j,j) | *> *> <= M(0) * product ( ( 1 + CNORM(i) ) / |A(i,i)| ) *> 1<=i<=j *> *> and we can safely call ZTRSV if 1/M(n) and 1/G(n) are both greater *> than max(underflow, 1/overflow). *> \endverbatim *> * ===================================================================== SUBROUTINE ZLATRS( UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, $ CNORM, INFO ) * * -- LAPACK auxiliary routine (version 3.8.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. CHARACTER DIAG, NORMIN, TRANS, UPLO INTEGER INFO, LDA, N DOUBLE PRECISION SCALE * .. * .. Array Arguments .. DOUBLE PRECISION CNORM( * ) COMPLEX*16 A( LDA, * ), X( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, HALF, ONE, TWO PARAMETER ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0, $ TWO = 2.0D+0 ) * .. * .. Local Scalars .. LOGICAL NOTRAN, NOUNIT, UPPER INTEGER I, IMAX, J, JFIRST, JINC, JLAST DOUBLE PRECISION BIGNUM, GROW, REC, SMLNUM, TJJ, TMAX, TSCAL, $ XBND, XJ, XMAX COMPLEX*16 CSUMJ, TJJS, USCAL, ZDUM * .. * .. External Functions .. LOGICAL LSAME INTEGER IDAMAX, IZAMAX DOUBLE PRECISION DLAMCH, DZASUM COMPLEX*16 ZDOTC, ZDOTU, ZLADIV EXTERNAL LSAME, IDAMAX, IZAMAX, DLAMCH, DZASUM, ZDOTC, $ ZDOTU, ZLADIV * .. * .. External Subroutines .. EXTERNAL DSCAL, XERBLA, ZAXPY, ZDSCAL, ZTRSV, DLABAD * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, MIN * .. * .. Statement Functions .. DOUBLE PRECISION CABS1, CABS2 * .. * .. Statement Function definitions .. CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) CABS2( ZDUM ) = ABS( DBLE( ZDUM ) / 2.D0 ) + $ ABS( DIMAG( ZDUM ) / 2.D0 ) * .. * .. Executable Statements .. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) NOTRAN = LSAME( TRANS, 'N' ) NOUNIT = LSAME( DIAG, 'N' ) * * Test the input parameters. * IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. $ LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -3 ELSE IF( .NOT.LSAME( NORMIN, 'Y' ) .AND. .NOT. $ LSAME( NORMIN, 'N' ) ) THEN INFO = -4 ELSE IF( N.LT.0 ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -7 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLATRS', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Determine machine dependent parameters to control overflow. * SMLNUM = DLAMCH( 'Safe minimum' ) BIGNUM = ONE / SMLNUM CALL DLABAD( SMLNUM, BIGNUM ) SMLNUM = SMLNUM / DLAMCH( 'Precision' ) BIGNUM = ONE / SMLNUM SCALE = ONE * IF( LSAME( NORMIN, 'N' ) ) THEN * * Compute the 1-norm of each column, not including the diagonal. * IF( UPPER ) THEN * * A is upper triangular. * DO 10 J = 1, N CNORM( J ) = DZASUM( J-1, A( 1, J ), 1 ) 10 CONTINUE ELSE * * A is lower triangular. * DO 20 J = 1, N - 1 CNORM( J ) = DZASUM( N-J, A( J+1, J ), 1 ) 20 CONTINUE CNORM( N ) = ZERO END IF END IF * * Scale the column norms by TSCAL if the maximum element in CNORM is * greater than BIGNUM/2. * IMAX = IDAMAX( N, CNORM, 1 ) TMAX = CNORM( IMAX ) IF( TMAX.LE.BIGNUM*HALF ) THEN TSCAL = ONE ELSE TSCAL = HALF / ( SMLNUM*TMAX ) CALL DSCAL( N, TSCAL, CNORM, 1 ) END IF * * Compute a bound on the computed solution vector to see if the * Level 2 BLAS routine ZTRSV can be used. * XMAX = ZERO DO 30 J = 1, N XMAX = MAX( XMAX, CABS2( X( J ) ) ) 30 CONTINUE XBND = XMAX * IF( NOTRAN ) THEN * * Compute the growth in A * x = b. * IF( UPPER ) THEN JFIRST = N JLAST = 1 JINC = -1 ELSE JFIRST = 1 JLAST = N JINC = 1 END IF * IF( TSCAL.NE.ONE ) THEN GROW = ZERO GO TO 60 END IF * IF( NOUNIT ) THEN * * A is non-unit triangular. * * Compute GROW = 1/G(j) and XBND = 1/M(j). * Initially, G(0) = max{x(i), i=1,...,n}. * GROW = HALF / MAX( XBND, SMLNUM ) XBND = GROW DO 40 J = JFIRST, JLAST, JINC * * Exit the loop if the growth factor is too small. * IF( GROW.LE.SMLNUM ) $ GO TO 60 * TJJS = A( J, J ) TJJ = CABS1( TJJS ) * IF( TJJ.GE.SMLNUM ) THEN * * M(j) = G(j-1) / abs(A(j,j)) * XBND = MIN( XBND, MIN( ONE, TJJ )*GROW ) ELSE * * M(j) could overflow, set XBND to 0. * XBND = ZERO END IF * IF( TJJ+CNORM( J ).GE.SMLNUM ) THEN * * G(j) = G(j-1)*( 1 + CNORM(j) / abs(A(j,j)) ) * GROW = GROW*( TJJ / ( TJJ+CNORM( J ) ) ) ELSE * * G(j) could overflow, set GROW to 0. * GROW = ZERO END IF 40 CONTINUE GROW = XBND ELSE * * A is unit triangular. * * Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. * GROW = MIN( ONE, HALF / MAX( XBND, SMLNUM ) ) DO 50 J = JFIRST, JLAST, JINC * * Exit the loop if the growth factor is too small. * IF( GROW.LE.SMLNUM ) $ GO TO 60 * * G(j) = G(j-1)*( 1 + CNORM(j) ) * GROW = GROW*( ONE / ( ONE+CNORM( J ) ) ) 50 CONTINUE END IF 60 CONTINUE * ELSE * * Compute the growth in A**T * x = b or A**H * x = b. * IF( UPPER ) THEN JFIRST = 1 JLAST = N JINC = 1 ELSE JFIRST = N JLAST = 1 JINC = -1 END IF * IF( TSCAL.NE.ONE ) THEN GROW = ZERO GO TO 90 END IF * IF( NOUNIT ) THEN * * A is non-unit triangular. * * Compute GROW = 1/G(j) and XBND = 1/M(j). * Initially, M(0) = max{x(i), i=1,...,n}. * GROW = HALF / MAX( XBND, SMLNUM ) XBND = GROW DO 70 J = JFIRST, JLAST, JINC * * Exit the loop if the growth factor is too small. * IF( GROW.LE.SMLNUM ) $ GO TO 90 * * G(j) = max( G(j-1), M(j-1)*( 1 + CNORM(j) ) ) * XJ = ONE + CNORM( J ) GROW = MIN( GROW, XBND / XJ ) * TJJS = A( J, J ) TJJ = CABS1( TJJS ) * IF( TJJ.GE.SMLNUM ) THEN * * M(j) = M(j-1)*( 1 + CNORM(j) ) / abs(A(j,j)) * IF( XJ.GT.TJJ ) $ XBND = XBND*( TJJ / XJ ) ELSE * * M(j) could overflow, set XBND to 0. * XBND = ZERO END IF 70 CONTINUE GROW = MIN( GROW, XBND ) ELSE * * A is unit triangular. * * Compute GROW = 1/G(j), where G(0) = max{x(i), i=1,...,n}. * GROW = MIN( ONE, HALF / MAX( XBND, SMLNUM ) ) DO 80 J = JFIRST, JLAST, JINC * * Exit the loop if the growth factor is too small. * IF( GROW.LE.SMLNUM ) $ GO TO 90 * * G(j) = ( 1 + CNORM(j) )*G(j-1) * XJ = ONE + CNORM( J ) GROW = GROW / XJ 80 CONTINUE END IF 90 CONTINUE END IF * IF( ( GROW*TSCAL ).GT.SMLNUM ) THEN * * Use the Level 2 BLAS solve if the reciprocal of the bound on * elements of X is not too small. * CALL ZTRSV( UPLO, TRANS, DIAG, N, A, LDA, X, 1 ) ELSE * * Use a Level 1 BLAS solve, scaling intermediate results. * IF( XMAX.GT.BIGNUM*HALF ) THEN * * Scale X so that its components are less than or equal to * BIGNUM in absolute value. * SCALE = ( BIGNUM*HALF ) / XMAX CALL ZDSCAL( N, SCALE, X, 1 ) XMAX = BIGNUM ELSE XMAX = XMAX*TWO END IF * IF( NOTRAN ) THEN * * Solve A * x = b * DO 120 J = JFIRST, JLAST, JINC * * Compute x(j) = b(j) / A(j,j), scaling x if necessary. * XJ = CABS1( X( J ) ) IF( NOUNIT ) THEN TJJS = A( J, J )*TSCAL ELSE TJJS = TSCAL IF( TSCAL.EQ.ONE ) $ GO TO 110 END IF TJJ = CABS1( TJJS ) IF( TJJ.GT.SMLNUM ) THEN * * abs(A(j,j)) > SMLNUM: * IF( TJJ.LT.ONE ) THEN IF( XJ.GT.TJJ*BIGNUM ) THEN * * Scale x by 1/b(j). * REC = ONE / XJ CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC XMAX = XMAX*REC END IF END IF X( J ) = ZLADIV( X( J ), TJJS ) XJ = CABS1( X( J ) ) ELSE IF( TJJ.GT.ZERO ) THEN * * 0 < abs(A(j,j)) <= SMLNUM: * IF( XJ.GT.TJJ*BIGNUM ) THEN * * Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM * to avoid overflow when dividing by A(j,j). * REC = ( TJJ*BIGNUM ) / XJ IF( CNORM( J ).GT.ONE ) THEN * * Scale by 1/CNORM(j) to avoid overflow when * multiplying x(j) times column j. * REC = REC / CNORM( J ) END IF CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC XMAX = XMAX*REC END IF X( J ) = ZLADIV( X( J ), TJJS ) XJ = CABS1( X( J ) ) ELSE * * A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and * scale = 0, and compute a solution to A*x = 0. * DO 100 I = 1, N X( I ) = ZERO 100 CONTINUE X( J ) = ONE XJ = ONE SCALE = ZERO XMAX = ZERO END IF 110 CONTINUE * * Scale x if necessary to avoid overflow when adding a * multiple of column j of A. * IF( XJ.GT.ONE ) THEN REC = ONE / XJ IF( CNORM( J ).GT.( BIGNUM-XMAX )*REC ) THEN * * Scale x by 1/(2*abs(x(j))). * REC = REC*HALF CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC END IF ELSE IF( XJ*CNORM( J ).GT.( BIGNUM-XMAX ) ) THEN * * Scale x by 1/2. * CALL ZDSCAL( N, HALF, X, 1 ) SCALE = SCALE*HALF END IF * IF( UPPER ) THEN IF( J.GT.1 ) THEN * * Compute the update * x(1:j-1) := x(1:j-1) - x(j) * A(1:j-1,j) * CALL ZAXPY( J-1, -X( J )*TSCAL, A( 1, J ), 1, X, $ 1 ) I = IZAMAX( J-1, X, 1 ) XMAX = CABS1( X( I ) ) END IF ELSE IF( J.LT.N ) THEN * * Compute the update * x(j+1:n) := x(j+1:n) - x(j) * A(j+1:n,j) * CALL ZAXPY( N-J, -X( J )*TSCAL, A( J+1, J ), 1, $ X( J+1 ), 1 ) I = J + IZAMAX( N-J, X( J+1 ), 1 ) XMAX = CABS1( X( I ) ) END IF END IF 120 CONTINUE * ELSE IF( LSAME( TRANS, 'T' ) ) THEN * * Solve A**T * x = b * DO 170 J = JFIRST, JLAST, JINC * * Compute x(j) = b(j) - sum A(k,j)*x(k). * k<>j * XJ = CABS1( X( J ) ) USCAL = TSCAL REC = ONE / MAX( XMAX, ONE ) IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN * * If x(j) could overflow, scale x by 1/(2*XMAX). * REC = REC*HALF IF( NOUNIT ) THEN TJJS = A( J, J )*TSCAL ELSE TJJS = TSCAL END IF TJJ = CABS1( TJJS ) IF( TJJ.GT.ONE ) THEN * * Divide by A(j,j) when scaling x if A(j,j) > 1. * REC = MIN( ONE, REC*TJJ ) USCAL = ZLADIV( USCAL, TJJS ) END IF IF( REC.LT.ONE ) THEN CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC XMAX = XMAX*REC END IF END IF * CSUMJ = ZERO IF( USCAL.EQ.DCMPLX( ONE ) ) THEN * * If the scaling needed for A in the dot product is 1, * call ZDOTU to perform the dot product. * IF( UPPER ) THEN CSUMJ = ZDOTU( J-1, A( 1, J ), 1, X, 1 ) ELSE IF( J.LT.N ) THEN CSUMJ = ZDOTU( N-J, A( J+1, J ), 1, X( J+1 ), 1 ) END IF ELSE * * Otherwise, use in-line code for the dot product. * IF( UPPER ) THEN DO 130 I = 1, J - 1 CSUMJ = CSUMJ + ( A( I, J )*USCAL )*X( I ) 130 CONTINUE ELSE IF( J.LT.N ) THEN DO 140 I = J + 1, N CSUMJ = CSUMJ + ( A( I, J )*USCAL )*X( I ) 140 CONTINUE END IF END IF * IF( USCAL.EQ.DCMPLX( TSCAL ) ) THEN * * Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) * was not used to scale the dotproduct. * X( J ) = X( J ) - CSUMJ XJ = CABS1( X( J ) ) IF( NOUNIT ) THEN TJJS = A( J, J )*TSCAL ELSE TJJS = TSCAL IF( TSCAL.EQ.ONE ) $ GO TO 160 END IF * * Compute x(j) = x(j) / A(j,j), scaling if necessary. * TJJ = CABS1( TJJS ) IF( TJJ.GT.SMLNUM ) THEN * * abs(A(j,j)) > SMLNUM: * IF( TJJ.LT.ONE ) THEN IF( XJ.GT.TJJ*BIGNUM ) THEN * * Scale X by 1/abs(x(j)). * REC = ONE / XJ CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC XMAX = XMAX*REC END IF END IF X( J ) = ZLADIV( X( J ), TJJS ) ELSE IF( TJJ.GT.ZERO ) THEN * * 0 < abs(A(j,j)) <= SMLNUM: * IF( XJ.GT.TJJ*BIGNUM ) THEN * * Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. * REC = ( TJJ*BIGNUM ) / XJ CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC XMAX = XMAX*REC END IF X( J ) = ZLADIV( X( J ), TJJS ) ELSE * * A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and * scale = 0 and compute a solution to A**T *x = 0. * DO 150 I = 1, N X( I ) = ZERO 150 CONTINUE X( J ) = ONE SCALE = ZERO XMAX = ZERO END IF 160 CONTINUE ELSE * * Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot * product has already been divided by 1/A(j,j). * X( J ) = ZLADIV( X( J ), TJJS ) - CSUMJ END IF XMAX = MAX( XMAX, CABS1( X( J ) ) ) 170 CONTINUE * ELSE * * Solve A**H * x = b * DO 220 J = JFIRST, JLAST, JINC * * Compute x(j) = b(j) - sum A(k,j)*x(k). * k<>j * XJ = CABS1( X( J ) ) USCAL = TSCAL REC = ONE / MAX( XMAX, ONE ) IF( CNORM( J ).GT.( BIGNUM-XJ )*REC ) THEN * * If x(j) could overflow, scale x by 1/(2*XMAX). * REC = REC*HALF IF( NOUNIT ) THEN TJJS = DCONJG( A( J, J ) )*TSCAL ELSE TJJS = TSCAL END IF TJJ = CABS1( TJJS ) IF( TJJ.GT.ONE ) THEN * * Divide by A(j,j) when scaling x if A(j,j) > 1. * REC = MIN( ONE, REC*TJJ ) USCAL = ZLADIV( USCAL, TJJS ) END IF IF( REC.LT.ONE ) THEN CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC XMAX = XMAX*REC END IF END IF * CSUMJ = ZERO IF( USCAL.EQ.DCMPLX( ONE ) ) THEN * * If the scaling needed for A in the dot product is 1, * call ZDOTC to perform the dot product. * IF( UPPER ) THEN CSUMJ = ZDOTC( J-1, A( 1, J ), 1, X, 1 ) ELSE IF( J.LT.N ) THEN CSUMJ = ZDOTC( N-J, A( J+1, J ), 1, X( J+1 ), 1 ) END IF ELSE * * Otherwise, use in-line code for the dot product. * IF( UPPER ) THEN DO 180 I = 1, J - 1 CSUMJ = CSUMJ + ( DCONJG( A( I, J ) )*USCAL )* $ X( I ) 180 CONTINUE ELSE IF( J.LT.N ) THEN DO 190 I = J + 1, N CSUMJ = CSUMJ + ( DCONJG( A( I, J ) )*USCAL )* $ X( I ) 190 CONTINUE END IF END IF * IF( USCAL.EQ.DCMPLX( TSCAL ) ) THEN * * Compute x(j) := ( x(j) - CSUMJ ) / A(j,j) if 1/A(j,j) * was not used to scale the dotproduct. * X( J ) = X( J ) - CSUMJ XJ = CABS1( X( J ) ) IF( NOUNIT ) THEN TJJS = DCONJG( A( J, J ) )*TSCAL ELSE TJJS = TSCAL IF( TSCAL.EQ.ONE ) $ GO TO 210 END IF * * Compute x(j) = x(j) / A(j,j), scaling if necessary. * TJJ = CABS1( TJJS ) IF( TJJ.GT.SMLNUM ) THEN * * abs(A(j,j)) > SMLNUM: * IF( TJJ.LT.ONE ) THEN IF( XJ.GT.TJJ*BIGNUM ) THEN * * Scale X by 1/abs(x(j)). * REC = ONE / XJ CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC XMAX = XMAX*REC END IF END IF X( J ) = ZLADIV( X( J ), TJJS ) ELSE IF( TJJ.GT.ZERO ) THEN * * 0 < abs(A(j,j)) <= SMLNUM: * IF( XJ.GT.TJJ*BIGNUM ) THEN * * Scale x by (1/abs(x(j)))*abs(A(j,j))*BIGNUM. * REC = ( TJJ*BIGNUM ) / XJ CALL ZDSCAL( N, REC, X, 1 ) SCALE = SCALE*REC XMAX = XMAX*REC END IF X( J ) = ZLADIV( X( J ), TJJS ) ELSE * * A(j,j) = 0: Set x(1:n) = 0, x(j) = 1, and * scale = 0 and compute a solution to A**H *x = 0. * DO 200 I = 1, N X( I ) = ZERO 200 CONTINUE X( J ) = ONE SCALE = ZERO XMAX = ZERO END IF 210 CONTINUE ELSE * * Compute x(j) := x(j) / A(j,j) - CSUMJ if the dot * product has already been divided by 1/A(j,j). * X( J ) = ZLADIV( X( J ), TJJS ) - CSUMJ END IF XMAX = MAX( XMAX, CABS1( X( J ) ) ) 220 CONTINUE END IF SCALE = SCALE / TSCAL END IF * * Scale the column norms by 1/TSCAL for return. * IF( TSCAL.NE.ONE ) THEN CALL DSCAL( N, ONE / TSCAL, CNORM, 1 ) END IF * RETURN * * End of ZLATRS * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/ztrti2.f0000644000000000000000000000013214061636515015262 xustar0030 mtime=1623670093.352103943 30 atime=1623670093.352103943 30 ctime=1623670093.352103943 elk-7.2.42/src/LAPACK/ztrti2.f0000644002504400250440000001343714061636515017327 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTRTI2 computes the inverse of a triangular matrix (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZTRTI2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZTRTI2( UPLO, DIAG, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTRTI2 computes the inverse of a complex upper or lower triangular *> matrix. *> *> This is the Level 2 BLAS version of the algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the matrix A is upper or lower triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> Specifies whether or not the matrix A is unit triangular. *> = 'N': Non-unit triangular *> = 'U': Unit triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the triangular matrix A. If UPLO = 'U', the *> leading n by n upper triangular part of the array A contains *> the upper triangular matrix, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n by n lower triangular part of the array A contains *> the lower triangular matrix, and the strictly upper *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. *> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZTRTI2( UPLO, DIAG, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER J COMPLEX*16 AJJ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZSCAL, ZTRMV * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) NOUNIT = LSAME( DIAG, 'N' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZTRTI2', -INFO ) RETURN END IF * IF( UPPER ) THEN * * Compute inverse of upper triangular matrix. * DO 10 J = 1, N IF( NOUNIT ) THEN A( J, J ) = ONE / A( J, J ) AJJ = -A( J, J ) ELSE AJJ = -ONE END IF * * Compute elements 1:j-1 of j-th column. * CALL ZTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA, $ A( 1, J ), 1 ) CALL ZSCAL( J-1, AJJ, A( 1, J ), 1 ) 10 CONTINUE ELSE * * Compute inverse of lower triangular matrix. * DO 20 J = N, 1, -1 IF( NOUNIT ) THEN A( J, J ) = ONE / A( J, J ) AJJ = -A( J, J ) ELSE AJJ = -ONE END IF IF( J.LT.N ) THEN * * Compute elements j+1:n of j-th column. * CALL ZTRMV( 'Lower', 'No transpose', DIAG, N-J, $ A( J+1, J+1 ), LDA, A( J+1, J ), 1 ) CALL ZSCAL( N-J, AJJ, A( J+1, J ), 1 ) END IF 20 CONTINUE END IF * RETURN * * End of ZTRTI2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zungl2.f0000644000000000000000000000013214061636515015245 xustar0030 mtime=1623670093.354103941 30 atime=1623670093.354103941 30 ctime=1623670093.354103941 elk-7.2.42/src/LAPACK/zungl2.f0000644002504400250440000001264514061636515017312 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNGL2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows, *> which is defined as the first m rows of a product of k elementary *> reflectors of order n *> *> Q = H(k)**H . . . H(2)**H H(1)**H *> *> as returned by ZGELQF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. N >= M. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. M >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the i-th row must contain the vector which defines *> the elementary reflector H(i), for i = 1,2,...,k, as returned *> by ZGELQF in the first k rows of its array argument A. *> On exit, the m by n matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGELQF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (M) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNGL2( M, N, K, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, J, L * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLACGV, ZLARF, ZSCAL * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNGL2', -INFO ) RETURN END IF * * Quick return if possible * IF( M.LE.0 ) $ RETURN * IF( K.LT.M ) THEN * * Initialise rows k+1:m to rows of the unit matrix * DO 20 J = 1, N DO 10 L = K + 1, M A( L, J ) = ZERO 10 CONTINUE IF( J.GT.K .AND. J.LE.M ) $ A( J, J ) = ONE 20 CONTINUE END IF * DO 40 I = K, 1, -1 * * Apply H(i)**H to A(i:m,i:n) from the right * IF( I.LT.N ) THEN CALL ZLACGV( N-I, A( I, I+1 ), LDA ) IF( I.LT.M ) THEN A( I, I ) = ONE CALL ZLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, $ DCONJG( TAU( I ) ), A( I+1, I ), LDA, WORK ) END IF CALL ZSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA ) CALL ZLACGV( N-I, A( I, I+1 ), LDA ) END IF A( I, I ) = ONE - DCONJG( TAU( I ) ) * * Set A(i,1:i-1) to zero * DO 30 L = 1, I - 1 A( I, L ) = ZERO 30 CONTINUE 40 CONTINUE RETURN * * End of ZUNGL2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zung2r.f0000644000000000000000000000013114061636515015252 xustar0030 mtime=1623670093.356103939 29 atime=1623670093.35510394 30 ctime=1623670093.356103939 elk-7.2.42/src/LAPACK/zung2r.f0000644002504400250440000001210014061636515017302 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNG2R * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNG2R + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNG2R generates an m by n complex matrix Q with orthonormal columns, *> which is defined as the first n columns of a product of k elementary *> reflectors of order m *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by ZGEQRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. M >= N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the i-th column must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by ZGEQRF in the first k columns of its array *> argument A. *> On exit, the m by n matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEQRF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNG2R( M, N, K, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, J, L * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF, ZSCAL * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNG2R', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.0 ) $ RETURN * * Initialise columns k+1:n to columns of the unit matrix * DO 20 J = K + 1, N DO 10 L = 1, M A( L, J ) = ZERO 10 CONTINUE A( J, J ) = ONE 20 CONTINUE * DO 40 I = K, 1, -1 * * Apply H(i) to A(i:m,i:n) from the left * IF( I.LT.N ) THEN A( I, I ) = ONE CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), $ A( I, I+1 ), LDA, WORK ) END IF IF( I.LT.M ) $ CALL ZSCAL( M-I, -TAU( I ), A( I+1, I ), 1 ) A( I, I ) = ONE - TAU( I ) * * Set A(1:i-1,i) to zero * DO 30 L = 1, I - 1 A( L, I ) = ZERO 30 CONTINUE 40 CONTINUE RETURN * * End of ZUNG2R * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zungql.f0000644000000000000000000000013214061636515015344 xustar0030 mtime=1623670093.358103937 30 atime=1623670093.357103938 30 ctime=1623670093.358103937 elk-7.2.42/src/LAPACK/zungql.f0000644002504400250440000002000614061636515017377 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNGQL * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNGQL + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNGQL generates an M-by-N complex matrix Q with orthonormal columns, *> which is defined as the last N columns of a product of K elementary *> reflectors of order M *> *> Q = H(k) . . . H(2) H(1) *> *> as returned by ZGEQLF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. M >= N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the (n-k+i)-th column must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by ZGEQLF in the last k columns of its array *> argument A. *> On exit, the M-by-N matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEQLF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY INTEGER I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT, $ NB, NBMIN, NX * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNG2L * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LQUERY = ( LWORK.EQ.-1 ) IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF * IF( INFO.EQ.0 ) THEN IF( N.EQ.0 ) THEN LWKOPT = 1 ELSE NB = ILAENV( 1, 'ZUNGQL', ' ', M, N, K, -1 ) LWKOPT = N*NB END IF WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN INFO = -8 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNGQL', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.LE.0 ) THEN RETURN END IF * NBMIN = 2 NX = 0 IWS = N IF( NB.GT.1 .AND. NB.LT.K ) THEN * * Determine when to cross over from blocked to unblocked code. * NX = MAX( 0, ILAENV( 3, 'ZUNGQL', ' ', M, N, K, -1 ) ) IF( NX.LT.K ) THEN * * Determine if workspace is large enough for blocked code. * LDWORK = N IWS = LDWORK*NB IF( LWORK.LT.IWS ) THEN * * Not enough workspace to use optimal NB: reduce NB and * determine the minimum value of NB. * NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZUNGQL', ' ', M, N, K, -1 ) ) END IF END IF END IF * IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN * * Use blocked code after the first block. * The last kk columns are handled by the block method. * KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB ) * * Set A(m-kk+1:m,1:n-kk) to zero. * DO 20 J = 1, N - KK DO 10 I = M - KK + 1, M A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE KK = 0 END IF * * Use unblocked code for the first or only block. * CALL ZUNG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO ) * IF( KK.GT.0 ) THEN * * Use blocked code * DO 50 I = K - KK + 1, K, NB IB = MIN( NB, K-I+1 ) IF( N-K+I.GT.1 ) THEN * * Form the triangular factor of the block reflector * H = H(i+ib-1) . . . H(i+1) H(i) * CALL ZLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB, $ A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK ) * * Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left * CALL ZLARFB( 'Left', 'No transpose', 'Backward', $ 'Columnwise', M-K+I+IB-1, N-K+I-1, IB, $ A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA, $ WORK( IB+1 ), LDWORK ) END IF * * Apply H to rows 1:m-k+i+ib-1 of current block * CALL ZUNG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA, $ TAU( I ), WORK, IINFO ) * * Set rows m-k+i+ib:m of current block to zero * DO 40 J = N - K + I, N - K + I + IB - 1 DO 30 L = M - K + I + IB, M A( L, J ) = ZERO 30 CONTINUE 40 CONTINUE 50 CONTINUE END IF * WORK( 1 ) = IWS RETURN * * End of ZUNGQL * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunmqr.f0000644000000000000000000000013214061636515015360 xustar0030 mtime=1623670093.359103936 30 atime=1623670093.359103936 30 ctime=1623670093.359103936 elk-7.2.42/src/LAPACK/zunmqr.f0000644002504400250440000002223114061636515017415 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNMQR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNMQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNMQR overwrites the general complex M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'C': Q**H * C C * Q**H *> *> where Q is a complex unitary matrix defined as the product of k *> elementary reflectors *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by ZGEQRF. Q is of order M if SIDE = 'L' and of order N *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left; *> = 'R': apply Q or Q**H from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'C': Conjugate transpose, apply Q**H. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> ZGEQRF in the first k columns of its array argument A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,M); *> if SIDE = 'R', LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEQRF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For good performance, LWORK should generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NBMAX, LDT, TSIZE PARAMETER ( NBMAX = 64, LDT = NBMAX+1, $ TSIZE = LDT*NBMAX ) * .. * .. Local Scalars .. LOGICAL LEFT, LQUERY, NOTRAN INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK, $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNM2R * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -12 END IF * IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * NB = MIN( NBMAX, ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N, K, $ -1 ) ) LWKOPT = MAX( 1, NW )*NB + TSIZE WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNMQR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NBMIN = 2 LDWORK = NW IF( NB.GT.1 .AND. NB.LT.K ) THEN IF( LWORK.LT.NW*NB+TSIZE ) THEN NB = (LWORK-TSIZE) / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZUNMQR', SIDE // TRANS, M, N, K, $ -1 ) ) END IF END IF * IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN * * Use unblocked code * CALL ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, $ IINFO ) ELSE * * Use blocked code * IWT = 1 + NW*NB IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN I1 = 1 I2 = K I3 = NB ELSE I1 = ( ( K-1 ) / NB )*NB + 1 I2 = 1 I3 = -NB END IF * IF( LEFT ) THEN NI = N JC = 1 ELSE MI = M IC = 1 END IF * DO 10 I = I1, I2, I3 IB = MIN( NB, K-I+1 ) * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL ZLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ), $ LDA, TAU( I ), WORK( IWT ), LDT ) IF( LEFT ) THEN * * H or H**H is applied to C(i:m,1:n) * MI = M - I + 1 IC = I ELSE * * H or H**H is applied to C(1:m,i:n) * NI = N - I + 1 JC = I END IF * * Apply H or H**H * CALL ZLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI, $ IB, A( I, I ), LDA, WORK( IWT ), LDT, $ C( IC, JC ), LDC, WORK, LDWORK ) 10 CONTINUE END IF WORK( 1 ) = LWKOPT RETURN * * End of ZUNMQR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunmlq.f0000644000000000000000000000013214061636515015352 xustar0030 mtime=1623670093.361103934 30 atime=1623670093.361103934 30 ctime=1623670093.361103934 elk-7.2.42/src/LAPACK/zunmlq.f0000644002504400250440000002250314061636515017411 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNMLQ * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNMLQ + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNMLQ overwrites the general complex M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'C': Q**H * C C * Q**H *> *> where Q is a complex unitary matrix defined as the product of k *> elementary reflectors *> *> Q = H(k)**H . . . H(2)**H H(1)**H *> *> as returned by ZGELQF. Q is of order M if SIDE = 'L' and of order N *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left; *> = 'R': apply Q or Q**H from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'C': Conjugate transpose, apply Q**H. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension *> (LDA,M) if SIDE = 'L', *> (LDA,N) if SIDE = 'R' *> The i-th row must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> ZGELQF in the first k rows of its array argument A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,K). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGELQF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For good performance, LWORK should generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NBMAX, LDT, TSIZE PARAMETER ( NBMAX = 64, LDT = NBMAX+1, $ TSIZE = LDT*NBMAX ) * .. * .. Local Scalars .. LOGICAL LEFT, LQUERY, NOTRAN CHARACTER TRANST INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK, $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNML2 * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -12 END IF * IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * NB = MIN( NBMAX, ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N, K, $ -1 ) ) LWKOPT = MAX( 1, NW )*NB + TSIZE WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNMLQ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NBMIN = 2 LDWORK = NW IF( NB.GT.1 .AND. NB.LT.K ) THEN IF( LWORK.LT.NW*NB+TSIZE ) THEN NB = (LWORK-TSIZE) / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZUNMLQ', SIDE // TRANS, M, N, K, $ -1 ) ) END IF END IF * IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN * * Use unblocked code * CALL ZUNML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, $ IINFO ) ELSE * * Use blocked code * IWT = 1 + NW*NB IF( ( LEFT .AND. NOTRAN ) .OR. $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN I1 = 1 I2 = K I3 = NB ELSE I1 = ( ( K-1 ) / NB )*NB + 1 I2 = 1 I3 = -NB END IF * IF( LEFT ) THEN NI = N JC = 1 ELSE MI = M IC = 1 END IF * IF( NOTRAN ) THEN TRANST = 'C' ELSE TRANST = 'N' END IF * DO 10 I = I1, I2, I3 IB = MIN( NB, K-I+1 ) * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL ZLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ), $ LDA, TAU( I ), WORK( IWT ), LDT ) IF( LEFT ) THEN * * H or H**H is applied to C(i:m,1:n) * MI = M - I + 1 IC = I ELSE * * H or H**H is applied to C(1:m,i:n) * NI = N - I + 1 JC = I END IF * * Apply H or H**H * CALL ZLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB, $ A( I, I ), LDA, WORK( IWT ), LDT, $ C( IC, JC ), LDC, WORK, LDWORK ) 10 CONTINUE END IF WORK( 1 ) = LWKOPT RETURN * * End of ZUNMLQ * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunmql.f0000644000000000000000000000013214061636515015352 xustar0030 mtime=1623670093.363103932 30 atime=1623670093.363103932 30 ctime=1623670093.363103932 elk-7.2.42/src/LAPACK/zunmql.f0000644002504400250440000002225314061636515017413 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNMQL * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNMQL + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNMQL overwrites the general complex M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'C': Q**H * C C * Q**H *> *> where Q is a complex unitary matrix defined as the product of k *> elementary reflectors *> *> Q = H(k) . . . H(2) H(1) *> *> as returned by ZGEQLF. Q is of order M if SIDE = 'L' and of order N *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left; *> = 'R': apply Q or Q**H from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'C': Transpose, apply Q**H. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> ZGEQLF in the last k columns of its array argument A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,M); *> if SIDE = 'R', LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEQLF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For good performance, LWORK should genreally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NBMAX, LDT, TSIZE PARAMETER ( NBMAX = 64, LDT = NBMAX+1, $ TSIZE = LDT*NBMAX ) * .. * .. Local Scalars .. LOGICAL LEFT, LQUERY, NOTRAN INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT, $ MI, NB, NBMIN, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNM2L * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = MAX( 1, N ) ELSE NQ = N NW = MAX( 1, M ) END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN INFO = -12 END IF * IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * IF( M.EQ.0 .OR. N.EQ.0 ) THEN LWKOPT = 1 ELSE NB = MIN( NBMAX, ILAENV( 1, 'ZUNMQL', SIDE // TRANS, M, N, $ K, -1 ) ) LWKOPT = NW*NB + TSIZE END IF WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNMQL', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) THEN RETURN END IF * NBMIN = 2 LDWORK = NW IF( NB.GT.1 .AND. NB.LT.K ) THEN IF( LWORK.LT.NW*NB+TSIZE ) THEN NB = (LWORK-TSIZE) / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'ZUNMQL', SIDE // TRANS, M, N, K, $ -1 ) ) END IF END IF * IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN * * Use unblocked code * CALL ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, $ IINFO ) ELSE * * Use blocked code * IWT = 1 + NW*NB IF( ( LEFT .AND. NOTRAN ) .OR. $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN I1 = 1 I2 = K I3 = NB ELSE I1 = ( ( K-1 ) / NB )*NB + 1 I2 = 1 I3 = -NB END IF * IF( LEFT ) THEN NI = N ELSE MI = M END IF * DO 10 I = I1, I2, I3 IB = MIN( NB, K-I+1 ) * * Form the triangular factor of the block reflector * H = H(i+ib-1) . . . H(i+1) H(i) * CALL ZLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB, $ A( 1, I ), LDA, TAU( I ), WORK( IWT ), LDT ) IF( LEFT ) THEN * * H or H**H is applied to C(1:m-k+i+ib-1,1:n) * MI = M - K + I + IB - 1 ELSE * * H or H**H is applied to C(1:m,1:n-k+i+ib-1) * NI = N - K + I + IB - 1 END IF * * Apply H or H**H * CALL ZLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI, $ IB, A( 1, I ), LDA, WORK( IWT ), LDT, C, LDC, $ WORK, LDWORK ) 10 CONTINUE END IF WORK( 1 ) = LWKOPT RETURN * * End of ZUNMQL * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zung2l.f0000644000000000000000000000013214061636515015245 xustar0030 mtime=1623670093.365103931 30 atime=1623670093.365103931 30 ctime=1623670093.365103931 elk-7.2.42/src/LAPACK/zung2l.f0000644002504400250440000001225014061636515017302 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNG2L + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNG2L generates an m by n complex matrix Q with orthonormal columns, *> which is defined as the last n columns of a product of k elementary *> reflectors of order m *> *> Q = H(k) . . . H(2) H(1) *> *> as returned by ZGEQLF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. M >= N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the (n-k+i)-th column must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by ZGEQLF in the last k columns of its array *> argument A. *> On exit, the m-by-n matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEQLF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNG2L( M, N, K, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, II, J, L * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF, ZSCAL * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNG2L', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.0 ) $ RETURN * * Initialise columns 1:n-k to columns of the unit matrix * DO 20 J = 1, N - K DO 10 L = 1, M A( L, J ) = ZERO 10 CONTINUE A( M-N+J, J ) = ONE 20 CONTINUE * DO 40 I = 1, K II = N - K + I * * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left * A( M-N+II, II ) = ONE CALL ZLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A, $ LDA, WORK ) CALL ZSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 ) A( M-N+II, II ) = ONE - TAU( I ) * * Set A(m-k+i+1:m,n-k+i) to zero * DO 30 L = M - N + II + 1, M A( L, II ) = ZERO 30 CONTINUE 40 CONTINUE RETURN * * End of ZUNG2L * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlarf.f0000644000000000000000000000013214061636515015142 xustar0030 mtime=1623670093.367103929 30 atime=1623670093.367103929 30 ctime=1623670093.367103929 elk-7.2.42/src/LAPACK/zlarf.f0000644002504400250440000001426714061636515017211 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLARF applies an elementary reflector to a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLARF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) * * .. Scalar Arguments .. * CHARACTER SIDE * INTEGER INCV, LDC, M, N * COMPLEX*16 TAU * .. * .. Array Arguments .. * COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLARF applies a complex elementary reflector H to a complex M-by-N *> matrix C, from either the left or the right. H is represented in the *> form *> *> H = I - tau * v * v**H *> *> where tau is a complex scalar and v is a complex vector. *> *> If tau = 0, then H is taken to be the unit matrix. *> *> To apply H**H, supply conjg(tau) instead *> tau. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': form H * C *> = 'R': form C * H *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is COMPLEX*16 array, dimension *> (1 + (M-1)*abs(INCV)) if SIDE = 'L' *> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' *> The vector v in the representation of H. V is not used if *> TAU = 0. *> \endverbatim *> *> \param[in] INCV *> \verbatim *> INCV is INTEGER *> The increment between elements of v. INCV <> 0. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 *> The value tau in the representation of H. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by the matrix H * C if SIDE = 'L', *> or C * H if SIDE = 'R'. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension *> (N) if SIDE = 'L' *> or (M) if SIDE = 'R' *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE INTEGER INCV, LDC, M, N COMPLEX*16 TAU * .. * .. Array Arguments .. COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), $ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL APPLYLEFT INTEGER I, LASTV, LASTC * .. * .. External Subroutines .. EXTERNAL ZGEMV, ZGERC * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAZLR, ILAZLC EXTERNAL LSAME, ILAZLR, ILAZLC * .. * .. Executable Statements .. * APPLYLEFT = LSAME( SIDE, 'L' ) LASTV = 0 LASTC = 0 IF( TAU.NE.ZERO ) THEN * Set up variables for scanning V. LASTV begins pointing to the end * of V. IF( APPLYLEFT ) THEN LASTV = M ELSE LASTV = N END IF IF( INCV.GT.0 ) THEN I = 1 + (LASTV-1) * INCV ELSE I = 1 END IF * Look for the last non-zero row in V. DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) LASTV = LASTV - 1 I = I - INCV END DO IF( APPLYLEFT ) THEN * Scan for the last non-zero column in C(1:lastv,:). LASTC = ILAZLC(LASTV, N, C, LDC) ELSE * Scan for the last non-zero row in C(:,1:lastv). LASTC = ILAZLR(M, LASTV, C, LDC) END IF END IF * Note that lastc.eq.0 renders the BLAS operations null; no special * case is needed at this level. IF( APPLYLEFT ) THEN * * Form H * C * IF( LASTV.GT.0 ) THEN * * w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1) * CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE, $ C, LDC, V, INCV, ZERO, WORK, 1 ) * * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H * CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) END IF ELSE * * Form C * H * IF( LASTV.GT.0 ) THEN * * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) * CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, $ V, INCV, ZERO, WORK, 1 ) * * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H * CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) END IF END IF RETURN * * End of ZLARF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed2.f0000644000000000000000000000013214061636515015157 xustar0030 mtime=1623670093.369103927 30 atime=1623670093.369103927 30 ctime=1623670093.369103927 elk-7.2.42/src/LAPACK/dlaed2.f0000644002504400250440000003723114061636515017222 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, * Q2, INDX, INDXC, INDXP, COLTYP, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDQ, N, N1 * DOUBLE PRECISION RHO * .. * .. Array Arguments .. * INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ), * $ INDXQ( * ) * DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), * $ W( * ), Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAED2 merges the two sets of eigenvalues together into a single *> sorted set. Then it tries to deflate the size of the problem. *> There are two ways in which deflation can occur: when two or more *> eigenvalues are close together or if there is a tiny entry in the *> Z vector. For each such occurrence the order of the related secular *> equation problem is reduced by one. *> \endverbatim * * Arguments: * ========== * *> \param[out] K *> \verbatim *> K is INTEGER *> The number of non-deflated eigenvalues, and the order of the *> related secular equation. 0 <= K <=N. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in] N1 *> \verbatim *> N1 is INTEGER *> The location of the last eigenvalue in the leading sub-matrix. *> min(1,N) <= N1 <= N/2. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, D contains the eigenvalues of the two submatrices to *> be combined. *> On exit, D contains the trailing (N-K) updated eigenvalues *> (those which were deflated) sorted into increasing order. *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDQ, N) *> On entry, Q contains the eigenvectors of two submatrices in *> the two square blocks with corners at (1,1), (N1,N1) *> and (N1+1, N1+1), (N,N). *> On exit, Q contains the trailing (N-K) updated eigenvectors *> (those which were deflated) in its last N-K columns. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[in,out] INDXQ *> \verbatim *> INDXQ is INTEGER array, dimension (N) *> The permutation which separately sorts the two sub-problems *> in D into ascending order. Note that elements in the second *> half of this permutation must first have N1 added to their *> values. Destroyed on exit. *> \endverbatim *> *> \param[in,out] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> On entry, the off-diagonal element associated with the rank-1 *> cut which originally split the two submatrices which are now *> being recombined. *> On exit, RHO has been modified to the value required by *> DLAED3. *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (N) *> On entry, Z contains the updating vector (the last *> row of the first sub-eigenvector matrix and the first row of *> the second sub-eigenvector matrix). *> On exit, the contents of Z have been destroyed by the updating *> process. *> \endverbatim *> *> \param[out] DLAMDA *> \verbatim *> DLAMDA is DOUBLE PRECISION array, dimension (N) *> A copy of the first K eigenvalues which will be used by *> DLAED3 to form the secular equation. *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> The first k values of the final deflation-altered z-vector *> which will be passed to DLAED3. *> \endverbatim *> *> \param[out] Q2 *> \verbatim *> Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2) *> A copy of the first K eigenvectors which will be used by *> DLAED3 in a matrix multiply (DGEMM) to solve for the new *> eigenvectors. *> \endverbatim *> *> \param[out] INDX *> \verbatim *> INDX is INTEGER array, dimension (N) *> The permutation used to sort the contents of DLAMDA into *> ascending order. *> \endverbatim *> *> \param[out] INDXC *> \verbatim *> INDXC is INTEGER array, dimension (N) *> The permutation used to arrange the columns of the deflated *> Q matrix into three groups: the first group contains non-zero *> elements only at and above N1, the second contains *> non-zero elements only below N1, and the third is dense. *> \endverbatim *> *> \param[out] INDXP *> \verbatim *> INDXP is INTEGER array, dimension (N) *> The permutation used to place deflated values of D at the end *> of the array. INDXP(1:K) points to the nondeflated D-values *> and INDXP(K+1:N) points to the deflated eigenvalues. *> \endverbatim *> *> \param[out] COLTYP *> \verbatim *> COLTYP is INTEGER array, dimension (N) *> During execution, a label which will indicate which of the *> following types a column in the Q2 matrix is: *> 1 : non-zero in the upper half only; *> 2 : dense; *> 3 : non-zero in the lower half only; *> 4 : deflated. *> On exit, COLTYP(i) is the number of columns of type i, *> for i=1 to 4 only. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA \n *> Modified by Francoise Tisseur, University of Tennessee *> * ===================================================================== SUBROUTINE DLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, $ Q2, INDX, INDXC, INDXP, COLTYP, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDQ, N, N1 DOUBLE PRECISION RHO * .. * .. Array Arguments .. INTEGER COLTYP( * ), INDX( * ), INDXC( * ), INDXP( * ), $ INDXQ( * ) DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), $ W( * ), Z( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION MONE, ZERO, ONE, TWO, EIGHT PARAMETER ( MONE = -1.0D0, ZERO = 0.0D0, ONE = 1.0D0, $ TWO = 2.0D0, EIGHT = 8.0D0 ) * .. * .. Local Arrays .. INTEGER CTOT( 4 ), PSM( 4 ) * .. * .. Local Scalars .. INTEGER CT, I, IMAX, IQ1, IQ2, J, JMAX, JS, K2, N1P1, $ N2, NJ, PJ DOUBLE PRECISION C, EPS, S, T, TAU, TOL * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DLAMCH, DLAPY2 EXTERNAL IDAMAX, DLAMCH, DLAPY2 * .. * .. External Subroutines .. EXTERNAL DCOPY, DLACPY, DLAMRG, DROT, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( MIN( 1, ( N / 2 ) ).GT.N1 .OR. ( N / 2 ).LT.N1 ) THEN INFO = -3 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAED2', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * N2 = N - N1 N1P1 = N1 + 1 * IF( RHO.LT.ZERO ) THEN CALL DSCAL( N2, MONE, Z( N1P1 ), 1 ) END IF * * Normalize z so that norm(z) = 1. Since z is the concatenation of * two normalized vectors, norm2(z) = sqrt(2). * T = ONE / SQRT( TWO ) CALL DSCAL( N, T, Z, 1 ) * * RHO = ABS( norm(z)**2 * RHO ) * RHO = ABS( TWO*RHO ) * * Sort the eigenvalues into increasing order * DO 10 I = N1P1, N INDXQ( I ) = INDXQ( I ) + N1 10 CONTINUE * * re-integrate the deflated parts from the last pass * DO 20 I = 1, N DLAMDA( I ) = D( INDXQ( I ) ) 20 CONTINUE CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDXC ) DO 30 I = 1, N INDX( I ) = INDXQ( INDXC( I ) ) 30 CONTINUE * * Calculate the allowable deflation tolerance * IMAX = IDAMAX( N, Z, 1 ) JMAX = IDAMAX( N, D, 1 ) EPS = DLAMCH( 'Epsilon' ) TOL = EIGHT*EPS*MAX( ABS( D( JMAX ) ), ABS( Z( IMAX ) ) ) * * If the rank-1 modifier is small enough, no more needs to be done * except to reorganize Q so that its columns correspond with the * elements in D. * IF( RHO*ABS( Z( IMAX ) ).LE.TOL ) THEN K = 0 IQ2 = 1 DO 40 J = 1, N I = INDX( J ) CALL DCOPY( N, Q( 1, I ), 1, Q2( IQ2 ), 1 ) DLAMDA( J ) = D( I ) IQ2 = IQ2 + N 40 CONTINUE CALL DLACPY( 'A', N, N, Q2, N, Q, LDQ ) CALL DCOPY( N, DLAMDA, 1, D, 1 ) GO TO 190 END IF * * If there are multiple eigenvalues then the problem deflates. Here * the number of equal eigenvalues are found. As each equal * eigenvalue is found, an elementary reflector is computed to rotate * the corresponding eigensubspace so that the corresponding * components of Z are zero in this new basis. * DO 50 I = 1, N1 COLTYP( I ) = 1 50 CONTINUE DO 60 I = N1P1, N COLTYP( I ) = 3 60 CONTINUE * * K = 0 K2 = N + 1 DO 70 J = 1, N NJ = INDX( J ) IF( RHO*ABS( Z( NJ ) ).LE.TOL ) THEN * * Deflate due to small z component. * K2 = K2 - 1 COLTYP( NJ ) = 4 INDXP( K2 ) = NJ IF( J.EQ.N ) $ GO TO 100 ELSE PJ = NJ GO TO 80 END IF 70 CONTINUE 80 CONTINUE J = J + 1 NJ = INDX( J ) IF( J.GT.N ) $ GO TO 100 IF( RHO*ABS( Z( NJ ) ).LE.TOL ) THEN * * Deflate due to small z component. * K2 = K2 - 1 COLTYP( NJ ) = 4 INDXP( K2 ) = NJ ELSE * * Check if eigenvalues are close enough to allow deflation. * S = Z( PJ ) C = Z( NJ ) * * Find sqrt(a**2+b**2) without overflow or * destructive underflow. * TAU = DLAPY2( C, S ) T = D( NJ ) - D( PJ ) C = C / TAU S = -S / TAU IF( ABS( T*C*S ).LE.TOL ) THEN * * Deflation is possible. * Z( NJ ) = TAU Z( PJ ) = ZERO IF( COLTYP( NJ ).NE.COLTYP( PJ ) ) $ COLTYP( NJ ) = 2 COLTYP( PJ ) = 4 CALL DROT( N, Q( 1, PJ ), 1, Q( 1, NJ ), 1, C, S ) T = D( PJ )*C**2 + D( NJ )*S**2 D( NJ ) = D( PJ )*S**2 + D( NJ )*C**2 D( PJ ) = T K2 = K2 - 1 I = 1 90 CONTINUE IF( K2+I.LE.N ) THEN IF( D( PJ ).LT.D( INDXP( K2+I ) ) ) THEN INDXP( K2+I-1 ) = INDXP( K2+I ) INDXP( K2+I ) = PJ I = I + 1 GO TO 90 ELSE INDXP( K2+I-1 ) = PJ END IF ELSE INDXP( K2+I-1 ) = PJ END IF PJ = NJ ELSE K = K + 1 DLAMDA( K ) = D( PJ ) W( K ) = Z( PJ ) INDXP( K ) = PJ PJ = NJ END IF END IF GO TO 80 100 CONTINUE * * Record the last eigenvalue. * K = K + 1 DLAMDA( K ) = D( PJ ) W( K ) = Z( PJ ) INDXP( K ) = PJ * * Count up the total number of the various types of columns, then * form a permutation which positions the four column types into * four uniform groups (although one or more of these groups may be * empty). * DO 110 J = 1, 4 CTOT( J ) = 0 110 CONTINUE DO 120 J = 1, N CT = COLTYP( J ) CTOT( CT ) = CTOT( CT ) + 1 120 CONTINUE * * PSM(*) = Position in SubMatrix (of types 1 through 4) * PSM( 1 ) = 1 PSM( 2 ) = 1 + CTOT( 1 ) PSM( 3 ) = PSM( 2 ) + CTOT( 2 ) PSM( 4 ) = PSM( 3 ) + CTOT( 3 ) K = N - CTOT( 4 ) * * Fill out the INDXC array so that the permutation which it induces * will place all type-1 columns first, all type-2 columns next, * then all type-3's, and finally all type-4's. * DO 130 J = 1, N JS = INDXP( J ) CT = COLTYP( JS ) INDX( PSM( CT ) ) = JS INDXC( PSM( CT ) ) = J PSM( CT ) = PSM( CT ) + 1 130 CONTINUE * * Sort the eigenvalues and corresponding eigenvectors into DLAMDA * and Q2 respectively. The eigenvalues/vectors which were not * deflated go into the first K slots of DLAMDA and Q2 respectively, * while those which were deflated go into the last N - K slots. * I = 1 IQ1 = 1 IQ2 = 1 + ( CTOT( 1 )+CTOT( 2 ) )*N1 DO 140 J = 1, CTOT( 1 ) JS = INDX( I ) CALL DCOPY( N1, Q( 1, JS ), 1, Q2( IQ1 ), 1 ) Z( I ) = D( JS ) I = I + 1 IQ1 = IQ1 + N1 140 CONTINUE * DO 150 J = 1, CTOT( 2 ) JS = INDX( I ) CALL DCOPY( N1, Q( 1, JS ), 1, Q2( IQ1 ), 1 ) CALL DCOPY( N2, Q( N1+1, JS ), 1, Q2( IQ2 ), 1 ) Z( I ) = D( JS ) I = I + 1 IQ1 = IQ1 + N1 IQ2 = IQ2 + N2 150 CONTINUE * DO 160 J = 1, CTOT( 3 ) JS = INDX( I ) CALL DCOPY( N2, Q( N1+1, JS ), 1, Q2( IQ2 ), 1 ) Z( I ) = D( JS ) I = I + 1 IQ2 = IQ2 + N2 160 CONTINUE * IQ1 = IQ2 DO 170 J = 1, CTOT( 4 ) JS = INDX( I ) CALL DCOPY( N, Q( 1, JS ), 1, Q2( IQ2 ), 1 ) IQ2 = IQ2 + N Z( I ) = D( JS ) I = I + 1 170 CONTINUE * * The deflated eigenvalues and their corresponding vectors go back * into the last N - K slots of D and Q respectively. * IF( K.LT.N ) THEN CALL DLACPY( 'A', N, CTOT( 4 ), Q2( IQ1 ), N, $ Q( 1, K+1 ), LDQ ) CALL DCOPY( N-K, Z( K+1 ), 1, D( K+1 ), 1 ) END IF * * Copy CTOT into COLTYP for referencing in DLAED3. * DO 180 J = 1, 4 COLTYP( J ) = CTOT( J ) 180 CONTINUE * 190 CONTINUE RETURN * * End of DLAED2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaruv.f0000644000000000000000000000013214061636515015321 xustar0030 mtime=1623670093.371103925 30 atime=1623670093.371103925 30 ctime=1623670093.371103925 elk-7.2.42/src/LAPACK/dlaruv.f0000644002504400250440000004407214061636515017365 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLARUV returns a vector of n random real numbers from a uniform distribution. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARUV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARUV( ISEED, N, X ) * * .. Scalar Arguments .. * INTEGER N * .. * .. Array Arguments .. * INTEGER ISEED( 4 ) * DOUBLE PRECISION X( N ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARUV returns a vector of n random real numbers from a uniform (0,1) *> distribution (n <= 128). *> *> This is an auxiliary routine called by DLARNV and ZLARNV. *> \endverbatim * * Arguments: * ========== * *> \param[in,out] ISEED *> \verbatim *> ISEED is INTEGER array, dimension (4) *> On entry, the seed of the random number generator; the array *> elements must be between 0 and 4095, and ISEED(4) must be *> odd. *> On exit, the seed is updated. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of random numbers to be generated. N <= 128. *> \endverbatim *> *> \param[out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension (N) *> The generated random numbers. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> This routine uses a multiplicative congruential method with modulus *> 2**48 and multiplier 33952834046453 (see G.S.Fishman, *> 'Multiplicative congruential random number generators with modulus *> 2**b: an exhaustive analysis for b = 32 and a partial analysis for *> b = 48', Math. Comp. 189, pp 331-344, 1990). *> *> 48-bit integers are stored in 4 integer array elements with 12 bits *> per element. Hence the routine is portable across machines with *> integers of 32 bits or more. *> \endverbatim *> * ===================================================================== SUBROUTINE DLARUV( ISEED, N, X ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION X( N ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) INTEGER LV, IPW2 DOUBLE PRECISION R PARAMETER ( LV = 128, IPW2 = 4096, R = ONE / IPW2 ) * .. * .. Local Scalars .. INTEGER I, I1, I2, I3, I4, IT1, IT2, IT3, IT4, J * .. * .. Local Arrays .. INTEGER MM( LV, 4 ) * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MIN, MOD * .. * .. Data statements .. DATA ( MM( 1, J ), J = 1, 4 ) / 494, 322, 2508, $ 2549 / DATA ( MM( 2, J ), J = 1, 4 ) / 2637, 789, 3754, $ 1145 / DATA ( MM( 3, J ), J = 1, 4 ) / 255, 1440, 1766, $ 2253 / DATA ( MM( 4, J ), J = 1, 4 ) / 2008, 752, 3572, $ 305 / DATA ( MM( 5, J ), J = 1, 4 ) / 1253, 2859, 2893, $ 3301 / DATA ( MM( 6, J ), J = 1, 4 ) / 3344, 123, 307, $ 1065 / DATA ( MM( 7, J ), J = 1, 4 ) / 4084, 1848, 1297, $ 3133 / DATA ( MM( 8, J ), J = 1, 4 ) / 1739, 643, 3966, $ 2913 / DATA ( MM( 9, J ), J = 1, 4 ) / 3143, 2405, 758, $ 3285 / DATA ( MM( 10, J ), J = 1, 4 ) / 3468, 2638, 2598, $ 1241 / DATA ( MM( 11, J ), J = 1, 4 ) / 688, 2344, 3406, $ 1197 / DATA ( MM( 12, J ), J = 1, 4 ) / 1657, 46, 2922, $ 3729 / DATA ( MM( 13, J ), J = 1, 4 ) / 1238, 3814, 1038, $ 2501 / DATA ( MM( 14, J ), J = 1, 4 ) / 3166, 913, 2934, $ 1673 / DATA ( MM( 15, J ), J = 1, 4 ) / 1292, 3649, 2091, $ 541 / DATA ( MM( 16, J ), J = 1, 4 ) / 3422, 339, 2451, $ 2753 / DATA ( MM( 17, J ), J = 1, 4 ) / 1270, 3808, 1580, $ 949 / DATA ( MM( 18, J ), J = 1, 4 ) / 2016, 822, 1958, $ 2361 / DATA ( MM( 19, J ), J = 1, 4 ) / 154, 2832, 2055, $ 1165 / DATA ( MM( 20, J ), J = 1, 4 ) / 2862, 3078, 1507, $ 4081 / DATA ( MM( 21, J ), J = 1, 4 ) / 697, 3633, 1078, $ 2725 / DATA ( MM( 22, J ), J = 1, 4 ) / 1706, 2970, 3273, $ 3305 / DATA ( MM( 23, J ), J = 1, 4 ) / 491, 637, 17, $ 3069 / DATA ( MM( 24, J ), J = 1, 4 ) / 931, 2249, 854, $ 3617 / DATA ( MM( 25, J ), J = 1, 4 ) / 1444, 2081, 2916, $ 3733 / DATA ( MM( 26, J ), J = 1, 4 ) / 444, 4019, 3971, $ 409 / DATA ( MM( 27, J ), J = 1, 4 ) / 3577, 1478, 2889, $ 2157 / DATA ( MM( 28, J ), J = 1, 4 ) / 3944, 242, 3831, $ 1361 / DATA ( MM( 29, J ), J = 1, 4 ) / 2184, 481, 2621, $ 3973 / DATA ( MM( 30, J ), J = 1, 4 ) / 1661, 2075, 1541, $ 1865 / DATA ( MM( 31, J ), J = 1, 4 ) / 3482, 4058, 893, $ 2525 / DATA ( MM( 32, J ), J = 1, 4 ) / 657, 622, 736, $ 1409 / DATA ( MM( 33, J ), J = 1, 4 ) / 3023, 3376, 3992, $ 3445 / DATA ( MM( 34, J ), J = 1, 4 ) / 3618, 812, 787, $ 3577 / DATA ( MM( 35, J ), J = 1, 4 ) / 1267, 234, 2125, $ 77 / DATA ( MM( 36, J ), J = 1, 4 ) / 1828, 641, 2364, $ 3761 / DATA ( MM( 37, J ), J = 1, 4 ) / 164, 4005, 2460, $ 2149 / DATA ( MM( 38, J ), J = 1, 4 ) / 3798, 1122, 257, $ 1449 / DATA ( MM( 39, J ), J = 1, 4 ) / 3087, 3135, 1574, $ 3005 / DATA ( MM( 40, J ), J = 1, 4 ) / 2400, 2640, 3912, $ 225 / DATA ( MM( 41, J ), J = 1, 4 ) / 2870, 2302, 1216, $ 85 / DATA ( MM( 42, J ), J = 1, 4 ) / 3876, 40, 3248, $ 3673 / DATA ( MM( 43, J ), J = 1, 4 ) / 1905, 1832, 3401, $ 3117 / DATA ( MM( 44, J ), J = 1, 4 ) / 1593, 2247, 2124, $ 3089 / DATA ( MM( 45, J ), J = 1, 4 ) / 1797, 2034, 2762, $ 1349 / DATA ( MM( 46, J ), J = 1, 4 ) / 1234, 2637, 149, $ 2057 / DATA ( MM( 47, J ), J = 1, 4 ) / 3460, 1287, 2245, $ 413 / DATA ( MM( 48, J ), J = 1, 4 ) / 328, 1691, 166, $ 65 / DATA ( MM( 49, J ), J = 1, 4 ) / 2861, 496, 466, $ 1845 / DATA ( MM( 50, J ), J = 1, 4 ) / 1950, 1597, 4018, $ 697 / DATA ( MM( 51, J ), J = 1, 4 ) / 617, 2394, 1399, $ 3085 / DATA ( MM( 52, J ), J = 1, 4 ) / 2070, 2584, 190, $ 3441 / DATA ( MM( 53, J ), J = 1, 4 ) / 3331, 1843, 2879, $ 1573 / DATA ( MM( 54, J ), J = 1, 4 ) / 769, 336, 153, $ 3689 / DATA ( MM( 55, J ), J = 1, 4 ) / 1558, 1472, 2320, $ 2941 / DATA ( MM( 56, J ), J = 1, 4 ) / 2412, 2407, 18, $ 929 / DATA ( MM( 57, J ), J = 1, 4 ) / 2800, 433, 712, $ 533 / DATA ( MM( 58, J ), J = 1, 4 ) / 189, 2096, 2159, $ 2841 / DATA ( MM( 59, J ), J = 1, 4 ) / 287, 1761, 2318, $ 4077 / DATA ( MM( 60, J ), J = 1, 4 ) / 2045, 2810, 2091, $ 721 / DATA ( MM( 61, J ), J = 1, 4 ) / 1227, 566, 3443, $ 2821 / DATA ( MM( 62, J ), J = 1, 4 ) / 2838, 442, 1510, $ 2249 / DATA ( MM( 63, J ), J = 1, 4 ) / 209, 41, 449, $ 2397 / DATA ( MM( 64, J ), J = 1, 4 ) / 2770, 1238, 1956, $ 2817 / DATA ( MM( 65, J ), J = 1, 4 ) / 3654, 1086, 2201, $ 245 / DATA ( MM( 66, J ), J = 1, 4 ) / 3993, 603, 3137, $ 1913 / DATA ( MM( 67, J ), J = 1, 4 ) / 192, 840, 3399, $ 1997 / DATA ( MM( 68, J ), J = 1, 4 ) / 2253, 3168, 1321, $ 3121 / DATA ( MM( 69, J ), J = 1, 4 ) / 3491, 1499, 2271, $ 997 / DATA ( MM( 70, J ), J = 1, 4 ) / 2889, 1084, 3667, $ 1833 / DATA ( MM( 71, J ), J = 1, 4 ) / 2857, 3438, 2703, $ 2877 / DATA ( MM( 72, J ), J = 1, 4 ) / 2094, 2408, 629, $ 1633 / DATA ( MM( 73, J ), J = 1, 4 ) / 1818, 1589, 2365, $ 981 / DATA ( MM( 74, J ), J = 1, 4 ) / 688, 2391, 2431, $ 2009 / DATA ( MM( 75, J ), J = 1, 4 ) / 1407, 288, 1113, $ 941 / DATA ( MM( 76, J ), J = 1, 4 ) / 634, 26, 3922, $ 2449 / DATA ( MM( 77, J ), J = 1, 4 ) / 3231, 512, 2554, $ 197 / DATA ( MM( 78, J ), J = 1, 4 ) / 815, 1456, 184, $ 2441 / DATA ( MM( 79, J ), J = 1, 4 ) / 3524, 171, 2099, $ 285 / DATA ( MM( 80, J ), J = 1, 4 ) / 1914, 1677, 3228, $ 1473 / DATA ( MM( 81, J ), J = 1, 4 ) / 516, 2657, 4012, $ 2741 / DATA ( MM( 82, J ), J = 1, 4 ) / 164, 2270, 1921, $ 3129 / DATA ( MM( 83, J ), J = 1, 4 ) / 303, 2587, 3452, $ 909 / DATA ( MM( 84, J ), J = 1, 4 ) / 2144, 2961, 3901, $ 2801 / DATA ( MM( 85, J ), J = 1, 4 ) / 3480, 1970, 572, $ 421 / DATA ( MM( 86, J ), J = 1, 4 ) / 119, 1817, 3309, $ 4073 / DATA ( MM( 87, J ), J = 1, 4 ) / 3357, 676, 3171, $ 2813 / DATA ( MM( 88, J ), J = 1, 4 ) / 837, 1410, 817, $ 2337 / DATA ( MM( 89, J ), J = 1, 4 ) / 2826, 3723, 3039, $ 1429 / DATA ( MM( 90, J ), J = 1, 4 ) / 2332, 2803, 1696, $ 1177 / DATA ( MM( 91, J ), J = 1, 4 ) / 2089, 3185, 1256, $ 1901 / DATA ( MM( 92, J ), J = 1, 4 ) / 3780, 184, 3715, $ 81 / DATA ( MM( 93, J ), J = 1, 4 ) / 1700, 663, 2077, $ 1669 / DATA ( MM( 94, J ), J = 1, 4 ) / 3712, 499, 3019, $ 2633 / DATA ( MM( 95, J ), J = 1, 4 ) / 150, 3784, 1497, $ 2269 / DATA ( MM( 96, J ), J = 1, 4 ) / 2000, 1631, 1101, $ 129 / DATA ( MM( 97, J ), J = 1, 4 ) / 3375, 1925, 717, $ 1141 / DATA ( MM( 98, J ), J = 1, 4 ) / 1621, 3912, 51, $ 249 / DATA ( MM( 99, J ), J = 1, 4 ) / 3090, 1398, 981, $ 3917 / DATA ( MM( 100, J ), J = 1, 4 ) / 3765, 1349, 1978, $ 2481 / DATA ( MM( 101, J ), J = 1, 4 ) / 1149, 1441, 1813, $ 3941 / DATA ( MM( 102, J ), J = 1, 4 ) / 3146, 2224, 3881, $ 2217 / DATA ( MM( 103, J ), J = 1, 4 ) / 33, 2411, 76, $ 2749 / DATA ( MM( 104, J ), J = 1, 4 ) / 3082, 1907, 3846, $ 3041 / DATA ( MM( 105, J ), J = 1, 4 ) / 2741, 3192, 3694, $ 1877 / DATA ( MM( 106, J ), J = 1, 4 ) / 359, 2786, 1682, $ 345 / DATA ( MM( 107, J ), J = 1, 4 ) / 3316, 382, 124, $ 2861 / DATA ( MM( 108, J ), J = 1, 4 ) / 1749, 37, 1660, $ 1809 / DATA ( MM( 109, J ), J = 1, 4 ) / 185, 759, 3997, $ 3141 / DATA ( MM( 110, J ), J = 1, 4 ) / 2784, 2948, 479, $ 2825 / DATA ( MM( 111, J ), J = 1, 4 ) / 2202, 1862, 1141, $ 157 / DATA ( MM( 112, J ), J = 1, 4 ) / 2199, 3802, 886, $ 2881 / DATA ( MM( 113, J ), J = 1, 4 ) / 1364, 2423, 3514, $ 3637 / DATA ( MM( 114, J ), J = 1, 4 ) / 1244, 2051, 1301, $ 1465 / DATA ( MM( 115, J ), J = 1, 4 ) / 2020, 2295, 3604, $ 2829 / DATA ( MM( 116, J ), J = 1, 4 ) / 3160, 1332, 1888, $ 2161 / DATA ( MM( 117, J ), J = 1, 4 ) / 2785, 1832, 1836, $ 3365 / DATA ( MM( 118, J ), J = 1, 4 ) / 2772, 2405, 1990, $ 361 / DATA ( MM( 119, J ), J = 1, 4 ) / 1217, 3638, 2058, $ 2685 / DATA ( MM( 120, J ), J = 1, 4 ) / 1822, 3661, 692, $ 3745 / DATA ( MM( 121, J ), J = 1, 4 ) / 1245, 327, 1194, $ 2325 / DATA ( MM( 122, J ), J = 1, 4 ) / 2252, 3660, 20, $ 3609 / DATA ( MM( 123, J ), J = 1, 4 ) / 3904, 716, 3285, $ 3821 / DATA ( MM( 124, J ), J = 1, 4 ) / 2774, 1842, 2046, $ 3537 / DATA ( MM( 125, J ), J = 1, 4 ) / 997, 3987, 2107, $ 517 / DATA ( MM( 126, J ), J = 1, 4 ) / 2573, 1368, 3508, $ 3017 / DATA ( MM( 127, J ), J = 1, 4 ) / 1148, 1848, 3525, $ 2141 / DATA ( MM( 128, J ), J = 1, 4 ) / 545, 2366, 3801, $ 1537 / * .. * .. Executable Statements .. * I1 = ISEED( 1 ) I2 = ISEED( 2 ) I3 = ISEED( 3 ) I4 = ISEED( 4 ) * DO 10 I = 1, MIN( N, LV ) * 20 CONTINUE * * Multiply the seed by i-th power of the multiplier modulo 2**48 * IT4 = I4*MM( I, 4 ) IT3 = IT4 / IPW2 IT4 = IT4 - IPW2*IT3 IT3 = IT3 + I3*MM( I, 4 ) + I4*MM( I, 3 ) IT2 = IT3 / IPW2 IT3 = IT3 - IPW2*IT2 IT2 = IT2 + I2*MM( I, 4 ) + I3*MM( I, 3 ) + I4*MM( I, 2 ) IT1 = IT2 / IPW2 IT2 = IT2 - IPW2*IT1 IT1 = IT1 + I1*MM( I, 4 ) + I2*MM( I, 3 ) + I3*MM( I, 2 ) + $ I4*MM( I, 1 ) IT1 = MOD( IT1, IPW2 ) * * Convert 48-bit integer to a real number in the interval (0,1) * X( I ) = R*( DBLE( IT1 )+R*( DBLE( IT2 )+R*( DBLE( IT3 )+R* $ DBLE( IT4 ) ) ) ) * IF (X( I ).EQ.1.0D0) THEN * If a real number has n bits of precision, and the first * n bits of the 48-bit integer above happen to be all 1 (which * will occur about once every 2**n calls), then X( I ) will * be rounded to exactly 1.0. * Since X( I ) is not supposed to return exactly 0.0 or 1.0, * the statistically correct thing to do in this situation is * simply to iterate again. * N.B. the case X( I ) = 0.0 should not be possible. I1 = I1 + 2 I2 = I2 + 2 I3 = I3 + 2 I4 = I4 + 2 GOTO 20 END IF * 10 CONTINUE * * Return final value of seed * ISEED( 1 ) = IT1 ISEED( 2 ) = IT2 ISEED( 3 ) = IT3 ISEED( 4 ) = IT4 RETURN * * End of DLARUV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasq2.f0000644000000000000000000000013214061636515015212 xustar0030 mtime=1623670093.374103922 30 atime=1623670093.373103923 30 ctime=1623670093.374103922 elk-7.2.42/src/LAPACK/dlasq2.f0000644002504400250440000004116714061636515017260 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASQ2 computes all the eigenvalues of the symmetric positive definite tridiagonal matrix associated with the qd Array Z to high relative accuracy. Used by sbdsqr and sstegr. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASQ2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASQ2( N, Z, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, N * .. * .. Array Arguments .. * DOUBLE PRECISION Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASQ2 computes all the eigenvalues of the symmetric positive *> definite tridiagonal matrix associated with the qd array Z to high *> relative accuracy are computed to high relative accuracy, in the *> absence of denormalization, underflow and overflow. *> *> To see the relation of Z to the tridiagonal matrix, let L be a *> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and *> let U be an upper bidiagonal matrix with 1's above and diagonal *> Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the *> symmetric tridiagonal to which it is similar. *> *> Note : DLASQ2 defines a logical variable, IEEE, which is true *> on machines which follow ieee-754 floating-point standard in their *> handling of infinities and NaNs, and false otherwise. This variable *> is passed to DLASQ3. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns in the matrix. N >= 0. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension ( 4*N ) *> On entry Z holds the qd array. On exit, entries 1 to N hold *> the eigenvalues in decreasing order, Z( 2*N+1 ) holds the *> trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If *> N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) *> holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of *> shifts that failed. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if the i-th argument is a scalar and had an illegal *> value, then INFO = -i, if the i-th argument is an *> array and the j-entry had an illegal value, then *> INFO = -(i*100+j) *> > 0: the algorithm failed *> = 1, a split was marked by a positive value in E *> = 2, current block of Z not diagonalized after 100*N *> iterations (in inner while loop). On exit Z holds *> a qd array with the same eigenvalues as the given Z. *> = 3, termination criterion of outer while loop not met *> (program created more than N unreduced blocks) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> Local Variables: I0:N0 defines a current unreduced segment of Z. *> The shifts are accumulated in SIGMA. Iteration count is in ITER. *> Ping-pong is controlled by PP (alternates between 0 and 1). *> \endverbatim *> * ===================================================================== SUBROUTINE DLASQ2( N, Z, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, N * .. * .. Array Arguments .. DOUBLE PRECISION Z( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION CBIAS PARAMETER ( CBIAS = 1.50D0 ) DOUBLE PRECISION ZERO, HALF, ONE, TWO, FOUR, HUNDRD PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, $ TWO = 2.0D0, FOUR = 4.0D0, HUNDRD = 100.0D0 ) * .. * .. Local Scalars .. LOGICAL IEEE INTEGER I0, I1, I4, IINFO, IPN4, ITER, IWHILA, IWHILB, $ K, KMIN, N0, N1, NBIG, NDIV, NFAIL, PP, SPLT, $ TTYPE DOUBLE PRECISION D, DEE, DEEMIN, DESIG, DMIN, DMIN1, DMIN2, DN, $ DN1, DN2, E, EMAX, EMIN, EPS, G, OLDEMN, QMAX, $ QMIN, S, SAFMIN, SIGMA, T, TAU, TEMP, TOL, $ TOL2, TRACE, ZMAX, TEMPE, TEMPQ * .. * .. External Subroutines .. EXTERNAL DLASQ3, DLASRT, XERBLA * .. * .. External Functions .. INTEGER ILAENV DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH, ILAENV * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input arguments. * (in case DLASQ2 is not called by DLASQ1) * INFO = 0 EPS = DLAMCH( 'Precision' ) SAFMIN = DLAMCH( 'Safe minimum' ) TOL = EPS*HUNDRD TOL2 = TOL**2 * IF( N.LT.0 ) THEN INFO = -1 CALL XERBLA( 'DLASQ2', 1 ) RETURN ELSE IF( N.EQ.0 ) THEN RETURN ELSE IF( N.EQ.1 ) THEN * * 1-by-1 case. * IF( Z( 1 ).LT.ZERO ) THEN INFO = -201 CALL XERBLA( 'DLASQ2', 2 ) END IF RETURN ELSE IF( N.EQ.2 ) THEN * * 2-by-2 case. * IF( Z( 2 ).LT.ZERO .OR. Z( 3 ).LT.ZERO ) THEN INFO = -2 CALL XERBLA( 'DLASQ2', 2 ) RETURN ELSE IF( Z( 3 ).GT.Z( 1 ) ) THEN D = Z( 3 ) Z( 3 ) = Z( 1 ) Z( 1 ) = D END IF Z( 5 ) = Z( 1 ) + Z( 2 ) + Z( 3 ) IF( Z( 2 ).GT.Z( 3 )*TOL2 ) THEN T = HALF*( ( Z( 1 )-Z( 3 ) )+Z( 2 ) ) S = Z( 3 )*( Z( 2 ) / T ) IF( S.LE.T ) THEN S = Z( 3 )*( Z( 2 ) / ( T*( ONE+SQRT( ONE+S / T ) ) ) ) ELSE S = Z( 3 )*( Z( 2 ) / ( T+SQRT( T )*SQRT( T+S ) ) ) END IF T = Z( 1 ) + ( S+Z( 2 ) ) Z( 3 ) = Z( 3 )*( Z( 1 ) / T ) Z( 1 ) = T END IF Z( 2 ) = Z( 3 ) Z( 6 ) = Z( 2 ) + Z( 1 ) RETURN END IF * * Check for negative data and compute sums of q's and e's. * Z( 2*N ) = ZERO EMIN = Z( 2 ) QMAX = ZERO ZMAX = ZERO D = ZERO E = ZERO * DO 10 K = 1, 2*( N-1 ), 2 IF( Z( K ).LT.ZERO ) THEN INFO = -( 200+K ) CALL XERBLA( 'DLASQ2', 2 ) RETURN ELSE IF( Z( K+1 ).LT.ZERO ) THEN INFO = -( 200+K+1 ) CALL XERBLA( 'DLASQ2', 2 ) RETURN END IF D = D + Z( K ) E = E + Z( K+1 ) QMAX = MAX( QMAX, Z( K ) ) EMIN = MIN( EMIN, Z( K+1 ) ) ZMAX = MAX( QMAX, ZMAX, Z( K+1 ) ) 10 CONTINUE IF( Z( 2*N-1 ).LT.ZERO ) THEN INFO = -( 200+2*N-1 ) CALL XERBLA( 'DLASQ2', 2 ) RETURN END IF D = D + Z( 2*N-1 ) QMAX = MAX( QMAX, Z( 2*N-1 ) ) ZMAX = MAX( QMAX, ZMAX ) * * Check for diagonality. * IF( E.EQ.ZERO ) THEN DO 20 K = 2, N Z( K ) = Z( 2*K-1 ) 20 CONTINUE CALL DLASRT( 'D', N, Z, IINFO ) Z( 2*N-1 ) = D RETURN END IF * TRACE = D + E * * Check for zero data. * IF( TRACE.EQ.ZERO ) THEN Z( 2*N-1 ) = ZERO RETURN END IF * * Check whether the machine is IEEE conformable. * IEEE = ILAENV( 10, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 .AND. $ ILAENV( 11, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 * * Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). * DO 30 K = 2*N, 2, -2 Z( 2*K ) = ZERO Z( 2*K-1 ) = Z( K ) Z( 2*K-2 ) = ZERO Z( 2*K-3 ) = Z( K-1 ) 30 CONTINUE * I0 = 1 N0 = N * * Reverse the qd-array, if warranted. * IF( CBIAS*Z( 4*I0-3 ).LT.Z( 4*N0-3 ) ) THEN IPN4 = 4*( I0+N0 ) DO 40 I4 = 4*I0, 2*( I0+N0-1 ), 4 TEMP = Z( I4-3 ) Z( I4-3 ) = Z( IPN4-I4-3 ) Z( IPN4-I4-3 ) = TEMP TEMP = Z( I4-1 ) Z( I4-1 ) = Z( IPN4-I4-5 ) Z( IPN4-I4-5 ) = TEMP 40 CONTINUE END IF * * Initial split checking via dqd and Li's test. * PP = 0 * DO 80 K = 1, 2 * D = Z( 4*N0+PP-3 ) DO 50 I4 = 4*( N0-1 ) + PP, 4*I0 + PP, -4 IF( Z( I4-1 ).LE.TOL2*D ) THEN Z( I4-1 ) = -ZERO D = Z( I4-3 ) ELSE D = Z( I4-3 )*( D / ( D+Z( I4-1 ) ) ) END IF 50 CONTINUE * * dqd maps Z to ZZ plus Li's test. * EMIN = Z( 4*I0+PP+1 ) D = Z( 4*I0+PP-3 ) DO 60 I4 = 4*I0 + PP, 4*( N0-1 ) + PP, 4 Z( I4-2*PP-2 ) = D + Z( I4-1 ) IF( Z( I4-1 ).LE.TOL2*D ) THEN Z( I4-1 ) = -ZERO Z( I4-2*PP-2 ) = D Z( I4-2*PP ) = ZERO D = Z( I4+1 ) ELSE IF( SAFMIN*Z( I4+1 ).LT.Z( I4-2*PP-2 ) .AND. $ SAFMIN*Z( I4-2*PP-2 ).LT.Z( I4+1 ) ) THEN TEMP = Z( I4+1 ) / Z( I4-2*PP-2 ) Z( I4-2*PP ) = Z( I4-1 )*TEMP D = D*TEMP ELSE Z( I4-2*PP ) = Z( I4+1 )*( Z( I4-1 ) / Z( I4-2*PP-2 ) ) D = Z( I4+1 )*( D / Z( I4-2*PP-2 ) ) END IF EMIN = MIN( EMIN, Z( I4-2*PP ) ) 60 CONTINUE Z( 4*N0-PP-2 ) = D * * Now find qmax. * QMAX = Z( 4*I0-PP-2 ) DO 70 I4 = 4*I0 - PP + 2, 4*N0 - PP - 2, 4 QMAX = MAX( QMAX, Z( I4 ) ) 70 CONTINUE * * Prepare for the next iteration on K. * PP = 1 - PP 80 CONTINUE * * Initialise variables to pass to DLASQ3. * TTYPE = 0 DMIN1 = ZERO DMIN2 = ZERO DN = ZERO DN1 = ZERO DN2 = ZERO G = ZERO TAU = ZERO * ITER = 2 NFAIL = 0 NDIV = 2*( N0-I0 ) * DO 160 IWHILA = 1, N + 1 IF( N0.LT.1 ) $ GO TO 170 * * While array unfinished do * * E(N0) holds the value of SIGMA when submatrix in I0:N0 * splits from the rest of the array, but is negated. * DESIG = ZERO IF( N0.EQ.N ) THEN SIGMA = ZERO ELSE SIGMA = -Z( 4*N0-1 ) END IF IF( SIGMA.LT.ZERO ) THEN INFO = 1 RETURN END IF * * Find last unreduced submatrix's top index I0, find QMAX and * EMIN. Find Gershgorin-type bound if Q's much greater than E's. * EMAX = ZERO IF( N0.GT.I0 ) THEN EMIN = ABS( Z( 4*N0-5 ) ) ELSE EMIN = ZERO END IF QMIN = Z( 4*N0-3 ) QMAX = QMIN DO 90 I4 = 4*N0, 8, -4 IF( Z( I4-5 ).LE.ZERO ) $ GO TO 100 IF( QMIN.GE.FOUR*EMAX ) THEN QMIN = MIN( QMIN, Z( I4-3 ) ) EMAX = MAX( EMAX, Z( I4-5 ) ) END IF QMAX = MAX( QMAX, Z( I4-7 )+Z( I4-5 ) ) EMIN = MIN( EMIN, Z( I4-5 ) ) 90 CONTINUE I4 = 4 * 100 CONTINUE I0 = I4 / 4 PP = 0 * IF( N0-I0.GT.1 ) THEN DEE = Z( 4*I0-3 ) DEEMIN = DEE KMIN = I0 DO 110 I4 = 4*I0+1, 4*N0-3, 4 DEE = Z( I4 )*( DEE /( DEE+Z( I4-2 ) ) ) IF( DEE.LE.DEEMIN ) THEN DEEMIN = DEE KMIN = ( I4+3 )/4 END IF 110 CONTINUE IF( (KMIN-I0)*2.LT.N0-KMIN .AND. $ DEEMIN.LE.HALF*Z(4*N0-3) ) THEN IPN4 = 4*( I0+N0 ) PP = 2 DO 120 I4 = 4*I0, 2*( I0+N0-1 ), 4 TEMP = Z( I4-3 ) Z( I4-3 ) = Z( IPN4-I4-3 ) Z( IPN4-I4-3 ) = TEMP TEMP = Z( I4-2 ) Z( I4-2 ) = Z( IPN4-I4-2 ) Z( IPN4-I4-2 ) = TEMP TEMP = Z( I4-1 ) Z( I4-1 ) = Z( IPN4-I4-5 ) Z( IPN4-I4-5 ) = TEMP TEMP = Z( I4 ) Z( I4 ) = Z( IPN4-I4-4 ) Z( IPN4-I4-4 ) = TEMP 120 CONTINUE END IF END IF * * Put -(initial shift) into DMIN. * DMIN = -MAX( ZERO, QMIN-TWO*SQRT( QMIN )*SQRT( EMAX ) ) * * Now I0:N0 is unreduced. * PP = 0 for ping, PP = 1 for pong. * PP = 2 indicates that flipping was applied to the Z array and * and that the tests for deflation upon entry in DLASQ3 * should not be performed. * NBIG = 100*( N0-I0+1 ) DO 140 IWHILB = 1, NBIG IF( I0.GT.N0 ) $ GO TO 150 * * While submatrix unfinished take a good dqds step. * CALL DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, $ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, $ DN2, G, TAU ) * PP = 1 - PP * * When EMIN is very small check for splits. * IF( PP.EQ.0 .AND. N0-I0.GE.3 ) THEN IF( Z( 4*N0 ).LE.TOL2*QMAX .OR. $ Z( 4*N0-1 ).LE.TOL2*SIGMA ) THEN SPLT = I0 - 1 QMAX = Z( 4*I0-3 ) EMIN = Z( 4*I0-1 ) OLDEMN = Z( 4*I0 ) DO 130 I4 = 4*I0, 4*( N0-3 ), 4 IF( Z( I4 ).LE.TOL2*Z( I4-3 ) .OR. $ Z( I4-1 ).LE.TOL2*SIGMA ) THEN Z( I4-1 ) = -SIGMA SPLT = I4 / 4 QMAX = ZERO EMIN = Z( I4+3 ) OLDEMN = Z( I4+4 ) ELSE QMAX = MAX( QMAX, Z( I4+1 ) ) EMIN = MIN( EMIN, Z( I4-1 ) ) OLDEMN = MIN( OLDEMN, Z( I4 ) ) END IF 130 CONTINUE Z( 4*N0-1 ) = EMIN Z( 4*N0 ) = OLDEMN I0 = SPLT + 1 END IF END IF * 140 CONTINUE * INFO = 2 * * Maximum number of iterations exceeded, restore the shift * SIGMA and place the new d's and e's in a qd array. * This might need to be done for several blocks * I1 = I0 N1 = N0 145 CONTINUE TEMPQ = Z( 4*I0-3 ) Z( 4*I0-3 ) = Z( 4*I0-3 ) + SIGMA DO K = I0+1, N0 TEMPE = Z( 4*K-5 ) Z( 4*K-5 ) = Z( 4*K-5 ) * (TEMPQ / Z( 4*K-7 )) TEMPQ = Z( 4*K-3 ) Z( 4*K-3 ) = Z( 4*K-3 ) + SIGMA + TEMPE - Z( 4*K-5 ) END DO * * Prepare to do this on the previous block if there is one * IF( I1.GT.1 ) THEN N1 = I1-1 DO WHILE( ( I1.GE.2 ) .AND. ( Z(4*I1-5).GE.ZERO ) ) I1 = I1 - 1 END DO SIGMA = -Z(4*N1-1) GO TO 145 END IF DO K = 1, N Z( 2*K-1 ) = Z( 4*K-3 ) * * Only the block 1..N0 is unfinished. The rest of the e's * must be essentially zero, although sometimes other data * has been stored in them. * IF( K.LT.N0 ) THEN Z( 2*K ) = Z( 4*K-1 ) ELSE Z( 2*K ) = 0 END IF END DO RETURN * * end IWHILB * 150 CONTINUE * 160 CONTINUE * INFO = 3 RETURN * * end IWHILA * 170 CONTINUE * * Move q's to the front. * DO 180 K = 2, N Z( K ) = Z( 4*K-3 ) 180 CONTINUE * * Sort and compute sum of eigenvalues. * CALL DLASRT( 'D', N, Z, IINFO ) * E = ZERO DO 190 K = N, 1, -1 E = E + Z( K ) 190 CONTINUE * * Store trace, sum(eigenvalues) and information on performance. * Z( 2*N+1 ) = TRACE Z( 2*N+2 ) = E Z( 2*N+3 ) = DBLE( ITER ) Z( 2*N+4 ) = DBLE( NDIV ) / DBLE( N**2 ) Z( 2*N+5 ) = HUNDRD*NFAIL / DBLE( ITER ) RETURN * * End of DLASQ2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlarfg.f0000644000000000000000000000013214061636515015263 xustar0030 mtime=1623670093.375103921 30 atime=1623670093.375103921 30 ctime=1623670093.375103921 elk-7.2.42/src/LAPACK/dlarfg.f0000644002504400250440000001162014061636515017320 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLARFG generates an elementary reflector (Householder matrix). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARFG + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) * * .. Scalar Arguments .. * INTEGER INCX, N * DOUBLE PRECISION ALPHA, TAU * .. * .. Array Arguments .. * DOUBLE PRECISION X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARFG generates a real elementary reflector H of order n, such *> that *> *> H * ( alpha ) = ( beta ), H**T * H = I. *> ( x ) ( 0 ) *> *> where alpha and beta are scalars, and x is an (n-1)-element real *> vector. H is represented in the form *> *> H = I - tau * ( 1 ) * ( 1 v**T ) , *> ( v ) *> *> where tau is a real scalar and v is a real (n-1)-element *> vector. *> *> If the elements of x are all zero, then tau = 0 and H is taken to be *> the unit matrix. *> *> Otherwise 1 <= tau <= 2. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the elementary reflector. *> \endverbatim *> *> \param[in,out] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION *> On entry, the value alpha. *> On exit, it is overwritten with the value beta. *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is DOUBLE PRECISION array, dimension *> (1+(N-2)*abs(INCX)) *> On entry, the vector x. *> On exit, it is overwritten with the vector v. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between elements of X. INCX > 0. *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is DOUBLE PRECISION *> The value tau. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup doubleOTHERauxiliary * * ===================================================================== SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) * * -- LAPACK auxiliary routine (version 3.8.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * * .. Scalar Arguments .. INTEGER INCX, N DOUBLE PRECISION ALPHA, TAU * .. * .. Array Arguments .. DOUBLE PRECISION X( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER J, KNT DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2 EXTERNAL DLAMCH, DLAPY2, DNRM2 * .. * .. Intrinsic Functions .. INTRINSIC ABS, SIGN * .. * .. External Subroutines .. EXTERNAL DSCAL * .. * .. Executable Statements .. * IF( N.LE.1 ) THEN TAU = ZERO RETURN END IF * XNORM = DNRM2( N-1, X, INCX ) * IF( XNORM.EQ.ZERO ) THEN * * H = I * TAU = ZERO ELSE * * general case * BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) KNT = 0 IF( ABS( BETA ).LT.SAFMIN ) THEN * * XNORM, BETA may be inaccurate; scale X and recompute them * RSAFMN = ONE / SAFMIN 10 CONTINUE KNT = KNT + 1 CALL DSCAL( N-1, RSAFMN, X, INCX ) BETA = BETA*RSAFMN ALPHA = ALPHA*RSAFMN IF( (ABS( BETA ).LT.SAFMIN) .AND. (KNT .LT. 20) ) $ GO TO 10 * * New BETA is at most 1, at least SAFMIN * XNORM = DNRM2( N-1, X, INCX ) BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA ) END IF TAU = ( BETA-ALPHA ) / BETA CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX ) * * If ALPHA is subnormal, it may lose relative accuracy * DO 20 J = 1, KNT BETA = BETA*SAFMIN 20 CONTINUE ALPHA = BETA END IF * RETURN * * End of DLARFG * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dorg2l.f0000644000000000000000000000012714061636515015221 xustar0029 mtime=1623670093.37710392 29 atime=1623670093.37710392 29 ctime=1623670093.37710392 elk-7.2.42/src/LAPACK/dorg2l.f0000644002504400250440000001220614061636515017253 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORG2L + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORG2L generates an m by n real matrix Q with orthonormal columns, *> which is defined as the last n columns of a product of k elementary *> reflectors of order m *> *> Q = H(k) . . . H(2) H(1) *> *> as returned by DGEQLF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. M >= N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the (n-k+i)-th column must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by DGEQLF in the last k columns of its array *> argument A. *> On exit, the m by n matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEQLF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, II, J, L * .. * .. External Subroutines .. EXTERNAL DLARF, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORG2L', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.0 ) $ RETURN * * Initialise columns 1:n-k to columns of the unit matrix * DO 20 J = 1, N - K DO 10 L = 1, M A( L, J ) = ZERO 10 CONTINUE A( M-N+J, J ) = ONE 20 CONTINUE * DO 40 I = 1, K II = N - K + I * * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left * A( M-N+II, II ) = ONE CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A, $ LDA, WORK ) CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 ) A( M-N+II, II ) = ONE - TAU( I ) * * Set A(m-k+i+1:m,n-k+i) to zero * DO 30 L = M - N + II + 1, M A( L, II ) = ZERO 30 CONTINUE 40 CONTINUE RETURN * * End of DORG2L * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlarft.f0000644000000000000000000000013214061636515015300 xustar0030 mtime=1623670093.379103918 30 atime=1623670093.379103918 30 ctime=1623670093.379103918 elk-7.2.42/src/LAPACK/dlarft.f0000644002504400250440000002402614061636515017341 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLARFT forms the triangular factor T of a block reflector H = I - vtvH * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARFT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) * * .. Scalar Arguments .. * CHARACTER DIRECT, STOREV * INTEGER K, LDT, LDV, N * .. * .. Array Arguments .. * DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARFT forms the triangular factor T of a real block reflector H *> of order n, which is defined as a product of k elementary reflectors. *> *> If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; *> *> If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. *> *> If STOREV = 'C', the vector which defines the elementary reflector *> H(i) is stored in the i-th column of the array V, and *> *> H = I - V * T * V**T *> *> If STOREV = 'R', the vector which defines the elementary reflector *> H(i) is stored in the i-th row of the array V, and *> *> H = I - V**T * T * V *> \endverbatim * * Arguments: * ========== * *> \param[in] DIRECT *> \verbatim *> DIRECT is CHARACTER*1 *> Specifies the order in which the elementary reflectors are *> multiplied to form the block reflector: *> = 'F': H = H(1) H(2) . . . H(k) (Forward) *> = 'B': H = H(k) . . . H(2) H(1) (Backward) *> \endverbatim *> *> \param[in] STOREV *> \verbatim *> STOREV is CHARACTER*1 *> Specifies how the vectors which define the elementary *> reflectors are stored (see also Further Details): *> = 'C': columnwise *> = 'R': rowwise *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the block reflector H. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The order of the triangular factor T (= the number of *> elementary reflectors). K >= 1. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is DOUBLE PRECISION array, dimension *> (LDV,K) if STOREV = 'C' *> (LDV,N) if STOREV = 'R' *> The matrix V. See further details. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V. *> If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i). *> \endverbatim *> *> \param[out] T *> \verbatim *> T is DOUBLE PRECISION array, dimension (LDT,K) *> The k by k triangular factor T of the block reflector. *> If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is *> lower triangular. The rest of the array is not used. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= K. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> The shape of the matrix V and the storage of the vectors which define *> the H(i) is best illustrated by the following example with n = 5 and *> k = 3. The elements equal to 1 are not stored. *> *> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': *> *> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) *> ( v1 1 ) ( 1 v2 v2 v2 ) *> ( v1 v2 1 ) ( 1 v3 v3 ) *> ( v1 v2 v3 ) *> ( v1 v2 v3 ) *> *> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': *> *> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) *> ( v1 v2 v3 ) ( v2 v2 v2 1 ) *> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) *> ( 1 v3 ) *> ( 1 ) *> \endverbatim *> * ===================================================================== SUBROUTINE DLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIRECT, STOREV INTEGER K, LDT, LDV, N * .. * .. Array Arguments .. DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, PREVLASTV, LASTV * .. * .. External Subroutines .. EXTERNAL DGEMV, DTRMV * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Executable Statements .. * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * IF( LSAME( DIRECT, 'F' ) ) THEN PREVLASTV = N DO I = 1, K PREVLASTV = MAX( I, PREVLASTV ) IF( TAU( I ).EQ.ZERO ) THEN * * H(i) = I * DO J = 1, I T( J, I ) = ZERO END DO ELSE * * general case * IF( LSAME( STOREV, 'C' ) ) THEN * Skip any trailing zeros. DO LASTV = N, I+1, -1 IF( V( LASTV, I ).NE.ZERO ) EXIT END DO DO J = 1, I-1 T( J, I ) = -TAU( I ) * V( I , J ) END DO J = MIN( LASTV, PREVLASTV ) * * T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i) * CALL DGEMV( 'Transpose', J-I, I-1, -TAU( I ), $ V( I+1, 1 ), LDV, V( I+1, I ), 1, ONE, $ T( 1, I ), 1 ) ELSE * Skip any trailing zeros. DO LASTV = N, I+1, -1 IF( V( I, LASTV ).NE.ZERO ) EXIT END DO DO J = 1, I-1 T( J, I ) = -TAU( I ) * V( J , I ) END DO J = MIN( LASTV, PREVLASTV ) * * T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T * CALL DGEMV( 'No transpose', I-1, J-I, -TAU( I ), $ V( 1, I+1 ), LDV, V( I, I+1 ), LDV, ONE, $ T( 1, I ), 1 ) END IF * * T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) * CALL DTRMV( 'Upper', 'No transpose', 'Non-unit', I-1, T, $ LDT, T( 1, I ), 1 ) T( I, I ) = TAU( I ) IF( I.GT.1 ) THEN PREVLASTV = MAX( PREVLASTV, LASTV ) ELSE PREVLASTV = LASTV END IF END IF END DO ELSE PREVLASTV = 1 DO I = K, 1, -1 IF( TAU( I ).EQ.ZERO ) THEN * * H(i) = I * DO J = I, K T( J, I ) = ZERO END DO ELSE * * general case * IF( I.LT.K ) THEN IF( LSAME( STOREV, 'C' ) ) THEN * Skip any leading zeros. DO LASTV = 1, I-1 IF( V( LASTV, I ).NE.ZERO ) EXIT END DO DO J = I+1, K T( J, I ) = -TAU( I ) * V( N-K+I , J ) END DO J = MAX( LASTV, PREVLASTV ) * * T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i) * CALL DGEMV( 'Transpose', N-K+I-J, K-I, -TAU( I ), $ V( J, I+1 ), LDV, V( J, I ), 1, ONE, $ T( I+1, I ), 1 ) ELSE * Skip any leading zeros. DO LASTV = 1, I-1 IF( V( I, LASTV ).NE.ZERO ) EXIT END DO DO J = I+1, K T( J, I ) = -TAU( I ) * V( J, N-K+I ) END DO J = MAX( LASTV, PREVLASTV ) * * T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T * CALL DGEMV( 'No transpose', K-I, N-K+I-J, $ -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV, $ ONE, T( I+1, I ), 1 ) END IF * * T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) * CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I, $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 ) IF( I.GT.1 ) THEN PREVLASTV = MIN( PREVLASTV, LASTV ) ELSE PREVLASTV = LASTV END IF END IF T( I, I ) = TAU( I ) END IF END DO END IF RETURN * * End of DLARFT * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlarfb.f0000644000000000000000000000013214061636515015256 xustar0030 mtime=1623670093.381103916 30 atime=1623670093.381103916 30 ctime=1623670093.381103916 elk-7.2.42/src/LAPACK/dlarfb.f0000644002504400250440000005142514061636515017322 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLARFB applies a block reflector or its transpose to a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARFB + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, * T, LDT, C, LDC, WORK, LDWORK ) * * .. Scalar Arguments .. * CHARACTER DIRECT, SIDE, STOREV, TRANS * INTEGER K, LDC, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), * $ WORK( LDWORK, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARFB applies a real block reflector H or its transpose H**T to a *> real m by n matrix C, from either the left or the right. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply H or H**T from the Left *> = 'R': apply H or H**T from the Right *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply H (No transpose) *> = 'T': apply H**T (Transpose) *> \endverbatim *> *> \param[in] DIRECT *> \verbatim *> DIRECT is CHARACTER*1 *> Indicates how H is formed from a product of elementary *> reflectors *> = 'F': H = H(1) H(2) . . . H(k) (Forward) *> = 'B': H = H(k) . . . H(2) H(1) (Backward) *> \endverbatim *> *> \param[in] STOREV *> \verbatim *> STOREV is CHARACTER*1 *> Indicates how the vectors which define the elementary *> reflectors are stored: *> = 'C': Columnwise *> = 'R': Rowwise *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The order of the matrix T (= the number of elementary *> reflectors whose product defines the block reflector). *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is DOUBLE PRECISION array, dimension *> (LDV,K) if STOREV = 'C' *> (LDV,M) if STOREV = 'R' and SIDE = 'L' *> (LDV,N) if STOREV = 'R' and SIDE = 'R' *> The matrix V. See Further Details. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V. *> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); *> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); *> if STOREV = 'R', LDV >= K. *> \endverbatim *> *> \param[in] T *> \verbatim *> T is DOUBLE PRECISION array, dimension (LDT,K) *> The triangular k by k matrix T in the representation of the *> block reflector. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= K. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> On entry, the m by n matrix C. *> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (LDWORK,K) *> \endverbatim *> *> \param[in] LDWORK *> \verbatim *> LDWORK is INTEGER *> The leading dimension of the array WORK. *> If SIDE = 'L', LDWORK >= max(1,N); *> if SIDE = 'R', LDWORK >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2013 * *> \ingroup doubleOTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> The shape of the matrix V and the storage of the vectors which define *> the H(i) is best illustrated by the following example with n = 5 and *> k = 3. The elements equal to 1 are not stored; the corresponding *> array elements are modified but restored on exit. The rest of the *> array is not used. *> *> DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': *> *> V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) *> ( v1 1 ) ( 1 v2 v2 v2 ) *> ( v1 v2 1 ) ( 1 v3 v3 ) *> ( v1 v2 v3 ) *> ( v1 v2 v3 ) *> *> DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': *> *> V = ( v1 v2 v3 ) V = ( v1 v1 1 ) *> ( v1 v2 v3 ) ( v2 v2 v2 1 ) *> ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) *> ( 1 v3 ) *> ( 1 ) *> \endverbatim *> * ===================================================================== SUBROUTINE DLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, $ T, LDT, C, LDC, WORK, LDWORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2013 * * .. Scalar Arguments .. CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER K, LDC, LDT, LDV, LDWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ), $ WORK( LDWORK, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. CHARACTER TRANST INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMM, DTRMM * .. * .. Executable Statements .. * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) $ RETURN * IF( LSAME( TRANS, 'N' ) ) THEN TRANST = 'T' ELSE TRANST = 'N' END IF * IF( LSAME( STOREV, 'C' ) ) THEN * IF( LSAME( DIRECT, 'F' ) ) THEN * * Let V = ( V1 ) (first K rows) * ( V2 ) * where V1 is unit lower triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**T * C where C = ( C1 ) * ( C2 ) * * W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) * * W := C1**T * DO 10 J = 1, K CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 10 CONTINUE * * W := W * V1 * CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, $ K, ONE, V, LDV, WORK, LDWORK ) IF( M.GT.K ) THEN * * W := W + C2**T * V2 * CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K, $ ONE, C( K+1, 1 ), LDC, V( K+1, 1 ), LDV, $ ONE, WORK, LDWORK ) END IF * * W := W * T**T or W * T * CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - V * W**T * IF( M.GT.K ) THEN * * C2 := C2 - V2 * W**T * CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K, $ -ONE, V( K+1, 1 ), LDV, WORK, LDWORK, ONE, $ C( K+1, 1 ), LDC ) END IF * * W := W * V1**T * CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K, $ ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W**T * DO 30 J = 1, K DO 20 I = 1, N C( J, I ) = C( J, I ) - WORK( I, J ) 20 CONTINUE 30 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**T where C = ( C1 C2 ) * * W := C * V = (C1*V1 + C2*V2) (stored in WORK) * * W := C1 * DO 40 J = 1, K CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 40 CONTINUE * * W := W * V1 * CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, $ K, ONE, V, LDV, WORK, LDWORK ) IF( N.GT.K ) THEN * * W := W + C2 * V2 * CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K, $ ONE, C( 1, K+1 ), LDC, V( K+1, 1 ), LDV, $ ONE, WORK, LDWORK ) END IF * * W := W * T or W * T**T * CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V**T * IF( N.GT.K ) THEN * * C2 := C2 - W * V2**T * CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K, $ -ONE, WORK, LDWORK, V( K+1, 1 ), LDV, ONE, $ C( 1, K+1 ), LDC ) END IF * * W := W * V1**T * CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K, $ ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W * DO 60 J = 1, K DO 50 I = 1, M C( I, J ) = C( I, J ) - WORK( I, J ) 50 CONTINUE 60 CONTINUE END IF * ELSE * * Let V = ( V1 ) * ( V2 ) (last K rows) * where V2 is unit upper triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**T * C where C = ( C1 ) * ( C2 ) * * W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK) * * W := C2**T * DO 70 J = 1, K CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) 70 CONTINUE * * W := W * V2 * CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, $ K, ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) IF( M.GT.K ) THEN * * W := W + C1**T * V1 * CALL DGEMM( 'Transpose', 'No transpose', N, K, M-K, $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF * * W := W * T**T or W * T * CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - V * W**T * IF( M.GT.K ) THEN * * C1 := C1 - V1 * W**T * CALL DGEMM( 'No transpose', 'Transpose', M-K, N, K, $ -ONE, V, LDV, WORK, LDWORK, ONE, C, LDC ) END IF * * W := W * V2**T * CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K, $ ONE, V( M-K+1, 1 ), LDV, WORK, LDWORK ) * * C2 := C2 - W**T * DO 90 J = 1, K DO 80 I = 1, N C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J ) 80 CONTINUE 90 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**T where C = ( C1 C2 ) * * W := C * V = (C1*V1 + C2*V2) (stored in WORK) * * W := C2 * DO 100 J = 1, K CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 100 CONTINUE * * W := W * V2 * CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, $ K, ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) IF( N.GT.K ) THEN * * W := W + C1 * V1 * CALL DGEMM( 'No transpose', 'No transpose', M, K, N-K, $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF * * W := W * T or W * T**T * CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V**T * IF( N.GT.K ) THEN * * C1 := C1 - W * V1**T * CALL DGEMM( 'No transpose', 'Transpose', M, N-K, K, $ -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) END IF * * W := W * V2**T * CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K, $ ONE, V( N-K+1, 1 ), LDV, WORK, LDWORK ) * * C2 := C2 - W * DO 120 J = 1, K DO 110 I = 1, M C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) 110 CONTINUE 120 CONTINUE END IF END IF * ELSE IF( LSAME( STOREV, 'R' ) ) THEN * IF( LSAME( DIRECT, 'F' ) ) THEN * * Let V = ( V1 V2 ) (V1: first K columns) * where V1 is unit upper triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**T * C where C = ( C1 ) * ( C2 ) * * W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) * * W := C1**T * DO 130 J = 1, K CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 ) 130 CONTINUE * * W := W * V1**T * CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', N, K, $ ONE, V, LDV, WORK, LDWORK ) IF( M.GT.K ) THEN * * W := W + C2**T * V2**T * CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE, $ C( K+1, 1 ), LDC, V( 1, K+1 ), LDV, ONE, $ WORK, LDWORK ) END IF * * W := W * T**T or W * T * CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit', N, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - V**T * W**T * IF( M.GT.K ) THEN * * C2 := C2 - V2**T * W**T * CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE, $ V( 1, K+1 ), LDV, WORK, LDWORK, ONE, $ C( K+1, 1 ), LDC ) END IF * * W := W * V1 * CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', N, $ K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W**T * DO 150 J = 1, K DO 140 I = 1, N C( J, I ) = C( J, I ) - WORK( I, J ) 140 CONTINUE 150 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H**T where C = ( C1 C2 ) * * W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) * * W := C1 * DO 160 J = 1, K CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 ) 160 CONTINUE * * W := W * V1**T * CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit', M, K, $ ONE, V, LDV, WORK, LDWORK ) IF( N.GT.K ) THEN * * W := W + C2 * V2**T * CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K, $ ONE, C( 1, K+1 ), LDC, V( 1, K+1 ), LDV, $ ONE, WORK, LDWORK ) END IF * * W := W * T or W * T**T * CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit', M, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V * IF( N.GT.K ) THEN * * C2 := C2 - W * V2 * CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K, $ -ONE, WORK, LDWORK, V( 1, K+1 ), LDV, ONE, $ C( 1, K+1 ), LDC ) END IF * * W := W * V1 * CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit', M, $ K, ONE, V, LDV, WORK, LDWORK ) * * C1 := C1 - W * DO 180 J = 1, K DO 170 I = 1, M C( I, J ) = C( I, J ) - WORK( I, J ) 170 CONTINUE 180 CONTINUE * END IF * ELSE * * Let V = ( V1 V2 ) (V2: last K columns) * where V2 is unit lower triangular. * IF( LSAME( SIDE, 'L' ) ) THEN * * Form H * C or H**T * C where C = ( C1 ) * ( C2 ) * * W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK) * * W := C2**T * DO 190 J = 1, K CALL DCOPY( N, C( M-K+J, 1 ), LDC, WORK( 1, J ), 1 ) 190 CONTINUE * * W := W * V2**T * CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', N, K, $ ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) IF( M.GT.K ) THEN * * W := W + C1**T * V1**T * CALL DGEMM( 'Transpose', 'Transpose', N, K, M-K, ONE, $ C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF * * W := W * T**T or W * T * CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - V**T * W**T * IF( M.GT.K ) THEN * * C1 := C1 - V1**T * W**T * CALL DGEMM( 'Transpose', 'Transpose', M-K, N, K, -ONE, $ V, LDV, WORK, LDWORK, ONE, C, LDC ) END IF * * W := W * V2 * CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', N, $ K, ONE, V( 1, M-K+1 ), LDV, WORK, LDWORK ) * * C2 := C2 - W**T * DO 210 J = 1, K DO 200 I = 1, N C( M-K+J, I ) = C( M-K+J, I ) - WORK( I, J ) 200 CONTINUE 210 CONTINUE * ELSE IF( LSAME( SIDE, 'R' ) ) THEN * * Form C * H or C * H' where C = ( C1 C2 ) * * W := C * V**T = (C1*V1**T + C2*V2**T) (stored in WORK) * * W := C2 * DO 220 J = 1, K CALL DCOPY( M, C( 1, N-K+J ), 1, WORK( 1, J ), 1 ) 220 CONTINUE * * W := W * V2**T * CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit', M, K, $ ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) IF( N.GT.K ) THEN * * W := W + C1 * V1**T * CALL DGEMM( 'No transpose', 'Transpose', M, K, N-K, $ ONE, C, LDC, V, LDV, ONE, WORK, LDWORK ) END IF * * W := W * T or W * T**T * CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, $ ONE, T, LDT, WORK, LDWORK ) * * C := C - W * V * IF( N.GT.K ) THEN * * C1 := C1 - W * V1 * CALL DGEMM( 'No transpose', 'No transpose', M, N-K, K, $ -ONE, WORK, LDWORK, V, LDV, ONE, C, LDC ) END IF * * W := W * V2 * CALL DTRMM( 'Right', 'Lower', 'No transpose', 'Unit', M, $ K, ONE, V( 1, N-K+1 ), LDV, WORK, LDWORK ) * * C1 := C1 - W * DO 240 J = 1, K DO 230 I = 1, M C( I, N-K+J ) = C( I, N-K+J ) - WORK( I, J ) 230 CONTINUE 240 CONTINUE * END IF * END IF END IF * RETURN * * End of DLARFB * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dorg2r.f0000644000000000000000000000013214061636515015223 xustar0030 mtime=1623670093.383103914 30 atime=1623670093.383103914 30 ctime=1623670093.383103914 elk-7.2.42/src/LAPACK/dorg2r.f0000644002504400250440000001222014061636515017255 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORG2R + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORG2R generates an m by n real matrix Q with orthonormal columns, *> which is defined as the first n columns of a product of k elementary *> reflectors of order m *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by DGEQRF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. M >= N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the i-th column must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by DGEQRF in the first k columns of its array *> argument A. *> On exit, the m-by-n matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEQRF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, L * .. * .. External Subroutines .. EXTERNAL DLARF, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORG2R', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.0 ) $ RETURN * * Initialise columns k+1:n to columns of the unit matrix * DO 20 J = K + 1, N DO 10 L = 1, M A( L, J ) = ZERO 10 CONTINUE A( J, J ) = ONE 20 CONTINUE * DO 40 I = K, 1, -1 * * Apply H(i) to A(i:m,i:n) from the left * IF( I.LT.N ) THEN A( I, I ) = ONE CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ), $ A( I, I+1 ), LDA, WORK ) END IF IF( I.LT.M ) $ CALL DSCAL( M-I, -TAU( I ), A( I+1, I ), 1 ) A( I, I ) = ONE - TAU( I ) * * Set A(1:i-1,i) to zero * DO 30 L = 1, I - 1 A( L, I ) = ZERO 30 CONTINUE 40 CONTINUE RETURN * * End of DORG2R * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dormql.f0000644000000000000000000000013214061636515015322 xustar0030 mtime=1623670093.385103912 30 atime=1623670093.385103912 30 ctime=1623670093.385103912 elk-7.2.42/src/LAPACK/dormql.f0000644002504400250440000002227514061636515017367 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORMQL * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORMQL + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORMQL overwrites the general real M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'T': Q**T * C C * Q**T *> *> where Q is a real orthogonal matrix defined as the product of k *> elementary reflectors *> *> Q = H(k) . . . H(2) H(1) *> *> as returned by DGEQLF. Q is of order M if SIDE = 'L' and of order N *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**T from the Left; *> = 'R': apply Q or Q**T from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'T': Transpose, apply Q**T. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> DGEQLF in the last k columns of its array argument A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,M); *> if SIDE = 'R', LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEQLF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For good performance, LWORK should generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NBMAX, LDT, TSIZE PARAMETER ( NBMAX = 64, LDT = NBMAX+1, $ TSIZE = LDT*NBMAX ) * .. * .. Local Scalars .. LOGICAL LEFT, LQUERY, NOTRAN INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT, $ MI, NB, NBMIN, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DLARFB, DLARFT, DORM2L, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = MAX( 1, N ) ELSE NQ = N NW = MAX( 1, M ) END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN INFO = -12 END IF * IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * IF( M.EQ.0 .OR. N.EQ.0 ) THEN LWKOPT = 1 ELSE NB = MIN( NBMAX, ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N, $ K, -1 ) ) LWKOPT = NW*NB + TSIZE END IF WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMQL', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 ) THEN RETURN END IF * NBMIN = 2 LDWORK = NW IF( NB.GT.1 .AND. NB.LT.K ) THEN IF( LWORK.LT.NW*NB+TSIZE ) THEN NB = (LWORK-TSIZE) / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DORMQL', SIDE // TRANS, M, N, K, $ -1 ) ) END IF END IF * IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN * * Use unblocked code * CALL DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, $ IINFO ) ELSE * * Use blocked code * IWT = 1 + NW*NB IF( ( LEFT .AND. NOTRAN ) .OR. $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN I1 = 1 I2 = K I3 = NB ELSE I1 = ( ( K-1 ) / NB )*NB + 1 I2 = 1 I3 = -NB END IF * IF( LEFT ) THEN NI = N ELSE MI = M END IF * DO 10 I = I1, I2, I3 IB = MIN( NB, K-I+1 ) * * Form the triangular factor of the block reflector * H = H(i+ib-1) . . . H(i+1) H(i) * CALL DLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB, $ A( 1, I ), LDA, TAU( I ), WORK( IWT ), LDT ) IF( LEFT ) THEN * * H or H**T is applied to C(1:m-k+i+ib-1,1:n) * MI = M - K + I + IB - 1 ELSE * * H or H**T is applied to C(1:m,1:n-k+i+ib-1) * NI = N - K + I + IB - 1 END IF * * Apply H or H**T * CALL DLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI, $ IB, A( 1, I ), LDA, WORK( IWT ), LDT, C, LDC, $ WORK, LDWORK ) 10 CONTINUE END IF WORK( 1 ) = LWKOPT RETURN * * End of DORMQL * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dormqr.f0000644000000000000000000000012714061636515015334 xustar0029 mtime=1623670093.38710391 29 atime=1623670093.38710391 29 ctime=1623670093.38710391 elk-7.2.42/src/LAPACK/dormqr.f0000644002504400250440000002224114061636515017366 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORMQR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORMQR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORMQR overwrites the general real M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'T': Q**T * C C * Q**T *> *> where Q is a real orthogonal matrix defined as the product of k *> elementary reflectors *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**T from the Left; *> = 'R': apply Q or Q**T from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': No transpose, apply Q; *> = 'T': Transpose, apply Q**T. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> DGEQRF in the first k columns of its array argument A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,M); *> if SIDE = 'R', LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEQRF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For good performance, LWORK should generally be larger. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NBMAX, LDT, TSIZE PARAMETER ( NBMAX = 64, LDT = NBMAX+1, $ TSIZE = LDT*NBMAX ) * .. * .. Local Scalars .. LOGICAL LEFT, LQUERY, NOTRAN INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK, $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DLARFB, DLARFT, DORM2R, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -12 END IF * IF( INFO.EQ.0 ) THEN * * Compute the workspace requirements * NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K, $ -1 ) ) LWKOPT = MAX( 1, NW )*NB + TSIZE WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMQR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * NBMIN = 2 LDWORK = NW IF( NB.GT.1 .AND. NB.LT.K ) THEN IF( LWORK.LT.NW*NB+TSIZE ) THEN NB = (LWORK-TSIZE) / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K, $ -1 ) ) END IF END IF * IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN * * Use unblocked code * CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, $ IINFO ) ELSE * * Use blocked code * IWT = 1 + NW*NB IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN I1 = 1 I2 = K I3 = NB ELSE I1 = ( ( K-1 ) / NB )*NB + 1 I2 = 1 I3 = -NB END IF * IF( LEFT ) THEN NI = N JC = 1 ELSE MI = M IC = 1 END IF * DO 10 I = I1, I2, I3 IB = MIN( NB, K-I+1 ) * * Form the triangular factor of the block reflector * H = H(i) H(i+1) . . . H(i+ib-1) * CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ), $ LDA, TAU( I ), WORK( IWT ), LDT ) IF( LEFT ) THEN * * H or H**T is applied to C(i:m,1:n) * MI = M - I + 1 IC = I ELSE * * H or H**T is applied to C(1:m,i:n) * NI = N - I + 1 JC = I END IF * * Apply H or H**T * CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI, $ IB, A( I, I ), LDA, WORK( IWT ), LDT, $ C( IC, JC ), LDC, WORK, LDWORK ) 10 CONTINUE END IF WORK( 1 ) = LWKOPT RETURN * * End of DORMQR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed0.f0000644000000000000000000000013214061636515015155 xustar0030 mtime=1623670093.389103908 30 atime=1623670093.389103908 30 ctime=1623670093.389103908 elk-7.2.42/src/LAPACK/dlaed0.f0000644002504400250440000003310614061636515017215 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED0 used by sstedc. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED0 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, * WORK, IWORK, INFO ) * * .. Scalar Arguments .. * INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ * .. * .. Array Arguments .. * INTEGER IWORK( * ) * DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), * $ WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAED0 computes all eigenvalues and corresponding eigenvectors of a *> symmetric tridiagonal matrix using the divide and conquer method. *> \endverbatim * * Arguments: * ========== * *> \param[in] ICOMPQ *> \verbatim *> ICOMPQ is INTEGER *> = 0: Compute eigenvalues only. *> = 1: Compute eigenvectors of original dense symmetric matrix *> also. On entry, Q contains the orthogonal matrix used *> to reduce the original matrix to tridiagonal form. *> = 2: Compute eigenvalues and eigenvectors of tridiagonal *> matrix. *> \endverbatim *> *> \param[in] QSIZ *> \verbatim *> QSIZ is INTEGER *> The dimension of the orthogonal matrix used to reduce *> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the main diagonal of the tridiagonal matrix. *> On exit, its eigenvalues. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is DOUBLE PRECISION array, dimension (N-1) *> The off-diagonal elements of the tridiagonal matrix. *> On exit, E has been destroyed. *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDQ, N) *> On entry, Q must contain an N-by-N orthogonal matrix. *> If ICOMPQ = 0 Q is not referenced. *> If ICOMPQ = 1 On entry, Q is a subset of the columns of the *> orthogonal matrix used to reduce the full *> matrix to tridiagonal form corresponding to *> the subset of the full matrix which is being *> decomposed at this time. *> If ICOMPQ = 2 On entry, Q will be the identity matrix. *> On exit, Q contains the eigenvectors of the *> tridiagonal matrix. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. If eigenvectors are *> desired, then LDQ >= max(1,N). In any case, LDQ >= 1. *> \endverbatim *> *> \param[out] QSTORE *> \verbatim *> QSTORE is DOUBLE PRECISION array, dimension (LDQS, N) *> Referenced only when ICOMPQ = 1. Used to store parts of *> the eigenvector matrix when the updating matrix multiplies *> take place. *> \endverbatim *> *> \param[in] LDQS *> \verbatim *> LDQS is INTEGER *> The leading dimension of the array QSTORE. If ICOMPQ = 1, *> then LDQS >= max(1,N). In any case, LDQS >= 1. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, *> If ICOMPQ = 0 or 1, the dimension of WORK must be at least *> 1 + 3*N + 2*N*lg N + 3*N**2 *> ( lg( N ) = smallest integer k *> such that 2^k >= N ) *> If ICOMPQ = 2, the dimension of WORK must be at least *> 4*N + N**2. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, *> If ICOMPQ = 0 or 1, the dimension of IWORK must be at least *> 6 + 6*N + 5*N*lg N. *> ( lg( N ) = smallest integer k *> such that 2^k >= N ) *> If ICOMPQ = 2, the dimension of IWORK must be at least *> 3 + 5*N. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: The algorithm failed to compute an eigenvalue while *> working on the submatrix lying in rows and columns *> INFO/(N+1) through mod(INFO,N+1). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA * * ===================================================================== SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, $ WORK, IWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ), $ WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO PARAMETER ( ZERO = 0.D0, ONE = 1.D0, TWO = 2.D0 ) * .. * .. Local Scalars .. INTEGER CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM, $ IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM, $ J, K, LGN, MATSIZ, MSD2, SMLSIZ, SMM1, SPM1, $ SPM2, SUBMAT, SUBPBS, TLVLS DOUBLE PRECISION TEMP * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMM, DLACPY, DLAED1, DLAED7, DSTEQR, $ XERBLA * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, INT, LOG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.2 ) THEN INFO = -1 ELSE IF( ( ICOMPQ.EQ.1 ) .AND. ( QSIZ.LT.MAX( 0, N ) ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAED0', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * SMLSIZ = ILAENV( 9, 'DLAED0', ' ', 0, 0, 0, 0 ) * * Determine the size and placement of the submatrices, and save in * the leading elements of IWORK. * IWORK( 1 ) = N SUBPBS = 1 TLVLS = 0 10 CONTINUE IF( IWORK( SUBPBS ).GT.SMLSIZ ) THEN DO 20 J = SUBPBS, 1, -1 IWORK( 2*J ) = ( IWORK( J )+1 ) / 2 IWORK( 2*J-1 ) = IWORK( J ) / 2 20 CONTINUE TLVLS = TLVLS + 1 SUBPBS = 2*SUBPBS GO TO 10 END IF DO 30 J = 2, SUBPBS IWORK( J ) = IWORK( J ) + IWORK( J-1 ) 30 CONTINUE * * Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 * using rank-1 modifications (cuts). * SPM1 = SUBPBS - 1 DO 40 I = 1, SPM1 SUBMAT = IWORK( I ) + 1 SMM1 = SUBMAT - 1 D( SMM1 ) = D( SMM1 ) - ABS( E( SMM1 ) ) D( SUBMAT ) = D( SUBMAT ) - ABS( E( SMM1 ) ) 40 CONTINUE * INDXQ = 4*N + 3 IF( ICOMPQ.NE.2 ) THEN * * Set up workspaces for eigenvalues only/accumulate new vectors * routine * TEMP = LOG( DBLE( N ) ) / LOG( TWO ) LGN = INT( TEMP ) IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IPRMPT = INDXQ + N + 1 IPERM = IPRMPT + N*LGN IQPTR = IPERM + N*LGN IGIVPT = IQPTR + N + 2 IGIVCL = IGIVPT + N*LGN * IGIVNM = 1 IQ = IGIVNM + 2*N*LGN IWREM = IQ + N**2 + 1 * * Initialize pointers * DO 50 I = 0, SUBPBS IWORK( IPRMPT+I ) = 1 IWORK( IGIVPT+I ) = 1 50 CONTINUE IWORK( IQPTR ) = 1 END IF * * Solve each submatrix eigenproblem at the bottom of the divide and * conquer tree. * CURR = 0 DO 70 I = 0, SPM1 IF( I.EQ.0 ) THEN SUBMAT = 1 MATSIZ = IWORK( 1 ) ELSE SUBMAT = IWORK( I ) + 1 MATSIZ = IWORK( I+1 ) - IWORK( I ) END IF IF( ICOMPQ.EQ.2 ) THEN CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ), $ Q( SUBMAT, SUBMAT ), LDQ, WORK, INFO ) IF( INFO.NE.0 ) $ GO TO 130 ELSE CALL DSTEQR( 'I', MATSIZ, D( SUBMAT ), E( SUBMAT ), $ WORK( IQ-1+IWORK( IQPTR+CURR ) ), MATSIZ, WORK, $ INFO ) IF( INFO.NE.0 ) $ GO TO 130 IF( ICOMPQ.EQ.1 ) THEN CALL DGEMM( 'N', 'N', QSIZ, MATSIZ, MATSIZ, ONE, $ Q( 1, SUBMAT ), LDQ, WORK( IQ-1+IWORK( IQPTR+ $ CURR ) ), MATSIZ, ZERO, QSTORE( 1, SUBMAT ), $ LDQS ) END IF IWORK( IQPTR+CURR+1 ) = IWORK( IQPTR+CURR ) + MATSIZ**2 CURR = CURR + 1 END IF K = 1 DO 60 J = SUBMAT, IWORK( I+1 ) IWORK( INDXQ+J ) = K K = K + 1 60 CONTINUE 70 CONTINUE * * Successively merge eigensystems of adjacent submatrices * into eigensystem for the corresponding larger matrix. * * while ( SUBPBS > 1 ) * CURLVL = 1 80 CONTINUE IF( SUBPBS.GT.1 ) THEN SPM2 = SUBPBS - 2 DO 90 I = 0, SPM2, 2 IF( I.EQ.0 ) THEN SUBMAT = 1 MATSIZ = IWORK( 2 ) MSD2 = IWORK( 1 ) CURPRB = 0 ELSE SUBMAT = IWORK( I ) + 1 MATSIZ = IWORK( I+2 ) - IWORK( I ) MSD2 = MATSIZ / 2 CURPRB = CURPRB + 1 END IF * * Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) * into an eigensystem of size MATSIZ. * DLAED1 is used only for the full eigensystem of a tridiagonal * matrix. * DLAED7 handles the cases in which eigenvalues only or eigenvalues * and eigenvectors of a full symmetric matrix (which was reduced to * tridiagonal form) are desired. * IF( ICOMPQ.EQ.2 ) THEN CALL DLAED1( MATSIZ, D( SUBMAT ), Q( SUBMAT, SUBMAT ), $ LDQ, IWORK( INDXQ+SUBMAT ), $ E( SUBMAT+MSD2-1 ), MSD2, WORK, $ IWORK( SUBPBS+1 ), INFO ) ELSE CALL DLAED7( ICOMPQ, MATSIZ, QSIZ, TLVLS, CURLVL, CURPRB, $ D( SUBMAT ), QSTORE( 1, SUBMAT ), LDQS, $ IWORK( INDXQ+SUBMAT ), E( SUBMAT+MSD2-1 ), $ MSD2, WORK( IQ ), IWORK( IQPTR ), $ IWORK( IPRMPT ), IWORK( IPERM ), $ IWORK( IGIVPT ), IWORK( IGIVCL ), $ WORK( IGIVNM ), WORK( IWREM ), $ IWORK( SUBPBS+1 ), INFO ) END IF IF( INFO.NE.0 ) $ GO TO 130 IWORK( I / 2+1 ) = IWORK( I+2 ) 90 CONTINUE SUBPBS = SUBPBS / 2 CURLVL = CURLVL + 1 GO TO 80 END IF * * end while * * Re-merge the eigenvalues/vectors which were deflated at the final * merge step. * IF( ICOMPQ.EQ.1 ) THEN DO 100 I = 1, N J = IWORK( INDXQ+I ) WORK( I ) = D( J ) CALL DCOPY( QSIZ, QSTORE( 1, J ), 1, Q( 1, I ), 1 ) 100 CONTINUE CALL DCOPY( N, WORK, 1, D, 1 ) ELSE IF( ICOMPQ.EQ.2 ) THEN DO 110 I = 1, N J = IWORK( INDXQ+I ) WORK( I ) = D( J ) CALL DCOPY( N, Q( 1, J ), 1, WORK( N*I+1 ), 1 ) 110 CONTINUE CALL DCOPY( N, WORK, 1, D, 1 ) CALL DLACPY( 'A', N, N, WORK( N+1 ), N, Q, LDQ ) ELSE DO 120 I = 1, N J = IWORK( INDXQ+I ) WORK( I ) = D( J ) 120 CONTINUE CALL DCOPY( N, WORK, 1, D, 1 ) END IF GO TO 140 * 130 CONTINUE INFO = SUBMAT*( N+1 ) + SUBMAT + MATSIZ - 1 * 140 CONTINUE RETURN * * End of DLAED0 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlacgv.f0000644000000000000000000000013214061636515015312 xustar0030 mtime=1623670093.391103906 30 atime=1623670093.391103906 30 ctime=1623670093.391103906 elk-7.2.42/src/LAPACK/zlacgv.f0000644002504400250440000000544414061636515017356 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLACGV conjugates a complex vector. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLACGV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLACGV( N, X, INCX ) * * .. Scalar Arguments .. * INTEGER INCX, N * .. * .. Array Arguments .. * COMPLEX*16 X( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLACGV conjugates a complex vector of length N. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The length of the vector X. N >= 0. *> \endverbatim *> *> \param[in,out] X *> \verbatim *> X is COMPLEX*16 array, dimension *> (1+(N-1)*abs(INCX)) *> On entry, the vector of length N to be conjugated. *> On exit, X is overwritten with conjg(X). *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The spacing between successive elements of X. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZLACGV( N, X, INCX ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX, N * .. * .. Array Arguments .. COMPLEX*16 X( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, IOFF * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. Executable Statements .. * IF( INCX.EQ.1 ) THEN DO 10 I = 1, N X( I ) = DCONJG( X( I ) ) 10 CONTINUE ELSE IOFF = 1 IF( INCX.LT.0 ) $ IOFF = 1 - ( N-1 )*INCX DO 20 I = 1, N X( IOFF ) = DCONJG( X( IOFF ) ) IOFF = IOFF + INCX 20 CONTINUE END IF RETURN * * End of ZLACGV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaed7.f0000644000000000000000000000013214061636515015212 xustar0030 mtime=1623670093.393103905 30 atime=1623670093.393103905 30 ctime=1623670093.393103905 elk-7.2.42/src/LAPACK/zlaed7.f0000644002504400250440000003036314061636515017254 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAED7 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, * LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, * GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, * INFO ) * * .. Scalar Arguments .. * INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, * $ TLVLS * DOUBLE PRECISION RHO * .. * .. Array Arguments .. * INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), * $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) * DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * ) * COMPLEX*16 Q( LDQ, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAED7 computes the updated eigensystem of a diagonal *> matrix after modification by a rank-one symmetric matrix. This *> routine is used only for the eigenproblem which requires all *> eigenvalues and optionally eigenvectors of a dense or banded *> Hermitian matrix that has been reduced to tridiagonal form. *> *> T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) *> *> where Z = Q**Hu, u is a vector of length N with ones in the *> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. *> *> The eigenvectors of the original matrix are stored in Q, and the *> eigenvalues are in D. The algorithm consists of three stages: *> *> The first stage consists of deflating the size of the problem *> when there are multiple eigenvalues or if there is a zero in *> the Z vector. For each such occurrence the dimension of the *> secular equation problem is reduced by one. This stage is *> performed by the routine DLAED2. *> *> The second stage consists of calculating the updated *> eigenvalues. This is done by finding the roots of the secular *> equation via the routine DLAED4 (as called by SLAED3). *> This routine also calculates the eigenvectors of the current *> problem. *> *> The final stage consists of computing the updated eigenvectors *> directly using the updated eigenvalues. The eigenvectors for *> the current problem are multiplied with the eigenvectors from *> the overall problem. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in] CUTPNT *> \verbatim *> CUTPNT is INTEGER *> Contains the location of the last eigenvalue in the leading *> sub-matrix. min(1,N) <= CUTPNT <= N. *> \endverbatim *> *> \param[in] QSIZ *> \verbatim *> QSIZ is INTEGER *> The dimension of the unitary matrix used to reduce *> the full matrix to tridiagonal form. QSIZ >= N. *> \endverbatim *> *> \param[in] TLVLS *> \verbatim *> TLVLS is INTEGER *> The total number of merging levels in the overall divide and *> conquer tree. *> \endverbatim *> *> \param[in] CURLVL *> \verbatim *> CURLVL is INTEGER *> The current level in the overall merge routine, *> 0 <= curlvl <= tlvls. *> \endverbatim *> *> \param[in] CURPBM *> \verbatim *> CURPBM is INTEGER *> The current problem in the current level in the overall *> merge routine (counting from upper left to lower right). *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the eigenvalues of the rank-1-perturbed matrix. *> On exit, the eigenvalues of the repaired matrix. *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDQ,N) *> On entry, the eigenvectors of the rank-1-perturbed matrix. *> On exit, the eigenvectors of the repaired tridiagonal matrix. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[in] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> Contains the subdiagonal element used to create the rank-1 *> modification. *> \endverbatim *> *> \param[out] INDXQ *> \verbatim *> INDXQ is INTEGER array, dimension (N) *> This contains the permutation which will reintegrate the *> subproblem just solved back into sorted order, *> ie. D( INDXQ( I = 1, N ) ) will be in ascending order. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (4*N) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, *> dimension (3*N+2*QSIZ*N) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (QSIZ*N) *> \endverbatim *> *> \param[in,out] QSTORE *> \verbatim *> QSTORE is DOUBLE PRECISION array, dimension (N**2+1) *> Stores eigenvectors of submatrices encountered during *> divide and conquer, packed together. QPTR points to *> beginning of the submatrices. *> \endverbatim *> *> \param[in,out] QPTR *> \verbatim *> QPTR is INTEGER array, dimension (N+2) *> List of indices pointing to beginning of submatrices stored *> in QSTORE. The submatrices are numbered starting at the *> bottom left of the divide and conquer tree, from left to *> right and bottom to top. *> \endverbatim *> *> \param[in] PRMPTR *> \verbatim *> PRMPTR is INTEGER array, dimension (N lg N) *> Contains a list of pointers which indicate where in PERM a *> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) *> indicates the size of the permutation and also the size of *> the full, non-deflated problem. *> \endverbatim *> *> \param[in] PERM *> \verbatim *> PERM is INTEGER array, dimension (N lg N) *> Contains the permutations (from deflation and sorting) to be *> applied to each eigenblock. *> \endverbatim *> *> \param[in] GIVPTR *> \verbatim *> GIVPTR is INTEGER array, dimension (N lg N) *> Contains a list of pointers which indicate where in GIVCOL a *> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) *> indicates the number of Givens rotations. *> \endverbatim *> *> \param[in] GIVCOL *> \verbatim *> GIVCOL is INTEGER array, dimension (2, N lg N) *> Each pair of numbers indicates a pair of columns to take place *> in a Givens rotation. *> \endverbatim *> *> \param[in] GIVNUM *> \verbatim *> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) *> Each number indicates the S value to be used in the *> corresponding Givens rotation. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, an eigenvalue did not converge *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, $ LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, $ GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, $ INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, $ TLVLS DOUBLE PRECISION RHO * .. * .. Array Arguments .. INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * ) COMPLEX*16 Q( LDQ, * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER COLTYP, CURR, I, IDLMDA, INDX, $ INDXC, INDXP, IQ, IW, IZ, K, N1, N2, PTR * .. * .. External Subroutines .. EXTERNAL DLAED9, DLAEDA, DLAMRG, XERBLA, ZLACRM, ZLAED8 * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * * IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN * INFO = -1 * ELSE IF( N.LT.0 ) THEN IF( N.LT.0 ) THEN INFO = -1 ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN INFO = -2 ELSE IF( QSIZ.LT.N ) THEN INFO = -3 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -9 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLAED7', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * The following values are for bookkeeping purposes only. They are * integer pointers which indicate the portion of the workspace * used by a particular array in DLAED2 and SLAED3. * IZ = 1 IDLMDA = IZ + N IW = IDLMDA + N IQ = IW + N * INDX = 1 INDXC = INDX + N COLTYP = INDXC + N INDXP = COLTYP + N * * Form the z-vector which consists of the last row of Q_1 and the * first row of Q_2. * PTR = 1 + 2**TLVLS DO 10 I = 1, CURLVL - 1 PTR = PTR + 2**( TLVLS-I ) 10 CONTINUE CURR = PTR + CURPBM CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, $ GIVCOL, GIVNUM, QSTORE, QPTR, RWORK( IZ ), $ RWORK( IZ+N ), INFO ) * * When solving the final problem, we no longer need the stored data, * so we will overwrite the data from this level onto the previously * used storage space. * IF( CURLVL.EQ.TLVLS ) THEN QPTR( CURR ) = 1 PRMPTR( CURR ) = 1 GIVPTR( CURR ) = 1 END IF * * Sort and Deflate eigenvalues. * CALL ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, RWORK( IZ ), $ RWORK( IDLMDA ), WORK, QSIZ, RWORK( IW ), $ IWORK( INDXP ), IWORK( INDX ), INDXQ, $ PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), $ GIVCOL( 1, GIVPTR( CURR ) ), $ GIVNUM( 1, GIVPTR( CURR ) ), INFO ) PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) * * Solve Secular Equation. * IF( K.NE.0 ) THEN CALL DLAED9( K, 1, K, N, D, RWORK( IQ ), K, RHO, $ RWORK( IDLMDA ), RWORK( IW ), $ QSTORE( QPTR( CURR ) ), K, INFO ) CALL ZLACRM( QSIZ, K, WORK, QSIZ, QSTORE( QPTR( CURR ) ), K, Q, $ LDQ, RWORK( IQ ) ) QPTR( CURR+1 ) = QPTR( CURR ) + K**2 IF( INFO.NE.0 ) THEN RETURN END IF * * Prepare the INDXQ sorting premutation. * N1 = K N2 = N - K CALL DLAMRG( N1, N2, D, 1, -1, INDXQ ) ELSE QPTR( CURR+1 ) = QPTR( CURR ) DO 20 I = 1, N INDXQ( I ) = I 20 CONTINUE END IF * RETURN * * End of ZLAED7 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zladiv.f0000644000000000000000000000013214061636515015315 xustar0030 mtime=1623670093.395103903 30 atime=1623670093.395103903 30 ctime=1623670093.395103903 elk-7.2.42/src/LAPACK/zladiv.f0000644002504400250440000000457114061636515017361 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLADIV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * COMPLEX*16 FUNCTION ZLADIV( X, Y ) * * .. Scalar Arguments .. * COMPLEX*16 X, Y * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLADIV := X / Y, where X and Y are complex. The computation of X / Y *> will not overflow on an intermediary step unless the results *> overflows. *> \endverbatim * * Arguments: * ========== * *> \param[in] X *> \verbatim *> X is COMPLEX*16 *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is COMPLEX*16 *> The complex scalars X and Y. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== COMPLEX*16 FUNCTION ZLADIV( X, Y ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. COMPLEX*16 X, Y * .. * * ===================================================================== * * .. Local Scalars .. DOUBLE PRECISION ZI, ZR * .. * .. External Subroutines .. EXTERNAL DLADIV * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, DIMAG * .. * .. Executable Statements .. * CALL DLADIV( DBLE( X ), DIMAG( X ), DBLE( Y ), DIMAG( Y ), ZR, $ ZI ) ZLADIV = DCMPLX( ZR, ZI ) * RETURN * * End of ZLADIV * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaqr3.f0000644000000000000000000000013214061636515015240 xustar0030 mtime=1623670093.397103901 30 atime=1623670093.396103902 30 ctime=1623670093.397103901 elk-7.2.42/src/LAPACK/zlaqr3.f0000644002504400250440000004311514061636515017301 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAQR3 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, * IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, * NV, WV, LDWV, WORK, LWORK ) * * .. Scalar Arguments .. * INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV, * $ LDZ, LWORK, N, ND, NH, NS, NV, NW * LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. * COMPLEX*16 H( LDH, * ), SH( * ), T( LDT, * ), V( LDV, * ), * $ WORK( * ), WV( LDWV, * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Aggressive early deflation: *> *> ZLAQR3 accepts as input an upper Hessenberg matrix *> H and performs an unitary similarity transformation *> designed to detect and deflate fully converged eigenvalues from *> a trailing principal submatrix. On output H has been over- *> written by a new Hessenberg matrix that is a perturbation of *> an unitary similarity transformation of H. It is to be *> hoped that the final version of H has many zero subdiagonal *> entries. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] WANTT *> \verbatim *> WANTT is LOGICAL *> If .TRUE., then the Hessenberg matrix H is fully updated *> so that the triangular Schur factor may be *> computed (in cooperation with the calling subroutine). *> If .FALSE., then only enough of H is updated to preserve *> the eigenvalues. *> \endverbatim *> *> \param[in] WANTZ *> \verbatim *> WANTZ is LOGICAL *> If .TRUE., then the unitary matrix Z is updated so *> so that the unitary Schur factor may be computed *> (in cooperation with the calling subroutine). *> If .FALSE., then Z is not referenced. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix H and (if WANTZ is .TRUE.) the *> order of the unitary matrix Z. *> \endverbatim *> *> \param[in] KTOP *> \verbatim *> KTOP is INTEGER *> It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. *> KBOT and KTOP together determine an isolated block *> along the diagonal of the Hessenberg matrix. *> \endverbatim *> *> \param[in] KBOT *> \verbatim *> KBOT is INTEGER *> It is assumed without a check that either *> KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together *> determine an isolated block along the diagonal of the *> Hessenberg matrix. *> \endverbatim *> *> \param[in] NW *> \verbatim *> NW is INTEGER *> Deflation window size. 1 <= NW <= (KBOT-KTOP+1). *> \endverbatim *> *> \param[in,out] H *> \verbatim *> H is COMPLEX*16 array, dimension (LDH,N) *> On input the initial N-by-N section of H stores the *> Hessenberg matrix undergoing aggressive early deflation. *> On output H has been transformed by a unitary *> similarity transformation, perturbed, and the returned *> to Hessenberg form that (it is to be hoped) has some *> zero subdiagonal entries. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> Leading dimension of H just as declared in the calling *> subroutine. N <= LDH *> \endverbatim *> *> \param[in] ILOZ *> \verbatim *> ILOZ is INTEGER *> \endverbatim *> *> \param[in] IHIZ *> \verbatim *> IHIZ is INTEGER *> Specify the rows of Z to which transformations must be *> applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ,N) *> IF WANTZ is .TRUE., then on output, the unitary *> similarity transformation mentioned above has been *> accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. *> If WANTZ is .FALSE., then Z is unreferenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of Z just as declared in the *> calling subroutine. 1 <= LDZ. *> \endverbatim *> *> \param[out] NS *> \verbatim *> NS is INTEGER *> The number of unconverged (ie approximate) eigenvalues *> returned in SR and SI that may be used as shifts by the *> calling subroutine. *> \endverbatim *> *> \param[out] ND *> \verbatim *> ND is INTEGER *> The number of converged eigenvalues uncovered by this *> subroutine. *> \endverbatim *> *> \param[out] SH *> \verbatim *> SH is COMPLEX*16 array, dimension (KBOT) *> On output, approximate eigenvalues that may *> be used for shifts are stored in SH(KBOT-ND-NS+1) *> through SR(KBOT-ND). Converged eigenvalues are *> stored in SH(KBOT-ND+1) through SH(KBOT). *> \endverbatim *> *> \param[out] V *> \verbatim *> V is COMPLEX*16 array, dimension (LDV,NW) *> An NW-by-NW work array. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of V just as declared in the *> calling subroutine. NW <= LDV *> \endverbatim *> *> \param[in] NH *> \verbatim *> NH is INTEGER *> The number of columns of T. NH >= NW. *> \endverbatim *> *> \param[out] T *> \verbatim *> T is COMPLEX*16 array, dimension (LDT,NW) *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of T just as declared in the *> calling subroutine. NW <= LDT *> \endverbatim *> *> \param[in] NV *> \verbatim *> NV is INTEGER *> The number of rows of work array WV available for *> workspace. NV >= NW. *> \endverbatim *> *> \param[out] WV *> \verbatim *> WV is COMPLEX*16 array, dimension (LDWV,NW) *> \endverbatim *> *> \param[in] LDWV *> \verbatim *> LDWV is INTEGER *> The leading dimension of W just as declared in the *> calling subroutine. NW <= LDV *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (LWORK) *> On exit, WORK(1) is set to an estimate of the optimal value *> of LWORK for the given values of N, NW, KTOP and KBOT. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. *> *> If LWORK = -1, then a workspace query is assumed; ZLAQR3 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned *> in WORK(1). No error message related to LWORK is issued *> by XERBLA. Neither H nor Z are accessed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Contributors: * ================== *> *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA *> * ===================================================================== SUBROUTINE ZLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, $ IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, $ NV, WV, LDWV, WORK, LWORK ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV, $ LDZ, LWORK, N, ND, NH, NS, NV, NW LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), SH( * ), T( LDT, * ), V( LDV, * ), $ WORK( * ), WV( LDWV, * ), Z( LDZ, * ) * .. * * ================================================================ * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), $ ONE = ( 1.0d0, 0.0d0 ) ) DOUBLE PRECISION RZERO, RONE PARAMETER ( RZERO = 0.0d0, RONE = 1.0d0 ) * .. * .. Local Scalars .. COMPLEX*16 BETA, CDUM, S, TAU DOUBLE PRECISION FOO, SAFMAX, SAFMIN, SMLNUM, ULP INTEGER I, IFST, ILST, INFO, INFQR, J, JW, KCOL, KLN, $ KNT, KROW, KWTOP, LTOP, LWK1, LWK2, LWK3, $ LWKOPT, NMIN * .. * .. External Functions .. DOUBLE PRECISION DLAMCH INTEGER ILAENV EXTERNAL DLAMCH, ILAENV * .. * .. External Subroutines .. EXTERNAL DLABAD, ZCOPY, ZGEHRD, ZGEMM, ZLACPY, ZLAHQR, $ ZLAQR4, ZLARF, ZLARFG, ZLASET, ZTREXC, ZUNMHR * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, MAX, MIN * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. Executable Statements .. * * ==== Estimate optimal workspace. ==== * JW = MIN( NW, KBOT-KTOP+1 ) IF( JW.LE.2 ) THEN LWKOPT = 1 ELSE * * ==== Workspace query call to ZGEHRD ==== * CALL ZGEHRD( JW, 1, JW-1, T, LDT, WORK, WORK, -1, INFO ) LWK1 = INT( WORK( 1 ) ) * * ==== Workspace query call to ZUNMHR ==== * CALL ZUNMHR( 'R', 'N', JW, JW, 1, JW-1, T, LDT, WORK, V, LDV, $ WORK, -1, INFO ) LWK2 = INT( WORK( 1 ) ) * * ==== Workspace query call to ZLAQR4 ==== * CALL ZLAQR4( .true., .true., JW, 1, JW, T, LDT, SH, 1, JW, V, $ LDV, WORK, -1, INFQR ) LWK3 = INT( WORK( 1 ) ) * * ==== Optimal workspace ==== * LWKOPT = MAX( JW+MAX( LWK1, LWK2 ), LWK3 ) END IF * * ==== Quick return in case of workspace query. ==== * IF( LWORK.EQ.-1 ) THEN WORK( 1 ) = DCMPLX( LWKOPT, 0 ) RETURN END IF * * ==== Nothing to do ... * ... for an empty active block ... ==== NS = 0 ND = 0 WORK( 1 ) = ONE IF( KTOP.GT.KBOT ) $ RETURN * ... nor for an empty deflation window. ==== IF( NW.LT.1 ) $ RETURN * * ==== Machine constants ==== * SAFMIN = DLAMCH( 'SAFE MINIMUM' ) SAFMAX = RONE / SAFMIN CALL DLABAD( SAFMIN, SAFMAX ) ULP = DLAMCH( 'PRECISION' ) SMLNUM = SAFMIN*( DBLE( N ) / ULP ) * * ==== Setup deflation window ==== * JW = MIN( NW, KBOT-KTOP+1 ) KWTOP = KBOT - JW + 1 IF( KWTOP.EQ.KTOP ) THEN S = ZERO ELSE S = H( KWTOP, KWTOP-1 ) END IF * IF( KBOT.EQ.KWTOP ) THEN * * ==== 1-by-1 deflation window: not much to do ==== * SH( KWTOP ) = H( KWTOP, KWTOP ) NS = 1 ND = 0 IF( CABS1( S ).LE.MAX( SMLNUM, ULP*CABS1( H( KWTOP, $ KWTOP ) ) ) ) THEN NS = 0 ND = 1 IF( KWTOP.GT.KTOP ) $ H( KWTOP, KWTOP-1 ) = ZERO END IF WORK( 1 ) = ONE RETURN END IF * * ==== Convert to spike-triangular form. (In case of a * . rare QR failure, this routine continues to do * . aggressive early deflation using that part of * . the deflation window that converged using INFQR * . here and there to keep track.) ==== * CALL ZLACPY( 'U', JW, JW, H( KWTOP, KWTOP ), LDH, T, LDT ) CALL ZCOPY( JW-1, H( KWTOP+1, KWTOP ), LDH+1, T( 2, 1 ), LDT+1 ) * CALL ZLASET( 'A', JW, JW, ZERO, ONE, V, LDV ) NMIN = ILAENV( 12, 'ZLAQR3', 'SV', JW, 1, JW, LWORK ) IF( JW.GT.NMIN ) THEN CALL ZLAQR4( .true., .true., JW, 1, JW, T, LDT, SH( KWTOP ), 1, $ JW, V, LDV, WORK, LWORK, INFQR ) ELSE CALL ZLAHQR( .true., .true., JW, 1, JW, T, LDT, SH( KWTOP ), 1, $ JW, V, LDV, INFQR ) END IF * * ==== Deflation detection loop ==== * NS = JW ILST = INFQR + 1 DO 10 KNT = INFQR + 1, JW * * ==== Small spike tip deflation test ==== * FOO = CABS1( T( NS, NS ) ) IF( FOO.EQ.RZERO ) $ FOO = CABS1( S ) IF( CABS1( S )*CABS1( V( 1, NS ) ).LE.MAX( SMLNUM, ULP*FOO ) ) $ THEN * * ==== One more converged eigenvalue ==== * NS = NS - 1 ELSE * * ==== One undeflatable eigenvalue. Move it up out of the * . way. (ZTREXC can not fail in this case.) ==== * IFST = NS CALL ZTREXC( 'V', JW, T, LDT, V, LDV, IFST, ILST, INFO ) ILST = ILST + 1 END IF 10 CONTINUE * * ==== Return to Hessenberg form ==== * IF( NS.EQ.0 ) $ S = ZERO * IF( NS.LT.JW ) THEN * * ==== sorting the diagonal of T improves accuracy for * . graded matrices. ==== * DO 30 I = INFQR + 1, NS IFST = I DO 20 J = I + 1, NS IF( CABS1( T( J, J ) ).GT.CABS1( T( IFST, IFST ) ) ) $ IFST = J 20 CONTINUE ILST = I IF( IFST.NE.ILST ) $ CALL ZTREXC( 'V', JW, T, LDT, V, LDV, IFST, ILST, INFO ) 30 CONTINUE END IF * * ==== Restore shift/eigenvalue array from T ==== * DO 40 I = INFQR + 1, JW SH( KWTOP+I-1 ) = T( I, I ) 40 CONTINUE * * IF( NS.LT.JW .OR. S.EQ.ZERO ) THEN IF( NS.GT.1 .AND. S.NE.ZERO ) THEN * * ==== Reflect spike back into lower triangle ==== * CALL ZCOPY( NS, V, LDV, WORK, 1 ) DO 50 I = 1, NS WORK( I ) = DCONJG( WORK( I ) ) 50 CONTINUE BETA = WORK( 1 ) CALL ZLARFG( NS, BETA, WORK( 2 ), 1, TAU ) WORK( 1 ) = ONE * CALL ZLASET( 'L', JW-2, JW-2, ZERO, ZERO, T( 3, 1 ), LDT ) * CALL ZLARF( 'L', NS, JW, WORK, 1, DCONJG( TAU ), T, LDT, $ WORK( JW+1 ) ) CALL ZLARF( 'R', NS, NS, WORK, 1, TAU, T, LDT, $ WORK( JW+1 ) ) CALL ZLARF( 'R', JW, NS, WORK, 1, TAU, V, LDV, $ WORK( JW+1 ) ) * CALL ZGEHRD( JW, 1, NS, T, LDT, WORK, WORK( JW+1 ), $ LWORK-JW, INFO ) END IF * * ==== Copy updated reduced window into place ==== * IF( KWTOP.GT.1 ) $ H( KWTOP, KWTOP-1 ) = S*DCONJG( V( 1, 1 ) ) CALL ZLACPY( 'U', JW, JW, T, LDT, H( KWTOP, KWTOP ), LDH ) CALL ZCOPY( JW-1, T( 2, 1 ), LDT+1, H( KWTOP+1, KWTOP ), $ LDH+1 ) * * ==== Accumulate orthogonal matrix in order update * . H and Z, if requested. ==== * IF( NS.GT.1 .AND. S.NE.ZERO ) $ CALL ZUNMHR( 'R', 'N', JW, NS, 1, NS, T, LDT, WORK, V, LDV, $ WORK( JW+1 ), LWORK-JW, INFO ) * * ==== Update vertical slab in H ==== * IF( WANTT ) THEN LTOP = 1 ELSE LTOP = KTOP END IF DO 60 KROW = LTOP, KWTOP - 1, NV KLN = MIN( NV, KWTOP-KROW ) CALL ZGEMM( 'N', 'N', KLN, JW, JW, ONE, H( KROW, KWTOP ), $ LDH, V, LDV, ZERO, WV, LDWV ) CALL ZLACPY( 'A', KLN, JW, WV, LDWV, H( KROW, KWTOP ), LDH ) 60 CONTINUE * * ==== Update horizontal slab in H ==== * IF( WANTT ) THEN DO 70 KCOL = KBOT + 1, N, NH KLN = MIN( NH, N-KCOL+1 ) CALL ZGEMM( 'C', 'N', JW, KLN, JW, ONE, V, LDV, $ H( KWTOP, KCOL ), LDH, ZERO, T, LDT ) CALL ZLACPY( 'A', JW, KLN, T, LDT, H( KWTOP, KCOL ), $ LDH ) 70 CONTINUE END IF * * ==== Update vertical slab in Z ==== * IF( WANTZ ) THEN DO 80 KROW = ILOZ, IHIZ, NV KLN = MIN( NV, IHIZ-KROW+1 ) CALL ZGEMM( 'N', 'N', KLN, JW, JW, ONE, Z( KROW, KWTOP ), $ LDZ, V, LDV, ZERO, WV, LDWV ) CALL ZLACPY( 'A', KLN, JW, WV, LDWV, Z( KROW, KWTOP ), $ LDZ ) 80 CONTINUE END IF END IF * * ==== Return the number of deflations ... ==== * ND = JW - NS * * ==== ... and the number of shifts. (Subtracting * . INFQR from the spike length takes care * . of the case of a rare QR failure while * . calculating eigenvalues of the deflation * . window.) ==== * NS = NS - INFQR * * ==== Return optimal workspace. ==== * WORK( 1 ) = DCMPLX( LWKOPT, 0 ) * * ==== End of ZLAQR3 ==== * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaqr4.f0000644000000000000000000000013214061636515015241 xustar0030 mtime=1623670093.399103899 30 atime=1623670093.399103899 30 ctime=1623670093.399103899 elk-7.2.42/src/LAPACK/zlaqr4.f0000644002504400250440000006076514061636515017314 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Schur decomposition. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAQR4 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, * IHIZ, Z, LDZ, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N * LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. * COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAQR4 implements one level of recursion for ZLAQR0. *> It is a complete implementation of the small bulge multi-shift *> QR algorithm. It may be called by ZLAQR0 and, for large enough *> deflation window size, it may be called by ZLAQR3. This *> subroutine is identical to ZLAQR0 except that it calls ZLAQR2 *> instead of ZLAQR3. *> *> ZLAQR4 computes the eigenvalues of a Hessenberg matrix H *> and, optionally, the matrices T and Z from the Schur decomposition *> H = Z T Z**H, where T is an upper triangular matrix (the *> Schur form), and Z is the unitary matrix of Schur vectors. *> *> Optionally Z may be postmultiplied into an input unitary *> matrix Q so that this routine can give the Schur factorization *> of a matrix A which has been reduced to the Hessenberg form H *> by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H. *> \endverbatim * * Arguments: * ========== * *> \param[in] WANTT *> \verbatim *> WANTT is LOGICAL *> = .TRUE. : the full Schur form T is required; *> = .FALSE.: only eigenvalues are required. *> \endverbatim *> *> \param[in] WANTZ *> \verbatim *> WANTZ is LOGICAL *> = .TRUE. : the matrix of Schur vectors Z is required; *> = .FALSE.: Schur vectors are not required. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix H. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> It is assumed that H is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N and, if ILO > 1, *> H(ILO,ILO-1) is zero. ILO and IHI are normally set by a *> previous call to ZGEBAL, and then passed to ZGEHRD when the *> matrix output by ZGEBAL is reduced to Hessenberg form. *> Otherwise, ILO and IHI should be set to 1 and N, *> respectively. If N > 0, then 1 <= ILO <= IHI <= N. *> If N = 0, then ILO = 1 and IHI = 0. *> \endverbatim *> *> \param[in,out] H *> \verbatim *> H is COMPLEX*16 array, dimension (LDH,N) *> On entry, the upper Hessenberg matrix H. *> On exit, if INFO = 0 and WANTT is .TRUE., then H *> contains the upper triangular matrix T from the Schur *> decomposition (the Schur form). If INFO = 0 and WANT is *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO > 0 is given under the *> description of INFO below.) *> *> This subroutine may explicitly set H(i,j) = 0 for i > j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> The leading dimension of the array H. LDH >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is COMPLEX*16 array, dimension (N) *> The computed eigenvalues of H(ILO:IHI,ILO:IHI) are stored *> in W(ILO:IHI). If WANTT is .TRUE., then the eigenvalues are *> stored in the same order as on the diagonal of the Schur *> form returned in H, with W(i) = H(i,i). *> \endverbatim *> *> \param[in] ILOZ *> \verbatim *> ILOZ is INTEGER *> \endverbatim *> *> \param[in] IHIZ *> \verbatim *> IHIZ is INTEGER *> Specify the rows of Z to which transformations must be *> applied if WANTZ is .TRUE.. *> 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ,IHI) *> If WANTZ is .FALSE., then Z is not referenced. *> If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is *> replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the *> orthogonal Schur factor of H(ILO:IHI,ILO:IHI). *> (The output value of Z when INFO > 0 is given under *> the description of INFO below.) *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of the array Z. if WANTZ is .TRUE. *> then LDZ >= MAX(1,IHIZ). Otherwise, LDZ >= 1. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension LWORK *> On exit, if LWORK = -1, WORK(1) returns an estimate of *> the optimal value for LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N) *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. *> *> If LWORK = -1, then ZLAQR4 does a workspace query. *> In this case, ZLAQR4 checks the input parameters and *> estimates the optimal workspace size for the given *> values of N, ILO and IHI. The estimate is returned *> in WORK(1). No error message related to LWORK is *> issued by XERBLA. Neither H nor Z are accessed. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = i, ZLAQR4 failed to compute all of *> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR *> and WI contain those eigenvalues which have been *> successfully computed. (Failures are rare.) *> *> If INFO > 0 and WANT is .FALSE., then on exit, *> the remaining unconverged eigenvalues are the eigen- *> values of the upper Hessenberg matrix rows and *> columns ILO through INFO of the final, output *> value of H. *> *> If INFO > 0 and WANTT is .TRUE., then on exit *> *> (*) (initial value of H)*U = U*(final value of H) *> *> where U is a unitary matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. *> *> If INFO > 0 and WANTZ is .TRUE., then on exit *> *> (final value of Z(ILO:IHI,ILOZ:IHIZ) *> = (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U *> *> where U is the unitary matrix in (*) (regard- *> less of the value of WANTT.) *> *> If INFO > 0 and WANTZ is .FALSE., then Z is not *> accessed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Contributors: * ================== *> *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA * *> \par References: * ================ *> *> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR *> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 *> Performance, SIAM Journal of Matrix Analysis, volume 23, pages *> 929--947, 2002. *> \n *> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR *> Algorithm Part II: Aggressive Early Deflation, SIAM Journal *> of Matrix Analysis, volume 23, pages 948--973, 2002. *> * ===================================================================== SUBROUTINE ZLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, $ IHIZ, Z, LDZ, WORK, LWORK, INFO ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * ) * .. * * ================================================================ * * .. Parameters .. * * ==== Matrices of order NTINY or smaller must be processed by * . ZLAHQR because of insufficient subdiagonal scratch space. * . (This is a hard limit.) ==== INTEGER NTINY PARAMETER ( NTINY = 11 ) * * ==== Exceptional deflation windows: try to cure rare * . slow convergence by varying the size of the * . deflation window after KEXNW iterations. ==== INTEGER KEXNW PARAMETER ( KEXNW = 5 ) * * ==== Exceptional shifts: try to cure rare slow convergence * . with ad-hoc exceptional shifts every KEXSH iterations. * . ==== INTEGER KEXSH PARAMETER ( KEXSH = 6 ) * * ==== The constant WILK1 is used to form the exceptional * . shifts. ==== DOUBLE PRECISION WILK1 PARAMETER ( WILK1 = 0.75d0 ) COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), $ ONE = ( 1.0d0, 0.0d0 ) ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0d0 ) * .. * .. Local Scalars .. COMPLEX*16 AA, BB, CC, CDUM, DD, DET, RTDISC, SWAP, TR2 DOUBLE PRECISION S INTEGER I, INF, IT, ITMAX, K, KACC22, KBOT, KDU, KS, $ KT, KTOP, KU, KV, KWH, KWTOP, KWV, LD, LS, $ LWKOPT, NDEC, NDFL, NH, NHO, NIBBLE, NMIN, NS, $ NSMAX, NSR, NVE, NW, NWMAX, NWR, NWUPBD LOGICAL SORTED CHARACTER JBCMPZ*2 * .. * .. External Functions .. INTEGER ILAENV EXTERNAL ILAENV * .. * .. Local Arrays .. COMPLEX*16 ZDUM( 1, 1 ) * .. * .. External Subroutines .. EXTERNAL ZLACPY, ZLAHQR, ZLAQR2, ZLAQR5 * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DIMAG, INT, MAX, MIN, MOD, $ SQRT * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. Executable Statements .. INFO = 0 * * ==== Quick return for N = 0: nothing to do. ==== * IF( N.EQ.0 ) THEN WORK( 1 ) = ONE RETURN END IF * IF( N.LE.NTINY ) THEN * * ==== Tiny matrices must use ZLAHQR. ==== * LWKOPT = 1 IF( LWORK.NE.-1 ) $ CALL ZLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, $ IHIZ, Z, LDZ, INFO ) ELSE * * ==== Use small bulge multi-shift QR with aggressive early * . deflation on larger-than-tiny matrices. ==== * * ==== Hope for the best. ==== * INFO = 0 * * ==== Set up job flags for ILAENV. ==== * IF( WANTT ) THEN JBCMPZ( 1: 1 ) = 'S' ELSE JBCMPZ( 1: 1 ) = 'E' END IF IF( WANTZ ) THEN JBCMPZ( 2: 2 ) = 'V' ELSE JBCMPZ( 2: 2 ) = 'N' END IF * * ==== NWR = recommended deflation window size. At this * . point, N .GT. NTINY = 11, so there is enough * . subdiagonal workspace for NWR.GE.2 as required. * . (In fact, there is enough subdiagonal space for * . NWR.GE.3.) ==== * NWR = ILAENV( 13, 'ZLAQR4', JBCMPZ, N, ILO, IHI, LWORK ) NWR = MAX( 2, NWR ) NWR = MIN( IHI-ILO+1, ( N-1 ) / 3, NWR ) * * ==== NSR = recommended number of simultaneous shifts. * . At this point N .GT. NTINY = 11, so there is at * . enough subdiagonal workspace for NSR to be even * . and greater than or equal to two as required. ==== * NSR = ILAENV( 15, 'ZLAQR4', JBCMPZ, N, ILO, IHI, LWORK ) NSR = MIN( NSR, ( N+6 ) / 9, IHI-ILO ) NSR = MAX( 2, NSR-MOD( NSR, 2 ) ) * * ==== Estimate optimal workspace ==== * * ==== Workspace query call to ZLAQR2 ==== * CALL ZLAQR2( WANTT, WANTZ, N, ILO, IHI, NWR+1, H, LDH, ILOZ, $ IHIZ, Z, LDZ, LS, LD, W, H, LDH, N, H, LDH, N, H, $ LDH, WORK, -1 ) * * ==== Optimal workspace = MAX(ZLAQR5, ZLAQR2) ==== * LWKOPT = MAX( 3*NSR / 2, INT( WORK( 1 ) ) ) * * ==== Quick return in case of workspace query. ==== * IF( LWORK.EQ.-1 ) THEN WORK( 1 ) = DCMPLX( LWKOPT, 0 ) RETURN END IF * * ==== ZLAHQR/ZLAQR0 crossover point ==== * NMIN = ILAENV( 12, 'ZLAQR4', JBCMPZ, N, ILO, IHI, LWORK ) NMIN = MAX( NTINY, NMIN ) * * ==== Nibble crossover point ==== * NIBBLE = ILAENV( 14, 'ZLAQR4', JBCMPZ, N, ILO, IHI, LWORK ) NIBBLE = MAX( 0, NIBBLE ) * * ==== Accumulate reflections during ttswp? Use block * . 2-by-2 structure during matrix-matrix multiply? ==== * KACC22 = ILAENV( 16, 'ZLAQR4', JBCMPZ, N, ILO, IHI, LWORK ) KACC22 = MAX( 0, KACC22 ) KACC22 = MIN( 2, KACC22 ) * * ==== NWMAX = the largest possible deflation window for * . which there is sufficient workspace. ==== * NWMAX = MIN( ( N-1 ) / 3, LWORK / 2 ) NW = NWMAX * * ==== NSMAX = the Largest number of simultaneous shifts * . for which there is sufficient workspace. ==== * NSMAX = MIN( ( N+6 ) / 9, 2*LWORK / 3 ) NSMAX = NSMAX - MOD( NSMAX, 2 ) * * ==== NDFL: an iteration count restarted at deflation. ==== * NDFL = 1 * * ==== ITMAX = iteration limit ==== * ITMAX = MAX( 30, 2*KEXSH )*MAX( 10, ( IHI-ILO+1 ) ) * * ==== Last row and column in the active block ==== * KBOT = IHI * * ==== Main Loop ==== * DO 70 IT = 1, ITMAX * * ==== Done when KBOT falls below ILO ==== * IF( KBOT.LT.ILO ) $ GO TO 80 * * ==== Locate active block ==== * DO 10 K = KBOT, ILO + 1, -1 IF( H( K, K-1 ).EQ.ZERO ) $ GO TO 20 10 CONTINUE K = ILO 20 CONTINUE KTOP = K * * ==== Select deflation window size: * . Typical Case: * . If possible and advisable, nibble the entire * . active block. If not, use size MIN(NWR,NWMAX) * . or MIN(NWR+1,NWMAX) depending upon which has * . the smaller corresponding subdiagonal entry * . (a heuristic). * . * . Exceptional Case: * . If there have been no deflations in KEXNW or * . more iterations, then vary the deflation window * . size. At first, because, larger windows are, * . in general, more powerful than smaller ones, * . rapidly increase the window to the maximum possible. * . Then, gradually reduce the window size. ==== * NH = KBOT - KTOP + 1 NWUPBD = MIN( NH, NWMAX ) IF( NDFL.LT.KEXNW ) THEN NW = MIN( NWUPBD, NWR ) ELSE NW = MIN( NWUPBD, 2*NW ) END IF IF( NW.LT.NWMAX ) THEN IF( NW.GE.NH-1 ) THEN NW = NH ELSE KWTOP = KBOT - NW + 1 IF( CABS1( H( KWTOP, KWTOP-1 ) ).GT. $ CABS1( H( KWTOP-1, KWTOP-2 ) ) )NW = NW + 1 END IF END IF IF( NDFL.LT.KEXNW ) THEN NDEC = -1 ELSE IF( NDEC.GE.0 .OR. NW.GE.NWUPBD ) THEN NDEC = NDEC + 1 IF( NW-NDEC.LT.2 ) $ NDEC = 0 NW = NW - NDEC END IF * * ==== Aggressive early deflation: * . split workspace under the subdiagonal into * . - an nw-by-nw work array V in the lower * . left-hand-corner, * . - an NW-by-at-least-NW-but-more-is-better * . (NW-by-NHO) horizontal work array along * . the bottom edge, * . - an at-least-NW-but-more-is-better (NHV-by-NW) * . vertical work array along the left-hand-edge. * . ==== * KV = N - NW + 1 KT = NW + 1 NHO = ( N-NW-1 ) - KT + 1 KWV = NW + 2 NVE = ( N-NW ) - KWV + 1 * * ==== Aggressive early deflation ==== * CALL ZLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, $ IHIZ, Z, LDZ, LS, LD, W, H( KV, 1 ), LDH, NHO, $ H( KV, KT ), LDH, NVE, H( KWV, 1 ), LDH, WORK, $ LWORK ) * * ==== Adjust KBOT accounting for new deflations. ==== * KBOT = KBOT - LD * * ==== KS points to the shifts. ==== * KS = KBOT - LS + 1 * * ==== Skip an expensive QR sweep if there is a (partly * . heuristic) reason to expect that many eigenvalues * . will deflate without it. Here, the QR sweep is * . skipped if many eigenvalues have just been deflated * . or if the remaining active block is small. * IF( ( LD.EQ.0 ) .OR. ( ( 100*LD.LE.NW*NIBBLE ) .AND. ( KBOT- $ KTOP+1.GT.MIN( NMIN, NWMAX ) ) ) ) THEN * * ==== NS = nominal number of simultaneous shifts. * . This may be lowered (slightly) if ZLAQR2 * . did not provide that many shifts. ==== * NS = MIN( NSMAX, NSR, MAX( 2, KBOT-KTOP ) ) NS = NS - MOD( NS, 2 ) * * ==== If there have been no deflations * . in a multiple of KEXSH iterations, * . then try exceptional shifts. * . Otherwise use shifts provided by * . ZLAQR2 above or from the eigenvalues * . of a trailing principal submatrix. ==== * IF( MOD( NDFL, KEXSH ).EQ.0 ) THEN KS = KBOT - NS + 1 DO 30 I = KBOT, KS + 1, -2 W( I ) = H( I, I ) + WILK1*CABS1( H( I, I-1 ) ) W( I-1 ) = W( I ) 30 CONTINUE ELSE * * ==== Got NS/2 or fewer shifts? Use ZLAHQR * . on a trailing principal submatrix to * . get more. (Since NS.LE.NSMAX.LE.(N+6)/9, * . there is enough space below the subdiagonal * . to fit an NS-by-NS scratch array.) ==== * IF( KBOT-KS+1.LE.NS / 2 ) THEN KS = KBOT - NS + 1 KT = N - NS + 1 CALL ZLACPY( 'A', NS, NS, H( KS, KS ), LDH, $ H( KT, 1 ), LDH ) CALL ZLAHQR( .false., .false., NS, 1, NS, $ H( KT, 1 ), LDH, W( KS ), 1, 1, ZDUM, $ 1, INF ) KS = KS + INF * * ==== In case of a rare QR failure use * . eigenvalues of the trailing 2-by-2 * . principal submatrix. Scale to avoid * . overflows, underflows and subnormals. * . (The scale factor S can not be zero, * . because H(KBOT,KBOT-1) is nonzero.) ==== * IF( KS.GE.KBOT ) THEN S = CABS1( H( KBOT-1, KBOT-1 ) ) + $ CABS1( H( KBOT, KBOT-1 ) ) + $ CABS1( H( KBOT-1, KBOT ) ) + $ CABS1( H( KBOT, KBOT ) ) AA = H( KBOT-1, KBOT-1 ) / S CC = H( KBOT, KBOT-1 ) / S BB = H( KBOT-1, KBOT ) / S DD = H( KBOT, KBOT ) / S TR2 = ( AA+DD ) / TWO DET = ( AA-TR2 )*( DD-TR2 ) - BB*CC RTDISC = SQRT( -DET ) W( KBOT-1 ) = ( TR2+RTDISC )*S W( KBOT ) = ( TR2-RTDISC )*S * KS = KBOT - 1 END IF END IF * IF( KBOT-KS+1.GT.NS ) THEN * * ==== Sort the shifts (Helps a little) ==== * SORTED = .false. DO 50 K = KBOT, KS + 1, -1 IF( SORTED ) $ GO TO 60 SORTED = .true. DO 40 I = KS, K - 1 IF( CABS1( W( I ) ).LT.CABS1( W( I+1 ) ) ) $ THEN SORTED = .false. SWAP = W( I ) W( I ) = W( I+1 ) W( I+1 ) = SWAP END IF 40 CONTINUE 50 CONTINUE 60 CONTINUE END IF END IF * * ==== If there are only two shifts, then use * . only one. ==== * IF( KBOT-KS+1.EQ.2 ) THEN IF( CABS1( W( KBOT )-H( KBOT, KBOT ) ).LT. $ CABS1( W( KBOT-1 )-H( KBOT, KBOT ) ) ) THEN W( KBOT-1 ) = W( KBOT ) ELSE W( KBOT ) = W( KBOT-1 ) END IF END IF * * ==== Use up to NS of the the smallest magnitude * . shifts. If there aren't NS shifts available, * . then use them all, possibly dropping one to * . make the number of shifts even. ==== * NS = MIN( NS, KBOT-KS+1 ) NS = NS - MOD( NS, 2 ) KS = KBOT - NS + 1 * * ==== Small-bulge multi-shift QR sweep: * . split workspace under the subdiagonal into * . - a KDU-by-KDU work array U in the lower * . left-hand-corner, * . - a KDU-by-at-least-KDU-but-more-is-better * . (KDU-by-NHo) horizontal work array WH along * . the bottom edge, * . - and an at-least-KDU-but-more-is-better-by-KDU * . (NVE-by-KDU) vertical work WV arrow along * . the left-hand-edge. ==== * KDU = 3*NS - 3 KU = N - KDU + 1 KWH = KDU + 1 NHO = ( N-KDU+1-4 ) - ( KDU+1 ) + 1 KWV = KDU + 4 NVE = N - KDU - KWV + 1 * * ==== Small-bulge multi-shift QR sweep ==== * CALL ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NS, $ W( KS ), H, LDH, ILOZ, IHIZ, Z, LDZ, WORK, $ 3, H( KU, 1 ), LDH, NVE, H( KWV, 1 ), LDH, $ NHO, H( KU, KWH ), LDH ) END IF * * ==== Note progress (or the lack of it). ==== * IF( LD.GT.0 ) THEN NDFL = 1 ELSE NDFL = NDFL + 1 END IF * * ==== End of main loop ==== 70 CONTINUE * * ==== Iteration limit exceeded. Set INFO to show where * . the problem occurred and exit. ==== * INFO = KBOT 80 CONTINUE END IF * * ==== Return the optimal value of LWORK. ==== * WORK( 1 ) = DCMPLX( LWKOPT, 0 ) * * ==== End of ZLAQR4 ==== * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaqr5.f0000644000000000000000000000013214061636515015242 xustar0030 mtime=1623670093.402103896 30 atime=1623670093.401103897 30 ctime=1623670093.402103896 elk-7.2.42/src/LAPACK/zlaqr5.f0000644002504400250440000010145114061636515017301 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAQR5 performs a single small-bulge multi-shift QR sweep. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAQR5 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, * H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, * WV, LDWV, NH, WH, LDWH ) * * .. Scalar Arguments .. * INTEGER IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV, * $ LDWH, LDWV, LDZ, N, NH, NSHFTS, NV * LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. * COMPLEX*16 H( LDH, * ), S( * ), U( LDU, * ), V( LDV, * ), * $ WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAQR5, called by ZLAQR0, performs a *> single small-bulge multi-shift QR sweep. *> \endverbatim * * Arguments: * ========== * *> \param[in] WANTT *> \verbatim *> WANTT is LOGICAL *> WANTT = .true. if the triangular Schur factor *> is being computed. WANTT is set to .false. otherwise. *> \endverbatim *> *> \param[in] WANTZ *> \verbatim *> WANTZ is LOGICAL *> WANTZ = .true. if the unitary Schur factor is being *> computed. WANTZ is set to .false. otherwise. *> \endverbatim *> *> \param[in] KACC22 *> \verbatim *> KACC22 is INTEGER with value 0, 1, or 2. *> Specifies the computation mode of far-from-diagonal *> orthogonal updates. *> = 0: ZLAQR5 does not accumulate reflections and does not *> use matrix-matrix multiply to update far-from-diagonal *> matrix entries. *> = 1: ZLAQR5 accumulates reflections and uses matrix-matrix *> multiply to update the far-from-diagonal matrix entries. *> = 2: ZLAQR5 accumulates reflections, uses matrix-matrix *> multiply to update the far-from-diagonal matrix entries, *> and takes advantage of 2-by-2 block structure during *> matrix multiplies. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> N is the order of the Hessenberg matrix H upon which this *> subroutine operates. *> \endverbatim *> *> \param[in] KTOP *> \verbatim *> KTOP is INTEGER *> \endverbatim *> *> \param[in] KBOT *> \verbatim *> KBOT is INTEGER *> These are the first and last rows and columns of an *> isolated diagonal block upon which the QR sweep is to be *> applied. It is assumed without a check that *> either KTOP = 1 or H(KTOP,KTOP-1) = 0 *> and *> either KBOT = N or H(KBOT+1,KBOT) = 0. *> \endverbatim *> *> \param[in] NSHFTS *> \verbatim *> NSHFTS is INTEGER *> NSHFTS gives the number of simultaneous shifts. NSHFTS *> must be positive and even. *> \endverbatim *> *> \param[in,out] S *> \verbatim *> S is COMPLEX*16 array, dimension (NSHFTS) *> S contains the shifts of origin that define the multi- *> shift QR sweep. On output S may be reordered. *> \endverbatim *> *> \param[in,out] H *> \verbatim *> H is COMPLEX*16 array, dimension (LDH,N) *> On input H contains a Hessenberg matrix. On output a *> multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied *> to the isolated diagonal block in rows and columns KTOP *> through KBOT. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> LDH is the leading dimension of H just as declared in the *> calling procedure. LDH >= MAX(1,N). *> \endverbatim *> *> \param[in] ILOZ *> \verbatim *> ILOZ is INTEGER *> \endverbatim *> *> \param[in] IHIZ *> \verbatim *> IHIZ is INTEGER *> Specify the rows of Z to which transformations must be *> applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ,IHIZ) *> If WANTZ = .TRUE., then the QR Sweep unitary *> similarity transformation is accumulated into *> Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. *> If WANTZ = .FALSE., then Z is unreferenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> LDA is the leading dimension of Z just as declared in *> the calling procedure. LDZ >= N. *> \endverbatim *> *> \param[out] V *> \verbatim *> V is COMPLEX*16 array, dimension (LDV,NSHFTS/2) *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> LDV is the leading dimension of V as declared in the *> calling procedure. LDV >= 3. *> \endverbatim *> *> \param[out] U *> \verbatim *> U is COMPLEX*16 array, dimension (LDU,3*NSHFTS-3) *> \endverbatim *> *> \param[in] LDU *> \verbatim *> LDU is INTEGER *> LDU is the leading dimension of U just as declared in the *> in the calling subroutine. LDU >= 3*NSHFTS-3. *> \endverbatim *> *> \param[in] NV *> \verbatim *> NV is INTEGER *> NV is the number of rows in WV agailable for workspace. *> NV >= 1. *> \endverbatim *> *> \param[out] WV *> \verbatim *> WV is COMPLEX*16 array, dimension (LDWV,3*NSHFTS-3) *> \endverbatim *> *> \param[in] LDWV *> \verbatim *> LDWV is INTEGER *> LDWV is the leading dimension of WV as declared in the *> in the calling subroutine. LDWV >= NV. *> \endverbatim * *> \param[in] NH *> \verbatim *> NH is INTEGER *> NH is the number of columns in array WH available for *> workspace. NH >= 1. *> \endverbatim *> *> \param[out] WH *> \verbatim *> WH is COMPLEX*16 array, dimension (LDWH,NH) *> \endverbatim *> *> \param[in] LDWH *> \verbatim *> LDWH is INTEGER *> Leading dimension of WH just as declared in the *> calling procedure. LDWH >= 3*NSHFTS-3. *> \endverbatim *> * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Contributors: * ================== *> *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA * *> \par References: * ================ *> *> K. Braman, R. Byers and R. Mathias, The Multi-Shift QR *> Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 *> Performance, SIAM Journal of Matrix Analysis, volume 23, pages *> 929--947, 2002. *> * ===================================================================== SUBROUTINE ZLAQR5( WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, $ H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, $ WV, LDWV, NH, WH, LDWH ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV, $ LDWH, LDWV, LDZ, N, NH, NSHFTS, NV LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), S( * ), U( LDU, * ), V( LDV, * ), $ WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * ) * .. * * ================================================================ * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), $ ONE = ( 1.0d0, 0.0d0 ) ) DOUBLE PRECISION RZERO, RONE PARAMETER ( RZERO = 0.0d0, RONE = 1.0d0 ) * .. * .. Local Scalars .. COMPLEX*16 ALPHA, BETA, CDUM, REFSUM DOUBLE PRECISION H11, H12, H21, H22, SAFMAX, SAFMIN, SCL, $ SMLNUM, TST1, TST2, ULP INTEGER I2, I4, INCOL, J, J2, J4, JBOT, JCOL, JLEN, $ JROW, JTOP, K, K1, KDU, KMS, KNZ, KRCOL, KZS, $ M, M22, MBOT, MEND, MSTART, MTOP, NBMPS, NDCOL, $ NS, NU LOGICAL ACCUM, BLK22, BMP22 * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. Intrinsic Functions .. * INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, MIN, MOD * .. * .. Local Arrays .. COMPLEX*16 VT( 3 ) * .. * .. External Subroutines .. EXTERNAL DLABAD, ZGEMM, ZLACPY, ZLAQR1, ZLARFG, ZLASET, $ ZTRMM * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. Executable Statements .. * * ==== If there are no shifts, then there is nothing to do. ==== * IF( NSHFTS.LT.2 ) $ RETURN * * ==== If the active block is empty or 1-by-1, then there * . is nothing to do. ==== * IF( KTOP.GE.KBOT ) $ RETURN * * ==== NSHFTS is supposed to be even, but if it is odd, * . then simply reduce it by one. ==== * NS = NSHFTS - MOD( NSHFTS, 2 ) * * ==== Machine constants for deflation ==== * SAFMIN = DLAMCH( 'SAFE MINIMUM' ) SAFMAX = RONE / SAFMIN CALL DLABAD( SAFMIN, SAFMAX ) ULP = DLAMCH( 'PRECISION' ) SMLNUM = SAFMIN*( DBLE( N ) / ULP ) * * ==== Use accumulated reflections to update far-from-diagonal * . entries ? ==== * ACCUM = ( KACC22.EQ.1 ) .OR. ( KACC22.EQ.2 ) * * ==== If so, exploit the 2-by-2 block structure? ==== * BLK22 = ( NS.GT.2 ) .AND. ( KACC22.EQ.2 ) * * ==== clear trash ==== * IF( KTOP+2.LE.KBOT ) $ H( KTOP+2, KTOP ) = ZERO * * ==== NBMPS = number of 2-shift bulges in the chain ==== * NBMPS = NS / 2 * * ==== KDU = width of slab ==== * KDU = 6*NBMPS - 3 * * ==== Create and chase chains of NBMPS bulges ==== * DO 210 INCOL = 3*( 1-NBMPS ) + KTOP - 1, KBOT - 2, 3*NBMPS - 2 NDCOL = INCOL + KDU IF( ACCUM ) $ CALL ZLASET( 'ALL', KDU, KDU, ZERO, ONE, U, LDU ) * * ==== Near-the-diagonal bulge chase. The following loop * . performs the near-the-diagonal part of a small bulge * . multi-shift QR sweep. Each 6*NBMPS-2 column diagonal * . chunk extends from column INCOL to column NDCOL * . (including both column INCOL and column NDCOL). The * . following loop chases a 3*NBMPS column long chain of * . NBMPS bulges 3*NBMPS-2 columns to the right. (INCOL * . may be less than KTOP and and NDCOL may be greater than * . KBOT indicating phantom columns from which to chase * . bulges before they are actually introduced or to which * . to chase bulges beyond column KBOT.) ==== * DO 140 KRCOL = INCOL, MIN( INCOL+3*NBMPS-3, KBOT-2 ) * * ==== Bulges number MTOP to MBOT are active double implicit * . shift bulges. There may or may not also be small * . 2-by-2 bulge, if there is room. The inactive bulges * . (if any) must wait until the active bulges have moved * . down the diagonal to make room. The phantom matrix * . paradigm described above helps keep track. ==== * MTOP = MAX( 1, ( ( KTOP-1 )-KRCOL+2 ) / 3+1 ) MBOT = MIN( NBMPS, ( KBOT-KRCOL ) / 3 ) M22 = MBOT + 1 BMP22 = ( MBOT.LT.NBMPS ) .AND. ( KRCOL+3*( M22-1 ) ).EQ. $ ( KBOT-2 ) * * ==== Generate reflections to chase the chain right * . one column. (The minimum value of K is KTOP-1.) ==== * DO 10 M = MTOP, MBOT K = KRCOL + 3*( M-1 ) IF( K.EQ.KTOP-1 ) THEN CALL ZLAQR1( 3, H( KTOP, KTOP ), LDH, S( 2*M-1 ), $ S( 2*M ), V( 1, M ) ) ALPHA = V( 1, M ) CALL ZLARFG( 3, ALPHA, V( 2, M ), 1, V( 1, M ) ) ELSE BETA = H( K+1, K ) V( 2, M ) = H( K+2, K ) V( 3, M ) = H( K+3, K ) CALL ZLARFG( 3, BETA, V( 2, M ), 1, V( 1, M ) ) * * ==== A Bulge may collapse because of vigilant * . deflation or destructive underflow. In the * . underflow case, try the two-small-subdiagonals * . trick to try to reinflate the bulge. ==== * IF( H( K+3, K ).NE.ZERO .OR. H( K+3, K+1 ).NE. $ ZERO .OR. H( K+3, K+2 ).EQ.ZERO ) THEN * * ==== Typical case: not collapsed (yet). ==== * H( K+1, K ) = BETA H( K+2, K ) = ZERO H( K+3, K ) = ZERO ELSE * * ==== Atypical case: collapsed. Attempt to * . reintroduce ignoring H(K+1,K) and H(K+2,K). * . If the fill resulting from the new * . reflector is too large, then abandon it. * . Otherwise, use the new one. ==== * CALL ZLAQR1( 3, H( K+1, K+1 ), LDH, S( 2*M-1 ), $ S( 2*M ), VT ) ALPHA = VT( 1 ) CALL ZLARFG( 3, ALPHA, VT( 2 ), 1, VT( 1 ) ) REFSUM = DCONJG( VT( 1 ) )* $ ( H( K+1, K )+DCONJG( VT( 2 ) )* $ H( K+2, K ) ) * IF( CABS1( H( K+2, K )-REFSUM*VT( 2 ) )+ $ CABS1( REFSUM*VT( 3 ) ).GT.ULP* $ ( CABS1( H( K, K ) )+CABS1( H( K+1, $ K+1 ) )+CABS1( H( K+2, K+2 ) ) ) ) THEN * * ==== Starting a new bulge here would * . create non-negligible fill. Use * . the old one with trepidation. ==== * H( K+1, K ) = BETA H( K+2, K ) = ZERO H( K+3, K ) = ZERO ELSE * * ==== Stating a new bulge here would * . create only negligible fill. * . Replace the old reflector with * . the new one. ==== * H( K+1, K ) = H( K+1, K ) - REFSUM H( K+2, K ) = ZERO H( K+3, K ) = ZERO V( 1, M ) = VT( 1 ) V( 2, M ) = VT( 2 ) V( 3, M ) = VT( 3 ) END IF END IF END IF 10 CONTINUE * * ==== Generate a 2-by-2 reflection, if needed. ==== * K = KRCOL + 3*( M22-1 ) IF( BMP22 ) THEN IF( K.EQ.KTOP-1 ) THEN CALL ZLAQR1( 2, H( K+1, K+1 ), LDH, S( 2*M22-1 ), $ S( 2*M22 ), V( 1, M22 ) ) BETA = V( 1, M22 ) CALL ZLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) ) ELSE BETA = H( K+1, K ) V( 2, M22 ) = H( K+2, K ) CALL ZLARFG( 2, BETA, V( 2, M22 ), 1, V( 1, M22 ) ) H( K+1, K ) = BETA H( K+2, K ) = ZERO END IF END IF * * ==== Multiply H by reflections from the left ==== * IF( ACCUM ) THEN JBOT = MIN( NDCOL, KBOT ) ELSE IF( WANTT ) THEN JBOT = N ELSE JBOT = KBOT END IF DO 30 J = MAX( KTOP, KRCOL ), JBOT MEND = MIN( MBOT, ( J-KRCOL+2 ) / 3 ) DO 20 M = MTOP, MEND K = KRCOL + 3*( M-1 ) REFSUM = DCONJG( V( 1, M ) )* $ ( H( K+1, J )+DCONJG( V( 2, M ) )* $ H( K+2, J )+DCONJG( V( 3, M ) )*H( K+3, J ) ) H( K+1, J ) = H( K+1, J ) - REFSUM H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M ) H( K+3, J ) = H( K+3, J ) - REFSUM*V( 3, M ) 20 CONTINUE 30 CONTINUE IF( BMP22 ) THEN K = KRCOL + 3*( M22-1 ) DO 40 J = MAX( K+1, KTOP ), JBOT REFSUM = DCONJG( V( 1, M22 ) )* $ ( H( K+1, J )+DCONJG( V( 2, M22 ) )* $ H( K+2, J ) ) H( K+1, J ) = H( K+1, J ) - REFSUM H( K+2, J ) = H( K+2, J ) - REFSUM*V( 2, M22 ) 40 CONTINUE END IF * * ==== Multiply H by reflections from the right. * . Delay filling in the last row until the * . vigilant deflation check is complete. ==== * IF( ACCUM ) THEN JTOP = MAX( KTOP, INCOL ) ELSE IF( WANTT ) THEN JTOP = 1 ELSE JTOP = KTOP END IF DO 80 M = MTOP, MBOT IF( V( 1, M ).NE.ZERO ) THEN K = KRCOL + 3*( M-1 ) DO 50 J = JTOP, MIN( KBOT, K+3 ) REFSUM = V( 1, M )*( H( J, K+1 )+V( 2, M )* $ H( J, K+2 )+V( 3, M )*H( J, K+3 ) ) H( J, K+1 ) = H( J, K+1 ) - REFSUM H( J, K+2 ) = H( J, K+2 ) - $ REFSUM*DCONJG( V( 2, M ) ) H( J, K+3 ) = H( J, K+3 ) - $ REFSUM*DCONJG( V( 3, M ) ) 50 CONTINUE * IF( ACCUM ) THEN * * ==== Accumulate U. (If necessary, update Z later * . with with an efficient matrix-matrix * . multiply.) ==== * KMS = K - INCOL DO 60 J = MAX( 1, KTOP-INCOL ), KDU REFSUM = V( 1, M )*( U( J, KMS+1 )+V( 2, M )* $ U( J, KMS+2 )+V( 3, M )*U( J, KMS+3 ) ) U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM U( J, KMS+2 ) = U( J, KMS+2 ) - $ REFSUM*DCONJG( V( 2, M ) ) U( J, KMS+3 ) = U( J, KMS+3 ) - $ REFSUM*DCONJG( V( 3, M ) ) 60 CONTINUE ELSE IF( WANTZ ) THEN * * ==== U is not accumulated, so update Z * . now by multiplying by reflections * . from the right. ==== * DO 70 J = ILOZ, IHIZ REFSUM = V( 1, M )*( Z( J, K+1 )+V( 2, M )* $ Z( J, K+2 )+V( 3, M )*Z( J, K+3 ) ) Z( J, K+1 ) = Z( J, K+1 ) - REFSUM Z( J, K+2 ) = Z( J, K+2 ) - $ REFSUM*DCONJG( V( 2, M ) ) Z( J, K+3 ) = Z( J, K+3 ) - $ REFSUM*DCONJG( V( 3, M ) ) 70 CONTINUE END IF END IF 80 CONTINUE * * ==== Special case: 2-by-2 reflection (if needed) ==== * K = KRCOL + 3*( M22-1 ) IF( BMP22 ) THEN IF ( V( 1, M22 ).NE.ZERO ) THEN DO 90 J = JTOP, MIN( KBOT, K+3 ) REFSUM = V( 1, M22 )*( H( J, K+1 )+V( 2, M22 )* $ H( J, K+2 ) ) H( J, K+1 ) = H( J, K+1 ) - REFSUM H( J, K+2 ) = H( J, K+2 ) - $ REFSUM*DCONJG( V( 2, M22 ) ) 90 CONTINUE * IF( ACCUM ) THEN KMS = K - INCOL DO 100 J = MAX( 1, KTOP-INCOL ), KDU REFSUM = V( 1, M22 )*( U( J, KMS+1 )+ $ V( 2, M22 )*U( J, KMS+2 ) ) U( J, KMS+1 ) = U( J, KMS+1 ) - REFSUM U( J, KMS+2 ) = U( J, KMS+2 ) - $ REFSUM*DCONJG( V( 2, M22 ) ) 100 CONTINUE ELSE IF( WANTZ ) THEN DO 110 J = ILOZ, IHIZ REFSUM = V( 1, M22 )*( Z( J, K+1 )+V( 2, M22 )* $ Z( J, K+2 ) ) Z( J, K+1 ) = Z( J, K+1 ) - REFSUM Z( J, K+2 ) = Z( J, K+2 ) - $ REFSUM*DCONJG( V( 2, M22 ) ) 110 CONTINUE END IF END IF END IF * * ==== Vigilant deflation check ==== * MSTART = MTOP IF( KRCOL+3*( MSTART-1 ).LT.KTOP ) $ MSTART = MSTART + 1 MEND = MBOT IF( BMP22 ) $ MEND = MEND + 1 IF( KRCOL.EQ.KBOT-2 ) $ MEND = MEND + 1 DO 120 M = MSTART, MEND K = MIN( KBOT-1, KRCOL+3*( M-1 ) ) * * ==== The following convergence test requires that * . the tradition small-compared-to-nearby-diagonals * . criterion and the Ahues & Tisseur (LAWN 122, 1997) * . criteria both be satisfied. The latter improves * . accuracy in some examples. Falling back on an * . alternate convergence criterion when TST1 or TST2 * . is zero (as done here) is traditional but probably * . unnecessary. ==== * IF( H( K+1, K ).NE.ZERO ) THEN TST1 = CABS1( H( K, K ) ) + CABS1( H( K+1, K+1 ) ) IF( TST1.EQ.RZERO ) THEN IF( K.GE.KTOP+1 ) $ TST1 = TST1 + CABS1( H( K, K-1 ) ) IF( K.GE.KTOP+2 ) $ TST1 = TST1 + CABS1( H( K, K-2 ) ) IF( K.GE.KTOP+3 ) $ TST1 = TST1 + CABS1( H( K, K-3 ) ) IF( K.LE.KBOT-2 ) $ TST1 = TST1 + CABS1( H( K+2, K+1 ) ) IF( K.LE.KBOT-3 ) $ TST1 = TST1 + CABS1( H( K+3, K+1 ) ) IF( K.LE.KBOT-4 ) $ TST1 = TST1 + CABS1( H( K+4, K+1 ) ) END IF IF( CABS1( H( K+1, K ) ).LE.MAX( SMLNUM, ULP*TST1 ) ) $ THEN H12 = MAX( CABS1( H( K+1, K ) ), $ CABS1( H( K, K+1 ) ) ) H21 = MIN( CABS1( H( K+1, K ) ), $ CABS1( H( K, K+1 ) ) ) H11 = MAX( CABS1( H( K+1, K+1 ) ), $ CABS1( H( K, K )-H( K+1, K+1 ) ) ) H22 = MIN( CABS1( H( K+1, K+1 ) ), $ CABS1( H( K, K )-H( K+1, K+1 ) ) ) SCL = H11 + H12 TST2 = H22*( H11 / SCL ) * IF( TST2.EQ.RZERO .OR. H21*( H12 / SCL ).LE. $ MAX( SMLNUM, ULP*TST2 ) )H( K+1, K ) = ZERO END IF END IF 120 CONTINUE * * ==== Fill in the last row of each bulge. ==== * MEND = MIN( NBMPS, ( KBOT-KRCOL-1 ) / 3 ) DO 130 M = MTOP, MEND K = KRCOL + 3*( M-1 ) REFSUM = V( 1, M )*V( 3, M )*H( K+4, K+3 ) H( K+4, K+1 ) = -REFSUM H( K+4, K+2 ) = -REFSUM*DCONJG( V( 2, M ) ) H( K+4, K+3 ) = H( K+4, K+3 ) - $ REFSUM*DCONJG( V( 3, M ) ) 130 CONTINUE * * ==== End of near-the-diagonal bulge chase. ==== * 140 CONTINUE * * ==== Use U (if accumulated) to update far-from-diagonal * . entries in H. If required, use U to update Z as * . well. ==== * IF( ACCUM ) THEN IF( WANTT ) THEN JTOP = 1 JBOT = N ELSE JTOP = KTOP JBOT = KBOT END IF IF( ( .NOT.BLK22 ) .OR. ( INCOL.LT.KTOP ) .OR. $ ( NDCOL.GT.KBOT ) .OR. ( NS.LE.2 ) ) THEN * * ==== Updates not exploiting the 2-by-2 block * . structure of U. K1 and NU keep track of * . the location and size of U in the special * . cases of introducing bulges and chasing * . bulges off the bottom. In these special * . cases and in case the number of shifts * . is NS = 2, there is no 2-by-2 block * . structure to exploit. ==== * K1 = MAX( 1, KTOP-INCOL ) NU = ( KDU-MAX( 0, NDCOL-KBOT ) ) - K1 + 1 * * ==== Horizontal Multiply ==== * DO 150 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH JLEN = MIN( NH, JBOT-JCOL+1 ) CALL ZGEMM( 'C', 'N', NU, JLEN, NU, ONE, U( K1, K1 ), $ LDU, H( INCOL+K1, JCOL ), LDH, ZERO, WH, $ LDWH ) CALL ZLACPY( 'ALL', NU, JLEN, WH, LDWH, $ H( INCOL+K1, JCOL ), LDH ) 150 CONTINUE * * ==== Vertical multiply ==== * DO 160 JROW = JTOP, MAX( KTOP, INCOL ) - 1, NV JLEN = MIN( NV, MAX( KTOP, INCOL )-JROW ) CALL ZGEMM( 'N', 'N', JLEN, NU, NU, ONE, $ H( JROW, INCOL+K1 ), LDH, U( K1, K1 ), $ LDU, ZERO, WV, LDWV ) CALL ZLACPY( 'ALL', JLEN, NU, WV, LDWV, $ H( JROW, INCOL+K1 ), LDH ) 160 CONTINUE * * ==== Z multiply (also vertical) ==== * IF( WANTZ ) THEN DO 170 JROW = ILOZ, IHIZ, NV JLEN = MIN( NV, IHIZ-JROW+1 ) CALL ZGEMM( 'N', 'N', JLEN, NU, NU, ONE, $ Z( JROW, INCOL+K1 ), LDZ, U( K1, K1 ), $ LDU, ZERO, WV, LDWV ) CALL ZLACPY( 'ALL', JLEN, NU, WV, LDWV, $ Z( JROW, INCOL+K1 ), LDZ ) 170 CONTINUE END IF ELSE * * ==== Updates exploiting U's 2-by-2 block structure. * . (I2, I4, J2, J4 are the last rows and columns * . of the blocks.) ==== * I2 = ( KDU+1 ) / 2 I4 = KDU J2 = I4 - I2 J4 = KDU * * ==== KZS and KNZ deal with the band of zeros * . along the diagonal of one of the triangular * . blocks. ==== * KZS = ( J4-J2 ) - ( NS+1 ) KNZ = NS + 1 * * ==== Horizontal multiply ==== * DO 180 JCOL = MIN( NDCOL, KBOT ) + 1, JBOT, NH JLEN = MIN( NH, JBOT-JCOL+1 ) * * ==== Copy bottom of H to top+KZS of scratch ==== * (The first KZS rows get multiplied by zero.) ==== * CALL ZLACPY( 'ALL', KNZ, JLEN, H( INCOL+1+J2, JCOL ), $ LDH, WH( KZS+1, 1 ), LDWH ) * * ==== Multiply by U21**H ==== * CALL ZLASET( 'ALL', KZS, JLEN, ZERO, ZERO, WH, LDWH ) CALL ZTRMM( 'L', 'U', 'C', 'N', KNZ, JLEN, ONE, $ U( J2+1, 1+KZS ), LDU, WH( KZS+1, 1 ), $ LDWH ) * * ==== Multiply top of H by U11**H ==== * CALL ZGEMM( 'C', 'N', I2, JLEN, J2, ONE, U, LDU, $ H( INCOL+1, JCOL ), LDH, ONE, WH, LDWH ) * * ==== Copy top of H to bottom of WH ==== * CALL ZLACPY( 'ALL', J2, JLEN, H( INCOL+1, JCOL ), LDH, $ WH( I2+1, 1 ), LDWH ) * * ==== Multiply by U21**H ==== * CALL ZTRMM( 'L', 'L', 'C', 'N', J2, JLEN, ONE, $ U( 1, I2+1 ), LDU, WH( I2+1, 1 ), LDWH ) * * ==== Multiply by U22 ==== * CALL ZGEMM( 'C', 'N', I4-I2, JLEN, J4-J2, ONE, $ U( J2+1, I2+1 ), LDU, $ H( INCOL+1+J2, JCOL ), LDH, ONE, $ WH( I2+1, 1 ), LDWH ) * * ==== Copy it back ==== * CALL ZLACPY( 'ALL', KDU, JLEN, WH, LDWH, $ H( INCOL+1, JCOL ), LDH ) 180 CONTINUE * * ==== Vertical multiply ==== * DO 190 JROW = JTOP, MAX( INCOL, KTOP ) - 1, NV JLEN = MIN( NV, MAX( INCOL, KTOP )-JROW ) * * ==== Copy right of H to scratch (the first KZS * . columns get multiplied by zero) ==== * CALL ZLACPY( 'ALL', JLEN, KNZ, H( JROW, INCOL+1+J2 ), $ LDH, WV( 1, 1+KZS ), LDWV ) * * ==== Multiply by U21 ==== * CALL ZLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, LDWV ) CALL ZTRMM( 'R', 'U', 'N', 'N', JLEN, KNZ, ONE, $ U( J2+1, 1+KZS ), LDU, WV( 1, 1+KZS ), $ LDWV ) * * ==== Multiply by U11 ==== * CALL ZGEMM( 'N', 'N', JLEN, I2, J2, ONE, $ H( JROW, INCOL+1 ), LDH, U, LDU, ONE, WV, $ LDWV ) * * ==== Copy left of H to right of scratch ==== * CALL ZLACPY( 'ALL', JLEN, J2, H( JROW, INCOL+1 ), LDH, $ WV( 1, 1+I2 ), LDWV ) * * ==== Multiply by U21 ==== * CALL ZTRMM( 'R', 'L', 'N', 'N', JLEN, I4-I2, ONE, $ U( 1, I2+1 ), LDU, WV( 1, 1+I2 ), LDWV ) * * ==== Multiply by U22 ==== * CALL ZGEMM( 'N', 'N', JLEN, I4-I2, J4-J2, ONE, $ H( JROW, INCOL+1+J2 ), LDH, $ U( J2+1, I2+1 ), LDU, ONE, WV( 1, 1+I2 ), $ LDWV ) * * ==== Copy it back ==== * CALL ZLACPY( 'ALL', JLEN, KDU, WV, LDWV, $ H( JROW, INCOL+1 ), LDH ) 190 CONTINUE * * ==== Multiply Z (also vertical) ==== * IF( WANTZ ) THEN DO 200 JROW = ILOZ, IHIZ, NV JLEN = MIN( NV, IHIZ-JROW+1 ) * * ==== Copy right of Z to left of scratch (first * . KZS columns get multiplied by zero) ==== * CALL ZLACPY( 'ALL', JLEN, KNZ, $ Z( JROW, INCOL+1+J2 ), LDZ, $ WV( 1, 1+KZS ), LDWV ) * * ==== Multiply by U12 ==== * CALL ZLASET( 'ALL', JLEN, KZS, ZERO, ZERO, WV, $ LDWV ) CALL ZTRMM( 'R', 'U', 'N', 'N', JLEN, KNZ, ONE, $ U( J2+1, 1+KZS ), LDU, WV( 1, 1+KZS ), $ LDWV ) * * ==== Multiply by U11 ==== * CALL ZGEMM( 'N', 'N', JLEN, I2, J2, ONE, $ Z( JROW, INCOL+1 ), LDZ, U, LDU, ONE, $ WV, LDWV ) * * ==== Copy left of Z to right of scratch ==== * CALL ZLACPY( 'ALL', JLEN, J2, Z( JROW, INCOL+1 ), $ LDZ, WV( 1, 1+I2 ), LDWV ) * * ==== Multiply by U21 ==== * CALL ZTRMM( 'R', 'L', 'N', 'N', JLEN, I4-I2, ONE, $ U( 1, I2+1 ), LDU, WV( 1, 1+I2 ), $ LDWV ) * * ==== Multiply by U22 ==== * CALL ZGEMM( 'N', 'N', JLEN, I4-I2, J4-J2, ONE, $ Z( JROW, INCOL+1+J2 ), LDZ, $ U( J2+1, I2+1 ), LDU, ONE, $ WV( 1, 1+I2 ), LDWV ) * * ==== Copy the result back to Z ==== * CALL ZLACPY( 'ALL', JLEN, KDU, WV, LDWV, $ Z( JROW, INCOL+1 ), LDZ ) 200 CONTINUE END IF END IF END IF 210 CONTINUE * * ==== End of ZLAQR5 ==== * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/ilazlc.f0000644000000000000000000000013214061636515015302 xustar0030 mtime=1623670093.404103894 30 atime=1623670093.404103894 30 ctime=1623670093.404103894 elk-7.2.42/src/LAPACK/ilazlc.f0000644002504400250440000000565714061636515017354 0ustar00dewhurstdewhurst00000000000000*> \brief \b ILAZLC scans a matrix for its last non-zero column. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ILAZLC + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * INTEGER FUNCTION ILAZLC( M, N, A, LDA ) * * .. Scalar Arguments .. * INTEGER M, N, LDA * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ILAZLC scans A for its last non-zero column. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The m by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== INTEGER FUNCTION ILAZLC( M, N, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER M, N, LDA * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) * .. * .. Local Scalars .. INTEGER I * .. * .. Executable Statements .. * * Quick test for the common case where one corner is non-zero. IF( N.EQ.0 ) THEN ILAZLC = N ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILAZLC = N ELSE * Now scan each column from the end, returning with the first non-zero. DO ILAZLC = N, 1, -1 DO I = 1, M IF( A(I, ILAZLC).NE.ZERO ) RETURN END DO END DO END IF RETURN END elk-7.2.42/src/LAPACK/PaxHeaders.21776/ilazlr.f0000644000000000000000000000013214061636515015321 xustar0030 mtime=1623670093.406103893 30 atime=1623670093.406103893 30 ctime=1623670093.406103893 elk-7.2.42/src/LAPACK/ilazlr.f0000644002504400250440000000574214061636515017366 0ustar00dewhurstdewhurst00000000000000*> \brief \b ILAZLR scans a matrix for its last non-zero row. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ILAZLR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * INTEGER FUNCTION ILAZLR( M, N, A, LDA ) * * .. Scalar Arguments .. * INTEGER M, N, LDA * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ILAZLR scans A for its last non-zero row. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The m by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== INTEGER FUNCTION ILAZLR( M, N, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER M, N, LDA * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) * .. * .. Local Scalars .. INTEGER I, J * .. * .. Executable Statements .. * * Quick test for the common case where one corner is non-zero. IF( M.EQ.0 ) THEN ILAZLR = M ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILAZLR = M ELSE * Scan up each column tracking the last zero row seen. ILAZLR = 0 DO J = 1, N I=M DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) I=I-1 ENDDO ILAZLR = MAX( ILAZLR, I ) END DO END IF RETURN END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlapy3.f0000644000000000000000000000013214061636515015220 xustar0030 mtime=1623670093.408103891 30 atime=1623670093.407103892 30 ctime=1623670093.408103891 elk-7.2.42/src/LAPACK/dlapy3.f0000644002504400250440000000526614061636515017266 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAPY3 returns sqrt(x2+y2+z2). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAPY3 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) * * .. Scalar Arguments .. * DOUBLE PRECISION X, Y, Z * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause *> unnecessary overflow. *> \endverbatim * * Arguments: * ========== * *> \param[in] X *> \verbatim *> X is DOUBLE PRECISION *> \endverbatim *> *> \param[in] Y *> \verbatim *> Y is DOUBLE PRECISION *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION *> X, Y and Z specify the values x, y and z. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION X, Y, Z * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) * .. * .. Local Scalars .. DOUBLE PRECISION W, XABS, YABS, ZABS * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * XABS = ABS( X ) YABS = ABS( Y ) ZABS = ABS( Z ) W = MAX( XABS, YABS, ZABS ) IF( W.EQ.ZERO ) THEN * W can be zero for max(0,nan,0) * adding all three entries together will make sure * NaN will not disappear. DLAPY3 = XABS + YABS + ZABS ELSE DLAPY3 = W*SQRT( ( XABS / W )**2+( YABS / W )**2+ $ ( ZABS / W )**2 ) END IF RETURN * * End of DLAPY3 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunml2.f0000644000000000000000000000012714061636515015257 xustar0029 mtime=1623670093.40910389 29 atime=1623670093.40910389 29 ctime=1623670093.40910389 elk-7.2.42/src/LAPACK/zunml2.f0000644002504400250440000001705014061636515017313 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNML2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNML2 overwrites the general complex m-by-n matrix C with *> *> Q * C if SIDE = 'L' and TRANS = 'N', or *> *> Q**H* C if SIDE = 'L' and TRANS = 'C', or *> *> C * Q if SIDE = 'R' and TRANS = 'N', or *> *> C * Q**H if SIDE = 'R' and TRANS = 'C', *> *> where Q is a complex unitary matrix defined as the product of k *> elementary reflectors *> *> Q = H(k)**H . . . H(2)**H H(1)**H *> *> as returned by ZGELQF. Q is of order m if SIDE = 'L' and of order n *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left *> = 'R': apply Q or Q**H from the Right *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply Q (No transpose) *> = 'C': apply Q**H (Conjugate transpose) *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension *> (LDA,M) if SIDE = 'L', *> (LDA,N) if SIDE = 'R' *> The i-th row must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> ZGELQF in the first k rows of its array argument A. *> A is modified by the routine but restored on exit. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,K). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGELQF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the m-by-n matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension *> (N) if SIDE = 'L', *> (M) if SIDE = 'R' *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LEFT, NOTRAN INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ COMPLEX*16 AII, TAUI * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLACGV, ZLARF * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) * * NQ is the order of Q * IF( LEFT ) THEN NQ = M ELSE NQ = N END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNML2', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) $ RETURN * IF( ( LEFT .AND. NOTRAN .OR. .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN I1 = 1 I2 = K I3 = 1 ELSE I1 = K I2 = 1 I3 = -1 END IF * IF( LEFT ) THEN NI = N JC = 1 ELSE MI = M IC = 1 END IF * DO 10 I = I1, I2, I3 IF( LEFT ) THEN * * H(i) or H(i)**H is applied to C(i:m,1:n) * MI = M - I + 1 IC = I ELSE * * H(i) or H(i)**H is applied to C(1:m,i:n) * NI = N - I + 1 JC = I END IF * * Apply H(i) or H(i)**H * IF( NOTRAN ) THEN TAUI = DCONJG( TAU( I ) ) ELSE TAUI = TAU( I ) END IF IF( I.LT.NQ ) $ CALL ZLACGV( NQ-I, A( I, I+1 ), LDA ) AII = A( I, I ) A( I, I ) = ONE CALL ZLARF( SIDE, MI, NI, A( I, I ), LDA, TAUI, C( IC, JC ), $ LDC, WORK ) A( I, I ) = AII IF( I.LT.NQ ) $ CALL ZLACGV( NQ-I, A( I, I+1 ), LDA ) 10 CONTINUE RETURN * * End of ZUNML2 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunm2l.f0000644000000000000000000000013214061636515015253 xustar0030 mtime=1623670093.411103888 30 atime=1623670093.411103888 30 ctime=1623670093.411103888 elk-7.2.42/src/LAPACK/zunm2l.f0000644002504400250440000001642314061636515017316 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNM2L + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNM2L overwrites the general complex m-by-n matrix C with *> *> Q * C if SIDE = 'L' and TRANS = 'N', or *> *> Q**H* C if SIDE = 'L' and TRANS = 'C', or *> *> C * Q if SIDE = 'R' and TRANS = 'N', or *> *> C * Q**H if SIDE = 'R' and TRANS = 'C', *> *> where Q is a complex unitary matrix defined as the product of k *> elementary reflectors *> *> Q = H(k) . . . H(2) H(1) *> *> as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left *> = 'R': apply Q or Q**H from the Right *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply Q (No transpose) *> = 'C': apply Q**H (Conjugate transpose) *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> ZGEQLF in the last k columns of its array argument A. *> A is modified by the routine but restored on exit. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,M); *> if SIDE = 'R', LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEQLF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the m-by-n matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension *> (N) if SIDE = 'L', *> (M) if SIDE = 'R' *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LEFT, NOTRAN INTEGER I, I1, I2, I3, MI, NI, NQ COMPLEX*16 AII, TAUI * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) * * NQ is the order of Q * IF( LEFT ) THEN NQ = M ELSE NQ = N END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNM2L', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) $ RETURN * IF( ( LEFT .AND. NOTRAN .OR. .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN I1 = 1 I2 = K I3 = 1 ELSE I1 = K I2 = 1 I3 = -1 END IF * IF( LEFT ) THEN NI = N ELSE MI = M END IF * DO 10 I = I1, I2, I3 IF( LEFT ) THEN * * H(i) or H(i)**H is applied to C(1:m-k+i,1:n) * MI = M - K + I ELSE * * H(i) or H(i)**H is applied to C(1:m,1:n-k+i) * NI = N - K + I END IF * * Apply H(i) or H(i)**H * IF( NOTRAN ) THEN TAUI = TAU( I ) ELSE TAUI = DCONJG( TAU( I ) ) END IF AII = A( NQ-K+I, I ) A( NQ-K+I, I ) = ONE CALL ZLARF( SIDE, MI, NI, A( 1, I ), 1, TAUI, C, LDC, WORK ) A( NQ-K+I, I ) = AII 10 CONTINUE RETURN * * End of ZUNM2L * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunm2r.f0000644000000000000000000000013214061636515015261 xustar0030 mtime=1623670093.413103886 30 atime=1623670093.413103886 30 ctime=1623670093.413103886 elk-7.2.42/src/LAPACK/zunm2r.f0000644002504400250440000001655214061636515017327 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNM2R + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNM2R overwrites the general complex m-by-n matrix C with *> *> Q * C if SIDE = 'L' and TRANS = 'N', or *> *> Q**H* C if SIDE = 'L' and TRANS = 'C', or *> *> C * Q if SIDE = 'R' and TRANS = 'N', or *> *> C * Q**H if SIDE = 'R' and TRANS = 'C', *> *> where Q is a complex unitary matrix defined as the product of k *> elementary reflectors *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by ZGEQRF. Q is of order m if SIDE = 'L' and of order n *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left *> = 'R': apply Q or Q**H from the Right *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply Q (No transpose) *> = 'C': apply Q**H (Conjugate transpose) *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> ZGEQRF in the first k columns of its array argument A. *> A is modified by the routine but restored on exit. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,M); *> if SIDE = 'R', LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEQRF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the m-by-n matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension *> (N) if SIDE = 'L', *> (M) if SIDE = 'R' *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LEFT, NOTRAN INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ COMPLEX*16 AII, TAUI * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) * * NQ is the order of Q * IF( LEFT ) THEN NQ = M ELSE NQ = N END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNM2R', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) $ RETURN * IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN I1 = 1 I2 = K I3 = 1 ELSE I1 = K I2 = 1 I3 = -1 END IF * IF( LEFT ) THEN NI = N JC = 1 ELSE MI = M IC = 1 END IF * DO 10 I = I1, I2, I3 IF( LEFT ) THEN * * H(i) or H(i)**H is applied to C(i:m,1:n) * MI = M - I + 1 IC = I ELSE * * H(i) or H(i)**H is applied to C(1:m,i:n) * NI = N - I + 1 JC = I END IF * * Apply H(i) or H(i)**H * IF( NOTRAN ) THEN TAUI = TAU( I ) ELSE TAUI = DCONJG( TAU( I ) ) END IF AII = A( I, I ) A( I, I ) = ONE CALL ZLARF( SIDE, MI, NI, A( I, I ), 1, TAUI, C( IC, JC ), LDC, $ WORK ) A( I, I ) = AII 10 CONTINUE RETURN * * End of ZUNM2R * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed5.f0000644000000000000000000000013214061636515015162 xustar0030 mtime=1623670093.415103884 30 atime=1623670093.414103885 30 ctime=1623670093.415103884 elk-7.2.42/src/LAPACK/dlaed5.f0000644002504400250440000001237314061636515017225 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED5 used by sstedc. Solves the 2-by-2 secular equation. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED5 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM ) * * .. Scalar Arguments .. * INTEGER I * DOUBLE PRECISION DLAM, RHO * .. * .. Array Arguments .. * DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> This subroutine computes the I-th eigenvalue of a symmetric rank-one *> modification of a 2-by-2 diagonal matrix *> *> diag( D ) + RHO * Z * transpose(Z) . *> *> The diagonal elements in the array D are assumed to satisfy *> *> D(i) < D(j) for i < j . *> *> We also assume RHO > 0 and that the Euclidean norm of the vector *> Z is one. *> \endverbatim * * Arguments: * ========== * *> \param[in] I *> \verbatim *> I is INTEGER *> The index of the eigenvalue to be computed. I = 1 or I = 2. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (2) *> The original eigenvalues. We assume D(1) < D(2). *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (2) *> The components of the updating vector. *> \endverbatim *> *> \param[out] DELTA *> \verbatim *> DELTA is DOUBLE PRECISION array, dimension (2) *> The vector DELTA contains the information necessary *> to construct the eigenvectors. *> \endverbatim *> *> \param[in] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> The scalar in the symmetric updating formula. *> \endverbatim *> *> \param[out] DLAM *> \verbatim *> DLAM is DOUBLE PRECISION *> The computed lambda_I, the I-th updated eigenvalue. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Ren-Cang Li, Computer Science Division, University of California *> at Berkeley, USA *> * ===================================================================== SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER I DOUBLE PRECISION DLAM, RHO * .. * .. Array Arguments .. DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO, FOUR PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ FOUR = 4.0D0 ) * .. * .. Local Scalars .. DOUBLE PRECISION B, C, DEL, TAU, TEMP, W * .. * .. Intrinsic Functions .. INTRINSIC ABS, SQRT * .. * .. Executable Statements .. * DEL = D( 2 ) - D( 1 ) IF( I.EQ.1 ) THEN W = ONE + TWO*RHO*( Z( 2 )*Z( 2 )-Z( 1 )*Z( 1 ) ) / DEL IF( W.GT.ZERO ) THEN B = DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) C = RHO*Z( 1 )*Z( 1 )*DEL * * B > ZERO, always * TAU = TWO*C / ( B+SQRT( ABS( B*B-FOUR*C ) ) ) DLAM = D( 1 ) + TAU DELTA( 1 ) = -Z( 1 ) / TAU DELTA( 2 ) = Z( 2 ) / ( DEL-TAU ) ELSE B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) C = RHO*Z( 2 )*Z( 2 )*DEL IF( B.GT.ZERO ) THEN TAU = -TWO*C / ( B+SQRT( B*B+FOUR*C ) ) ELSE TAU = ( B-SQRT( B*B+FOUR*C ) ) / TWO END IF DLAM = D( 2 ) + TAU DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) DELTA( 2 ) = -Z( 2 ) / TAU END IF TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) DELTA( 1 ) = DELTA( 1 ) / TEMP DELTA( 2 ) = DELTA( 2 ) / TEMP ELSE * * Now I=2 * B = -DEL + RHO*( Z( 1 )*Z( 1 )+Z( 2 )*Z( 2 ) ) C = RHO*Z( 2 )*Z( 2 )*DEL IF( B.GT.ZERO ) THEN TAU = ( B+SQRT( B*B+FOUR*C ) ) / TWO ELSE TAU = TWO*C / ( -B+SQRT( B*B+FOUR*C ) ) END IF DLAM = D( 2 ) + TAU DELTA( 1 ) = -Z( 1 ) / ( DEL+TAU ) DELTA( 2 ) = -Z( 2 ) / TAU TEMP = SQRT( DELTA( 1 )*DELTA( 1 )+DELTA( 2 )*DELTA( 2 ) ) DELTA( 1 ) = DELTA( 1 ) / TEMP DELTA( 2 ) = DELTA( 2 ) / TEMP END IF RETURN * * End OF DLAED5 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed7.f0000644000000000000000000000013214061636515015164 xustar0030 mtime=1623670093.417103882 30 atime=1623670093.416103883 30 ctime=1623670093.417103882 elk-7.2.42/src/LAPACK/dlaed7.f0000644002504400250440000003172314061636515017227 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED7 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, * LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, * PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, * INFO ) * * .. Scalar Arguments .. * INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, * $ QSIZ, TLVLS * DOUBLE PRECISION RHO * .. * .. Array Arguments .. * INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), * $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) * DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), * $ QSTORE( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAED7 computes the updated eigensystem of a diagonal *> matrix after modification by a rank-one symmetric matrix. This *> routine is used only for the eigenproblem which requires all *> eigenvalues and optionally eigenvectors of a dense symmetric matrix *> that has been reduced to tridiagonal form. DLAED1 handles *> the case in which all eigenvalues and eigenvectors of a symmetric *> tridiagonal matrix are desired. *> *> T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) *> *> where Z = Q**Tu, u is a vector of length N with ones in the *> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. *> *> The eigenvectors of the original matrix are stored in Q, and the *> eigenvalues are in D. The algorithm consists of three stages: *> *> The first stage consists of deflating the size of the problem *> when there are multiple eigenvalues or if there is a zero in *> the Z vector. For each such occurrence the dimension of the *> secular equation problem is reduced by one. This stage is *> performed by the routine DLAED8. *> *> The second stage consists of calculating the updated *> eigenvalues. This is done by finding the roots of the secular *> equation via the routine DLAED4 (as called by DLAED9). *> This routine also calculates the eigenvectors of the current *> problem. *> *> The final stage consists of computing the updated eigenvectors *> directly using the updated eigenvalues. The eigenvectors for *> the current problem are multiplied with the eigenvectors from *> the overall problem. *> \endverbatim * * Arguments: * ========== * *> \param[in] ICOMPQ *> \verbatim *> ICOMPQ is INTEGER *> = 0: Compute eigenvalues only. *> = 1: Compute eigenvectors of original dense symmetric matrix *> also. On entry, Q contains the orthogonal matrix used *> to reduce the original matrix to tridiagonal form. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in] QSIZ *> \verbatim *> QSIZ is INTEGER *> The dimension of the orthogonal matrix used to reduce *> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. *> \endverbatim *> *> \param[in] TLVLS *> \verbatim *> TLVLS is INTEGER *> The total number of merging levels in the overall divide and *> conquer tree. *> \endverbatim *> *> \param[in] CURLVL *> \verbatim *> CURLVL is INTEGER *> The current level in the overall merge routine, *> 0 <= CURLVL <= TLVLS. *> \endverbatim *> *> \param[in] CURPBM *> \verbatim *> CURPBM is INTEGER *> The current problem in the current level in the overall *> merge routine (counting from upper left to lower right). *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the eigenvalues of the rank-1-perturbed matrix. *> On exit, the eigenvalues of the repaired matrix. *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDQ, N) *> On entry, the eigenvectors of the rank-1-perturbed matrix. *> On exit, the eigenvectors of the repaired tridiagonal matrix. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[out] INDXQ *> \verbatim *> INDXQ is INTEGER array, dimension (N) *> The permutation which will reintegrate the subproblem just *> solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) *> will be in ascending order. *> \endverbatim *> *> \param[in] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> The subdiagonal element used to create the rank-1 *> modification. *> \endverbatim *> *> \param[in] CUTPNT *> \verbatim *> CUTPNT is INTEGER *> Contains the location of the last eigenvalue in the leading *> sub-matrix. min(1,N) <= CUTPNT <= N. *> \endverbatim *> *> \param[in,out] QSTORE *> \verbatim *> QSTORE is DOUBLE PRECISION array, dimension (N**2+1) *> Stores eigenvectors of submatrices encountered during *> divide and conquer, packed together. QPTR points to *> beginning of the submatrices. *> \endverbatim *> *> \param[in,out] QPTR *> \verbatim *> QPTR is INTEGER array, dimension (N+2) *> List of indices pointing to beginning of submatrices stored *> in QSTORE. The submatrices are numbered starting at the *> bottom left of the divide and conquer tree, from left to *> right and bottom to top. *> \endverbatim *> *> \param[in] PRMPTR *> \verbatim *> PRMPTR is INTEGER array, dimension (N lg N) *> Contains a list of pointers which indicate where in PERM a *> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) *> indicates the size of the permutation and also the size of *> the full, non-deflated problem. *> \endverbatim *> *> \param[in] PERM *> \verbatim *> PERM is INTEGER array, dimension (N lg N) *> Contains the permutations (from deflation and sorting) to be *> applied to each eigenblock. *> \endverbatim *> *> \param[in] GIVPTR *> \verbatim *> GIVPTR is INTEGER array, dimension (N lg N) *> Contains a list of pointers which indicate where in GIVCOL a *> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) *> indicates the number of Givens rotations. *> \endverbatim *> *> \param[in] GIVCOL *> \verbatim *> GIVCOL is INTEGER array, dimension (2, N lg N) *> Each pair of numbers indicates a pair of columns to take place *> in a Givens rotation. *> \endverbatim *> *> \param[in] GIVNUM *> \verbatim *> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) *> Each number indicates the S value to be used in the *> corresponding Givens rotation. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (3*N+2*QSIZ*N) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (4*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, an eigenvalue did not converge *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA * * ===================================================================== SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, $ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, $ PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, $ INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, $ QSIZ, TLVLS DOUBLE PRECISION RHO * .. * .. Array Arguments .. INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), $ QSTORE( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) * .. * .. Local Scalars .. INTEGER COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP, $ IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR * .. * .. External Subroutines .. EXTERNAL DGEMM, DLAED8, DLAED9, DLAEDA, DLAMRG, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN INFO = -3 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -9 ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN INFO = -12 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAED7', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * The following values are for bookkeeping purposes only. They are * integer pointers which indicate the portion of the workspace * used by a particular array in DLAED8 and DLAED9. * IF( ICOMPQ.EQ.1 ) THEN LDQ2 = QSIZ ELSE LDQ2 = N END IF * IZ = 1 IDLMDA = IZ + N IW = IDLMDA + N IQ2 = IW + N IS = IQ2 + N*LDQ2 * INDX = 1 INDXC = INDX + N COLTYP = INDXC + N INDXP = COLTYP + N * * Form the z-vector which consists of the last row of Q_1 and the * first row of Q_2. * PTR = 1 + 2**TLVLS DO 10 I = 1, CURLVL - 1 PTR = PTR + 2**( TLVLS-I ) 10 CONTINUE CURR = PTR + CURPBM CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, $ GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ), $ WORK( IZ+N ), INFO ) * * When solving the final problem, we no longer need the stored data, * so we will overwrite the data from this level onto the previously * used storage space. * IF( CURLVL.EQ.TLVLS ) THEN QPTR( CURR ) = 1 PRMPTR( CURR ) = 1 GIVPTR( CURR ) = 1 END IF * * Sort and Deflate eigenvalues. * CALL DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, $ WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2, $ WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), $ GIVCOL( 1, GIVPTR( CURR ) ), $ GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ), $ IWORK( INDX ), INFO ) PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) * * Solve Secular Equation. * IF( K.NE.0 ) THEN CALL DLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ), $ WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO ) IF( INFO.NE.0 ) $ GO TO 30 IF( ICOMPQ.EQ.1 ) THEN CALL DGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2, $ QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ ) END IF QPTR( CURR+1 ) = QPTR( CURR ) + K**2 * * Prepare the INDXQ sorting permutation. * N1 = K N2 = N - K CALL DLAMRG( N1, N2, D, 1, -1, INDXQ ) ELSE QPTR( CURR+1 ) = QPTR( CURR ) DO 20 I = 1, N INDXQ( I ) = I 20 CONTINUE END IF * 30 CONTINUE RETURN * * End of DLAED7 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasq3.f0000644000000000000000000000013214061636515015213 xustar0030 mtime=1623670093.419103881 30 atime=1623670093.418103881 30 ctime=1623670093.419103881 elk-7.2.42/src/LAPACK/dlasq3.f0000644002504400250440000002474314061636515017262 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASQ3 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, * ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, * DN2, G, TAU ) * * .. Scalar Arguments .. * LOGICAL IEEE * INTEGER I0, ITER, N0, NDIV, NFAIL, PP * DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, * $ QMAX, SIGMA, TAU * .. * .. Array Arguments .. * DOUBLE PRECISION Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. *> In case of failure it changes shifts, and tries again until output *> is positive. *> \endverbatim * * Arguments: * ========== * *> \param[in] I0 *> \verbatim *> I0 is INTEGER *> First index. *> \endverbatim *> *> \param[in,out] N0 *> \verbatim *> N0 is INTEGER *> Last index. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension ( 4*N0 ) *> Z holds the qd array. *> \endverbatim *> *> \param[in,out] PP *> \verbatim *> PP is INTEGER *> PP=0 for ping, PP=1 for pong. *> PP=2 indicates that flipping was applied to the Z array *> and that the initial tests for deflation should not be *> performed. *> \endverbatim *> *> \param[out] DMIN *> \verbatim *> DMIN is DOUBLE PRECISION *> Minimum value of d. *> \endverbatim *> *> \param[out] SIGMA *> \verbatim *> SIGMA is DOUBLE PRECISION *> Sum of shifts used in current segment. *> \endverbatim *> *> \param[in,out] DESIG *> \verbatim *> DESIG is DOUBLE PRECISION *> Lower order part of SIGMA *> \endverbatim *> *> \param[in] QMAX *> \verbatim *> QMAX is DOUBLE PRECISION *> Maximum value of q. *> \endverbatim *> *> \param[in,out] NFAIL *> \verbatim *> NFAIL is INTEGER *> Increment NFAIL by 1 each time the shift was too big. *> \endverbatim *> *> \param[in,out] ITER *> \verbatim *> ITER is INTEGER *> Increment ITER by 1 for each iteration. *> \endverbatim *> *> \param[in,out] NDIV *> \verbatim *> NDIV is INTEGER *> Increment NDIV by 1 for each division. *> \endverbatim *> *> \param[in] IEEE *> \verbatim *> IEEE is LOGICAL *> Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). *> \endverbatim *> *> \param[in,out] TTYPE *> \verbatim *> TTYPE is INTEGER *> Shift type. *> \endverbatim *> *> \param[in,out] DMIN1 *> \verbatim *> DMIN1 is DOUBLE PRECISION *> \endverbatim *> *> \param[in,out] DMIN2 *> \verbatim *> DMIN2 is DOUBLE PRECISION *> \endverbatim *> *> \param[in,out] DN *> \verbatim *> DN is DOUBLE PRECISION *> \endverbatim *> *> \param[in,out] DN1 *> \verbatim *> DN1 is DOUBLE PRECISION *> \endverbatim *> *> \param[in,out] DN2 *> \verbatim *> DN2 is DOUBLE PRECISION *> \endverbatim *> *> \param[in,out] G *> \verbatim *> G is DOUBLE PRECISION *> \endverbatim *> *> \param[in,out] TAU *> \verbatim *> TAU is DOUBLE PRECISION *> *> These are passed as arguments in order to save their values *> between calls to DLASQ3. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, $ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, $ DN2, G, TAU ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. LOGICAL IEEE INTEGER I0, ITER, N0, NDIV, NFAIL, PP DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, $ QMAX, SIGMA, TAU * .. * .. Array Arguments .. DOUBLE PRECISION Z( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION CBIAS PARAMETER ( CBIAS = 1.50D0 ) DOUBLE PRECISION ZERO, QURTR, HALF, ONE, TWO, HUNDRD PARAMETER ( ZERO = 0.0D0, QURTR = 0.250D0, HALF = 0.5D0, $ ONE = 1.0D0, TWO = 2.0D0, HUNDRD = 100.0D0 ) * .. * .. Local Scalars .. INTEGER IPN4, J4, N0IN, NN, TTYPE DOUBLE PRECISION EPS, S, T, TEMP, TOL, TOL2 * .. * .. External Subroutines .. EXTERNAL DLASQ4, DLASQ5, DLASQ6 * .. * .. External Function .. DOUBLE PRECISION DLAMCH LOGICAL DISNAN EXTERNAL DISNAN, DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Executable Statements .. * N0IN = N0 EPS = DLAMCH( 'Precision' ) TOL = EPS*HUNDRD TOL2 = TOL**2 * * Check for deflation. * 10 CONTINUE * IF( N0.LT.I0 ) $ RETURN IF( N0.EQ.I0 ) $ GO TO 20 NN = 4*N0 + PP IF( N0.EQ.( I0+1 ) ) $ GO TO 40 * * Check whether E(N0-1) is negligible, 1 eigenvalue. * IF( Z( NN-5 ).GT.TOL2*( SIGMA+Z( NN-3 ) ) .AND. $ Z( NN-2*PP-4 ).GT.TOL2*Z( NN-7 ) ) $ GO TO 30 * 20 CONTINUE * Z( 4*N0-3 ) = Z( 4*N0+PP-3 ) + SIGMA N0 = N0 - 1 GO TO 10 * * Check whether E(N0-2) is negligible, 2 eigenvalues. * 30 CONTINUE * IF( Z( NN-9 ).GT.TOL2*SIGMA .AND. $ Z( NN-2*PP-8 ).GT.TOL2*Z( NN-11 ) ) $ GO TO 50 * 40 CONTINUE * IF( Z( NN-3 ).GT.Z( NN-7 ) ) THEN S = Z( NN-3 ) Z( NN-3 ) = Z( NN-7 ) Z( NN-7 ) = S END IF T = HALF*( ( Z( NN-7 )-Z( NN-3 ) )+Z( NN-5 ) ) IF( Z( NN-5 ).GT.Z( NN-3 )*TOL2.AND.T.NE.ZERO ) THEN S = Z( NN-3 )*( Z( NN-5 ) / T ) IF( S.LE.T ) THEN S = Z( NN-3 )*( Z( NN-5 ) / $ ( T*( ONE+SQRT( ONE+S / T ) ) ) ) ELSE S = Z( NN-3 )*( Z( NN-5 ) / ( T+SQRT( T )*SQRT( T+S ) ) ) END IF T = Z( NN-7 ) + ( S+Z( NN-5 ) ) Z( NN-3 ) = Z( NN-3 )*( Z( NN-7 ) / T ) Z( NN-7 ) = T END IF Z( 4*N0-7 ) = Z( NN-7 ) + SIGMA Z( 4*N0-3 ) = Z( NN-3 ) + SIGMA N0 = N0 - 2 GO TO 10 * 50 CONTINUE IF( PP.EQ.2 ) $ PP = 0 * * Reverse the qd-array, if warranted. * IF( DMIN.LE.ZERO .OR. N0.LT.N0IN ) THEN IF( CBIAS*Z( 4*I0+PP-3 ).LT.Z( 4*N0+PP-3 ) ) THEN IPN4 = 4*( I0+N0 ) DO 60 J4 = 4*I0, 2*( I0+N0-1 ), 4 TEMP = Z( J4-3 ) Z( J4-3 ) = Z( IPN4-J4-3 ) Z( IPN4-J4-3 ) = TEMP TEMP = Z( J4-2 ) Z( J4-2 ) = Z( IPN4-J4-2 ) Z( IPN4-J4-2 ) = TEMP TEMP = Z( J4-1 ) Z( J4-1 ) = Z( IPN4-J4-5 ) Z( IPN4-J4-5 ) = TEMP TEMP = Z( J4 ) Z( J4 ) = Z( IPN4-J4-4 ) Z( IPN4-J4-4 ) = TEMP 60 CONTINUE IF( N0-I0.LE.4 ) THEN Z( 4*N0+PP-1 ) = Z( 4*I0+PP-1 ) Z( 4*N0-PP ) = Z( 4*I0-PP ) END IF DMIN2 = MIN( DMIN2, Z( 4*N0+PP-1 ) ) Z( 4*N0+PP-1 ) = MIN( Z( 4*N0+PP-1 ), Z( 4*I0+PP-1 ), $ Z( 4*I0+PP+3 ) ) Z( 4*N0-PP ) = MIN( Z( 4*N0-PP ), Z( 4*I0-PP ), $ Z( 4*I0-PP+4 ) ) QMAX = MAX( QMAX, Z( 4*I0+PP-3 ), Z( 4*I0+PP+1 ) ) DMIN = -ZERO END IF END IF * * Choose a shift. * CALL DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, DN1, $ DN2, TAU, TTYPE, G ) * * Call dqds until DMIN > 0. * 70 CONTINUE * CALL DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, $ DN1, DN2, IEEE, EPS ) * NDIV = NDIV + ( N0-I0+2 ) ITER = ITER + 1 * * Check status. * IF( DMIN.GE.ZERO .AND. DMIN1.GE.ZERO ) THEN * * Success. * GO TO 90 * ELSE IF( DMIN.LT.ZERO .AND. DMIN1.GT.ZERO .AND. $ Z( 4*( N0-1 )-PP ).LT.TOL*( SIGMA+DN1 ) .AND. $ ABS( DN ).LT.TOL*SIGMA ) THEN * * Convergence hidden by negative DN. * Z( 4*( N0-1 )-PP+2 ) = ZERO DMIN = ZERO GO TO 90 ELSE IF( DMIN.LT.ZERO ) THEN * * TAU too big. Select new TAU and try again. * NFAIL = NFAIL + 1 IF( TTYPE.LT.-22 ) THEN * * Failed twice. Play it safe. * TAU = ZERO ELSE IF( DMIN1.GT.ZERO ) THEN * * Late failure. Gives excellent shift. * TAU = ( TAU+DMIN )*( ONE-TWO*EPS ) TTYPE = TTYPE - 11 ELSE * * Early failure. Divide by 4. * TAU = QURTR*TAU TTYPE = TTYPE - 12 END IF GO TO 70 ELSE IF( DISNAN( DMIN ) ) THEN * * NaN. * IF( TAU.EQ.ZERO ) THEN GO TO 80 ELSE TAU = ZERO GO TO 70 END IF ELSE * * Possible underflow. Play it safe. * GO TO 80 END IF * * Risk of underflow. * 80 CONTINUE CALL DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, DN1, DN2 ) NDIV = NDIV + ( N0-I0+2 ) ITER = ITER + 1 TAU = ZERO * 90 CONTINUE IF( TAU.LT.SIGMA ) THEN DESIG = DESIG + TAU T = SIGMA + DESIG DESIG = DESIG - ( T-SIGMA ) ELSE T = SIGMA + TAU DESIG = SIGMA - ( T-TAU ) + DESIG END IF SIGMA = T * RETURN * * End of DLASQ3 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlarf.f0000644000000000000000000000013214061636515015114 xustar0030 mtime=1623670093.421103879 30 atime=1623670093.421103879 30 ctime=1623670093.421103879 elk-7.2.42/src/LAPACK/dlarf.f0000644002504400250440000001411014061636515017146 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLARF applies an elementary reflector to a general rectangular matrix. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) * * .. Scalar Arguments .. * CHARACTER SIDE * INTEGER INCV, LDC, M, N * DOUBLE PRECISION TAU * .. * .. Array Arguments .. * DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLARF applies a real elementary reflector H to a real m by n matrix *> C, from either the left or the right. H is represented in the form *> *> H = I - tau * v * v**T *> *> where tau is a real scalar and v is a real vector. *> *> If tau = 0, then H is taken to be the unit matrix. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': form H * C *> = 'R': form C * H *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. *> \endverbatim *> *> \param[in] V *> \verbatim *> V is DOUBLE PRECISION array, dimension *> (1 + (M-1)*abs(INCV)) if SIDE = 'L' *> or (1 + (N-1)*abs(INCV)) if SIDE = 'R' *> The vector v in the representation of H. V is not used if *> TAU = 0. *> \endverbatim *> *> \param[in] INCV *> \verbatim *> INCV is INTEGER *> The increment between elements of v. INCV <> 0. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION *> The value tau in the representation of H. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> On entry, the m by n matrix C. *> On exit, C is overwritten by the matrix H * C if SIDE = 'L', *> or C * H if SIDE = 'R'. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension *> (N) if SIDE = 'L' *> or (M) if SIDE = 'R' *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERauxiliary * * ===================================================================== SUBROUTINE DLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE INTEGER INCV, LDC, M, N DOUBLE PRECISION TAU * .. * .. Array Arguments .. DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL APPLYLEFT INTEGER I, LASTV, LASTC * .. * .. External Subroutines .. EXTERNAL DGEMV, DGER * .. * .. External Functions .. LOGICAL LSAME INTEGER ILADLR, ILADLC EXTERNAL LSAME, ILADLR, ILADLC * .. * .. Executable Statements .. * APPLYLEFT = LSAME( SIDE, 'L' ) LASTV = 0 LASTC = 0 IF( TAU.NE.ZERO ) THEN ! Set up variables for scanning V. LASTV begins pointing to the end ! of V. IF( APPLYLEFT ) THEN LASTV = M ELSE LASTV = N END IF IF( INCV.GT.0 ) THEN I = 1 + (LASTV-1) * INCV ELSE I = 1 END IF ! Look for the last non-zero row in V. DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO ) LASTV = LASTV - 1 I = I - INCV END DO IF( APPLYLEFT ) THEN ! Scan for the last non-zero column in C(1:lastv,:). LASTC = ILADLC(LASTV, N, C, LDC) ELSE ! Scan for the last non-zero row in C(:,1:lastv). LASTC = ILADLR(M, LASTV, C, LDC) END IF END IF ! Note that lastc.eq.0 renders the BLAS operations null; no special ! case is needed at this level. IF( APPLYLEFT ) THEN * * Form H * C * IF( LASTV.GT.0 ) THEN * * w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1) * CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV, $ ZERO, WORK, 1 ) * * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T * CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC ) END IF ELSE * * Form C * H * IF( LASTV.GT.0 ) THEN * * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1) * CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC, $ V, INCV, ZERO, WORK, 1 ) * * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T * CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC ) END IF END IF RETURN * * End of DLARF * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dorm2l.f0000644000000000000000000000013214061636515015223 xustar0030 mtime=1623670093.423103877 30 atime=1623670093.422103878 30 ctime=1623670093.423103877 elk-7.2.42/src/LAPACK/dorm2l.f0000644002504400250440000001622114061636515017262 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORM2L + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORM2L overwrites the general real m by n matrix C with *> *> Q * C if SIDE = 'L' and TRANS = 'N', or *> *> Q**T * C if SIDE = 'L' and TRANS = 'T', or *> *> C * Q if SIDE = 'R' and TRANS = 'N', or *> *> C * Q**T if SIDE = 'R' and TRANS = 'T', *> *> where Q is a real orthogonal matrix defined as the product of k *> elementary reflectors *> *> Q = H(k) . . . H(2) H(1) *> *> as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**T from the Left *> = 'R': apply Q or Q**T from the Right *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply Q (No transpose) *> = 'T': apply Q**T (Transpose) *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> DGEQLF in the last k columns of its array argument A. *> A is modified by the routine but restored on exit. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,M); *> if SIDE = 'R', LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEQLF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> On entry, the m by n matrix C. *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension *> (N) if SIDE = 'L', *> (M) if SIDE = 'R' *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LEFT, NOTRAN INTEGER I, I1, I2, I3, MI, NI, NQ DOUBLE PRECISION AII * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DLARF, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) * * NQ is the order of Q * IF( LEFT ) THEN NQ = M ELSE NQ = N END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORM2L', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) $ RETURN * IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) $ THEN I1 = 1 I2 = K I3 = 1 ELSE I1 = K I2 = 1 I3 = -1 END IF * IF( LEFT ) THEN NI = N ELSE MI = M END IF * DO 10 I = I1, I2, I3 IF( LEFT ) THEN * * H(i) is applied to C(1:m-k+i,1:n) * MI = M - K + I ELSE * * H(i) is applied to C(1:m,1:n-k+i) * NI = N - K + I END IF * * Apply H(i) * AII = A( NQ-K+I, I ) A( NQ-K+I, I ) = ONE CALL DLARF( SIDE, MI, NI, A( 1, I ), 1, TAU( I ), C, LDC, $ WORK ) A( NQ-K+I, I ) = AII 10 CONTINUE RETURN * * End of DORM2L * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dorm2r.f0000644000000000000000000000013214061636515015231 xustar0030 mtime=1623670093.424103876 30 atime=1623670093.424103876 30 ctime=1623670093.424103876 elk-7.2.42/src/LAPACK/dorm2r.f0000644002504400250440000001632214061636515017272 0ustar00dewhurstdewhurst00000000000000*> \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORM2R + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, * WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORM2R overwrites the general real m by n matrix C with *> *> Q * C if SIDE = 'L' and TRANS = 'N', or *> *> Q**T* C if SIDE = 'L' and TRANS = 'T', or *> *> C * Q if SIDE = 'R' and TRANS = 'N', or *> *> C * Q**T if SIDE = 'R' and TRANS = 'T', *> *> where Q is a real orthogonal matrix defined as the product of k *> elementary reflectors *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by DGEQRF. Q is of order m if SIDE = 'L' and of order n *> if SIDE = 'R'. *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**T from the Left *> = 'R': apply Q or Q**T from the Right *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply Q (No transpose) *> = 'T': apply Q**T (Transpose) *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines *> the matrix Q. *> If SIDE = 'L', M >= K >= 0; *> if SIDE = 'R', N >= K >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,K) *> The i-th column must contain the vector which defines the *> elementary reflector H(i), for i = 1,2,...,k, as returned by *> DGEQRF in the first k columns of its array argument A. *> A is modified by the routine but restored on exit. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> If SIDE = 'L', LDA >= max(1,M); *> if SIDE = 'R', LDA >= max(1,N). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGEQRF. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> On entry, the m by n matrix C. *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension *> (N) if SIDE = 'L', *> (M) if SIDE = 'R' *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, $ WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER INFO, K, LDA, LDC, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LEFT, NOTRAN INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ DOUBLE PRECISION AII * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DLARF, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) * * NQ is the order of Q * IF( LEFT ) THEN NQ = M ELSE NQ = N END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN INFO = -5 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORM2R', -INFO ) RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) $ RETURN * IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. ( .NOT.LEFT .AND. NOTRAN ) ) $ THEN I1 = 1 I2 = K I3 = 1 ELSE I1 = K I2 = 1 I3 = -1 END IF * IF( LEFT ) THEN NI = N JC = 1 ELSE MI = M IC = 1 END IF * DO 10 I = I1, I2, I3 IF( LEFT ) THEN * * H(i) is applied to C(i:m,1:n) * MI = M - I + 1 IC = I ELSE * * H(i) is applied to C(1:m,i:n) * NI = N - I + 1 JC = I END IF * * Apply H(i) * AII = A( I, I ) A( I, I ) = ONE CALL DLARF( SIDE, MI, NI, A( I, I ), 1, TAU( I ), C( IC, JC ), $ LDC, WORK ) A( I, I ) = AII 10 CONTINUE RETURN * * End of DORM2R * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dladiv.f0000644000000000000000000000013214061636515015267 xustar0030 mtime=1623670093.426103874 30 atime=1623670093.426103874 30 ctime=1623670093.426103874 elk-7.2.42/src/LAPACK/dladiv.f0000644002504400250440000001370614061636515017333 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLADIV + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLADIV( A, B, C, D, P, Q ) * * .. Scalar Arguments .. * DOUBLE PRECISION A, B, C, D, P, Q * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLADIV performs complex division in real arithmetic *> *> a + i*b *> p + i*q = --------- *> c + i*d *> *> The algorithm is due to Michael Baudin and Robert L. Smith *> and can be found in the paper *> "A Robust Complex Division in Scilab" *> \endverbatim * * Arguments: * ========== * *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION *> \endverbatim *> *> \param[in] B *> \verbatim *> B is DOUBLE PRECISION *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION *> The scalars a, b, c, and d in the above expression. *> \endverbatim *> *> \param[out] P *> \verbatim *> P is DOUBLE PRECISION *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is DOUBLE PRECISION *> The scalars p and q in the above expression. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date January 2013 * *> \ingroup doubleOTHERauxiliary * * ===================================================================== SUBROUTINE DLADIV( A, B, C, D, P, Q ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * January 2013 * * .. Scalar Arguments .. DOUBLE PRECISION A, B, C, D, P, Q * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION BS PARAMETER ( BS = 2.0D0 ) DOUBLE PRECISION HALF PARAMETER ( HALF = 0.5D0 ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0D0 ) * * .. Local Scalars .. DOUBLE PRECISION AA, BB, CC, DD, AB, CD, S, OV, UN, BE, EPS * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DLADIV1 * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * AA = A BB = B CC = C DD = D AB = MAX( ABS(A), ABS(B) ) CD = MAX( ABS(C), ABS(D) ) S = 1.0D0 OV = DLAMCH( 'Overflow threshold' ) UN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Epsilon' ) BE = BS / (EPS*EPS) IF( AB >= HALF*OV ) THEN AA = HALF * AA BB = HALF * BB S = TWO * S END IF IF( CD >= HALF*OV ) THEN CC = HALF * CC DD = HALF * DD S = HALF * S END IF IF( AB <= UN*BS/EPS ) THEN AA = AA * BE BB = BB * BE S = S / BE END IF IF( CD <= UN*BS/EPS ) THEN CC = CC * BE DD = DD * BE S = S * BE END IF IF( ABS( D ).LE.ABS( C ) ) THEN CALL DLADIV1(AA, BB, CC, DD, P, Q) ELSE CALL DLADIV1(BB, AA, DD, CC, P, Q) Q = -Q END IF P = P * S Q = Q * S * RETURN * * End of DLADIV * END *> \ingroup doubleOTHERauxiliary SUBROUTINE DLADIV1( A, B, C, D, P, Q ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * January 2013 * * .. Scalar Arguments .. DOUBLE PRECISION A, B, C, D, P, Q * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) * * .. Local Scalars .. DOUBLE PRECISION R, T * .. * .. External Functions .. DOUBLE PRECISION DLADIV2 EXTERNAL DLADIV2 * .. * .. Executable Statements .. * R = D / C T = ONE / (C + D * R) P = DLADIV2(A, B, C, D, R, T) A = -A Q = DLADIV2(B, A, C, D, R, T) * RETURN * * End of DLADIV1 * END *> \ingroup doubleOTHERauxiliary DOUBLE PRECISION FUNCTION DLADIV2( A, B, C, D, R, T ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * January 2013 * * .. Scalar Arguments .. DOUBLE PRECISION A, B, C, D, R, T * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) * * .. Local Scalars .. DOUBLE PRECISION BR * .. * .. Executable Statements .. * IF( R.NE.ZERO ) THEN BR = B * R IF( BR.NE.ZERO ) THEN DLADIV2 = (A + BR) * T ELSE DLADIV2 = A * T + (B * T) * R END IF ELSE DLADIV2 = (A + D * (B / C)) * T END IF * RETURN * * End of DLADIV12 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaeda.f0000644000000000000000000000013214061636515015236 xustar0030 mtime=1623670093.428103872 30 atime=1623670093.428103872 30 ctime=1623670093.428103872 elk-7.2.42/src/LAPACK/dlaeda.f0000644002504400250440000002324014061636515017274 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAEDA + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, * GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) * * .. Scalar Arguments .. * INTEGER CURLVL, CURPBM, INFO, N, TLVLS * .. * .. Array Arguments .. * INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), * $ PRMPTR( * ), QPTR( * ) * DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAEDA computes the Z vector corresponding to the merge step in the *> CURLVLth step of the merge process with TLVLS steps for the CURPBMth *> problem. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in] TLVLS *> \verbatim *> TLVLS is INTEGER *> The total number of merging levels in the overall divide and *> conquer tree. *> \endverbatim *> *> \param[in] CURLVL *> \verbatim *> CURLVL is INTEGER *> The current level in the overall merge routine, *> 0 <= curlvl <= tlvls. *> \endverbatim *> *> \param[in] CURPBM *> \verbatim *> CURPBM is INTEGER *> The current problem in the current level in the overall *> merge routine (counting from upper left to lower right). *> \endverbatim *> *> \param[in] PRMPTR *> \verbatim *> PRMPTR is INTEGER array, dimension (N lg N) *> Contains a list of pointers which indicate where in PERM a *> level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) *> indicates the size of the permutation and incidentally the *> size of the full, non-deflated problem. *> \endverbatim *> *> \param[in] PERM *> \verbatim *> PERM is INTEGER array, dimension (N lg N) *> Contains the permutations (from deflation and sorting) to be *> applied to each eigenblock. *> \endverbatim *> *> \param[in] GIVPTR *> \verbatim *> GIVPTR is INTEGER array, dimension (N lg N) *> Contains a list of pointers which indicate where in GIVCOL a *> level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) *> indicates the number of Givens rotations. *> \endverbatim *> *> \param[in] GIVCOL *> \verbatim *> GIVCOL is INTEGER array, dimension (2, N lg N) *> Each pair of numbers indicates a pair of columns to take place *> in a Givens rotation. *> \endverbatim *> *> \param[in] GIVNUM *> \verbatim *> GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) *> Each number indicates the S value to be used in the *> corresponding Givens rotation. *> \endverbatim *> *> \param[in] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (N**2) *> Contains the square eigenblocks from previous levels, the *> starting positions for blocks are given by QPTR. *> \endverbatim *> *> \param[in] QPTR *> \verbatim *> QPTR is INTEGER array, dimension (N+2) *> Contains a list of pointers which indicate where in Q an *> eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates *> the size of the block. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (N) *> On output this vector contains the updating vector (the last *> row of the first sub-eigenvector matrix and the first row of *> the second sub-eigenvector matrix). *> \endverbatim *> *> \param[out] ZTEMP *> \verbatim *> ZTEMP is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA * * ===================================================================== SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, $ GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER CURLVL, CURPBM, INFO, N, TLVLS * .. * .. Array Arguments .. INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), $ PRMPTR( * ), QPTR( * ) DOUBLE PRECISION GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, HALF, ONE PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER BSIZ1, BSIZ2, CURR, I, K, MID, PSIZ1, PSIZ2, $ PTR, ZPTR1 * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMV, DROT, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, INT, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( N.LT.0 ) THEN INFO = -1 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAEDA', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * * Determine location of first number in second half. * MID = N / 2 + 1 * * Gather last/first rows of appropriate eigenblocks into center of Z * PTR = 1 * * Determine location of lowest level subproblem in the full storage * scheme * CURR = PTR + CURPBM*2**CURLVL + 2**( CURLVL-1 ) - 1 * * Determine size of these matrices. We add HALF to the value of * the SQRT in case the machine underestimates one of these square * roots. * BSIZ1 = INT( HALF+SQRT( DBLE( QPTR( CURR+1 )-QPTR( CURR ) ) ) ) BSIZ2 = INT( HALF+SQRT( DBLE( QPTR( CURR+2 )-QPTR( CURR+1 ) ) ) ) DO 10 K = 1, MID - BSIZ1 - 1 Z( K ) = ZERO 10 CONTINUE CALL DCOPY( BSIZ1, Q( QPTR( CURR )+BSIZ1-1 ), BSIZ1, $ Z( MID-BSIZ1 ), 1 ) CALL DCOPY( BSIZ2, Q( QPTR( CURR+1 ) ), BSIZ2, Z( MID ), 1 ) DO 20 K = MID + BSIZ2, N Z( K ) = ZERO 20 CONTINUE * * Loop through remaining levels 1 -> CURLVL applying the Givens * rotations and permutation and then multiplying the center matrices * against the current Z. * PTR = 2**TLVLS + 1 DO 70 K = 1, CURLVL - 1 CURR = PTR + CURPBM*2**( CURLVL-K ) + 2**( CURLVL-K-1 ) - 1 PSIZ1 = PRMPTR( CURR+1 ) - PRMPTR( CURR ) PSIZ2 = PRMPTR( CURR+2 ) - PRMPTR( CURR+1 ) ZPTR1 = MID - PSIZ1 * * Apply Givens at CURR and CURR+1 * DO 30 I = GIVPTR( CURR ), GIVPTR( CURR+1 ) - 1 CALL DROT( 1, Z( ZPTR1+GIVCOL( 1, I )-1 ), 1, $ Z( ZPTR1+GIVCOL( 2, I )-1 ), 1, GIVNUM( 1, I ), $ GIVNUM( 2, I ) ) 30 CONTINUE DO 40 I = GIVPTR( CURR+1 ), GIVPTR( CURR+2 ) - 1 CALL DROT( 1, Z( MID-1+GIVCOL( 1, I ) ), 1, $ Z( MID-1+GIVCOL( 2, I ) ), 1, GIVNUM( 1, I ), $ GIVNUM( 2, I ) ) 40 CONTINUE PSIZ1 = PRMPTR( CURR+1 ) - PRMPTR( CURR ) PSIZ2 = PRMPTR( CURR+2 ) - PRMPTR( CURR+1 ) DO 50 I = 0, PSIZ1 - 1 ZTEMP( I+1 ) = Z( ZPTR1+PERM( PRMPTR( CURR )+I )-1 ) 50 CONTINUE DO 60 I = 0, PSIZ2 - 1 ZTEMP( PSIZ1+I+1 ) = Z( MID+PERM( PRMPTR( CURR+1 )+I )-1 ) 60 CONTINUE * * Multiply Blocks at CURR and CURR+1 * * Determine size of these matrices. We add HALF to the value of * the SQRT in case the machine underestimates one of these * square roots. * BSIZ1 = INT( HALF+SQRT( DBLE( QPTR( CURR+1 )-QPTR( CURR ) ) ) ) BSIZ2 = INT( HALF+SQRT( DBLE( QPTR( CURR+2 )-QPTR( CURR+ $ 1 ) ) ) ) IF( BSIZ1.GT.0 ) THEN CALL DGEMV( 'T', BSIZ1, BSIZ1, ONE, Q( QPTR( CURR ) ), $ BSIZ1, ZTEMP( 1 ), 1, ZERO, Z( ZPTR1 ), 1 ) END IF CALL DCOPY( PSIZ1-BSIZ1, ZTEMP( BSIZ1+1 ), 1, Z( ZPTR1+BSIZ1 ), $ 1 ) IF( BSIZ2.GT.0 ) THEN CALL DGEMV( 'T', BSIZ2, BSIZ2, ONE, Q( QPTR( CURR+1 ) ), $ BSIZ2, ZTEMP( PSIZ1+1 ), 1, ZERO, Z( MID ), 1 ) END IF CALL DCOPY( PSIZ2-BSIZ2, ZTEMP( PSIZ1+BSIZ2+1 ), 1, $ Z( MID+BSIZ2 ), 1 ) * PTR = PTR + 2**( TLVLS-K ) 70 CONTINUE * RETURN * * End of DLAEDA * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaed8.f0000644000000000000000000000012714061636515015217 xustar0029 mtime=1623670093.43010387 29 atime=1623670093.43010387 29 ctime=1623670093.43010387 elk-7.2.42/src/LAPACK/zlaed8.f0000644002504400250440000003522514061636515017257 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAED8 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, * Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, * GIVCOL, GIVNUM, INFO ) * * .. Scalar Arguments .. * INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ * DOUBLE PRECISION RHO * .. * .. Array Arguments .. * INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), * $ INDXQ( * ), PERM( * ) * DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), * $ Z( * ) * COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAED8 merges the two sets of eigenvalues together into a single *> sorted set. Then it tries to deflate the size of the problem. *> There are two ways in which deflation can occur: when two or more *> eigenvalues are close together or if there is a tiny element in the *> Z vector. For each such occurrence the order of the related secular *> equation problem is reduced by one. *> \endverbatim * * Arguments: * ========== * *> \param[out] K *> \verbatim *> K is INTEGER *> Contains the number of non-deflated eigenvalues. *> This is the order of the related secular equation. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in] QSIZ *> \verbatim *> QSIZ is INTEGER *> The dimension of the unitary matrix used to reduce *> the dense or band matrix to tridiagonal form. *> QSIZ >= N if ICOMPQ = 1. *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDQ,N) *> On entry, Q contains the eigenvectors of the partially solved *> system which has been previously updated in matrix *> multiplies with other partially solved eigensystems. *> On exit, Q contains the trailing (N-K) updated eigenvectors *> (those which were deflated) in its last N-K columns. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max( 1, N ). *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, D contains the eigenvalues of the two submatrices to *> be combined. On exit, D contains the trailing (N-K) updated *> eigenvalues (those which were deflated) sorted into increasing *> order. *> \endverbatim *> *> \param[in,out] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> Contains the off diagonal element associated with the rank-1 *> cut which originally split the two submatrices which are now *> being recombined. RHO is modified during the computation to *> the value required by DLAED3. *> \endverbatim *> *> \param[in] CUTPNT *> \verbatim *> CUTPNT is INTEGER *> Contains the location of the last eigenvalue in the leading *> sub-matrix. MIN(1,N) <= CUTPNT <= N. *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (N) *> On input this vector contains the updating vector (the last *> row of the first sub-eigenvector matrix and the first row of *> the second sub-eigenvector matrix). The contents of Z are *> destroyed during the updating process. *> \endverbatim *> *> \param[out] DLAMDA *> \verbatim *> DLAMDA is DOUBLE PRECISION array, dimension (N) *> Contains a copy of the first K eigenvalues which will be used *> by DLAED3 to form the secular equation. *> \endverbatim *> *> \param[out] Q2 *> \verbatim *> Q2 is COMPLEX*16 array, dimension (LDQ2,N) *> If ICOMPQ = 0, Q2 is not referenced. Otherwise, *> Contains a copy of the first K eigenvectors which will be used *> by DLAED7 in a matrix multiply (DGEMM) to update the new *> eigenvectors. *> \endverbatim *> *> \param[in] LDQ2 *> \verbatim *> LDQ2 is INTEGER *> The leading dimension of the array Q2. LDQ2 >= max( 1, N ). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> This will hold the first k values of the final *> deflation-altered z-vector and will be passed to DLAED3. *> \endverbatim *> *> \param[out] INDXP *> \verbatim *> INDXP is INTEGER array, dimension (N) *> This will contain the permutation used to place deflated *> values of D at the end of the array. On output INDXP(1:K) *> points to the nondeflated D-values and INDXP(K+1:N) *> points to the deflated eigenvalues. *> \endverbatim *> *> \param[out] INDX *> \verbatim *> INDX is INTEGER array, dimension (N) *> This will contain the permutation used to sort the contents of *> D into ascending order. *> \endverbatim *> *> \param[in] INDXQ *> \verbatim *> INDXQ is INTEGER array, dimension (N) *> This contains the permutation which separately sorts the two *> sub-problems in D into ascending order. Note that elements in *> the second half of this permutation must first have CUTPNT *> added to their values in order to be accurate. *> \endverbatim *> *> \param[out] PERM *> \verbatim *> PERM is INTEGER array, dimension (N) *> Contains the permutations (from deflation and sorting) to be *> applied to each eigenblock. *> \endverbatim *> *> \param[out] GIVPTR *> \verbatim *> GIVPTR is INTEGER *> Contains the number of Givens rotations which took place in *> this subproblem. *> \endverbatim *> *> \param[out] GIVCOL *> \verbatim *> GIVCOL is INTEGER array, dimension (2, N) *> Each pair of numbers indicates a pair of columns to take place *> in a Givens rotation. *> \endverbatim *> *> \param[out] GIVNUM *> \verbatim *> GIVNUM is DOUBLE PRECISION array, dimension (2, N) *> Each number indicates the S value to be used in the *> corresponding Givens rotation. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, $ Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, $ GIVCOL, GIVNUM, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ DOUBLE PRECISION RHO * .. * .. Array Arguments .. INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), $ INDXQ( * ), PERM( * ) DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), $ Z( * ) COMPLEX*16 Q( LDQ, * ), Q2( LDQ2, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION MONE, ZERO, ONE, TWO, EIGHT PARAMETER ( MONE = -1.0D0, ZERO = 0.0D0, ONE = 1.0D0, $ TWO = 2.0D0, EIGHT = 8.0D0 ) * .. * .. Local Scalars .. INTEGER I, IMAX, J, JLAM, JMAX, JP, K2, N1, N1P1, N2 DOUBLE PRECISION C, EPS, S, T, TAU, TOL * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DLAMCH, DLAPY2 EXTERNAL IDAMAX, DLAMCH, DLAPY2 * .. * .. External Subroutines .. EXTERNAL DCOPY, DLAMRG, DSCAL, XERBLA, ZCOPY, ZDROT, $ ZLACPY * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( N.LT.0 ) THEN INFO = -2 ELSE IF( QSIZ.LT.N ) THEN INFO = -3 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( CUTPNT.LT.MIN( 1, N ) .OR. CUTPNT.GT.N ) THEN INFO = -8 ELSE IF( LDQ2.LT.MAX( 1, N ) ) THEN INFO = -12 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLAED8', -INFO ) RETURN END IF * * Need to initialize GIVPTR to O here in case of quick exit * to prevent an unspecified code behavior (usually sigfault) * when IWORK array on entry to *stedc is not zeroed * (or at least some IWORK entries which used in *laed7 for GIVPTR). * GIVPTR = 0 * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * N1 = CUTPNT N2 = N - N1 N1P1 = N1 + 1 * IF( RHO.LT.ZERO ) THEN CALL DSCAL( N2, MONE, Z( N1P1 ), 1 ) END IF * * Normalize z so that norm(z) = 1 * T = ONE / SQRT( TWO ) DO 10 J = 1, N INDX( J ) = J 10 CONTINUE CALL DSCAL( N, T, Z, 1 ) RHO = ABS( TWO*RHO ) * * Sort the eigenvalues into increasing order * DO 20 I = CUTPNT + 1, N INDXQ( I ) = INDXQ( I ) + CUTPNT 20 CONTINUE DO 30 I = 1, N DLAMDA( I ) = D( INDXQ( I ) ) W( I ) = Z( INDXQ( I ) ) 30 CONTINUE I = 1 J = CUTPNT + 1 CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDX ) DO 40 I = 1, N D( I ) = DLAMDA( INDX( I ) ) Z( I ) = W( INDX( I ) ) 40 CONTINUE * * Calculate the allowable deflation tolerance * IMAX = IDAMAX( N, Z, 1 ) JMAX = IDAMAX( N, D, 1 ) EPS = DLAMCH( 'Epsilon' ) TOL = EIGHT*EPS*ABS( D( JMAX ) ) * * If the rank-1 modifier is small enough, no more needs to be done * -- except to reorganize Q so that its columns correspond with the * elements in D. * IF( RHO*ABS( Z( IMAX ) ).LE.TOL ) THEN K = 0 DO 50 J = 1, N PERM( J ) = INDXQ( INDX( J ) ) CALL ZCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 ) 50 CONTINUE CALL ZLACPY( 'A', QSIZ, N, Q2( 1, 1 ), LDQ2, Q( 1, 1 ), LDQ ) RETURN END IF * * If there are multiple eigenvalues then the problem deflates. Here * the number of equal eigenvalues are found. As each equal * eigenvalue is found, an elementary reflector is computed to rotate * the corresponding eigensubspace so that the corresponding * components of Z are zero in this new basis. * K = 0 K2 = N + 1 DO 60 J = 1, N IF( RHO*ABS( Z( J ) ).LE.TOL ) THEN * * Deflate due to small z component. * K2 = K2 - 1 INDXP( K2 ) = J IF( J.EQ.N ) $ GO TO 100 ELSE JLAM = J GO TO 70 END IF 60 CONTINUE 70 CONTINUE J = J + 1 IF( J.GT.N ) $ GO TO 90 IF( RHO*ABS( Z( J ) ).LE.TOL ) THEN * * Deflate due to small z component. * K2 = K2 - 1 INDXP( K2 ) = J ELSE * * Check if eigenvalues are close enough to allow deflation. * S = Z( JLAM ) C = Z( J ) * * Find sqrt(a**2+b**2) without overflow or * destructive underflow. * TAU = DLAPY2( C, S ) T = D( J ) - D( JLAM ) C = C / TAU S = -S / TAU IF( ABS( T*C*S ).LE.TOL ) THEN * * Deflation is possible. * Z( J ) = TAU Z( JLAM ) = ZERO * * Record the appropriate Givens rotation * GIVPTR = GIVPTR + 1 GIVCOL( 1, GIVPTR ) = INDXQ( INDX( JLAM ) ) GIVCOL( 2, GIVPTR ) = INDXQ( INDX( J ) ) GIVNUM( 1, GIVPTR ) = C GIVNUM( 2, GIVPTR ) = S CALL ZDROT( QSIZ, Q( 1, INDXQ( INDX( JLAM ) ) ), 1, $ Q( 1, INDXQ( INDX( J ) ) ), 1, C, S ) T = D( JLAM )*C*C + D( J )*S*S D( J ) = D( JLAM )*S*S + D( J )*C*C D( JLAM ) = T K2 = K2 - 1 I = 1 80 CONTINUE IF( K2+I.LE.N ) THEN IF( D( JLAM ).LT.D( INDXP( K2+I ) ) ) THEN INDXP( K2+I-1 ) = INDXP( K2+I ) INDXP( K2+I ) = JLAM I = I + 1 GO TO 80 ELSE INDXP( K2+I-1 ) = JLAM END IF ELSE INDXP( K2+I-1 ) = JLAM END IF JLAM = J ELSE K = K + 1 W( K ) = Z( JLAM ) DLAMDA( K ) = D( JLAM ) INDXP( K ) = JLAM JLAM = J END IF END IF GO TO 70 90 CONTINUE * * Record the last eigenvalue. * K = K + 1 W( K ) = Z( JLAM ) DLAMDA( K ) = D( JLAM ) INDXP( K ) = JLAM * 100 CONTINUE * * Sort the eigenvalues and corresponding eigenvectors into DLAMDA * and Q2 respectively. The eigenvalues/vectors which were not * deflated go into the first K slots of DLAMDA and Q2 respectively, * while those which were deflated go into the last N - K slots. * DO 110 J = 1, N JP = INDXP( J ) DLAMDA( J ) = D( JP ) PERM( J ) = INDXQ( INDX( JP ) ) CALL ZCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 ) 110 CONTINUE * * The deflated eigenvalues and their corresponding vectors go back * into the last N - K slots of D and Q respectively. * IF( K.LT.N ) THEN CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 ) CALL ZLACPY( 'A', QSIZ, N-K, Q2( 1, K+1 ), LDQ2, Q( 1, K+1 ), $ LDQ ) END IF * RETURN * * End of ZLAED8 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/Makefile0000644000000000000000000000013214061636515015315 xustar0030 mtime=1623670093.432103868 30 atime=1623670093.432103868 30 ctime=1623670093.432103868 elk-7.2.42/src/LAPACK/Makefile0000644002504400250440000000524414061636515017357 0ustar00dewhurstdewhurst00000000000000 AR = ar include ../../make.inc #------------------------------------------------------------------------------- # Suffix Rules #------------------------------------------------------------------------------- .SUFFIXES: .o .f .f.o: $(F77) $(F77_OPTS) -c $< #------------------------------------------------------------------------------- # File dependencies #------------------------------------------------------------------------------- SRC = \ dcombssq.f dgesv.f dgetrf2.f dgetrf.f dgetri.f dgetrs.f \ disnan.f dlabad.f dlacpy.f dladiv.f dlae2.f dlaebz.f \ dlaed0.f dlaed1.f dlaed2.f dlaed3.f dlaed4.f dlaed5.f \ dlaed6.f dlaed7.f dlaed8.f dlaed9.f dlaeda.f dlaev2.f \ dlagtf.f dlagts.f dlaisnan.f dlamch.f dlamrg.f dlanst.f \ dlansy.f dlapy2.f dlapy3.f dlarfb.f dlarf.f dlarfg.f \ dlarft.f dlarnv.f dlartg.f dlaruv.f dlas2.f dlascl.f \ dlaset.f dlasq1.f dlasq2.f dlasq3.f dlasq4.f dlasq5.f \ dlasq6.f dlasr.f dlasrt.f dlassq.f dlasv2.f dlaswp.f \ dlatrd.f dorg2l.f dorg2r.f dorgql.f dorgqr.f dorgtr.f \ dorm2l.f dorm2r.f dormql.f dormqr.f dormtr.f dpotrf2.f \ dpotrf.f dstebz.f dstedc.f dstein.f dsteqr.f dsterf.f \ dsyev.f dsyevx.f dsygs2.f dsygst.f dsygvx.f dsytd2.f \ dsytrd.f dtrti2.f dtrtri.f ieeeck.f iladlc.f iladlr.f \ ilaenv.f ilazlc.f ilazlr.f iparam2stage.f iparmq.f xerbla.f \ zbdsqr.f zgebak.f zgebal.f zgebd2.f zgebrd.f zgeev.f \ zgehd2.f zgehrd.f zgelq2.f zgelqf.f zgeqr2.f zgeqrf.f \ zgesvd.f zgesv.f zgetrf2.f zgetrf.f zgetri.f zgetrs.f \ zheevd.f zheev.f zheevx.f zhegs2.f zhegst.f zhegv.f \ zhegvx.f zhetd2.f zhetrd.f zhpevx.f zhpgst.f zhpgvx.f \ zhptrd.f zhseqr.f zlabrd.f zlacgv.f zlacpy.f zlacrm.f \ zladiv.f zlaed0.f zlaed7.f zlaed8.f zlahqr.f zlahr2.f \ zlange.f zlanhe.f zlanhp.f zlaqr0.f zlaqr1.f zlaqr2.f \ zlaqr3.f zlaqr4.f zlaqr5.f zlarfb.f zlarf.f zlarfg.f \ zlarft.f zlartg.f zlascl.f zlaset.f zlasr.f zlassq.f \ zlaswp.f zlatrd.f zlatrs.f zpotrf2.f zpotrf.f zpptrf.f \ zrot.f zstedc.f zstein.f zsteqr.f ztrevc3.f ztrexc.f \ ztrti2.f ztrtri.f zung2l.f zung2r.f zungbr.f zunghr.f \ zungl2.f zunglq.f zungql.f zungqr.f zungtr.f zunm2l.f \ zunm2r.f zunmbr.f zunmhr.f zunml2.f zunmlq.f zunmql.f \ zunmqr.f zunmtr.f zupgtr.f zupmtr.f OBJ = $(SRC:.f=.o) lapack: $(OBJ) $(AR) -rc lapack.a $(OBJ) clean: rm -f *.o *.mod *~ *.a ifc* *.gcno gmon.out ls: ls -x --tabsize=0 --width=80 *.f elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed9.f0000644000000000000000000000013214061636515015166 xustar0030 mtime=1623670093.434103867 30 atime=1623670093.434103867 30 ctime=1623670093.434103867 elk-7.2.42/src/LAPACK/dlaed9.f0000644002504400250440000002072214061636515017226 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED9 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED9 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, * S, LDS, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N * DOUBLE PRECISION RHO * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), * $ W( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAED9 finds the roots of the secular equation, as defined by the *> values in D, Z, and RHO, between KSTART and KSTOP. It makes the *> appropriate calls to DLAED4 and then stores the new matrix of *> eigenvectors for use in calculating the next level of Z vectors. *> \endverbatim * * Arguments: * ========== * *> \param[in] K *> \verbatim *> K is INTEGER *> The number of terms in the rational function to be solved by *> DLAED4. K >= 0. *> \endverbatim *> *> \param[in] KSTART *> \verbatim *> KSTART is INTEGER *> \endverbatim *> *> \param[in] KSTOP *> \verbatim *> KSTOP is INTEGER *> The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP *> are to be computed. 1 <= KSTART <= KSTOP <= K. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns in the Q matrix. *> N >= K (delation may result in N > K). *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> D(I) contains the updated eigenvalues *> for KSTART <= I <= KSTOP. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDQ,N) *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max( 1, N ). *> \endverbatim *> *> \param[in] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> The value of the parameter in the rank one update equation. *> RHO >= 0 required. *> \endverbatim *> *> \param[in] DLAMDA *> \verbatim *> DLAMDA is DOUBLE PRECISION array, dimension (K) *> The first K elements of this array contain the old roots *> of the deflated updating problem. These are the poles *> of the secular equation. *> \endverbatim *> *> \param[in] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (K) *> The first K elements of this array contain the components *> of the deflation-adjusted updating vector. *> \endverbatim *> *> \param[out] S *> \verbatim *> S is DOUBLE PRECISION array, dimension (LDS, K) *> Will contain the eigenvectors of the repaired matrix which *> will be stored for subsequent Z vector calculation and *> multiplied by the previously accumulated eigenvectors *> to update the system. *> \endverbatim *> *> \param[in] LDS *> \verbatim *> LDS is INTEGER *> The leading dimension of S. LDS >= max( 1, K ). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, an eigenvalue did not converge *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA * * ===================================================================== SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, $ S, LDS, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N DOUBLE PRECISION RHO * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), $ W( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION TEMP * .. * .. External Functions .. DOUBLE PRECISION DLAMC3, DNRM2 EXTERNAL DLAMC3, DNRM2 * .. * .. External Subroutines .. EXTERNAL DCOPY, DLAED4, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, SIGN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( K.LT.0 ) THEN INFO = -1 ELSE IF( KSTART.LT.1 .OR. KSTART.GT.MAX( 1, K ) ) THEN INFO = -2 ELSE IF( MAX( 1, KSTOP ).LT.KSTART .OR. KSTOP.GT.MAX( 1, K ) ) $ THEN INFO = -3 ELSE IF( N.LT.K ) THEN INFO = -4 ELSE IF( LDQ.LT.MAX( 1, K ) ) THEN INFO = -7 ELSE IF( LDS.LT.MAX( 1, K ) ) THEN INFO = -12 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAED9', -INFO ) RETURN END IF * * Quick return if possible * IF( K.EQ.0 ) $ RETURN * * Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can * be computed with high relative accuracy (barring over/underflow). * This is a problem on machines without a guard digit in * add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). * The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), * which on any of these machines zeros out the bottommost * bit of DLAMDA(I) if it is 1; this makes the subsequent * subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation * occurs. On binary machines with a guard digit (almost all * machines) it does not change DLAMDA(I) at all. On hexadecimal * and decimal machines with a guard digit, it slightly * changes the bottommost bits of DLAMDA(I). It does not account * for hexadecimal or decimal machines without guard digits * (we know of none). We use a subroutine call to compute * 2*DLAMBDA(I) to prevent optimizing compilers from eliminating * this code. * DO 10 I = 1, N DLAMDA( I ) = DLAMC3( DLAMDA( I ), DLAMDA( I ) ) - DLAMDA( I ) 10 CONTINUE * DO 20 J = KSTART, KSTOP CALL DLAED4( K, J, DLAMDA, W, Q( 1, J ), RHO, D( J ), INFO ) * * If the zero finder fails, the computation is terminated. * IF( INFO.NE.0 ) $ GO TO 120 20 CONTINUE * IF( K.EQ.1 .OR. K.EQ.2 ) THEN DO 40 I = 1, K DO 30 J = 1, K S( J, I ) = Q( J, I ) 30 CONTINUE 40 CONTINUE GO TO 120 END IF * * Compute updated W. * CALL DCOPY( K, W, 1, S, 1 ) * * Initialize W(I) = Q(I,I) * CALL DCOPY( K, Q, LDQ+1, W, 1 ) DO 70 J = 1, K DO 50 I = 1, J - 1 W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) ) 50 CONTINUE DO 60 I = J + 1, K W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) ) 60 CONTINUE 70 CONTINUE DO 80 I = 1, K W( I ) = SIGN( SQRT( -W( I ) ), S( I, 1 ) ) 80 CONTINUE * * Compute eigenvectors of the modified rank-1 modification. * DO 110 J = 1, K DO 90 I = 1, K Q( I, J ) = W( I ) / Q( I, J ) 90 CONTINUE TEMP = DNRM2( K, Q( 1, J ), 1 ) DO 100 I = 1, K S( I, J ) = Q( I, J ) / TEMP 100 CONTINUE 110 CONTINUE * 120 CONTINUE RETURN * * End of DLAED9 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlamrg.f0000644000000000000000000000013214061636515015272 xustar0030 mtime=1623670093.436103865 30 atime=1623670093.436103865 30 ctime=1623670093.436103865 elk-7.2.42/src/LAPACK/dlamrg.f0000644002504400250440000001071314061636515017331 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAMRG creates a permutation list to merge the entries of two independently sorted sets into a single set sorted in ascending order. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAMRG + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAMRG( N1, N2, A, DTRD1, DTRD2, INDEX ) * * .. Scalar Arguments .. * INTEGER DTRD1, DTRD2, N1, N2 * .. * .. Array Arguments .. * INTEGER INDEX( * ) * DOUBLE PRECISION A( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAMRG will create a permutation list which will merge the elements *> of A (which is composed of two independently sorted sets) into a *> single set which is sorted in ascending order. *> \endverbatim * * Arguments: * ========== * *> \param[in] N1 *> \verbatim *> N1 is INTEGER *> \endverbatim *> *> \param[in] N2 *> \verbatim *> N2 is INTEGER *> These arguments contain the respective lengths of the two *> sorted lists to be merged. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (N1+N2) *> The first N1 elements of A contain a list of numbers which *> are sorted in either ascending or descending order. Likewise *> for the final N2 elements. *> \endverbatim *> *> \param[in] DTRD1 *> \verbatim *> DTRD1 is INTEGER *> \endverbatim *> *> \param[in] DTRD2 *> \verbatim *> DTRD2 is INTEGER *> These are the strides to be taken through the array A. *> Allowable strides are 1 and -1. They indicate whether a *> subset of A is sorted in ascending (DTRDx = 1) or descending *> (DTRDx = -1) order. *> \endverbatim *> *> \param[out] INDEX *> \verbatim *> INDEX is INTEGER array, dimension (N1+N2) *> On exit this array will contain a permutation such that *> if B( I ) = A( INDEX( I ) ) for I=1,N1+N2, then B will be *> sorted in ascending order. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DLAMRG( N1, N2, A, DTRD1, DTRD2, INDEX ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER DTRD1, DTRD2, N1, N2 * .. * .. Array Arguments .. INTEGER INDEX( * ) DOUBLE PRECISION A( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, IND1, IND2, N1SV, N2SV * .. * .. Executable Statements .. * N1SV = N1 N2SV = N2 IF( DTRD1.GT.0 ) THEN IND1 = 1 ELSE IND1 = N1 END IF IF( DTRD2.GT.0 ) THEN IND2 = 1 + N1 ELSE IND2 = N1 + N2 END IF I = 1 * while ( (N1SV > 0) & (N2SV > 0) ) 10 CONTINUE IF( N1SV.GT.0 .AND. N2SV.GT.0 ) THEN IF( A( IND1 ).LE.A( IND2 ) ) THEN INDEX( I ) = IND1 I = I + 1 IND1 = IND1 + DTRD1 N1SV = N1SV - 1 ELSE INDEX( I ) = IND2 I = I + 1 IND2 = IND2 + DTRD2 N2SV = N2SV - 1 END IF GO TO 10 END IF * end while IF( N1SV.EQ.0 ) THEN DO 20 N1SV = 1, N2SV INDEX( I ) = IND2 I = I + 1 IND2 = IND2 + DTRD2 20 CONTINUE ELSE * N2SV .EQ. 0 DO 30 N2SV = 1, N1SV INDEX( I ) = IND1 I = I + 1 IND1 = IND1 + DTRD1 30 CONTINUE END IF * RETURN * * End of DLAMRG * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zunmhr.f0000644000000000000000000000013214061636515015347 xustar0030 mtime=1623670093.438103863 30 atime=1623670093.437103864 30 ctime=1623670093.438103863 elk-7.2.42/src/LAPACK/zunmhr.f0000644002504400250440000002024714061636515017411 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZUNMHR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZUNMHR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZUNMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, * LDC, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER SIDE, TRANS * INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZUNMHR overwrites the general complex M-by-N matrix C with *> *> SIDE = 'L' SIDE = 'R' *> TRANS = 'N': Q * C C * Q *> TRANS = 'C': Q**H * C C * Q**H *> *> where Q is a complex unitary matrix of order nq, with nq = m if *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of *> IHI-ILO elementary reflectors, as returned by ZGEHRD: *> *> Q = H(ilo) H(ilo+1) . . . H(ihi-1). *> \endverbatim * * Arguments: * ========== * *> \param[in] SIDE *> \verbatim *> SIDE is CHARACTER*1 *> = 'L': apply Q or Q**H from the Left; *> = 'R': apply Q or Q**H from the Right. *> \endverbatim *> *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> = 'N': apply Q (No transpose) *> = 'C': apply Q**H (Conjugate transpose) *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix C. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix C. N >= 0. *> \endverbatim *> *> \param[in] ILO *> \verbatim *> ILO is INTEGER *> \endverbatim *> *> \param[in] IHI *> \verbatim *> IHI is INTEGER *> *> ILO and IHI must have the same values as in the previous call *> of ZGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). *> If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and *> ILO = 1 and IHI = 0, if M = 0; *> if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and *> ILO = 1 and IHI = 0, if N = 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX*16 array, dimension *> (LDA,M) if SIDE = 'L' *> (LDA,N) if SIDE = 'R' *> The vectors which define the elementary reflectors, as *> returned by ZGEHRD. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. *> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension *> (M-1) if SIDE = 'L' *> (N-1) if SIDE = 'R' *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by ZGEHRD. *> \endverbatim *> *> \param[in,out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDC,N) *> On entry, the M-by-N matrix C. *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,M). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. *> If SIDE = 'L', LWORK >= max(1,N); *> if SIDE = 'R', LWORK >= max(1,M). *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. *> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error *> message related to LWORK is issued by XERBLA. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZUNMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, $ LDC, WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER SIDE, TRANS INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL LEFT, LQUERY INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZUNMQR * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 NH = IHI - ILO LEFT = LSAME( SIDE, 'L' ) LQUERY = ( LWORK.EQ.-1 ) * * NQ is the order of Q and NW is the minimum dimension of WORK * IF( LEFT ) THEN NQ = M NW = N ELSE NQ = N NW = M END IF IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN INFO = -1 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) $ THEN INFO = -2 ELSE IF( M.LT.0 ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN INFO = -5 ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN INFO = -6 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -8 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -11 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN IF( LEFT ) THEN NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, NH, N, NH, -1 ) ELSE NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, NH, NH, -1 ) END IF LWKOPT = MAX( 1, NW )*NB WORK( 1 ) = LWKOPT END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZUNMHR', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF * IF( LEFT ) THEN MI = NH NI = N I1 = ILO + 1 I2 = 1 ELSE MI = M NI = NH I1 = 1 I2 = ILO + 1 END IF * CALL ZUNMQR( SIDE, TRANS, MI, NI, NH, A( ILO+1, ILO ), LDA, $ TAU( ILO ), C( I1, I2 ), LDC, WORK, LWORK, IINFO ) * WORK( 1 ) = LWKOPT RETURN * * End of ZUNMHR * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/ztrexc.f0000644000000000000000000000013214061636515015343 xustar0030 mtime=1623670093.440103861 30 atime=1623670093.439103862 30 ctime=1623670093.440103861 elk-7.2.42/src/LAPACK/ztrexc.f0000644002504400250440000001456314061636515017411 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZTREXC * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZTREXC + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO ) * * .. Scalar Arguments .. * CHARACTER COMPQ * INTEGER IFST, ILST, INFO, LDQ, LDT, N * .. * .. Array Arguments .. * COMPLEX*16 Q( LDQ, * ), T( LDT, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTREXC reorders the Schur factorization of a complex matrix *> A = Q*T*Q**H, so that the diagonal element of T with row index IFST *> is moved to row ILST. *> *> The Schur form T is reordered by a unitary similarity transformation *> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by *> postmultplying it with Z. *> \endverbatim * * Arguments: * ========== * *> \param[in] COMPQ *> \verbatim *> COMPQ is CHARACTER*1 *> = 'V': update the matrix Q of Schur vectors; *> = 'N': do not update Q. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix T. N >= 0. *> If N == 0 arguments ILST and IFST may be any value. *> \endverbatim *> *> \param[in,out] T *> \verbatim *> T is COMPLEX*16 array, dimension (LDT,N) *> On entry, the upper triangular matrix T. *> On exit, the reordered upper triangular matrix. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= max(1,N). *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDQ,N) *> On entry, if COMPQ = 'V', the matrix Q of Schur vectors. *> On exit, if COMPQ = 'V', Q has been postmultiplied by the *> unitary transformation matrix Z which reorders T. *> If COMPQ = 'N', Q is not referenced. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= 1, and if *> COMPQ = 'V', LDQ >= max(1,N). *> \endverbatim *> *> \param[in] IFST *> \verbatim *> IFST is INTEGER *> \endverbatim *> *> \param[in] ILST *> \verbatim *> ILST is INTEGER *> *> Specify the reordering of the diagonal elements of T: *> The element with row index IFST is moved to row ILST by a *> sequence of transpositions between adjacent elements. *> 1 <= IFST <= N; 1 <= ILST <= N. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERcomputational * * ===================================================================== SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER COMPQ INTEGER IFST, ILST, INFO, LDQ, LDT, N * .. * .. Array Arguments .. COMPLEX*16 Q( LDQ, * ), T( LDT, * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL WANTQ INTEGER K, M1, M2, M3 DOUBLE PRECISION CS COMPLEX*16 SN, T11, T22, TEMP * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARTG, ZROT * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Decode and test the input parameters. * INFO = 0 WANTQ = LSAME( COMPQ, 'V' ) IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDT.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN INFO = -6 ELSE IF(( IFST.LT.1 .OR. IFST.GT.N ).AND.( N.GT.0 )) THEN INFO = -7 ELSE IF(( ILST.LT.1 .OR. ILST.GT.N ).AND.( N.GT.0 )) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZTREXC', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.1 .OR. IFST.EQ.ILST ) $ RETURN * IF( IFST.LT.ILST ) THEN * * Move the IFST-th diagonal element forward down the diagonal. * M1 = 0 M2 = -1 M3 = 1 ELSE * * Move the IFST-th diagonal element backward up the diagonal. * M1 = -1 M2 = 0 M3 = -1 END IF * DO 10 K = IFST + M1, ILST + M2, M3 * * Interchange the k-th and (k+1)-th diagonal elements. * T11 = T( K, K ) T22 = T( K+1, K+1 ) * * Determine the transformation to perform the interchange. * CALL ZLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP ) * * Apply transformation to the matrix T. * IF( K+2.LE.N ) $ CALL ZROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS, $ SN ) CALL ZROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS, $ DCONJG( SN ) ) * T( K, K ) = T22 T( K+1, K+1 ) = T11 * IF( WANTQ ) THEN * * Accumulate transformation in the matrix Q. * CALL ZROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS, $ DCONJG( SN ) ) END IF * 10 CONTINUE * RETURN * * End of ZTREXC * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaqr2.f0000644000000000000000000000013114061636515015236 xustar0030 mtime=1623670093.442103859 29 atime=1623670093.44110386 30 ctime=1623670093.442103859 elk-7.2.42/src/LAPACK/zlaqr2.f0000644002504400250440000004223614061636515017303 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAQR2 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAQR2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, * IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, * NV, WV, LDWV, WORK, LWORK ) * * .. Scalar Arguments .. * INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV, * $ LDZ, LWORK, N, ND, NH, NS, NV, NW * LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. * COMPLEX*16 H( LDH, * ), SH( * ), T( LDT, * ), V( LDV, * ), * $ WORK( * ), WV( LDWV, * ), Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAQR2 is identical to ZLAQR3 except that it avoids *> recursion by calling ZLAHQR instead of ZLAQR4. *> *> Aggressive early deflation: *> *> ZLAQR2 accepts as input an upper Hessenberg matrix *> H and performs an unitary similarity transformation *> designed to detect and deflate fully converged eigenvalues from *> a trailing principal submatrix. On output H has been over- *> written by a new Hessenberg matrix that is a perturbation of *> an unitary similarity transformation of H. It is to be *> hoped that the final version of H has many zero subdiagonal *> entries. *> *> \endverbatim * * Arguments: * ========== * *> \param[in] WANTT *> \verbatim *> WANTT is LOGICAL *> If .TRUE., then the Hessenberg matrix H is fully updated *> so that the triangular Schur factor may be *> computed (in cooperation with the calling subroutine). *> If .FALSE., then only enough of H is updated to preserve *> the eigenvalues. *> \endverbatim *> *> \param[in] WANTZ *> \verbatim *> WANTZ is LOGICAL *> If .TRUE., then the unitary matrix Z is updated so *> so that the unitary Schur factor may be computed *> (in cooperation with the calling subroutine). *> If .FALSE., then Z is not referenced. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix H and (if WANTZ is .TRUE.) the *> order of the unitary matrix Z. *> \endverbatim *> *> \param[in] KTOP *> \verbatim *> KTOP is INTEGER *> It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. *> KBOT and KTOP together determine an isolated block *> along the diagonal of the Hessenberg matrix. *> \endverbatim *> *> \param[in] KBOT *> \verbatim *> KBOT is INTEGER *> It is assumed without a check that either *> KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together *> determine an isolated block along the diagonal of the *> Hessenberg matrix. *> \endverbatim *> *> \param[in] NW *> \verbatim *> NW is INTEGER *> Deflation window size. 1 <= NW <= (KBOT-KTOP+1). *> \endverbatim *> *> \param[in,out] H *> \verbatim *> H is COMPLEX*16 array, dimension (LDH,N) *> On input the initial N-by-N section of H stores the *> Hessenberg matrix undergoing aggressive early deflation. *> On output H has been transformed by a unitary *> similarity transformation, perturbed, and the returned *> to Hessenberg form that (it is to be hoped) has some *> zero subdiagonal entries. *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> Leading dimension of H just as declared in the calling *> subroutine. N <= LDH *> \endverbatim *> *> \param[in] ILOZ *> \verbatim *> ILOZ is INTEGER *> \endverbatim *> *> \param[in] IHIZ *> \verbatim *> IHIZ is INTEGER *> Specify the rows of Z to which transformations must be *> applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N. *> \endverbatim *> *> \param[in,out] Z *> \verbatim *> Z is COMPLEX*16 array, dimension (LDZ,N) *> IF WANTZ is .TRUE., then on output, the unitary *> similarity transformation mentioned above has been *> accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. *> If WANTZ is .FALSE., then Z is unreferenced. *> \endverbatim *> *> \param[in] LDZ *> \verbatim *> LDZ is INTEGER *> The leading dimension of Z just as declared in the *> calling subroutine. 1 <= LDZ. *> \endverbatim *> *> \param[out] NS *> \verbatim *> NS is INTEGER *> The number of unconverged (ie approximate) eigenvalues *> returned in SR and SI that may be used as shifts by the *> calling subroutine. *> \endverbatim *> *> \param[out] ND *> \verbatim *> ND is INTEGER *> The number of converged eigenvalues uncovered by this *> subroutine. *> \endverbatim *> *> \param[out] SH *> \verbatim *> SH is COMPLEX*16 array, dimension (KBOT) *> On output, approximate eigenvalues that may *> be used for shifts are stored in SH(KBOT-ND-NS+1) *> through SR(KBOT-ND). Converged eigenvalues are *> stored in SH(KBOT-ND+1) through SH(KBOT). *> \endverbatim *> *> \param[out] V *> \verbatim *> V is COMPLEX*16 array, dimension (LDV,NW) *> An NW-by-NW work array. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of V just as declared in the *> calling subroutine. NW <= LDV *> \endverbatim *> *> \param[in] NH *> \verbatim *> NH is INTEGER *> The number of columns of T. NH >= NW. *> \endverbatim *> *> \param[out] T *> \verbatim *> T is COMPLEX*16 array, dimension (LDT,NW) *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of T just as declared in the *> calling subroutine. NW <= LDT *> \endverbatim *> *> \param[in] NV *> \verbatim *> NV is INTEGER *> The number of rows of work array WV available for *> workspace. NV >= NW. *> \endverbatim *> *> \param[out] WV *> \verbatim *> WV is COMPLEX*16 array, dimension (LDWV,NW) *> \endverbatim *> *> \param[in] LDWV *> \verbatim *> LDWV is INTEGER *> The leading dimension of W just as declared in the *> calling subroutine. NW <= LDV *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (LWORK) *> On exit, WORK(1) is set to an estimate of the optimal value *> of LWORK for the given values of N, NW, KTOP and KBOT. *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. *> *> If LWORK = -1, then a workspace query is assumed; ZLAQR2 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned *> in WORK(1). No error message related to LWORK is issued *> by XERBLA. Neither H nor Z are accessed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complex16OTHERauxiliary * *> \par Contributors: * ================== *> *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA *> * ===================================================================== SUBROUTINE ZLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, $ IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, $ NV, WV, LDWV, WORK, LWORK ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV, $ LDZ, LWORK, N, ND, NH, NS, NV, NW LOGICAL WANTT, WANTZ * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), SH( * ), T( LDT, * ), V( LDV, * ), $ WORK( * ), WV( LDWV, * ), Z( LDZ, * ) * .. * * ================================================================ * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), $ ONE = ( 1.0d0, 0.0d0 ) ) DOUBLE PRECISION RZERO, RONE PARAMETER ( RZERO = 0.0d0, RONE = 1.0d0 ) * .. * .. Local Scalars .. COMPLEX*16 BETA, CDUM, S, TAU DOUBLE PRECISION FOO, SAFMAX, SAFMIN, SMLNUM, ULP INTEGER I, IFST, ILST, INFO, INFQR, J, JW, KCOL, KLN, $ KNT, KROW, KWTOP, LTOP, LWK1, LWK2, LWKOPT * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DLABAD, ZCOPY, ZGEHRD, ZGEMM, ZLACPY, ZLAHQR, $ ZLARF, ZLARFG, ZLASET, ZTREXC, ZUNMHR * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, MAX, MIN * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. Executable Statements .. * * ==== Estimate optimal workspace. ==== * JW = MIN( NW, KBOT-KTOP+1 ) IF( JW.LE.2 ) THEN LWKOPT = 1 ELSE * * ==== Workspace query call to ZGEHRD ==== * CALL ZGEHRD( JW, 1, JW-1, T, LDT, WORK, WORK, -1, INFO ) LWK1 = INT( WORK( 1 ) ) * * ==== Workspace query call to ZUNMHR ==== * CALL ZUNMHR( 'R', 'N', JW, JW, 1, JW-1, T, LDT, WORK, V, LDV, $ WORK, -1, INFO ) LWK2 = INT( WORK( 1 ) ) * * ==== Optimal workspace ==== * LWKOPT = JW + MAX( LWK1, LWK2 ) END IF * * ==== Quick return in case of workspace query. ==== * IF( LWORK.EQ.-1 ) THEN WORK( 1 ) = DCMPLX( LWKOPT, 0 ) RETURN END IF * * ==== Nothing to do ... * ... for an empty active block ... ==== NS = 0 ND = 0 WORK( 1 ) = ONE IF( KTOP.GT.KBOT ) $ RETURN * ... nor for an empty deflation window. ==== IF( NW.LT.1 ) $ RETURN * * ==== Machine constants ==== * SAFMIN = DLAMCH( 'SAFE MINIMUM' ) SAFMAX = RONE / SAFMIN CALL DLABAD( SAFMIN, SAFMAX ) ULP = DLAMCH( 'PRECISION' ) SMLNUM = SAFMIN*( DBLE( N ) / ULP ) * * ==== Setup deflation window ==== * JW = MIN( NW, KBOT-KTOP+1 ) KWTOP = KBOT - JW + 1 IF( KWTOP.EQ.KTOP ) THEN S = ZERO ELSE S = H( KWTOP, KWTOP-1 ) END IF * IF( KBOT.EQ.KWTOP ) THEN * * ==== 1-by-1 deflation window: not much to do ==== * SH( KWTOP ) = H( KWTOP, KWTOP ) NS = 1 ND = 0 IF( CABS1( S ).LE.MAX( SMLNUM, ULP*CABS1( H( KWTOP, $ KWTOP ) ) ) ) THEN NS = 0 ND = 1 IF( KWTOP.GT.KTOP ) $ H( KWTOP, KWTOP-1 ) = ZERO END IF WORK( 1 ) = ONE RETURN END IF * * ==== Convert to spike-triangular form. (In case of a * . rare QR failure, this routine continues to do * . aggressive early deflation using that part of * . the deflation window that converged using INFQR * . here and there to keep track.) ==== * CALL ZLACPY( 'U', JW, JW, H( KWTOP, KWTOP ), LDH, T, LDT ) CALL ZCOPY( JW-1, H( KWTOP+1, KWTOP ), LDH+1, T( 2, 1 ), LDT+1 ) * CALL ZLASET( 'A', JW, JW, ZERO, ONE, V, LDV ) CALL ZLAHQR( .true., .true., JW, 1, JW, T, LDT, SH( KWTOP ), 1, $ JW, V, LDV, INFQR ) * * ==== Deflation detection loop ==== * NS = JW ILST = INFQR + 1 DO 10 KNT = INFQR + 1, JW * * ==== Small spike tip deflation test ==== * FOO = CABS1( T( NS, NS ) ) IF( FOO.EQ.RZERO ) $ FOO = CABS1( S ) IF( CABS1( S )*CABS1( V( 1, NS ) ).LE.MAX( SMLNUM, ULP*FOO ) ) $ THEN * * ==== One more converged eigenvalue ==== * NS = NS - 1 ELSE * * ==== One undeflatable eigenvalue. Move it up out of the * . way. (ZTREXC can not fail in this case.) ==== * IFST = NS CALL ZTREXC( 'V', JW, T, LDT, V, LDV, IFST, ILST, INFO ) ILST = ILST + 1 END IF 10 CONTINUE * * ==== Return to Hessenberg form ==== * IF( NS.EQ.0 ) $ S = ZERO * IF( NS.LT.JW ) THEN * * ==== sorting the diagonal of T improves accuracy for * . graded matrices. ==== * DO 30 I = INFQR + 1, NS IFST = I DO 20 J = I + 1, NS IF( CABS1( T( J, J ) ).GT.CABS1( T( IFST, IFST ) ) ) $ IFST = J 20 CONTINUE ILST = I IF( IFST.NE.ILST ) $ CALL ZTREXC( 'V', JW, T, LDT, V, LDV, IFST, ILST, INFO ) 30 CONTINUE END IF * * ==== Restore shift/eigenvalue array from T ==== * DO 40 I = INFQR + 1, JW SH( KWTOP+I-1 ) = T( I, I ) 40 CONTINUE * * IF( NS.LT.JW .OR. S.EQ.ZERO ) THEN IF( NS.GT.1 .AND. S.NE.ZERO ) THEN * * ==== Reflect spike back into lower triangle ==== * CALL ZCOPY( NS, V, LDV, WORK, 1 ) DO 50 I = 1, NS WORK( I ) = DCONJG( WORK( I ) ) 50 CONTINUE BETA = WORK( 1 ) CALL ZLARFG( NS, BETA, WORK( 2 ), 1, TAU ) WORK( 1 ) = ONE * CALL ZLASET( 'L', JW-2, JW-2, ZERO, ZERO, T( 3, 1 ), LDT ) * CALL ZLARF( 'L', NS, JW, WORK, 1, DCONJG( TAU ), T, LDT, $ WORK( JW+1 ) ) CALL ZLARF( 'R', NS, NS, WORK, 1, TAU, T, LDT, $ WORK( JW+1 ) ) CALL ZLARF( 'R', JW, NS, WORK, 1, TAU, V, LDV, $ WORK( JW+1 ) ) * CALL ZGEHRD( JW, 1, NS, T, LDT, WORK, WORK( JW+1 ), $ LWORK-JW, INFO ) END IF * * ==== Copy updated reduced window into place ==== * IF( KWTOP.GT.1 ) $ H( KWTOP, KWTOP-1 ) = S*DCONJG( V( 1, 1 ) ) CALL ZLACPY( 'U', JW, JW, T, LDT, H( KWTOP, KWTOP ), LDH ) CALL ZCOPY( JW-1, T( 2, 1 ), LDT+1, H( KWTOP+1, KWTOP ), $ LDH+1 ) * * ==== Accumulate orthogonal matrix in order update * . H and Z, if requested. ==== * IF( NS.GT.1 .AND. S.NE.ZERO ) $ CALL ZUNMHR( 'R', 'N', JW, NS, 1, NS, T, LDT, WORK, V, LDV, $ WORK( JW+1 ), LWORK-JW, INFO ) * * ==== Update vertical slab in H ==== * IF( WANTT ) THEN LTOP = 1 ELSE LTOP = KTOP END IF DO 60 KROW = LTOP, KWTOP - 1, NV KLN = MIN( NV, KWTOP-KROW ) CALL ZGEMM( 'N', 'N', KLN, JW, JW, ONE, H( KROW, KWTOP ), $ LDH, V, LDV, ZERO, WV, LDWV ) CALL ZLACPY( 'A', KLN, JW, WV, LDWV, H( KROW, KWTOP ), LDH ) 60 CONTINUE * * ==== Update horizontal slab in H ==== * IF( WANTT ) THEN DO 70 KCOL = KBOT + 1, N, NH KLN = MIN( NH, N-KCOL+1 ) CALL ZGEMM( 'C', 'N', JW, KLN, JW, ONE, V, LDV, $ H( KWTOP, KCOL ), LDH, ZERO, T, LDT ) CALL ZLACPY( 'A', JW, KLN, T, LDT, H( KWTOP, KCOL ), $ LDH ) 70 CONTINUE END IF * * ==== Update vertical slab in Z ==== * IF( WANTZ ) THEN DO 80 KROW = ILOZ, IHIZ, NV KLN = MIN( NV, IHIZ-KROW+1 ) CALL ZGEMM( 'N', 'N', KLN, JW, JW, ONE, Z( KROW, KWTOP ), $ LDZ, V, LDV, ZERO, WV, LDWV ) CALL ZLACPY( 'A', KLN, JW, WV, LDWV, Z( KROW, KWTOP ), $ LDZ ) 80 CONTINUE END IF END IF * * ==== Return the number of deflations ... ==== * ND = JW - NS * * ==== ... and the number of shifts. (Subtracting * . INFQR from the spike length takes care * . of the case of a rare QR failure while * . calculating eigenvalues of the deflation * . window.) ==== * NS = NS - INFQR * * ==== Return optimal workspace. ==== * WORK( 1 ) = DCMPLX( LWKOPT, 0 ) * * ==== End of ZLAQR2 ==== * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlaqr1.f0000644000000000000000000000013214061636515015236 xustar0030 mtime=1623670093.443103858 30 atime=1623670093.443103858 30 ctime=1623670093.443103858 elk-7.2.42/src/LAPACK/zlaqr1.f0000644002504400250440000001152214061636515017274 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLAQR1 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, V ) * * .. Scalar Arguments .. * COMPLEX*16 S1, S2 * INTEGER LDH, N * .. * .. Array Arguments .. * COMPLEX*16 H( LDH, * ), V( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Given a 2-by-2 or 3-by-3 matrix H, ZLAQR1 sets v to a *> scalar multiple of the first column of the product *> *> (*) K = (H - s1*I)*(H - s2*I) *> *> scaling to avoid overflows and most underflows. *> *> This is useful for starting double implicit shift bulges *> in the QR algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> Order of the matrix H. N must be either 2 or 3. *> \endverbatim *> *> \param[in] H *> \verbatim *> H is COMPLEX*16 array, dimension (LDH,N) *> The 2-by-2 or 3-by-3 matrix H in (*). *> \endverbatim *> *> \param[in] LDH *> \verbatim *> LDH is INTEGER *> The leading dimension of H as declared in *> the calling procedure. LDH >= N *> \endverbatim *> *> \param[in] S1 *> \verbatim *> S1 is COMPLEX*16 *> \endverbatim *> *> \param[in] S2 *> \verbatim *> S2 is COMPLEX*16 *> *> S1 and S2 are the shifts defining K in (*) above. *> \endverbatim *> *> \param[out] V *> \verbatim *> V is COMPLEX*16 array, dimension (N) *> A scalar multiple of the first column of the *> matrix K in (*). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup complex16OTHERauxiliary * *> \par Contributors: * ================== *> *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA *> * ===================================================================== SUBROUTINE ZLAQR1( N, H, LDH, S1, S2, V ) * * -- LAPACK auxiliary routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. COMPLEX*16 S1, S2 INTEGER LDH, N * .. * .. Array Arguments .. COMPLEX*16 H( LDH, * ), V( * ) * .. * * ================================================================ * * .. Parameters .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ) ) DOUBLE PRECISION RZERO PARAMETER ( RZERO = 0.0d0 ) * .. * .. Local Scalars .. COMPLEX*16 CDUM, H21S, H31S DOUBLE PRECISION S * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DIMAG * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function definitions .. CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) * .. * .. Executable Statements .. * * Quick return if possible * IF( N.NE.2 .AND. N.NE.3 ) THEN RETURN END IF * IF( N.EQ.2 ) THEN S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) ) IF( S.EQ.RZERO ) THEN V( 1 ) = ZERO V( 2 ) = ZERO ELSE H21S = H( 2, 1 ) / S V( 1 ) = H21S*H( 1, 2 ) + ( H( 1, 1 )-S1 )* $ ( ( H( 1, 1 )-S2 ) / S ) V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 ) END IF ELSE S = CABS1( H( 1, 1 )-S2 ) + CABS1( H( 2, 1 ) ) + $ CABS1( H( 3, 1 ) ) IF( S.EQ.ZERO ) THEN V( 1 ) = ZERO V( 2 ) = ZERO V( 3 ) = ZERO ELSE H21S = H( 2, 1 ) / S H31S = H( 3, 1 ) / S V( 1 ) = ( H( 1, 1 )-S1 )*( ( H( 1, 1 )-S2 ) / S ) + $ H( 1, 2 )*H21S + H( 1, 3 )*H31S V( 2 ) = H21S*( H( 1, 1 )+H( 2, 2 )-S1-S2 ) + H( 2, 3 )*H31S V( 3 ) = H31S*( H( 1, 1 )+H( 3, 3 )-S1-S2 ) + H21S*H( 3, 2 ) END IF END IF END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed3.f0000644000000000000000000000013214061636515015160 xustar0030 mtime=1623670093.445103856 30 atime=1623670093.445103856 30 ctime=1623670093.445103856 elk-7.2.42/src/LAPACK/dlaed3.f0000644002504400250440000002530014061636515017215 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED3 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, * CTOT, W, S, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDQ, N, N1 * DOUBLE PRECISION RHO * .. * .. Array Arguments .. * INTEGER CTOT( * ), INDX( * ) * DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), * $ S( * ), W( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAED3 finds the roots of the secular equation, as defined by the *> values in D, W, and RHO, between 1 and K. It makes the *> appropriate calls to DLAED4 and then updates the eigenvectors by *> multiplying the matrix of eigenvectors of the pair of eigensystems *> being combined by the matrix of eigenvectors of the K-by-K system *> which is solved here. *> *> This code makes very mild assumptions about floating point *> arithmetic. It will work on machines with a guard digit in *> add/subtract, or on those binary machines without guard digits *> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. *> It could conceivably fail on hexadecimal or decimal machines *> without guard digits, but we know of none. *> \endverbatim * * Arguments: * ========== * *> \param[in] K *> \verbatim *> K is INTEGER *> The number of terms in the rational function to be solved by *> DLAED4. K >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns in the Q matrix. *> N >= K (deflation may result in N>K). *> \endverbatim *> *> \param[in] N1 *> \verbatim *> N1 is INTEGER *> The location of the last eigenvalue in the leading submatrix. *> min(1,N) <= N1 <= N/2. *> \endverbatim *> *> \param[out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> D(I) contains the updated eigenvalues for *> 1 <= I <= K. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDQ,N) *> Initially the first K columns are used as workspace. *> On output the columns 1 to K contain *> the updated eigenvectors. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[in] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> The value of the parameter in the rank one update equation. *> RHO >= 0 required. *> \endverbatim *> *> \param[in,out] DLAMDA *> \verbatim *> DLAMDA is DOUBLE PRECISION array, dimension (K) *> The first K elements of this array contain the old roots *> of the deflated updating problem. These are the poles *> of the secular equation. May be changed on output by *> having lowest order bit set to zero on Cray X-MP, Cray Y-MP, *> Cray-2, or Cray C-90, as described above. *> \endverbatim *> *> \param[in] Q2 *> \verbatim *> Q2 is DOUBLE PRECISION array, dimension (LDQ2*N) *> The first K columns of this matrix contain the non-deflated *> eigenvectors for the split problem. *> \endverbatim *> *> \param[in] INDX *> \verbatim *> INDX is INTEGER array, dimension (N) *> The permutation used to arrange the columns of the deflated *> Q matrix into three groups (see DLAED2). *> The rows of the eigenvectors found by DLAED4 must be likewise *> permuted before the matrix multiply can take place. *> \endverbatim *> *> \param[in] CTOT *> \verbatim *> CTOT is INTEGER array, dimension (4) *> A count of the total number of the various types of columns *> in Q, as described in INDX. The fourth column type is any *> column which has been deflated. *> \endverbatim *> *> \param[in,out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (K) *> The first K elements of this array contain the components *> of the deflation-adjusted updating vector. Destroyed on *> output. *> \endverbatim *> *> \param[out] S *> \verbatim *> S is DOUBLE PRECISION array, dimension (N1 + 1)*K *> Will contain the eigenvectors of the repaired matrix which *> will be multiplied by the previously accumulated eigenvectors *> to update the system. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, an eigenvalue did not converge *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA \n *> Modified by Francoise Tisseur, University of Tennessee *> * ===================================================================== SUBROUTINE DLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, $ CTOT, W, S, INFO ) * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. INTEGER INFO, K, LDQ, N, N1 DOUBLE PRECISION RHO * .. * .. Array Arguments .. INTEGER CTOT( * ), INDX( * ) DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), $ S( * ), W( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) * .. * .. Local Scalars .. INTEGER I, II, IQ2, J, N12, N2, N23 DOUBLE PRECISION TEMP * .. * .. External Functions .. DOUBLE PRECISION DLAMC3, DNRM2 EXTERNAL DLAMC3, DNRM2 * .. * .. External Subroutines .. EXTERNAL DCOPY, DGEMM, DLACPY, DLAED4, DLASET, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, SIGN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( K.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.K ) THEN INFO = -2 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAED3', -INFO ) RETURN END IF * * Quick return if possible * IF( K.EQ.0 ) $ RETURN * * Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can * be computed with high relative accuracy (barring over/underflow). * This is a problem on machines without a guard digit in * add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). * The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), * which on any of these machines zeros out the bottommost * bit of DLAMDA(I) if it is 1; this makes the subsequent * subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation * occurs. On binary machines with a guard digit (almost all * machines) it does not change DLAMDA(I) at all. On hexadecimal * and decimal machines with a guard digit, it slightly * changes the bottommost bits of DLAMDA(I). It does not account * for hexadecimal or decimal machines without guard digits * (we know of none). We use a subroutine call to compute * 2*DLAMBDA(I) to prevent optimizing compilers from eliminating * this code. * DO 10 I = 1, K DLAMDA( I ) = DLAMC3( DLAMDA( I ), DLAMDA( I ) ) - DLAMDA( I ) 10 CONTINUE * DO 20 J = 1, K CALL DLAED4( K, J, DLAMDA, W, Q( 1, J ), RHO, D( J ), INFO ) * * If the zero finder fails, the computation is terminated. * IF( INFO.NE.0 ) $ GO TO 120 20 CONTINUE * IF( K.EQ.1 ) $ GO TO 110 IF( K.EQ.2 ) THEN DO 30 J = 1, K W( 1 ) = Q( 1, J ) W( 2 ) = Q( 2, J ) II = INDX( 1 ) Q( 1, J ) = W( II ) II = INDX( 2 ) Q( 2, J ) = W( II ) 30 CONTINUE GO TO 110 END IF * * Compute updated W. * CALL DCOPY( K, W, 1, S, 1 ) * * Initialize W(I) = Q(I,I) * CALL DCOPY( K, Q, LDQ+1, W, 1 ) DO 60 J = 1, K DO 40 I = 1, J - 1 W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) ) 40 CONTINUE DO 50 I = J + 1, K W( I ) = W( I )*( Q( I, J ) / ( DLAMDA( I )-DLAMDA( J ) ) ) 50 CONTINUE 60 CONTINUE DO 70 I = 1, K W( I ) = SIGN( SQRT( -W( I ) ), S( I ) ) 70 CONTINUE * * Compute eigenvectors of the modified rank-1 modification. * DO 100 J = 1, K DO 80 I = 1, K S( I ) = W( I ) / Q( I, J ) 80 CONTINUE TEMP = DNRM2( K, S, 1 ) DO 90 I = 1, K II = INDX( I ) Q( I, J ) = S( II ) / TEMP 90 CONTINUE 100 CONTINUE * * Compute the updated eigenvectors. * 110 CONTINUE * N2 = N - N1 N12 = CTOT( 1 ) + CTOT( 2 ) N23 = CTOT( 2 ) + CTOT( 3 ) * CALL DLACPY( 'A', N23, K, Q( CTOT( 1 )+1, 1 ), LDQ, S, N23 ) IQ2 = N1*N12 + 1 IF( N23.NE.0 ) THEN CALL DGEMM( 'N', 'N', N2, K, N23, ONE, Q2( IQ2 ), N2, S, N23, $ ZERO, Q( N1+1, 1 ), LDQ ) ELSE CALL DLASET( 'A', N2, K, ZERO, ZERO, Q( N1+1, 1 ), LDQ ) END IF * CALL DLACPY( 'A', N12, K, Q, LDQ, S, N12 ) IF( N12.NE.0 ) THEN CALL DGEMM( 'N', 'N', N1, K, N12, ONE, Q2, N1, S, N12, ZERO, Q, $ LDQ ) ELSE CALL DLASET( 'A', N1, K, ZERO, ZERO, Q( 1, 1 ), LDQ ) END IF * * 120 CONTINUE RETURN * * End of DLAED3 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed8.f0000644000000000000000000000013214061636515015165 xustar0030 mtime=1623670093.447103854 30 atime=1623670093.447103854 30 ctime=1623670093.447103854 elk-7.2.42/src/LAPACK/dlaed8.f0000644002504400250440000003726214061636515017234 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED8 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, * CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, * GIVCOL, GIVNUM, INDXP, INDX, INFO ) * * .. Scalar Arguments .. * INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, * $ QSIZ * DOUBLE PRECISION RHO * .. * .. Array Arguments .. * INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), * $ INDXQ( * ), PERM( * ) * DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), * $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAED8 merges the two sets of eigenvalues together into a single *> sorted set. Then it tries to deflate the size of the problem. *> There are two ways in which deflation can occur: when two or more *> eigenvalues are close together or if there is a tiny element in the *> Z vector. For each such occurrence the order of the related secular *> equation problem is reduced by one. *> \endverbatim * * Arguments: * ========== * *> \param[in] ICOMPQ *> \verbatim *> ICOMPQ is INTEGER *> = 0: Compute eigenvalues only. *> = 1: Compute eigenvectors of original dense symmetric matrix *> also. On entry, Q contains the orthogonal matrix used *> to reduce the original matrix to tridiagonal form. *> \endverbatim *> *> \param[out] K *> \verbatim *> K is INTEGER *> The number of non-deflated eigenvalues, and the order of the *> related secular equation. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the symmetric tridiagonal matrix. N >= 0. *> \endverbatim *> *> \param[in] QSIZ *> \verbatim *> QSIZ is INTEGER *> The dimension of the orthogonal matrix used to reduce *> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the eigenvalues of the two submatrices to be *> combined. On exit, the trailing (N-K) updated eigenvalues *> (those which were deflated) sorted into increasing order. *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDQ,N) *> If ICOMPQ = 0, Q is not referenced. Otherwise, *> on entry, Q contains the eigenvectors of the partially solved *> system which has been previously updated in matrix *> multiplies with other partially solved eigensystems. *> On exit, Q contains the trailing (N-K) updated eigenvectors *> (those which were deflated) in its last N-K columns. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= max(1,N). *> \endverbatim *> *> \param[in] INDXQ *> \verbatim *> INDXQ is INTEGER array, dimension (N) *> The permutation which separately sorts the two sub-problems *> in D into ascending order. Note that elements in the second *> half of this permutation must first have CUTPNT added to *> their values in order to be accurate. *> \endverbatim *> *> \param[in,out] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> On entry, the off-diagonal element associated with the rank-1 *> cut which originally split the two submatrices which are now *> being recombined. *> On exit, RHO has been modified to the value required by *> DLAED3. *> \endverbatim *> *> \param[in] CUTPNT *> \verbatim *> CUTPNT is INTEGER *> The location of the last eigenvalue in the leading *> sub-matrix. min(1,N) <= CUTPNT <= N. *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (N) *> On entry, Z contains the updating vector (the last row of *> the first sub-eigenvector matrix and the first row of the *> second sub-eigenvector matrix). *> On exit, the contents of Z are destroyed by the updating *> process. *> \endverbatim *> *> \param[out] DLAMDA *> \verbatim *> DLAMDA is DOUBLE PRECISION array, dimension (N) *> A copy of the first K eigenvalues which will be used by *> DLAED3 to form the secular equation. *> \endverbatim *> *> \param[out] Q2 *> \verbatim *> Q2 is DOUBLE PRECISION array, dimension (LDQ2,N) *> If ICOMPQ = 0, Q2 is not referenced. Otherwise, *> a copy of the first K eigenvectors which will be used by *> DLAED7 in a matrix multiply (DGEMM) to update the new *> eigenvectors. *> \endverbatim *> *> \param[in] LDQ2 *> \verbatim *> LDQ2 is INTEGER *> The leading dimension of the array Q2. LDQ2 >= max(1,N). *> \endverbatim *> *> \param[out] W *> \verbatim *> W is DOUBLE PRECISION array, dimension (N) *> The first k values of the final deflation-altered z-vector and *> will be passed to DLAED3. *> \endverbatim *> *> \param[out] PERM *> \verbatim *> PERM is INTEGER array, dimension (N) *> The permutations (from deflation and sorting) to be applied *> to each eigenblock. *> \endverbatim *> *> \param[out] GIVPTR *> \verbatim *> GIVPTR is INTEGER *> The number of Givens rotations which took place in this *> subproblem. *> \endverbatim *> *> \param[out] GIVCOL *> \verbatim *> GIVCOL is INTEGER array, dimension (2, N) *> Each pair of numbers indicates a pair of columns to take place *> in a Givens rotation. *> \endverbatim *> *> \param[out] GIVNUM *> \verbatim *> GIVNUM is DOUBLE PRECISION array, dimension (2, N) *> Each number indicates the S value to be used in the *> corresponding Givens rotation. *> \endverbatim *> *> \param[out] INDXP *> \verbatim *> INDXP is INTEGER array, dimension (N) *> The permutation used to place deflated values of D at the end *> of the array. INDXP(1:K) points to the nondeflated D-values *> and INDXP(K+1:N) points to the deflated eigenvalues. *> \endverbatim *> *> \param[out] INDX *> \verbatim *> INDX is INTEGER array, dimension (N) *> The permutation used to sort the contents of D into ascending *> order. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Jeff Rutter, Computer Science Division, University of California *> at Berkeley, USA * * ===================================================================== SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, $ CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, $ GIVCOL, GIVNUM, INDXP, INDX, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, $ QSIZ DOUBLE PRECISION RHO * .. * .. Array Arguments .. INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), $ INDXQ( * ), PERM( * ) DOUBLE PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), $ Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION MONE, ZERO, ONE, TWO, EIGHT PARAMETER ( MONE = -1.0D0, ZERO = 0.0D0, ONE = 1.0D0, $ TWO = 2.0D0, EIGHT = 8.0D0 ) * .. * .. Local Scalars .. * INTEGER I, IMAX, J, JLAM, JMAX, JP, K2, N1, N1P1, N2 DOUBLE PRECISION C, EPS, S, T, TAU, TOL * .. * .. External Functions .. INTEGER IDAMAX DOUBLE PRECISION DLAMCH, DLAPY2 EXTERNAL IDAMAX, DLAMCH, DLAPY2 * .. * .. External Subroutines .. EXTERNAL DCOPY, DLACPY, DLAMRG, DROT, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 * IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN INFO = -4 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN INFO = -7 ELSE IF( CUTPNT.LT.MIN( 1, N ) .OR. CUTPNT.GT.N ) THEN INFO = -10 ELSE IF( LDQ2.LT.MAX( 1, N ) ) THEN INFO = -14 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLAED8', -INFO ) RETURN END IF * * Need to initialize GIVPTR to O here in case of quick exit * to prevent an unspecified code behavior (usually sigfault) * when IWORK array on entry to *stedc is not zeroed * (or at least some IWORK entries which used in *laed7 for GIVPTR). * GIVPTR = 0 * * Quick return if possible * IF( N.EQ.0 ) $ RETURN * N1 = CUTPNT N2 = N - N1 N1P1 = N1 + 1 * IF( RHO.LT.ZERO ) THEN CALL DSCAL( N2, MONE, Z( N1P1 ), 1 ) END IF * * Normalize z so that norm(z) = 1 * T = ONE / SQRT( TWO ) DO 10 J = 1, N INDX( J ) = J 10 CONTINUE CALL DSCAL( N, T, Z, 1 ) RHO = ABS( TWO*RHO ) * * Sort the eigenvalues into increasing order * DO 20 I = CUTPNT + 1, N INDXQ( I ) = INDXQ( I ) + CUTPNT 20 CONTINUE DO 30 I = 1, N DLAMDA( I ) = D( INDXQ( I ) ) W( I ) = Z( INDXQ( I ) ) 30 CONTINUE I = 1 J = CUTPNT + 1 CALL DLAMRG( N1, N2, DLAMDA, 1, 1, INDX ) DO 40 I = 1, N D( I ) = DLAMDA( INDX( I ) ) Z( I ) = W( INDX( I ) ) 40 CONTINUE * * Calculate the allowable deflation tolerance * IMAX = IDAMAX( N, Z, 1 ) JMAX = IDAMAX( N, D, 1 ) EPS = DLAMCH( 'Epsilon' ) TOL = EIGHT*EPS*ABS( D( JMAX ) ) * * If the rank-1 modifier is small enough, no more needs to be done * except to reorganize Q so that its columns correspond with the * elements in D. * IF( RHO*ABS( Z( IMAX ) ).LE.TOL ) THEN K = 0 IF( ICOMPQ.EQ.0 ) THEN DO 50 J = 1, N PERM( J ) = INDXQ( INDX( J ) ) 50 CONTINUE ELSE DO 60 J = 1, N PERM( J ) = INDXQ( INDX( J ) ) CALL DCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 ) 60 CONTINUE CALL DLACPY( 'A', QSIZ, N, Q2( 1, 1 ), LDQ2, Q( 1, 1 ), $ LDQ ) END IF RETURN END IF * * If there are multiple eigenvalues then the problem deflates. Here * the number of equal eigenvalues are found. As each equal * eigenvalue is found, an elementary reflector is computed to rotate * the corresponding eigensubspace so that the corresponding * components of Z are zero in this new basis. * K = 0 K2 = N + 1 DO 70 J = 1, N IF( RHO*ABS( Z( J ) ).LE.TOL ) THEN * * Deflate due to small z component. * K2 = K2 - 1 INDXP( K2 ) = J IF( J.EQ.N ) $ GO TO 110 ELSE JLAM = J GO TO 80 END IF 70 CONTINUE 80 CONTINUE J = J + 1 IF( J.GT.N ) $ GO TO 100 IF( RHO*ABS( Z( J ) ).LE.TOL ) THEN * * Deflate due to small z component. * K2 = K2 - 1 INDXP( K2 ) = J ELSE * * Check if eigenvalues are close enough to allow deflation. * S = Z( JLAM ) C = Z( J ) * * Find sqrt(a**2+b**2) without overflow or * destructive underflow. * TAU = DLAPY2( C, S ) T = D( J ) - D( JLAM ) C = C / TAU S = -S / TAU IF( ABS( T*C*S ).LE.TOL ) THEN * * Deflation is possible. * Z( J ) = TAU Z( JLAM ) = ZERO * * Record the appropriate Givens rotation * GIVPTR = GIVPTR + 1 GIVCOL( 1, GIVPTR ) = INDXQ( INDX( JLAM ) ) GIVCOL( 2, GIVPTR ) = INDXQ( INDX( J ) ) GIVNUM( 1, GIVPTR ) = C GIVNUM( 2, GIVPTR ) = S IF( ICOMPQ.EQ.1 ) THEN CALL DROT( QSIZ, Q( 1, INDXQ( INDX( JLAM ) ) ), 1, $ Q( 1, INDXQ( INDX( J ) ) ), 1, C, S ) END IF T = D( JLAM )*C*C + D( J )*S*S D( J ) = D( JLAM )*S*S + D( J )*C*C D( JLAM ) = T K2 = K2 - 1 I = 1 90 CONTINUE IF( K2+I.LE.N ) THEN IF( D( JLAM ).LT.D( INDXP( K2+I ) ) ) THEN INDXP( K2+I-1 ) = INDXP( K2+I ) INDXP( K2+I ) = JLAM I = I + 1 GO TO 90 ELSE INDXP( K2+I-1 ) = JLAM END IF ELSE INDXP( K2+I-1 ) = JLAM END IF JLAM = J ELSE K = K + 1 W( K ) = Z( JLAM ) DLAMDA( K ) = D( JLAM ) INDXP( K ) = JLAM JLAM = J END IF END IF GO TO 80 100 CONTINUE * * Record the last eigenvalue. * K = K + 1 W( K ) = Z( JLAM ) DLAMDA( K ) = D( JLAM ) INDXP( K ) = JLAM * 110 CONTINUE * * Sort the eigenvalues and corresponding eigenvectors into DLAMDA * and Q2 respectively. The eigenvalues/vectors which were not * deflated go into the first K slots of DLAMDA and Q2 respectively, * while those which were deflated go into the last N - K slots. * IF( ICOMPQ.EQ.0 ) THEN DO 120 J = 1, N JP = INDXP( J ) DLAMDA( J ) = D( JP ) PERM( J ) = INDXQ( INDX( JP ) ) 120 CONTINUE ELSE DO 130 J = 1, N JP = INDXP( J ) DLAMDA( J ) = D( JP ) PERM( J ) = INDXQ( INDX( JP ) ) CALL DCOPY( QSIZ, Q( 1, PERM( J ) ), 1, Q2( 1, J ), 1 ) 130 CONTINUE END IF * * The deflated eigenvalues and their corresponding vectors go back * into the last N - K slots of D and Q respectively. * IF( K.LT.N ) THEN IF( ICOMPQ.EQ.0 ) THEN CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 ) ELSE CALL DCOPY( N-K, DLAMDA( K+1 ), 1, D( K+1 ), 1 ) CALL DLACPY( 'A', QSIZ, N-K, Q2( 1, K+1 ), LDQ2, $ Q( 1, K+1 ), LDQ ) END IF END IF * RETURN * * End of DLAED8 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed4.f0000644000000000000000000000013214061636515015161 xustar0030 mtime=1623670093.449103853 30 atime=1623670093.449103853 30 ctime=1623670093.449103853 elk-7.2.42/src/LAPACK/dlaed4.f0000644002504400250440000006463114061636515017230 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED4 used by sstedc. Finds a single root of the secular equation. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED4 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) * * .. Scalar Arguments .. * INTEGER I, INFO, N * DOUBLE PRECISION DLAM, RHO * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ), DELTA( * ), Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> This subroutine computes the I-th updated eigenvalue of a symmetric *> rank-one modification to a diagonal matrix whose elements are *> given in the array d, and that *> *> D(i) < D(j) for i < j *> *> and that RHO > 0. This is arranged by the calling routine, and is *> no loss in generality. The rank-one modified system is thus *> *> diag( D ) + RHO * Z * Z_transpose. *> *> where we assume the Euclidean norm of Z is 1. *> *> The method consists of approximating the rational functions in the *> secular equation by simpler interpolating rational functions. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The length of all arrays. *> \endverbatim *> *> \param[in] I *> \verbatim *> I is INTEGER *> The index of the eigenvalue to be computed. 1 <= I <= N. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The original eigenvalues. It is assumed that they are in *> order, D(I) < D(J) for I < J. *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (N) *> The components of the updating vector. *> \endverbatim *> *> \param[out] DELTA *> \verbatim *> DELTA is DOUBLE PRECISION array, dimension (N) *> If N > 2, DELTA contains (D(j) - lambda_I) in its j-th *> component. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5 *> for detail. The vector DELTA contains the information necessary *> to construct the eigenvectors by DLAED3 and DLAED9. *> \endverbatim *> *> \param[in] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> The scalar in the symmetric updating formula. *> \endverbatim *> *> \param[out] DLAM *> \verbatim *> DLAM is DOUBLE PRECISION *> The computed lambda_I, the I-th updated eigenvalue. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = 1, the updating process failed. *> \endverbatim * *> \par Internal Parameters: * ========================= *> *> \verbatim *> Logical variable ORGATI (origin-at-i?) is used for distinguishing *> whether D(i) or D(i+1) is treated as the origin. *> *> ORGATI = .true. origin at i *> ORGATI = .false. origin at i+1 *> *> Logical variable SWTCH3 (switch-for-3-poles?) is for noting *> if we are working with THREE poles! *> *> MAXIT is the maximum number of iterations allowed for each *> eigenvalue. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Contributors: * ================== *> *> Ren-Cang Li, Computer Science Division, University of California *> at Berkeley, USA *> * ===================================================================== SUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER I, INFO, N DOUBLE PRECISION DLAM, RHO * .. * .. Array Arguments .. DOUBLE PRECISION D( * ), DELTA( * ), Z( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER MAXIT PARAMETER ( MAXIT = 30 ) DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, EIGHT, TEN PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ THREE = 3.0D0, FOUR = 4.0D0, EIGHT = 8.0D0, $ TEN = 10.0D0 ) * .. * .. Local Scalars .. LOGICAL ORGATI, SWTCH, SWTCH3 INTEGER II, IIM1, IIP1, IP1, ITER, J, NITER DOUBLE PRECISION A, B, C, DEL, DLTLB, DLTUB, DPHI, DPSI, DW, $ EPS, ERRETM, ETA, MIDPT, PHI, PREW, PSI, $ RHOINV, TAU, TEMP, TEMP1, W * .. * .. Local Arrays .. DOUBLE PRECISION ZZ( 3 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL DLAED5, DLAED6 * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Executable Statements .. * * Since this routine is called in an inner loop, we do no argument * checking. * * Quick return for N=1 and 2. * INFO = 0 IF( N.EQ.1 ) THEN * * Presumably, I=1 upon entry * DLAM = D( 1 ) + RHO*Z( 1 )*Z( 1 ) DELTA( 1 ) = ONE RETURN END IF IF( N.EQ.2 ) THEN CALL DLAED5( I, D, Z, DELTA, RHO, DLAM ) RETURN END IF * * Compute machine epsilon * EPS = DLAMCH( 'Epsilon' ) RHOINV = ONE / RHO * * The case I = N * IF( I.EQ.N ) THEN * * Initialize some basic variables * II = N - 1 NITER = 1 * * Calculate initial guess * MIDPT = RHO / TWO * * If ||Z||_2 is not one, then TEMP should be set to * RHO * ||Z||_2^2 / TWO * DO 10 J = 1, N DELTA( J ) = ( D( J )-D( I ) ) - MIDPT 10 CONTINUE * PSI = ZERO DO 20 J = 1, N - 2 PSI = PSI + Z( J )*Z( J ) / DELTA( J ) 20 CONTINUE * C = RHOINV + PSI W = C + Z( II )*Z( II ) / DELTA( II ) + $ Z( N )*Z( N ) / DELTA( N ) * IF( W.LE.ZERO ) THEN TEMP = Z( N-1 )*Z( N-1 ) / ( D( N )-D( N-1 )+RHO ) + $ Z( N )*Z( N ) / RHO IF( C.LE.TEMP ) THEN TAU = RHO ELSE DEL = D( N ) - D( N-1 ) A = -C*DEL + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N ) B = Z( N )*Z( N )*DEL IF( A.LT.ZERO ) THEN TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A ) ELSE TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C ) END IF END IF * * It can be proved that * D(N)+RHO/2 <= LAMBDA(N) < D(N)+TAU <= D(N)+RHO * DLTLB = MIDPT DLTUB = RHO ELSE DEL = D( N ) - D( N-1 ) A = -C*DEL + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N ) B = Z( N )*Z( N )*DEL IF( A.LT.ZERO ) THEN TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A ) ELSE TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C ) END IF * * It can be proved that * D(N) < D(N)+TAU < LAMBDA(N) < D(N)+RHO/2 * DLTLB = ZERO DLTUB = MIDPT END IF * DO 30 J = 1, N DELTA( J ) = ( D( J )-D( I ) ) - TAU 30 CONTINUE * * Evaluate PSI and the derivative DPSI * DPSI = ZERO PSI = ZERO ERRETM = ZERO DO 40 J = 1, II TEMP = Z( J ) / DELTA( J ) PSI = PSI + Z( J )*TEMP DPSI = DPSI + TEMP*TEMP ERRETM = ERRETM + PSI 40 CONTINUE ERRETM = ABS( ERRETM ) * * Evaluate PHI and the derivative DPHI * TEMP = Z( N ) / DELTA( N ) PHI = Z( N )*TEMP DPHI = TEMP*TEMP ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + $ ABS( TAU )*( DPSI+DPHI ) * W = RHOINV + PHI + PSI * * Test for convergence * IF( ABS( W ).LE.EPS*ERRETM ) THEN DLAM = D( I ) + TAU GO TO 250 END IF * IF( W.LE.ZERO ) THEN DLTLB = MAX( DLTLB, TAU ) ELSE DLTUB = MIN( DLTUB, TAU ) END IF * * Calculate the new step * NITER = NITER + 1 C = W - DELTA( N-1 )*DPSI - DELTA( N )*DPHI A = ( DELTA( N-1 )+DELTA( N ) )*W - $ DELTA( N-1 )*DELTA( N )*( DPSI+DPHI ) B = DELTA( N-1 )*DELTA( N )*W IF( C.LT.ZERO ) $ C = ABS( C ) IF( C.EQ.ZERO ) THEN * ETA = B/A * ETA = RHO - TAU ETA = DLTUB - TAU ELSE IF( A.GE.ZERO ) THEN ETA = ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) ELSE ETA = TWO*B / ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) END IF * * Note, eta should be positive if w is negative, and * eta should be negative otherwise. However, * if for some reason caused by roundoff, eta*w > 0, * we simply use one Newton step instead. This way * will guarantee eta*w < 0. * IF( W*ETA.GT.ZERO ) $ ETA = -W / ( DPSI+DPHI ) TEMP = TAU + ETA IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN IF( W.LT.ZERO ) THEN ETA = ( DLTUB-TAU ) / TWO ELSE ETA = ( DLTLB-TAU ) / TWO END IF END IF DO 50 J = 1, N DELTA( J ) = DELTA( J ) - ETA 50 CONTINUE * TAU = TAU + ETA * * Evaluate PSI and the derivative DPSI * DPSI = ZERO PSI = ZERO ERRETM = ZERO DO 60 J = 1, II TEMP = Z( J ) / DELTA( J ) PSI = PSI + Z( J )*TEMP DPSI = DPSI + TEMP*TEMP ERRETM = ERRETM + PSI 60 CONTINUE ERRETM = ABS( ERRETM ) * * Evaluate PHI and the derivative DPHI * TEMP = Z( N ) / DELTA( N ) PHI = Z( N )*TEMP DPHI = TEMP*TEMP ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + $ ABS( TAU )*( DPSI+DPHI ) * W = RHOINV + PHI + PSI * * Main loop to update the values of the array DELTA * ITER = NITER + 1 * DO 90 NITER = ITER, MAXIT * * Test for convergence * IF( ABS( W ).LE.EPS*ERRETM ) THEN DLAM = D( I ) + TAU GO TO 250 END IF * IF( W.LE.ZERO ) THEN DLTLB = MAX( DLTLB, TAU ) ELSE DLTUB = MIN( DLTUB, TAU ) END IF * * Calculate the new step * C = W - DELTA( N-1 )*DPSI - DELTA( N )*DPHI A = ( DELTA( N-1 )+DELTA( N ) )*W - $ DELTA( N-1 )*DELTA( N )*( DPSI+DPHI ) B = DELTA( N-1 )*DELTA( N )*W IF( A.GE.ZERO ) THEN ETA = ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) ELSE ETA = TWO*B / ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) END IF * * Note, eta should be positive if w is negative, and * eta should be negative otherwise. However, * if for some reason caused by roundoff, eta*w > 0, * we simply use one Newton step instead. This way * will guarantee eta*w < 0. * IF( W*ETA.GT.ZERO ) $ ETA = -W / ( DPSI+DPHI ) TEMP = TAU + ETA IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN IF( W.LT.ZERO ) THEN ETA = ( DLTUB-TAU ) / TWO ELSE ETA = ( DLTLB-TAU ) / TWO END IF END IF DO 70 J = 1, N DELTA( J ) = DELTA( J ) - ETA 70 CONTINUE * TAU = TAU + ETA * * Evaluate PSI and the derivative DPSI * DPSI = ZERO PSI = ZERO ERRETM = ZERO DO 80 J = 1, II TEMP = Z( J ) / DELTA( J ) PSI = PSI + Z( J )*TEMP DPSI = DPSI + TEMP*TEMP ERRETM = ERRETM + PSI 80 CONTINUE ERRETM = ABS( ERRETM ) * * Evaluate PHI and the derivative DPHI * TEMP = Z( N ) / DELTA( N ) PHI = Z( N )*TEMP DPHI = TEMP*TEMP ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + $ ABS( TAU )*( DPSI+DPHI ) * W = RHOINV + PHI + PSI 90 CONTINUE * * Return with INFO = 1, NITER = MAXIT and not converged * INFO = 1 DLAM = D( I ) + TAU GO TO 250 * * End for the case I = N * ELSE * * The case for I < N * NITER = 1 IP1 = I + 1 * * Calculate initial guess * DEL = D( IP1 ) - D( I ) MIDPT = DEL / TWO DO 100 J = 1, N DELTA( J ) = ( D( J )-D( I ) ) - MIDPT 100 CONTINUE * PSI = ZERO DO 110 J = 1, I - 1 PSI = PSI + Z( J )*Z( J ) / DELTA( J ) 110 CONTINUE * PHI = ZERO DO 120 J = N, I + 2, -1 PHI = PHI + Z( J )*Z( J ) / DELTA( J ) 120 CONTINUE C = RHOINV + PSI + PHI W = C + Z( I )*Z( I ) / DELTA( I ) + $ Z( IP1 )*Z( IP1 ) / DELTA( IP1 ) * IF( W.GT.ZERO ) THEN * * d(i)< the ith eigenvalue < (d(i)+d(i+1))/2 * * We choose d(i) as origin. * ORGATI = .TRUE. A = C*DEL + Z( I )*Z( I ) + Z( IP1 )*Z( IP1 ) B = Z( I )*Z( I )*DEL IF( A.GT.ZERO ) THEN TAU = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) ELSE TAU = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) END IF DLTLB = ZERO DLTUB = MIDPT ELSE * * (d(i)+d(i+1))/2 <= the ith eigenvalue < d(i+1) * * We choose d(i+1) as origin. * ORGATI = .FALSE. A = C*DEL - Z( I )*Z( I ) - Z( IP1 )*Z( IP1 ) B = Z( IP1 )*Z( IP1 )*DEL IF( A.LT.ZERO ) THEN TAU = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) ) ELSE TAU = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C ) END IF DLTLB = -MIDPT DLTUB = ZERO END IF * IF( ORGATI ) THEN DO 130 J = 1, N DELTA( J ) = ( D( J )-D( I ) ) - TAU 130 CONTINUE ELSE DO 140 J = 1, N DELTA( J ) = ( D( J )-D( IP1 ) ) - TAU 140 CONTINUE END IF IF( ORGATI ) THEN II = I ELSE II = I + 1 END IF IIM1 = II - 1 IIP1 = II + 1 * * Evaluate PSI and the derivative DPSI * DPSI = ZERO PSI = ZERO ERRETM = ZERO DO 150 J = 1, IIM1 TEMP = Z( J ) / DELTA( J ) PSI = PSI + Z( J )*TEMP DPSI = DPSI + TEMP*TEMP ERRETM = ERRETM + PSI 150 CONTINUE ERRETM = ABS( ERRETM ) * * Evaluate PHI and the derivative DPHI * DPHI = ZERO PHI = ZERO DO 160 J = N, IIP1, -1 TEMP = Z( J ) / DELTA( J ) PHI = PHI + Z( J )*TEMP DPHI = DPHI + TEMP*TEMP ERRETM = ERRETM + PHI 160 CONTINUE * W = RHOINV + PHI + PSI * * W is the value of the secular function with * its ii-th element removed. * SWTCH3 = .FALSE. IF( ORGATI ) THEN IF( W.LT.ZERO ) $ SWTCH3 = .TRUE. ELSE IF( W.GT.ZERO ) $ SWTCH3 = .TRUE. END IF IF( II.EQ.1 .OR. II.EQ.N ) $ SWTCH3 = .FALSE. * TEMP = Z( II ) / DELTA( II ) DW = DPSI + DPHI + TEMP*TEMP TEMP = Z( II )*TEMP W = W + TEMP ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + $ THREE*ABS( TEMP ) + ABS( TAU )*DW * * Test for convergence * IF( ABS( W ).LE.EPS*ERRETM ) THEN IF( ORGATI ) THEN DLAM = D( I ) + TAU ELSE DLAM = D( IP1 ) + TAU END IF GO TO 250 END IF * IF( W.LE.ZERO ) THEN DLTLB = MAX( DLTLB, TAU ) ELSE DLTUB = MIN( DLTUB, TAU ) END IF * * Calculate the new step * NITER = NITER + 1 IF( .NOT.SWTCH3 ) THEN IF( ORGATI ) THEN C = W - DELTA( IP1 )*DW - ( D( I )-D( IP1 ) )* $ ( Z( I ) / DELTA( I ) )**2 ELSE C = W - DELTA( I )*DW - ( D( IP1 )-D( I ) )* $ ( Z( IP1 ) / DELTA( IP1 ) )**2 END IF A = ( DELTA( I )+DELTA( IP1 ) )*W - $ DELTA( I )*DELTA( IP1 )*DW B = DELTA( I )*DELTA( IP1 )*W IF( C.EQ.ZERO ) THEN IF( A.EQ.ZERO ) THEN IF( ORGATI ) THEN A = Z( I )*Z( I ) + DELTA( IP1 )*DELTA( IP1 )* $ ( DPSI+DPHI ) ELSE A = Z( IP1 )*Z( IP1 ) + DELTA( I )*DELTA( I )* $ ( DPSI+DPHI ) END IF END IF ETA = B / A ELSE IF( A.LE.ZERO ) THEN ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) ELSE ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) END IF ELSE * * Interpolation using THREE most relevant poles * TEMP = RHOINV + PSI + PHI IF( ORGATI ) THEN TEMP1 = Z( IIM1 ) / DELTA( IIM1 ) TEMP1 = TEMP1*TEMP1 C = TEMP - DELTA( IIP1 )*( DPSI+DPHI ) - $ ( D( IIM1 )-D( IIP1 ) )*TEMP1 ZZ( 1 ) = Z( IIM1 )*Z( IIM1 ) ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )* $ ( ( DPSI-TEMP1 )+DPHI ) ELSE TEMP1 = Z( IIP1 ) / DELTA( IIP1 ) TEMP1 = TEMP1*TEMP1 C = TEMP - DELTA( IIM1 )*( DPSI+DPHI ) - $ ( D( IIP1 )-D( IIM1 ) )*TEMP1 ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )* $ ( DPSI+( DPHI-TEMP1 ) ) ZZ( 3 ) = Z( IIP1 )*Z( IIP1 ) END IF ZZ( 2 ) = Z( II )*Z( II ) CALL DLAED6( NITER, ORGATI, C, DELTA( IIM1 ), ZZ, W, ETA, $ INFO ) IF( INFO.NE.0 ) $ GO TO 250 END IF * * Note, eta should be positive if w is negative, and * eta should be negative otherwise. However, * if for some reason caused by roundoff, eta*w > 0, * we simply use one Newton step instead. This way * will guarantee eta*w < 0. * IF( W*ETA.GE.ZERO ) $ ETA = -W / DW TEMP = TAU + ETA IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN IF( W.LT.ZERO ) THEN ETA = ( DLTUB-TAU ) / TWO ELSE ETA = ( DLTLB-TAU ) / TWO END IF END IF * PREW = W * DO 180 J = 1, N DELTA( J ) = DELTA( J ) - ETA 180 CONTINUE * * Evaluate PSI and the derivative DPSI * DPSI = ZERO PSI = ZERO ERRETM = ZERO DO 190 J = 1, IIM1 TEMP = Z( J ) / DELTA( J ) PSI = PSI + Z( J )*TEMP DPSI = DPSI + TEMP*TEMP ERRETM = ERRETM + PSI 190 CONTINUE ERRETM = ABS( ERRETM ) * * Evaluate PHI and the derivative DPHI * DPHI = ZERO PHI = ZERO DO 200 J = N, IIP1, -1 TEMP = Z( J ) / DELTA( J ) PHI = PHI + Z( J )*TEMP DPHI = DPHI + TEMP*TEMP ERRETM = ERRETM + PHI 200 CONTINUE * TEMP = Z( II ) / DELTA( II ) DW = DPSI + DPHI + TEMP*TEMP TEMP = Z( II )*TEMP W = RHOINV + PHI + PSI + TEMP ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + $ THREE*ABS( TEMP ) + ABS( TAU+ETA )*DW * SWTCH = .FALSE. IF( ORGATI ) THEN IF( -W.GT.ABS( PREW ) / TEN ) $ SWTCH = .TRUE. ELSE IF( W.GT.ABS( PREW ) / TEN ) $ SWTCH = .TRUE. END IF * TAU = TAU + ETA * * Main loop to update the values of the array DELTA * ITER = NITER + 1 * DO 240 NITER = ITER, MAXIT * * Test for convergence * IF( ABS( W ).LE.EPS*ERRETM ) THEN IF( ORGATI ) THEN DLAM = D( I ) + TAU ELSE DLAM = D( IP1 ) + TAU END IF GO TO 250 END IF * IF( W.LE.ZERO ) THEN DLTLB = MAX( DLTLB, TAU ) ELSE DLTUB = MIN( DLTUB, TAU ) END IF * * Calculate the new step * IF( .NOT.SWTCH3 ) THEN IF( .NOT.SWTCH ) THEN IF( ORGATI ) THEN C = W - DELTA( IP1 )*DW - $ ( D( I )-D( IP1 ) )*( Z( I ) / DELTA( I ) )**2 ELSE C = W - DELTA( I )*DW - ( D( IP1 )-D( I ) )* $ ( Z( IP1 ) / DELTA( IP1 ) )**2 END IF ELSE TEMP = Z( II ) / DELTA( II ) IF( ORGATI ) THEN DPSI = DPSI + TEMP*TEMP ELSE DPHI = DPHI + TEMP*TEMP END IF C = W - DELTA( I )*DPSI - DELTA( IP1 )*DPHI END IF A = ( DELTA( I )+DELTA( IP1 ) )*W - $ DELTA( I )*DELTA( IP1 )*DW B = DELTA( I )*DELTA( IP1 )*W IF( C.EQ.ZERO ) THEN IF( A.EQ.ZERO ) THEN IF( .NOT.SWTCH ) THEN IF( ORGATI ) THEN A = Z( I )*Z( I ) + DELTA( IP1 )* $ DELTA( IP1 )*( DPSI+DPHI ) ELSE A = Z( IP1 )*Z( IP1 ) + $ DELTA( I )*DELTA( I )*( DPSI+DPHI ) END IF ELSE A = DELTA( I )*DELTA( I )*DPSI + $ DELTA( IP1 )*DELTA( IP1 )*DPHI END IF END IF ETA = B / A ELSE IF( A.LE.ZERO ) THEN ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) ELSE ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) END IF ELSE * * Interpolation using THREE most relevant poles * TEMP = RHOINV + PSI + PHI IF( SWTCH ) THEN C = TEMP - DELTA( IIM1 )*DPSI - DELTA( IIP1 )*DPHI ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )*DPSI ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )*DPHI ELSE IF( ORGATI ) THEN TEMP1 = Z( IIM1 ) / DELTA( IIM1 ) TEMP1 = TEMP1*TEMP1 C = TEMP - DELTA( IIP1 )*( DPSI+DPHI ) - $ ( D( IIM1 )-D( IIP1 ) )*TEMP1 ZZ( 1 ) = Z( IIM1 )*Z( IIM1 ) ZZ( 3 ) = DELTA( IIP1 )*DELTA( IIP1 )* $ ( ( DPSI-TEMP1 )+DPHI ) ELSE TEMP1 = Z( IIP1 ) / DELTA( IIP1 ) TEMP1 = TEMP1*TEMP1 C = TEMP - DELTA( IIM1 )*( DPSI+DPHI ) - $ ( D( IIP1 )-D( IIM1 ) )*TEMP1 ZZ( 1 ) = DELTA( IIM1 )*DELTA( IIM1 )* $ ( DPSI+( DPHI-TEMP1 ) ) ZZ( 3 ) = Z( IIP1 )*Z( IIP1 ) END IF END IF CALL DLAED6( NITER, ORGATI, C, DELTA( IIM1 ), ZZ, W, ETA, $ INFO ) IF( INFO.NE.0 ) $ GO TO 250 END IF * * Note, eta should be positive if w is negative, and * eta should be negative otherwise. However, * if for some reason caused by roundoff, eta*w > 0, * we simply use one Newton step instead. This way * will guarantee eta*w < 0. * IF( W*ETA.GE.ZERO ) $ ETA = -W / DW TEMP = TAU + ETA IF( TEMP.GT.DLTUB .OR. TEMP.LT.DLTLB ) THEN IF( W.LT.ZERO ) THEN ETA = ( DLTUB-TAU ) / TWO ELSE ETA = ( DLTLB-TAU ) / TWO END IF END IF * DO 210 J = 1, N DELTA( J ) = DELTA( J ) - ETA 210 CONTINUE * TAU = TAU + ETA PREW = W * * Evaluate PSI and the derivative DPSI * DPSI = ZERO PSI = ZERO ERRETM = ZERO DO 220 J = 1, IIM1 TEMP = Z( J ) / DELTA( J ) PSI = PSI + Z( J )*TEMP DPSI = DPSI + TEMP*TEMP ERRETM = ERRETM + PSI 220 CONTINUE ERRETM = ABS( ERRETM ) * * Evaluate PHI and the derivative DPHI * DPHI = ZERO PHI = ZERO DO 230 J = N, IIP1, -1 TEMP = Z( J ) / DELTA( J ) PHI = PHI + Z( J )*TEMP DPHI = DPHI + TEMP*TEMP ERRETM = ERRETM + PHI 230 CONTINUE * TEMP = Z( II ) / DELTA( II ) DW = DPSI + DPHI + TEMP*TEMP TEMP = Z( II )*TEMP W = RHOINV + PHI + PSI + TEMP ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + $ THREE*ABS( TEMP ) + ABS( TAU )*DW IF( W*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN ) $ SWTCH = .NOT.SWTCH * 240 CONTINUE * * Return with INFO = 1, NITER = MAXIT and not converged * INFO = 1 IF( ORGATI ) THEN DLAM = D( I ) + TAU ELSE DLAM = D( IP1 ) + TAU END IF * END IF * 250 CONTINUE * RETURN * * End of DLAED4 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/iladlc.f0000644000000000000000000000013014061636515015252 xustar0029 mtime=1623670093.45210385 30 atime=1623670093.451103851 29 ctime=1623670093.45210385 elk-7.2.42/src/LAPACK/iladlc.f0000644002504400250440000000564214061636515017320 0ustar00dewhurstdewhurst00000000000000*> \brief \b ILADLC scans a matrix for its last non-zero column. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ILADLC + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * INTEGER FUNCTION ILADLC( M, N, A, LDA ) * * .. Scalar Arguments .. * INTEGER M, N, LDA * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ILADLC scans A for its last non-zero column. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The m by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== INTEGER FUNCTION ILADLC( M, N, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER M, N, LDA * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I * .. * .. Executable Statements .. * * Quick test for the common case where one corner is non-zero. IF( N.EQ.0 ) THEN ILADLC = N ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILADLC = N ELSE * Now scan each column from the end, returning with the first non-zero. DO ILADLC = N, 1, -1 DO I = 1, M IF( A(I, ILADLC).NE.ZERO ) RETURN END DO END DO END IF RETURN END elk-7.2.42/src/LAPACK/PaxHeaders.21776/iladlr.f0000644000000000000000000000013214061636515015273 xustar0030 mtime=1623670093.453103849 30 atime=1623670093.453103849 30 ctime=1623670093.453103849 elk-7.2.42/src/LAPACK/iladlr.f0000644002504400250440000000572514061636515017341 0ustar00dewhurstdewhurst00000000000000*> \brief \b ILADLR scans a matrix for its last non-zero row. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ILADLR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * INTEGER FUNCTION ILADLR( M, N, A, LDA ) * * .. Scalar Arguments .. * INTEGER M, N, LDA * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ILADLR scans A for its last non-zero row. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The m by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup OTHERauxiliary * * ===================================================================== INTEGER FUNCTION ILADLR( M, N, A, LDA ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER M, N, LDA * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J * .. * .. Executable Statements .. * * Quick test for the common case where one corner is non-zero. IF( M.EQ.0 ) THEN ILADLR = M ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN ILADLR = M ELSE * Scan up each column tracking the last zero row seen. ILADLR = 0 DO J = 1, N I=M DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) I=I-1 ENDDO ILADLR = MAX( ILADLR, I ) END DO END IF RETURN END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasq4.f0000644000000000000000000000013214061636515015214 xustar0030 mtime=1623670093.455103847 30 atime=1623670093.455103847 30 ctime=1623670093.455103847 elk-7.2.42/src/LAPACK/dlasq4.f0000644002504400250440000002663414061636515017264 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASQ4 computes an approximation to the smallest eigenvalue using values of d from the previous transform. Used by sbdsqr. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASQ4 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, * DN1, DN2, TAU, TTYPE, G ) * * .. Scalar Arguments .. * INTEGER I0, N0, N0IN, PP, TTYPE * DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU * .. * .. Array Arguments .. * DOUBLE PRECISION Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASQ4 computes an approximation TAU to the smallest eigenvalue *> using values of d from the previous transform. *> \endverbatim * * Arguments: * ========== * *> \param[in] I0 *> \verbatim *> I0 is INTEGER *> First index. *> \endverbatim *> *> \param[in] N0 *> \verbatim *> N0 is INTEGER *> Last index. *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension ( 4*N0 ) *> Z holds the qd array. *> \endverbatim *> *> \param[in] PP *> \verbatim *> PP is INTEGER *> PP=0 for ping, PP=1 for pong. *> \endverbatim *> *> \param[in] N0IN *> \verbatim *> N0IN is INTEGER *> The value of N0 at start of EIGTEST. *> \endverbatim *> *> \param[in] DMIN *> \verbatim *> DMIN is DOUBLE PRECISION *> Minimum value of d. *> \endverbatim *> *> \param[in] DMIN1 *> \verbatim *> DMIN1 is DOUBLE PRECISION *> Minimum value of d, excluding D( N0 ). *> \endverbatim *> *> \param[in] DMIN2 *> \verbatim *> DMIN2 is DOUBLE PRECISION *> Minimum value of d, excluding D( N0 ) and D( N0-1 ). *> \endverbatim *> *> \param[in] DN *> \verbatim *> DN is DOUBLE PRECISION *> d(N) *> \endverbatim *> *> \param[in] DN1 *> \verbatim *> DN1 is DOUBLE PRECISION *> d(N-1) *> \endverbatim *> *> \param[in] DN2 *> \verbatim *> DN2 is DOUBLE PRECISION *> d(N-2) *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is DOUBLE PRECISION *> This is the shift. *> \endverbatim *> *> \param[out] TTYPE *> \verbatim *> TTYPE is INTEGER *> Shift type. *> \endverbatim *> *> \param[in,out] G *> \verbatim *> G is DOUBLE PRECISION *> G is passed as an argument in order to save its value between *> calls to DLASQ4. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup auxOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> CNST1 = 9/16 *> \endverbatim *> * ===================================================================== SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, $ DN1, DN2, TAU, TTYPE, G ) * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2016 * * .. Scalar Arguments .. INTEGER I0, N0, N0IN, PP, TTYPE DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU * .. * .. Array Arguments .. DOUBLE PRECISION Z( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION CNST1, CNST2, CNST3 PARAMETER ( CNST1 = 0.5630D0, CNST2 = 1.010D0, $ CNST3 = 1.050D0 ) DOUBLE PRECISION QURTR, THIRD, HALF, ZERO, ONE, TWO, HUNDRD PARAMETER ( QURTR = 0.250D0, THIRD = 0.3330D0, $ HALF = 0.50D0, ZERO = 0.0D0, ONE = 1.0D0, $ TWO = 2.0D0, HUNDRD = 100.0D0 ) * .. * .. Local Scalars .. INTEGER I4, NN, NP DOUBLE PRECISION A2, B1, B2, GAM, GAP1, GAP2, S * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, SQRT * .. * .. Executable Statements .. * * A negative DMIN forces the shift to take that absolute value * TTYPE records the type of shift. * IF( DMIN.LE.ZERO ) THEN TAU = -DMIN TTYPE = -1 RETURN END IF * NN = 4*N0 + PP IF( N0IN.EQ.N0 ) THEN * * No eigenvalues deflated. * IF( DMIN.EQ.DN .OR. DMIN.EQ.DN1 ) THEN * B1 = SQRT( Z( NN-3 ) )*SQRT( Z( NN-5 ) ) B2 = SQRT( Z( NN-7 ) )*SQRT( Z( NN-9 ) ) A2 = Z( NN-7 ) + Z( NN-5 ) * * Cases 2 and 3. * IF( DMIN.EQ.DN .AND. DMIN1.EQ.DN1 ) THEN GAP2 = DMIN2 - A2 - DMIN2*QURTR IF( GAP2.GT.ZERO .AND. GAP2.GT.B2 ) THEN GAP1 = A2 - DN - ( B2 / GAP2 )*B2 ELSE GAP1 = A2 - DN - ( B1+B2 ) END IF IF( GAP1.GT.ZERO .AND. GAP1.GT.B1 ) THEN S = MAX( DN-( B1 / GAP1 )*B1, HALF*DMIN ) TTYPE = -2 ELSE S = ZERO IF( DN.GT.B1 ) $ S = DN - B1 IF( A2.GT.( B1+B2 ) ) $ S = MIN( S, A2-( B1+B2 ) ) S = MAX( S, THIRD*DMIN ) TTYPE = -3 END IF ELSE * * Case 4. * TTYPE = -4 S = QURTR*DMIN IF( DMIN.EQ.DN ) THEN GAM = DN A2 = ZERO IF( Z( NN-5 ) .GT. Z( NN-7 ) ) $ RETURN B2 = Z( NN-5 ) / Z( NN-7 ) NP = NN - 9 ELSE NP = NN - 2*PP GAM = DN1 IF( Z( NP-4 ) .GT. Z( NP-2 ) ) $ RETURN A2 = Z( NP-4 ) / Z( NP-2 ) IF( Z( NN-9 ) .GT. Z( NN-11 ) ) $ RETURN B2 = Z( NN-9 ) / Z( NN-11 ) NP = NN - 13 END IF * * Approximate contribution to norm squared from I < NN-1. * A2 = A2 + B2 DO 10 I4 = NP, 4*I0 - 1 + PP, -4 IF( B2.EQ.ZERO ) $ GO TO 20 B1 = B2 IF( Z( I4 ) .GT. Z( I4-2 ) ) $ RETURN B2 = B2*( Z( I4 ) / Z( I4-2 ) ) A2 = A2 + B2 IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) $ GO TO 20 10 CONTINUE 20 CONTINUE A2 = CNST3*A2 * * Rayleigh quotient residual bound. * IF( A2.LT.CNST1 ) $ S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 ) END IF ELSE IF( DMIN.EQ.DN2 ) THEN * * Case 5. * TTYPE = -5 S = QURTR*DMIN * * Compute contribution to norm squared from I > NN-2. * NP = NN - 2*PP B1 = Z( NP-2 ) B2 = Z( NP-6 ) GAM = DN2 IF( Z( NP-8 ).GT.B2 .OR. Z( NP-4 ).GT.B1 ) $ RETURN A2 = ( Z( NP-8 ) / B2 )*( ONE+Z( NP-4 ) / B1 ) * * Approximate contribution to norm squared from I < NN-2. * IF( N0-I0.GT.2 ) THEN B2 = Z( NN-13 ) / Z( NN-15 ) A2 = A2 + B2 DO 30 I4 = NN - 17, 4*I0 - 1 + PP, -4 IF( B2.EQ.ZERO ) $ GO TO 40 B1 = B2 IF( Z( I4 ) .GT. Z( I4-2 ) ) $ RETURN B2 = B2*( Z( I4 ) / Z( I4-2 ) ) A2 = A2 + B2 IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) $ GO TO 40 30 CONTINUE 40 CONTINUE A2 = CNST3*A2 END IF * IF( A2.LT.CNST1 ) $ S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 ) ELSE * * Case 6, no information to guide us. * IF( TTYPE.EQ.-6 ) THEN G = G + THIRD*( ONE-G ) ELSE IF( TTYPE.EQ.-18 ) THEN G = QURTR*THIRD ELSE G = QURTR END IF S = G*DMIN TTYPE = -6 END IF * ELSE IF( N0IN.EQ.( N0+1 ) ) THEN * * One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. * IF( DMIN1.EQ.DN1 .AND. DMIN2.EQ.DN2 ) THEN * * Cases 7 and 8. * TTYPE = -7 S = THIRD*DMIN1 IF( Z( NN-5 ).GT.Z( NN-7 ) ) $ RETURN B1 = Z( NN-5 ) / Z( NN-7 ) B2 = B1 IF( B2.EQ.ZERO ) $ GO TO 60 DO 50 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4 A2 = B1 IF( Z( I4 ).GT.Z( I4-2 ) ) $ RETURN B1 = B1*( Z( I4 ) / Z( I4-2 ) ) B2 = B2 + B1 IF( HUNDRD*MAX( B1, A2 ).LT.B2 ) $ GO TO 60 50 CONTINUE 60 CONTINUE B2 = SQRT( CNST3*B2 ) A2 = DMIN1 / ( ONE+B2**2 ) GAP2 = HALF*DMIN2 - A2 IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) ELSE S = MAX( S, A2*( ONE-CNST2*B2 ) ) TTYPE = -8 END IF ELSE * * Case 9. * S = QURTR*DMIN1 IF( DMIN1.EQ.DN1 ) $ S = HALF*DMIN1 TTYPE = -9 END IF * ELSE IF( N0IN.EQ.( N0+2 ) ) THEN * * Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. * * Cases 10 and 11. * IF( DMIN2.EQ.DN2 .AND. TWO*Z( NN-5 ).LT.Z( NN-7 ) ) THEN TTYPE = -10 S = THIRD*DMIN2 IF( Z( NN-5 ).GT.Z( NN-7 ) ) $ RETURN B1 = Z( NN-5 ) / Z( NN-7 ) B2 = B1 IF( B2.EQ.ZERO ) $ GO TO 80 DO 70 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4 IF( Z( I4 ).GT.Z( I4-2 ) ) $ RETURN B1 = B1*( Z( I4 ) / Z( I4-2 ) ) B2 = B2 + B1 IF( HUNDRD*B1.LT.B2 ) $ GO TO 80 70 CONTINUE 80 CONTINUE B2 = SQRT( CNST3*B2 ) A2 = DMIN2 / ( ONE+B2**2 ) GAP2 = Z( NN-7 ) + Z( NN-9 ) - $ SQRT( Z( NN-11 ) )*SQRT( Z( NN-9 ) ) - A2 IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) ELSE S = MAX( S, A2*( ONE-CNST2*B2 ) ) END IF ELSE S = QURTR*DMIN2 TTYPE = -11 END IF ELSE IF( N0IN.GT.( N0+2 ) ) THEN * * Case 12, more than two eigenvalues deflated. No information. * S = ZERO TTYPE = -12 END IF * TAU = S RETURN * * End of DLASQ4 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasq5.f0000644000000000000000000000013214061636515015215 xustar0030 mtime=1623670093.457103845 30 atime=1623670093.457103845 30 ctime=1623670093.457103845 elk-7.2.42/src/LAPACK/dlasq5.f0000644002504400250440000002625514061636515017264 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASQ5 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN, * DNM1, DNM2, IEEE, EPS ) * * .. Scalar Arguments .. * LOGICAL IEEE * INTEGER I0, N0, PP * DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS * .. * .. Array Arguments .. * DOUBLE PRECISION Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASQ5 computes one dqds transform in ping-pong form, one *> version for IEEE machines another for non IEEE machines. *> \endverbatim * * Arguments: * ========== * *> \param[in] I0 *> \verbatim *> I0 is INTEGER *> First index. *> \endverbatim *> *> \param[in] N0 *> \verbatim *> N0 is INTEGER *> Last index. *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension ( 4*N ) *> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid *> an extra argument. *> \endverbatim *> *> \param[in] PP *> \verbatim *> PP is INTEGER *> PP=0 for ping, PP=1 for pong. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION *> This is the shift. *> \endverbatim *> *> \param[in] SIGMA *> \verbatim *> SIGMA is DOUBLE PRECISION *> This is the accumulated shift up to this step. *> \endverbatim *> *> \param[out] DMIN *> \verbatim *> DMIN is DOUBLE PRECISION *> Minimum value of d. *> \endverbatim *> *> \param[out] DMIN1 *> \verbatim *> DMIN1 is DOUBLE PRECISION *> Minimum value of d, excluding D( N0 ). *> \endverbatim *> *> \param[out] DMIN2 *> \verbatim *> DMIN2 is DOUBLE PRECISION *> Minimum value of d, excluding D( N0 ) and D( N0-1 ). *> \endverbatim *> *> \param[out] DN *> \verbatim *> DN is DOUBLE PRECISION *> d(N0), the last value of d. *> \endverbatim *> *> \param[out] DNM1 *> \verbatim *> DNM1 is DOUBLE PRECISION *> d(N0-1). *> \endverbatim *> *> \param[out] DNM2 *> \verbatim *> DNM2 is DOUBLE PRECISION *> d(N0-2). *> \endverbatim *> *> \param[in] IEEE *> \verbatim *> IEEE is LOGICAL *> Flag for IEEE or non IEEE arithmetic. *> \endverbatim *> *> \param[in] EPS *> \verbatim *> EPS is DOUBLE PRECISION *> This is the value of epsilon used. *> \endverbatim *> * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2017 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, $ DN, DNM1, DNM2, IEEE, EPS ) * * -- LAPACK computational routine (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. Scalar Arguments .. LOGICAL IEEE INTEGER I0, N0, PP DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, $ SIGMA, EPS * .. * .. Array Arguments .. DOUBLE PRECISION Z( * ) * .. * * ===================================================================== * * .. Parameter .. DOUBLE PRECISION ZERO, HALF PARAMETER ( ZERO = 0.0D0, HALF = 0.5 ) * .. * .. Local Scalars .. INTEGER J4, J4P2 DOUBLE PRECISION D, EMIN, TEMP, DTHRESH * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( ( N0-I0-1 ).LE.0 ) $ RETURN * DTHRESH = EPS*(SIGMA+TAU) IF( TAU.LT.DTHRESH*HALF ) TAU = ZERO IF( TAU.NE.ZERO ) THEN J4 = 4*I0 + PP - 3 EMIN = Z( J4+4 ) D = Z( J4 ) - TAU DMIN = D DMIN1 = -Z( J4 ) * IF( IEEE ) THEN * * Code for IEEE arithmetic. * IF( PP.EQ.0 ) THEN DO 10 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-2 ) = D + Z( J4-1 ) TEMP = Z( J4+1 ) / Z( J4-2 ) D = D*TEMP - TAU DMIN = MIN( DMIN, D ) Z( J4 ) = Z( J4-1 )*TEMP EMIN = MIN( Z( J4 ), EMIN ) 10 CONTINUE ELSE DO 20 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-3 ) = D + Z( J4 ) TEMP = Z( J4+2 ) / Z( J4-3 ) D = D*TEMP - TAU DMIN = MIN( DMIN, D ) Z( J4-1 ) = Z( J4 )*TEMP EMIN = MIN( Z( J4-1 ), EMIN ) 20 CONTINUE END IF * * Unroll last two steps. * DNM2 = D DMIN2 = DMIN J4 = 4*( N0-2 ) - PP J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM2 + Z( J4P2 ) Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU DMIN = MIN( DMIN, DNM1 ) * DMIN1 = DMIN J4 = J4 + 4 J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM1 + Z( J4P2 ) Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU DMIN = MIN( DMIN, DN ) * ELSE * * Code for non IEEE arithmetic. * IF( PP.EQ.0 ) THEN DO 30 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-2 ) = D + Z( J4-1 ) IF( D.LT.ZERO ) THEN RETURN ELSE Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU END IF DMIN = MIN( DMIN, D ) EMIN = MIN( EMIN, Z( J4 ) ) 30 CONTINUE ELSE DO 40 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-3 ) = D + Z( J4 ) IF( D.LT.ZERO ) THEN RETURN ELSE Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU END IF DMIN = MIN( DMIN, D ) EMIN = MIN( EMIN, Z( J4-1 ) ) 40 CONTINUE END IF * * Unroll last two steps. * DNM2 = D DMIN2 = DMIN J4 = 4*( N0-2 ) - PP J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM2 + Z( J4P2 ) IF( DNM2.LT.ZERO ) THEN RETURN ELSE Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU END IF DMIN = MIN( DMIN, DNM1 ) * DMIN1 = DMIN J4 = J4 + 4 J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM1 + Z( J4P2 ) IF( DNM1.LT.ZERO ) THEN RETURN ELSE Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU END IF DMIN = MIN( DMIN, DN ) * END IF ELSE * This is the version that sets d's to zero if they are small enough J4 = 4*I0 + PP - 3 EMIN = Z( J4+4 ) D = Z( J4 ) - TAU DMIN = D DMIN1 = -Z( J4 ) IF( IEEE ) THEN * * Code for IEEE arithmetic. * IF( PP.EQ.0 ) THEN DO 50 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-2 ) = D + Z( J4-1 ) TEMP = Z( J4+1 ) / Z( J4-2 ) D = D*TEMP - TAU IF( D.LT.DTHRESH ) D = ZERO DMIN = MIN( DMIN, D ) Z( J4 ) = Z( J4-1 )*TEMP EMIN = MIN( Z( J4 ), EMIN ) 50 CONTINUE ELSE DO 60 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-3 ) = D + Z( J4 ) TEMP = Z( J4+2 ) / Z( J4-3 ) D = D*TEMP - TAU IF( D.LT.DTHRESH ) D = ZERO DMIN = MIN( DMIN, D ) Z( J4-1 ) = Z( J4 )*TEMP EMIN = MIN( Z( J4-1 ), EMIN ) 60 CONTINUE END IF * * Unroll last two steps. * DNM2 = D DMIN2 = DMIN J4 = 4*( N0-2 ) - PP J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM2 + Z( J4P2 ) Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU DMIN = MIN( DMIN, DNM1 ) * DMIN1 = DMIN J4 = J4 + 4 J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM1 + Z( J4P2 ) Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU DMIN = MIN( DMIN, DN ) * ELSE * * Code for non IEEE arithmetic. * IF( PP.EQ.0 ) THEN DO 70 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-2 ) = D + Z( J4-1 ) IF( D.LT.ZERO ) THEN RETURN ELSE Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU END IF IF( D.LT.DTHRESH) D = ZERO DMIN = MIN( DMIN, D ) EMIN = MIN( EMIN, Z( J4 ) ) 70 CONTINUE ELSE DO 80 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-3 ) = D + Z( J4 ) IF( D.LT.ZERO ) THEN RETURN ELSE Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU END IF IF( D.LT.DTHRESH) D = ZERO DMIN = MIN( DMIN, D ) EMIN = MIN( EMIN, Z( J4-1 ) ) 80 CONTINUE END IF * * Unroll last two steps. * DNM2 = D DMIN2 = DMIN J4 = 4*( N0-2 ) - PP J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM2 + Z( J4P2 ) IF( DNM2.LT.ZERO ) THEN RETURN ELSE Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU END IF DMIN = MIN( DMIN, DNM1 ) * DMIN1 = DMIN J4 = J4 + 4 J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM1 + Z( J4P2 ) IF( DNM1.LT.ZERO ) THEN RETURN ELSE Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU END IF DMIN = MIN( DMIN, DN ) * END IF END IF * Z( J4+2 ) = DN Z( 4*N0-PP ) = EMIN RETURN * * End of DLASQ5 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlasq6.f0000644000000000000000000000013214061636515015216 xustar0030 mtime=1623670093.459103843 30 atime=1623670093.459103843 30 ctime=1623670093.459103843 elk-7.2.42/src/LAPACK/dlasq6.f0000644002504400250440000001521414061636515017256 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLASQ6 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, * DNM1, DNM2 ) * * .. Scalar Arguments .. * INTEGER I0, N0, PP * DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 * .. * .. Array Arguments .. * DOUBLE PRECISION Z( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLASQ6 computes one dqd (shift equal to zero) transform in *> ping-pong form, with protection against underflow and overflow. *> \endverbatim * * Arguments: * ========== * *> \param[in] I0 *> \verbatim *> I0 is INTEGER *> First index. *> \endverbatim *> *> \param[in] N0 *> \verbatim *> N0 is INTEGER *> Last index. *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension ( 4*N ) *> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid *> an extra argument. *> \endverbatim *> *> \param[in] PP *> \verbatim *> PP is INTEGER *> PP=0 for ping, PP=1 for pong. *> \endverbatim *> *> \param[out] DMIN *> \verbatim *> DMIN is DOUBLE PRECISION *> Minimum value of d. *> \endverbatim *> *> \param[out] DMIN1 *> \verbatim *> DMIN1 is DOUBLE PRECISION *> Minimum value of d, excluding D( N0 ). *> \endverbatim *> *> \param[out] DMIN2 *> \verbatim *> DMIN2 is DOUBLE PRECISION *> Minimum value of d, excluding D( N0 ) and D( N0-1 ). *> \endverbatim *> *> \param[out] DN *> \verbatim *> DN is DOUBLE PRECISION *> d(N0), the last value of d. *> \endverbatim *> *> \param[out] DNM1 *> \verbatim *> DNM1 is DOUBLE PRECISION *> d(N0-1). *> \endverbatim *> *> \param[out] DNM2 *> \verbatim *> DNM2 is DOUBLE PRECISION *> d(N0-2). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * * ===================================================================== SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, $ DNM1, DNM2 ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER I0, N0, PP DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 * .. * .. Array Arguments .. DOUBLE PRECISION Z( * ) * .. * * ===================================================================== * * .. Parameter .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) * .. * .. Local Scalars .. INTEGER J4, J4P2 DOUBLE PRECISION D, EMIN, SAFMIN, TEMP * .. * .. External Function .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( ( N0-I0-1 ).LE.0 ) $ RETURN * SAFMIN = DLAMCH( 'Safe minimum' ) J4 = 4*I0 + PP - 3 EMIN = Z( J4+4 ) D = Z( J4 ) DMIN = D * IF( PP.EQ.0 ) THEN DO 10 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-2 ) = D + Z( J4-1 ) IF( Z( J4-2 ).EQ.ZERO ) THEN Z( J4 ) = ZERO D = Z( J4+1 ) DMIN = D EMIN = ZERO ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND. $ SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN TEMP = Z( J4+1 ) / Z( J4-2 ) Z( J4 ) = Z( J4-1 )*TEMP D = D*TEMP ELSE Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) D = Z( J4+1 )*( D / Z( J4-2 ) ) END IF DMIN = MIN( DMIN, D ) EMIN = MIN( EMIN, Z( J4 ) ) 10 CONTINUE ELSE DO 20 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-3 ) = D + Z( J4 ) IF( Z( J4-3 ).EQ.ZERO ) THEN Z( J4-1 ) = ZERO D = Z( J4+2 ) DMIN = D EMIN = ZERO ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND. $ SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN TEMP = Z( J4+2 ) / Z( J4-3 ) Z( J4-1 ) = Z( J4 )*TEMP D = D*TEMP ELSE Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) D = Z( J4+2 )*( D / Z( J4-3 ) ) END IF DMIN = MIN( DMIN, D ) EMIN = MIN( EMIN, Z( J4-1 ) ) 20 CONTINUE END IF * * Unroll last two steps. * DNM2 = D DMIN2 = DMIN J4 = 4*( N0-2 ) - PP J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM2 + Z( J4P2 ) IF( Z( J4-2 ).EQ.ZERO ) THEN Z( J4 ) = ZERO DNM1 = Z( J4P2+2 ) DMIN = DNM1 EMIN = ZERO ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. $ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN TEMP = Z( J4P2+2 ) / Z( J4-2 ) Z( J4 ) = Z( J4P2 )*TEMP DNM1 = DNM2*TEMP ELSE Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) END IF DMIN = MIN( DMIN, DNM1 ) * DMIN1 = DMIN J4 = J4 + 4 J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM1 + Z( J4P2 ) IF( Z( J4-2 ).EQ.ZERO ) THEN Z( J4 ) = ZERO DN = Z( J4P2+2 ) DMIN = DN EMIN = ZERO ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. $ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN TEMP = Z( J4P2+2 ) / Z( J4-2 ) Z( J4 ) = Z( J4P2 )*TEMP DN = DNM1*TEMP ELSE Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) END IF DMIN = MIN( DMIN, DN ) * Z( J4+2 ) = DN Z( 4*N0-PP ) = EMIN RETURN * * End of DLASQ6 * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zlartg.f0000644000000000000000000000013214061636515015327 xustar0030 mtime=1623670093.461103841 30 atime=1623670093.461103841 30 ctime=1623670093.461103841 elk-7.2.42/src/LAPACK/zlartg.f0000644002504400250440000001632214061636515017370 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZLARTG generates a plane rotation with real cosine and complex sine. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLARTG + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZLARTG( F, G, CS, SN, R ) * * .. Scalar Arguments .. * DOUBLE PRECISION CS * COMPLEX*16 F, G, R, SN * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLARTG generates a plane rotation so that *> *> [ CS SN ] [ F ] [ R ] *> [ __ ] . [ ] = [ ] where CS**2 + |SN|**2 = 1. *> [ -SN CS ] [ G ] [ 0 ] *> *> This is a faster version of the BLAS1 routine ZROTG, except for *> the following differences: *> F and G are unchanged on return. *> If G=0, then CS=1 and SN=0. *> If F=0, then CS=0 and SN is chosen so that R is real. *> \endverbatim * * Arguments: * ========== * *> \param[in] F *> \verbatim *> F is COMPLEX*16 *> The first component of vector to be rotated. *> \endverbatim *> *> \param[in] G *> \verbatim *> G is COMPLEX*16 *> The second component of vector to be rotated. *> \endverbatim *> *> \param[out] CS *> \verbatim *> CS is DOUBLE PRECISION *> The cosine of the rotation. *> \endverbatim *> *> \param[out] SN *> \verbatim *> SN is COMPLEX*16 *> The sine of the rotation. *> \endverbatim *> *> \param[out] R *> \verbatim *> R is COMPLEX*16 *> The nonzero component of the rotated vector. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * *> \par Further Details: * ===================== *> *> \verbatim *> *> 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel *> *> This version has a few statements commented out for thread safety *> (machine parameters are computed on each entry). 10 feb 03, SJH. *> \endverbatim *> * ===================================================================== SUBROUTINE ZLARTG( F, G, CS, SN, R ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. DOUBLE PRECISION CS COMPLEX*16 F, G, R, SN * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION TWO, ONE, ZERO PARAMETER ( TWO = 2.0D+0, ONE = 1.0D+0, ZERO = 0.0D+0 ) COMPLEX*16 CZERO PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. * LOGICAL FIRST INTEGER COUNT, I DOUBLE PRECISION D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN, $ SAFMN2, SAFMX2, SCALE COMPLEX*16 FF, FS, GS * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLAPY2 LOGICAL DISNAN EXTERNAL DLAMCH, DLAPY2, DISNAN * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, LOG, $ MAX, SQRT * .. * .. Statement Functions .. DOUBLE PRECISION ABS1, ABSSQ * .. * .. Statement Function definitions .. ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) ) ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2 * .. * .. Executable Statements .. * SAFMIN = DLAMCH( 'S' ) EPS = DLAMCH( 'E' ) SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / $ LOG( DLAMCH( 'B' ) ) / TWO ) SAFMX2 = ONE / SAFMN2 SCALE = MAX( ABS1( F ), ABS1( G ) ) FS = F GS = G COUNT = 0 IF( SCALE.GE.SAFMX2 ) THEN 10 CONTINUE COUNT = COUNT + 1 FS = FS*SAFMN2 GS = GS*SAFMN2 SCALE = SCALE*SAFMN2 IF( SCALE.GE.SAFMX2 ) $ GO TO 10 ELSE IF( SCALE.LE.SAFMN2 ) THEN IF( G.EQ.CZERO.OR.DISNAN( ABS( G ) ) ) THEN CS = ONE SN = CZERO R = F RETURN END IF 20 CONTINUE COUNT = COUNT - 1 FS = FS*SAFMX2 GS = GS*SAFMX2 SCALE = SCALE*SAFMX2 IF( SCALE.LE.SAFMN2 ) $ GO TO 20 END IF F2 = ABSSQ( FS ) G2 = ABSSQ( GS ) IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN * * This is a rare case: F is very small. * IF( F.EQ.CZERO ) THEN CS = ZERO R = DLAPY2( DBLE( G ), DIMAG( G ) ) * Do complex/real division explicitly with two real divisions D = DLAPY2( DBLE( GS ), DIMAG( GS ) ) SN = DCMPLX( DBLE( GS ) / D, -DIMAG( GS ) / D ) RETURN END IF F2S = DLAPY2( DBLE( FS ), DIMAG( FS ) ) * G2 and G2S are accurate * G2 is at least SAFMIN, and G2S is at least SAFMN2 G2S = SQRT( G2 ) * Error in CS from underflow in F2S is at most * UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS * If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN, * and so CS .lt. sqrt(SAFMIN) * If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN * and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS) * Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S CS = F2S / G2S * Make sure abs(FF) = 1 * Do complex/real division explicitly with 2 real divisions IF( ABS1( F ).GT.ONE ) THEN D = DLAPY2( DBLE( F ), DIMAG( F ) ) FF = DCMPLX( DBLE( F ) / D, DIMAG( F ) / D ) ELSE DR = SAFMX2*DBLE( F ) DI = SAFMX2*DIMAG( F ) D = DLAPY2( DR, DI ) FF = DCMPLX( DR / D, DI / D ) END IF SN = FF*DCMPLX( DBLE( GS ) / G2S, -DIMAG( GS ) / G2S ) R = CS*F + SN*G ELSE * * This is the most common case. * Neither F2 nor F2/G2 are less than SAFMIN * F2S cannot overflow, and it is accurate * F2S = SQRT( ONE+G2 / F2 ) * Do the F2S(real)*FS(complex) multiply with two real multiplies R = DCMPLX( F2S*DBLE( FS ), F2S*DIMAG( FS ) ) CS = ONE / F2S D = F2 + G2 * Do complex/real division explicitly with two real divisions SN = DCMPLX( DBLE( R ) / D, DIMAG( R ) / D ) SN = SN*DCONJG( GS ) IF( COUNT.NE.0 ) THEN IF( COUNT.GT.0 ) THEN DO 30 I = 1, COUNT R = R*SAFMX2 30 CONTINUE ELSE DO 40 I = 1, -COUNT R = R*SAFMN2 40 CONTINUE END IF END IF END IF RETURN * * End of ZLARTG * END elk-7.2.42/src/LAPACK/PaxHeaders.21776/zrot.f0000644000000000000000000000012714061636515015026 xustar0029 mtime=1623670093.46310384 29 atime=1623670093.46310384 29 ctime=1623670093.46310384 elk-7.2.42/src/LAPACK/zrot.f0000644002504400250440000001013414061636515017056 0ustar00dewhurstdewhurst00000000000000*> \brief \b ZROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZROT + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZROT( N, CX, INCX, CY, INCY, C, S ) * * .. Scalar Arguments .. * INTEGER INCX, INCY, N * DOUBLE PRECISION C * COMPLEX*16 S * .. * .. Array Arguments .. * COMPLEX*16 CX( * ), CY( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZROT applies a plane rotation, where the cos (C) is real and the *> sin (S) is complex, and the vectors CX and CY are complex. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The number of elements in the vectors CX and CY. *> \endverbatim *> *> \param[in,out] CX *> \verbatim *> CX is COMPLEX*16 array, dimension (N) *> On input, the vector X. *> On output, CX is overwritten with C*X + S*Y. *> \endverbatim *> *> \param[in] INCX *> \verbatim *> INCX is INTEGER *> The increment between successive values of CY. INCX <> 0. *> \endverbatim *> *> \param[in,out] CY *> \verbatim *> CY is COMPLEX*16 array, dimension (N) *> On input, the vector Y. *> On output, CY is overwritten with -CONJG(S)*X + C*Y. *> \endverbatim *> *> \param[in] INCY *> \verbatim *> INCY is INTEGER *> The increment between successive values of CY. INCX <> 0. *> \endverbatim *> *> \param[in] C *> \verbatim *> C is DOUBLE PRECISION *> \endverbatim *> *> \param[in] S *> \verbatim *> S is COMPLEX*16 *> C and S define a rotation *> [ C S ] *> [ -conjg(S) C ] *> where C*C + S*CONJG(S) = 1.0. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16OTHERauxiliary * * ===================================================================== SUBROUTINE ZROT( N, CX, INCX, CY, INCY, C, S ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INCX, INCY, N DOUBLE PRECISION C COMPLEX*16 S * .. * .. Array Arguments .. COMPLEX*16 CX( * ), CY( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, IX, IY COMPLEX*16 STEMP * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. Executable Statements .. * IF( N.LE.0 ) $ RETURN IF( INCX.EQ.1 .AND. INCY.EQ.1 ) $ GO TO 20 * * Code for unequal increments or equal increments not equal to 1 * IX = 1 IY = 1 IF( INCX.LT.0 ) $ IX = ( -N+1 )*INCX + 1 IF( INCY.LT.0 ) $ IY = ( -N+1 )*INCY + 1 DO 10 I = 1, N STEMP = C*CX( IX ) + S*CY( IY ) CY( IY ) = C*CY( IY ) - DCONJG( S )*CX( IX ) CX( IX ) = STEMP IX = IX + INCX IY = IY + INCY 10 CONTINUE RETURN * * Code for both increments equal to 1 * 20 CONTINUE DO 30 I = 1, N STEMP = C*CX( I ) + S*CY( I ) CY( I ) = C*CY( I ) - DCONJG( S )*CX( I ) CX( I ) = STEMP 30 CONTINUE RETURN END elk-7.2.42/src/LAPACK/PaxHeaders.21776/dlaed6.f0000644000000000000000000000013214061636515015163 xustar0030 mtime=1623670093.465103838 30 atime=1623670093.464103839 30 ctime=1623670093.465103838 elk-7.2.42/src/LAPACK/dlaed6.f0000644002504400250440000002655314061636515017233 0ustar00dewhurstdewhurst00000000000000*> \brief \b DLAED6 used by sstedc. Computes one Newton step in solution of the secular equation. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAED6 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO ) * * .. Scalar Arguments .. * LOGICAL ORGATI * INTEGER INFO, KNITER * DOUBLE PRECISION FINIT, RHO, TAU * .. * .. Array Arguments .. * DOUBLE PRECISION D( 3 ), Z( 3 ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAED6 computes the positive or negative root (closest to the origin) *> of *> z(1) z(2) z(3) *> f(x) = rho + --------- + ---------- + --------- *> d(1)-x d(2)-x d(3)-x *> *> It is assumed that *> *> if ORGATI = .true. the root is between d(2) and d(3); *> otherwise it is between d(1) and d(2) *> *> This routine will be called by DLAED4 when necessary. In most cases, *> the root sought is the smallest in magnitude, though it might not be *> in some extremely rare situations. *> \endverbatim * * Arguments: * ========== * *> \param[in] KNITER *> \verbatim *> KNITER is INTEGER *> Refer to DLAED4 for its significance. *> \endverbatim *> *> \param[in] ORGATI *> \verbatim *> ORGATI is LOGICAL *> If ORGATI is true, the needed root is between d(2) and *> d(3); otherwise it is between d(1) and d(2). See *> DLAED4 for further details. *> \endverbatim *> *> \param[in] RHO *> \verbatim *> RHO is DOUBLE PRECISION *> Refer to the equation f(x) above. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (3) *> D satisfies d(1) < d(2) < d(3). *> \endverbatim *> *> \param[in] Z *> \verbatim *> Z is DOUBLE PRECISION array, dimension (3) *> Each of the elements in z must be positive. *> \endverbatim *> *> \param[in] FINIT *> \verbatim *> FINIT is DOUBLE PRECISION *> The value of f at 0. It is more accurate than the one *> evaluated inside this routine (if someone wants to do *> so). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is DOUBLE PRECISION *> The root of the equation f(x). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = 1, failure to converge *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup auxOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> 10/02/03: This version has a few statements commented out for thread *> safety (machine parameters are computed on each entry). SJH. *> *> 05/10/06: Modified from a new version of Ren-Cang Li, use *> Gragg-Thornton-Warner cubic convergent scheme for better stability. *> \endverbatim * *> \par Contributors: * ================== *> *> Ren-Cang Li, Computer Science Division, University of California *> at Berkeley, USA *> * ===================================================================== SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. LOGICAL ORGATI INTEGER INFO, KNITER DOUBLE PRECISION FINIT, RHO, TAU * .. * .. Array Arguments .. DOUBLE PRECISION D( 3 ), Z( 3 ) * .. * * ===================================================================== * * .. Parameters .. INTEGER MAXIT PARAMETER ( MAXIT = 40 ) DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, EIGHT PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ THREE = 3.0D0, FOUR = 4.0D0, EIGHT = 8.0D0 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. Local Arrays .. DOUBLE PRECISION DSCALE( 3 ), ZSCALE( 3 ) * .. * .. Local Scalars .. LOGICAL SCALE INTEGER I, ITER, NITER DOUBLE PRECISION A, B, BASE, C, DDF, DF, EPS, ERRETM, ETA, F, $ FC, SCLFAC, SCLINV, SMALL1, SMALL2, SMINV1, $ SMINV2, TEMP, TEMP1, TEMP2, TEMP3, TEMP4, $ LBD, UBD * .. * .. Intrinsic Functions .. INTRINSIC ABS, INT, LOG, MAX, MIN, SQRT * .. * .. Executable Statements .. * INFO = 0 * IF( ORGATI ) THEN LBD = D(2) UBD = D(3) ELSE LBD = D(1) UBD = D(2) END IF IF( FINIT .LT. ZERO )THEN LBD = ZERO ELSE UBD = ZERO END IF * NITER = 1 TAU = ZERO IF( KNITER.EQ.2 ) THEN IF( ORGATI ) THEN TEMP = ( D( 3 )-D( 2 ) ) / TWO C = RHO + Z( 1 ) / ( ( D( 1 )-D( 2 ) )-TEMP ) A = C*( D( 2 )+D( 3 ) ) + Z( 2 ) + Z( 3 ) B = C*D( 2 )*D( 3 ) + Z( 2 )*D( 3 ) + Z( 3 )*D( 2 ) ELSE TEMP = ( D( 1 )-D( 2 ) ) / TWO C = RHO + Z( 3 ) / ( ( D( 3 )-D( 2 ) )-TEMP ) A = C*( D( 1 )+D( 2 ) ) + Z( 1 ) + Z( 2 ) B = C*D( 1 )*D( 2 ) + Z( 1 )*D( 2 ) + Z( 2 )*D( 1 ) END IF TEMP = MAX( ABS( A ), ABS( B ), ABS( C ) ) A = A / TEMP B = B / TEMP C = C / TEMP IF( C.EQ.ZERO ) THEN TAU = B / A ELSE IF( A.LE.ZERO ) THEN TAU = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) ELSE TAU = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) END IF IF( TAU .LT. LBD .OR. TAU .GT. UBD ) $ TAU = ( LBD+UBD )/TWO IF( D(1).EQ.TAU .OR. D(2).EQ.TAU .OR. D(3).EQ.TAU ) THEN TAU = ZERO ELSE TEMP = FINIT + TAU*Z(1)/( D(1)*( D( 1 )-TAU ) ) + $ TAU*Z(2)/( D(2)*( D( 2 )-TAU ) ) + $ TAU*Z(3)/( D(3)*( D( 3 )-TAU ) ) IF( TEMP .LE. ZERO )THEN LBD = TAU ELSE UBD = TAU END IF IF( ABS( FINIT ).LE.ABS( TEMP ) ) $ TAU = ZERO END IF END IF * * get machine parameters for possible scaling to avoid overflow * * modified by Sven: parameters SMALL1, SMINV1, SMALL2, * SMINV2, EPS are not SAVEd anymore between one call to the * others but recomputed at each call * EPS = DLAMCH( 'Epsilon' ) BASE = DLAMCH( 'Base' ) SMALL1 = BASE**( INT( LOG( DLAMCH( 'SafMin' ) ) / LOG( BASE ) / $ THREE ) ) SMINV1 = ONE / SMALL1 SMALL2 = SMALL1*SMALL1 SMINV2 = SMINV1*SMINV1 * * Determine if scaling of inputs necessary to avoid overflow * when computing 1/TEMP**3 * IF( ORGATI ) THEN TEMP = MIN( ABS( D( 2 )-TAU ), ABS( D( 3 )-TAU ) ) ELSE TEMP = MIN( ABS( D( 1 )-TAU ), ABS( D( 2 )-TAU ) ) END IF SCALE = .FALSE. IF( TEMP.LE.SMALL1 ) THEN SCALE = .TRUE. IF( TEMP.LE.SMALL2 ) THEN * * Scale up by power of radix nearest 1/SAFMIN**(2/3) * SCLFAC = SMINV2 SCLINV = SMALL2 ELSE * * Scale up by power of radix nearest 1/SAFMIN**(1/3) * SCLFAC = SMINV1 SCLINV = SMALL1 END IF * * Scaling up safe because D, Z, TAU scaled elsewhere to be O(1) * DO 10 I = 1, 3 DSCALE( I ) = D( I )*SCLFAC ZSCALE( I ) = Z( I )*SCLFAC 10 CONTINUE TAU = TAU*SCLFAC LBD = LBD*SCLFAC UBD = UBD*SCLFAC ELSE * * Copy D and Z to DSCALE and ZSCALE * DO 20 I = 1, 3 DSCALE( I ) = D( I ) ZSCALE( I ) = Z( I ) 20 CONTINUE END IF * FC = ZERO DF = ZERO DDF = ZERO DO 30 I = 1, 3 TEMP = ONE / ( DSCALE( I )-TAU ) TEMP1 = ZSCALE( I )*TEMP TEMP2 = TEMP1*TEMP TEMP3 = TEMP2*TEMP FC = FC + TEMP1 / DSCALE( I ) DF = DF + TEMP2 DDF = DDF + TEMP3 30 CONTINUE F = FINIT + TAU*FC * IF( ABS( F ).LE.ZERO ) $ GO TO 60 IF( F .LE. ZERO )THEN LBD = TAU ELSE UBD = TAU END IF * * Iteration begins -- Use Gragg-Thornton-Warner cubic convergent * scheme * * It is not hard to see that * * 1) Iterations will go up monotonically * if FINIT < 0; * * 2) Iterations will go down monotonically * if FINIT > 0. * ITER = NITER + 1 * DO 50 NITER = ITER, MAXIT * IF( ORGATI ) THEN TEMP1 = DSCALE( 2 ) - TAU TEMP2 = DSCALE( 3 ) - TAU ELSE TEMP1 = DSCALE( 1 ) - TAU TEMP2 = DSCALE( 2 ) - TAU END IF A = ( TEMP1+TEMP2 )*F - TEMP1*TEMP2*DF B = TEMP1*TEMP2*F C = F - ( TEMP1+TEMP2 )*DF + TEMP1*TEMP2*DDF TEMP = MAX( ABS( A ), ABS( B ), ABS( C ) ) A = A / TEMP B = B / TEMP C = C / TEMP IF( C.EQ.ZERO ) THEN ETA = B / A ELSE IF( A.LE.ZERO ) THEN ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) ELSE ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) END IF IF( F*ETA.GE.ZERO ) THEN ETA = -F / DF END IF * TAU = TAU + ETA IF( TAU .LT. LBD .OR. TAU .GT. UBD ) $ TAU = ( LBD + UBD )/TWO * FC = ZERO ERRETM = ZERO DF = ZERO DDF = ZERO DO 40 I = 1, 3 IF ( ( DSCALE( I )-TAU ).NE.ZERO ) THEN TEMP = ONE / ( DSCALE( I )-TAU ) TEMP1 = ZSCALE( I )*TEMP TEMP2 = TEMP1*TEMP TEMP3 = TEMP2*TEMP TEMP4 = TEMP1 / DSCALE( I ) FC = FC + TEMP4 ERRETM = ERRETM + ABS( TEMP4 ) DF = DF + TEMP2 DDF = DDF + TEMP3 ELSE GO TO 60 END IF 40 CONTINUE F = FINIT + TAU*FC ERRETM = EIGHT*( ABS( FINIT )+ABS( TAU )*ERRETM ) + $ ABS( TAU )*DF IF( ( ABS( F ).LE.FOUR*EPS*ERRETM ) .OR. $ ( (UBD-LBD).LE.FOUR*EPS*ABS(TAU) ) ) $ GO TO 60 IF( F .LE. ZERO )THEN LBD = TAU ELSE UBD = TAU END IF 50 CONTINUE INFO = 1 60 CONTINUE * * Undo scaling * IF( SCALE ) $ TAU = TAU*SCLINV RETURN * * End of DLAED6 * END elk-7.2.42/src/PaxHeaders.21776/fftlib0000644000000000000000000000013214061636515014113 xustar0030 mtime=1623670093.474103829 30 atime=1623670093.471103832 30 ctime=1623670093.474103829 elk-7.2.42/src/fftlib/0000755002504400250440000000000014061636515016225 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/src/fftlib/PaxHeaders.21776/Makefile0000644000000000000000000000012714061636515015634 xustar0029 mtime=1623670093.47310383 29 atime=1623670093.47310383 29 ctime=1623670093.47310383 elk-7.2.42/src/fftlib/Makefile0000644002504400250440000000107514061636515017670 0ustar00dewhurstdewhurst00000000000000 AR = ar include ../../make.inc #------------------------------------------------------------------------------- # Suffix Rules #------------------------------------------------------------------------------- .SUFFIXES: .o .f90 .f90.o: $(F90) $(F90_OPTS) -c $< #------------------------------------------------------------------------------- # File dependencies #------------------------------------------------------------------------------- SRC = cfftnd.f90 OBJ = $(SRC:.f90=.o) fftlib: $(OBJ) $(AR) -rc fftlib.a $(OBJ) clean: rm -f *.o *.mod *~ *.a ifc* *.gcno elk-7.2.42/src/fftlib/PaxHeaders.21776/cfftnd.f900000644000000000000000000000013214061636515015754 xustar0030 mtime=1623670093.475103829 30 atime=1623670093.474103829 30 ctime=1623670093.475103829 elk-7.2.42/src/fftlib/cfftnd.f900000644002504400250440000016417414061636515020026 0ustar00dewhurstdewhurst00000000000000module fftpack5 integer, parameter :: prec=kind(1.d0) end module subroutine cfftnd(nd,n,sgn,c) ! ! DESCRIPTION: ! In-place fast Fourier transform for complex arrays in $n_d$ dimensions. The ! forward transform is scaled by one over the size of the array. Uses a ! modified version of the FFTPACK5 library. ! ! INPUT/OUTPUT PARAMETERS: ! nd : number of dimensions (in,integer) ! n : mesh size (in,integer(nd)) ! sgn : FFT direction, -1: forward, 1: backward (in,integer) ! c : array to transform (inout,complex(n(1)*n(2)*...*n(nd))) ! ! Copyright (C) 2005 J. K. Dewhurst ! Distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! use fftpack5 implicit none ! arguments integer, intent(in) :: nd integer, intent(in) :: n(nd) integer, intent(in) :: sgn complex(prec), intent(inout) :: c(*) ! local variables integer i,j,k,l,p,q,iw,iw1,ni integer lensav,lenwrk ! allocatable arrays real(prec), allocatable :: wsave(:) real(prec), allocatable :: work(:) if (nd.le.0) then write(*,*) write(*,'("Error(cfftnd): invalid number of dimensions : ",I8)') nd write(*,*) stop end if p=1 lensav=1 do i=1,nd if (n(i).le.0) then write(*,*) write(*,'("Error(cfftnd): invalid n : ",I8)') n(i) write(*,'(" for dimension ",I4)') i write(*,*) stop end if p=p*n(i) lensav=max(lensav,2*n(i)+int(log(real(n(i),prec)))+4) end do lenwrk=2*p allocate(wsave(lensav)) allocate(work(lenwrk)) if (sgn.gt.0) then q=1 do i=1,nd ni=n(i) if (ni.gt.1) then iw=ni+ni+1 iw1=iw+1 p=p/ni call cfftmi(ni,wsave,lensav) j=1 k=q*ni do l=1,p call cmfm1b(q,1,ni,q,c(j),work,wsave,wsave(iw),wsave(iw1)) j=j+k end do q=k end if end do else q=1 do i=1,nd ni=n(i) if (ni.gt.1) then iw=ni+ni+1 iw1=iw+1 p=p/ni call cfftmi(ni,wsave,lensav) j=1 k=q*ni do l=1,p call cmfm1f(q,1,ni,q,c(j),work,wsave,wsave(iw),wsave(iw1)) j=j+k end do q=k end if end do end if deallocate(wsave,work) return end subroutine subroutine cfftmi ( n, wsave, lensav ) !******************************************************************************* ! !! CFFTMI: initialization for CFFTMB and CFFTMF. ! ! Discussion: ! ! CFFTMI initializes array WSAVE for use in its companion routines ! CFFTMB and CFFTMF. CFFTMI must be called before the first call ! to CFFTMB or CFFTMF, and after whenever the value of integer N changes. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Modified: ! ! 24 March 2005 ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! ! Input, integer N, the length of each sequence to be transformed. ! The transform is most efficient when N is a product of small primes. ! ! Input, integer LENSAV, the dimension of the WSAVE array. LENSAV must be ! at least 2*N + INT(LOG(REAL(N))) + 4. ! ! Output, real WSAVE(LENSAV), containing the prime factors of N and ! also containing certain trigonometric values which will be used in ! routines CFFTMB or CFFTMF. ! ! use fftpack5 implicit none integer lensav integer iw1 integer n real(prec) wsave(lensav) if ( n == 1 ) then return end if iw1 = n + n + 1 call mcfti1 ( n, wsave, wsave(iw1), wsave(iw1+1) ) return end subroutine mcfti1 ( n, wa, fnf, fac ) !******************************************************************************* ! !! MCFTI1 is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none real(prec) fac(*) real(prec) fnf integer ido integer ip integer iw integer k1 integer l1 integer l2 integer n integer nf real(prec) wa(*) ! ! Get the factorization of N. ! call factor ( n, nf, fac ) fnf = real ( nf, prec ) iw = 1 l1 = 1 ! ! Set up the trigonometric tables. ! do k1 = 1, nf ip = int ( fac(k1) ) l2 = l1 * ip ido = n / l2 call tables ( ido, ip, wa(iw) ) iw = iw + ( ip - 1 ) * ( ido + ido ) l1 = l2 end do return end subroutine factor ( n, nf, fac ) !******************************************************************************* ! !! FACTOR determines the factors of an integer. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Modified: ! ! 28 March 2005 ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! ! Input, integer N, the number for which factorization and other information ! is needed. ! ! Output, integer NF, the number of factors. ! ! Output, real FAC(*), a list of factors of N. ! use fftpack5 implicit none real(prec) fac(*) integer j integer n integer nf integer nl integer nq integer nr integer ntry nl = n nf = 0 j = 0 do while ( 1 < nl ) j = j + 1 if ( j == 1 ) then ntry = 4 else if ( j == 2 ) then ntry = 2 else if ( j == 3 ) then ntry = 3 else if ( j == 4 ) then ntry = 5 else ntry = ntry + 2 end if do nq = nl / ntry nr = nl - ntry * nq if ( nr /= 0 ) then exit end if nf = nf + 1 fac(nf) = ntry nl = nq end do end do return end subroutine tables ( ido, ip, wa ) !******************************************************************************* ! !! TABLES computes trigonometric tables needed by the FFT routines. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer ip real(prec) arg1 real(prec) arg2 real(prec) arg3 real(prec) arg4 real(prec) argz integer i integer j real(prec) tpi real(prec) wa(ido,ip-1,2) tpi = 8.0E+00_prec * atan ( 1.0E+00_prec ) argz = tpi / real ( ip, prec ) arg1 = tpi / real ( ido * ip, prec ) do j = 2, ip arg2 = real ( j - 1, prec ) * arg1 do i = 1, ido arg3 = real ( i - 1, prec ) * arg2 wa(i,j-1,1) = cos ( arg3 ) wa(i,j-1,2) = sin ( arg3 ) end do if ( 5 < ip ) then arg4 = real ( j - 1, prec ) * argz wa(1,j-1,1) = cos ( arg4 ) wa(1,j-1,2) = sin ( arg4 ) end if end do return end subroutine cmfm1b ( lot, jump, n, inc, c, ch, wa, fnf, fac ) !******************************************************************************* ! !! CMFM1B is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none complex(prec) c(*) real(prec) ch(*) real(prec) fac(*) real(prec) fnf integer ido integer inc integer ip integer iw integer jump integer k1 integer l1 integer l2 integer lid integer lot integer n integer na integer nbr integer nf real(prec) wa(*) nf = int ( fnf ) na = 0 l1 = 1 iw = 1 do k1 = 1, nf ip = int ( fac(k1) ) l2 = ip * l1 ido = n / l2 lid = l1 * ido nbr = 1 + na + 2 * min ( ip - 2, 4 ) if ( nbr == 1 ) then call cmf2kb ( lot, ido, l1, na, c, jump, inc, ch, 1, lot, wa(iw) ) else if ( nbr == 2 ) then call cmf2kb ( lot, ido, l1, na, ch, 1, lot, c, jump, inc, wa(iw) ) else if ( nbr == 3 ) then call cmf3kb ( lot, ido, l1, na, c, jump, inc, ch, 1, lot, wa(iw) ) else if ( nbr == 4 ) then call cmf3kb ( lot, ido, l1, na, ch, 1, lot, c, jump, inc, wa(iw) ) else if ( nbr == 5 ) then call cmf4kb ( lot, ido, l1, na, c, jump, inc, ch, 1, lot, wa(iw) ) else if ( nbr == 6 ) then call cmf4kb ( lot, ido, l1, na, ch, 1, lot, c, jump, inc, wa(iw) ) else if ( nbr == 7 ) then call cmf5kb ( lot, ido, l1, na, c, jump, inc, ch, 1, lot, wa(iw) ) else if ( nbr == 8 ) then call cmf5kb ( lot, ido, l1, na, ch, 1, lot, c, jump, inc, wa(iw) ) else if ( nbr == 9 ) then call cmfgkb ( lot, ido, ip, l1, lid, na, c, c, jump, inc, ch, ch, & 1, lot, wa(iw) ) else if ( nbr == 10 ) then call cmfgkb ( lot, ido, ip, l1, lid, na, ch, ch, 1, lot, c, c, & jump, inc, wa(iw) ) end if l1 = l2 iw = iw + ( ip - 1 ) * ( ido + ido ) if ( ip <= 5 ) then na = 1 - na end if end do return end subroutine cmfm1f ( lot, jump, n, inc, c, ch, wa, fnf, fac ) !******************************************************************************* ! !! CMFM1F is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none complex(prec) c(*) real(prec) ch(*) real(prec) fac(*) real(prec) fnf integer ido integer inc integer ip integer iw integer jump integer k1 integer l1 integer l2 integer lid integer lot integer n integer na integer nbr integer nf real(prec) wa(*) nf = int ( fnf ) na = 0 l1 = 1 iw = 1 do k1 = 1, nf ip = int ( fac(k1) ) l2 = ip * l1 ido = n / l2 lid = l1 * ido nbr = 1 + na + 2 * min ( ip - 2, 4 ) if ( nbr == 1 ) then call cmf2kf ( lot, ido, l1, na, c, jump, inc, ch, 1, lot, wa(iw) ) else if ( nbr == 2 ) then call cmf2kf ( lot, ido, l1, na, ch, 1, lot, c, jump, inc, wa(iw) ) else if ( nbr == 3 ) then call cmf3kf ( lot, ido, l1, na, c, jump, inc, ch, 1, lot, wa(iw) ) else if ( nbr == 4 ) then call cmf3kf ( lot, ido, l1, na, ch, 1, lot, c, jump, inc, wa(iw) ) else if ( nbr == 5 ) then call cmf4kf ( lot, ido, l1, na, c, jump, inc, ch, 1, lot, wa(iw) ) else if ( nbr == 6 ) then call cmf4kf ( lot, ido, l1, na, ch, 1, lot, c, jump, inc, wa(iw) ) else if ( nbr == 7 ) then call cmf5kf ( lot, ido, l1, na, c, jump, inc, ch, 1, lot, wa(iw) ) else if ( nbr == 8 ) then call cmf5kf ( lot, ido, l1, na, ch, 1, lot, c, jump, inc, wa(iw) ) else if ( nbr == 9 ) then call cmfgkf ( lot, ido, ip, l1, lid, na, c, c, jump, inc, ch, ch, & 1, lot, wa(iw) ) else if ( nbr == 10 ) then call cmfgkf ( lot, ido, ip, l1, lid, na, ch, ch, 1, lot, c, c, & jump, inc, wa(iw) ) end if l1 = l2 iw = iw + ( ip - 1 ) * ( ido + ido ) if ( ip <= 5 ) then na = 1 - na end if end do return end subroutine cmf2kb ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa ) !******************************************************************************* ! !! CMF2KB is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer l1 real(prec) cc(2,in1,l1,ido,2) real(prec) ch(2,in2,l1,2,ido) real(prec) chold1 real(prec) chold2 integer i integer im1 integer im2 integer k integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) ti2 real(prec) tr2 real(prec) wa(ido,1,2) m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 if ( 1 < ido .or. na == 1 ) then do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch(1,m2,k,1,1) = cc(1,m1,k,1,1) + cc(1,m1,k,1,2) ch(1,m2,k,2,1) = cc(1,m1,k,1,1) - cc(1,m1,k,1,2) ch(2,m2,k,1,1) = cc(2,m1,k,1,1) + cc(2,m1,k,1,2) ch(2,m2,k,2,1) = cc(2,m1,k,1,1) - cc(2,m1,k,1,2) end do end do do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch(1,m2,k,1,i) = cc(1,m1,k,i,1)+cc(1,m1,k,i,2) tr2 = cc(1,m1,k,i,1)-cc(1,m1,k,i,2) ch(2,m2,k,1,i) = cc(2,m1,k,i,1)+cc(2,m1,k,i,2) ti2 = cc(2,m1,k,i,1)-cc(2,m1,k,i,2) ch(2,m2,k,2,i) = wa(i,1,1)*ti2+wa(i,1,2)*tr2 ch(1,m2,k,2,i) = wa(i,1,1)*tr2-wa(i,1,2)*ti2 end do end do end do else do k = 1, l1 do m1 = 1, m1d, im1 chold1 = cc(1,m1,k,1,1) + cc(1,m1,k,1,2) cc(1,m1,k,1,2) = cc(1,m1,k,1,1) - cc(1,m1,k,1,2) cc(1,m1,k,1,1) = chold1 chold2 = cc(2,m1,k,1,1) + cc(2,m1,k,1,2) cc(2,m1,k,1,2) = cc(2,m1,k,1,1) - cc(2,m1,k,1,2) cc(2,m1,k,1,1) = chold2 end do end do end if return end subroutine cmf2kf ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa ) !******************************************************************************* ! !! CMF2KF is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer l1 real(prec) cc(2,in1,l1,ido,2) real(prec) ch(2,in2,l1,2,ido) real(prec) chold1 real(prec) chold2 integer i integer im1 integer im2 integer k integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) sn real(prec) ti2 real(prec) tr2 real(prec) wa(ido,1,2) m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 if ( 1 < ido ) then do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch(1,m2,k,1,1) = cc(1,m1,k,1,1)+cc(1,m1,k,1,2) ch(1,m2,k,2,1) = cc(1,m1,k,1,1)-cc(1,m1,k,1,2) ch(2,m2,k,1,1) = cc(2,m1,k,1,1)+cc(2,m1,k,1,2) ch(2,m2,k,2,1) = cc(2,m1,k,1,1)-cc(2,m1,k,1,2) end do end do do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch(1,m2,k,1,i) = cc(1,m1,k,i,1)+cc(1,m1,k,i,2) tr2 = cc(1,m1,k,i,1)-cc(1,m1,k,i,2) ch(2,m2,k,1,i) = cc(2,m1,k,i,1)+cc(2,m1,k,i,2) ti2 = cc(2,m1,k,i,1)-cc(2,m1,k,i,2) ch(2,m2,k,2,i) = wa(i,1,1)*ti2-wa(i,1,2)*tr2 ch(1,m2,k,2,i) = wa(i,1,1)*tr2+wa(i,1,2)*ti2 end do end do end do else if ( na == 1 ) then sn = 1.0E+00_prec / real ( 2 * l1, prec ) do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch(1,m2,k,1,1) = sn * ( cc(1,m1,k,1,1) + cc(1,m1,k,1,2) ) ch(1,m2,k,2,1) = sn * ( cc(1,m1,k,1,1) - cc(1,m1,k,1,2) ) ch(2,m2,k,1,1) = sn * ( cc(2,m1,k,1,1) + cc(2,m1,k,1,2) ) ch(2,m2,k,2,1) = sn * ( cc(2,m1,k,1,1) - cc(2,m1,k,1,2) ) end do end do else sn = 1.0E+00_prec / real ( 2 * l1, prec ) do k = 1, l1 do m1 = 1, m1d, im1 chold1 = sn * ( cc(1,m1,k,1,1) + cc(1,m1,k,1,2) ) cc(1,m1,k,1,2) = sn * ( cc(1,m1,k,1,1) - cc(1,m1,k,1,2) ) cc(1,m1,k,1,1) = chold1 chold2 = sn * ( cc(2,m1,k,1,1) + cc(2,m1,k,1,2) ) cc(2,m1,k,1,2) = sn * ( cc(2,m1,k,1,1) - cc(2,m1,k,1,2) ) cc(2,m1,k,1,1) = chold2 end do end do end if return end subroutine cmf3kb ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa ) !******************************************************************************* ! !! CMF3KB is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer l1 real(prec) cc(2,in1,l1,ido,3) real(prec) ch(2,in2,l1,3,ido) real(prec) ci2 real(prec) ci3 real(prec) cr2 real(prec) cr3 real(prec) di2 real(prec) di3 real(prec) dr2 real(prec) dr3 integer i integer im1 integer im2 integer k integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec), parameter :: taui = 0.866025403784439E+00_prec real(prec), parameter :: taur = -0.5E+00_prec real(prec) ti2 real(prec) tr2 real(prec) wa(ido,2,2) m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 if ( 1 < ido .or. na == 1 ) then do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,3) cr2 = cc(1,m1,k,1,1)+taur*tr2 ch(1,m2,k,1,1) = cc(1,m1,k,1,1)+tr2 ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,3) ci2 = cc(2,m1,k,1,1)+taur*ti2 ch(2,m2,k,1,1) = cc(2,m1,k,1,1)+ti2 cr3 = taui * (cc(1,m1,k,1,2)-cc(1,m1,k,1,3)) ci3 = taui * (cc(2,m1,k,1,2)-cc(2,m1,k,1,3)) ch(1,m2,k,2,1) = cr2-ci3 ch(1,m2,k,3,1) = cr2+ci3 ch(2,m2,k,2,1) = ci2+cr3 ch(2,m2,k,3,1) = ci2-cr3 end do end do do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 tr2 = cc(1,m1,k,i,2)+cc(1,m1,k,i,3) cr2 = cc(1,m1,k,i,1)+taur*tr2 ch(1,m2,k,1,i) = cc(1,m1,k,i,1)+tr2 ti2 = cc(2,m1,k,i,2)+cc(2,m1,k,i,3) ci2 = cc(2,m1,k,i,1)+taur*ti2 ch(2,m2,k,1,i) = cc(2,m1,k,i,1)+ti2 cr3 = taui*(cc(1,m1,k,i,2)-cc(1,m1,k,i,3)) ci3 = taui*(cc(2,m1,k,i,2)-cc(2,m1,k,i,3)) dr2 = cr2-ci3 dr3 = cr2+ci3 di2 = ci2+cr3 di3 = ci2-cr3 ch(2,m2,k,2,i) = wa(i,1,1)*di2+wa(i,1,2)*dr2 ch(1,m2,k,2,i) = wa(i,1,1)*dr2-wa(i,1,2)*di2 ch(2,m2,k,3,i) = wa(i,2,1)*di3+wa(i,2,2)*dr3 ch(1,m2,k,3,i) = wa(i,2,1)*dr3-wa(i,2,2)*di3 end do end do end do else do k = 1, l1 do m1 = 1, m1d, im1 tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,3) cr2 = cc(1,m1,k,1,1)+taur*tr2 cc(1,m1,k,1,1) = cc(1,m1,k,1,1)+tr2 ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,3) ci2 = cc(2,m1,k,1,1)+taur*ti2 cc(2,m1,k,1,1) = cc(2,m1,k,1,1)+ti2 cr3 = taui*(cc(1,m1,k,1,2)-cc(1,m1,k,1,3)) ci3 = taui*(cc(2,m1,k,1,2)-cc(2,m1,k,1,3)) cc(1,m1,k,1,2) = cr2-ci3 cc(1,m1,k,1,3) = cr2+ci3 cc(2,m1,k,1,2) = ci2+cr3 cc(2,m1,k,1,3) = ci2-cr3 end do end do end if return end subroutine cmf3kf ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa ) !******************************************************************************* ! !! CMF3KF is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer l1 real(prec) cc(2,in1,l1,ido,3) real(prec) ch(2,in2,l1,3,ido) real(prec) ci2 real(prec) ci3 real(prec) cr2 real(prec) cr3 real(prec) di2 real(prec) di3 real(prec) dr2 real(prec) dr3 integer i integer im1 integer im2 integer k integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) sn real(prec), parameter :: taui = -0.866025403784439E+00_prec real(prec), parameter :: taur = -0.5E+00_prec real(prec) ti2 real(prec) tr2 real(prec) wa(ido,2,2) m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 if ( 1 < ido ) then do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,3) cr2 = cc(1,m1,k,1,1)+taur*tr2 ch(1,m2,k,1,1) = cc(1,m1,k,1,1)+tr2 ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,3) ci2 = cc(2,m1,k,1,1)+taur*ti2 ch(2,m2,k,1,1) = cc(2,m1,k,1,1)+ti2 cr3 = taui*(cc(1,m1,k,1,2)-cc(1,m1,k,1,3)) ci3 = taui*(cc(2,m1,k,1,2)-cc(2,m1,k,1,3)) ch(1,m2,k,2,1) = cr2-ci3 ch(1,m2,k,3,1) = cr2+ci3 ch(2,m2,k,2,1) = ci2+cr3 ch(2,m2,k,3,1) = ci2-cr3 end do end do do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 tr2 = cc(1,m1,k,i,2)+cc(1,m1,k,i,3) cr2 = cc(1,m1,k,i,1)+taur*tr2 ch(1,m2,k,1,i) = cc(1,m1,k,i,1)+tr2 ti2 = cc(2,m1,k,i,2)+cc(2,m1,k,i,3) ci2 = cc(2,m1,k,i,1)+taur*ti2 ch(2,m2,k,1,i) = cc(2,m1,k,i,1)+ti2 cr3 = taui*(cc(1,m1,k,i,2)-cc(1,m1,k,i,3)) ci3 = taui*(cc(2,m1,k,i,2)-cc(2,m1,k,i,3)) dr2 = cr2-ci3 dr3 = cr2+ci3 di2 = ci2+cr3 di3 = ci2-cr3 ch(2,m2,k,2,i) = wa(i,1,1)*di2-wa(i,1,2)*dr2 ch(1,m2,k,2,i) = wa(i,1,1)*dr2+wa(i,1,2)*di2 ch(2,m2,k,3,i) = wa(i,2,1)*di3-wa(i,2,2)*dr3 ch(1,m2,k,3,i) = wa(i,2,1)*dr3+wa(i,2,2)*di3 end do end do end do else if ( na == 1 ) then sn = 1.0E+00_prec / real ( 3 * l1, prec ) do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,3) cr2 = cc(1,m1,k,1,1)+taur*tr2 ch(1,m2,k,1,1) = sn*(cc(1,m1,k,1,1)+tr2) ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,3) ci2 = cc(2,m1,k,1,1)+taur*ti2 ch(2,m2,k,1,1) = sn*(cc(2,m1,k,1,1)+ti2) cr3 = taui*(cc(1,m1,k,1,2)-cc(1,m1,k,1,3)) ci3 = taui*(cc(2,m1,k,1,2)-cc(2,m1,k,1,3)) ch(1,m2,k,2,1) = sn*(cr2-ci3) ch(1,m2,k,3,1) = sn*(cr2+ci3) ch(2,m2,k,2,1) = sn*(ci2+cr3) ch(2,m2,k,3,1) = sn*(ci2-cr3) end do end do else sn = 1.0E+00_prec / real ( 3 * l1, prec ) do k = 1, l1 do m1 = 1, m1d, im1 tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,3) cr2 = cc(1,m1,k,1,1)+taur*tr2 cc(1,m1,k,1,1) = sn*(cc(1,m1,k,1,1)+tr2) ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,3) ci2 = cc(2,m1,k,1,1)+taur*ti2 cc(2,m1,k,1,1) = sn*(cc(2,m1,k,1,1)+ti2) cr3 = taui*(cc(1,m1,k,1,2)-cc(1,m1,k,1,3)) ci3 = taui*(cc(2,m1,k,1,2)-cc(2,m1,k,1,3)) cc(1,m1,k,1,2) = sn*(cr2-ci3) cc(1,m1,k,1,3) = sn*(cr2+ci3) cc(2,m1,k,1,2) = sn*(ci2+cr3) cc(2,m1,k,1,3) = sn*(ci2-cr3) end do end do end if return end subroutine cmf4kb ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa ) !******************************************************************************* ! !! CMF4KB is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer l1 real(prec) cc(2,in1,l1,ido,4) real(prec) ch(2,in2,l1,4,ido) real(prec) ci2 real(prec) ci3 real(prec) ci4 real(prec) cr2 real(prec) cr3 real(prec) cr4 integer i integer im1 integer im2 integer k integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) ti1 real(prec) ti2 real(prec) ti3 real(prec) ti4 real(prec) tr1 real(prec) tr2 real(prec) tr3 real(prec) tr4 real(prec) wa(ido,3,2) m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 if ( 1 < ido .or. na == 1 ) then do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti1 = cc(2,m1,k,1,1)-cc(2,m1,k,1,3) ti2 = cc(2,m1,k,1,1)+cc(2,m1,k,1,3) tr4 = cc(2,m1,k,1,4)-cc(2,m1,k,1,2) ti3 = cc(2,m1,k,1,2)+cc(2,m1,k,1,4) tr1 = cc(1,m1,k,1,1)-cc(1,m1,k,1,3) tr2 = cc(1,m1,k,1,1)+cc(1,m1,k,1,3) ti4 = cc(1,m1,k,1,2)-cc(1,m1,k,1,4) tr3 = cc(1,m1,k,1,2)+cc(1,m1,k,1,4) ch(1,m2,k,1,1) = tr2+tr3 ch(1,m2,k,3,1) = tr2-tr3 ch(2,m2,k,1,1) = ti2+ti3 ch(2,m2,k,3,1) = ti2-ti3 ch(1,m2,k,2,1) = tr1+tr4 ch(1,m2,k,4,1) = tr1-tr4 ch(2,m2,k,2,1) = ti1+ti4 ch(2,m2,k,4,1) = ti1-ti4 end do end do do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti1 = cc(2,m1,k,i,1)-cc(2,m1,k,i,3) ti2 = cc(2,m1,k,i,1)+cc(2,m1,k,i,3) ti3 = cc(2,m1,k,i,2)+cc(2,m1,k,i,4) tr4 = cc(2,m1,k,i,4)-cc(2,m1,k,i,2) tr1 = cc(1,m1,k,i,1)-cc(1,m1,k,i,3) tr2 = cc(1,m1,k,i,1)+cc(1,m1,k,i,3) ti4 = cc(1,m1,k,i,2)-cc(1,m1,k,i,4) tr3 = cc(1,m1,k,i,2)+cc(1,m1,k,i,4) ch(1,m2,k,1,i) = tr2+tr3 cr3 = tr2-tr3 ch(2,m2,k,1,i) = ti2+ti3 ci3 = ti2-ti3 cr2 = tr1+tr4 cr4 = tr1-tr4 ci2 = ti1+ti4 ci4 = ti1-ti4 ch(1,m2,k,2,i) = wa(i,1,1)*cr2-wa(i,1,2)*ci2 ch(2,m2,k,2,i) = wa(i,1,1)*ci2+wa(i,1,2)*cr2 ch(1,m2,k,3,i) = wa(i,2,1)*cr3-wa(i,2,2)*ci3 ch(2,m2,k,3,i) = wa(i,2,1)*ci3+wa(i,2,2)*cr3 ch(1,m2,k,4,i) = wa(i,3,1)*cr4-wa(i,3,2)*ci4 ch(2,m2,k,4,i) = wa(i,3,1)*ci4+wa(i,3,2)*cr4 end do end do end do else do k = 1, l1 do m1 = 1, m1d, im1 ti1 = cc(2,m1,k,1,1)-cc(2,m1,k,1,3) ti2 = cc(2,m1,k,1,1)+cc(2,m1,k,1,3) tr4 = cc(2,m1,k,1,4)-cc(2,m1,k,1,2) ti3 = cc(2,m1,k,1,2)+cc(2,m1,k,1,4) tr1 = cc(1,m1,k,1,1)-cc(1,m1,k,1,3) tr2 = cc(1,m1,k,1,1)+cc(1,m1,k,1,3) ti4 = cc(1,m1,k,1,2)-cc(1,m1,k,1,4) tr3 = cc(1,m1,k,1,2)+cc(1,m1,k,1,4) cc(1,m1,k,1,1) = tr2+tr3 cc(1,m1,k,1,3) = tr2-tr3 cc(2,m1,k,1,1) = ti2+ti3 cc(2,m1,k,1,3) = ti2-ti3 cc(1,m1,k,1,2) = tr1+tr4 cc(1,m1,k,1,4) = tr1-tr4 cc(2,m1,k,1,2) = ti1+ti4 cc(2,m1,k,1,4) = ti1-ti4 end do end do end if return end subroutine cmf4kf ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa ) !******************************************************************************* ! !! CMF4KF is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer l1 real(prec) cc(2,in1,l1,ido,4) real(prec) ch(2,in2,l1,4,ido) real(prec) ci2 real(prec) ci3 real(prec) ci4 real(prec) cr2 real(prec) cr3 real(prec) cr4 integer i integer im1 integer im2 integer k integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) sn real(prec) ti1 real(prec) ti2 real(prec) ti3 real(prec) ti4 real(prec) tr1 real(prec) tr2 real(prec) tr3 real(prec) tr4 real(prec) wa(ido,3,2) m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 if ( 1 < ido ) then do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti1 = cc(2,m1,k,1,1)-cc(2,m1,k,1,3) ti2 = cc(2,m1,k,1,1)+cc(2,m1,k,1,3) tr4 = cc(2,m1,k,1,2)-cc(2,m1,k,1,4) ti3 = cc(2,m1,k,1,2)+cc(2,m1,k,1,4) tr1 = cc(1,m1,k,1,1)-cc(1,m1,k,1,3) tr2 = cc(1,m1,k,1,1)+cc(1,m1,k,1,3) ti4 = cc(1,m1,k,1,4)-cc(1,m1,k,1,2) tr3 = cc(1,m1,k,1,2)+cc(1,m1,k,1,4) ch(1,m2,k,1,1) = tr2+tr3 ch(1,m2,k,3,1) = tr2-tr3 ch(2,m2,k,1,1) = ti2+ti3 ch(2,m2,k,3,1) = ti2-ti3 ch(1,m2,k,2,1) = tr1+tr4 ch(1,m2,k,4,1) = tr1-tr4 ch(2,m2,k,2,1) = ti1+ti4 ch(2,m2,k,4,1) = ti1-ti4 end do end do do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti1 = cc(2,m1,k,i,1)-cc(2,m1,k,i,3) ti2 = cc(2,m1,k,i,1)+cc(2,m1,k,i,3) ti3 = cc(2,m1,k,i,2)+cc(2,m1,k,i,4) tr4 = cc(2,m1,k,i,2)-cc(2,m1,k,i,4) tr1 = cc(1,m1,k,i,1)-cc(1,m1,k,i,3) tr2 = cc(1,m1,k,i,1)+cc(1,m1,k,i,3) ti4 = cc(1,m1,k,i,4)-cc(1,m1,k,i,2) tr3 = cc(1,m1,k,i,2)+cc(1,m1,k,i,4) ch(1,m2,k,1,i) = tr2+tr3 cr3 = tr2-tr3 ch(2,m2,k,1,i) = ti2+ti3 ci3 = ti2-ti3 cr2 = tr1+tr4 cr4 = tr1-tr4 ci2 = ti1+ti4 ci4 = ti1-ti4 ch(1,m2,k,2,i) = wa(i,1,1)*cr2+wa(i,1,2)*ci2 ch(2,m2,k,2,i) = wa(i,1,1)*ci2-wa(i,1,2)*cr2 ch(1,m2,k,3,i) = wa(i,2,1)*cr3+wa(i,2,2)*ci3 ch(2,m2,k,3,i) = wa(i,2,1)*ci3-wa(i,2,2)*cr3 ch(1,m2,k,4,i) = wa(i,3,1)*cr4+wa(i,3,2)*ci4 ch(2,m2,k,4,i) = wa(i,3,1)*ci4-wa(i,3,2)*cr4 end do end do end do else if ( na == 1 ) then sn = 1.0E+00_prec / real ( 4 * l1, prec ) do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti1 = cc(2,m1,k,1,1)-cc(2,m1,k,1,3) ti2 = cc(2,m1,k,1,1)+cc(2,m1,k,1,3) tr4 = cc(2,m1,k,1,2)-cc(2,m1,k,1,4) ti3 = cc(2,m1,k,1,2)+cc(2,m1,k,1,4) tr1 = cc(1,m1,k,1,1)-cc(1,m1,k,1,3) tr2 = cc(1,m1,k,1,1)+cc(1,m1,k,1,3) ti4 = cc(1,m1,k,1,4)-cc(1,m1,k,1,2) tr3 = cc(1,m1,k,1,2)+cc(1,m1,k,1,4) ch(1,m2,k,1,1) = sn*(tr2+tr3) ch(1,m2,k,3,1) = sn*(tr2-tr3) ch(2,m2,k,1,1) = sn*(ti2+ti3) ch(2,m2,k,3,1) = sn*(ti2-ti3) ch(1,m2,k,2,1) = sn*(tr1+tr4) ch(1,m2,k,4,1) = sn*(tr1-tr4) ch(2,m2,k,2,1) = sn*(ti1+ti4) ch(2,m2,k,4,1) = sn*(ti1-ti4) end do end do else sn = 1.0E+00_prec / real ( 4 * l1, prec ) do k = 1, l1 do m1 = 1, m1d, im1 ti1 = cc(2,m1,k,1,1)-cc(2,m1,k,1,3) ti2 = cc(2,m1,k,1,1)+cc(2,m1,k,1,3) tr4 = cc(2,m1,k,1,2)-cc(2,m1,k,1,4) ti3 = cc(2,m1,k,1,2)+cc(2,m1,k,1,4) tr1 = cc(1,m1,k,1,1)-cc(1,m1,k,1,3) tr2 = cc(1,m1,k,1,1)+cc(1,m1,k,1,3) ti4 = cc(1,m1,k,1,4)-cc(1,m1,k,1,2) tr3 = cc(1,m1,k,1,2)+cc(1,m1,k,1,4) cc(1,m1,k,1,1) = sn*(tr2+tr3) cc(1,m1,k,1,3) = sn*(tr2-tr3) cc(2,m1,k,1,1) = sn*(ti2+ti3) cc(2,m1,k,1,3) = sn*(ti2-ti3) cc(1,m1,k,1,2) = sn*(tr1+tr4) cc(1,m1,k,1,4) = sn*(tr1-tr4) cc(2,m1,k,1,2) = sn*(ti1+ti4) cc(2,m1,k,1,4) = sn*(ti1-ti4) end do end do end if return end subroutine cmf5kb ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa ) !******************************************************************************* ! !! CMF5KB is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer l1 real(prec) cc(2,in1,l1,ido,5) real(prec) ch(2,in2,l1,5,ido) real(prec) chold1 real(prec) chold2 real(prec) ci2 real(prec) ci3 real(prec) ci4 real(prec) ci5 real(prec) cr2 real(prec) cr3 real(prec) cr4 real(prec) cr5 real(prec) di2 real(prec) di3 real(prec) di4 real(prec) di5 real(prec) dr2 real(prec) dr3 real(prec) dr4 real(prec) dr5 integer i integer im1 integer im2 integer k integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) ti2 real(prec) ti3 real(prec) ti4 real(prec) ti5 real(prec), parameter :: ti11 = 0.9510565162951536E+00_prec real(prec), parameter :: ti12 = 0.5877852522924731E+00_prec real(prec) tr2 real(prec) tr3 real(prec) tr4 real(prec) tr5 real(prec), parameter :: tr11 = 0.3090169943749474E+00_prec real(prec), parameter :: tr12 = -0.8090169943749474E+00_prec real(prec) wa(ido,4,2) m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 if ( 1 < ido .or. na == 1 ) then do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti5 = cc(2,m1,k,1,2)-cc(2,m1,k,1,5) ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,5) ti4 = cc(2,m1,k,1,3)-cc(2,m1,k,1,4) ti3 = cc(2,m1,k,1,3)+cc(2,m1,k,1,4) tr5 = cc(1,m1,k,1,2)-cc(1,m1,k,1,5) tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,5) tr4 = cc(1,m1,k,1,3)-cc(1,m1,k,1,4) tr3 = cc(1,m1,k,1,3)+cc(1,m1,k,1,4) ch(1,m2,k,1,1) = cc(1,m1,k,1,1)+tr2+tr3 ch(2,m2,k,1,1) = cc(2,m1,k,1,1)+ti2+ti3 cr2 = cc(1,m1,k,1,1)+tr11*tr2+tr12*tr3 ci2 = cc(2,m1,k,1,1)+tr11*ti2+tr12*ti3 cr3 = cc(1,m1,k,1,1)+tr12*tr2+tr11*tr3 ci3 = cc(2,m1,k,1,1)+tr12*ti2+tr11*ti3 cr5 = ti11*tr5+ti12*tr4 ci5 = ti11*ti5+ti12*ti4 cr4 = ti12*tr5-ti11*tr4 ci4 = ti12*ti5-ti11*ti4 ch(1,m2,k,2,1) = cr2-ci5 ch(1,m2,k,5,1) = cr2+ci5 ch(2,m2,k,2,1) = ci2+cr5 ch(2,m2,k,3,1) = ci3+cr4 ch(1,m2,k,3,1) = cr3-ci4 ch(1,m2,k,4,1) = cr3+ci4 ch(2,m2,k,4,1) = ci3-cr4 ch(2,m2,k,5,1) = ci2-cr5 end do end do do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti5 = cc(2,m1,k,i,2)-cc(2,m1,k,i,5) ti2 = cc(2,m1,k,i,2)+cc(2,m1,k,i,5) ti4 = cc(2,m1,k,i,3)-cc(2,m1,k,i,4) ti3 = cc(2,m1,k,i,3)+cc(2,m1,k,i,4) tr5 = cc(1,m1,k,i,2)-cc(1,m1,k,i,5) tr2 = cc(1,m1,k,i,2)+cc(1,m1,k,i,5) tr4 = cc(1,m1,k,i,3)-cc(1,m1,k,i,4) tr3 = cc(1,m1,k,i,3)+cc(1,m1,k,i,4) ch(1,m2,k,1,i) = cc(1,m1,k,i,1)+tr2+tr3 ch(2,m2,k,1,i) = cc(2,m1,k,i,1)+ti2+ti3 cr2 = cc(1,m1,k,i,1)+tr11*tr2+tr12*tr3 ci2 = cc(2,m1,k,i,1)+tr11*ti2+tr12*ti3 cr3 = cc(1,m1,k,i,1)+tr12*tr2+tr11*tr3 ci3 = cc(2,m1,k,i,1)+tr12*ti2+tr11*ti3 cr5 = ti11*tr5+ti12*tr4 ci5 = ti11*ti5+ti12*ti4 cr4 = ti12*tr5-ti11*tr4 ci4 = ti12*ti5-ti11*ti4 dr3 = cr3-ci4 dr4 = cr3+ci4 di3 = ci3+cr4 di4 = ci3-cr4 dr5 = cr2+ci5 dr2 = cr2-ci5 di5 = ci2-cr5 di2 = ci2+cr5 ch(1,m2,k,2,i) = wa(i,1,1) * dr2 - wa(i,1,2) * di2 ch(2,m2,k,2,i) = wa(i,1,1) * di2 + wa(i,1,2) * dr2 ch(1,m2,k,3,i) = wa(i,2,1) * dr3 - wa(i,2,2) * di3 ch(2,m2,k,3,i) = wa(i,2,1) * di3 + wa(i,2,2) * dr3 ch(1,m2,k,4,i) = wa(i,3,1) * dr4 - wa(i,3,2) * di4 ch(2,m2,k,4,i) = wa(i,3,1) * di4 + wa(i,3,2) * dr4 ch(1,m2,k,5,i) = wa(i,4,1) * dr5 - wa(i,4,2) * di5 ch(2,m2,k,5,i) = wa(i,4,1) * di5 + wa(i,4,2) * dr5 end do end do end do else do k = 1, l1 do m1 = 1, m1d, im1 ti5 = cc(2,m1,k,1,2)-cc(2,m1,k,1,5) ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,5) ti4 = cc(2,m1,k,1,3)-cc(2,m1,k,1,4) ti3 = cc(2,m1,k,1,3)+cc(2,m1,k,1,4) tr5 = cc(1,m1,k,1,2)-cc(1,m1,k,1,5) tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,5) tr4 = cc(1,m1,k,1,3)-cc(1,m1,k,1,4) tr3 = cc(1,m1,k,1,3)+cc(1,m1,k,1,4) chold1 = cc(1,m1,k,1,1) + tr2 + tr3 chold2 = cc(2,m1,k,1,1) + ti2 + ti3 cr2 = cc(1,m1,k,1,1) + tr11 * tr2 + tr12 * tr3 ci2 = cc(2,m1,k,1,1) + tr11 * ti2 + tr12 * ti3 cr3 = cc(1,m1,k,1,1) + tr12 * tr2 + tr11 * tr3 ci3 = cc(2,m1,k,1,1) + tr12 * ti2 + tr11 * ti3 cc(1,m1,k,1,1) = chold1 cc(2,m1,k,1,1) = chold2 cr5 = ti11*tr5 + ti12*tr4 ci5 = ti11*ti5 + ti12*ti4 cr4 = ti12*tr5 - ti11*tr4 ci4 = ti12*ti5 - ti11*ti4 cc(1,m1,k,1,2) = cr2-ci5 cc(1,m1,k,1,5) = cr2+ci5 cc(2,m1,k,1,2) = ci2+cr5 cc(2,m1,k,1,3) = ci3+cr4 cc(1,m1,k,1,3) = cr3-ci4 cc(1,m1,k,1,4) = cr3+ci4 cc(2,m1,k,1,4) = ci3-cr4 cc(2,m1,k,1,5) = ci2-cr5 end do end do end if return end subroutine cmf5kf ( lot, ido, l1, na, cc, im1, in1, ch, im2, in2, wa ) !******************************************************************************* ! !! CMF5KF is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer l1 real(prec) cc(2,in1,l1,ido,5) real(prec) ch(2,in2,l1,5,ido) real(prec) chold1 real(prec) chold2 real(prec) ci2 real(prec) ci3 real(prec) ci4 real(prec) ci5 real(prec) cr2 real(prec) cr3 real(prec) cr4 real(prec) cr5 real(prec) di2 real(prec) di3 real(prec) di4 real(prec) di5 real(prec) dr2 real(prec) dr3 real(prec) dr4 real(prec) dr5 integer i integer im1 integer im2 integer k integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) sn real(prec) ti2 real(prec) ti3 real(prec) ti4 real(prec) ti5 real(prec), parameter :: ti11 = -0.9510565162951536E+00_prec real(prec), parameter :: ti12 = -0.5877852522924731E+00_prec real(prec) tr2 real(prec) tr3 real(prec) tr4 real(prec) tr5 real(prec), parameter :: tr11 = 0.3090169943749474E+00_prec real(prec), parameter :: tr12 = -0.8090169943749474E+00_prec real(prec) wa(ido,4,2) m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 if ( 1 < ido ) then do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti5 = cc(2,m1,k,1,2)-cc(2,m1,k,1,5) ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,5) ti4 = cc(2,m1,k,1,3)-cc(2,m1,k,1,4) ti3 = cc(2,m1,k,1,3)+cc(2,m1,k,1,4) tr5 = cc(1,m1,k,1,2)-cc(1,m1,k,1,5) tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,5) tr4 = cc(1,m1,k,1,3)-cc(1,m1,k,1,4) tr3 = cc(1,m1,k,1,3)+cc(1,m1,k,1,4) ch(1,m2,k,1,1) = cc(1,m1,k,1,1)+tr2+tr3 ch(2,m2,k,1,1) = cc(2,m1,k,1,1)+ti2+ti3 cr2 = cc(1,m1,k,1,1)+tr11*tr2+tr12*tr3 ci2 = cc(2,m1,k,1,1)+tr11*ti2+tr12*ti3 cr3 = cc(1,m1,k,1,1)+tr12*tr2+tr11*tr3 ci3 = cc(2,m1,k,1,1)+tr12*ti2+tr11*ti3 cr5 = ti11*tr5+ti12*tr4 ci5 = ti11*ti5+ti12*ti4 cr4 = ti12*tr5-ti11*tr4 ci4 = ti12*ti5-ti11*ti4 ch(1,m2,k,2,1) = cr2-ci5 ch(1,m2,k,5,1) = cr2+ci5 ch(2,m2,k,2,1) = ci2+cr5 ch(2,m2,k,3,1) = ci3+cr4 ch(1,m2,k,3,1) = cr3-ci4 ch(1,m2,k,4,1) = cr3+ci4 ch(2,m2,k,4,1) = ci3-cr4 ch(2,m2,k,5,1) = ci2-cr5 end do end do do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti5 = cc(2,m1,k,i,2)-cc(2,m1,k,i,5) ti2 = cc(2,m1,k,i,2)+cc(2,m1,k,i,5) ti4 = cc(2,m1,k,i,3)-cc(2,m1,k,i,4) ti3 = cc(2,m1,k,i,3)+cc(2,m1,k,i,4) tr5 = cc(1,m1,k,i,2)-cc(1,m1,k,i,5) tr2 = cc(1,m1,k,i,2)+cc(1,m1,k,i,5) tr4 = cc(1,m1,k,i,3)-cc(1,m1,k,i,4) tr3 = cc(1,m1,k,i,3)+cc(1,m1,k,i,4) ch(1,m2,k,1,i) = cc(1,m1,k,i,1)+tr2+tr3 ch(2,m2,k,1,i) = cc(2,m1,k,i,1)+ti2+ti3 cr2 = cc(1,m1,k,i,1)+tr11*tr2+tr12*tr3 ci2 = cc(2,m1,k,i,1)+tr11*ti2+tr12*ti3 cr3 = cc(1,m1,k,i,1)+tr12*tr2+tr11*tr3 ci3 = cc(2,m1,k,i,1)+tr12*ti2+tr11*ti3 cr5 = ti11*tr5+ti12*tr4 ci5 = ti11*ti5+ti12*ti4 cr4 = ti12*tr5-ti11*tr4 ci4 = ti12*ti5-ti11*ti4 dr3 = cr3-ci4 dr4 = cr3+ci4 di3 = ci3+cr4 di4 = ci3-cr4 dr5 = cr2+ci5 dr2 = cr2-ci5 di5 = ci2-cr5 di2 = ci2+cr5 ch(1,m2,k,2,i) = wa(i,1,1)*dr2+wa(i,1,2)*di2 ch(2,m2,k,2,i) = wa(i,1,1)*di2-wa(i,1,2)*dr2 ch(1,m2,k,3,i) = wa(i,2,1)*dr3+wa(i,2,2)*di3 ch(2,m2,k,3,i) = wa(i,2,1)*di3-wa(i,2,2)*dr3 ch(1,m2,k,4,i) = wa(i,3,1)*dr4+wa(i,3,2)*di4 ch(2,m2,k,4,i) = wa(i,3,1)*di4-wa(i,3,2)*dr4 ch(1,m2,k,5,i) = wa(i,4,1)*dr5+wa(i,4,2)*di5 ch(2,m2,k,5,i) = wa(i,4,1)*di5-wa(i,4,2)*dr5 end do end do end do else if ( na == 1 ) then sn = 1.0E+00_prec / real ( 5 * l1, prec ) do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ti5 = cc(2,m1,k,1,2)-cc(2,m1,k,1,5) ti2 = cc(2,m1,k,1,2)+cc(2,m1,k,1,5) ti4 = cc(2,m1,k,1,3)-cc(2,m1,k,1,4) ti3 = cc(2,m1,k,1,3)+cc(2,m1,k,1,4) tr5 = cc(1,m1,k,1,2)-cc(1,m1,k,1,5) tr2 = cc(1,m1,k,1,2)+cc(1,m1,k,1,5) tr4 = cc(1,m1,k,1,3)-cc(1,m1,k,1,4) tr3 = cc(1,m1,k,1,3)+cc(1,m1,k,1,4) ch(1,m2,k,1,1) = sn*(cc(1,m1,k,1,1)+tr2+tr3) ch(2,m2,k,1,1) = sn*(cc(2,m1,k,1,1)+ti2+ti3) cr2 = cc(1,m1,k,1,1)+tr11*tr2+tr12*tr3 ci2 = cc(2,m1,k,1,1)+tr11*ti2+tr12*ti3 cr3 = cc(1,m1,k,1,1)+tr12*tr2+tr11*tr3 ci3 = cc(2,m1,k,1,1)+tr12*ti2+tr11*ti3 cr5 = ti11*tr5+ti12*tr4 ci5 = ti11*ti5+ti12*ti4 cr4 = ti12*tr5-ti11*tr4 ci4 = ti12*ti5-ti11*ti4 ch(1,m2,k,2,1) = sn*(cr2-ci5) ch(1,m2,k,5,1) = sn*(cr2+ci5) ch(2,m2,k,2,1) = sn*(ci2+cr5) ch(2,m2,k,3,1) = sn*(ci3+cr4) ch(1,m2,k,3,1) = sn*(cr3-ci4) ch(1,m2,k,4,1) = sn*(cr3+ci4) ch(2,m2,k,4,1) = sn*(ci3-cr4) ch(2,m2,k,5,1) = sn*(ci2-cr5) end do end do else sn = 1.0E+00_prec / real ( 5 * l1, prec ) do k = 1, l1 do m1 = 1, m1d, im1 ti5 = cc(2,m1,k,1,2) - cc(2,m1,k,1,5) ti2 = cc(2,m1,k,1,2) + cc(2,m1,k,1,5) ti4 = cc(2,m1,k,1,3) - cc(2,m1,k,1,4) ti3 = cc(2,m1,k,1,3) + cc(2,m1,k,1,4) tr5 = cc(1,m1,k,1,2) - cc(1,m1,k,1,5) tr2 = cc(1,m1,k,1,2) + cc(1,m1,k,1,5) tr4 = cc(1,m1,k,1,3) - cc(1,m1,k,1,4) tr3 = cc(1,m1,k,1,3) + cc(1,m1,k,1,4) chold1 = sn * ( cc(1,m1,k,1,1) + tr2 + tr3 ) chold2 = sn * ( cc(2,m1,k,1,1) + ti2 + ti3 ) cr2 = cc(1,m1,k,1,1) + tr11 * tr2 + tr12 * tr3 ci2 = cc(2,m1,k,1,1) + tr11 * ti2 + tr12 * ti3 cr3 = cc(1,m1,k,1,1) + tr12 * tr2 + tr11 * tr3 ci3 = cc(2,m1,k,1,1) + tr12 * ti2 + tr11 * ti3 cc(1,m1,k,1,1) = chold1 cc(2,m1,k,1,1) = chold2 cr5 = ti11 * tr5 + ti12 * tr4 ci5 = ti11 * ti5 + ti12 * ti4 cr4 = ti12 * tr5 - ti11 * tr4 ci4 = ti12 * ti5 - ti11 * ti4 cc(1,m1,k,1,2) = sn * ( cr2 - ci5 ) cc(1,m1,k,1,5) = sn * ( cr2 + ci5 ) cc(2,m1,k,1,2) = sn * ( ci2 + cr5 ) cc(2,m1,k,1,3) = sn * ( ci3 + cr4 ) cc(1,m1,k,1,3) = sn * ( cr3 - ci4 ) cc(1,m1,k,1,4) = sn * ( cr3 + ci4 ) cc(2,m1,k,1,4) = sn * ( ci3 - cr4 ) cc(2,m1,k,1,5) = sn * ( ci2 - cr5 ) end do end do end if return end subroutine cmfgkb ( lot, ido, ip, l1, lid, na, cc, cc1, im1, in1, & ch, ch1, im2, in2, wa ) !******************************************************************************* ! !! CMFGKB is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer ip integer l1 integer lid real(prec) cc(2,in1,l1,ip,ido) real(prec) cc1(2,in1,lid,ip) real(prec) ch(2,in2,l1,ido,ip) real(prec) ch1(2,in2,lid,ip) real(prec) chold1 real(prec) chold2 integer i integer idlj integer im1 integer im2 integer ipp2 integer ipph integer j integer jc integer k integer ki integer l integer lc integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) wa(ido,ip-1,2) real(prec) wai real(prec) war m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 ipp2 = ip + 2 ipph = ( ip + 1 ) / 2 do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,1) = cc1(1,m1,ki,1) ch1(2,m2,ki,1) = cc1(2,m1,ki,1) end do end do do j = 2, ipph jc = ipp2 - j do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,j) = cc1(1,m1,ki,j) + cc1(1,m1,ki,jc) ch1(1,m2,ki,jc) = cc1(1,m1,ki,j) - cc1(1,m1,ki,jc) ch1(2,m2,ki,j) = cc1(2,m1,ki,j) + cc1(2,m1,ki,jc) ch1(2,m2,ki,jc) = cc1(2,m1,ki,j) - cc1(2,m1,ki,jc) end do end do end do do j = 2, ipph do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc1(1,m1,ki,1) = cc1(1,m1,ki,1) + ch1(1,m2,ki,j) cc1(2,m1,ki,1) = cc1(2,m1,ki,1) + ch1(2,m2,ki,j) end do end do end do do l = 2, ipph lc = ipp2 - l do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc1(1,m1,ki,l) = ch1(1,m2,ki,1) + wa(1,l-1,1) * ch1(1,m2,ki,2) cc1(1,m1,ki,lc) = wa(1,l-1,2) * ch1(1,m2,ki,ip) cc1(2,m1,ki,l) = ch1(2,m2,ki,1) + wa(1,l-1,1) * ch1(2,m2,ki,2) cc1(2,m1,ki,lc) = wa(1,l-1,2) * ch1(2,m2,ki,ip) end do end do do j = 3, ipph jc = ipp2 - j idlj = mod ( ( l - 1 ) * ( j - 1 ), ip ) war = wa(1,idlj,1) wai = wa(1,idlj,2) do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc1(1,m1,ki,l) = cc1(1,m1,ki,l) + war * ch1(1,m2,ki,j) cc1(1,m1,ki,lc) = cc1(1,m1,ki,lc) + wai * ch1(1,m2,ki,jc) cc1(2,m1,ki,l) = cc1(2,m1,ki,l) + war * ch1(2,m2,ki,j) cc1(2,m1,ki,lc) = cc1(2,m1,ki,lc) + wai * ch1(2,m2,ki,jc) end do end do end do end do if( 1 < ido .or. na == 1 ) then do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,1) = cc1(1,m1,ki,1) ch1(2,m2,ki,1) = cc1(2,m1,ki,1) end do end do do j = 2, ipph jc = ipp2 - j do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,j) = cc1(1,m1,ki,j) - cc1(2,m1,ki,jc) ch1(1,m2,ki,jc) = cc1(1,m1,ki,j) + cc1(2,m1,ki,jc) ch1(2,m2,ki,jc) = cc1(2,m1,ki,j) - cc1(1,m1,ki,jc) ch1(2,m2,ki,j) = cc1(2,m1,ki,j) + cc1(1,m1,ki,jc) end do end do end do if ( ido == 1 ) then return end if do i = 1, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc(1,m1,k,1,i) = ch(1,m2,k,i,1) cc(2,m1,k,1,i) = ch(2,m2,k,i,1) end do end do end do do j = 2, ip do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc(1,m1,k,j,1) = ch(1,m2,k,1,j) cc(2,m1,k,j,1) = ch(2,m2,k,1,j) end do end do end do do j = 2, ip do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc(1,m1,k,j,i) = wa(i,j-1,1) * ch(1,m2,k,i,j) & - wa(i,j-1,2) * ch(2,m2,k,i,j) cc(2,m1,k,j,i) = wa(i,j-1,1) * ch(2,m2,k,i,j) & + wa(i,j-1,2) * ch(1,m2,k,i,j) end do end do end do end do else do j = 2, ipph jc = ipp2 - j do ki = 1, lid do m1 = 1, m1d, im1 chold1 = cc1(1,m1,ki,j) - cc1(2,m1,ki,jc) chold2 = cc1(1,m1,ki,j) + cc1(2,m1,ki,jc) cc1(1,m1,ki,j) = chold1 cc1(2,m1,ki,jc) = cc1(2,m1,ki,j) - cc1(1,m1,ki,jc) cc1(2,m1,ki,j) = cc1(2,m1,ki,j) + cc1(1,m1,ki,jc) cc1(1,m1,ki,jc) = chold2 end do end do end do end if return end subroutine cmfgkf ( lot, ido, ip, l1, lid, na, cc, cc1, im1, in1, & ch, ch1, im2, in2, wa ) !******************************************************************************* ! !! CMFGKF is an FFTPACK5 auxiliary routine. ! ! License: ! ! Licensed under the GNU General Public License (GPL). ! Copyright (C) 1995-2004, Scientific Computing Division, ! University Corporation for Atmospheric Research ! ! Author: ! ! Paul Swarztrauber ! Richard Valent ! ! Reference: ! ! Paul Swarztrauber, ! Vectorizing the Fast Fourier Transforms, ! in Parallel Computations, ! edited by G. Rodrigue, ! Academic Press, 1982. ! ! Paul Swarztrauber, ! Fast Fourier Transform Algorithms for Vector Computers, ! Parallel Computing, pages 45-63, 1984. ! ! Parameters: ! use fftpack5 implicit none integer ido integer in1 integer in2 integer ip integer l1 integer lid real(prec) cc(2,in1,l1,ip,ido) real(prec) cc1(2,in1,lid,ip) real(prec) ch(2,in2,l1,ido,ip) real(prec) ch1(2,in2,lid,ip) real(prec) chold1 real(prec) chold2 integer i integer idlj integer im1 integer im2 integer ipp2 integer ipph integer j integer jc integer k integer ki integer l integer lc integer lot integer m1 integer m1d integer m2 integer m2s integer na real(prec) sn real(prec) wa(ido,ip-1,2) real(prec) wai real(prec) war m1d = ( lot - 1 ) * im1 + 1 m2s = 1 - im2 ipp2 = ip + 2 ipph = ( ip + 1 ) / 2 do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,1) = cc1(1,m1,ki,1) ch1(2,m2,ki,1) = cc1(2,m1,ki,1) end do end do do j = 2, ipph jc = ipp2 - j do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,j) = cc1(1,m1,ki,j) + cc1(1,m1,ki,jc) ch1(1,m2,ki,jc) = cc1(1,m1,ki,j) - cc1(1,m1,ki,jc) ch1(2,m2,ki,j) = cc1(2,m1,ki,j) + cc1(2,m1,ki,jc) ch1(2,m2,ki,jc) = cc1(2,m1,ki,j) - cc1(2,m1,ki,jc) end do end do end do do j = 2, ipph do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc1(1,m1,ki,1) = cc1(1,m1,ki,1) + ch1(1,m2,ki,j) cc1(2,m1,ki,1) = cc1(2,m1,ki,1) + ch1(2,m2,ki,j) end do end do end do do l = 2, ipph lc = ipp2 - l do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc1(1,m1,ki,l) = ch1(1,m2,ki,1) + wa(1,l-1,1) * ch1(1,m2,ki,2) cc1(1,m1,ki,lc) = - wa(1,l-1,2) * ch1(1,m2,ki,ip) cc1(2,m1,ki,l) = ch1(2,m2,ki,1) + wa(1,l-1,1) * ch1(2,m2,ki,2) cc1(2,m1,ki,lc) = - wa(1,l-1,2) * ch1(2,m2,ki,ip) end do end do do j = 3, ipph jc = ipp2 - j idlj = mod ( ( l - 1 ) * ( j - 1 ), ip ) war = wa(1,idlj,1) wai = -wa(1,idlj,2) do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc1(1,m1,ki,l) = cc1(1,m1,ki,l) + war * ch1(1,m2,ki,j) cc1(1,m1,ki,lc) = cc1(1,m1,ki,lc) + wai * ch1(1,m2,ki,jc) cc1(2,m1,ki,l) = cc1(2,m1,ki,l) + war * ch1(2,m2,ki,j) cc1(2,m1,ki,lc) = cc1(2,m1,ki,lc) + wai * ch1(2,m2,ki,jc) end do end do end do end do if ( 1 < ido ) then do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,1) = cc1(1,m1,ki,1) ch1(2,m2,ki,1) = cc1(2,m1,ki,1) end do end do do j = 2, ipph jc = ipp2 - j do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,j) = cc1(1,m1,ki,j) - cc1(2,m1,ki,jc) ch1(2,m2,ki,j) = cc1(2,m1,ki,j) + cc1(1,m1,ki,jc) ch1(1,m2,ki,jc) = cc1(1,m1,ki,j) + cc1(2,m1,ki,jc) ch1(2,m2,ki,jc) = cc1(2,m1,ki,j) - cc1(1,m1,ki,jc) end do end do end do do i = 1, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc(1,m1,k,1,i) = ch(1,m2,k,i,1) cc(2,m1,k,1,i) = ch(2,m2,k,i,1) end do end do end do do j = 2, ip do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc(1,m1,k,j,1) = ch(1,m2,k,1,j) cc(2,m1,k,j,1) = ch(2,m2,k,1,j) end do end do end do do j = 2, ip do i = 2, ido do k = 1, l1 m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc(1,m1,k,j,i) = wa(i,j-1,1) * ch(1,m2,k,i,j) & + wa(i,j-1,2) * ch(2,m2,k,i,j) cc(2,m1,k,j,i) = wa(i,j-1,1) * ch(2,m2,k,i,j) & - wa(i,j-1,2) * ch(1,m2,k,i,j) end do end do end do end do else if ( na == 1 ) then sn = 1.0E+00_prec / real ( ip * l1, prec ) do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,1) = sn * cc1(1,m1,ki,1) ch1(2,m2,ki,1) = sn * cc1(2,m1,ki,1) end do end do do j = 2, ipph jc = ipp2 - j do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 ch1(1,m2,ki,j) = sn * ( cc1(1,m1,ki,j) - cc1(2,m1,ki,jc) ) ch1(2,m2,ki,j) = sn * ( cc1(2,m1,ki,j) + cc1(1,m1,ki,jc) ) ch1(1,m2,ki,jc) = sn * ( cc1(1,m1,ki,j) + cc1(2,m1,ki,jc) ) ch1(2,m2,ki,jc) = sn * ( cc1(2,m1,ki,j) - cc1(1,m1,ki,jc) ) end do end do end do else sn = 1.0E+00_prec / real ( ip * l1, prec ) do ki = 1, lid m2 = m2s do m1 = 1, m1d, im1 m2 = m2 + im2 cc1(1,m1,ki,1) = sn * cc1(1,m1,ki,1) cc1(2,m1,ki,1) = sn * cc1(2,m1,ki,1) end do end do do j = 2, ipph jc = ipp2 - j do ki = 1, lid do m1 = 1, m1d, im1 chold1 = sn * ( cc1(1,m1,ki,j) - cc1(2,m1,ki,jc) ) chold2 = sn * ( cc1(1,m1,ki,j) + cc1(2,m1,ki,jc) ) cc1(1,m1,ki,j) = chold1 cc1(2,m1,ki,jc) = sn * ( cc1(2,m1,ki,j) - cc1(1,m1,ki,jc) ) cc1(2,m1,ki,j) = sn * ( cc1(2,m1,ki,j) + cc1(1,m1,ki,jc) ) cc1(1,m1,ki,jc) = chold2 end do end do end do end if return end elk-7.2.42/src/PaxHeaders.21776/eos0000644000000000000000000000013214061636515013433 xustar0030 mtime=1623670093.500103805 30 atime=1623670093.481103823 30 ctime=1623670093.500103805 elk-7.2.42/src/eos/0000755002504400250440000000000014061636515015545 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/src/eos/PaxHeaders.21776/Makefile0000644000000000000000000000013214061636515015150 xustar0030 mtime=1623670093.483103821 30 atime=1623670093.482103822 30 ctime=1623670093.483103821 elk-7.2.42/src/eos/Makefile0000644002504400250440000000134614061636515017211 0ustar00dewhurstdewhurst00000000000000 include ../../make.inc #------------------------------------------------------------------------------- # Suffix rules #------------------------------------------------------------------------------- .SUFFIXES: .o .f90 .f90.o: $(F90) $(F90_OPTS) -c $< #------------------------------------------------------------------------------- # Source files #------------------------------------------------------------------------------- SRC = modmain.f90 eos.f90 eveos.f90 pveos.f90 readinput.f90 getedata.f90 \ fitdata.f90 output.f90 minf_nm.f90 fmin_nm.f90 OBJ = $(SRC:.f90=.o) EXE = eos eos: $(OBJ) $(F90) $(F90_OPTS) -o $(EXE) $(OBJ) clean: rm -f *.o *.mod *~ fort.* ifc* *.gcno *.OUT gmon.out $(EXE) spaces: ../rmspaces $(SRC) elk-7.2.42/src/eos/PaxHeaders.21776/README0000644000000000000000000000012714061636515014374 xustar0029 mtime=1623670093.48410382 29 atime=1623670093.48410382 29 ctime=1623670093.48410382 elk-7.2.42/src/eos/README0000644002504400250440000000254414061636515016432 0ustar00dewhurstdewhurst00000000000000 +---------------------------+ | EOS Version 1.4.0 | +---------------------------+ Equation of state (EOS) program for fitting energy-volume data. The following variables are set in the file eos.in: cname : name of crystal up to 256 characters natoms : number of atoms in unit cell etype : equation of state type (see below) vplt1, vplt2, nvplt : volume interval over which to plot energy, pressure etc. as well as the number of points in the plot nevpt : number of energy-volume points to be inputted vpt(i) ept(i) : energy-volume points (atomic units) Note that the input units are atomic - Bohr and Hartree (NOT Rydbergs). The equations of state currently implemented are: 1. Universal EOS (Vinet P et al., J. Phys.: Condens. Matter 1, p1941 (1989)) 2. Murnaghan EOS (Murnaghan F D, Am. J. Math. 49, p235 (1937)) 3. Birch-Murnaghan 3rd-order EOS (Birch F, Phys. Rev. 71, p809 (1947)) 4. Birch-Murnaghan 4th-order EOS 5. Natural strain 3rd-order EOS (Poirier J-P and Tarantola A, Phys. Earth Planet Int. 109, p1 (1998)) 6. Natural strain 4th-order EOS 7. Cubic polynomial in (V-V0) -------------------------------------------------------------------------------- J. K. Dewhurst August 2005 elk-7.2.42/src/eos/PaxHeaders.21776/eos.f900000644000000000000000000000013214061636515014616 xustar0030 mtime=1623670093.486103818 30 atime=1623670093.486103818 30 ctime=1623670093.486103818 elk-7.2.42/src/eos/eos.f900000644002504400250440000000051714061636515016656 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. program eos use modmain implicit none call readinput call getedata(etype,nparam,ename,pname) call fitdata call output stop end program elk-7.2.42/src/eos/PaxHeaders.21776/eos.in0000644000000000000000000000013214061636515014626 xustar0030 mtime=1623670093.487103817 30 atime=1623670093.487103817 30 ctime=1623670093.487103817 elk-7.2.42/src/eos/eos.in0000644002504400250440000000063514061636515016667 0ustar00dewhurstdewhurst00000000000000 "Silicon" : cname 2 : natoms 1 : etype 140.0 450.0 1000 : vplt1, vplt2, nvplt 8 : nevpt 165.8207473 -578.0660968 196.8383062 -578.1728409 231.5010189 -578.2305598 270.0113940 -578.2548962 312.5719400 -578.2566194 359.3851654 -578.2453281 410.6535788 -578.2253154 466.5796888 -578.2028836 elk-7.2.42/src/eos/PaxHeaders.21776/eveos.f900000644000000000000000000000013214061636515015151 xustar0030 mtime=1623670093.489103815 30 atime=1623670093.489103815 30 ctime=1623670093.489103815 elk-7.2.42/src/eos/eveos.f900000644002504400250440000000455614061636515017220 0ustar00dewhurstdewhurst00000000000000real(8) function eveos(etype,param,v) implicit none ! arguments integer, intent(in) :: etype real(8), intent(in) :: param(*) real(8), intent(in) :: v ! local variables real(8) v0,e0,b0,b0p,b0pp real(8) t1,t2,t3,t4,t5,t6,t7 eveos=0.d0 select case(etype) case(1) ! Universal equation of state v0=param(1) e0=param(2) b0=param(3) b0p=param(4) if (v0.lt.1.d-5) v0=1.d-5 if (abs(b0p-1.d0).lt.1.d-5) b0p=b0p+1.d-5 t1=b0*v0 t2=b0p-1.d0 t3=(v/v0)**(1.d0/3.d0) t4=exp(-3.d0/2.d0*t2*(-1.d0+t3)) t5=t2**2 t6=1.d0/t5 eveos=-2.d0*t1*t4*(3.d0*t3*b0p-3.d0*t3+5.d0-3.d0*b0p)*t6+4.d0*t1*t6+e0 case(2) ! Murnaghan equation of state v0=param(1) e0=param(2) b0=param(3) b0p=param(4) if (v0.lt.1.d-5) v0=1.d-5 if (abs(b0p).lt.1.d-5) b0p=1.d-5 if (abs(b0p-1.d0).lt.1.d-5) b0p=b0p+1.d-5 t1=(v0/v)**b0p t2=1.d0/(b0p-1.d0) eveos=b0*(b0p-1.d0+t1)/b0p*t2*v-b0*v0*t2+e0 case(3) ! Birch-Murnaghan third-order equation of state v0=param(1) e0=param(2) b0=param(3) b0p=param(4) if (v0.lt.1.d-5) v0=1.d-5 t1=(v0/v)**(1.d0/3.d0) t2=t1**2 t3=t2-1.d0 eveos=9.d0/8.d0*b0*v0*t3**2*(b0p*t3/2.d0-2.d0*t2+3.d0)+e0 case(4) ! Birch-Murnaghan fourth-order equation of state v0=param(1) e0=param(2) b0=param(3) b0p=param(4) b0pp=param(5) if (v0.lt.1.d-5) v0=1.d-5 t1=(v0/v)**(1.d0/3.d0) t2=t1**2 t3=t2-1.d0 t4=t3**2/4.d0 t5=b0p**2 eveos=3.d0/8.d0*b0*v0*t4*(9.d0*t4*b0*b0pp+9.d0*t4*t5-63.d0*t4*b0p+143.d0*t4 & +6.d0*b0p*t3-24.d0*t2+36.d0)+e0 case(5) ! Natural strain third-order equation of state v0=param(1) e0=param(2) b0=param(3) b0p=param(4) if (v0.lt.1.d-5) v0=1.d-5 t1=b0*v0 t2=log(v0/v) t3=t2**2 t4=t3*t2 eveos=t1*t3/2.d0+t1*t4*b0p/6.d0-t1*t4/3.d0+e0 case(6) ! Natural strain fourth-order equation of state v0=param(1) e0=param(2) b0=param(3) b0p=param(4) b0pp=param(5) if (v0.lt.1.d-5) v0=1.d-5 t1=b0*v0 t2=log(v0/v) t3=t2**2 t4=t3**2 t5=b0**2 t6=b0p**2 t7=t3*t2 eveos=t1*t4/8.d0+t5*v0*t4*b0pp/24.d0-t1*t4*b0p/8.d0+t1*t4*t6/24.d0 & +t1*t7*b0p/6.d0-t1*t7/3.d0+t1*t3/2.d0+e0 case(7) ! cubic polynomial v0=param(1) e0=param(2) b0=param(3) b0p=param(4) if (v0.lt.1.d-5) v0=1.d-5 t1=v0**2 t2=v0-v t3=t2**2 eveos=(1.d0+b0p)*b0/t1*t3*t2/6.d0+b0/v0*t3/2.d0+e0 case default write(*,*) write(*,'("Error(eveos): etype not defined : ",I4)') etype write(*,*) stop end select return end function elk-7.2.42/src/eos/PaxHeaders.21776/fitdata.f900000644000000000000000000000013214061636515015444 xustar0030 mtime=1623670093.490103815 30 atime=1623670093.490103815 30 ctime=1623670093.490103815 elk-7.2.42/src/eos/fitdata.f900000644002504400250440000000173214061636515017504 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine fitdata use modmain implicit none ! local variables integer, parameter :: maxit=1000000 integer i,iter real(8), parameter :: eps=1.d-14 ! automatic arrays real(8) x(nparam,nparam+1) ! initial guess: it is assumed that param(1)=V0, param(2)=E0 and param(3)=B0 x(:,1)=0.d0 x(1,1)=vpt(1) x(2,1)=ept(1) x(3,1)=0.003d0 ! fit V0 and E0 do i=1,nparam x(:,i+1)=x(:,1) end do x(1,2)=x(1,2)+1.d0 x(2,3)=x(2,3)+0.1d0 call minf_nm(nparam,x,maxit,iter,eps) ! fit V0, E0 and B0 do i=1,nparam x(:,i+1)=x(:,1) end do x(1,2)=x(1,2)+1.d0 x(2,3)=x(2,3)+0.1d0 x(3,4)=x(3,4)+0.001d0 call minf_nm(nparam,x,maxit,iter,eps) ! fit everything do i=1,nparam x(:,i+1)=x(:,1) x(i,i+1)=x(i,i+1)+0.1d0 end do call minf_nm(nparam,x,maxit,iter,eps) popt(1:nparam)=x(1:nparam,1) return end subroutine elk-7.2.42/src/eos/PaxHeaders.21776/fmin_nm.f900000644000000000000000000000013214061636515015453 xustar0030 mtime=1623670093.492103813 30 atime=1623670093.492103813 30 ctime=1623670093.492103813 elk-7.2.42/src/eos/fmin_nm.f900000644002504400250440000000074614061636515017517 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. real(8) function fmin_nm(x) use modmain implicit none ! arguments real(8), intent(in) :: x ! local variables integer i real(8) sum ! external functions real(8) eveos external eveos sum=0.d0 do i=1,nevpt sum=sum+(eveos(etype,x,vpt(i))-ept(i))**2 end do fmin_nm=sum return end function elk-7.2.42/src/eos/PaxHeaders.21776/getedata.f900000644000000000000000000000013214061636515015606 xustar0030 mtime=1623670093.493103812 30 atime=1623670093.493103812 30 ctime=1623670093.493103812 elk-7.2.42/src/eos/getedata.f900000644002504400250440000000325114061636515017644 0ustar00dewhurstdewhurst00000000000000subroutine getedata(etype,nparam,ename,pname) ! get eos name and number of parameters implicit none ! arguments integer, intent(in) :: etype integer, intent(out) :: nparam character(256), intent(out) :: ename(2) character(256), intent(out) :: pname(*) select case(etype) case(1) ename(1)="Universal EOS" ename(2)="Vinet P et al., J. Phys.: Condens. Matter 1, p1941 (1989)" nparam=4 pname(1)="V0" pname(2)="E0" pname(3)="B0" pname(4)="B0'" case(2) ename(1)="Murnaghan EOS" ename(2)="Murnaghan F D, Am. J. Math. 49, p235 (1937)" nparam=4 pname(1)="V0" pname(2)="E0" pname(3)="B0" pname(4)="B0'" case(3) ename(1)="Birch-Murnaghan 3rd-order EOS" ename(2)="Birch F, Phys. Rev. 71, p809 (1947)" nparam=4 pname(1)="V0" pname(2)="E0" pname(3)="B0" pname(4)="B0'" case(4) ename(1)="Birch-Murnaghan 4th-order EOS" ename(2)="Birch F, Phys. Rev. 71, p809 (1947)" nparam=5 pname(1)="V0" pname(2)="E0" pname(3)="B0" pname(4)="B0'" pname(5)="B0''" case(5) ename(1)="Natural strain 3rd-order EOS" ename(2)="Poirier J-P and Tarantola A, Phys. Earth Planet Int. 109, p1 (1998)" nparam=4 pname(1)="V0" pname(2)="E0" pname(3)="B0" pname(4)="B0'" case(6) ename(1)="Natural strain 4th-order EOS" ename(2)="Poirier J-P and Tarantola A, Phys. Earth Planet Int. 109, p1 (1998)" nparam=5 pname(1)="V0" pname(2)="E0" pname(3)="B0" pname(4)="B0'" pname(5)="B0''" case(7) ename(1)="Cubic polynomial in (V-V0)" ename(2)="" nparam=4 pname(1)="V0" pname(2)="E0" pname(3)="B0" pname(4)="B0'" case default write(*,*) write(*,'("Error(getedata): etype not defined : ",I4)') etype write(*,*) stop end select return end subroutine elk-7.2.42/src/eos/PaxHeaders.21776/minf_nm.f900000644000000000000000000000012714061636515015457 xustar0029 mtime=1623670093.49510381 29 atime=1623670093.49510381 29 ctime=1623670093.49510381 elk-7.2.42/src/eos/minf_nm.f900000644002504400250440000000371214061636515017513 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst and D. W. H. Rankin. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine minf_nm(n,x,maxit,iter,eps) implicit none ! arguments integer, intent(in) :: n real(8), intent(inout) :: x(n,n+1) integer, intent(in) :: maxit integer, intent(out) :: iter real(8), intent(in) :: eps ! local variables integer i,j,il,iu ! Nelder-Mead parmeters real(8), parameter :: alpha=1.d0,gamma=2.d0 real(8), parameter :: beta=0.5d0,sigma=0.5d0 real(8) fr,fe,fc,sum,t1 ! automatic arrays real(8) f(n+1),xm(n),xr(n),xe(n),xc(n) ! external functions real(8) fmin_nm external fmin_nm if (n.lt.0) then write(*,*) write(*,'("Error(minf_nm): n <= 0 : ",I8)') n write(*,*) stop end if ! evaluate the function at each vertex do i=1,n+1 f(i)=fmin_nm(x(:,i)) end do iter=0 10 continue iter=iter+1 if (iter.ge.maxit) return ! find the lowest and highest vertex il=1 iu=1 do i=2,n+1 if (f(i).lt.f(il)) il=i if (f(i).gt.f(iu)) iu=i end do ! check for convergence if ((f(iu)-f(il)).lt.eps) return ! compute the mean of the n lowest vertices t1=1.d0/dble(n) do i=1,n sum=0.d0 do j=1,iu-1 sum=sum+x(i,j) end do do j=iu+1,n+1 sum=sum+x(i,j) end do xm(i)=t1*sum end do xr(:)=xm(:)+alpha*(xm(:)-x(:,iu)) fr=fmin_nm(xr) if (f(il).gt.fr) goto 30 if ((f(il).le.fr).and.(fr.lt.f(iu))) then ! reflection x(:,iu)=xr(:) f(iu)=fr goto 10 else goto 40 end if 30 continue xe(:)=xm(:)+gamma*(xr(:)-xm(:)) fe=fmin_nm(xe) if (fr.gt.fe) then ! expansion x(:,iu)=xe(:) f(iu)=fe else ! reflection x(:,iu)=xr(:) f(iu)=fr end if goto 10 40 continue xc(:)=xm(:)+beta*(x(:,iu)-xm(:)) fc=fmin_nm(xc) if (fc.lt.f(iu)) then ! contraction x(:,iu)=xc(:) f(iu)=fc goto 10 end if ! shrinkage do j=1,il-1 x(:,j)=x(:,il)+sigma*(x(:,j)-x(:,il)) f(j)=fmin_nm(x(1,j)) end do do j=il+1,n+1 x(:,j)=x(:,il)+sigma*(x(:,j)-x(:,il)) f(j)=fmin_nm(x(1,j)) end do goto 10 return end subroutine elk-7.2.42/src/eos/PaxHeaders.21776/modmain.f900000644000000000000000000000013214061636515015454 xustar0030 mtime=1623670093.496103809 30 atime=1623670093.496103809 30 ctime=1623670093.496103809 elk-7.2.42/src/eos/modmain.f900000644002504400250440000000276214061636515017520 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modmain ! crystal name character(256) cname ! number of atoms integer natoms ! EOS type integer etype ! number of volume points to plot integer nvplt ! volume plot range real(8) vplt1,vplt2 ! number of energy data points to fit integer nevpt ! volume and energy data point sets real(8), allocatable :: vpt(:) real(8), allocatable :: ept(:) ! maximum number of parameters for an EOS integer, parameter :: maxparam=100 ! number of parameters integer nparam ! EOS name character(256) ename(2) ! optimized parameter set real(8) popt(maxparam) ! parameter names character(256) pname(maxparam) !-----------------------------! ! numerical constants ! !-----------------------------! real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: twopi=6.2831853071795864769d0 ! CODATA 2006 constants ! Bohr in SI units real(8), parameter :: bohr_si=0.52917720859d-10 ! electron mass in SI units real(8), parameter :: emass_si=9.10938215d-31 ! atomic unit of time in SI units real(8), parameter :: autime_si=2.418884326505d-17 ! atomic pressure unit in GPa real(8), parameter :: aupress_gpa=1.d-9*emass_si/(bohr_si*autime_si**2) !---------------------------------! ! miscellaneous variables ! !---------------------------------! ! code version integer version(3) data version /1,4,0/ end module elk-7.2.42/src/eos/PaxHeaders.21776/output.f900000644000000000000000000000013214061636515015370 xustar0030 mtime=1623670093.498103807 30 atime=1623670093.498103807 30 ctime=1623670093.498103807 elk-7.2.42/src/eos/output.f900000644002504400250440000000505614061636515017433 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine output use modmain implicit none ! local variables integer ip,ipt,iplt real(8) v ! external functions real(8) eveos,pveos external eveos,pveos ! output parameters open(60,file='PARAM.OUT') write(60,*) write(60,'(A)') trim(cname) write(60,*) write(60,'(A)') trim(ename(1)) write(60,'(A)') trim(ename(2)) write(60,*) write(60,'("(Default units are atomic: Hartree, Bohr etc.) ")') write(60,*) do ip=1,nparam write(60,'(" ",A,T20,"=",T30,G18.10)') trim(pname(ip)),popt(ip) end do write(60,*) do ip=1,nparam if (trim(pname(ip)).eq."B0") then write(60,'(" B0 (GPa)",T20,"=",T30,G18.10)') popt(ip)*aupress_gpa end if if (trim(pname(ip)).eq."B0''") then write(60,'(A4," (/GPa)",T20,"=",T30,G18.10)') "B0''",popt(ip)/aupress_gpa end if end do write(60,*) close(60) ! output energy vs volume per atom at data points open(60,file='EVPAP.OUT') do ipt=1,nevpt write(60,*) vpt(ipt)/dble(natoms),ept(ipt)/dble(natoms) end do close(60) ! output energy vs volume per atom over volume interval open(60,file='EVPAI.OUT') do iplt=1,nvplt v=(vplt2-vplt1)*dble(iplt)/dble(nvplt)+vplt1 write(60,*) v/dble(natoms),eveos(etype,popt,v)/dble(natoms) end do close(60) ! output pressure vs volume per atom at data points open(60,file='PVPAP.OUT') do ipt=1,nevpt write(60,*) vpt(ipt)/dble(natoms),pveos(etype,popt,vpt(ipt))*aupress_gpa end do close(60) ! output pressure vs volume per atom over volume interval open(60,file='PVPAI.OUT') do iplt=1,nvplt v=(vplt2-vplt1)*dble(iplt)/dble(nvplt)+vplt1 write(60,*) v/dble(natoms),pveos(etype,popt,v)*aupress_gpa end do close(60) ! output enthalpy vs pressure per atom over volume interval open(60,file='HPPAI.OUT') do iplt=1,nvplt v=(vplt2-vplt1)*dble(iplt)/dble(nvplt)+vplt1 write(60,*) pveos(etype,popt,v)*aupress_gpa, & (eveos(etype,popt,v)+pveos(etype,popt,v)*v)/dble(natoms) end do close(60) write(*,*) write(*,'("All units are atomic unless otherwise stated")') write(*,'("EOS parameters written to PARAM.OUT")') write(*,'("Energy-volume per atom at data points written to EVPAP.OUT")') write(*,'("Energy-volume per atom over interval written to EVPAI.OUT")') write(*,'("Pressure(GPa)-volume per atom at data points written to PVPAP.OUT")') write(*,'("Pressure(GPa)-volume per atom over interval written to PVPAI.OUT")') write(*,'("Enthalpy-pressure(GPa) per atom over interval written to HPPAI.OUT")') write(*,*) return end subroutine elk-7.2.42/src/eos/PaxHeaders.21776/pveos.f900000644000000000000000000000013214061636515015164 xustar0030 mtime=1623670093.499103806 30 atime=1623670093.499103806 30 ctime=1623670093.499103806 elk-7.2.42/src/eos/pveos.f900000644002504400250440000000066114061636515017224 0ustar00dewhurstdewhurst00000000000000real(8) function pveos(etype,param,v) ! pressure-volume equation of state function implicit none ! arguments integer, intent(in) :: etype real(8), intent(in) :: param(*) real(8), intent(in) :: v ! local variables real(8) vm,vp,pm,pp,dv ! external functions real(8) eveos external eveos ! use central differences dv=1.d-3 vm=v-dv vp=v+dv pm=eveos(etype,param,vm) pp=eveos(etype,param,vp) pveos=-(pp-pm)/(2.d0*dv) return end function elk-7.2.42/src/eos/PaxHeaders.21776/readinput.f900000644000000000000000000000013214061636515016023 xustar0030 mtime=1623670093.501103804 30 atime=1623670093.501103804 30 ctime=1623670093.501103804 elk-7.2.42/src/eos/readinput.f900000644002504400250440000000144014061636515020057 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readinput use modmain implicit none ! local variables integer ipt open(50,file='eos.in',action='READ',status='OLD',form='FORMATTED') read(50,*) cname read(50,*) natoms if (natoms.le.0) then write(*,*) write(*,'("Error(readinput): natoms <= 0 : ",I8)') natoms write(*,*) stop end if read(50,*) etype read(50,*) vplt1,vplt2,nvplt read(50,*) nevpt if (nevpt.le.0) then write(*,*) write(*,'("Error(readinput): nevpt <= 0 : ",I8)') nevpt write(*,*) stop end if allocate(vpt(nevpt),ept(nevpt)) do ipt=1,nevpt read(50,*) vpt(ipt),ept(ipt) end do close(50) return end subroutine elk-7.2.42/src/PaxHeaders.21776/spacegroup0000644000000000000000000000013014061636515015013 xustar0029 mtime=1623670093.53810377 30 atime=1623670093.508103798 29 ctime=1623670093.53810377 elk-7.2.42/src/spacegroup/0000755002504400250440000000000014061636515017127 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/src/spacegroup/PaxHeaders.21776/spacegroup.in0000644000000000000000000000013214061636515017572 xustar0030 mtime=1623670093.510103796 30 atime=1623670093.509103797 30 ctime=1623670093.510103796 elk-7.2.42/src/spacegroup/spacegroup.in0000644002504400250440000000101714061636515021626 0ustar00dewhurstdewhurst00000000000000 'Bmab' : hrmg 10.0605232 10.0605232 24.972729 : a, b, c 90.0 90.0 90.0 : bc, ac, ab 1 1 1 : ncell .true. : primcell 3 : nspecies 'La' : spsymb 1 : nwpos 0.0000 0.0000 0.3608 : wpos 'Cu' 1 0.0000 0.0000 0.0000 'O' 2 0.2500 0.2500 0.0000 0.0000 0.0000 0.1820 elk-7.2.42/src/spacegroup/PaxHeaders.21776/Makefile0000644000000000000000000000013214061636515016532 xustar0030 mtime=1623670093.511103795 30 atime=1623670093.511103795 30 ctime=1623670093.511103795 elk-7.2.42/src/spacegroup/Makefile0000644002504400250440000000216714061636515020575 0ustar00dewhurstdewhurst00000000000000 include ../../make.inc #------------------------------------------------------------------------------- # Suffix rules #------------------------------------------------------------------------------- .SUFFIXES: .o .f90 .f90.o: $(F90) $(F90_OPTS) -c $< #------------------------------------------------------------------------------- # Source files #------------------------------------------------------------------------------- SRC_modules = modmain.f90 SRC_main = main.f90 SRC_routines = readinput.f90 gencrystal.f90 sgsymb.f90 seitzgen.f90 \ gengroup.f90 seitzeq.f90 seitzmul.f90 writegeom.f90 geomplot.f90 \ findprimcell.f90 r3frac.f90 r3mv.f90 r3cross.f90 r3minv.f90 r3mm.f90 SRC = $(SRC_modules) $(SRC_main) $(SRC_routines) OBJ = $(SRC:.f90=.o) EXE = spacegroup spacegroup: $(OBJ) $(F90) $(F90_OPTS) -o $(EXE) $(OBJ) clean: rm -f *.o *.mod *~ fort.* ifc* *.gcno *.OUT *.xsf *.ascii gmon.out \ *.aux *.dvi *.log *.pdf *.tex *.toc *.out $(EXE) doc: ../protex -s $(SRC_main) $(SRC_modules) $(SRC_routines) > spacegroup.tex pdflatex spacegroup;pdflatex spacegroup;pdflatex spacegroup spaces: ../rmspaces $(SRC) elk-7.2.42/src/spacegroup/PaxHeaders.21776/findprimcell.f900000644000000000000000000000013214061636515020062 xustar0030 mtime=1623670093.513103793 30 atime=1623670093.512103794 30 ctime=1623670093.513103793 elk-7.2.42/src/spacegroup/findprimcell.f900000644002504400250440000000735614061636515022132 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: findprimcell ! !INTERFACE: subroutine findprimcell ! !USES: use modmain ! !DESCRIPTION: ! This routine finds the smallest primitive cell which produces the same ! crystal structure as the conventional cell. This is done by searching ! through all the vectors which connect atomic positions and finding those ! which leave the crystal structure invariant. Of these, the three shortest ! which produce a non-zero unit cell volume are chosen. ! ! !REVISION HISTORY: ! Created April 2007 (JKD) !EOP !BOC implicit none ! local variables integer is,js,ia,ja,ka,na integer i1,i2,i3,i,j,n real(8) v1(3),v2(3),v3(3) real(8) t1,t2 ! allocatable arrays real(8), allocatable :: dp(:) real(8), allocatable :: vp(:,:) do is=1,nspecies do ia=1,natoms(is) ! make sure all atomic coordinates are in [0,1) call r3frac(epslat,atposl(:,ia,is)) ! determine atomic Cartesian coordinates call r3mv(avec,atposl(:,ia,is),atposc(:,ia,is)) end do end do ! find the smallest set of atoms is=1 do js=1,nspecies ! if a species has only one atom the cell must be primitive if (natoms(js).eq.1) return if (natoms(js).lt.natoms(is)) is=js end do n=27*natoms(is) allocate(dp(n),vp(3,n)) ! generate set of possible lattice vectors n=0 do ia=1,natoms(is) v1(:)=atposl(:,ia,is)-atposl(:,1,is) do i1=-1,1 v2(1)=v1(1)+dble(i1) do i2=-1,1 v2(2)=v1(2)+dble(i2) do i3=-1,1 v2(3)=v1(3)+dble(i3) t1=abs(v2(1))+abs(v2(2))+abs(v2(3)) if (t1.lt.epslat) goto 20 ! check if vector v2 leaves conventional cell invariant do js=1,nspecies do ja=1,natoms(js) v3(:)=atposl(:,ja,js)+v2(:) call r3frac(epslat,v3) do ka=1,natoms(js) ! check both positions and magnetic fields are the same t1=sum(abs(atposl(:,ka,js)-v3(:))) t2=sum(abs(bfcmt0(:,ja,js)-bfcmt0(:,ka,js))) if ((t1.lt.epslat).and.(t2.lt.epslat)) goto 10 end do ! atom ja has no equivalent under translation by v2 goto 20 10 continue end do end do ! cell invariant under translation by v2, so add to list n=n+1 call r3mv(avec,v2,vp(:,n)) dp(n)=sqrt(vp(1,n)**2+vp(2,n)**2+vp(3,n)**2) 20 continue end do end do end do end do if (n.eq.0) then write(*,*) write(*,'("Error(findprimcell): cannot find any lattice vectors")') write(*,*) stop end if ! find the shortest lattice vector j=1 t1=1.d8 do i=1,n if (dp(i).lt.t1+epslat) then j=i t1=dp(i) end if end do avec(:,1)=vp(:,j) ! find the next shortest lattice vector not parallel to the first j=1 t1=1.d8 do i=1,n call r3cross(avec(:,1),vp(:,i),v1) t2=sqrt(v1(1)**2+v1(2)**2+v1(3)**2) if (t2.gt.epslat) then if (dp(i).lt.t1+epslat) then j=i t1=dp(i) end if end if end do avec(:,2)=vp(:,j) ! find the next shortest lattice vector which gives non-zero unit cell volume call r3cross(avec(:,1),avec(:,2),v1) j=1 t1=1.d8 do i=1,n t2=dot_product(vp(:,i),v1(:)) if (abs(t2).gt.epslat) then if (dp(i).lt.t1+epslat) then j=i t1=dp(i) end if end if end do avec(:,3)=vp(:,j) call r3minv(avec,ainv) ! remove redundant atoms do is=1,nspecies na=0 do ia=1,natoms(is) call r3mv(ainv,atposc(:,ia,is),v1) call r3frac(epslat,v1) do ja=1,na t1=sum(abs(atposl(:,ja,is)-v1(:))) if (t1.lt.epslat) goto 30 end do na=na+1 atposl(:,na,is)=v1(:) call r3mv(avec,atposl(:,na,is),atposc(:,na,is)) bfcmt0(:,na,is)=bfcmt0(:,ia,is) 30 continue end do natoms(is)=na end do deallocate(dp,vp) return end subroutine !EOC elk-7.2.42/src/spacegroup/PaxHeaders.21776/gencrystal.f900000644000000000000000000000013214061636515017565 xustar0030 mtime=1623670093.514103792 30 atime=1623670093.514103792 30 ctime=1623670093.514103792 elk-7.2.42/src/spacegroup/gencrystal.f900000644002504400250440000000577314061636515021636 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gencrystal use modmain implicit none ! local variables integer is,ia,ip,i,j integer i1,i2,i3 integer ngen,ngrp real(8) abr,acr,bcr real(8) sab,cab,cac,cbc real(8) v1(3),v2(3),t1 ! space group generator Seitz matrices real(8) srgen(3,3,12),stgen(3,12) ! space group Seitz matrices real(8) srgrp(3,3,192),stgrp(3,192) ! convert angles from degrees to radians abr=ab*(pi/180.d0) acr=ac*(pi/180.d0) bcr=bc*(pi/180.d0) ! setup lattice vectors sab=sin(abr) if (abs(sab).lt.epslat) then write(*,*) write(*,'("Error(gencrystal): degenerate lattice vectors")') write(*,*) stop end if cab=cos(abr) cac=cos(acr) cbc=cos(bcr) avec(1,1)=a avec(2,1)=0.d0 avec(3,1)=0.d0 avec(1,2)=b*cab avec(2,2)=b*sab avec(3,2)=0.d0 avec(1,3)=c*cac avec(2,3)=c*(cbc-cab*cac)/sab avec(3,3)=c*sqrt(sab**2-cac**2+2.d0*cab*cac*cbc-cbc**2)/sab do i=1,3 do j=1,3 if (abs(avec(i,j)).lt.epslat) avec(i,j)=0.d0 end do end do ! scale lattice vectors by the number of unit cells do i=1,3 avec(:,i)=avec(:,i)*dble(ncell(i)) end do ! determine the Hall symbol from the Hermann-Mauguin symbol call sgsymb(hrmg,num,schn,hall) ! determine the space group generators call seitzgen(hall,ngen,srgen,stgen) ! compute the space group operations call gengroup(ngen,srgen,stgen,ngrp,srgrp,stgrp) ! compute the equivalent atomic positions do is=1,nspecies natoms(is)=0 do ip=1,nwpos(is) do j=1,ngrp ! apply the space group operation call r3mv(srgrp(:,1,j),wpos(:,ip,is),v1) v1(:)=v1(:)+stgrp(:,j) do i1=0,ncell(1)-1 do i2=0,ncell(2)-1 do i3=0,ncell(3)-1 v2(1)=(v1(1)+dble(i1))/dble(ncell(1)) v2(2)=(v1(2)+dble(i2))/dble(ncell(2)) v2(3)=(v1(3)+dble(i3))/dble(ncell(3)) call r3frac(epslat,v2) ! check if new position already exists do ia=1,natoms(is) t1=sum(abs(v2(:)-atposl(:,ia,is))) if (t1.lt.epslat) goto 30 end do ! add new position to list natoms(is)=natoms(is)+1 if (natoms(is).gt.maxatoms) then write(*,*) write(*,'("Error(gencrystal): natoms too large")') write(*,'(" for species ",I4)') is write(*,'("Adjust maxatoms and recompile code")') write(*,*) stop end if atposl(:,natoms(is),is)=v2(:) end do end do end do 30 continue end do end do natmtot=natmtot+natoms(is) end do ! set magnetic fields to zero bfcmt0(:,:,:)=0.d0 ! reduce conventional cell to primitive cell if required if (primcell) call findprimcell ! find the total number of atoms natmtot=0 do is=1,nspecies natmtot=natmtot+natoms(is) end do ! determine the Cartesian atomic coordinates do is=1,nspecies do ia=1,natoms(is) call r3mv(avec,atposl(:,ia,is),atposc(:,ia,is)) end do end do return end subroutine elk-7.2.42/src/spacegroup/PaxHeaders.21776/gengroup.f900000644000000000000000000000013014061636515017236 xustar0029 mtime=1623670093.51610379 30 atime=1623670093.515103791 29 ctime=1623670093.51610379 elk-7.2.42/src/spacegroup/gengroup.f900000644002504400250440000000331714061636515021301 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gengroup(ngen,srgen,stgen,ngrp,srgrp,stgrp) implicit none ! arguments integer, intent(in) :: ngen real(8), intent(in) :: srgen(3,3,ngen) real(8), intent(in) :: stgen(3,ngen) integer, intent(out) :: ngrp real(8), intent(out) :: srgrp(3,3,192) real(8), intent(out) :: stgrp(3,192) ! local variables integer i,j,k real(8), parameter :: eps=1.d-6 real(8) sr(3,3),st(3) ! external functions logical seitzeq external seitzeq ! store the identity ngrp=1 srgrp(1,1,1)=1.d0; srgrp(1,2,1)=0.d0; srgrp(1,3,1)=0.d0 srgrp(2,1,1)=0.d0; srgrp(2,2,1)=1.d0; srgrp(2,3,1)=0.d0 srgrp(3,1,1)=0.d0; srgrp(3,2,1)=0.d0; srgrp(3,3,1)=1.d0 stgrp(:,1)=0.d0 10 continue ! right multiply by the generators do i=1,ngen do j=1,ngrp call seitzmul(eps,srgrp(:,:,j),stgrp(:,j),srgen(:,:,i),stgen(:,i),sr,st) ! check if the new element already exists do k=1,ngrp if (seitzeq(eps,srgrp(:,:,k),stgrp(:,k),sr,st)) goto 20 end do goto 40 20 continue end do end do ! left multiply by the generators do i=1,ngen do j=1,ngrp call seitzmul(eps,srgen(:,:,i),stgen(:,i),srgrp(:,:,j),stgrp(:,j),sr,st) ! check if the new element already exists do k=1,ngrp if (seitzeq(eps,srgrp(:,:,k),stgrp(:,k),sr,st)) goto 30 end do goto 40 30 continue end do end do ! all elements accounted for return 40 continue ! add new element ngrp=ngrp+1 if (ngrp.gt.192) then write(*,*) write(*,'("Error(gengroup): more than 192 group elements")') write(*,*) stop end if srgrp(:,:,ngrp)=sr(:,:) stgrp(:,ngrp)=st(:) goto 10 return end subroutine elk-7.2.42/src/spacegroup/PaxHeaders.21776/geomplot.f900000644000000000000000000000012714061636515017244 xustar0029 mtime=1623670093.51710379 29 atime=1623670093.51710379 29 ctime=1623670093.51710379 elk-7.2.42/src/spacegroup/geomplot.f900000644002504400250440000000445314061636515021303 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine geomplot use modmain implicit none ! local variables integer is,ia ! Bohr to Angstroms (CODATA 2002) real(8), parameter :: au_to_ang=0.5291772108d0 real(8) v1(3),v2(3),v3(3),v4(3),t1 real(8) dxx,dyx,dyy,dzx,dzy,dzz !------------------------------------------------! ! write the XCrysden file to crystal.xsf ! !------------------------------------------------! open(50,file='crystal.xsf',action='WRITE',form='FORMATTED') write(50,*) write(50,'("CRYSTAL")') write(50,*) write(50,'("PRIMVEC")') write(50,'(3G18.10)') avec(:,1)*au_to_ang write(50,'(3G18.10)') avec(:,2)*au_to_ang write(50,'(3G18.10)') avec(:,3)*au_to_ang write(50,*) write(50,'("PRIMCOORD")') write(50,'(2I8)') natmtot,1 do is=1,nspecies do ia=1,natoms(is) call r3mv(avec,atposl(:,ia,is),v1) write(50,'(A,3G18.10)') trim(spsymb(is)),v1(:)*au_to_ang end do end do close(50) write(*,*) write(*,'("Info(writexsf):")') write(*,'(" XCrysDen file written to crystal.xsf")') !-----------------------------------------------! ! write the V_Sim file to crystal.ascii ! !-----------------------------------------------! ! determine coordinate system vectors t1=sqrt(avec(1,1)**2+avec(2,1)**2+avec(3,1)**2) v1(:)=avec(:,1)/t1 t1=sqrt(avec(1,2)**2+avec(2,2)**2+avec(3,2)**2) v2(:)=avec(:,2)/t1 call r3cross(v1,v2,v3) t1=sqrt(v3(1)**2+v3(2)**2+v3(3)**2) v3(:)=v3(:)/t1 call r3cross(v3,v1,v2) t1=sqrt(v2(1)**2+v2(2)**2+v2(3)**2) v2(:)=v2(:)/t1 dxx=dot_product(avec(:,1),v1(:)) dyx=dot_product(avec(:,2),v1(:)) dyy=dot_product(avec(:,2),v2(:)) dzx=dot_product(avec(:,3),v1(:)) dzy=dot_product(avec(:,3),v2(:)) dzz=dot_product(avec(:,3),v3(:)) open(50,file='crystal.ascii',action='WRITE',form='FORMATTED') write(50,*) write(50,'(3G18.10)') dxx,dyx,dyy write(50,'(3G18.10)') dzx,dzy,dzz write(50,*) do is=1,nspecies do ia=1,natoms(is) v4(1)=dot_product(atposc(:,ia,is),v1(:)) v4(2)=dot_product(atposc(:,ia,is),v2(:)) v4(3)=dot_product(atposc(:,ia,is),v3(:)) write(50,'(3G18.10," ",A)') v4,trim(spsymb(is)) end do end do close(50) write(*,*) write(*,'("Info(writevsim):")') write(*,'(" V_Sim file written to crystal.ascii")') return end subroutine elk-7.2.42/src/spacegroup/PaxHeaders.21776/main.f900000644000000000000000000000013214061636515016336 xustar0030 mtime=1623670093.519103788 30 atime=1623670093.518103789 30 ctime=1623670093.519103788 elk-7.2.42/src/spacegroup/main.f900000644002504400250440000013267614061636515020412 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. program main implicit none ! read the input parameters from spacegroup.in call readinput ! generate the lattice and atomic basis call gencrystal ! write the structural data to GEOMETRY.OUT call writegeom ! write the XCrySDen and V_Sim files for plotting call geomplot stop end program !BOI ! !TITLE: {\huge{\sc The Spacegroup Manual}}\\ \Large{\sc Version 1.2.1} ! !AUTHORS: {\sc J. K. Dewhurst, S. Sharma and L. Nordstr\"{o}m} ! !AFFILIATION: ! !INTRODUCTION: Introduction ! Spacegroup is a utility which produces crystal geometry for use with the Elk ! code, from the space group defined by its Hermann-Mauguin symbol and lattice ! vector lengths and angles. Spacegroup recognises all 230 space groups in ! various coordinate settings giving a total of 530 possible symbols, which are ! tabulated below. The code also provides output compatible with the XCrysDen or ! V\_Sim packages for visualisation of the crystal structure. ! \section{Usage} ! Only one input file, {\tt spacegroup.in}, is required. The structure of this ! file is illustrated by the following example for the high $T_c$ superconductor ! La$_2$CuO$_4$: ! \begin{verbatim} ! 'Bmab' : hrmg ! 10.0605232 10.0605232 24.972729 : a, b, c ! 90.0 90.0 90.0 : bc, ac, ab ! 1 1 1 : ncell ! .true. : primcell ! 3 : nspecies ! 'La' : spsymb ! 1 : nwpos ! 0.0000 0.0000 0.3608 : wpos ! 'Cu' ! 1 ! 0.0000 0.0000 0.0000 ! 'O' ! 2 ! 0.2500 0.2500 0.0000 ! 0.0000 0.0000 0.1820 ! \end{verbatim} ! The input parameters are defined as follows: ! \vskip 6pt ! {\tt hrmg}\\ ! The Hermann-Mauguin symbol of a space group listed in the table below. ! (case-sensitive) ! \vskip 6pt ! {\tt a}, {\tt b}, {\tt c}\\ ! Lattice vector lengths in Bohr (i.e. atomic units, {\bf NOT} \AA ngstroms). ! \vskip 6pt ! {\tt bc}, {\tt ac}, {\tt ab}\\ ! Angles in degrees between lattice vectors ${\bf b}$ and ${\bf c}$ ($\alpha$); ! ${\bf a}$ and ${\bf c}$ ($\beta$); and ${\bf a}$ and ${\bf b}$ ($\gamma$). ! \vskip 6pt ! {\tt ncell}\\ ! The number of unit cells required in each direction. ! \vskip 6pt ! {\tt primcell}\\ ! Set to {\tt .true.} if the primitive unit cell should be found. ! \vskip 6pt ! {\tt nspecies}\\ ! Number of atomic species. ! \vskip 6pt ! {\tt spsymb}\\ ! The atomic species symbol. ! \vskip 6pt ! {\tt nwpos}\\ ! The number of Wyckoff positional coordinates. ! \vskip 6pt ! {\tt wpos}\\ ! Wyckoff positional coordinates in fractions of the lattice vectors. ! \vskip 6pt ! Note that {\tt nwpos} and {\tt wpos} are repeated as many times as there are ! species. After creating the input file, the {\tt spacegroup} command is run ! and the files {\tt GEOMETRY.OUT} and {\tt crystal.xsf} should be produced. ! The {\tt GEOMETRY.OUT} file can simply be appended to an {\tt elk.in} file. If ! XCrysDen is available, then use the command ! \vskip 6pt ! \hskip 24pt {\tt xcrysden --xsf crystal.xsf} ! \vskip 6pt ! to render the unit cell. ! \section{Table of space group symbols} ! We acknowledge Ralf W. Grosse-Kunstleve ({\tt http://cci.lbl.gov/sginfo/}) ! for the following table which associates space group numbers, Sch\"{o}nflies ! symbols, Hermann-Mauguin symbols, and Hall symbols. ! \newpage ! \begin{center} ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 1 & C$_{1}^{1}$ & P1 & P 1 \\ ! 2 & C$_{i}^{1}$ & P-1 & -P 1 \\ ! 3:b & C$_{2}^{1}$ & P2:b = P121 & P 2y \\ ! 3:c & C$_{2}^{1}$ & P2:c = P112 & P 2 \\ ! 3:a & C$_{2}^{1}$ & P2:a = P211 & P 2x \\ ! 4:b & C$_{2}^{2}$ & P21:b = P1211 & P 2yb \\ ! 4:c & C$_{2}^{2}$ & P21:c = P1121 & P 2c \\ ! 4:a & C$_{2}^{2}$ & P21:a = P2111 & P 2xa \\ ! 5:b1 & C$_{2}^{3}$ & C2:b1 = C121 & C 2y \\ ! 5:b2 & C$_{2}^{3}$ & C2:b2 = A121 & A 2y \\ ! 5:b3 & C$_{2}^{3}$ & C2:b3 = I121 & I 2y \\ ! 5:c1 & C$_{2}^{3}$ & C2:c1 = A112 & A 2 \\ ! 5:c2 & C$_{2}^{3}$ & C2:c2 = B112 = B2 & B 2 \\ ! 5:c3 & C$_{2}^{3}$ & C2:c3 = I112 & I 2 \\ ! 5:a1 & C$_{2}^{3}$ & C2:a1 = B211 & B 2x \\ ! 5:a2 & C$_{2}^{3}$ & C2:a2 = C211 & C 2x \\ ! 5:a3 & C$_{2}^{3}$ & C2:a3 = I211 & I 2x \\ ! 6:b & C$_{s}^{1}$ & Pm:b = P1m1 & P -2y \\ ! 6:c & C$_{s}^{1}$ & Pm:c = P11m & P -2 \\ ! 6:a & C$_{s}^{1}$ & Pm:a = Pm11 & P -2x \\ ! 7:b1 & C$_{s}^{2}$ & Pc:b1 = P1c1 & P -2yc \\ ! 7:b2 & C$_{s}^{2}$ & Pc:b2 = P1n1 & P -2yac \\ ! 7:b3 & C$_{s}^{2}$ & Pc:b3 = P1a1 & P -2ya \\ ! 7:c1 & C$_{s}^{2}$ & Pc:c1 = P11a & P -2a \\ ! 7:c2 & C$_{s}^{2}$ & Pc:c2 = P11n & P -2ab \\ ! 7:c3 & C$_{s}^{2}$ & Pc:c3 = P11b = Pb & P -2b \\ ! 7:a1 & C$_{s}^{2}$ & Pc:a1 = Pb11 & P -2xb \\ ! 7:a2 & C$_{s}^{2}$ & Pc:a2 = Pn11 & P -2xbc \\ ! 7:a3 & C$_{s}^{2}$ & Pc:a3 = Pc11 & P -2xc \\ ! 8:b1 & C$_{s}^{3}$ & Cm:b1 = C1m1 & C -2y \\ ! 8:b2 & C$_{s}^{3}$ & Cm:b2 = A1m1 & A -2y \\ ! 8:b3 & C$_{s}^{3}$ & Cm:b3 = I1m1 & I -2y \\ ! 8:c1 & C$_{s}^{3}$ & Cm:c1 = A11m & A -2 \\ ! 8:c2 & C$_{s}^{3}$ & Cm:c2 = B11m = Bm & B -2 \\ ! 8:c3 & C$_{s}^{3}$ & Cm:c3 = I11m & I -2 \\ ! 8:a1 & C$_{s}^{3}$ & Cm:a1 = Bm11 & B -2x \\ ! 8:a2 & C$_{s}^{3}$ & Cm:a2 = Cm11 & C -2x \\ ! 8:a3 & C$_{s}^{3}$ & Cm:a3 = Im11 & I -2x \\ ! 9:b1 & C$_{s}^{4}$ & Cc:b1 = C1c1 & C -2yc \\ ! 9:b2 & C$_{s}^{4}$ & Cc:b2 = A1n1 & A -2yac \\ ! 9:b3 & C$_{s}^{4}$ & Cc:b3 = I1a1 & I -2ya \\ ! 9:-b1 & C$_{s}^{4}$ & Cc:-b1 = A1a1 & A -2ya \\ ! 9:-b2 & C$_{s}^{4}$ & Cc:-b2 = C1n1 & C -2ybc \\ ! 9:-b3 & C$_{s}^{4}$ & Cc:-b3 = I1c1 & I -2yc \\ ! 9:c1 & C$_{s}^{4}$ & Cc:c1 = A11a & A -2a \\ ! 9:c2 & C$_{s}^{4}$ & Cc:c2 = B11n & B -2bc \\ ! 9:c3 & C$_{s}^{4}$ & Cc:c3 = I11b & I -2b \\ ! 9:-c1 & C$_{s}^{4}$ & Cc:-c1 = B11b = Bb & B -2b \\ ! 9:-c2 & C$_{s}^{4}$ & Cc:-c2 = A11n & A -2ac \\ ! 9:-c3 & C$_{s}^{4}$ & Cc:-c3 = I11a & I -2a \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 9:a1 & C$_{s}^{4}$ & Cc:a1 = Bb11 & B -2xb \\ ! 9:a2 & C$_{s}^{4}$ & Cc:a2 = Cn11 & C -2xbc \\ ! 9:a3 & C$_{s}^{4}$ & Cc:a3 = Ic11 & I -2xc \\ ! 9:-a1 & C$_{s}^{4}$ & Cc:-a1 = Cc11 & C -2xc \\ ! 9:-a2 & C$_{s}^{4}$ & Cc:-a2 = Bn11 & B -2xbc \\ ! 9:-a3 & C$_{s}^{4}$ & Cc:-a3 = Ib11 & I -2xb \\ ! 10:b & C$_{2h}^{1}$ & P2/m:b = P12/m1 & -P 2y \\ ! 10:c & C$_{2h}^{1}$ & P2/m:c = P112/m & -P 2 \\ ! 10:a & C$_{2h}^{1}$ & P2/m:a = P2/m11 & -P 2x \\ ! 11:b & C$_{2h}^{2}$ & P21/m:b = P121/m1 & -P 2yb \\ ! 11:c & C$_{2h}^{2}$ & P21/m:c = P1121/m & -P 2c \\ ! 11:a & C$_{2h}^{2}$ & P21/m:a = P21/m11 & -P 2xa \\ ! 12:b1 & C$_{2h}^{3}$ & C2/m:b1 = C12/m1 & -C 2y \\ ! 12:b2 & C$_{2h}^{3}$ & C2/m:b2 = A12/m1 & -A 2y \\ ! 12:b3 & C$_{2h}^{3}$ & C2/m:b3 = I12/m1 & -I 2y \\ ! 12:c1 & C$_{2h}^{3}$ & C2/m:c1 = A112/m & -A 2 \\ ! 12:c2 & C$_{2h}^{3}$ & C2/m:c2 = B112/m = B2/m & -B 2 \\ ! 12:c3 & C$_{2h}^{3}$ & C2/m:c3 = I112/m & -I 2 \\ ! 12:a1 & C$_{2h}^{3}$ & C2/m:a1 = B2/m11 & -B 2x \\ ! 12:a2 & C$_{2h}^{3}$ & C2/m:a2 = C2/m11 & -C 2x \\ ! 12:a3 & C$_{2h}^{3}$ & C2/m:a3 = I2/m11 & -I 2x \\ ! 13:b1 & C$_{2h}^{4}$ & P2/c:b1 = P12/c1 & -P 2yc \\ ! 13:b2 & C$_{2h}^{4}$ & P2/c:b2 = P12/n1 & -P 2yac \\ ! 13:b3 & C$_{2h}^{4}$ & P2/c:b3 = P12/a1 & -P 2ya \\ ! 13:c1 & C$_{2h}^{4}$ & P2/c:c1 = P112/a & -P 2a \\ ! 13:c2 & C$_{2h}^{4}$ & P2/c:c2 = P112/n & -P 2ab \\ ! 13:c3 & C$_{2h}^{4}$ & P2/c:c3 = P112/b = P2/b & -P 2b \\ ! 13:a1 & C$_{2h}^{4}$ & P2/c:a1 = P2/b11 & -P 2xb \\ ! 13:a2 & C$_{2h}^{4}$ & P2/c:a2 = P2/n11 & -P 2xbc \\ ! 13:a3 & C$_{2h}^{4}$ & P2/c:a3 = P2/c11 & -P 2xc \\ ! 14:b1 & C$_{2h}^{5}$ & P21/c:b1 = P121/c1 & -P 2ybc \\ ! 14:b2 & C$_{2h}^{5}$ & P21/c:b2 = P121/n1 & -P 2yn \\ ! 14:b3 & C$_{2h}^{5}$ & P21/c:b3 = P121/a1 & -P 2yab \\ ! 14:c1 & C$_{2h}^{5}$ & P21/c:c1 = P1121/a & -P 2ac \\ ! 14:c2 & C$_{2h}^{5}$ & P21/c:c2 = P1121/n & -P 2n \\ ! 14:c3 & C$_{2h}^{5}$ & P21/c:c3 = P1121/b = P21/b & -P 2bc \\ ! 14:a1 & C$_{2h}^{5}$ & P21/c:a1 = P21/b11 & -P 2xab \\ ! 14:a2 & C$_{2h}^{5}$ & P21/c:a2 = P21/n11 & -P 2xn \\ ! 14:a3 & C$_{2h}^{5}$ & P21/c:a3 = P21/c11 & -P 2xac \\ ! 15:b1 & C$_{2h}^{6}$ & C2/c:b1 = C12/c1 & -C 2yc \\ ! 15:b2 & C$_{2h}^{6}$ & C2/c:b2 = A12/n1 & -A 2yac \\ ! 15:b3 & C$_{2h}^{6}$ & C2/c:b3 = I12/a1 & -I 2ya \\ ! 15:-b1 & C$_{2h}^{6}$ & C2/c:-b1 = A12/a1 & -A 2ya \\ ! 15:-b2 & C$_{2h}^{6}$ & C2/c:-b2 = C12/n1 & -C 2ybc \\ ! 15:-b3 & C$_{2h}^{6}$ & C2/c:-b3 = I12/c1 & -I 2yc \\ ! 15:c1 & C$_{2h}^{6}$ & C2/c:c1 = A112/a & -A 2a \\ ! 15:c2 & C$_{2h}^{6}$ & C2/c:c2 = B112/n & -B 2bc \\ ! 15:c3 & C$_{2h}^{6}$ & C2/c:c3 = I112/b & -I 2b \\ ! 15:-c1 & C$_{2h}^{6}$ & C2/c:-c1 = B112/b = B2/b & -B 2b \\ ! 15:-c2 & C$_{2h}^{6}$ & C2/c:-c2 = A112/n & -A 2ac \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 15:-c3 & C$_{2h}^{6}$ & C2/c:-c3 = I112/a & -I 2a \\ ! 15:a1 & C$_{2h}^{6}$ & C2/c:a1 = B2/b11 & -B 2xb \\ ! 15:a2 & C$_{2h}^{6}$ & C2/c:a2 = C2/n11 & -C 2xbc \\ ! 15:a3 & C$_{2h}^{6}$ & C2/c:a3 = I2/c11 & -I 2xc \\ ! 15:-a1 & C$_{2h}^{6}$ & C2/c:-a1 = C2/c11 & -C 2xc \\ ! 15:-a2 & C$_{2h}^{6}$ & C2/c:-a2 = B2/n11 & -B 2xbc \\ ! 15:-a3 & C$_{2h}^{6}$ & C2/c:-a3 = I2/b11 & -I 2xb \\ ! 16 & D$_{2}^{1}$ & P222 & P 2 2 \\ ! 17 & D$_{2}^{2}$ & P2221 & P 2c 2 \\ ! 17:cab & D$_{2}^{2}$ & P2122 & P 2a 2a \\ ! 17:bca & D$_{2}^{2}$ & P2212 & P 2 2b \\ ! 18 & D$_{2}^{3}$ & P21212 & P 2 2ab \\ ! 18:cab & D$_{2}^{3}$ & P22121 & P 2bc 2 \\ ! 18:bca & D$_{2}^{3}$ & P21221 & P 2ac 2ac \\ ! 19 & D$_{2}^{4}$ & P212121 & P 2ac 2ab \\ ! 20 & D$_{2}^{5}$ & C2221 & C 2c 2 \\ ! 20:cab & D$_{2}^{5}$ & A2122 & A 2a 2a \\ ! 20:bca & D$_{2}^{5}$ & B2212 & B 2 2b \\ ! 21 & D$_{2}^{6}$ & C222 & C 2 2 \\ ! 21:cab & D$_{2}^{6}$ & A222 & A 2 2 \\ ! 21:bca & D$_{2}^{6}$ & B222 & B 2 2 \\ ! 22 & D$_{2}^{7}$ & F222 & F 2 2 \\ ! 23 & D$_{2}^{8}$ & I222 & I 2 2 \\ ! 24 & D$_{2}^{9}$ & I212121 & I 2b 2c \\ ! 25 & C$_{2v}^{1}$ & Pmm2 & P 2 -2 \\ ! 25:cab & C$_{2v}^{1}$ & P2mm & P -2 2 \\ ! 25:bca & C$_{2v}^{1}$ & Pm2m & P -2 -2 \\ ! 26 & C$_{2v}^{2}$ & Pmc21 & P 2c -2 \\ ! 26:ba-c & C$_{2v}^{2}$ & Pcm21 & P 2c -2c \\ ! 26:cab & C$_{2v}^{2}$ & P21ma & P -2a 2a \\ ! 26:-cba & C$_{2v}^{2}$ & P21am & P -2 2a \\ ! 26:bca & C$_{2v}^{2}$ & Pb21m & P -2 -2b \\ ! 26:a-cb & C$_{2v}^{2}$ & Pm21b & P -2b -2 \\ ! 27 & C$_{2v}^{3}$ & Pcc2 & P 2 -2c \\ ! 27:cab & C$_{2v}^{3}$ & P2aa & P -2a 2 \\ ! 27:bca & C$_{2v}^{3}$ & Pb2b & P -2b -2b \\ ! 28 & C$_{2v}^{4}$ & Pma2 & P 2 -2a \\ ! 28:ba-c & C$_{2v}^{4}$ & Pbm2 & P 2 -2b \\ ! 28:cab & C$_{2v}^{4}$ & P2mb & P -2b 2 \\ ! 28:-cba & C$_{2v}^{4}$ & P2cm & P -2c 2 \\ ! 28:bca & C$_{2v}^{4}$ & Pc2m & P -2c -2c \\ ! 28:a-cb & C$_{2v}^{4}$ & Pm2a & P -2a -2a \\ ! 29 & C$_{2v}^{5}$ & Pca21 & P 2c -2ac \\ ! 29:ba-c & C$_{2v}^{5}$ & Pbc21 & P 2c -2b \\ ! 29:cab & C$_{2v}^{5}$ & P21ab & P -2b 2a \\ ! 29:-cba & C$_{2v}^{5}$ & P21ca & P -2ac 2a \\ ! 29:bca & C$_{2v}^{5}$ & Pc21b & P -2bc -2c \\ ! 29:a-cb & C$_{2v}^{5}$ & Pb21a & P -2a -2ab \\ ! 30 & C$_{2v}^{6}$ & Pnc2 & P 2 -2bc \\ ! 30:ba-c & C$_{2v}^{6}$ & Pcn2 & P 2 -2ac \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 30:cab & C$_{2v}^{6}$ & P2na & P -2ac 2 \\ ! 30:-cba & C$_{2v}^{6}$ & P2an & P -2ab 2 \\ ! 30:bca & C$_{2v}^{6}$ & Pb2n & P -2ab -2ab \\ ! 30:a-cb & C$_{2v}^{6}$ & Pn2b & P -2bc -2bc \\ ! 31 & C$_{2v}^{7}$ & Pmn21 & P 2ac -2 \\ ! 31:ba-c & C$_{2v}^{7}$ & Pnm21 & P 2bc -2bc \\ ! 31:cab & C$_{2v}^{7}$ & P21mn & P -2ab 2ab \\ ! 31:-cba & C$_{2v}^{7}$ & P21nm & P -2 2ac \\ ! 31:bca & C$_{2v}^{7}$ & Pn21m & P -2 -2bc \\ ! 31:a-cb & C$_{2v}^{7}$ & Pm21n & P -2ab -2 \\ ! 32 & C$_{2v}^{8}$ & Pba2 & P 2 -2ab \\ ! 32:cab & C$_{2v}^{8}$ & P2cb & P -2bc 2 \\ ! 32:bca & C$_{2v}^{8}$ & Pc2a & P -2ac -2ac \\ ! 33 & C$_{2v}^{9}$ & Pna21 & P 2c -2n \\ ! 33:ba-c & C$_{2v}^{9}$ & Pbn21 & P 2c -2ab \\ ! 33:cab & C$_{2v}^{9}$ & P21nb & P -2bc 2a \\ ! 33:-cba & C$_{2v}^{9}$ & P21cn & P -2n 2a \\ ! 33:bca & C$_{2v}^{9}$ & Pc21n & P -2n -2ac \\ ! 33:a-cb & C$_{2v}^{9}$ & Pn21a & P -2ac -2n \\ ! 34 & C$_{2v}^{10}$ & Pnn2 & P 2 -2n \\ ! 34:cab & C$_{2v}^{10}$ & P2nn & P -2n 2 \\ ! 34:bca & C$_{2v}^{10}$ & Pn2n & P -2n -2n \\ ! 35 & C$_{2v}^{11}$ & Cmm2 & C 2 -2 \\ ! 35:cab & C$_{2v}^{11}$ & A2mm & A -2 2 \\ ! 35:bca & C$_{2v}^{11}$ & Bm2m & B -2 -2 \\ ! 36 & C$_{2v}^{12}$ & Cmc21 & C 2c -2 \\ ! 36:ba-c & C$_{2v}^{12}$ & Ccm21 & C 2c -2c \\ ! 36:cab & C$_{2v}^{12}$ & A21ma & A -2a 2a \\ ! 36:-cba & C$_{2v}^{12}$ & A21am & A -2 2a \\ ! 36:bca & C$_{2v}^{12}$ & Bb21m & B -2 -2b \\ ! 36:a-cb & C$_{2v}^{12}$ & Bm21b & B -2b -2 \\ ! 37 & C$_{2v}^{13}$ & Ccc2 & C 2 -2c \\ ! 37:cab & C$_{2v}^{13}$ & A2aa & A -2a 2 \\ ! 37:bca & C$_{2v}^{13}$ & Bb2b & B -2b -2b \\ ! 38 & C$_{2v}^{14}$ & Amm2 & A 2 -2 \\ ! 38:ba-c & C$_{2v}^{14}$ & Bmm2 & B 2 -2 \\ ! 38:cab & C$_{2v}^{14}$ & B2mm & B -2 2 \\ ! 38:-cba & C$_{2v}^{14}$ & C2mm & C -2 2 \\ ! 38:bca & C$_{2v}^{14}$ & Cm2m & C -2 -2 \\ ! 38:a-cb & C$_{2v}^{14}$ & Am2m & A -2 -2 \\ ! 39 & C$_{2v}^{15}$ & Abm2 & A 2 -2c \\ ! 39:ba-c & C$_{2v}^{15}$ & Bma2 & B 2 -2c \\ ! 39:cab & C$_{2v}^{15}$ & B2cm & B -2c 2 \\ ! 39:-cba & C$_{2v}^{15}$ & C2mb & C -2b 2 \\ ! 39:bca & C$_{2v}^{15}$ & Cm2a & C -2b -2b \\ ! 39:a-cb & C$_{2v}^{15}$ & Ac2m & A -2c -2c \\ ! 40 & C$_{2v}^{16}$ & Ama2 & A 2 -2a \\ ! 40:ba-c & C$_{2v}^{16}$ & Bbm2 & B 2 -2b \\ ! 40:cab & C$_{2v}^{16}$ & B2mb & B -2b 2 \\ ! 40:-cba & C$_{2v}^{16}$ & C2cm & C -2c 2 \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 40:bca & C$_{2v}^{16}$ & Cc2m & C -2c -2c \\ ! 40:a-cb & C$_{2v}^{16}$ & Am2a & A -2a -2a \\ ! 41 & C$_{2v}^{17}$ & Aba2 & A 2 -2ac \\ ! 41:ba-c & C$_{2v}^{17}$ & Bba2 & B 2 -2bc \\ ! 41:cab & C$_{2v}^{17}$ & B2cb & B -2bc 2 \\ ! 41:-cba & C$_{2v}^{17}$ & C2cb & C -2bc 2 \\ ! 41:bca & C$_{2v}^{17}$ & Cc2a & C -2bc -2bc \\ ! 41:a-cb & C$_{2v}^{17}$ & Ac2a & A -2ac -2ac \\ ! 42 & C$_{2v}^{18}$ & Fmm2 & F 2 -2 \\ ! 42:cab & C$_{2v}^{18}$ & F2mm & F -2 2 \\ ! 42:bca & C$_{2v}^{18}$ & Fm2m & F -2 -2 \\ ! 43 & C$_{2v}^{19}$ & Fdd2 & F 2 -2d \\ ! 43:cab & C$_{2v}^{19}$ & F2dd & F -2d 2 \\ ! 43:bca & C$_{2v}^{19}$ & Fd2d & F -2d -2d \\ ! 44 & C$_{2v}^{20}$ & Imm2 & I 2 -2 \\ ! 44:cab & C$_{2v}^{20}$ & I2mm & I -2 2 \\ ! 44:bca & C$_{2v}^{20}$ & Im2m & I -2 -2 \\ ! 45 & C$_{2v}^{21}$ & Iba2 & I 2 -2c \\ ! 45:cab & C$_{2v}^{21}$ & I2cb & I -2a 2 \\ ! 45:bca & C$_{2v}^{21}$ & Ic2a & I -2b -2b \\ ! 46 & C$_{2v}^{22}$ & Ima2 & I 2 -2a \\ ! 46:ba-c & C$_{2v}^{22}$ & Ibm2 & I 2 -2b \\ ! 46:cab & C$_{2v}^{22}$ & I2mb & I -2b 2 \\ ! 46:-cba & C$_{2v}^{22}$ & I2cm & I -2c 2 \\ ! 46:bca & C$_{2v}^{22}$ & Ic2m & I -2c -2c \\ ! 46:a-cb & C$_{2v}^{22}$ & Im2a & I -2a -2a \\ ! 47 & D$_{2h}^{1}$ & Pmmm & -P 2 2 \\ ! 48:1 & D$_{2h}^{2}$ & Pnnn:1 & P 2 2 -1n \\ ! 48:2 & D$_{2h}^{2}$ & Pnnn:2 & -P 2ab 2bc \\ ! 49 & D$_{2h}^{3}$ & Pccm & -P 2 2c \\ ! 49:cab & D$_{2h}^{3}$ & Pmaa & -P 2a 2 \\ ! 49:bca & D$_{2h}^{3}$ & Pbmb & -P 2b 2b \\ ! 50:1 & D$_{2h}^{4}$ & Pban:1 & P 2 2 -1ab \\ ! 50:2 & D$_{2h}^{4}$ & Pban:2 & -P 2ab 2b \\ ! 50:1cab & D$_{2h}^{4}$ & Pncb:1 & P 2 2 -1bc \\ ! 50:2cab & D$_{2h}^{4}$ & Pncb:2 & -P 2b 2bc \\ ! 50:1bca & D$_{2h}^{4}$ & Pcna:1 & P 2 2 -1ac \\ ! 50:2bca & D$_{2h}^{4}$ & Pcna:2 & -P 2a 2c \\ ! 51 & D$_{2h}^{5}$ & Pmma & -P 2a 2a \\ ! 51:ba-c & D$_{2h}^{5}$ & Pmmb & -P 2b 2 \\ ! 51:cab & D$_{2h}^{5}$ & Pbmm & -P 2 2b \\ ! 51:-cba & D$_{2h}^{5}$ & Pcmm & -P 2c 2c \\ ! 51:bca & D$_{2h}^{5}$ & Pmcm & -P 2c 2 \\ ! 51:a-cb & D$_{2h}^{5}$ & Pmam & -P 2 2a \\ ! 52 & D$_{2h}^{6}$ & Pnna & -P 2a 2bc \\ ! 52:ba-c & D$_{2h}^{6}$ & Pnnb & -P 2b 2n \\ ! 52:cab & D$_{2h}^{6}$ & Pbnn & -P 2n 2b \\ ! 52:-cba & D$_{2h}^{6}$ & Pcnn & -P 2ab 2c \\ ! 52:bca & D$_{2h}^{6}$ & Pncn & -P 2ab 2n \\ ! 52:a-cb & D$_{2h}^{6}$ & Pnan & -P 2n 2bc \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 53 & D$_{2h}^{7}$ & Pmna & -P 2ac 2 \\ ! 53:ba-c & D$_{2h}^{7}$ & Pnmb & -P 2bc 2bc \\ ! 53:cab & D$_{2h}^{7}$ & Pbmn & -P 2ab 2ab \\ ! 53:-cba & D$_{2h}^{7}$ & Pcnm & -P 2 2ac \\ ! 53:bca & D$_{2h}^{7}$ & Pncm & -P 2 2bc \\ ! 53:a-cb & D$_{2h}^{7}$ & Pman & -P 2ab 2 \\ ! 54 & D$_{2h}^{8}$ & Pcca & -P 2a 2ac \\ ! 54:ba-c & D$_{2h}^{8}$ & Pccb & -P 2b 2c \\ ! 54:cab & D$_{2h}^{8}$ & Pbaa & -P 2a 2b \\ ! 54:-cba & D$_{2h}^{8}$ & Pcaa & -P 2ac 2c \\ ! 54:bca & D$_{2h}^{8}$ & Pbcb & -P 2bc 2b \\ ! 54:a-cb & D$_{2h}^{8}$ & Pbab & -P 2b 2ab \\ ! 55 & D$_{2h}^{9}$ & Pbam & -P 2 2ab \\ ! 55:cab & D$_{2h}^{9}$ & Pmcb & -P 2bc 2 \\ ! 55:bca & D$_{2h}^{9}$ & Pcma & -P 2ac 2ac \\ ! 56 & D$_{2h}^{10}$ & Pccn & -P 2ab 2ac \\ ! 56:cab & D$_{2h}^{10}$ & Pnaa & -P 2ac 2bc \\ ! 56:bca & D$_{2h}^{10}$ & Pbnb & -P 2bc 2ab \\ ! 57 & D$_{2h}^{11}$ & Pbcm & -P 2c 2b \\ ! 57:ba-c & D$_{2h}^{11}$ & Pcam & -P 2c 2ac \\ ! 57:cab & D$_{2h}^{11}$ & Pmca & -P 2ac 2a \\ ! 57:-cba & D$_{2h}^{11}$ & Pmab & -P 2b 2a \\ ! 57:bca & D$_{2h}^{11}$ & Pbma & -P 2a 2ab \\ ! 57:a-cb & D$_{2h}^{11}$ & Pcmb & -P 2bc 2c \\ ! 58 & D$_{2h}^{12}$ & Pnnm & -P 2 2n \\ ! 58:cab & D$_{2h}^{12}$ & Pmnn & -P 2n 2 \\ ! 58:bca & D$_{2h}^{12}$ & Pnmn & -P 2n 2n \\ ! 59:1 & D$_{2h}^{13}$ & Pmmn:1 & P 2 2ab -1ab \\ ! 59:2 & D$_{2h}^{13}$ & Pmmn:2 & -P 2ab 2a \\ ! 59:1cab & D$_{2h}^{13}$ & Pnmm:1 & P 2bc 2 -1bc \\ ! 59:2cab & D$_{2h}^{13}$ & Pnmm:2 & -P 2c 2bc \\ ! 59:1bca & D$_{2h}^{13}$ & Pmnm:1 & P 2ac 2ac -1ac \\ ! 59:2bca & D$_{2h}^{13}$ & Pmnm:2 & -P 2c 2a \\ ! 60 & D$_{2h}^{14}$ & Pbcn & -P 2n 2ab \\ ! 60:ba-c & D$_{2h}^{14}$ & Pcan & -P 2n 2c \\ ! 60:cab & D$_{2h}^{14}$ & Pnca & -P 2a 2n \\ ! 60:-cba & D$_{2h}^{14}$ & Pnab & -P 2bc 2n \\ ! 60:bca & D$_{2h}^{14}$ & Pbna & -P 2ac 2b \\ ! 60:a-cb & D$_{2h}^{14}$ & Pcnb & -P 2b 2ac \\ ! 61 & D$_{2h}^{15}$ & Pbca & -P 2ac 2ab \\ ! 61:ba-c & D$_{2h}^{15}$ & Pcab & -P 2bc 2ac \\ ! 62 & D$_{2h}^{16}$ & Pnma & -P 2ac 2n \\ ! 62:ba-c & D$_{2h}^{16}$ & Pmnb & -P 2bc 2a \\ ! 62:cab & D$_{2h}^{16}$ & Pbnm & -P 2c 2ab \\ ! 62:-cba & D$_{2h}^{16}$ & Pcmn & -P 2n 2ac \\ ! 62:bca & D$_{2h}^{16}$ & Pmcn & -P 2n 2a \\ ! 62:a-cb & D$_{2h}^{16}$ & Pnam & -P 2c 2n \\ ! 63 & D$_{2h}^{17}$ & Cmcm & -C 2c 2 \\ ! 63:ba-c & D$_{2h}^{17}$ & Ccmm & -C 2c 2c \\ ! 63:cab & D$_{2h}^{17}$ & Amma & -A 2a 2a \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 63:-cba & D$_{2h}^{17}$ & Amam & -A 2 2a \\ ! 63:bca & D$_{2h}^{17}$ & Bbmm & -B 2 2b \\ ! 63:a-cb & D$_{2h}^{17}$ & Bmmb & -B 2b 2 \\ ! 64 & D$_{2h}^{18}$ & Cmca & -C 2bc 2 \\ ! 64:ba-c & D$_{2h}^{18}$ & Ccmb & -C 2bc 2bc \\ ! 64:cab & D$_{2h}^{18}$ & Abma & -A 2ac 2ac \\ ! 64:-cba & D$_{2h}^{18}$ & Acam & -A 2 2ac \\ ! 64:bca & D$_{2h}^{18}$ & Bbcm & -B 2 2bc \\ ! 64:a-cb & D$_{2h}^{18}$ & Bmab & -B 2bc 2 \\ ! 65 & D$_{2h}^{19}$ & Cmmm & -C 2 2 \\ ! 65:cab & D$_{2h}^{19}$ & Ammm & -A 2 2 \\ ! 65:bca & D$_{2h}^{19}$ & Bmmm & -B 2 2 \\ ! 66 & D$_{2h}^{20}$ & Cccm & -C 2 2c \\ ! 66:cab & D$_{2h}^{20}$ & Amaa & -A 2a 2 \\ ! 66:bca & D$_{2h}^{20}$ & Bbmb & -B 2b 2b \\ ! 67 & D$_{2h}^{21}$ & Cmma & -C 2b 2 \\ ! 67:ba-c & D$_{2h}^{21}$ & Cmmb & -C 2b 2b \\ ! 67:cab & D$_{2h}^{21}$ & Abmm & -A 2c 2c \\ ! 67:-cba & D$_{2h}^{21}$ & Acmm & -A 2 2c \\ ! 67:bca & D$_{2h}^{21}$ & Bmcm & -B 2 2c \\ ! 67:a-cb & D$_{2h}^{21}$ & Bmam & -B 2c 2 \\ ! 68:1 & D$_{2h}^{22}$ & Ccca:1 & C 2 2 -1bc \\ ! 68:2 & D$_{2h}^{22}$ & Ccca:2 & -C 2b 2bc \\ ! 68:1ba-c & D$_{2h}^{22}$ & Cccb:1 & C 2 2 -1bc \\ ! 68:2ba-c & D$_{2h}^{22}$ & Cccb:2 & -C 2b 2c \\ ! 68:1cab & D$_{2h}^{22}$ & Abaa:1 & A 2 2 -1ac \\ ! 68:2cab & D$_{2h}^{22}$ & Abaa:2 & -A 2a 2c \\ ! 68:1-cba & D$_{2h}^{22}$ & Acaa:1 & A 2 2 -1ac \\ ! 68:2-cba & D$_{2h}^{22}$ & Acaa:2 & -A 2ac 2c \\ ! 68:1bca & D$_{2h}^{22}$ & Bbcb:1 & B 2 2 -1bc \\ ! 68:2bca & D$_{2h}^{22}$ & Bbcb:2 & -B 2bc 2b \\ ! 68:1a-cb & D$_{2h}^{22}$ & Bbab:1 & B 2 2 -1bc \\ ! 68:2a-cb & D$_{2h}^{22}$ & Bbab:2 & -B 2b 2bc \\ ! 69 & D$_{2h}^{23}$ & Fmmm & -F 2 2 \\ ! 70:1 & D$_{2h}^{24}$ & Fddd:1 & F 2 2 -1d \\ ! 70:2 & D$_{2h}^{24}$ & Fddd:2 & -F 2uv 2vw \\ ! 71 & D$_{2h}^{25}$ & Immm & -I 2 2 \\ ! 72 & D$_{2h}^{26}$ & Ibam & -I 2 2c \\ ! 72:cab & D$_{2h}^{26}$ & Imcb & -I 2a 2 \\ ! 72:bca & D$_{2h}^{26}$ & Icma & -I 2b 2b \\ ! 73 & D$_{2h}^{27}$ & Ibca & -I 2b 2c \\ ! 73:ba-c & D$_{2h}^{27}$ & Icab & -I 2a 2b \\ ! 74 & D$_{2h}^{28}$ & Imma & -I 2b 2 \\ ! 74:ba-c & D$_{2h}^{28}$ & Immb & -I 2a 2a \\ ! 74:cab & D$_{2h}^{28}$ & Ibmm & -I 2c 2c \\ ! 74:-cba & D$_{2h}^{28}$ & Icmm & -I 2 2b \\ ! 74:bca & D$_{2h}^{28}$ & Imcm & -I 2 2a \\ ! 74:a-cb & D$_{2h}^{28}$ & Imam & -I 2c 2 \\ ! 75 & C$_{4}^{1}$ & P4 & P 4 \\ ! 76 & C$_{4}^{2}$ & P41 & P 4w \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 77 & C$_{4}^{3}$ & P42 & P 4c \\ ! 78 & C$_{4}^{4}$ & P43 & P 4cw \\ ! 79 & C$_{4}^{5}$ & I4 & I 4 \\ ! 80 & C$_{4}^{6}$ & I41 & I 4bw \\ ! 81 & S$_{4}^{1}$ & P-4 & P -4 \\ ! 82 & S$_{4}^{2}$ & I-4 & I -4 \\ ! 83 & C$_{4h}^{1}$ & P4/m & -P 4 \\ ! 84 & C$_{4h}^{2}$ & P42/m & -P 4c \\ ! 85:1 & C$_{4h}^{3}$ & P4/n:1 & P 4ab -1ab \\ ! 85:2 & C$_{4h}^{3}$ & P4/n:2 & -P 4a \\ ! 86:1 & C$_{4h}^{4}$ & P42/n:1 & P 4n -1n \\ ! 86:2 & C$_{4h}^{4}$ & P42/n:2 & -P 4bc \\ ! 87 & C$_{4h}^{5}$ & I4/m & -I 4 \\ ! 88:1 & C$_{4h}^{6}$ & I41/a:1 & I 4bw -1bw \\ ! 88:2 & C$_{4h}^{6}$ & I41/a:2 & -I 4ad \\ ! 89 & D$_{4}^{1}$ & P422 & P 4 2 \\ ! 90 & D$_{4}^{2}$ & P4212 & P 4ab 2ab \\ ! 91 & D$_{4}^{3}$ & P4122 & P 4w 2c \\ ! 92 & D$_{4}^{4}$ & P41212 & P 4abw 2nw \\ ! 93 & D$_{4}^{5}$ & P4222 & P 4c 2 \\ ! 94 & D$_{4}^{6}$ & P42212 & P 4n 2n \\ ! 95 & D$_{4}^{7}$ & P4322 & P 4cw 2c \\ ! 96 & D$_{4}^{8}$ & P43212 & P 4nw 2abw \\ ! 97 & D$_{4}^{9}$ & I422 & I 4 2 \\ ! 98 & D$_{4}^{10}$ & I4122 & I 4bw 2bw \\ ! 99 & C$_{4v}^{1}$ & P4mm & P 4 -2 \\ ! 100 & C$_{4v}^{2}$ & P4bm & P 4 -2ab \\ ! 101 & C$_{4v}^{3}$ & P42cm & P 4c -2c \\ ! 102 & C$_{4v}^{4}$ & P42nm & P 4n -2n \\ ! 103 & C$_{4v}^{5}$ & P4cc & P 4 -2c \\ ! 104 & C$_{4v}^{6}$ & P4nc & P 4 -2n \\ ! 105 & C$_{4v}^{7}$ & P42mc & P 4c -2 \\ ! 106 & C$_{4v}^{8}$ & P42bc & P 4c -2ab \\ ! 107 & C$_{4v}^{9}$ & I4mm & I 4 -2 \\ ! 108 & C$_{4v}^{10}$ & I4cm & I 4 -2c \\ ! 109 & C$_{4v}^{11}$ & I41md & I 4bw -2 \\ ! 110 & C$_{4v}^{12}$ & I41cd & I 4bw -2c \\ ! 111 & D$_{2d}^{1}$ & P-42m & P -4 2 \\ ! 112 & D$_{2d}^{2}$ & P-42c & P -4 2c \\ ! 113 & D$_{2d}^{3}$ & P-421m & P -4 2ab \\ ! 114 & D$_{2d}^{4}$ & P-421c & P -4 2n \\ ! 115 & D$_{2d}^{5}$ & P-4m2 & P -4 -2 \\ ! 116 & D$_{2d}^{6}$ & P-4c2 & P -4 -2c \\ ! 117 & D$_{2d}^{7}$ & P-4b2 & P -4 -2ab \\ ! 118 & D$_{2d}^{8}$ & P-4n2 & P -4 -2n \\ ! 119 & D$_{2d}^{9}$ & I-4m2 & I -4 -2 \\ ! 120 & D$_{2d}^{10}$ & I-4c2 & I -4 -2c \\ ! 121 & D$_{2d}^{11}$ & I-42m & I -4 2 \\ ! 122 & D$_{2d}^{12}$ & I-42d & I -4 2bw \\ ! 123 & D$_{4h}^{1}$ & P4/mmm & -P 4 2 \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 124 & D$_{4h}^{2}$ & P4/mcc & -P 4 2c \\ ! 125:1 & D$_{4h}^{3}$ & P4/nbm:1 & P 4 2 -1ab \\ ! 125:2 & D$_{4h}^{3}$ & P4/nbm:2 & -P 4a 2b \\ ! 126:1 & D$_{4h}^{4}$ & P4/nnc:1 & P 4 2 -1n \\ ! 126:2 & D$_{4h}^{4}$ & P4/nnc:2 & -P 4a 2bc \\ ! 127 & D$_{4h}^{5}$ & P4/mbm & -P 4 2ab \\ ! 128 & D$_{4h}^{6}$ & P4/mnc & -P 4 2n \\ ! 129:1 & D$_{4h}^{7}$ & P4/nmm:1 & P 4ab 2ab -1ab \\ ! 129:2 & D$_{4h}^{7}$ & P4/nmm:2 & -P 4a 2a \\ ! 130:1 & D$_{4h}^{8}$ & P4/ncc:1 & P 4ab 2n -1ab \\ ! 130:2 & D$_{4h}^{8}$ & P4/ncc:2 & -P 4a 2ac \\ ! 131 & D$_{4h}^{9}$ & P42/mmc & -P 4c 2 \\ ! 132 & D$_{4h}^{10}$ & P42/mcm & -P 4c 2c \\ ! 133:1 & D$_{4h}^{11}$ & P42/nbc:1 & P 4n 2c -1n \\ ! 133:2 & D$_{4h}^{11}$ & P42/nbc:2 & -P 4ac 2b \\ ! 134:1 & D$_{4h}^{12}$ & P42/nnm:1 & P 4n 2 -1n \\ ! 134:2 & D$_{4h}^{12}$ & P42/nnm:2 & -P 4ac 2bc \\ ! 135 & D$_{4h}^{13}$ & P42/mbc & -P 4c 2ab \\ ! 136 & D$_{4h}^{14}$ & P42/mnm & -P 4n 2n \\ ! 137:1 & D$_{4h}^{15}$ & P42/nmc:1 & P 4n 2n -1n \\ ! 137:2 & D$_{4h}^{15}$ & P42/nmc:2 & -P 4ac 2a \\ ! 138:1 & D$_{4h}^{16}$ & P42/ncm:1 & P 4n 2ab -1n \\ ! 138:2 & D$_{4h}^{16}$ & P42/ncm:2 & -P 4ac 2ac \\ ! 139 & D$_{4h}^{17}$ & I4/mmm & -I 4 2 \\ ! 140 & D$_{4h}^{18}$ & I4/mcm & -I 4 2c \\ ! 141:1 & D$_{4h}^{19}$ & I41/amd:1 & I 4bw 2bw -1bw \\ ! 141:2 & D$_{4h}^{19}$ & I41/amd:2 & -I 4bd 2 \\ ! 142:1 & D$_{4h}^{20}$ & I41/acd:1 & I 4bw 2aw -1bw \\ ! 142:2 & D$_{4h}^{20}$ & I41/acd:2 & -I 4bd 2c \\ ! 143 & C$_{3}^{1}$ & P3 & P 3 \\ ! 144 & C$_{3}^{2}$ & P31 & P 31 \\ ! 145 & C$_{3}^{3}$ & P32 & P 32 \\ ! 146:H & C$_{3}^{4}$ & R3:H & R 3 \\ ! 146:R & C$_{3}^{4}$ & R3:R & P 3* \\ ! 147 & C$_{3i}^{1}$ & P-3 & -P 3 \\ ! 148:H & C$_{3i}^{2}$ & R-3:H & -R 3 \\ ! 148:R & C$_{3i}^{2}$ & R-3:R & -P 3* \\ ! 149 & D$_{3}^{1}$ & P312 & P 3 2 \\ ! 150 & D$_{3}^{2}$ & P321 & P 3 2$''$ \\ ! 151 & D$_{3}^{3}$ & P3112 & P 31 2c (0 0 1) \\ ! 152 & D$_{3}^{4}$ & P3121 & P 31 2$''$ \\ ! 153 & D$_{3}^{5}$ & P3212 & P 32 2c (0 0 -1) \\ ! 154 & D$_{3}^{6}$ & P3221 & P 32 2$''$ \\ ! 155:H & D$_{3}^{7}$ & R32:H & R 3 2$''$ \\ ! 155:R & D$_{3}^{7}$ & R32:R & P 3* 2 \\ ! 156 & C$_{3v}^{1}$ & P3m1 & P 3 -2$''$ \\ ! 157 & C$_{3v}^{2}$ & P31m & P 3 -2 \\ ! 158 & C$_{3v}^{3}$ & P3c1 & P 3 -2$''$c \\ ! 159 & C$_{3v}^{4}$ & P31c & P 3 -2c \\ ! 160:H & C$_{3v}^{5}$ & R3m:H & R 3 -2$''$ \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 160:R & C$_{3v}^{5}$ & R3m:R & P 3* -2 \\ ! 161:H & C$_{3v}^{6}$ & R3c:H & R 3 -2$''$c \\ ! 161:R & C$_{3v}^{6}$ & R3c:R & P 3* -2n \\ ! 162 & D$_{3d}^{1}$ & P-31m & -P 3 2 \\ ! 163 & D$_{3d}^{2}$ & P-31c & -P 3 2c \\ ! 164 & D$_{3d}^{3}$ & P-3m1 & -P 3 2$''$ \\ ! 165 & D$_{3d}^{4}$ & P-3c1 & -P 3 2$''$c \\ ! 166:H & D$_{3d}^{5}$ & R-3m:H & -R 3 2$''$ \\ ! 166:R & D$_{3d}^{5}$ & R-3m:R & -P 3* 2 \\ ! 167:H & D$_{3d}^{6}$ & R-3c:H & -R 3 2$''$c \\ ! 167:R & D$_{3d}^{6}$ & R-3c:R & -P 3* 2n \\ ! 168 & C$_{6}^{1}$ & P6 & P 6 \\ ! 169 & C$_{6}^{2}$ & P61 & P 61 \\ ! 170 & C$_{6}^{3}$ & P65 & P 65 \\ ! 171 & C$_{6}^{4}$ & P62 & P 62 \\ ! 172 & C$_{6}^{5}$ & P64 & P 64 \\ ! 173 & C$_{6}^{6}$ & P63 & P 6c \\ ! 174 & C$_{3h}^{1}$ & P-6 & P -6 \\ ! 175 & C$_{6h}^{1}$ & P6/m & -P 6 \\ ! 176 & C$_{6h}^{2}$ & P63/m & -P 6c \\ ! 177 & D$_{6}^{1}$ & P622 & P 6 2 \\ ! 178 & D$_{6}^{2}$ & P6122 & P 61 2 (0 0 -1) \\ ! 179 & D$_{6}^{3}$ & P6522 & P 65 2 (0 0 1) \\ ! 180 & D$_{6}^{4}$ & P6222 & P 62 2c (0 0 1) \\ ! 181 & D$_{6}^{5}$ & P6422 & P 64 2c (0 0 -1) \\ ! 182 & D$_{6}^{6}$ & P6322 & P 6c 2c \\ ! 183 & C$_{6v}^{1}$ & P6mm & P 6 -2 \\ ! 184 & C$_{6v}^{2}$ & P6cc & P 6 -2c \\ ! 185 & C$_{6v}^{3}$ & P63cm & P 6c -2 \\ ! 186 & C$_{6v}^{4}$ & P63mc & P 6c -2c \\ ! 187 & D$_{3h}^{1}$ & P-6m2 & P -6 2 \\ ! 188 & D$_{3h}^{2}$ & P-6c2 & P -6c 2 \\ ! 189 & D$_{3h}^{3}$ & P-62m & P -6 -2 \\ ! 190 & D$_{3h}^{4}$ & P-62c & P -6c -2c \\ ! 191 & D$_{6h}^{1}$ & P6/mmm & -P 6 2 \\ ! 192 & D$_{6h}^{2}$ & P6/mcc & -P 6 2c \\ ! 193 & D$_{6h}^{3}$ & P63/mcm & -P 6c 2 \\ ! 194 & D$_{6h}^{4}$ & P63/mmc & -P 6c 2c \\ ! 195 & T$_{}^{1}$ & P23 & P 2 2 3 \\ ! 196 & T$_{}^{2}$ & F23 & F 2 2 3 \\ ! 197 & T$_{}^{3}$ & I23 & I 2 2 3 \\ ! 198 & T$_{}^{4}$ & P213 & P 2ac 2ab 3 \\ ! 199 & T$_{}^{5}$ & I213 & I 2b 2c 3 \\ ! 200 & T$_{h}^{1}$ & Pm-3 & -P 2 2 3 \\ ! 201:1 & T$_{h}^{2}$ & Pn-3:1 & P 2 2 3 -1n \\ ! 201:2 & T$_{h}^{2}$ & Pn-3:2 & -P 2ab 2bc 3 \\ ! 202 & T$_{h}^{3}$ & Fm-3 & -F 2 2 3 \\ ! 203:1 & T$_{h}^{4}$ & Fd-3:1 & F 2 2 3 -1d \\ ! 203:2 & T$_{h}^{4}$ & Fd-3:2 & -F 2uv 2vw 3 \\ ! 204 & T$_{h}^{5}$ & Im-3 & -I 2 2 3 \\ ! \hline ! \end{tabular} ! \newpage ! \begin{tabular}{|l|l|l|l|} ! \hline ! Number & Schoenflies & Hermann-Mauguin & Hall \\ ! \hline ! 205 & T$_{h}^{6}$ & Pa-3 & -P 2ac 2ab 3 \\ ! 206 & T$_{h}^{7}$ & Ia-3 & -I 2b 2c 3 \\ ! 207 & O$^{1}$ & P432 & P 4 2 3 \\ ! 208 & O$^{2}$ & P4232 & P 4n 2 3 \\ ! 209 & O$^{3}$ & F432 & F 4 2 3 \\ ! 210 & O$^{4}$ & F4132 & F 4d 2 3 \\ ! 211 & O$^{5}$ & I432 & I 4 2 3 \\ ! 212 & O$^{6}$ & P4332 & P 4acd 2ab 3 \\ ! 213 & O$^{7}$ & P4132 & P 4bd 2ab 3 \\ ! 214 & O$^{8}$ & I4132 & I 4bd 2c 3 \\ ! 215 & T$_{d}^{1}$ & P-43m & P -4 2 3 \\ ! 216 & T$_{d}^{2}$ & F-43m & F -4 2 3 \\ ! 217 & T$_{d}^{3}$ & I-43m & I -4 2 3 \\ ! 218 & T$_{d}^{4}$ & P-43n & P -4n 2 3 \\ ! 219 & T$_{d}^{5}$ & F-43c & F -4c 2 3 \\ ! 220 & T$_{d}^{6}$ & I-43d & I -4bd 2c 3 \\ ! 221 & O$_{h}^{1}$ & Pm-3m & -P 4 2 3 \\ ! 222:1 & O$_{h}^{2}$ & Pn-3n:1 & P 4 2 3 -1n \\ ! 222:2 & O$_{h}^{2}$ & Pn-3n:2 & -P 4a 2bc 3 \\ ! 223 & O$_{h}^{3}$ & Pm-3n & -P 4n 2 3 \\ ! 224:1 & O$_{h}^{4}$ & Pn-3m:1 & P 4n 2 3 -1n \\ ! 224:2 & O$_{h}^{4}$ & Pn-3m:2 & -P 4bc 2bc 3 \\ ! 225 & O$_{h}^{5}$ & Fm-3m & -F 4 2 3 \\ ! 226 & O$_{h}^{6}$ & Fm-3c & -F 4c 2 3 \\ ! 227:1 & O$_{h}^{7}$ & Fd-3m:1 & F 4d 2 3 -1d \\ ! 227:2 & O$_{h}^{7}$ & Fd-3m:2 & -F 4vw 2vw 3 \\ ! 228:1 & O$_{h}^{8}$ & Fd-3c:1 & F 4d 2 3 -1cd \\ ! 228:2 & O$_{h}^{8}$ & Fd-3c:2 & -F 4cvw 2vw 3 \\ ! 229 & O$_{h}^{9}$ & Im-3m & -I 4 2 3 \\ ! 230 & O$_{h}^{10}$ & Ia-3d & -I 4bd 2c 3 \\ ! \hline ! \end{tabular} ! \end{center} ! !EOI elk-7.2.42/src/spacegroup/PaxHeaders.21776/modmain.f900000644000000000000000000000013214061636515017036 xustar0030 mtime=1623670093.521103786 30 atime=1623670093.521103786 30 ctime=1623670093.521103786 elk-7.2.42/src/spacegroup/modmain.f900000644002504400250440000000454314061636515021101 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !MODULE: modmain ! !DESCRIPTION: ! Contains all the global variables required by the spacegroup code. ! ! !REVISION HISTORY: ! Created October 2006 (JKD) !EOP !BOC module modmain !-------------------------------! ! space group variables ! !-------------------------------! ! Hermann-Mauguin symbol character(20) hrmg ! space-group number character(20) num ! Schoenflies symbol character(20) schn ! Hall symbol character(20) hall !----------------------------! ! lattice parameters ! !----------------------------! ! number of unit cells integer ncell(3) ! lattice vector lengths real(8) a,b,c ! lattice vector angles real(8) ab,ac,bc ! lattice vectors stored column-wise real(8) avec(3,3) ! inverse of lattice vector matrix real(8) ainv(3,3) ! any vector with length less than epslat is considered zero real(8), parameter :: epslat=1.d-6 !--------------------------! ! atomic variables ! !--------------------------! ! maximum allowed species integer, parameter :: maxspecies=8 ! maximum allowed atoms per species integer, parameter :: maxatoms=1000 ! number of species integer nspecies ! number of atoms for each species integer natoms(maxspecies) ! total number of atoms integer natmtot ! primcell is .true. if primitive unit cell is to be found automatically logical primcell ! maximum allowed Wyckoff positions integer, parameter :: maxwpos=100 ! number of Wyckoff positions integer nwpos(maxspecies) ! Wyckoff positions real(8) wpos(3,maxwpos,maxspecies) ! atomic positions in lattice coordinates real(8) atposl(3,maxatoms,maxspecies) ! atomic positions in Cartesian coordinates real(8) atposc(3,maxatoms,maxspecies) ! magnetic fields real(8) bfcmt0(3,maxatoms,maxspecies) !----------------------------------! ! atomic species variables ! !----------------------------------! ! species symbol character(256) spsymb(maxspecies) !-----------------------------! ! numerical constants ! !-----------------------------! real(8), parameter :: pi=3.1415926535897932385d0 !---------------------------------! ! miscellaneous variables ! !---------------------------------! ! code version integer version(3) data version / 1,2,1 / end module !EOC elk-7.2.42/src/spacegroup/PaxHeaders.21776/r3cross.f900000644000000000000000000000013214061636515017010 xustar0030 mtime=1623670093.523103784 30 atime=1623670093.522103785 30 ctime=1623670093.523103784 elk-7.2.42/src/spacegroup/r3cross.f900000644002504400250440000000137314061636515021051 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3cross ! !INTERFACE: subroutine r3cross(x,y,z) ! !INPUT/OUTPUT PARAMETERS: ! x : input vector 1 (in,real(3)) ! y : input vector 2 (in,real(3)) ! z : output cross-product (out,real(3)) ! !DESCRIPTION: ! Returns the cross product of two real 3-vectors. ! ! !REVISION HISTORY: ! Created September 2002 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: x(3) real(8), intent(in) :: y(3) real(8), intent(out) :: z(3) z(1)=x(2)*y(3)-x(3)*y(2) z(2)=x(3)*y(1)-x(1)*y(3) z(3)=x(1)*y(2)-x(2)*y(1) return end subroutine !EOC elk-7.2.42/src/spacegroup/PaxHeaders.21776/r3frac.f900000644000000000000000000000013214061636515016572 xustar0030 mtime=1623670093.524103783 30 atime=1623670093.524103783 30 ctime=1623670093.524103783 elk-7.2.42/src/spacegroup/r3frac.f900000644002504400250440000000176014061636515020633 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3frac ! !INTERFACE: subroutine r3frac(eps,v) ! !INPUT/OUTPUT PARAMETERS: ! eps : zero component tolerance (in,real) ! v : input vector (inout,real(3)) ! !DESCRIPTION: ! Finds the fractional part of each component of a real 3-vector using the ! function ${\rm frac}\,(x)=x-\lfloor x\rfloor$. A component is taken to be ! zero if it lies within the intervals $[0,\epsilon)$ or $(1-\epsilon,1]$. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) ! Removed iv, September 2011 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: eps real(8), intent(inout) :: v(3) ! local variables integer i do i=1,3 v(i)=v(i)-int(v(i)) if (v(i).lt.0.d0) v(i)=v(i)+1.d0 if ((1.d0-v(i)).lt.eps) v(i)=0.d0 if (v(i).lt.eps) v(i)=0.d0 end do return end subroutine !EOC elk-7.2.42/src/spacegroup/PaxHeaders.21776/r3minv.f900000644000000000000000000000013214061636515016630 xustar0030 mtime=1623670093.526103781 30 atime=1623670093.525103782 30 ctime=1623670093.526103781 elk-7.2.42/src/spacegroup/r3minv.f900000644002504400250440000000236214061636515020670 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3minv ! !INTERFACE: subroutine r3minv(a,b) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix (in,real(3,3)) ! b : output matrix (in,real(3,3)) ! !DESCRIPTION: ! Computes the inverse of a real $3\times 3$ matrix. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: a(3,3) real(8), intent(out) :: b(3,3) ! local variables real(8) t1 t1=a(1,2)*a(2,3)*a(3,1)-a(1,3)*a(2,2)*a(3,1)+a(1,3)*a(2,1)*a(3,2) & -a(1,1)*a(2,3)*a(3,2)+a(1,1)*a(2,2)*a(3,3)-a(1,2)*a(2,1)*a(3,3) if (abs(t1).lt.1.d-40) then write(*,*) write(*,'("Error(r3minv): singular matrix")') write(*,*) stop end if t1=1.d0/t1 b(1,1)=(a(2,2)*a(3,3)-a(2,3)*a(3,2))*t1 b(1,2)=(a(1,3)*a(3,2)-a(1,2)*a(3,3))*t1 b(1,3)=(a(1,2)*a(2,3)-a(1,3)*a(2,2))*t1 b(2,1)=(a(2,3)*a(3,1)-a(2,1)*a(3,3))*t1 b(2,2)=(a(1,1)*a(3,3)-a(1,3)*a(3,1))*t1 b(2,3)=(a(1,3)*a(2,1)-a(1,1)*a(2,3))*t1 b(3,1)=(a(2,1)*a(3,2)-a(2,2)*a(3,1))*t1 b(3,2)=(a(1,2)*a(3,1)-a(1,1)*a(3,2))*t1 b(3,3)=(a(1,1)*a(2,2)-a(1,2)*a(2,1))*t1 return end subroutine !EOC elk-7.2.42/src/spacegroup/PaxHeaders.21776/r3mm.f900000644000000000000000000000012714061636515016274 xustar0029 mtime=1623670093.52710378 29 atime=1623670093.52710378 29 ctime=1623670093.52710378 elk-7.2.42/src/spacegroup/r3mm.f900000644002504400250440000000213514061636515020326 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3mm ! !INTERFACE: subroutine r3mm(a,b,c) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix 1 (in,real(3,3)) ! b : input matrix 2 (in,real(3,3)) ! c : output matrix (out,real(3,3)) ! !DESCRIPTION: ! Multiplies two real $3\times 3$ matrices. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: a(3,3) real(8), intent(in) :: b(3,3) real(8), intent(out) :: c(3,3) c(1,1)=a(1,1)*b(1,1)+a(1,2)*b(2,1)+a(1,3)*b(3,1) c(2,1)=a(2,1)*b(1,1)+a(2,2)*b(2,1)+a(2,3)*b(3,1) c(3,1)=a(3,1)*b(1,1)+a(3,2)*b(2,1)+a(3,3)*b(3,1) c(1,2)=a(1,1)*b(1,2)+a(1,2)*b(2,2)+a(1,3)*b(3,2) c(2,2)=a(2,1)*b(1,2)+a(2,2)*b(2,2)+a(2,3)*b(3,2) c(3,2)=a(3,1)*b(1,2)+a(3,2)*b(2,2)+a(3,3)*b(3,2) c(1,3)=a(1,1)*b(1,3)+a(1,2)*b(2,3)+a(1,3)*b(3,3) c(2,3)=a(2,1)*b(1,3)+a(2,2)*b(2,3)+a(2,3)*b(3,3) c(3,3)=a(3,1)*b(1,3)+a(3,2)*b(2,3)+a(3,3)*b(3,3) return end subroutine !EOC elk-7.2.42/src/spacegroup/PaxHeaders.21776/r3mv.f900000644000000000000000000000013214061636515016301 xustar0030 mtime=1623670093.528103779 30 atime=1623670093.528103779 30 ctime=1623670093.528103779 elk-7.2.42/src/spacegroup/r3mv.f900000644002504400250440000000143714061636515020343 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3mv ! !INTERFACE: subroutine r3mv(a,x,y) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix (in,real(3,3)) ! x : input vector (in,real(3)) ! y : output vector (out,real(3)) ! !DESCRIPTION: ! Multiplies a real $3\times 3$ matrix with a vector. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: a(3,3) real(8), intent(in) :: x(3) real(8), intent(out) :: y(3) y(1)=a(1,1)*x(1)+a(1,2)*x(2)+a(1,3)*x(3) y(2)=a(2,1)*x(1)+a(2,2)*x(2)+a(2,3)*x(3) y(3)=a(3,1)*x(1)+a(3,2)*x(2)+a(3,3)*x(3) return end subroutine !EOC elk-7.2.42/src/spacegroup/PaxHeaders.21776/readinput.f900000644000000000000000000000013214061636515017405 xustar0030 mtime=1623670093.530103777 30 atime=1623670093.530103777 30 ctime=1623670093.530103777 elk-7.2.42/src/spacegroup/readinput.f900000644002504400250440000000300314061636515021436 0ustar00dewhurstdewhurst00000000000000subroutine readinput use modmain implicit none ! local variables integer is,ip open(50,file='spacegroup.in',action='READ',status='OLD',form='FORMATTED') ! read the Hermann-Mauguin symbol read(50,*) hrmg hrmg=adjustl(hrmg) ! read lattice vector lengths read(50,*) a,b,c ! read angles between lattice vectors: alpha, beta, gamma ! (convention fixed by F. Cricchio) read(50,*) bc,ac,ab ! read number of unit cells read(50,*) ncell if ((ncell(1).lt.1).or.(ncell(2).lt.1).or.(ncell(3).lt.1)) then write(*,*) write(*,'("Error(readinput): invalid ncell : ",3I8)') ncell write(*,*) stop end if read(50,*) primcell read(50,*) nspecies if (nspecies.le.0) then write(*,*) write(*,'("Error(readinput): nspecies <= 0 : ",I8)') nspecies write(*,*) stop end if if (nspecies.gt.maxspecies) then write(*,*) write(*,'("Error(readinput): nspecies too large : ",I8)') nspecies write(*,'("Adjust maxspecies and recompile code")') write(*,*) stop end if do is=1,nspecies read(50,*) spsymb(is) read(50,*) nwpos(is) if (nwpos(is).le.0) then write(*,*) write(*,'("Error(readinput): nwpos <= 0 : ",I8)') nwpos(is) write(*,'(" for species ",I4)') is write(*,*) stop end if if (nwpos(is).gt.maxwpos) then write(*,*) write(*,'("Error(readinput): nwpos too large : ",I8)') nwpos(is) write(*,'(" for species ",I4)') is write(*,'("Adjust maxwpos and reompile code")') write(*,*) stop end if do ip=1,nwpos(is) read(50,*) wpos(:,ip,is) end do end do close(50) return end subroutine elk-7.2.42/src/spacegroup/PaxHeaders.21776/seitzeq.f900000644000000000000000000000013214061636515017076 xustar0030 mtime=1623670093.531103777 30 atime=1623670093.531103777 30 ctime=1623670093.531103777 elk-7.2.42/src/spacegroup/seitzeq.f900000644002504400250440000000127114061636515021134 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. logical function seitzeq(eps,sr1,st1,sr2,st2) implicit none ! arguments real(8), intent(in) :: eps real(8), intent(in) :: sr1(3,3) real(8), intent(in) :: st1(3) real(8), intent(in) :: sr2(3,3) real(8), intent(in) :: st2(3) ! local variables integer j real(8) v1(3),v2(3) seitzeq=.false. do j=1,3 v1(:)=sr1(:,j)+st1(:) v2(:)=sr2(:,j)+st2(:) if ((abs(v1(1)-v2(1)).gt.eps).or. & (abs(v1(2)-v2(2)).gt.eps).or. & (abs(v1(3)-v2(3)).gt.eps)) return end do seitzeq=.true. return end function elk-7.2.42/src/spacegroup/PaxHeaders.21776/seitzgen.f900000644000000000000000000000013214061636515017242 xustar0030 mtime=1623670093.533103775 30 atime=1623670093.533103775 30 ctime=1623670093.533103775 elk-7.2.42/src/spacegroup/seitzgen.f900000644002504400250440000002566714061636515021317 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine seitzgen(hall,ngen,srgen,stgen) implicit none character(20), intent(in) :: hall integer, intent(out) :: ngen real(8), intent(out) :: srgen(3,3,12) real(8), intent(out) :: stgen(3,12) ! local variables logical pr integer i,m,n,no,nop,axis ! zero vector tolerance real(8), parameter :: eps=1.d-6 real(8) av(3),r(3,3),t1 real(8) v1(3),v2(3),v3(3) character(20) str1,str2,str3 str1=trim(adjustl(hall))//' ' no=0 nop=0 axis=0 n=0 10 continue ! check for origin shift vector if (scan(str1,'(').eq.1) then if (index(str1,'(0 0 1)').ne.0) then v1(1)=0.d0; v1(2)=0.d0; v1(3)=1.d0 else if (index(str1,'(0 0 -1)').ne.0) then v1(1)=0.d0; v1(2)=0.d0; v1(3)=-1.d0 else write(*,*) write(*,'("Error(seitzgen): origin-shift not available : ",A)') trim(str1) write(*,*) stop end if v1(:)=v1(:)/12.d0 ! apply vector shift to all Seitz matrices do i=1,ngen v3(:)=-v1(:) call r3mv(srgen(:,:,i),v3,v2) v2(:)=v2(:)+stgen(:,i) stgen(:,i)=v2(:)+v1(:) end do goto 20 end if m=scan(str1,' ') if (m.le.1) goto 20 str2=str1(1:m-1) n=n+1 !------------------------------! ! lattice translations ! !------------------------------! if (n.eq.1) then stgen(:,1)=0.d0 if (scan(str2,'P').ne.0) then ngen=1 else if (scan(str2,'A').ne.0) then stgen(1,2)=0.d0 stgen(2,2)=0.5d0 stgen(3,2)=0.5d0 ngen=2 else if (scan(str2,'B').ne.0) then stgen(1,2)=0.5d0 stgen(2,2)=0.d0 stgen(3,2)=0.5d0 ngen=2 else if (scan(str2,'C').ne.0) then stgen(1,2)=0.5d0 stgen(2,2)=0.5d0 stgen(3,2)=0.d0 ngen=2 else if (scan(str2,'I').ne.0) then stgen(:,2)=0.5d0 ngen=2 else if (scan(str2,'R').ne.0) then stgen(1,2)=0.6666666666666666667d0 stgen(2,2)=0.3333333333333333333d0 stgen(3,2)=0.3333333333333333333d0 stgen(1,3)=0.3333333333333333333d0 stgen(2,3)=0.6666666666666666667d0 stgen(3,3)=0.6666666666666666667d0 ngen=3 else if (scan(str2,'S').ne.0) then stgen(1,2)=0.3333333333333333333d0 stgen(2,2)=0.3333333333333333333d0 stgen(3,2)=0.6666666666666666667d0 stgen(1,3)=0.6666666666666666667d0 stgen(2,3)=0.6666666666666666667d0 stgen(3,3)=0.3333333333333333333d0 ngen=3 else if (scan(str2,'T').ne.0) then stgen(1,2)=0.3333333333333333333d0 stgen(2,2)=0.6666666666666666667d0 stgen(3,2)=0.3333333333333333333d0 stgen(1,3)=0.6666666666666666667d0 stgen(2,3)=0.3333333333333333333d0 stgen(3,3)=0.6666666666666666667d0 ngen=3 else if (scan(str2,'F').ne.0) then stgen(1,2)=0.d0 stgen(2,2)=0.5d0 stgen(3,2)=0.5d0 stgen(1,3)=0.5d0 stgen(2,3)=0.d0 stgen(3,3)=0.5d0 stgen(1,4)=0.5d0 stgen(2,4)=0.5d0 stgen(3,4)=0.d0 ngen=4 else write(*,*) write(*,'("Error(seitzgen): Lattice symbol ''",A,"'' not found")') & trim(str2) write(*,*) stop end if ! set the rotations to the identity do i=1,ngen srgen(1,1,i)=1.d0; srgen(1,2,i)=0.d0; srgen(1,3,i)=0.d0 srgen(2,1,i)=0.d0; srgen(2,2,i)=1.d0; srgen(2,3,i)=0.d0 srgen(3,1,i)=0.d0; srgen(3,2,i)=0.d0; srgen(3,3,i)=1.d0 end do ! check if lattice is centrosymmetric if (scan(str2,'-').ne.0) then do i=ngen+1,2*ngen srgen(:,:,i)=-srgen(:,:,i-ngen) stgen(:,i)=stgen(:,i-ngen) end do ngen=2*ngen end if end if !-------------------------------! ! rotation-translations ! !-------------------------------! if (n.ge.2) then ! determine if rotation is proper or improper if (scan(str2,'-').eq.1) then pr=.false. ! remove the minus sign str3=str2(2:) str2=str3 else pr=.true. end if ! determine the order of rotation if (scan(str2,'1').eq.1) then no=1 else if (scan(str2,'2').eq.1) then no=2 else if (scan(str2,'3').eq.1) then no=3 else if (scan(str2,'4').eq.1) then no=4 else if (scan(str2,'6').eq.1) then no=6 else write(*,*) write(*,'("Error(seitzgen): invalid rotation order for Hall symbol ''",A,& &"''")') trim(hall) write(*,*) stop end if ! determine the axis of rotation if (scan(str2,'x').ne.0) then ! a axis axis=1 else if (scan(str2,'y').ne.0) then ! b axis axis=2 else if (scan(str2,'z').ne.0) then ! c axis axis=3 else if (scan(str2,'"').ne.0) then ! a+b axis=5 else if (scan(str2,'*').ne.0) then ! a+b+c axis axis=6 else if (n.eq.2) then ! default first rotation is along c axis=3 else if ((n.eq.3).and.(no.eq.2)) then ! default second rotation if ((nop.eq.2).or.(nop.eq.4)) then ! a axis axis=1 else if ((nop.eq.3).or.(nop.eq.6)) then ! a-b axis axis=4 else write(*,*) write(*,'("Error(seitzgen): malformed Hall symbol ''",A,"''")') trim(hall) write(*,'(" for default second rotation")') write(*,*) stop end if else if ((n.eq.4).and.(no.eq.3)) then ! third rotation around a+b+c axis axis=6 else if (no.eq.1) then ! arbitrary axis for identity axis=1 else write(*,*) write(*,'("Error(seitzgen): malformed Hall symbol ''",A,"''")') trim(hall) write(*,*) stop end if ! determine axis vector av(:)=0.d0 if (axis.eq.1) then ! a axis av(1)=1.d0 else if (axis.eq.2) then ! b axis av(2)=1.d0 else if (axis.eq.3) then ! c axis av(3)=1.d0 else if (axis.eq.4) then ! a-b axis av(1)=1.d0 av(2)=-1.d0 else if (axis.eq.5) then ! a+b axis av(1)=1.d0 av(2)=1.d0 else if (axis.eq.6) then ! a+b+c axis av(:)=1.d0 end if ! compute the rotation part of the Seitz matrix if (axis.eq.1) then ! a axis if (no.eq.1) then r(1,1)= 1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)= 1.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)= 1.d0 else if (no.eq.2) then r(1,1)= 1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)=-1.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)=-1.d0 else if (no.eq.3) then r(1,1)= 1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)= 0.d0; r(2,3)=-1.d0 r(3,1)= 0.d0; r(3,2)= 1.d0; r(3,3)=-1.d0 else if (no.eq.4) then r(1,1)= 1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)= 0.d0; r(2,3)=-1.d0 r(3,1)= 0.d0; r(3,2)= 1.d0; r(3,3)= 0.d0 else if (no.eq.6) then r(1,1)= 1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)= 1.d0; r(2,3)=-1.d0 r(3,1)= 0.d0; r(3,2)= 1.d0; r(3,3)= 0.d0 end if else if (axis.eq.2) then ! b axis if (no.eq.1) then r(1,1)= 1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)= 1.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)= 1.d0 else if (no.eq.2) then r(1,1)=-1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)= 1.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)=-1.d0 else if (no.eq.3) then r(1,1)=-1.d0; r(1,2)= 0.d0; r(1,3)= 1.d0 r(2,1)= 0.d0; r(2,2)= 1.d0; r(2,3)= 0.d0 r(3,1)=-1.d0; r(3,2)= 0.d0; r(3,3)= 0.d0 else if (no.eq.4) then r(1,1)= 0.d0; r(1,2)= 0.d0; r(1,3)= 1.d0 r(2,1)= 0.d0; r(2,2)= 1.d0; r(2,3)= 0.d0 r(3,1)=-1.d0; r(3,2)= 0.d0; r(3,3)= 0.d0 else if (no.eq.6) then r(1,1)= 0.d0; r(1,2)= 0.d0; r(1,3)= 1.d0 r(2,1)= 0.d0; r(2,2)= 1.d0; r(2,3)= 0.d0 r(3,1)=-1.d0; r(3,2)= 0.d0; r(3,3)= 1.d0 end if else if (axis.eq.3) then ! c axis if (no.eq.1) then r(1,1)= 1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)= 1.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)= 1.d0 else if (no.eq.2) then r(1,1)=-1.d0; r(1,2)= 0.d0; r(1,3)= 0.d0 r(2,1)= 0.d0; r(2,2)=-1.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)= 1.d0 else if (no.eq.3) then r(1,1)= 0.d0; r(1,2)=-1.d0; r(1,3)= 0.d0 r(2,1)= 1.d0; r(2,2)=-1.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)= 1.d0 else if (no.eq.4) then r(1,1)= 0.d0; r(1,2)=-1.d0; r(1,3)= 0.d0 r(2,1)= 1.d0; r(2,2)= 0.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)= 1.d0 else if (no.eq.6) then r(1,1)= 1.d0; r(1,2)=-1.d0; r(1,3)= 0.d0 r(2,1)= 1.d0; r(2,2)= 0.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)= 1.d0 end if else if (axis.eq.4) then ! a-b axis r(1,1)= 0.d0; r(1,2)=-1.d0; r(1,3)= 0.d0 r(2,1)=-1.d0; r(2,2)= 0.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)=-1.d0 else if (axis.eq.5) then ! a+b axis r(1,1)= 0.d0; r(1,2)= 1.d0; r(1,3)= 0.d0 r(2,1)= 1.d0; r(2,2)= 0.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 0.d0; r(3,3)=-1.d0 else if (axis.eq.6) then ! a+b+c axis r(1,1)= 0.d0; r(1,2)= 0.d0; r(1,3)= 1.d0 r(2,1)= 1.d0; r(2,2)= 0.d0; r(2,3)= 0.d0 r(3,1)= 0.d0; r(3,2)= 1.d0; r(3,3)= 0.d0 end if ! check if axis is invariant with respect to rotation call r3mv(r,av,v1) t1=sum(abs(av(:)-v1(:))) if (t1.gt.eps) then write(*,*) write(*,'("Error(seitzgen): axis not invariant with respect to rotation")') write(*,'(" for Hall symbol ''",A,"''")') trim(hall) write(*,*) stop end if ! apply inverse for improper rotation if (.not.pr) r(:,:)=-r(:,:) ! increment Seitz matrix count ngen=ngen+1 ! store rotation in main array srgen(:,:,ngen)=r(:,:) ! remove rotation symbol str3=str2(2:) str2=str3 ! determine translations stgen(:,ngen)=0.d0 if (scan(str2,'a').ne.0) then stgen(1,ngen)=stgen(1,ngen)+0.5d0 end if if (scan(str2,'b').ne.0) then stgen(2,ngen)=stgen(2,ngen)+0.5d0 end if if (scan(str2,'c').ne.0) then stgen(3,ngen)=stgen(3,ngen)+0.5d0 end if if (scan(str2,'n').ne.0) then stgen(:,ngen)=stgen(:,ngen)+0.5d0 end if if (scan(str2,'u').ne.0) then stgen(1,ngen)=stgen(1,ngen)+0.25d0 end if if (scan(str2,'v').ne.0) then stgen(2,ngen)=stgen(2,ngen)+0.25d0 end if if (scan(str2,'w').ne.0) then stgen(3,ngen)=stgen(3,ngen)+0.25d0 end if if (scan(str2,'d').ne.0) then stgen(:,ngen)=stgen(:,ngen)+0.25d0 end if if (scan(str2,'1').ne.0) then if (no.eq.3) then stgen(:,ngen)=stgen(:,ngen)+0.3333333333333333333d0*av(:) else if (no.eq.4) then stgen(:,ngen)=stgen(:,ngen)+0.25d0*av(:) else if (no.eq.6) then stgen(:,ngen)=stgen(:,ngen)+0.1666666666666666667d0*av(:) end if else if (scan(str2,'2').ne.0) then if (no.eq.3) then stgen(:,ngen)=stgen(:,ngen)+0.6666666666666666667d0*av(:) else if (no.eq.6) then stgen(:,ngen)=stgen(:,ngen)+0.3333333333333333333d0*av(:) end if else if (scan(str2,'3').ne.0) then if (no.eq.4) then stgen(:,ngen)=stgen(:,ngen)+0.75d0*av(:) end if else if (scan(str2,'4').ne.0) then if (no.eq.6) then stgen(:,ngen)=stgen(:,ngen)+0.6666666666666666667d0*av(:) end if else if (scan(str2,'5').ne.0) then if (no.eq.6) then stgen(:,ngen)=stgen(:,ngen)+0.8333333333333333333d0*av(:) end if end if end if str3=adjustl(str1(m:)) str1=str3 nop=no goto 10 20 continue ! map translations to [0,1) do i=1,ngen call r3frac(eps,stgen(:,i)) end do return end subroutine elk-7.2.42/src/spacegroup/PaxHeaders.21776/seitzmul.f900000644000000000000000000000013214061636515017266 xustar0030 mtime=1623670093.535103773 30 atime=1623670093.534103774 30 ctime=1623670093.535103773 elk-7.2.42/src/spacegroup/seitzmul.f900000644002504400250440000000112314061636515021320 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine seitzmul(eps,sr1,st1,sr2,st2,sr3,st3) implicit none ! arguments real(8), intent(in) :: eps real(8), intent(in) :: sr1(3,3) real(8), intent(in) :: st1(3) real(8), intent(in) :: sr2(3,3) real(8), intent(in) :: st2(3) real(8), intent(out) :: sr3(3,3) real(8), intent(out) :: st3(3) call r3mv(sr1,st2,st3) st3(:)=st3(:)+st1(:) call r3frac(eps,st3) call r3mm(sr1,sr2,sr3) return end subroutine elk-7.2.42/src/spacegroup/PaxHeaders.21776/sgsymb.f900000644000000000000000000000013214061636515016716 xustar0030 mtime=1623670093.536103772 30 atime=1623670093.536103772 30 ctime=1623670093.536103772 elk-7.2.42/src/spacegroup/sgsymb.f900000644002504400250440000010040014061636515020746 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: sgsymb ! !INTERFACE: subroutine sgsymb(hrmg,num,schn,hall) ! !INPUT/OUTPUT PARAMETERS: ! hrmg : Hermann-Mauguin symbol (in,character(20)) ! num : space group number (out,character(20)) ! schn : Schoenflies symbol (out,character(20)) ! hall : Hall symbol (out,character(20)) ! !DESCRIPTION: ! Returns the space group number, Schoenflies and Hall symbols given the ! Hermann-Mauguin symbol. The routine is case-sensitive. With acknowledgements ! to Ralf W. Grosse-Kunstleve and the tables available at ! {\tt http://cci.lbl.gov/sginfo/}. ! ! !REVISION HISTORY: ! Created October 2006 (JKD) !EOP !BOC implicit none ! arguments character(20), intent(in) :: hrmg character(20), intent(out) :: num character(20), intent(out) :: schn character(20), intent(out) :: hall select case(trim(adjustl(hrmg))) case('P1') num='1' schn='C1^1' hall='P 1' case('P-1') num='2' schn='Ci^1' hall='-P 1' case('P2:b') num='3:b' schn='C2^1' hall='P 2y' case('P2:c') num='3:c' schn='C2^1' hall='P 2' case('P2:a') num='3:a' schn='C2^1' hall='P 2x' case('P21:b') num='4:b' schn='C2^2' hall='P 2yb' case('P21:c') num='4:c' schn='C2^2' hall='P 2c' case('P21:a') num='4:a' schn='C2^2' hall='P 2xa' case('C2:b1') num='5:b1' schn='C2^3' hall='C 2y' case('C2:b2') num='5:b2' schn='C2^3' hall='A 2y' case('C2:b3') num='5:b3' schn='C2^3' hall='I 2y' case('C2:c1') num='5:c1' schn='C2^3' hall='A 2' case('C2:c2') num='5:c2' schn='C2^3' hall='B 2' case('C2:c3') num='5:c3' schn='C2^3' hall='I 2' case('C2:a1') num='5:a1' schn='C2^3' hall='B 2x' case('C2:a2') num='5:a2' schn='C2^3' hall='C 2x' case('C2:a3') num='5:a3' schn='C2^3' hall='I 2x' case('Pm:b') num='6:b' schn='Cs^1' hall='P -2y' case('Pm:c') num='6:c' schn='Cs^1' hall='P -2' case('Pm:a') num='6:a' schn='Cs^1' hall='P -2x' case('Pc:b1') num='7:b1' schn='Cs^2' hall='P -2yc' case('Pc:b2') num='7:b2' schn='Cs^2' hall='P -2yac' case('Pc:b3') num='7:b3' schn='Cs^2' hall='P -2ya' case('Pc:c1') num='7:c1' schn='Cs^2' hall='P -2a' case('Pc:c2') num='7:c2' schn='Cs^2' hall='P -2ab' case('Pc:c3') num='7:c3' schn='Cs^2' hall='P -2b' case('Pc:a1') num='7:a1' schn='Cs^2' hall='P -2xb' case('Pc:a2') num='7:a2' schn='Cs^2' hall='P -2xbc' case('Pc:a3') num='7:a3' schn='Cs^2' hall='P -2xc' case('Cm:b1') num='8:b1' schn='Cs^3' hall='C -2y' case('Cm:b2') num='8:b2' schn='Cs^3' hall='A -2y' case('Cm:b3') num='8:b3' schn='Cs^3' hall='I -2y' case('Cm:c1') num='8:c1' schn='Cs^3' hall='A -2' case('Cm:c2') num='8:c2' schn='Cs^3' hall='B -2' case('Cm:c3') num='8:c3' schn='Cs^3' hall='I -2' case('Cm:a1') num='8:a1' schn='Cs^3' hall='B -2x' case('Cm:a2') num='8:a2' schn='Cs^3' hall='C -2x' case('Cm:a3') num='8:a3' schn='Cs^3' hall='I -2x' case('Cc:b1') num='9:b1' schn='Cs^4' hall='C -2yc' case('Cc:b2') num='9:b2' schn='Cs^4' hall='A -2yac' case('Cc:b3') num='9:b3' schn='Cs^4' hall='I -2ya' case('Cc:-b1') num='9:-b1' schn='Cs^4' hall='A -2ya' case('Cc:-b2') num='9:-b2' schn='Cs^4' hall='C -2ybc' case('Cc:-b3') num='9:-b3' schn='Cs^4' hall='I -2yc' case('Cc:c1') num='9:c1' schn='Cs^4' hall='A -2a' case('Cc:c2') num='9:c2' schn='Cs^4' hall='B -2bc' case('Cc:c3') num='9:c3' schn='Cs^4' hall='I -2b' case('Cc:-c1') num='9:-c1' schn='Cs^4' hall='B -2b' case('Cc:-c2') num='9:-c2' schn='Cs^4' hall='A -2ac' case('Cc:-c3') num='9:-c3' schn='Cs^4' hall='I -2a' case('Cc:a1') num='9:a1' schn='Cs^4' hall='B -2xb' case('Cc:a2') num='9:a2' schn='Cs^4' hall='C -2xbc' case('Cc:a3') num='9:a3' schn='Cs^4' hall='I -2xc' case('Cc:-a1') num='9:-a1' schn='Cs^4' hall='C -2xc' case('Cc:-a2') num='9:-a2' schn='Cs^4' hall='B -2xbc' case('Cc:-a3') num='9:-a3' schn='Cs^4' hall='I -2xb' case('P2/m:b') num='10:b' schn='C2h^1' hall='-P 2y' case('P2/m:c') num='10:c' schn='C2h^1' hall='-P 2' case('P2/m:a') num='10:a' schn='C2h^1' hall='-P 2x' case('P21/m:b') num='11:b' schn='C2h^2' hall='-P 2yb' case('P21/m:c') num='11:c' schn='C2h^2' hall='-P 2c' case('P21/m:a') num='11:a' schn='C2h^2' hall='-P 2xa' case('C2/m:b1') num='12:b1' schn='C2h^3' hall='-C 2y' case('C2/m:b2') num='12:b2' schn='C2h^3' hall='-A 2y' case('C2/m:b3') num='12:b3' schn='C2h^3' hall='-I 2y' case('C2/m:c1') num='12:c1' schn='C2h^3' hall='-A 2' case('C2/m:c2') num='12:c2' schn='C2h^3' hall='-B 2' case('C2/m:c3') num='12:c3' schn='C2h^3' hall='-I 2' case('C2/m:a1') num='12:a1' schn='C2h^3' hall='-B 2x' case('C2/m:a2') num='12:a2' schn='C2h^3' hall='-C 2x' case('C2/m:a3') num='12:a3' schn='C2h^3' hall='-I 2x' case('P2/c:b1') num='13:b1' schn='C2h^4' hall='-P 2yc' case('P2/c:b2') num='13:b2' schn='C2h^4' hall='-P 2yac' case('P2/c:b3') num='13:b3' schn='C2h^4' hall='-P 2ya' case('P2/c:c1') num='13:c1' schn='C2h^4' hall='-P 2a' case('P2/c:c2') num='13:c2' schn='C2h^4' hall='-P 2ab' case('P2/c:c3') num='13:c3' schn='C2h^4' hall='-P 2b' case('P2/c:a1') num='13:a1' schn='C2h^4' hall='-P 2xb' case('P2/c:a2') num='13:a2' schn='C2h^4' hall='-P 2xbc' case('P2/c:a3') num='13:a3' schn='C2h^4' hall='-P 2xc' case('P21/c:b1') num='14:b1' schn='C2h^5' hall='-P 2ybc' case('P21/c:b2') num='14:b2' schn='C2h^5' hall='-P 2yn' case('P21/c:b3') num='14:b3' schn='C2h^5' hall='-P 2yab' case('P21/c:c1') num='14:c1' schn='C2h^5' hall='-P 2ac' case('P21/c:c2') num='14:c2' schn='C2h^5' hall='-P 2n' case('P21/c:c3') num='14:c3' schn='C2h^5' hall='-P 2bc' case('P21/c:a1') num='14:a1' schn='C2h^5' hall='-P 2xab' case('P21/c:a2') num='14:a2' schn='C2h^5' hall='-P 2xn' case('P21/c:a3') num='14:a3' schn='C2h^5' hall='-P 2xac' case('C2/c:b1') num='15:b1' schn='C2h^6' hall='-C 2yc' case('C2/c:b2') num='15:b2' schn='C2h^6' hall='-A 2yac' case('C2/c:b3') num='15:b3' schn='C2h^6' hall='-I 2ya' case('C2/c:-b1') num='15:-b1' schn='C2h^6' hall='-A 2ya' case('C2/c:-b2') num='15:-b2' schn='C2h^6' hall='-C 2ybc' case('C2/c:-b3') num='15:-b3' schn='C2h^6' hall='-I 2yc' case('C2/c:c1') num='15:c1' schn='C2h^6' hall='-A 2a' case('C2/c:c2') num='15:c2' schn='C2h^6' hall='-B 2bc' case('C2/c:c3') num='15:c3' schn='C2h^6' hall='-I 2b' case('C2/c:-c1') num='15:-c1' schn='C2h^6' hall='-B 2b' case('C2/c:-c2') num='15:-c2' schn='C2h^6' hall='-A 2ac' case('C2/c:-c3') num='15:-c3' schn='C2h^6' hall='-I 2a' case('C2/c:a1') num='15:a1' schn='C2h^6' hall='-B 2xb' case('C2/c:a2') num='15:a2' schn='C2h^6' hall='-C 2xbc' case('C2/c:a3') num='15:a3' schn='C2h^6' hall='-I 2xc' case('C2/c:-a1') num='15:-a1' schn='C2h^6' hall='-C 2xc' case('C2/c:-a2') num='15:-a2' schn='C2h^6' hall='-B 2xbc' case('C2/c:-a3') num='15:-a3' schn='C2h^6' hall='-I 2xb' case('P222') num='16' schn='D2^1' hall='P 2 2' case('P2221') num='17' schn='D2^2' hall='P 2c 2' case('P2122') num='17:cab' schn='D2^2' hall='P 2a 2a' case('P2212') num='17:bca' schn='D2^2' hall='P 2 2b' case('P21212') num='18' schn='D2^3' hall='P 2 2ab' case('P22121') num='18:cab' schn='D2^3' hall='P 2bc 2' case('P21221') num='18:bca' schn='D2^3' hall='P 2ac 2ac' case('P212121') num='19' schn='D2^4' hall='P 2ac 2ab' case('C2221') num='20' schn='D2^5' hall='C 2c 2' case('A2122') num='20:cab' schn='D2^5' hall='A 2a 2a' case('B2212') num='20:bca' schn='D2^5' hall='B 2 2b' case('C222') num='21' schn='D2^6' hall='C 2 2' case('A222') num='21:cab' schn='D2^6' hall='A 2 2' case('B222') num='21:bca' schn='D2^6' hall='B 2 2' case('F222') num='22' schn='D2^7' hall='F 2 2' case('I222') num='23' schn='D2^8' hall='I 2 2' case('I212121') num='24' schn='D2^9' hall='I 2b 2c' case('Pmm2') num='25' schn='C2v^1' hall='P 2 -2' case('P2mm') num='25:cab' schn='C2v^1' hall='P -2 2' case('Pm2m') num='25:bca' schn='C2v^1' hall='P -2 -2' case('Pmc21') num='26' schn='C2v^2' hall='P 2c -2' case('Pcm21') num='26:ba-c' schn='C2v^2' hall='P 2c -2c' case('P21ma') num='26:cab' schn='C2v^2' hall='P -2a 2a' case('P21am') num='26:-cba' schn='C2v^2' hall='P -2 2a' case('Pb21m') num='26:bca' schn='C2v^2' hall='P -2 -2b' case('Pm21b') num='26:a-cb' schn='C2v^2' hall='P -2b -2' case('Pcc2') num='27' schn='C2v^3' hall='P 2 -2c' case('P2aa') num='27:cab' schn='C2v^3' hall='P -2a 2' case('Pb2b') num='27:bca' schn='C2v^3' hall='P -2b -2b' case('Pma2') num='28' schn='C2v^4' hall='P 2 -2a' case('Pbm2') num='28:ba-c' schn='C2v^4' hall='P 2 -2b' case('P2mb') num='28:cab' schn='C2v^4' hall='P -2b 2' case('P2cm') num='28:-cba' schn='C2v^4' hall='P -2c 2' case('Pc2m') num='28:bca' schn='C2v^4' hall='P -2c -2c' case('Pm2a') num='28:a-cb' schn='C2v^4' hall='P -2a -2a' case('Pca21') num='29' schn='C2v^5' hall='P 2c -2ac' case('Pbc21') num='29:ba-c' schn='C2v^5' hall='P 2c -2b' case('P21ab') num='29:cab' schn='C2v^5' hall='P -2b 2a' case('P21ca') num='29:-cba' schn='C2v^5' hall='P -2ac 2a' case('Pc21b') num='29:bca' schn='C2v^5' hall='P -2bc -2c' case('Pb21a') num='29:a-cb' schn='C2v^5' hall='P -2a -2ab' case('Pnc2') num='30' schn='C2v^6' hall='P 2 -2bc' case('Pcn2') num='30:ba-c' schn='C2v^6' hall='P 2 -2ac' case('P2na') num='30:cab' schn='C2v^6' hall='P -2ac 2' case('P2an') num='30:-cba' schn='C2v^6' hall='P -2ab 2' case('Pb2n') num='30:bca' schn='C2v^6' hall='P -2ab -2ab' case('Pn2b') num='30:a-cb' schn='C2v^6' hall='P -2bc -2bc' case('Pmn21') num='31' schn='C2v^7' hall='P 2ac -2' case('Pnm21') num='31:ba-c' schn='C2v^7' hall='P 2bc -2bc' case('P21mn') num='31:cab' schn='C2v^7' hall='P -2ab 2ab' case('P21nm') num='31:-cba' schn='C2v^7' hall='P -2 2ac' case('Pn21m') num='31:bca' schn='C2v^7' hall='P -2 -2bc' case('Pm21n') num='31:a-cb' schn='C2v^7' hall='P -2ab -2' case('Pba2') num='32' schn='C2v^8' hall='P 2 -2ab' case('P2cb') num='32:cab' schn='C2v^8' hall='P -2bc 2' case('Pc2a') num='32:bca' schn='C2v^8' hall='P -2ac -2ac' case('Pna21') num='33' schn='C2v^9' hall='P 2c -2n' case('Pbn21') num='33:ba-c' schn='C2v^9' hall='P 2c -2ab' case('P21nb') num='33:cab' schn='C2v^9' hall='P -2bc 2a' case('P21cn') num='33:-cba' schn='C2v^9' hall='P -2n 2a' case('Pc21n') num='33:bca' schn='C2v^9' hall='P -2n -2ac' case('Pn21a') num='33:a-cb' schn='C2v^9' hall='P -2ac -2n' case('Pnn2') num='34' schn='C2v^10' hall='P 2 -2n' case('P2nn') num='34:cab' schn='C2v^10' hall='P -2n 2' case('Pn2n') num='34:bca' schn='C2v^10' hall='P -2n -2n' case('Cmm2') num='35' schn='C2v^11' hall='C 2 -2' case('A2mm') num='35:cab' schn='C2v^11' hall='A -2 2' case('Bm2m') num='35:bca' schn='C2v^11' hall='B -2 -2' case('Cmc21') num='36' schn='C2v^12' hall='C 2c -2' case('Ccm21') num='36:ba-c' schn='C2v^12' hall='C 2c -2c' case('A21ma') num='36:cab' schn='C2v^12' hall='A -2a 2a' case('A21am') num='36:-cba' schn='C2v^12' hall='A -2 2a' case('Bb21m') num='36:bca' schn='C2v^12' hall='B -2 -2b' case('Bm21b') num='36:a-cb' schn='C2v^12' hall='B -2b -2' case('Ccc2') num='37' schn='C2v^13' hall='C 2 -2c' case('A2aa') num='37:cab' schn='C2v^13' hall='A -2a 2' case('Bb2b') num='37:bca' schn='C2v^13' hall='B -2b -2b' case('Amm2') num='38' schn='C2v^14' hall='A 2 -2' case('Bmm2') num='38:ba-c' schn='C2v^14' hall='B 2 -2' case('B2mm') num='38:cab' schn='C2v^14' hall='B -2 2' case('C2mm') num='38:-cba' schn='C2v^14' hall='C -2 2' case('Cm2m') num='38:bca' schn='C2v^14' hall='C -2 -2' case('Am2m') num='38:a-cb' schn='C2v^14' hall='A -2 -2' case('Abm2') num='39' schn='C2v^15' hall='A 2 -2c' case('Bma2') num='39:ba-c' schn='C2v^15' hall='B 2 -2c' case('B2cm') num='39:cab' schn='C2v^15' hall='B -2c 2' case('C2mb') num='39:-cba' schn='C2v^15' hall='C -2b 2' case('Cm2a') num='39:bca' schn='C2v^15' hall='C -2b -2b' case('Ac2m') num='39:a-cb' schn='C2v^15' hall='A -2c -2c' case('Ama2') num='40' schn='C2v^16' hall='A 2 -2a' case('Bbm2') num='40:ba-c' schn='C2v^16' hall='B 2 -2b' case('B2mb') num='40:cab' schn='C2v^16' hall='B -2b 2' case('C2cm') num='40:-cba' schn='C2v^16' hall='C -2c 2' case('Cc2m') num='40:bca' schn='C2v^16' hall='C -2c -2c' case('Am2a') num='40:a-cb' schn='C2v^16' hall='A -2a -2a' case('Aba2') num='41' schn='C2v^17' hall='A 2 -2ac' case('Bba2') num='41:ba-c' schn='C2v^17' hall='B 2 -2bc' case('B2cb') num='41:cab' schn='C2v^17' hall='B -2bc 2' case('C2cb') num='41:-cba' schn='C2v^17' hall='C -2bc 2' case('Cc2a') num='41:bca' schn='C2v^17' hall='C -2bc -2bc' case('Ac2a') num='41:a-cb' schn='C2v^17' hall='A -2ac -2ac' case('Fmm2') num='42' schn='C2v^18' hall='F 2 -2' case('F2mm') num='42:cab' schn='C2v^18' hall='F -2 2' case('Fm2m') num='42:bca' schn='C2v^18' hall='F -2 -2' case('Fdd2') num='43' schn='C2v^19' hall='F 2 -2d' case('F2dd') num='43:cab' schn='C2v^19' hall='F -2d 2' case('Fd2d') num='43:bca' schn='C2v^19' hall='F -2d -2d' case('Imm2') num='44' schn='C2v^20' hall='I 2 -2' case('I2mm') num='44:cab' schn='C2v^20' hall='I -2 2' case('Im2m') num='44:bca' schn='C2v^20' hall='I -2 -2' case('Iba2') num='45' schn='C2v^21' hall='I 2 -2c' case('I2cb') num='45:cab' schn='C2v^21' hall='I -2a 2' case('Ic2a') num='45:bca' schn='C2v^21' hall='I -2b -2b' case('Ima2') num='46' schn='C2v^22' hall='I 2 -2a' case('Ibm2') num='46:ba-c' schn='C2v^22' hall='I 2 -2b' case('I2mb') num='46:cab' schn='C2v^22' hall='I -2b 2' case('I2cm') num='46:-cba' schn='C2v^22' hall='I -2c 2' case('Ic2m') num='46:bca' schn='C2v^22' hall='I -2c -2c' case('Im2a') num='46:a-cb' schn='C2v^22' hall='I -2a -2a' case('Pmmm') num='47' schn='D2h^1' hall='-P 2 2' case('Pnnn:1') num='48:1' schn='D2h^2' hall='P 2 2 -1n' case('Pnnn:2') num='48:2' schn='D2h^2' hall='-P 2ab 2bc' case('Pccm') num='49' schn='D2h^3' hall='-P 2 2c' case('Pmaa') num='49:cab' schn='D2h^3' hall='-P 2a 2' case('Pbmb') num='49:bca' schn='D2h^3' hall='-P 2b 2b' case('Pban:1') num='50:1' schn='D2h^4' hall='P 2 2 -1ab' case('Pban:2') num='50:2' schn='D2h^4' hall='-P 2ab 2b' case('Pncb:1') num='50:1cab' schn='D2h^4' hall='P 2 2 -1bc' case('Pncb:2') num='50:2cab' schn='D2h^4' hall='-P 2b 2bc' case('Pcna:1') num='50:1bca' schn='D2h^4' hall='P 2 2 -1ac' case('Pcna:2') num='50:2bca' schn='D2h^4' hall='-P 2a 2c' case('Pmma') num='51' schn='D2h^5' hall='-P 2a 2a' case('Pmmb') num='51:ba-c' schn='D2h^5' hall='-P 2b 2' case('Pbmm') num='51:cab' schn='D2h^5' hall='-P 2 2b' case('Pcmm') num='51:-cba' schn='D2h^5' hall='-P 2c 2c' case('Pmcm') num='51:bca' schn='D2h^5' hall='-P 2c 2' case('Pmam') num='51:a-cb' schn='D2h^5' hall='-P 2 2a' case('Pnna') num='52' schn='D2h^6' hall='-P 2a 2bc' case('Pnnb') num='52:ba-c' schn='D2h^6' hall='-P 2b 2n' case('Pbnn') num='52:cab' schn='D2h^6' hall='-P 2n 2b' case('Pcnn') num='52:-cba' schn='D2h^6' hall='-P 2ab 2c' case('Pncn') num='52:bca' schn='D2h^6' hall='-P 2ab 2n' case('Pnan') num='52:a-cb' schn='D2h^6' hall='-P 2n 2bc' case('Pmna') num='53' schn='D2h^7' hall='-P 2ac 2' case('Pnmb') num='53:ba-c' schn='D2h^7' hall='-P 2bc 2bc' case('Pbmn') num='53:cab' schn='D2h^7' hall='-P 2ab 2ab' case('Pcnm') num='53:-cba' schn='D2h^7' hall='-P 2 2ac' case('Pncm') num='53:bca' schn='D2h^7' hall='-P 2 2bc' case('Pman') num='53:a-cb' schn='D2h^7' hall='-P 2ab 2' case('Pcca') num='54' schn='D2h^8' hall='-P 2a 2ac' case('Pccb') num='54:ba-c' schn='D2h^8' hall='-P 2b 2c' case('Pbaa') num='54:cab' schn='D2h^8' hall='-P 2a 2b' case('Pcaa') num='54:-cba' schn='D2h^8' hall='-P 2ac 2c' case('Pbcb') num='54:bca' schn='D2h^8' hall='-P 2bc 2b' case('Pbab') num='54:a-cb' schn='D2h^8' hall='-P 2b 2ab' case('Pbam') num='55' schn='D2h^9' hall='-P 2 2ab' case('Pmcb') num='55:cab' schn='D2h^9' hall='-P 2bc 2' case('Pcma') num='55:bca' schn='D2h^9' hall='-P 2ac 2ac' case('Pccn') num='56' schn='D2h^10' hall='-P 2ab 2ac' case('Pnaa') num='56:cab' schn='D2h^10' hall='-P 2ac 2bc' case('Pbnb') num='56:bca' schn='D2h^10' hall='-P 2bc 2ab' case('Pbcm') num='57' schn='D2h^11' hall='-P 2c 2b' case('Pcam') num='57:ba-c' schn='D2h^11' hall='-P 2c 2ac' case('Pmca') num='57:cab' schn='D2h^11' hall='-P 2ac 2a' case('Pmab') num='57:-cba' schn='D2h^11' hall='-P 2b 2a' case('Pbma') num='57:bca' schn='D2h^11' hall='-P 2a 2ab' case('Pcmb') num='57:a-cb' schn='D2h^11' hall='-P 2bc 2c' case('Pnnm') num='58' schn='D2h^12' hall='-P 2 2n' case('Pmnn') num='58:cab' schn='D2h^12' hall='-P 2n 2' case('Pnmn') num='58:bca' schn='D2h^12' hall='-P 2n 2n' case('Pmmn:1') num='59:1' schn='D2h^13' hall='P 2 2ab -1ab' case('Pmmn:2') num='59:2' schn='D2h^13' hall='-P 2ab 2a' case('Pnmm:1') num='59:1cab' schn='D2h^13' hall='P 2bc 2 -1bc' case('Pnmm:2') num='59:2cab' schn='D2h^13' hall='-P 2c 2bc' case('Pmnm:1') num='59:1bca' schn='D2h^13' hall='P 2ac 2ac -1ac' case('Pmnm:2') num='59:2bca' schn='D2h^13' hall='-P 2c 2a' case('Pbcn') num='60' schn='D2h^14' hall='-P 2n 2ab' case('Pcan') num='60:ba-c' schn='D2h^14' hall='-P 2n 2c' case('Pnca') num='60:cab' schn='D2h^14' hall='-P 2a 2n' case('Pnab') num='60:-cba' schn='D2h^14' hall='-P 2bc 2n' case('Pbna') num='60:bca' schn='D2h^14' hall='-P 2ac 2b' case('Pcnb') num='60:a-cb' schn='D2h^14' hall='-P 2b 2ac' case('Pbca') num='61' schn='D2h^15' hall='-P 2ac 2ab' case('Pcab') num='61:ba-c' schn='D2h^15' hall='-P 2bc 2ac' case('Pnma') num='62' schn='D2h^16' hall='-P 2ac 2n' case('Pmnb') num='62:ba-c' schn='D2h^16' hall='-P 2bc 2a' case('Pbnm') num='62:cab' schn='D2h^16' hall='-P 2c 2ab' case('Pcmn') num='62:-cba' schn='D2h^16' hall='-P 2n 2ac' case('Pmcn') num='62:bca' schn='D2h^16' hall='-P 2n 2a' case('Pnam') num='62:a-cb' schn='D2h^16' hall='-P 2c 2n' case('Cmcm') num='63' schn='D2h^17' hall='-C 2c 2' case('Ccmm') num='63:ba-c' schn='D2h^17' hall='-C 2c 2c' case('Amma') num='63:cab' schn='D2h^17' hall='-A 2a 2a' case('Amam') num='63:-cba' schn='D2h^17' hall='-A 2 2a' case('Bbmm') num='63:bca' schn='D2h^17' hall='-B 2 2b' case('Bmmb') num='63:a-cb' schn='D2h^17' hall='-B 2b 2' case('Cmca') num='64' schn='D2h^18' hall='-C 2bc 2' case('Ccmb') num='64:ba-c' schn='D2h^18' hall='-C 2bc 2bc' case('Abma') num='64:cab' schn='D2h^18' hall='-A 2ac 2ac' case('Acam') num='64:-cba' schn='D2h^18' hall='-A 2 2ac' case('Bbcm') num='64:bca' schn='D2h^18' hall='-B 2 2bc' case('Bmab') num='64:a-cb' schn='D2h^18' hall='-B 2bc 2' case('Cmmm') num='65' schn='D2h^19' hall='-C 2 2' case('Ammm') num='65:cab' schn='D2h^19' hall='-A 2 2' case('Bmmm') num='65:bca' schn='D2h^19' hall='-B 2 2' case('Cccm') num='66' schn='D2h^20' hall='-C 2 2c' case('Amaa') num='66:cab' schn='D2h^20' hall='-A 2a 2' case('Bbmb') num='66:bca' schn='D2h^20' hall='-B 2b 2b' case('Cmma') num='67' schn='D2h^21' hall='-C 2b 2' case('Cmmb') num='67:ba-c' schn='D2h^21' hall='-C 2b 2b' case('Abmm') num='67:cab' schn='D2h^21' hall='-A 2c 2c' case('Acmm') num='67:-cba' schn='D2h^21' hall='-A 2 2c' case('Bmcm') num='67:bca' schn='D2h^21' hall='-B 2 2c' case('Bmam') num='67:a-cb' schn='D2h^21' hall='-B 2c 2' case('Ccca:1') num='68:1' schn='D2h^22' hall='C 2 2 -1bc' case('Ccca:2') num='68:2' schn='D2h^22' hall='-C 2b 2bc' case('Cccb:1') num='68:1ba-c' schn='D2h^22' hall='C 2 2 -1bc' case('Cccb:2') num='68:2ba-c' schn='D2h^22' hall='-C 2b 2c' case('Abaa:1') num='68:1cab' schn='D2h^22' hall='A 2 2 -1ac' case('Abaa:2') num='68:2cab' schn='D2h^22' hall='-A 2a 2c' case('Acaa:1') num='68:1-cba' schn='D2h^22' hall='A 2 2 -1ac' case('Acaa:2') num='68:2-cba' schn='D2h^22' hall='-A 2ac 2c' case('Bbcb:1') num='68:1bca' schn='D2h^22' hall='B 2 2 -1bc' case('Bbcb:2') num='68:2bca' schn='D2h^22' hall='-B 2bc 2b' case('Bbab:1') num='68:1a-cb' schn='D2h^22' hall='B 2 2 -1bc' case('Bbab:2') num='68:2a-cb' schn='D2h^22' hall='-B 2b 2bc' case('Fmmm') num='69' schn='D2h^23' hall='-F 2 2' case('Fddd:1') num='70:1' schn='D2h^24' hall='F 2 2 -1d' case('Fddd:2') num='70:2' schn='D2h^24' hall='-F 2uv 2vw' case('Immm') num='71' schn='D2h^25' hall='-I 2 2' case('Ibam') num='72' schn='D2h^26' hall='-I 2 2c' case('Imcb') num='72:cab' schn='D2h^26' hall='-I 2a 2' case('Icma') num='72:bca' schn='D2h^26' hall='-I 2b 2b' case('Ibca') num='73' schn='D2h^27' hall='-I 2b 2c' case('Icab') num='73:ba-c' schn='D2h^27' hall='-I 2a 2b' case('Imma') num='74' schn='D2h^28' hall='-I 2b 2' case('Immb') num='74:ba-c' schn='D2h^28' hall='-I 2a 2a' case('Ibmm') num='74:cab' schn='D2h^28' hall='-I 2c 2c' case('Icmm') num='74:-cba' schn='D2h^28' hall='-I 2 2b' case('Imcm') num='74:bca' schn='D2h^28' hall='-I 2 2a' case('Imam') num='74:a-cb' schn='D2h^28' hall='-I 2c 2' case('P4') num='75' schn='C4^1' hall='P 4' case('P41') num='76' schn='C4^2' hall='P 4w' case('P42') num='77' schn='C4^3' hall='P 4c' case('P43') num='78' schn='C4^4' hall='P 4cw' case('I4') num='79' schn='C4^5' hall='I 4' case('I41') num='80' schn='C4^6' hall='I 4bw' case('P-4') num='81' schn='S4^1' hall='P -4' case('I-4') num='82' schn='S4^2' hall='I -4' case('P4/m') num='83' schn='C4h^1' hall='-P 4' case('P42/m') num='84' schn='C4h^2' hall='-P 4c' case('P4/n:1') num='85:1' schn='C4h^3' hall='P 4ab -1ab' case('P4/n:2') num='85:2' schn='C4h^3' hall='-P 4a' case('P42/n:1') num='86:1' schn='C4h^4' hall='P 4n -1n' case('P42/n:2') num='86:2' schn='C4h^4' hall='-P 4bc' case('I4/m') num='87' schn='C4h^5' hall='-I 4' case('I41/a:1') num='88:1' schn='C4h^6' hall='I 4bw -1bw' case('I41/a:2') num='88:2' schn='C4h^6' hall='-I 4ad' case('P422') num='89' schn='D4^1' hall='P 4 2' case('P4212') num='90' schn='D4^2' hall='P 4ab 2ab' case('P4122') num='91' schn='D4^3' hall='P 4w 2c' case('P41212') num='92' schn='D4^4' hall='P 4abw 2nw' case('P4222') num='93' schn='D4^5' hall='P 4c 2' case('P42212') num='94' schn='D4^6' hall='P 4n 2n' case('P4322') num='95' schn='D4^7' hall='P 4cw 2c' case('P43212') num='96' schn='D4^8' hall='P 4nw 2abw' case('I422') num='97' schn='D4^9' hall='I 4 2' case('I4122') num='98' schn='D4^10' hall='I 4bw 2bw' case('P4mm') num='99' schn='C4v^1' hall='P 4 -2' case('P4bm') num='100' schn='C4v^2' hall='P 4 -2ab' case('P42cm') num='101' schn='C4v^3' hall='P 4c -2c' case('P42nm') num='102' schn='C4v^4' hall='P 4n -2n' case('P4cc') num='103' schn='C4v^5' hall='P 4 -2c' case('P4nc') num='104' schn='C4v^6' hall='P 4 -2n' case('P42mc') num='105' schn='C4v^7' hall='P 4c -2' case('P42bc') num='106' schn='C4v^8' hall='P 4c -2ab' case('I4mm') num='107' schn='C4v^9' hall='I 4 -2' case('I4cm') num='108' schn='C4v^10' hall='I 4 -2c' case('I41md') num='109' schn='C4v^11' hall='I 4bw -2' case('I41cd') num='110' schn='C4v^12' hall='I 4bw -2c' case('P-42m') num='111' schn='D2d^1' hall='P -4 2' case('P-42c') num='112' schn='D2d^2' hall='P -4 2c' case('P-421m') num='113' schn='D2d^3' hall='P -4 2ab' case('P-421c') num='114' schn='D2d^4' hall='P -4 2n' case('P-4m2') num='115' schn='D2d^5' hall='P -4 -2' case('P-4c2') num='116' schn='D2d^6' hall='P -4 -2c' case('P-4b2') num='117' schn='D2d^7' hall='P -4 -2ab' case('P-4n2') num='118' schn='D2d^8' hall='P -4 -2n' case('I-4m2') num='119' schn='D2d^9' hall='I -4 -2' case('I-4c2') num='120' schn='D2d^10' hall='I -4 -2c' case('I-42m') num='121' schn='D2d^11' hall='I -4 2' case('I-42d') num='122' schn='D2d^12' hall='I -4 2bw' case('P4/mmm') num='123' schn='D4h^1' hall='-P 4 2' case('P4/mcc') num='124' schn='D4h^2' hall='-P 4 2c' case('P4/nbm:1') num='125:1' schn='D4h^3' hall='P 4 2 -1ab' case('P4/nbm:2') num='125:2' schn='D4h^3' hall='-P 4a 2b' case('P4/nnc:1') num='126:1' schn='D4h^4' hall='P 4 2 -1n' case('P4/nnc:2') num='126:2' schn='D4h^4' hall='-P 4a 2bc' case('P4/mbm') num='127' schn='D4h^5' hall='-P 4 2ab' case('P4/mnc') num='128' schn='D4h^6' hall='-P 4 2n' case('P4/nmm:1') num='129:1' schn='D4h^7' hall='P 4ab 2ab -1ab' case('P4/nmm:2') num='129:2' schn='D4h^7' hall='-P 4a 2a' case('P4/ncc:1') num='130:1' schn='D4h^8' hall='P 4ab 2n -1ab' case('P4/ncc:2') num='130:2' schn='D4h^8' hall='-P 4a 2ac' case('P42/mmc') num='131' schn='D4h^9' hall='-P 4c 2' case('P42/mcm') num='132' schn='D4h^10' hall='-P 4c 2c' case('P42/nbc:1') num='133:1' schn='D4h^11' hall='P 4n 2c -1n' case('P42/nbc:2') num='133:2' schn='D4h^11' hall='-P 4ac 2b' case('P42/nnm:1') num='134:1' schn='D4h^12' hall='P 4n 2 -1n' case('P42/nnm:2') num='134:2' schn='D4h^12' hall='-P 4ac 2bc' case('P42/mbc') num='135' schn='D4h^13' hall='-P 4c 2ab' case('P42/mnm') num='136' schn='D4h^14' hall='-P 4n 2n' case('P42/nmc:1') num='137:1' schn='D4h^15' hall='P 4n 2n -1n' case('P42/nmc:2') num='137:2' schn='D4h^15' hall='-P 4ac 2a' case('P42/ncm:1') num='138:1' schn='D4h^16' hall='P 4n 2ab -1n' case('P42/ncm:2') num='138:2' schn='D4h^16' hall='-P 4ac 2ac' case('I4/mmm') num='139' schn='D4h^17' hall='-I 4 2' case('I4/mcm') num='140' schn='D4h^18' hall='-I 4 2c' case('I41/amd:1') num='141:1' schn='D4h^19' hall='I 4bw 2bw -1bw' case('I41/amd:2') num='141:2' schn='D4h^19' hall='-I 4bd 2' case('I41/acd:1') num='142:1' schn='D4h^20' hall='I 4bw 2aw -1bw' case('I41/acd:2') num='142:2' schn='D4h^20' hall='-I 4bd 2c' case('P3') num='143' schn='C3^1' hall='P 3' case('P31') num='144' schn='C3^2' hall='P 31' case('P32') num='145' schn='C3^3' hall='P 32' case('R3:H') num='146:H' schn='C3^4' hall='R 3' case('R3:R') num='146:R' schn='C3^4' hall='P 3*' case('P-3') num='147' schn='C3i^1' hall='-P 3' case('R-3:H') num='148:H' schn='C3i^2' hall='-R 3' case('R-3:R') num='148:R' schn='C3i^2' hall='-P 3*' case('P312') num='149' schn='D3^1' hall='P 3 2' case('P321') num='150' schn='D3^2' hall='P 3 2"' case('P3112') num='151' schn='D3^3' hall='P 31 2c (0 0 1)' case('P3121') num='152' schn='D3^4' hall='P 31 2"' case('P3212') num='153' schn='D3^5' hall='P 32 2c (0 0 -1)' case('P3221') num='154' schn='D3^6' hall='P 32 2"' case('R32:H') num='155:H' schn='D3^7' hall='R 3 2"' case('R32:R') num='155:R' schn='D3^7' hall='P 3* 2' case('P3m1') num='156' schn='C3v^1' hall='P 3 -2"' case('P31m') num='157' schn='C3v^2' hall='P 3 -2' case('P3c1') num='158' schn='C3v^3' hall='P 3 -2"c' case('P31c') num='159' schn='C3v^4' hall='P 3 -2c' case('R3m:H') num='160:H' schn='C3v^5' hall='R 3 -2"' case('R3m:R') num='160:R' schn='C3v^5' hall='P 3* -2' case('R3c:H') num='161:H' schn='C3v^6' hall='R 3 -2"c' case('R3c:R') num='161:R' schn='C3v^6' hall='P 3* -2n' case('P-31m') num='162' schn='D3d^1' hall='-P 3 2' case('P-31c') num='163' schn='D3d^2' hall='-P 3 2c' case('P-3m1') num='164' schn='D3d^3' hall='-P 3 2"' case('P-3c1') num='165' schn='D3d^4' hall='-P 3 2"c' case('R-3m:H') num='166:H' schn='D3d^5' hall='-R 3 2"' case('R-3m:R') num='166:R' schn='D3d^5' hall='-P 3* 2' case('R-3c:H') num='167:H' schn='D3d^6' hall='-R 3 2"c' case('R-3c:R') num='167:R' schn='D3d^6' hall='-P 3* 2n' case('P6') num='168' schn='C6^1' hall='P 6' case('P61') num='169' schn='C6^2' hall='P 61' case('P65') num='170' schn='C6^3' hall='P 65' case('P62') num='171' schn='C6^4' hall='P 62' case('P64') num='172' schn='C6^5' hall='P 64' case('P63') num='173' schn='C6^6' hall='P 6c' case('P-6') num='174' schn='C3h^1' hall='P -6' case('P6/m') num='175' schn='C6h^1' hall='-P 6' case('P63/m') num='176' schn='C6h^2' hall='-P 6c' case('P622') num='177' schn='D6^1' hall='P 6 2' case('P6122') num='178' schn='D6^2' hall='P 61 2 (0 0 -1)' case('P6522') num='179' schn='D6^3' hall='P 65 2 (0 0 1)' case('P6222') num='180' schn='D6^4' hall='P 62 2c (0 0 1)' case('P6422') num='181' schn='D6^5' hall='P 64 2c (0 0 -1)' case('P6322') num='182' schn='D6^6' hall='P 6c 2c' case('P6mm') num='183' schn='C6v^1' hall='P 6 -2' case('P6cc') num='184' schn='C6v^2' hall='P 6 -2c' case('P63cm') num='185' schn='C6v^3' hall='P 6c -2' case('P63mc') num='186' schn='C6v^4' hall='P 6c -2c' case('P-6m2') num='187' schn='D3h^1' hall='P -6 2' case('P-6c2') num='188' schn='D3h^2' hall='P -6c 2' case('P-62m') num='189' schn='D3h^3' hall='P -6 -2' case('P-62c') num='190' schn='D3h^4' hall='P -6c -2c' case('P6/mmm') num='191' schn='D6h^1' hall='-P 6 2' case('P6/mcc') num='192' schn='D6h^2' hall='-P 6 2c' case('P63/mcm') num='193' schn='D6h^3' hall='-P 6c 2' case('P63/mmc') num='194' schn='D6h^4' hall='-P 6c 2c' case('P23') num='195' schn='T^1' hall='P 2 2 3' case('F23') num='196' schn='T^2' hall='F 2 2 3' case('I23') num='197' schn='T^3' hall='I 2 2 3' case('P213') num='198' schn='T^4' hall='P 2ac 2ab 3' case('I213') num='199' schn='T^5' hall='I 2b 2c 3' case('Pm-3') num='200' schn='Th^1' hall='-P 2 2 3' case('Pn-3:1') num='201:1' schn='Th^2' hall='P 2 2 3 -1n' case('Pn-3:2') num='201:2' schn='Th^2' hall='-P 2ab 2bc 3' case('Fm-3') num='202' schn='Th^3' hall='-F 2 2 3' case('Fd-3:1') num='203:1' schn='Th^4' hall='F 2 2 3 -1d' case('Fd-3:2') num='203:2' schn='Th^4' hall='-F 2uv 2vw 3' case('Im-3') num='204' schn='Th^5' hall='-I 2 2 3' case('Pa-3') num='205' schn='Th^6' hall='-P 2ac 2ab 3' case('Ia-3') num='206' schn='Th^7' hall='-I 2b 2c 3' case('P432') num='207' schn='O^1' hall='P 4 2 3' case('P4232') num='208' schn='O^2' hall='P 4n 2 3' case('F432') num='209' schn='O^3' hall='F 4 2 3' case('F4132') num='210' schn='O^4' hall='F 4d 2 3' case('I432') num='211' schn='O^5' hall='I 4 2 3' case('P4332') num='212' schn='O^6' hall='P 4acd 2ab 3' case('P4132') num='213' schn='O^7' hall='P 4bd 2ab 3' case('I4132') num='214' schn='O^8' hall='I 4bd 2c 3' case('P-43m') num='215' schn='Td^1' hall='P -4 2 3' case('F-43m') num='216' schn='Td^2' hall='F -4 2 3' case('I-43m') num='217' schn='Td^3' hall='I -4 2 3' case('P-43n') num='218' schn='Td^4' hall='P -4n 2 3' case('F-43c') num='219' schn='Td^5' hall='F -4c 2 3' case('I-43d') num='220' schn='Td^6' hall='I -4bd 2c 3' case('Pm-3m') num='221' schn='Oh^1' hall='-P 4 2 3' case('Pn-3n:1') num='222:1' schn='Oh^2' hall='P 4 2 3 -1n' case('Pn-3n:2') num='222:2' schn='Oh^2' hall='-P 4a 2bc 3' case('Pm-3n') num='223' schn='Oh^3' hall='-P 4n 2 3' case('Pn-3m:1') num='224:1' schn='Oh^4' hall='P 4n 2 3 -1n' case('Pn-3m:2') num='224:2' schn='Oh^4' hall='-P 4bc 2bc 3' case('Fm-3m') num='225' schn='Oh^5' hall='-F 4 2 3' case('Fm-3c') num='226' schn='Oh^6' hall='-F 4c 2 3' case('Fd-3m:1') num='227:1' schn='Oh^7' hall='F 4d 2 3 -1d' case('Fd-3m:2') num='227:2' schn='Oh^7' hall='-F 4vw 2vw 3' case('Fd-3c:1') num='228:1' schn='Oh^8' hall='F 4d 2 3 -1cd' case('Fd-3c:2') num='228:2' schn='Oh^8' hall='-F 4cvw 2vw 3' case('Im-3m') num='229' schn='Oh^9' hall='-I 4 2 3' case('Ia-3d') num='230' schn='Oh^10' hall='-I 4bd 2c 3' case default write(*,*) write(*,'("Error(sgsymb): Hermann-Mauguin symbol ''",A,"'' not found")') & trim(adjustl(hrmg)) write(*,*) stop end select return end subroutine !EOC elk-7.2.42/src/spacegroup/PaxHeaders.21776/writegeom.f900000644000000000000000000000012714061636515017420 xustar0029 mtime=1623670093.53810377 29 atime=1623670093.53810377 29 ctime=1623670093.53810377 elk-7.2.42/src/spacegroup/writegeom.f900000644002504400250440000000334614061636515021457 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writegeom use modmain implicit none ! local variables integer is,ia,ip open(50,file='GEOMETRY.OUT',action='WRITE',form='FORMATTED') write(50,*) write(50,'("! Atomic positions generated by spacegroup version ",& &I1.1,".",I1.1,".",I2.2)') version write(50,'("! Hermann-Mauguin symbol : ",A)') trim(hrmg) write(50,'("! Hall symbol : ",A)') trim(hall) write(50,'("! Schoenflies symbol : ",A)') trim(schn) write(50,'("! space group number : ",A)') trim(num) write(50,'("! lattice constants (a,b,c) : ",3G18.10)') a,b,c write(50,'("! angles in degrees (bc,ac,ab) : ",3G18.10)') bc,ac,ab write(50,'("! number of conventional unit cells : ",3I4)') ncell write(50,'("! reduction to primitive cell : ",L1)') primcell write(50,'("! Wyckoff positions :")') do is=1,nspecies write(50,'("! species : ",I4,", ",A)') is,trim(spsymb(is)) do ip=1,nwpos(is) write(50,'("! ",3G18.10)') wpos(:,ip,is) end do end do write(50,*) write(50,'("avec")') write(50,'(3G18.10)') avec(:,1) write(50,'(3G18.10)') avec(:,2) write(50,'(3G18.10)') avec(:,3) write(50,*) write(50,'("atoms")') write(50,'(I4,T40," : nspecies")') nspecies do is=1,nspecies write(50,'("''",A,"''",T40," : spfname")') trim(spsymb(is))//'.in' write(50,'(I4,T40," : natoms; atposl, bfcmt below")') natoms(is) do ia=1,natoms(is) write(50,'(3F14.8," ",3F12.8)') atposl(:,ia,is),bfcmt0(:,ia,is) end do end do close(50) write(*,*) write(*,'("Info(writegeom):")') write(*,'(" Elk lattice vectors and atomic positions written to GEOMETRY.OUT")') return end subroutine elk-7.2.42/src/PaxHeaders.21776/modmain.f900000644000000000000000000000013214061636516014667 xustar0030 mtime=1623670094.832102569 30 atime=1623670093.546103763 30 ctime=1623670094.832102569 elk-7.2.42/src/modmain.f900000644002504400250440000012014514061636516016727 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2009 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modmain !----------------------------! ! lattice parameters ! !----------------------------! ! lattice vectors stored column-wise real(8) avec(3,3) ! magnitude of random displacements added to lattice vectors real(8) rndavec ! inverse of lattice vector matrix real(8) ainv(3,3) ! reciprocal lattice vectors real(8) bvec(3,3) ! inverse of reciprocal lattice vector matrix real(8) binv(3,3) ! unit cell volume real(8) omega ! Brillouin zone volume real(8) omegabz ! any vector with length less than epslat is considered zero real(8) epslat !--------------------------! ! atomic variables ! !--------------------------! ! maximum allowed species integer, parameter :: maxspecies=8 ! maximum allowed atoms per species integer, parameter :: maxatoms=200 ! number of species integer nspecies ! number of atoms for each species integer natoms(maxspecies) ! maximum number of atoms over all the species integer natmmax ! total number of atoms integer natmtot ! index to atoms and species integer idxas(maxatoms,maxspecies) ! inverse atoms and species indices integer idxis(maxatoms*maxspecies) integer idxia(maxatoms*maxspecies) ! molecule is .true. is the system is an isolated molecule logical molecule ! primcell is .true. if primitive unit cell is to be found automatically logical primcell ! atomic positions in lattice coordinates real(8) atposl(3,maxatoms,maxspecies) ! atomic positions in Cartesian coordinates real(8) atposc(3,maxatoms,maxspecies) ! magnitude of random displacements added to the atomic positions real(8) rndatposc ! tdatpos is .true. if small amplitude displacements are to be included when ! calculating the Coulomb potential logical :: tdatpos=.false. ! trddatpos is .true. if the small amplitude displacements and velocities are to ! be read from file logical :: trddatpos=.false. ! small amplitude atomic displacements and velocities real(8) datposc(3,0:1,maxatoms,maxspecies) !----------------------------------! ! atomic species variables ! !----------------------------------! ! species files path character(256) sppath ! species filenames character(256) spfname(maxspecies) ! species name character(256) spname(maxspecies) ! species symbol character(256) spsymb(maxspecies) ! species nuclear charge real(8) spzn(maxspecies) ! ptnucl is .true. if the nuclei are to be treated as point charges, if .false. ! the nuclei have a finite spherical distribution logical ptnucl ! nuclear radius real(8) rnucl(maxspecies) ! nuclear volume real(8) volnucl(maxspecies) ! number of radial mesh points to nuclear radius integer nrnucl(maxspecies) ! nuclear Coulomb potential real(8), allocatable :: vcln(:,:) ! species electronic charge real(8) spze(maxspecies) ! species mass real(8) spmass(maxspecies) ! smallest radial point for each species real(8) rminsp(maxspecies) ! effective infinity for species real(8) rmaxsp(maxspecies) ! number of radial points to effective infinity for each species integer nrsp(maxspecies) ! maximum nrsp over all the species integer nrspmax ! maximum allowed states for each species integer, parameter :: maxstsp=40 ! number of states for each species integer nstsp(maxspecies) ! maximum nstsp over all the species integer nstspmax ! core-valence cut-off energy for species file generation real(8) ecvcut ! semi-core-valence cut-off energy for species file generation real(8) esccut ! state principle quantum number for each species integer nsp(maxstsp,maxspecies) ! state l value for each species integer lsp(maxstsp,maxspecies) ! state k value for each species integer ksp(maxstsp,maxspecies) ! spcore is .true. if species state is core logical spcore(maxstsp,maxspecies) ! total number of core states integer nstcr ! state eigenvalue for each species real(8) evalsp(maxstsp,maxspecies) ! state occupancy for each species real(8) occsp(maxstsp,maxspecies) ! species radial mesh to effective infinity real(8), allocatable :: rsp(:,:) ! species charge density real(8), allocatable :: rhosp(:,:) ! species self-consistent potential real(8), allocatable :: vrsp(:,:) ! exchange-correlation type for atomic species (the converged ground-state of ! the crystal does not depend on this choice) integer xctsp(3) !---------------------------------------------------------------! ! muffin-tin radial mesh and angular momentum variables ! !---------------------------------------------------------------! ! scale factor for number of muffin-tin points real(8) nrmtscf ! number of muffin-tin radial points for each species integer nrmt(maxspecies) ! maximum nrmt over all the species integer nrmtmax ! optional default muffin-tin radius for all atoms real(8) rmtall ! minimum allowed distance between muffin-tin surfaces real(8) rmtdelta ! muffin-tin radii real(8) rmt(maxspecies) ! total muffin-tin volume real(8) omegamt ! radial step length for coarse mesh integer lradstp ! number of coarse radial mesh points integer nrcmt(maxspecies) ! maximum nrcmt over all the species integer nrcmtmax ! coarse muffin-tin radial mesh real(8), allocatable :: rcmt(:,:) ! r^l on fine radial mesh real(8), allocatable :: rlmt(:,:,:) ! r^l on coarse radial mesh real(8), allocatable :: rlcmt(:,:,:) ! weights for spline integration on fine radial mesh real(8), allocatable :: wrmt(:,:) ! weights for spline partial integration on fine radial mesh real(8), allocatable :: wprmt(:,:,:) ! weights for spline coefficients on fine radial mesh real(8), allocatable :: wcrmt(:,:,:) ! weights for spline integration on coarse radial mesh real(8), allocatable :: wrcmt(:,:) ! weights for spline partial integration on coarse radial mesh real(8), allocatable :: wprcmt(:,:,:) ! weights for spline coefficients on coarse radial mesh real(8), allocatable :: wcrcmt(:,:,:) ! maximum allowable angular momentum for augmented plane waves integer, parameter :: maxlapw=30 ! maximum angular momentum for augmented plane waves integer lmaxapw ! (lmaxapw+1)^2 integer lmmaxapw ! maximum angular momentum on the outer part of the muffin-tin integer lmaxo ! (lmaxo+1)^2 integer lmmaxo ! maximum angular momentum on the inner part of the muffin-tin integer lmaxi ! (lmaxi+1)^2 integer lmmaxi ! fraction of muffin-tin radius which constitutes the inner part real(8) fracinr ! number of fine/coarse radial points on the inner part of the muffin-tin integer nrmti(maxspecies),nrcmti(maxspecies) ! number of fine/coarse points in packed muffin-tins integer npmti(maxspecies),npmt(maxspecies) integer npcmti(maxspecies),npcmt(maxspecies) ! maximum number of points over all packed muffin-tins integer npmtmax,npcmtmax !--------------------------------! ! spin related variables ! !--------------------------------! ! spinpol is .true. for spin-polarised calculations logical spinpol ! spinorb is .true. for spin-orbit coupling logical spinorb ! scale factor of spin-orbit coupling term in Hamiltonian real(8) socscf ! dimension of magnetisation and magnetic vector fields (1 or 3) integer ndmag ! ncmag is .true. if the magnetisation is non-collinear, i.e. when ndmag = 3 logical ncmag ! if cmagz is .true. then collinear magnetism along the z-axis is enforced logical cmagz ! spcpl is .true. if the up and down spins are coupled logical spcpl ! fixed spin moment type ! 0 : none ! 1 (-1) : total moment (direction) ! 2 (-2) : individual muffin-tin moments (direction) ! 3 (-3) : total and muffin-tin moments (direction) integer fsmtype ! fixed total spin magnetic moment real(8) momfix(3) ! fixed spin moment global effective field in Cartesian coordinates real(8) bfsmc(3) ! muffin-tin fixed spin moments real(8) mommtfix(3,maxatoms,maxspecies) ! muffin-tin fixed spin moment effective fields in Cartesian coordinates real(8), allocatable :: bfsmcmt(:,:) ! fixed spin moment field step size real(8) taufsm ! second-variational spinor dimension (1 or 2) integer nspinor ! global external magnetic field in Cartesian coordinates real(8) bfieldc(3) ! initial field real(8) bfieldc0(3) ! external magnetic field in each muffin-tin in Cartesian coordinates real(8) bfcmt(3,maxatoms,maxspecies) ! initial field as read in from input file real(8) bfcmt0(3,maxatoms,maxspecies) ! magnitude of random vectors added to muffin-tin fields real(8) rndbfcmt ! external magnetic fields are multiplied by reducebf after each s.c. loop real(8) reducebf ! spinsprl is .true. if a spin-spiral is to be calculated logical spinsprl ! ssdph is .true. if the muffin-tin spin-spiral magnetisation is de-phased logical ssdph ! spin-spiral phase factor for each atom complex(8), allocatable :: zqss(:) ! number of spin-dependent first-variational functions per state integer nspnfv ! map from second- to first-variational spin index integer jspnfv(2) ! spin-spiral q-vector in lattice coordinates real(8) vqlss(3) ! spin-spiral q-vector in Cartesian coordinates real(8) vqcss(3) ! current q-point in spin-spiral supercell calculation integer iqss ! number of primitive unit cells in spin-spiral supercell integer nscss ! number of fixed spin direction points on the sphere for finding the magnetic ! anisotropy energy (MAE) integer npmae0,npmae ! (theta,phi) coordinates for each MAE direction real(8), allocatable :: tpmae(:,:) !---------------------------------------------! ! electric field and vector potential ! !---------------------------------------------! ! tefield is .true. if a polarising constant electric field is applied logical tefield ! electric field vector in Cartesian coordinates real(8) efieldc(3) ! electric field vector in lattice coordinates real(8) efieldl(3) ! tafield is .true. if a constant vector potential is applied logical tafield ! vector potential A-field which couples to paramagnetic current real(8) afieldc(3) ! A-field in lattice coordinates real(8) afieldl(3) !----------------------------! ! symmetry variables ! !----------------------------! ! type of symmetry allowed for the crystal ! 0 : only the identity element is used ! 1 : full symmetry group is used ! 2 : only symmorphic symmetries are allowed integer symtype ! number of Bravais lattice point group symmetries integer nsymlat ! Bravais lattice point group symmetries integer symlat(3,3,48) ! determinants of lattice symmetry matrices (1 or -1) integer symlatd(48) ! index to inverses of the lattice symmetries integer isymlat(48) ! lattice point group symmetries in Cartesian coordinates real(8) symlatc(3,3,48) ! tshift is .true. if atomic basis is allowed to be shifted logical tshift ! tsyminv is .true. if the crystal has inversion symmetry logical tsyminv ! maximum of symmetries allowed integer, parameter :: maxsymcrys=192 ! number of crystal symmetries integer nsymcrys ! crystal symmetry translation vector in lattice and Cartesian coordinates real(8) vtlsymc(3,maxsymcrys) real(8) vtcsymc(3,maxsymcrys) ! tv0symc is .true. if the translation vector is zero logical tv0symc(maxsymcrys) ! spatial rotation element in lattice point group for each crystal symmetry integer lsplsymc(maxsymcrys) ! global spin rotation element in lattice point group for each crystal symmetry integer lspnsymc(maxsymcrys) ! equivalent atom index for each crystal symmetry integer, allocatable :: ieqatom(:,:,:) ! eqatoms(ia,ja,is) is .true. if atoms ia and ja are equivalent logical, allocatable :: eqatoms(:,:,:) ! number of site symmetries integer, allocatable :: nsymsite(:) ! site symmetry spatial rotation element in lattice point group integer, allocatable :: lsplsyms(:,:) ! site symmetry global spin rotation element in lattice point group integer, allocatable :: lspnsyms(:,:) !----------------------------! ! G-vector variables ! !----------------------------! ! G-vector cut-off for interstitial potential and density real(8) gmaxvr ! G-vector grid sizes integer ngridg(3) ! G-vector grid sizes for coarse grid (G < 2*gkmax) integer ngdgc(3) ! total number of G-vectors integer ngtot ! total number of G-vectors for coarse grid (G < 2*gkmax) integer ngtc ! integer grid intervals for each direction integer intgv(2,3) ! number of G-vectors with G < gmaxvr integer ngvec ! number of G-vectors for coarse grid (G < 2*gkmax) integer ngvc ! G-vector integer coordinates (i1,i2,i3) integer, allocatable :: ivg(:,:) ! map from (i1,i2,i3) to G-vector index integer, allocatable :: ivgig(:,:,:) ! map from G-vector index to FFT array integer, allocatable :: igfft(:) ! map from G-vector index to FFT array for coarse grid (G < 2*gkmax) integer, allocatable :: igfc(:) ! G-vectors in Cartesian coordinates real(8), allocatable :: vgc(:,:) ! length of G-vectors real(8), allocatable :: gc(:) ! Coulomb Green's function in G-space = 4 pi / G^2 real(8), allocatable :: gclg(:) ! spherical Bessel functions j_l(|G|R_mt) real(8), allocatable :: jlgrmt(:,:,:) ! spherical harmonics of the G-vectors complex(8), allocatable :: ylmg(:,:) ! structure factors for the G-vectors complex(8), allocatable :: sfacg(:,:) ! smooth step function form factors for all species and G-vectors real(8), allocatable :: ffacg(:,:) ! characteristic function in G-space: 0 inside the muffin-tins and 1 outside complex(8), allocatable :: cfunig(:) ! characteristic function in real-space: 0 inside the muffin-tins and 1 outside real(8), allocatable :: cfunir(:) ! characteristic function in real-space for coarse grid (G < 2*gkmax) real(8), allocatable :: cfrc(:) !---------------------------! ! k-point variables ! !---------------------------! ! autokpt is .true. if the k-point set is determined automatically logical autokpt ! radius of sphere used to determine k-point density when autokpt is .true. real(8) radkpt ! k-point grid sizes integer ngridk(3) ! k-point offset real(8) vkloff(3) ! type of reduction to perform on k-point set ! 0 : no reduction ! 1 : reduce with full crystal symmetry group ! 2 : reduce with symmorphic symmetries only integer reducek ! number of point group symmetries used for k-point reduction integer nsymkpt ! point group symmetry matrices used for k-point reduction integer symkpt(3,3,48) ! total number of reduced k-points integer nkpt ! total number of non-reduced k-points integer nkptnr ! locations of k-points on integer grid integer, allocatable :: ivk(:,:) ! map from integer grid to reduced k-point index integer, allocatable :: ivkik(:,:,:) ! map from integer grid to non-reduced k-point index integer, allocatable :: ivkiknr(:,:,:) ! k-points in lattice coordinates real(8), allocatable :: vkl(:,:) ! k-points in Cartesian coordinates real(8), allocatable :: vkc(:,:) ! reduced k-point weights real(8), allocatable :: wkpt(:) ! weight of each non-reduced k-point real(8) wkptnr ! k-point at which to determine effective mass tensor real(8) vklem(3) ! displacement size for computing the effective mass tensor real(8) deltaem ! number of displacements in each direction integer ndspem ! number of k-points subdivision used for calculating the polarisation phase integer nkspolar !------------------------------! ! G+k-vector variables ! !------------------------------! ! species for which the muffin-tin radius will be used for calculating gkmax integer isgkmax ! smallest muffin-tin radius times gkmax real(8) rgkmax ! maximum |G+k| cut-off for APW functions real(8) gkmax ! number of G+k-vectors for augmented plane waves integer, allocatable :: ngk(:,:) ! maximum number of G+k-vectors over all k-points integer ngkmax ! index from G+k-vectors to G-vectors integer, allocatable :: igkig(:,:,:) ! G+k-vectors in lattice coordinates real(8), allocatable :: vgkl(:,:,:,:) ! G+k-vectors in Cartesian coordinates real(8), allocatable :: vgkc(:,:,:,:) ! length of G+k-vectors real(8), allocatable :: gkc(:,:,:) ! structure factors for the G+k-vectors complex(8), allocatable :: sfacgk(:,:,:,:) !---------------------------! ! q-point variables ! !---------------------------! ! q-point grid sizes integer ngridq(3) ! integer grid intervals for the q-points integer intq(2,3) ! type of reduction to perform on q-point set (see reducek) integer reduceq ! number of point group symmetries used for q-point reduction integer nsymqpt ! point group symmetry matrices used for q-point reduction integer symqpt(3,3,48) ! total number of reduced q-points integer nqpt ! total number of non-reduced q-points integer nqptnr ! locations of q-points on integer grid integer, allocatable :: ivq(:,:) ! map from integer grid to reduced index integer, allocatable :: ivqiq(:,:,:) ! map from integer grid to non-reduced index integer, allocatable :: ivqiqnr(:,:,:) ! map from q-vector index to complex-complex FFT array integer, allocatable :: iqfft(:) ! number of complex FFT elements for real-complex transforms integer nfqrz ! map from q-point index to real-complex FFT index integer, allocatable :: ifqrz(:) ! map from real-complex FFT index to q-point index integer, allocatable :: iqrzf(:) ! q-points in lattice coordinates real(8), allocatable :: vql(:,:) ! q-points in Cartesian coordinates real(8), allocatable :: vqc(:,:) ! q-point weights real(8), allocatable :: wqpt(:) ! weight for each non-reduced q-point real(8) wqptnr ! regularised Coulomb Green's function in q-space real(8), allocatable :: gclq(:) ! if t0gclq0 is .true. then the Coulomb Green's function at q = 0 is set to zero logical t0gclq0 !-----------------------------------------------------! ! spherical harmonic transform (SHT) matrices ! !-----------------------------------------------------! ! trotsht is .true. if the spherical cover used for the SHT is to be rotated logical :: trotsht=.false. ! spherical cover rotation matrix real(8) rotsht(3,3) ! real backward SHT matrix for lmaxi real(8), allocatable :: rbshti(:,:) ! real forward SHT matrix for lmaxi real(8), allocatable :: rfshti(:,:) ! real backward SHT matrix for lmaxo real(8), allocatable :: rbshto(:,:) ! real forward SHT matrix for lmaxo real(8), allocatable :: rfshto(:,:) ! complex backward SHT matrix for lmaxi complex(8), allocatable :: zbshti(:,:) ! complex forward SHT matrix for lmaxi complex(8), allocatable :: zfshti(:,:) ! complex backward SHT matrix for lmaxo complex(8), allocatable :: zbshto(:,:) ! complex forward SHT matrix for lmaxo complex(8), allocatable :: zfshto(:,:) !---------------------------------------------------------------! ! density, potential and exchange-correlation variables ! !---------------------------------------------------------------! ! exchange-correlation functional type integer xctype(3) ! exchange-correlation functional description character(512) xcdescr ! exchange-correlation functional spin requirement integer xcspin ! exchange-correlation functional density gradient requirement integer xcgrad ! small constant used to stabilise non-collinear GGA real(8) dncgga ! muffin-tin and interstitial charge density real(8), allocatable :: rhomt(:,:),rhoir(:) ! trhonorm is .true. if the density is to be normalised after every iteration logical trhonorm ! muffin-tin and interstitial magnetisation vector field real(8), allocatable :: magmt(:,:,:),magir(:,:) ! tjr is .true. if the current density j(r) is to be calculated logical tjr ! muffin-tin and interstitial gauge-invariant current density vector field real(8), allocatable :: jrmt(:,:,:),jrir(:,:) ! amount of smoothing to be applied to the exchange-correlation potentials and ! magnetic field integer msmooth ! muffin-tin and interstitial Coulomb potential real(8), allocatable :: vclmt(:,:),vclir(:) ! Poisson solver pseudocharge density constant integer npsd ! lmaxo+npsd+1 integer lnpsd ! muffin-tin and interstitial exchange energy density real(8), allocatable :: exmt(:,:),exir(:) ! muffin-tin and interstitial correlation energy density real(8), allocatable :: ecmt(:,:),ecir(:) ! muffin-tin and interstitial exchange-correlation potential real(8), allocatable :: vxcmt(:,:),vxcir(:) ! muffin-tin and interstitial exchange-correlation magnetic field real(8), allocatable :: bxcmt(:,:,:),bxcir(:,:) ! muffin-tin and interstitial magnetic dipole field real(8), allocatable :: bdmt(:,:,:),bdir(:,:) ! tbdip is .true. if the spin and current dipole fields are to be added to the ! Kohn-Sham magnetic field logical tbdip ! combined target array for vsmt, vsir, bsmt and bsir real(8), allocatable, target :: vsbs(:) ! muffin-tin and interstitial Kohn-Sham effective potential real(8), pointer :: vsmt(:,:),vsir(:) ! muffin-tin Kohn-Sham effective magnetic field in spherical coordinates and on ! a coarse radial mesh real(8), pointer :: bsmt(:,:,:) ! interstitial Kohn-Sham effective magnetic field real(8), pointer :: bsir(:,:) ! G-space interstitial Kohn-Sham effective potential complex(8), allocatable :: vsig(:) ! nosource is .true. if the field is to be made source-free logical nosource ! tssxc is .true. if scaled spin exchange-correlation is to be used logical tssxc ! spin exchange-correlation scaling factor real(8) sxcscf ! spin-orbit coupling radial function real(8), allocatable :: socfr(:,:) ! kinetic energy density real(8), allocatable :: taumt(:,:,:),tauir(:,:) ! core kinetic energy density real(8), allocatable :: taucr(:,:,:) ! taudft is .true. if meta-GGA is to be treated as a meta-GGA functional logical taudft ! meta-GGA exchange-correlation potential real(8), allocatable :: wxcmt(:,:),wxcir(:) ! meta-GGA Kohn-Sham potential real(8), allocatable :: wsmt(:,:),wsir(:) ! Tran-Blaha '09 constant c [Phys. Rev. Lett. 102, 226401 (2009)] real(8) c_tb09 ! tc_tb09 is .true. if the Tran-Blaha constant has been read in logical tc_tb09 ! if trdstate is .true. the density and potential can be read from STATE.OUT logical :: trdstate=.false. ! temperature in degrees Kelvin real(8) tempk !--------------------------! ! mixing variables ! !--------------------------! ! type of mixing to use for the potential integer mixtype ! mixing type description character(256) mixdescr ! adaptive mixing parameters (formerly beta0 and betamax) real(8) amixpm(2) ! subspace dimension for Broyden mixing integer mixsdb ! Broyden mixing parameters alpha and w0 real(8) broydpm(2) !----------------------------------------------! ! charge, moment and current variables ! !----------------------------------------------! ! tolerance for error in total charge real(8) epschg ! total nuclear charge real(8) chgzn ! core charges real(8) chgcr(maxspecies) ! total core charge real(8) chgcrtot ! core leakage charge real(8), allocatable :: chgcrlk(:) ! total valence charge real(8) chgval ! excess charge real(8) chgexs ! total charge real(8) chgtot ! calculated total charge real(8) chgcalc ! interstitial region charge real(8) chgir ! muffin-tin charges real(8), allocatable :: chgmt(:) ! total muffin-tin charge real(8) chgmttot ! effective Wigner radius real(8) rwigner ! total moment real(8) momtot(3) ! total moment magnitude real(8) momtotm ! interstitial region moment real(8) momir(3) ! muffin-tin moments real(8), allocatable :: mommt(:,:) ! total muffin-tin moment real(8) mommttot(3) ! total gauge-invariant current and its magnitude real(8) jtot(3),jtotm !-----------------------------------------! ! APW and local-orbital variables ! !-----------------------------------------! ! energy step used for numerical calculation of energy derivatives real(8) deapwlo ! maximum allowable APW order integer, parameter :: maxapword=4 ! APW order integer apword(0:maxlapw,maxspecies) ! maximum of apword over all angular momenta and species integer apwordmax ! total number of APW coefficients (l, m and order) for each species integer lmoapw(maxspecies) ! polynomial order used for APW radial derivatives integer npapw ! APW initial linearisation energies real(8) apwe0(maxapword,0:maxlapw,maxspecies) ! APW linearisation energies real(8), allocatable :: apwe(:,:,:) ! APW derivative order integer apwdm(maxapword,0:maxlapw,maxspecies) ! apwve is .true. if the linearisation energies are allowed to vary logical apwve(maxapword,0:maxlapw,maxspecies) ! APW radial functions real(8), allocatable :: apwfr(:,:,:,:,:) ! derivate of radial functions at the muffin-tin surface real(8), allocatable :: apwdfr(:,:,:) ! maximum number of local-orbitals integer, parameter :: maxlorb=200 ! maximum allowable local-orbital order integer, parameter :: maxlorbord=5 ! number of local-orbitals integer nlorb(maxspecies) ! maximum nlorb over all species integer nlomax ! total number of local-orbitals integer nlotot ! local-orbital order integer lorbord(maxlorb,maxspecies) ! maximum lorbord over all species integer lorbordmax ! polynomial order used for local-orbital radial derivatives integer nplorb ! local-orbital angular momentum integer lorbl(maxlorb,maxspecies) ! maximum lorbl over all species integer lolmax ! (lolmax+1)^2 integer lolmmax ! local-orbital initial energies real(8) lorbe0(maxlorbord,maxlorb,maxspecies) ! local-orbital energies real(8), allocatable :: lorbe(:,:,:) ! local-orbital derivative order integer lorbdm(maxlorbord,maxlorb,maxspecies) ! lorbve is .true. if the linearisation energies are allowed to vary logical lorbve(maxlorbord,maxlorb,maxspecies) ! local-orbital radial functions real(8), allocatable :: lofr(:,:,:,:) ! band energy search tolerance real(8) epsband ! maximum allowed change in energy during band energy search; enforced only if ! default energy is less than zero real(8) demaxbnd ! minimum default linearisation energy over all APWs and local-orbitals real(8) e0min ! if autolinengy is .true. then the fixed linearisation energies are set to the ! Fermi energy minus dlefe logical autolinengy ! difference between linearisation and Fermi energies when autolinengy is .true. real(8) dlefe ! lorbcnd is .true. if conduction state local-orbitals should be added logical lorbcnd ! conduction state local-orbital order integer lorbordc ! excess order of the APW and local-orbital functions integer nxoapwlo ! excess local orbitals integer nxlo !-------------------------------------------! ! overlap and Hamiltonian variables ! !-------------------------------------------! ! overlap and Hamiltonian matrices sizes at each k-point integer, allocatable :: nmat(:,:) ! maximum nmat over all k-points integer nmatmax ! index to the position of the local-orbitals in the H and O matrices integer, allocatable :: idxlo(:,:,:) ! APW-local-orbital overlap integrals real(8), allocatable :: oalo(:,:,:) ! local-orbital-local-orbital overlap integrals real(8), allocatable :: ololo(:,:,:) ! APW-APW Hamiltonian integrals real(8), allocatable :: haa(:,:,:,:,:,:) ! local-orbital-APW Hamiltonian integrals real(8), allocatable :: hloa(:,:,:,:,:) ! local-orbital-local-orbital Hamiltonian integrals real(8), allocatable :: hlolo(:,:,:,:) ! complex Gaunt coefficient array complex(8), allocatable :: gntyry(:,:,:) ! tefvr is .true. if the first-variational eigenvalue equation is to be solved ! as a real symmetric problem logical tefvr ! tefvit is .true. if the first-variational eigenvalue equation is to be solved ! iteratively logical tefvit ! minimum and maximum allowed number of eigenvalue equation iterations integer minitefv,maxitefv ! eigenvalue mixing parameter for iterative solver real(8) befvit ! iterative solver convergence tolerance real(8) epsefvit !--------------------------------------------! ! eigenvalue and occupancy variables ! !--------------------------------------------! ! number of empty states per atom and spin real(8) nempty0 ! number of empty states integer nempty ! number of first-variational states integer nstfv ! number of second-variational states integer nstsv ! smearing type integer stype ! smearing function description character(256) sdescr ! smearing width real(8) swidth ! autoswidth is .true. if the smearing width is to be determined automatically logical autoswidth ! effective mass used in smearing width formula real(8) mstar ! maximum allowed occupancy (1 or 2) real(8) occmax ! convergence tolerance for occupancies real(8) epsocc ! second-variational occupation numbers real(8), allocatable :: occsv(:,:) ! Fermi energy for second-variational states real(8) efermi ! scissor correction applied when computing response functions real(8) scissor ! density of states at the Fermi energy real(8) fermidos ! estimated indirect and direct band gaps real(8) bandgap(2) ! k-points of indirect and direct gaps integer ikgap(3) ! error tolerance for the first-variational eigenvalues real(8) evaltol ! second-variational eigenvalues real(8), allocatable :: evalsv(:,:) ! tevecsv is .true. if second-variational eigenvectors are calculated logical tevecsv ! maximum number of k-point and states indices in user-defined list integer, parameter :: maxkst=20 ! number of k-point and states indices in user-defined list integer nkstlist ! user-defined list of k-point and state indices integer kstlist(2,maxkst) !------------------------------! ! core state variables ! !------------------------------! ! occupancies for core states real(8), allocatable :: occcr(:,:) ! eigenvalues for core states real(8), allocatable :: evalcr(:,:) ! radial wavefunctions for core states real(8), allocatable :: rwfcr(:,:,:,:) ! radial charge density for core states real(8), allocatable :: rhocr(:,:,:) ! spincore is .true. if the core is to be treated as spin-polarised logical spincore ! number of core spin-channels integer nspncr !--------------------------! ! energy variables ! !--------------------------! ! eigenvalue sum real(8) evalsum ! electron kinetic energy real(8) engykn ! core electron kinetic energy real(8) engykncr ! nuclear-nuclear energy real(8) engynn ! electron-nuclear energy real(8) engyen ! Hartree energy real(8) engyhar ! Coulomb energy (E_nn + E_en + E_H) real(8) engycl ! electronic Coulomb potential energy real(8) engyvcl ! Madelung term real(8) engymad ! exchange-correlation potential energy real(8) engyvxc ! exchange-correlation effective field energy real(8) engybxc ! energy of external global magnetic field real(8) engybext ! exchange energy real(8) engyx ! correlation energy real(8) engyc ! electronic entropy real(8) entrpy ! entropic contribution to free energy real(8) engyts ! total energy real(8) engytot !--------------------------------------------! ! force, stress and strain variables ! !--------------------------------------------! ! tforce is .true. if force should be calculated logical tforce ! Hellmann-Feynman force on each atom real(8), allocatable :: forcehf(:,:) ! incomplete basis set (IBS) force on each atom real(8), allocatable :: forceibs(:,:) ! total force on each atom real(8), allocatable :: forcetot(:,:) ! previous total force on each atom real(8), allocatable :: forcetotp(:,:) ! maximum force magnitude over all atoms real(8) forcemax ! tfav0 is .true. if the average force should be zero in order to prevent ! translation of the atomic basis logical tfav0 ! average force real(8) forceav(3) ! atomic position optimisation type ! 0 : no optimisation ! 1 : unconstrained optimisation integer atpopt ! maximum number of atomic position optimisation steps integer maxatpstp ! default step size parameter for atomic position optimisation real(8) tau0atp ! step size parameters for each atom real(8), allocatable :: tauatp(:) ! number of strain tensors integer nstrain ! current strain tensor integer :: istrain=0 ! strain tensors real(8) strain(3,3,9) ! infinitesimal displacement parameter multiplied by the strain tensor for ! computing the stress tensor real(8) deltast ! symmetry reduced stress tensor components real(8) stress(9) ! previous stress tensor real(8) stressp(9) ! stress tensor component magnitude maximum real(8) stressmax ! lattice vector optimisation type ! 0 : no optimisation ! 1 : unconstrained optimisation ! 2 : iso-volumetric optimisation integer latvopt ! maximum number of lattice vector optimisation steps integer maxlatvstp ! default step size parameter for lattice vector optimisation real(8) tau0latv ! step size for each stress tensor component acting on the lattice vectors real(8) taulatv(9) !-------------------------------! ! convergence variables ! !-------------------------------! ! maximum number of self-consistent loops integer maxscl ! current self-consistent loop number integer iscl ! Kohn-Sham potential convergence tolerance real(8) epspot ! energy convergence tolerance real(8) epsengy ! force convergence tolerance real(8) epsforce ! stress tensor convergence tolerance real(8) epsstress !----------------------------------------------------------! ! density of states, optics and response variables ! !----------------------------------------------------------! ! number of energy intervals in the DOS/optics function plot integer nwplot ! fine k-point grid size for integration of functions in the Brillouin zone integer ngrkf ! smoothing level for DOS/optics function plot integer nswplot ! energy interval for DOS/optics function plot real(8) wplot(2) ! maximum angular momentum for the partial DOS plot integer lmaxdos ! dosocc is .true. if the DOS is to be weighted by the occupancy logical dosocc ! dosmsum is .true. if the partial DOS is to be summed over m logical dosmsum ! dosssum is .true. if the partial DOS is to be summed over spin logical dosssum ! number of optical matrix components required integer noptcomp ! required optical matrix components integer optcomp(3,27) ! intraband is .true. if the intraband term is to be added to the optical matrix logical intraband ! lmirep is .true. if the (l,m) band characters should correspond to the ! irreducible representations of the site symmetries logical lmirep ! spin-quantisation axis in Cartesian coordinates used when plotting the ! spin-resolved DOS (z-axis by default) real(8) sqados(3) ! q-vector in lattice and Cartesian coordinates for calculating the matrix ! elements < i,k+q | exp(iq.r) | j,k > real(8) vecql(3),vecqc(3) ! maximum initial-state energy allowed in ELNES transitions real(8) emaxelnes ! structure factor energy window real(8) wsfac(2) !-------------------------------------! ! 1D/2D/3D plotting variables ! !-------------------------------------! ! number of vertices in 1D plot integer nvp1d ! total number of points in 1D plot integer npp1d ! vertices in lattice coordinates for 1D plot real(8), allocatable :: vvlp1d(:,:) ! distance to vertices in 1D plot real(8), allocatable :: dvp1d(:) ! plot vectors in lattice coordinates for 1D plot real(8), allocatable :: vplp1d(:,:) ! distance to points in 1D plot real(8), allocatable :: dpp1d(:) ! corner vectors of 2D plot in lattice coordinates real(8) vclp2d(3,0:2) ! grid sizes of 2D plot integer np2d(2) ! corner vectors of 3D plot in lattice coordinates real(8) vclp3d(3,0:3) ! grid sizes of 3D plot integer np3d(3) !----------------------------------------! ! OEP and Hartree-Fock variables ! !----------------------------------------! ! maximum number of core states over all species integer ncrmax ! maximum number of OEP iterations integer maxitoep ! OEP step size and fraction of previous potential to be used as starting point real(8) tauoep(2) ! magnitude of the OEP residual real(8) resoep ! exchange potential and magnetic field real(8), allocatable :: vxmt(:,:),vxir(:) real(8), allocatable :: bxmt(:,:,:),bxir(:,:) ! hybrid is .true. if a hybrid functional is to be used logical hybrid,hybrid0 ! hybrid functional mixing coefficient real(8) hybridc !-------------------------------------------------------------! ! response function and perturbation theory variables ! !-------------------------------------------------------------! ! |G| cut-off for response functions real(8) gmaxrf ! energy cut-off for response functions real(8) emaxrf ! number of G-vectors for response functions integer ngrf ! number of response function frequencies integer nwrf ! complex response function frequencies complex(8), allocatable :: wrf(:) ! maximum number of spherical Bessel functions on the coarse radial mesh over ! all species integer njcmax !-------------------------------------------------! ! Bethe-Salpeter equation (BSE) variables ! !-------------------------------------------------! ! number of valence and conduction states for transitions integer nvbse,ncbse ! default number of valence and conduction states integer nvbse0,ncbse0 ! maximum number of extra valence and conduction states integer, parameter :: maxxbse=20 ! number of extra valence and conduction states integer nvxbse,ncxbse ! extra valence and conduction states integer istxbse(maxxbse),jstxbse(maxxbse) ! total number of transitions integer nvcbse ! size of blocks in BSE Hamiltonian matrix integer nbbse ! size of BSE matrix (= 2*nbbse) integer nmbse ! index from BSE valence states to second-variational states integer, allocatable :: istbse(:,:) ! index from BSE conduction states to second-variational states integer, allocatable :: jstbse(:,:) ! index from BSE valence-conduction pair and k-point to location in BSE matrix integer, allocatable :: ijkbse(:,:,:) ! BSE Hamiltonian complex(8), allocatable :: hmlbse(:,:) ! BSE Hamiltonian eigenvalues real(8), allocatable :: evalbse(:) ! if bsefull is .true. then the full BSE Hamiltonian is calculated, otherwise ! only the Hermitian block logical bsefull ! if hxbse/hdbse is .true. then the exchange/direct term is included in the BSE ! Hamiltonian logical hxbse,hdbse !--------------------------! ! timing variables ! !--------------------------! ! initialisation real(8) timeinit ! Hamiltonian and overlap matrix set up real(8) timemat ! first-variational calculation real(8) timefv ! second-variational calculation real(8) timesv ! charge density calculation real(8) timerho ! potential calculation real(8) timepot ! force calculation real(8) timefor !-----------------------------! ! numerical constants ! !-----------------------------! real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: twopi=6.2831853071795864769d0 real(8), parameter :: fourpi=12.566370614359172954d0 ! spherical harmonic for l=m=0 real(8), parameter :: y00=0.28209479177387814347d0 ! complex constants complex(8), parameter :: zzero=(0.d0,0.d0) complex(8), parameter :: zone=(1.d0,0.d0) complex(8), parameter :: zi=(0.d0,1.d0) ! array of i^l and (-i)^l values integer, private :: l complex(8), parameter :: zil(0:maxlapw)=[((0.d0,1.d0)**l,l=0,maxlapw)] complex(8), parameter :: zilc(0:maxlapw)=[((0.d0,-1.d0)**l,l=0,maxlapw)] ! Pauli spin matrices: ! sigma_x = ( 0 1 ) sigma_y = ( 0 -i ) sigma_z = ( 1 0 ) ! ( 1 0 ) ( i 0 ) ( 0 -1 ) ! Planck constant in SI units (exact, CODATA 2018) real(8), parameter :: h_si=6.62607015d-34 ! reduced Planck constant in SI units real(8), parameter :: hbar_si=h_si/twopi ! speed of light in SI units (exact, CODATA 2018) real(8), parameter :: sol_si=299792458d0 ! speed of light in atomic units (=1/alpha) (CODATA 2018) real(8), parameter :: sol=137.035999084d0 ! scaled speed of light real(8) solsc ! Hartree in SI units (CODATA 2018) real(8), parameter :: ha_si=4.3597447222071d-18 ! Hartree in eV (CODATA 2018) real(8), parameter :: ha_ev=27.211386245988d0 ! Hartree in inverse meters real(8), parameter :: ha_im=ha_si/(h_si*sol_si) ! Boltzmann constant in SI units (exact, CODATA 2018) real(8), parameter :: kb_si=1.380649d-23 ! Boltzmann constant in Hartree/kelvin real(8), parameter :: kboltz=kb_si/ha_si ! electron charge in SI units (exact, CODATA 2018) real(8), parameter :: e_si=1.602176634d-19 ! Bohr radius in SI units (CODATA 2018) real(8), parameter :: br_si=0.529177210903d-10 ! Bohr radius in Angstroms real(8), parameter :: br_ang=br_si*1.d10 ! atomic unit of magnetic flux density in SI real(8), parameter :: b_si=hbar_si/(e_si*br_si**2) ! atomic unit of electric field in SI real(8), parameter :: ef_si=ha_si/(e_si*br_si) ! atomic unit of time in SI real(8), parameter :: t_si=hbar_si/ha_si ! electron g-factor (CODATA 2018) real(8), parameter :: gfacte=2.00231930436256d0 ! electron mass in SI (CODATA 2018) real(8), parameter :: em_si=9.1093837015d-31 ! atomic mass unit in SI (CODATA 2018) real(8), parameter :: amu_si=1.66053906660d-27 ! atomic mass unit in electron masses real(8), parameter :: amu=amu_si/em_si !---------------------------------! ! miscellaneous variables ! !---------------------------------! ! code version integer, parameter :: version(3)=[7,2,42] ! maximum number of tasks integer, parameter :: maxtasks=40 ! number of tasks integer ntasks ! task array integer tasks(maxtasks) ! current task integer task ! tlast is .true. if the calculation is on the last self-consistent loop logical tlast ! tstop is .true. if the STOP file exists logical tstop ! number of self-consistent loops after which STATE.OUT is written integer nwrite ! filename extension for files generated by gndstate character(256) :: filext='.OUT' ! scratch space path character(256) scrpath ! number of note lines integer notelns ! notes to include in INFO.OUT character(256), allocatable :: notes(:) end module elk-7.2.42/src/PaxHeaders.21776/mpi_stub.f900000644000000000000000000000013114061636517015065 xustar0030 mtime=1623670095.967101515 29 atime=1623670093.54910376 30 ctime=1623670095.967101515 elk-7.2.42/src/mpi_stub.f900000644002504400250440000000353014061636517017124 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! Stub routines for MPI. module mpi integer mpi_comm_world integer mpi_in_place integer mpi_sum integer mpi_logical integer mpi_integer integer mpi_double_precision integer mpi_double_complex end module subroutine mpi_init(ierror) implicit none integer, intent(out) :: ierror ierror=0 end subroutine subroutine mpi_finalize(ierror) implicit none integer, intent(out) :: ierror ierror=0 end subroutine subroutine mpi_comm_dup(comm,newcomm,ierror) implicit none integer, intent(in) :: comm integer, intent(out) :: newcomm integer, intent(out) :: ierror newcomm=comm ierror=0 end subroutine subroutine mpi_comm_size(comm,size,ierror) implicit none integer, intent(in) :: comm integer, intent(out) :: size integer, intent(out) :: ierror size=1 ierror=0 end subroutine subroutine mpi_comm_rank(comm,rank,ierror) implicit none integer, intent(in) :: comm integer, intent(out) :: rank integer, intent(out) :: ierror rank=0 ierror=0 end subroutine subroutine mpi_barrier(comm,ierror) implicit none integer, intent(in) :: comm integer, intent(out) :: ierror ierror=0 end subroutine subroutine mpi_bcast(buffer,count,datatype,root,comm,ierror) implicit none real(8), intent(in) :: buffer(*) integer, intent(in) :: count integer, intent(in) :: datatype integer, intent(in) :: root integer, intent(in) :: comm integer, intent(out) :: ierror ierror=0 end subroutine subroutine mpi_allreduce(sendbuf,recvbuf,count,datatype,op,comm,ierror) implicit none real(8), intent(in) :: sendbuf(*) real(8), intent(in) :: recvbuf(*) integer, intent(in) :: count integer, intent(in) :: datatype integer, intent(in) :: op integer, intent(in) :: comm integer, intent(out) :: ierror ierror=0 end subroutine elk-7.2.42/src/PaxHeaders.21776/modmpi.f900000644000000000000000000000013214061636516014530 xustar0030 mtime=1623670094.836102565 30 atime=1623670093.551103758 30 ctime=1623670094.836102565 elk-7.2.42/src/modmpi.f900000644002504400250440000000074214061636516016570 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modmpi use mpi ! MPI communicator for main code integer mpicom ! number of MPI processes integer np_mpi ! local MPI process number integer lp_mpi ! mp_mpi is .true. if the local MPI process is the master (0) logical mp_mpi ! commonly used error variable integer ierror end module elk-7.2.42/src/PaxHeaders.21776/modramdisk.f900000644000000000000000000000013214061636516015375 xustar0030 mtime=1623670094.838102563 30 atime=1623670093.553103756 30 ctime=1623670094.838102563 elk-7.2.42/src/modramdisk.f900000644002504400250440000001636314061636516017443 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modramdisk ! ramdisk is .true. if the RAM disk should be used logical ramdisk ! maximum allowed number of files in the RAM disk integer, parameter, private :: maxfiles=20 ! maximum number of records per file integer, parameter, private :: maxrec=10000 ! record data stored as 4-byte words type, private :: rec_t integer(4), allocatable :: dat(:) end type ! RAM disk file consisting of the filename and an array of records type, private :: file_t character(256) fname type(rec_t), allocatable :: rec(:) end type ! arrays of files constituting the RAM disk type(file_t), allocatable, private :: file(:) ! private subroutines private findfile,openfile contains subroutine initrd ! this subroutine should not be called from a parallel region implicit none ! local variables integer i if (allocated(file)) then write(*,*) write(*,'("Error(initrd): RAM disk already initialised")') write(*,*) stop end if allocate(file(maxfiles)) do i=1,maxfiles file(i)%fname='' end do end subroutine subroutine findfile(fname,fnum) implicit none ! arguments character(*), intent(in) :: fname integer, intent(out) :: fnum ! local variables integer i if (.not.allocated(file)) then write(*,*) write(*,'("Error(findfile): RAM disk not initialised")') write(*,*) stop end if fnum=0 do i=1,maxfiles if (file(i)%fname.eq.fname) then fnum=i return end if end do end subroutine subroutine openfile(fname,fnum) implicit none ! arguments character(*), intent(in) :: fname integer, intent(out) :: fnum ! local variables integer i ! check to see if the file already exists call findfile(fname,fnum) if (fnum.ne.0) return ! use the first available file number do i=1,maxfiles if (file(i)%fname.eq.'') then ! assign the filename file(i)%fname=fname ! allocate the record array allocate(file(i)%rec(maxrec)) fnum=i return end if end do write(*,*) write(*,'("Error(openfile): too many RAM disk files open : ",I8)') maxfiles write(*,*) stop end subroutine subroutine delfrd(fname) ! this subroutine should not be called from a parallel region implicit none ! arguments character(*), intent(in) :: fname ! local variables integer fnum,i ! determine the file number call findfile(fname,fnum) ! return if the file does not exist if (fnum.eq.0) return ! erase filename file(fnum)%fname='' ! deallocate associated arrays do i=1,maxrec if (allocated(file(fnum)%rec(i)%dat)) then deallocate(file(fnum)%rec(i)%dat) end if end do deallocate(file(fnum)%rec) end subroutine subroutine putrd(fname,irec,n1,n2,n3,v1,v2,nrv,rva,nzv,zva) ! this subroutine should be called from a critical section implicit none ! arguments character(*), intent(in) :: fname integer, intent(in) :: irec integer, optional, intent(in) :: n1,n2,n3 real(8), optional, intent(in) :: v1(3),v2(3) integer, optional, intent(in) :: nrv real(8), optional, intent(in) :: rva(*) integer, optional, intent(in) :: nzv complex(8), optional, intent(in) :: zva(*) ! local variables integer fnum,n,i if (irec.gt.maxrec) return ! find the record length in 4-byte words n=0 if (present(n1)) n=n+1 if (present(n2)) n=n+1 if (present(n3)) n=n+1 if (present(v1)) n=n+6 if (present(v2)) n=n+6 if (present(rva)) then if (present(nrv)) then n=n+2*nrv else write(*,*) write(*,'("Error(putrd): missing argument nrv")') write(*,*) stop end if end if if (present(zva)) then if (present(nzv)) then n=n+4*nzv else write(*,*) write(*,'("Error(putrd): missing argument nzv")') write(*,*) stop end if end if ! open the file call openfile(fname,fnum) ! allocate the record data array if required if (allocated(file(fnum)%rec(irec)%dat)) then if (size(file(fnum)%rec(irec)%dat).lt.n) then deallocate(file(fnum)%rec(irec)%dat) end if end if if (.not.allocated(file(fnum)%rec(irec)%dat)) then allocate(file(fnum)%rec(irec)%dat(n)) end if i=1 if (present(n1)) then file(fnum)%rec(irec)%dat(i)=n1 i=i+1 end if if (present(n2)) then file(fnum)%rec(irec)%dat(i)=n2 i=i+1 end if if (present(n3)) then file(fnum)%rec(irec)%dat(i)=n3 i=i+1 end if if (present(v1)) then call dcopy(3,v1,1,file(fnum)%rec(irec)%dat(i),1) i=i+6 end if if (present(v2)) then call dcopy(3,v2,1,file(fnum)%rec(irec)%dat(i),1) i=i+6 end if if (present(rva)) then call dcopy(nrv,rva,1,file(fnum)%rec(irec)%dat(i),1) i=i+2*nrv end if if (present(zva)) then call zcopy(nzv,zva,1,file(fnum)%rec(irec)%dat(i),1) end if end subroutine subroutine getrd(fname,irec,tgs,n1,n2,n3,v1,v2,nrv,rva,nzv,zva) implicit none ! arguments character(*), intent(in) :: fname integer, intent(in) :: irec logical, intent(out) :: tgs integer, optional, intent(out) :: n1,n2,n3 real(8), optional, intent(out) :: v1(3),v2(3) integer, optional, intent(in) :: nrv real(8), optional, intent(out) :: rva(*) integer, optional, intent(in) :: nzv complex(8), optional, intent(out) :: zva(*) ! local variables integer fnum,n,i if (present(rva)) then if (.not.present(nrv)) then write(*,*) write(*,'("Error(getrd): missing argument nrv")') write(*,*) stop end if end if if (present(zva)) then if (.not.present(nzv)) then write(*,*) write(*,'("Error(getrd): missing argument nzv")') write(*,*) stop end if end if tgs=.false. if (irec.gt.maxrec) return ! determine the file number call findfile(fname,fnum) ! return unsuccessfully if file is not found or record is unavailable if (fnum.eq.0) return if (.not.allocated(file(fnum)%rec(irec)%dat)) return n=size(file(fnum)%rec(irec)%dat) i=1 if (present(n1)) then if (n.lt.1) return n1=file(fnum)%rec(irec)%dat(i) i=i+1 n=n-1 end if if (present(n2)) then if (n.lt.1) return n2=file(fnum)%rec(irec)%dat(i) i=i+1 n=n-1 end if if (present(n3)) then if (n.lt.1) return n3=file(fnum)%rec(irec)%dat(i) i=i+1 n=n-1 end if if (present(v1)) then if (n.lt.6) return call dcopy(3,file(fnum)%rec(irec)%dat(i),1,v1,1) i=i+6 n=n-6 end if if (present(v2)) then if (n.lt.6) return call dcopy(3,file(fnum)%rec(irec)%dat(i),1,v2,1) i=i+6 n=n-6 end if if (present(rva)) then if (n.lt.2*nrv) return call dcopy(nrv,file(fnum)%rec(irec)%dat(i),1,rva,1) i=i+2*nrv n=n-2*nrv end if if (present(zva)) then if (n.lt.4*nzv) return call zcopy(nzv,file(fnum)%rec(irec)%dat(i),1,zva,1) end if ! flag the get operation as successful tgs=.true. end subroutine subroutine rdstatus ! this subroutine should not be called from a parallel region implicit none ! local variables integer nf,nr,i,j integer(8) m,n write(*,*) write(*,'("Info(rdstatus):")') if (.not.allocated(file)) then write(*,'(" RAM disk not initialised")') return end if nf=0 n=0 do i=1,maxfiles if (file(i)%fname.ne.'') then write(*,*) write(*,'(" Filename : ",A)') trim(file(i)%fname) nf=nf+1 nr=0 m=0 do j=1,maxrec if (allocated(file(i)%rec(j)%dat)) then nr=nr+1 m=m+size(file(i)%rec(j)%dat) end if end do n=n+m write(*,'(" number of records : ",I8)') nr write(*,'(" total number of bytes : ",I14)') 4*m end if end do write(*,*) write(*,'(" Number of files on RAM disk : ",I4)') nf write(*,'(" Total number of bytes used by RAM disk : ",I14)') 4*n end subroutine end module elk-7.2.42/src/PaxHeaders.21776/libxcifc_stub.f900000644000000000000000000000013214061636517016064 xustar0030 mtime=1623670095.987101497 30 atime=1623670093.555103754 30 ctime=1623670095.987101497 elk-7.2.42/src/libxcifc_stub.f900000644002504400250440000000416314061636517020125 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! Stub routines for libxc. See Elk manual for libxc installation instructions. module libxcifc integer libxcv(3) integer, parameter :: XC_MGGA_X_TB09=208 contains subroutine xcifc_libxc(xctype,n,c_tb09,tempa,rho,rhoup,rhodn,g2rho,g2up,g2dn, & grho2,gup2,gdn2,gupdn,tau,tauup,taudn,ex,ec,vx,vc,vxup,vxdn,vcup,vcdn,dxdgr2, & dxdgu2,dxdgd2,dxdgud,dcdgr2,dcdgu2,dcdgd2,dcdgud,dxdg2r,dxdg2u,dxdg2d,dcdg2r, & dcdg2u,dcdg2d,wx,wxup,wxdn,wc,wcup,wcdn) implicit none ! mandatory arguments integer, intent(in) :: xctype(3),n ! optional arguments real(8), optional :: c_tb09,tempa real(8), optional :: rho(n),rhoup(n),rhodn(n) real(8), optional :: g2rho(n),g2up(n),g2dn(n) real(8), optional :: grho2(n),gup2(n),gdn2(n),gupdn(n) real(8), optional :: tau(n),tauup(n),taudn(n) real(8), optional :: ex(n),ec(n),vx(n),vc(n) real(8), optional :: vxup(n),vxdn(n),vcup(n),vcdn(n) real(8), optional :: dxdgr2(n),dxdgu2(n),dxdgd2(n),dxdgud(n) real(8), optional :: dcdgr2(n),dcdgu2(n),dcdgd2(n),dcdgud(n) real(8), optional :: dxdg2r(n),dxdg2u(n),dxdg2d(n) real(8), optional :: dcdg2r(n),dcdg2u(n),dcdg2d(n) real(8), optional :: wx(n),wxup(n),wxdn(n) real(8), optional :: wc(n),wcup(n),wcdn(n) write(*,*) write(*,'("Error(libxcifc): libxc not or improperly installed")') write(*,*) stop end subroutine subroutine fxcifc_libxc(fxctype,n,rho,rhoup,rhodn,fxc,fxcuu,fxcud,fxcdd) implicit none ! mandatory arguments integer, intent(in) :: fxctype(3),n ! optional arguments real(8), optional :: rho(n),rhoup(n),rhodn(n) real(8), optional :: fxc(n),fxcuu(n),fxcud(n),fxcdd(n) write(*,*) write(*,'("Error(libxcifc): libxc not or improperly installed")') write(*,*) stop end subroutine subroutine xcdata_libxc(xctype,xcdescr,xcspin,xcgrad,hybrid,hybridc) implicit none ! arguments integer xctype(3) character(512) xcdescr integer xcspin integer xcgrad logical hybrid real(8) hybridc write(*,*) write(*,'("Error(libxcifc): libxc not or improperly installed")') write(*,*) stop end subroutine !EOC end module elk-7.2.42/src/PaxHeaders.21776/modxcifc.f900000644000000000000000000000013214061636516015037 xustar0030 mtime=1623670094.841102561 30 atime=1623670093.556103753 30 ctime=1623670094.841102561 elk-7.2.42/src/modxcifc.f900000644002504400250440000004073114061636516017101 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modxcifc use libxcifc contains !BOP ! !ROUTINE: xcifc ! !INTERFACE: subroutine xcifc(xctype,n,c_tb09,tempa,rho,rhoup,rhodn,grho,gup,gdn,g2rho, & g2up,g2dn,g3rho,g3up,g3dn,grho2,gup2,gdn2,gupdn,tau,tauup,taudn,ex,ec,vx,vc, & vxup,vxdn,vcup,vcdn,dxdgr2,dxdgu2,dxdgd2,dxdgud,dcdgr2,dcdgu2,dcdgd2,dcdgud, & dxdg2r,dxdg2u,dxdg2d,dcdg2r,dcdg2u,dcdg2d,wx,wxup,wxdn,wc,wcup,wcdn) ! !INPUT/OUTPUT PARAMETERS: ! xctype : type of exchange-correlation functional (in,integer(3)) ! n : number of density points (in,integer) ! c_tb09 : Tran-Blaha '09 constant c (in,real,optional) ! tempa : temperature in atomic units (in,real,optional) ! rho : spin-unpolarised charge density (in,real(n),optional) ! rhoup : spin-up charge density (in,real(n),optional) ! rhodn : spin-down charge density (in,real(n),optional) ! grho : |grad rho| (in,real(n),optional) ! gup : |grad rhoup| (in,real(n),optional) ! gdn : |grad rhodn| (in,real(n),optional) ! g2rho : grad^2 rho (in,real(n),optional) ! g2up : grad^2 rhoup (in,real(n),optional) ! g2dn : grad^2 rhodn (in,real(n),optional) ! g3rho : (grad rho).(grad |grad rho|) (in,real(n),optional) ! g3up : (grad rhoup).(grad |grad rhoup|) (in,real(n),optional) ! g3dn : (grad rhodn).(grad |grad rhodn|) (in,real(n),optional) ! grho2 : |grad rho|^2 (in,real(n),optional) ! gup2 : |grad rhoup|^2 (in,real(n),optional) ! gdn2 : |grad rhodn|^2 (in,real(n),optional) ! gupdn : (grad rhoup).(grad rhodn) (in,real(n),optional) ! tau : kinetic energy density (in,real(n),optional) ! tauup : spin-up kinetic energy density (in,real(n),optional) ! taudn : spin-down kinetic energy density (in,real(n),optional) ! ex : exchange energy density (out,real(n),optional) ! ec : correlation energy density (out,real(n),optional) ! vx : spin-unpolarised exchange potential (out,real(n),optional) ! vc : spin-unpolarised correlation potential (out,real(n),optional) ! vxup : spin-up exchange potential (out,real(n),optional) ! vxdn : spin-down exchange potential (out,real(n),optional) ! vcup : spin-up correlation potential (out,real(n),optional) ! vcdn : spin-down correlation potential (out,real(n),optional) ! dxdgr2 : de_x/d(|grad rho|^2) (out,real(n),optional) ! dxdgu2 : de_x/d(|grad rhoup|^2) (out,real(n),optional) ! dxdgd2 : de_x/d(|grad rhodn|^2) (out,real(n),optional) ! dxdgud : de_x/d((grad rhoup).(grad rhodn)) (out,real(n),optional) ! dcdgr2 : de_c/d(|grad rho|^2) (out,real(n),optional) ! dcdgu2 : de_c/d(|grad rhoup|^2) (out,real(n),optional) ! dcdgd2 : de_c/d(|grad rhodn|^2) (out,real(n),optional) ! dcdgud : de_c/d((grad rhoup).(grad rhodn)) (out,real(n),optional) ! dxdg2r : de_x/d(grad^2 rho) (out,real(n),optional) ! dxdg2u : de_x/d(grad^2 rhoup) (out,real(n),optional) ! dxdg2d : de_x/d(grad^2 rhodn) (out,real(n),optional) ! dcdg2r : de_c/d(grad^2 rho) (out,real(n),optional) ! dcdg2u : de_c/d(grad^2 rhoup) (out,real(n),optional) ! dcdg2d : de_c/d(grad^2 rhodn) (out,real(n),optional) ! wx : de_x/dtau (out,real(n),optional) ! wxup : de_x/dtauup (out,real(n),optional) ! wxdn : de_x/dtaudn (out,real(n),optional) ! wc : de_c/dtau (out,real(n),optional) ! wcup : de_c/dtauup (out,real(n),optional) ! wcdn : de_c/dtaudn (out,real(n),optional) ! !DESCRIPTION: ! Interface to the exchange-correlation routines. In the most general case ! (meta-GGA), the exchange-correlation energy is given by ! $$ E_{xc}[\rho^{\uparrow},\rho^{\downarrow}]=\int d^3r\, ! \rho({\bf r})\,\varepsilon_{xc}(\rho^{\uparrow},\rho^{\downarrow}, ! |\nabla\rho|,|\nabla\rho^{\uparrow}|,|\nabla\rho^{\downarrow}|, ! \nabla^2\rho^{\uparrow},\nabla^2\rho^{\downarrow},\tau), $$ ! where $\rho({\bf r})=\rho^{\uparrow}({\bf r})+\rho^{\downarrow}({\bf r})$ is ! the density; ! $$ \tau({\bf r})\equiv\sum_{i\;{\rm occ}}\nabla\psi({\bf r})\cdot ! \nabla\psi({\bf r}) $$ ! is twice the spin-contracted kinetic energy density; and $\varepsilon_{xc}$ ! is the exchange-correlation energy per electron. ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! mandatory arguments integer, intent(in) :: xctype(3) integer, intent(in) :: n ! optional arguments real(8), optional, intent(in) :: c_tb09,tempa real(8), optional, intent(in) :: rho(n),rhoup(n),rhodn(n) real(8), optional, intent(in) :: grho(n),gup(n),gdn(n) real(8), optional, intent(in) :: g2rho(n),g2up(n),g2dn(n) real(8), optional, intent(in) :: g3rho(n),g3up(n),g3dn(n) real(8), optional, intent(in) :: grho2(n),gup2(n),gdn2(n),gupdn(n) real(8), optional, intent(in) :: tau(n),tauup(n),taudn(n) real(8), optional, intent(out) :: ex(n),ec(n),vx(n),vc(n) real(8), optional, intent(out) :: vxup(n),vxdn(n),vcup(n),vcdn(n) real(8), optional, intent(out) :: dxdgr2(n),dxdgu2(n),dxdgd2(n),dxdgud(n) real(8), optional, intent(out) :: dxdg2r(n),dxdg2u(n),dxdg2d(n) real(8), optional, intent(out) :: wx(n),wxup(n),wxdn(n) real(8), optional, intent(out) :: dcdgr2(n),dcdgu2(n),dcdgd2(n),dcdgud(n) real(8), optional, intent(out) :: dcdg2r(n),dcdg2u(n),dcdg2d(n) real(8), optional, intent(out) :: wc(n),wcup(n),wcdn(n) ! local variables real(8) kappa,mu,beta ! allocatable arrays real(8), allocatable :: ra(:,:) if (n.le.0) then write(*,*) write(*,'("Error(xcifc): n <= 0 : ",I8)') n write(*,*) stop end if select case(abs(xctype(1))) case(1) ! No density-derived exchange-correlation energy or potential if (present(ex)) ex(:)=0.d0 if (present(ec)) ec(:)=0.d0 if (present(vx)) vx(:)=0.d0 if (present(vc)) vc(:)=0.d0 if (present(vxup)) vxup(:)=0.d0 if (present(vxdn)) vxdn(:)=0.d0 if (present(vcup)) vcup(:)=0.d0 if (present(vcdn)) vcdn(:)=0.d0 case(2) ! Perdew-Zunger parameterisation of Ceperley-Alder electron gas ! J. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981) ! D. M. Ceperly and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980) if (present(rho).and.present(ex).and.present(ec).and.present(vx) & .and.present(vc)) then call xc_pzca(n,rho,ex,ec,vx,vc) else goto 10 end if case(3) ! Perdew-Wang parameterisation of the spin-polarised Ceperley-Alder electron gas ! J. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992) ! D. M. Ceperly and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980) if (present(rhoup).and.present(rhodn).and.present(ex).and.present(ec) & .and.present(vxup).and.present(vxdn).and.present(vcup) & .and.present(vcdn)) then ! spin-polarised density call xc_pwca(n,rhoup,rhodn,ex,ec,vxup,vxdn,vcup,vcdn) else if (present(rho).and.present(ex).and.present(ec).and.present(vx) & .and.present(vc)) then ! divide spin-unpolarised density into up and down allocate(ra(n,1)) ra(:,1)=0.5d0*rho(:) call xc_pwca(n,ra,ra,ex,ec,vx,vx,vc,vc) deallocate(ra) else goto 10 end if case(4) ! X-alpha approximation ! J. C. Slater, Phys. Rev. 81, 385 (1951) if (present(rho).and.present(ex).and.present(ec).and.present(vx) & .and.present(vc)) then call xc_xalpha(n,rho,ex,vx) ! set correlation energy and potential to zero ec(:)=0.d0 vc(:)=0.d0 else goto 10 end if case(5) ! U. von Barth and L. Hedin parameterisation of LSDA ! J. Phys. C, 5, 1629 (1972) if (present(rhoup).and.present(rhodn).and.present(ex).and.present(ec) & .and.present(vxup).and.present(vxdn).and.present(vcup) & .and.present(vcdn)) then ! spin-polarised density call xc_vbh(n,rhoup,rhodn,ex,ec,vxup,vxdn,vcup,vcdn) else if (present(rho).and.present(ex).and.present(ec).and.present(vx) & .and.present(vc)) then ! divide spin-unpolarised density into up and down allocate(ra(n,1)) ra(:,1)=0.5d0*rho(:) call xc_vbh(n,ra,ra,ex,ec,vx,vx,vc,vc) deallocate(ra) else goto 10 end if case(20,21,22) ! original PBE kappa kappa=0.804d0 if (xctype(1).eq.21) then ! Zhang-Yang kappa kappa=1.245d0 end if ! original PBE mu and beta mu=0.2195149727645171d0 beta=0.06672455060314922d0 if (xctype(1).eq.22) then ! PBEsol parameters mu=10.d0/81.d0 beta=0.046d0 end if ! Perdew-Burke-Ernzerhof generalised gradient approximation ! Phys. Rev. Lett. 77, 3865 (1996); 78, 1396(E) (1997) ! Revised PBE, Zhang-Yang, Phys. Rev. Lett. 80, 890 (1998) if (present(rhoup).and.present(rhodn).and.present(grho).and.present(gup) & .and.present(gdn).and.present(g2up).and.present(g2dn).and.present(g3rho) & .and.present(g3up).and.present(g3dn).and.present(ex).and.present(ec) & .and.present(vxup).and.present(vxdn).and.present(vcup) & .and.present(vcdn)) then call xc_pbe(n,kappa,mu,beta,rhoup,rhodn,grho,gup,gdn,g2up,g2dn,g3rho,g3up, & g3dn,ex,ec,vxup,vxdn,vcup,vcdn) else if (present(rho).and.present(grho).and.present(g2rho) & .and.present(g3rho).and.present(ex).and.present(ec).and.present(vx) & .and.present(vc)) then allocate(ra(n,6)) ra(:,1)=0.5d0*rho(:) ra(:,2)=0.5d0*grho(:) ra(:,3)=0.5d0*g2rho(:) ra(:,4)=0.25d0*g3rho(:) call xc_pbe(n,kappa,mu,beta,ra,ra,grho,ra(:,2),ra(:,2),ra(:,3),ra(:,3), & g3rho,ra(:,4),ra(:,4),ex,ec,vx,ra(:,5),vc,ra(:,6)) deallocate(ra) else goto 10 end if case(26) ! Wu-Cohen exchange with PBE correlation generalised gradient functional ! Zhigang Wu and R. E. Cohen, Phys. Rev. B 73, 235116 (2006) if (present(rho).and.present(grho).and.present(g2rho).and.present(g3rho) & .and.present(ex).and.present(ec).and.present(vx).and.present(vc)) then call xc_wc06(n,rho,grho,g2rho,g3rho,ex,ec,vx,vc) else goto 10 end if case(30) ! Armiento-Mattsson generalised gradient functional ! R. Armiento and A. E. Mattsson, Phys. Rev. B 72, 085108 (2005) if (present(rho).and.present(grho).and.present(g2rho).and.present(g3rho) & .and.present(ex).and.present(ec).and.present(vx).and.present(vc)) then call xc_am05(n,rho,grho,g2rho,g3rho,ex,ec,vx,vc) else goto 10 end if case(100) ! libxc library functionals if (present(rhoup).and.present(rhodn).and.present(g2up).and.present(g2dn) & .and.present(gup2).and.present(gdn2).and.present(gupdn).and.present(tauup) & .and.present(taudn).and.present(ex).and.present(ec).and.present(vxup) & .and.present(vxdn).and.present(vcup).and.present(vcdn).and.present(dxdgu2) & .and.present(dxdgd2).and.present(dxdgud).and.present(dcdgu2) & .and.present(dcdgd2).and.present(dcdgud).and.present(dxdg2u) & .and.present(dxdg2d).and.present(dcdg2u).and.present(dcdg2d) & .and.present(wxup).and.present(wxdn).and.present(wcup) & .and.present(wcdn)) then ! spin-polarised energy meta-GGA call xcifc_libxc(xctype,n,rhoup=rhoup,rhodn=rhodn,g2up=g2up,g2dn=g2dn, & gup2=gup2,gdn2=gdn2,gupdn=gupdn,tauup=tauup,taudn=taudn,ex=ex,ec=ec, & vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn,dxdgu2=dxdgu2,dxdgd2=dxdgd2, & dxdgud=dxdgud,dcdgu2=dcdgu2,dcdgd2=dcdgd2,dcdgud=dcdgud,dxdg2u=dxdg2u, & dxdg2d=dxdg2d,dcdg2u=dcdg2u,dcdg2d=dcdg2d,wxup=wxup,wxdn=wxdn,wcup=wcup, & wcdn=wcdn) else if (present(rhoup).and.present(rhodn).and.present(g2up) & .and.present(g2dn).and.present(gup2).and.present(gdn2).and.present(gupdn) & .and.present(tauup).and.present(taudn).and.present(vxup).and.present(vxdn) & .and.present(vcup).and.present(vcdn)) then ! spin-polarised potential-only meta-GGA call xcifc_libxc(xctype,n,c_tb09=c_tb09,rhoup=rhoup,rhodn=rhodn,g2up=g2up, & g2dn=g2dn,gup2=gup2,gdn2=gdn2,gupdn=gupdn,tauup=tauup,taudn=taudn, & vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn) else if (present(rhoup).and.present(rhodn).and.present(gup2) & .and.present(gdn2).and.present(gupdn).and.present(ex).and.present(ec) & .and.present(vxup).and.present(vxdn).and.present(vcup).and.present(vcdn) & .and.present(dxdgu2).and.present(dxdgd2).and.present(dxdgud) & .and.present(dcdgu2).and.present(dcdgd2).and.present(dcdgud)) then ! spin-polarised GGA call xcifc_libxc(xctype,n,rhoup=rhoup,rhodn=rhodn,gup2=gup2,gdn2=gdn2, & gupdn=gupdn,ex=ex,ec=ec,vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn, & dxdgu2=dxdgu2,dxdgd2=dxdgd2,dxdgud=dxdgud,dcdgu2=dcdgu2,dcdgd2=dcdgd2, & dcdgud=dcdgud) else if (present(rhoup).and.present(rhodn).and.present(ex).and.present(ec) & .and.present(vxup).and.present(vxdn).and.present(vcup) & .and.present(vcdn)) then ! LSDA call xcifc_libxc(xctype,n,tempa=tempa,rhoup=rhoup,rhodn=rhodn,ex=ex,ec=ec, & vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn) else if (present(rho).and.present(g2rho).and.present(grho2).and.present(tau) & .and.present(ex).and.present(ec).and.present(vx).and.present(vc) & .and.present(dxdgr2).and.present(dcdgr2).and.present(dxdg2r) & .and.present(dcdg2r).and.present(wx).and.present(wc)) then ! spin-unpolarised energy meta-GGA call xcifc_libxc(xctype,n,rho=rho,g2rho=g2rho,grho2=grho2,tau=tau,ex=ex, & ec=ec,vx=vx,vc=vc,dxdgr2=dxdgr2,dcdgr2=dcdgr2,dxdg2r=dxdg2r, & dcdg2r=dcdg2r,wx=wx,wc=wc) else if (present(rho).and.present(g2rho).and.present(grho2).and.present(tau) & .and.present(vx).and.present(vc)) then ! spin-unpolarised potential-only meta-GGA call xcifc_libxc(xctype,n,c_tb09=c_tb09,rho=rho,g2rho=g2rho,grho2=grho2, & tau=tau,vx=vx,vc=vc) else if (present(rho).and.present(grho2).and.present(ex).and.present(ec) & .and.present(vx).and.present(vc).and.present(dxdgr2) & .and.present(dcdgr2)) then ! spin-unpolarised GGA call xcifc_libxc(xctype,n,rho=rho,grho2=grho2,ex=ex,ec=ec,vx=vx,vc=vc, & dxdgr2=dxdgr2,dcdgr2=dcdgr2) else if (present(rho).and.present(ex).and.present(ec).and.present(vx) & .and.present(vc)) then ! LDA call xcifc_libxc(xctype,n,tempa=tempa,rho=rho,ex=ex,ec=ec,vx=vx,vc=vc) else goto 10 end if case default write(*,*) write(*,'("Error(xcifc): xctype not defined : ",I8)') xctype(1) write(*,*) stop end select ! set exchange potential to zero for EXX if (xctype(1).le.-2) then if (present(vx)) vx(:)=0.d0 if (present(vxup)) vxup(:)=0.d0 if (present(vxdn)) vxdn(:)=0.d0 end if return 10 continue write(*,*) write(*,'("Error(xcifc): missing arguments for exchange-correlation type ",& &3I6)') xctype(:) write(*,*) stop end subroutine !EOC !BOP ! !ROUTINE: getxcdata ! !INTERFACE: subroutine getxcdata(xctype,xcdescr,xcspin,xcgrad,hybrid,hybridc) ! !INPUT/OUTPUT PARAMETERS: ! xctype : type of exchange-correlation functional (in,integer(3)) ! xcdescr : description of functional (out,character(512)) ! xcspin : spin treatment (out,integer) ! xcgrad : gradient treatment (out,integer) ! hybrid : .true. if functional a hybrid (out,logical) ! hybridc : hybrid exact exchange mixing coefficient (out,real(8)) ! !DESCRIPTION: ! Returns data on the exchange-correlation functional labeled by {\tt xctype}. ! The character array {\tt xcdescr} contains a short description of the ! functional including journal references. The variable {\tt xcspin} is set to ! 1 or 0 for spin-polarised or -unpolarised functionals, respectively. For ! functionals which require the gradients of the density {\tt xcgrad} is set ! to 1, otherwise it is set to 0. ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: xctype(3) character(512), intent(out) :: xcdescr integer, intent(out) :: xcspin,xcgrad logical, intent(out) :: hybrid real(8), intent(out) :: hybridc select case(abs(xctype(1))) case(1) xcdescr='No density-derived exchange-correlation energy or potential' ! spin-polarisation or gradient status not required xcspin=-1 xcgrad=-1 case(2) xcdescr='Perdew-Zunger/Ceperley-Alder, Phys. Rev. B 23, 5048 (1981)' xcspin=0 xcgrad=0 case(3) xcdescr='Perdew-Wang/Ceperley-Alder, Phys. Rev. B 45, 13244 (1992)' xcspin=1 xcgrad=0 case(4) xcdescr='X-alpha approximation, J. C. Slater, Phys. Rev. 81, 385 (1951)' xcspin=0 xcgrad=0 case(5) xcdescr='von Barth-Hedin, J. Phys. C 5, 1629 (1972)' xcspin=1 xcgrad=0 case(20) xcdescr='Perdew-Burke-Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)' xcspin=1 xcgrad=1 case(21) xcdescr='Revised PBE, Zhang-Yang, Phys. Rev. Lett. 80, 890 (1998)' xcspin=1 xcgrad=1 case(22) xcdescr='PBEsol, Phys. Rev. Lett. 100, 136406 (2008)' xcspin=1 xcgrad=1 case(26) xcdescr='Wu-Cohen exchange + PBE correlation, Phys. Rev. B 73, 235116 (2006)' xcspin=0 xcgrad=1 case(30) xcdescr='Armiento-Mattsson functional, Phys. Rev. B 72, 85108 (2005)' xcspin=0 xcgrad=1 case(100) ! libxc library functionals call xcdata_libxc(xctype,xcdescr,xcspin,xcgrad,hybrid,hybridc) case default write(*,*) write(*,'("Error(getxcdata): xctype not defined : ",I8)') xctype(1) write(*,*) stop end select end subroutine !EOC end module elk-7.2.42/src/PaxHeaders.21776/modfxcifc.f900000644000000000000000000000013214061636516015205 xustar0030 mtime=1623670094.843102559 30 atime=1623670093.558103751 30 ctime=1623670094.843102559 elk-7.2.42/src/modfxcifc.f900000644002504400250440000000412714061636516017246 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modfxcifc use libxcifc contains subroutine fxcifc(fxctype,n,rho,rhoup,rhodn,fxc,fxcuu,fxcud,fxcdd) implicit none ! mandatory arguments integer, intent(in) :: fxctype(3),n ! optional arguments real(8), optional, intent(in) :: rho(n),rhoup(n),rhodn(n) real(8), optional, intent(out) :: fxc(n),fxcuu(n),fxcud(n),fxcdd(n) ! allocatable arrays real(8), allocatable :: ra(:,:) if (n.le.0) then write(*,*) write(*,'("Error(fxcifc): n <= 0 : ",I8)') n write(*,*) stop end if select case(abs(fxctype(1))) case(0,1) ! f_xc = 0 if (present(fxcuu).and.present(fxcud).and.present(fxcdd)) then fxcuu(:)=0.d0 fxcud(:)=0.d0 fxcdd(:)=0.d0 else if (present(fxc)) then fxc(:)=0.d0 else goto 10 end if case(3) ! Perdew-Wang-Ceperley-Alder if (present(rhoup).and.present(rhodn).and.present(fxcuu).and.present(fxcud) & .and.present(fxcdd)) then ! spin-polarised density call fxc_pwca(n,rhoup,rhodn,fxcuu,fxcud,fxcdd) else if (present(rho).and.present(fxc)) then ! divide spin-unpolarised density into up and down allocate(ra(n,4)) ra(:,1)=0.5d0*rho(:) call fxc_pwca(n,ra(:,1),ra(:,1),ra(:,2),ra(:,3),ra(:,4)) fxc(:)=0.5d0*(ra(:,2)+ra(:,3)) deallocate(ra) else goto 10 end if case(100) ! libxc library functionals if (present(rhoup).and.present(rhodn).and.present(fxcuu).and.present(fxcud) & .and.present(fxcdd)) then ! LSDA call fxcifc_libxc(fxctype,n,rhoup=rhoup,rhodn=rhodn,fxcuu=fxcuu, & fxcud=fxcud,fxcdd=fxcdd) else if (present(rho).and.present(fxc)) then ! LDA call fxcifc_libxc(fxctype,n,rho=rho,fxc=fxc) else goto 10 end if case default write(*,*) write(*,'("Error(fxcifc): response function unavailable for fxctype ",3I8)') & fxctype write(*,*) stop end select return 10 continue write(*,*) write(*,'("Error(fxcifc): missing arguments for exchange-correlation type ",& &3I6)') fxctype(:) write(*,*) stop end subroutine end module elk-7.2.42/src/PaxHeaders.21776/moddftu.f900000644000000000000000000000013114061636516014704 xustar0030 mtime=1623670094.844102558 29 atime=1623670093.56010375 30 ctime=1623670094.844102558 elk-7.2.42/src/moddftu.f900000644002504400250440000000627714061636516016756 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module moddftu use modmain !-----------------------------------------------------------! ! muffin-tin density and potential matrix variables ! !-----------------------------------------------------------! ! maximum angular momentum for muffin-tin density matrix integer, parameter :: lmaxdm=3 integer, parameter :: lmmaxdm=(lmaxdm+1)**2 ! density matrix in each muffin-tin complex(8), allocatable :: dmatmt(:,:,:,:,:) ! potential matrix in each muffin-tin complex(8), allocatable :: vmatmt(:,:,:,:,:) ! tvmatmt is .true. if the potential matrices are calculated logical tvmatmt ! tvmmt is .true. if the potential matrix for that l and atom is non-zero logical, allocatable :: tvmmt(:,:) !-------------------------! ! DFT+U variables ! !-------------------------! ! type of DFT+U to use (0 = none) integer dftu ! input type for DFT+U calculation (1:5) integer inpdftu ! maximum number of DFT+U entries integer, parameter :: maxdftu=40 ! number of DFT+U entries integer ndftu ! species and angular momentum for each entry integer idftu(2,maxdftu) ! U and J values for each entry real(8) ujdu(2,maxdftu) ! interpolation constant alpha for each atom and entry [PRB 67, 153106 (2003)] real(8), allocatable :: alphadu(:,:) ! readadu is .true. if alphadu is to be read from file logical readadu ! DFT+U energy for each atom and entry real(8), allocatable :: engyadu(:,:) ! energy from the DFT+U correction real(8) engydu ! Slater parameters real(8) fdu(0:2*lmaxdm,maxdftu) ! Racah parameters real(8) edu(0:lmaxdm,maxdftu) ! screening length of Yukawa potential to calculate Slater integrals real(8) lambdadu(maxdftu) ! energies to calculate radial functions for Slater integrals real(8), allocatable :: fdue(:,:) ! radial functions to calculate Slater integrals real(8), allocatable :: fdufr(:,:,:) ! fixed value of U for which screening length has to be determined real(8) udufix(maxdftu) ! initial values of screening length if U is fixed real(8) lambdadu0(maxdftu) !---------------------------------! ! tensor moment variables ! !---------------------------------! ! tmwrite is .true. if tensor moments are written out at every s.c. loop logical tmwrite ! fixed tensor moment type ! 0 : none ! 2 (-2) : fixed 2-index tensor moment (or just lowering the symmetry) ! 3 (-3) : fixed 3-index tensor moment (or just lowering the symmetry) integer ftmtype ! number of fixed tensor moment entries integer ntmfix ! tensor moment indices for each entry: is, ia, l, n and k, p, x, y for the ! 2-index tensor or k, p, r, t for the 3-index tensor integer, allocatable :: itmfix(:,:) ! tensor component complex(8), allocatable :: tmfix(:) ! spatial and spin rotation matrices of tensor real(8), allocatable :: rtmfix(:,:,:,:) ! density matrices corresponding to the fixed tensor moments complex(8), allocatable :: dmftm(:,:,:,:,:) ! fixed tensor moment potential matrix complex(8), allocatable :: vmftm(:,:,:,:,:) ! fixed tensor moment step size real(8) tauftm ! number of self-consistent loops after which FTM field is updated integer ftmstep end module elk-7.2.42/src/PaxHeaders.21776/modrdm.f900000644000000000000000000000013214061636516014525 xustar0030 mtime=1623670094.846102556 30 atime=1623670093.562103748 30 ctime=1623670094.846102556 elk-7.2.42/src/modrdm.f900000644002504400250440000000213214061636516016560 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modrdm use modmain !--------------------------------------------------------------------! ! reduced density matrix functional theory (RDMFT) variables ! !--------------------------------------------------------------------! ! Coulomb potential matrix elements complex(8), allocatable :: vclmat(:,:,:) ! derivative of kinetic energy w.r.t. natural orbital coefficients complex(8), allocatable :: dkdc(:,:,:) ! step size for occupation numbers real(8) taurdmn ! step size for natural orbital coefficients real(8) taurdmc ! xc functional integer rdmxctype ! maximum number of self-consistent loops integer rdmmaxscl ! maximum number of iterations for occupation number optimisation integer maxitn ! maximum number of iteration for natural orbital optimisation integer maxitc ! exponent for the power and hybrid functional real(8) rdmalpha ! temperature real(8) rdmtemp ! entropy real(8) rdmentrpy end module elk-7.2.42/src/PaxHeaders.21776/modphonon.f900000644000000000000000000000013214061636516015244 xustar0030 mtime=1623670094.847102555 30 atime=1623670093.564103746 30 ctime=1623670094.847102555 elk-7.2.42/src/modphonon.f900000644002504400250440000001261114061636516017302 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modphonon use modmain !--------------------------! ! phonon variables ! !--------------------------! ! number of phonon branches (3*natmtot) integer nbph ! current phonon q-point, species, atom and polarisation index integer iqph,isph,iaph,iasph,ipph ! tphq0 is .true. if q = 0 logical tphq0 ! number of vectors for writing out frequencies and eigenvectors integer nphwrt ! vectors in lattice coordinates for writing out frequencies and eigenvectors real(8), allocatable :: vqlwrt(:,:) ! Coulomb pseudopotential real(8) mustar ! number of temperatures for the Eliashberg equations and thermal properties integer ntemp ! phonon frequencies for all q-points real(8), allocatable :: wphq(:,:) !-----------------------------! ! supercell variables ! !-----------------------------! ! number of primitive unit cells in phonon supercell integer nscph ! Cartesian offset vectors for each primitive cell in the supercell real(8), allocatable :: vscph(:,:) ! phonon displacement distance real(8) deltaph !---------------------! ! k+q-vectors ! !---------------------! ! k+q-vectors in lattice coordinates real(8), allocatable :: vkql(:,:) ! k+q-vectors in Cartesian coordinates real(8), allocatable :: vkqc(:,:) !------------------------------! ! G+q-vector variables ! !------------------------------! ! G+q-vectors in Cartesian coordinates real(8), allocatable :: vgqc(:,:) ! G+q-vector lengths real(8), allocatable :: gqc(:) ! regularised Coulomb Green's function in G+q-space real(8), allocatable :: gclgq(:) ! spherical Bessel functions j_l(|G+q|R_mt) real(8), allocatable :: jlgqrmt(:,:,:) ! spherical harmonics for G+q-vectors complex(8), allocatable :: ylmgq(:,:) ! structure factors for G+q-vectors complex(8), allocatable :: sfacgq(:,:) ! smooth step function form factors for all species and G+q-vectors real(8), allocatable :: ffacgq(:,:) ! characteristic function derivative in G- and G+q-space complex(8), allocatable :: dcfunig(:) ! characteristic function derivative in real-space complex(8), allocatable :: dcfunir(:) !--------------------------------! ! G+k+q-vector variables ! !--------------------------------! ! number of G+k+q-vector for each k-point integer, allocatable :: ngkq(:,:) ! index from G+k+q-vectors to G-vectors integer, allocatable :: igkqig(:,:,:) ! G+k+q-vectors in lattice and Cartesian coordinates real(8), allocatable :: vgkql(:,:,:,:),vgkqc(:,:,:,:) ! G+k+q-vector lengths real(8), allocatable :: gkqc(:,:,:) ! structure factors for the G+k+q-vectors complex(8), allocatable :: sfacgkq(:,:,:,:) !----------------------------------------------------------! ! density functional perturbation theory variables ! !----------------------------------------------------------! ! density derivative complex(8), allocatable :: drhomt(:,:),drhoir(:) ! magnetisation derivative complex(8), allocatable :: dmagmt(:,:,:),dmagir(:,:) ! Coulomb potential derivative complex(8), allocatable :: dvclmt(:,:),dvclir(:) ! if tphdyn is .true. then the phonon dynamical matrix is being calculated logical :: tphdyn=.false. ! nuclear potential without the self-term; used for the phonon dynamical matrix complex(8), allocatable :: zvnmt(:) ! gradient of vsmt for the displaced muffin-tin complex(8), allocatable :: gvsmt(:) ! combined target array for dvsmt, dvsir, dbsmt and dbsir complex(8), allocatable, target :: dvsbs(:) ! Kohn-Sham potential derivative complex(8), pointer :: dvsmt(:,:),dvsir(:) ! Kohn-Sham effective magnetic field derivative complex(8), pointer :: dbsmt(:,:,:),dbsir(:,:) ! G+q-space interstitial Kohn-Sham potential derivative complex(8), allocatable :: dvsig(:) ! spin-orbit coupling radial function derivative complex(8), allocatable :: dsocfr(:,:) ! APW-APW Hamiltonian integral derivatives complex(8), allocatable :: dhaa(:,:,:,:,:,:) ! local-orbital-APW Hamiltonian integral derivatives complex(8), allocatable :: dhloa(:,:,:,:,:) ! local-orbital-local-orbital Hamiltonian integral derivatives complex(8), allocatable :: dhlolo(:,:,:,:) ! real Gaunt coefficient array real(8), allocatable :: gntyyy(:,:,:) ! smallest allowed perturbation theory denominator for eigenvector derivatives real(8) epsdev ! Fermi energy derivative real(8) defermi ! first-variational eigenvalue derivatives real(8), allocatable :: devalfv(:,:,:) ! second-variational eigenvalue derivatives real(8), allocatable :: devalsv(:,:) ! second-variational occupation number derivatives real(8), allocatable :: doccsv(:,:) !-------------------------------------------+ ! electron-phonon mean-field theory | !-------------------------------------------+ ! energy change of the electron system real(8) dengye ! energy change of the phonon system real(8) dengyph ! sum of energy changes in electron and phonon systems real(8) dengy ! phonon frequency cut-off below which modes are neglected real(8) wphcut ! scale factor of the electron-phonon term and its mixing parameter real(8) ephscf(2) ! anomalous is .true. if only the anomalous density matrix is to be used in the ! construction of the electron-phonon Hamiltonian logical anomalous ! tephde is .true. if D = D0 + E, otherwise D = D0 logical tephde ! single-precision electron-phonon matrix element array for each k- and q-point complex(4), allocatable :: ephmkq(:,:,:,:,:) end module elk-7.2.42/src/PaxHeaders.21776/modtest.f900000644000000000000000000000013214061636516014722 xustar0030 mtime=1623670094.849102553 30 atime=1623670093.565103745 30 ctime=1623670094.849102553 elk-7.2.42/src/modtest.f900000644002504400250440000000470214061636516016762 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modtest use modmpi ! if test is .true. then the test variables are written to file logical test contains subroutine writetest(id,descr,nv,iv,iva,tol,rv,rva,zv,zva) implicit none ! arguments integer, intent(in) :: id character(*), intent(in) :: descr integer, optional, intent(in) :: nv integer, optional, intent(in) :: iv integer, optional, intent(in) :: iva(*) real(8), optional, intent(in) :: tol real(8), optional, intent(in) :: rv real(8), optional, intent(in) :: rva(*) complex(8), optional, intent(in) :: zv complex(8), optional, intent(in) :: zva(*) ! local variables integer j character(256) fname if (.not.test) return if (.not.mp_mpi) return if ((id.lt.0).or.(id.gt.999)) then write(*,*) write(*,'("Error(writetest): id out of range : ",I8)') id write(*,*) stop end if if ((present(iva)).or.(present(rva)).or.(present(zva))) then if (.not.present(nv)) then write(*,*) write(*,'("Error(writetest): missing argument nv")') write(*,*) stop else if (nv.le.0) then write(*,*) write(*,'("Error(writetest): nv <= 0 : ",I8)') nv write(*,*) stop end if end if end if if ((present(rv)).or.(present(rva)).or.(present(zv)).or.(present(zva))) then if (.not.present(tol)) then write(*,*) write(*,'("Error(writetest): missing argument tol")') write(*,*) stop end if end if write(fname,'("TEST_",I3.3,".OUT")') id !$OMP CRITICAL(writetest_) open(90,file=trim(fname),form='FORMATTED',action='WRITE') write(90,'("''",A,"''")') trim(descr) if (present(iv)) then write(90,'(2I8)') 1,1 write(90,'(2I8)') 1,iv else if (present(rv)) then write(90,'(2I8)') 2,1 write(90,'(G22.12)') tol write(90,'(I8,G22.12)') 1,rv else if (present(zv)) then write(90,'(2I8)') 3,1 write(90,'(G22.12)') tol write(90,'(I8,2G22.12)') 1,dble(zv),aimag(zv) else if (present(iva)) then write(90,'(2I8)') 1,nv do j=1,nv write(90,'(2I8)') j,iva(j) end do else if (present(rva)) then write(90,'(2I8)') 2,nv write(90,'(G22.12)') tol do j=1,nv write(90,'(I8,G22.12)') j,rva(j) end do else if (present(zva)) then write(90,'(2I8)') 3,nv write(90,'(G22.12)') tol do j=1,nv write(90,'(I8,2G22.12)') j,dble(zva(j)),aimag(zva(j)) end do end if close(90) !$OMP END CRITICAL(writetest_) end subroutine end module elk-7.2.42/src/PaxHeaders.21776/modrandom.f900000644000000000000000000000013214061636516015223 xustar0030 mtime=1623670094.851102551 30 atime=1623670093.567103743 30 ctime=1623670094.851102551 elk-7.2.42/src/modrandom.f900000644002504400250440000000251414061636516017262 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modrandom ! random number generator state integer(8) :: rndstate(0:5)=[799047353, 1322018920, 1014372120, 1198189977, & 832907020, 5678910] contains !BOP ! !ROUTINE: randomu ! !INTERFACE: real(8) function randomu() ! !DESCRIPTION: ! Generates random numbers with a uniform distribution in the interval $[0,1]$ ! using the fifth-order multiple recursive generator of P. L'Ecuyer, ! F. Blouin, and R. Coutre, {\it ACM Trans. Modeling Comput. Simulation} ! {\bf 3}, 87 (1993). The sequence of numbers $r_i$ is produced from ! $$ x_i=(a_1 x_{i-1}+a_5 x_{i-5})\mod m $$ ! with $r_i=x_i/m$. The period is about $2^{155}$. ! ! !REVISION HISTORY: ! Created January 2012 (JKD) ! Changed initial state, April 2017 (JKD) !EOP !BOC implicit none ! local variables ! parameters taken from the GNU Scientific Library (GSL) integer(8), parameter :: a1=107374182, a5=104480, m=2147483647 integer(8) :: i=0 integer(8) i1,i5 !$OMP CRITICAL(randomu_) i=modulo(i+1,6_8) i1=modulo(i-1,6_8) i5=modulo(i-5,6_8) rndstate(i)=int(mod(a1*rndstate(i1)+a5*rndstate(i5),m)) randomu=dble(rndstate(i))/dble(m) !$OMP END CRITICAL(randomu_) end function !EOC end module elk-7.2.42/src/PaxHeaders.21776/modstore.f900000644000000000000000000000013014061636516015075 xustar0029 mtime=1623670094.85210255 30 atime=1623670093.569103741 29 ctime=1623670094.85210255 elk-7.2.42/src/modstore.f900000644002504400250440000000220514061636516017133 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !---------------------------------------------------------! ! variables for storing original input parameters ! !---------------------------------------------------------! module modstore use modmain real(8) avec_(3,3) real(8) bvec_(3,3),binv_(3,3) real(8) omega_ logical tshift_ logical primcell_ integer natoms_(maxspecies) integer natmtot_ integer idxis_(maxatoms*maxspecies) real(8) atposl_(3,maxatoms,maxspecies) real(8) atposc_(3,maxatoms,maxspecies) integer ngridg_(3),ngtot_ integer, allocatable :: ivg_(:,:),igfft_(:) logical spinpol_,spinorb_,cmagz_,spinsprl_ real(8) bfieldc0_(3) real(8) bfcmt0_(3,maxatoms,maxspecies) real(8) afieldc_(3) real(8) reducebf_ integer fsmtype_ real(8) momfix_(3) real(8) mommtfix_(3,maxatoms,maxspecies) logical tforce_ logical autokpt_ integer ngridk_(3) real(8) vkloff_(3) integer lmaxi_ logical tfav0_ real(8) vqlss_(3) integer msmooth_ integer reducek_ integer maxscl_ logical tjr_ real(8) swidth_ end module elk-7.2.42/src/PaxHeaders.21776/modpw.f900000644000000000000000000000013214061636516014371 xustar0030 mtime=1623670094.854102548 30 atime=1623670093.571103739 30 ctime=1623670094.854102548 elk-7.2.42/src/modpw.f900000644002504400250440000000320214061636516016423 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modpw !----------------------------! ! H-vector variables ! !----------------------------! ! reduceh is .true. if the H-vectors are reduced with the crystal symmetries logical reduceh ! H-vector cut-off for interstitial potential and density real(8) hmaxvr ! H-vector grid sizes integer ngridh(3) ! total number of H-vectors integer nhtot ! integer grid intervals for each direction integer inthv(2,3) ! number of H-vectors with |H| < hmaxvr integer nhvec ! H-vector integer coordinates (i1,i2,i3) integer, allocatable :: ivh(:,:) ! H-vector multiplicity after symmetry reduction integer, allocatable :: mulh(:) ! H-vectors in Cartesian coordinates real(8), allocatable :: vhc(:,:) ! length of H-vectors real(8), allocatable :: hc(:) ! H-vector transformation matrix real(8) vhmat(3,3) !------------------------------! ! H+k-vector variables ! !------------------------------! ! maximum |H+k| cut-off for plane wave real(8) hkmax ! number of H+k-vectors for plane waves integer, allocatable :: nhk(:,:) ! maximum number of H+k-vectors over all k-points integer nhkmax ! index from H+k-vectors to G-vectors integer, allocatable :: ihkig(:,:,:) ! H+k-vectors in lattice coordinates real(8), allocatable :: vhkl(:,:,:,:) ! H+k-vectors in Cartesian coordinates real(8), allocatable :: vhkc(:,:,:,:) ! length of H+k-vectors real(8), allocatable :: hkc(:,:,:) ! structure factors for the H+k-vectors complex(8), allocatable :: sfachk(:,:,:,:) end module elk-7.2.42/src/PaxHeaders.21776/modvars.f900000644000000000000000000000013214061636516014716 xustar0030 mtime=1623670094.855102548 30 atime=1623670093.572103738 30 ctime=1623670094.855102548 elk-7.2.42/src/modvars.f900000644002504400250440000000465014061636516016760 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modvars use modmpi ! if wrtvars is .true. then variables are written to VARIABLES.OUT logical wrtvars contains subroutine delvars implicit none if (.not.mp_mpi) return ! delete existing variables file open(95,file='VARIABLES.OUT') close(95,status='DELETE') end subroutine subroutine writevars(vname,l,m,nv,iv,iva,rv,rva,zv,zva,sv,sva) implicit none ! arguments character(*), intent(in) :: vname integer, optional, intent(in) :: l,m integer, optional, intent(in) :: nv integer, optional, intent(in) :: iv integer, optional, intent(in) :: iva(*) real(8), optional, intent(in) :: rv real(8), optional, intent(in) :: rva(*) complex(8), optional, intent(in) :: zv complex(8), optional, intent(in) :: zva(*) character(*), optional, intent(in) :: sv character(*), optional, intent(in) :: sva(*) ! local variables integer i if (.not.wrtvars) return if (.not.mp_mpi) return if ((present(iva)).or.(present(rva)).or.(present(zva)).or.(present(sva))) then if (.not.present(nv)) then write(*,*) write(*,'("Error(writevars): missing argument nv")') write(*,*) stop else if (nv.lt.0) then write(*,*) write(*,'("Error(writevars): nv < 0 : ",I8)') nv write(*,*) stop end if end if end if open(95,file='VARIABLES.OUT',position='APPEND',form='FORMATTED',action='WRITE') write(95,*) write(95,'(A)',advance='NO') trim(vname) if (present(l)) write(95,'(I8)',advance='NO') l if (present(m)) write(95,'(I8)',advance='NO') m write(95,*) if (present(iv)) then write(95,'(2I8)') 1,1 write(95,'(I8)') iv else if (present(rv)) then write(95,'(2I8)') 2,1 write(95,'(G22.12)') rv else if (present(zv)) then write(95,'(2I8)') 3,1 write(95,'(2G22.12)') dble(zv),aimag(zv) else if (present(sv)) then write(95,'(2I8)') 4,1 write(95,'(A)') trim(sv) else if (present(iva)) then write(95,'(2I8)') 1,nv do i=1,nv write(95,'(I8)') iva(i) end do else if (present(rva)) then write(95,'(2I8)') 2,nv do i=1,nv write(95,'(G22.12)') rva(i) end do else if (present(zva)) then write(95,'(2I8)') 3,nv do i=1,nv write(95,'(2G22.12)') dble(zva(i)),aimag(zva(i)) end do else if (present(sva)) then write(95,'(2I8)') 4,nv do i=1,nv write(95,'(A)') trim(sva(i)) end do end if close(95) end subroutine end module elk-7.2.42/src/PaxHeaders.21776/modtddft.f900000644000000000000000000000013214061636516015050 xustar0030 mtime=1623670094.857102546 30 atime=1623670093.574103737 30 ctime=1623670094.857102546 elk-7.2.42/src/modtddft.f900000644002504400250440000000607714061636516017117 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modtddft !-----------------------------------------! ! TDDFT linear response variables ! !-----------------------------------------! ! exchange-correlation kernel type integer fxctype(3) ! parameters for long-range correction (LRC) kernel real(8) fxclrc(2) ! number of independent spin components of the f_xc spin tensor integer nscfxc ! magnetic linear dichroism (MLD) angle between the electric and magnetic fields real(8) thetamld !---------------------------------------------! ! TDDFT real-time evolution variables ! !---------------------------------------------! ! number of laser pulses defining the time-dependent A-field integer npulse ! laser pulse parameters: vector amplitude, peak time, full-width at ! half-maximum, frequency and phase real(8), allocatable :: pulse(:,:) ! number of A-field ramps integer nramp ! ramp parameters: vector amplitude, ramp start time, linear, quadratic, cubic, ! etc. coefficients real(8), allocatable :: ramp(:,:) ! total simulation time real(8) tstime ! time step length real(8) dtimes ! number of time steps integer ntimes ! current time step integer itimes ! time steps real(8), allocatable :: times(:) ! phase defining complex direction of time evolution real(8) tdphi ! number of time steps after which the time-dependent eigenvectors are backed up integer ntsbackup ! tafieldt is .true. if a time-dependent vector potential is applied logical tafieldt ! time-dependent total A-field (external plus induced) real(8), allocatable :: afieldt(:,:) ! induced A-field and its time derivative at the current time step real(8) afindt(3,0:1) ! induced A-field scale factor real(8) afindscf ! if tafindt is .true. then the induced A-field is determined from Maxwell's ! equation and added to the total logical tafindt ! electric field at current time step real(8) efieldt(3) ! observables are written to file every ntswrite(1) time steps; this begins ! at or after time step ntswrite(2); writing occurs at the first time step ! irrespective of ntswrite integer ntswrite(2) ! static charge density real(8), allocatable :: rhosmt(:,:,:),rhosir(:,:) ! total static charge real(8) chgstot(3) ! muffin-tin static charge real(8), allocatable :: chgsmt(:,:) ! gradient of the Coulomb potential of the nucleus plus static density complex(8), allocatable :: gvclns(:,:,:) ! the following variables are .true. if the corresponding quantities are to be ! written every ntswrite time steps logical tdrho1d,tdrho2d,tdrho3d logical tdmag1d,tdmag2d,tdmag3d logical tdjr1d,tdjr2d,tdjr3d logical tddos,tdlsj ! magnitude of complex numbers added to initial eigenvectors real(8) rndevt0 ! starting time for the Fourier transform when calculating the linear response ! dielectric function from the real-time evolved current real(8) t0tdlr ! number of time steps between force calculations integer ntsforce ! total atomic forces at each time step real(8), allocatable :: forcet(:,:,:) end module elk-7.2.42/src/PaxHeaders.21776/modgw.f900000644000000000000000000000013214061636516014360 xustar0030 mtime=1623670094.858102545 30 atime=1623670093.576103735 30 ctime=1623670094.858102545 elk-7.2.42/src/modgw.f900000644002504400250440000000242714061636516016422 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. module modgw ! maximum Matsubara frequency for the GW calculation real(8) wmaxgw ! maximum number of Matsubara frequencies integer nwgw ! integer grid intervals for Matsubara frequencies integer intwgw(2) ! map from frequency index to FFT array integer, allocatable :: iwfft(:) ! maximum fermionic Matsubara frequency index to be used for the GW calculation integer nwfm ! maximum bosonic frequency index integer nwbs ! imaginary frequencies used for the GW calculation real(8), allocatable :: wgw(:) ! complex fermionic frequencies complex(8), allocatable :: wfm(:) ! twdiag is .true. if the screened interaction W is taken to be diagonal logical twdiag ! tsediag is .true. if the GW self-energy is taken to be diagonal logical tsediag ! type of analytic continuation to be used for determining the self-energy on ! the real axis integer actype ! number of poles used for fitting the self-energy matrix elements integer npole ! number of complex shifts used in averaging the Pade approximant for the ! analytic continuation of the self-energy to the real axis integer nspade end module elk-7.2.42/src/PaxHeaders.21776/modulr.f900000644000000000000000000000013214061636516014545 xustar0030 mtime=1623670094.860102543 30 atime=1623670093.577103734 30 ctime=1623670094.860102543 elk-7.2.42/src/modulr.f900000644002504400250440000000626514061636516016613 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modulr !-----------------------------! ! ultracell variables ! !-----------------------------! ! ultracell lattice vectors stored column-wise real(8) avecu(3,3) ! ultracell reciprocal lattice vectors real(8) bvecu(3,3) ! ultracell volume and Brillouin zone volume real(8) omegau,omegabzu ! original number of k-points integer nkpt0 ! kappa-point grid sizes integer ngridkpa(3) ! integer grid intervals for the kappa-points integer intkpa(2,3) ! number of kappa-points integer nkpa ! R-vectors in Cartesian coordinates spanning the ultracell real(8), allocatable :: vrcu(:,:) !------------------------------! ! G+Q-vector variables ! !------------------------------! ! small Q cut-off for non-zero Q-vectors real(8) q0cut ! G+Q-vectors in Cartesian coordinates real(8), allocatable :: vgqc(:,:,:) ! |G+Q| for all G+Q-vectors real(8), allocatable :: gqc(:,:) ! Coulomb Green's function in G+Q-space = 4 pi / |G+Q|^2 real(8), allocatable :: gclgq(:,:) ! spherical Bessel functions j_l(|G+Q|R_mt) real(8), allocatable :: jlgqrmt(:,:,:,:) ! spherical harmonics of the G+Q-vectors complex(8), allocatable :: ylmgq(:,:,:) ! structure factors for the G+Q-vectors complex(8), allocatable :: sfacgq(:,:,:) ! phase factor functions exp(iQ.r) in each muffin-tin complex(8), allocatable :: expqmt(:,:,:) !---------------------------------------------------! ! ultra long-range densities and potentials ! !---------------------------------------------------! ! trdvclr is .true. if the real-space external Coulomb potential should be read ! in from file logical trdvclr ! Q-dependent external Coulomb potential (FFT ordering) complex(8), allocatable :: vclq(:) ! Q-dependent external magnetic field complex(8), allocatable :: bfcq(:,:) ! Q-dependent external muffin-tin magnetic fields complex(8), allocatable :: bfcmtq(:,:,:) ! electric field vector in Cartesian coordinates real(8) efielduc(3) ! R-dependent density and magnetisation real(8), allocatable :: rhormt(:,:,:),rhorir(:,:) real(8), allocatable :: magrmt(:,:,:,:),magrir(:,:,:) ! muffin-tin charges and moments for each R-vector real(8), allocatable :: chgmtru(:,:) real(8), allocatable :: mommtru(:,:,:) ! Q-dependent density and magnetisation complex(8), allocatable :: rhoqmt(:,:,:),rhoqir(:,:) complex(8), allocatable :: magqmt(:,:,:,:),magqir(:,:,:) ! Q-dependent Kohn-Sham potential and magnetic field complex(8), allocatable, target :: vsbsq(:) complex(8), pointer :: vsqmt(:,:,:),vsqir(:,:) complex(8), pointer :: bsqmt(:,:,:,:),bsqir(:,:,:) ! random amplitude used for initialising the long-range magnetic field real(8) rndbfcu ! if tplotq0 is .true. then the Q=0 term is included when generating plots logical tplotq0 !----------------------------------------------! ! eigenvalue and eigenvector variables ! !----------------------------------------------! ! number of ultra long-range states integer nstulr ! long-range eigenvalues real(8), allocatable :: evalu(:,:) ! long-range occupation numbers real(8), allocatable :: occulr(:,:) end module elk-7.2.42/src/PaxHeaders.21776/modbog.f900000644000000000000000000000013214061636516014512 xustar0030 mtime=1623670094.861102542 30 atime=1623670093.579103732 30 ctime=1623670094.861102542 elk-7.2.42/src/modbog.f900000644002504400250440000000231214061636516016545 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modbog ! combined target array for fermionic and bosonic density matrices complex(8), allocatable, target :: duvwx(:) !----------------------------------------! ! fermionic Bogoliubov variables ! !----------------------------------------! ! Bogoliubov equation eigenvalues real(8), allocatable :: evaluv(:,:) ! V-norm for each state and k-point real(8), allocatable :: vnorm(:,:) ! Fermi energy adjustment step size real(8) tauefm ! Fermi energy convergence tolerance real(8) epsefm ! Hartree-Fock-Bogoliubov coupling constant real(8) ehfb ! density matrices VV† and UV† complex(8), pointer :: dvv(:,:,:),duv(:,:,:) ! fermionic anomalous correlation entropy real(8) face ! bdiag is .true. if the matrix B is taken to be diagonal logical bdiag !--------------------------------------! ! bosonic Bogoliubov variables ! !--------------------------------------! ! Bogoliubov equation eigenvalues real(8), allocatable :: evalwx(:,:) ! density matrices XX† and WX† complex(8), pointer :: dxx(:,:,:),dwx(:,:,:) end module elk-7.2.42/src/PaxHeaders.21776/moddelf.f900000644000000000000000000000012714061636516014661 xustar0029 mtime=1623670094.86310254 29 atime=1623670093.58110373 29 ctime=1623670094.86310254 elk-7.2.42/src/moddelf.f900000644002504400250440000000517014061636516016715 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module moddelf use modramdisk use modmpi contains subroutine delfiles(evec,devec,eval,occ,pmat,epsi) use modphonon implicit none ! arguments logical, optional, intent(in) :: evec,devec,eval,occ,pmat,epsi ! local variables integer ios character(256) fext,fname if (present(evec)) then ! delete the first-variational eigenvector file fname=trim(scrpath)//'EVECFV'//trim(filext) if (mp_mpi) then open(202,file=fname,form='UNFORMATTED',iostat=ios) close(202,status='DELETE',iostat=ios) end if if (ramdisk) call delfrd(fname) ! delete the second-variational eigenvector file fname=trim(scrpath)//'EVECSV'//trim(filext) if (mp_mpi) then open(206,file=fname,form='UNFORMATTED',iostat=ios) close(206,status='DELETE',iostat=ios) end if if (ramdisk) call delfrd(fname) end if if (present(devec)) then ! construct the dynamical matrix file extension call dynfext(iqph,isph,iaph,ipph,fext) ! delete the eigenvector derivative files fname=trim(scrpath)//'DEVECFV'//trim(fext) if (mp_mpi) then open(222,file=fname,form='UNFORMATTED',iostat=ios) close(222,status='DELETE',iostat=ios) end if if (ramdisk) call delfrd(fname) fname=trim(scrpath)//'DEVECSV'//trim(fext) if (mp_mpi) then open(226,file=fname,form='UNFORMATTED',iostat=ios) close(226,status='DELETE',iostat=ios) end if if (ramdisk) call delfrd(fname) end if if (present(eval)) then ! delete the first-variational eigenvalue file fname='EVALFV'//trim(filext) if (mp_mpi) then open(200,file=fname,form='UNFORMATTED',iostat=ios) close(200,status='DELETE',iostat=ios) end if if (ramdisk) call delfrd(fname) ! delete the second-variational eigenvalue file if (mp_mpi) then open(204,file='EVALSV'//trim(filext),form='UNFORMATTED',iostat=ios) close(204,status='DELETE',iostat=ios) end if end if if (present(occ)) then ! delete the occupation number file if (mp_mpi) then open(208,file='OCCSV'//trim(filext),form='UNFORMATTED',iostat=ios) close(208,status='DELETE',iostat=ios) end if end if if (present(pmat)) then ! delete the momentum matrix elements file if (mp_mpi) then open(230,file='PMAT.OUT',form='UNFORMATTED',iostat=ios) close(230,status='DELETE',iostat=ios) end if if (ramdisk) call delfrd('PMAT.OUT') end if if (present(epsi)) then ! delete the inverse epsilon file if (mp_mpi) then open(245,file='EPSINV.OUT',form='UNFORMATTED',iostat=ios) close(245,status='DELETE',iostat=ios) end if end if end subroutine end module elk-7.2.42/src/PaxHeaders.21776/modomp.f900000644000000000000000000000013214061636516014536 xustar0030 mtime=1623670094.864102539 30 atime=1623670093.582103729 30 ctime=1623670094.864102539 elk-7.2.42/src/modomp.f900000644002504400250440000000735014061636516016600 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module modomp ! maximum number of OpenMP threads available integer maxthd ! maximum number of OpenMP threads for the first nesting level integer maxthd1 ! maximum number of threads available to MKL integer maxthdmkl ! maximum OpenMP nesting level integer maxlvl ! number of active OpenMP threads for each nesting level integer, allocatable, protected :: nathd(:) interface integer function omp_get_num_procs() end function integer function omp_get_max_threads() end function integer function omp_get_num_threads() end function integer function omp_get_thread_num() end function integer function omp_get_max_active_levels() end function logical function omp_get_dynamic() end function integer function omp_get_level() end function subroutine omp_set_num_threads(num_threads) integer, intent(in) :: num_threads end subroutine integer function mkl_set_num_threads_local(num_threads) integer, intent(in) :: num_threads end function subroutine omp_set_nested(nested) logical, intent(in) :: nested end subroutine subroutine omp_set_max_active_levels(max_levels) integer, intent(in) :: max_levels end subroutine subroutine omp_set_dynamic(dynamic_threads) logical, intent(in) :: dynamic_threads end subroutine end interface contains subroutine omp_init implicit none ! determine the maximum number of available threads select case(maxthd) case(:-1) ! set the number of threads equal to a fraction of the number of processors maxthd=omp_get_num_procs()/abs(maxthd) maxthd=max(maxthd,1) call omp_set_num_threads(maxthd) case(0) ! use the system default number of threads maxthd=omp_get_max_threads() case default ! use the number of threads specified in the input file call omp_set_num_threads(maxthd) end select ! determine the maximum number of threads available at first nesting level select case(maxthd1) case(:-1) maxthd1=maxthd/abs(maxthd1) maxthd1=max(maxthd1,1) case(0) maxthd1=maxthd case default maxthd1=min(maxthd1,maxthd) end select ! switch off dynamic allocation of threads call omp_set_dynamic(.false.) ! allow nested parallelism (deprecated in OpenMP version 5) call omp_set_nested(.true.) ! set the maximum nesting level call omp_set_max_active_levels(maxlvl) ! allocate the number of active threads array if (allocated(nathd)) deallocate(nathd) allocate(nathd(0:maxlvl)) ! initialise the number of active threads call omp_reset end subroutine subroutine omp_reset implicit none ! number of active threads at each nesting level nathd(0)=1 nathd(1:)=0 end subroutine subroutine holdthd(nloop,nthd) implicit none ! arguments integer, intent(in) :: nloop integer, intent(out) :: nthd ! local variables integer lvl,na,n ! current nesting level lvl=omp_get_level() if ((lvl.lt.0).or.(lvl.ge.maxlvl)) then nthd=1 return end if !$OMP CRITICAL(modomp_) ! determine number of active threads at the current nesting level na=nathd(lvl) na=max(min(na,maxthd),1) ! number of threads allowed for this loop nthd=maxthd/na if (mod(maxthd,na).gt.0) nthd=nthd+1 if (lvl.eq.0) nthd=min(nthd,maxthd1) nthd=max(min(nthd,maxthd,nloop),1) ! add to number of active threads in next nesting level n=nathd(lvl+1)+nthd n=max(min(n,maxthd),0) nathd(lvl+1)=n !$OMP END CRITICAL(modomp_) end subroutine subroutine freethd(nthd) implicit none ! arguments integer, intent(in) :: nthd ! local variables integer lvl,n ! current nesting level lvl=omp_get_level() if ((lvl.lt.0).or.(lvl.ge.maxlvl)) return !$OMP CRITICAL(modomp_) ! subtract from the number of active threads in next nesting level n=nathd(lvl+1)-nthd n=max(min(n,maxthd),0) nathd(lvl+1)=n !$OMP END CRITICAL(modomp_) end subroutine end module elk-7.2.42/src/PaxHeaders.21776/mkl_stub.f900000644000000000000000000000013214061636517015064 xustar0030 mtime=1623670095.970101513 30 atime=1623670093.584103727 30 ctime=1623670095.970101513 elk-7.2.42/src/mkl_stub.f900000644002504400250440000000107714061636517017126 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! Stub routines for Intel MKL subroutine mkl_set_num_threads(num_threads) implicit none integer, intent(in) :: num_threads end subroutine integer function mkl_set_num_threads_local(num_threads) implicit none integer, intent(in) :: num_threads mkl_set_num_threads_local=0 end function subroutine mkl_set_dynamic(dynamic) implicit none logical, intent(in) :: dynamic end subroutine elk-7.2.42/src/PaxHeaders.21776/mkl_init.f900000644000000000000000000000013214061636516015051 xustar0030 mtime=1623670094.867102536 30 atime=1623670093.586103725 30 ctime=1623670094.867102536 elk-7.2.42/src/mkl_init.f900000644002504400250440000000117614061636516017113 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine mkl_init use modomp implicit none ! set the initial global number of MKL threads equal to one call mkl_set_num_threads(1) ! set the maximum number of threads available to MKL select case(maxthdmkl) case(:-1) maxthdmkl=maxthd/abs(maxthdmkl) maxthdmkl=max(maxthdmkl,1) case(0) maxthdmkl=maxthd case default maxthdmkl=min(maxthdmkl,maxthd) end select ! enable dynamic thread allocation call mkl_set_dynamic(.true.) end subroutine elk-7.2.42/src/PaxHeaders.21776/oblas_stub.f900000644000000000000000000000013214061636517015401 xustar0030 mtime=1623670095.972101511 30 atime=1623670093.587103725 30 ctime=1623670095.972101511 elk-7.2.42/src/oblas_stub.f900000644002504400250440000000051714061636517017441 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! Stub routines for OpenBLAS subroutine openblas_set_num_threads(num_threads) implicit none integer, intent(in) :: num_threads end subroutine elk-7.2.42/src/PaxHeaders.21776/oblas_init.f900000644000000000000000000000013214061636516015366 xustar0030 mtime=1623670094.870102534 30 atime=1623670093.589103723 30 ctime=1623670094.870102534 elk-7.2.42/src/oblas_init.f900000644002504400250440000000051614061636516017425 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine oblas_init implicit none ! set the initial number of OpenBLAS threads equal to one call openblas_set_num_threads(1) end subroutine elk-7.2.42/src/PaxHeaders.21776/blis_stub.f900000644000000000000000000000013014061636517015230 xustar0029 mtime=1623670095.97310151 30 atime=1623670093.591103721 29 ctime=1623670095.97310151 elk-7.2.42/src/blis_stub.f900000644002504400250440000000051514061636517017270 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! Stub routines for BLIS subroutine bli_thread_set_num_threads(num_threads) implicit none integer, intent(in) :: num_threads end subroutine elk-7.2.42/src/PaxHeaders.21776/blis_init.f900000644000000000000000000000013114061636516015216 xustar0030 mtime=1623670094.873102531 29 atime=1623670093.59210372 30 ctime=1623670094.873102531 elk-7.2.42/src/blis_init.f900000644002504400250440000000051314061636516017253 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine blis_init implicit none ! set the initial number of BLIS threads equal to one call bli_thread_set_num_threads(1) end subroutine elk-7.2.42/src/PaxHeaders.21776/w90_stub.f900000644000000000000000000000013214061636517014720 xustar0030 mtime=1623670095.975101508 30 atime=1623670093.594103718 30 ctime=1623670095.975101508 elk-7.2.42/src/w90_stub.f900000644002504400250440000000322114061636517016753 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin and Lars Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! Stub routines for Wannier90 library. subroutine wannier_setup(seed__name,mp_grid_loc,num_kpts_loc, & real_lattice_loc,recip_lattice_loc,kpt_latt_loc,num_bands_tot, & num_atoms_loc,atom_symbols_loc,atoms_cart_loc, gamma_only_loc,spinors_loc, & nntot_loc,nnlist_loc,nncell_loc,num_bands_loc,num_wann_loc, & proj_site_loc,proj_l_loc,proj_m_loc,proj_radial_loc,proj_z_loc, & proj_x_loc,proj_zona_loc,exclude_bands_loc,proj_s_loc,proj_s_qaxis_loc) implicit none ! arguments character(*) seed__name integer mp_grid_loc(3) integer num_kpts_loc real(8) real_lattice_loc(3,3) real(8) recip_lattice_loc(3,3) real(8) kpt_latt_loc(3,num_kpts_loc) integer num_bands_tot integer num_atoms_loc character(*) atom_symbols_loc(num_atoms_loc) real(8) atoms_cart_loc(3,num_atoms_loc) logical gamma_only_loc logical spinors_loc integer nntot_loc integer nnlist_loc(num_kpts_loc,*) integer nncell_loc(3,num_kpts_loc,*) integer num_bands_loc integer num_wann_loc real(8) proj_site_loc(3,num_bands_tot) integer proj_l_loc(num_bands_tot) integer proj_m_loc(num_bands_tot) integer proj_radial_loc(num_bands_tot) real(8) proj_z_loc(3,num_bands_tot) real(8) proj_x_loc(3,num_bands_tot) real(8) proj_zona_loc(num_bands_tot) integer exclude_bands_loc(num_bands_tot) integer, optional :: proj_s_loc(num_bands_tot) real(8), optional :: proj_s_qaxis_loc(3,num_bands_tot) write(*,*) write(*,'("Error(wannier_setup): libwannier not or improperly installed")') write(*,*) error stop end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/modw90.f900000644000000000000000000000013214061636516014362 xustar0030 mtime=1623670094.876102528 30 atime=1623670093.596103716 30 ctime=1623670094.876102528 elk-7.2.42/src/modw90.f900000644002504400250440000000227414061636516016424 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 Jon Lafuente and Manh Duc Le; 2017-18 Arsenii Gerasimov, ! Yaroslav Kvashnin and Lars Nordstrom. This file is distributed under the terms ! of the GNU General Public License. See the file COPYING for license details. module modw90 !---------------------------------------! ! Wannier90 interface variables ! !---------------------------------------! ! seedname for all Wannier90 files character(256) seedname ! number of extra lines to write to .win file integer nxlwin ! extra lines to write to .win file character(256), allocatable :: xlwin(:) ! number of Wannier functions to calculate integer num_wann ! number of bands to pass to Wannier90 integer num_bands ! index to bands integer, allocatable :: idxw90(:) ! number of iterations for the minimisation of omega integer num_iter ! trial step for the line search minimisation real(8) trial_step ! maximum number of nearest neighbours per k-point integer, parameter :: num_nnmax=12 ! total number of nearest neighbours for each k-point integer nntot ! list of nearest neighbours for each k-point integer, allocatable :: nnlist(:,:) ! G-vector offset for each nearest neighbour integer, allocatable :: nncell(:,:,:) end module elk-7.2.42/src/PaxHeaders.21776/zfftifc.f900000644000000000000000000000013014061636517014675 xustar0029 mtime=1623670095.99410149 30 atime=1623670093.597103715 29 ctime=1623670095.99410149 elk-7.2.42/src/zfftifc.f900000644002504400250440000000234714061636517016742 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zfftifc ! !INTERFACE: subroutine zfftifc(nd,n,sgn,z) ! !INPUT/OUTPUT PARAMETERS: ! nd : number of dimensions (in,integer) ! n : grid sizes (in,integer(nd)) ! sgn : FFT direction, -1: forward; 1: backward (in,integer) ! z : array to transform (inout,complex(n(1)*n(2)*...*n(nd))) ! !DESCRIPTION: ! Interface to the double-precision complex fast Fourier transform routine. ! This is to allow machine-optimised routines to be used without affecting the ! rest of the code. See routine {\tt nfftifc}. ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nd,n(nd),sgn complex(8), intent(inout) :: z(*) ! interface to modified FFTPACK5 call cfftnd(nd,n,sgn,z) end subroutine !EOC subroutine rzfftifc(nd,n,sgn,r,z) implicit none ! arguments integer, intent(in) :: nd,n(nd),sgn real(8), intent(inout) :: r(*) complex(8), intent(inout) :: z(*) write(*,*) write(*,'("Error(rzfftifc): FFTW or MKL required for real to complex FFT")') write(*,*) stop end subroutine elk-7.2.42/src/PaxHeaders.21776/elk.f900000644000000000000000000000013214061636516014016 xustar0030 mtime=1623670094.880102524 30 atime=1623670093.599103713 30 ctime=1623670094.880102524 elk-7.2.42/src/elk.f900000644002504400250440000024622714061636516016070 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2011 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! main routine for the Elk code program elk use modmain use modmpi use modomp use modvars use modramdisk implicit none ! local variables logical exist integer itask ! initialise MPI execution environment call mpi_init(ierror) ! duplicate mpi_comm_world call mpi_comm_dup(mpi_comm_world,mpicom,ierror) ! determine the number of MPI processes call mpi_comm_size(mpicom,np_mpi,ierror) ! determine the local MPI process number call mpi_comm_rank(mpicom,lp_mpi,ierror) ! determine if the local process is the master if (lp_mpi.eq.0) then mp_mpi=.true. write(*,*) write(*,'("Elk code version ",I1.1,".",I1.1,".",I2.2," started")') version else mp_mpi=.false. end if ! read input files call readinput ! initialise OpenMP variables call omp_init ! initialise the MKL library call mkl_init ! initialise the OpenBLAS library call oblas_init ! initialise the BLIS library call blis_init if (mp_mpi) then write(*,*) write(*,'("Number of MPI processes : ",I6)') np_mpi write(*,'("Number of OpenMP threads per MPI process : ",I4)') maxthd write(*,'("Total number of threads (MPI x OpenMP) : ",I6)') np_mpi*maxthd write(*,'("Maximum OpenMP nesting level : ",I4)') maxlvl write(*,'("Number of OpenMP threads at first nesting level : ",I4)') maxthd1 write(*,'("Number of MKL threads : ",I4)') maxthdmkl end if ! delete the VARIABLES.OUT file call delvars ! write version number to VARIABLES.OUT call writevars('version',nv=3,iva=version) ! check if Elk is already running in this directory if (mp_mpi) then inquire(file='RUNNING',exist=exist) if (exist) then write(*,*) write(*,'("Info(elk): several copies of Elk may be running in this path")') write(*,'("(this could be intentional, or result from a previous crash,")') write(*,'(" or arise from an incorrect MPI compilation)")') else open(50,file='RUNNING') close(50) end if end if ! initialise the RAM disk if required if (ramdisk) then call initrd if (mp_mpi) then write(*,*) write(*,'("RAM disk enabled")') end if end if ! perform the tasks do itask=1,ntasks task=tasks(itask) if (mp_mpi) then write(*,*) write(*,'("Info(elk): current task : ",I6)') task end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! check if task can be run with MPI if (lp_mpi.gt.0) then if (any(task.eq.[0,1,2,3,5,15,16,28,29,61,62,63,110,120,135,136,162,170, & 180,185,188,200,201,205,208,240,241,270,271,300,320,330,331,350,351,371, & 372,373,440,460,461,462,463,471,478,600,610,620,630,640,700,701,800, & 801])) then continue else write(*,'("Info(elk): MPI process ",I6," idle for task ",I6)') lp_mpi,task cycle end if end if ! write task to VARIABLES.OUT call writevars('task',iv=task) select case(task) case(0,1) call gndstate case(2,3) call geomopt case(5) call hartfock case(10) call writedos case(14) call writesf case(15,16) call writelsj case(20,21,22,23) call bandstr case(25) call effmass case(28,29) call mae case(31,32,33) call rhoplot case(41,42,43) call potplot case(51,52,53) call elfplot case(61,62,63,162) call wfplot case(65) call wfcrplot case(68) call rdstatus case(71,72,73,81,82,83,141,142,143,151,152,153) call vecplot case(91,92,93) call dbxcplot case(100,101) call fermisurf case(102) call fermisurfbxsf case(105) call nesting case(110) call mossbauer case(115) call writeefg case(120) call writepmat case(121) call dielectric case(122) call moke case(125) call nonlinopt case(130) call writeexpmat case(135) call writewfpw case(140) call elnes case(150) call writeevsp case(160) call torque case(170) call writeemd case(171,172,173) call emdplot case(180) call writeepsinv case(185) call writehmlbse case(186) call writeevbse case(187) call dielectric_bse case(190) call geomplot case(195) call sfacrho case(196) call sfacmag case(200,201,202) call phononsc case(205) call phonon case(208,209) call bornechg case(210) call phdos case(220) call phdisp case(230) call writephn case(240,241) call ephcouple case(245) call phlwidth case(250) call alpha2f case(260) call eliashberg case(270,271) call gndsteph case(280) call ephdos case(285) call aceplot case(300) call rdmft case(320) call tddftlr case(330,331) call tddftsplr case(341,342,343) call wxcplot case(350,351,352) call spiralsc case(371,372,373) call jprplot case(400) call writetmdu case(430) call writestrain case(440) call writestress case(450) call genafieldt case(460,461,462,463) call tddft case(471) call rhosplot case(478) call bornectd case(480,481) call dielectric_tdrt case(500) call testcheck case(550) call writew90 case(600) call gwsefm case(610) call gwspecf case(620) call gwbandstr case(630) call gwscrho case(640) call gwdmat case(700,701) call gndstulr case(731,732,733) call rhouplot case(741,742,743) call potuplot case(771,772,773) call maguplot case(800,801) !*********** case default write(*,*) write(*,'("Error(elk): task not defined : ",I8)') task write(*,*) stop end select ! reset the OpenMP thread variables call omp_reset ! close all opened files call closefiles end do if (mp_mpi) then open(50,file='RUNNING') close(50,status='DELETE') write(*,*) write(*,'("Elk code stopped")') end if ! terminate MPI execution environment call mpi_finalize(ierror) end program !BOI ! !TITLE: {\huge{\sc The Elk Code Manual}}\\ \Large{\sc Version 7.2.42}\\ \vskip 20pt \includegraphics[height=1cm]{elk_silhouette.pdf} ! !AUTHORS: {\sc J. K. Dewhurst, S. Sharma} \\ {\sc L. Nordstr\"{o}m, F. Cricchio, O. Gr\aa n\"{a}s} \\ {\sc E. K. U. Gross} ! !AFFILIATION: ! !INTRODUCTION: Introduction ! Welcome to the Elk Code! Elk is an all-electron full-potential linearised ! augmented-plane-wave (FP-LAPW) code for determining the properties of ! crystalline solids. It was developed originally at the ! Karl-Franzens-Universit\"{a}t Graz as part of the EXCITING EU Research and ! Training Network project\footnote{EXCITING code developed under the Research ! and Training Network EXCITING funded by the EU, contract No. ! HPRN-CT-2002-00317}. The guiding philosophy during the implementation of the ! code was to keep it as simple as possible for both users and developers ! without compromising on its capabilities. All the routines are released ! under either the GNU General Public License (GPL) or the GNU Lesser General ! Public License (LGPL) in the hope that they may inspire other scientists to ! implement new developments in the field of density functional theory and ! beyond. ! ! \section{Acknowledgments} ! Lots of people contributed to the Elk code with ideas, checking and testing, ! writing code or documentation and general encouragement. They include ! Claudia Ambrosch-Draxl, Clas Persson, Fredrik Bultmark, Christian Brouder, ! Rickard Armiento, Andrew Chizmeshya, Per Anderson, Igor Nekrasov, Sushil ! Auluck, Frank Wagner, Fateh Kalarasse, J\"{u}rgen Spitaler, Stefano ! Pittalis, Nektarios Lathiotakis, Tobias Burnus, Stephan Sagmeister, ! Christian Meisenbichler, S\'{e}bastien Leb\`{e}gue, Yigang Zhang, Fritz ! K\"{o}rmann, Alexey Baranov, Anton Kozhevnikov, Shigeru Suehara, Frank ! Essenberger, Antonio Sanna, Tyrel McQueen, Tim Baldsiefen, Marty Blaber, ! Anton Filanovich, Torbj\"{o}rn Bj\"{o}rkman, Martin Stankovski, Jerzy ! Goraus, Markus Meinert, Daniel Rohr, Vladimir Nazarov, Kevin Krieger, Pink ! Floyd, Arkardy Davydov, Florian Eich, Aldo Romero Castro, Koichi Kitahara, ! James Glasbrenner, Konrad Bussmann, Igor Mazin, Matthieu Verstraete, David ! Ernsting, Stephen Dugdale, Peter Elliott, Marcin Dulak, Jos\'{e} A. Flores ! Livas, Stefaan Cottenier, Yasushi Shinohara, Michael Fechner, Yaroslav ! Kvashnin, Tristan M\"uller, Arsenii Gerasimov, Manh Duc Le, Jon Lafuente ! Bartolom\'{e}, Ren\'{e} Wirnata, Jagdish Kumar, Andrew Shyichuk, Nisha ! Singh, Pietro Bonfa, Ronald Cohen and Alyn James. Special mention of David ! Singh's very useful book on the LAPW method\footnote{D. J. Singh, ! {\it Planewaves, Pseudopotentials and the LAPW Method} (Kluwer Academic ! Publishers, Boston, 1994).} must also be made. Finally we would like to ! acknowledge the generous support of Karl-Franzens-Universit\"{a}t Graz, the ! EU Marie-Curie Research Training Networks initiative, the Max Born Institute ! and the Max Planck Society. ! ! \vspace{24pt} ! Kay Dewhurst\newline ! Sangeeta Sharma\newline ! Lars Nordstr\"{o}m\newline ! Francesco Cricchio\newline ! Oscar Gr\aa n\"{a}s\newline ! Hardy Gross ! ! \vspace{12pt} ! Berlin, Halle, Jerusalem and Uppsala, June 2021 ! \newpage ! ! \section{Units} ! Unless explicitly stated otherwise, Elk uses atomic units. In this system ! $\hbar=1$, the electron mass $m=1$, the Bohr radius $a_0=1$ and the electron ! charge $e=1$ (note that the electron charge is positive, so that the atomic ! numbers $Z$ are negative). Thus the atomic unit of length is ! 0.529177210903(80) \AA, and the atomic unit of energy is the Hartree which ! equals 27.211386245988(53) eV. The unit of the external magnetic fields is ! defined such that one unit of magnetic field in {\tt elk.in} equals ! 1715.255541 Tesla. ! ! \section{Compiling and running Elk} ! \subsection{Compiling the code} ! Unpack the code from the archive file. Run the command ! \begin{verbatim} ! setup ! \end{verbatim} ! in the {\tt elk} directory and select the appropriate system and compiler. ! We highly recommend that you edit the file {\tt make.inc} and tune the ! compiler options for your computer system. In particular, use of ! machine-optimised BLAS/LAPACK libraries can result in significant increase ! in performance, but make sure they are of version $3.x$. Following this, run ! \begin{verbatim} ! make ! \end{verbatim} ! This will hopefully compile the entire code and all the libraries into one ! executable, {\tt elk}, located in the {\tt elk/src} directory. It will also ! compile two useful auxiliary programs, namely {\tt spacegroup} for producing ! crystal geometries from spacegroup data and {\tt eos} for fitting equations ! of state to energy-volume data. If you want to compile everything all over ! again, then run {\tt make clean} from the {\tt elk} directory, followed by ! {\tt make}. ! \subsubsection{Parallelism in Elk} ! Three forms of parallelism are implemented in Elk, and all can be used in ! combination with each other, with efficiency depending on the particular ! task, crystal structure and computer system. You may need to contact your ! system administrator for assistance with running Elk in parallel. ! \begin{enumerate} ! \item ! OpenMP works for symmetric multiprocessors, i.e. computers that have many ! cores with the same unified memory accessible to each. It is enabled by ! setting the appropriate command-line options (e.g. {\tt -qopenmp} for the ! Intel compiler) before compiling, and also at runtime by the environment ! variable ! \begin{verbatim} ! export OMP_NUM_THREADS=n ! \end{verbatim} ! where n is the number of cores available on a particular node. The same can ! be accomplished in {\tt elk.in} with ! \begin{verbatim} ! maxthd ! n ! \end{verbatim} ! In addition, some vendor-supplied BLAS/LAPACK libraries use OpenMP ! internally. The maximum number of threads used for LAPACK operations by ! Intel's MKL can be set with ! \begin{verbatim} ! maxthdmkl ! n ! \end{verbatim} ! \item ! The message passing interface (MPI) is particularly suitable for running ! Elk across multiple nodes of a cluster, with scaling to hundreds of ! processors possible. To enable MPI, comment out the lines indicated in ! {\tt elk/make.inc}. Then run {\tt make clean} followed by {\tt make}. If ! $y$ is the number of nodes and $x$ is the number of cores per node, then at ! runtime envoke ! \begin{verbatim} ! mpirun -np z ./elk ! \end{verbatim} ! where $z=x y$ is the total number of cores available on the machine. ! Highest efficiency is obtained by using hybrid parallelism with OpenMP on ! each node and MPI across nodes. This can be done by compiling the code ! using the MPI Fortran compiler in combination with the OpenMP command-line ! option. At runtime set {\tt export OMP\_NUM\_THREADS=x} and start the MPI ! run with {\em one process per node} as follows ! \begin{verbatim} ! mpirun -pernode -np y ./elk ! \end{verbatim} ! The number of MPI processes is reported in the file {\tt INFO.OUT} which ! serves as a check that MPI is running correctly. Note that version 2 of the ! MPI libraries is required to run Elk. ! \item ! Phonon calculations use a simple form of parallelism by just examining the ! run directory for dynamical matrix files. These files are of the form ! \begin{verbatim} ! DYN_Qqqqq_qqqq_qqqq_Sss_Aaa_Pp.OUT ! \end{verbatim} ! and contain a single row of a particular dynamical matrix. Elk simply finds ! which {\tt DYN} files do not exist, chooses one and runs it. This way many ! independent runs of Elk can be started in the same directory on a networked ! file system (NFS), and will run until all the dynamical matrices files are ! completed. Should a particular run crash, then delete the associated empty ! {\tt DYN} file and rerun Elk. ! \end{enumerate} ! ! \subsection{Memory requirements} ! Elk is a memory-bound code and runs best on processors with large caches and ! a large number of memory channels per core. Some tasks in Elk require a ! considerable amount of memory which can exceed the physical memory of the ! computer. In such cases, the number of threads at the first nesting level ! can be reduced with (for example) ! \begin{verbatim} ! maxthd1 ! -4 ! \end{verbatim} ! which restricts the number of threads at the first nesting level to ! maxthd/4. Deeper nesting levels, which generally require less memory, will ! still utilise the full compliment of available threads. ! \subsubsection{Stack space} ! The latest versions of Elk use stack space aggressively. This is because ! accessing variables is faster on the stack than on the heap. This can, ! however, result in the code crashing as threads run out of their stack ! space. To avoid this, increase the stack size for each OpenMP thread with ! (for example) ! \begin{verbatim} ! export OMP_STACKSIZE=64M ! \end{verbatim} ! before running the code. ! ! \subsection{Linking with the Libxc functional library} ! Libxc is the ETSF library of exchange-correlation functionals. Elk can use ! the complete set of LDA and GGA functionals available in Libxc as well as ! the potential-only metaGGA's. In order to enable this, first download and ! compile Libxc version 5. This should have produced the files {\tt libxc.a} ! and {\tt libxcf90.a}. Copy these files to the {\tt elk/src} directory and ! then uncomment the lines indicated for Libxc in the file {\tt elk/make.inc}. ! Once this is done, run {\tt make clean} followed by {\tt make}. To select a ! particular functional of Libxc, use the block ! \begin{verbatim} ! xctype ! 100 nx nc ! \end{verbatim} ! where {\tt nx} and {\tt nc} are, respectively, the numbers of the exchange ! and correlation functionals in the Libxc library. See the file ! {\tt elk/src/libxcf90.f90} for a list of the functionals and their ! associated numbers. ! ! \subsection{Running the code} ! As a rule, all input files for the code are in lower case and end with the ! extension {\tt .in}. All output files are uppercase and have the extension ! {\tt .OUT}. For most cases, the user will only need to modify the file ! {\tt elk.in}. In this file input parameters are arranged in blocks. ! Each block consists of a block name on one line and the block variables on ! subsequent lines. Almost all blocks are optional: the code uses reasonable ! default values in cases where they are absent. Blocks can appear in any ! order, if a block is repeated then the second instance is used. Comment ! lines can be included in the input file and begin with the {\tt !} ! character. ! ! \subsubsection{Species files} ! The only other input files are those describing the atomic species which go ! into the crystal. These files are found in the {\tt species} directory and ! are named with the element symbol and the extension {\tt .in}, for example ! {\tt Sb.in}. They contain parameters like the atomic charge, mass, ! muffin-tin radius, occupied atomic states and the type of linearisation ! required. Here as an example is the copper species file {\tt Cu.in}: ! \begin{verbatim} ! 'Cu' : spsymb ! 'copper' : spname ! -29.0000 : spzn ! 115837.2716 : spmass ! 0.371391E-06 2.0000 34.8965 500 : rminsp, rmt, rmaxsp, nrmt ! 10 : nstsp ! 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore ! 2 0 1 2.00000 T ! 2 1 1 2.00000 T ! 2 1 2 4.00000 T ! 3 0 1 2.00000 T ! 3 1 1 2.00000 F ! 3 1 2 4.00000 F ! 3 2 2 4.00000 F ! 3 2 3 6.00000 F ! 4 0 1 1.00000 F ! 1 : apword ! 0.1500 0 F : apwe0, apwdm, apwve ! 1 : nlx ! 2 2 : lx, apword ! 0.1500 0 T : apwe0, apwdm, apwve ! 0.1500 1 T ! 4 : nlorb ! 0 2 : lorbl, lorbord ! 0.1500 0 F : lorbe0, lorbdm, lorbve ! 0.1500 1 F ! 1 2 ! 0.1500 0 F ! 0.1500 1 F ! 2 2 ! 0.1500 0 F ! 0.1500 1 F ! 1 3 ! 0.1500 0 F ! 0.1500 1 F ! -2.8652 0 T ! \end{verbatim} ! The input parameters are defined as follows: ! \vskip 6pt ! {\tt spsymb} \\ ! The symbol of the element. ! \vskip 6pt ! {\tt spname} \\ ! The name of the element. ! \vskip 6pt ! {\tt spzn} \\ ! Nuclear charge: should be negative since the electron charge is taken to be ! postive in the code; it can also be fractional for purposes of doping. ! \vskip 6pt ! {\tt spmass} \\ ! Nuclear mass in atomic units. ! \vskip 6pt ! {\tt rminsp}, {\tt rmt}, {\tt rmaxsp}, {\tt nrmt} \\ ! Respectively, the minimum radius on logarithmic radial mesh; muffin-tin ! radius; effective infinity for atomic radial mesh; and number of radial mesh ! points to muffin-tin radius. ! \vskip 6pt ! {\tt nstsp} \\ ! Number of atomic states. ! \vskip 6pt ! {\tt nsp}, {\tt lsp}, {\tt ksp}, {\tt occsp}, {\tt spcore} \\ ! Respectively, the principal quantum number of the radial Dirac equation; ! quantum number $l$; quantum number $k$ ($l$ or $l+1$); occupancy of atomic ! state (can be fractional); {\tt .T.} if state is in the core and therefore ! treated with the Dirac equation in the spherical part of the muffin-tin ! Kohn-Sham potential. ! \vskip 6pt ! {\tt apword} \\ ! Default APW function order, i.e. the number of radial functions and ! therefore the order of the radial derivative matching at the muffin-tin ! surface. ! \vskip 6pt ! {\tt apwe0}, {\tt apwdm}, {\tt apwve} \\ ! Respectively, the default APW linearisation energy; the order of the energy ! derivative of the APW radial function $\partial^m u(r)/\partial E^m$; and ! {\tt .T.} if the linearisation energy is allowed to vary. ! \vskip 6pt ! {\tt nlx} \\ ! The number of exceptions to the default APW configuration. These should be ! listed on subsequent lines for particular angular momenta. In this example, ! the fixed energy APW with angular momentum $d$ ({\tt lx} $=2$) is replaced ! with a LAPW, which has variable linearisation energy. ! \vskip 6pt ! {\tt nlorb} \\ ! Number of local-orbitals. ! \vskip 6pt ! {\tt lorbl}, {\tt lorbord} \\ ! Respectively, the angular momentum $l$ of the local-orbital; and the order ! of the radial derivative which goes to zero at the muffin-tin surface. ! \vskip 6pt ! {\tt lorbe0}, {\tt lorbdm}, {\tt lorbve} \\ ! Respectively, the default local-orbital linearisation energy; the order of ! the energy derivative of the local-orbital radial function; and {\tt .T.} if ! the linearisation energy is allowed to vary. ! ! \subsubsection{Examples} ! The best way to learn to use Elk is to run the examples included with the ! package. These can be found in the {\tt examples} directory and use many of ! the code's capabilities. The following section which describes all the input ! parameters will be of invaluable assistance. ! ! \section{Input blocks} ! This section lists all the input blocks available. It is arranged with the ! name of the block followed by a table which lists each parameter name, what ! the parameter does, its type and default value. A horizontal line in the ! table indicates a new line in {\tt elk.in}. Below the table is a brief ! overview of the block's function. ! ! \block{atoms}{ ! {\tt nspecies} & number of species & integer & 0 \\ ! \hline ! {\tt spfname(i)} & species filename for species $i$ & string & - \\ ! \hline ! {\tt natoms(i)} & number of atoms for species $i$ & integer & - \\ ! \hline ! {\tt atposl(j,i)} & atomic position in lattice coordinates for atom $j$ ! & real(3) & - \\ ! {\tt bfcmt(j,i)} & muffin-tin external magnetic field in Cartesian ! coordinates for atom $j$ & real(3) & -} ! Defines the atomic species as well as their positions in the unit cell and ! the external magnetic field applied throughout the muffin-tin. These fields ! are used to break spin symmetry and should be considered infinitesimal as ! they do not contribute directly to the total energy. Collinear calculations ! are more efficient if the field is applied in the $z$-direction. One could, ! for example, set up an antiferromagnetic crystal by pointing the field on ! one atom in the positive $z$-direction and in the opposite direction on ! another atom. If {\tt molecule} is {\tt .true.} then the atomic positions ! are assumed to be in Cartesian coordinates. See also {\tt sppath}, ! {\tt bfieldc} and {\tt molecule}. ! ! \block{autokpt}{ ! {\tt autokpt} & {\tt .true.} if the $k$-point set is to be determined ! automatically & logical & {\tt .false.}} ! See {\tt radkpt} for details. ! ! \block{autolinengy}{ ! {\tt autolinengy} & {\tt .true.} if the fixed linearisation energies are ! to be determined automatically & logical & {\tt .false.}} ! See {\tt dlefe} for details. ! ! \block{autoswidth}{ ! {\tt autoswidth} & {\tt .true.} if the smearing parameter {\tt swidth} ! should be determined automatically & logical & {\tt .false.}} ! Calculates the smearing width from the $k$-point density, $V_{\rm BZ}/n_k$; ! the valence band width, $W$; and an effective mass parameter, $m^{*}$; ! according to ! $$ \sigma=\frac{\sqrt{2W}}{m^{*}}\left(\frac{3}{4\pi} ! \frac{V_{\rm BZ}}{n_k}\right)^{1/3}. $$ ! The variable {\tt mstar} then replaces {\tt swidth} as the control parameter ! of the smearing width. A large value of $m^{*}$ gives a narrower smearing ! function. Since {\tt swidth} is adjusted according to the fineness of the ! ${\bf k}$-mesh, the smearing parameter can then be eliminated. It is not ! recommended that {\tt autoswidth} be used in conjunction with the ! Fermi-Dirac smearing function, since the electronic temperature will then be ! a function of the $k$-point mesh. See T. Bj\"orkman and O. Gr\aa n\"as, ! {\it Int. J. Quant. Chem.} DOI: 10.1002/qua.22476 (2010) for details. See ! also {\tt stype} and {\tt swidth}. ! ! \block{avec}{ ! {\tt avec(1)} & first lattice vector & real(3) & $(1.0,0.0,0.0)$ \\ ! \hline ! {\tt avec(2)} & second lattice vector & real(3) & $(0.0,1.0,0.0)$ \\ ! \hline ! {\tt avec(3)} & third lattice vector & real(3) & $(0.0,0.0,1.0)$} ! Lattice vectors of the crystal in atomic units (Bohr). ! ! \block{beta0}{ ! {\tt beta0} & adaptive mixing parameter & real & $0.05$} ! This determines how much of the potential from the previous self-consistent ! loop is mixed with the potential from the current loop. It should be made ! smaller if the calculation is unstable. See {\tt betamax} and also the ! routine {\tt mixadapt}. ! ! \block{betamax}{ ! {\tt betamax} & maximum adaptive mixing parameter & real & $0.5$} ! Maximum allowed mixing parameter used in routine {\tt mixadapt}. ! ! \block{bfieldc}{ ! {\tt bfieldc} & global external magnetic field in Cartesian coordinates & ! real(3) & $(0.0,0.0,0.0)$} ! This is a constant magnetic field applied throughout the entire unit cell ! and enters the second-variational Hamiltonian as ! $$ \frac{g_e}{4c}\,\vec{\sigma}\cdot{\bf B}_{\rm ext}, $$ ! where $g_e$ is the electron $g$-factor. This field is normally used to break ! spin symmetry for spin-polarised calculations and considered to be ! infinitesimal with no direct contribution to the total energy. In cases ! where the magnetic field is finite (for example when computing magnetic ! response) the external ${\bf B}$-field energy reported in {\tt INFO.OUT} ! should be added to the total by hand. This field is applied throughout the ! entire unit cell. To apply magnetic fields in particular muffin-tins use the ! {\tt bfcmt} vectors in the {\tt atoms} block. Collinear calculations are ! more efficient if the field is applied in the $z$-direction. ! ! \block{broydpm}{ ! {\tt broydpm} & Broyden mixing parameters $\alpha$ and $w_0$ & real & ! $(0.4,0.15)$} ! See {\tt mixtype} and {\tt mixsdb}. ! ! \block{c\_tb09}{ ! {\tt c\_tb09} & Tran-Blaha constant $c$ & real & -} ! Sets the constant $c$ in the Tran-Blaha '09 functional. Normally this is ! calculated from the density, but there may be situations where this needs to ! be adjusted by hand. See {\it Phys. Rev. Lett.} {\bf 102}, 226401 (2009). ! ! \block{chgexs}{ ! {\tt chgexs} & excess electronic charge & real & $0.0$} ! This controls the amount of charge in the unit cell beyond that required to ! maintain neutrality. It can be set positive or negative depending on whether ! electron or hole doping is required. ! ! \block{cmagz}{ ! {\tt cmagz} & .true. if $z$-axis collinear magnetism is to be enforced & ! logical & {\tt .false.}} ! This variable can be set to .true. in cases where the magnetism is ! predominantly collinear in the $z$-direction, for example a ferromagnet with ! spin-orbit coupling. This will make the calculation considerably faster at ! the slight expense of precision. ! ! \block{deltaem}{ ! {\tt deltaem} & the size of the ${\bf k}$-vector displacement used when ! calculating numerical derivatives for the effective mass tensor & real & ! $0.025$} ! See {\tt ndspem} and {\tt vklem}. ! ! \block{deltaph}{ ! {\tt deltaph} & size of the atomic displacement used for calculating ! dynamical matrices & real & $0.01$} ! Phonon calculations are performed by constructing a supercell corresponding ! to a particular ${\bf q}$-vector and making a small periodic displacement of ! the atoms. The magnitude of this displacement is given by {\tt deltaph}. ! This should not be made too large, as anharmonic terms could then become ! significant, neither should it be too small as this can introduce numerical ! error. ! ! \block{deltast}{ ! {\tt deltast} & size of the change in lattice vectors used for calculating ! the stress tensor & real & $0.005$} ! The stress tensor is computed by changing the lattice vector matrix $A$ by ! $$ A\rightarrow (1+\delta t\,e_i)A, $$ ! where $dt$ is an infinitesimal equal in practice to {\tt deltast} and $e_i$ ! is the $i^{\rm th}$ strain tensor. Numerical finite differences are used to ! compute the stress tensor as the derivative of the total energy $dE_i/dt$. ! ! \block{dft+u}{ ! {\tt dftu} & type of DFT+$U$ calculation & integer & 0 \\ ! {\tt inpdftu} & type of input for DFT+U calculation & integer & 1 \\ ! \hline ! {\tt is} & species number & integer & - \\ ! {\tt l} & angular momentum value & integer & -1 \\ ! {\tt u} & the desired $U$ value & real & $0.0$ \\ ! {\tt j} & the desired $J$ value & real & $0.0$} ! This block contains the parameters required for an DFT+$U$ calculation, with ! the list of parameters for each species terminated with a blank line. The ! type of double counting required is set with the parameter {\tt dftu}. ! Currently implemented are: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! 0 & No DFT+$U$ calculation \\ ! 1 & Fully localised limit (FLL) \\ ! 2 & Around mean field (AFM) \\ ! 3 & An interpolation between FLL and AFM \\ ! \end{tabularx} ! \vskip 6pt ! The type of input parameters is set with the parameter {\tt inpdftu}. ! The current possibilities are: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! 1 & U and J \\ ! 2 & Slater parameters \\ ! 3 & Racah parameters \\ ! 4 & Yukawa screening length \\ ! 5 & U and determination of corresponding Yukawa screening length ! \end{tabularx} ! \vskip 6pt ! See (amongst others) {\it Phys. Rev. B} {\bf 67}, 153106 (2003), ! {\it Phys. Rev. B} {\bf 52}, R5467 (1995), {\it Phys. Rev. B} {\bf 60}, ! 10763 (1999), and {\it Phys. Rev. B} {\bf 80}, 035121 (2009). ! ! \block{dlefe}{ ! {\tt dlefe} & difference between the fixed linearisation energy and the ! Fermi energy & real & $-0.1$} ! When {\tt autolinengy} is {\tt .true.} then the fixed linearisation energies ! are set to the Fermi energy plus {\tt dlefe}. ! ! \block{dncgga}{ ! {\tt dncgga} & small constant used to stabilise non-collinear GGA & ! real & $1\times 10^{-8}$} ! This small constant, $d$, is required in order to remove the infinite ! gradients obtained when using `Kubler's trick' in conjunction with GGA and ! non-collinear magnetism. It is applied by calculating the up and down ! densities as ! $$ \rho^{\uparrow}({\bf r})=\rho({\bf r})+\widetilde{m}({\bf r}) ! \qquad \rho^{\downarrow}({\bf r})=\rho({\bf r})-\widetilde{m}({\bf r}), $$ ! where $\widetilde{m}({\bf r})=\sqrt{{\bf m}^2({\bf r})+d}$, ! and should be taken as the smallest value for which the exchange-correlation ! magnetic field ${\bf B}_{\rm xc}$ is smooth. ! ! \block{dosmsum}{ ! {\tt dosmsum} & {\tt .true.} if the partial DOS is to be summed over $m$ & ! logical & {\tt .false.}} ! By default, the partial density of states is resolved over $(l,m)$ quantum ! numbers. If {\tt dosmsum} is set to {\tt .true.} then the partial DOS is ! summed over $m$, and thus depends only on $l$. ! ! \block{dosssum}{ ! {\tt dosssum} & {\tt .true.} if the partial DOS is to be summed over spin & ! logical & {\tt .false.}} ! By default, the partial density of states for spin-polarised systems is spin ! resolved. ! ! \block{dtimes}{ ! {\tt dtimes} & time step used in time evolution run & real & $0.1$} ! See also {\tt tstime}. ! ! \block{epsband}{ ! {\tt epsband} & convergence tolerance for determining band energies & real & ! $1\times 10^{-12}$} ! APW and local-orbital linearisation energies are determined from the band ! energies. This is done by first searching upwards in energy until the radial ! wavefunction at the muffin-tin radius is zero. This is the energy at the top ! of the band, denoted $E_{\rm t}$. A downward search is now performed from ! $E_{\rm t}$ until the slope of the radial wavefunction at the muffin-tin ! radius is zero. This energy, $E_{\rm b}$, is at the bottom of the band. The ! band energy is taken as $(E_{\rm t}+E_{\rm b})/2$. If either $E_{\rm t}$ or ! $E_{\rm b}$ is not found, then the band energy is set to the default value. ! ! \block{epschg}{ ! {\tt epschg} & maximum allowed error in the calculated total charge beyond ! which a warning message will be issued & real & $1\times 10^{-3}$} ! ! \block{epsengy}{ ! {\tt epsengy} & convergence criterion for the total energy & real & ! $1\times 10^{-4}$} ! See {\tt epspot}. ! ! \block{epsforce}{ ! {\tt epsforce} & convergence tolerance for the forces during a geometry ! optimisation run & real & $2\times 10^{-3}$} ! If the mean absolute value of the atomic forces is less than {\tt epsforce} ! then the geometry optimisation run is ended. See also {\tt tasks} and ! {\tt latvopt}. ! ! \block{epslat}{ ! {\tt epslat } & vectors with lengths less than this are considered zero & ! real & $10^{-6}$} ! Sets the tolerance for determining if a vector or its components are zero. ! This is to account for any numerical error in real or reciprocal space ! vectors. ! ! \block{epsocc}{ ! {\tt epsocc} & smallest occupancy for which a state will contribute to the ! density & real & $1\times 10^{-8}$} ! ! \block{epspot}{ ! {\tt epspot} & convergence criterion for the Kohn-Sham potential and field & ! real & $1\times 10^{-6}$} ! If the RMS change in the Kohn-Sham potential and magnetic field is smaller ! than {\tt epspot} and the absolute change in the total energy is less than ! {\tt epsengy}, then the self-consistent loop is considered converged ! and exited. For geometry optimisation runs this results in the forces being ! calculated, the atomic positions updated and the loop restarted. See also ! {\tt epsengy} and {\tt maxscl}. ! ! \block{epsstress}{ ! {\tt epsstress} & convergence tolerance for the stress tensor during a ! geometry optimisation run with lattice vector relaxation & real & ! $5\times 10^{-4}$} ! See also {\tt epsforce} and {\tt latvopt}. ! ! \block{emaxelnes}{ ! {\tt emaxelnes} & maximum allowed initial-state eigenvalue for ELNES ! calculations & real & $-1.2$} ! ! \block{emaxrf}{ ! {\tt emaxrf} & energy cut-off used when calculating Kohn-Sham response ! functions & real & $10^6$} ! A typical Kohn-Sham response function is of the form ! \begin{align*} ! \chi_s({\bf r},{\bf r}',\omega) ! \equiv\frac{\delta\rho({\bf r},\omega)}{\delta v_s({\bf r}',\omega)} ! =\frac{1}{N_k}\sum_{i{\bf k},j{\bf k}'}(f_{i{\bf k}}-f_{j{\bf k}'}) ! \frac{\langle i{\bf k}|\hat{\rho}({\bf r})|j{\bf k}'\rangle ! \langle j{\bf k}'|\hat{\rho}({\bf r}')|i{\bf k}\rangle} ! {w+(\varepsilon_{i{\bf k}}-\varepsilon_{j{\bf k}'})+i\eta}, ! \end{align*} ! where $\hat{\rho}$ is the density operator; $N_k$ is the number of ! $k$-points; $\varepsilon_{i{\bf k}}$ and $f_{i{\bf k}}$ are the eigenvalues ! and occupation numbers, respectively. The variable {\tt emaxrf} is an energy ! window which limits the summation over states in the formula above so that ! $|\varepsilon_{i{\bf k}}-\varepsilon_{\rm Fermi}|<{\tt emaxrf}$. Reducing ! this can result in a faster calculation at the expense of accuracy. ! ! \block{fracinr}{ ! {\tt fracinr} & fraction of the muffin-tin radius up to which {\tt lmaxi} ! is used as the angular momentum cut-off & real & $0.01$} ! If {\tt fracinr} is negative then the fraction is determined from ! $f=\sqrt{({\tt lmaxi}+1)^2/({\tt lmaxo}+1)^2}$ in order to ! maintain a minimum density of points throughout the muffin-tin. See ! {\tt lmaxi} and {\tt lmaxo}. ! ! \block{fsmtype}{ ! {\tt fsmtype} & 0 for no fixed spin moment (FSM), 1 for total FSM, 2 for ! local muffin-tin FSM, and 3 for both total and local FSM & integer & 0} ! Set to 1, 2 or 3 for fixed spin moment calculations. To fix only the ! direction and not the magnitude set to $-1$, $-2$ or $-3$. See also ! {\tt momfix}, {\tt mommtfix}, {\tt taufsm} and {\tt spinpol}. ! ! \block{ftmtype}{ ! {\tt ftmtype} & 1 to enable a fixed tensor moment (FTM) calculation, ! 0 otherwise & integer & 0} ! If {\tt ftmtype} is $-1$ then the symmetry corresponding to the tensor ! moment is broken but no FTM calculation is performed. See {\it Phys. Rev. ! Lett.} {\bf 103}, 107202 (2009) and also {\tt tmomfix}. ! ! \block{fxclrc}{ ! {\tt fxclrc} & parameters for the dynamical long-range contribution (LRC) to ! the TDDFT exchange-correlation kernel & real(2) & $(0.0,0.0)$} ! These are the parameters $\alpha$ and $\beta$ for the kernel proposed in ! {\it Phys. Rev. B} {\bf 72}, 125203 (2005), namely ! $$ f_{xc}({\bf G},{\bf G}',{\bf q},\omega)=-\frac{\alpha+\beta\omega^2}{q^2} ! \delta_{{\bf G},{\bf G}'}\delta_{{\bf G},{\bf 0}}. $$ ! ! \block{fxctype}{ ! {\tt fxctype} & integer defining the type of exchange-correlation kernel ! $f_{\rm xc}$ & integer & $-1$} ! The acceptable values are: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! $-1$ & $f_{\rm xc}$ defined by {\tt xctype} \\ ! 0,1 & RPA ($f_{\rm xc}=0$) \\ ! 200 & Long-range contribution (LRC) kernel, S. Botti {\it et al.}, ! {\it Phys. Rev. B} {\bf 72}, 125203 (2005); see {\tt fxclrc} \\ ! 210 & `Bootstrap' kernel, S. Sharma, J. K. Dewhurst, A. Sanna and ! E. K. U. Gross, {\it Phys. Rev. Lett.} {\bf 107}, 186401 (2011) \\ ! 211 & Single iteration bootstrap ! \end{tabularx} ! ! \block{gmaxrf}{ ! {\tt gmaxrf} & maximum length of $|{\bf G}|$ for computing response ! functions & real & $3.0$} ! ! \block{gmaxvr}{ ! {\tt gmaxvr} & maximum length of $|{\bf G}|$ for expanding the interstitial ! density and potential & real & $12.0$} ! This variable has a lower bound which is enforced by the code as follows: ! $$ {\rm gmaxvr}\rightarrow\max\,({\rm gmaxvr},2\times{\rm gkmax} ! +{\rm epslat}) $$ ! See {\tt rgkmax}. ! ! \block{hdbse}{ ! {\tt hdbse} & {\tt .true.} if the direct term is to be included in the BSE ! Hamiltonian & logical & {\tt .true.}} ! ! \block{highq}{ ! {\tt highq} & {\tt .true.} if a high quality parameter set should be used & ! logical & {\tt .false.}} ! Setting this to {\tt .true.} results in some default parameters being ! changed to ensure good convergence in most situations. These changes can be ! overruled by subsequent blocks in the input file. See also {\tt vhighq}. ! ! \block{hmaxvr}{ ! {\tt hmaxvr} & maximum length of ${\bf H}$-vectors & real & $6.0$} ! The ${\bf H}$-vectors are used for calculating X-ray and magnetic structure ! factors. They are also used in linear response phonon calculations for ! expanding the density and potential in plane waves. See also {\tt gmaxvr}, ! {\tt vhmat}, {\tt reduceh}, {\tt wsfac} and {\tt hkmax}. ! ! \block{hxbse}{ ! {\tt hxbse} & {\tt .true.} if the exchange term is to be included in the BSE ! Hamiltonian & {\tt .true.}} ! ! \block{hybrid}{ ! {\tt hybrid} & {\tt .true} if a hybrid functional is to be used when running ! a Hartree-Fock calculation & logical & {\tt .false}} ! See also {\tt hybridc} and {\tt xctype}. ! ! \block{hybridc}{ ! {\tt hybridc} & hybrid functional mixing coefficient & real & $1.0$} ! ! \block{intraband}{ ! {\tt intraband} & {\tt .true.} if the intraband (Drude-like) contribution is ! to be added to the dieletric tensor & logical & {\tt .false.}} ! ! \block{isgkmax}{ ! {\tt isgkmax} & species for which the muffin-tin radius will be used for ! calculating {\tt gkmax} & integer & $-1$} ! The APW cut-off is determined from ${\tt gkmax}={\tt rgkmax}/R$. The ! variable {\tt isgkmax} determines which muffin-tin radius is to be used for ! $R$. These are the options: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! -4 & Use the largest radius \\ ! -3 & Use the smallest radius \\ ! -2 & Use the fixed value $R=2.0$ \\ ! -1 & Use the average of the muffin-tin radii \\ ! $n\ge 1$ & Use the radius of species $n$ ! \end{tabularx} ! ! \block{kstlist}{ ! {\tt kstlist(i)} & $i$th $k$-point and state pair & integer(2) & $(1,1)$} ! This is a user-defined list of $k$-point and state index pairs which are ! those used for plotting wavefunctions and writing ${\bf L}$, ${\bf S}$ and ! ${\bf J}$ expectation values. Only the first pair is used by the ! aforementioned tasks. The list should be terminated by a blank line. ! ! \block{latvopt}{ ! {\tt latvopt} & type of lattice vector optimisation to be performed during ! structural relaxation & integer & 0} ! Optimisation of the lattice vectors will be performed with ${\tt task}=2,3$ ! when ${\tt latvopt}\ne 0$. When ${\tt latvopt}=1$ the lattice vector ! optimisation will be constrained only by symmetry. Optimisation over all ! symmetry-preserving strains except isotropic scaling is performed when ! ${\tt latvopt}=2$. If ${\tt latvopt}<0$ then the optimisation will be over ! strain number $|{\tt latvopt}|$. The list of symmetric strain tensors can be ! produced with ${\tt task}=430$. By default (${\tt latvopt}=0$) no lattice ! vector optimisation is performed during structural relaxation. See also ! {\tt tau0latv} and {\tt atpopt}. ! ! \block{lmaxapw}{ ! {\tt lmaxapw} & angular momentum cut-off for the APW functions & integer & ! $8$} ! ! \block{lmaxdos}{ ! {\tt lmaxdos} & angular momentum cut-off for the partial DOS plot & ! integer & $3$} ! ! \block{lmaxi}{ ! {\tt lmaxi} & angular momentum cut-off for the muffin-tin density and ! potential on the inner part of the muffin-tin & integer & 2} ! Close to the nucleus, the density and potential is almost spherical and ! therefore the spherical harmonic expansion can be truncated a low angular ! momentum. See also {\tt fracinr}. ! ! \block{lmaxo}{ ! {\tt lmaxo} & angular momentum cut-off for the muffin-tin density and ! potential & integer & 6} ! ! \block{lmirep}{ ! {\tt lmirep} & {\tt .true.} if the $Y_{lm}$ basis is to be transformed ! into the basis of irreducible representations of the site symmetries for ! DOS plotting & logical & {\tt .true.}} ! When lmirep is set to .true., the spherical harmonic basis is transformed ! into one in which the site symmetries are block diagonal. Band characters ! determined from the density matrix expressed in this basis correspond to ! irreducible representations, and allow the partial DOS to be resolved into ! physically relevant contributions, for example $e_g$ and $t_{2g}$. ! ! \block{lorbcnd}{ ! {\tt lorbcnd} & {\tt .true.} if conduction state local-orbitals are to be ! automatically added to the basis & logical & {\tt .false.}} ! Adding these higher energy local-orbitals can improve calculations which ! rely on accurate unoccupied states, such as the response function. See also ! {\tt lorbordc}. ! ! \block{lorbordc}{ ! {\tt lorbordc} & the order of the conduction state local-orbitals & ! integer & 2} ! See {\tt lorbcnd}. ! ! \block{lradstp}{ ! {\tt lradstp} & radial step length for determining coarse radial mesh & ! integer & 4} ! Some muffin-tin functions (such as the density) are calculated on a coarse ! radial mesh and then interpolated onto a fine mesh. This is done for the ! sake of efficiency. {\tt lradstp} defines the step size in going from the ! fine to the coarse radial mesh. If it is too large, loss of precision may ! occur. ! ! \block{maxitoep}{ ! {\tt maxitoep} & maximum number of iterations when solving the exact ! exchange integral equations & integer & 300} ! See {\tt tau0oep}. ! ! \block{maxscl}{ ! {\tt maxscl } & maximum number of self-consistent loops allowed & integer & ! 200} ! This determines after how many loops the self-consistent cycle will ! terminate if the convergence criterion is not met. If {\tt maxscl} is $1$ ! then the density and potential file, {\tt STATE.OUT}, will {\bf not} be ! written to disk at the end of the loop. See {\tt epspot}. ! ! \block{mixtype}{ ! {\tt mixtype } & type of mixing required for the potential & integer & 1} ! Currently implemented are: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! 0 & Linear mixing \\ ! 1 & Adaptive linear mixing \\ ! 3 & Broyden mixing, {\it J. Phys. A: Math. Gen.} {\bf 17}, L317 (1984) ! \end{tabularx} ! ! \block{mixsdb}{ ! {\tt mixsdb} & subspace dimension for Broyden mixing & integer & 5} ! This is the number of mixing vectors which define the subspace in which the ! Hessian matrix is calculated. See {\tt mixtype} and {\tt broydpm}. ! ! \block{molecule}{ ! {\tt molecule} & {\tt .true.} if the system is an isolated molecule & ! logical & {\tt .false.}} ! If {\tt molecule} is {\tt .true.}, then the atomic positions, ${\bf a}$, ! given in the {\tt atoms} block are assumed to be in Cartesian coordinates. ! ! \block{momfix}{ ! {\tt momfix} & the desired total moment for a FSM calculation & ! real(3) & $(0.0,0.0,0.0)$} ! Note that all three components must be specified (even for collinear ! calculations). See {\tt fsmtype}, {\tt taufsm} and {\tt spinpol}. ! ! \block{mommtfix}{ ! {\tt is} & species number & integer & 0 \\ ! {\tt ia} & atom number & integer & 0 \\ ! {\tt mommtfix} & the desired muffin-tin moment for a FSM calculation & ! real(3) & $(0.0,0.0,0.0)$} ! The local muffin-tin moments are specified for a subset of atoms, with the ! list terminated with a blank line. Note that all three components must be ! specified (even for collinear calculations). See {\tt fsmtype}, {\tt taufsm} ! and {\tt spinpol}. ! ! \block{msmooth}{ ! {\tt msmooth} & amount of smoothing to be applied to the ! exchange-correlation potentials and magnetic field & integer & 0} ! Smoothing operations can be applied to the exchange-correlation potentials ! $v_{xc}$, $w_{xc}$ and the magnetic field ${\bf B}_{xc}$ in order to improve ! convergence. In the muffin-tin, this smoothing takes the form of $m$ ! successive three-point running averages applied to the radial component. In ! the interstitial region, the potential is first Fourier transformed to ! $G$-space, then a low-pass filter of the form $\exp[-2m(G/G_{\rm max})^8]$ ! is applied and the function is transformed back to real-space. ! ! \block{mstar}{ ! {\tt mstar} & value of the effective mass parameter used for adaptive ! determination of {\tt swidth} & real & $10.0$} ! See {\tt autoswidth}. ! ! \block{mustar}{ ! {\tt mustar} & Coulomb pseudopotential, $\mu^*$, used in the ! McMillan-Allen-Dynes equation & real & $0.15$} ! This is used when calculating the superconducting critical temperature with ! the formula {\it Phys. Rev. B 12, 905 (1975)} ! $$ T_c=\frac{\omega_{\rm log}}{1.2 k_B}\exp\left[\frac{-1.04(1+\lambda)} ! {\lambda-\mu^*(1+0.62\lambda)}\right], $$ ! where $\omega_{\rm log}$ is the logarithmic average frequency and $\lambda$ ! is the electron-phonon coupling constant. ! ! \block{ncbse}{ ! {\tt ncbse} & number of conduction states to be used for BSE calculations & ! integer & 3} ! See also {\tt nvbse}. ! ! \block{ndspem}{ ! {\tt ndspem} & the number of {\bf k}-vector displacements in each direction ! around {\tt vklem} when computing the numerical derivatives for the ! effective mass tensor & integer & 1} ! See {\tt deltaem} and {\tt vklem}. ! ! \block{nempty}{ ! {\tt nempty} & the number of empty states per atom and spin & real & $4.0$ } ! Defines the number of eigenstates beyond that required for charge ! neutrality. When running metals it is not known {\it a priori} how many ! states will be below the Fermi energy for each $k$-point. Setting ! {\tt nempty} greater than zero allows the additional states to act as a ! buffer in such cases. Furthermore, magnetic calculations use the ! first-variational eigenstates as a basis for setting up the ! second-variational Hamiltonian, and thus {\tt nempty} will determine the ! size of this basis set. Convergence with respect to this quantity should be ! checked. ! ! \block{ngridk}{ ! {\tt ngridk } & the $k$-point mesh sizes & integer(3) & $(1,1,1)$} ! The ${\bf k}$-vectors are generated using ! $$ {\bf k}=(\frac{i_1+v_1}{n_1},\frac{i_2+v_2}{n_2},\frac{i_3+v_3}{n_3}), $$ ! where $i_j$ runs from 0 to $n_j-1$ and $0\le v_j<1$ for $j=1,2,3$. The ! vector ${\bf v}$ is given by the variable {\tt vkloff}. See also ! {\tt reducek}. ! ! \block{ngridq}{ ! {\tt ngridq } & the phonon $q$-point mesh sizes & integer(3) & $(1,1,1)$} ! Same as {\tt ngridk}, except that this mesh is for the phonon $q$-points ! and other tasks. See also {\tt reduceq}. ! ! \block{nosource}{ ! {\tt nosource} & when set to {\tt .true.}, source fields are projected out ! of the exchange-correlation magnetic field & logical & {\tt .false.}} ! Experimental feature. ! ! \block{notes}{ ! {\tt notes(i)} & the $i$th line of the notes & string & -} ! This block allows users to add their own notes to the file {\tt INFO.OUT}. ! The block should be terminated with a blank line, and no line should exceed ! 80 characters. ! ! \block{npmae}{ ! {\tt npmae } & number or distribution of directions for MAE calculations & ! integer & $-1$} ! Automatic determination of the magnetic anisotropy energy (MAE) requires ! that the total energy is determined for a set of directions of the total ! magnetic moment. This variable controls the number or distribution of these ! directions. The convention is: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! $-4,-3,-2,-1$ & Cardinal directions given by the primitive translation ! vectors $n_1{\bf A}_1+n_2{\bf A}_2+n_3{\bf A}_3$, where ! $1\le n_i\le|{\tt npmae}|$ \\ ! 2 & Cartesian $x$ and $z$ directions \\ ! 3 & Cartesian $x$, $y$ and $z$ directions \\ ! $4,5,\ldots$ & Even distribution of {\tt npmae} directions ! \end{tabularx} ! ! \block{ntemp}{ ! {\tt ntemp} & number of temperature steps & integer & 40} ! This is the number of temperature steps to be used in the Eliashberg gap ! and thermodynamic properties calculations. ! ! \block{nvbse}{ ! {\tt nvbse} & number of valence states to be used for BSE calculations & ! integer & 2} ! See also {\tt ncbse}. ! ! \block{nwrite}{ ! {\tt nwrite} & number of self-consistent loops after which {\tt STATE.OUT} ! is to be written & integer & 0} ! Normally, the density and potentials are written to the file {\tt STATE.OUT} ! only after completion of the self-consistent loop. By setting {\tt nwrite} ! to a positive integer the file will instead be written every {\tt nwrite} ! loops. ! ! \block{nxoapwlo}{ ! {\tt nxoapwlo} & extra order of radial functions to be added to the existing ! APW and local-orbital set & integer & 0} ! Setting this variable will result in the APWs and local-orbitals for all ! species becoming higher order with corresponding increase in derivative ! matching at the muffin-tin surface. For example, setting {\tt nxoapwlo}=1 ! turns all APWs into LAPWs. ! ! \block{optcomp}{ ! {\tt optcomp} & the components of the first- or second-order optical tensor ! to be calculated & integer(3) & $(1,1,1)$} ! This selects which components of the optical tensor you would like to plot. ! Only the first two are used for the first-order tensor. Several components ! can be listed one after the other with a blank line terminating the list. ! ! \block{phwrite}{ ! {\tt nphwrt} & number of $q$-points for which phonon modes are to be found & ! integer & 1 \\ ! \hline ! {\tt vqlwrt(i)} & the $i$th $q$-point in lattice coordinates & real(3) & ! $(0.0,0.0,0.0)$} ! This is used in conjunction with {\tt task}=230. The code will write the ! phonon frequencies and eigenvectors to the file {\tt PHONON.OUT} for all the ! $q$-points in the list. The $q$-points can be anywhere in the Brillouin zone ! and do not have to lie on the mesh defined by {\tt ngridq}. Obviously, all ! the dynamical matrices have to be computed first using {\tt task}=200. ! ! \block{plot1d}{ ! {\tt nvp1d} & number of vertices & integer & 2 \\ ! {\tt npp1d} & number of plotting points & integer & 200 \\ ! \hline ! {\tt vvlp1d(i)} & lattice coordinates for vertex $i$ & real(3) & ! $(0.0,0.0,0.0)\rightarrow(1.0,1.0,1.0)$} ! Defines the path in either real or reciprocal space along which the 1D plot ! is to be produced. The user should provide {\tt nvp1d} vertices in lattice ! coordinates. ! ! \block{plot2d}{ ! {\tt vclp2d(0)} & zeroth corner (origin) & real(3) & $(0.0,0.0,0.0)$ \\ ! \hline ! {\tt vclp2d(1)} & first corner & real(3) & $(1.0,0.0,0.0)$ \\ ! \hline ! {\tt vclp2d(2)} & second corner & real(3) & $(0.0,1.0,0.0)$ \\ ! \hline ! {\tt np2d} & number of plotting points in both directions & integer(2) & ! $(40,40)$} ! Defines the corners of a parallelogram and the grid size used for producing ! 2D plots. ! ! \block{plot3d}{ ! {\tt vclp3d(0)} & zeroth corner (origin) & real(3) & $(0.0,0.0,0.0)$ \\ ! \hline ! {\tt vclp3d(1)} & first corner & real(3) & $(1.0,0.0,0.0)$ \\ ! \hline ! {\tt vclp3d(2)} & second corner & real(3) & $(0.0,1.0,0.0)$ \\ ! \hline ! {\tt vclp3d(3)} & third corner & real(3) & $(0.0,0.0,1.0)$ \\ ! \hline ! {\tt np3d} & number of plotting points each direction & integer(3) & ! $(20,20,20)$} ! Defines the corners of a box and the grid size used for producing 3D plots. ! ! \block{primcell}{ ! {\tt primcell} & {\tt .true.} if the primitive unit cell should be found ! & logical & {\tt .false.}} ! Allows the primitive unit cell to be determined automatically from the ! conventional cell. This is done by searching for lattice vectors among all ! those which connect atomic sites, and using the three shortest which produce ! a unit cell with non-zero volume. ! ! \block{pulse}{ ! {\tt n} & number of pulses & integer & - \\ ! \hline ! {\tt a0(i)} & polarisation vector (including amplitude) & real(3) & - \\ ! {\tt w(i)} & frequency & real & - \\ ! {\tt phi(i)} & phase in degrees & real & - \\ ! {\tt rc(i)} & chirp rate & real & - \\ ! {\tt t0(i)} & peak time & real & - \\ ! {\tt d(i)} & full-width at half-maximum & real & -} ! Parameters used to generate a time-dependent vector potential ${\bf A}(t)$ ! representing a laser pulse. The total vector potential is the sum of ! individual pulses and is given by the formula ! $$ {\bf A}(t)=\sum_{i=1}^n {\bf A}_0^i\exp ! \left[-(t-t_0^i)^2/2\sigma_i^2\right] ! \sin\left[w_i(t-t_0^i)+\phi_i+r_{\rm c}^i t^2/2\right], $$ ! where $\sigma=d/2\sqrt{2\ln 2}$. See also {\tt ramp}. ! ! \block{radkpt}{ ! {\tt radkpt } & radius of sphere used to determine $k$-point density & ! real & $40.0$} ! Used for the automatic determination of the $k$-point mesh. If {\tt autokpt} ! is set to {\tt .true.} then the mesh sizes will be determined by ! $n_i=R_k|{\bf B}_i|+1$, where ${\bf B}_i$ are the primitive reciprocal ! lattice vectors. ! ! \block{ramp}{ ! {\tt n} & number of ramps & integer & - \\ ! \hline ! {\tt a0(i)} & polarisation vector (including amplitude) & real(3) & - \\ ! {\tt t0(i)} & ramp start time & real & - \\ ! {\tt c1(i)} & linear coefficient of ${\bf A}(t)$ & real & - \\ ! {\tt c2(i)} & quadratic coefficient & real & -} ! Parameters used to generate a time-dependent vector potential ${\bf A}(t)$ ! representing a constant or linearly increasing electric field ! ${\bf E}(t)=-\partial{\bf A}(t)/\partial t$. The vector potential is given ! by ! $$ {\bf A}(t)=\sum_{i=1}^n {\bf A}_0^i ! \left[c_1(t-t_0)+c_2(t-t_0)^2\right]\Theta(t-t_0). $$ ! ! \block{readadu}{ ! {\tt readadu} & set to {\tt .true.} if the interpolation constant for ! DFT+$U$ should be read from file rather than calculated & logical & ! {\tt .false.}} ! When {\tt dftu}=3, the DFT+$U$ energy and potential are interpolated ! between FLL and AFM. The interpolation constant, $\alpha$, is normally ! calculated from the density matrix, but can also be read in from the file ! {\tt ALPHADU.OUT}. This allows the user to fix $\alpha$, but is also ! necessary when calculating forces, since the contribution of the potential ! of the variation of $\alpha$ with respect to the density matrix is not ! computed. See {\tt dft+u}. ! ! \block{reducebf}{ ! {\tt reducebf} & reduction factor for the external magnetic fields & real & ! $1.0$} ! After each self-consistent loop, the external magnetic fields are multiplied ! with {\tt reducebf}. This allows for a large external magnetic field at the ! start of the self-consistent loop to break spin symmetry, while at the end ! of the loop the field will be effectively zero, i.e. infinitesimal. See ! {\tt bfieldc} and {\tt atoms}. ! ! \block{reduceh}{ ! {\tt reduceh} & set to {\tt .true.} if the reciprocal ${\bf H}$-vectors ! should be reduced by the symmorphic crystal symmetries & logical & .true.} ! See {\tt hmaxvr} and {\tt vmat}. ! ! \block{reducek}{ ! {\tt reducek} & type of reduction of the $k$-point set & integer & 1} ! Types of reduction are defined by the symmetry group used: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! 0 & no reduction \\ ! 1 & reduce with full crystal symmetry group (including non-symmorphic ! symmetries) \\ ! 2 & reduce with symmorphic symmetries only ! \end{tabularx} ! \vskip 6pt ! See also {\tt ngridk} and {\tt vkloff}. ! ! \block{reduceq}{ ! {\tt reduceq} & type of reduction of the $q$-point set & integer & 1} ! See {\tt reducek} and {\tt ngridq}. ! ! \block{rgkmax}{ ! {\tt rgkmax} & $R^{\rm MT}_{\rm min}\times\max\{|{\bf G}+{\bf k}|\}$ & ! real & $7.0$} ! This sets the maximum length for the ${\bf G}+{\bf k}$ vectors, defined as ! {\tt rgkmax} divided by the average muffin-tin radius. See {\tt isgkmax}. ! ! \block{rotavec}{ ! {\tt axang} & axis-angle representation of lattice vector rotation & ! real(4) & $(0.0,0.0,0.0,0.0)$} ! This determines the rotation matrix which is applied to the lattice vectors ! prior to any calculation. The first three components specify the axis and ! the last component is the angle in degrees. The `right-hand rule' convention ! is followed. ! ! \block{scale}{ ! {\tt scale } & lattice vector scaling factor & real & $1.0$} ! Scaling factor for all three lattice vectors. Applied in conjunction with ! {\tt scale1}, {\tt scale2} and {\tt scale3}. ! ! \block{scale1/2/3}{ ! {\tt scale1/2/3 } & separate scaling factors for each lattice vector & ! real & $1.0$} ! ! \block{scissor}{ ! {\tt scissor} & the scissor correction & real & $0.0$} ! This is the scissor shift applied to states above the Fermi energy ! {\it Phys. Rev. B} {\bf 43}, 4187 (1991). Affects optics calculations only. ! ! \block{scrpath}{ ! {\tt scrpath} & scratch space path & string & null} ! This is the scratch space path where the eigenvector files {\tt EVALFV.OUT} ! and {\tt EVALSV.OUT} will be written. If the run directory is accessed via a ! network then {\tt scrpath} can be set to a directory on the local disk, for ! example {\tt /tmp/}. Note that the forward slash {\tt /} at the end of the ! path must be included. ! ! \block{socscf}{ ! {\tt socscf} & scaling factor for the spin-orbit coupling term in the ! Hamiltonian & real & $1.0$} ! This can be used to enhance the effect of spin-orbit coupling in order to ! accurately determine the magnetic anisotropy energy (MAE). ! ! \block{spincore}{ ! {\tt spincore} & set to {\tt .true.} if the core should be spin-polarised ! & logical & {\tt .false.}} ! ! \block{spinorb}{ ! {\tt spinorb} & set to {\tt .true.} if a spin-orbit coupling is required ! & logical & {\tt .false.}} ! If {\tt spinorb} is {\tt .true.}, then a $\boldsymbol\sigma\cdot{\bf L}$ ! term is added to the second-variational Hamiltonian. See {\tt spinpol}. ! ! \block{spinpol}{ ! {\tt spinpol} & set to {\tt .true.} if a spin-polarised calculation is ! required & logical & {\tt .false.}} ! If {\tt spinpol} is {\tt .true.}, then the spin-polarised Hamiltonian is ! solved as a second-variational step using two-component spinors in the ! Kohn-Sham magnetic field. The first variational scalar wavefunctions are ! used as a basis for setting this Hamiltonian. ! ! \block{spinsprl}{ ! {\tt spinsprl} & set to {\tt .true.} if a spin-spiral calculation is ! required & logical & {\tt .false.}} ! Experimental feature for the calculation of spin-spiral states. See ! {\tt vqlss} for details. ! ! \block{sppath}{ ! {\tt sppath} & path where the species files can be found & string & null} ! Note that the forward slash {\tt /} at the end of the path must be included. ! ! \block{ssdph}{ ! {\tt ssdph} & set to {\tt .true.} if a complex de-phasing factor is to be ! used in spin-spiral calculations & logical & {\tt .true.}} ! If this is {\tt .true.} then spin-spiral wavefunctions in each muffin-tin at ! position ${\bf r}_{\alpha}$ are de-phased by the matrix ! $$ \begin{pmatrix} e^{-i{\bf q}\cdot{\bf r}_{\alpha}/2} & 0 \\ ! 0 & e^{i{\bf q}\cdot{\bf r}_{\alpha}/2} \end{pmatrix}. $$ ! In simple situations, this has the advantage of producing magnon dynamical ! matrices which are already in diagonal form. This option should be used with ! care, and a full understanding of the spin-spiral configuration is required. ! See {\tt spinsprl}. ! ! \block{stype}{ ! {\tt stype} & integer defining the type of smearing to be used & integer & ! $3$} ! A smooth approximation to the Dirac delta function is needed to compute the ! occupancies of the Kohn-Sham states. The variable {\tt swidth} determines ! the width of the approximate delta function. Currently implemented are ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! 0 & Gaussian \\ ! 1 & Methfessel-Paxton order 1, Phys. Rev. B {\bf 40}, 3616 (1989) \\ ! 2 & Methfessel-Paxton order 2 \\ ! 3 & Fermi-Dirac ! \end{tabularx} ! \vskip 6pt ! See also {\tt autoswidth}, {\tt swidth} and {\tt tempk}. ! ! \block{swidth}{ ! {\tt swidth} & width of the smooth approximation to the Dirac delta ! function & real & $0.001$} ! See {\tt stype} for details and the variable {\tt tempk}. ! ! \newpage ! \block{tasks}{ ! {\tt task(i) } & the $i$th task & integer & $-1$} ! A list of tasks for the code to perform sequentially. The list should be ! terminated with a blank line. Each task has an associated integer as ! follows: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! -1 & Write out the version number of the code. \\ ! 0 & Ground state run starting from the atomic densities. \\ ! 1 & Resumption of ground-state run using density in {\tt STATE.OUT}. \\ ! 2 & Geometry optimisation run starting from the atomic densities, with ! atomic positions written to {\tt GEOMETRY.OUT}. \\ ! 3 & Resumption of geometry optimisation run using density in {\tt STATE.OUT} ! but with positions from {\tt elk.in}. \\ ! 5 & Ground state Hartree-Fock run. \\ ! 10 & Total, partial and interstitial density of states (DOS). \\ ! 14 & Plots the smooth Dirac delta and Heaviside step functions used by the ! code to calculate occupancies. \\ ! 15 & Output ${\bf L}$, ${\bf S}$ and ${\bf J}$ total expectation values. \\ ! 16 & Output ${\bf L}$, ${\bf S}$ and ${\bf J}$ expectation values for each ! $k$-point and state in {\tt kstlist}. \\ ! 20 & Band structure plot. \\ ! 21 & Band structure plot which includes total and angular momentum ! characters for every atom. \\ ! 22 & Band structure plot which includes $(l,m)$ character for every atom. \\ ! 23 & Band structure plot which includes spin character for every atom. \\ ! 25 & Compute the effective mass tensor at the $k$-point given by ! {\tt vklem}. \\ ! 31, 32, 33 & 1/2/3D charge density plot. \\ ! 41, 42, 43 & 1/2/3D exchange-correlation and Coulomb potential plots. \\ ! 51, 52, 53 & 1/2/3D electron localisation function (ELF) plot. \\ ! 61, 62, 63 & 1/2/3D wavefunction plot: ! $\left|\Psi_{i{\bf k}}({\bf r})\right|^2$. \\ ! 65 & Write the core wavefunctions to file for plotting. \\ ! 71, 72, 73 & 1/2/3D plot of magnetisation vector field, ! ${\bf m}({\bf r})$. \\ ! 81, 82, 83 & 1/2/3D plot of exchange-correlation magnetic vector field, ! ${\bf B}_{\rm xc}({\bf r})$. \\ ! 91, 92, 93 & 1/2/3D plot of $\nabla\cdot{\bf B}_{\rm xc}({\bf r})$. \\ ! 100 & 3D Fermi surface plot using the scalar product ! $p({\bf k})=\Pi_i(\epsilon_{i{\bf k}}-\epsilon_{\rm F})$. \\ ! 101 & 3D Fermi surface plot using separate bands (minus the Fermi ! energy). \\ ! 102 & 3D Fermi surface which can be plotted with XCrysDen. \\ ! 105 & 3D nesting function plot. \\ ! 110 & Calculation of M\"{o}ssbauer contact charge densities and magnetic ! fields at the nuclear sites. \\ ! 115 & Calculation of the electric field gradient (EFG) at the nuclear ! sites. \\ ! 120 & Output of the momentum matrix elements ! $\langle\Psi_{i{\bf k}}|-i\nabla|\Psi_{j{\bf k}}\rangle$. \\ ! 121 & Linear optical dielectric response tensor calculated within the random ! phase approximation (RPA) and in the $q\rightarrow 0$ limit, with no ! microscopic contributions. \\ ! 122 & Magneto optical Kerr effect (MOKE) angle. \\ ! 125 & Non-linear optical second harmonic generation. ! \end{tabularx} ! ! \begin{tabularx}{\textwidth}[h]{lX} ! 130 & Output matrix elements of the type ! $\langle\Psi_{i{\bf k+q}}|\exp[i({\bf G+q})\cdot{\bf r}]| ! \Psi_{j{\bf k}}\rangle$. \\ ! 135 & Output all wavefunctions expanded in the plane wave basis up to a ! cut-off defined by {\tt rgkmax}. \\ ! 140 & Energy loss near edge structure (ELNES). \\ ! 141, 142, 143 & 1/2/3D plot of the electric field ! ${\bf E}({\bf r})\equiv\nabla V_{\rm C}({\bf r})$. \\ ! 151, 152, 153 & 1/2/3D plot of ! ${\bf m}({\bf r})\times{\bf B}_{\rm xc}({\bf r})$. \\ ! 162 & Scanning-tunneling microscopy (STM) image. \\ ! 180 & Generate the RPA inverse dielectric function with local contributions ! and write it to file. \\ ! 185 & Write the Bethe-Salpeter equation (BSE) Hamiltonian to file. \\ ! 186 & Diagonalise the BSE Hamiltonian and write the eigenvectors and ! eigenvalues to file. \\ ! 187 & Output the BSE dielectric response function. \\ ! 190 & Write the atomic geometry to file for plotting with XCrySDen and ! V\_Sim. \\ ! 195 & Calculation of X-ray density structure factors. \\ ! 196 & Calculation of magnetic structure factors. \\ ! 200 & Calculation of phonon dynamical matrices on a $q$-point set defined by ! {\tt ngridq} using the supercell method. \\ ! 202 & Phonon dry run: just produce a set of empty DYN files. \\ ! 205 & Calculation of phonon dynamical matrices using density functional ! perturbation theory (DFPT). \\ ! 210 & Phonon density of states. \\ ! 220 & Phonon dispersion plot. \\ ! 230 & Phonon frequencies and eigenvectors for an arbitrary $q$-point. \\ ! 240, 241 & Generate the ${\bf q}$-dependent phonon linewidths and ! electron-phonon coupling constants and write them to file. \\ ! 245 & Phonon linewidths plot. \\ ! 250 & Eliashberg function $\alpha^2F(\omega)$, electron-phonon coupling ! constant $\lambda$, and the McMillan-Allen-Dynes critical temperature ! $T_c$. \\ ! 300 & Reduced density matrix functional theory (RDMFT) calculation. \\ ! 320 & Time-dependent density functional theory (TDDFT) calculation of the ! dielectric response function including microscopic contributions. \\ ! 330, 331 & TDDFT calculation of the spin-polarised response function for ! arbitrary ${\bf q}$-vectors. Task 331 writes the entire response function ! $\overleftrightarrow{\chi}({\bf G},{\bf G}',q,\omega)$ to file. \\ ! 400 & Calculation of tensor moments and corresponding DFT+$U$ Hartree-Fock ! energy contributions. \\ ! 450 & Generates a laser pulse in the form of a time-dependent vector ! potential ${\bf A}(t)$ and writes it to AFIELDT.OUT. \\ ! 460 & Time evolution run using TDDFT under the influence of ${\bf A}(t)$. ! \end{tabularx} ! ! \block{tau0atp}{ ! {\tt tau0atp} & the step size to be used for atomic position optimisation & ! real & $0.25$} ! The position of atom $\alpha$ is updated on step $m$ of a geometry ! optimisation run using ! $$ {\bf r}_{\alpha}^{m+1}={\bf r}_{\alpha}^m+\tau_{\alpha}^m ! \left({\bf F}_{\alpha}^m+{\bf F}_{\alpha}^{m-1}\right), $$ ! where $\tau_{\alpha}$ is set to {\tt tau0atp} for $m=0$, and incremented by ! the same amount if the atom is moving in the same direction between steps. ! If the direction changes then $\tau_{\alpha}$ is reset to {\tt tau0atp}. ! ! \block{tau0latv}{ ! {\tt tau0latv} & the step size to be used for lattice vector optimisation & ! real & $0.25$} ! This parameter is used for lattice vector optimisation in a procedure ! identical to that for atomic position optimisation. See {\tt tau0atp} and ! {\tt latvopt}. ! ! \block{tauoep}{ ! {\tt tauoep} & step length and starting fraction for the OEP iterative ! solver & real(2) & $(0.05, 0.95)$} ! The optimised effective potential is determined using an interative method ! [Phys. Rev. Lett. 98, 196405 (2007)]. This variable sets the step length ! described in the article. The second number defines the fraction of the ! existing potential to be used as the starting point of the iterative ! procedure. These parameters are also used for inverting the Kohn-Sham ! equations as required by the self-consistent density $GW$ method. See ! {\tt maxitoep}. ! ! \block{taufsm}{ ! {\tt taufsm} & the step size to be used when finding the effective magnetic ! field in fixed spin moment calculations & real & $0.01$} ! An effective magnetic field, ${\bf B}_{\rm FSM}$, is required for fixing the ! spin moment to a given value, ${\bf M}_{\rm FSM}$. This is found by adding a ! vector to the field which is proportional to the difference between the ! moment calculated in the $i$th self-consistent loop and the required moment: ! $$ {\bf B}_{\rm FSM}^{i+1}={\bf B}_{\rm FSM}^i+\lambda\left({\bf M}^i ! -{\bf M}_{\rm FSM}\right), $$ ! where $\lambda$ is proportional to {\tt taufsm}. See also {\tt fsmtype}, ! {\tt momfix} and {\tt spinpol}. ! ! \block{tempk}{ ! {\tt tempk} & temperature $T$ of the electronic system in kelvin & real & -} ! Assigning a value to this variable sets {\tt stype} to 3 (Fermi-Dirac) and ! the smearing width to $k_{\rm B}T$. ! ! \block{tforce}{ ! {\tt tforce} & set to {\tt .true.} if the force should be calculated at the ! end of the self-consistent cycle & logical & {\tt .false.}} ! This variable is automatically set to {\tt .true.} when performing geometry ! optimisation. ! ! \block{tefvit}{ ! {\tt tefvit} & set to {\tt .true.} if the first-variational eigenvalue ! equation should be solved iteratively & logical & {\tt .false.}} ! ! \block{tefvr}{ ! {\tt tefvr} & set to {\tt .true.} if a real symmetric eigenvalue solver ! should be used for crystals which have inversion symmetry & logical & ! {\tt .true.}} ! For crystals with inversion symmetry, the first-variational Hamiltonian and ! overlap matrices can be made real by using appropriate transformations. In ! this case, a real symmetric (instead of complex Hermitian) eigenvalue solver ! can be used. This makes the calculation about three times faster. ! ! \block{tmomfix}{ ! {\tt ntmfix} & number of tensor moments (TM) to be fixed & integer & 0 \\ ! \hline ! {\tt is(i)} & species number for entry $i$ & integer & - \\ ! {\tt ia(i)} & atom number & integer & - \\ ! {\tt (l, n)(i)} & $l$ and $n$ indices of TM & integer & - \\ ! \hline ! {\tt (k, p, x, y)(i)} or & & & \\ ! {\tt (k, p, r, t)(i)} & indices for the 2-index or 3-index TM, ! respectively & integer & - \\ ! \hline ! {\tt z(i)} & complex TM value & complex & - \\ ! \hline ! {\tt p(i)} & parity of spatial rotation & integer & - \\ ! {\tt aspl(i)} & Euler angles of spatial rotation & real(3) & - \\ ! {\tt aspn(i)} & Euler angles of spin rotation & real(3) & - } ! This block sets up the fixed tensor moment (FTM). There should be as many ! TM entries as {\tt ntmfix}. See {\it Phys. Rev. Lett.} {\bf 103}, 107202 ! (2009) for the tensor moment indexing convention. This is a highly ! complicated feature of the code, and should only be attempted with a full ! understanding of tensor moments. ! ! \block{tmwrite}{ ! {\tt tmwrite} & set to {\tt .true.} if the tensor moments and the ! corresponding decomposition of DFT+$U$ energy should be calculated ! at every loop of the self-consistent cycle & logical & {\tt .false.}} ! This variable is useful to check the convergence of the tensor moments in ! DFT+$U$ caculations. Alternatively, with {\tt task} equal to 400, one can ! calculate the tensor moments and corresponding DFT+$U$ energy contributions ! from a given density matrix and set of Slater parameters at the end of the ! self-consistent cycle. ! ! \block{tsediag}{ ! {\tt tsediag} & set to {\tt .true.} if the self-energy matrix should be ! treated as diagonal & logical & {\tt .true.}} ! When this variable is {\tt .true.}, the self-energy used in a $GW$ ! calculation $\Sigma_{ij}({\bf k},\omega)$ is taken to be diagonal in the ! Kohn-Sham state indices $i$ and $j$. When {\tt tsediag} is {\tt .false.}, ! the entire matrix is used. See also {\tt twdiag}. ! ! \block{tshift}{ ! {\tt tshift} & set to {\tt .true.} if the crystal can be shifted so that the ! atom closest to the origin is exactly at the origin & ! logical & {\tt .true.}} ! ! \block{tstime}{ ! {\tt tstime} & total simulation time of time evolution run & real & ! $1000.0$} ! See also {\tt dtimes}. ! ! \block{twdiag}{ ! {\tt twdiag} & set to {\tt .true.} if the screened interaction matrix should ! be treated as diagonal & logical & {\tt .false.}} ! When this variable is {\tt .true.}, the screened interaction used in a $GW$ ! calculation $W({\bf G},{\bf G}',{\bf q},\omega)$ is taken to be diagonal in ! the plane wave indices ${\bf G}$ and ${\bf G}'$. See also {\tt tsediag}. ! ! \block{vhmat}{ ! {\tt vhmat(1)} & matrix row 1 & real(3) & $(1.0,0.0,0.0)$ \\ ! \hline ! {\tt vhmat(2)} & matrix row 2 & real(3) & $(0.0,1.0,0.0)$ \\ ! \hline ! {\tt vhmat(3)} & matrix row 3 & real(3) & $(0.0,0.0,1.0)$} ! This is the transformation matrix $M$ applied to every vector $\bf H$ in the ! structure factor output files {\tt SFACRHO.OUT} and {\tt SFACMAG.OUT}. It is ! stored in the usual row-column setting and applied directly as ! ${\bf H}'=M{\bf H}$ to every vector but {\em only} when writing the output ! files. See also {\tt hmaxvr} and {\tt reduceh}. ! ! \block{vhighq}{ ! {\tt vhighq} & {\tt .true.} if a very high quality parameter set should be ! used & logical & {\tt .false.}} ! Setting this to {\tt .true.} results in some default parameters being ! changed to ensure excellent convergence in most situations. See also ! {\tt highq}. ! ! \block{vklem}{ ! {\tt vklem} & the $k$-point in lattice coordinates at which to compute the ! effective mass tensors & real(3) & $(0.0,0.0,0.0)$} ! See {\tt deltaem} and {\tt ndspem}. ! ! \block{vkloff}{ ! {\tt vkloff } & the $k$-point offset vector in lattice coordinates & ! real(3) & $(0.0,0.0,0.0)$} ! See {\tt ngridk}. ! ! \block{vqlss}{ ! {\tt vqlss} & the ${\bf q}$-vector of the spin-spiral state in lattice ! coordinates & real(3) & $(0.0,0.0,0.0)$} ! Spin-spirals arise from spinor states assumed to be of the form ! $$ \Psi^{\bf q}_{\bf k}({\bf r})= ! \left( \begin{array}{c} ! U^{{\bf q}\uparrow}_{\bf k}({\bf r})e^{i({\bf k+q/2})\cdot{\bf r}} \\ ! U^{{\bf q}\downarrow}_{\bf k}({\bf r})e^{i({\bf k-q/2})\cdot{\bf r}} \\ ! \end{array} \right). $$ ! These are determined using a second-variational approach, and give rise to a ! magnetisation density of the form ! $$ {\bf m}^{\bf q}({\bf r})=(m_x({\bf r})\cos({\bf q \cdot r}), ! m_y({\bf r})\sin({\bf q \cdot r}),m_z({\bf r})), $$ ! where $m_x$, $m_y$ and $m_z$ are lattice periodic. See also {\tt spinsprl}. ! ! \block{wmaxgw}{ ! {\tt wmaxgw} & maximum Matsubara frequency for $GW$ calculations & real & ! $-5.0$} ! This defines the cut-off of the Matsubara frequencies on the imaginary ! axis for calculating the $GW$ self-energy and solving the Dyson equation. ! If this number is negative then the cut-off is taken to be ! $|{\tt wmaxgw}|\times\Delta\epsilon$, where $\Delta\epsilon$ is the ! difference between the largest and smallest Kohn-Sham valence eigenvalues. ! ! \block{wplot}{ ! {\tt nwplot} & number of frequency/energy points in the DOS or optics plot & ! integer & $500$ \\ ! {\tt ngrkf} & fine $k$-point grid size used for integrating functions in the ! Brillouin zone & integer & $100$ \\ ! {\tt nswplot} & level of smoothing applied to DOS/optics output & integer & ! $1$ \\ ! \hline ! {\tt wplot} & frequency/energy window for the DOS or optics plot & real(2) & ! $(-0.5,0.5)$} ! DOS and optics plots require integrals of the kind ! $$ g(\omega_i)=\frac{\Omega}{(2\pi)^3}\int_{\rm BZ} f({\bf k}) ! \delta(\omega_i-e({\bf k}))d{\bf k}. $$ ! These are calculated by first interpolating the functions $e({\bf k})$ and ! $f({\bf k})$ with the trilinear method on a much finer mesh whose size is ! determined by {\tt ngrkf}. Then the $\omega$-dependent histogram of the ! integrand is accumulated over the fine mesh. If the output function is noisy ! then either {\tt ngrkf} should be increased or {\tt nwplot} decreased. ! Alternatively, the output function can be artificially smoothed up to a ! level given by {\tt nswplot}. This is the number of successive 3-point ! averages to be applied to the function $g$. ! ! \block{wsfac}{ ! {\tt wsfac} & energy window to be used when calculating density or magnetic ! structure factors & real(2) & $(-10^6,10^6)$} ! Only those states with eigenvalues within this window will contribute to the ! density or magnetisation. See also {\tt hmaxvr} and {\tt vhmat}. ! ! \block{xctype}{ ! {\tt xctype} & integers defining the type of exchange-correlation functional ! to be used & integer(3) & $(3,0,0)$} ! Normally only the first value is used to define the functional type. The ! other value may be used for external libraries. Currently implemented are: ! \vskip 6pt ! \begin{tabularx}{\textwidth}[h]{lX} ! $-n$ & Exact-exchange optimised effective potential (EXX-OEP) method with ! correlation energy and potential given by functional number $n$ \\ ! 1 & No exchange-correlation funtional ($E_{\rm xc}\equiv 0$) \\ ! 2 & LDA, Perdew-Zunger/Ceperley-Alder, {\it Phys. Rev. B} {\bf 23}, 5048 ! (1981) \\ ! 3 & LSDA, Perdew-Wang/Ceperley-Alder, {\it Phys. Rev. B} {\bf 45}, 13244 ! (1992) \\ ! 4 & LDA, X-alpha approximation, J. C. Slater, {\it Phys. Rev.} {\bf 81}, 385 ! (1951) \\ ! 5 & LSDA, von Barth-Hedin, {\it J. Phys. C} {\bf 5}, 1629 (1972) \\ ! 20 & GGA, Perdew-Burke-Ernzerhof, {\it Phys. Rev. Lett.} {\bf 77}, 3865 ! (1996) \\ ! 21 & GGA, Revised PBE, Zhang-Yang, {\it Phys. Rev. Lett.} {\bf 80}, 890 ! (1998) \\ ! 22 & GGA, PBEsol, Phys. Rev. Lett. 100, 136406 (2008) \\ ! 26 & GGA, Wu-Cohen exchange (WC06) with PBE correlation, {\it Phys. Rev. B} ! {\bf 73}, 235116 (2006) \\ ! 30 & GGA, Armiento-Mattsson (AM05) spin-unpolarised functional, ! {\it Phys. Rev. B} {\bf 72}, 085108 (2005) \\ ! 100 & Libxc functionals; the second and third values of {\tt xctype} define ! the exchange and correlation functionals in the Libxc library, ! respectively \\ ! \end{tabularx} ! ! \section{Contributing to Elk} ! Please bear in mind when writing code for the Elk project that it should be ! an exercise in physics and not software engineering. All code should ! therefore be kept as simple and concise as possible, and above all it should ! be easy for anyone to locate and follow the Fortran representation of the ! original mathematics. We would also appreciate the following conventions ! being adhered to: ! \begin{itemize} ! \item Strict Fortran 2003 should be used. Features which are marked as ! obsolescent in Fortran 2003 should be avoided. These include assigned ! format specifiers, labeled do-loops, computed goto statements and statement ! functions. ! \item Modules should be used in place of common blocks for declaring ! global variables. Use the existing modules to declare new global variables. ! \item Any code should be written in lower-case free form style, starting ! from column one. Try and keep the length of each line to fewer than 80 ! characters using the \& character for line continuation. ! \item Every function or subroutine, no matter how small, should be in its ! own file named {\tt routine.f90}, where {\tt routine} is the function or ! subroutine name. It is recommended that the routines are named so as to ! make their purpose apparent from the name alone. ! \item Use of {\tt implicit none} is mandatory. Remember also to define the ! {\tt intent} of any passed arguments. ! \item Local allocatable arrays must be deallocated on exit of the routine to ! prevent memory leakage. Use of automatic arrays should be limited to arrays ! of small size. ! \item Every function or subroutine must be documented with the Protex source ! code documentation system. This should include a short \LaTeX\ description ! of the algorithms and methods involved. Equations which need to be ! referenced should be labeled with {\tt routine\_1}, {\tt routine\_2}, etc. ! The authorship of each new piece of code or modification should be ! indicated in the {\tt REVISION HISTORY} part of the header. See the Protex ! documentation for details. ! \item Ensure as much as possible that a routine will terminate the program ! when given improper input instead of continuing with erroneous results. ! Specifically, functions should have a well-defined domain for which they ! return accurate results. Input outside that domain should result in an ! error message and termination. ! \item Report errors prior to termination with a short description, for ! example: ! \begin{verbatim} ! write(*,*) ! write(*,'("Error(readinput): natoms <= 0 : ",I8)') natoms(is) ! write(*,'(" for species ",I4)') is ! write(*,*) ! stop ! \end{verbatim} ! \item Wherever possible, real numbers outputted as ASCII data should be ! formatted with the {\tt G18.10} specifier. ! \item Avoid redundant or repeated code: check to see if the routine you need ! already exists, before writing a new one. ! \item All reading in of ASCII data should be done in the subroutine ! {\tt readinput}. For binary data, separate routines for reading and writing ! should be used (for example {\tt writestate} and {\tt readstate}). ! \item Input filenames should be in lowercase and have the extension ! {\tt .in} . All output filenames should be in uppercase with the extension ! {\tt .OUT} . ! \item All internal units should be atomic. Input and output units should be ! atomic by default and clearly stated otherwise. Rydbergs should not be used ! under any circumstances. ! \end{itemize} ! \subsection{Licensing} ! Routines which constitute the main part of the code are released under the ! GNU General Public License (GPL). Library routines are released under the ! less restrictive GNU Lesser General Public License (LGPL). Both licenses ! are contained in the file {\tt COPYING}. Any contribution to the code must ! be licensed at the authors' discretion under either the GPL or LGPL. ! Author(s) of the code retain the copyrights. Copyright and (L)GPL ! information must be included at the beginning of every file, and no code ! will be accepted without this. ! !EOI elk-7.2.42/src/PaxHeaders.21776/olpistl.f900000644000000000000000000000013214061636516014731 xustar0030 mtime=1623670094.883102522 30 atime=1623670093.602103711 30 ctime=1623670094.883102522 elk-7.2.42/src/olpistl.f900000644002504400250440000000237514061636516016775 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: olpistl ! !INTERFACE: pure subroutine olpistl(ngp,igpig,ld,o) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ngp : number of G+p-vectors (in,integer) ! igpig : index from G+p-vectors to G-vectors (in,integer(ngkmax)) ! ld : leading dimension of o (in,integer) ! o : overlap matrix (inout,complex(*)) ! !DESCRIPTION: ! Computes the interstitial contribution to the overlap matrix for the APW ! basis functions. The overlap is given by ! $$ O^{\rm I}({\bf G+k,G'+k})=\tilde{\Theta}({\bf G-G'}), $$ ! where $\tilde{\Theta}$ is the characteristic function. See routine ! {\tt gencfun}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: ngp,igpig(ngkmax) integer, intent(in) :: ld complex(8), intent(inout) :: o(ld,*) ! local variables integer ig,j1,j2,j3,i,j do j=1,ngp ig=igpig(j) j1=ivg(1,ig); j2=ivg(2,ig); j3=ivg(3,ig) do i=1,j ig=igpig(i) ig=ivgig(ivg(1,ig)-j1,ivg(2,ig)-j2,ivg(3,ig)-j3) o(i,j)=o(i,j)+cfunig(ig) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/hmlistl.f900000644000000000000000000000013114061636516014716 xustar0030 mtime=1623670094.884102521 29 atime=1623670093.60310371 30 ctime=1623670094.884102521 elk-7.2.42/src/hmlistl.f900000644002504400250440000000316314061636516016757 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: hmlistl ! !INTERFACE: pure subroutine hmlistl(ngp,igpig,vgpc,ld,h) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ngp : number of G+p-vectors (in,integer) ! igpig : index from G+p-vectors to G-vectors (in,integer(ngkmax)) ! vgpc : G+p-vectors in Cartesian coordinates (in,real(3,ngkmax)) ! ld : leading dimension of h (in,integer) ! h : Hamiltonian matrix (inout,complex(*)) ! !DESCRIPTION: ! Computes the interstitial contribution to the Hamiltonian matrix for the APW ! basis functions. The Hamiltonian is given by ! $$ H^{\rm I}({\bf G+k,G'+k})=\frac{1}{2}({\bf G+k})\cdot({\bf G'+k}) ! \tilde{\Theta}({\bf G-G'})+V_s({\bf G-G'}), $$ ! where $V_s$ is the interstitial Kohn-Sham potential and $\tilde{\Theta}$ is ! the characteristic function. See routine {\tt gencfun}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: ngp,igpig(ngkmax) real(8), intent(in) :: vgpc(3,ngkmax) integer, intent(in) :: ld complex(8), intent(inout) :: h(ld,*) ! local variables integer ig,j1,j2,j3,i,j real(8) v1,v2,v3,t1 do j=1,ngp ig=igpig(j) j1=ivg(1,ig); j2=ivg(2,ig); j3=ivg(3,ig) v1=0.5d0*vgpc(1,j); v2=0.5d0*vgpc(2,j); v3=0.5d0*vgpc(3,j) do i=1,j ig=igpig(i) ig=ivgig(ivg(1,ig)-j1,ivg(2,ig)-j2,ivg(3,ig)-j3) t1=vgpc(1,i)*v1+vgpc(2,i)*v2+vgpc(3,i)*v3 h(i,j)=h(i,j)+vsig(ig)+t1*cfunig(ig) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/olpalo.f900000644000000000000000000000013014061636516014527 xustar0029 mtime=1623670094.88510252 30 atime=1623670093.605103708 29 ctime=1623670094.88510252 elk-7.2.42/src/olpalo.f900000644002504400250440000000136314061636516016571 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine olpalo(is,ias,ngp,apwalm,ld,o) use modmain implicit none ! arguments integer, intent(in) :: is,ias,ngp complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: o(ld,*) ! local variables integer ilo,io,l,lm,i,j real(8) t1 do ilo=1,nlorb(is) l=lorbl(ilo,is) do lm=l**2+1,(l+1)**2 j=ngp+idxlo(lm,ilo,ias) do io=1,apword(l,is) t1=oalo(io,ilo,ias) do i=1,ngp o(i,j)=o(i,j)+t1*conjg(apwalm(i,io,lm)) end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlalo.f900000644000000000000000000000013214061636516014517 xustar0030 mtime=1623670094.887102518 30 atime=1623670093.607103706 30 ctime=1623670094.887102518 elk-7.2.42/src/hmlalo.f900000644002504400250440000000237214061636516016560 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine hmlalo(is,ias,ngp,apwalm,ld,h) use modmain implicit none ! arguments integer, intent(in) :: is,ias,ngp complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: h(ld,*) ! local variables integer io,ilo,i,j integer l1,l2,l3 integer lm1,lm2,lm3 complex(8) z1 do ilo=1,nlorb(is) l1=lorbl(ilo,is) do lm1=l1**2+1,(l1+1)**2 j=ngp+idxlo(lm1,ilo,ias) do l3=0,lmaxapw do lm3=l3**2+1,(l3+1)**2 do io=1,apword(l3,is) z1=0.d0 do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyry(lm2,lm3,lm1)*hloa(lm2,io,l3,ilo,ias) end do end if end do ! note that what is actually computed is the Hermitian conjugate of if (abs(dble(z1))+abs(aimag(z1)).gt.1.d-14) then do i=1,ngp h(i,j)=h(i,j)+conjg(z1*apwalm(i,io,lm3)) end do end if end do end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/olplolo.f900000644000000000000000000000013214061636516014723 xustar0030 mtime=1623670094.888102517 30 atime=1623670093.608103705 30 ctime=1623670094.888102517 elk-7.2.42/src/olplolo.f900000644002504400250440000000125714061636516016765 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine olplolo(is,ias,ngp,ld,o) use modmain implicit none ! arguments integer, intent(in) :: is,ias,ngp,ld complex(8), intent(inout) :: o(ld,*) ! local variables integer ilo,jlo,l,lm,i,j do ilo=1,nlorb(is) l=lorbl(ilo,is) do jlo=1,nlorb(is) if (lorbl(jlo,is).eq.l) then do lm=l**2+1,(l+1)**2 i=ngp+idxlo(lm,ilo,ias) j=ngp+idxlo(lm,jlo,ias) if (i.le.j) o(i,j)=o(i,j)+ololo(ilo,jlo,ias) end do end if end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/hmllolo.f900000644000000000000000000000013214061636516014711 xustar0030 mtime=1623670094.890102515 30 atime=1623670093.610103703 30 ctime=1623670094.890102515 elk-7.2.42/src/hmllolo.f900000644002504400250440000000172614061636516016754 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine hmllolo(is,ias,ngp,ld,h) use modmain implicit none ! arguments integer, intent(in) :: is,ias,ngp,ld complex(8), intent(inout) :: h(ld,*) ! local variables integer ilo,jlo,i,j integer l1,l2,l3 integer lm1,lm2,lm3 complex(8) z1 do jlo=1,nlorb(is) l3=lorbl(jlo,is) do lm3=l3**2+1,(l3+1)**2 j=ngp+idxlo(lm3,jlo,ias) do ilo=1,nlorb(is) l1=lorbl(ilo,is) do lm1=l1**2+1,(l1+1)**2 i=ngp+idxlo(lm1,ilo,ias) if (i.gt.j) cycle z1=0.d0 do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyry(lm2,lm3,lm1)*hlolo(lm2,jlo,ilo,ias) end do end if end do h(i,j)=h(i,j)+z1 end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/olpaa.f900000644000000000000000000000013214061636516014337 xustar0030 mtime=1623670094.891102514 30 atime=1623670093.612103701 30 ctime=1623670094.891102514 elk-7.2.42/src/olpaa.f900000644002504400250440000000134414061636516016376 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine olpaa(tor,is,ngp,apwalm,ld,o) use modmain implicit none ! arguments logical, intent(in) :: tor integer, intent(in) :: is,ngp complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: o(*) ! local variables integer io,l,lm,i ! automatic arrays complex(8) a(lmoapw(is),ngp) i=0 do l=0,lmaxapw do lm=l**2+1,(l+1)**2 do io=1,apword(l,is) i=i+1 a(i,1:ngp)=apwalm(1:ngp,io,lm) end do end do end do call zmctmu(tor,lmoapw(is),ngp,a,a,ld,o) end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlaa.f900000644000000000000000000000013014061636516014323 xustar0030 mtime=1623670094.893102512 28 atime=1623670093.6131037 30 ctime=1623670094.893102512 elk-7.2.42/src/hmlaa.f900000644002504400250440000000426014061636516016364 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: hmlaa ! !INTERFACE: subroutine hmlaa(thr,is,ias,ngp,apwalm,ld,h) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! thr : .true. if the matrix h is real valued (in,logical) ! is : species number (in,integer) ! ias : joint atom and species number (in,integer) ! ngp : number of G+p-vectors (in,integer) ! apwalm : APW matching coefficients (in,complex(ngkmax,apwordmax,lmmaxapw)) ! ld : leading dimension of h (in,integer) ! h : Hamiltonian matrix (inout,complex(*)) ! !DESCRIPTION: ! Calculates the APW-APW contribution to the Hamiltonian matrix. ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! arguments logical, intent(in) :: thr integer, intent(in) :: is,ias,ngp complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: h(*) ! local variables integer lmo,io,jo,i integer l1,l2,l3 integer lm1,lm2,lm3 real(8) t0 complex(8) z1 ! automatic arrays complex(8) a(lmoapw(is),ngp),b(lmoapw(is),ngp) lmo=lmoapw(is) t0=0.5d0*rmt(is)**2 i=0 do l1=0,lmaxapw do lm1=l1**2+1,(l1+1)**2 do io=1,apword(l1,is) i=i+1 b(i,:)=0.d0 do l3=0,lmaxapw do lm3=l3**2+1,(l3+1)**2 do jo=1,apword(l3,is) z1=0.d0 ! kinetic and potential contribution do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyry(lm2,lm3,lm1)*haa(lm2,jo,l3,io,l1,ias) end do end if end do ! kinetic surface contribution if (lm1.eq.lm3) then z1=z1+t0*apwfr(nrmt(is),1,io,l1,ias)*apwdfr(jo,l1,ias) end if if (abs(dble(z1))+abs(aimag(z1)).gt.1.d-14) then call zaxpy(ngp,z1,apwalm(:,jo,lm3),1,b(i,1),lmo) end if end do end do end do a(i,1:ngp)=apwalm(1:ngp,io,lm1) end do end do end do call zmctmu(thr,lmo,ngp,a,b,ld,h) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gengclg.f900000644000000000000000000000013214061636516014651 xustar0030 mtime=1623670094.894102511 30 atime=1623670093.615103699 30 ctime=1623670094.894102511 elk-7.2.42/src/gengclg.f900000644002504400250440000000057314061636516016713 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gengclg use modmain implicit none ! local variables if (allocated(gclg)) deallocate(gclg) allocate(gclg(ngvec)) gclg(1)=0.d0 gclg(2:ngvec)=fourpi/gc(2:ngvec)**2 end subroutine elk-7.2.42/src/PaxHeaders.21776/rhomagsh.f900000644000000000000000000000013014061636516015051 xustar0029 mtime=1623670094.89610251 30 atime=1623670093.617103697 29 ctime=1623670094.89610251 elk-7.2.42/src/rhomagsh.f900000644002504400250440000000235714061636516017117 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rhomagsh ! !INTERFACE: subroutine rhomagsh ! !USES: use modmain use modomp ! !DESCRIPTION: ! Converts the muffin-tin density and magnetisation from spherical coordinates ! to a spherical harmonic expansion. See {\tt rhomagk}. ! ! !REVISION HISTORY: ! Created January 2009 (JKD) !EOP !BOC implicit none ! local variables integer idm,is,ias integer npc,nthd ! automatic arrays real(8) rfmt(npcmtmax) call holdthd(natmtot,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(rfmt,is,npc,idm) & !$OMP NUM_THREADS(nthd) !$OMP DO do ias=1,natmtot is=idxis(ias) npc=npcmt(is) ! convert the density to spherical harmonics rfmt(1:npc)=rhomt(1:npc,ias) call rfsht(nrcmt(is),nrcmti(is),rfmt,rhomt(:,ias)) end do !$OMP END DO NOWAIT do idm=1,ndmag !$OMP DO do ias=1,natmtot is=idxis(ias) npc=npcmt(is) ! convert the magnetisation to spherical harmonics rfmt(1:npc)=magmt(1:npc,ias,idm) call rfsht(nrcmt(is),nrcmti(is),rfmt,magmt(:,ias,idm)) end do !$OMP END DO end do !$OMP END PARALLEL call freethd(nthd) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/charge.f900000644000000000000000000000013214061636516014474 xustar0030 mtime=1623670094.897102509 30 atime=1623670093.618103696 30 ctime=1623670094.897102509 elk-7.2.42/src/charge.f900000644002504400250440000000201114061636516016523 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: charge ! !INTERFACE: subroutine charge ! !USES: use modmain use modtest ! !DESCRIPTION: ! Computes the muffin-tin, interstitial and total charges by integrating the ! density. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! local variables integer is,ias real(8) t1 ! external functions real(8), external :: rfmtint ! find the muffin-tin charges chgmttot=0.d0 do ias=1,natmtot is=idxis(ias) chgmt(ias)=rfmtint(nrmt(is),nrmti(is),wrmt(:,is),rhomt(:,ias)) chgmttot=chgmttot+chgmt(ias) end do ! find the interstitial charge t1=dot_product(rhoir(1:ngtot),cfunir(1:ngtot)) chgir=t1*omega/dble(ngtot) ! total calculated charge chgcalc=chgmttot+chgir ! write total calculated charge to test file call writetest(400,'calculated total charge',tol=1.d-6,rv=chgcalc) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/moment.f900000644000000000000000000000013214061636516014542 xustar0030 mtime=1623670094.899102507 30 atime=1623670093.620103694 30 ctime=1623670094.899102507 elk-7.2.42/src/moment.f900000644002504400250440000000253714061636516016606 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: moment ! !INTERFACE: subroutine moment ! !USES: use modmain use modtest ! !DESCRIPTION: ! Computes the muffin-tin, interstitial and total moments by integrating the ! magnetisation. ! ! !REVISION HISTORY: ! Created January 2005 (JKD) !EOP !BOC implicit none ! local variables integer idm,is,ias real(8) t1 ! external functions real(8), external :: rfmtint if (.not.spinpol) then mommt(:,:)=0.d0 mommttot(:)=0.d0 momir(:)=0.d0 momtot(:)=0.d0 momtotm=0.d0 return end if ! find the muffin-tin moments mommttot(:)=0.d0 do idm=1,ndmag do ias=1,natmtot is=idxis(ias) mommt(idm,ias)=rfmtint(nrmt(is),nrmti(is),wrmt(:,is),magmt(:,ias,idm)) mommttot(idm)=mommttot(idm)+mommt(idm,ias) end do end do ! find the interstitial moments do idm=1,ndmag t1=dot_product(magir(1:ngtot,idm),cfunir(1:ngtot)) momir(idm)=t1*omega/dble(ngtot) end do momtot(:)=mommttot(:)+momir(:) ! total moment magnitude if (ncmag) then momtotm=sqrt(momtot(1)**2+momtot(2)**2+momtot(3)**2) else momtotm=abs(momtot(1)) end if ! write total moment magnitude to test file call writetest(450,'total moment magnitude',tol=1.d-3,rv=momtotm) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rfint0.f900000644000000000000000000000013214061636516014445 xustar0030 mtime=1623670094.900102506 30 atime=1623670093.622103692 30 ctime=1623670094.900102506 elk-7.2.42/src/rfint0.f900000644002504400250440000000136714061636516016511 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rfint0(rf0,rfmt,rfir) use modmain implicit none ! arguments real(8), intent(in) :: rf0 real(8), intent(inout) :: rfmt(npmtmax,natmtot),rfir(ngtot) ! local variables integer is,ias integer nr,nri,ir,i real(8) t1 ! external functions real(8), external :: rfint t1=rfint(rfmt,rfir) t1=rf0-t1/omega rfir(:)=rfir(:)+t1 t1=t1/y00 do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) i=1 do ir=1,nri rfmt(i,ias)=rfmt(i,ias)+t1 i=i+lmmaxi end do do ir=nri+1,nr rfmt(i,ias)=rfmt(i,ias)+t1 i=i+lmmaxo end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/potnucl.f900000644000000000000000000000013214061636516014727 xustar0030 mtime=1623670094.902102504 30 atime=1623670093.623103691 30 ctime=1623670094.902102504 elk-7.2.42/src/potnucl.f900000644002504400250440000000313214061636516016763 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: potnucl ! !INTERFACE: subroutine potnucl(ptnucl,nr,r,zn,vn) ! !INPUT/OUTPUT PARAMETERS: ! ptnucl : .true. if the nucleus is a point charge (in,logical) ! nr : number of radial mesh points (in,integer) ! r : radial mesh (in,real(nr)) ! zn : nuclear charge (in,real) ! vn : potential on radial mesh (out,real(nr)) ! !DESCRIPTION: ! Computes the nuclear Coulomb potential on a radial mesh. The nuclear radius ! $R$ is estimated from the nuclear charge $Z$ and the potential is given by ! $$ V(r)=\begin{cases} ! Z(3R^2-r^2)/2R^3 & r nstrain : ",2I8)') i,nstrain write(*,*) stop end if strain(:,:,1)=strain(:,:,i) nstrain=1 end if end if end subroutine elk-7.2.42/src/PaxHeaders.21776/symmetry.f900000644000000000000000000000013214061636517015135 xustar0030 mtime=1623670095.012102402 30 atime=1623670093.744103579 30 ctime=1623670095.012102402 elk-7.2.42/src/symmetry.f900000644002504400250440000000204514061636517017173 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine symmetry use modmain use modvars implicit none ! inverse of the lattice vector matrix call r3minv(avec,ainv) ! find Bravais lattice symmetries call findsymlat ! use only the identity if required if (symtype.eq.0) nsymlat=1 ! find the crystal symmetries and shift atomic positions if required call findsymcrys ! find the site symmetries call findsymsite ! check if fixed spin moments are invariant under the symmetry group call checkfsm ! check if real symmetric first-variational eigen solver can be used if (.not.tsyminv) tefvr=.false. ! write to VARIABLES.OUT call writevars('nsymlat',iv=nsymlat) call writevars('symlat',nv=9*nsymlat,iva=symlat) call writevars('nsymcrys',iv=nsymcrys) call writevars('vtlsymc',nv=3*nsymcrys,rva=vtlsymc) call writevars('lsplsymc',nv=nsymcrys,iva=lsplsymc) call writevars('lspnsymc',nv=nsymcrys,iva=lspnsymc) end subroutine elk-7.2.42/src/PaxHeaders.21776/linengy.f900000644000000000000000000000013214061636517014711 xustar0030 mtime=1623670095.013102401 30 atime=1623670093.746103577 30 ctime=1623670095.013102401 elk-7.2.42/src/linengy.f900000644002504400250440000000671214061636517016754 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: linengy ! !INTERFACE: subroutine linengy ! !USES: use modmain use modmpi ! !DESCRIPTION: ! Calculates the new linearisation energies for both the APW and local-orbital ! radial functions. See the routine {\tt findband}. ! ! !REVISION HISTORY: ! Created May 2003 (JKD) !EOP !BOC implicit none ! local variables logical fnd integer is,ia,ja,ias,jas integer nr,nri,iro,ir,l,i integer ilo,io,jo,nnf ! automatic arrays logical done(natmmax) real(8) vr(nrmtmax) nnf=0 ! begin loops over atoms and species do is=1,nspecies nr=nrmt(is) nri=nrmti(is) iro=nri+1 done(:)=.false. do ia=1,natoms(is) if (done(ia)) cycle ias=idxas(ia,is) i=1 do ir=1,nri vr(ir)=vsmt(i,ias)*y00 i=i+lmmaxi end do do ir=iro,nr vr(ir)=vsmt(i,ias)*y00 i=i+lmmaxo end do !-----------------------! ! APW functions ! !-----------------------! do l=0,lmaxapw do io=1,apword(l,is) if (apwve(io,l,is)) then ! check if previous radial functions have same default energies do jo=1,io-1 if (apwve(jo,l,is)) then if (abs(apwe0(io,l,is)-apwe0(jo,l,is)).lt.1.d-4) then apwe(io,l,ias)=apwe(jo,l,ias) goto 10 end if end if end do ! find the band energy starting from default apwe(io,l,ias)=apwe0(io,l,is) call findband(solsc,l,nr,rlmt(:,1,is),vr,epsband,demaxbnd, & apwe(io,l,ias),fnd) if (.not.fnd) nnf=nnf+1 else ! set linearisation energy automatically if (autolinengy) apwe(io,l,ias)=efermi+dlefe end if 10 continue end do end do !---------------------------------! ! local-orbital functions ! !---------------------------------! do ilo=1,nlorb(is) do io=1,lorbord(ilo,is) if (lorbve(io,ilo,is)) then ! check if previous radial functions have same default energies do jo=1,io-1 if (lorbve(jo,ilo,is)) then if (abs(lorbe0(io,ilo,is)-lorbe0(jo,ilo,is)).lt.1.d-4) then lorbe(io,ilo,ias)=lorbe(jo,ilo,ias) goto 20 end if end if end do l=lorbl(ilo,is) ! find the band energy starting from default lorbe(io,ilo,ias)=lorbe0(io,ilo,is) call findband(solsc,l,nr,rlmt(:,1,is),vr,epsband,demaxbnd, & lorbe(io,ilo,ias),fnd) if (.not.fnd) nnf=nnf+1 else ! set linearisation energy automatically if (autolinengy) lorbe(io,ilo,ias)=efermi+dlefe end if 20 continue end do end do done(ia)=.true. ! copy to equivalent atoms do ja=1,natoms(is) if ((.not.done(ja)).and.(eqatoms(ia,ja,is))) then jas=idxas(ja,is) do l=0,lmaxapw do io=1,apword(l,is) apwe(io,l,jas)=apwe(io,l,ias) end do end do do ilo=1,nlorb(is) do io=1,lorbord(ilo,is) lorbe(io,ilo,jas)=lorbe(io,ilo,ias) end do end do done(ja)=.true. end if end do ! end loops over atoms and species end do end do if (mp_mpi.and.(nnf.gt.0)) then write(*,*) write(*,'("Warning(linengy): could not find ",I3," linearisation energies & &in s.c. loop ",I5)') nnf,iscl end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writestress.f900000644000000000000000000000013214061636517015642 xustar0030 mtime=1623670095.015102399 30 atime=1623670093.748103575 30 ctime=1623670095.015102399 elk-7.2.42/src/writestress.f900000644002504400250440000000245214061636517017702 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writestress use modmain use modmpi use modtest implicit none ! local variables integer i,j,k ! initialise universal variables call init0 ! start from the atomic densities trdstate=.false. ! generate the stress tensors call genstress ! write the stress tensors to file if (mp_mpi) then open(50,file='STRESS.OUT',form='FORMATTED',action='WRITE') write(50,*) write(50,'("Lattice vector matrix, A, changed by")') write(50,*) write(50,'(" A --> A + e_i dt,")') write(50,*) write(50,'("where dt is an infinitesimal scalar and e_i is a strain tensor")') write(50,*) write(50,'("Stress is given by the derivative of the total energy dE/dt")') do k=1,nstrain write(50,*) write(50,'("Strain tensor : ",I1)') k do j=1,3 write(50,'(3G18.10)') (strain(i,j,k),i=1,3) end do write(50,'("Stress : ",G18.10)') stress(k) end do close(50) write(*,*) write(*,'("Info(writestress):")') write(*,'(" Stress tensor components written to STRESS.OUT")') end if ! write test file if required call writetest(440,'Stress tensor components',nv=nstrain,tol=1.d-2,rva=stress) end subroutine elk-7.2.42/src/PaxHeaders.21776/eulerrot.f900000644000000000000000000000013214061636517015105 xustar0030 mtime=1623670095.016102398 30 atime=1623670093.749103574 30 ctime=1623670095.016102398 elk-7.2.42/src/eulerrot.f900000644002504400250440000000215714061636517017147 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: eulerrot ! !INTERFACE: pure subroutine eulerrot(ang,rot) ! !INPUT/OUTPUT PARAMETERS: ! ang : Euler angles (alpha, beta, gamma) (in,real(3)) ! rot : rotation matrix (out,real(3,3)) ! !DESCRIPTION: ! Given a set of Euler angles, $(\alpha,\beta,\gamma)$, this routine ! determines the corresponding $3\times 3$ rotation matrix. The so-called ! `y-convention' is taken for the Euler angles. See the routine {\tt roteuler} ! for details. ! ! !REVISION HISTORY: ! Created January 2014 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: ang(3) real(8), intent(out) :: rot(3,3) ! local variables real(8) sa,sb,sg,ca,cb,cg sa=sin(ang(1)); ca=cos(ang(1)) sb=sin(ang(2)); cb=cos(ang(2)) sg=sin(ang(3)); cg=cos(ang(3)) rot(1,1)=cg*cb*ca-sg*sa rot(2,1)=-sg*cb*ca-cg*sa rot(3,1)=sb*ca rot(1,2)=cg*cb*sa+sg*ca rot(2,2)=-sg*cb*sa+cg*ca rot(3,2)=sb*sa rot(1,3)=-cg*sb rot(2,3)=sg*sb rot(3,3)=cb end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/zftwfir.f900000644000000000000000000000013214061636517014737 xustar0030 mtime=1623670095.018102396 30 atime=1623670093.751103572 30 ctime=1623670095.018102396 elk-7.2.42/src/zftwfir.f900000644002504400250440000000173614061636517017003 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zftwfir(ngp,igpig,wfir) use modmain use modomp implicit none ! arguments integer, intent(in) :: ngp(nspnfv),igpig(ngkmax,nspnfv) complex(8), intent(inout) :: wfir(ngtc,nspinor,nstsv) ! local variables integer ist,ispn,jspn integer igp,ifg,nthd real(8) t0 ! automatic arrays complex(8) z(ngkmax) t0=1.d0/sqrt(omega) call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(z,ispn,jspn,igp,ifg) & !$OMP NUM_THREADS(nthd) do ist=1,nstsv do ispn=1,nspinor jspn=jspnfv(ispn) call zcopy(ngp(jspn),wfir(:,ispn,ist),1,z,1) wfir(:,ispn,ist)=0.d0 do igp=1,ngp(jspn) ifg=igfc(igpig(igp,jspn)) wfir(ifg,ispn,ist)=t0*z(igp) end do call zfftifc(3,ngdgc,1,wfir(:,ispn,ist)) end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/rschrodint.f900000644000000000000000000000013214061636517015423 xustar0030 mtime=1623670095.019102395 30 atime=1623670093.752103571 30 ctime=1623670095.019102395 elk-7.2.42/src/rschrodint.f900000644002504400250440000001051214061636517017457 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2015 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rschrodint ! !INTERFACE: pure subroutine rschrodint(sol,l,e,nr,r,vr,nn,p0,p1,q0,q1) ! !INPUT/OUTPUT PARAMETERS: ! sol : speed of light in atomic units (in,real) ! l : angular momentum quantum number (in,integer) ! e : energy (in,real) ! nr : number of radial mesh points (in,integer) ! r : radial mesh (in,real(nr)) ! vr : potential on radial mesh (in,real(nr)) ! nn : number of nodes (out,integer) ! p0 : m th energy derivative of P (out,real(nr)) ! p1 : radial derivative of p0 (out,real(nr)) ! q0 : m th energy derivative of Q (out,real(nr)) ! q1 : radial derivative of q0 (out,real(nr)) ! !DESCRIPTION: ! Integrates the scalar relativistic radial Schr\"{o}dinger equation from ! $r=0$ outwards. This involves using the predictor-corrector method to solve ! the coupled first-order equations (in atomic units) ! \begin{align*} ! \frac{d}{dr}P_l&=2MQ_l+\frac{1}{r}P_l\\ ! \frac{d}{dr}Q_l&=-\frac{1}{r}Q_l+\left[\frac{l(l+1)}{2Mr^2} ! +(V-E)\right]P_l, ! \end{align*} ! where $V$ is the external potential, $E$ is the eigen energy and ! $M=1+(E-V)/2c^2$. Following the convention of Koelling and Harmon, ! {\it J. Phys. C: Solid State Phys.} {\bf 10}, 3107 (1977), the functions ! $P_l$ and $Q_l$ are defined by ! \begin{align*} ! P_l&=rg_l\\ ! Q_l&=\frac{r}{2M}\frac{dg_l}{dr}, ! \end{align*} ! where $g_l$ is the major component of the Dirac equation (see the routine ! {\tt rdiracint}). ! ! !REVISION HISTORY: ! Created October 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: sol integer, intent(in) :: l real(8), intent(in) :: e integer, intent(in) :: nr real(8), intent(in) :: r(nr),vr(nr) integer, intent(out) :: nn real(8), intent(out) :: p0(nr),p1(nr) real(8), intent(out) :: q0(nr),q1(nr) ! local variables integer ir,ir0 real(8) ri,t1,t2,t3,t4 t1=1.d0/sol**2 t2=dble(l*(l+1)) ! determine the r -> 0 boundary values of P and Q ri=1.d0/r(1) t3=2.d0+t1*(e-vr(1)) t4=t2/(t3*r(1)**2)+vr(1)-e q0(1)=1.d0 q1(1)=0.d0 p0(1)=(q1(1)+q0(1)*ri)/t4 p1(1)=t3*q0(1)+p0(1)*ri ! extrapolate to the first four points p1(2:4)=p1(1) q1(2:4)=q1(1) nn=0 do ir=2,nr ri=1.d0/r(ir) t3=2.d0+t1*(e-vr(ir)) t4=t2/(t3*r(ir)**2)+vr(ir)-e ir0=ir-3 if (ir0.lt.1) ir0=1 p1(ir)=poly3(r(ir0),p1(ir0),r(ir)) q1(ir)=poly3(r(ir0),q1(ir0),r(ir)) ! integrate to find wavefunction p0(ir)=poly4i(r(ir0),p1(ir0),r(ir))+p0(ir0) q0(ir)=poly4i(r(ir0),q1(ir0),r(ir))+q0(ir0) ! compute the derivatives p1(ir)=t3*q0(ir)+p0(ir)*ri q1(ir)=t4*p0(ir)-q0(ir)*ri ! integrate for correction p0(ir)=poly4i(r(ir0),p1(ir0),r(ir))+p0(ir0) q0(ir)=poly4i(r(ir0),q1(ir0),r(ir))+q0(ir0) ! compute the derivatives again p1(ir)=t3*q0(ir)+p0(ir)*ri q1(ir)=t4*p0(ir)-q0(ir)*ri ! check for overflow if ((abs(p0(ir)).gt.1.d100).or.(abs(p1(ir)).gt.1.d100).or. & (abs(q0(ir)).gt.1.d100).or.(abs(q1(ir)).gt.1.d100)) then p0(ir:nr)=p0(ir) p1(ir:nr)=p1(ir) q0(ir:nr)=q0(ir) q1(ir:nr)=q1(ir) return end if ! check for node if (p0(ir-1)*p0(ir).lt.0.d0) nn=nn+1 end do return contains pure real(8) function poly3(xa,ya,x) implicit none ! arguments real(8), intent(in) :: xa(3),ya(3),x ! local variables real(8) x0,x1,x2,y0,y1,y2 real(8) c1,c2,t0,t1,t2 ! evaluate the polynomial coefficients x0=xa(1) x1=xa(2)-x0; x2=xa(3)-x0 y0=ya(1) y1=ya(2)-y0; y2=ya(3)-y0 t0=1.d0/(x1*x2*(x2-x1)) t1=x1*y2; t2=x2*y1 c1=x2*t2-x1*t1 c2=t1-t2 t1=x-x0 ! evaluate the polynomial poly3=y0+t0*t1*(c1+c2*t1) end function pure real(8) function poly4i(xa,ya,x) implicit none ! arguments real(8), intent(in) :: xa(4),ya(4),x ! local variables real(8) x0,x1,x2,x3,y0,y1,y2,y3 real(8) c1,c2,c3,t0,t1,t2,t3,t4,t5,t6 ! evaluate the polynomial coefficients x0=xa(1) x1=xa(2)-x0; x2=xa(3)-x0; x3=xa(4)-x0 y0=ya(1) y1=ya(2)-y0; y2=ya(3)-y0; y3=ya(4)-y0 t4=x1-x2; t5=x1-x3; t6=x2-x3 t1=x1*x2*y3; t2=x2*x3*y1; t3=x1*x3 t0=1.d0/(x2*t3*t4*t5*t6) t3=t3*y2 c3=t1*t4+t2*t6-t3*t5 t4=x1**2; t5=x2**2; t6=x3**2 c2=t1*(t5-t4)+t2*(t6-t5)+t3*(t4-t6) c1=t1*(x2*t4-x1*t5)+t2*(x3*t5-x2*t6)+t3*(x1*t6-x3*t4) t1=x-x0 ! integrate the polynomial poly4i=t1*(y0+t0*t1*(0.5d0*c1+t1*(0.3333333333333333333d0*c2+0.25d0*c3*t1))) end function end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writegclq.f900000644000000000000000000000013214061636517015245 xustar0030 mtime=1623670095.021102393 30 atime=1623670093.754103569 30 ctime=1623670095.021102393 elk-7.2.42/src/writegclq.f900000644002504400250440000000201314061636517017276 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writegclq ! !INTERFACE: subroutine writegclq ! !USES: use modmain ! !DESCRIPTION: ! Outputs the volume-averaged integral of $4\pi/q^2$ in the small ! parallelepiped around each discrete $q$-point to the file {\tt GCLQ.OUT}. ! These represent the regularised Coulomb Green's function in reciprocal ! space for small $q$. See the routine gengclq. ! ! !REVISION HISTORY: ! Created June 2005 (JKD) !EOP !BOC implicit none ! local variables integer iq real(8) t1 open(50,file='GCLQ'//trim(filext),form='FORMATTED',action='WRITE') write(50,'(I6," : nqpt; q-point, vql, gclq, 4π/q² below")') nqpt do iq=1,nqpt t1=vqc(1,iq)**2+vqc(2,iq)**2+vqc(3,iq)**2 if (t1.gt.1.d-12) then t1=fourpi/t1 else t1=0.d0 end if write(50,'(I6,5G18.10)') iq,vql(:,iq),gclq(iq),t1 end do close(50) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writegeom.f900000644000000000000000000000013214061636517015246 xustar0030 mtime=1623670095.022102393 30 atime=1623670093.756103568 30 ctime=1623670095.022102393 elk-7.2.42/src/writegeom.f900000644002504400250440000000346214061636517017310 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writegeom ! !INTERFACE: subroutine writegeom(fnum) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! fnum : file number for writing output (in,integer) ! !DESCRIPTION: ! Outputs the lattice vectors and atomic positions to file, in a format ! which may be then used directly in {\tt elk.in}. ! ! !REVISION HISTORY: ! Created January 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: fnum ! local variables integer is,ia,i real(8) v1(3),v2(3) write(fnum,*) write(fnum,'("scale")') write(fnum,'(" 1.0")') write(fnum,*) write(fnum,'("scale1")') write(fnum,'(" 1.0")') write(fnum,*) write(fnum,'("scale2")') write(fnum,'(" 1.0")') write(fnum,*) write(fnum,'("scale3")') write(fnum,'(" 1.0")') write(fnum,*) write(fnum,'("avec")') write(fnum,'(3G18.10)') avec(:,1) write(fnum,'(3G18.10)') avec(:,2) write(fnum,'(3G18.10)') avec(:,3) if (molecule) then write(fnum,*) write(fnum,'("molecule")') write(fnum,'(" ",L1)') molecule end if write(fnum,*) write(fnum,'("atoms")') write(fnum,'(I4,T40," : nspecies")') nspecies do is=1,nspecies write(fnum,'("''",A,"''",T40," : spfname")') trim(spfname(is)) write(fnum,'(I4,T40," : natoms; atpos, bfcmt below")') natoms(is) do ia=1,natoms(is) if (molecule) then ! map lattice coordinates to [-0.5,0.5) and write as Cartesian coordinates v1(:)=atposl(:,ia,is) do i=1,3 if (v1(i).gt.0.5d0) v1(i)=v1(i)-1.d0 end do call r3mv(avec,v1,v2) else ! otherwise write lattice coordinates v2(:)=atposl(:,ia,is) end if write(fnum,'(3F14.8," ",3F12.8)') v2(:),bfcmt(:,ia,is) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writemom.f900000644000000000000000000000013214061636517015107 xustar0030 mtime=1623670095.023102392 30 atime=1623670093.757103567 30 ctime=1623670095.023102392 elk-7.2.42/src/writemom.f900000644002504400250440000000152614061636517017150 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine writemom(fnum) use modmain implicit none ! arguments integer, intent(in) :: fnum ! local variables integer is,ia,ias write(fnum,*) write(fnum,'("Moments :")') write(fnum,'(" interstitial",T30,": ",3G18.10)') momir(1:ndmag) write(fnum,'(" muffin-tins")') do is=1,nspecies write(fnum,'(" species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) ias=idxas(ia,is) write(fnum,'(" atom ",I4,T30,": ",3G18.10)') ia,mommt(1:ndmag,ias) end do end do write(fnum,'(" total in muffin-tins",T30,": ",3G18.10)') mommttot(1:ndmag) write(fnum,'(" total moment",T30,": ",3G18.10)') momtot(1:ndmag) flush(fnum) end subroutine elk-7.2.42/src/PaxHeaders.21776/gendmat.f900000644000000000000000000000013014061636517014661 xustar0029 mtime=1623670095.02510239 30 atime=1623670093.759103565 29 ctime=1623670095.02510239 elk-7.2.42/src/gendmat.f900000644002504400250440000000435014061636517016722 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gendmat(tspndg,tlmdg,lmin,lmax,ld,dmat) use modmain use modmpi use modomp implicit none ! arguments logical, intent(in) :: tspndg,tlmdg integer, intent(in) :: lmin,lmax,ld complex(8), intent(out) :: dmat(ld,nspinor,ld,nspinor,natmtot) ! local variables integer ik,ispn,ist integer ias,n,nthd real(8) wo ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:,:),evecfv(:,:,:),evecsv(:,:) complex(8), allocatable :: dmatk(:,:,:,:,:) ! zero the density matrix dmat(:,:,:,:,:)=0.d0 ! begin parallel loop over k-points call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(apwalm,evecfv,evecsv,dmatk) & !$OMP PRIVATE(ispn,ias,ist,wo) & !$OMP NUM_THREADS(nthd) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv),evecsv(nstsv,nstsv)) allocate(dmatk(ld,nspinor,ld,nspinor,nstsv)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! find the matching coefficients do ispn=1,nspnfv call match(ngk(ispn,ik),vgkc(:,:,ispn,ik),gkc(:,ispn,ik), & sfacgk(:,:,ispn,ik),apwalm(:,:,:,:,ispn)) end do ! get the eigenvectors from file call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! begin loop over atoms and species do ias=1,natmtot call gendmatk(tspndg,tlmdg,lmin,lmax,ias,ngk(:,ik),apwalm,evecfv,evecsv, & ld,dmatk) do ist=1,nstsv wo=occsv(ist,ik) if (abs(wo).lt.epsocc) cycle wo=wo*wkpt(ik) !$OMP CRITICAL(gendmat_) dmat(:,:,:,:,ias)=dmat(:,:,:,:,ias)+wo*dmatk(:,:,:,:,ist) !$OMP END CRITICAL(gendmat_) end do end do end do !$OMP END DO deallocate(apwalm,evecfv,evecsv,dmatk) !$OMP END PARALLEL call freethd(nthd) ! add density matrices from each process and redistribute if (np_mpi.gt.1) then n=((ld*nspinor)**2)*natmtot call mpi_allreduce(mpi_in_place,dmat,n,mpi_double_complex,mpi_sum,mpicom, & ierror) end if ! symmetrise the density matrix call symdmat(lmax,ld,dmat) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/curlrvf.f900000644000000000000000000000013214061636517014727 xustar0030 mtime=1623670095.027102388 30 atime=1623670093.761103563 30 ctime=1623670095.027102388 elk-7.2.42/src/curlrvf.f900000644002504400250440000000265714061636517016776 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine curlrvf(rvfmt,rvfir,curlmt,curlir) use modmain use modomp implicit none ! arguments real(8), intent(in) :: rvfmt(npmtmax,natmtot,3),rvfir(ngtot,3) real(8), intent(out) :: curlmt(npmtmax,natmtot,3),curlir(ngtot,3) ! local variables integer is,ias,np,i,nthd ! allocatable arrays real(8), allocatable :: grfmt(:,:,:,:),grfir(:,:,:) allocate(grfmt(npmtmax,natmtot,3,3),grfir(ngtot,3,3)) ! compute the gradients call holdthd(3,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do i=1,3 call gradrf(rvfmt(:,:,i),rvfir(:,i),grfmt(:,:,:,i),grfir(:,:,i)) end do !$OMP END PARALLEL DO call freethd(nthd) ! determine the muffin-tin and interstitial curl call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP PRIVATE(ias,is,np) & !$OMP NUM_THREADS(nthd) !$OMP SECTION do ias=1,natmtot is=idxis(ias) np=npmt(is) curlmt(1:np,ias,1)=grfmt(1:np,ias,2,3)-grfmt(1:np,ias,3,2) curlmt(1:np,ias,2)=grfmt(1:np,ias,3,1)-grfmt(1:np,ias,1,3) curlmt(1:np,ias,3)=grfmt(1:np,ias,1,2)-grfmt(1:np,ias,2,1) end do !$OMP SECTION curlir(:,1)=grfir(:,2,3)-grfir(:,3,2) curlir(:,2)=grfir(:,3,1)-grfir(:,1,3) curlir(:,3)=grfir(:,1,2)-grfir(:,2,1) !$OMP END PARALLEL SECTIONS call freethd(nthd) deallocate(grfmt,grfir) end subroutine elk-7.2.42/src/PaxHeaders.21776/genzvclmt.f900000644000000000000000000000013214061636517015255 xustar0030 mtime=1623670095.028102387 30 atime=1623670093.762103562 30 ctime=1623670095.028102387 elk-7.2.42/src/genzvclmt.f900000644002504400250440000000164214061636517017315 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genzvclmt(nr,nri,ld1,rl,wpr,ld2,zrhomt,zvclmt) use modmain use modomp implicit none ! arguments integer, intent(in) :: nr(nspecies),nri(nspecies) integer, intent(in) :: ld1 real(8), intent(in) :: rl(ld1,-lmaxo-1:lmaxo+2,nspecies) real(8), intent(in) :: wpr(4,ld1,nspecies) integer, intent(in) :: ld2 complex(8), intent(in) :: zrhomt(ld2,natmtot) complex(8), intent(out) :: zvclmt(ld2,natmtot) ! local variables integer is,ias,nthd call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) call zpotclmt(nr(is),nri(is),ld1,rl(:,:,is),wpr(:,:,is),zrhomt(:,ias), & zvclmt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/genjtot.f900000644000000000000000000000013114061636517014715 xustar0030 mtime=1623670095.030102385 29 atime=1623670093.76410356 30 ctime=1623670095.030102385 elk-7.2.42/src/genjtot.f900000644002504400250440000000077014061636517016757 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genjtot use modmain implicit none ! local variables integer i ! external functions real(8), external :: rfint if (.not.tjr) return ! compute the total current in the unit cell do i=1,3 jtot(i)=rfint(jrmt(:,:,i),jrir(:,i)) end do ! total current magnitude jtotm=sqrt(jtot(1)**2+jtot(2)**2+jtot(3)**2) end subroutine elk-7.2.42/src/PaxHeaders.21776/symvec.f900000644000000000000000000000013214061636517014552 xustar0030 mtime=1623670095.031102384 30 atime=1623670093.766103558 30 ctime=1623670095.031102384 elk-7.2.42/src/symvec.f900000644002504400250440000000104214061636517016604 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine symvec(vc) use modmain implicit none ! arguments real(8), intent(inout) :: vc(3) ! local variables integer isym,lspl real(8) vs(3),v(3),t1 ! make symmetric average vs(:)=0.d0 do isym=1,nsymcrys lspl=lsplsymc(isym) call r3mv(symlatc(:,:,lspl),vc,v) vs(:)=vs(:)+v(:) end do ! normalise t1=1.d0/dble(nsymcrys) vc(:)=t1*vs(:) end subroutine elk-7.2.42/src/PaxHeaders.21776/checkwrite.f900000644000000000000000000000013214061636517015374 xustar0030 mtime=1623670095.033102382 30 atime=1623670093.767103558 30 ctime=1623670095.033102382 elk-7.2.42/src/checkwrite.f900000644002504400250440000000075214061636517017435 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine checkwrite(twrite) use modmain implicit none ! arguments logical, intent(out) :: twrite ! check for WRITE file inquire(file='WRITE',exist=twrite) if (twrite) then write(*,*) write(*,'("Info(checkwrite): WRITE file exists")') open(50,file='WRITE') close(50,status='DELETE') end if end subroutine elk-7.2.42/src/PaxHeaders.21776/genjprk.f900000644000000000000000000000013214061636517014704 xustar0030 mtime=1623670095.034102381 30 atime=1623670093.769103556 30 ctime=1623670095.034102381 elk-7.2.42/src/genjprk.f900000644002504400250440000000717314061636517016751 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genjprk(ik,lock) use modmain implicit none ! arguments integer, intent(in) :: ik integer(8), intent(in) :: lock(natmtot) ! local variables integer ispn,jspn,nst,ist,jst integer is,ia,ias,nrc,nrci,npc integer igk,ifg,i real(8) wo complex(8) z1 ! automatic arrays integer idx(nstsv) real(8) rfmt(npcmtmax) complex(8) gzfmt(npcmtmax,3),zfmt1(npcmtmax),zfmt2(npcmtmax) ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfgp(:,:,:) complex(8), allocatable :: zfft1(:),zfft2(:) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) ! find the matching coefficients do ispn=1,nspnfv call match(ngk(ispn,ik),vgkc(:,:,ispn,ik),gkc(:,ispn,ik), & sfacgk(:,:,ispn,ik),apwalm(:,:,:,:,ispn)) end do ! get the eigenvectors from file call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! count and index the occupied states nst=0 do ist=1,nstsv if (abs(occsv(ist,ik)).lt.epsocc) cycle nst=nst+1 idx(nst)=ist end do ! calculate the second-variational wavefunctions for occupied states allocate(wfmt(npcmtmax,natmtot,nspinor,nst),wfgp(ngkmax,nspinor,nst)) call genwfsv(.true.,.true.,nst,idx,ngdgc,igfc,ngk(:,ik),igkig(:,:,ik),apwalm, & evecfv,evecsv,wfmt,ngkmax,wfgp) deallocate(apwalm,evecfv,evecsv) !-------------------------------------------------! ! muffin-tin paramagnetic current density ! !-------------------------------------------------! do ist=1,nst jst=idx(ist) wo=wkpt(ik)*occsv(jst,ik) do ispn=1,nspinor do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) ! compute the gradient of the wavefunction call gradzfmt(nrc,nrci,rlcmt(:,-1,is),wcrcmt(:,:,is), & wfmt(:,ias,ispn,ist),npcmtmax,gzfmt) ! convert wavefunction to spherical coordinates and conjugate call zbsht(nrc,nrci,wfmt(:,ias,ispn,ist),zfmt1) zfmt1(1:npc)=conjg(zfmt1(1:npc)) do i=1,3 ! convert wavefunction gradient to spherical coordinates call zbsht(nrc,nrci,gzfmt(:,i),zfmt2) ! compute the partial current density rfmt(1:npc)=aimag(zfmt1(1:npc)*zfmt2(1:npc)) call omp_set_lock(lock(ias)) call daxpy(npc,wo,rfmt,1,jrmt(:,ias,i),1) call omp_unset_lock(lock(ias)) end do end do end do end do end do deallocate(wfmt) !---------------------------------------------------! ! interstitial paramagnetic current density ! !---------------------------------------------------! allocate(zfft1(ngtc),zfft2(ngtc)) do ist=1,nst jst=idx(ist) wo=wkpt(ik)*occsv(jst,ik)/omega do ispn=1,nspinor jspn=jspnfv(ispn) ! Fourier transform to real-space and conjugate zfft1(:)=0.d0 do igk=1,ngk(jspn,ik) ifg=igfc(igkig(igk,jspn,ik)) zfft1(ifg)=wfgp(igk,ispn,ist) end do call zfftifc(3,ngdgc,1,zfft1) zfft1(:)=conjg(zfft1(:)) do i=1,3 ! compute the gradient of the wavefunction zfft2(:)=0.d0 do igk=1,ngk(jspn,ik) ifg=igfc(igkig(igk,jspn,ik)) z1=wfgp(igk,ispn,ist) zfft2(ifg)=vgkc(i,igk,jspn,ik)*cmplx(-aimag(z1),dble(z1),8) end do call zfftifc(3,ngdgc,1,zfft2) !$OMP CRITICAL(currentk_) jrir(1:ngtc,i)=jrir(1:ngtc,i)+wo*aimag(zfft1(1:ngtc)*zfft2(1:ngtc)) !$OMP END CRITICAL(currentk_) end do end do end do deallocate(wfgp,zfft1,zfft2) end subroutine elk-7.2.42/src/PaxHeaders.21776/proj2d.f900000644000000000000000000000013014061636517014442 xustar0029 mtime=1623670095.03610238 30 atime=1623670093.771103554 29 ctime=1623670095.03610238 elk-7.2.42/src/proj2d.f900000644002504400250440000000254514061636517016507 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine proj2d(np,fp) use modmain implicit none ! arguments integer, intent(in) :: np real(8), intent(inout) :: fp(np,3) ! local variables integer i real(8) vl1(3),vl2(3),t1,t2,t3 real(8) vc1(3),vc2(3),vc3(3),vc4(3) ! determine the 2D plotting plane vectors in Cartesian coordinates vl1(:)=vclp2d(:,1)-vclp2d(:,0) vl2(:)=vclp2d(:,2)-vclp2d(:,0) call r3mv(avec,vl1,vc1) call r3mv(avec,vl2,vc2) ! the z axis is orthogonal to the plotting plane vectors call r3cross(vc1,vc2,vc3) t1=sqrt(vc1(1)**2+vc1(2)**2+vc1(3)**2) t2=sqrt(vc2(1)**2+vc2(2)**2+vc2(3)**2) t3=sqrt(vc3(1)**2+vc3(2)**2+vc3(3)**2) if ((t1.lt.epslat).or.(t2.lt.epslat).or.(t3.lt.epslat)) then write(*,*) write(*,'("Error(proj2d): degenerate 2D plotting directions")') write(*,*) stop end if ! normalise the x and z axes vc1(:)=vc1(:)/t1 vc3(:)=vc3(:)/t3 ! create new y axis orthogonal to x and z axes call r3cross(vc3,vc1,vc2) t1=sqrt(vc2(1)**2+vc2(2)**2+vc2(3)**2) vc2(:)=vc2(:)/t1 ! project the vector function onto the orthogonalised plotting plane axes do i=1,np vc4(:)=fp(i,:) fp(i,1)=dot_product(vc4(:),vc1(:)) fp(i,2)=dot_product(vc4(:),vc2(:)) fp(i,3)=dot_product(vc4(:),vc3(:)) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/genidxbse.f900000644000000000000000000000013214061636517015214 xustar0030 mtime=1623670095.037102379 30 atime=1623670093.772103553 30 ctime=1623670095.037102379 elk-7.2.42/src/genidxbse.f900000644002504400250440000000756714061636517017270 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genidxbse use modmain implicit none integer ik,jk,a,ntop integer ist,jst,i,j,k ! automatic arrays integer idx(nstsv) ! check if the BSE extra valence or conduction states are in range do i=1,nvxbse ist=istxbse(i) if ((ist.lt.1).or.(ist.gt.nstsv)) then write(*,*) write(*,'("Error(genidxbse): extra valence state out of range : ",I8)') ist write(*,*) stop end if end do do j=1,ncxbse jst=jstxbse(j) if ((jst.lt.1).or.(jst.gt.nstsv)) then write(*,*) write(*,'("Error(genidxbse): extra conduction state out of range : ",I8)') & jst write(*,*) stop end if end do ! number of valence states for transitions nvbse=nvbse0+nvxbse ! number of conduction states for transitions ncbse=ncbse0+ncxbse if ((nvbse.le.0).or.(ncbse.le.0)) then write(*,*) write(*,'("Error(genidxbse): invalid number of valence or conduction & &transition states : ",2I8)') nvbse,ncbse write(*,*) stop end if ! total number of transitions nvcbse=nvbse*ncbse ! block size in BSE matrix nbbse=nvcbse*nkptnr ! BSE matrix size if (bsefull) then nmbse=2*nbbse else nmbse=nbbse end if ! allocate global BSE index arrays if (allocated(istbse)) deallocate(istbse) allocate(istbse(nvbse,nkptnr)) if (allocated(jstbse)) deallocate(jstbse) allocate(jstbse(ncbse,nkptnr)) if (allocated(ijkbse)) deallocate(ijkbse) allocate(ijkbse(nvbse,ncbse,nkptnr)) a=0 ! loop over non-reduced k-points do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! index for sorting the eigenvalues into ascending order call sortidx(nstsv,evalsv(:,jk),idx) ! find the topmost occupied band ntop=nstsv do ist=nstsv,1,-1 if (evalsv(idx(ist),jk).lt.efermi) then ntop=ist exit end if end do if ((ntop-nvbse0+1).lt.1) then write(*,*) write(*,'("Error(genidxbse): not enough valence states, reduce nvbse")') write(*,*) stop end if if ((ntop+ncbse0).gt.nstsv) then write(*,*) write(*,'("Error(genidxbse): not enough conduction states")') write(*,'(" reduce ncbse or increase nempty")') write(*,*) stop end if ! index from BSE valence states to second-variational state numbers do i=1,nvbse0 istbse(i,ik)=idx(ntop-nvbse0+i) end do ! index from BSE conduction states to second-variational state numbers do j=1,ncbse0 jstbse(j,ik)=idx(ntop+j) end do ! add extra states to the list do i=1,nvxbse ist=istxbse(i) if (evalsv(ist,jk).gt.efermi) then write(*,*) write(*,'("Error(genidxbse): extra valence state above Fermi energy : ",& &I6)') ist write(*,'(" for k-point ",I8)') jk write(*,*) stop end if do k=1,nvbse0+i-1 if (ist.eq.istbse(k,ik)) then write(*,*) write(*,'("Error(genidxbse): redundant extra valence state : ",I6)') ist write(*,'(" for k-point ",I8)') jk write(*,*) stop end if end do istbse(nvbse0+i,ik)=ist end do do j=1,ncxbse jst=jstxbse(j) if (evalsv(jst,jk).lt.efermi) then write(*,*) write(*,'("Error(genidxbse): extra conduction state below Fermi & &energy : ",I6)') jst write(*,'(" for k-point ",I8)') jk write(*,*) stop end if do k=1,ncbse0+j-1 if (jst.eq.jstbse(k,ik)) then write(*,*) write(*,'("Error(genidxbse): redundant extra conduction state : ",& &I6)') jst write(*,'(" for k-point ",I8)') jk write(*,*) stop end if end do jstbse(ncbse0+j,ik)=jst end do ! index from BSE valence-conduction pair and k-point to location in BSE matrix do i=1,nvbse do j=1,ncbse a=a+1 ijkbse(i,j,ik)=a end do end do ! end loop over non-reduced k-points end do end subroutine elk-7.2.42/src/PaxHeaders.21776/symrvfir.f900000644000000000000000000000013214061636517015125 xustar0030 mtime=1623670095.039102377 30 atime=1623670093.774103551 30 ctime=1623670095.039102377 elk-7.2.42/src/symrvfir.f900000644002504400250440000001020614061636517017161 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: symrvfir subroutine symrvfir(tspin,tnc,ngdg,ngt,ngv,igf,ld,rvfir) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! tspin : .true. if spin rotations should be used (in,logical) ! tnc : .true. if the vector field is non-collinear, otherwise it is ! collinear along the z-axis (in,logical) ! ngdg : G-vector grid sizes (in,integer(3)) ! ngt : total number of G-vectors (in,integer) ! ngv : number of G-vectors within cut-off (in,integer) ! igf : map from G-vector index to FFT array (in,integer(ngv)) ! ld : leading dimension (in,integer) ! rvfir : real interstitial vector function (inout,real(ld,*)) ! !DESCRIPTION: ! Symmetrises a real interstitial vector function. See routines {\tt symrvf} ! and {\tt symrfir} for details. ! ! !REVISION HISTORY: ! Created July 2007 (JKD) !EOP !BOC implicit none ! arguments logical, intent(in) :: tspin,tnc integer, intent(in) :: ngdg(3),ngt,ngv,igf(ngv) integer, intent(in) :: ld real(8), intent(inout) :: rvfir(ld,*) ! local variables logical tv0 integer nd,isym,lspl,ilspl,lspn integer sym(3,3),ig,ifg,jfg integer i1,i2,i3,j1,j2,j3,i real(8) sc(3,3),v1,v2,v3,t1 complex(8) x1,x2,x3,z1 ! allocatable arrays complex(8), allocatable :: zfft1(:,:),zfft2(:,:) ! dimension of the vector field if (tnc) then nd=3 else nd=1 end if allocate(zfft1(ngt,nd),zfft2(ngt,nd)) ! Fourier transform vector function to G-space do i=1,nd zfft1(1:ngt,i)=rvfir(1:ngt,i) call zfftifc(3,ngdg,-1,zfft1(:,i)) end do zfft2(:,:)=0.d0 do isym=1,nsymcrys ! zero translation vector flag tv0=tv0symc(isym) ! translation vector in Cartesian coordinates if (.not.tv0) then v1=vtcsymc(1,isym) v2=vtcsymc(2,isym) v3=vtcsymc(3,isym) end if ! index to spatial rotation lattice symmetry lspl=lsplsymc(isym) ! inverse rotation required for rotation of G-vectors ilspl=isymlat(lspl) sym(:,:)=symlat(:,:,ilspl) if (tspin) then ! global spin proper rotation in Cartesian coordinates lspn=lspnsymc(isym) sc(:,:)=symlatd(lspn)*symlatc(:,:,lspn) else ! set spin rotation equal to spatial rotation lspn=lspl sc(:,:)=symlatc(:,:,lspl) end if do ig=1,ngv ifg=igf(ig) ! multiply the transpose of the inverse symmetry matrix with the G-vector if (lspl.eq.1) then jfg=ifg else i1=ivg(1,ig); i2=ivg(2,ig); i3=ivg(3,ig) j1=sym(1,1)*i1+sym(2,1)*i2+sym(3,1)*i3 j2=sym(1,2)*i1+sym(2,2)*i2+sym(3,2)*i3 j3=sym(1,3)*i1+sym(2,3)*i2+sym(3,3)*i3 jfg=igf(ivgig(j1,j2,j3)) end if ! translation, spatial rotation and global spin rotation if (tv0) then ! zero translation vector if (lspn.eq.1) then ! global spin symmetry is the identity zfft2(jfg,:)=zfft2(jfg,:)+zfft1(ifg,:) else if (tnc) then ! non-collinear case x1=zfft1(ifg,1); x2=zfft1(ifg,2); x3=zfft1(ifg,3) zfft2(jfg,1)=zfft2(jfg,1)+sc(1,1)*x1+sc(1,2)*x2+sc(1,3)*x3 zfft2(jfg,2)=zfft2(jfg,2)+sc(2,1)*x1+sc(2,2)*x2+sc(2,3)*x3 zfft2(jfg,3)=zfft2(jfg,3)+sc(3,1)*x1+sc(3,2)*x2+sc(3,3)*x3 else ! collinear case zfft2(jfg,1)=zfft2(jfg,1)+sc(3,3)*zfft1(ifg,1) end if end if else ! complex phase factor for translation t1=-(vgc(1,ig)*v1+vgc(2,ig)*v2+vgc(3,ig)*v3) z1=cmplx(cos(t1),sin(t1),8) if (lspn.eq.1) then zfft2(jfg,:)=zfft2(jfg,:)+z1*zfft1(ifg,:) else if (tnc) then x1=zfft1(ifg,1); x2=zfft1(ifg,2); x3=zfft1(ifg,3) zfft2(jfg,1)=zfft2(jfg,1)+z1*(sc(1,1)*x1+sc(1,2)*x2+sc(1,3)*x3) zfft2(jfg,2)=zfft2(jfg,2)+z1*(sc(2,1)*x1+sc(2,2)*x2+sc(2,3)*x3) zfft2(jfg,3)=zfft2(jfg,3)+z1*(sc(3,1)*x1+sc(3,2)*x2+sc(3,3)*x3) else zfft2(jfg,1)=zfft2(jfg,1)+sc(3,3)*z1*zfft1(ifg,1) end if end if end if end do end do ! Fourier transform to real-space and normalise t1=1.d0/dble(nsymcrys) do i=1,nd call zfftifc(3,ngdg,1,zfft2(:,i)) rvfir(1:ngt,i)=t1*dble(zfft2(1:ngt,i)) end do deallocate(zfft1,zfft2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genjpr.f900000644000000000000000000000013214061636517014531 xustar0030 mtime=1623670095.040102376 30 atime=1623670093.776103549 30 ctime=1623670095.040102376 elk-7.2.42/src/genjpr.f900000644002504400250440000000442714061636517016575 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genjpr use modmain use modmpi use modomp implicit none ! local variables integer ik,is,ias integer nrc,nrci,npc integer n,i,nthd ! automatic arrays integer(8) lock(natmtot) real(8) rfmt(npcmtmax) ! set the current density to zero do i=1,3 do ias=1,natmtot is=idxis(ias) jrmt(1:npcmt(is),ias,i)=0.d0 end do end do jrir(1:ngtc,:)=0.d0 ! current density cannot be computed if wavefunctions do not exist if (iscl.le.0) return ! initialise the OpenMP locks do ias=1,natmtot call omp_init_lock(lock(ias)) end do call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call genjprk(ik,lock) end do !$OMP END PARALLEL DO call freethd(nthd) ! destroy the OpenMP locks do ias=1,natmtot call omp_destroy_lock(lock(ias)) end do ! convert muffin-tin current density to spherical harmonics call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(rfmt,is,nrc,nrci,npc,i) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do i=1,3 rfmt(1:npc)=jrmt(1:npc,ias,i) call rfsht(nrc,nrci,rfmt,jrmt(:,ias,i)) end do end do !$OMP END PARALLEL DO call freethd(nthd) ! symmetrise the current density call symrvf(.false.,.true.,nrcmt,nrcmti,npcmt,ngdgc,ngtc,ngvc,igfc,npmtmax, & jrmt,ngtot,jrir) ! convert muffin-tin and interstitial current density from coarse to fine grids call holdthd(3,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP DO do i=1,3 call rfmtctof(jrmt(:,:,i)) end do !$OMP END DO NOWAIT !$OMP DO do i=1,3 call rfirctof(jrir(:,i),jrir(:,i)) end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) ! add current densities from each process and redistribute if (np_mpi.gt.1) then n=npmtmax*natmtot*3 call mpi_allreduce(mpi_in_place,jrmt,n,mpi_double_precision,mpi_sum,mpicom, & ierror) n=ngtot*3 call mpi_allreduce(mpi_in_place,jrir,n,mpi_double_precision,mpi_sum,mpicom, & ierror) end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqnfvr.f900000644000000000000000000000013214061636517015100 xustar0030 mtime=1623670095.042102374 30 atime=1623670093.777103548 30 ctime=1623670095.042102374 elk-7.2.42/src/eveqnfvr.f900000644002504400250440000001677514061636517017155 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: eveqnfvr ! !INTERFACE: subroutine eveqnfvr(nmatp,ngp,vpc,h,o,evalfv,evecfv) ! !USES: use modmain use modomp ! !INPUT/OUTPUT PARAMETERS: ! nmatp : order of overlap and Hamiltonian matrices (in,integer) ! ngp : number of G+p-vectors (in,integer) ! vpc : p-vector in Cartesian coordinates (in,real(3)) ! h,o : Hamiltonian and overlap matrices in upper triangular form ! (in,complex(*)) ! evalfv : first-variational eigenvalues (out,real(nstfv)) ! evecfv : first-variational eigenvectors (out,complex(nmatmax,nstfv)) ! !DESCRIPTION: ! This routine solves the first-variational eigenvalue equation for the ! special case when inversion symmetry is present. In this case the ! Hamiltonian and overlap matrices can be made real by using appropriate ! linear combinations of the local-orbitals for atoms related by inversion ! symmetry. These are derived from the effect of parity and complex ! conjugation on the spherical harmonics: $P Y_{lm}=(-1)^l Y_{lm}$ and ! $(Y_{lm})^*=(-1)^mY_{l-m}$. ! ! !REVISION HISTORY: ! Created May 2011 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nmatp,ngp real(8), intent(in) :: vpc(3) complex(8), intent(in) :: h(*),o(*) real(8), intent(out) :: evalfv(nstfv) complex(8), intent(out) :: evecfv(nmatmax,nstfv) ! local variables integer is,ia,ja,jas integer ilo,i,j,k,l,m integer i1,i2,j1,j2 integer k1,k2,k3,k4 integer l1,l2,m1,m2 integer lwork,info integer nthd,nts real(8) v(3),vl,vu real(8) t1,t2,t3,t4 real(8) ts0,ts1 complex(8) h1,h2,o1,o2,z1 ! automatic arrays logical tr(nlotot),tp(nlotot) integer idx(nlotot),s(nlotot) integer iwork(5*nmatp),ifail(nmatp) real(8) w(nmatp) complex(8) zp(nlotot) ! allocatable arrays real(8), allocatable :: rh(:),ro(:),rv(:,:),work(:) call timesec(ts0) tp(:)=.false. i=0 do is=1,nspecies do ia=1,natoms(is) ! symmetry equivalent atom, mapped with inversion ja=ieqatom(ia,is,2) jas=idxas(ja,is) ! residual phase factor v(:)=atposc(:,ia,is)+atposc(:,ja,is) t1=0.5d0*(vpc(1)*v(1)+vpc(2)*v(2)+vpc(3)*v(3)) z1=cmplx(cos(t1),sin(t1),8) do ilo=1,nlorb(is) l=lorbl(ilo,is) do m=-l,l i=i+1 ! index to conjugate local-orbital in symmetry equivalent atom idx(i)=idxlo(l*(l+1)-m+1,ilo,jas) if (ia.ne.ja) then ! sign of parity and conjugation operators if (mod(l+m,2).eq.0) then s(i)=1 else s(i)=-1 end if if (ia.lt.ja) then ! if ia < ja use the real part of the sum of matrix elements tr(i)=.true. else if (ia.gt.ja) then ! if ia > ja use the imaginary part of the difference of matrix elements s(i)=-s(i) tr(i)=.false. end if else ! if ia = ja then use real function when l even and imaginary when l is odd if (mod(m,2).eq.0) then s(i)=1 else s(i)=-1 end if ! new function should be real if symmetric or imaginary if antisymmetric if (mod(l,2).eq.0) then ! l even if (m.ge.0) then tr(i)=.true. else s(i)=-s(i) tr(i)=.false. end if else ! l odd if (m.ge.0) then tr(i)=.false. else s(i)=-s(i) tr(i)=.true. end if end if end if ! phase factors if required if (abs(t1).gt.1.d-8) then zp(i)=z1 tp(i)=.true. end if end do end do end do end do !---------------------------------! ! real Hamiltonian matrix ! !---------------------------------! allocate(rh(nmatp**2)) ! do j=1,ngp k=(j-1)*nmatp+1 rh(k:k+j-1)=dble(h(k:k+j-1)) end do ! do m1=1,nlotot j1=ngp+m1 j2=ngp+idx(m1) do i=1,ngp k1=i+(j1-1)*nmatp k2=i+(j2-1)*nmatp h1=h(k1); h2=h(k2) if (tp(m1)) then h1=h1*zp(m1); h2=h2*zp(m1) end if if (tr(m1)) then rh(k1)=dble(h1)+s(m1)*dble(h2) else rh(k1)=aimag(h1)+s(m1)*aimag(h2) end if end do end do ! do m1=1,nlotot m2=idx(m1) do l1=1,m1 l2=idx(l1) k1=map(l1,m1); k2=map(l1,m2); k3=map(l2,m1); k4=map(l2,m2) if ((tr(l1).and.tr(m1)).or.((.not.tr(l1)).and.(.not.tr(m1)))) then rh(k1)=dble(h(k1))+s(m1)*dble(h(k2))+s(l1)*(dble(h(k3))+s(m1)*dble(h(k4))) else t2=aimag(h(k2)) if (l1.gt.m2) t2=-t2 t3=aimag(h(k3)) if (l2.gt.m1) t3=-t3 t4=aimag(h(k4)) if (l2.gt.m2) t4=-t4 rh(k1)=aimag(h(k1))+s(m1)*t2+s(l1)*(t3+s(m1)*t4) if (.not.tr(l1)) rh(k1)=-rh(k1) end if end do end do !-----------------------------! ! real overlap matrix ! !-----------------------------! allocate(ro(nmatp**2)) ! do j=1,ngp k=(j-1)*nmatp+1 ro(k:k+j-1)=dble(o(k:k+j-1)) end do ! do m1=1,nlotot j1=ngp+m1 j2=ngp+idx(m1) do i=1,ngp k1=i+(j1-1)*nmatp k2=i+(j2-1)*nmatp o1=o(k1); o2=o(k2) if (tp(m1)) then o1=o1*zp(m1); o2=o2*zp(m1) end if if (tr(m1)) then ro(k1)=dble(o1)+s(m1)*dble(o2) else ro(k1)=aimag(o1)+s(m1)*aimag(o2) end if end do end do ! do m1=1,nlotot m2=idx(m1) do l1=1,m1 l2=idx(l1) k1=map(l1,m1); k2=map(l1,m2); k3=map(l2,m1); k4=map(l2,m2) if ((tr(l1).and.tr(m1)).or.((.not.tr(l1)).and.(.not.tr(m1)))) then ro(k1)=dble(o(k1))+s(m1)*dble(o(k2))+s(l1)*(dble(o(k3))+s(m1)*dble(o(k4))) else t2=aimag(o(k2)) if (l1.gt.m2) t2=-t2 t3=aimag(o(k3)) if (l2.gt.m1) t3=-t3 t4=aimag(o(k4)) if (l2.gt.m2) t4=-t4 ro(k1)=aimag(o(k1))+s(m1)*t2+s(l1)*(t3+s(m1)*t4) if (.not.tr(l1)) ro(k1)=-ro(k1) end if end do end do ! solve the generalised eigenvalue problem for real symmetric matrices allocate(rv(nmatp,nstfv)) lwork=8*nmatp allocate(work(lwork)) ! enable MKL parallelism call holdthd(maxthdmkl,nthd) nts=mkl_set_num_threads_local(nthd) ! diagonalise the matrix call dsygvx(1,'V','I','U',nmatp,rh,nmatp,ro,nmatp,vl,vu,1,nstfv,evaltol,m,w, & rv,nmatp,work,lwork,iwork,ifail,info) nts=mkl_set_num_threads_local(0) call freethd(nthd) if (info.ne.0) then write(*,*) write(*,'("Error(eveqnfvr): diagonalisation failed")') write(*,'(" DSYGVX returned INFO = ",I8)') info if (info.gt.nmatp) then i=info-nmatp write(*,'(" The leading minor of the overlap matrix of order ",I8)') i write(*,'(" is not positive definite")') write(*,'(" Order of overlap matrix : ",I8)') nmatp end if write(*,*) stop end if evalfv(1:nstfv)=w(1:nstfv) ! reconstruct the complex eigenvectors do j=1,nstfv evecfv(1:ngp,j)=rv(1:ngp,j) evecfv(ngp+1:nmatp,j)=0.d0 do l1=1,nlotot i1=ngp+l1 i2=ngp+idx(l1) t1=rv(i1,j) if (tr(l1)) then evecfv(i1,j)=evecfv(i1,j)+t1 evecfv(i2,j)=evecfv(i2,j)+s(l1)*t1 else evecfv(i1,j)=evecfv(i1,j)-cmplx(0.d0,t1,8) evecfv(i2,j)=evecfv(i2,j)-cmplx(0.d0,s(l1)*t1,8) end if end do do l1=1,nlotot if (tp(l1)) then i1=ngp+l1 evecfv(i1,j)=evecfv(i1,j)*zp(l1) end if end do end do deallocate(rh,ro,rv,work) call timesec(ts1) !$OMP ATOMIC timefv=timefv+ts1-ts0 contains elemental integer function map(i,j) implicit none ! arguments integer, intent(in) :: i,j ! map from local-orbital indices to position in matrix if (i.le.j) then map=ngp+i+(ngp+j-1)*nmatp else map=ngp+j+(ngp+i-1)*nmatp end if end function end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gentau.f900000644000000000000000000000013214061636517014527 xustar0030 mtime=1623670095.043102373 30 atime=1623670093.779103546 30 ctime=1623670095.043102373 elk-7.2.42/src/gentau.f900000644002504400250440000000634014061636517016567 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gentau use modmain use modmpi use modomp implicit none ! local variables integer ik,ispn,is,ias integer np,npc,n,nthd ! allocatable arrays real(8), allocatable :: rfmt(:,:),rfir(:) real(8), allocatable :: rvfmt(:,:,:),rvfir(:,:) ! set the kinetic energy density to zero do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) taumt(1:npcmt(is),ias,ispn)=0.d0 end do end do tauir(1:ngtc,:)=0.d0 ! tau cannot be computed if wavefunctions do not exist if (iscl.le.0) return call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call gentauk(ik) end do !$OMP END PARALLEL DO call freethd(nthd) allocate(rfmt(npcmtmax,natmtot)) ! convert taumt to spherical harmonics do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) call dcopy(npcmt(is),taumt(:,ias,ispn),1,rfmt,1) call rfsht(nrcmt(is),nrcmti(is),rfmt,taumt(:,ias,ispn)) end do end do ! symmetrise tau if (spinpol) then ! spin-polarised case: convert to scalar-vector form allocate(rvfmt(npcmtmax,natmtot,ndmag)) allocate(rvfir(ngtc,ndmag),rfir(ngtc)) do ias=1,natmtot is=idxis(ias) npc=npcmt(is) rfmt(1:npc,ias)=taumt(1:npc,ias,1)+taumt(1:npc,ias,2) rvfmt(1:npc,ias,1:ndmag-1)=0.d0 rvfmt(1:npc,ias,ndmag)=taumt(1:npc,ias,1)-taumt(1:npc,ias,2) end do rfir(1:ngtc)=tauir(1:ngtc,1)+tauir(1:ngtc,2) rvfir(1:ngtc,1:ndmag-1)=0.d0 rvfir(1:ngtc,ndmag)=tauir(1:ngtc,1)-tauir(1:ngtc,2) call symrf(nrcmt,nrcmti,npcmt,ngdgc,ngtc,ngvc,igfc,npcmtmax,rfmt,rfir) call symrvf(.true.,ncmag,nrcmt,nrcmti,npcmt,ngdgc,ngtc,ngvc,igfc,npcmtmax,& rvfmt,ngtc,rvfir) do ias=1,natmtot is=idxis(ias) npc=npcmt(is) taumt(1:npc,ias,1)=0.5d0*(rfmt(1:npc,ias)+rvfmt(1:npc,ias,ndmag)) taumt(1:npc,ias,2)=0.5d0*(rfmt(1:npc,ias)-rvfmt(1:npc,ias,ndmag)) end do tauir(1:ngtc,1)=0.5d0*(rfir(1:ngtc)+rvfir(1:ngtc,ndmag)) tauir(1:ngtc,2)=0.5d0*(rfir(1:ngtc)-rvfir(1:ngtc,ndmag)) deallocate(rvfmt,rvfir,rfir) else ! spin-unpolarised case call symrf(nrcmt,nrcmti,npcmt,ngdgc,ngtc,ngvc,igfc,npmtmax,taumt,tauir) end if ! convert muffin-tin tau from coarse to fine radial mesh do ispn=1,nspinor call rfmtctof(taumt(:,:,ispn)) end do ! convert interstitial tau from coarse to fine grid do ispn=1,nspinor call rfirctof(tauir(:,ispn),tauir(:,ispn)) end do ! add tau from each process and redistribute if (np_mpi.gt.1) then n=npmtmax*natmtot*nspinor call mpi_allreduce(mpi_in_place,taumt,n,mpi_double_precision,mpi_sum,mpicom, & ierror) n=ngtot*nspinor call mpi_allreduce(mpi_in_place,tauir,n,mpi_double_precision,mpi_sum,mpicom, & ierror) end if ! generate the core kinetic energy density call gentaucr do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) np=npmt(is) ! add the core contribution taumt(1:np,ias,ispn)=taumt(1:np,ias,ispn)+taucr(1:np,ias,ispn) ! zero tau on the inner part of the muffin-tin taumt(1:npmti(is),ias,ispn)=0.d0 end do end do deallocate(rfmt) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/genjlgpr.f900000644000000000000000000000013214061636517015054 xustar0030 mtime=1623670095.045102371 30 atime=1623670093.781103544 30 ctime=1623670095.045102371 elk-7.2.42/src/genjlgpr.f900000644002504400250440000000211414061636517017107 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genjlgpr(ngp,gpc,jlgpr) use modmain use modomp implicit none ! arguments integer, intent(in) :: ngp real(8), intent(in) :: gpc(ngp) real(8), intent(out) :: jlgpr(njcmax,nspecies,ngp) ! local variables integer ig,is,n,i,nthd integer nrc,nrci,irc real(8) t1,t2 ! generate spherical Bessel functions on the coarse radial mesh over all species call holdthd(ngp,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(t1,t2,is,nrc) & !$OMP PRIVATE(nrci,n,i,irc) & !$OMP NUM_THREADS(nthd) do ig=1,ngp t1=gpc(ig) do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) n=lmaxi+1 i=1 do irc=1,nrci t2=t1*rcmt(irc,is) call sbessel(lmaxi,t2,jlgpr(i,is,ig)) i=i+n end do n=lmaxo+1 do irc=nrci+1,nrc t2=t1*rcmt(irc,is) call sbessel(lmaxo,t2,jlgpr(i,is,ig)) i=i+n end do end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/writestrain.f900000644000000000000000000000013014061636517015615 xustar0029 mtime=1623670095.04610237 30 atime=1623670093.782103544 29 ctime=1623670095.04610237 elk-7.2.42/src/writestrain.f900000644002504400250440000000142314061636517017654 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writestrain use modmain implicit none ! local variables integer i,j,k ! initialise universal variables call init0 ! generate the strain tensors call genstrain ! write the strain tensors to file open(50,file='STRAIN.OUT',form='FORMATTED',action='WRITE') do k=1,nstrain write(50,*) write(50,'("Strain tensor : ",I1)') k do j=1,3 write(50,'(3G18.10)') (strain(i,j,k),i=1,3) end do end do close(50) write(*,*) write(*,'("Info(writestrain)")') write(*,'(" Strain tensors written to STRAIN.OUT")') write(*,'(" (the first strain tensor is isotropic expansion)")') end subroutine elk-7.2.42/src/PaxHeaders.21776/writefermi.f900000644000000000000000000000013214061636517015421 xustar0030 mtime=1623670095.048102368 30 atime=1623670093.784103542 30 ctime=1623670095.048102368 elk-7.2.42/src/writefermi.f900000644002504400250440000000106214061636517017455 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writefermi ! !INTERFACE: subroutine writefermi ! !USES: use modmain ! !DESCRIPTION: ! Writes the Fermi energy to the file {\tt EFERMI.OUT}. ! ! !REVISION HISTORY: ! Created March 2005 (JKD) !EOP !BOC implicit none open(50,file='EFERMI'//trim(filext),form='FORMATTED',action='WRITE') write(50,'(G18.10)') efermi close(50) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rfmtctof.f900000644000000000000000000000013114061636517015067 xustar0030 mtime=1623670095.049102368 29 atime=1623670093.78610354 30 ctime=1623670095.049102368 elk-7.2.42/src/rfmtctof.f900000644002504400250440000000432214061636517017126 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rfmtctof ! !INTERFACE: subroutine rfmtctof(rfmt) ! !USES: use modmain use modomp ! !INPUT/OUTPUT PARAMETERS: ! rfmt : real muffin-tin function (in,real(npmtmax,natmtot)) ! !DESCRIPTION: ! Converts a real muffin-tin function from a coarse to a fine radial mesh by ! using cubic spline interpolation. See {\tt rfinterp} and {\tt spline}. ! ! !REVISION HISTORY: ! Created October 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(inout) :: rfmt(npmtmax,natmtot) ! local variables integer is,ias,lm,nthd integer nr,nri,nro integer iro,ir,npi,i integer nrc,nrci,nrco integer irco,irc,npci ! automatic arrays real(8) rfmt1(npcmtmax),fr(nrmtmax),frc(nrcmtmax) if (lradstp.eq.1) return call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(rfmt1,fr,frc,is,nr,nri,nro) & !$OMP PRIVATE(iro,npi,nrc,nrci,nrco) & !$OMP PRIVATE(irco,npci,lm,i,irc,ir) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) nro=nr-nri iro=nri+1 npi=npmti(is) nrc=nrcmt(is) nrci=nrcmti(is) nrco=nrc-nrci irco=nrci+1 npci=npcmti(is) ! copy the input function call dcopy(npcmt(is),rfmt(:,ias),1,rfmt1,1) ! interpolate up to lmaxi over entire muffin-tin do lm=1,lmmaxi i=lm do irc=1,nrci frc(irc)=rfmt1(i) i=i+lmmaxi end do do irc=irco,nrc frc(irc)=rfmt1(i) i=i+lmmaxo end do call rfinterp(nrc,rcmt(:,is),wcrcmt(:,:,is),frc,nr,rlmt(:,1,is),fr) i=lm do ir=1,nri rfmt(i,ias)=fr(ir) i=i+lmmaxi end do do ir=iro,nr rfmt(i,ias)=fr(ir) i=i+lmmaxo end do end do ! interpolate up to lmaxo on outer part of muffin-tin do lm=lmmaxi+1,lmmaxo i=npci+lm do irc=irco,nrc frc(irc)=rfmt1(i) i=i+lmmaxo end do call rfinterp(nrco,rcmt(irco,is),wcrcmt(:,irco,is),frc(irco),nro, & rsp(iro,is),fr(iro)) i=npi+lm do ir=iro,nr rfmt(i,ias)=fr(ir) i=i+lmmaxo end do end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/findsym.f900000644000000000000000000000013214061636517014715 xustar0030 mtime=1623670095.051102366 30 atime=1623670093.787103539 30 ctime=1623670095.051102366 elk-7.2.42/src/findsym.f900000644002504400250440000001265314061636517016761 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: findsym ! !INTERFACE: subroutine findsym(apl1,apl2,nsym,lspl,lspn,iea) ! !USES: use modmain use moddftu ! !INPUT/OUTPUT PARAMETERS: ! apl1 : first set of atomic positions in lattice coordinates ! (in,real(3,maxatoms,maxspecies)) ! apl2 : second set of atomic positions in lattice coordinates ! (in,real(3,maxatoms,maxspecies)) ! nsym : number of symmetries (out,integer) ! lspl : spatial rotation element in lattice point group for each symmetry ! (out,integer(48)) ! lspn : spin rotation element in lattice point group for each symmetry ! (out,integer(48)) ! iea : equivalent atom index for each symmetry ! (out,integer(iea(natmmax,nspecies,48)) ! !DESCRIPTION: ! Finds the symmetries which rotate one set of atomic positions into another. ! Both sets of positions differ only by a translation vector and have the same ! muffin-tin magnetic fields (stored in the global array {\tt bfcmt}). Any ! symmetry element consists of a spatial rotation of the atomic position ! vectors followed by a global magnetic rotation: $\{\alpha_S|\alpha_R\}$. In ! the case of spin-orbit coupling $\alpha_S=\alpha_R$. The symmetries are ! returned as indices of elements in the Bravais lattice point group. An ! index to equivalent atoms is stored in the array {\tt iea}. ! ! !REVISION HISTORY: ! Created April 2007 (JKD) ! Fixed use of proper rotations for spin, February 2008 (L. Nordstrom) !EOP !BOC implicit none ! arguments real(8), intent(in) :: apl1(3,maxatoms,maxspecies) real(8), intent(in) :: apl2(3,maxatoms,maxspecies) integer, intent(out) :: nsym,lspl(48),lspn(48) integer, intent(out) :: iea(natmmax,nspecies,48) ! local variables integer isym,jsym,jsym0,jsym1 integer is,ia,ias,ja,jas,md,n real(8) sl(3,3),sc(3,3),v(3),t1 ! automatic arrays integer jea(natmmax,nspecies) real(8) apl3(3,natmmax) complex(8) dmat(lmmaxdm,nspinor,lmmaxdm,nspinor) ! external functions real(8), external :: dnrm2 nsym=0 ! loop over lattice symmetries (spatial rotations) do isym=1,nsymlat ! make real copy of lattice rotation symmetry sl(:,:)=dble(symlat(:,:,isym)) ! loop over species do is=1,nspecies ! map apl1 coordinates to [0,1) and store in apl3 do ia=1,natoms(is) apl3(:,ia)=apl1(:,ia,is) call r3frac(epslat,apl3(:,ia)) end do do ja=1,natoms(is) ! apply lattice symmetry to atomic positions v(:)=sl(:,1)*apl2(1,ja,is)+sl(:,2)*apl2(2,ja,is)+sl(:,3)*apl2(3,ja,is) ! map coordinates to [0,1) call r3frac(epslat,v) ! check if atomic positions are invariant do ia=1,natoms(is) t1=abs(apl3(1,ia)-v(1))+abs(apl3(2,ia)-v(2))+abs(apl3(3,ia)-v(3)) if (t1.lt.epslat) then ! equivalent atom index jea(ia,is)=ja goto 10 end if end do ! not invariant so try new spatial rotation goto 40 10 continue end do end do ! all atomic positions invariant at this point jsym=1 ! spin polarised case if (spinpol) then ! check invariance of magnetic fields under global spin rotation if (spinorb) then ! with spin-orbit coupling spin rotation equals spatial rotation jsym0=isym jsym1=isym else ! without spin-orbit coupling spin rotation independent of spatial rotation jsym0=1 jsym1=nsymlat end if do jsym=jsym0,jsym1 ! determinant of the symmetry matrix md=symlatd(jsym) sc(:,:)=dble(md)*symlatc(:,:,jsym) ! rotate global field and check invariance using proper part of symmetry matrix v(:)=sc(:,1)*bfieldc0(1)+sc(:,2)*bfieldc0(2)+sc(:,3)*bfieldc0(3) t1=abs(bfieldc0(1)-v(1))+abs(bfieldc0(2)-v(2))+abs(bfieldc0(3)-v(3)) ! if not invariant try a different global spin rotation if (t1.gt.epslat) goto 20 ! rotate muffin-tin magnetic fields and check invariance do is=1,nspecies do ia=1,natoms(is) ! equivalent atom ja=jea(ia,is) v(:)=sc(:,1)*bfcmt0(1,ja,is) & +sc(:,2)*bfcmt0(2,ja,is) & +sc(:,3)*bfcmt0(3,ja,is) t1=abs(bfcmt0(1,ia,is)-v(1)) & +abs(bfcmt0(2,ia,is)-v(2)) & +abs(bfcmt0(3,ia,is)-v(3)) ! if not invariant try a different global spin rotation if (t1.gt.epslat) goto 20 end do end do ! all fields invariant goto 30 20 continue ! end loop over global spin rotations end do ! magnetic fields not invariant so try different spatial rotation goto 40 end if 30 continue ! check invariance of density matrices for fixed tensor moment calculations if (ftmtype.ne.0) then n=2*(lmmaxdm*nspinor)**2 do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) ! equivalent atom ja=jea(ia,is) jas=idxas(ja,is) ! rotate the fixed tensor moment density matrix dmat(:,:,:,:)=0.d0 call rotdmat(symlatc(:,:,isym),symlatc(:,:,jsym),lmaxdm,nspinor, & lmmaxdm,dmftm(:,:,:,:,jas),dmat) ! check invariance call daxpy(n,-1.d0,dmftm(:,:,:,:,ias),1,dmat,1) t1=dnrm2(n,dmat,1)/dble(n) if (t1.gt.epslat) goto 40 end do end do end if ! everything invariant so add symmetry to set nsym=nsym+1 lspl(nsym)=isym lspn(nsym)=jsym do is=1,nspecies do ia=1,natoms(is) iea(ia,is,nsym)=jea(ia,is) end do end do 40 continue ! end loop over spatial rotations end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/zfsht.f900000644000000000000000000000013214061636517014402 xustar0030 mtime=1623670095.052102365 30 atime=1623670093.789103537 30 ctime=1623670095.052102365 elk-7.2.42/src/zfsht.f900000644002504400250440000000261414061636517016442 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zfsht ! !INTERFACE: subroutine zfsht(nr,nri,zfmt1,zfmt2) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial mesh points (in,integer) ! nri : number of points on the inner part of the muffin-tin (in,integer) ! zfmt1 : input complex muffin-tin function in spherical coordinates ! (in,complex(*)) ! zfmt2 : output complex muffin-tin function in spherical harmonics ! (out,complex(*)) ! !DESCRIPTION: ! Performs a forward spherical harmonic transform (SHT) on a complex ! muffin-tin function in spherical coordinates to obtain a function expressed ! in spherical harmonics. See also {\tt genshtmat} and {\tt zbsht}. ! !REVISION HISTORY: ! Created October 2013 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr,nri complex(8), intent(in) :: zfmt1(*) complex(8), intent(out) :: zfmt2(*) ! local variables integer i ! transform the inner part of the muffin-tin call zgemm('N','N',lmmaxi,nri,lmmaxi,zone,zfshti,lmmaxi,zfmt1,lmmaxi,zzero, & zfmt2,lmmaxi) ! transform the outer part of the muffin-tin i=lmmaxi*nri+1 call zgemm('N','N',lmmaxo,nr-nri,lmmaxo,zone,zfshto,lmmaxo,zfmt1(i),lmmaxo, & zzero,zfmt2(i),lmmaxo) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rhonorm.f900000644000000000000000000000013214061636517014730 xustar0030 mtime=1623670095.054102363 30 atime=1623670093.791103535 30 ctime=1623670095.054102363 elk-7.2.42/src/rhonorm.f900000644002504400250440000000341614061636517016771 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rhonorm ! !INTERFACE: subroutine rhonorm ! !USES: use modmain ! !DESCRIPTION: ! Loss of precision of the calculated total charge can result because the ! muffin-tin density is computed on a set of $(\theta,\phi)$ points and then ! transformed to a spherical harmonic representation. This routine adds a ! constant to the density so that the total charge is correct. If the error in ! total charge exceeds a certain tolerance then a warning is issued. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) ! Changed from rescaling to adding, September 2006 (JKD) !EOP !BOC implicit none ! local variables integer is,ia,ias integer nr,nri,ir,i real(8) t1,t2 if (.not.trhonorm) return ! check error in total charge t1=chgcalc/chgtot-1.d0 if (abs(t1).gt.epschg) then write(*,*) write(*,'("Warning(rhonorm): total charge density incorrect for s.c. & &loop ",I5)') iscl write(*,'(" Calculated : ",G18.10)') chgcalc write(*,'(" Required : ",G18.10)') chgtot end if ! error in average density t1=(chgtot-chgcalc)/omega ! add the constant difference to the density t2=t1/y00 do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) i=1 do ir=1,nri rhomt(i,ias)=rhomt(i,ias)+t2 i=i+lmmaxi end do do ir=nri+1,nr rhomt(i,ias)=rhomt(i,ias)+t2 i=i+lmmaxo end do end do rhoir(1:ngtot)=rhoir(1:ngtot)+t1 ! add the difference to the charges t1=t1*(fourpi/3.d0) do is=1,nspecies t2=t1*rmt(is)**3 do ia=1,natoms(is) ias=idxas(ia,is) chgmt(ias)=chgmt(ias)+t2 chgmttot=chgmttot+t2 end do end do chgir=chgtot-chgmttot end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genvchi0.f900000644000000000000000000000013214061636517014747 xustar0030 mtime=1623670095.055102362 30 atime=1623670093.792103534 30 ctime=1623670095.055102362 elk-7.2.42/src/genvchi0.f900000644002504400250440000001277114061636517017014 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genvchi0(t3hw,ik,lock,ssr,vqpl,gclgq,jlgqr,ylmgq,sfacgq,nm,vchi0) use modmain use modomp implicit none ! local variables logical, intent(in) :: t3hw integer, intent(in) :: ik integer(8), intent(in) :: lock(nwrf) real(8), intent(in) :: ssr,vqpl(3),gclgq(ngrf) real(8), intent(in) :: jlgqr(njcmax,nspecies,ngrf) complex(8), intent(in) :: ylmgq(lmmaxo,ngrf) complex(8), intent(in) :: sfacgq(ngrf,natmtot) integer, intent(in) :: nm complex(8), intent(inout) :: vchi0(nm,nm,nwrf) ! local variables logical tq0,tssr integer isym,jk,jkq,iw integer nst,nstq,ist,jst,kst,lst integer nm2,ig,jg,i,j,nthd real(8) vkql(3),ei,ej,eij,t1,t2 complex(8) a(3,3),z1 ! automatic arrays integer idx(nstsv),idxq(nstsv) integer ngp(nspnfv),ngpq(nspnfv) ! allocatable arrays integer, allocatable :: igpig(:,:),igpqig(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfir(:,:,:) complex(8), allocatable :: wfmtq(:,:,:,:),wfirq(:,:,:) complex(8), allocatable :: zrhomt(:,:),zrhoir(:),zrhoig(:) complex(8), allocatable :: pmat(:,:,:),zw(:),b(:,:) ! check if q=0 tq0=.false. if (sum(abs(vqpl(:))).lt.epslat) tq0=.true. ! k+q-vector in lattice coordinates vkql(:)=vkl(:,ik)+vqpl(:) ! equivalent reduced k-points for k and k+q jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) call findkpt(vkql,isym,jkq) ! count and index states at k and k+q in energy window nst=0 do ist=1,nstsv if (abs(evalsv(ist,jk)-efermi).lt.emaxrf) then nst=nst+1 idx(nst)=ist end if end do nstq=0 do jst=1,nstsv if (abs(evalsv(jst,jkq)-efermi).lt.emaxrf) then nstq=nstq+1 idxq(nstq)=jst end if end do ! set flag for scissor operator if (abs(ssr).gt.1.d-8) then tssr=.true. else tssr=.false. end if ! generate the wavefunctions for all states at k and k+q in energy window allocate(igpig(ngkmax,nspnfv)) allocate(wfmt(npcmtmax,natmtot,nspinor,nst),wfir(ngtc,nspinor,nst)) call genwfsvp(.false.,.false.,nst,idx,ngdgc,igfc,vkl(:,ik),ngp,igpig,wfmt,ngtc,& wfir) deallocate(igpig) allocate(igpqig(ngkmax,nspnfv)) allocate(wfmtq(npcmtmax,natmtot,nspinor,nstq),wfirq(ngtc,nspinor,nstq)) call genwfsvp(.false.,.false.,nstq,idxq,ngdgc,igfc,vkql,ngpq,igpqig,wfmtq,ngtc,& wfirq) deallocate(igpqig) ! read the momentum matrix elements from file for q=0 if (tq0) then allocate(pmat(nstsv,nstsv,3)) call getpmat(vkl(:,ik),pmat) ! divide by unit cell volume t1=1.d0/omega pmat(:,:,:)=t1*pmat(:,:,:) end if nm2=nm**2 call holdthd(nst,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zrhomt,zrhoir,zrhoig,zw,b) & !$OMP PRIVATE(jst,kst,lst,ei,ej,eij,t1,t2) & !$OMP PRIVATE(iw,ig,jg,z1,i,j,a) & !$OMP NUM_THREADS(nthd) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) allocate(zrhoig(ngrf),zw(nwrf)) if (tq0.and.t3hw) then allocate(b(-1:ngrf,-1:ngrf)) else allocate(b(ngrf,ngrf)) end if !$OMP DO do ist=1,nst kst=idx(ist) ei=evalsv(kst,jk) do jst=1,nstq lst=idxq(jst) t1=wkptnr*omega*(occsv(kst,jk)-occsv(lst,jkq)) if (abs(t1).lt.1.d-8) cycle ej=evalsv(lst,jkq) eij=ei-ej ! scissor operator if (tssr) then t2=eij if ((ei.gt.efermi).and.(ej.le.efermi)) then eij=eij+ssr else if ((ei.le.efermi).and.(ej.gt.efermi)) then eij=eij-ssr end if t2=eij/t2 ! scale the momentum matrix elements for q=0 if (tq0) pmat(kst,lst,1:3)=t2*pmat(kst,lst,1:3) end if ! frequency-dependent part in response function formula for all frequencies do iw=1,nwrf zw(iw)=t1/(eij+wrf(iw)) end do ! compute the complex density in G+q-space call genzrho(.true.,.true.,ngtc,wfmt(:,:,:,ist),wfir(:,:,ist), & wfmtq(:,:,:,jst),wfirq(:,:,jst),zrhomt,zrhoir) call zftzf(ngrf,jlgqr,ylmgq,ngrf,sfacgq,zrhomt,zrhoir,zrhoig) ! Hermitian part of body do jg=1,ngrf do ig=1,jg-1 b(ig,jg)=conjg(b(jg,ig)) end do z1=gclgq(jg)*conjg(zrhoig(jg)) do ig=jg,ngrf b(ig,jg)=gclgq(ig)*zrhoig(ig)*z1 end do end do ! case of q=0 if (tq0) then if (t3hw) then b(-1:1,-1:1)=0.d0 ! calculate 3 x ngrf wings of matrix t1=-sqrt(fourpi)/eij do i=-1,1 z1=t1*pmat(kst,lst,i+2) b(i,2:)=z1*conjg(zrhoig(2:))*gclgq(2:) b(2:,i)=conjg(b(i,2:)) end do else ! use trace of 3 x 3 head of matrix t1=sum(dble(pmat(kst,lst,1:3))**2+aimag(pmat(kst,lst,1:3))**2)/3.d0 b(1,1)=(fourpi/eij**2)*t1 ! wings of matrix t1=-sqrt(fourpi)/eij z1=(t1/3.d0)*(pmat(kst,lst,1)+pmat(kst,lst,2)+pmat(kst,lst,3)) b(1,2:)=z1*conjg(zrhoig(2:))*gclgq(2:) b(2:,1)=conjg(b(1,2:)) end if end if ! add to body and wings of the response function do iw=1,nwrf call omp_set_lock(lock(iw)) call zaxpy(nm2,zw(iw),b,1,vchi0(1,1,iw),1) call omp_unset_lock(lock(iw)) end do ! calculate 3 x 3 head if (tq0.and.t3hw) then t1=-fourpi/eij zw(1:nwrf)=zw(1:nwrf)/wrf(1:nwrf) do j=1,3 do i=1,3 a(i,j)=t1*pmat(kst,lst,i)*conjg(pmat(kst,lst,j)) end do end do ! add to the head of the response function do iw=1,nwrf call omp_set_lock(lock(iw)) vchi0(1:3,1:3,iw)=vchi0(1:3,1:3,iw)+a(1:3,1:3)*zw(iw) call omp_unset_lock(lock(iw)) end do end if ! end loop over jst end do ! end loop over ist end do !$OMP END DO deallocate(zrhomt,zrhoir,zrhoig,zw,b) !$OMP END PARALLEL call freethd(nthd) deallocate(wfmt,wfir,wfmtq,wfirq) if (tq0) deallocate(pmat) end subroutine elk-7.2.42/src/PaxHeaders.21776/zfmtconj.f900000644000000000000000000000013014061636517015074 xustar0029 mtime=1623670095.05710236 30 atime=1623670093.794103532 29 ctime=1623670095.05710236 elk-7.2.42/src/zfmtconj.f900000644002504400250440000000376514061636517017146 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine zfmtconj(nr,nri,np,zfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri,np complex(8), intent(inout) :: zfmt(np) ! local variables integer i ! automatic arrays complex(8) zfmt1(np) zfmt1(:)=zfmt(:) call zflmnconj(lmaxi,nri,lmmaxi,zfmt1,zfmt) i=lmmaxi*nri+1 call zflmnconj(lmaxo,nr-nri,lmmaxo,zfmt1(i),zfmt(i)) return contains !BOP ! !ROUTINE: zflmnconj ! !INTERFACE: pure subroutine zflmnconj(lmax,n,ld,zflm1,zflm2) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum angular momentum (in,integer) ! n : number of functions to conjugate (in,integer) ! ld : leading dimension (in,integer) ! zflm1 : coefficients of input complex spherical harmonic expansion ! (in,complex((lmax+1)**2))) ! zflm2 : coefficients of output complex spherical harmonic expansion ! (out,complex((lmax+1)**2))) ! !DESCRIPTION: ! Returns the complex conjugate of a function expanded in spherical harmonics. ! In other words, given the input function coefficients $z_{lm}$, the routine ! returns $z'_{lm}=(-1)^m z^*_{l-m}$ so that ! $$ \sum_{lm}z'_{lm}Y_{lm}(\theta,\phi)=\left(\sum_{lm}z_{lm}Y_{lm} ! (\theta,\phi)\right)^* $$ ! for all $(\theta,\phi)$. ! ! !REVISION HISTORY: ! Created April 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: lmax,n,ld complex(8), intent(in) :: zflm1(ld,n) complex(8), intent(out) :: zflm2(ld,n) ! local variables integer l,m,lm1,lm2 do l=0,lmax lm1=l**2 lm2=(l+1)**2+1 do m=-l,-1 lm1=lm1+1 lm2=lm2-1 if (mod(m,2).eq.0) then zflm2(lm1,:)=conjg(zflm1(lm2,:)) zflm2(lm2,:)=conjg(zflm1(lm1,:)) else zflm2(lm1,:)=-conjg(zflm1(lm2,:)) zflm2(lm2,:)=-conjg(zflm1(lm1,:)) end if end do ! m=0 case lm1=lm1+1 zflm2(lm1,:)=conjg(zflm1(lm1,:)) end do end subroutine !EOC end subroutine elk-7.2.42/src/PaxHeaders.21776/stheta_sq.f900000644000000000000000000000013214061636517015237 xustar0030 mtime=1623670095.058102359 30 atime=1623670093.796103531 30 ctime=1623670095.058102359 elk-7.2.42/src/stheta_sq.f900000644002504400250440000000160114061636517017272 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: stheta_sq ! !INTERFACE: elemental real(8) function stheta_sq(x) ! !INPUT/OUTPUT PARAMETERS: ! x : real argument (in,real) ! !DESCRIPTION: ! Returns the Heaviside step function corresponding to the square-wave pulse ! approximation to the Dirac delta function ! $$ \tilde\Theta(x)=\left\{\begin{array}{ll} ! 0 & \quad x \le -1/2 \\ ! x+1/2 & \quad -1/2 < x < 1/2 \\ ! 1 & \quad x\ge 1 \end{array}\right. $$ ! ! !REVISION HISTORY: ! Created July 2008 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: x if (x.le.-0.5d0) then stheta_sq=0.d0 return end if if (x.lt.0.5d0) then stheta_sq=x+0.5d0 else stheta_sq=1.d0 end if end function !EOC elk-7.2.42/src/PaxHeaders.21776/sdelta_lr.f900000644000000000000000000000013114061636517015214 xustar0030 mtime=1623670095.060102357 29 atime=1623670093.79710353 30 ctime=1623670095.060102357 elk-7.2.42/src/sdelta_lr.f900000644002504400250440000000063114061636517017252 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. elemental real(8) function sdelta_lr(x) implicit none ! arguments real(8), intent(in) :: x ! local variables real(8), parameter :: twopi=6.2831853071795864769d0 sdelta_lr=1.d0/(twopi*(x**2+0.25d0)) end function elk-7.2.42/src/PaxHeaders.21776/stheta_lr.f900000644000000000000000000000013214061636517015231 xustar0030 mtime=1623670095.061102356 30 atime=1623670093.799103528 30 ctime=1623670095.061102356 elk-7.2.42/src/stheta_lr.f900000644002504400250440000000062114061636517017265 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. elemental real(8) function stheta_lr(x) implicit none ! arguments real(8), intent(in) :: x ! local variables real(8), parameter :: pi=3.1415926535897932385d0 stheta_lr=0.5d0+atan(2.d0*x)/pi end function elk-7.2.42/src/PaxHeaders.21776/findsymsite.f900000644000000000000000000000013214061636517015602 xustar0030 mtime=1623670095.063102355 30 atime=1623670093.800103527 30 ctime=1623670095.063102355 elk-7.2.42/src/findsymsite.f900000644002504400250440000000163614061636517017645 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine findsymsite use modmain implicit none ! local variables integer is,js,ia,ja,ias real(8) apl(3,maxatoms,maxspecies) ! automatic arrays real(8) iea(natmmax,nspecies,48) ! allocate the site symmetry arrays if (allocated(nsymsite)) deallocate(nsymsite) allocate(nsymsite(natmtot)) if (allocated(lsplsyms)) deallocate(lsplsyms) allocate(lsplsyms(48,natmtot)) if (allocated(lspnsyms)) deallocate(lspnsyms) allocate(lspnsyms(48,natmtot)) do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) do js=1,nspecies do ja=1,natoms(js) apl(:,ja,js)=atposl(:,ja,js)-atposl(:,ia,is) end do end do call findsym(apl,apl,nsymsite(ias),lsplsyms(:,ias),lspnsyms(:,ias),iea) end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/genlmirep.f900000644000000000000000000000013214061636517015226 xustar0030 mtime=1623670095.064102354 30 atime=1623670093.802103525 30 ctime=1623670095.064102354 elk-7.2.42/src/genlmirep.f900000644002504400250440000000430414061636517017264 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genlmirep(lmax,ld,elm,ulm) use modmain implicit none ! arguments integer, intent(in) :: lmax integer, intent(in) :: ld real(8), intent(out) :: elm(ld,natmtot) complex(8), intent(out) :: ulm(ld,ld,natmtot) ! local variables integer isym,lspl,is,ia,ias integer lmmax,i,j,l,lm,n,p integer info,lwork ! allocatable arrays real(8), allocatable :: rwork(:) complex(8), allocatable :: ulat(:,:,:) complex(8), allocatable :: a(:,:),b(:,:) complex(8), allocatable :: h(:,:),work(:) lmmax=(lmax+1)**2 allocate(rwork(3*lmmax)) allocate(ulat(lmmax,lmmax,nsymlat)) allocate(a(lmmax,lmmax),b(lmmax,lmmax)) allocate(h(lmmax,lmmax)) lwork=2*lmmax allocate(work(lwork)) ! construct (l,m) rotation matrix for each lattice symmetry a(:,:)=0.d0 do i=1,lmmax a(i,i)=1.d0 end do do isym=1,nsymlat call rotzflm(symlatc(:,:,isym),0,lmax,lmmax,lmmax,lmmax,a,ulat(:,:,isym)) end do ! set up pseudorandom symmetric matrix H h(:,:)=0.d0 p=1 do l=0,lmax n=2*l+1 lm=l*(l+1)-l+1 do i=lm,lm+n-1 do j=i,lm+n-1 ! Park and Miller linear congruential generator p=mod(p*171,30269) h(i,j)=mod(p,lmmax) h(j,i)=h(i,j) end do end do end do ! loop over species and atoms do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) ! symmetrise H with site symmetries b(:,:)=0.d0 do isym=1,nsymsite(ias) ! spatial rotation element in lattice point group lspl=lsplsyms(isym,ias) ! apply lattice symmetry as U*H*conjg(U') call zgemm('N','N',lmmax,lmmax,lmmax,zone,ulat(:,:,lspl),lmmax,h,lmmax, & zzero,a,lmmax) call zgemm('N','C',lmmax,lmmax,lmmax,zone,a,lmmax,ulat(:,:,lspl),lmmax, & zone,b,lmmax) end do ! block diagonalise symmetrised H do l=0,lmax n=2*l+1 lm=l*(l+1)-l+1 call zheev('V','U',n,b(lm,lm),lmmax,elm(lm,ias),work,lwork,rwork,info) end do ! the unitary matrix U is the transpose of the eigenvector array do i=1,lmmax do j=1,lmmax ulm(i,j,ias)=b(j,i) end do end do end do end do deallocate(rwork,ulat,a,b,h,work) end subroutine elk-7.2.42/src/PaxHeaders.21776/writespecies.f900000644000000000000000000000013214061636517015752 xustar0030 mtime=1623670095.066102352 30 atime=1623670093.804103523 30 ctime=1623670095.066102352 elk-7.2.42/src/writespecies.f900000644002504400250440000000526414061636517020016 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writespecies(symb,name,zn,mass,rmin,rm,rmax,nrm,nst,n,l,k,occ,eval) use modmain use modmpi implicit none ! arguments character(*), intent(in) :: symb,name real(8), intent(in) :: zn,mass real(8), intent(in) :: rmin,rm,rmax integer, intent(in) :: nrm,nst integer, intent(in) :: n(nst),l(nst),k(nst) real(8), intent(in) :: occ(nst) real(8), intent(in) :: eval(nst) ! local variables integer lmax,nlo integer ist,jst,i logical core(maxstsp),lorb(maxstsp) ! default APW band energy real(8), parameter :: e0=0.15d0 ! find which states belong to core do ist=1,nst if (eval(ist).lt.ecvcut) then core(ist)=.true. else core(ist)=.false. end if end do ! check that the state for same n and l but different k is also core do ist=1,nst if (core(ist)) then do jst=1,nst if ((n(ist).eq.n(jst)).and.(l(ist).eq.l(jst))) core(jst)=.true. end do end if end do lmax=1 do ist=1,nst if (.not.core(ist)) lmax=max(lmax,l(ist)) end do ! determine the local orbitals nlo=lmax+1 lorb(:)=.false. do ist=1,nst if (.not.core(ist)) then if ((l(ist).eq.0).or.(l(ist).lt.k(ist))) then if ((eval(ist).lt.esccut).or.(l(ist).ge.2)) then lorb(ist)=.true. nlo=nlo+1 end if end if end if end do if (mp_mpi) then open(55,file=trim(symb)//'.in',form='FORMATTED') write(55,'(" ''",A,"''",T45,": spsymb")') trim(symb) write(55,'(" ''",A,"''",T45,": spname")') trim(name) write(55,'(G14.6,T45,": spzn")') zn write(55,'(G18.10,T45,": spmass")') mass write(55,'(G14.6,2F10.4,I6,T45,": rminsp, rmt, rmaxsp, nrmt")') rmin,rm, & rmax,nrm write(55,'(I4,T45,": nstsp")') nst write(55,'(3I4,G14.6,L1,T45,": nsp, lsp, ksp, occsp, spcore")') n(1),l(1), & k(1),occ(1),core(1) do ist=2,nst write(55,'(3I4,G14.6,L1)') n(ist),l(ist),k(ist),occ(ist),core(ist) end do write(55,'(I4,T45,": apword")') 1 write(55,'(F10.4,I4," ",L1,T45,": apwe0, apwdm, apwve")') e0,0,.false. write(55,'(I4,T45,": nlx")') 0 write(55,'(I4,T45,": nlorb")') nlo do i=0,lmax write(55,'(2I4,T45,": lorbl, lorbord")') i,2 write(55,'(F10.4,I4," ",L1,T45,": lorbe0, lorbdm, lorbve")') e0,0,.false. write(55,'(F10.4,I4," ",L1)') e0,1,.false. end do do ist=1,nst if (lorb(ist)) then write(55,'(2I4,T45,": lorbl, lorbord")') l(ist),2 write(55,'(F10.4,I4," ",L1,T45,": lorbe0, lorbdm, lorbve")') e0,0,.false. write(55,'(F10.4,I4," ",L1)') eval(ist),0,.true. end if end do close(55) end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/rhomagk.f900000644000000000000000000000013214061636517014674 xustar0030 mtime=1623670095.067102351 30 atime=1623670093.805103522 30 ctime=1623670095.067102351 elk-7.2.42/src/rhomagk.f900000644002504400250440000001706114061636517016736 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2010 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rhomagk ! !INTERFACE: subroutine rhomagk(ngp,igpig,lock,wppt,occsvp,apwalm,evecfv,evecsv) ! !USES: use modmain use modomp ! !INPUT/OUTPUT PARAMETERS: ! ngp : number of G+p-vectors (in,integer(nspnfv)) ! igpig : index from G+p-vectors to G-vectors (in,integer(ngkmax,nspnfv)) ! lock : OpenMP lock for each atom (in,integer(natmtot)) ! wppt : weight of input p-point (in,real) ! occsvp : occupation number for each state (in,real(nstsv)) ! apwalm : APW matching coefficients ! (in,complex(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) ! evecfv : first-variational eigenvectors (in,complex(nmatmax,nstfv,nspnfv)) ! evecsv : second-variational eigenvectors (in,complex(nstsv,nstsv)) ! !DESCRIPTION: ! Generates the partial valence charge density and magnetisation from the ! eigenvectors at a particular $k$-point. In the muffin-tin region, the ! wavefunction is obtained in terms of its $(l,m)$-components from both the ! APW and local-orbital functions. Using a backward spherical harmonic ! transform (SHT), the wavefunction is converted to real-space and the density ! obtained from its modulus squared. A similar proccess is used for the ! intersitial density in which the wavefunction in real-space is obtained from ! a Fourier transform of the APW functions. See routines {\tt wavefmt}, ! {\tt genshtmat} and {\tt eveqn}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) ! Removed conversion to spherical harmonics, January 2009 (JKD) ! Partially de-phased the muffin-tin magnetisation for spin-spirals, ! February 2009 (FC, FB & LN) ! Optimisations, July 2010 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: ngp(nspnfv),igpig(ngkmax,nspnfv) integer(8), intent(in) :: lock(natmtot) real(8), intent(in) :: wppt,occsvp(nstsv) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv) complex(8), intent(in) :: evecfv(nmatmax,nstfv,nspnfv),evecsv(nstsv,nstsv) ! local variables integer ispn,jspn,ist integer is,ias,i,j,n,nthd integer nrc,nrci,npc real(8) wo real(8) ts0,ts1 complex(8) zq(2),z1 ! automatic arrays logical done(nstfv,nspnfv) complex(8) wfmt1(npcmtmax),wfmt2(npcmtmax,nspinor) complex(8) wfir(ngtc,nspinor),wfgp(ngkmax) ! allocatable arrays complex(8), allocatable :: wfmt3(:,:,:) call timesec(ts0) !----------------------------------------------! ! muffin-tin density and magnetisation ! !----------------------------------------------! call holdthd(natmtot,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfmt1,wfmt2,wfmt3) & !$OMP PRIVATE(is,nrc,nrci,npc) & !$OMP PRIVATE(zq,done,i,j,wo) & !$OMP PRIVATE(ispn,jspn,n,ist,z1) & !$OMP NUM_THREADS(nthd) if (tevecsv) allocate(wfmt3(npcmtmax,nstfv,nspnfv)) !$OMP DO do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) ! de-phasing factor for spin-spirals if (ssdph) then zq(1)=zqss(ias) zq(2)=conjg(zq(1)) end if done(:,:)=.false. do j=1,nstsv wo=occsvp(j) if (abs(wo).lt.epsocc) cycle wo=wo*wppt if (tevecsv) then ! generate spinor wavefunction from second-variational eigenvectors i=0 do ispn=1,nspinor jspn=jspnfv(ispn) n=ngp(jspn) wfmt2(1:npc,ispn)=0.d0 do ist=1,nstfv i=i+1 z1=evecsv(i,j) if (abs(dble(z1))+abs(aimag(z1)).lt.epsocc) cycle if (ssdph) z1=z1*zq(ispn) if (.not.done(ist,jspn)) then call wavefmt(lradstp,ias,n,apwalm(:,:,:,ias,jspn), & evecfv(:,ist,jspn),wfmt1) ! convert to spherical coordinates call zbsht(nrc,nrci,wfmt1,wfmt3(:,ist,jspn)) done(ist,jspn)=.true. end if ! add to spinor wavefunction call zaxpy(npc,z1,wfmt3(:,ist,jspn),1,wfmt2(:,ispn),1) end do end do else ! spin-unpolarised wavefunction call wavefmt(lradstp,ias,ngp,apwalm(:,:,:,ias,1),evecfv(:,j,1),wfmt1) ! convert to spherical coordinates call zbsht(nrc,nrci,wfmt1,wfmt2) end if ! add to density and magnetisation call omp_set_lock(lock(ias)) if (spinpol) then ! spin-polarised if (ncmag) then ! non-collinear call rmk1(npc,wo,wfmt2,wfmt2(:,2),rhomt(:,ias),magmt(:,ias,1), & magmt(:,ias,2),magmt(:,ias,3)) else ! collinear call rmk2(npc,wo,wfmt2,wfmt2(:,2),rhomt(:,ias),magmt(:,ias,1)) end if else ! spin-unpolarised call rmk3(npc,wo,wfmt2,rhomt(:,ias)) end if call omp_unset_lock(lock(ias)) end do ! end loop over atoms end do !$OMP END DO if (tevecsv) deallocate(wfmt3) !$OMP END PARALLEL call freethd(nthd) !------------------------------------------------! ! interstitial density and magnetisation ! !------------------------------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(wfir,wfgp,wo,i) & !$OMP PRIVATE(ispn,jspn,n,ist,z1) & !$OMP NUM_THREADS(nthd) do j=1,nstsv wo=occsvp(j) if (abs(wo).lt.epsocc) cycle wo=wo*wppt/omega if (tevecsv) then ! generate spinor wavefunction from second-variational eigenvectors i=0 do ispn=1,nspinor jspn=jspnfv(ispn) n=ngp(jspn) wfgp(1:n)=0.d0 do ist=1,nstfv i=i+1 z1=evecsv(i,j) if (abs(dble(z1))+abs(aimag(z1)).lt.epsocc) cycle call zaxpy(n,z1,evecfv(:,ist,jspn),1,wfgp,1) end do wfir(:,ispn)=0.d0 wfir(igfc(igpig(1:n,jspn)),ispn)=wfgp(1:n) ! Fourier transform wavefunction to real-space call zfftifc(3,ngdgc,1,wfir(:,ispn)) end do else ! spin-unpolarised wavefunction wfir(:,1)=0.d0 wfir(igfc(igpig(1:ngp(1),1)),1)=evecfv(1:ngp(1),j,1) call zfftifc(3,ngdgc,1,wfir) end if ! add to density and magnetisation !$OMP CRITICAL(rhomagk_) if (spinpol) then ! spin-polarised if (ncmag) then ! non-collinear call rmk1(ngtc,wo,wfir,wfir(:,2),rhoir,magir,magir(:,2),magir(:,3)) else ! collinear call rmk2(ngtc,wo,wfir,wfir(:,2),rhoir,magir) end if else ! spin-unpolarised call rmk3(ngtc,wo,wfir,rhoir) end if !$OMP END CRITICAL(rhomagk_) end do !$OMP END PARALLEL DO call freethd(nthd) call timesec(ts1) !$OMP ATOMIC timerho=timerho+ts1-ts0 return contains pure subroutine rmk1(n,wo,wf1,wf2,rho,mag1,mag2,mag3) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf1(n),wf2(n) real(8), intent(inout) :: rho(n),mag1(n),mag2(n),mag3(n) ! local variables integer i real(8) wo2,t1,t2 real(8) a1,b1,a2,b2 wo2=2.d0*wo !$OMP SIMD PRIVATE(a1,b1,a2,b2,t1,t2) SIMDLEN(8) do i=1,n a1=dble(wf1(i)); b1=aimag(wf1(i)) a2=dble(wf2(i)); b2=aimag(wf2(i)) t1=a1**2+b1**2; t2=a2**2+b2**2 mag1(i)=mag1(i)+wo2*(a1*a2+b1*b2) mag2(i)=mag2(i)+wo2*(a1*b2-b1*a2) mag3(i)=mag3(i)+wo*(t1-t2) rho(i)=rho(i)+wo*(t1+t2) end do end subroutine pure subroutine rmk2(n,wo,wf1,wf2,rho,mag) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf1(n),wf2(n) real(8), intent(inout) :: rho(n),mag(n) ! local variables integer i real(8) t1,t2 !$OMP SIMD PRIVATE(t1,t2) SIMDLEN(8) do i=1,n t1=dble(wf1(i))**2+aimag(wf1(i))**2 t2=dble(wf2(i))**2+aimag(wf2(i))**2 mag(i)=mag(i)+wo*(t1-t2) rho(i)=rho(i)+wo*(t1+t2) end do end subroutine pure subroutine rmk3(n,wo,wf,rho) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf(n) real(8), intent(inout) :: rho(n) rho(:)=rho(:)+wo*(dble(wf(:))**2+aimag(wf(:))**2) end subroutine end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/symrvfmt.f900000644000000000000000000000013114061636517015132 xustar0030 mtime=1623670095.069102349 29 atime=1623670093.80710352 30 ctime=1623670095.069102349 elk-7.2.42/src/symrvfmt.f900000644002504400250440000000720114061636517017170 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine symrvfmt(tspin,tnc,nr,nri,np,ld,rvfmt) use modmain implicit none ! arguments logical, intent(in) :: tspin,tnc integer, intent(in) :: nr(nspecies),nri(nspecies),np(nspecies) integer, intent(in) :: ld real(8), intent(inout) :: rvfmt(ld,natmtot,*) ! local variables integer is,ia,ja,ias,jas integer nd,isym,lspl,lspn,i real(8) sc(3,3),t0 real(8) x1,x2,x3,y1,y2,y3 ! automatic arrays logical done(natmmax) ! allocatable arrays real(8), allocatable :: rvfmt1(:,:,:),rvfmt2(:,:) ! dimension of the vector field if (tnc) then nd=3 else nd=1 end if allocate(rvfmt1(ld,natmmax,nd),rvfmt2(ld,nd)) t0=1.d0/dble(nsymcrys) do is=1,nspecies ! make copy of vector field for all atoms of current species do i=1,nd do ia=1,natoms(is) ias=idxas(ia,is) call dcopy(np(is),rvfmt(:,ias,i),1,rvfmt1(:,ia,i),1) end do end do done(:)=.false. do ia=1,natoms(is) if (done(ia)) cycle ias=idxas(ia,is) rvfmt(1:np(is),ias,1:nd)=0.d0 ! begin loop over crystal symmetries do isym=1,nsymcrys ! equivalent atom ja=ieqatom(ia,is,isym) ! parallel transport of vector field lspl=lsplsymc(isym) do i=1,nd call rotrfmt(symlatc(:,:,lspl),nr(is),nri(is),rvfmt1(:,ja,i), & rvfmt2(:,i)) end do if (tspin) then ! global spin proper rotation matrix in Cartesian coordinates lspn=lspnsymc(isym) sc(:,:)=symlatd(lspn)*symlatc(:,:,lspn) else ! set spin rotation equal to spatial rotation lspn=lspl sc(:,:)=symlatc(:,:,lspl) end if ! global spin rotation of vector field if (tnc) then ! non-collinear case do i=1,np(is) x1=rvfmt2(i,1); x2=rvfmt2(i,2); x3=rvfmt2(i,3) y1=sc(1,1)*x1+sc(1,2)*x2+sc(1,3)*x3 y2=sc(2,1)*x1+sc(2,2)*x2+sc(2,3)*x3 y3=sc(3,1)*x1+sc(3,2)*x2+sc(3,3)*x3 rvfmt(i,ias,1)=rvfmt(i,ias,1)+y1 rvfmt(i,ias,2)=rvfmt(i,ias,2)+y2 rvfmt(i,ias,3)=rvfmt(i,ias,3)+y3 end do else ! collinear case call daxpy(np(is),sc(3,3),rvfmt2,1,rvfmt(:,ias,1),1) end if ! end loop over crystal symmetries end do ! normalise do i=1,nd call dscal(np(is),t0,rvfmt(:,ias,i),1) end do ! mark atom as done done(ia)=.true. ! rotate into equivalent atoms do isym=1,nsymcrys ja=ieqatom(ia,is,isym) if (done(ja)) cycle jas=idxas(ja,is) ! parallel transport of vector field (using operation inverse) lspl=isymlat(lsplsymc(isym)) do i=1,nd call rotrfmt(symlatc(:,:,lspl),nr(is),nri(is),rvfmt(:,ias,i), & rvfmt(:,jas,i)) end do if (tspin) then ! inverse of global proper rotation matrix in Cartesian coordinates lspn=isymlat(lspnsymc(isym)) sc(:,:)=symlatd(lspn)*symlatc(:,:,lspn) else ! set spin rotation equal to spatial rotation lspn=lspl sc(:,:)=symlatc(:,:,lspl) end if ! global spin rotation of vector field if (tnc) then ! non-collinear case do i=1,np(is) x1=rvfmt(i,jas,1); x2=rvfmt(i,jas,2); x3=rvfmt(i,jas,3) y1=sc(1,1)*x1+sc(1,2)*x2+sc(1,3)*x3 y2=sc(2,1)*x1+sc(2,2)*x2+sc(2,3)*x3 y3=sc(3,1)*x1+sc(3,2)*x2+sc(3,3)*x3 rvfmt(i,jas,1)=y1; rvfmt(i,jas,2)=y2; rvfmt(i,jas,3)=y3 end do else ! collinear case call dscal(np(is),sc(3,3),rvfmt(:,jas,1),1) end if ! mark atom as done done(ja)=.true. end do ! end loop over atoms and species end do end do deallocate(rvfmt1,rvfmt2) end subroutine elk-7.2.42/src/PaxHeaders.21776/wigner3jf.f900000644000000000000000000000013214061636517015142 xustar0030 mtime=1623670095.070102348 30 atime=1623670093.808103519 30 ctime=1623670095.070102348 elk-7.2.42/src/wigner3jf.f900000644002504400250440000000523014061636517017177 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: wigner3jf ! !INTERFACE: real(8) function wigner3jf(j12,j22,j32,m12,m22,m32) ! !INPUT/OUTPUT PARAMETERS: ! j12, j22, j32 : angular momentum quantum numbers times 2 (in,integer) ! m12, m22, m32 : magnetic quantum numbers times 2 (in,integer) ! !DESCRIPTION: ! Returns the Wigner $3j$-symbol for the case where the arguments may be ! fractional, i.e. multiples of $\frac{1}{2}$. The input parameters to this ! function are taken to be twice their actual values, which allows them to ! remain integers. The formula used is identical to that in {\tt wigner3j}. ! ! !REVISION HISTORY: ! Created January 2014 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: j12,j22,j32 integer, intent(in) :: m12,m22,m32 ! local variables integer jm1,jm2,jm3,n1,n2 integer l12,l22,l32,l42 integer k,k1,k2,l1,l2,l3 real(8) sgn,sm,t1 ! external functions real(8), external :: factnm,factr ! check input variables if ((j12.lt.0).or.(j22.lt.0).or.(j32.lt.0).or.(abs(m12).gt.j12).or. & (abs(m22).gt.j22).or.(abs(m32).gt.j32)) then write(*,*) write(*,'("Error(wigner3jf): invalid arguments :")') write(*,'("j12 = ",I8," j22 = ",I8," j32 = ",I8)') j12,j22,j32 write(*,'("m12 = ",I8," m22 = ",I8," m32 = ",I8)') m12,m22,m32 write(*,*) stop end if if ((j12.eq.0).and.(j22.eq.0).and.(j32.eq.0)) then wigner3jf=1.d0 return end if if ((j12.gt.100).or.(j22.gt.100).or.(j32.gt.100)) then write(*,*) write(*,'("Error(wigner3jf): angular momenta out of range : ",3I8)') j12, & j22,j32 write(*,*) stop end if jm1=j12+m12 jm2=j22+m22 jm3=j32+m32 if ((mod(jm1,2).ne.0).or.(mod(jm2,2).ne.0).or.(mod(jm3,2).ne.0)) then wigner3jf=0.d0 return end if l12=j22-j12+j32 l22=j12-j22+j32 l32=j12+j22-j32 l42=j12+j22+j32 if ((mod(l12,2).ne.0).or.(mod(l22,2).ne.0).or.(mod(l32,2).ne.0).or. & (mod(l42,2).ne.0)) then wigner3jf=0.d0 return end if l1=l12/2 l2=l22/2 l3=l32/2 if ((m12+m22+m32.ne.0).or.(l1.lt.0).or.(l2.lt.0).or.(l3.lt.0)) then wigner3jf=0.d0 return end if n1=(j12-m12)/2 n2=(j22+m22)/2 k1=max(0,n1-l2,n2-l1) k2=min(l3,n1,n2) k=k1+(j22-j12+m32)/2 if (mod(k,2).ne.0) then sgn=-1.d0 else sgn=1.d0 end if sm=0.d0 do k=k1,k2 t1=sgn*factr(l1,l1-n2+k)*factr(l2,l2-n1+k)*factr(l3,l3-k) sm=sm+t1/(factnm(k,1)*factnm(n1-k,1)*factnm(n2-k,1)) sgn=-sgn end do jm1=jm1/2 jm2=jm2/2 jm3=jm3/2 t1=factr(jm1,l1)*factr(jm2,l2)*factr(jm3,l3) jm1=(j12-m12)/2 jm2=(j22-m22)/2 jm3=(j32-m32)/2 t1=t1*factr(jm3,1+l42/2)*factnm(jm1,1)*factnm(jm2,1) wigner3jf=sm*sqrt(t1) end function !EOC elk-7.2.42/src/PaxHeaders.21776/wigner6j.f900000644000000000000000000000013214061636517014777 xustar0030 mtime=1623670095.072102346 30 atime=1623670093.810103517 30 ctime=1623670095.072102346 elk-7.2.42/src/wigner6j.f900000644002504400250440000000610714061636517017040 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: wigner6j ! !INTERFACE: real(8) function wigner6j(j1,j2,j3,k1,k2,k3) ! !INPUT/OUTPUT PARAMETERS: ! j1, j2, j3 : angular momentum quantum numbers (in,integer) ! k1, k2, k3 : angular momentum quantum numbers (in,integer) ! !DESCRIPTION: ! Returns the Wigner $6j$-symbol for integer arguments. This is computed using ! the Racah formula: ! \begin{align*} ! &\left\{\begin{matrix} j_1 & j_2 & j_3 \\ k_1 & k_2 & k_3 \end{matrix} ! \right\}=\sqrt{\Delta(j_1\,j_2\,j_3)\Delta(j_1\,k_2\,k_3) ! \Delta(k_1\,j_2\,k_3)\Delta(k_1\,k_2\,j_3)}\, ! \sum_n\frac{(-1)^n(n+1)!}{f(n)}, ! \end{align*} ! where ! \begin{align*} ! f(n)=&(n-j_1-j_2-j_3)!\,(n-j_1-k_2-k_3)!\,(n-k_1-j_2-k_3)!\, ! (n-k_1-k_2-j_3)! \\ ! &\times(j_1+j_2+k_1+k_2-n)!\,(j_2+j_3+k_2+k_3-n)!\,(j_1+j_3+k_1+k_3-n)! ! \end{align*} ! and ! $$ \Delta(a,b,c)=\frac{(a+b-c)!\,(a-b+c)!\,(-a+b+c)!}{(a+b+c+1)!} $$ ! is the triangle coefficient, and where the sum is over all integers $n$ for ! which the factorials in $f(n)$ have non-negative arguments. The Wigner-$6j$ ! function is zero unless each triad, $(j_1\,j_2\,j_3)$, $(j_1\,k_2\,k_3)$, ! $(k_1\,j_2\,k_3)$ and $(k_1\,k_2\,j_3)$, satifies the triangle inequalities: ! $$ |x-y|\le z \le x+y, $$ ! for triad $(x,y,z)$. See, for example, A. Messiah, {\it Quantum Mechanics}, ! Vol. 2., 1061-1066 (1962). ! ! !REVISION HISTORY: ! Created August 2009 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: j1,j2,j3 integer, intent(in) :: k1,k2,k3 ! local variables integer n0,n1,n real(8) sm,t1,t2 ! external functions real(8), external :: factnm,factr wigner6j=0.d0 if ((abs(j1-j2).gt.j3).or.((j1+j2).lt.j3)) return if ((abs(j1-k2).gt.k3).or.((j1+k2).lt.k3)) return if ((abs(k1-j2).gt.k3).or.((k1+j2).lt.k3)) return if ((abs(k1-k2).gt.j3).or.((k1+k2).lt.j3)) return if ((abs(j1).gt.50).or.(abs(j2).gt.50).or.(abs(j3).gt.50).or. & (abs(k1).gt.50).or.(abs(k2).gt.50).or.(abs(k3).gt.50)) then write(*,*) write(*,'("Error(wigner6j): arguments out of range :")') write(*,'(" j1, j2, j3 = ",3I8)') j1,j2,j3 write(*,'(" k1, k2, k3 = ",3I8)') k1,k2,k3 write(*,*) stop end if ! range for summation n0=max(j1+j2+j3,j1+k2+k3,k1+j2+k3,k1+k2+j3) n1=min(j1+j2+k1+k2,j2+j3+k2+k3,j1+j3+k1+k3) ! Racah formula summation sm=0.d0 do n=n0,n1 t1=dble((-1)**n)*factr(n+1,n-(j1+j2+j3)) t2=factnm(n-(j1+k2+k3),1)*factnm(n-(k1+j2+k3),1)*factnm(n-(k1+k2+j3),1) t2=t2*factnm(j1+j2+k1+k2-n,1)*factnm(j2+j3+k2+k3-n,1)*factnm(j1+j3+k1+k3-n,1) sm=sm+t1/t2 end do ! multiply by prefactor wigner6j=sqrt(triangle(j1,j2,j3)*triangle(j1,k2,k3) & *triangle(k1,j2,k3)*triangle(k1,k2,j3))*sm return contains real(8) function triangle(a,b,c) implicit none ! arguments integer, intent(in) :: a,b,c ! external functions real(8), external :: factnm,factr triangle=factr(a+b-c,a+b+c+1)*factnm(a-b+c,1)*factnm(-a+b+c,1) end function end function !EOC elk-7.2.42/src/PaxHeaders.21776/genhvec.f900000644000000000000000000000013214061636517014663 xustar0030 mtime=1623670095.073102345 30 atime=1623670093.812103516 30 ctime=1623670095.073102345 elk-7.2.42/src/genhvec.f900000644002504400250440000000611214061636517016720 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 Alexey I. Baranov. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genhvec use modmain use modpw implicit none ! local variables logical lsym(48) integer ih,jh,kh,lh,k integer i1,i2,i3,iv(3) integer nsym,isym,sym(3,3,48) real(8) v1(3),v2(3),v3(3) ! allocatable arrays integer, allocatable :: idx(:),ivh0(:,:) real(8), allocatable :: vhc0(:,:),hc0(:) ! find the H-vector grid sizes call gridsize(avec,hmaxvr,ngridh,nhtot,inthv) ! allocate global H-vector arrays if (allocated(ivh)) deallocate(ivh) allocate(ivh(3,nhtot)) if (allocated(mulh)) deallocate(mulh) allocate(mulh(nhtot)) if (allocated(vhc)) deallocate(vhc) allocate(vhc(3,nhtot)) if (allocated(hc)) deallocate(hc) allocate(hc(nhtot)) ! allocate local arrays allocate(idx(nhtot),ivh0(3,nhtot)) allocate(vhc0(3,nhtot),hc0(nhtot)) ih=0 do i1=inthv(1,1),inthv(2,1) v1(:)=dble(i1)*bvec(:,1) do i2=inthv(1,2),inthv(2,2) v2(:)=v1(:)+dble(i2)*bvec(:,2) do i3=inthv(1,3),inthv(2,3) v3(:)=v2(:)+dble(i3)*bvec(:,3) ih=ih+1 ! map from H-vector to (i1,i2,i3) index ivh0(1,ih)=i1 ivh0(2,ih)=i2 ivh0(3,ih)=i3 ! H-vector in Cartesian coordinates vhc0(:,ih)=v3(:) ! length of each H-vector hc0(ih)=sqrt(v3(1)**2+v3(2)**2+v3(3)**2) end do end do end do ! sort by vector length call sortidx(nhtot,hc0,idx) ! reorder arrays do ih=1,nhtot jh=idx(ih) ivh(:,ih)=ivh0(:,jh) hc(ih)=hc0(jh) vhc(:,ih)=vhc0(:,jh) end do ! find the number of vectors with H < hmaxvr nhvec=1 do ih=nhtot,1,-1 if (hc(ih).lt.hmaxvr) then nhvec=ih exit end if end do ! find the subgroup of symmorphic, non-magnetic symmetries lsym(:)=.false. do isym=1,nsymcrys if (tv0symc(isym).and.(lspnsymc(isym).eq.1)) lsym(lsplsymc(isym))=.true. end do nsym=0 do isym=1,nsymlat if (lsym(isym)) then nsym=nsym+1 sym(:,:,nsym)=symlat(:,:,isym) end if end do if (reduceh) then ! find the subgroup of symmorphic, non-magnetic symmetries lsym(:)=.false. do isym=1,nsymcrys if (tv0symc(isym).and.(lspnsymc(isym).eq.1)) lsym(lsplsymc(isym))=.true. end do nsym=0 do isym=1,nsymlat if (lsym(isym)) then nsym=nsym+1 sym(:,:,nsym)=symlat(:,:,isym) end if end do else ! use only the identity element if no reduction is required nsym=1 end if ! reduce the H-vector set with the symmetries if required if (nsym.gt.1) then ivh0(:,1:nhvec)=ivh(:,1:nhvec) hc0(1:nhvec)=hc(1:nhvec) vhc0(:,1:nhvec)=vhc(:,1:nhvec) kh=0 lh=nhvec do ih=1,nhvec do isym=1,nsym call i3mtv(sym(:,:,isym),ivh0(:,ih),iv(:)) do jh=1,kh k=abs(ivh(1,jh)-iv(1))+abs(ivh(2,jh)-iv(2))+abs(ivh(3,jh)-iv(3)) if (k.eq.0) then ivh(:,lh)=ivh0(:,ih) hc(lh)=hc0(ih) vhc(:,lh)=vhc0(:,ih) lh=lh-1 mulh(jh)=mulh(jh)+1 goto 10 end if end do end do kh=kh+1 ivh(:,kh)=ivh0(:,ih) hc(kh)=hc0(ih) vhc(:,kh)=vhc0(:,ih) mulh(kh)=1 10 continue end do nhvec=kh else mulh(:)=1 end if deallocate(idx,ivh0,vhc0,hc0) end subroutine elk-7.2.42/src/PaxHeaders.21776/ylmrot.f900000644000000000000000000000013214061636517014572 xustar0030 mtime=1623670095.075102343 30 atime=1623670093.813103515 30 ctime=1623670095.075102343 elk-7.2.42/src/ylmrot.f900000644002504400250440000000407214061636517016632 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: ylmrot ! !INTERFACE: subroutine ylmrot(p,ang,lmax,ld,d) ! !INPUT/OUTPUT PARAMETERS: ! p : if p=-1 then the rotation matrix is improper (in,integer) ! ang : Euler angles; alpha, beta, gamma (in,real(3)) ! lmax : maximum angular momentum (in,integer) ! ld : leading dimension (in,integer) ! d : complex spherical harmonic rotation matrix (out,complex(ld,*)) ! !DESCRIPTION: ! Returns the rotation matrix in the basis of complex spherical harmonics ! given the three Euler angles, $(\alpha,\beta,\gamma)$, and the parity, $p$, ! of the rotation. The matrix is given by the formula ! $$ D^l_{m_1m_2}(\alpha,\beta,\gamma)=d^l_{m_1m_2}(\beta) ! e^{-i(m_1\alpha+m_2\gamma)}, $$ ! where $d$ is the rotation matrix about the $y$-axis. For improper rotations, ! i.e. those which are a combination of a rotation and inversion, $D$ is ! modified with $D^l_{m_1m_2}\rightarrow(-1)^l D^l_{m_1m_2}$. See the routines ! {\tt roteuler} and {\tt ylmroty}. ! ! !REVISION HISTORY: ! Created December 2008 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: p real(8), intent(in) :: ang(3) integer, intent(in) :: lmax,ld complex(8), intent(out) :: d(ld,*) ! local variables integer l,m1,m2 integer lm1,lm2,n real(8) t1 ! automatic arrays real(8) dy(ld,ld) if (lmax.lt.0) then write(*,*) write(*,'("Error(ylmrot): lmax < 0 : ",I8)') lmax write(*,*) stop end if ! generate the rotation matrix about the y-axis call ylmroty(ang(2),lmax,ld,dy) ! apply inversion if required if (p.eq.-1) then do l=1,lmax,2 lm1=l**2+1 lm2=lm1+2*l dy(lm1:lm2,lm1:lm2)=-dy(lm1:lm2,lm1:lm2) end do end if ! rotation by alpha and gamma do l=0,lmax n=l*(l+1)+1 do m1=-l,l lm1=n+m1 do m2=-l,l lm2=n+m2 t1=-dble(m1)*ang(1)-dble(m2)*ang(3) d(lm1,lm2)=dy(lm1,lm2)*cmplx(cos(t1),sin(t1),8) end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/wxcplot.f900000644000000000000000000000013214061636517014744 xustar0030 mtime=1623670095.076102343 30 atime=1623670093.815103513 30 ctime=1623670095.076102343 elk-7.2.42/src/wxcplot.f900000644002504400250440000000252214061636517017002 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine wxcplot use modmain implicit none ! initialise universal variables call init0 if (xcgrad.ne.4) then write(*,*) write(*,'("Error(wxcplot): meta-GGA not in use")') write(*,*) stop end if ! read the density and potentials from file call readstate ! write the potential plots to file select case(task) case(341) open(50,file='WXC1D.OUT',form='FORMATTED') open(51,file='WLINES.OUT',form='FORMATTED') call plot1d(50,51,1,wxcmt,wxcir) close(50) close(51) write(*,*) write(*,'("Info(wxcplot):")') write(*,'(" 1D meta-GGA exchange-correlation potential written to & &WXC1D.OUT")') write(*,'(" vertex location lines written to WLINES.OUT")') case(342) open(50,file='WXC2D.OUT',form='FORMATTED') call plot2d(.false.,50,1,wxcmt,wxcir) close(50) write(*,*) write(*,'("Info(wxcplot):")') write(*,'(" 2D meta-GGA exchange-correlation potential written to & &WXC2D.OUT")') case(343) open(50,file='WXC3D.OUT',form='FORMATTED') call plot3d(50,1,wxcmt,wxcir) close(50) write(*,*) write(*,'("Info(wxcplot):")') write(*,'(" 3D meta-GGA exchange-correlation potential written to & &WXC3D.OUT")') end select end subroutine elk-7.2.42/src/PaxHeaders.21776/massnucl.f900000644000000000000000000000013214061636517015071 xustar0030 mtime=1623670095.078102341 30 atime=1623670093.816103512 30 ctime=1623670095.078102341 elk-7.2.42/src/massnucl.f900000644002504400250440000000373514061636517017136 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: massnucl ! !INTERFACE: elemental real(8) function massnucl(z) ! !INPUT/OUTPUT PARAMETERS: ! z : atomic number (in,real) ! !DESCRIPTION: ! Computes an approximate nuclear mass from the atomic number $Z$. The nuclear ! mass number, $A$, is first estimated using ! $$ A=4.467\times 10^{-3}Z^2+2.163 Z-1.168, $$ ! [D. Andrae in {\it Relativistic Electronic Structure Theory - Fundamentals} ! {\bf 11}, 203 (2002)]. Then the nuclear mass can be determined from: ! $$ M=Z m_p+N m_n-\frac{B}{c^2}, $$ ! where $m_p$ is the proton mass, $m_n$ is the neutron mass and $B$ is the ! nuclear binding energy. The binding energy is approximated by the ! Weizs\"{a}cker formula: ! $$ B=a_V A-a_S A^{2/3}-a_C Z^2 A^{-1/3}-a_{\rm sym}(Z-N)^2A^{-1} ! +B_p+B_{\rm shell}. $$ ! See F. Yang and J. H. Hamilton in {\it Modern Atomic and Nuclear Physics}, ! Revised Edition 2010, for details on the quantities in this formula. In this ! implementation, $B_p$ and $B_{\rm shell}$ are set to zero. ! ! !REVISION HISTORY: ! Created February 2014 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: z ! local variables ! coefficients for computing mass number real(8), parameter :: c2=4.467d-3, c1=2.163d0, c0=-1.168d0 ! Weizsacker coefficients in MeV real(8), parameter :: av=15.8d0, as=18.3d0, ac=0.72d0, asym=23.2d0 ! proton and neutron masses in MeV/c^2 (CODATA 2018) real(8), parameter :: mp=938.27208816d0 real(8), parameter :: mn=939.56542052d0 ! atomic mass unit in MeV/c^2 (CODATA 2018) real(8), parameter :: mu=931.49410242d0 real(8) za,n,a,b za=abs(z) ! approximate nuclear mass number if (za.le.1.d0) then a=1.d0 else a=abs(c2*za**2+c1*za+c0) end if n=a-za b=av*a-as*a**(2.d0/3.d0)-ac*(za**2)/a**(1.d0/3.d0)-asym*(za-n)**2/a massnucl=(za*mp+n*mn-b)/mu end function !EOC elk-7.2.42/src/PaxHeaders.21776/gendmatk.f900000644000000000000000000000012714061636517015042 xustar0029 mtime=1623670095.07910234 29 atime=1623670093.81810351 29 ctime=1623670095.07910234 elk-7.2.42/src/gendmatk.f900000644002504400250440000000674014061636517017102 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gendmatk(tspndg,tlmdg,lmin,lmax,ias,ngp,apwalm,evecfv,evecsv,ld,dmat) use modmain implicit none ! arguments logical, intent(in) :: tspndg,tlmdg integer, intent(in) :: lmin,lmax integer, intent(in) :: ias integer, intent(in) :: ngp(nspnfv) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv) complex(8), intent(in) :: evecfv(nmatmax,nstfv,nspnfv) complex(8), intent(in) :: evecsv(nstsv,nstsv) integer, intent(in) :: ld complex(8), intent(out) :: dmat(ld,nspinor,ld,nspinor,nstsv) ! local variables integer ist,ispn,jspn,is integer nrc,nrci,irco,irc integer l,lma,lmb,lm1,lm2 integer npc,npci,i1,i2,i,j complex(8) zq(2),zsm,z1 ! automatic arrays logical done(nstfv,nspnfv) ! allocatable arrays complex(8), allocatable :: wfmt1(:,:,:),wfmt2(:,:) if (lmin.lt.0) then write(*,*) write(*,'("Error(gendmatk): lmin < 0 : ",I8)') lmin write(*,*) stop end if if (lmax.gt.lmaxo) then write(*,*) write(*,'("Error(gendmatk): lmax > lmaxo : ",2I8)') lmax,lmaxo write(*,*) stop end if ! allocate local arrays allocate(wfmt1(npcmtmax,nstfv,nspnfv),wfmt2(npcmtmax,nspinor)) ! species and atom numbers is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) irco=nrci+1 npc=npcmt(is) npci=npcmti(is) ! de-phasing factor for spin-spirals if (ssdph) then zq(1)=zqss(ias) zq(2)=conjg(zq(1)) end if ! zero the density matrix dmat(:,:,:,:,:)=0.d0 done(:,:)=.false. ! begin loop over second-variational states do j=1,nstsv if (tevecsv) then ! generate spinor wavefunction from second-variational eigenvectors wfmt2(1:npc,:)=0.d0 i=0 do ispn=1,nspinor jspn=jspnfv(ispn) do ist=1,nstfv i=i+1 z1=evecsv(i,j) if (ssdph) z1=z1*zq(ispn) if (abs(dble(z1))+abs(aimag(z1)).gt.epsocc) then if (.not.done(ist,jspn)) then call wavefmt(lradstp,ias,ngp(jspn),apwalm(:,:,:,ias,jspn), & evecfv(:,ist,jspn),wfmt1(:,ist,jspn)) done(ist,jspn)=.true. end if ! add to spinor wavefunction wfmt2(1:npc,ispn)=wfmt2(1:npc,ispn)+z1*wfmt1(1:npc,ist,jspn) end if end do end do else ! spin-unpolarised wavefunction call wavefmt(lradstp,ias,ngp,apwalm(:,:,:,ias,1),evecfv(:,j,1),wfmt2) end if do ispn=1,nspinor do jspn=1,nspinor if (tspndg.and.(ispn.ne.jspn)) cycle do l=lmin,lmax lma=l**2+1; lmb=lma+2*l do lm1=lma,lmb do lm2=lma,lmb if (tlmdg.and.(lm1.ne.lm2)) cycle if (l.le.lmaxi) then zsm=0.d0 i1=lm1; i2=lm2 do irc=1,nrci zsm=zsm+wfmt2(i1,ispn)*conjg(wfmt2(i2,jspn))*wrcmt(irc,is) i1=i1+lmmaxi; i2=i2+lmmaxi end do do irc=irco,nrc zsm=zsm+wfmt2(i1,ispn)*conjg(wfmt2(i2,jspn))*wrcmt(irc,is) i1=i1+lmmaxo; i2=i2+lmmaxo end do else zsm=0.d0 i1=npci+lm1; i2=npci+lm2 do irc=irco,nrc zsm=zsm+wfmt2(i1,ispn)*conjg(wfmt2(i2,jspn))*wrcmt(irc,is) i1=i1+lmmaxo; i2=i2+lmmaxo end do end if dmat(lm1,ispn,lm2,jspn,j)=zsm end do end do end do end do end do ! end loop over second-variational states end do deallocate(wfmt1,wfmt2) end subroutine elk-7.2.42/src/PaxHeaders.21776/rfplot.f900000644000000000000000000000013214061636517014552 xustar0030 mtime=1623670095.081102338 30 atime=1623670093.820103508 30 ctime=1623670095.081102338 elk-7.2.42/src/rfplot.f900000644002504400250440000000756414061636517016623 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rfplot(np,vpl,rfmt,rfir,fp) use modmain use modomp implicit none ! arguments integer, intent(in) :: np real(8), intent(in) :: vpl(3,np) real(8), intent(in) :: rfmt(npmtmax,natmtot),rfir(ngtot) real(8), intent(out) :: fp(np) ! local variables integer ias,is,ip,nthd ! allocatable arrays real(8), allocatable :: rfmt1(:,:,:) complex(8), allocatable :: zfft(:) ! unpack the muffin-tin function allocate(rfmt1(lmmaxo,nrmtmax,natmtot)) call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) call rfmtpack(.false.,nrmt(is),nrmti(is),rfmt(:,ias),rfmt1(:,:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! Fourier transform rfir to G-space allocate(zfft(ngtot)) zfft(:)=rfir(:) call zfftifc(3,ngridg,-1,zfft) ! begin loop over all points call holdthd(np,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ip=1,np call rfip(ip) end do !$OMP END PARALLEL DO call freethd(nthd) deallocate(rfmt1,zfft) return contains subroutine rfip(ip) implicit none ! arguments integer, intent(in) :: ip ! local variables integer is,ia,ias,nr,nri integer ir0,ir,lmax,l,m,lm integer ig,ifg,i1,i2,i3,i,j real(8) rmt2,r,sm,ya(4),t1 real(8) v1(3),v2(3),v3(3),v4(3),v5(3) ! automatic arrays real(8) rlm(lmmaxo) v2(:)=vpl(:,ip) call r3frac(epslat,v2) ! convert point to Cartesian coordinates call r3mv(avec,v2,v1) ! check if point is in a muffin-tin do is=1,nspecies nr=nrmt(is) nri=nrmti(is) rmt2=rmt(is)**2 do ia=1,natoms(is) ias=idxas(ia,is) v2(:)=v1(:)-atposc(:,ia,is) do i1=-1,1 v3(:)=v2(:)+dble(i1)*avec(:,1) do i2=-1,1 v4(:)=v3(:)+dble(i2)*avec(:,2) do i3=-1,1 v5(:)=v4(:)+dble(i3)*avec(:,3) t1=v5(1)**2+v5(2)**2+v5(3)**2 if (t1.lt.rmt2) then r=sqrt(t1) call genrlmv(lmaxo,v5,rlm) do ir=1,nr if (rsp(ir,is).ge.r) then if (ir.le.3) then ir0=1 else if (ir.gt.nr-2) then ir0=nr-3 else ir0=ir-2 end if r=max(r,rsp(1,is)) if (ir0.le.nri) then lmax=lmaxi else lmax=lmaxo end if sm=0.d0 lm=0 do l=0,lmax do m=-l,l lm=lm+1 do j=1,4 i=ir0+j-1 ya(j)=rfmt1(lm,i,ias) end do t1=poly4(rsp(ir0,is),ya,r) sm=sm+t1*rlm(lm) end do end do goto 10 end if end do end if end do end do end do end do end do ! otherwise use direct Fourier transform of interstitial function sm=0.d0 do ig=1,ngvec ifg=igfft(ig) t1=vgc(1,ig)*v1(1)+vgc(2,ig)*v1(2)+vgc(3,ig)*v1(3) sm=sm+dble(zfft(ifg)*cmplx(cos(t1),sin(t1),8)) end do 10 continue fp(ip)=sm end subroutine pure real(8) function poly4(xa,ya,x) implicit none ! arguments real(8), intent(in) :: xa(4),ya(4),x ! local variables real(8) x0,x1,x2,x3,y0,y1,y2,y3 real(8) c1,c2,c3,t0,t1,t2,t3,t4,t5,t6 ! evaluate the polynomial coefficients x0=xa(1) x1=xa(2)-x0; x2=xa(3)-x0; x3=xa(4)-x0 t4=x1-x2; t5=x1-x3; t6=x2-x3 y0=ya(1) y1=ya(2)-y0; y2=ya(3)-y0; y3=ya(4)-y0 t1=x1*x2*y3; t2=x2*x3*y1; t3=x1*x3 t0=1.d0/(x2*t3*t4*t5*t6) t3=t3*y2 c3=t1*t4+t2*t6-t3*t5 t4=x1**2; t5=x2**2; t6=x3**2 c2=t1*(t5-t4)+t2*(t6-t5)+t3*(t4-t6) c1=t1*(x2*t4-x1*t5)+t2*(x3*t5-x2*t6)+t3*(x1*t6-x3*t4) t1=x-x0 ! evaluate the polynomial poly4=y0+t0*t1*(c1+t1*(c2+c3*t1)) end function end subroutine elk-7.2.42/src/PaxHeaders.21776/straingkq.f900000644000000000000000000000013214061636517015247 xustar0030 mtime=1623670095.082102337 30 atime=1623670093.821103507 30 ctime=1623670095.082102337 elk-7.2.42/src/straingkq.f900000644002504400250440000000443314061636517017310 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine straingkq use modmain use modulr use modstore implicit none integer is,ia,ig integer nppt,ik,igk integer jspn,iq real(8) ta(3,3),tb(3,3),vc(3) if ((istrain.lt.1).or.(istrain.gt.nstrain)) return ! compute the strained lattice vectors avec(:,:)=avec_(:,:)+deltast*strain(:,:,istrain) ! generate the strained reciprocal lattice vectors and unit cell volume call reciplat(avec,bvec,omega,omegabz) ! determine the transformation matrix to the strained vectors call r3mm(avec,ainv,ta) call r3mm(bvec,binv,tb) ! recalculate all required variables which depend on avec call r3minv(avec,ainv) call r3minv(bvec,binv) call r3mv(bvec,vqlss,vqcss) do is=1,nspecies do ia=1,natoms(is) call r3mv(avec,atposl(:,ia,is),atposc(:,ia,is)) end do end do call r3mv(bvec,vecql,vecqc) call r3mv(ainv,efieldc,efieldl) call r3mv(ainv,afieldc,afieldl) call symmetry ! apply the transformation matrix to the G-vectors do ig=1,ngtot vc(:)=vgc(:,ig) call r3mv(tb,vc,vgc(:,ig)) gc(ig)=sqrt(vgc(1,ig)**2+vgc(2,ig)**2+vgc(3,ig)**2) end do ! recalculate variables which depend on the G-vectors call gengclg call genjlgprmt(lnpsd,ngvec,gc,ngvec,jlgrmt) call genylmg call gensfacgp(ngvec,vgc,ngvec,sfacg) do is=1,nspecies call genffacgp(is,gc,ffacg(:,is)) end do call gencfun call gencfrc call energynn ! apply the transformation to the k-vectors do ik=1,nkptnr vc(:)=vkc(:,ik) call r3mv(tb,vc,vkc(:,ik)) end do ! apply the transformation to G+k-vectors and recalculate dependent variables if (xctype(1).lt.0) then nppt=nkptnr else nppt=nkpt end if do ik=1,nppt do jspn=1,nspnfv do igk=1,ngk(jspn,ik) vc(:)=vgkc(:,igk,jspn,ik) call r3mv(tb,vc,vgkc(:,igk,jspn,ik)) gkc(igk,jspn,ik)=sqrt(vgkc(1,igk,jspn,ik)**2 & +vgkc(2,igk,jspn,ik)**2 & +vgkc(3,igk,jspn,ik)**2) end do call gensfacgp(ngk(jspn,ik),vgkc(:,:,jspn,ik),ngkmax,sfacgk(:,:,jspn,ik)) end do end do ! apply the transformation to the q-vectors if required if (xctype(1).lt.0) then do iq=1,nqptnr vc(:)=vqc(:,iq) call r3mv(tb,vc,vqc(:,iq)) end do call gengclq end if end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqnit.f900000644000000000000000000000013214061636517014717 xustar0030 mtime=1623670095.084102335 30 atime=1623670093.823103505 30 ctime=1623670095.084102335 elk-7.2.42/src/eveqnit.f900000644002504400250440000001351114061636517016755 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine eveqnit(nmatp,ngp,igpig,vpl,vgpl,vgpc,apwalm,evalfv,evecfv) use modmain use modomp implicit none ! arguments integer, intent(in) :: nmatp,ngp integer, intent(in) :: igpig(ngkmax) real(8), intent(in) :: vpl(3) real(8), intent(in) :: vgpl(3,ngkmax),vgpc(3,ngkmax) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot) real(8), intent(out) :: evalfv(nstfv) complex(8), intent(out) :: evecfv(nmatmax,nstfv) ! local variables integer n2,ns,ist,i integer is,ias,it,nthd integer lwork,info real(8) rmax,t1 real(8) ts1,ts0 ! allocatable arrays real(8), allocatable :: w(:),rwork(:) complex(8), allocatable :: h(:,:),o(:,:),hv(:,:),ov(:,:) complex(8), allocatable :: u(:,:),hu(:,:),ou(:,:) complex(8), allocatable :: hs(:,:),os(:,:),work(:) ! external functions complex(8), external :: zdotc n2=2*nmatp ns=2*nstfv if (iscl.ge.2) then ! read in the eigenvalues/vectors from file call getevalfv(filext,0,vpl,evalfv) call getevecfv(filext,0,vpl,vgpl,evecfv) else ! initialise the eigenvectors to canonical basis vectors evecfv(1:nmatp,:)=0.d0 do ist=1,nstfv evecfv(ist,ist)=1.d0 end do end if ! compute Hamiltonian and overlap matrices call timesec(ts0) allocate(h(nmatp,nmatp),o(nmatp,nmatp)) call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP PRIVATE(i,ias,is) & !$OMP NUM_THREADS(nthd) !$OMP SECTION ! Hamiltonian do i=1,nmatp h(1:i,i)=0.d0 end do do ias=1,natmtot is=idxis(ias) call hmlaa(tefvr,is,ias,ngp,apwalm(:,:,:,ias),nmatp,h) call hmlalo(is,ias,ngp,apwalm(:,:,:,ias),nmatp,h) call hmllolo(is,ias,ngp,nmatp,h) end do call hmlistl(ngp,igpig,vgpc,nmatp,h) !$OMP SECTION ! overlap do i=1,nmatp o(1:i,i)=0.d0 end do do ias=1,natmtot is=idxis(ias) call olpaa(tefvr,is,ngp,apwalm(:,:,:,ias),nmatp,o) call olpalo(is,ias,ngp,apwalm(:,:,:,ias),nmatp,o) call olplolo(is,ias,ngp,nmatp,o) end do call olpistl(ngp,igpig,nmatp,o) !$OMP END PARALLEL SECTIONS call freethd(nthd) call timesec(ts1) !$OMP ATOMIC timemat=timemat+ts1-ts0 call timesec(ts0) allocate(w(ns),rwork(3*ns)) allocate(hv(nmatp,nstfv),ov(nmatp,nstfv)) allocate(u(nmatp,nstfv),hu(nmatp,nstfv),ou(nmatp,nstfv)) allocate(hs(ns,ns),os(ns,ns)) lwork=2*ns allocate(work(lwork)) ! start iteration loop do it=1,maxitefv rmax=0.d0 call holdthd(nstfv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(t1) & !$OMP NUM_THREADS(nthd) do ist=1,nstfv ! operate with O on the current eigenvector call zhemv('U',nmatp,zone,o,nmatp,evecfv(:,ist),1,zzero,ov(:,ist),1) ! normalise the eigenvector t1=dble(zdotc(nmatp,evecfv(:,ist),1,ov(:,ist),1)) if (t1.gt.0.d0) then t1=1.d0/sqrt(t1) call dscal(n2,t1,evecfv(:,ist),1) call dscal(n2,t1,ov(:,ist),1) end if ! operate with H on the current eigenvector call zhemv('U',nmatp,zone,h,nmatp,evecfv(:,ist),1,zzero,hv(:,ist),1) ! estimate the eigenvalue t1=dble(zdotc(nmatp,evecfv(:,ist),1,hv(:,ist),1)) if ((iscl.le.1).and.(it.eq.1)) then evalfv(ist)=t1 else evalfv(ist)=(1.d0-befvit)*evalfv(ist)+befvit*t1 end if ! compute the residual |u> = (H - eO)|v> call zcopy(nmatp,hv(:,ist),1,u(:,ist),1) call daxpy(n2,-evalfv(ist),ov(:,ist),1,u(:,ist),1) ! apply the overlap matrix to the residual call zhemv('U',nmatp,zone,o,nmatp,u(:,ist),1,zzero,ou(:,ist),1) ! compute the overlap of the residual with itself t1=dble(zdotc(nmatp,u(:,ist),1,ou(:,ist),1)) !$OMP CRITICAL(eveqnit_) if (t1.gt.rmax) rmax=t1 !$OMP END CRITICAL(eveqnit_) ! normalise the residual if (t1.gt.0.d0) then t1=1.d0/sqrt(t1) call dscal(n2,t1,u(:,ist),1) call dscal(n2,t1,ou(:,ist),1) end if ! apply the Hamiltonian matrix to the residual call zhemv('U',nmatp,zone,h,nmatp,u(:,ist),1,zzero,hu(:,ist),1) end do !$OMP END PARALLEL DO call freethd(nthd) ! compute the Hamiltonian and overlap matrices in the subspace formed by the ! eigenvectors and their residuals call holdthd(nstfv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ist=1,nstfv call zgemv('C',nmatp,nstfv,zone,evecfv,nmatmax,hv(:,ist),1,zzero, & hs(1,ist),1) call zgemv('C',nmatp,nstfv,zone,evecfv,nmatmax,hu(:,ist),1,zzero, & hs(1,nstfv+ist),1) call zgemv('C',nmatp,nstfv,zone,u,nmatp,hu(:,ist),1,zzero, & hs(nstfv+1,nstfv+ist),1) end do !$OMP END PARALLEL DO call freethd(nthd) call holdthd(nstfv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ist=1,nstfv call zgemv('C',nmatp,nstfv,zone,evecfv,nmatmax,ov(:,ist),1,zzero, & os(1,ist),1) call zgemv('C',nmatp,nstfv,zone,evecfv,nmatmax,ou(:,ist),1,zzero, & os(1,nstfv+ist),1) call zgemv('C',nmatp,nstfv,zone,u,nmatp,ou(:,ist),1,zzero, & os(nstfv+1,nstfv+ist),1) end do !$OMP END PARALLEL DO call freethd(nthd) ! solve the generalised eigenvalue problem in the subspace call zhegv(1,'V','U',ns,hs,ns,os,ns,w,work,lwork,rwork,info) if (info.ne.0) exit ! construct the new eigenvectors call holdthd(nstfv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ist=1,nstfv call zgemv('N',nmatp,nstfv,zone,evecfv,nmatmax,hs(1,ist),1,zzero, & ov(:,ist),1) call zgemv('N',nmatp,nstfv,zone,u,nmatp,hs(nstfv+1,ist),1,zone,ov(:,ist),1) end do !$OMP END PARALLEL DO call freethd(nthd) call holdthd(nstfv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ist=1,nstfv call zcopy(nmatp,ov(:,ist),1,evecfv(:,ist),1) end do !$OMP END PARALLEL DO call freethd(nthd) ! check for convergence rmax=sqrt(abs(rmax)/dble(nmatp)) if ((it.ge.minitefv).and.(rmax.lt.epsefvit)) exit ! end iteration loop end do deallocate(w,rwork,h,o,hv,ov) deallocate(u,hu,ou,hs,os,work) call timesec(ts1) !$OMP ATOMIC timefv=timefv+ts1-ts0 end subroutine elk-7.2.42/src/PaxHeaders.21776/oepmain.f900000644000000000000000000000013214061636517014674 xustar0030 mtime=1623670095.085102334 30 atime=1623670093.825103504 30 ctime=1623670095.085102334 elk-7.2.42/src/oepmain.f900000644002504400250440000001321414061636517016732 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine oepmain use modmain use modmpi use modomp implicit none ! local variables integer ik,idm,is,ias integer nrc,nrci,np,npc integer n,nthd,it real(8) tau,t1 ! allocatable arrays real(8), allocatable :: dvxmt(:,:),dvxir(:) real(8), allocatable :: dbxmt(:,:,:),dbxir(:,:) real(8), allocatable :: rfmt1(:,:),rfmt2(:),rfir(:) real(8), allocatable :: rvfmt(:,:,:),rvfir(:,:) complex(8), allocatable :: vclcv(:,:,:,:),vclvv(:,:,:) ! external functions real(8), external :: rfint,rfinpc if (iscl.le.0) return ! calculate Coulomb matrix elements allocate(vclcv(ncrmax,natmtot,nstsv,nkpt),vclvv(nstsv,nstsv,nkpt)) call oepvcl(vclcv,vclvv) ! allocate local arrays allocate(dvxmt(npcmtmax,natmtot),dvxir(ngtot)) allocate(rfmt1(npmtmax,natmtot),rfir(ngtot)) if (spinpol) then allocate(dbxmt(npcmtmax,natmtot,ndmag),dbxir(ngtot,ndmag)) allocate(rvfmt(npmtmax,natmtot,ndmag),rvfir(ngtot,ndmag)) end if ! initialise the exchange potential and magnetic field tau=tauoep(2) vxmt(:,:)=tau*vxmt(:,:) vxir(:)=tau*vxir(:) if (spinpol) then bxmt(:,:,:)=tau*bxmt(:,:,:) bxir(:,:)=tau*bxir(:,:) end if ! iterative method step size tau=tauoep(1) !------------------------------! ! start iteration loop ! !------------------------------! do it=1,maxitoep if (mp_mpi.and.(mod(it,10).eq.0)) then write(*,'("Info(oepmain): done ",I4," iterations of ",I4)') it,maxitoep end if ! zero the residuals dvxmt(:,:)=0.d0 dvxir(:)=0.d0 if (spinpol) then dbxmt(:,:,:)=0.d0 dbxir(:,:)=0.d0 end if ! calculate the k-dependent residuals call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call oepresk(ik,vclcv,vclvv,dvxmt,dvxir,dbxmt,dbxir) end do !$OMP END PARALLEL DO call freethd(nthd) ! add residuals from each process and redistribute if (np_mpi.gt.1) then n=npcmtmax*natmtot call mpi_allreduce(mpi_in_place,dvxmt,n,mpi_double_precision,mpi_sum, & mpicom,ierror) call mpi_allreduce(mpi_in_place,dvxir,ngtot,mpi_double_precision, & mpi_sum,mpicom,ierror) if (spinpol) then n=n*ndmag call mpi_allreduce(mpi_in_place,dbxmt,n,mpi_double_precision,mpi_sum, & mpicom,ierror) n=ngtot*ndmag call mpi_allreduce(mpi_in_place,dbxir,n,mpi_double_precision,mpi_sum, & mpicom,ierror) end if end if ! convert muffin-tin residuals to spherical harmonics call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is,nrc,nrci,idm) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) call rfsht(nrc,nrci,dvxmt(:,ias),rfmt1(:,ias)) do idm=1,ndmag call rfsht(nrc,nrci,dbxmt(:,ias,idm),rvfmt(:,ias,idm)) end do end do !$OMP END PARALLEL DO call freethd(nthd) ! symmetrise the residuals call symrf(nrcmt,nrcmti,npcmt,ngridg,ngtot,ngvec,igfft,npmtmax,rfmt1,dvxir) if (spinpol) call symrvf(.true.,ncmag,nrcmt,nrcmti,npcmt,ngridg,ngtot,ngvec, & igfft,npmtmax,rvfmt,ngtot,dbxir) ! magnitude of residuals resoep=rfinpc(npmtmax,rfmt1,dvxir,rfmt1,dvxir) do idm=1,ndmag t1=rfinpc(npmtmax,rvfmt(:,:,idm),dbxir(:,idm),rvfmt(:,:,idm),dbxir(:,idm)) resoep=resoep+t1 end do resoep=sqrt(resoep)/omega ! update exchange potential and magnetic field call holdthd(natmtot,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(rfmt2,is,nrc,nrci,npc,idm) & !$OMP NUM_THREADS(nthd) allocate(rfmt2(npcmtmax)) !$OMP DO do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) ! convert residual to spherical coordinates call rbsht(nrc,nrci,rfmt1(:,ias),rfmt2) ! subtract from exchange potential vxmt(1:npc,ias)=vxmt(1:npc,ias)-tau*rfmt2(1:npc) ! repeat for exchange magnetic field do idm=1,ndmag call rbsht(nrc,nrci,rvfmt(:,ias,idm),rfmt2) bxmt(1:npc,ias,idm)=bxmt(1:npc,ias,idm)-tau*rfmt2(1:npc) end do end do !$OMP END DO deallocate(rfmt2) !$OMP END PARALLEL call freethd(nthd) vxir(:)=vxir(:)-tau*dvxir(:) do idm=1,ndmag bxir(:,idm)=bxir(:,idm)-tau*dbxir(:,idm) end do ! end iteration loop end do ! convert the exchange potential and field to spherical harmonics call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is,nrc,nrci,idm) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) call rfsht(nrc,nrci,vxmt(:,ias),rfmt1(:,ias)) do idm=1,ndmag call rfsht(nrc,nrci,bxmt(:,ias,idm),rvfmt(:,ias,idm)) end do end do !$OMP END PARALLEL DO call freethd(nthd) ! convert potential and field from a coarse to a fine radial mesh call rfmtctof(rfmt1) do idm=1,ndmag call rfmtctof(rvfmt(:,:,idm)) end do ! add to existing (density derived) correlation potential and field do ias=1,natmtot is=idxis(ias) np=npmt(is) vxcmt(1:np,ias)=vxcmt(1:np,ias)+rfmt1(1:np,ias) do idm=1,ndmag bxcmt(1:np,ias,idm)=bxcmt(1:np,ias,idm)+rvfmt(1:np,ias,idm) end do end do vxcir(:)=vxcir(:)+vxir(:) do idm=1,ndmag bxcir(:,idm)=bxcir(:,idm)+bxir(:,idm) end do ! symmetrise the exchange potential and field call symrf(nrmt,nrmti,npmt,ngridg,ngtot,ngvec,igfft,npmtmax,vxcmt,vxcir) if (spinpol) call symrvf(.true.,ncmag,nrmt,nrmti,npmt,ngridg,ngtot,ngvec,igfft,& npmtmax,bxcmt,ngtot,bxcir) deallocate(rfmt1,rfir,vclcv,vclvv) deallocate(dvxmt,dvxir) if (spinpol) then deallocate(rvfmt,rvfir) deallocate(dbxmt,dbxir) end if ! set the constant part of the exchange potential equal to zero call rfint0(0.d0,vxcmt,vxcir) end subroutine elk-7.2.42/src/PaxHeaders.21776/rdirac.f900000644000000000000000000000013214061636517014510 xustar0030 mtime=1623670095.087102332 30 atime=1623670093.826103503 30 ctime=1623670095.087102332 elk-7.2.42/src/rdirac.f900000644002504400250440000000714514061636517016554 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rdirac ! !INTERFACE: subroutine rdirac(sol,n,l,k,nr,r,vr,eval,g0,f0) ! !INPUT/OUTPUT PARAMETERS: ! sol : speed of light in atomic units (in,real) ! n : principal quantum number (in,integer) ! l : quantum number l (in,integer) ! k : quantum number k (l or l+1) (in,integer) ! nr : number of radial mesh points (in,integer) ! r : radial mesh (in,real(nr)) ! vr : potential on radial mesh (in,real(nr)) ! eval : eigenvalue without rest-mass energy (inout,real) ! g0 : major component of the radial wavefunction (out,real(nr)) ! f0 : minor component of the radial wavefunction (out,real(nr)) ! !DESCRIPTION: ! Finds the solution to the radial Dirac equation for a given potential $v(r)$ ! and quantum numbers $n$, $k$ and $l$. The method involves integrating the ! equation using the predictor-corrector method and adjusting $E$ until the ! number of nodes in the wavefunction equals $n-l-1$. The calling routine must ! provide an initial estimate for the eigenvalue. Note that the arrays ! {\tt g0} and {\tt f0} represent the radial functions multiplied by $r$. ! ! !REVISION HISTORY: ! Created September 2002 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: sol integer, intent(in) :: n,l,k,nr real(8), intent(in) :: r(nr),vr(nr) real(8), intent(inout) :: eval real(8), intent(out) :: g0(nr),f0(nr) ! local variables integer, parameter :: maxit=2000 integer kpa,it,ir integer nn,nnd,nndp ! energy convergence tolerance real(8), parameter :: eps=1.d-12 real(8) t1,de ! automatic arrays real(8) g1(nr),f1(nr),fr(nr) ! external functions real(8), external :: splint if (k.le.0) then write(*,*) write(*,'("Error(rdirac): k <= 0 : ",I8)') k write(*,*) stop end if if (k.gt.n) then write(*,*) write(*,'("Error(rdirac): incompatible n and k : ",2I8)') n,k write(*,*) stop end if if ((k.eq.n).and.(l.ne.k-1)) then write(*,*) write(*,'("Error(rdirac): incompatible n, k and l : ",3I8)') n,k,l write(*,*) stop end if if (k.eq.l) then kpa=k else if (k.eq.l+1) then kpa=-k else write(*,*) write(*,'("Error(rdirac): incompatible l and k : ",2I8)') l,k write(*,*) stop end if if (nr.lt.4) then write(*,*) write(*,'("Error(rdirac): nr < 4 : ",I8)') nr write(*,*) stop end if de=1.d0 nndp=0 do it=1,maxit ! integrate the Dirac equation call rdiracint(sol,kpa,eval,nr,r,vr,nn,g0,g1,f0,f1) ! check the number of nodes nnd=nn-(n-l-1) if (nnd.gt.0) then eval=eval-de else eval=eval+de end if if (it.gt.1) then if ((nnd.ne.0).or.(nndp.ne.0)) then if (nnd*nndp.le.0) then de=de*0.5d0 else de=de*1.1d0 end if end if end if nndp=nnd if (de.lt.eps*(abs(eval)+1.d0)) goto 20 end do write(*,*) write(*,'("Warning(rdirac): maximum iterations exceeded")') 20 continue ! find effective infinity and set wavefunction to zero after that point ! major component do ir=nr,2,-1 if ((g0(ir-1)*g0(ir).lt.0.d0).or.(g1(ir-1)*g1(ir).lt.0.d0)) then g0(ir:nr)=0.d0 exit end if end do ! minor component do ir=nr,2,-1 if ((f0(ir-1)*f0(ir).lt.0.d0).or.(f1(ir-1)*f1(ir).lt.0.d0)) then f0(ir:nr)=0.d0 exit end if end do ! normalise do ir=1,nr fr(ir)=g0(ir)**2+f0(ir)**2 end do t1=splint(nr,r,fr) t1=sqrt(abs(t1)) if (t1.le.0.d0) then write(*,*) write(*,'("Error(rdirac): zero wavefunction")') write(*,*) stop end if t1=1.d0/t1 call dscal(nr,t1,g0,1) call dscal(nr,t1,f0,1) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/unitary.f900000644000000000000000000000013214061636517014737 xustar0030 mtime=1623670095.088102331 30 atime=1623670093.828103501 30 ctime=1623670095.088102331 elk-7.2.42/src/unitary.f900000644002504400250440000000203314061636517016772 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine unitary(n,a) implicit none ! arguments integer, intent(in) :: n complex(8), intent(inout) :: a(n,n) ! local variables integer lwork,info complex(8), parameter :: zzero=(0.d0,0.d0) complex(8), parameter :: zone=(1.d0,0.d0) ! allocatable arrays real(8), allocatable :: s(:),rwork(:) complex(8), allocatable :: u(:,:),vt(:,:),work(:) ! perform singular value decomposition on matrix lwork=3*n allocate(s(n),rwork(5*n)) allocate(u(n,n),vt(n,n),work(lwork)) call zgesvd('A','A',n,n,a,n,s,u,n,vt,n,work,lwork,rwork,info) if (info.ne.0) then write(*,*) write(*,'("Error(unitary): singular value decomposition failed")') write(*,'(" ZGESVD returned INFO = ",I8)') info write(*,*) stop end if ! multiply the two unitary matrices together and store in the input matrix call zgemm('N','N',n,n,n,zone,u,n,vt,n,zzero,a,n) deallocate(s,rwork,u,vt,work) end subroutine elk-7.2.42/src/PaxHeaders.21776/bandstr.f900000644000000000000000000000013014061636517014677 xustar0030 mtime=1623670095.090102329 28 atime=1623670093.8291035 30 ctime=1623670095.090102329 elk-7.2.42/src/bandstr.f900000644002504400250440000001563314061636517016746 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: bandstr ! !INTERFACE: subroutine bandstr ! !USES: use modmain use modomp ! !DESCRIPTION: ! Produces a band structure along the path in reciprocal space which connects ! the vertices in the array {\tt vvlp1d}. The band structure is obtained from ! the second-variational eigenvalues and is written to the file {\tt BAND.OUT} ! with the Fermi energy set to zero. If required, band structures are plotted ! to files {\tt BAND\_Sss\_Aaaaa.OUT} for atom {\tt aaaa} of species {\tt ss}, ! which include the band characters for each $l$ component of that atom in ! columns 4 onwards. Column 3 contains the sum over $l$ of the characters. ! Vertex location lines are written to {\tt BANDLINES.OUT}. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! local variables integer ik,ist,ispn,is,ia,ias integer lmax,lmmax,l,m,lm,iv,nthd real(8) emin,emax,sm character(256) fname ! allocatable arrays real(8), allocatable :: evalfv(:,:),e(:,:) ! low precision for band character array saves memory real(4), allocatable :: bc(:,:,:,:) complex(8), allocatable :: dmat(:,:,:,:,:),apwalm(:,:,:,:,:) complex(8), allocatable :: evecfv(:,:,:),evecsv(:,:) ! initialise universal variables call init0 call init1 ! allocate array for storing the eigenvalues allocate(e(nstsv,nkpt)) ! maximum angular momentum for band character lmax=min(3,lmaxo) lmmax=(lmax+1)**2 if (task.eq.21) then allocate(bc(0:lmax,natmtot,nstsv,nkpt)) else if (task.eq.22) then allocate(bc(lmmax,natmtot,nstsv,nkpt)) else allocate(bc(nspinor,natmtot,nstsv,nkpt)) end if ! read density and potentials from file call readstate ! Fourier transform Kohn-Sham potential to G-space call genvsig ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! generate the spin-orbit coupling radial functions call gensocfr emin=1.d5 emax=-1.d5 ! begin parallel loop over k-points call holdthd(nkpt,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evalfv,evecfv,evecsv) & !$OMP PRIVATE(dmat,apwalm,ist,ispn) & !$OMP PRIVATE(ias,l,m,lm,sm) & !$OMP NUM_THREADS(nthd) allocate(evalfv(nstfv,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv),evecsv(nstsv,nstsv)) if (task.ge.21) then allocate(dmat(lmmax,nspinor,lmmax,nspinor,nstsv)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) end if !$OMP DO do ik=1,nkpt !$OMP CRITICAL(bandstr_1) write(*,'("Info(bandstr): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(bandstr_1) ! solve the first- and second-variational eigenvalue equations call eveqn(ik,evalfv,evecfv,evecsv) do ist=1,nstsv ! subtract the Fermi energy e(ist,ik)=evalsv(ist,ik)-efermi !$OMP CRITICAL(bandstr_2) emin=min(emin,e(ist,ik)) emax=max(emax,e(ist,ik)) !$OMP END CRITICAL(bandstr_2) end do ! compute the band characters if required if (task.ge.21) then ! find the matching coefficients do ispn=1,nspnfv call match(ngk(ispn,ik),vgkc(:,:,ispn,ik),gkc(:,ispn,ik), & sfacgk(:,:,ispn,ik),apwalm(:,:,:,:,ispn)) end do ! average band character over spin and m for all atoms do ias=1,natmtot ! generate the diagonal of the density matrix call gendmatk(.true.,.true.,0,lmax,ias,ngk(:,ik),apwalm,evecfv,evecsv, & lmmax,dmat) do ist=1,nstsv if (task.eq.21) then ! l character of band lm=0 do l=0,lmax sm=0.d0 do m=-l,l lm=lm+1 do ispn=1,nspinor sm=sm+dble(dmat(lm,ispn,lm,ispn,ist)) end do end do bc(l,ias,ist,ik)=real(sm) end do else if (task.eq.22) then ! (l,m) character of band lm=0 do l=0,lmax do m=-l,l lm=lm+1 sm=0.d0 do ispn=1,nspinor sm=sm+dble(dmat(lm,ispn,lm,ispn,ist)) end do bc(lm,ias,ist,ik)=real(sm) end do end do else ! spin character of band do ispn=1,nspinor sm=0.d0 lm=0 do l=0,lmax do m=-l,l lm=lm+1 sm=sm+dble(dmat(lm,ispn,lm,ispn,ist)) end do end do bc(ispn,ias,ist,ik)=real(sm) end do end if end do end do end if ! end loop over k-points end do !$OMP END DO deallocate(evalfv,evecfv,evecsv) if (task.ge.21) deallocate(dmat,apwalm) !$OMP END PARALLEL call freethd(nthd) emax=emax+(emax-emin)*0.5d0 emin=emin-(emax-emin)*0.5d0 ! output the band structure if (task.eq.20) then open(50,file='BAND.OUT',form='FORMATTED',action='WRITE') do ist=1,nstsv do ik=1,nkpt write(50,'(2G18.10)') dpp1d(ik),e(ist,ik) end do write(50,*) end do close(50) write(*,*) write(*,'("Info(bandstr):")') write(*,'(" band structure plot written to BAND.OUT")') else do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) write(fname,'("BAND_S",I2.2,"_A",I4.4,".OUT")') is,ia open(50,file=trim(fname),form='FORMATTED',action='WRITE') do ist=1,nstsv do ik=1,nkpt if (task.eq.21) then ! sum band character over l to find total atomic character sm=0.d0 do l=0,lmax sm=sm+bc(l,ias,ist,ik) end do write(50,'(2G18.10,5F12.6)') dpp1d(ik),e(ist,ik),sm, & (bc(l,ias,ist,ik),l=0,lmax) else if (task.eq.22) then write(50,'(2G18.10,16F12.6)') dpp1d(ik),e(ist,ik), & (bc(lm,ias,ist,ik),lm=1,lmmax) else write(50,'(2G18.10,2F12.6)') dpp1d(ik),e(ist,ik), & (bc(ispn,ias,ist,ik),ispn=1,nspinor) end if end do write(50,*) end do close(50) end do end do write(*,*) write(*,'("Info(bandstr):")') write(*,'(" Band structure plot written to BAND_Sss_Aaaaa.OUT")') write(*,'(" for all species and atoms")') write(*,*) write(*,'(" Columns in the file are :")') if (task.eq.21) then write(*,'(" distance, eigenvalue, total atomic character, l character & &(l = 0...",I1,")")') lmax else if (task.eq.22) then write(*,'(" distance, eigenvalue, (l,m) character & &(l = 0...",I1,", m = -l...l)")') lmax else write(*,'(" distance, eigenvalue, spin-up and spin-down characters")') end if end if write(*,*) write(*,'(" Fermi energy is at zero in plot")') ! output the vertex location lines open(50,file='BANDLINES.OUT',form='FORMATTED',action='WRITE') do iv=1,nvp1d write(50,'(2G18.10)') dvp1d(iv),emin write(50,'(2G18.10)') dvp1d(iv),emax write(50,*) end do close(50) write(*,*) write(*,'(" Vertex location lines written to BANDLINES.OUT")') deallocate(e) if (task.ge.21) deallocate(bc) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/sfacinit.f900000644000000000000000000000013214061636517015044 xustar0030 mtime=1623670095.092102328 30 atime=1623670093.831103498 30 ctime=1623670095.092102328 elk-7.2.42/src/sfacinit.f900000644002504400250440000000353014061636517017102 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 A. I. Baranov and F. Wagner. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine sfacinit use modmain use modpw implicit none ! local variables logical trhonorm0 integer ik,ist,is,ias ! allocatable arrays real(8), allocatable :: occcr0(:,:) ! initialise universal variables call init0 call init1 ! read density and potentials from file call readstate ! use existing density if wsfac is default if ((wsfac(1).le.-1.d6).or.(wsfac(2).ge.1.d6)) goto 10 ! make a copy of the core state occupancies allocate(occcr0(nstspmax,natmtot)) occcr0(:,:)=occcr(:,:) ! zero the core state occupancies for eigenvalues not in energy window do ias=1,natmtot is=idxis(ias) do ist=1,nstsp(is) if (spcore(ist,is)) then if ((evalcr(ist,ias).lt.wsfac(1)).or.(evalcr(ist,ias).gt.wsfac(2))) then occcr(ist,ias)=0.d0 end if end if end do end do ! generate the core wavefunctions and densities call gencore ! restore the core state occupancies occcr(:,:)=occcr0(:,:) deallocate(occcr0) ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr do ik=1,nkpt ! get the eigenvalues and occupancies from file call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) ! zero occupancies for eigenvalues not in energy window do ist=1,nstsv if ((evalsv(ist,ik).lt.wsfac(1)).or.(evalsv(ist,ik).gt.wsfac(2))) then occsv(ist,ik)=0.d0 end if end do end do ! computed density should not be normalised trhonorm0=trhonorm trhonorm=.false. ! generate the density and magnetisation call rhomag trhonorm=trhonorm0 10 continue ! generate the H-vectors call genhvec end subroutine elk-7.2.42/src/PaxHeaders.21776/findscq.f900000644000000000000000000000013214061636517014673 xustar0030 mtime=1623670095.093102327 30 atime=1623670093.833103496 30 ctime=1623670095.093102327 elk-7.2.42/src/findscq.f900000644002504400250440000000705314061636517016735 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine findscq(iq,avec0,nsc,vsc) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq real(8), intent(in) :: avec0(3,3) integer, intent(out) :: nsc real(8), intent(out) :: vsc(3,nqptnr) ! local variables integer i1,i2,i3 integer scl(3,3),i,n real(8) dmin,t1 real(8) v1(3),v2(3) ! check for Gamma-point phonon if (tphq0) then scl(:,:)=0 scl(1,1)=1 scl(2,2)=1 scl(3,3)=1 nsc=1 goto 10 end if ! find the first lattice vector dmin=1.d8 do i1=-ngridq(1),ngridq(1) do i2=-ngridq(2),ngridq(2) do i3=-ngridq(3),ngridq(3) t1=dble(i1)*vql(1,iq)+dble(i2)*vql(2,iq)+dble(i3)*vql(3,iq) if (abs(t1-nint(t1)).lt.epslat) then v1(:)=dble(i1)*avec0(:,1)+dble(i2)*avec0(:,2)+dble(i3)*avec0(:,3) t1=sqrt(v1(1)**2+v1(2)**2+v1(3)**2) if ((t1.lt.dmin).and.(t1.gt.epslat)) then scl(1,1)=i1 scl(2,1)=i2 scl(3,1)=i3 dmin=t1 end if end if end do end do end do ! find the second lattice vector dmin=1.d8 do i1=-ngridq(1),ngridq(1) do i2=-ngridq(2),ngridq(2) do i3=-ngridq(3),ngridq(3) t1=dble(i1)*vql(1,iq)+dble(i2)*vql(2,iq)+dble(i3)*vql(3,iq) if (abs(t1-nint(t1)).lt.epslat) then ! area defined by first two lattice vectors n=(i2*scl(3,1)-i3*scl(2,1))**2 & +(i3*scl(1,1)-i1*scl(3,1))**2 & +(i1*scl(2,1)-i2*scl(1,1))**2 if (n.ne.0) then v1(:)=dble(i1)*avec0(:,1)+dble(i2)*avec0(:,2)+dble(i3)*avec0(:,3) t1=v1(1)**2+v1(2)**2+v1(3)**2 if (t1.lt.dmin) then scl(1,2)=i1 scl(2,2)=i2 scl(3,2)=i3 dmin=t1 end if end if end if end do end do end do ! find the third lattice vector nsc=0 dmin=1.d8 do i1=-ngridq(1),ngridq(1) do i2=-ngridq(2),ngridq(2) do i3=-ngridq(3),ngridq(3) t1=dble(i1)*vql(1,iq)+dble(i2)*vql(2,iq)+dble(i3)*vql(3,iq) if (abs(t1-nint(t1)).lt.epslat) then ! number of primitive unit cells in supercell n=scl(1,2)*(i2*scl(3,1)-i3*scl(2,1)) & +scl(2,2)*(i3*scl(1,1)-i1*scl(3,1)) & +scl(3,2)*(i1*scl(2,1)-i2*scl(1,1)) if (n.ne.0) then v1(:)=dble(i1)*avec0(:,1)+dble(i2)*avec0(:,2)+dble(i3)*avec0(:,3) t1=v1(1)**2+v1(2)**2+v1(3)**2 if (t1.lt.dmin) then nsc=abs(n) scl(1,3)=i1 scl(2,3)=i2 scl(3,3)=i3 dmin=t1 end if end if end if end do end do end do if (nsc.eq.0) goto 30 10 continue ! new lattice vectors do i=1,3 avec(:,i)=dble(scl(1,i))*avec0(:,1) & +dble(scl(2,i))*avec0(:,2) & +dble(scl(3,i))*avec0(:,3) end do ! inverse of lattice vector matrix call r3minv(avec,ainv) ! generate offset vectors for each primitive cell in the supercell n=1 vsc(:,1)=0.d0 do i1=-ngridq(1),ngridq(1) do i2=-ngridq(2),ngridq(2) do i3=-ngridq(3),ngridq(3) if (n.eq.nsc) return v1(:)=dble(i1)*avec0(:,1)+dble(i2)*avec0(:,2)+dble(i3)*avec0(:,3) call r3mv(ainv,v1,v2) call r3frac(epslat,v2) call r3mv(avec,v2,v1) do i=1,n t1=abs(v1(1)-vsc(1,i))+abs(v1(2)-vsc(2,i))+abs(v1(3)-vsc(3,i)) if (t1.lt.epslat) goto 20 end do n=n+1 vsc(:,n)=v1(:) 20 continue end do end do end do 30 continue write(*,*) write(*,'("Error(findscq): unable to generate supercell")') write(*,*) stop end subroutine elk-7.2.42/src/PaxHeaders.21776/plot1d.f900000644000000000000000000000013214061636517014447 xustar0030 mtime=1623670095.095102325 30 atime=1623670093.834103495 30 ctime=1623670095.095102325 elk-7.2.42/src/plot1d.f900000644002504400250440000000351214061636517016505 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: plot1d ! !INTERFACE: subroutine plot1d(fnum1,fnum2,nf,rfmt,rfir) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! fnum1 : plot file number (in,integer) ! fnum2 : vertex location file number (in,integer) ! nf : number of functions (in,integer) ! rfmt : real muffin-tin function (in,real(npmtmax,natmtot,nf)) ! rfir : real intersitial function (in,real(ngtot,nf)) ! !DESCRIPTION: ! Produces a 1D plot of the real functions contained in arrays {\tt rfmt} and ! {\tt rfir} along the lines connecting the vertices in the global array ! {\tt vvlp1d}. See routine {\tt rfplot}. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: fnum1,fnum2,nf real(8), intent(in) :: rfmt(npmtmax,natmtot,nf),rfir(ngtot,nf) ! local variables integer jf,ip,iv real(8) fmin,fmax,t1 ! allocatable arrays real(8), allocatable :: fp(:,:) if ((nf.lt.1).or.(nf.gt.4)) then write(*,*) write(*,'("Error(plot1d): invalid number of functions : ",I8)') nf write(*,*) stop end if allocate(fp(npp1d,nf)) ! connect the 1D plotting vertices call plotpt1d(avec,nvp1d,npp1d,vvlp1d,vplp1d,dvp1d,dpp1d) do jf=1,nf ! evaluate function at each point call rfplot(npp1d,vplp1d,rfmt(:,:,jf),rfir(:,jf),fp(:,jf)) end do do ip=1,npp1d ! write the point distances and function to file write(fnum1,'(5G18.10)') dpp1d(ip),(fp(ip,jf),jf=1,nf) end do ! write the vertex location lines fmin=minval(fp(:,:)) fmax=maxval(fp(:,:)) t1=0.5d0*(fmax-fmin) do iv=1,nvp1d write(fnum2,'(2G18.10)') dvp1d(iv),fmax+t1 write(fnum2,'(2G18.10)') dvp1d(iv),fmin-t1 write(fnum2,*) end do deallocate(fp) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/plot2d.f900000644000000000000000000000013214061636517014450 xustar0030 mtime=1623670095.096102324 30 atime=1623670093.836103493 30 ctime=1623670095.096102324 elk-7.2.42/src/plot2d.f900000644002504400250440000000367514061636517016520 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: plot2d ! !INTERFACE: subroutine plot2d(tproj,fnum,nf,rfmt,rfir) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! tproj : .true. if nf=3 and the vector function should be projected onto the ! 2D plotting plane axes (in,logical) ! fnum : plot file number (in,integer) ! nf : number of functions (in,integer) ! rfmt : real muffin-tin function (in,real(npmtmax,natmtot,nf)) ! rfir : real intersitial function (in,real(ngtot,nf)) ! !DESCRIPTION: ! Produces a 2D plot of the real functions contained in arrays {\tt rfmt} and ! {\tt rfir} on the parallelogram defined by the corner vertices in the global ! array {\tt vclp2d}. See routine {\tt rfplot}. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! arguments logical, intent(in) :: tproj integer, intent(in) :: fnum,nf real(8), intent(in) :: rfmt(npmtmax,natmtot,nf),rfir(ngtot,nf) ! local variables integer np,jf,ip real(8) vpnl(3) ! allocatable arrays real(8), allocatable :: vpl(:,:),vppc(:,:),fp(:,:) if ((nf.lt.1).or.(nf.gt.4)) then write(*,*) write(*,'("Error(plot2d): invalid number of functions : ",I8)') nf write(*,*) stop end if ! allocate local arrays np=np2d(1)*np2d(2) allocate(vpl(3,np),vppc(2,np),fp(np,nf)) ! generate the 2D plotting points call plotpt2d(avec,ainv,vpnl,vpl,vppc) ! evaluate the functions at the grid points do jf=1,nf call rfplot(np,vpl,rfmt(:,:,jf),rfir(:,jf),fp(:,jf)) end do ! project the vector function onto the 2D plotting plane axes if required if (tproj.and.(nf.eq.3)) then call proj2d(np,fp) end if ! write the functions to file write(fnum,'(2I6," : grid size")') np2d(:) do ip=1,np write(fnum,'(6G18.10)') vppc(1,ip),vppc(2,ip),(fp(ip,jf),jf=1,nf) end do deallocate(vpl,vppc,fp) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/plot3d.f900000644000000000000000000000013214061636517014451 xustar0030 mtime=1623670095.098102322 30 atime=1623670093.837103492 30 ctime=1623670095.098102322 elk-7.2.42/src/plot3d.f900000644002504400250440000000333114061636517016506 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: plot3d ! !INTERFACE: subroutine plot3d(fnum,nf,rfmt,rfir) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! fnum : plot file number (in,integer) ! nf : number of functions (in,integer) ! rfmt : real muffin-tin function (in,real(npmtmax,natmtot,nf)) ! rfir : real intersitial function (in,real(ngtot,nf)) ! !DESCRIPTION: ! Produces a 3D plot of the real functions contained in arrays {\tt rfmt} and ! {\tt rfir} in the parallelepiped defined by the corner vertices in the ! global array {\tt vclp3d}. See routine {\tt rfarray}. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) ! Modified, October 2008 (F. Bultmark, F. Cricchio, L. Nordstrom) !EOP !BOC implicit none ! arguments integer, intent(in) :: fnum,nf real(8), intent(in) :: rfmt(npmtmax,natmtot,nf),rfir(ngtot,nf) ! local variables integer np,jf,ip real(8) v1(3) ! allocatable arrays real(8), allocatable :: vpl(:,:),fp(:,:) if ((nf.lt.1).or.(nf.gt.4)) then write(*,*) write(*,'("Error(plot3d): invalid number of functions : ",I8)') nf write(*,*) stop end if ! total number of plot points np=np3d(1)*np3d(2)*np3d(3) ! allocate local arrays allocate(vpl(3,np),fp(np,nf)) ! generate the 3D plotting points call plotpt3d(vpl) ! evaluate the functions at the grid points do jf=1,nf call rfplot(np,vpl,rfmt(:,:,jf),rfir(:,jf),fp(:,jf)) end do ! write functions to file write(fnum,'(3I6," : grid size")') np3d(:) do ip=1,np call r3mv(avec,vpl(:,ip),v1) write(fnum,'(7G18.10)') v1(:),(fp(ip,jf),jf=1,nf) end do deallocate(vpl,fp) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/init0.f900000644000000000000000000000013214061636517014267 xustar0030 mtime=1623670095.099102321 30 atime=1623670093.839103491 30 ctime=1623670095.099102321 elk-7.2.42/src/init0.f900000644002504400250440000005115214061636517016330 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: init0 ! !INTERFACE: subroutine init0 ! !USES: use modmain use modxcifc use moddftu use modtddft use modphonon use modulr use modtest use modvars use modmpi use modomp ! !DESCRIPTION: ! Performs basic consistency checks as well as allocating and initialising ! global variables not dependent on the $k$-point set. ! ! !REVISION HISTORY: ! Created January 2004 (JKD) !EOP !BOC implicit none ! local variables integer is,ia,ias,n integer ist,nr,l,i real(8) t1 real(8) ts0,ts1 !-------------------------------! ! zero timing variables ! !-------------------------------! timeinit=0.d0 timemat=0.d0 timefv=0.d0 timesv=0.d0 timerho=0.d0 timepot=0.d0 timefor=0.d0 call timesec(ts0) !------------------------------------! ! angular momentum variables ! !------------------------------------! if (lmaxo.gt.lmaxapw) then write(*,*) write(*,'("Error(init0): lmaxo > lmaxapw : ",2I8)') lmaxo,lmaxapw write(*,*) stop end if lmaxi=min(lmaxi,lmaxo) lmmaxapw=(lmaxapw+1)**2 lmmaxi=(lmaxi+1)**2 lmmaxo=(lmaxo+1)**2 ! check DOS lmax is within range lmaxdos=min(lmaxdos,lmaxo) ! write to VARIABLES.OUT call writevars('lmaxapw',iv=lmaxapw) call writevars('lmaxi',iv=lmaxi) call writevars('lmaxo',iv=lmaxo) !------------------------------------! ! index to atoms and species ! !------------------------------------! natmmax=0 ias=0 do is=1,nspecies do ia=1,natoms(is) ias=ias+1 idxas(ia,is)=ias idxis(ias)=is idxia(ias)=ia end do ! maximum number of atoms over all species natmmax=max(natmmax,natoms(is)) end do ! total number of atoms natmtot=ias ! number of phonon branches nbph=3*natmtot ! write to VARIABLES.OUT call writevars('nspecies',iv=nspecies) call writevars('natoms',nv=nspecies,iva=natoms) call writevars('spsymb',nv=nspecies,sva=spsymb) call writevars('spname',nv=nspecies,sva=spname) call writevars('spzn',nv=nspecies,rva=spzn) !------------------------! ! spin variables ! !------------------------! if (spinsprl) then spinpol=.true. spinorb=.false. if (any(task.eq.[5,51,52,53,61,62,63,700,701,800,801])) then write(*,*) write(*,'("Error(init0): spin-spirals do not work with task ",I4)') task write(*,*) stop end if if (xctype(1).lt.0) then write(*,*) write(*,'("Error(init0): spin-spirals do not work with the OEP method")') write(*,*) stop end if if (tefvit) then write(*,*) write(*,'("Error(init0): spin-spirals do not work with iterative & &diagonalisation")') write(*,*) stop end if end if ! de-phasing required only for spin-spirals if (.not.spinsprl) ssdph=.false. ! spin-orbit coupling, fixed spin moment, spin spirals or spin-polarised cores ! requires a spin-polarised calculation if ((spinorb).or.(fsmtype.ne.0).or.(spinsprl).or.(spincore)) spinpol=.true. ! number of spinor components and maximum allowed occupancy if (spinpol) then nspinor=2 occmax=1.d0 else nspinor=1 occmax=2.d0 end if ! number of spin-dependent first-variational functions per state and map from ! second- to first-variational spin index if (spinsprl) then nspnfv=2 jspnfv(1)=1 jspnfv(2)=2 else nspnfv=1 jspnfv(1)=1 jspnfv(2)=1 end if ! no calculation of second-variational eigenvectors by default tevecsv=.false. ! spin-polarised calculations require second-variational eigenvectors if (spinpol) tevecsv=.true. ! Hartree-Fock/RDMFT/TDDFT/GW requires second-variational eigenvectors if (any(task.eq.[5,10,170,300,460,461,462,463,600,620,630,800,801])) then tevecsv=.true. end if ! get exchange-correlation functional data call getxcdata(xctype,xcdescr,xcspin,xcgrad,hybrid0,hybridc) if ((spinpol).and.(xcspin.eq.0)) then write(*,*) write(*,'("Error(init0): requested spin-polarised run with & &spin-unpolarised")') write(*,'(" exchange-correlation functional")') write(*,*) stop end if ! set flag for hybrid functional if (task.eq.5) then hybrid=hybrid0 else hybrid=.false. end if ! check for collinearity in the z-direction and set the dimension of the ! magnetisation and exchange-correlation vector fields if (spinpol) then ndmag=1 if ((abs(bfieldc0(1)).gt.epslat).or.(abs(bfieldc0(2)).gt.epslat)) ndmag=3 do is=1,nspecies do ia=1,natoms(is) if ((abs(bfcmt0(1,ia,is)).gt.epslat).or. & (abs(bfcmt0(2,ia,is)).gt.epslat)) ndmag=3 end do end do ! spin-orbit coupling is non-collinear in general if (spinorb) ndmag=3 ! source-free fields and spin-spirals must be non-collinear if ((nosource).or.(spinsprl)) then ndmag=3 cmagz=.false. end if ! force collinear magnetism along the z-axis if required if (cmagz) ndmag=1 else ndmag=0 end if ! set the non-collinear flag if (ndmag.eq.3) then ncmag=.true. else ncmag=.false. end if ! check for meta-GGA with non-collinearity if (((xcgrad.eq.3).or.(xcgrad.eq.4)).and.ncmag) then write(*,*) write(*,'("Error(init0): meta-GGA is not valid for non-collinear magnetism")') write(*,*) stop end if if (ncmag.or.spinorb) then ! spins are coupled in the second-variational Hamiltonian spcpl=.true. else ! spins are decoupled spcpl=.false. end if ! spin-polarised cores if (.not.spinpol) spincore=.false. if (fsmtype.ne.0) then ! set fixed spin moment effective field to zero bfsmc(:)=0.d0 ! set muffin-tin FSM fields to zero if (allocated(bfsmcmt)) deallocate(bfsmcmt) allocate(bfsmcmt(3,natmtot)) bfsmcmt(:,:)=0.d0 if (mp_mpi.and.(mixtype.ne.1)) then write(*,*) write(*,'("Info(init0): mixtype changed to 1 for FSM calculation")') end if mixtype=1 end if ! number of independent spin components of the f_xc spin tensor if (spinpol) then if (ncmag) then nscfxc=10 else nscfxc=3 end if else nscfxc=1 end if ! set the magnetic fields to the initial values bfieldc(:)=bfieldc0(:) bfcmt(:,:,:)=bfcmt0(:,:,:) ! if reducebf < 1 then reduce the external magnetic fields immediately for ! non-self-consistent calculations or resumptions if (reducebf.lt.1.d0-1.d-4) then if (all(task.ne.[0,1,2,3,5,28,200,201,350,351,630])) then bfieldc(:)=0.d0 bfcmt(:,:,:)=0.d0 end if end if ! set the fixed tensor moment spatial and spin rotation matrices equal for the ! case of spin-orbit coupling; parity for spin is ignored by rotdmat if (spinorb) then do i=1,ntmfix rtmfix(:,:,2,i)=rtmfix(:,:,1,i) end do end if ! generate the fixed tensor moment density matrices if required call gendmftm ! write to VARIABLES.OUT call writevars('nspinor',iv=nspinor) call writevars('ndmag',iv=ndmag) !----------------------------------! ! crystal structure set up ! !----------------------------------! ! generate the reciprocal lattice vectors and unit cell volume call reciplat(avec,bvec,omega,omegabz) ! inverse of the lattice vector matrix call r3minv(avec,ainv) ! inverse of the reciprocal vector matrix call r3minv(bvec,binv) ! Cartesian coordinates of the spin-spiral vector call r3mv(bvec,vqlss,vqcss) do is=1,nspecies do ia=1,natoms(is) ! map atomic lattice coordinates to [0,1) call r3frac(epslat,atposl(:,ia,is)) ! determine atomic Cartesian coordinates call r3mv(avec,atposl(:,ia,is),atposc(:,ia,is)) end do end do ! check for overlapping muffin-tins and adjust radii if required call checkmt ! compute the total muffin-tin volume (M. Meinert) omegamt=0.d0 do is=1,nspecies omegamt=omegamt+dble(natoms(is))*(fourpi/3.d0)*rmt(is)**3 end do ! input q-vector in Cartesian coordinates call r3mv(bvec,vecql,vecqc) ! write to VARIABLES.OUT call writevars('avec',nv=9,rva=avec) call writevars('bvec',nv=9,rva=bvec) call writevars('omega',rv=omega) do is=1,nspecies call writevars('atposl',l=is,nv=3*natoms(is),rva=atposl(:,:,is)) end do !-------------------------------! ! vector fields E and A ! !-------------------------------! tefield=.false. if (sum(abs(efieldc(:))).gt.epslat) then ! no shift of the atomic positions tshift=.false. ! electric field vector in lattice coordinates call r3mv(ainv,efieldc,efieldl) tefield=.true. end if tafield=.false. if (sum(abs(afieldc(:))).gt.epslat) then tafield=.true. ! A-field in lattice coordinates call r3mv(ainv,afieldc,afieldl) ! vector potential added in second-variational step tevecsv=.true. end if tafieldt=.false. if (any(task.eq.[460,461,462,463,480,481])) then ! read time-dependent A-field from file call readafieldt tafieldt=.true. ! zero the induced A-field and its time derivative afindt(:,:)=0.d0 end if !---------------------------------! ! crystal symmetry set up ! !---------------------------------! call symmetry !-----------------------! ! radial meshes ! !-----------------------! nrmtmax=1 nrcmtmax=1 do is=1,nspecies ! make the muffin-tin mesh commensurate with lradstp nrmt(is)=nrmt(is)-mod(nrmt(is)-1,lradstp) nrmtmax=max(nrmtmax,nrmt(is)) ! number of coarse radial mesh points nrcmt(is)=(nrmt(is)-1)/lradstp+1 nrcmtmax=max(nrcmtmax,nrcmt(is)) end do ! set up atomic and muffin-tin radial meshes call genrmesh ! number of points in packed muffin-tins npmtmax=1 npcmtmax=1 do is=1,nspecies npmti(is)=lmmaxi*nrmti(is) npmt(is)=npmti(is)+lmmaxo*(nrmt(is)-nrmti(is)) npmtmax=max(npmtmax,npmt(is)) npcmti(is)=lmmaxi*nrcmti(is) npcmt(is)=npcmti(is)+lmmaxo*(nrcmt(is)-nrcmti(is)) npcmtmax=max(npcmtmax,npcmt(is)) end do !--------------------------------------! ! charges and number of states ! !--------------------------------------! chgzn=0.d0 chgcrtot=0.d0 chgval=0.d0 nstspmax=0 nstcr=0 do is=1,nspecies ! nuclear charge chgzn=chgzn+spzn(is)*natoms(is) ! find the maximum number of atomic states nstspmax=max(nstspmax,nstsp(is)) ! compute the electronic charge for each species, as well as the total core and ! valence charge spze(is)=0.d0 chgcr(is)=0.d0 do ist=1,nstsp(is) spze(is)=spze(is)+occsp(ist,is) if (spcore(ist,is)) then chgcr(is)=chgcr(is)+occsp(ist,is) nstcr=nstcr+2*ksp(ist,is)*natoms(is) else chgval=chgval+occsp(ist,is)*natoms(is) end if end do chgcrtot=chgcrtot+chgcr(is)*natoms(is) end do ! add excess charge chgval=chgval+chgexs ! total charge chgtot=chgcrtot+chgval if (chgtot.lt.1.d-8) then write(*,*) write(*,'("Error(init0): zero total charge")') write(*,*) stop end if ! effective Wigner radius rwigner=(3.d0/(fourpi*(chgtot/omega)))**(1.d0/3.d0) ! write to VARIABLES.OUT call writevars('spze',nv=nspecies,rva=spze) call writevars('chgcr',nv=nspecies,rva=chgcr) call writevars('chgexs',rv=chgexs) call writevars('chgval',rv=chgtot) !-------------------------! ! G-vector arrays ! !-------------------------! ! determine gkmax from rgkmax if (nspecies.eq.0) isgkmax=-2 select case(isgkmax) case(:-4) ! use largest muffin-tin radius gkmax=rgkmax/maxval(rmt(1:nspecies)) case(-3) ! use smallest muffin-tin radius gkmax=rgkmax/minval(rmt(1:nspecies)) case(-2) ! use the fixed value of 2.0 gkmax=rgkmax/2.d0 case(-1) ! use average muffin-tin radius t1=sum(natoms(1:nspecies)*rmt(1:nspecies))/dble(natmtot) gkmax=rgkmax/t1 case(1:) ! use user-specified muffin-tin radius if (isgkmax.le.nspecies) then gkmax=rgkmax/rmt(isgkmax) else write(*,*) write(*,'("Error(init0): isgkmax > nspecies : ",2I8)') isgkmax,nspecies write(*,*) stop end if end select ! generate the G-vectors call gengvec ! write number of G-vectors to test file call writetest(900,'number of G-vectors',iv=ngvec) ! Poisson solver pseudocharge density constant if (nspecies.gt.0) then t1=0.25d0*gmaxvr*maxval(rmt(1:nspecies)) else t1=0.25d0*gmaxvr*2.d0 end if npsd=max(nint(t1),1) lnpsd=lmaxo+npsd+1 ! generate the Coulomb Green's function in G-space = fourpi / G^2 call gengclg ! compute the spherical Bessel functions j_l(|G|R_mt) if (allocated(jlgrmt)) deallocate(jlgrmt) allocate(jlgrmt(0:lnpsd,ngvec,nspecies)) call genjlgprmt(lnpsd,ngvec,gc,ngvec,jlgrmt) ! generate the spherical harmonics of the G-vectors call genylmg ! allocate structure factor array for G-vectors if (allocated(sfacg)) deallocate(sfacg) allocate(sfacg(ngvec,natmtot)) ! generate structure factors for G-vectors call gensfacgp(ngvec,vgc,ngvec,sfacg) ! generate the smooth step function form factors if (allocated(ffacg)) deallocate(ffacg) allocate(ffacg(ngtot,nspecies)) do is=1,nspecies call genffacgp(is,gc,ffacg(:,is)) end do ! generate the characteristic function call gencfun ! G-vector variables for coarse grid (G < 2*gkmax) call gengvc ! generate the characteristic function on the coarse grid call gencfrc ! write to VARIABLES.OUT call writevars('gmaxvr',rv=gmaxvr) call writevars('ngridg',nv=3,iva=ngridg) call writevars('intgv',nv=6,iva=intgv) call writevars('ngvec',iv=ngvec) call writevars('ivg',nv=3*ngtot,iva=ivg) call writevars('igfft',nv=ngtot,iva=igfft) !-------------------------! ! atoms and cores ! !-------------------------! ! determine the nuclear Coulomb potential if (allocated(vcln)) deallocate(vcln) allocate(vcln(nrspmax,nspecies)) t1=1.d0/y00 do is=1,nspecies nr=nrsp(is) call potnucl(ptnucl,nr,rsp(:,is),spzn(is),vcln(:,is)) vcln(1:nr,is)=t1*vcln(1:nr,is) end do ! solve the Kohn-Sham-Dirac equations for all atoms call allatoms ! allocate core state occupancy and eigenvalue arrays and set to default if (allocated(occcr)) deallocate(occcr) allocate(occcr(nstspmax,natmtot)) if (allocated(evalcr)) deallocate(evalcr) allocate(evalcr(nstspmax,natmtot)) do ias=1,natmtot is=idxis(ias) do ist=1,nstsp(is) occcr(ist,ias)=occsp(ist,is) evalcr(ist,ias)=evalsp(ist,is) end do end do ! allocate core state radial wavefunction array if (allocated(rwfcr)) deallocate(rwfcr) allocate(rwfcr(nrspmax,2,nstspmax,natmtot)) ! number of core spin channels if (spincore) then nspncr=2 else nspncr=1 end if ! allocate core state charge density array if (allocated(rhocr)) deallocate(rhocr) allocate(rhocr(nrmtmax,natmtot,nspncr)) !-------------------------------------------------------------! ! charge density, potentials and exchange-correlation ! !-------------------------------------------------------------! ! allocate charge density arrays if (allocated(rhomt)) deallocate(rhomt) allocate(rhomt(npmtmax,natmtot)) if (allocated(rhoir)) deallocate(rhoir) allocate(rhoir(ngtot)) ! allocate magnetisation arrays if (allocated(magmt)) deallocate(magmt) if (allocated(magir)) deallocate(magir) if (spinpol) then allocate(magmt(npmtmax,natmtot,ndmag)) allocate(magir(ngtot,ndmag)) end if ! check if the current density j(r) should be calculated if (tafield.or.tdjr1d.or.tdjr2d.or.tdjr3d.or.(any(task.eq.[371,372,373]))) then tjr=.true. end if ! allocate current density arrays if (allocated(jrmt)) deallocate(jrmt) if (allocated(jrir)) deallocate(jrir) if (tjr) then allocate(jrmt(npmtmax,natmtot,3),jrir(ngtot,3)) end if ! Coulomb potential if (allocated(vclmt)) deallocate(vclmt) allocate(vclmt(npmtmax,natmtot)) if (allocated(vclir)) deallocate(vclir) allocate(vclir(ngtot)) ! exchange energy density if (allocated(exmt)) deallocate(exmt) allocate(exmt(npmtmax,natmtot)) if (allocated(exir)) deallocate(exir) allocate(exir(ngtot)) ! correlation energy density if (allocated(ecmt)) deallocate(ecmt) allocate(ecmt(npmtmax,natmtot)) if (allocated(ecir)) deallocate(ecir) allocate(ecir(ngtot)) ! exchange-correlation potential if (allocated(vxcmt)) deallocate(vxcmt) allocate(vxcmt(npmtmax,natmtot)) if (allocated(vxcir)) deallocate(vxcir) allocate(vxcir(ngtot)) ! exchange-correlation and dipole magnetic fields if (allocated(bxcmt)) deallocate(bxcmt) if (allocated(bxcir)) deallocate(bxcir) if (allocated(bdmt)) deallocate(bdmt) if (allocated(bdir)) deallocate(bdir) if (spinpol) then allocate(bxcmt(npmtmax,natmtot,ndmag),bxcir(ngtot,ndmag)) if (tbdip) allocate(bdmt(npmtmax,natmtot,ndmag),bdir(ngtot,ndmag)) end if ! combined target array for Kohn-Sham potential and magnetic field if (allocated(vsbs)) deallocate(vsbs) n=npmtmax*natmtot+ngtot if (spinpol) n=n+(npcmtmax*natmtot+ngtot)*ndmag allocate(vsbs(n)) ! zero the array vsbs(:)=0.d0 ! associate pointer arrays with target vsmt(1:npmtmax,1:natmtot)=>vsbs(1:) i=npmtmax*natmtot+1 vsir(1:ngtot)=>vsbs(i:) if (spinpol) then i=i+ngtot bsmt(1:npcmtmax,1:natmtot,1:ndmag)=>vsbs(i:) i=i+npcmtmax*natmtot*ndmag bsir(1:ngtot,1:ndmag)=>vsbs(i:) end if ! effective Kohn-Sham potential in G-space if (allocated(vsig)) deallocate(vsig) allocate(vsig(ngvec)) ! kinetic energy density if (allocated(taumt)) deallocate(taumt) if (allocated(tauir)) deallocate(tauir) if (allocated(taucr)) deallocate(taucr) if ((xcgrad.eq.3).or.(xcgrad.eq.4)) then allocate(taumt(npmtmax,natmtot,nspinor),tauir(ngtot,nspinor)) allocate(taucr(npmtmax,natmtot,nspinor)) end if ! meta-GGA exchange-correlation and Kohn-Sham potentials if (allocated(wxcmt)) deallocate(wxcmt) if (allocated(wxcir)) deallocate(wxcir) if (allocated(wsmt)) deallocate(wsmt) if (allocated(wsir)) deallocate(wsir) if (xcgrad.eq.4) then allocate(wxcmt(npmtmax,natmtot),wxcir(ngtot)) allocate(wsmt(npcmtmax,natmtot),wsir(ngtot)) tevecsv=.true. end if ! spin-orbit coupling radial function if (allocated(socfr)) deallocate(socfr) if (spinorb) then allocate(socfr(nrcmtmax,natmtot)) end if ! allocate muffin-tin charge and moment arrays if (allocated(chgcrlk)) deallocate(chgcrlk) allocate(chgcrlk(natmtot)) if (allocated(chgmt)) deallocate(chgmt) allocate(chgmt(natmtot)) if (allocated(mommt)) deallocate(mommt) allocate(mommt(3,natmtot)) ! check if scaled spin exchange-correlation should be used if (abs(sxcscf-1.d0).gt.1.d-6) then tssxc=.true. else tssxc=.false. end if ! spin-spiral phase factors if (ssdph) then if (allocated(zqss)) deallocate(zqss) allocate(zqss(natmtot)) do ias=1,natmtot is=idxis(ias) ia=idxia(ias) t1=-0.5d0*dot_product(vqcss(:),atposc(:,ia,is)) zqss(ias)=cmplx(cos(t1),sin(t1),8) end do end if !-------------------------! ! force variables ! !-------------------------! if (tforce) then if (allocated(forcehf)) deallocate(forcehf) allocate(forcehf(3,natmtot)) if (allocated(forceibs)) deallocate(forceibs) allocate(forceibs(3,natmtot)) if (allocated(forcetot)) deallocate(forcetot) allocate(forcetot(3,natmtot)) end if !-------------------------------------------------! ! DFT+U and fixed tensor moment variables ! !-------------------------------------------------! if ((dftu.ne.0).or.(ftmtype.ne.0)) then ! density matrix elements in each muffin-tin if (allocated(dmatmt)) deallocate(dmatmt) allocate(dmatmt(lmmaxdm,nspinor,lmmaxdm,nspinor,natmtot)) ! potential matrix elements in each muffin-tin if (allocated(vmatmt)) deallocate(vmatmt) allocate(vmatmt(lmmaxdm,nspinor,lmmaxdm,nspinor,natmtot)) ! zero the potential matrix vmatmt(:,:,:,:,:)=0.d0 ! require the potential matrix elements be calculated tvmatmt=.true. ! flags for non-zero muffin-tin potential matrices if (allocated(tvmmt)) deallocate(tvmmt) allocate(tvmmt(0:lmaxdm,natmtot)) tvmmt(:,:)=.false. ! require second-variational eigenvectors tevecsv=.true. end if if (dftu.ne.0) then ! DFT+U energy for each atom if (allocated(engyadu)) deallocate(engyadu) allocate(engyadu(natmmax,ndftu)) ! interpolation constants (alpha) if (allocated(alphadu)) deallocate(alphadu) allocate(alphadu(natmmax,ndftu)) ! flag the muffin-tin potential matrices which are non-zero do i=1,ndftu is=idftu(1,i) if (is.gt.nspecies) then write(*,*) write(*,'("Error(init0): invalid species number : ",I8)') is write(*,*) stop end if l=idftu(2,i) do ia=1,natoms(is) ias=idxas(ia,is) tvmmt(l,ias)=.true. end do end do end if if (ftmtype.ne.0) then ! allocate and zero the fixed tensor moment potential array if (allocated(vmftm)) deallocate(vmftm) allocate(vmftm(lmmaxdm,nspinor,lmmaxdm,nspinor,natmtot)) vmftm(:,:,:,:,:)=0.d0 ! flag the muffin-tin potential matrices which are non-zero do i=1,ntmfix is=itmfix(1,i) ia=itmfix(2,i) ias=idxas(ia,is) l=itmfix(3,i) tvmmt(l,ias)=.true. end do end if !-----------------------! ! miscellaneous ! !-----------------------! ! determine nuclear radii and volumes call nuclei ! determine the nuclear-nuclear energy call energynn ! get smearing function description call getsdata(stype,sdescr) ! get mixing type description call getmixdata(mixtype,mixdescr) ! generate the spherical harmonic transform (SHT) matrices call genshtmat ! find the maximum size of the spherical Bessel function array over all species call findnjcmax ! allocate 1D plotting arrays if (allocated(dvp1d)) deallocate(dvp1d) allocate(dvp1d(nvp1d)) if (allocated(vplp1d)) deallocate(vplp1d) allocate(vplp1d(3,npp1d)) if (allocated(dpp1d)) deallocate(dpp1d) allocate(dpp1d(npp1d)) ! initial self-consistent loop number iscl=1 tlast=.false. ! set the Fermi energy to zero efermi=0.d0 ! set the temperature from the smearing width tempk=swidth/kboltz call timesec(ts1) timeinit=timeinit+ts1-ts0 end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/readstate.f900000644000000000000000000000013214061636517015220 xustar0030 mtime=1623670095.101102319 30 atime=1623670093.841103489 30 ctime=1623670095.101102319 elk-7.2.42/src/readstate.f900000644002504400250440000002327214061636517017263 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: readstate ! !INTERFACE: subroutine readstate ! !USES: use modmain use moddftu ! !DESCRIPTION: ! Reads in the charge density and other relevant variables from the file ! {\tt STATE.OUT}. Checks for version and parameter compatibility. ! ! !REVISION HISTORY: ! Created May 2003 (JKD) !EOP !BOC implicit none ! local variables logical spinpol_ integer is,ia,ias,lmmax,lm,ir,jr integer idm,jdm,mapidm(3),ios integer i1,i2,i3,j1,j2,j3,n integer version_(3) integer nspecies_,natoms_,lmmaxo_ integer nrmt_(maxspecies),nrmtmax_ integer nrcmt_(maxspecies),nrcmtmax_ integer ngridg_(3),ngtot_,ngvec_ integer ndmag_,nspinor_,fsmtype_,ftmtype_ integer dftu_,lmmaxdm_,xcgrad_ real(8) t1 ! allocatable arrays integer, allocatable :: mapir(:) real(8), allocatable :: rsp_(:,:),rcmt_(:,:) real(8), allocatable :: wcrmt_(:,:,:),wcrcmt_(:,:,:) real(8), allocatable :: rfmt_(:,:,:),rfir_(:) real(8), allocatable :: rvfmt_(:,:,:,:),rvfir_(:,:) real(8), allocatable :: rvfcmt_(:,:,:,:),rfmt(:,:) real(8), allocatable :: bfsmcmt_(:,:),fi(:),fo(:) complex(8), allocatable :: vsig_(:) complex(8), allocatable :: vmatmt_(:,:,:,:,:),vmftm_(:,:,:,:,:) open(100,file='STATE'//trim(filext),form='UNFORMATTED',action='READ', & status='OLD',iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readstate): error opening ",A)') 'STATE'//trim(filext) write(*,*) stop end if read(100) version_ if (version_(1).lt.2) then write(*,*) write(*,'("Error(readstate): unable to read STATE.OUT from versions earlier & &than 2.0.0")') write(*,*) stop end if if (any(version(:).ne.version_(:))) then write(*,*) write(*,'("Warning(readstate): different versions")') write(*,'(" current : ",I3.3,".",I3.3,".",I3.3)') version write(*,'(" STATE.OUT : ",I3.3,".",I3.3,".",I3.3)') version_ end if read(100) spinpol_ read(100) nspecies_ if (nspecies.ne.nspecies_) then write(*,*) write(*,'("Error(readstate): differing nspecies")') write(*,'(" current : ",I4)') nspecies write(*,'(" STATE.OUT : ",I4)') nspecies_ write(*,*) stop end if read(100) lmmaxo_ lmmax=min(lmmaxo,lmmaxo_) read(100) nrmtmax_ read(100) nrcmtmax_ allocate(rsp_(nrmtmax_,nspecies)) allocate(rcmt_(nrcmtmax_,nspecies)) do is=1,nspecies read(100) natoms_ if (natoms(is).ne.natoms_) then write(*,*) write(*,'("Error(readstate): differing natoms for species ",I4)') is write(*,'(" current : ",I4)') natoms(is) write(*,'(" STATE.OUT : ",I4)') natoms_ write(*,*) stop end if read(100) nrmt_(is) read(100) rsp_(1:nrmt_(is),is) read(100) nrcmt_(is) read(100) rcmt_(1:nrcmt_(is),is) end do read(100) ngridg_ read(100) ngvec_ read(100) ndmag_ if ((spinpol_).and.(ndmag_.ne.1).and.(ndmag_.ne.3)) then write(*,*) write(*,'("Error(readstate): invalid ndmag in STATE.OUT : ",I8)') ndmag_ write(*,*) stop end if read(100) nspinor_ read(100) fsmtype_ if ((version_(1).gt.2).or.(version_(2).ge.3)) then read(100) ftmtype_ else ftmtype_=0 end if read(100) dftu_ read(100) lmmaxdm_ if ((version_(1).gt.5).or.((version_(1).eq.5).and.(version_(2).ge.1))) then read(100) xcgrad_ else xcgrad_=0 end if ngtot_=ngridg_(1)*ngridg_(2)*ngridg_(3) ! map from old interstitial grid to new allocate(mapir(ngtot)) ir=0 do i3=0,ngridg(3)-1 t1=dble(i3*ngridg_(3))/dble(ngridg(3)) j3=modulo(nint(t1),ngridg_(3)) do i2=0,ngridg(2)-1 t1=dble(i2*ngridg_(2))/dble(ngridg(2)) j2=modulo(nint(t1),ngridg_(2)) do i1=0,ngridg(1)-1 t1=dble(i1*ngridg_(1))/dble(ngridg(1)) j1=modulo(nint(t1),ngridg_(1)) ir=ir+1 jr=j3*ngridg_(2)*ngridg_(1)+j2*ngridg_(1)+j1+1 mapir(ir)=jr end do end do end do ! determine the spline coefficient weights on the old radial mesh allocate(wcrmt_(12,nrmtmax_,nspecies)) allocate(wcrcmt_(12,nrcmtmax_,nspecies)) do is=1,nspecies call wspline(nrmt_(is),rsp_(:,is),wcrmt_(:,:,is)) call wspline(nrcmt_(is),rcmt_(:,is),wcrcmt_(:,:,is)) end do allocate(rfmt_(lmmaxo_,nrmtmax_,natmtot),rfir_(ngtot_)) allocate(rfmt(lmmaxo,nrmtmax)) n=max(nrmtmax,nrmtmax_) allocate(fi(n),fo(n)) ! read the muffin-tin density read(100) rfmt_,rfir_ ! regrid and pack the muffin-tin function call rgfmt(rhomt) ! regrid the interstitial function rhoir(:)=rfir_(mapir(:)) ! read the Coulomb potential, regrid and pack read(100) rfmt_,rfir_ call rgfmt(vclmt) vclir(:)=rfir_(mapir(:)) ! read the exchange-correlation potential, regrid and pack read(100) rfmt_,rfir_ call rgfmt(vxcmt) vxcir(:)=rfir_(mapir(:)) ! read the Kohn-Sham effective potential, regrid and pack if ((version_(1).gt.2).or.(version_(2).ge.2)) then read(100) rfmt_,rfir_ else allocate(vsig_(ngvec_)) read(100) rfmt_,rfir_,vsig_ deallocate(vsig_) end if call rgfmt(vsmt) vsir(:)=rfir_(mapir(:)) ! read the magnetisation, exchange-correlation and effective magnetic fields if (spinpol_) then ! component map for spin-polarised case mapidm(:)=0 if (ndmag.eq.ndmag_) then do idm=1,ndmag mapidm(idm)=idm end do else mapidm(ndmag)=ndmag_ end if allocate(rvfmt_(lmmaxo_,nrmtmax_,natmtot,ndmag_)) allocate(rvfir_(ngtot_,ndmag_)) allocate(rvfcmt_(lmmaxo_,nrcmtmax_,natmtot,ndmag_)) read(100) rvfmt_,rvfir_ call rgvfmt(magmt) call rgvir(magir) read(100) rvfmt_,rvfir_ call rgvfmt(bxcmt) call rgvir(bxcir) read(100) rvfcmt_,rvfir_ call rgvfcmt(bsmt) call rgvir(bsir) deallocate(rvfmt_,rvfir_,rvfcmt_) ! read fixed spin moment effective fields if (fsmtype_.ne.0) then allocate(bfsmcmt_(3,natmtot)) read(100) bfsmc read(100) bfsmcmt_ if (fsmtype.ne.0) bfsmcmt(:,:)=bfsmcmt_(:,:) ! make sure that the constraining fields are perpendicular to the fixed moments ! for fixed direction calculations (Y. Kvashnin and LN) if (fsmtype.lt.0) then if (ncmag) then call r3vo(momfix,bfsmc) do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) call r3vo(mommtfix(:,ia,is),bfsmcmt(:,ias)) end do end do else bfsmc(:)=0.d0 bfsmcmt(:,:)=0.d0 end if end if deallocate(bfsmcmt_) end if end if if (xcgrad.eq.4) then if (xcgrad_.eq.4) then read(100) rfmt_,rfir_ call rgfmt(wxcmt) wxcir(:)=rfir_(mapir(:)) else wxcmt(:,:)=0.d0 wxcir(:)=0.d0 end if call genws end if deallocate(wcrmt_,wcrcmt_,rfmt_,rfir_,rfmt,fi,fo) ! read DFT+U potential matrix in each muffin-tin if (((dftu.ne.0).and.(dftu_.ne.0)).or. & ((ftmtype.ne.0).and.(ftmtype_.ne.0))) then allocate(vmatmt_(lmmaxdm_,nspinor_,lmmaxdm_,nspinor_,natmtot)) read(100) vmatmt_ lmmax=min(lmmaxdm,lmmaxdm_) vmatmt(:,:,:,:,:)=0.d0 if (nspinor.eq.nspinor_) then vmatmt(1:lmmax,:,1:lmmax,:,:)=vmatmt_(1:lmmax,:,1:lmmax,:,:) else if ((nspinor.eq.1).and.(nspinor_.eq.2)) then vmatmt(1:lmmax,1,1:lmmax,1,:)=0.5d0*(vmatmt_(1:lmmax,1,1:lmmax,1,:) & +vmatmt_(1:lmmax,2,1:lmmax,2,:)) else vmatmt(1:lmmax,1,1:lmmax,1,:)=vmatmt_(1:lmmax,1,1:lmmax,1,:) vmatmt(1:lmmax,2,1:lmmax,2,:)=vmatmt_(1:lmmax,1,1:lmmax,1,:) end if deallocate(vmatmt_) end if ! read fixed tensor moment potential matrix elements if ((ftmtype.ne.0).and.(ftmtype_.ne.0)) then allocate(vmftm_(lmmaxdm_,nspinor_,lmmaxdm_,nspinor_,natmtot)) read(100) vmftm_ lmmax=min(lmmaxdm,lmmaxdm_) vmftm_(:,:,:,:,:)=0.d0 if (nspinor.eq.nspinor_) then vmftm(1:lmmax,:,1:lmmax,:,:)=vmftm_(1:lmmax,:,1:lmmax,:,:) else if ((nspinor.eq.1).and.(nspinor_.eq.2)) then vmftm(1:lmmax,1,1:lmmax,1,:)=0.5d0*(vmftm_(1:lmmax,1,1:lmmax,1,:) & +vmftm_(1:lmmax,2,1:lmmax,2,:)) else vmftm(1:lmmax,1,1:lmmax,1,:)=vmftm_(1:lmmax,1,1:lmmax,1,:) vmftm(1:lmmax,2,1:lmmax,2,:)=vmftm_(1:lmmax,1,1:lmmax,1,:) end if deallocate(vmftm_) end if close(100) return contains subroutine rgfmt(rfmtp) implicit none ! arguments real(8), intent(out) :: rfmtp(npmtmax,natmtot) do ias=1,natmtot is=idxis(ias) ! regrid the muffin-tin function do lm=1,lmmax fi(1:nrmt_(is))=rfmt_(lm,1:nrmt_(is),ias) call rfinterp(nrmt_(is),rsp_(:,is),wcrmt_(:,:,is),fi,nrmt(is),rsp(:,is),fo) rfmt(lm,1:nrmt(is))=fo(1:nrmt(is)) end do rfmt(lmmax+1:lmmaxo,1:nrmt(is))=0.d0 ! pack the muffin-tin function call rfmtpack(.true.,nrmt(is),nrmti(is),rfmt,rfmtp(:,ias)) end do end subroutine subroutine rgvfmt(rvfmt) implicit none ! arguments real(8), intent(out) :: rvfmt(npmtmax,natmtot,ndmag) do idm=1,ndmag jdm=mapidm(idm) if (jdm.eq.0) then rvfmt(:,:,idm)=0.d0 cycle end if do ias=1,natmtot is=idxis(ias) do lm=1,lmmax fi(1:nrmt_(is))=rvfmt_(lm,1:nrmt_(is),ias,jdm) call rfinterp(nrmt_(is),rsp_(:,is),wcrmt_(:,:,is),fi,nrmt(is),rsp(:,is), & fo) rfmt(lm,1:nrmt(is))=fo(1:nrmt(is)) end do rfmt(lmmax+1:lmmaxo,1:nrmt(is))=0.d0 call rfmtpack(.true.,nrmt(is),nrmti(is),rfmt,rvfmt(:,ias,idm)) end do end do end subroutine subroutine rgvfcmt(rvfcmt) implicit none ! arguments real(8), intent(out) :: rvfcmt(npcmtmax,natmtot,ndmag) do idm=1,ndmag jdm=mapidm(idm) if (jdm.eq.0) then rvfcmt(:,:,idm)=0.d0 cycle end if do ias=1,natmtot is=idxis(ias) do lm=1,lmmax fi(1:nrcmt_(is))=rvfcmt_(lm,1:nrcmt_(is),ias,jdm) call rfinterp(nrcmt_(is),rcmt_(:,is),wcrcmt_(:,:,is),fi,nrcmt(is), & rcmt(:,is),fo) rfmt(lm,1:nrcmt(is))=fo(1:nrcmt(is)) end do rfmt(lmmax+1:lmmaxo,1:nrcmt(is))=0.d0 call rfmtpack(.true.,nrcmt(is),nrcmti(is),rfmt,rvfcmt(:,ias,idm)) end do end do end subroutine subroutine rgvir(rvfir) implicit none ! arguments real(8), intent(out) :: rvfir(ngtot,ndmag) do idm=1,ndmag jdm=mapidm(idm) if (jdm.eq.0) then rvfir(:,idm)=0.d0 cycle end if rvfir(:,idm)=rvfir_(mapir(:),jdm) end do end subroutine end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/eveqnhf.f900000644000000000000000000000013214061636517014700 xustar0030 mtime=1623670095.103102317 30 atime=1623670093.843103487 30 ctime=1623670095.103102317 elk-7.2.42/src/eveqnhf.f900000644002504400250440000001475514061636517016751 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine eveqnhf(ikp,vmt,vir,bmt,bir,evecsvp) use modmain use modomp implicit none ! arguments integer, intent(in) :: ikp real(8), intent(in) :: vmt(npcmtmax,natmtot),vir(ngtot) real(8), intent(in) :: bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag) complex(8), intent(inout) :: evecsvp(nstsv,nstsv) ! local variables integer ik,jk,ist1,ist2,ist3 integer iv(3),iq,ig,nthd real(8) vc(3),t1 complex(8) z1 ! automatic arrays integer idx(nstsv) ! allocatable arrays real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqrmt(:,:,:) complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: h(:,:),v(:,:),kmat(:,:) complex(8), allocatable :: wfmt1(:,:,:,:),wfir1(:,:,:) complex(8), allocatable :: wfmt2(:,:,:,:),wfir2(:,:,:) complex(8), allocatable :: zrhomt(:,:,:),zrhoir(:,:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) ! external functions complex(8), external :: zfinp !$OMP CRITICAL(eveqnhf_) write(*,'("Info(eveqnhf): ",I6," of ",I6," k-points")') ikp,nkpt !$OMP END CRITICAL(eveqnhf_) ! allocate local arrays allocate(vgqc(3,ngvc),gqc(ngvc),gclgq(ngvc)) allocate(jlgqrmt(0:lnpsd,ngvc,nspecies)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) allocate(ylmgq(lmmaxo,ngvc),sfacgq(ngvc,natmtot)) allocate(h(nstsv,nstsv),v(nstsv,nstsv)) allocate(wfmt1(npcmtmax,natmtot,nspinor,nstsv),wfir1(ngtc,nspinor,nstsv)) allocate(wfmt2(npcmtmax,natmtot,nspinor,nstsv),wfir2(ngtc,nspinor,nstsv)) allocate(zrhomt(npcmtmax,natmtot,nstsv),zrhoir(ngtc,nstsv)) ! get the first-variational eigenvectors from file for input reduced k-point call getevecfv(filext,ikp,vkl(:,ikp),vgkl(:,:,1,ikp),evecfv) ! find the matching coefficients call match(ngk(1,ikp),vgkc(:,:,1,ikp),gkc(:,1,ikp),sfacgk(:,:,1,ikp),apwalm) ! index to all states do ist1=1,nstsv idx(ist1)=ist1 end do ! calculate the wavefunctions for all states of the input k-point call genwfsv(.false.,.true.,nstsv,idx,ngdgc,igfc,ngk(1,ikp),igkig(:,1,ikp), & apwalm,evecfv,evecsvp,wfmt1,ngtc,wfir1) !-----------------------------------------! ! local potential matrix elements ! !-----------------------------------------! if (hybrid.and.spinpol) then ! magnetic field matrix elements in hybrid case call genvbmatk(vmt,vir,bmt,bir,ngk(1,ikp),igkig(:,1,ikp),wfmt1,ngtc,wfir1,h) else call genvmatk(vmt,vir,ngk(1,ikp),igkig(:,1,ikp),wfmt1,ngtc,wfir1,h) end if ! Fourier transform wavefunctions to real-space call zftwfir(ngk(1,ikp),igkig(:,1,ikp),wfir1) !---------------------------------! ! kinetic matrix elements ! !---------------------------------! allocate(kmat(nstsv,nstsv)) call getkmat(ikp,kmat) call zgemm('N','N',nstsv,nstsv,nstsv,zone,kmat,nstsv,evecsvp,nstsv,zzero,v, & nstsv) call zgemm('C','N',nstsv,nstsv,nstsv,zone,evecsvp,nstsv,v,nstsv,zone,h,nstsv) deallocate(kmat) !------------------------------! ! Fock matrix elements ! !------------------------------! v(:,:)=0.d0 ! loop over non-reduced k-point set do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! determine the q-vector iv(:)=ivk(:,ikp)-ivk(:,ik) iv(:)=modulo(iv(:),ngridk(:)) ! check if the q-point is in user-defined set iv(:)=iv(:)*ngridq(:) if (any(modulo(iv(:),ngridk(:)).ne.0)) cycle iv(:)=iv(:)/ngridk(:) iq=ivqiq(iv(1),iv(2),iv(3)) vc(:)=vkc(:,ikp)-vkc(:,ik) do ig=1,ngvc ! determine the G+q-vectors vgqc(:,ig)=vgc(:,ig)+vc(:) ! G+q-vector length gqc(ig)=sqrt(vgqc(1,ig)**2+vgqc(2,ig)**2+vgqc(3,ig)**2) ! spherical harmonics for G+q-vectors call genylmv(lmaxo,vgqc(:,ig),ylmgq(:,ig)) end do ! structure factors for G+q call gensfacgp(ngvc,vgqc,ngvc,sfacgq) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.true.,iq,ngvc,gqc,gclgq) ! compute the required spherical Bessel functions call genjlgprmt(lnpsd,ngvc,gqc,ngvc,jlgqrmt) ! find the matching coefficients call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! get the eigenvectors from file for non-reduced k-point call getevecfv(filext,0,vkl(:,ik),vgkl(:,:,1,ik),evecfv) call getevecsv(filext,0,vkl(:,ik),evecsv) ! calculate the wavefunctions for all states call genwfsv(.false.,.false.,nstsv,idx,ngdgc,igfc,ngk(1,ik),igkig(:,1,ik), & apwalm,evecfv,evecsv,wfmt2,ngtc,wfir2) do ist3=1,nstsv if (abs(occsv(ist3,jk)).lt.epsocc) cycle ! calculate the complex overlap densities for all states (T. McQueen) call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ist1=1,nstsv call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,ist3),wfir2(:,:,ist3), & wfmt1(:,:,:,ist1),wfir1(:,:,ist1),zrhomt(:,:,ist1),zrhoir(:,ist1)) end do !$OMP END PARALLEL DO call freethd(nthd) t1=wqptnr*occsv(ist3,jk)/occmax call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zvclmt,zvclir) & !$OMP PRIVATE(ist1,z1) & !$OMP NUM_THREADS(nthd) allocate(zvclmt(npcmtmax,natmtot),zvclir(ngtc)) !$OMP DO do ist2=1,nstsv ! calculate the Coulomb potential call genzvclmt(nrcmt,nrcmti,nrcmtmax,rlcmt,wprcmt,npcmtmax, & zrhomt(:,:,ist2),zvclmt) call zpotcoul(nrcmt,nrcmti,npcmt,npcmti,nrcmtmax,rlcmt,ngdgc,igfc,ngvc, & gqc,gclgq,ngvc,jlgqrmt,ylmgq,sfacgq,zrhoir(:,ist2),npcmtmax,zvclmt, & zvclir) zvclir(:)=zvclir(:)*cfrc(:) do ist1=1,ist2 z1=zfinp(zrhomt(:,:,ist1),zrhoir(:,ist1),zvclmt,zvclir) v(ist1,ist2)=v(ist1,ist2)-t1*z1 end do end do !$OMP END DO deallocate(zvclmt,zvclir) !$OMP END PARALLEL call freethd(nthd) end do ! end loop over non-reduced k-point set end do deallocate(vgqc,gqc,gclgq,jlgqrmt) deallocate(ylmgq,sfacgq,apwalm,evecfv) deallocate(wfmt1,wfir1,wfmt2,wfir2) deallocate(zrhomt,zrhoir) ! scale the Coulomb matrix elements in the case of a hybrid functional if (hybrid) v(:,:)=hybridc*v(:,:) ! add the Coulomb matrix elements to Hamiltonian h(:,:)=h(:,:)+v(:,:) !----------------------------------------------! ! diagonalise Hartree-Fock Hamiltonian ! !----------------------------------------------! call eveqnzh(nstsv,nstsv,h,evalsv(:,ikp)) ! apply unitary transformation to the third-variational states so that they ! refer to the first-variational basis evecsv(:,:)=evecsvp(:,:) call zgemm('N','N',nstsv,nstsv,nstsv,zone,evecsv,nstsv,h,nstsv,zzero,evecsvp, & nstsv) deallocate(evecsv,h,v) end subroutine elk-7.2.42/src/PaxHeaders.21776/zbsht.f900000644000000000000000000000013214061636517014376 xustar0030 mtime=1623670095.105102316 30 atime=1623670093.845103485 30 ctime=1623670095.105102316 elk-7.2.42/src/zbsht.f900000644002504400250440000000261614061636517016440 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zbsht ! !INTERFACE: subroutine zbsht(nr,nri,zfmt1,zfmt2) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial mesh points (in,integer) ! nri : number of points on the inner part of the muffin-tin (in,integer) ! zfmt1 : input complex muffin-tin function in spherical harmonics ! (in,complex(*)) ! zfmt2 : output complex muffin-tin function in spherical coordinates ! (out,complex(*)) ! !DESCRIPTION: ! Performs a backward spherical harmonic transform (SHT) on a complex ! muffin-tin function expressed in spherical harmonics to obtain a function in ! spherical coordinates. See also {\tt genshtmat} and {\tt zfsht}. ! ! !REVISION HISTORY: ! Created October 2013 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr,nri complex(8), intent(in) :: zfmt1(*) complex(8), intent(out) :: zfmt2(*) ! local variables integer i ! transform the inner part of the muffin-tin call zgemm('N','N',lmmaxi,nri,lmmaxi,zone,zbshti,lmmaxi,zfmt1,lmmaxi,zzero, & zfmt2,lmmaxi) ! transform the outer part of the muffin-tin i=lmmaxi*nri+1 call zgemm('N','N',lmmaxo,nr-nri,lmmaxo,zone,zbshto,lmmaxo,zfmt1(i),lmmaxo, & zzero,zfmt2(i),lmmaxo) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/i3mtv.f900000644000000000000000000000013214061636517014306 xustar0030 mtime=1623670095.106102315 30 atime=1623670093.846103484 30 ctime=1623670095.106102315 elk-7.2.42/src/i3mtv.f900000644002504400250440000000143714061636517016350 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: i3mtv ! !INTERFACE: pure subroutine i3mtv(a,x,y) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix (in,integer(3,3)) ! x : input vector (in,integer(3)) ! y : output vector (out,integer(3)) ! !DESCRIPTION: ! Multiplies the transpose of an integer $3\times 3$ matrix with a vector. ! ! !REVISION HISTORY: ! Created April 2007 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: a(3,3),x(3) integer, intent(out) :: y(3) y(1)=a(1,1)*x(1)+a(2,1)*x(2)+a(3,1)*x(3) y(2)=a(1,2)*x(1)+a(2,2)*x(2)+a(3,2)*x(3) y(3)=a(1,3)*x(1)+a(2,3)*x(2)+a(3,3)*x(3) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/spline.f900000644000000000000000000000013214061636517014536 xustar0030 mtime=1623670095.108102313 30 atime=1623670093.848103482 30 ctime=1623670095.108102313 elk-7.2.42/src/spline.f900000644002504400250440000000564614061636517016606 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: spline ! !INTERFACE: subroutine spline(n,x,f,cf) ! !INPUT/OUTPUT PARAMETERS: ! n : number of points (in,integer) ! x : abscissa array (in,real(n)) ! f : input data array (in,real(n)) ! cf : cubic spline coefficients (out,real(3,n)) ! !DESCRIPTION: ! Calculates the coefficients of a cubic spline fitted to input data. In other ! words, given a set of data points $f_i$ defined at $x_i$, where ! $i=1\ldots n$, the coefficients $c_j^i$ are determined such that ! $$ y_i(x)=f_i+c_1^i(x-x_i)+c_2^i(x-x_i)^2+c_3^i(x-x_i)^3, $$ ! is the interpolating function for $x\in[x_i,x_{i+1})$. The coefficients are ! determined piecewise by fitting a cubic polynomial to adjacent points. ! ! !REVISION HISTORY: ! Created November 2011 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: x(n),f(n) real(8), intent(out) :: cf(3,n) ! local variables integer i real(8) x0,x1,x2,x3,y0,y1,y2,y3 real(8) t0,t1,t2,t3,t4,t5,t6,t7 if (n.le.0) then write(*,*) write(*,'("Error(spline): n <= 0 : ",I8)') n write(*,*) stop end if if (n.eq.1) then cf(:,1)=0.d0 return end if if (n.eq.2) then cf(1,1)=(f(2)-f(1))/(x(2)-x(1)) cf(2:3,1)=0.d0 cf(1,2)=cf(1,1) cf(2:3,2)=0.d0 return end if if (n.eq.3) then x0=x(1) x1=x(2)-x0; x2=x(3)-x0 y0=f(1) y1=f(2)-y0; y2=f(3)-y0 t0=1.d0/(x1*x2*(x2-x1)) t3=x1*y2; t4=x2*y1 t1=t0*(x2*t4-x1*t3) t2=t0*(t3-t4) cf(1,1)=t1 cf(2,1)=t2 cf(3,1)=0.d0 t3=2.d0*t2 cf(1,2)=t1+t3*x1 cf(2,2)=t2 cf(3,2)=0.d0 cf(1,3)=t1+t3*x2 cf(2,3)=t2 cf(3,3)=0.d0 return end if x0=x(1) x1=x(2)-x0; x2=x(3)-x0; x3=x(4)-x0 t4=x1-x2; t5=x1-x3; t6=x2-x3 y0=f(1) y1=f(2)-y0; y2=f(3)-y0; y3=f(4)-y0 t1=x1*x2*y3; t2=x2*x3*y1; t3=x1*x3 t0=1.d0/(x2*t3*t4*t5*t6) t3=t3*y2 t7=t0*(t1*t4+t2*t6-t3*t5) t4=x1**2; t5=x2**2; t6=x3**2 y1=t3*t6-t1*t5; y3=t2*t5-t3*t4; y2=t1*t4-t2*t6 t1=t0*(x1*y1+x2*y2+x3*y3) t2=-t0*(y1+y2+y3) cf(1,1)=t1; cf(2,1)=t2; cf(3,1)=t7 cf(1,2)=t1+2.d0*t2*x1+3.d0*t7*t4 cf(2,2)=t2+3.d0*t7*x1 cf(3,2)=t7 if (n.eq.4) then cf(1,3)=t1+2.d0*t2*x2+3.d0*t7*t5 cf(2,3)=t2+3.d0*t7*x2 cf(3,3)=t7 cf(1,4)=t1+2.d0*t2*x3+3.d0*t7*t6 cf(2,4)=t2+3.d0*t7*x3 cf(3,4)=t7 return end if do i=3,n-2 x0=x(i) x1=x(i-1)-x0; x2=x(i+1)-x0; x3=x(i+2)-x0 t4=x1-x2; t5=x1-x3; t6=x2-x3 y0=f(i) y1=f(i-1)-y0; y2=f(i+1)-y0; y3=f(i+2)-y0 t1=x1*x2*y3; t2=x2*x3*y1; t3=x1*x3 t0=1.d0/(x2*t3*t4*t5*t6) t3=t3*y2 t7=t0*(t1*t4+t2*t6-t3*t5) t4=x1**2; t5=x2**2; t6=x3**2 y1=t3*t6-t1*t5; y2=t1*t4-t2*t6; y3=t2*t5-t3*t4 t1=t0*(x1*y1+x2*y2+x3*y3) t2=-t0*(y1+y2+y3) cf(1,i)=t1; cf(2,i)=t2; cf(3,i)=t7 end do cf(1,n-1)=t1+2.d0*t2*x2+3.d0*t7*t5 cf(2,n-1)=t2+3.d0*t7*x2 cf(3,n-1)=t7 cf(1,n)=t1+2.d0*t2*x3+3.d0*t7*t6 cf(2,n)=t2+3.d0*t7*x3 cf(3,n)=t7 end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gauntyry.f900000644000000000000000000000013114061636517015125 xustar0030 mtime=1623670095.109102312 29 atime=1623670093.85010348 30 ctime=1623670095.109102312 elk-7.2.42/src/gauntyry.f900000644002504400250440000000302314061636517017161 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: gauntyry ! !INTERFACE: complex(8) function gauntyry(l1,l2,l3,m1,m2,m3) ! !INPUT/OUTPUT PARAMETERS: ! l1, l2, l3 : angular momentum quantum numbers (in,integer) ! m1, m2, m3 : magnetic quantum numbers (in,integer) ! !DESCRIPTION: ! Returns the complex Gaunt-like coefficient given by ! $\langle Y^{l_1}_{m_1}|R^{l_2}_{m_2}|Y^{l_3}_{m_3}\rangle$, where $Y_{lm}$ ! and $R_{lm}$ are the complex and real spherical harmonics, respectively. ! Suitable for $l_i$ less than 50. See routine {\tt genrlm}. ! ! !REVISION HISTORY: ! Created November 2002 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: l1,l2,l3 integer, intent(in) :: m1,m2,m3 ! local variables ! real constant sqrt(2)/2 real(8), parameter :: c1=0.7071067811865475244d0 real(8) t1 ! external functions real(8), external :: gaunt if (m2.gt.0) then if (mod(m2,2).eq.0) then t1=c1*(gaunt(l1,l2,l3,m1,m2,m3)+gaunt(l1,l2,l3,m1,-m2,m3)) else t1=c1*(gaunt(l1,l2,l3,m1,m2,m3)-gaunt(l1,l2,l3,m1,-m2,m3)) end if gauntyry=cmplx(t1,0.d0,8) else if (m2.lt.0) then if (mod(m2,2).eq.0) then t1=c1*(gaunt(l1,l2,l3,m1,m2,m3)-gaunt(l1,l2,l3,m1,-m2,m3)) else t1=c1*(gaunt(l1,l2,l3,m1,m2,m3)+gaunt(l1,l2,l3,m1,-m2,m3)) end if gauntyry=cmplx(0.d0,-t1,8) else gauntyry=cmplx(gaunt(l1,l2,l3,m1,m2,m3),0.d0,8) end if end function !EOC elk-7.2.42/src/PaxHeaders.21776/findnjcmax.f900000644000000000000000000000013014061636517015363 xustar0029 mtime=1623670095.11110231 30 atime=1623670093.851103479 29 ctime=1623670095.11110231 elk-7.2.42/src/findnjcmax.f900000644002504400250440000000074514061636517017430 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine findnjcmax use modmain implicit none ! local variables integer is,n ! find the maximum size of the spherical Bessel function array over all species njcmax=1 do is=1,nspecies n=(lmaxi+1)*nrcmti(is)+(lmaxo+1)*(nrcmt(is)-nrcmti(is)) if (n.gt.njcmax) njcmax=n end do end subroutine elk-7.2.42/src/PaxHeaders.21776/gndstate.f900000644000000000000000000000013214061636517015055 xustar0030 mtime=1623670095.113102308 30 atime=1623670093.853103478 30 ctime=1623670095.113102308 elk-7.2.42/src/gndstate.f900000644002504400250440000002730214061636517017116 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2013 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: gndstate ! !INTERFACE: subroutine gndstate ! !USES: use modmain use moddftu use modulr use modmpi use modomp ! !DESCRIPTION: ! Computes the self-consistent Kohn-Sham ground-state. General information is ! written to the file {\tt INFO.OUT}. First- and second-variational ! eigenvalues, eigenvectors and occupancies are written to the unformatted ! files {\tt EVALFV.OUT}, {\tt EVALSV.OUT}, {\tt EVECFV.OUT}, {\tt EVECSV.OUT} ! and {\tt OCCSV.OUT}. The density, magnetisation, Kohn-Sham potential and ! magnetic field are written to {\tt STATE.OUT}. ! ! !REVISION HISTORY: ! Created October 2002 (JKD) ! Added MPI, August 2010 (JKD) !EOP !BOC implicit none ! local variables logical twrite integer ik,nmix,nwork real(8) dv,etp,de,timetot ! allocatable arrays real(8), allocatable :: work(:) ! initialise global variables call init0 call init1 ! initialise q-vector-dependent variables if required if (xctype(1).lt.0) call init2 ! apply strain to the G, k, G+k and q-vectors if required call straingkq if (task.eq.0) trdstate=.false. if (task.eq.1) trdstate=.true. ! only the MPI master process should write files if (mp_mpi) then ! write the real and reciprocal lattice vectors to file call writelat ! write symmetry matrices to file call writesym ! output the k-point set to file call writekpts ! write lattice vectors and atomic positions to file open(50,file='GEOMETRY'//trim(filext),form='FORMATTED') call writegeom(50) close(50) ! write interatomic distances to file open(50,file='IADIST'//trim(filext),form='FORMATTED') call writeiad(50) close(50) ! open INFO.OUT file open(60,file='INFO'//trim(filext),form='FORMATTED') ! write out general information to INFO.OUT call writeinfo(60) write(60,*) ! open TOTENERGY.OUT open(61,file='TOTENERGY'//trim(filext),form='FORMATTED') ! open FERMIDOS.OUT open(62,file='FERMIDOS'//trim(filext),form='FORMATTED') ! open MOMENT.OUT if required if (spinpol) open(63,file='MOMENT'//trim(filext),form='FORMATTED') ! open GAP.OUT open(64,file='GAP'//trim(filext),form='FORMATTED') ! open RMSDVS.OUT open(65,file='RMSDVS'//trim(filext),form='FORMATTED') ! open DTOTENERGY.OUT open(66,file='DTOTENERGY'//trim(filext),form='FORMATTED') ! open TMDFTU.OUT if (tmwrite) open(67,file='TMDFTU'//trim(filext),form='FORMATTED') ! open MOMENTM.OUT if (spinpol) open(68,file='MOMENTM'//trim(filext),form='FORMATTED') ! open RESIDUAL.OUT if (xctype(1).lt.0) open(69,file='RESIDUAL'//trim(filext),form='FORMATTED') end if iscl=0 if (trdstate) then ! read the Kohn-Sham potential and fields from file call readstate if (mp_mpi) then write(60,'("Potential read in from STATE.OUT")') end if if (autolinengy) call readfermi else ! initialise the density and magnetisation from atomic data call rhoinit call maginit ! generate the Kohn-Sham potential and magnetic field call potks(.true.) if (mp_mpi) then write(60,'("Kohn-Sham potential initialised from atomic data")') end if end if if (mp_mpi) flush(60) call genvsig ! size of mixing vector nmix=size(vsbs) ! determine the size of the mixer work array nwork=-1 call mixerifc(mixtype,nmix,vsbs,dv,nwork,vsbs) allocate(work(nwork)) ! initialise the mixer iscl=0 call mixerifc(mixtype,nmix,vsbs,dv,nwork,work) ! set the stop signal to .false. tstop=.false. ! set last self-consistent loop flag tlast=.false. etp=0.d0 ! begin the self-consistent loop if (mp_mpi) then write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop started |")') write(60,'("+------------------------------+")') end if do iscl=1,maxscl if (mp_mpi) then write(60,*) write(60,'("+--------------------+")') write(60,'("| Loop number : ",I4," |")') iscl write(60,'("+--------------------+")') end if if (iscl.ge.maxscl) then if (mp_mpi) then write(60,*) write(60,'("Reached self-consistent loops maximum")') end if if (maxscl.gt.1) then write(*,*) write(*,'("Warning(gndstate): failed to reach self-consistency after ", & &I4," loops")') iscl end if tlast=.true. end if if (mp_mpi) flush(60) ! reset the OpenMP thread variables call omp_reset ! generate the core wavefunctions and densities call gencore ! find the new linearisation energies call linengy ! write out the linearisation energies if (mp_mpi) call writelinen ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! generate the spin-orbit coupling radial functions call gensocfr ! generate the first- and second-variational eigenvectors and eigenvalues call genevfsv ! find the occupation numbers and Fermi energy call occupy if (mp_mpi) then if (autoswidth) then write(60,*) write(60,'("New smearing width : ",G18.10)') swidth end if ! write the occupation numbers to file do ik=1,nkpt call putoccsv(filext,ik,occsv(:,ik)) end do ! write eigenvalues to file call writeeval ! write the Fermi energy to file call writefermi end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! generate the density and magnetisation call rhomag ! DFT+U or fixed tensor moment calculation if ((dftu.ne.0).or.(ftmtype.ne.0)) then ! generate the muffin-tin density matrix used for computing the potential matrix call gendmatmt ! write the FTM tensor moments to file if (ftmtype.ne.0) call writeftm ! generate the DFT+U or FTM muffin-tin potential matrices call genvmatmt end if if (dftu.ne.0) then if (mp_mpi) then ! write the DFT+U matrices to file call writedftu ! calculate and write tensor moments to file if (tmwrite) then if (spinorb) then call writetm3du(67) else call writetm2du(67) end if end if end if end if ! compute the Kohn-Sham potentials and magnetic fields call potks(.true.) if (mp_mpi) then if ((xcgrad.eq.3).and.(c_tb09.ne.0.d0)) then write(60,*) write(60,'("Tran-Blaha ''09 constant c : ",G18.10)') c_tb09 end if end if ! mix the old effective potential and field with the new call mixerifc(mixtype,nmix,vsbs,dv,nwork,work) ! calculate and add the fixed spin moment effective field (after mixing) call fsmbfield call addbfsm ! Fourier transform Kohn-Sham potential to G-space call genvsig ! reduce the external magnetic fields if required if (reducebf.lt.1.d0) then bfieldc(:)=bfieldc(:)*reducebf bfcmt(:,:,:)=bfcmt(:,:,:)*reducebf end if ! compute the energy components call energy if (mp_mpi) then ! output energy components call writeengy(60) write(60,*) write(60,'("Density of states at Fermi energy : ",G18.10)') fermidos write(60,'(" (states/Hartree/unit cell)")') write(60,*) write(60,'("Estimated indirect band gap : ",G18.10)') bandgap(1) write(60,'(" from k-point ",I6," to k-point ",I6)') ikgap(1),ikgap(2) write(60,'("Estimated direct band gap : ",G18.10)') bandgap(2) write(60,'(" at k-point ",I6)') ikgap(3) ! write total energy to TOTENERGY.OUT write(61,'(G22.12)') engytot flush(61) ! write DOS at Fermi energy to FERMIDOS.OUT write(62,'(G18.10)') fermidos flush(62) ! output charges and moments call writechg(60) if (spinpol) then call writemom(60) ! write total moment to MOMENT.OUT write(63,'(3G18.10)') momtot(1:ndmag) flush(63) ! write total moment magnitude to MOMENTM.OUT write(68,'(G18.10)') momtotm flush(68) end if ! write estimated Kohn-Sham indirect band gap write(64,'(G22.12)') bandgap(1) flush(64) ! output effective fields for fixed spin moment calculations if (fsmtype.ne.0) call writefsm(60) ! check for WRITE file call checkwrite(twrite) ! write STATE.OUT file if required if (twrite.or.((nwrite.ge.1).and.(mod(iscl,nwrite).eq.0))) then call writestate write(60,*) write(60,'("Wrote STATE.OUT")') end if ! write OEP residual if (xctype(1).lt.0) then write(60,*) write(60,'("Magnitude of OEP residual : ",G18.10)') resoep write(69,'(G18.10)') resoep flush(69) end if end if ! exit self-consistent loop if required if (tlast) goto 10 ! check for convergence if (iscl.ge.2) then de=abs(engytot-etp) if (mp_mpi) then write(60,*) write(60,'("RMS change in Kohn-Sham potential (target) : ",G18.10," (",& &G18.10,")")') dv,epspot write(65,'(G18.10)') dv flush(65) write(60,'("Absolute change in total energy (target) : ",G18.10," (",& &G18.10,")")') de,epsengy write(66,'(G18.10)') de flush(66) if ((dv.lt.epspot).and.(de.lt.epsengy)) then write(60,*) write(60,'("Convergence targets achieved")') tlast=.true. end if end if end if ! average the current and previous total energies and store if (iscl.gt.1) then etp=0.75d0*engytot+0.25d0*etp else etp=engytot end if ! check for STOP file call checkstop if (tstop) tlast=.true. ! broadcast tlast from master process to all other processes call mpi_bcast(tlast,1,mpi_logical,0,mpicom,ierror) ! output the current total CPU time timetot=timeinit+timemat+timefv+timesv+timerho+timepot+timefor if (mp_mpi) then write(60,*) write(60,'("Time (CPU seconds) : ",F12.2)') timetot end if ! end the self-consistent loop end do 10 continue ! synchronise MPI processes call mpi_barrier(mpicom,ierror) if (mp_mpi) then write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop stopped |")') write(60,'("+------------------------------+")') ! write density and potentials to file only if maxscl > 1 if (maxscl.gt.1) then call writestate write(60,*) write(60,'("Wrote STATE.OUT")') end if end if ! compute forces if required if (tforce) then call force ! output forces to INFO.OUT if (mp_mpi) call writeforces(60) end if ! compute the paramagnetic current density and total current if required if (tjr) then call genjpr call genjtot if (mp_mpi) then write(60,*) write(60,'("Total paramagnetic current per unit cell")') write(60,'(3G18.10)') jtot write(60,'(" magnitude : ",G18.10)') jtotm end if end if ! total time used timetot=timeinit+timemat+timefv+timesv+timerho+timepot+timefor if (mp_mpi) then ! output timing information write(60,*) write(60,'("Timings (CPU seconds) :")') write(60,'(" initialisation",T40,": ",F12.2)') timeinit write(60,'(" Hamiltonian and overlap matrix set up",T40,": ",F12.2)') timemat write(60,'(" first-variational eigenvalue equation",T40,": ",F12.2)') timefv if (tevecsv) then write(60,'(" second-variational calculation",T40,": ",F12.2)') timesv end if write(60,'(" charge density calculation",T40,": ",F12.2)') timerho write(60,'(" potential calculation",T40,": ",F12.2)') timepot if (tforce) then write(60,'(" force calculation",T40,": ",F12.2)') timefor end if write(60,'(" total",T40,": ",F12.2)') timetot write(60,*) write(60,'("+----------------------------+")') write(60,'("| Elk version ",I1.1,".",I1.1,".",I2.2," stopped |")') version write(60,'("+----------------------------+")') ! close the INFO.OUT file close(60) ! close the TOTENERGY.OUT file close(61) ! close the FERMIDOS.OUT file close(62) ! close the MOMENT.OUT and MOMENTM.OUT files if (spinpol) then close(63); close(68) end if ! close the GAP.OUT file close(64) ! close the RMSDVS.OUT file close(65) ! close the DTOTENERGY.OUT file close(66) ! close TMDFTU.OUT file if (tmwrite) close(67) ! close the RESIDUAL.OUT file if (xctype(1).lt.0) close(69) end if deallocate(work) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/sstask.f900000644000000000000000000000013214061636517014554 xustar0030 mtime=1623670095.114102307 30 atime=1623670093.855103476 30 ctime=1623670095.114102307 elk-7.2.42/src/sstask.f900000644002504400250440000000166714061636517016623 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine sstask(fnum,fext) use modmain use modmpi implicit none ! arguments integer, intent(in) :: fnum character(*), intent(out) :: fext ! local variables logical exist ! only master process should search for file if (.not.mp_mpi) goto 10 do iqss=1,nqpt ! construct the spin-spiral file extension call ssfext(iqss,fext) ! determine if the SS file exists inquire(file='SS'//trim(fext),exist=exist) if (.not.exist) then open(fnum,file='SS'//trim(fext),form='FORMATTED') goto 10 end if end do iqss=0 write(*,*) write(*,'("Info(sstask): nothing more to do")') 10 continue ! broadcast to all other processes call mpi_bcast(iqss,1,mpi_integer,0,mpicom,ierror) if (iqss.eq.0) then fext='.OUT' else call ssfext(iqss,fext) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/fermisurf.f900000644000000000000000000000013214061636517015246 xustar0030 mtime=1623670095.116102305 30 atime=1623670093.856103475 30 ctime=1623670095.116102305 elk-7.2.42/src/fermisurf.f900000644002504400250440000001023414061636517017303 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine fermisurf use modmain use modomp implicit none ! local variables integer ik,nst,ist integer ist0,ist1,jst0,jst1 integer i1,i2,i3,nf,f integer np,i,nthd real(8) e0,e1,prd,v(3) ! allocatable arrays integer, allocatable :: idx(:) real(8), allocatable :: evalfv(:,:),e(:),vpc(:,:) complex(8), allocatable :: evecfv(:,:,:) complex(8), allocatable :: evecsv(:,:) ! initialise universal variables call init0 call init1 ! read density and potentials from file call readstate ! Fourier transform Kohn-Sham potential to G-space call genvsig ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! generate the spin-orbit coupling radial functions call gensocfr ! begin parallel loop over reduced k-points set call holdthd(nkpt,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evalfv,evecfv,evecsv) & !$OMP NUM_THREADS(nthd) allocate(evalfv(nstfv,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv)) allocate(evecsv(nstsv,nstsv)) !$OMP DO do ik=1,nkpt !$OMP CRITICAL(fermisurf_) write(*,'("Info(fermisurf): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(fermisurf_) ! solve the first- and second-variational eigenvalue equations call eveqn(ik,evalfv,evecfv,evecsv) ! end loop over reduced k-points set end do !$OMP END DO deallocate(evalfv,evecfv,evecsv) !$OMP END PARALLEL call freethd(nthd) ! if iterative diagonalisation is used the eigenvalues must be reordered if (tefvit.and.(.not.spinpol)) then allocate(idx(nstsv),e(nstsv)) do ik=1,nkpt e(:)=evalsv(:,ik) call sortidx(nstsv,e,idx) evalsv(1:nstsv,ik)=e(idx(1:nstsv)) end do deallocate(idx,e) end if ! generate the plotting point grid in Cartesian coordinates (this has the same ! arrangement as the k-point grid) np=np3d(1)*np3d(2)*np3d(3) allocate(vpc(3,np)) call plotpt3d(vpc) do i=1,np v(:)=vpc(:,i) call r3mv(bvec,v,vpc(:,i)) end do ! number of files to plot (2 for collinear magnetism, 1 otherwise) if (ndmag.eq.1) then nf=2 else nf=1 end if do f=1,nf if (nf.eq.2) then if (f.eq.1) then open(50,file='FERMISURF_UP.OUT',form='FORMATTED',action='WRITE') jst0=1; jst1=nstfv else open(50,file='FERMISURF_DN.OUT',form='FORMATTED',action='WRITE') jst0=nstfv+1; jst1=2*nstfv end if else open(50,file='FERMISURF.OUT',form='FORMATTED',action='WRITE') jst0=1; jst1=nstsv end if ! find the range of eigenvalues which contribute to the Fermi surface (Lars) ist0=jst1; ist1=jst0 do ist=jst0,jst1 e0=minval(evalsv(ist,:)); e1=maxval(evalsv(ist,:)) ! determine if the band crosses the Fermi energy if ((e0.lt.efermi).and.(e1.gt.efermi)) then ist0=min(ist0,ist); ist1=max(ist1,ist) end if end do nst=ist1-ist0+1 if (task.eq.100) then ! write product of eigenstates minus the Fermi energy write(50,'(3I6," : grid size")') np3d(:) i=0 do i3=0,ngridk(3)-1 do i2=0,ngridk(2)-1 do i1=0,ngridk(1)-1 i=i+1 ik=ivkik(i1,i2,i3) prd=product(evalsv(ist0:ist1,ik)-efermi) write(50,'(4G18.10)') vpc(:,i),prd end do end do end do else ! write the eigenvalues minus the Fermi energy separately write(50,'(4I6," : grid size, number of states")') np3d(:),nst i=0 do i3=0,ngridk(3)-1 do i2=0,ngridk(2)-1 do i1=0,ngridk(1)-1 i=i+1 ik=ivkik(i1,i2,i3) write(50,'(3G18.10,40F14.8)') vpc(:,i),evalsv(ist0:ist1,ik)-efermi end do end do end do end if close(50) end do write(*,*) write(*,'("Info(fermisurf):")') if (ndmag.eq.1) then write(*,'(" 3D Fermi surface data written to FERMISURF_UP.OUT and & &FERMISURF_DN.OUT")') else write(*,'(" 3D Fermi surface data written to FERMISURF.OUT")') end if if (task.eq.100) then write(*,'(" in terms of the product of eigenvalues minus the Fermi energy")') else write(*,'(" in terms of separate eigenvalues minus the Fermi energy")') end if deallocate(vpc) end subroutine elk-7.2.42/src/PaxHeaders.21776/spiralsc.f900000644000000000000000000000013214061636517015064 xustar0030 mtime=1623670095.117102304 30 atime=1623670093.858103473 30 ctime=1623670095.117102304 elk-7.2.42/src/spiralsc.f900000644002504400250440000000457514061636517017134 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine spiralsc use modmain use modmpi use modstore use moddelf implicit none ! local variables integer nq,iq,jq real(8) q ! store original parameters natoms_(:)=natoms(:) avec_(:,:)=avec(:,:) atposl_(:,:,:)=atposl(:,:,:) bfcmt0_(:,:,:)=bfcmt0(:,:,:) mommtfix_(:,:,:)=mommtfix(:,:,:) autokpt_=autokpt ngridk_(:)=ngridk ! initialise universal variables call init0 ! initialise q-point dependent variables call init2 ! store original parameters atposc_(:,:,:)=atposc(:,:,:) 10 continue call sstask(80,filext) ! if nothing more to do then restore input parameters and return if (iqss.eq.0) then filext='.OUT' natoms(:)=natoms_(:) avec(:,:)=avec_(:,:) atposl(:,:,:)=atposl_(:,:,:) bfcmt0(:,:,:)=bfcmt0_(:,:,:) mommtfix(:,:,:)=mommtfix_(:,:,:) autokpt=autokpt_ ngridk(:)=ngridk_(:) return end if ! spiral dry run: just generate empty SS files if (task.eq.352) goto 10 if (mp_mpi) then write(*,'("Info(spiralsc): working on ",A)') 'SS'//trim(filext) end if ! determine k-point grid size from radkpt autokpt=.true. ! generate the spin-spiral supercell call genscss ! initialise or read the charge density and potentials from file if (task.eq.350) then trdstate=.false. else trdstate=.true. end if ! run the ground-state calculation call gndstate if (mp_mpi) then write(80,'(I6,T20," : number of unit cells in supercell")') nscss write(80,'(G18.10,T20," : total energy per unit cell")') engytot/dble(nscss) write(80,*) write(80,'("q-point in lattice and Cartesian coordinates :")') write(80,'(3G18.10)') vql(:,iqss) write(80,'(3G18.10)') vqc(:,iqss) q=sqrt(vqc(1,iqss)**2+vqc(2,iqss)**2+vqc(3,iqss)**2) write(80,'(G18.10,T20," : length of q-vector")') q write(80,*) nq=nint(dble(nqptnr)*wqpt(iqss)) write(80,'(I6,T20," : number of equivalent q-points")') nq write(80,'("Equivalent q-points in lattice and Cartesian coordinates :")') do iq=1,nqptnr jq=ivqiq(ivq(1,iq),ivq(2,iq),ivq(3,iq)) if (jq.eq.iqss) then write(80,'(3G18.10)') vql(:,iq) write(80,'(3G18.10)') vqc(:,iq) write(80,*) end if end do close(80) end if ! delete the eigenvector files call delfiles(evec=.true.) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) goto 10 end subroutine elk-7.2.42/src/PaxHeaders.21776/atom.f900000644000000000000000000000013214061636517014204 xustar0030 mtime=1623670095.119102302 30 atime=1623670093.860103471 30 ctime=1623670095.119102302 elk-7.2.42/src/atom.f900000644002504400250440000001405114061636517016242 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: atom ! !INTERFACE: subroutine atom(sol,ptnucl,zn,nst,n,l,k,occ,xctype,xcgrad,nr,r,eval,rho,vr,rwf) ! !USES: use modxcifc ! !INPUT/OUTPUT PARAMETERS: ! sol : speed of light in atomic units (in,real) ! ptnucl : .true. if the nucleus is a point particle (in,logical) ! zn : nuclear charge (in,real) ! nst : number of states to solve for (in,integer) ! n : priciple quantum number of each state (in,integer(nst)) ! l : quantum number l of each state (in,integer(nst)) ! k : quantum number k (l or l+1) of each state (in,integer(nst)) ! occ : occupancy of each state (inout,real(nst)) ! xctype : exchange-correlation type (in,integer(3)) ! xcgrad : 1 for GGA functional, 0 otherwise (in,integer) ! nr : number of radial mesh points (in,integer) ! r : radial mesh (in,real(nr)) ! eval : eigenvalue without rest-mass energy for each state (out,real(nst)) ! rho : charge density (out,real(nr)) ! vr : self-constistent potential (out,real(nr)) ! rwf : major and minor components of radial wavefunctions for each state ! (out,real(nr,2,nst)) ! !DESCRIPTION: ! Solves the Dirac-Kohn-Sham equations for an atom using the ! exchange-correlation functional {\tt xctype} and returns the self-consistent ! radial wavefunctions, eigenvalues, charge densities and potentials. Requires ! the exchange-correlation interface routine {\tt xcifc}. ! ! !REVISION HISTORY: ! Created September 2002 (JKD) ! Fixed s.c. convergence problem, October 2003 (JKD) ! Added support for GGA functionals, June 2006 (JKD) ! !EOP !BOC implicit none ! arguments real(8), intent(in) :: sol logical, intent(in) :: ptnucl real(8), intent(in) :: zn integer, intent(in) :: nst integer, intent(in) :: n(nst),l(nst),k(nst) real(8), intent(inout) :: occ(nst) integer, intent(in) :: xctype(3),xcgrad integer, intent(in) :: nr real(8), intent(in) :: r(nr) real(8), intent(out) :: eval(nst) real(8), intent(out) :: rho(nr),vr(nr) real(8), intent(out) :: rwf(nr,2,nst) ! local variables integer, parameter :: maxscl=200 integer ir,ist,iscl real(8), parameter :: fourpi=12.566370614359172954d0 ! potential convergence tolerance real(8), parameter :: eps=1.d-6 real(8) sm,dv,dvp,ze,beta,t1 ! allocatable arrays real(8), allocatable :: vn(:),vh(:),ex(:),ec(:),vx(:),vc(:),vrp(:) real(8), allocatable :: ri(:),wpr(:,:),fr1(:),fr2(:),gr1(:),gr2(:) real(8), allocatable :: grho(:),g2rho(:),g3rho(:) if (nst.le.0) then write(*,*) write(*,'("Error(atom): invalid nst : ",I8)') nst write(*,*) stop end if ! allocate local arrays allocate(vn(nr),vh(nr),ex(nr),ec(nr),vx(nr),vc(nr),vrp(nr)) allocate(ri(nr),wpr(4,nr),fr1(nr),fr2(nr),gr1(nr),gr2(nr)) if (xcgrad.eq.1) then allocate(grho(nr),g2rho(nr),g3rho(nr)) end if ! find total electronic charge ze=0.d0 do ist=1,nst ze=ze+occ(ist) end do ! set up nuclear potential call potnucl(ptnucl,nr,r,zn,vn) do ir=1,nr ri(ir)=1.d0/r(ir) ! initialise the Kohn-Sham potential to the nuclear potential vr(ir)=vn(ir) end do ! determine the weights for radial integration call wsplintp(nr,r,wpr) dvp=0.d0 vrp(:)=0.d0 ! initialise mixing parameter beta=0.5d0 ! initialise eigenvalues to relativistic values (minus the rest mass energy) do ist=1,nst t1=sqrt(dble(k(ist)**2)-(zn/sol)**2) t1=(dble(n(ist)-abs(k(ist)))+t1)**2 t1=1.d0+((zn/sol)**2)/t1 eval(ist)=sol**2/sqrt(t1)-sol**2 end do ! start of self-consistent loop do iscl=1,maxscl ! solve the Dirac equation for each state !$OMP PARALLEL DO DEFAULT(SHARED) do ist=1,nst call rdirac(sol,n(ist),l(ist),k(ist),nr,r,vr,eval(ist),rwf(:,1,ist), & rwf(:,2,ist)) end do !$OMP END PARALLEL DO ! compute the charge density do ir=1,nr sm=0.d0 do ist=1,nst sm=sm+occ(ist)*(rwf(ir,1,ist)**2+rwf(ir,2,ist)**2) end do fr1(ir)=sm fr2(ir)=sm*ri(ir) rho(ir)=(1.d0/fourpi)*sm*ri(ir)**2 end do call splintwp(nr,wpr,fr1,gr1) call splintwp(nr,wpr,fr2,gr2) ! find the Hartree potential t1=gr2(nr) do ir=1,nr vh(ir)=gr1(ir)*ri(ir)+t1-gr2(ir) end do ! normalise charge density and potential t1=ze/gr1(nr) rho(:)=t1*rho(:) vh(:)=t1*vh(:) ! compute the exchange-correlation energy and potential if (xcgrad.eq.1) then ! GGA functional ! |grad rho| call fderiv(1,nr,r,rho,grho) ! grad^2 rho call fderiv(2,nr,r,rho,g2rho) do ir=1,nr g2rho(ir)=g2rho(ir)+2.d0*ri(ir)*grho(ir) end do ! approximate (grad rho).(grad |grad rho|) do ir=1,nr g3rho(ir)=grho(ir)*g2rho(ir) end do call xcifc(xctype,nr,rho=rho,grho=grho,g2rho=g2rho,g3rho=g3rho,ex=ex,ec=ec,& vx=vx,vc=vc) else ! LDA functional call xcifc(xctype,nr,rho=rho,ex=ex,ec=ec,vx=vx,vc=vc) end if ! self-consistent potential vr(:)=vh(:)+vx(:)+vc(:) ! determine change in potential sm=0.d0 do ir=1,nr sm=sm+(vr(ir)-vrp(ir))**2 end do dv=sqrt(sm)/dble(nr) if (iscl.gt.2) then ! reduce beta if change in potential is diverging if (dv.gt.dvp) beta=beta*0.8d0 beta=max(beta,0.01d0) end if dvp=dv do ir=1,nr ! mix old and new potentials vr(ir)=(1.d0-beta)*vrp(ir)+beta*vr(ir) vrp(ir)=vr(ir) ! add nuclear potential vr(ir)=vr(ir)+vn(ir) end do ! check for convergence if ((iscl.gt.2).and.(dv.lt.eps)) goto 10 ! end self-consistent loop end do write(*,*) write(*,'("Warning(atom): maximum iterations exceeded")') 10 continue deallocate(vn,vh,ex,ec,vx,vc,vrp) deallocate(ri,wpr,fr1,fr2,gr1,gr2) if (xcgrad.eq.1) deallocate(grho,g2rho,g3rho) return contains pure subroutine splintwp(n,wp,f,g) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wp(*),f(n) real(8), intent(out) :: g(n) ! local variables integer i,j real(8) sm g(1)=0.d0 sm=wp(5)*f(1)+wp(6)*f(2)+wp(7)*f(3)+wp(8)*f(4) g(2)=sm do i=3,n-1 j=(i-1)*4+1 sm=sm+wp(j)*f(i-2)+wp(j+1)*f(i-1)+wp(j+2)*f(i)+wp(j+3)*f(i+1) g(i)=sm end do j=(n-1)*4+1 g(n)=sm+wp(j)*f(n-3)+wp(j+1)*f(n-2)+wp(j+2)*f(n-1)+wp(j+3)*f(n) end subroutine end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/maginit.f900000644000000000000000000000013214061636517014674 xustar0030 mtime=1623670095.120102302 30 atime=1623670093.862103469 30 ctime=1623670095.120102302 elk-7.2.42/src/maginit.f900000644002504400250440000000205614061636517016734 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine maginit use modmain implicit none ! local variables integer idm,is,ia,ias,np ! magnetisation as fraction of density real(8), parameter :: fmr=0.15d0 real(8) v(3),t1 if (.not.spinpol) return ! initialise muffin-tin magnetisation do ias=1,natmtot is=idxis(ias) ia=idxia(ias) np=npmt(is) v(:)=bfcmt(:,ia,is)+bfieldc(:) t1=sqrt(v(1)**2+v(2)**2+v(3)**2) if (t1.gt.1.d-8) then t1=-fmr/t1 v(:)=t1*v(:) if (.not.ncmag) v(1)=v(3) do idm=1,ndmag t1=v(idm) magmt(1:np,ias,idm)=t1*rhomt(1:np,ias) end do else magmt(1:np,ias,:)=0.d0 end if end do ! initialise interstitial magnetisation v(:)=bfieldc(:) t1=sqrt(v(1)**2+v(2)**2+v(3)**2) if (t1.gt.1.d-8) then t1=-fmr/t1 v(:)=t1*v(:) if (.not.ncmag) v(1)=v(3) do idm=1,ndmag t1=v(idm) magir(:,idm)=t1*rhoir(:) end do else magir(:,:)=0.d0 end if end subroutine elk-7.2.42/src/PaxHeaders.21776/exxengyk.f900000644000000000000000000000012614061636517015111 xustar0028 mtime=1623670095.1221023 30 atime=1623670093.863103468 28 ctime=1623670095.1221023 elk-7.2.42/src/exxengyk.f900000644002504400250440000001465214061636517017153 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine exxengyk(ikp) use modmain implicit none ! arguments integer, intent(in) :: ikp ! local variables integer iq,ik,jk,m integer nst1,nst2,ist,jst integer is,ia,ias integer nrc,nrci,npc integer iv(3),ig real(8) ex,vc(3) complex(8) z1 ! automatic arrays integer idx(nstsv) ! allocatable arrays real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqrmt(:,:,:) complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: wfmt1(:,:,:,:),wfir1(:,:,:) complex(8), allocatable :: wfmt2(:,:,:,:),wfir2(:,:,:) complex(8), allocatable :: wfcr(:,:),zfmt(:) complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) ! external functions complex(8), external :: zfinp,zfmtinp ! allocate local arrays allocate(vgqc(3,ngvc),gqc(ngvc),gclgq(ngvc)) allocate(jlgqrmt(0:lnpsd,ngvc,nspecies)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) allocate(ylmgq(lmmaxo,ngvc),sfacgq(ngvc,natmtot)) allocate(wfmt2(npcmtmax,natmtot,nspinor,nstsv)) allocate(wfir2(ngtc,nspinor,nstsv)) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) allocate(zvclmt(npcmtmax,natmtot),zvclir(ngtc)) ! get the eigenvectors from file for input reduced k-point call getevecfv(filext,ikp,vkl(:,ikp),vgkl(:,:,:,ikp),evecfv) call getevecsv(filext,ikp,vkl(:,ikp),evecsv) ! find the matching coefficients call match(ngk(1,ikp),vgkc(:,:,1,ikp),gkc(:,1,ikp),sfacgk(:,:,1,ikp),apwalm) ! count and index the occupied states nst1=0 do ist=1,nstsv if (evalsv(ist,ikp).lt.efermi) then nst1=nst1+1 idx(nst1)=ist end if end do ! calculate the wavefunctions for occupied states of the input k-point allocate(wfmt1(npcmtmax,natmtot,nspinor,nst1),wfir1(ngtc,nspinor,nst1)) call genwfsv(.false.,.false.,nst1,idx,ngdgc,igfc,ngk(1,ikp),igkig(:,1,ikp), & apwalm,evecfv,evecsv,wfmt1,ngtc,wfir1) ! zero the local exchange energy variable ex=0.d0 ! start loop over non-reduced k-point set do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! determine the q-vector iv(:)=ivk(:,ikp)-ivk(:,ik) iv(:)=modulo(iv(:),ngridk(:)) ! check if the q-point is in user-defined set iv(:)=iv(:)*ngridq(:) if (any(modulo(iv(:),ngridk(:)).ne.0)) cycle iv(:)=iv(:)/ngridk(:) iq=ivqiq(iv(1),iv(2),iv(3)) vc(:)=vkc(:,ikp)-vkc(:,ik) do ig=1,ngvc ! determine the G+q-vectors vgqc(:,ig)=vgc(:,ig)+vc(:) ! G+q-vector length gqc(ig)=sqrt(vgqc(1,ig)**2+vgqc(2,ig)**2+vgqc(3,ig)**2) ! spherical harmonics for G+q-vectors call genylmv(lmaxo,vgqc(:,ig),ylmgq(:,ig)) end do ! structure factors for G+q call gensfacgp(ngvc,vgqc,ngvc,sfacgq) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.true.,iq,ngvc,gqc,gclgq) ! compute the required spherical Bessel functions call genjlgprmt(lnpsd,ngvc,gqc,ngvc,jlgqrmt) ! find the matching coefficients call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! get the eigenvectors from file for non-reduced k-point call getevecfv(filext,0,vkl(:,ik),vgkl(:,:,1,ik),evecfv) call getevecsv(filext,0,vkl(:,ik),evecsv) ! count and index the occupied states nst2=0 do jst=1,nstsv if (evalsv(jst,jk).lt.efermi) then nst2=nst2+1 idx(nst2)=jst end if end do ! calculate the wavefunctions for occupied states call genwfsv(.false.,.false.,nst2,idx,ngdgc,igfc,ngk(1,ik),igkig(:,1,ik), & apwalm,evecfv,evecsv,wfmt2,ngtc,wfir2) !--------------------------------------------! ! valence-valence-valence contribution ! !--------------------------------------------! do jst=1,nst2 do ist=1,nst1 ! calculate the complex overlap density call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,jst),wfir2(:,:,jst), & wfmt1(:,:,:,ist),wfir1(:,:,ist),zrhomt,zrhoir) ! calculate the Coulomb potential call genzvclmt(nrcmt,nrcmti,nrcmtmax,rlcmt,wprcmt,npcmtmax,zrhomt,zvclmt) call zpotcoul(nrcmt,nrcmti,npcmt,npcmti,nrcmtmax,rlcmt,ngdgc,igfc,ngvc, & gqc,gclgq,ngvc,jlgqrmt,ylmgq,sfacgq,zrhoir,npcmtmax,zvclmt,zvclir) zvclir(:)=zvclir(:)*cfrc(:) z1=zfinp(zrhomt,zrhoir,zvclmt,zvclir) ex=ex-0.5d0*occmax*wkpt(ikp)*wqptnr*dble(z1) end do end do ! end loop over non-reduced k-point set end do deallocate(vgqc,gqc,gclgq,jlgqrmt) deallocate(evecfv,evecsv) deallocate(apwalm,ylmgq,sfacgq) deallocate(wfmt2,wfir2) !-----------------------------------------! ! valence-core-valence contribution ! !-----------------------------------------! allocate(wfcr(npcmtmax,2),zfmt(npcmtmax)) ! begin loops over atoms and species do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) do jst=1,nstsp(is) if (spcore(jst,is)) then do m=-ksp(jst,is),ksp(jst,is)-1 ! generate the core wavefunction in spherical coordinates (pass in m-1/2) call wavefcr(.false.,lradstp,is,ia,jst,m,npcmtmax,wfcr) do ist=1,nst1 ! calculate the complex overlap density in spherical harmonics if (spinpol) then call zrho2(npc,wfcr,wfcr(:,2),wfmt1(:,ias,1,ist), & wfmt1(:,ias,2,ist),zfmt) else call zrho1(npc,wfcr,wfmt1(:,ias,1,ist),zfmt) end if call zfsht(nrc,nrci,zfmt,zrhomt(:,ias)) ! calculate the Coulomb potential call zpotclmt(nrc,nrci,nrcmtmax,rlcmt(:,:,is),wprcmt(:,:,is), & zrhomt(:,ias),zvclmt(:,ias)) z1=zfmtinp(nrc,nrci,wrcmt(:,is),zrhomt(:,ias),zvclmt(:,ias)) ex=ex-occmax*wkpt(ikp)*dble(z1) end do ! end loop over m end do ! end loop over jst end if end do ! end loops over atoms and species end do end do ! add to global exchange energy !$OMP CRITICAL(exxengyk_) engyx=engyx+ex !$OMP END CRITICAL(exxengyk_) deallocate(wfmt1,wfir1,wfcr,zfmt) deallocate(zrhomt,zrhoir,zvclmt,zvclir) return contains pure subroutine zrho1(n,x,y,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x(n),y(n) complex(8), intent(out) :: z(n) z(:)=conjg(x(:))*y(:) end subroutine pure subroutine zrho2(n,x1,x2,y1,y2,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x1(n),x2(n),y1(n),y2(n) complex(8), intent(out) :: z(n) z(:)=conjg(x1(:))*y1(:)+conjg(x2(:))*y2(:) end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/xc_c_tb09.f900000644000000000000000000000013214061636517015016 xustar0030 mtime=1623670095.124102298 30 atime=1623670093.865103467 30 ctime=1623670095.124102298 elk-7.2.42/src/xc_c_tb09.f900000644002504400250440000000334014061636517017053 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine xc_c_tb09 use modmain use libxcifc implicit none ! local variables integer is,ias,i integer nr,nri,ir real(8), parameter :: alpha=-0.012d0, beta=1.023d0 real(8) t1 ! allocatable arrays real(8), allocatable :: grfmt(:,:,:),grfir(:,:) real(8), allocatable :: rfmt(:,:),rfir(:) real(8), allocatable :: rfmt1(:),rfmt2(:,:) ! external functions real(8), external :: rfint ! check that the Tran-Blaha functional is being used (A. Shyichuk) if (xctype(2).ne.XC_MGGA_X_TB09) return ! if Tran-Blaha constant has been read in return if (tc_tb09) return ! compute the gradient of the density allocate(grfmt(npmtmax,natmtot,3),grfir(ngtot,3)) call gradrf(rhomt,rhoir,grfmt,grfir) allocate(rfmt(npmtmax,natmtot),rfmt1(npmtmax),rfmt2(npmtmax,3)) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) ! convert muffin-tin density to spherical coordinates call rbsht(nr,nri,rhomt(:,ias),rfmt1) ! convert muffin-tin gradient to spherical coordinates do i=1,3 call rbsht(nr,nri,grfmt(:,ias,i),rfmt2(:,i)) end do ! integrand in muffin-tin do i=1,npmt(is) t1=sqrt(rfmt2(i,1)**2+rfmt2(i,2)**2+rfmt2(i,3)**2) rfmt1(i)=t1/rfmt1(i) end do ! convert to spherical harmonics call rfsht(nr,nri,rfmt1,rfmt(:,ias)) end do deallocate(grfmt,rfmt1,rfmt2) ! integrand in interstitial allocate(rfir(ngtot)) do ir=1,ngtot t1=sqrt(grfir(ir,1)**2+grfir(ir,2)**2+grfir(ir,3)**2) rfir(ir)=t1/rhoir(ir) end do ! integrate over the unit cell t1=rfint(rfmt,rfir) ! set the constant c_tb09=alpha+beta*sqrt(abs(t1)/omega) deallocate(grfir,rfmt,rfir) end subroutine elk-7.2.42/src/PaxHeaders.21776/moke.f900000644000000000000000000000013214061636517014177 xustar0030 mtime=1623670095.125102297 30 atime=1623670093.867103465 30 ctime=1623670095.125102297 elk-7.2.42/src/moke.f900000644002504400250440000000412214061636517016233 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 S. Sharma, J. K. Dewhurst and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine moke use modmain implicit none ! local variables integer iw,ios complex(8) z1,z2,z3 ! allocatable arrays real(8), allocatable :: w(:),sig1(:,:),sig2(:,:) complex(8), allocatable :: kerr(:) ! calculate dielectric function for the 11 and 12 components noptcomp=2 optcomp(1,1)=1 optcomp(2,1)=1 optcomp(1,2)=1 optcomp(2,2)=2 call dielectric ! allocate local arrays allocate(w(nwplot)) allocate(sig1(nwplot,2),sig2(nwplot,2)) allocate(kerr(nwplot)) ! read diagonal contribution to optical conductivity open(50,file='SIGMA_11.OUT',status='OLD',form='FORMATTED',iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(moke): error opening SIGMA_11.OUT")') write(*,*) stop end if do iw=1,nwplot read(50,'(2G18.10)') w(iw),sig1(iw,1) end do read(50,*) do iw=1,nwplot read(50,'(2G18.10)') w(iw),sig2(iw,1) end do close(50) ! read off-diagonal contribution to optical conductivity open(50,file='SIGMA_12.OUT',status='OLD',form='FORMATTED',iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(moke): error opening SIGMA_12.OUT")') write(*,*) stop end if do iw=1,nwplot read(50,'(2G18.10)') w(iw),sig1(iw,2) end do read(50,*) do iw=1,nwplot read(50,'(2G18.10)') w(iw),sig2(iw,2) end do close(50) ! calculate the complex Kerr angle do iw=1,nwplot if (w(iw).gt.0.d0) then z1=cmplx(sig1(iw,1),sig2(iw,1),8) z2=cmplx(sig1(iw,2),sig2(iw,2),8) z3=z1*sqrt(1.d0+fourpi*zi*z1/w(iw)) if (abs(z3).gt.1.d-8) then kerr(iw)=-z2/z3 else kerr(iw)=0.d0 end if else kerr(iw)=0.d0 end if end do open(50,file='KERR.OUT',form='FORMATTED') do iw=1,nwplot write(50,'(2G18.10)') w(iw),dble(kerr(iw))*180.d0/pi end do write(50,'(" ")') do iw=1,nwplot write(50,'(2G18.10)') w(iw),aimag(kerr(iw))*180.d0/pi end do close(50) write(*,*) write(*,'("Info(moke):")') write(*,'(" complex Kerr angle in degrees written to KERR.OUT")') deallocate(w,sig1,sig2,kerr) end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlrad.f900000644000000000000000000000013214061636517014513 xustar0030 mtime=1623670095.127102295 30 atime=1623670093.868103464 30 ctime=1623670095.127102295 elk-7.2.42/src/hmlrad.f900000644002504400250440000001360514061636517016555 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2016 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: hmlrad ! !INTERFACE: subroutine hmlrad ! !USES: use modmain use modomp ! !DESCRIPTION: ! Calculates the radial Hamiltonian integrals of the APW and local-orbital ! basis functions. In other words, for atom $\alpha$, it computes integrals of ! the form ! $$ h^{\alpha}_{qq';ll'l''m''}=\begin{cases} ! \int_0^{R_i}u^{\alpha}_{q;l}(r)H u^{\alpha}_{q';l'}(r)r^2dr & l''=0 \\ ! \int_0^{R_i}u^{\alpha}_{q;l}(r)V^{\alpha}_{l''m''}(r) ! u^{\alpha}_{q';l'}(r)r^2dr & l''>0 \end{cases}, $$ ! where $u^{\alpha}_{q;l}$ is the $q$th APW radial function for angular ! momentum $l$; $H$ is the Hamiltonian of the radial Schr\"{o}dinger equation; ! and $V^{\alpha}_{l''m''}$ is the muffin-tin Kohn-Sham potential. Similar ! integrals are calculated for APW-local-orbital and ! local-orbital-local-orbital contributions. ! ! !REVISION HISTORY: ! Created December 2003 (JKD) ! Updated for compressed muffin-tin functions, March 2016 (JKD) !EOP !BOC implicit none ! local variables integer is,ias,nthd integer nr,nri,iro integer ir,npi,i integer l1,l2,l3,m2,lm2 integer io,jo,ilo,jlo real(8) sm,t1 ! begin loops over atoms and species call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is,nr,nri,iro,npi) & !$OMP PRIVATE(l1,l2,l3,io,jo,sm) & !$OMP PRIVATE(lm2,m2,i,ir,t1,ilo,jlo) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) iro=nri+1 npi=npmti(is) !---------------------------! ! APW-APW integrals ! !---------------------------! do l1=0,lmaxapw do io=1,apword(l1,is) do l3=0,lmaxapw do jo=1,apword(l3,is) if (l1.eq.l3) then sm=sum(apwfr(1:nr,1,io,l1,ias)*apwfr(1:nr,2,jo,l3,ias) & *wrmt(1:nr,is)) haa(1,jo,l3,io,l1,ias)=sm/y00 else haa(1,jo,l3,io,l1,ias)=0.d0 end if if (l1.ge.l3) then lm2=1 do l2=1,lmaxi do m2=-l2,l2 lm2=lm2+1 sm=0.d0 i=lm2 do ir=1,nri t1=apwfr(ir,1,io,l1,ias)*apwfr(ir,1,jo,l3,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxi end do do ir=iro,nr t1=apwfr(ir,1,io,l1,ias)*apwfr(ir,1,jo,l3,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxo end do haa(lm2,jo,l3,io,l1,ias)=sm haa(lm2,io,l1,jo,l3,ias)=sm end do end do do l2=lmaxi+1,lmaxo do m2=-l2,l2 lm2=lm2+1 sm=0.d0 i=npi+lm2 do ir=iro,nr t1=apwfr(ir,1,io,l1,ias)*apwfr(ir,1,jo,l3,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxo end do haa(lm2,jo,l3,io,l1,ias)=sm haa(lm2,io,l1,jo,l3,ias)=sm end do end do end if end do end do end do end do !-------------------------------------! ! local-orbital-APW integrals ! !-------------------------------------! do ilo=1,nlorb(is) l1=lorbl(ilo,is) do l3=0,lmaxapw do io=1,apword(l3,is) if (l1.eq.l3) then sm=sum(lofr(1:nr,1,ilo,ias)*apwfr(1:nr,2,io,l3,ias)*wrmt(1:nr,is)) hloa(1,io,l3,ilo,ias)=sm/y00 else hloa(1,io,l3,ilo,ias)=0.d0 end if lm2=1 do l2=1,lmaxi do m2=-l2,l2 lm2=lm2+1 sm=0.d0 i=lm2 do ir=1,nri t1=lofr(ir,1,ilo,ias)*apwfr(ir,1,io,l3,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxi end do do ir=nri+1,nr t1=lofr(ir,1,ilo,ias)*apwfr(ir,1,io,l3,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxo end do hloa(lm2,io,l3,ilo,ias)=sm end do end do do l2=lmaxi+1,lmaxo do m2=-l2,l2 lm2=lm2+1 sm=0.d0 i=npi+lm2 do ir=iro,nr t1=lofr(ir,1,ilo,ias)*apwfr(ir,1,io,l3,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxo end do hloa(lm2,io,l3,ilo,ias)=sm end do end do end do end do end do !-----------------------------------------------! ! local-orbital-local-orbital integrals ! !-----------------------------------------------! do ilo=1,nlorb(is) l1=lorbl(ilo,is) do jlo=1,nlorb(is) l3=lorbl(jlo,is) if (l1.eq.l3) then sm=sum(lofr(1:nr,1,ilo,ias)*lofr(1:nr,2,jlo,ias)*wrmt(1:nr,is)) hlolo(1,jlo,ilo,ias)=sm/y00 else hlolo(1,jlo,ilo,ias)=0.d0 end if lm2=1 do l2=1,lmaxi do m2=-l2,l2 lm2=lm2+1 sm=0.d0 i=lm2 do ir=1,nri t1=lofr(ir,1,ilo,ias)*lofr(ir,1,jlo,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxi end do do ir=iro,nr t1=lofr(ir,1,ilo,ias)*lofr(ir,1,jlo,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxo end do hlolo(lm2,jlo,ilo,ias)=sm end do end do do l2=lmaxi+1,lmaxo do m2=-l2,l2 lm2=lm2+1 sm=0.d0 i=npi+lm2 do ir=iro,nr t1=lofr(ir,1,ilo,ias)*lofr(ir,1,jlo,ias)*wrmt(ir,is) sm=sm+t1*vsmt(i,ias) i=i+lmmaxo end do hlolo(lm2,jlo,ilo,ias)=sm end do end do end do end do ! end loops over atoms and species end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/dos.f900000644000000000000000000000013214061636517014031 xustar0030 mtime=1623670095.128102294 30 atime=1623670093.870103462 30 ctime=1623670095.128102294 elk-7.2.42/src/dos.f900000644002504400250440000002554714061636517016103 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: dos ! !INTERFACE: subroutine dos(fext,tocc,occsvp) ! !USES: use modmain use modomp use modtest ! !INPUT/OUTPUT PARAMETERS: ! fext : filename extension (in,character(*)) ! tocc : .true. if just the occupied orbitals should contribute to the DOS ! (in,logical) ! occsvp : occupation numbers of second-variational orbitals ! (in,real(nstsv,nkpt)) ! !DESCRIPTION: ! Produces a total and partial density of states (DOS) for plotting. The total ! DOS is written to the file {\tt TDOS.OUT} while the partial DOS is written ! to the file {\tt PDOS\_Sss\_Aaaaa.OUT} for atom {\tt aaaa} of species ! {\tt ss}. In the case of the partial DOS, each symmetrised ! $(l,m)$-projection is written consecutively and separated by blank lines. ! If the global variable {\tt lmirep} is {\tt .true.}, then the density matrix ! from which the $(l,m)$-projections are obtained is first rotated into a ! irreducible representation basis, i.e. one that block diagonalises all the ! site symmetry matrices in the $Y_{lm}$ basis. Eigenvalues of a quasi-random ! matrix in the $Y_{lm}$ basis which has been symmetrised with the site ! symmetries are written to {\tt ELMIREP.OUT}. This allows for identification ! of the irreducible representations of the site symmetries, for example $e_g$ ! or $t_{2g}$, by the degeneracies of the eigenvalues. In the plot, spin-up is ! made positive and spin-down negative. See the routines {\tt gendmatk} and ! {\tt brzint}. ! ! !REVISION HISTORY: ! Created January 2004 (JKD) ! Parallelised and included sum over m, November 2009 (F. Cricchio) !EOP !BOC implicit none ! arguments character(*), intent(in) :: fext logical, intent(in) :: tocc real(8), intent(in) :: occsvp(nstsv,nkpt) ! local variables logical tsqaz integer nsk(3),ik,jk,ist,iw,ld integer nsd,ispn,jspn,is,ia,ias integer lmmax,l0,l1,l,m,lm,nthd real(8) dw,th,sps(2),vl(3),vc(3) real(8) v1(3),v2(3),v3(3),t1 complex(8) su2(2,2),b(2,2),c(2,2) character(256) fname ! low precision for band/spin character array saves memory real(4), allocatable :: bc(:,:,:,:,:),sc(:,:,:) real(8), allocatable :: w(:),e(:,:,:),f(:,:),g(:) real(8), allocatable :: dt(:,:),dp(:,:,:),elm(:,:) complex(8), allocatable :: ulm(:,:,:),a(:,:) complex(8), allocatable :: dmat(:,:,:,:,:),sdmat(:,:,:) complex(8), allocatable :: apwalm(:,:,:,:,:) complex(8), allocatable :: evecfv(:,:,:),evecsv(:,:) lmmax=(lmaxdos+1)**2 ld=lmmax*nspinor if (dosssum) then nsd=1 else nsd=nspinor end if if (dosmsum) then l0=0; l1=lmaxdos else l0=1; l1=lmmax end if allocate(bc(lmmax,nspinor,natmtot,nstsv,nkptnr)) allocate(sc(nspinor,nstsv,nkptnr)) ! generate unitary matrices which convert the (l,m) basis into the irreducible ! representation basis of the symmetry group at each atomic site if (lmirep) then allocate(elm(lmmax,natmtot)) allocate(ulm(lmmax,lmmax,natmtot)) call genlmirep(lmaxdos,lmmax,elm,ulm) end if ! compute the SU(2) operator used for rotating the density matrix to the ! desired spin-quantisation axis v1(:)=sqados(:) t1=sqrt(v1(1)**2+v1(2)**2+v1(3)**2) if (t1.le.epslat) then write(*,*) write(*,'("Error(dos): spin-quantisation axis (sqados) has zero length")') write(*,*) stop end if v1(:)=v1(:)/t1 if (v1(3).ge.1.d0-epslat) then tsqaz=.true. else tsqaz=.false. v2(1:2)=0.d0 v2(3)=1.d0 call r3cross(v1,v2,v3) ! note that the spin-quantisation axis is rotated, so the density matrix should ! be rotated in the opposite direction th=-acos(v1(3)) call axangsu2(v3,th,su2) end if ! begin parallel loop over k-points call holdthd(nkptnr,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(apwalm,evecfv,evecsv,dmat,sdmat,a) & !$OMP PRIVATE(jk,ispn,jspn,vl,vc) & !$OMP PRIVATE(is,ia,ias,ist,lm,b,c,t1) & !$OMP NUM_THREADS(nthd) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv),evecsv(nstsv,nstsv)) allocate(dmat(lmmax,nspinor,lmmax,nspinor,nstsv)) allocate(sdmat(nspinor,nspinor,nstsv),a(lmmax,lmmax)) !$OMP DO do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! loop over first-variational spins do ispn=1,nspnfv vl(:)=vkl(:,ik) vc(:)=vkc(:,ik) ! spin-spiral case if (spinsprl) then if (ispn.eq.1) then vl(:)=vl(:)+0.5d0*vqlss(:) vc(:)=vc(:)+0.5d0*vqcss(:) else vl(:)=vl(:)-0.5d0*vqlss(:) vc(:)=vc(:)-0.5d0*vqcss(:) end if end if ! find the matching coefficients call match(ngk(ispn,ik),vgkc(:,:,ispn,ik),gkc(:,ispn,ik), & sfacgk(:,:,ispn,ik),apwalm(:,:,:,:,ispn)) end do ! get the eigenvectors from file for non-reduced k-point call getevecfv('.OUT',0,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv('.OUT',0,vkl(:,ik),evecsv) do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) ! generate the density matrix call gendmatk(.false.,.false.,0,lmaxdos,ias,ngk(:,ik),apwalm,evecfv, & evecsv,lmmax,dmat) ! convert (l,m) part to an irreducible representation if required if (lmirep) then do ist=1,nstsv do ispn=1,nspinor do jspn=1,nspinor call zgemm('N','N',lmmax,lmmax,lmmax,zone,ulm(:,:,ias),lmmax, & dmat(:,ispn,1,jspn,ist),ld,zzero,a,lmmax) call zgemm('N','C',lmmax,lmmax,lmmax,zone,a,lmmax,ulm(:,:,ias), & lmmax,zzero,dmat(:,ispn,1,jspn,ist),ld) end do end do end do end if ! spin rotate the density matrices to desired spin-quantisation axis if (spinpol.and.(.not.tsqaz)) then do ist=1,nstsv do lm=1,lmmax b(:,:)=dmat(lm,:,lm,:,ist) call z2mm(su2,b,c) call z2mmct(c,su2,b) dmat(lm,:,lm,:,ist)=b(:,:) end do end do end if ! determine the band characters from the density matrix do ist=1,nstsv do ispn=1,nspinor do lm=1,lmmax t1=dble(dmat(lm,ispn,lm,ispn,ist)) bc(lm,ispn,ias,ist,ik)=real(t1) end do end do end do end do end do ! compute the spin density matrices of the second-variational states call gensdmat(evecsv,sdmat) ! spin rotate the density matrices to desired spin-quantisation axis if (spinpol.and.(.not.tsqaz)) then do ist=1,nstsv call z2mm(su2,sdmat(:,:,ist),b) call z2mmct(b,su2,sdmat(:,:,ist)) end do end if do ist=1,nstsv do ispn=1,nspinor t1=dble(sdmat(ispn,ispn,ist)) sc(ispn,ist,ik)=real(t1) end do end do end do !$OMP END DO deallocate(apwalm,evecfv,evecsv,dmat,sdmat,a) !$OMP END PARALLEL call freethd(nthd) allocate(w(nwplot),e(nstsv,nkptnr,nspinor)) allocate(dt(nwplot,nsd),dp(nwplot,l0:l1,nsd)) ! generate frequency grid dw=(wplot(2)-wplot(1))/dble(nwplot) do iw=1,nwplot w(iw)=dw*dble(iw-1)+wplot(1) end do ! number of subdivisions used for interpolation in the Brillouin zone nsk(:)=max(ngrkf/ngridk(:),1) ! sign for spin in DOS sps(1)=1.d0 sps(2)=-1.d0 !-------------------! ! total DOS ! !-------------------! allocate(f(nstsv,nkptnr),g(nwplot)) dt(:,:)=0.d0 do ispn=1,nspinor do ik=1,nkptnr jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) do ist=1,nstsv ! subtract the Fermi energy e(ist,ik,ispn)=evalsv(ist,jk)-efermi ! use diagonal of spin density matrix for weight f(ist,ik)=sc(ispn,ist,ik) if (tocc) then f(ist,ik)=f(ist,ik)*occsvp(ist,jk) else f(ist,ik)=f(ist,ik)*occmax end if end do end do ! integrate over the Brillouin zone call brzint(nswplot,ngridk,nsk,ivkiknr,nwplot,wplot,nstsv,nstsv,e(:,:,ispn), & f,g) if (dosssum) then dt(:,1)=dt(:,1)+g(:) else dt(:,ispn)=g(:) end if end do deallocate(f,g) ! output to file open(50,file='TDOS'//trim(fext),form='FORMATTED',action='WRITE') do ispn=1,nsd do iw=1,nwplot write(50,'(2G18.10)') w(iw),dt(iw,ispn)*sps(ispn) end do write(50,*) end do close(50) !---------------------! ! partial DOS ! !---------------------! do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) dp(:,:,:)=0.d0 do ispn=1,nspinor call holdthd(lmaxdos+1,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(f,g,lm,ik,jk,ist) & !$OMP NUM_THREADS(nthd) allocate(f(nstsv,nkptnr),g(nwplot)) !$OMP DO do l=0,lmaxdos do lm=l**2+1,(l+1)**2 do ik=1,nkptnr jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) do ist=1,nstsv f(ist,ik)=bc(lm,ispn,ias,ist,ik) if (tocc) then f(ist,ik)=f(ist,ik)*occsvp(ist,jk) else f(ist,ik)=f(ist,ik)*occmax end if end do end do call brzint(nswplot,ngridk,nsk,ivkiknr,nwplot,wplot,nstsv,nstsv, & e(:,:,ispn),f,g) if (dosmsum) then if (dosssum) then dp(:,l,1)=dp(:,l,1)+g(:) else dp(:,l,ispn)=dp(:,l,ispn)+g(:) end if else if (dosssum) then dp(:,lm,1)=dp(:,lm,1)+g(:) else dp(:,lm,ispn)=g(:) end if end if ! subtract from interstitial DOS !$OMP CRITICAL(dos_) if (dosssum) then dt(:,1)=dt(:,1)-g(:) else dt(:,ispn)=dt(:,ispn)-g(:) end if !$OMP END CRITICAL(dos_) end do end do !$OMP END DO deallocate(f,g) !$OMP END PARALLEL call freethd(nthd) end do ! output to file write(fname,'("PDOS_S",I2.2,"_A",I4.4)') is,ia open(50,file=trim(fname)//trim(fext),form='FORMATTED',action='WRITE') do ispn=1,nsd do l=l0,l1 do iw=1,nwplot write(50,'(2G18.10)') w(iw),dp(iw,l,ispn)*sps(ispn) end do write(50,*) end do end do close(50) end do end do !------------------------------------------! ! irreducible representations file ! !------------------------------------------! if (lmirep) then open(50,file='ELMIREP'//trim(fext),form='FORMATTED',action='WRITE') do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) write(50,*) write(50,'("Species : ",I4," (",A,"), atom : ",I4)') is, & trim(spsymb(is)),ia do l=0,lmaxdos do m=-l,l lm=l*(l+1)+m+1 write(50,'(" l = ",I2,", m = ",I2,", lm= ",I3," : ",G18.10)') l,m, & lm,elm(lm,ias) end do end do end do end do close(50) end if !--------------------------! ! interstitial DOS ! !--------------------------! open(50,file='IDOS'//trim(fext),form='FORMATTED',action='WRITE') do ispn=1,nsd do iw=1,nwplot write(50,'(2G18.10)') w(iw),dt(iw,ispn)*sps(ispn) end do write(50,*) end do close(50) ! write the total DOS to test file call writetest(10,'total DOS',nv=nwplot*nsd,tol=2.d-2,rva=dt) deallocate(bc,sc,w,e,dt,dp) if (lmirep) deallocate(elm,ulm) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/findprimcell.f900000644000000000000000000000013114061636517015713 xustar0030 mtime=1623670095.130102292 29 atime=1623670093.87210346 30 ctime=1623670095.130102292 elk-7.2.42/src/findprimcell.f900000644002504400250440000000750014061636517017753 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: findprimcell ! !INTERFACE: subroutine findprimcell ! !USES: use modmain ! !DESCRIPTION: ! This routine finds the smallest primitive cell which produces the same ! crystal structure as the conventional cell. This is done by searching ! through all the vectors which connect atomic positions and finding those ! which leave the crystal structure invariant. Of these, the three shortest ! which produce a non-zero unit cell volume are chosen. ! ! !REVISION HISTORY: ! Created April 2007 (JKD) !EOP !BOC implicit none ! local variables integer is,js,ia,ja,ka,na integer i1,i2,i3,i,j,n real(8) v1(3),v2(3),v3(3) real(8) t1,t2 ! allocatable arrays real(8), allocatable :: dp(:),vp(:,:) do is=1,nspecies do ia=1,natoms(is) ! make sure all atomic coordinates are in [0,1) call r3frac(epslat,atposl(:,ia,is)) ! determine atomic Cartesian coordinates call r3mv(avec,atposl(:,ia,is),atposc(:,ia,is)) end do end do ! find the smallest set of atoms is=1 do js=1,nspecies ! if a species has only one atom the cell must be primitive if (natoms(js).eq.1) return if (natoms(js).lt.natoms(is)) is=js end do n=27*natoms(is) allocate(dp(n),vp(3,n)) ! generate set of possible lattice vectors n=0 do ia=1,natoms(is) v1(:)=atposl(:,ia,is)-atposl(:,1,is) do i1=-1,1 v2(1)=v1(1)+dble(i1) do i2=-1,1 v2(2)=v1(2)+dble(i2) do i3=-1,1 v2(3)=v1(3)+dble(i3) t1=abs(v2(1))+abs(v2(2))+abs(v2(3)) if (t1.lt.epslat) goto 20 ! check if vector v2 leaves conventional cell invariant do js=1,nspecies do ja=1,natoms(js) v3(:)=atposl(:,ja,js)+v2(:) call r3frac(epslat,v3) do ka=1,natoms(js) ! check both positions and magnetic fields are the same t1=sum(abs(atposl(:,ka,js)-v3(:))) t2=sum(abs(bfcmt0(:,ja,js)-bfcmt0(:,ka,js))) if ((t1.lt.epslat).and.(t2.lt.epslat)) goto 10 end do ! atom ja has no equivalent under translation by v2 goto 20 10 continue end do end do ! cell invariant under translation by v2, so add to list n=n+1 call r3mv(avec,v2,vp(:,n)) dp(n)=sqrt(vp(1,n)**2+vp(2,n)**2+vp(3,n)**2) 20 continue end do end do end do end do if (n.eq.0) then write(*,*) write(*,'("Error(findprimcell): cannot find any lattice vectors")') write(*,*) stop end if ! find the shortest lattice vector j=1 t1=1.d8 do i=1,n if (dp(i).lt.t1+epslat) then j=i t1=dp(i) end if end do avec(:,1)=vp(:,j) ! find the next shortest lattice vector not parallel to the first j=1 t1=1.d8 do i=1,n call r3cross(avec(:,1),vp(:,i),v1) t2=sqrt(v1(1)**2+v1(2)**2+v1(3)**2) if (t2.gt.epslat) then if (dp(i).lt.t1+epslat) then j=i t1=dp(i) end if end if end do avec(:,2)=vp(:,j) ! find the next shortest lattice vector which gives non-zero unit cell volume call r3cross(avec(:,1),avec(:,2),v1) j=1 t1=1.d8 do i=1,n t2=dot_product(vp(:,i),v1(:)) if (abs(t2).gt.epslat) then if (dp(i).lt.t1+epslat) then j=i t1=dp(i) end if end if end do avec(:,3)=vp(:,j) call r3minv(avec,ainv) ! remove redundant atoms do is=1,nspecies na=0 do ia=1,natoms(is) call r3mv(ainv,atposc(:,ia,is),v1) call r3frac(epslat,v1) do ja=1,na t1=sum(abs(atposl(:,ja,is)-v1(:))) if (t1.lt.epslat) goto 30 end do na=na+1 atposl(:,na,is)=v1(:) call r3mv(avec,atposl(:,na,is),atposc(:,na,is)) ! re-index external magnetic fields bfcmt0(:,na,is)=bfcmt0(:,ia,is) ! re-index fixed spin moment vectors mommtfix(:,na,is)=mommtfix(:,ia,is) 30 continue end do natoms(is)=na end do deallocate(dp,vp) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/plotpt2d.f900000644000000000000000000000013214061636517015014 xustar0030 mtime=1623670095.131102291 30 atime=1623670093.874103458 30 ctime=1623670095.131102291 elk-7.2.42/src/plotpt2d.f900000644002504400250440000000277614061636517017065 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine plotpt2d(cvec,cinv,vpnl,vpl,vppc) use modmain implicit none ! arguments real(8), intent(in) :: cvec(3,3),cinv(3,3) real(8), intent(out) :: vpnl(3) real(8), intent(out) :: vpl(3,np2d(1)*np2d(2)) real(8), intent(out) :: vppc(2,np2d(1)*np2d(2)) ! local variables integer ip,i1,i2 real(8) vl1(3),vl2(3) real(8) vc1(3),vc2(3),vc3(3) real(8) d1,d2,d12,t1,t2 vl1(:)=vclp2d(:,1)-vclp2d(:,0) vl2(:)=vclp2d(:,2)-vclp2d(:,0) call r3mv(cvec,vl1,vc1) call r3mv(cvec,vl2,vc2) d1=sqrt(vc1(1)**2+vc1(2)**2+vc1(3)**2) d2=sqrt(vc2(1)**2+vc2(2)**2+vc2(3)**2) if ((d1.lt.epslat).or.(d2.lt.epslat)) then write(*,*) write(*,'("Error(plotpt2d): zero length plotting vectors")') write(*,*) stop end if d12=(vc1(1)*vc2(1)+vc1(2)*vc2(2)+vc1(3)*vc2(3))/(d1*d2) ! vector normal to plane call r3cross(vc1,vc2,vc3) t1=sqrt(vc3(1)**2+vc3(2)**2+vc3(3)**2) if (t1.lt.epslat) then write(*,*) write(*,'("Error(plotpt2d): 2D plotting plane vectors are collinear")') write(*,*) stop end if vc3(:)=vc3(:)/t1 call r3mv(cinv,vc3,vpnl) ip=0 do i2=0,np2d(2)-1 do i1=0,np2d(1)-1 ip=ip+1 t1=dble(i1)/dble(np2d(1)) t2=dble(i2)/dble(np2d(2)) ! plot points in 3D space vpl(:,ip)=t1*vl1(:)+t2*vl2(:)+vclp2d(:,0) ! plot points on the plane vppc(1,ip)=t1*d1+t2*d2*d12 vppc(2,ip)=t2*d2*sqrt(abs(1.d0-d12**2)) end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/sfacrho.f900000644000000000000000000000013014061636517014667 xustar0029 mtime=1623670095.13310229 30 atime=1623670093.875103457 29 ctime=1623670095.13310229 elk-7.2.42/src/sfacrho.f900000644002504400250440000000510314061636517016725 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 A. I. Baranov and F. Wagner. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: sfacrho ! !INTERFACE: subroutine sfacrho ! !USES: use modmain use modpw use modtest ! !DESCRIPTION: ! Outputs X-ray structure factors, i.e. the Fourier transform coefficients of ! the total electron density ! $$ F({\bf H})=\int_{\Omega}d^3r\,\rho({\bf r})e^{i{\bf H}\cdot{\bf r}}, $$ ! to the file {\tt SFACRHO.OUT}. The lattice coordinates $(h,k,l)$ of the ! $\bf H$-vectors in this file are transformed by the matrix {\tt vhmat}. If ! and energy window is set using the variable {\tt wsfac}, then only those ! states within the window are used to compute the density. See also routines ! {\tt zftrf} and {\tt genhvec}. ! ! !REVISION HISTORY: ! Created July 2010 (Alexey I. Baranov) ! Added multiplicity of the H-vectors, Oct. 2010 (Alexey I. Baranov) !EOP !BOC implicit none ! local variables integer ih,iv(3) real(8) v(3),a,b,r ! allocatable arrays complex(8), allocatable :: zrhoh(:) ! initialise the structure factor specific variables call sfacinit ! calculate the density structure factors allocate(zrhoh(nhvec)) call zftrf(nhvec,ivh,vhc,rhomt,rhoir,zrhoh) open(50,file='SFACRHO.OUT',form='FORMATTED') write(50,*) write(50,'("h k l indices transformed by vhmat matrix:")') write(50,'(3G18.10)') vhmat(:,1) write(50,'(3G18.10)') vhmat(:,2) write(50,'(3G18.10)') vhmat(:,3) write(50,*) write(50,'(" h k l multipl. |H| Re(F)& & Im(F) |F|")') write(50,*) do ih=1,nhvec ! apply transformation matrix v(:)=vhmat(:,1)*dble(ivh(1,ih)) & +vhmat(:,2)*dble(ivh(2,ih)) & +vhmat(:,3)*dble(ivh(3,ih)) ! in crystallography the forward Fourier transform of real-space density is ! usually done with positive phase and without 1/omega prefactor a=dble(zrhoh(ih))*omega b=-aimag(zrhoh(ih))*omega r=abs(zrhoh(ih))*omega iv(:)=nint(v(:)) if ((abs(v(1)-iv(1)).le.epslat).and. & (abs(v(2)-iv(2)).le.epslat).and. & (abs(v(3)-iv(3)).le.epslat)) then ! integer hkl write(50,'(4I7,4G16.8)') iv(:),mulh(ih),hc(ih),a,b,r else ! non-integer hkl write(50,'(3F7.2,I7,4G16.8)') v(:),mulh(ih),hc(ih),a,b,r end if end do close(50) write(*,*) write(*,'("Info(sfacrho): density structure factors written to SFACRHO.OUT")') write(*,*) write(*,'(" Energy window : ",2G18.10)') wsfac(:) ! write the structure factors to test file call writetest(195,'density structure factors',nv=nhvec,tol=1.d-5,zva=zrhoh(:)) deallocate(zrhoh) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/bdipole.f900000644000000000000000000000013214061636517014662 xustar0030 mtime=1623670095.134102289 30 atime=1623670093.877103455 30 ctime=1623670095.134102289 elk-7.2.42/src/bdipole.f900000644002504400250440000000526414061636517016726 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine bdipole use modmain implicit none ! local variables integer idm,is,ias integer nrc,nrci,npc real(8) cb,t1 ! automatic arrays real(8) rfmt1(npcmtmax),rfmt2(npcmtmax) ! allocatable arrays real(8), allocatable :: rvfmt(:,:,:),rvfir(:,:) complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) if (.not.ncmag) then write(*,*) write(*,'("Error(bdipole): non-collinear magnetism required for inclusion of & &the dipole field")') write(*,*) stop end if ! prefactor for the spin dipole magnetic field cb=gfacte/(4.d0*solsc) ! compute the gauge invariant current density if required if (tjr) call genjr ! allocate local arrays allocate(rvfmt(npmtmax,natmtot,3),rvfir(ngtot,3)) allocate(zrhomt(npmtmax,natmtot),zrhoir(ngtot)) allocate(zvclmt(npmtmax,natmtot),zvclir(ngtot)) ! compute the curl of the magnetisation density, i.e. the magnetisation current call curlrvf(magmt,magir,rvfmt,rvfir) ! multiply by prefactor rvfmt(:,:,:)=cb*rvfmt(:,:,:) rvfir(:,:)=cb*rvfir(:,:) ! add the current density if required if (tjr) then t1=1.d0/solsc rvfmt(:,:,:)=rvfmt(:,:,:)+t1*jrmt(:,:,:) rvfir(:,:)=rvfir(:,:)+t1*jrir(:,:) end if do idm=1,3 ! transform to complex spherical harmonics do ias=1,natmtot is=idxis(ias) call rtozfmt(nrmt(is),nrmti(is),rvfmt(:,ias,idm),zrhomt(:,ias)) end do ! solve Poisson's equation in the muffin-tin to find the A-field call genzvclmt(nrmt,nrmti,nrmtmax,rlmt,wprmt,npmtmax,zrhomt,zvclmt) zrhoir(:)=rvfir(:,idm) ! solve in the entire unit cell call zpotcoul(nrmt,nrmti,npmt,npmti,nrmtmax,rlmt,ngridg,igfft,ngvec,gc,gclg, & ngvec,jlgrmt,ylmg,sfacg,zrhoir,npmtmax,zvclmt,zvclir) ! convert muffin-tin A-field to real spherical harmonics do ias=1,natmtot is=idxis(ias) call ztorfmt(nrmt(is),nrmti(is),zvclmt(:,ias),rvfmt(:,ias,idm)) end do ! store the real part of the interstitial A-field rvfir(:,idm)=dble(zvclir(:)) end do ! compute the curl of A to obtain the dipole B-field call curlrvf(rvfmt,rvfir,bdmt,bdir) ! add to the Kohn-Sham field do idm=1,3 do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) ! convert to coarse radial mesh call rfmtftoc(nrc,nrci,bdmt(:,ias,idm),rfmt1) ! convert to spherical coordinates call rbsht(nrc,nrci,rfmt1,rfmt2) bsmt(1:npc,ias,idm)=bsmt(1:npc,ias,idm)+cb*rfmt2(1:npc) end do end do do idm=1,3 bsir(:,idm)=bsir(:,idm)+cb*bdir(:,idm)*cfunir(:) end do deallocate(rvfmt,rvfir) deallocate(zrhomt,zrhoir,zvclmt,zvclir) end subroutine elk-7.2.42/src/PaxHeaders.21776/dielectric.f900000644000000000000000000000013214061636517015353 xustar0030 mtime=1623670095.136102287 30 atime=1623670093.879103453 30 ctime=1623670095.136102287 elk-7.2.42/src/dielectric.f900000644002504400250440000001171314061636517017413 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2009 S. Sharma, J. K. Dewhurst and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: dielectric ! !INTERFACE: subroutine dielectric ! !USES: use modmain use modtest use modomp ! !DESCRIPTION: ! Computes the dielectric tensor, optical conductivity and plasma frequency. ! The formulae are taken from {\it Physica Scripta} {\bf T109}, 170 (2004). ! ! !REVISION HISTORY: ! Created November 2005 (SS and JKD) ! Added plasma frequency and intraband contribution (S. Lebegue) ! Complete rewrite, 2008 (JKD) ! Fixed problem with plasma frequency, 2009 (Marty Blaber and JKD) ! Parallelised, 2009 (M. Blaber) !EOP !BOC implicit none ! local variables logical tssr integer ik,jk,ist,jst integer iw,i,j,l,nthd real(8) w1,w2,wplas,x real(8) ei,ej,eji,t1,t2 complex(8) eta,z1 character(256) fname ! allocatable arrays real(8), allocatable :: w(:) complex(8), allocatable :: pmat(:,:,:),sigma(:) ! external functions real(8), external :: sdelta ! initialise universal variables call init0 call init1 ! read Fermi energy from file call readfermi ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! allocate local arrays allocate(w(nwplot),sigma(nwplot)) ! generate energy grid (always non-negative) w1=max(wplot(1),0.d0) w2=max(wplot(2),w1) t1=(w2-w1)/dble(nwplot) do iw=1,nwplot w(iw)=w1+t1*dble(iw-1) end do ! i divided by the complex relaxation time eta=cmplx(0.d0,swidth,8) ! set flag for scissor operator if (abs(scissor).gt.1.d-8) then tssr=.true. else tssr=.false. end if ! loop over dielectric tensor components do l=1,noptcomp i=optcomp(1,l) j=optcomp(2,l) wplas=0.d0 sigma(:)=0.d0 ! parallel loop over non-reduced k-points call holdthd(nkptnr,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(pmat,jk,ist,jst) & !$OMP PRIVATE(ei,ej,eji,z1,t1,x) & !$OMP REDUCTION(+:wplas,sigma) & !$OMP NUM_THREADS(nthd) allocate(pmat(nstsv,nstsv,3)) !$OMP DO do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! read in the momentum matrix elements call getpmat(vkl(:,ik),pmat) ! valance states do ist=1,nstsv ei=evalsv(ist,jk) ! conduction states do jst=1,nstsv ej=evalsv(jst,jk) eji=ej-ei z1=pmat(ist,jst,i)*conjg(pmat(ist,jst,j)) ! scissor correction if (tssr) then if ((ei.le.efermi).and.(ej.gt.efermi)) then t1=(eji+scissor)/eji z1=z1*t1**2 eji=eji+scissor end if end if if (abs(eji).gt.1.d-8) then t1=occsv(ist,jk)*(1.d0-occsv(jst,jk)/occmax)/eji sigma(:)=sigma(:)+t1*(z1/(w(:)-eji+eta)+conjg(z1)/(w(:)+eji+eta)) end if ! add to the plasma frequency if (intraband) then if (i.eq.j) then if (ist.eq.jst) then x=(ei-efermi)/swidth t1=wkptnr*dble(z1)*sdelta(stype,x)/swidth wplas=wplas+t1 end if end if end if end do end do end do !$OMP END DO deallocate(pmat) !$OMP END PARALLEL call freethd(nthd) z1=zi*wkptnr/omega sigma(:)=z1*sigma(:) ! intraband contribution if (intraband) then if (i.eq.j) then wplas=sqrt(occmax*abs(wplas)*fourpi/omega) ! write the plasma frequency to file write(fname,'("PLASMA_",2I1,".OUT")') i,j open(50,file=trim(fname),form='FORMATTED') write(50,'(G18.10," : plasma frequency")') wplas close(50) ! add the intraband contribution to sigma t1=wplas**2/fourpi do iw=1,nwplot sigma(iw)=sigma(iw)+t1/(swidth-zi*w(iw)) end do end if end if ! write the optical conductivity to file write(fname,'("SIGMA_",2I1,".OUT")') i,j open(50,file=trim(fname),form='FORMATTED') do iw=1,nwplot write(50,'(2G18.10)') w(iw),dble(sigma(iw)) end do write(50,*) do iw=1,nwplot write(50,'(2G18.10)') w(iw),aimag(sigma(iw)) end do close(50) ! write the dielectric function to file write(fname,'("EPSILON_",2I1,".OUT")') i,j open(50,file=trim(fname),form='FORMATTED') t1=0.d0 if (i.eq.j) t1=1.d0 do iw=1,nwplot t2=t1-fourpi*aimag(sigma(iw)/(w(iw)+eta)) write(50,'(2G18.10)') w(iw),t2 end do write(50,*) do iw=1,nwplot t2=fourpi*dble(sigma(iw)/(w(iw)+eta)) write(50,'(2G18.10)') w(iw),t2 end do close(50) ! end loop over tensor components end do write(*,*) write(*,'("Info(dielectric):")') write(*,'(" dielectric tensor written to EPSILON_ij.OUT")') write(*,'(" optical conductivity written to SIGMA_ij.OUT")') if (intraband) then write(*,'(" plasma frequency written to PLASMA_ij.OUT")') end if write(*,'(" for components")') do l=1,noptcomp write(*,'(" i = ",I1,", j = ",I1)') optcomp(1:2,l) end do ! write sigma to test file if required call writetest(121,'optical conductivity',nv=nwplot,tol=1.d-2,zva=sigma) deallocate(w,sigma) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/elfplot.f900000644000000000000000000000013214061636517014711 xustar0030 mtime=1623670095.137102286 30 atime=1623670093.880103453 30 ctime=1623670095.137102286 elk-7.2.42/src/elfplot.f900000644002504400250440000001266114061636517016754 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: elfplot ! !INTERFACE: subroutine elfplot ! !USES: use modmain ! !DESCRIPTION: ! Outputs the electron localisation function (ELF) for 1D, 2D or 3D plotting. ! The spin-averaged ELF is given by ! $$ f_{\rm ELF}({\bf r})=\frac{1}{1+[D({\bf r})/D^0({\bf r})]^2}, $$ ! where ! $$ D({\bf r})=\frac{1}{2}\left(\tau({\bf r})-\frac{1}{4} ! \frac{[\nabla n({\bf r})]^2}{n({\bf r})}\right) $$ ! and ! $$ \tau({\bf r})=\sum_{i=1}^N \left|\nabla\Psi_i({\bf r}) ! \right|^2 $$ ! is the spin-averaged kinetic energy density from the spinor wavefunctions. ! The function $D^0$ is the kinetic energy density for the homogeneous ! electron gas evaluated for $n({\bf r})$: ! $$ D^0({\bf r})=\frac{3}{5}(6\pi^2)^{2/3}\left(\frac{n({\bf r})}{2} ! \right)^{5/3}. $$ ! The ELF is useful for the topological classification of bonding. See for ! example T. Burnus, M. A. L. Marques and E. K. U. Gross [Phys. Rev. A 71, ! 10501 (2005)]. ! ! !REVISION HISTORY: ! Created September 2003 (JKD) ! Fixed bug found by F. Wagner (JKD) !EOP !BOC implicit none ! local variables integer ik,is,ias integer nr,nri,ir integer ig,ifg,i real(8) r,t1,t2 complex(8) z1 ! allocatable arrays real(8), allocatable :: gwf2mt(:,:),gwf2ir(:) real(8), allocatable :: rfmt1(:),rfmt2(:),grfir(:) real(8), allocatable :: grfmt1(:,:),grfmt2(:,:) real(8), allocatable :: elfmt(:,:),elfir(:) complex(8), allocatable :: evecfv(:,:),evecsv(:,:) complex(8), allocatable :: zfft1(:),zfft2(:) ! initialise universal variables call init0 call init1 ! allocate local arrays allocate(gwf2mt(npmtmax,natmtot),gwf2ir(ngtot)) allocate(rfmt1(npmtmax),rfmt2(npmtmax),grfir(ngtot)) allocate(grfmt1(npmtmax,3),grfmt2(npmtmax,3)) allocate(elfmt(npmtmax,natmtot),elfir(ngtot)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) allocate(zfft1(ngtot),zfft2(ngtot)) ! read density and potentials from file call readstate ! generate the core wavefunctions and densities call gencore ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! set the gradient squared to zero gwf2mt(:,:)=0.d0 gwf2ir(:)=0.d0 do ik=1,nkpt ! get the eigenvectors and occupancies from file call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! add the valence wavefunction gradient squared call gradwf2(ik,evecfv,evecsv,gwf2mt,gwf2ir) end do ! add core wavefunction gradient squared call gradwfcr2(gwf2mt) !------------------------! ! muffin-tin ELF ! !------------------------! do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) ! convert rho from spherical harmonics to spherical coordinates call rbsht(nr,nri,rhomt(:,ias),rfmt1) ! compute the gradient of the density call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rhomt(:,ias),npmtmax,grfmt1) ! convert gradient to spherical coordinates do i=1,3 call rbsht(nr,nri,grfmt1(:,i),grfmt2(:,i)) end do do i=1,npmt(is) r=abs(rfmt1(i)) ! square of gradient of rho t1=grfmt2(i,1)**2+grfmt2(i,2)**2+grfmt2(i,3)**2 ! D for inhomogeneous density t1=(1.d0/2.d0)*(gwf2mt(i,ias)-(1.d0/4.d0)*t1/r) ! D0 for uniform electron gas t2=(3.d0/5.d0)*((6.d0*pi**2)**(2.d0/3.d0))*(r/2.d0)**(5.d0/3.d0) ! ELF function rfmt2(i)=1.d0/(1.d0+(t1/t2)**2) end do ! convert ELF from spherical coordinates to spherical harmonics call rfsht(nr,nri,rfmt2,elfmt(:,ias)) end do !--------------------------! ! interstitial ELF ! !--------------------------! ! Fourier transform density to G-space zfft1(:)=rhoir(:) call zfftifc(3,ngridg,-1,zfft1) ! calculate the square of gradient of rho grfir(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) ! take the gradient z1=zfft1(ifg) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(z1),dble(z1),8) end do ! Fourier transform gradient to real-space call zfftifc(3,ngridg,1,zfft2) do ir=1,ngtot grfir(ir)=grfir(ir)+dble(zfft2(ir))**2 end do end do do ir=1,ngtot r=abs(rhoir(ir)) ! D for inhomogeneous density t1=(1.d0/2.d0)*(gwf2ir(ir)-(1.d0/4.d0)*grfir(ir)/r) ! D0 for homogeneous electron gas t2=(3.d0/5.d0)*((6.d0*pi**2)**(2.d0/3.d0))*(r/2.d0)**(5.d0/3.d0) ! ELF function elfir(ir)=1.d0/(1.d0+(t1/t2)**2) end do ! symmetrise the ELF call symrf(nrmt,nrmti,npmt,ngridg,ngtot,ngvec,igfft,npmtmax,elfmt,elfir) ! plot the ELF to file select case(task) case(51) open(50,file='ELF1D.OUT',form='FORMATTED') open(51,file='ELFLINES.OUT',form='FORMATTED') call plot1d(50,51,1,elfmt,elfir) close(50) close(51) write(*,*) write(*,'("Info(elfplot):")') write(*,'(" 1D ELF plot written to ELF1D.OUT")') write(*,'(" vertex location lines written to ELFLINES.OUT")') case(52) open(50,file='ELF2D.OUT',form='FORMATTED') call plot2d(.false.,50,1,elfmt,elfir) close(50) write(*,*) write(*,'("Info(elfplot): 2D ELF plot written to ELF2D.OUT")') case(53) open(50,file='ELF3D.OUT',form='FORMATTED') call plot3d(50,1,elfmt,elfir) close(50) write(*,*) write(*,'("Info(elfplot): 3D ELF plot written to ELF3D.OUT")') end select deallocate(gwf2mt,gwf2ir,rfmt1,rfmt2,grfir) deallocate(grfmt1,grfmt2,elfmt,elfir) deallocate(evecfv,evecsv,zfft1,zfft2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/vclcore.f900000644000000000000000000000013214061636517014701 xustar0030 mtime=1623670095.139102284 30 atime=1623670093.882103451 30 ctime=1623670095.139102284 elk-7.2.42/src/vclcore.f900000644002504400250440000000551714061636517016746 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine vclcore(wfmt,vmat) use modmain use modomp implicit none ! arguments complex(8), intent(in) :: wfmt(npcmtmax,natmtot,nspinor,nstsv) complex(8), intent(inout) :: vmat(nstsv,nstsv) ! local variables integer ist1,ist2,ist3 integer is,ia,ias,m,nthd integer nrc,nrci,npc ! automatic arrays complex(8) wfcr(npcmtmax,2),zfmt(npcmtmax),v(nstsv,nstsv) ! allocatable arrays complex(8), allocatable :: zrhomt(:,:) ! external functions complex(8), external :: zdotc allocate(zrhomt(npcmtmax,nstsv)) v(:,:)=0.d0 do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) do ist3=1,nstsp(is) if (spcore(ist3,is)) then do m=-ksp(ist3,is),ksp(ist3,is)-1 ! generate the core wavefunction in spherical coordinates (pass in m-1/2) call wavefcr(.false.,lradstp,is,ia,ist3,m,npcmtmax,wfcr) call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(zfmt) & !$OMP NUM_THREADS(nthd) do ist1=1,nstsv ! calculate the complex overlap density in spherical harmonics if (spinpol) then call zrho2(npc,wfcr,wfcr(:,2),wfmt(:,ias,1,ist1), & wfmt(:,ias,2,ist1),zfmt) else call zrho1(npc,wfcr,wfmt(:,ias,1,ist1),zfmt) end if call zfsht(nrc,nrci,zfmt,zrhomt(:,ist1)) end do !$OMP END PARALLEL DO call freethd(nthd) call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(zfmt,ist1) & !$OMP NUM_THREADS(nthd) do ist2=1,nstsv call zpotclmt(nrc,nrci,nrcmtmax,rlcmt(:,:,is),wprcmt(:,:,is), & zrhomt(:,ist2),zfmt) call zfmtwr(nrc,nrci,wrcmt(:,is),zfmt) do ist1=1,ist2 v(ist1,ist2)=v(ist1,ist2)-zdotc(npc,zrhomt(:,ist1),1,zfmt,1) end do end do !$OMP END PARALLEL DO call freethd(nthd) end do end if end do end do end do ! set the lower triangular part of the matrix do ist1=1,nstsv do ist2=1,ist1-1 v(ist1,ist2)=conjg(v(ist2,ist1)) end do end do ! scale the Coulomb matrix elements in the case of a hybrid functional if (hybrid) v(:,:)=hybridc*v(:,:) ! add to input matrix vmat(:,:)=vmat(:,:)+v(:,:) deallocate(zrhomt) return contains pure subroutine zrho1(n,x,y,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x(n),y(n) complex(8), intent(out) :: z(n) z(:)=conjg(x(:))*y(:) end subroutine pure subroutine zrho2(n,x1,x2,y1,y2,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x1(n),x2(n),y1(n),y2(n) complex(8), intent(out) :: z(n) z(:)=conjg(x1(:))*y1(:)+conjg(x2(:))*y2(:) end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/zfmtwr.f900000644000000000000000000000013214061636517014575 xustar0030 mtime=1623670095.140102283 30 atime=1623670093.884103449 30 ctime=1623670095.140102283 elk-7.2.42/src/zfmtwr.f900000644002504400250440000000123414061636517016632 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine zfmtwr(nr,nri,wr,zfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: wr(nr) complex(8), intent(inout) :: zfmt(*) ! local variables integer n,ir,i i=1 if (lmaxi.eq.1) then do ir=1,nri zfmt(i:i+3)=wr(ir)*zfmt(i:i+3) i=i+4 end do else n=lmmaxi-1 do ir=1,nri zfmt(i:i+n)=wr(ir)*zfmt(i:i+n) i=i+lmmaxi end do end if n=lmmaxo-1 do ir=nri+1,nr zfmt(i:i+n)=wr(ir)*zfmt(i:i+n) i=i+lmmaxo end do end subroutine elk-7.2.42/src/PaxHeaders.21776/zvcldisp.f900000644000000000000000000000013214061636517015102 xustar0030 mtime=1623670095.142102281 30 atime=1623670093.885103448 30 ctime=1623670095.142102281 elk-7.2.42/src/zvcldisp.f900000644002504400250440000000122214061636517017134 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zvcldisp(zvclmt) use modmain use modtddft implicit none ! arguments complex(8), intent(inout) :: zvclmt(npmtmax,natmtot) ! local variables integer is,ia,ias,np,i real(8) t1 do is=1,nspecies np=npmt(is) do ia=1,natoms(is) ias=idxas(ia,is) do i=1,3 t1=-datposc(i,0,ia,is) ! add the gradient of the Coulomb potential of the nucleus plus static density zvclmt(1:np,ias)=zvclmt(1:np,ias)+t1*gvclns(1:np,i,ias) end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/vecfbz.f900000644000000000000000000000013014061636517014521 xustar0029 mtime=1623670095.14310228 30 atime=1623670093.887103446 29 ctime=1623670095.14310228 elk-7.2.42/src/vecfbz.f900000644002504400250440000000270714061636517016566 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: vecfbz ! !INTERFACE: subroutine vecfbz(eps,bvec,vpl) ! !INPUT/OUTPUT PARAMETERS: ! eps : zero component tolerance (in,real) ! bvec : reciprocal lattice vectors (in,real(3,3)) ! vpl : input vector in lattice coordinates (inout,real(3)) ! !DESCRIPTION: ! Maps a vector in lattice coordinates to the first Brillouin zone. This is ! done by first removing its integer components and then adding primitive ! reciprocal lattice vectors until the shortest vector is found. ! ! !REVISION HISTORY: ! Created September 2008 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: eps,bvec(3,3) real(8), intent(inout) :: vpl(3) ! local variables integer i1,i2,i3,j1,j2,j3 real(8) v0(3),v1(3),v2(3),v3(3),t1,t2 ! map vector to [0,1) interval call r3frac(eps,vpl) v0(:)=bvec(:,1)*vpl(1)+bvec(:,2)*vpl(2)+bvec(:,3)*vpl(3) t1=v0(1)**2+v0(2)**2+v0(3)**2 j1=0; j2=0; j3=0 do i1=-1,0 v1(:)=v0(:)+dble(i1)*bvec(:,1) do i2=-1,0 v2(:)=v1(:)+dble(i2)*bvec(:,2) do i3=-1,0 v3(:)=v2(:)+dble(i3)*bvec(:,3) t2=v3(1)**2+v3(2)**2+v3(3)**2 if (t2.lt.t1+eps) then j1=i1; j2=i2; j3=i3 t1=t2 end if end do end do end do vpl(1)=vpl(1)+dble(j1) vpl(2)=vpl(2)+dble(j2) vpl(3)=vpl(3)+dble(j3) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gcd.f900000644000000000000000000000013214061636517014001 xustar0030 mtime=1623670095.145102278 30 atime=1623670093.889103444 30 ctime=1623670095.145102278 elk-7.2.42/src/gcd.f900000644002504400250440000000156314061636517016043 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: gcd ! !INTERFACE: integer function gcd(x,y) ! !INPUT/OUTPUT PARAMETERS: ! x : first integer (in,integer) ! y : second integer (in,integer) ! !DESCRIPTION: ! Computes the greatest common divisor (GCD) of two integers using Euclid's ! algorithm. ! ! !REVISION HISTORY: ! Created September 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: x,y ! local variables integer a,b,c if ((x.le.0).or.(y.le.0)) then write(*,*) write(*,'("Error(gcd): x <= 0 or y <= 0 : ",2I8)') x,y write(*,*) stop end if if (x.ge.y) then a=x b=y else a=y b=x end if 10 continue c=mod(a,b) a=b b=c if (c.gt.0) goto 10 gcd=a end function !EOC elk-7.2.42/src/PaxHeaders.21776/lopzflmn.f900000644000000000000000000000013214061636517015105 xustar0030 mtime=1623670095.146102277 30 atime=1623670093.890103443 30 ctime=1623670095.146102277 elk-7.2.42/src/lopzflmn.f900000644002504400250440000000220314061636517017137 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine lopzflmn(lmax,n,ld,zflm,zlflm1,zlflm2,zlflm3) implicit none ! arguments integer, intent(in) :: lmax,n,ld complex(8), intent(in) :: zflm(ld,n) complex(8), intent(out) :: zlflm1(ld,n),zlflm2(ld,n),zlflm3(ld,n) ! local variables integer l,m,lm,i real(8) t1 complex(8) z1 lm=0 do l=0,lmax do m=-l,l lm=lm+1 if (m.eq.-l) then zlflm1(lm,:)=0.d0 zlflm2(lm,:)=0.d0 end if if (m.lt.l) then t1=0.5d0*sqrt(dble((l-m)*(l+m+1))) do i=1,n z1=t1*zflm(lm,i) zlflm1(lm+1,i)=z1 zlflm2(lm+1,i)=cmplx(aimag(z1),-dble(z1),8) end do end if if (m.gt.-l) then t1=0.5d0*sqrt(dble((l+m)*(l-m+1))) do i=1,n z1=t1*zflm(lm,i) zlflm1(lm-1,i)=zlflm1(lm-1,i)+z1 zlflm2(lm-1,i)=zlflm2(lm-1,i)+cmplx(-aimag(z1),dble(z1),8) end do end if if (m.ne.0) then zlflm3(lm,:)=dble(m)*zflm(lm,:) else zlflm3(lm,:)=0.d0 end if end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/zpotclmt.f900000644000000000000000000000013214061636517015120 xustar0030 mtime=1623670095.148102276 30 atime=1623670093.892103441 30 ctime=1623670095.148102276 elk-7.2.42/src/zpotclmt.f900000644002504400250440000000757314061636517017171 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zpotclmt ! !INTERFACE: pure subroutine zpotclmt(nr,nri,ld,rl,wpr,zrhomt,zvclmt) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial mesh points (in,integer) ! nri : number of points on inner part of muffin-tin (in,integer) ! ld : leading dimension (in,integer) ! rl : r^l on the radial mesh (in,real(ld,-lmaxo-1:lmaxo+2)) ! wpr : weights for partial integration on radial mesh (in,real(4,nr)) ! zrhomt : muffin-tin charge density (in,complex(*)) ! zvclmt : muffin-tin Coulomb potential (out,complex(*)) ! !DESCRIPTION: ! Solves the Poisson equation for the charge density contained in an isolated ! muffin-tin using the Green's function approach. In other words, the ! spherical harmonic expansion of the Coulomb potential, $V_{lm}$, is obtained ! from the density expansion, $\rho_{lm}$, by ! $$ V_{lm}(r)=\frac{4\pi}{2l+1}\left(\frac{1}{r^{l+1}}\int_0^r\rho_{lm}(r') ! {r'}^{l+2}dr'+r^l\int_r^R\frac{\rho_{lm}(r')}{{r'}^{l-1}}dr'\right) $$ ! where $R$ is the muffin-tin radius. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr,nri,ld real(8), intent(in) :: rl(ld,-lmaxo-1:lmaxo+2),wpr(4,nr) complex(8), intent(in) :: zrhomt(*) complex(8), intent(out) :: zvclmt(*) ! local variables integer nro,iro,ir integer l,l1,l2,l3 integer lm,npi,i real(8) r1,r2,t0,t1,t2,t3,t4 ! automatic arrays real(8) f1(nr),f2(nr),f3(nr),f4(nr),f5(nr) nro=nr-nri iro=nri+1 npi=lmmaxi*nri do l=0,lmaxi l1=l+2 l2=-l+1 l3=-l-1 t0=fourpi/dble(2*l+1) do lm=l**2+1,(l+1)**2 i=lm do ir=1,nri t1=dble(zrhomt(i)); t2=aimag(zrhomt(i)) r1=rl(ir,l1); r2=rl(ir,l2) f1(ir)=t1*r1; f2(ir)=t2*r1 f3(ir)=t1*r2; f4(ir)=t2*r2 i=i+lmmaxi end do do ir=iro,nr t1=dble(zrhomt(i)); t2=aimag(zrhomt(i)) r1=rl(ir,l1); r2=rl(ir,l2) f1(ir)=t1*r1; f2(ir)=t2*r1 f3(ir)=t1*r2; f4(ir)=t2*r2 i=i+lmmaxo end do call splintwp(nr,wpr,f1,f5) call splintwp(nr,wpr,f2,f1) call splintwp(nr,wpr,f3,f2) call splintwp(nr,wpr,f4,f3) t1=f2(nr); t2=f3(nr) i=lm do ir=1,nri r1=t0*rl(ir,l3); r2=t0*rl(ir,l) t3=r1*f5(ir)+r2*(t1-f2(ir)) t4=r1*f1(ir)+r2*(t2-f3(ir)) zvclmt(i)=cmplx(t3,t4,8) i=i+lmmaxi end do do ir=iro,nr r1=t0*rl(ir,l3); r2=t0*rl(ir,l) t3=r1*f5(ir)+r2*(t1-f2(ir)) t4=r1*f1(ir)+r2*(t2-f3(ir)) zvclmt(i)=cmplx(t3,t4,8) i=i+lmmaxo end do end do end do do l=lmaxi+1,lmaxo l1=l+2 l2=-l+1 l3=-l-1 t0=fourpi/dble(2*l+1) do lm=l**2+1,(l+1)**2 i=npi+lm do ir=iro,nr t1=dble(zrhomt(i)); t2=aimag(zrhomt(i)) r1=rl(ir,l1); r2=rl(ir,l2) f1(ir)=t1*r1; f2(ir)=t2*r1 f3(ir)=t1*r2; f4(ir)=t2*r2 i=i+lmmaxo end do call splintwp(nro,wpr(1,iro),f1(iro),f5(iro)) call splintwp(nro,wpr(1,iro),f2(iro),f1(iro)) call splintwp(nro,wpr(1,iro),f3(iro),f2(iro)) call splintwp(nro,wpr(1,iro),f4(iro),f3(iro)) t1=f2(nr); t2=f3(nr) i=npi+lm do ir=iro,nr r1=t0*rl(ir,l3); r2=t0*rl(ir,l) t3=r1*f5(ir)+r2*(t1-f2(ir)) t4=r1*f1(ir)+r2*(t2-f3(ir)) zvclmt(i)=cmplx(t3,t4,8) i=i+lmmaxo end do end do end do return contains pure subroutine splintwp(n,wp,f,g) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wp(*),f(n) real(8), intent(out) :: g(n) ! local variables integer i,j real(8) sm g(1)=0.d0 sm=wp(5)*f(1)+wp(6)*f(2)+wp(7)*f(3)+wp(8)*f(4) g(2)=sm do i=3,n-1 j=(i-1)*4+1 sm=sm+wp(j)*f(i-2)+wp(j+1)*f(i-1)+wp(j+2)*f(i)+wp(j+3)*f(i+1) g(i)=sm end do j=(n-1)*4+1 g(n)=sm+wp(j)*f(n-3)+wp(j+1)*f(n-2)+wp(j+2)*f(n-1)+wp(j+3)*f(n) end subroutine end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/readfermi.f900000644000000000000000000000013114061636517015201 xustar0030 mtime=1623670095.149102275 29 atime=1623670093.89410344 30 ctime=1623670095.149102275 elk-7.2.42/src/readfermi.f900000644002504400250440000000157214061636517017244 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: readfermi ! !INTERFACE: subroutine readfermi ! !USES: use modmain ! !DESCRIPTION: ! Reads the Fermi energy from the file {\tt EFERMI.OUT}. ! ! !REVISION HISTORY: ! Created March 2005 (JKD) !EOP !BOC implicit none ! local variables integer ios open(50,file='EFERMI'//trim(filext),form='FORMATTED',action='READ', & status='OLD',iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readfermi): error opening ",A)') 'EFERMI'//trim(filext) write(*,*) stop end if read(50,*,iostat=ios) efermi if (ios.ne.0) then write(*,*) write(*,'("Error(readfermi): error reading Fermi energy from EFERMI.OUT")') write(*,*) stop end if close(50) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gensdmat.f900000644000000000000000000000013214061636517015046 xustar0030 mtime=1623670095.151102273 30 atime=1623670093.895103439 30 ctime=1623670095.151102273 elk-7.2.42/src/gensdmat.f900000644002504400250440000000212314061636517017101 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: gensdmat ! !INTERFACE: pure subroutine gensdmat(evecsv,sdmat) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! evecsv : second-variational eigenvectors (in,complex(nstsv,nstsv)) ! sdmat : spin density matrices (out,complex(nspinor,nspinor,nstsv)) ! !DESCRIPTION: ! Computes the spin density matrices for a set of second-variational states. ! ! !REVISION HISTORY: ! Created September 2008 (JKD) !EOP !BOC implicit none ! arguments complex(8), intent(in) :: evecsv(nstsv,nstsv) complex(8), intent(out) :: sdmat(nspinor,nspinor,nstsv) ! local variables integer ispn,jspn,ist,j complex(8) z1,z2 sdmat(:,:,:)=0.d0 do j=1,nstsv do ispn=1,nspinor do jspn=1,nspinor do ist=1,nstfv z1=evecsv(ist+nstfv*(ispn-1),j) z2=evecsv(ist+nstfv*(jspn-1),j) sdmat(ispn,jspn,j)=sdmat(ispn,jspn,j)+z1*conjg(z2) end do end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/symrfmt.f900000644000000000000000000000013214061636517014745 xustar0030 mtime=1623670095.152102272 30 atime=1623670093.897103437 30 ctime=1623670095.152102272 elk-7.2.42/src/symrfmt.f900000644002504400250440000000354114061636517017005 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine symrfmt(nr,nri,np,ld,rfmt) use modmain implicit none ! arguments integer, intent(in) :: nr(nspecies),nri(nspecies),np(nspecies) integer, intent(in) :: ld real(8), intent(inout) :: rfmt(ld,natmtot) ! local variables integer is,ia,ja,ias,jas integer isym,lspl real(8) t0 ! automatic arrays logical done(natmmax) ! allocatable arrays real(8), allocatable :: rfmt1(:,:),rfmt2(:) allocate(rfmt1(ld,natmmax),rfmt2(ld)) t0=1.d0/dble(nsymcrys) do is=1,nspecies ! make a copy of the input function do ia=1,natoms(is) ias=idxas(ia,is) call dcopy(np(is),rfmt(:,ias),1,rfmt1(:,ia),1) end do done(:)=.false. ! loop over atoms do ia=1,natoms(is) if (done(ia)) cycle ias=idxas(ia,is) rfmt(1:np(is),ias)=0.d0 ! loop over crystal symmetries do isym=1,nsymcrys ! index to spatial rotation lattice symmetry lspl=lsplsymc(isym) ! equivalent atom index (symmetry rotates atom ja into atom ia) ja=ieqatom(ia,is,isym) ! apply the rotation to the muffin-tin function call rotrfmt(symlatc(:,:,lspl),nr(is),nri(is),rfmt1(:,ja),rfmt2) ! accumulate in original function array rfmt(1:np(is),ias)=rfmt(1:np(is),ias)+rfmt2(1:np(is)) end do ! normalise call dscal(np(is),t0,rfmt(:,ias),1) done(ia)=.true. ! rotate into equivalent atoms do isym=1,nsymcrys ja=ieqatom(ia,is,isym) if (done(ja)) cycle jas=idxas(ja,is) ! inverse symmetry (which rotates atom ia into atom ja) lspl=isymlat(lsplsymc(isym)) ! rotate symmetrised function into equivalent muffin-tin call rotrfmt(symlatc(:,:,lspl),nr(is),nri(is),rfmt(:,ias),rfmt(:,jas)) done(ja)=.true. end do end do end do deallocate(rfmt1,rfmt2) end subroutine elk-7.2.42/src/PaxHeaders.21776/sphcrd.f900000644000000000000000000000013014061636517014525 xustar0029 mtime=1623670095.15410227 30 atime=1623670093.899103435 29 ctime=1623670095.15410227 elk-7.2.42/src/sphcrd.f900000644002504400250440000000222514061636517016565 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: sphcrd ! !INTERFACE: pure subroutine sphcrd(v,r,tp) ! !INPUT/OUTPUT PARAMETERS: ! v : input vector (in,real(3)) ! r : length of v (out,real) ! tp : (theta, phi) coordinates (out,real(2)) ! !DESCRIPTION: ! Returns the spherical coordinates $(r,\theta,\phi)$ of a vector ! $$ {\bf v}=(r\sin(\theta)\cos(\phi), r\sin(\theta)\sin(\phi), ! r\cos(\theta)). $$ ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: v(3) real(8), intent(out) :: r,tp(2) ! local variables real(8), parameter :: eps=1.d-14 real(8) t1 r=sqrt(v(1)**2+v(2)**2+v(3)**2) if (r.gt.eps) then t1=v(3)/r if (t1.ge.1.d0) then tp(1)=0.d0 else if (t1.le.-1.d0) then tp(1)=3.1415926535897932385d0 else tp(1)=acos(t1) end if if ((abs(v(1)).gt.eps).or.(abs(v(2)).gt.eps)) then tp(2)=atan2(v(2),v(1)) else tp(2)=0.d0 end if else tp(1)=0.d0 tp(2)=0.d0 end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/potcoul.f900000644000000000000000000000013214061636517014731 xustar0030 mtime=1623670095.155102269 30 atime=1623670093.900103434 30 ctime=1623670095.155102269 elk-7.2.42/src/potcoul.f900000644002504400250440000000500214061636517016763 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: potcoul ! !INTERFACE: subroutine potcoul ! !USES: use modmain use modomp ! !DESCRIPTION: ! Calculates the Coulomb potential of the real charge density stored in the ! global variables {\tt rhomt} and {\tt rhoir} by solving Poisson's equation. ! These variables are coverted to complex representations and passed to the ! routine {\tt zpotcoul}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! local variables integer is,ias,nthd integer nr,nri,ir,i ! allocatable arrays complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) allocate(zrhomt(npmtmax,natmtot)) ! convert real muffin-tin charge density to complex spherical harmonic expansion call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) call rtozfmt(nrmt(is),nrmti(is),rhomt(:,ias),zrhomt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! solve the complex Poisson's equation in the muffin-tins allocate(zvclmt(npmtmax,natmtot)) call genzvclmt(nrmt,nrmti,nrmtmax,rlmt,wprmt,npmtmax,zrhomt,zvclmt) deallocate(zrhomt) ! add the nuclear monopole potentials do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) i=1 do ir=1,nri zvclmt(i,ias)=zvclmt(i,ias)+vcln(ir,is) i=i+lmmaxi end do do ir=nri+1,nr zvclmt(i,ias)=zvclmt(i,ias)+vcln(ir,is) i=i+lmmaxo end do end do ! apply atomic displacement potential if required if (tdatpos) call zvcldisp(zvclmt) allocate(zrhoir(ngtot),zvclir(ngtot)) ! store real interstitial charge density in complex array zrhoir(:)=rhoir(:) ! solve Poisson's equation in the entire unit cell call zpotcoul(nrmt,nrmti,npmt,npmti,nrmtmax,rlmt,ngridg,igfft,ngvec,gc,gclg, & ngvec,jlgrmt,ylmg,sfacg,zrhoir,npmtmax,zvclmt,zvclir) ! convert complex muffin-tin potential to real spherical harmonic expansion call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) call ztorfmt(nrmt(is),nrmti(is),zvclmt(:,ias),vclmt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! store complex interstitial potential in real array vclir(:)=dble(zvclir(:)) deallocate(zrhoir,zvclmt,zvclir) ! apply constant electric field if required if (tefield) call potefield end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genzrm.f900000644000000000000000000000013214061636517014546 xustar0030 mtime=1623670095.157102267 30 atime=1623670093.902103432 30 ctime=1623670095.157102267 elk-7.2.42/src/genzrm.f900000644002504400250440000000222514061636517016604 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine genzrm(n,wf11,wf12,wf21,wf22,zrho,ld,zmag) use modmain implicit none ! arguments integer, intent(in) :: n complex(8), intent(in) :: wf11(n),wf12(n),wf21(n),wf22(n) complex(8), intent(out) :: zrho(n) integer, intent(in) :: ld complex(8), intent(out) :: zmag(ld,ndmag) ! local variables integer i complex(8) z11,z12,z21,z22,z1,z2 if (ncmag) then ! non-collinear case do i=1,n z11=wf11(i); z12=wf12(i) z21=wf21(i); z22=wf22(i) ! up-dn spin density z1=conjg(z11)*z22 ! dn-up spin density z2=conjg(z12)*z21 ! x-component: up-dn + dn-up zmag(i,1)=z1+z2 ! y-component: i*(dn-up - up-dn) z1=z2-z1 zmag(i,2)=cmplx(-aimag(z1),dble(z1),8) z1=conjg(z11)*z21 z2=conjg(z12)*z22 ! z-component: up-up - dn-dn zmag(i,3)=z1-z2 ! density: up-up + dn-dn zrho(i)=z1+z2 end do else ! collinear case do i=1,n z1=conjg(wf11(i))*wf21(i) z2=conjg(wf12(i))*wf22(i) zmag(i,1)=z1-z2 zrho(i)=z1+z2 end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/rfmtftoc.f900000644000000000000000000000013114061636517015067 xustar0030 mtime=1623670095.158102266 29 atime=1623670093.90410343 30 ctime=1623670095.158102266 elk-7.2.42/src/rfmtftoc.f900000644002504400250440000000122714061636517017127 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine rfmtftoc(nrc,nrci,rfmt,rfcmt) use modmain implicit none ! arguments integer, intent(in) :: nrc,nrci real(8), intent(in) :: rfmt(*) real(8), intent(out) :: rfcmt(*) ! local variables integer irc,i,j,m,n i=1 j=1 m=lmmaxi*lradstp n=lmmaxi-1 do irc=1,nrci rfcmt(i:i+n)=rfmt(j:j+n) i=i+lmmaxi j=j+m end do j=j+(lradstp-1)*(lmmaxo-lmmaxi) m=lmmaxo*lradstp n=lmmaxo-1 do irc=nrci+1,nrc rfcmt(i:i+n)=rfmt(j:j+n) i=i+lmmaxo j=j+m end do end subroutine elk-7.2.42/src/PaxHeaders.21776/rminv.f900000644000000000000000000000013214061636517014377 xustar0030 mtime=1623670095.160102264 30 atime=1623670093.905103429 30 ctime=1623670095.160102264 elk-7.2.42/src/rminv.f900000644002504400250440000000143014061636517016432 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rminv(n,a) implicit none ! arguments integer, intent(in) :: n real(8), intent(inout) :: a(n,n) ! local variables integer info ! automatic arrays integer ipiv(n) real(8) work(n) call dgetrf(n,n,a,n,ipiv,info) if (info.ne.0) then write(*,*) write(*,'("Error(rminv): unable to invert matrix")') write(*,'(" DGETRF returned INFO = ",I8)') info write(*,*) stop end if call dgetri(n,a,n,ipiv,work,n,info) if (info.ne.0) then write(*,*) write(*,'("Error(rminv): unable to invert matrix")') write(*,'(" DGETRI returned INFO = ",I8)') info write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/zminv.f900000644000000000000000000000013214061636517014407 xustar0030 mtime=1623670095.161102264 30 atime=1623670093.907103428 30 ctime=1623670095.161102264 elk-7.2.42/src/zminv.f900000644002504400250440000000170014061636517016442 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zminv(n,a) use modomp implicit none ! arguments integer, intent(in) :: n complex(8), intent(inout) :: a(n,n) ! local variables integer info,nthd,nts ! automatic arrays integer ipiv(n) complex(8) work(n) ! enable MKL parallelism call holdthd(maxthdmkl,nthd) nts=mkl_set_num_threads_local(nthd) call zgetrf(n,n,a,n,ipiv,info) if (info.ne.0) then write(*,*) write(*,'("Error(zminv): unable to invert matrix")') write(*,'(" ZGETRF returned INFO = ",I8)') info write(*,*) stop end if call zgetri(n,a,n,ipiv,work,n,info) if (info.ne.0) then write(*,*) write(*,'("Error(zminv): unable to invert matrix")') write(*,'(" ZGETRI returned INFO = ",I8)') info write(*,*) stop end if nts=mkl_set_num_threads_local(0) call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/rtozfmt.f900000644000000000000000000000013214061636517014751 xustar0030 mtime=1623670095.162102263 30 atime=1623670093.909103426 30 ctime=1623670095.162102263 elk-7.2.42/src/rtozfmt.f900000644002504400250440000000416514061636517017014 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine rtozfmt(nr,nri,rfmt,zfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: rfmt(*) complex(8), intent(out) :: zfmt(*) ! local variables integer i call rtozflmn(lmaxi,nri,lmmaxi,rfmt,zfmt) i=lmmaxi*nri+1 call rtozflmn(lmaxo,nr-nri,lmmaxo,rfmt(i),zfmt(i)) return contains !BOP ! !ROUTINE: rtozflmn ! !INTERFACE: pure subroutine rtozflmn(lmax,n,ld,rflm,zflm) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum angular momentum (in,integer) ! n : number of functions to convert (in,integer) ! ld : leading dimension (in,integer) ! rflm : coefficients of real spherical harmonic expansion (in,real(ld,n)) ! zflm : coefficients of complex spherical harmonic expansion ! (out,complex(ld,n)) ! !DESCRIPTION: ! Converts a real function, $r_{lm}$, expanded in terms of real spherical ! harmonics into a complex spherical harmonic expansion, $z_{lm}$: ! $$ z_{lm}=\begin{cases} \frac{1}{\sqrt{2}}(r_{lm}+i(-1)^mr_{l-m}) & m>0 \\ ! \frac{1}{\sqrt{2}}((-1)^mr_{l-m}-ir_{lm}) & m<0 \\ ! r_{lm} & m=0 \end{cases}\;. $$ ! See routine {\tt genrlm}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: lmax,n,ld real(8), intent(in) :: rflm(ld,n) complex(8), intent(out) :: zflm(ld,n) ! local variables integer l,m,lm1,lm2 ! real constant 1/sqrt(2) real(8), parameter :: c1=0.7071067811865475244d0 lm1=0 do l=0,lmax lm2=lm1+2*(l+1) do m=-l,-1 lm1=lm1+1 lm2=lm2-1 if (mod(m,2).ne.0) then zflm(lm1,:)=c1*cmplx(-rflm(lm2,:),-rflm(lm1,:),8) else zflm(lm1,:)=c1*cmplx(rflm(lm2,:),-rflm(lm1,:),8) end if end do lm1=lm1+1 lm2=lm2-1 zflm(lm1,:)=rflm(lm1,:) do m=1,l lm1=lm1+1 lm2=lm2-1 if (mod(m,2).ne.0) then zflm(lm1,:)=c1*cmplx(rflm(lm1,:),-rflm(lm2,:),8) else zflm(lm1,:)=c1*cmplx(rflm(lm1,:),rflm(lm2,:),8) end if end do end do end subroutine !EOC end subroutine elk-7.2.42/src/PaxHeaders.21776/genwfsvp.f900000644000000000000000000000013214061636517015103 xustar0030 mtime=1623670095.164102261 30 atime=1623670093.910103425 30 ctime=1623670095.164102261 elk-7.2.42/src/genwfsvp.f900000644002504400250440000000376314061636517017151 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genwfsvp(tsh,tgp,nst,idx,ngdg,igf,vpl,ngp,igpig,wfmt,ld,wfir) use modmain implicit none ! arguments logical, intent(in) :: tsh,tgp integer, intent(in) :: nst,idx(nst),ngdg(3),igf(*) real(8), intent(in) :: vpl(3) integer, intent(out) :: ngp(nspnfv),igpig(ngkmax,nspnfv) complex(8), intent(out) :: wfmt(npcmtmax,natmtot,nspinor,nst) integer, intent(in) :: ld complex(8), intent(out) :: wfir(ld,nspinor,nst) ! local variables integer ispn real(8) vl(3),vc(3) ! automatic arrays real(8) vgpl(3,ngkmax,nspnfv),vgpc(3,ngkmax),gpc(ngkmax) ! allocatable arrays complex(8), allocatable :: sfacgp(:,:),apwalm(:,:,:,:,:) complex(8), allocatable :: evecfv(:,:,:),evecsv(:,:) allocate(sfacgp(ngkmax,natmtot)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) ! loop over first-variational spins do ispn=1,nspnfv vl(:)=vpl(:) vc(:)=bvec(:,1)*vpl(1)+bvec(:,2)*vpl(2)+bvec(:,3)*vpl(3) ! spin-spiral case if (spinsprl) then if (ispn.eq.1) then vl(:)=vl(:)+0.5d0*vqlss(:) vc(:)=vc(:)+0.5d0*vqcss(:) else vl(:)=vl(:)-0.5d0*vqlss(:) vc(:)=vc(:)-0.5d0*vqcss(:) end if end if ! generate the G+p-vectors call gengkvec(ngvc,ivg,vgc,vl,vc,gkmax,ngkmax,ngp(ispn),igpig(:,ispn), & vgpl(:,:,ispn),vgpc,gpc) ! generate structure factors for G+p-vectors call gensfacgp(ngp(ispn),vgpc,ngkmax,sfacgp) ! find the matching coefficients call match(ngp(ispn),vgpc,gpc,sfacgp,apwalm(:,:,:,:,ispn)) end do deallocate(sfacgp) ! get the first- and second-variational eigenvectors from file allocate(evecfv(nmatmax,nstfv,nspnfv),evecsv(nstsv,nstsv)) call getevecfv(filext,0,vpl,vgpl,evecfv) call getevecsv(filext,0,vpl,evecsv) ! calculate the second-variational wavefunctions call genwfsv(tsh,tgp,nst,idx,ngdg,igf,ngp,igpig,apwalm,evecfv,evecsv,wfmt,ld, & wfir) deallocate(apwalm,evecfv,evecsv) end subroutine elk-7.2.42/src/PaxHeaders.21776/rdiracint.f900000644000000000000000000000013014061636517015221 xustar0029 mtime=1623670095.16510226 30 atime=1623670093.912103423 29 ctime=1623670095.16510226 elk-7.2.42/src/rdiracint.f900000644002504400250440000001100214061636517017252 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2015 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rdiracint ! !INTERFACE: pure subroutine rdiracint(sol,kpa,e,nr,r,vr,nn,g0,g1,f0,f1) ! !INPUT/OUTPUT PARAMETERS: ! sol : speed of light in atomic units (in,real) ! kpa : quantum number kappa (in,integer) ! e : energy (in,real) ! nr : number of radial mesh points (in,integer) ! r : radial mesh (in,real(nr)) ! vr : potential on radial mesh (in,real(nr)) ! nn : number of nodes (out,integer) ! g0 : m th energy derivative of the major component multiplied by r ! (out,real(nr)) ! g1 : radial derivative of g0 (out,real(nr)) ! f0 : m th energy derivative of the minor component multiplied by r ! (out,real(nr)) ! f1 : radial derivative of f0 (out,real(nr)) ! !DESCRIPTION: ! Integrates the radial Dirac equation from $r=0$ outwards. This involves ! using the predictor-corrector method to solve the coupled first-order ! equations (in atomic units) ! \begin{align*} ! \left(\frac{d}{dr}+\frac{\kappa}{r}\right)G_{\kappa}&=\frac{1}{c} ! \{2E_0+E-V\}F_{\kappa}\\ ! \left(\frac{d}{dr}-\frac{\kappa}{r}\right)F_{\kappa}&= ! -\frac{1}{c}\{E-V\}G_{\kappa}, ! \end{align*} ! where $G_{\kappa}=rg_{\kappa}$ and $F_{\kappa}=rf_{\kappa}$ are the major ! and minor components multiplied by $r$, respectively; $V$ is the external ! potential; $E_0$ is the electron rest energy; $E$ is the eigen energy ! (excluding $E_0$); and $\kappa=l$ for $j=l-\frac{1}{2}$ or $\kappa=-(l+1)$ ! for $j=l+\frac{1}{2}$. ! ! !REVISION HISTORY: ! Created September 2002 (JKD) ! Polynomial order fixed to 3, September 2013 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: sol integer, intent(in) :: kpa real(8), intent(in) :: e integer, intent(in) :: nr real(8), intent(in) :: r(nr),vr(nr) integer, intent(out) :: nn real(8), intent(out) :: g0(nr),g1(nr) real(8), intent(out) :: f0(nr),f1(nr) ! local variables integer ir,ir0 ! rescaling limit real(8), parameter :: rsc=1.d100 real(8) ci,e0,t1,t2,t3,t4 ! inverse speed of light ci=1.d0/sol ! electron rest energy e0=sol**2 t1=2.d0*e0+e ! determine the r -> 0 boundary values of F and G t2=dble(kpa)/r(1) t3=ci*(t1-vr(1)) t4=ci*(vr(1)-e) f0(1)=1.d0 f1(1)=0.d0 g0(1)=(f1(1)-t2*f0(1))/t4 g1(1)=t3*f0(1)-t2*g0(1) ! extrapolate to the first four points g1(2:4)=g1(1) f1(2:4)=f1(1) nn=0 do ir=2,nr t2=dble(kpa)/r(ir) t3=ci*(t1-vr(ir)) t4=ci*(vr(ir)-e) ir0=ir-3 if (ir0.lt.1) ir0=1 g1(ir)=poly3(r(ir0),g1(ir0),r(ir)) f1(ir)=poly3(r(ir0),f1(ir0),r(ir)) ! integrate to find wavefunction g0(ir)=poly4i(r(ir0),g1(ir0),r(ir))+g0(ir0) f0(ir)=poly4i(r(ir0),f1(ir0),r(ir))+f0(ir0) ! compute the derivatives g1(ir)=t3*f0(ir)-t2*g0(ir) f1(ir)=t4*g0(ir)+t2*f0(ir) ! integrate for correction g0(ir)=poly4i(r(ir0),g1(ir0),r(ir))+g0(ir0) f0(ir)=poly4i(r(ir0),f1(ir0),r(ir))+f0(ir0) ! compute the derivatives again g1(ir)=t3*f0(ir)-t2*g0(ir) f1(ir)=t4*g0(ir)+t2*f0(ir) ! check for overflow if ((abs(g0(ir)).gt.rsc).or.(abs(g1(ir)).gt.rsc).or. & (abs(f0(ir)).gt.rsc).or.(abs(f1(ir)).gt.rsc)) then ! set the remaining points and return g0(ir:nr)=g0(ir) g1(ir:nr)=g1(ir) f0(ir:nr)=f0(ir) f1(ir:nr)=f1(ir) return end if ! check for node if (g0(ir-1)*g0(ir).lt.0.d0) nn=nn+1 end do return contains pure real(8) function poly3(xa,ya,x) implicit none ! arguments real(8), intent(in) :: xa(3),ya(3),x ! local variables real(8) x0,x1,x2,y0,y1,y2 real(8) c1,c2,t0,t1,t2 ! evaluate the polynomial coefficients x0=xa(1) x1=xa(2)-x0; x2=xa(3)-x0 y0=ya(1) y1=ya(2)-y0; y2=ya(3)-y0 t0=1.d0/(x1*x2*(x2-x1)) t1=x1*y2; t2=x2*y1 c1=x2*t2-x1*t1 c2=t1-t2 t1=x-x0 ! evaluate the polynomial poly3=y0+t0*t1*(c1+c2*t1) end function pure real(8) function poly4i(xa,ya,x) implicit none ! arguments real(8), intent(in) :: xa(4),ya(4),x ! local variables real(8) x0,x1,x2,x3,y0,y1,y2,y3 real(8) c1,c2,c3,t0,t1,t2,t3,t4,t5,t6 ! evaluate the polynomial coefficients x0=xa(1) x1=xa(2)-x0; x2=xa(3)-x0; x3=xa(4)-x0 y0=ya(1) y1=ya(2)-y0; y2=ya(3)-y0; y3=ya(4)-y0 t4=x1-x2; t5=x1-x3; t6=x2-x3 t1=x1*x2*y3; t2=x2*x3*y1; t3=x1*x3 t0=1.d0/(x2*t3*t4*t5*t6) t3=t3*y2 c3=t1*t4+t2*t6-t3*t5 t4=x1**2; t5=x2**2; t6=x3**2 c2=t1*(t5-t4)+t2*(t6-t5)+t3*(t4-t6) c1=t1*(x2*t4-x1*t5)+t2*(x3*t5-x2*t6)+t3*(x1*t6-x3*t4) t1=x-x0 ! integrate the polynomial poly4i=t1*(y0+t0*t1*(0.5d0*c1+t1*(0.3333333333333333333d0*c2+0.25d0*c3*t1))) end function end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/findngkmax.f900000644000000000000000000000013214061636517015372 xustar0030 mtime=1623670095.167102258 30 atime=1623670093.914103421 30 ctime=1623670095.167102258 elk-7.2.42/src/findngkmax.f900000644002504400250440000000424314061636517017432 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2012 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: findngkmax ! !INTERFACE: pure subroutine findngkmax(nkpt,vkc,nspnfv,vqcss,ngv,vgc,gkmax,ngkmax) ! !INPUT/OUTPUT PARAMETERS: ! nkpt : number of k-points (in,integer) ! vkc : k-point vectors in Cartesian coordinates (in,real(3,nkpt)) ! nspnfv : number of first-variational spin components: 1 normal case, 2 for ! spin-spiral case (in,integer) ! vqcss : spin-spiral q-vector, not referenced if nspnfv=1 (in,integer) ! ngv : number of G-vectors (in,integer) ! vgc : G-vectors in Cartesian coordinates (in,real(3,ngv)) ! gkmax : maximum allowed |G+k| (in,real) ! ngkmax : maximum number of G+k-vectors over all k-points (out,integer) ! !DESCRIPTION: ! Determines the largest number of ${\bf G+k}$-vectors with length less than ! {\tt gkmax} over all the $k$-points. This variable is used for allocating ! arrays. ! ! !REVISION HISTORY: ! Created October 2004 (JKD) ! Modified, August 2012 (JKD) ! Removed modmain and added arguments, September 2012 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nkpt real(8), intent(in) :: vkc(3,nkpt) integer, intent(in) :: nspnfv real(8), intent(in) :: vqcss(3) integer, intent(in) :: ngv real(8), intent(in) :: vgc(3,ngv),gkmax integer, intent(out) :: ngkmax ! local variables integer ispn,ik,n,ig real(8) v1,v2,v3,w1,w2,w3,t0,t1 t0=gkmax**2+1.d-6 ngkmax=0 do ispn=1,nspnfv do ik=1,nkpt if (nspnfv.eq.2) then ! spin-spiral case if (ispn.eq.1) then v1=vkc(1,ik)+0.5d0*vqcss(1) v2=vkc(2,ik)+0.5d0*vqcss(2) v3=vkc(3,ik)+0.5d0*vqcss(3) else v1=vkc(1,ik)-0.5d0*vqcss(1) v2=vkc(2,ik)-0.5d0*vqcss(2) v3=vkc(3,ik)-0.5d0*vqcss(3) end if else v1=vkc(1,ik) v2=vkc(2,ik) v3=vkc(3,ik) end if n=0 do ig=1,ngv w1=vgc(1,ig)+v1 w2=vgc(2,ig)+v2 w3=vgc(3,ig)+v3 t1=w1**2+w2**2+w3**2 if (t1.lt.t0) n=n+1 end do ngkmax=max(ngkmax,n) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rotzflm.f900000644000000000000000000000013214061636517014741 xustar0030 mtime=1623670095.168102257 30 atime=1623670093.916103419 30 ctime=1623670095.168102257 elk-7.2.42/src/rotzflm.f900000644002504400250440000000547214061636517017006 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rotzflm ! !INTERFACE: subroutine rotzflm(rot,lmin,lmax,lmmax,n,ld,zflm1,zflm2) ! !INPUT/OUTPUT PARAMETERS: ! rot : rotation matrix (in,real(3,3)) ! lmin : minimum angular momentum (in,integer) ! lmax : maximum angular momentum (in,integer) ! lmmax : (lmax+1)^2 or larger (in,integer) ! n : number of functions to rotate (in,integer) ! ld : leading dimension (in,integer) ! zflm1 : coefficients of the complex spherical harmonic expansion for each ! function (in,complex(ld,n)) ! zflm2 : coefficients of rotated functions (out,complex(ld,n)) ! !DESCRIPTION: ! Rotates a set of complex functions ! $$ f_i({\bf r})=\sum_{lm}f_{lm}^iY_{lm}(\hat{\bf r}) $$ ! for all $i$, given the coefficients $f_{lm}^i$ and a rotation matrix $R$. ! This is done by first the computing the Euler angles $(\alpha,\beta,\gamma)$ ! of $R^{-1}$ (see routine {\tt roteuler}) and then applying the spherical ! harmonic rotation matrix generated by the routine {\tt ylmrot}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) ! Modified, December 2008 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: rot(3,3) integer, intent(in) :: lmin,lmax,lmmax,n,ld complex(8), intent(in) :: zflm1(ld,n) complex(8), intent(out) :: zflm2(ld,n) ! local variables integer l,lm1,lm2,nm,p real(8) det,rotp(3,3) real(8) ang(3),angi(3) complex(8), parameter :: zzero=(0.d0,0.d0),zone=(1.d0,0.d0) ! automatic arrays complex(8) d(lmmax,lmmax) if (lmin.lt.0) then write(*,*) write(*,'("Error(rotzflm): lmin < 0 : ",I8)') lmin write(*,*) stop end if if (lmin.gt.lmax) then write(*,*) write(*,'("Error(rotzflm): lmin > lmax : ",2I8)') lmin,lmax write(*,*) stop end if if (n.eq.0) return if (n.lt.0) then write(*,*) write(*,'("Error(rotzflm): n < 0 : ",I8)') n write(*,*) stop end if ! find the determinant det=rot(1,1)*(rot(2,2)*rot(3,3)-rot(3,2)*rot(2,3)) & +rot(2,1)*(rot(3,2)*rot(1,3)-rot(1,2)*rot(3,3)) & +rot(3,1)*(rot(1,2)*rot(2,3)-rot(2,2)*rot(1,3)) ! make the rotation proper p=1 if (det.lt.0.d0) p=-1 rotp(:,:)=dble(p)*rot(:,:) ! compute the Euler angles of the rotation matrix call roteuler(rotp,ang) ! inverse rotation: the function is to be rotated, not the spherical harmonics angi(1)=-ang(3) angi(2)=-ang(2) angi(3)=-ang(1) ! determine the rotation matrix for complex spherical harmonics call ylmrot(p,angi,lmax,lmmax,d) ! apply rotation matrix (d and zflm may have different starting indices) lm1=lmin**2+1 lm2=1 do l=lmin,lmax nm=2*l+1 call zgemm('N','N',nm,n,nm,zone,d(lm1,lm1),lmmax,zflm1(lm2,1),ld,zzero, & zflm2(lm2,1),ld) lm1=lm1+nm lm2=lm2+nm end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/zfinp.f900000644000000000000000000000013214061636517014372 xustar0030 mtime=1623670095.169102256 30 atime=1623670093.917103418 30 ctime=1623670095.169102256 elk-7.2.42/src/zfinp.f900000644002504400250440000000372114061636517016432 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zfinp ! !INTERFACE: complex(8) function zfinp(zfmt1,zfir1,zfmt2,zfir2) ! !USES: use modmain use modomp ! !INPUT/OUTPUT PARAMETERS: ! zfmt1 : first complex function in spherical harmonics/coordinates for all ! muffin-tins (in,complex(npcmtmax,natmtot)) ! zfir1 : first complex interstitial function in real-space ! (in,complex(ngtc)) ! zfmt2 : second complex function in spherical harmonics/coordinates for all ! muffin-tins (in,complex(npcmtmax,natmtot)) ! zfir2 : second complex interstitial function in real-space ! (in,complex(ngtc)) ! !DESCRIPTION: ! Calculates the inner product of two complex fuctions over the entire unit ! cell. The muffin-tin functions should be stored on the coarse radial grid. ! In the interstitial region, the integrand is multiplied with the ! characteristic function to remove the contribution from the muffin-tin. See ! routines {\tt zfmtinp} and {\tt gencfun}. ! ! !REVISION HISTORY: ! Created July 2004 (Sharma) !EOP !BOC implicit none ! arguments complex(8), intent(in) :: zfmt1(npcmtmax,natmtot),zfir1(ngtc) complex(8), intent(in) :: zfmt2(npcmtmax,natmtot),zfir2(ngtc) ! local variables integer is,ias,nthd ! external functions complex(8), external :: zdotc,zfmtinp ! interstitial contribution (requires that one of the functions has been ! multiplied by the characteristic function) zfinp=zdotc(ngtc,zfir1,1,zfir2,1) zfinp=zfinp*omega/dble(ngtc) ! muffin-tin contribution call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) REDUCTION(+:zfinp) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) zfinp=zfinp+zfmtinp(nrcmt(is),nrcmti(is),wrcmt(:,is),zfmt1(:,ias), & zfmt2(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) end function !EOC elk-7.2.42/src/PaxHeaders.21776/latvstep.f900000644000000000000000000000013214061636517015106 xustar0030 mtime=1623670095.171102254 30 atime=1623670093.919103416 30 ctime=1623670095.171102254 elk-7.2.42/src/latvstep.f900000644002504400250440000000202514061636517017142 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine latvstep use modmain use modmpi use modstore implicit none ! local variables integer i real(8) t1 do i=1,nstrain ! compute product of current and previous stress tensor components t1=stress(i)*stressp(i) ! if component is in the same direction then increase step size parameter if (t1.gt.0.d0) then taulatv(i)=taulatv(i)+tau0latv else taulatv(i)=tau0latv end if t1=taulatv(i)*(stress(i)+stressp(i)) avec(:,:)=avec(:,:)-t1*strain(:,:,i) end do ! compute the new unit cell volume call reciplat(avec,bvec,omega,omegabz) ! preserve the volume if required (added by Ronald Cohen) if (latvopt.eq.2) then t1=(omega_/omega)**(1.d0/3.d0) avec(:,:)=t1*avec(:,:) omega=omega_ end if ! each MPI process should have numerically identical lattice vectors call mpi_bcast(avec,9,mpi_double_precision,0,mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/gradzfmt.f900000644000000000000000000000013214061636517015062 xustar0030 mtime=1623670095.172102253 30 atime=1623670093.921103414 30 ctime=1623670095.172102253 elk-7.2.42/src/gradzfmt.f900000644002504400250440000001375414061636517017131 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2009 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: gradzfmt ! !INTERFACE: subroutine gradzfmt(nr,nri,ri,wcr,zfmt,ld,gzfmt) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial mesh points (in,integer) ! nri : number of points on inner part of muffin-tin (in,integer) ! ri : 1/r on the radial mesh (in,real(nr)) ! wcr : weights for spline coefficients on radial mesh (in,real(12,nr)) ! zfmt : complex muffin-tin function (in,complex(*)) ! ld : leading dimension (in,integer) ! gzfmt : gradient of zfmt (out,complex(ld,3)) ! !DESCRIPTION: ! Calculates the gradient of a complex muffin-tin function. In other words, ! given the spherical harmonic expansion coefficients, $f_{lm}(r)$, of a ! function $f({\bf r})$, the routine returns ${\bf F}_{lm}$ where ! $$ \sum_{lm}{\bf F}_{lm}(r)Y_{lm}(\hat{\bf r})=\nabla f({\bf r}). $$ ! This is done using the gradient formula (see, for example, V. Devanathan, ! {\em Angular Momentum Techniques In Quantum Mechanics}) ! \begin{align*} ! \nabla f_{lm}(r)Y_{lm}(\hat{\bf r})&=-\sqrt{\frac{l+1}{2l+1}} ! \left(\frac{d}{dr}-\frac{l}{r}\right)f_{lm}(r) ! {\bf Y}_{lm}^{l+1}(\hat{\bf r})\\ ! &+\sqrt{\frac{l}{2l+1}}\left(\frac{d}{dr}+\frac{l+1}{r}\right)f_{lm}(r) ! {\bf Y}_{lm}^{l-1}(\hat{\bf r}), ! \end{align*} ! where the vector spherical harmonics are determined from Clebsch-Gordan ! coefficients as follows: ! $$ {\bf Y}_{lm}^{l'}(\hat{\bf r})=\sum_{m'\mu} ! \begin{bmatrix} l' & 1 & l \\ m' & \mu & m \end{bmatrix} ! Y_{lm}(\hat{\bf r})\hat{\bf e}^{\mu} $$ ! and the (contravariant) spherical unit vectors are given by ! $$ \hat{\bf e}_{+1}=-\frac{\hat{\bf x}+i\hat{\bf y}}{\sqrt{2}}, ! \qquad\hat{\bf e}_0=\hat{\bf z},\qquad ! \hat{\bf e}_{-1}=\frac{\hat{\bf x}-i\hat{\bf y}}{\sqrt{2}}. $$ ! ! !REVISION HISTORY: ! Rewritten May 2009 (JKD) ! Modified, February 2020 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: ri(nr),wcr(12,nr) complex(8), intent(in) :: zfmt(*) integer, intent(in) :: ld complex(8), intent(out) :: gzfmt(ld,3) ! local variables integer nro,iro,ir,mu integer np,npi,i,i1,j integer l,m,lm,lm1 ! real constant 1/sqrt(2) real(8), parameter :: c1=0.7071067811865475244d0 real(8) t1,t2,t3 complex(8) z1 ! automatic arrays real(8) f1(nr),f2(nr),g1(nr),g2(nr) complex(8) drmt(ld) ! external functions real(8), external :: clebgor nro=nr-nri iro=nri+1 npi=lmmaxi*nri np=npi+lmmaxo*nro !----------------------------------------! ! compute the radial derivatives ! !----------------------------------------! do lm=1,lmmaxi i=lm do ir=1,nri f1(ir)=dble(zfmt(i)) f2(ir)=aimag(zfmt(i)) i=i+lmmaxi end do do ir=iro,nr f1(ir)=dble(zfmt(i)) f2(ir)=aimag(zfmt(i)) i=i+lmmaxo end do call splined(nr,wcr,f1,g1) call splined(nr,wcr,f2,g2) i=lm do ir=1,nri drmt(i)=cmplx(g1(ir),g2(ir),8) i=i+lmmaxi end do do ir=iro,nr drmt(i)=cmplx(g1(ir),g2(ir),8) i=i+lmmaxo end do end do do lm=lmmaxi+1,lmmaxo i=npi+lm do ir=iro,nr f1(ir)=dble(zfmt(i)) f2(ir)=aimag(zfmt(i)) i=i+lmmaxo end do call splined(nro,wcr(1,iro),f1(iro),g1(iro)) call splined(nro,wcr(1,iro),f2(iro),g2(iro)) i=npi+lm do ir=iro,nr drmt(i)=cmplx(g1(ir),g2(ir),8) i=i+lmmaxo end do end do !-----------------------------------------------------! ! compute the gradient in the spherical basis ! !-----------------------------------------------------! ! zero the gradient array gzfmt(1:np,:)=0.d0 ! inner part of muffin-tin lm=0 do l=0,lmaxi t1=-sqrt(dble(l+1)/dble(2*l+1)) if (l.gt.0) then t2=sqrt(dble(l)/dble(2*l+1)) else t2=0.d0 end if do m=-l,l lm=lm+1 j=1 do mu=-1,1 if (mu.eq.0) j=3 if (mu.eq.1) j=2 if (l+1.le.lmaxi) then ! index to (l,m) is l*(l+1)+m+1, therefore index to (l+1,m-mu) is lm1=(l+1)*(l+2)+(m-mu)+1 t3=t1*clebgor(l+1,1,l,m-mu,mu,m) i=lm; i1=lm1 do ir=1,nri gzfmt(i1,j)=gzfmt(i1,j)+t3*(drmt(i)-dble(l)*ri(ir)*zfmt(i)) i=i+lmmaxi; i1=i1+lmmaxi end do end if if (abs(m-mu).le.l-1) then ! index to (l-1,m-mu) lm1=(l-1)*l+(m-mu)+1 t3=t2*clebgor(l-1,1,l,m-mu,mu,m) i=lm; i1=lm1 do ir=1,nri gzfmt(i1,j)=gzfmt(i1,j)+t3*(drmt(i)+dble(l+1)*ri(ir)*zfmt(i)) i=i+lmmaxi; i1=i1+lmmaxi end do end if end do end do end do ! outer part of muffin-tin lm=0 do l=0,lmaxo t1=-sqrt(dble(l+1)/dble(2*l+1)) if (l.gt.0) then t2=sqrt(dble(l)/dble(2*l+1)) else t2=0.d0 end if do m=-l,l lm=lm+1 j=1 do mu=-1,1 if (mu.eq.0) j=3 if (mu.eq.1) j=2 if (l+1.le.lmaxo) then lm1=(l+1)*(l+2)+(m-mu)+1 t3=t1*clebgor(l+1,1,l,m-mu,mu,m) i=npi+lm; i1=npi+lm1 do ir=iro,nr gzfmt(i1,j)=gzfmt(i1,j)+t3*(drmt(i)-dble(l)*ri(ir)*zfmt(i)) i=i+lmmaxo; i1=i1+lmmaxo end do end if if (abs(m-mu).le.l-1) then lm1=(l-1)*l+(m-mu)+1 t3=t2*clebgor(l-1,1,l,m-mu,mu,m) i=npi+lm; i1=npi+lm1 do ir=iro,nr gzfmt(i1,j)=gzfmt(i1,j)+t3*(drmt(i)+dble(l+1)*ri(ir)*zfmt(i)) i=i+lmmaxo; i1=i1+lmmaxo end do end if end do end do end do !---------------------------------------------------! ! convert from spherical to Cartesian basis ! !---------------------------------------------------! ! note that the gradient transforms as a covariant vector, i.e. y -> -y i=0 do ir=1,nri do lm=1,lmmaxi i=i+1 z1=gzfmt(i,1) gzfmt(i,1)=c1*(z1-gzfmt(i,2)) z1=c1*(z1+gzfmt(i,2)) gzfmt(i,2)=cmplx(aimag(z1),-dble(z1),8) end do end do do ir=iro,nr do lm=1,lmmaxo i=i+1 z1=gzfmt(i,1) gzfmt(i,1)=c1*(z1-gzfmt(i,2)) z1=c1*(z1+gzfmt(i,2)) gzfmt(i,2)=cmplx(aimag(z1),-dble(z1),8) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/eveqnfv.f900000644000000000000000000000013214061636517014716 xustar0030 mtime=1623670095.174102252 30 atime=1623670093.922103414 30 ctime=1623670095.174102252 elk-7.2.42/src/eveqnfv.f900000644002504400250440000000463014061636517016756 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: eveqnfv ! !INTERFACE: subroutine eveqnfv(nmatp,ngp,igpig,vpc,vgpc,apwalm,evalfv,evecfv) ! !USES: use modmain use modomp ! !INPUT/OUTPUT PARAMETERS: ! nmatp : order of overlap and Hamiltonian matrices (in,integer) ! ngp : number of G+p-vectors (in,integer) ! igpig : index from G+p-vectors to G-vectors (in,integer(ngkmax)) ! vpc : p-vector in Cartesian coordinates (in,real(3)) ! vgpc : G+p-vectors in Cartesian coordinates (in,real(3,ngkmax)) ! apwalm : APW matching coefficients ! (in,complex(ngkmax,apwordmax,lmmaxapw,natmtot)) ! evalfv : first-variational eigenvalues (out,real(nstfv)) ! evecfv : first-variational eigenvectors (out,complex(nmatmax,nstfv)) ! !DESCRIPTION: ! Solves the eigenvalue equation, ! $$ (H-\epsilon O)b=0, $$ ! for the all the first-variational states of the input $p$-point. ! ! !REVISION HISTORY: ! Created March 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nmatp,ngp,igpig(ngkmax) real(8), intent(in) :: vpc(3),vgpc(3,ngkmax) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot) real(8), intent(out) :: evalfv(nstfv) complex(8), intent(out) :: evecfv(nmatmax,nstfv) ! local variables integer nthd real(8) ts0,ts1 ! allocatable arrays complex(8), allocatable :: h(:,:),o(:,:) !-----------------------------------------------! ! Hamiltonian and overlap matrix set up ! !-----------------------------------------------! call timesec(ts0) allocate(h(nmatp,nmatp),o(nmatp,nmatp)) call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP SECTION ! Hamiltonian call hmlfv(nmatp,ngp,igpig,vgpc,apwalm,h) !$OMP SECTION ! overlap call olpfv(nmatp,ngp,igpig,apwalm,o) !$OMP END PARALLEL SECTIONS call freethd(nthd) call timesec(ts1) !$OMP ATOMIC timemat=timemat+ts1-ts0 !---------------------------------------! ! solve the eigenvalue equation ! !---------------------------------------! if (tefvr) then ! system has inversion symmetry: use real symmetric matrix eigen solver call eveqnfvr(nmatp,ngp,vpc,h,o,evalfv,evecfv) else ! no inversion symmetry: use complex Hermitian matrix eigen solver call eveqnfvz(nmatp,h,o,evalfv,evecfv) end if deallocate(h,o) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/symdmat.f900000644000000000000000000000013014061636517014720 xustar0029 mtime=1623670095.17510225 30 atime=1623670093.924103412 29 ctime=1623670095.17510225 elk-7.2.42/src/symdmat.f900000644002504400250440000000357714061636517016773 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine symdmat(lmax,ld,dmat) use modmain implicit none ! arguments integer, intent(in) :: lmax integer, intent(in) :: ld complex(8), intent(inout) :: dmat(ld,nspinor,ld,nspinor,natmtot) ! local variables integer is,ia,ja,ias,jas integer isym,lspl,lspn,lmmax real(8) t1 ! automatic arrays logical done(natmmax) ! allocatable arrays complex(8), allocatable :: dm(:,:,:,:,:) lmmax=(lmax+1)**2 ! allocate local arrays allocate(dm(ld,nspinor,ld,nspinor,natmmax)) t1=1.d0/dble(nsymcrys) do is=1,nspecies ! make copy of the density matrices do ia=1,natoms(is) ias=idxas(ia,is) dm(1:lmmax,:,1:lmmax,:,ia)=dmat(1:lmmax,:,1:lmmax,:,ias) end do done(:)=.false. do ia=1,natoms(is) if (done(ia)) cycle ias=idxas(ia,is) dmat(:,:,:,:,ias)=0.d0 do isym=1,nsymcrys lspl=lsplsymc(isym) lspn=lspnsymc(isym) ! equivalent atom index (symmetry rotates atom ja into atom ia) ja=ieqatom(ia,is,isym) call rotdmat(symlatc(:,:,lspl),symlatc(:,:,lspn),lmax,nspinor,ld, & dm(:,:,:,:,ja),dmat(:,:,:,:,ias)) ! end loop over crystal symmetries end do ! normalise dmat(:,:,:,:,ias)=t1*dmat(:,:,:,:,ias) done(ia)=.true. ! rotate into equivalent atoms do isym=1,nsymcrys ja=ieqatom(ia,is,isym) if (.not.done(ja)) then jas=idxas(ja,is) ! inverse symmetry (which rotates atom ia into atom ja) lspl=isymlat(lsplsymc(isym)) lspn=isymlat(lspnsymc(isym)) dmat(:,:,:,:,jas)=0.d0 call rotdmat(symlatc(:,:,lspl),symlatc(:,:,lspn),lmax,nspinor,ld, & dmat(:,:,:,:,ias),dmat(:,:,:,:,jas)) done(ja)=.true. end if end do ! end loop over atoms and species end do end do deallocate(dm) end subroutine elk-7.2.42/src/PaxHeaders.21776/z2mm.f900000644000000000000000000000013114061636517014130 xustar0030 mtime=1623670095.177102249 29 atime=1623670093.92610341 30 ctime=1623670095.177102249 elk-7.2.42/src/z2mm.f900000644002504400250440000000155314061636517016172 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: z2mm ! !INTERFACE: pure subroutine z2mm(a,b,c) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix 1 (in,complex(2,2)) ! b : input matrix 2 (in,complex(2,2)) ! c : output matrix (out,complex(2,2)) ! !DESCRIPTION: ! Multiplies two complex $2\times 2$ matrices. Note that the output matrix ! cannot be one of the input matrices. ! ! !REVISION HISTORY: ! Created October 2007 (JKD) !EOP !BOC implicit none ! arguments complex(8), intent(in) :: a(2,2),b(2,2) complex(8), intent(out) :: c(2,2) c(1,1)=a(1,1)*b(1,1)+a(1,2)*b(2,1) c(2,1)=a(2,1)*b(1,1)+a(2,2)*b(2,1) c(1,2)=a(1,1)*b(1,2)+a(1,2)*b(2,2) c(2,2)=a(2,1)*b(1,2)+a(2,2)*b(2,2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/z2mctm.f900000644000000000000000000000013214061636517014460 xustar0030 mtime=1623670095.178102248 30 atime=1623670093.927103409 30 ctime=1623670095.178102248 elk-7.2.42/src/z2mctm.f900000644002504400250440000000171514061636517016521 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: z2mctm ! !INTERFACE: pure subroutine z2mctm(a,b,c) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix 1 (in,complex(2,2)) ! b : input matrix 2 (in,complex(2,2)) ! c : output matrix (out,complex(2,2)) ! !DESCRIPTION: ! Multiplies the conjugate transpose of one complex $2\times 2$ matrix with ! another. Note that the output matrix cannot be one of the input matrices. ! ! !REVISION HISTORY: ! Created October 2007 (JKD) !EOP !BOC implicit none ! arguments complex(8), intent(in) :: a(2,2),b(2,2) complex(8), intent(out) :: c(2,2) c(1,1)=conjg(a(1,1))*b(1,1)+conjg(a(2,1))*b(2,1) c(2,1)=conjg(a(1,2))*b(1,1)+conjg(a(2,2))*b(2,1) c(1,2)=conjg(a(1,1))*b(1,2)+conjg(a(2,1))*b(2,2) c(2,2)=conjg(a(1,2))*b(1,2)+conjg(a(2,2))*b(2,2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/z2mmct.f900000644000000000000000000000013214061636517014460 xustar0030 mtime=1623670095.179102247 30 atime=1623670093.929103407 30 ctime=1623670095.179102247 elk-7.2.42/src/z2mmct.f900000644002504400250440000000170314061636517016516 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: z2mmct ! !INTERFACE: pure subroutine z2mmct(a,b,c) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix 1 (in,complex(2,2)) ! b : input matrix 2 (in,complex(2,2)) ! c : output matrix (out,complex(2,2)) ! !DESCRIPTION: ! Multiplies a $2\times 2$ matrix with the conjugate transpose of another. ! Note that the output matrix cannot be one of the input matrices. ! ! !REVISION HISTORY: ! Created October 2007 (JKD) !EOP !BOC implicit none ! arguments complex(8), intent(in) :: a(2,2),b(2,2) complex(8), intent(out) :: c(2,2) c(1,1)=a(1,1)*conjg(b(1,1))+a(1,2)*conjg(b(1,2)) c(2,1)=a(2,1)*conjg(b(1,1))+a(2,2)*conjg(b(1,2)) c(1,2)=a(1,1)*conjg(b(2,1))+a(1,2)*conjg(b(2,2)) c(2,2)=a(2,1)*conjg(b(2,1))+a(2,2)*conjg(b(2,2)) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/axangsu2.f900000644000000000000000000000013214061636517014774 xustar0030 mtime=1623670095.181102245 30 atime=1623670093.931103405 30 ctime=1623670095.181102245 elk-7.2.42/src/axangsu2.f900000644002504400250440000000246214061636517017035 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: axangsu2 subroutine axangsu2(v,th,su2) ! !INPUT/OUTPUT PARAMETERS: ! v : rotation axis vector (in,real(3)) ! th : rotation angle (in,real) ! su2 : SU(2) representation of rotation (out,complex(2,2)) ! !DESCRIPTION: ! Finds the complex ${\rm SU}(2)$ representation of a rotation defined by an ! axis vector $\hat{\bf v}$ and angle $\theta$. The spinor rotation matrix is ! given explicitly by ! $$ R^{1/2}(\hat{\bf v},\theta)=I\cos\frac{\theta}{2} ! -i(\hat{\bf v}\cdot\vec{\sigma})\sin\frac{\theta}{2}. $$ ! ! !REVISION HISTORY: ! Created August 2007 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: v(3),th complex(8), intent(out) :: su2(2,2) ! local variables real(8) x,y,z,cs,sn,t1 x=v(1); y=v(2); z=v(3) t1=sqrt(x**2+y**2+z**2) if (t1.lt.1.d-8) then write(*,*) write(*,'("Error(axangsu2): zero length axis vector")') write(*,*) stop end if ! normalise the vector t1=1.d0/t1 x=x*t1; y=y*t1; z=z*t1 cs=cos(0.5d0*th) sn=sin(0.5d0*th) su2(1,1)=cmplx(cs,-z*sn,8) su2(2,1)=cmplx(y*sn,-x*sn,8) su2(1,2)=cmplx(-y*sn,-x*sn,8) su2(2,2)=cmplx(cs,z*sn,8) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gradzvcln.f900000644000000000000000000000013214061636517015236 xustar0030 mtime=1623670095.182102244 30 atime=1623670093.933103403 30 ctime=1623670095.182102244 elk-7.2.42/src/gradzvcln.f900000644002504400250440000000140314061636517017271 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gradzvcln(is,gzfmt) use modmain implicit none ! arguments integer, intent(in) :: is complex(8), intent(out) :: gzfmt(npmtmax,3) ! local variables integer nr,nri,ir,i ! automatic arrays complex(8) zvclmt(npmtmax) nr=nrmt(is) nri=nrmti(is) ! convert nuclear Coulomb potential to complex spherical harmonics expansion zvclmt(1:npmt(is))=0.d0 i=1 do ir=1,nri zvclmt(i)=vcln(ir,is) i=i+lmmaxi end do do ir=nri+1,nr zvclmt(i)=vcln(ir,is) i=i+lmmaxo end do ! compute the gradient of the potential call gradzfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),zvclmt,npmtmax,gzfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/gentpmae.f900000644000000000000000000000013214061636517015044 xustar0030 mtime=1623670095.184102242 30 atime=1623670093.934103402 30 ctime=1623670095.184102242 elk-7.2.42/src/gentpmae.f900000644002504400250440000000355314061636517017107 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gentpmae use modmain implicit none ! local variables integer na,n,i1,i2,i3,i integer isym,lspl real(8) v1(3),v2(3),t1 ! allocatable arrays real(8), allocatable :: vp(:,:) if (allocated(tpmae)) deallocate(tpmae) select case(npmae0) case(4:) ! distribute points evenly on a sphere npmae=npmae0 allocate(tpmae(2,npmae)) call sphcover(npmae,tpmae) case(-4:-1) ! use symmetry reduced cardinal directions na=abs(npmae0) n=(2*na+1)**3 allocate(vp(3,n)) npmae=0 do i1=-na,na v1(1)=dble(i1) do i2=-na,na v1(2)=dble(i2) do i3=-na,na v1(3)=dble(i3) if ((i1.eq.0).and.(i2.eq.0).and.(i3.eq.0)) cycle do isym=1,nsymcrys lspl=lsplsymc(isym) v2(:)=symlat(:,1,lspl)*v1(1) & +symlat(:,2,lspl)*v1(2) & +symlat(:,3,lspl)*v1(3) do i=1,npmae t1=abs(vp(1,i)-v2(1))+abs(vp(2,i)-v2(2))+abs(vp(3,i)-v2(3)) if (t1.lt.epslat) goto 10 end do end do npmae=npmae+1 vp(:,npmae)=v1(:) 10 continue end do end do end do ! convert vectors to spherical coordinates allocate(tpmae(2,npmae)) do i=1,npmae call sphcrd(vp(:,i),t1,tpmae(:,i)) end do deallocate(vp) case(2) ! use x- and z-directions npmae=2 allocate(tpmae(2,npmae)) tpmae(1,1)=pi/2.d0 tpmae(2,1)=0.d0 tpmae(1,2)=0.d0 tpmae(2,2)=0.d0 case(3) ! use x-, y- and z-directions npmae=3 allocate(tpmae(2,npmae)) tpmae(1,1)=pi/2.d0 tpmae(2,1)=0.d0 tpmae(1,2)=pi/2.d0 tpmae(2,2)=pi/2.d0 tpmae(1,3)=0.d0 tpmae(2,3)=0.d0 case default write(*,*) write(*,'("Error(gentpmae): invalid npmae : ",I8)') npmae0 write(*,*) stop end select end subroutine elk-7.2.42/src/PaxHeaders.21776/zfcmtwr.f900000644000000000000000000000013214061636517014740 xustar0030 mtime=1623670095.185102241 30 atime=1623670093.936103401 30 ctime=1623670095.185102241 elk-7.2.42/src/zfcmtwr.f900000644002504400250440000000134714061636517017002 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine zfcmtwr(nr,nri,wr,zfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: wr(nr) complex(8), intent(inout) :: zfmt(*) ! local variables integer n,ir,i real(8) t1 i=1 if (lmaxi.eq.1) then do ir=1,nri zfmt(i:i+3)=(pi*wr(ir))*zfmt(i:i+3) i=i+4 end do else t1=fourpi/dble(lmmaxi) n=lmmaxi-1 do ir=1,nri zfmt(i:i+n)=(t1*wr(ir))*zfmt(i:i+n) i=i+lmmaxi end do end if t1=fourpi/dble(lmmaxo) n=lmmaxo-1 do ir=nri+1,nr zfmt(i:i+n)=(t1*wr(ir))*zfmt(i:i+n) i=i+lmmaxo end do end subroutine elk-7.2.42/src/PaxHeaders.21776/projsbf.f900000644000000000000000000000013014061636517014707 xustar0029 mtime=1623670095.18610224 30 atime=1623670093.938103399 29 ctime=1623670095.18610224 elk-7.2.42/src/projsbf.f900000644002504400250440000000372014061636517016750 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine projsbf use modmain implicit none ! local variables integer idm,is,ias,np real(8) t1 ! allocatable arrays real(8), allocatable :: rfmt(:,:),rfir(:) real(8), allocatable :: grfmt(:,:,:),grfir(:,:) complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) allocate(rfmt(npmtmax,natmtot),rfir(ngtot)) allocate(grfmt(npmtmax,natmtot,3),grfir(ngtot,3)) allocate(zrhomt(npmtmax,natmtot),zrhoir(ngtot)) allocate(zvclmt(npmtmax,natmtot),zvclir(ngtot)) ! compute the divergence of B_xc rfmt(:,:)=0.d0 rfir(:)=0.d0 do idm=1,3 call gradrf(bxcmt(:,:,idm),bxcir(:,idm),grfmt,grfir) do ias=1,natmtot is=idxis(ias) np=npmt(is) rfmt(1:np,ias)=rfmt(1:np,ias)+grfmt(1:np,ias,idm) end do rfir(:)=rfir(:)+grfir(:,idm) end do ! convert real muffin-tin divergence to complex spherical harmonic expansion do ias=1,natmtot is=idxis(ias) call rtozfmt(nrmt(is),nrmti(is),rfmt(:,ias),zrhomt(:,ias)) end do ! store real interstitial divergence in a complex array zrhoir(:)=rfir(:) ! solve the complex Poisson's equation call genzvclmt(nrmt,nrmti,nrmtmax,rlmt,wprmt,npmtmax,zrhomt,zvclmt) call zpotcoul(nrmt,nrmti,npmt,npmti,nrmtmax,rlmt,ngridg,igfft,ngvec,gc,gclg, & ngvec,jlgrmt,ylmg,sfacg,zrhoir,npmtmax,zvclmt,zvclir) ! convert complex muffin-tin potential to real spherical harmonic expansion do ias=1,natmtot is=idxis(ias) call ztorfmt(nrmt(is),nrmti(is),zvclmt(:,ias),rfmt(:,ias)) end do ! store complex interstitial potential in real array rfir(:)=dble(zvclir(:)) ! compute the gradient call gradrf(rfmt,rfir,grfmt,grfir) ! add gradient over 4*pi to existing B_xc t1=1.d0/fourpi bxcmt(:,:,:)=bxcmt(:,:,:)+t1*grfmt(:,:,:) bxcir(:,:)=bxcir(:,:)+t1*grfir(:,:) deallocate(rfmt,rfir,grfmt,grfir) deallocate(zrhomt,zrhoir,zvclmt,zvclir) end subroutine elk-7.2.42/src/PaxHeaders.21776/splinew.f900000644000000000000000000000013214061636517014725 xustar0030 mtime=1623670095.188102238 30 atime=1623670093.940103397 30 ctime=1623670095.188102238 elk-7.2.42/src/splinew.f900000644002504400250440000000265714061636517016774 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine splinew(n,wc,f,cf) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wc(4,3,n),f(n) real(8), intent(out) :: cf(3,n) ! local variables integer i real(8) f1,f2,f3,f4 f1=f(1); f2=f(2); f3=f(3); f4=f(4) cf(1,1)=wc(1,1,1)*f1+wc(2,1,1)*f2+wc(3,1,1)*f3+wc(4,1,1)*f4 cf(2,1)=wc(1,2,1)*f1+wc(2,2,1)*f2+wc(3,2,1)*f3+wc(4,2,1)*f4 cf(3,1)=wc(1,3,1)*f1+wc(2,3,1)*f2+wc(3,3,1)*f3+wc(4,3,1)*f4 cf(1,2)=wc(1,1,2)*f1+wc(2,1,2)*f2+wc(3,1,2)*f3+wc(4,1,2)*f4 cf(2,2)=wc(1,2,2)*f1+wc(2,2,2)*f2+wc(3,2,2)*f3+wc(4,2,2)*f4 cf(3,2)=wc(1,3,2)*f1+wc(2,3,2)*f2+wc(3,3,2)*f3+wc(4,3,2)*f4 !$OMP SIMD LASTPRIVATE(f1,f2,f3,f4) do i=3,n-2 f1=f(i-1); f2=f(i); f3=f(i+1); f4=f(i+2) cf(1,i)=wc(1,1,i)*f1+wc(2,1,i)*f2+wc(3,1,i)*f3+wc(4,1,i)*f4 cf(2,i)=wc(1,2,i)*f1+wc(2,2,i)*f2+wc(3,2,i)*f3+wc(4,2,i)*f4 cf(3,i)=wc(1,3,i)*f1+wc(2,3,i)*f2+wc(3,3,i)*f3+wc(4,3,i)*f4 end do i=n-1 cf(1,i)=wc(1,1,i)*f1+wc(2,1,i)*f2+wc(3,1,i)*f3+wc(4,1,i)*f4 cf(2,i)=wc(1,2,i)*f1+wc(2,2,i)*f2+wc(3,2,i)*f3+wc(4,2,i)*f4 cf(3,i)=wc(1,3,i)*f1+wc(2,3,i)*f2+wc(3,3,i)*f3+wc(4,3,i)*f4 cf(1,n)=wc(1,1,n)*f1+wc(2,1,n)*f2+wc(3,1,n)*f3+wc(4,1,n)*f4 cf(2,n)=wc(1,2,n)*f1+wc(2,2,n)*f2+wc(3,2,n)*f3+wc(4,2,n)*f4 cf(3,n)=wc(1,3,n)*f1+wc(2,3,n)*f2+wc(3,3,n)*f3+wc(4,3,n)*f4 end subroutine elk-7.2.42/src/PaxHeaders.21776/gradzf.f900000644000000000000000000000013214061636517014521 xustar0030 mtime=1623670095.189102238 30 atime=1623670093.941103396 30 ctime=1623670095.189102238 elk-7.2.42/src/gradzf.f900000644002504400250440000000250014061636517016553 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gradzf(zfmt,zfir,gzfmt,gzfir) use modmain use modomp implicit none ! arguments complex(8), intent(in) :: zfmt(npmtmax,natmtot),zfir(ngtot) complex(8), intent(out) :: gzfmt(npmtmax,natmtot,3),gzfir(ngtot,3) ! local variables integer is,ias,ld,i integer ig,ifg,nthd complex(8) z1 ! allocatable arrays complex(8), allocatable :: zfft(:) ! muffin-tin gradient ld=npmtmax*natmtot call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) call gradzfmt(nrmt(is),nrmti(is),rlmt(:,-1,is),wcrmt(:,:,is),zfmt(:,ias),ld, & gzfmt(1,ias,1)) end do !$OMP END PARALLEL DO call freethd(nthd) ! interstitial gradient allocate(zfft(ngtot)) call zcopy(ngtot,zfir,1,zfft,1) call zfftifc(3,ngridg,-1,zfft) call holdthd(3,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ig,ifg,z1) & !$OMP NUM_THREADS(nthd) do i=1,3 gzfir(:,i)=0.d0 do ig=1,ngvec ifg=igfft(ig) z1=zfft(ifg) gzfir(ifg,i)=vgc(i,ig)*cmplx(-aimag(z1),dble(z1),8) end do call zfftifc(3,ngridg,1,gzfir(:,i)) end do !$OMP END PARALLEL DO call freethd(nthd) deallocate(zfft) end subroutine elk-7.2.42/src/PaxHeaders.21776/mixerifc.f900000644000000000000000000000013214061636517015052 xustar0030 mtime=1623670095.191102236 30 atime=1623670093.943103394 30 ctime=1623670095.191102236 elk-7.2.42/src/mixerifc.f900000644002504400250440000000306014061636517017106 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine mixerifc(mtype,n,v,dv,nwork,work) use modmain implicit none ! arguments integer, intent(in) :: mtype,n real(8), intent(inout) :: v(n) real(8), intent(out) :: dv integer, intent(inout) :: nwork real(8), intent(inout) :: work(*) ! local variables select case(mtype) case(0) ! linear mixing if (nwork.le.0) then nwork=n return end if call mixlinear(iscl,amixpm(1),n,v,work,dv) case(1) ! adaptive linear mixing if (nwork.le.0) then nwork=3*n return end if call mixadapt(iscl,amixpm(1),amixpm(2),n,v,work,work(n+1),work(2*n+1),dv) case(3) ! Broyden mixing if (nwork.le.0) then nwork=(4+2*mixsdb)*n+mixsdb**2 return end if call mixbroyden(iscl,n,mixsdb,broydpm(1),broydpm(2),v,work,work(2*n+1), & work(4*n+1),work((4+mixsdb)*n+1),work((4+2*mixsdb)*n+1),dv) case default write(*,*) write(*,'("Error(mixerifc): mtype not defined : ",I8)') mtype write(*,*) stop end select end subroutine subroutine getmixdata(mtype,mixdescr) implicit none ! arguments integer, intent(in) :: mtype character(*), intent(out) :: mixdescr select case(mtype) case(0) mixdescr='Linear mixing' case(1) mixdescr='Adaptive linear mixing' case(3) mixdescr='Broyden mixing, J. Phys. A: Math. Gen. 17, L317 (1984)' case default write(*,*) write(*,'("Error(getmixdata): mixtype not defined : ",I8)') mtype write(*,*) stop end select end subroutine elk-7.2.42/src/PaxHeaders.21776/genvsig.f900000644000000000000000000000013214061636517014706 xustar0030 mtime=1623670095.192102235 30 atime=1623670093.945103392 30 ctime=1623670095.192102235 elk-7.2.42/src/genvsig.f900000644002504400250440000000164514061636517016751 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genvsig ! !INTERFACE: subroutine genvsig ! !USES: use modmain ! !DESCRIPTION: ! Generates the Fourier transform of the Kohn-Sham effective potential in the ! interstitial region. The potential is first multiplied by the characteristic ! function which zeros it in the muffin-tins. See routine {\tt gencfun}. ! ! !REVISION HISTORY: ! Created January 2004 (JKD) !EOP !BOC implicit none ! allocatable arrays complex(8), allocatable :: zfft(:) allocate(zfft(ngtot)) ! multiply potential by characteristic function in real-space zfft(:)=vsir(:)*cfunir(:) ! Fourier transform to G-space call zfftifc(3,ngridg,-1,zfft) ! store in global array vsig(1:ngvec)=zfft(igfft(1:ngvec)) deallocate(zfft) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/timesec.f900000644000000000000000000000013214061636517014675 xustar0030 mtime=1623670095.193102234 30 atime=1623670093.946103391 30 ctime=1623670095.193102234 elk-7.2.42/src/timesec.f900000644002504400250440000000122214061636517016727 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: timesec ! !INTERFACE: subroutine timesec(ts) ! !INPUT/OUTPUT PARAMETERS: ! ts : system time in seconds (out,real) ! !DESCRIPTION: ! Outputs the system time in seconds. ! ! !REVISION HISTORY: ! Created September 2010 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(out) :: ts ! local variables integer count,count_rate call system_clock(count=count,count_rate=count_rate) ts=dble(count)/dble(count_rate) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/zfmtftoc.f900000644000000000000000000000013214061636517015100 xustar0030 mtime=1623670095.195102232 30 atime=1623670093.948103389 30 ctime=1623670095.195102232 elk-7.2.42/src/zfmtftoc.f900000644002504400250440000000123514061636517017136 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine zfmtftoc(nrc,nrci,zfmt,zfcmt) use modmain implicit none ! arguments integer, intent(in) :: nrc,nrci complex(8), intent(in) :: zfmt(*) complex(8), intent(out) :: zfcmt(*) ! local variables integer irc,i,j,m,n i=1 j=1 m=lmmaxi*lradstp n=lmmaxi-1 do irc=1,nrci zfcmt(i:i+n)=zfmt(j:j+n) i=i+lmmaxi j=j+m end do j=j+(lradstp-1)*(lmmaxo-lmmaxi) m=lmmaxo*lradstp n=lmmaxo-1 do irc=nrci+1,nrc zfcmt(i:i+n)=zfmt(j:j+n) i=i+lmmaxo j=j+m end do end subroutine elk-7.2.42/src/PaxHeaders.21776/ztorfmt.f900000644000000000000000000000013214061636517014751 xustar0030 mtime=1623670095.196102231 30 atime=1623670093.950103388 30 ctime=1623670095.196102231 elk-7.2.42/src/ztorfmt.f900000644002504400250440000000423314061636517017010 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine ztorfmt(nr,nri,zfmt,rfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri complex(8), intent(in) :: zfmt(*) real(8), intent(out) :: rfmt(*) ! local variables integer i call ztorflmn(lmaxi,nri,lmmaxi,zfmt,rfmt) i=lmmaxi*nri+1 call ztorflmn(lmaxo,nr-nri,lmmaxo,zfmt(i),rfmt(i)) return contains !BOP ! !ROUTINE: ztorflmn ! !INTERFACE: pure subroutine ztorflmn(lmax,n,ld,zflm,rflm) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum angular momentum (in,integer) ! n : number of functions to convert (in,integer) ! ld : leading dimension (in,integer) ! zflm : coefficients of complex spherical harmonic expansion ! (in,complex(ld,n)) ! rflm : coefficients of real spherical harmonic expansion (out,real(ld,n)) ! !DESCRIPTION: ! Converts a real function, $z_{lm}$, expanded in terms of complex spherical ! harmonics into a real spherical harmonic expansion, $r_{lm}$: ! $$ r_{lm}=\begin{cases}\frac{1}{\sqrt{2}}\Re(z_{lm}+(-1)^m z_{l-m}) & m>0 \\ ! \frac{1}{\sqrt{2}}\Im(-z_{lm}+(-1)^m z_{l-m}) & m<0 \\ ! \Re(z_{lm}) & m=0 \end{cases}\;. $$ ! See routine {\tt genrlm}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: lmax,n,ld complex(8), intent(in) :: zflm(ld,n) real(8), intent(out) :: rflm(ld,n) ! local variables integer l,m,lm1,lm2 ! real constant 1/sqrt(2) real(8), parameter :: c1=0.7071067811865475244d0 lm1=0 do l=0,lmax lm2=lm1+2*(l+1) do m=-l,-1 lm1=lm1+1 lm2=lm2-1 if (mod(m,2).ne.0) then rflm(lm1,:)=-c1*(aimag(zflm(lm1,:))+aimag(zflm(lm2,:))) else rflm(lm1,:)=c1*(aimag(zflm(lm2,:))-aimag(zflm(lm1,:))) end if end do lm1=lm1+1 lm2=lm2-1 rflm(lm1,:)=dble(zflm(lm1,:)) do m=1,l lm1=lm1+1 lm2=lm2-1 if (mod(m,2).ne.0) then rflm(lm1,:)=c1*(dble(zflm(lm1,:))-dble(zflm(lm2,:))) else rflm(lm1,:)=c1*(dble(zflm(lm1,:))+dble(zflm(lm2,:))) end if end do end do end subroutine !EOC end subroutine elk-7.2.42/src/PaxHeaders.21776/zfmtctof.f900000644000000000000000000000013214061636517015100 xustar0030 mtime=1623670095.198102229 30 atime=1623670093.951103387 30 ctime=1623670095.198102229 elk-7.2.42/src/zfmtctof.f900000644002504400250440000000434714061636517017145 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine zfmtctof(zfmt) use modmain use modomp implicit none ! arguments complex(8), intent(inout) :: zfmt(npmtmax,natmtot) ! local variables integer is,ias,lm integer nr,nri,nro integer iro,ir,npi integer nrc,nrci,nrco integer irco,irc,npci integer i,nthd ! automatic arrays real(8) fi1(nrcmtmax),fi2(nrcmtmax) real(8) fo1(nrmtmax),fo2(nrmtmax) complex(8) zfmt1(npcmtmax) if (lradstp.eq.1) return call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(zfmt1,fi1,fi2,fo1,fo2) & !$OMP PRIVATE(is,nr,nri,nro,iro,npi) & !$OMP PRIVATE(nrc,nrci,nrco,irco,npci) & !$OMP PRIVATE(lm,i,irc,ir) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) nro=nr-nri iro=nri+1 npi=npmti(is) nrc=nrcmt(is) nrci=nrcmti(is) nrco=nrc-nrci irco=nrci+1 npci=npcmti(is) ! copy the input function call zcopy(npcmt(is),zfmt(:,ias),1,zfmt1,1) ! interpolate up to lmaxi over entire muffin-tin do lm=1,lmmaxi i=lm do irc=1,nrci fi1(irc)=dble(zfmt1(i)); fi2(irc)=aimag(zfmt1(i)) i=i+lmmaxi end do do irc=irco,nrc fi1(irc)=dble(zfmt1(i)); fi2(irc)=aimag(zfmt1(i)) i=i+lmmaxo end do call rfinterp(nrc,rcmt(:,is),wcrcmt(:,:,is),fi1,nr,rlmt(:,1,is),fo1) call rfinterp(nrc,rcmt(:,is),wcrcmt(:,:,is),fi2,nr,rlmt(:,1,is),fo2) i=lm do ir=1,nri zfmt(i,ias)=cmplx(fo1(ir),fo2(ir),8) i=i+lmmaxi end do do ir=iro,nr zfmt(i,ias)=cmplx(fo1(ir),fo2(ir),8) i=i+lmmaxo end do end do ! interpolate up to lmaxo on outer part of muffin-tin do lm=lmmaxi+1,lmmaxo i=npci+lm do irc=irco,nrc fi1(irc)=dble(zfmt1(i)); fi2(irc)=aimag(zfmt1(i)) i=i+lmmaxo end do call rfinterp(nrco,rcmt(irco,is),wcrcmt(:,irco,is),fi1(irco),nro, & rsp(iro,is),fo1(iro)) call rfinterp(nrco,rcmt(irco,is),wcrcmt(:,irco,is),fi2(irco),nro, & rsp(iro,is),fo2(iro)) i=npi+lm do ir=iro,nr zfmt(i,ias)=cmplx(fo1(ir),fo2(ir),8) i=i+lmmaxo end do end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqnfvz.f900000644000000000000000000000013214061636517015110 xustar0030 mtime=1623670095.199102228 30 atime=1623670093.953103385 30 ctime=1623670095.199102228 elk-7.2.42/src/eveqnfvz.f900000644002504400250440000000304514061636517017147 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine eveqnfvz(nmatp,h,o,evalfv,evecfv) use modmain use modomp implicit none ! arguments integer, intent(in) :: nmatp complex(8), intent(in) :: h(*),o(*) real(8), intent(out) :: evalfv(nstfv) complex(8), intent(out) :: evecfv(nmatmax,nstfv) ! local variables integer lwork,info integer m,i,nthd,nts real(8) vl,vu real(8) ts0,ts1 ! automatic arrays integer iwork(5*nmatp),ifail(nmatp) ! allocatable arrays real(8), allocatable :: w(:),rwork(:) complex(8), allocatable :: work(:) call timesec(ts0) allocate(w(nmatp),rwork(7*nmatp)) lwork=2*nmatp allocate(work(lwork)) ! enable MKL parallelism call holdthd(maxthdmkl,nthd) nts=mkl_set_num_threads_local(nthd) ! diagonalise the matrix call zhegvx(1,'V','I','U',nmatp,h,nmatp,o,nmatp,vl,vu,1,nstfv,evaltol,m,w, & evecfv,nmatmax,work,lwork,rwork,iwork,ifail,info) nts=mkl_set_num_threads_local(0) call freethd(nthd) if (info.ne.0) then write(*,*) write(*,'("Error(eveqnfvz): diagonalisation failed")') write(*,'(" ZHEGVX returned INFO = ",I8)') info if (info.gt.nmatp) then i=info-nmatp write(*,'(" The leading minor of the overlap matrix of order ",I8)') i write(*,'(" is not positive definite")') write(*,'(" Order of overlap matrix : ",I8)') nmatp end if write(*,*) stop end if evalfv(1:nstfv)=w(1:nstfv) deallocate(w,rwork,work) call timesec(ts1) !$OMP ATOMIC timefv=timefv+ts1-ts0 end subroutine elk-7.2.42/src/PaxHeaders.21776/energynn.f900000644000000000000000000000013214061636517015071 xustar0030 mtime=1623670095.200102227 30 atime=1623670093.955103383 30 ctime=1623670095.200102227 elk-7.2.42/src/energynn.f900000644002504400250440000000225714061636517017134 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine energynn use modmain implicit none ! local variables integer is,ias,i integer nr,nri,ir real(8) t1 ! allocatable arrays complex(8), allocatable :: zvclmt(:,:),zvclir(:),zrhoir(:) allocate(zvclmt(npmtmax,natmtot)) ! generate the nuclear monopole potentials do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) zvclmt(1:npmt(is),ias)=0.d0 i=1 do ir=1,nri zvclmt(i,ias)=vcln(ir,is) i=i+lmmaxi end do do ir=nri+1,nr zvclmt(i,ias)=vcln(ir,is) i=i+lmmaxo end do end do allocate(zrhoir(ngtot),zvclir(ngtot)) ! set the interstitial density to zero zrhoir(:)=0.d0 ! solve the complex Poisson's equation call zpotcoul(nrmt,nrmti,npmt,npmti,nrmtmax,rlmt,ngridg,igfft,ngvec,gc,gclg, & ngvec,jlgrmt,ylmg,sfacg,zrhoir,npmtmax,zvclmt,zvclir) ! compute the nuclear-nuclear energy engynn=0.d0 do ias=1,natmtot is=idxis(ias) t1=(dble(zvclmt(1,ias))-vcln(1,is))*y00 engynn=engynn+spzn(is)*t1 end do engynn=0.5d0*engynn deallocate(zvclmt,zvclir,zrhoir) end subroutine elk-7.2.42/src/PaxHeaders.21776/gaunt.f900000644000000000000000000000013214061636517014362 xustar0030 mtime=1623670095.202102225 30 atime=1623670093.957103381 30 ctime=1623670095.202102225 elk-7.2.42/src/gaunt.f900000644002504400250440000000413014061636517016415 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: gaunt ! !INTERFACE: real(8) function gaunt(l1,l2,l3,m1,m2,m3) ! !INPUT/OUTPUT PARAMETERS: ! l1, l2, l3 : angular momentum quantum numbers (in,integer) ! m1, m2, m3 : magnetic quantum numbers (in,integer) ! !DESCRIPTION: ! Returns the Gaunt coefficient given by ! $$ \langle Y^{l_1}_{m_1}|Y^{l_2}_{m_2}|Y^{l_3}_{m_3} \rangle ! = (-1)^{m_1}\left[\frac{(2l_1+1)(2l_2+1)(2l_3+1)}{4\pi} \right] ! ^{\frac{1}{2}} ! \begin{pmatrix} l_1 & l_2 & l_3 \\ 0 & 0 & 0 \end{pmatrix} ! \begin{pmatrix} l_1 & l_2 & l_3 \\ -m_1 & m_2 & m_3 \end{pmatrix}. $$ ! Suitable for $l_i$ less than 50. ! ! !REVISION HISTORY: ! Created November 2002 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: l1,l2,l3 integer, intent(in) :: m1,m2,m3 ! local variables integer j,j1,j2,j3,jh real(8) t1 ! real constant 1/sqrt(4*pi) real(8), parameter :: c1=0.28209479177387814347d0 ! external functions real(8), external :: wigner3j,factnm,factr if ((l1.lt.0).or.(l2.lt.0).or.(l3.lt.0).or.(abs(m1).gt.l1).or.(abs(m2).gt.l2) & .or.(abs(m3).gt.l3)) then write(*,*) write(*,'("Error(gaunt): non-physical arguments :")') write(*,'("l1 = ",I8," l2 = ",I8," l3 = ",I8)') l1,l2,l3 write(*,'("m1 = ",I8," m2 = ",I8," m3 = ",I8)') m1,m2,m3 write(*,*) stop end if if ((l1.gt.50).or.(l2.gt.50).or.(l3.gt.50)) then write(*,*) write(*,'("Error(gaunt): angular momenta out of range : ",3I8)') l1,l2,l3 write(*,*) stop end if if (m1-m2-m3.ne.0) then gaunt=0.d0 return end if j1=l2-l1+l3 j2=l1-l2+l3 j3=l1+l2-l3 if ((j1.lt.0).or.(j2.lt.0).or.(j3.lt.0)) then gaunt=0.d0 return end if j=l1+l2+l3 if (mod(j,2).ne.0) then gaunt=0.d0 return end if jh=j/2 t1=sqrt(dble((2*l1+1)*(2*l2+1)*(2*l3+1))*factr(j1,j+1)*factnm(j2,1) & *factnm(j3,1)) t1=t1*factr(jh,jh-l1)/(factnm(jh-l2,1)*factnm(jh-l3,1)) gaunt=t1*c1*wigner3j(l1,l2,l3,-m1,m2,m3) if (mod(m1+jh,2).ne.0) gaunt=-gaunt end function !EOC elk-7.2.42/src/PaxHeaders.21776/potxcmt.f900000644000000000000000000000013114061636517014741 xustar0030 mtime=1623670095.203102225 29 atime=1623670093.95810338 30 ctime=1623670095.203102225 elk-7.2.42/src/potxcmt.f900000644002504400250440000002470114061636517017003 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potxcmt(tsh,ias,xctype_,rhomt_,magmt_,taumt_,exmt_,ecmt_,vxcmt_, & bxcmt_,wxcmt_) use modmain use modxcifc implicit none ! arguments logical, intent(in) :: tsh integer, intent(in) :: ias,xctype_(3) real(8), intent(in) :: rhomt_(npmtmax,natmtot),magmt_(npmtmax,natmtot,ndmag) real(8), intent(in) :: taumt_(npmtmax,natmtot,nspinor) real(8), intent(out) :: exmt_(npmtmax,natmtot),ecmt_(npmtmax,natmtot) real(8), intent(out) :: vxcmt_(npmtmax,natmtot),bxcmt_(npmtmax,natmtot,ndmag) real(8), intent(out) :: wxcmt_(npmtmax,natmtot) ! local variables integer ispn,idm,is integer nr,nri,n,i real(8) t0,t1,t2,t3,t4 ! allocatable arrays real(8), allocatable :: rho(:),rhoup(:),rhodn(:) real(8), allocatable :: gvrho(:,:),gvup(:,:),gvdn(:,:) real(8), allocatable :: grho(:),gup(:),gdn(:) real(8), allocatable :: g2rho(:),g2up(:),g2dn(:) real(8), allocatable :: g3rho(:),g3up(:),g3dn(:) real(8), allocatable :: grho2(:),gup2(:),gdn2(:),gupdn(:) real(8), allocatable :: ex(:),ec(:),vxc(:) real(8), allocatable :: vx(:),vxup(:),vxdn(:) real(8), allocatable :: vc(:),vcup(:),vcdn(:) real(8), allocatable :: mag(:,:),bxc(:,:),tau(:,:) real(8), allocatable :: dxdgr2(:),dxdgu2(:),dxdgd2(:),dxdgud(:) real(8), allocatable :: dcdgr2(:),dcdgu2(:),dcdgd2(:),dcdgud(:) real(8), allocatable :: dxdg2r(:),dxdg2u(:),dxdg2d(:) real(8), allocatable :: dcdg2r(:),dcdg2u(:),dcdg2d(:) real(8), allocatable :: wx(:),wxup(:),wxdn(:) real(8), allocatable :: wc(:),wcup(:),wcdn(:) is=idxis(ias) n=npmt(is) ! allocate local arrays allocate(rho(n),ex(n),ec(n),vxc(n)) if ((xcgrad.eq.3).or.(xcgrad.eq.4)) allocate(tau(n,nspinor)) if (spinpol) then allocate(mag(n,3),bxc(n,3)) end if if (spinpol) then allocate(rhoup(n),rhodn(n)) allocate(vxup(n),vxdn(n),vcup(n),vcdn(n)) if (xcgrad.eq.1) then allocate(grho(n),gup(n),gdn(n)) allocate(g2up(n),g2dn(n)) allocate(g3rho(n),g3up(n),g3dn(n)) else if (xcgrad.eq.2) then allocate(g2up(n),g2dn(n)) allocate(gvup(n,3),gvdn(n,3)) allocate(gup2(n),gdn2(n),gupdn(n)) allocate(dxdgu2(n),dxdgd2(n),dxdgud(n)) allocate(dcdgu2(n),dcdgd2(n),dcdgud(n)) else if (xcgrad.eq.3) then allocate(g2up(n),g2dn(n)) allocate(gvup(n,3),gvdn(n,3)) allocate(gup2(n),gdn2(n),gupdn(n)) else if (xcgrad.eq.4) then allocate(g2up(n),g2dn(n)) allocate(gvup(n,3),gvdn(n,3)) allocate(gup2(n),gdn2(n),gupdn(n)) allocate(dxdgu2(n),dxdgd2(n),dxdgud(n)) allocate(dcdgu2(n),dcdgd2(n),dcdgud(n)) allocate(dxdg2u(n),dxdg2d(n)) allocate(dcdg2u(n),dcdg2d(n)) allocate(wxup(n),wxdn(n),wcup(n),wcdn(n)) end if else allocate(vx(n),vc(n)) if (xcgrad.eq.1) then allocate(grho(n),g2rho(n),g3rho(n)) else if (xcgrad.eq.2) then allocate(g2rho(n),gvrho(n,3),grho2(n)) allocate(dxdgr2(n),dcdgr2(n)) else if (xcgrad.eq.3) then allocate(g2rho(n),gvrho(n,3),grho2(n)) else if (xcgrad.eq.4) then allocate(g2rho(n),gvrho(n,3),grho2(n)) allocate(dxdgr2(n),dcdgr2(n)) allocate(dxdg2r(n),dcdg2r(n)) allocate(wx(n),wc(n)) end if end if nr=nrmt(is) nri=nrmti(is) if (tsh) then ! convert the density to spherical coordinates call rbsht(nr,nri,rhomt_(:,ias),rho) else rho(1:n)=rhomt_(1:n,ias) end if ! convert tau to spherical coordinates if required if ((xcgrad.eq.3).or.(xcgrad.eq.4)) then do ispn=1,nspinor if (tsh) then call rbsht(nr,nri,taumt_(:,ias,ispn),tau(:,ispn)) else tau(1:n,ispn)=taumt_(1:n,ias,ispn) end if end do end if if (spinpol) then !------------------------! ! spin-polarised ! !------------------------! ! magnetisation in spherical coordinates do idm=1,ndmag if (tsh) then call rbsht(nr,nri,magmt_(:,ias,idm),mag(:,idm)) else mag(1:n,idm)=magmt_(1:n,ias,idm) end if end do ! use scaled spin exchange-correlation if required if (tssxc) mag(:,1:ndmag)=mag(:,1:ndmag)*sxcscf if (ncmag) then ! non-collinear (use Kubler's trick) if (xcgrad.eq.0) then ! LSDA do i=1,n ! compute rhoup=(rho+|m|)/2 and rhodn=(rho-|m|)/2 t0=rho(i) t1=sqrt(mag(i,1)**2+mag(i,2)**2+mag(i,3)**2) rhoup(i)=0.5d0*(t0+t1) rhodn(i)=0.5d0*(t0-t1) end do else ! functionals which require gradients do i=1,n t0=rho(i) t1=sqrt(mag(i,1)**2+mag(i,2)**2+mag(i,3)**2+dncgga) rhoup(i)=0.5d0*(t0+t1) rhodn(i)=0.5d0*(t0-t1) end do end if else ! collinear do i=1,n ! compute rhoup=(rho+m_z)/2 and rhodn=(rho-m_z)/2 t0=rho(i) t1=mag(i,1) rhoup(i)=0.5d0*(t0+t1) rhodn(i)=0.5d0*(t0-t1) end do end if ! call the exchange-correlation interface routine if (xcgrad.le.0) then call xcifc(xctype_,n,tempa=swidth,rhoup=rhoup,rhodn=rhodn,ex=ex,ec=ec, & vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn) else if (xcgrad.eq.1) then call ggamt_sp_1(is,n,rhoup,rhodn,grho,gup,gdn,g2up,g2dn,g3rho,g3up,g3dn) call xcifc(xctype_,n,rhoup=rhoup,rhodn=rhodn,grho=grho,gup=gup,gdn=gdn, & g2up=g2up,g2dn=g2dn,g3rho=g3rho,g3up=g3up,g3dn=g3dn,ex=ex,ec=ec,vxup=vxup,& vxdn=vxdn,vcup=vcup,vcdn=vcdn) else if (xcgrad.eq.2) then call ggamt_sp_2a(is,n,rhoup,rhodn,g2up,g2dn,gvup,gvdn,gup2,gdn2,gupdn) call xcifc(xctype_,n,rhoup=rhoup,rhodn=rhodn,gup2=gup2,gdn2=gdn2, & gupdn=gupdn,ex=ex,ec=ec,vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn, & dxdgu2=dxdgu2,dxdgd2=dxdgd2,dxdgud=dxdgud,dcdgu2=dcdgu2,dcdgd2=dcdgd2, & dcdgud=dcdgud) call ggamt_sp_2b(is,n,g2up,g2dn,gvup,gvdn,vxup,vxdn,vcup,vcdn,dxdgu2, & dxdgd2,dxdgud,dcdgu2,dcdgd2,dcdgud) else if (xcgrad.eq.3) then call ggamt_sp_2a(is,n,rhoup,rhodn,g2up,g2dn,gvup,gvdn,gup2,gdn2,gupdn) call xcifc(xctype_,n,c_tb09=c_tb09,rhoup=rhoup,rhodn=rhodn,g2up=g2up, & g2dn=g2dn,gup2=gup2,gdn2=gdn2,gupdn=gupdn,tauup=tau(:,1),taudn=tau(:,2), & vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn) ex(:)=0.d0; ec(:)=0.d0 else if (xcgrad.eq.4) then call ggamt_sp_2a(is,n,rhoup,rhodn,g2up,g2dn,gvup,gvdn,gup2,gdn2,gupdn) call xcifc(xctype_,n,rhoup=rhoup,rhodn=rhodn,g2up=g2up,g2dn=g2dn,gup2=gup2,& gdn2=gdn2,gupdn=gupdn,tauup=tau(:,1),taudn=tau(:,2),ex=ex,ec=ec,vxup=vxup,& vxdn=vxdn,vcup=vcup,vcdn=vcdn,dxdgu2=dxdgu2,dxdgd2=dxdgd2,dxdgud=dxdgud, & dcdgu2=dcdgu2,dcdgd2=dcdgd2,dcdgud=dcdgud,dxdg2u=dxdg2u,dxdg2d=dxdg2d, & dcdg2u=dcdg2u,dcdg2d=dcdg2d,wxup=wxup,wxdn=wxdn,wcup=wcup,wcdn=wcdn) call ggamt_sp_2b(is,n,g2up,g2dn,gvup,gvdn,vxup,vxdn,vcup,vcdn,dxdgu2, & dxdgd2,dxdgud,dcdgu2,dcdgd2,dcdgud) wxup(:)=0.5d0*(wxup(:)+wxdn(:)+wcup(:)+wcdn(:)) if (tsh) then call rfsht(nr,nri,wxup,wxcmt_(:,ias)) else wxcmt_(1:n,ias)=wxup(1:n) end if end if ! hybrid functionals if (hybrid) then t1=1.d0-hybridc ! scale exchange part of energy ex(:)=t1*ex(:) ! scale exchange part of potential vxup(:)=t1*vxup(:) vxdn(:)=t1*vxdn(:) end if if (ncmag) then ! non-collinear: locally spin rotate the exchange-correlation potential do i=1,n t1=vxup(i)+vcup(i) t2=vxdn(i)+vcdn(i) vxc(i)=0.5d0*(t1+t2) ! determine the exchange-correlation magnetic field t3=0.5d0*(t1-t2) ! |m| = rhoup - rhodn t4=rhoup(i)-rhodn(i) if (abs(t4).gt.1.d-8) t4=t3/t4 bxc(i,1:3)=mag(i,1:3)*t4 end do else ! collinear do i=1,n t1=vxup(i)+vcup(i) t2=vxdn(i)+vcdn(i) vxc(i)=0.5d0*(t1+t2) bxc(i,1)=0.5d0*(t1-t2) end do end if ! scale B_xc for if required if (tssxc) bxc(:,1:ndmag)=bxc(:,1:ndmag)*sxcscf do idm=1,ndmag if (tsh) then ! convert field to spherical harmonics call rfsht(nr,nri,bxc(:,idm),bxcmt_(:,ias,idm)) else bxcmt_(1:n,ias,idm)=bxc(1:n,idm) end if end do else !--------------------------! ! spin-unpolarised ! !--------------------------! if (xcgrad.le.0) then call xcifc(xctype_,n,tempa=swidth,rho=rho,ex=ex,ec=ec,vx=vx,vc=vc) else if (xcgrad.eq.1) then call ggamt_1(tsh,is,n,rhomt_(:,ias),grho,g2rho,g3rho) call xcifc(xctype_,n,rho=rho,grho=grho,g2rho=g2rho,g3rho=g3rho,ex=ex,ec=ec,& vx=vx,vc=vc) else if (xcgrad.eq.2) then call ggamt_2a(tsh,is,n,rhomt_(:,ias),g2rho,gvrho,grho2) call xcifc(xctype_,n,rho=rho,grho2=grho2,ex=ex,ec=ec,vx=vx,vc=vc, & dxdgr2=dxdgr2,dcdgr2=dcdgr2) call ggamt_2b(is,n,g2rho,gvrho,vx,vc,dxdgr2,dcdgr2) else if (xcgrad.eq.3) then call ggamt_2a(tsh,is,n,rhomt_(:,ias),g2rho,gvrho,grho2) call xcifc(xctype_,n,c_tb09=c_tb09,rho=rho,g2rho=g2rho,grho2=grho2,tau=tau,& vx=vx,vc=vc) ex(:)=0.d0; ec(:)=0.d0 else if (xcgrad.eq.4) then call ggamt_2a(tsh,is,n,rhomt_(:,ias),g2rho,gvrho,grho2) call xcifc(xctype_,n,rho=rho,g2rho=g2rho,grho2=grho2,tau=tau,ex=ex,ec=ec, & vx=vx,vc=vc,dxdgr2=dxdgr2,dcdgr2=dcdgr2,dxdg2r=dxdg2r,dcdg2r=dcdg2r,wx=wx,& wc=wc) call ggamt_2b(is,n,g2rho,gvrho,vx,vc,dxdgr2,dcdgr2) wx(:)=wx(:)+wc(:) if (tsh) then call rfsht(nr,nri,wx,wxcmt_(:,ias)) else wxcmt_(1:n,ias)=wx(1:n) end if end if ! hybrid functionals if (hybrid) then t1=1.d0-hybridc ! scale exchange part of energy ex(:)=t1*ex(:) ! scale exchange part of potential vxc(:)=t1*vx(:)+vc(:) else vxc(:)=vx(:)+vc(:) end if end if if (tsh) then ! convert exchange and correlation energy densities to spherical harmonics call rfsht(nr,nri,ex,exmt_(:,ias)) call rfsht(nr,nri,ec,ecmt_(:,ias)) ! convert exchange-correlation potential to spherical harmonics call rfsht(nr,nri,vxc,vxcmt_(:,ias)) else exmt_(1:n,ias)=ex(1:n) ecmt_(1:n,ias)=ec(1:n) vxcmt_(1:n,ias)=vxc(1:n) end if deallocate(rho,ex,ec,vxc) if ((xcgrad.eq.3).or.(xcgrad.eq.4)) deallocate(tau) if (spinpol) then deallocate(mag,bxc) deallocate(rhoup,rhodn,vxup,vxdn,vcup,vcdn) if (xcgrad.eq.1) then deallocate(grho,gup,gdn,g2up,g2dn,g3rho,g3up,g3dn) else if (xcgrad.eq.2) then deallocate(g2up,g2dn) deallocate(gvup,gvdn) deallocate(gup2,gdn2,gupdn) deallocate(dxdgu2,dxdgd2,dxdgud) deallocate(dcdgu2,dcdgd2,dcdgud) else if (xcgrad.eq.3) then deallocate(g2up,g2dn) deallocate(gvup,gvdn) deallocate(gup2,gdn2,gupdn) end if else deallocate(vx,vc) if (xcgrad.eq.1) then deallocate(grho,g2rho,g3rho) else if (xcgrad.eq.2) then deallocate(g2rho,gvrho,grho2) deallocate(dxdgr2,dcdgr2) else if (xcgrad.eq.3) then deallocate(g2rho,gvrho,grho2) else if (xcgrad.eq.4) then deallocate(g2rho,gvrho,grho2) deallocate(dxdgr2,dcdgr2,dxdg2r,dcdg2r) deallocate(wx,wc) end if end if end subroutine elk-7.2.42/src/PaxHeaders.21776/sdelta_mp.f900000644000000000000000000000013214061636517015214 xustar0030 mtime=1623670095.205102223 30 atime=1623670093.960103378 30 ctime=1623670095.205102223 elk-7.2.42/src/sdelta_mp.f900000644002504400250440000000336514061636517017260 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: sdelta_mp ! !INTERFACE: real(8) function sdelta_mp(n,x) ! !INPUT/OUTPUT PARAMETERS: ! n : order (in,integer) ! x : real argument (in,real) ! !DESCRIPTION: ! Returns the smooth approximation to the Dirac delta function of order $N$ ! given by Methfessel and Paxton, {\it Phys. Rev. B} {\bf 40}, 3616 (1989), ! $$ \tilde\delta(x)=\sum_{i=0}^N \frac{(-1)^i}{i!4^n\sqrt\pi} H_{2i}(x) ! e^{-x^2},$$ ! where $H_j$ is the $j$th-order Hermite polynomial. This function has the ! property ! $$ \int_{-\infty}^{\infty}\tilde\delta(x)P(x)=P(0), $$ ! where $P(x)$ is any polynomial of degree $2N+1$ or less. The case $N=0$ ! corresponds to Gaussian smearing. This procedure is numerically stable ! and accurate to near machine precision for $N\le 10$. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: x ! local variables integer i real(8), parameter :: sqpi=1.7724538509055160273d0 real(8) sm,t0,t1 ! external functions real(8), external :: factnm,hermite if (n.eq.0) then sdelta_mp=exp(-x**2)/sqpi return end if if (n.lt.0) then write(*,*) write(*,'("Error(sdelta_mp): n < 0 : ",I8)') n write(*,*) stop end if if (n.gt.10) then write(*,*) write(*,'("Error(sdelta_mp): n out of range : ",I8)') n write(*,*) stop end if if (abs(x).gt.12.d0) then sdelta_mp=0.d0 return end if t0=exp(-x**2)/sqpi sm=t0 do i=1,n t1=t0/(factnm(i,1)*dble(4**i)) if (mod(i,2).ne.0) t1=-t1 sm=sm+t1*hermite(2*i,x) end do sdelta_mp=sm end function !EOC elk-7.2.42/src/PaxHeaders.21776/stheta_mp.f900000644000000000000000000000013214061636517015230 xustar0030 mtime=1623670095.206102222 30 atime=1623670093.962103376 30 ctime=1623670095.206102222 elk-7.2.42/src/stheta_mp.f900000644002504400250440000000336214061636517017271 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: stheta_mp ! !INTERFACE: real(8) function stheta_mp(n,x) ! !INPUT/OUTPUT PARAMETERS: ! n : order (in,integer) ! x : real argument (in,real) ! !DESCRIPTION: ! Returns the smooth approximation to the Heaviside step function of order ! $N$ given by Methfessel and Paxton, {\it Phys. Rev. B} {\bf 40}, 3616 ! (1989), ! $$ \tilde\Theta(x)=1-S_N(x) $$ ! where ! \begin{align*} ! S_N(x)&=S_0(x)+\sum_{i=1}^N \frac{(-1)^i}{i!4^n\sqrt\pi} H_{2i-1}(x) ! e^{-x^2},\\ ! S_0(x)&=\frac{1}{2}(1-{\rm erf}(x)) ! \end{align*} ! and $H_j$ is the $j$th-order Hermite polynomial. This procedure is ! numerically stable and accurate to near machine precision for $N\le 10$. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: x ! local variables integer i real(8), parameter :: sqpi=1.7724538509055160273d0 real(8) sm,t0,t1 ! external functions real(8), external :: factnm,hermite,erf if (n.eq.0) then stheta_mp=0.5d0*(1.d0+erf(x)) return end if if (n.lt.0) then write(*,*) write(*,'("Error(stheta_mp): n < 0 : ",I8)') n write(*,*) stop end if if (n.gt.10) then write(*,*) write(*,'("Error(stheta_mp): n out of range : ",I8)') n write(*,*) stop end if if (x.lt.-12.d0) then stheta_mp=0.d0 return end if if (x.gt.12.d0) then stheta_mp=1.d0 return end if t0=-exp(-x**2)/sqpi sm=0.5d0*(1.d0+erf(x)) do i=1,n t1=t0/(factnm(i,1)*dble(4**i)) if (mod(i,2).ne.0) t1=-t1 sm=sm+t1*hermite(2*i-1,x) end do stheta_mp=sm end function !EOC elk-7.2.42/src/PaxHeaders.21776/sdelta_fd.f900000644000000000000000000000013014061636517015167 xustar0029 mtime=1623670095.20810222 30 atime=1623670093.964103375 29 ctime=1623670095.20810222 elk-7.2.42/src/sdelta_fd.f900000644002504400250440000000135314061636517017230 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: sdelta_fd ! !INTERFACE: elemental real(8) function sdelta_fd(x) ! !INPUT/OUTPUT PARAMETERS: ! x : real argument (in,real) ! !DESCRIPTION: ! Returns the Fermi-Dirac approximation to the Dirac delta function ! $$ \tilde\delta(x)=\frac{e^{-x}}{(1+e^{-x})^2}. $$ ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: x ! local variables real(8) t1 if (abs(x).gt.50.d0) then sdelta_fd=0.d0 return end if t1=exp(-x) sdelta_fd=t1/((1.d0+t1)**2) end function !EOC elk-7.2.42/src/PaxHeaders.21776/stheta_fd.f900000644000000000000000000000013214061636517015205 xustar0030 mtime=1623670095.209102219 30 atime=1623670093.966103373 30 ctime=1623670095.209102219 elk-7.2.42/src/stheta_fd.f900000644002504400250440000000136114061636517017243 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: stheta_fd ! !INTERFACE: elemental real(8) function stheta_fd(x) ! !INPUT/OUTPUT PARAMETERS: ! x : real argument (in,real) ! !DESCRIPTION: ! Returns the Fermi-Dirac approximation to the Heaviside step function ! $$ \tilde\Theta(x)=\frac{1}{1+e^{-x}}. $$ ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: x if (x.gt.50.d0) then stheta_fd=1.d0 return end if if (x.lt.-50.d0) then stheta_fd=0.d0 return end if stheta_fd=1.d0/(1.d0+exp(-x)) end function !EOC elk-7.2.42/src/PaxHeaders.21776/writelsj.f900000644000000000000000000000013214061636517015107 xustar0030 mtime=1623670095.210102218 30 atime=1623670093.967103372 30 ctime=1623670095.210102218 elk-7.2.42/src/writelsj.f900000644002504400250440000001001314061636517017137 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma, C. Ambrosch-Draxl and ! F. Cricchio. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine writelsj use modmain use moddftu use modmpi use modtest implicit none ! local variables integer kst,ik,ist integer is,ia,ias real(8) xl(3),xs(3) ! allocatable arrays real(8), allocatable :: xj(:,:) complex(8), allocatable :: dmat(:,:,:,:,:) ! initialise universal variables call init0 call init1 ! read density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! allocate local arrays allocate(xj(3,natmtot)) allocate(dmat(lmmaxo,nspinor,lmmaxo,nspinor,natmtot)) if (task.eq.15) then ! compute total L, S and J ! read in the occupation numbers do ik=1,nkpt call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! generate the density matrix in each muffin-tin call gendmat(.false.,.false.,0,lmaxo,lmmaxo,dmat) if (mp_mpi) then open(50,file='LSJ.OUT',form='FORMATTED',action='WRITE') write(50,*) write(50,'("Expectation values are computed only over the muffin-tin")') ! loop over species and atoms do is=1,nspecies write(50,*) write(50,'("Species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) ias=idxas(ia,is) ! calculate the expectation value of L and S call dmatls(dmat(:,:,:,:,ias),xl,xs) ! J = L + S xj(:,ias)=xl(:)+xs(:) write(50,'(" atom : ",I4)') ia write(50,'(" L : ",3G18.10)') xl(:) write(50,'(" S : ",3G18.10)') xs(:) write(50,'(" J : ",3G18.10)') xj(:,ias) ! end loop over atoms and species end do end do close(50) write(*,*) write(*,'("Info(writelsj):")') write(*,'(" muffin-tin L, S and J expectation values written to LSJ.OUT")') end if ! write J to test file call writetest(15,'total muffin-tin angular momentum',nv=3*natmtot,tol=1.d-3,& rva=xj) else ! compute L, S and J for all states in kstlist if (mp_mpi) then open(50,file='LSJ_KST.OUT',form='FORMATTED',action='WRITE') write(50,*) write(50,'("Expectation values are computed only over the muffin-tin")') end if do kst=1,nkstlist ik=kstlist(1,kst) ist=kstlist(2,kst) if ((ik.le.0).or.(ik.gt.nkpt)) then write(*,*) write(*,'("Error(writelsj): k-point out of range : ",I8)') ik write(*,*) stop end if if ((ist.le.0).or.(ist.gt.nstsv)) then write(*,*) write(*,'("Error(writelsj): state out of range : ",I8)') ist write(*,*) stop end if ! select a particular wavefunction using its occupancy occsv(:,:)=0.d0 occsv(ist,ik)=1.d0/wkpt(ik) ! no symmetrisation required nsymcrys=1 ! generate the density matrix in each muffin-tin call gendmat(.false.,.false.,0,lmaxo,lmmaxo,dmat) if (mp_mpi) then ! loop over species and atoms do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) ! calculate the expectation value of L and S call dmatls(dmat(:,:,:,:,ias),xl,xs) ! J = L + S xj(:,ias)=xl(:)+xs(:) write(50,*) write(50,'("k-point : ",I6,3G18.10)') ik,vkl(:,ik) write(50,'("state : ",I6)') ist write(50,'("species : ",I4," (",A,"), atom : ",I4)') is, & trim(spsymb(is)),ia write(50,'(" L : ",3G18.10)') xl(:) write(50,'(" S : ",3G18.10)') xs(:) write(50,'(" J : ",3G18.10)') xj(:,ias) end do end do end if end do if (mp_mpi) then close(50) write(*,*) write(*,'("Info(writelsj):")') write(*,'(" muffin-tin L, S and J expectation values for each k-point and & &state")') write(*,'(" in kstlist written to LSJ_KST.OUT")') end if ! write J to test file call writetest(16,'muffin-tin angular momentum for one state',nv=3*natmtot, & tol=1.d-3,rva=xj) end if deallocate(xj,dmat) end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqnzh.f900000644000000000000000000000013114061636517014723 xustar0030 mtime=1623670095.212102216 29 atime=1623670093.96910337 30 ctime=1623670095.212102216 elk-7.2.42/src/eveqnzh.f900000644002504400250440000000210514061636517016757 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine eveqnzh(n,ld,a,w) use modmain use modomp implicit none ! arguments integer, intent(in) :: n,ld complex(8), intent(inout) :: a(ld,n) real(8), intent(out) :: w(n) ! local variables integer lrwork,lwork,info integer nthd,nts ! automatic arrays integer iwork(5*n+3) ! allocatable arrays real(8), allocatable :: rwork(:) complex(8), allocatable :: work(:) ! use the divide-and-conquer LAPACK routine zheevd lrwork=2*n**2+5*n+1 lwork=n**2+2*n allocate(rwork(lrwork),work(lwork)) ! enable MKL parallelism call holdthd(maxthdmkl,nthd) nts=mkl_set_num_threads_local(nthd) call zheevd('V','U',n,a,ld,w,work,lwork,rwork,lrwork,iwork,5*n+3,info) nts=mkl_set_num_threads_local(0) call freethd(nthd) if (info.ne.0) then write(*,*) write(*,'("Error(eveqnzh): diagonalisation failed")') write(*,'(" ZHEEVD returned INFO = ",I8)') info write(*,*) stop end if deallocate(rwork,work) end subroutine elk-7.2.42/src/PaxHeaders.21776/gensmatk.f900000644000000000000000000000013214061636517015055 xustar0030 mtime=1623670095.213102215 30 atime=1623670093.971103368 30 ctime=1623670095.213102215 elk-7.2.42/src/gensmatk.f900000644002504400250440000000210014061636517017103 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gensmatk(vpl,smat) use modmain implicit none ! arguments real(8), intent(in) :: vpl(3) complex(8), intent(out) :: smat(2,2,nstsv,nstsv) ! local variables integer ist,jst,n ! allocatable arrays complex(8), allocatable :: evecsv(:,:) ! external functions complex(8), external :: zdotc if (.not.spinpol) then write(*,*) write(*,'("Error(gensmatk): spin-unpolarised calculation")') write(*,*) stop end if allocate(evecsv(nstsv,nstsv)) ! get the second-variational eigenvectors from file call getevecsv(filext,0,vpl,evecsv) n=nstfv+1 do jst=1,nstsv do ist=1,jst smat(1,1,ist,jst)=zdotc(nstfv,evecsv(1,ist),1,evecsv(1,jst),1) smat(2,1,ist,jst)=zdotc(nstfv,evecsv(n,ist),1,evecsv(1,jst),1) smat(1,2,ist,jst)=zdotc(nstfv,evecsv(1,ist),1,evecsv(n,jst),1) smat(2,2,ist,jst)=zdotc(nstfv,evecsv(n,ist),1,evecsv(n,jst),1) end do end do deallocate(evecsv) end subroutine elk-7.2.42/src/PaxHeaders.21776/gensfacgp.f900000644000000000000000000000013214061636517015201 xustar0030 mtime=1623670095.215102213 30 atime=1623670093.972103367 30 ctime=1623670095.215102213 elk-7.2.42/src/gensfacgp.f900000644002504400250440000000247014061636517017241 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: gensfacgp ! !INTERFACE: pure subroutine gensfacgp(ngp,vgpc,ld,sfacgp) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ngp : number of G+p-vectors (in,integer) ! vgpc : G+p-vectors in Cartesian coordinates (in,real(3,*)) ! ld : leading dimension (in,integer) ! sfacgp : structure factors of G+p-vectors (out,complex(ld,natmtot)) ! !DESCRIPTION: ! Generates the atomic structure factors for a set of ${\bf G+p}$-vectors: ! $$ S_{\alpha}({\bf G+p})=\exp(i({\bf G+p})\cdot{\bf r}_{\alpha}), $$ ! where ${\bf r}_{\alpha}$ is the position of atom $\alpha$. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: ngp real(8), intent(in) :: vgpc(3,ngp) integer, intent(in) :: ld complex(8), intent(out) :: sfacgp(ld,natmtot) ! local variables integer is,ia,ias,igp real(8) v1,v2,v3,t1 do ias=1,natmtot is=idxis(ias) ia=idxia(ias) v1=atposc(1,ia,is); v2=atposc(2,ia,is); v3=atposc(3,ia,is) do igp=1,ngp t1=vgpc(1,igp)*v1+vgpc(2,igp)*v2+vgpc(3,igp)*v3 sfacgp(igp,ias)=cmplx(cos(t1),sin(t1),8) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rhomag.f900000644000000000000000000000013214061636517014521 xustar0030 mtime=1623670095.216102213 30 atime=1623670093.974103365 30 ctime=1623670095.216102213 elk-7.2.42/src/rhomag.f900000644002504400250440000000141214061636517016554 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rhomag use modmain use modmpi use modomp implicit none ! local variables integer nthd ! calculate the valence density and magnetisation call rhomagv ! add the core density and magnetisation to the total call rhocore call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP SECTION ! calculate the charges call charge ! normalise the density call rhonorm !$OMP SECTION ! calculate the moments if (spinpol) call moment !$OMP END PARALLEL SECTIONS call freethd(nthd) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/wsplintp.f900000644000000000000000000000013214061636517015124 xustar0030 mtime=1623670095.217102211 30 atime=1623670093.976103364 30 ctime=1623670095.217102211 elk-7.2.42/src/wsplintp.f900000644002504400250440000000306514061636517017165 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine wsplintp(n,x,wp) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: x(n) real(8), intent(out) :: wp(4,n) ! local variables integer i real(8) f(4),t1,t2 ! external functions real(8), external :: polynm if (n.lt.4) then write(*,*) write(*,'("Error(wsplintp): n < 4 : ",I8)') n write(*,*) stop end if wp(:,1)=0.d0 f(1)=1.d0 f(2:)=0.d0 wp(1,2)=polynm(-1,4,x,f,x(2)) f(1)=0.d0 f(2)=1.d0 wp(2,2)=polynm(-1,4,x,f,x(2)) f(2)=0.d0 f(3)=1.d0 wp(3,2)=polynm(-1,4,x,f,x(2)) f(3)=0.d0 f(4)=1.d0 wp(4,2)=polynm(-1,4,x,f,x(2)) do i=3,n-1 f(1)=1.d0 f(2:)=0.d0 t1=polynm(-1,4,x(i-2),f,x(i-1)) t2=polynm(-1,4,x(i-2),f,x(i)) wp(1,i)=t2-t1 f(1)=0.d0 f(2)=1.d0 t1=polynm(-1,4,x(i-2),f,x(i-1)) t2=polynm(-1,4,x(i-2),f,x(i)) wp(2,i)=t2-t1 f(2)=0.d0 f(3)=1.d0 t1=polynm(-1,4,x(i-2),f,x(i-1)) t2=polynm(-1,4,x(i-2),f,x(i)) wp(3,i)=t2-t1 f(3)=0.d0 f(4)=1.d0 t1=polynm(-1,4,x(i-2),f,x(i-1)) t2=polynm(-1,4,x(i-2),f,x(i)) wp(4,i)=t2-t1 end do f(1)=1.d0 f(2:)=0.d0 t1=polynm(-1,4,x(n-3),f,x(n-1)) t2=polynm(-1,4,x(n-3),f,x(n)) wp(1,n)=t2-t1 f(1)=0.d0 f(2)=1.d0 t1=polynm(-1,4,x(n-3),f,x(n-1)) t2=polynm(-1,4,x(n-3),f,x(n)) wp(2,n)=t2-t1 f(2)=0.d0 f(3)=1.d0 t1=polynm(-1,4,x(n-3),f,x(n-1)) t2=polynm(-1,4,x(n-3),f,x(n)) wp(3,n)=t2-t1 f(3)=0.d0 f(4)=1.d0 t1=polynm(-1,4,x(n-3),f,x(n-1)) t2=polynm(-1,4,x(n-3),f,x(n)) wp(4,n)=t2-t1 end subroutine elk-7.2.42/src/PaxHeaders.21776/checkmt.f900000644000000000000000000000013014061636517014660 xustar0029 mtime=1623670095.21910221 30 atime=1623670093.977103362 29 ctime=1623670095.21910221 elk-7.2.42/src/checkmt.f900000644002504400250440000000324314061636517016721 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: checkmt ! !INTERFACE: subroutine checkmt ! !USES: use modmain use modmpi use modvars ! !DESCRIPTION: ! Checks for muffin-tins which are too close together or intersecting. If any ! such muffin-tins are found then the radii of their associated atomic species ! are adjusted so that the minimum distance between their surfaces is ! {\tt rmtdelta}. ! ! !REVISION HISTORY: ! Created May 2003 (JKD) ! Modified, October 2011 (JKD) !EOP !BOC implicit none ! local variables integer is,js real(8) dmin,t1,t2 ! automatic arrays real(8) rmt0(nspecies) rmt0(1:nspecies)=rmt(1:nspecies) 10 continue ! find the minimum distance between muffin-tin surfaces call mtdmin(is,js,dmin) ! adjust muffin-tin radii if required if (dmin.lt.rmtdelta-epslat) then t1=rmt(is)+rmt(js) t2=(t1+dmin-rmtdelta)/t1 rmt(is)=rmt(is)*t2 if (is.ne.js) rmt(js)=rmt(js)*t2 goto 10 end if do is=1,nspecies if (rmt(is).lt.0.25d0) then write(*,*) write(*,'("Error(checkmt): muffin-tin radius too small for species ",I4,& &" (",A,")")') is,trim(spsymb(is)) write(*,'(" Radius : ",G18.10)') rmt(is) write(*,*) stop end if if (rmt(is).lt.rmt0(is)) then if (mp_mpi) then write(*,*) write(*,'("Info(checkmt): reduced muffin-tin radius of species ",I3,& &" (",A,") from ",F8.4," to ",F8.4)') is,trim(spsymb(is)),rmt0(is), & rmt(is) end if end if end do ! write to VARIABLES.OUT call writevars('rmt',nv=nspecies,rva=rmt) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rhomagv.f900000644000000000000000000000013214061636517014707 xustar0030 mtime=1623670095.220102209 30 atime=1623670093.979103361 30 ctime=1623670095.220102209 elk-7.2.42/src/rhomagv.f900000644002504400250440000000630614061636517016751 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rhomagv use modmain use modmpi use modomp implicit none ! local variables integer ik,ispn,idm integer is,ias,n,nthd ! automatic arrays integer(8) lock(natmtot) ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:,:),evecfv(:,:,:),evecsv(:,:) ! set the charge density and magnetisation to zero do ias=1,natmtot is=idxis(ias) rhomt(1:npcmt(is),ias)=0.d0 end do rhoir(1:ngtc)=0.d0 do idm=1,ndmag do ias=1,natmtot is=idxis(ias) magmt(1:npcmt(is),ias,idm)=0.d0 end do magir(1:ngtc,idm)=0.d0 end do ! initialise the OpenMP locks do ias=1,natmtot call omp_init_lock(lock(ias)) end do call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(apwalm,evecfv,evecsv,ispn) & !$OMP NUM_THREADS(nthd) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv),evecsv(nstsv,nstsv)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! get the eigenvectors from file call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! find the matching coefficients do ispn=1,nspnfv call match(ngk(ispn,ik),vgkc(:,:,ispn,ik),gkc(:,ispn,ik), & sfacgk(:,:,ispn,ik),apwalm(:,:,:,:,ispn)) end do ! add to the density and magnetisation call rhomagk(ngk(:,ik),igkig(:,:,ik),lock,wkpt(ik),occsv(:,ik),apwalm, & evecfv,evecsv) end do !$OMP END DO deallocate(apwalm,evecfv,evecsv) !$OMP END PARALLEL call freethd(nthd) ! destroy the OpenMP locks do ias=1,natmtot call omp_destroy_lock(lock(ias)) end do ! convert muffin-tin density/magnetisation to spherical harmonics call rhomagsh call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP PRIVATE(idm) & !$OMP NUM_THREADS(nthd) !$OMP SECTION ! symmetrise the density call symrf(nrcmt,nrcmti,npcmt,ngdgc,ngtc,ngvc,igfc,npmtmax,rhomt,rhoir) ! convert the muffin-tin density from coarse to fine radial mesh call rfmtctof(rhomt) ! convert the interstitial density from coarse to fine grid call rfirctof(rhoir,rhoir) !$OMP SECTION if (spinpol) then ! symmetrise the magnetisation call symrvf(.true.,ncmag,nrcmt,nrcmti,npcmt,ngdgc,ngtc,ngvc,igfc,npmtmax, & magmt,ngtot,magir) ! convert the muffin-tin magnetisation from coarse to fine radial mesh do idm=1,ndmag call rfmtctof(magmt(:,:,idm)) end do ! convert the interstitial magnetisation from coarse to fine grid do idm=1,ndmag call rfirctof(magir(:,idm),magir(:,idm)) end do end if !$OMP END PARALLEL SECTIONS call freethd(nthd) ! add densities from each process and redistribute if (np_mpi.gt.1) then n=npmtmax*natmtot call mpi_allreduce(mpi_in_place,rhomt,n,mpi_double_precision,mpi_sum,mpicom, & ierror) call mpi_allreduce(mpi_in_place,rhoir,ngtot,mpi_double_precision,mpi_sum, & mpicom,ierror) if (spinpol) then n=n*ndmag call mpi_allreduce(mpi_in_place,magmt,n,mpi_double_precision,mpi_sum, & mpicom,ierror) n=ngtot*ndmag call mpi_allreduce(mpi_in_place,magir,n,mpi_double_precision,mpi_sum, & mpicom,ierror) end if end if end subroutine elk-7.2.42/src/PaxHeaders.21776/reciplat.f900000644000000000000000000000013214061636517015047 xustar0030 mtime=1623670095.222102207 30 atime=1623670093.981103359 30 ctime=1623670095.222102207 elk-7.2.42/src/reciplat.f900000644002504400250440000000336714061636517017115 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: reciplat ! !INTERFACE: subroutine reciplat(avec,bvec,omega,omegabz) ! !INPUT/OUTPUT PARAMETERS: ! avec : lattice vectors (in,real(3,3)) ! bvec : reciprocal lattice vectors (out,real(3,3)) ! omega : unit cell volume (out,real) ! omegabz : Brillouin zone volume (out,real) ! !DESCRIPTION: ! Generates the reciprocal lattice vectors from the real-space lattice vectors ! \begin{align*} ! {\bf b}_1&=\frac{2\pi}{s}({\bf a}_2\times{\bf a}_3)\\ ! {\bf b}_2&=\frac{2\pi}{s}({\bf a}_3\times{\bf a}_1)\\ ! {\bf b}_3&=\frac{2\pi}{s}({\bf a}_1\times{\bf a}_2) ! \end{align*} ! and finds the unit cell volume $\Omega=|s|$, where ! $s={\bf a}_1\cdot({\bf a}_2\times{\bf a}_3)$, and the Brillouin zone volume ! $\Omega_{\rm BZ}=(2\pi)^3/\Omega$. ! ! !REVISION HISTORY: ! Created September 2002 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: avec(3,3) real(8), intent(out) :: bvec(3,3) real(8), intent(out) :: omega,omegabz ! local variables real(8), parameter :: twopi=6.2831853071795864769d0 real(8) t1 call r3cross(avec(:,2),avec(:,3),bvec(:,1)) call r3cross(avec(:,3),avec(:,1),bvec(:,2)) call r3cross(avec(:,1),avec(:,2),bvec(:,3)) t1=avec(1,1)*bvec(1,1)+avec(2,1)*bvec(2,1)+avec(3,1)*bvec(3,1) ! unit cell volume omega=abs(t1) if (omega.lt.1.d-6) then write(*,*) write(*,'("Error(reciplat) omega too small : ",G18.10)') omega write(*,'(" Lattice vectors may be collinear")') write(*,*) stop end if bvec(:,:)=(twopi/t1)*bvec(:,:) ! Brillouin zone volume omegabz=(twopi**3)/omega end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gradrf.f900000644000000000000000000000013214061636517014511 xustar0030 mtime=1623670095.223102206 30 atime=1623670093.982103358 30 ctime=1623670095.223102206 elk-7.2.42/src/gradrf.f900000644002504400250440000000231514061636517016547 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gradrf(rfmt,rfir,grfmt,grfir) use modmain use modomp implicit none ! arguments real(8), intent(in) :: rfmt(npmtmax,natmtot),rfir(ngtot) real(8), intent(out) :: grfmt(npmtmax,natmtot,3),grfir(ngtot,3) ! local variables integer is,ias,ld,i integer ig,ifg,nthd complex(8) z1 ! allocatable arrays complex(8), allocatable :: zfft1(:),zfft2(:) ! muffin-tin gradient ld=npmtmax*natmtot call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) call gradrfmt(nrmt(is),nrmti(is),rlmt(:,-1,is),wcrmt(:,:,is),rfmt(:,ias),ld, & grfmt(1,ias,1)) end do !$OMP END PARALLEL DO call freethd(nthd) ! interstitial gradient allocate(zfft1(ngtot),zfft2(ngtot)) zfft1(:)=rfir(:) call zfftifc(3,ngridg,-1,zfft1) do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) z1=zfft1(ifg) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(z1),dble(z1),8) end do call zfftifc(3,ngridg,1,zfft2) grfir(:,i)=dble(zfft2(:)) end do deallocate(zfft1,zfft2) end subroutine elk-7.2.42/src/PaxHeaders.21776/genzfrm.f900000644000000000000000000000013214061636517014714 xustar0030 mtime=1623670095.225102204 30 atime=1623670093.984103356 30 ctime=1623670095.225102204 elk-7.2.42/src/genzfrm.f900000644002504400250440000000255614061636517016761 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2010 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genzfrm(wfmt11,wfmt12,wfir11,wfir12,wfmt21,wfmt22,wfir21,wfir22, & zrhomt,zrhoir,zmagmt,zmagir) use modmain use modomp implicit none ! arguments complex(8), intent(in) :: wfmt11(npcmtmax,natmtot),wfmt12(npcmtmax,natmtot) complex(8), intent(in) :: wfir11(ngtot),wfir12(ngtot) complex(8), intent(in) :: wfmt21(npcmtmax,natmtot),wfmt22(npcmtmax,natmtot) complex(8), intent(in) :: wfir21(ngtot),wfir22(ngtot) complex(8), intent(out) :: zrhomt(npcmtmax,natmtot),zrhoir(ngtot) complex(8), intent(out) :: zmagmt(npcmtmax,natmtot,ndmag),zmagir(ngtot,ndmag) ! local variables integer ld,is,ias,nthd !-------------------------! ! muffin-tin part ! !-------------------------! ld=npcmtmax*natmtot call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) call genzrm(npcmt(is),wfmt11(:,ias),wfmt12(:,ias),wfmt21(:,ias), & wfmt22(:,ias),zrhomt(:,ias),ld,zmagmt(:,ias,1)) end do !$OMP END PARALLEL DO call freethd(nthd) !---------------------------! ! interstitial part ! !---------------------------! call genzrm(ngtot,wfir11,wfir12,wfir21,wfir22,zrhoir,ngtot,zmagir) end subroutine elk-7.2.42/src/PaxHeaders.21776/mixadapt.f900000644000000000000000000000013214061636517015053 xustar0030 mtime=1623670095.226102203 30 atime=1623670093.986103354 30 ctime=1623670095.226102203 elk-7.2.42/src/mixadapt.f900000644002504400250440000000504214061636517017111 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: mixadapt ! !INTERFACE: pure subroutine mixadapt(iscl,beta0,betamax,n,nu,mu,beta,f,d) ! !INPUT/OUTPUT PARAMETERS: ! iscl : self-consistent loop number (in,integer) ! beta0 : mixing parameter (in,real) ! betamax : maximum mixing parameter (in,real) ! n : vector length (in,integer) ! nu : current output vector as well as the next input vector of the ! self-consistent loop (inout,real(n)) ! mu : used internally (inout,real(n)) ! beta : used internally (inout,real(n)) ! f : used internally (inout,real(n)) ! d : RMS difference between old and new output vectors (out,real) ! !DESCRIPTION: ! Given the input vector $\mu^i$ and output vector $\nu^i$ of the $i$th ! self-consistent loop, this routine generates the next input vector to the ! loop using an adaptive mixing scheme. The $j$th component of the output ! vector is mixed with a fraction of the same component of the input vector: ! $$ \mu^{i+1}_j=\beta^i_j\nu^i_j+(1-\beta^i_j)\mu^i_j, $$ ! where $\beta^{i+1}_j=\beta^i_j+\beta_0$ if $f^i_j\equiv\nu^i_j-\mu^i_j$ does ! not change sign between loops. If $f^i_j$ does change sign, then ! $\beta^{i+1}_j=(\beta^i_j+\beta_0)/2$. Note that the array {\tt nu} serves ! for both input and output, and the arrays {\tt mu}, {\tt beta} and {\tt f} ! are used internally and should not be changed between calls. The routine is ! thread-safe so long as each thread has its own independent work arrays. ! Complex arrays may be passed as real arrays with $n$ doubled. ! ! !REVISION HISTORY: ! Created March 2003 (JKD) ! Modified, September 2008 (JKD) ! Modified, August 2011 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: iscl real(8), intent(in) :: beta0,betamax integer, intent(in) :: n real(8), intent(inout) :: nu(n),mu(n) real(8), intent(inout) :: beta(n),f(n) real(8), intent(out) :: d ! local variables integer i real(8) t1 if (n.le.0) return ! initialise mixer if (iscl.le.0) then mu(:)=nu(:) f(:)=0.d0 beta(:)=beta0 d=1.d0 return end if d=0.d0 do i=1,n t1=nu(i)-mu(i) d=d+t1**2 if (t1*f(i).ge.0.d0) then beta(i)=beta(i)+beta0 if (beta(i).gt.betamax) beta(i)=betamax else beta(i)=0.5d0*(beta(i)+beta0) end if f(i)=t1 nu(i)=beta(i)*nu(i)+(1.d0-beta(i))*mu(i) mu(i)=nu(i) end do d=sqrt(d/dble(n)) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/zftrf.f900000644000000000000000000000013214061636517014377 xustar0030 mtime=1623670095.227102202 30 atime=1623670093.987103353 30 ctime=1623670095.227102202 elk-7.2.42/src/zftrf.f900000644002504400250440000001215314061636517016436 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 Alexey I. Baranov. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zftrf ! !INTERFACE: subroutine zftrf(npv,ivp,vpc,rfmt,rfir,zfp) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! npv : number of P-vectors (in,integer) ! ivp : integer coordinates of the P-vectors (in,integer(3,npv)) ! vpc : P-vectors in Cartesian coordinates (in,real(3,npv)) ! rfmt : real muffin-tin function (in,real(npmtmax,natmtot)) ! rfir : real interstitial function (in,real(ngtot)) ! zfp : Fourier expansion coefficients of the real-space function ! (out,complex(npv)) ! !DESCRIPTION: ! Given a real function periodic in the unit cell, $f({\bf r})$, this routine ! calculates its complex Fourier expansion coefficients: ! $$ f({\bf P})=\frac{1}{\Omega}\int d^3r\,f({\bf r})\tilde{\Theta}({\bf r}) ! e^{-i{\bf P}\cdot{\bf r}} ! +\frac{4\pi}{\Omega}\sum_{\alpha}e^{-i{\bf P}\cdot{\bf R}_{\alpha}} ! \sum_{lm}(-i)^l Y_{lm}(\hat{\bf P}) ! \int_{0}^{R_{\alpha}}dr\,r^2 j_{l}(|{\bf P}|r)f_{lm}^{\alpha}(r), $$ ! where $\tilde{\Theta}$ is the smooth characteristic function of the ! interstitial region, $\Omega$ is the unit cell volume and $R_{\alpha}$ is ! the muffin-tin radius of atom $\alpha$. ! ! !REVISION HISTORY: ! Created July 2010 (Alexey I. Baranov) ! Modified, November 2010 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: npv,ivp(3,npv) real(8), intent(in) :: vpc(3,npv) real(8), intent(in) :: rfmt(npmtmax,natmtot),rfir(ngtot) complex(8), intent(out) :: zfp(npv) ! local variables integer is,ia,ias integer nrc,nrci,irco,irc integer lmax,l,m,lm,npci,i integer ip,ig,ifg real(8) p,t0,t1 complex(8) zsm,z1,z2,z3 ! automatic arrays real(8) jl(0:lmaxo,nrcmtmax),rfmt1(npcmtmax) complex(8) ylm(lmmaxo) ! allocatable arrays complex(8), allocatable :: zfft(:),zfmt(:,:) allocate(zfft(ngtot),zfmt(npcmtmax,natmtot)) ! zero the coefficients zfp(:)=0.d0 !---------------------------! ! interstitial part ! !---------------------------! ! Fourier transform to G-space zfft(:)=rfir(:) call zfftifc(3,ngridg,-1,zfft) ! find coefficients for all required input vectors do ip=1,npv if ((ivp(1,ip).ge.intgv(1,1)).and.(ivp(1,ip).le.intgv(2,1)).and. & (ivp(2,ip).ge.intgv(1,2)).and.(ivp(2,ip).le.intgv(2,2)).and. & (ivp(3,ip).ge.intgv(1,3)).and.(ivp(3,ip).le.intgv(2,3))) then ig=ivgig(ivp(1,ip),ivp(2,ip),ivp(3,ip)) zfp(ip)=zfft(igfft(ig)) end if end do !-------------------------! ! muffin-tin part ! !-------------------------! ! convert function from real to complex spherical harmonic expansion on coarse ! radial mesh do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) call rfmtftoc(nrc,nrci,rfmt(:,ias),rfmt1) call rtozfmt(nrc,nrci,rfmt1,zfmt(:,ias)) end do ! remove continuation of interstitial function into muffin-tin do ig=1,ngtot ifg=igfft(ig) ! conjugate spherical harmonics Y_lm*(G) call genylmv(lmaxo,vgc(:,ig),ylm) ylm(:)=conjg(ylm(:)) do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) irco=nrci+1 npci=npcmti(is) ! generate spherical Bessel functions lmax=lmaxi do irc=1,nrc t1=gc(ig)*rcmt(irc,is) call sbessel(lmax,t1,jl(:,irc)) if (irc.eq.nrci) lmax=lmaxo end do do ia=1,natoms(is) ias=idxas(ia,is) ! structure factor t1=dot_product(vgc(:,ig),atposc(:,ia,is)) z1=fourpi*zfft(ifg)*cmplx(cos(t1),sin(t1),8) lm=0 do l=0,lmaxi z2=z1*zil(l) do m=-l,l lm=lm+1 z3=z2*ylm(lm) i=lm do irc=1,nrci zfmt(i,ias)=zfmt(i,ias)-z3*jl(l,irc) i=i+lmmaxi end do end do end do lm=0 do l=0,lmaxo z2=z1*zil(l) do m=-l,l lm=lm+1 z3=z2*ylm(lm) i=npci+lm do irc=irco,nrc zfmt(i,ias)=zfmt(i,ias)-z3*jl(l,irc) i=i+lmmaxo end do end do end do end do end do end do t0=fourpi/omega ! loop over input P-vectors do ip=1,npv ! length of P-vector p=sqrt(vpc(1,ip)**2+vpc(2,ip)**2+vpc(3,ip)**2) ! spherical harmonics Y_lm(P) call genylmv(lmaxo,vpc(:,ip),ylm) do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) ! generate spherical Bessel functions lmax=lmaxi do irc=1,nrc t1=p*rcmt(irc,is) call sbessel(lmax,t1,jl(:,irc)) if (irc.eq.nrci) lmax=lmaxo end do do ia=1,natoms(is) ias=idxas(ia,is) zsm=0.d0 lmax=lmaxi i=0 do irc=1,nrc i=i+1 z1=jl(0,irc)*zfmt(i,ias)*ylm(1) lm=1 do l=1,lmax lm=lm+1 i=i+1 z2=zfmt(i,ias)*ylm(lm) do m=1-l,l lm=lm+1 i=i+1 z2=z2+zfmt(i,ias)*ylm(lm) end do z1=z1+jl(l,irc)*zilc(l)*z2 end do zsm=zsm+wrcmt(irc,is)*z1 if (irc.eq.nrci) lmax=lmaxo end do ! conjugate structure factor t1=-dot_product(vpc(:,ip),atposc(:,ia,is)) z1=t0*cmplx(cos(t1),sin(t1),8) zfp(ip)=zfp(ip)+z1*zsm end do end do end do deallocate(zfft,zfmt) end subroutine ! EOC elk-7.2.42/src/PaxHeaders.21776/sbessel.f900000644000000000000000000000012614061636517014707 xustar0028 mtime=1623670095.2291022 30 atime=1623670093.989103351 28 ctime=1623670095.2291022 elk-7.2.42/src/sbessel.f900000644002504400250440000000520014061636517016736 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: sbessel ! !INTERFACE: subroutine sbessel(lmax,x,jl) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum order of Bessel function (in,integer) ! x : real argument (in,real) ! jl : array of returned values (out,real(0:lmax)) ! !DESCRIPTION: ! Computes the spherical Bessel functions of the first kind, $j_l(x)$, for ! argument $x$ and $l=0,1,\ldots,l_{\rm max}$. The recursion relation ! $$ j_{l+1}(x)=\frac{2l+1}{x}j_l(x)-j_{l-1}(x) $$ ! is used either downwards for $x= lmax recurse up jl(0)=sin(x)*xi if (lmax.eq.0) return jl(1)=(jl(0)-cos(x))*xi if (lmax.eq.1) return j0=jl(0) j1=jl(1) do l=2,lmax jt=(2*l-1)*j1*xi-j0 j0=j1 j1=jt jl(l)=j1 end do end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gengclgq.f900000644000000000000000000000013114061636517015032 xustar0030 mtime=1623670095.230102199 29 atime=1623670093.99010335 30 ctime=1623670095.230102199 elk-7.2.42/src/gengclgq.f900000644002504400250440000000167014061636517017074 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine gengclgq(treg,iq,ngq,gqc,gclgq) use modmain implicit none ! arguments logical, intent(in) :: treg integer, intent(in) :: iq,ngq real(8), intent(in) :: gqc(ngq) real(8), intent(out) :: gclgq(ngq) ! local variables integer ig real(8) t1,t2 if (treg) then ! regularise 1/(G+q)^2 for G+q in the first Brillouin zone t1=sqrt(vqc(1,iq)**2+vqc(2,iq)**2+vqc(3,iq)**2) do ig=1,ngq t2=gqc(ig) if (abs(t1-t2).lt.epslat) then gclgq(ig)=gclq(iq) else if (t2.gt.epslat) then gclgq(ig)=fourpi/t2**2 else gclgq(ig)=0.d0 end if end do else ! no regularisation do ig=1,ngq t1=gqc(ig) if (t1.gt.epslat) then gclgq(ig)=fourpi/t1**2 else gclgq(ig)=0.d0 end if end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/gencfun.f900000644000000000000000000000013214061636517014671 xustar0030 mtime=1623670095.231102199 30 atime=1623670093.992103349 30 ctime=1623670095.231102199 elk-7.2.42/src/gencfun.f900000644002504400250440000000403014061636517016723 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: gencfun ! !INTERFACE: subroutine gencfun ! !USES: use modmain ! !DESCRIPTION: ! Generates the smooth characteristic function. This is the function which is ! 0 within the muffin-tins and 1 in the intersitial region and is constructed ! from radial step function form factors with $GG_{\rm max}\end{cases} $$ ! where $R_i$ is the muffin-tin radius of the $i$th species and $\Omega$ is ! the unit cell volume. Therefore the characteristic function in $G$-space is ! $$ \tilde{\Theta}({\bf G})=\delta_{G,0}-\sum_{ij}\exp(-i{\bf G}\cdot ! {\bf r}_{ij})\tilde{\Theta}_i(G), $$ ! where ${\bf r}_{ij}$ is the position of the $j$th atom of the $i$th species. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) !EOP !BOC implicit none ! local variables integer is,ia,ig real(8) v1,v2,v3,t1 complex(8) z1 ! allocatable arrays complex(8), allocatable :: zfft(:) ! allocate global characteristic function arrays if (allocated(cfunig)) deallocate(cfunig) allocate(cfunig(ngtot)) if (allocated(cfunir)) deallocate(cfunir) allocate(cfunir(ngtot)) cfunig(1)=1.d0 cfunig(2:)=0.d0 ! begin loop over species do is=1,nspecies ! loop over atoms do ia=1,natoms(is) v1=atposc(1,ia,is); v2=atposc(2,ia,is); v3=atposc(3,ia,is) do ig=1,ngtot ! structure factor t1=vgc(1,ig)*v1+vgc(2,ig)*v2+vgc(3,ig)*v3 z1=cmplx(cos(t1),-sin(t1),8) ! add to characteristic function in G-space cfunig(ig)=cfunig(ig)-ffacg(ig,is)*z1 end do end do end do allocate(zfft(ngtot)) zfft(igfft(:))=cfunig(:) ! Fourier transform to real-space call zfftifc(3,ngridg,1,zfft) cfunir(:)=dble(zfft(:)) deallocate(zfft) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writeeval.f900000644000000000000000000000013214061636517015246 xustar0030 mtime=1623670095.233102197 30 atime=1623670093.994103347 30 ctime=1623670095.233102197 elk-7.2.42/src/writeeval.f900000644002504400250440000000264114061636517017306 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writeeval ! !INTERFACE: subroutine writeeval ! !USES: use modmain ! !DESCRIPTION: ! Outputs the second-variational eigenvalues and occupation numbers to the ! file {\tt EIGVAL.OUT}. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! local variables integer ik,ist,is,ia,ias ! write out the valence eigenvalues open(50,file='EIGVAL'//trim(filext),form='FORMATTED') write(50,'(I6," : nkpt")') nkpt write(50,'(I6," : nstsv")') nstsv do ik=1,nkpt write(50,*) write(50,'(I6,3G18.10," : k-point, vkl")') ik,vkl(:,ik) write(50,'(" (state, eigenvalue and occupancy below)")') do ist=1,nstsv write(50,'(I6,2G18.10)') ist,evalsv(ist,ik),occsv(ist,ik) end do write(50,*) end do close(50) ! write out the core eigenvalues open(50,file='EVALCORE'//trim(filext),form='FORMATTED') do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) write(50,*) write(50,'("Species : ",I4," (",A,"), atom : ",I4)') is,trim(spsymb(is)),ia do ist=1,nstsp(is) if (spcore(ist,is)) then write(50,'(" n = ",I2,", l = ",I2,", k = ",I2," : ",G18.10)') & nsp(ist,is),lsp(ist,is),ksp(ist,is),evalcr(ist,ias) end if end do end do end do close(50) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/factr.f900000644000000000000000000000013214061636517014343 xustar0030 mtime=1623670095.234102196 30 atime=1623670093.995103346 30 ctime=1623670095.234102196 elk-7.2.42/src/factr.f900000644002504400250440000000175714061636517016412 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: factr ! !INTERFACE: real(8) function factr(n,d) ! !INPUT/OUTPUT PARAMETERS: ! n : numerator (in,integer) ! d : denominator (in,integer) ! !DESCRIPTION: ! Returns the ratio $n!/d!$ for $n,d\ge 0$. Performs no under- or overflow ! checking. ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n,d ! local variables integer i ! external functions real(8), external :: factnm if (d.eq.1) then factr=factnm(n,1) return end if if ((n.lt.0).or.(d.lt.0)) then factr=0.d0 return end if if (n.lt.d) then factr=dble(n+1) do i=n+2,d factr=factr*dble(i) end do factr=1.d0/factr else if (n.eq.d) then factr=1.d0 else factr=dble(d+1) do i=d+2,n factr=factr*dble(i) end do end if end function !EOC elk-7.2.42/src/PaxHeaders.21776/genstress.f900000644000000000000000000000013214061636517015261 xustar0030 mtime=1623670095.236102194 30 atime=1623670093.997103344 30 ctime=1623670095.236102194 elk-7.2.42/src/genstress.f900000644002504400250440000000252614061636517017323 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genstress use modmain use modmpi use modstore implicit none ! local variables integer i real(8) et0,t1 ! store original parameters avec_(:,:)=avec(:,:) tforce_=tforce tforce=.false. ! restore original symmetries call symmetry ! generate the strain tensors call genstrain ! zero the stress tensor components stress(:)=0.d0 ! run the ground-state calculation call gndstate ! check for stop signal if (tstop) goto 10 ! subsequent calculations will read STATE.OUT trdstate=.true. ! store the total energy et0=engytot ! loop over strain tensors do istrain=1,nstrain if (mp_mpi) then write(*,'("Info(genstress): strain tensor ",I1," of ",I1)') istrain,nstrain end if ! restore the lattice vectors avec(:,:)=avec_(:,:) ! run the ground-state calculation call gndstate ! check for stop signal if (tstop) goto 10 ! compute the stress tensor component stress(istrain)=(engytot-et0)/deltast end do 10 continue istrain=0 ! compute the maximum stress magnitude over all lattice vectors stressmax=0.d0 do i=1,nstrain t1=abs(stress(i)) if (t1.gt.stressmax) stressmax=t1 end do ! restore original parameters avec(:,:)=avec_(:,:) tforce=tforce_ end subroutine elk-7.2.42/src/PaxHeaders.21776/rfcopy.f900000644000000000000000000000013214061636517014546 xustar0030 mtime=1623670095.237102193 30 atime=1623670093.999103342 30 ctime=1623670095.237102193 elk-7.2.42/src/rfcopy.f900000644002504400250440000000104514061636517016603 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine rfcopy(rfmt1,rfir1,rfmt2,rfir2) use modmain implicit none ! arguments real(8), intent(in) :: rfmt1(npmtmax,natmtot),rfir1(ngtot) real(8), intent(out) :: rfmt2(npmtmax,natmtot),rfir2(ngtot) ! local variables integer is,ias do ias=1,natmtot is=idxis(ias) rfmt2(1:npmt(is),ias)=rfmt1(1:npmt(is),ias) end do rfir2(:)=rfir1(:) end subroutine elk-7.2.42/src/PaxHeaders.21776/force.f900000644000000000000000000000013214061636517014342 xustar0030 mtime=1623670095.239102191 30 atime=1623670094.000103341 30 ctime=1623670095.239102191 elk-7.2.42/src/force.f900000644002504400250440000002154714061636517016410 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: force ! !INTERFACE: subroutine force ! !USES: use modmain use modtddft use modtest use modmpi use modomp ! !DESCRIPTION: ! Computes the various contributions to the atomic forces. In principle, the ! force acting on a nucleus is simply the gradient at that site of the ! classical electrostatic potential from the other nuclei and the electronic ! density. This is a result of the Hellmann-Feynman theorem. However because ! the basis set is dependent on the nuclear coordinates and is not complete, ! the Hellman-Feynman force is inacurate and corrections to it are required. ! The first is the core correction which arises because the core wavefunctions ! were determined by neglecting the non-spherical parts of the Kohn-Sham ! potential $v_s$. Explicitly this is given by ! $$ {\bf F}_{\rm core}^{\alpha}=\int_{\rm MT_{\alpha}} v_s({\bf r}) ! \nabla\rho_{\rm core}^{\alpha}({\bf r})\,d{\bf r} $$ ! for atom $\alpha$. The second, which is the incomplete basis set (IBS) ! correction, is due to the position dependence of the APW functions, and is ! derived by considering the change in total energy if the eigenvector ! coefficients were fixed and the APW functions themselves were changed. This ! would result in changes to the first-variational Hamiltonian and overlap ! matrices given by ! \begin{align*} ! \delta H_{\bf G,G'}^{\alpha}&=i({\bf G-G'}) ! \left(H^{\alpha}_{\bf G+k,G'+k}-\frac{1}{2}({\bf G+k})\cdot({\bf G'+k}) ! \tilde{\Theta}_{\alpha}({\bf G-G'})e^{-i({\bf G-G'})\cdot{\bf r}_{\alpha}} ! \right)\\ ! \delta O_{\bf G,G'}^{\alpha}&=i({\bf G-G'})\left(O^{\alpha}_{\bf G+k,G'+k} ! -\tilde{\Theta}_{\alpha}({\bf G-G'})e^{-i({\bf G-G'})\cdot{\bf r}_{\alpha}} ! \right) ! \end{align*} ! where both ${\bf G}$ and ${\bf G'}$ run over the APW indices; ! $\tilde{\Theta}_{\alpha}$ is the form factor of the smooth step function for ! muffin-tin $\alpha$; and $H^{\alpha}$ and $O^{\alpha}$ are the muffin-tin ! Hamiltonian and overlap matrices, respectively. The APW-local-orbital part ! is given by ! \begin{align*} ! \delta H_{\bf G,G'}^{\alpha}&=i({\bf G+k})H^{\alpha}_{\bf G+k,G'+k}\\ ! \delta O_{\bf G,G'}^{\alpha}&=i({\bf G+k})O^{\alpha}_{\bf G+k,G'+k} ! \end{align*} ! where ${\bf G}$ runs over the APW indices and ${\bf G'}$ runs over the ! local-orbital indices. There is no contribution from the ! local-orbital-local-orbital part of the matrices. We can now write the IBS ! correction in terms of the basis of first-variational states as ! \begin{align*} ! {\bf F}_{ij}^{\alpha{\bf k}}=\sum_{\bf G,G'} ! b^{i{\bf k}*}_{\bf G}b^{j{\bf k}}_{\bf G'}\left( ! \delta H_{\bf G,G'}^{\alpha}-\epsilon_j\delta O_{\bf G,G'}^{\alpha}\right), ! \end{align*} ! where $b^{i{\bf k}}$ is the first-variational eigenvector. ! Finally, the ${\bf F}_{ij}^{\alpha{\bf k}}$ matrix elements can be ! multiplied by the second-variational coefficients, and contracted over all ! indices to obtain the IBS force: ! \begin{align*} ! {\bf F}_{\rm IBS}^{\alpha}=\sum_{\bf k}w_{\bf k}\sum_{l\sigma}n_{l{\bf k}} ! \sum_{ij}c_{\sigma i}^{l{\bf k}*}c_{\sigma j}^{l{\bf k}} ! {\bf F}_{ij}^{\alpha{\bf k}} ! +\int_{\rm MT_{\alpha}}v_s({\bf r})\nabla\left[\rho({\bf r}) ! -\rho^{\alpha}_{\rm core}({\bf r})\right]\,d{\bf r}, ! \end{align*} ! where $c^{l{\bf k}}$ are the second-variational coefficients, $w_{\bf k}$ ! are the $k$-point weights, $n_{l{\bf k}}$ are the occupancies. ! ! !REVISION HISTORY: ! Created January 2004 (JKD) ! Fixed problem with second-variational forces, May 2008 (JKD) !EOP !BOC implicit none ! local variables integer ik,idm,ispn integer is,ias,nr,nri integer np,i,j,nthd real(8) ca,t1,t2 real(8) ts0,ts1 ! allocatable arrays real(8), allocatable :: rfmt1(:,:),rfmt2(:),grfmt(:,:) complex(8), allocatable :: zfmt(:),gzfmt(:,:) ! external functions real(8), external :: rfmtinp,rfmtint call timesec(ts0) allocate(zfmt(npmtmax),gzfmt(npmtmax,3)) ! coupling constant of the external A-field (-1/c) ca=-1.d0/solsc !---------------------------------! ! Hellmann-Feynman forces ! !---------------------------------! do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) call rtozfmt(nr,nri,vclmt(:,ias),zfmt) call gradzfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),zfmt,npmtmax,gzfmt) ! force from Coulomb potential forcehf(:,ias)=-spzn(is)*dble(gzfmt(1,:))*y00 ! force on nuclei from time-dependent E-field if (tafieldt) then do i=1,3 t1=(chgcr(is)+spzn(is))*efieldt(i) forcehf(i,ias)=forcehf(i,ias)+t1 end do end if end do deallocate(zfmt,gzfmt) ! symmetrise Hellmann-Feynman forces call symveca(forcehf) !----------------------------------! ! IBS correction to forces ! !----------------------------------! allocate(grfmt(npmtmax,3)) ! set the IBS forces to zero forceibs(:,:)=0.d0 ! compute k-point dependent contribution to the IBS forces call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call forcek(ik) end do !$OMP END PARALLEL DO call freethd(nthd) ! add IBS forces from each process and redistribute if (np_mpi.gt.1) then call mpi_allreduce(mpi_in_place,forceibs,3*natmtot,mpi_double_precision, & mpi_sum,mpicom,ierror) end if if (tafieldt) then t2=afieldt(1,itimes)**2+afieldt(2,itimes)**2+afieldt(3,itimes)**2 t2=t2*ca**2 end if ! integral of Kohn-Sham potential with gradient of density do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rhomt(:,ias),npmtmax,grfmt) do i=1,3 t1=rfmtinp(nr,nri,wrmt(:,is),vsmt(:,ias),grfmt(:,i)) ! remove contribution from gauge correction to the current density if (tafieldt) then t1=t1-t2*rfmtint(nr,nri,wrmt(:,is),grfmt(:,i)) end if forceibs(i,ias)=forceibs(i,ias)+t1 end do end do ! integral of Kohn-Sham magnetic field with magnetisation gradient if (spinpol) then allocate(rfmt1(npmtmax,natmtot)) do idm=1,ndmag do ias=1,natmtot is=idxis(ias) call rfsht(nrcmt(is),nrcmti(is),bsmt(:,ias,idm),rfmt1(:,ias)) end do call rfmtctof(rfmt1) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),magmt(:,ias,idm), & npmtmax,grfmt) do i=1,3 t1=rfmtinp(nr,nri,wrmt(:,is),rfmt1(:,ias),grfmt(:,i)) forceibs(i,ias)=forceibs(i,ias)+t1 end do end do end do deallocate(rfmt1) end if ! integral of Kohn-Sham meta-GGA potential with kinetic energy density gradient if (xcgrad.eq.4) then allocate(rfmt1(npmtmax,natmtot),rfmt2(npmtmax)) do ias=1,natmtot is=idxis(ias) call rfsht(nrcmt(is),nrcmti(is),wsmt(:,ias),rfmt1(:,ias)) end do call rfmtctof(rfmt1) do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) np=npmt(is) rfmt2(1:np)=taumt(1:np,ias,ispn)-taucr(1:np,ias,ispn) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt2,npmtmax,grfmt) do i=1,3 t1=rfmtinp(nr,nri,wrmt(:,is),rfmt1(:,ias),grfmt(:,i)) forceibs(i,ias)=forceibs(i,ias)+t1 end do end do end do deallocate(rfmt1,rfmt2) end if ! time-dependent vector potential times integral of the gradient of the current ! density over the muffin-tin if (tafieldt) then do j=1,3 t1=ca*afieldt(j,itimes) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),jrmt(:,ias,j),npmtmax, & grfmt) do i=1,3 t2=rfmtint(nr,nri,wrmt(:,is),grfmt(:,i)) forceibs(i,ias)=forceibs(i,ias)+t1*t2 end do end do end do end if ! symmetrise IBS forces call symveca(forceibs) ! total force on each atom do ias=1,natmtot forcetot(:,ias)=forcehf(:,ias)+forceibs(:,ias) end do ! symmetrise total forces call symveca(forcetot) ! compute the average force do i=1,3 forceav(i)=0.d0 do ias=1,natmtot forceav(i)=forceav(i)+forcetot(i,ias) end do forceav(i)=forceav(i)/dble(natmtot) end do ! remove the average force, if required, to prevent translation of atomic basis if (tfav0) then do ias=1,natmtot forcetot(:,ias)=forcetot(:,ias)-forceav(:) end do end if ! zero force on atoms with negative mass do ias=1,natmtot is=idxis(ias) if (spmass(is).le.0.d0) forcetot(:,ias)=0.d0 end do ! compute maximum force magnitude over all atoms forcemax=0.d0 do ias=1,natmtot t1=sqrt(forcetot(1,ias)**2+forcetot(2,ias)**2+forcetot(3,ias)**2) if (t1.gt.forcemax) forcemax=t1 end do deallocate(grfmt) call timesec(ts1) timefor=timefor+ts1-ts0 ! write total forces to test file call writetest(750,'total forces',nv=3*natmtot,tol=1.d-3,rva=forcetot) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genvbmatk.f900000644000000000000000000000013014061636517015220 xustar0029 mtime=1623670095.24010219 30 atime=1623670094.002103339 29 ctime=1623670095.24010219 elk-7.2.42/src/genvbmatk.f900000644002504400250440000001021014061636517017251 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genvbmatk(vmt,vir,bmt,bir,ngp,igpig,wfmt,ld,wfgp,vbmat) use modmain use modomp implicit none ! arguments ! the potential and field are multiplied by the radial integration weights in ! the muffin-tin and by the characteristic function in the interstitial region real(8), intent(in) :: vmt(npcmtmax,natmtot),vir(ngtot) real(8), intent(in) :: bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag) integer, intent(in) :: ngp(nspnfv),igpig(ngkmax,nspnfv) complex(8), intent(in) :: wfmt(npcmtmax,natmtot,nspinor,nstsv) integer, intent(in) :: ld complex(8), intent(in) :: wfgp(ld,nspinor,nstsv) complex(8), intent(out) :: vbmat(nstsv,nstsv) ! local variables integer ist,jst,ispn,jspn integer is,ias,npc,igp,nthd ! automatic arrays complex(8) wfmt2(npcmtmax,nspinor),z(ngkmax) ! allocatable arrays complex(8), allocatable :: wfir1(:,:),wfir2(:,:) ! external functions complex(8), external :: zdotc ! zero the matrix elements vbmat(:,:)=0.d0 !-------------------------! ! muffin-tin part ! !-------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(wfmt2,ias,is,npc,ist) & !$OMP NUM_THREADS(nthd) do jst=1,nstsv do ias=1,natmtot is=idxis(ias) npc=npcmt(is) ! apply local potential and magnetic field to spinor wavefunction if (ncmag) then ! non-collinear case call vbmk1(npc,vmt(:,ias),bmt(:,ias,1),bmt(:,ias,2),bmt(:,ias,3), & wfmt(:,ias,1,jst),wfmt(:,ias,2,jst),wfmt2,wfmt2(:,2)) else ! collinear case call vbmk2(npc,vmt(:,ias),bmt(:,ias,1),wfmt(:,ias,1,jst), & wfmt(:,ias,2,jst),wfmt2,wfmt2(:,2)) end if ! compute the inner products do ist=1,jst vbmat(ist,jst)=vbmat(ist,jst) & +zdotc(npc,wfmt(:,ias,1,ist),1,wfmt2,1) & +zdotc(npc,wfmt(:,ias,2,ist),1,wfmt2(:,2),1) end do end do end do !$OMP END PARALLEL DO call freethd(nthd) !---------------------------! ! interstitial part ! !---------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfir1,wfir2,z) & !$OMP PRIVATE(ispn,jspn,igp,ist) & !$OMP NUM_THREADS(nthd) allocate(wfir1(ngtot,nspinor),wfir2(ngtot,nspinor)) !$OMP DO do jst=1,nstsv ! Fourier transform wavefunction to real-space do ispn=1,nspinor jspn=jspnfv(ispn) wfir1(:,ispn)=0.d0 do igp=1,ngp(jspn) wfir1(igfft(igpig(igp,jspn)),ispn)=wfgp(igp,ispn,jst) end do call zfftifc(3,ngridg,1,wfir1(:,ispn)) end do ! apply local potential and magnetic field to spinor wavefunction if (ncmag) then ! non-collinear case call vbmk1(ngtot,vir,bir,bir(:,2),bir(:,3),wfir1,wfir1(:,2),wfir2, & wfir2(:,2)) else ! collinear case call vbmk2(ngtot,vir,bir,wfir1,wfir1(:,2),wfir2,wfir2(:,2)) end if do ispn=1,nspinor jspn=jspnfv(ispn) ! Fourier transform to G+p-space call zfftifc(3,ngridg,-1,wfir2(:,ispn)) do igp=1,ngp(jspn) z(igp)=wfir2(igfft(igpig(igp,jspn)),ispn) end do do ist=1,jst vbmat(ist,jst)=vbmat(ist,jst)+zdotc(ngp(jspn),wfgp(:,ispn,ist),1,z,1) end do end do end do !$OMP END DO deallocate(wfir1,wfir2) !$OMP END PARALLEL call freethd(nthd) ! lower triangular part do ist=1,nstsv do jst=1,ist-1 vbmat(ist,jst)=conjg(vbmat(jst,ist)) end do end do return contains pure subroutine vbmk1(n,v,b1,b2,b3,wf11,wf12,wf21,wf22) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: v(n),b1(n),b2(n),b3(n) complex(8), intent(in) :: wf11(n),wf12(n) complex(8), intent(out) :: wf21(n),wf22(n) ! local variables integer i complex(8) z1 do i=1,n z1=cmplx(b1(i),b2(i),8) wf21(i)=(v(i)+b3(i))*wf11(i)+conjg(z1)*wf12(i) wf22(i)=(v(i)-b3(i))*wf12(i)+z1*wf11(i) end do end subroutine pure subroutine vbmk2(n,v,b,wf11,wf12,wf21,wf22) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: v(n),b(n) complex(8), intent(in) :: wf11(n),wf12(n) complex(8), intent(out) :: wf21(n),wf22(n) ! local variables integer i do i=1,n wf21(i)=(v(i)+b(i))*wf11(i) wf22(i)=(v(i)-b(i))*wf12(i) end do end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqn.f900000644000000000000000000000013214061636517014362 xustar0030 mtime=1623670095.242102188 30 atime=1623670094.004103337 30 ctime=1623670095.242102188 elk-7.2.42/src/eveqn.f900000644002504400250440000000416214061636517016422 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: eveqn subroutine eveqn(ik,evalfv,evecfv,evecsv) ! !USES: use modmain use modulr ! !INPUT/OUTPUT PARAMETERS: ! ik : k-point number (in,integer) ! evalfv : first-variational eigenvalues (out,real(nstfv)) ! evecfv : first-variational eigenvectors (out,complex(nmatmax,nstfv)) ! evecsv : second-variational eigenvectors (out,complex(nstsv,nstsv)) ! !DESCRIPTION: ! Solves the first- and second-variational eigenvalue equations. See routines ! {\tt match}, {\tt eveqnfv}, {\tt eveqnss} and {\tt eveqnsv}. ! ! !REVISION HISTORY: ! Created March 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: ik real(8), intent(out) :: evalfv(nstfv,nspnfv) complex(8), intent(out) :: evecfv(nmatmax,nstfv,nspnfv),evecsv(nstsv,nstsv) ! local variables integer jspn ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:,:) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) ! loop over first-variational spins (nspnfv=2 for spin-spirals only) do jspn=1,nspnfv ! find the matching coefficients call match(ngk(jspn,ik),vgkc(:,:,jspn,ik),gkc(:,jspn,ik), & sfacgk(:,:,jspn,ik),apwalm(:,:,:,:,jspn)) ! solve the first-variational eigenvalue equation if (tefvit) then ! iteratively call eveqnit(nmat(jspn,ik),ngk(jspn,ik),igkig(:,jspn,ik),vkl(:,ik), & vgkl(:,:,jspn,ik),vgkc(:,:,jspn,ik),apwalm(:,:,:,:,jspn),evalfv(:,jspn), & evecfv(:,:,jspn)) else ! directly call eveqnfv(nmat(jspn,ik),ngk(jspn,ik),igkig(:,jspn,ik),vkc(:,ik), & vgkc(:,:,jspn,ik),apwalm(:,:,:,:,jspn),evalfv(:,jspn),evecfv(:,:,jspn)) end if end do if (spinsprl) then ! solve the spin-spiral second-variational eigenvalue equation call eveqnss(ngk(:,ik),igkig(:,:,ik),apwalm,evalfv,evecfv,evalsv(:,ik),evecsv) else ! solve the second-variational eigenvalue equation call eveqnsv(ngk(1,ik),igkig(:,1,ik),vgkc(:,:,1,ik),apwalm,evalfv,evecfv, & evalsv(:,ik),evecsv) end if deallocate(apwalm) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/forcek.f900000644000000000000000000000013214061636517014515 xustar0030 mtime=1623670095.243102188 30 atime=1623670094.006103336 30 ctime=1623670095.243102188 elk-7.2.42/src/forcek.f900000644002504400250440000001176314061636517016562 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: forcek ! !INTERFACE: subroutine forcek(ik) ! !USES: use modmain use modomp ! !INPUT/OUTPUT PARAMETERS: ! ik : reduced k-point number (in,integer) ! !DESCRIPTION: ! Computes the {\bf k}-dependent contribution to the incomplete basis set ! (IBS) force. See the calling routine {\tt force} for a full description. ! ! !REVISION HISTORY: ! Created June 2006 (JKD) ! Updated for spin-spiral case, May 2007 (Francesco Cricchio and JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: ik ! local variables integer ispn0,ispn1,ispn,jspn integer n,nm,nm2,is,ias,ist,jst integer j1,j2,j3,ig,i,j,k,l integer nthd real(8) v1,v2,v3,sm,t1 complex(8) z1,z2 ! automatic arrays real(8) evalfv(nstfv,nspnfv) complex(8) vh(nmatmax),vo(nmatmax) complex(8) ffv(nstfv,nstfv),y(nstfv) ! allocatable arrays integer, allocatable :: ijg(:) real(8), allocatable :: dp(:) complex(8), allocatable :: apwalm(:,:,:,:) complex(8), allocatable :: evecfv(:,:,:),evecsv(:,:) complex(8), allocatable :: h(:),o(:),dlh(:),dlo(:) ! external functions complex(8), external :: zdotc nm2=nmatmax**2 ! allocate local arrays allocate(ijg(nm2),dp(nm2)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(evecfv(nmatmax,nstfv,nspnfv)) allocate(h(nm2),o(nm2),dlh(nm2),dlo(nm2)) ! get the eigenvalues/vectors from file call getevalfv(filext,ik,vkl(:,ik),evalfv) call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) if (tevecsv) then allocate(evecsv(nstsv,nstsv)) call getevecsv(filext,ik,vkl(:,ik),evecsv) end if ! loop over first-variational spin components do jspn=1,nspnfv if (spinsprl) then ispn0=jspn; ispn1=jspn else ispn0=1; ispn1=nspinor end if n=ngk(jspn,ik) nm=nmat(jspn,ik) do j=1,n k=(j-1)*nm ig=igkig(j,jspn,ik) j1=ivg(1,ig); j2=ivg(2,ig); j3=ivg(3,ig) v1=0.5d0*vgkc(1,j,jspn,ik) v2=0.5d0*vgkc(2,j,jspn,ik) v3=0.5d0*vgkc(3,j,jspn,ik) do i=1,j k=k+1 ig=igkig(i,jspn,ik) ijg(k)=ivgig(ivg(1,ig)-j1,ivg(2,ig)-j2,ivg(3,ig)-j3) dp(k)=vgkc(1,i,jspn,ik)*v1 & +vgkc(2,i,jspn,ik)*v2 & +vgkc(3,i,jspn,ik)*v3 end do end do ! find the matching coefficients call match(n,vgkc(:,:,jspn,ik),gkc(:,jspn,ik),sfacgk(:,:,jspn,ik),apwalm) ! zero the local-orbital-local-orbital contribution do j=n+1,nm k=(j-1)*nm+n do i=n+1,j k=k+1 dlh(k)=0.d0 dlo(k)=0.d0 end do end do ! loop over species and atoms do ias=1,natmtot is=idxis(ias) ! Hamiltonian and overlap matrices h(:)=0.d0 call hmlaa(.false.,is,ias,n,apwalm(:,:,:,ias),nm,h) call hmlalo(is,ias,n,apwalm(:,:,:,ias),nm,h) o(:)=0.d0 call olpaa(.false.,is,n,apwalm(:,:,:,ias),nm,o) call olpalo(is,ias,n,apwalm(:,:,:,ias),nm,o) ! loop over Cartesian directions do l=1,3 ! APW-APW contribution do j=1,n k=(j-1)*nm do i=1,j k=k+1 ig=ijg(k) t1=vgc(l,ig) z1=-ffacg(ig,is)*conjg(sfacg(ig,ias)) z2=t1*(dp(k)*z1+h(k)) dlh(k)=cmplx(-aimag(z2),dble(z2),8) z2=t1*(z1+o(k)) dlo(k)=cmplx(-aimag(z2),dble(z2),8) end do end do ! APW-local-orbital contribution do j=n+1,nm k=(j-1)*nm do i=1,n k=k+1 t1=vgkc(l,i,jspn,ik) z1=t1*h(k) dlh(k)=cmplx(-aimag(z1),dble(z1),8) z1=t1*o(k) dlo(k)=cmplx(-aimag(z1),dble(z1),8) end do end do ! compute the force matrix elements in the first-variational basis call holdthd(nstfv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(vh,vo,t1,ist,z1,z2) & !$OMP NUM_THREADS(nthd) do jst=1,nstfv call zhemv('U',nm,zone,dlh,nm,evecfv(:,jst,jspn),1,zzero,vh,1) call zhemv('U',nm,zone,dlo,nm,evecfv(:,jst,jspn),1,zzero,vo,1) t1=evalfv(jst,jspn) do ist=1,nstfv z1=zdotc(nm,evecfv(:,ist,jspn),1,vh,1) z2=zdotc(nm,evecfv(:,ist,jspn),1,vo,1) ffv(ist,jst)=z1-t1*z2 end do end do !$OMP END PARALLEL DO call freethd(nthd) ! compute the force using the second-variational coefficients if required sm=0.d0 if (tevecsv) then ! spin-polarised case do j=1,nstsv do ispn=ispn0,ispn1 i=(ispn-1)*nstfv+1 call zgemv('N',nstfv,nstfv,zone,ffv,nstfv,evecsv(i,j),1,zzero,y,1) z1=zdotc(nstfv,evecsv(i,j),1,y,1) sm=sm+occsv(j,ik)*dble(z1) end do end do else ! spin-unpolarised case do j=1,nstsv sm=sm+occsv(j,ik)*dble(ffv(j,j)) end do end if !$OMP ATOMIC forceibs(l,ias)=forceibs(l,ias)+wkpt(ik)*sm ! end loop over Cartesian components end do ! end loop over atoms and species end do ! end loop over first-variational spins end do deallocate(ijg,dp,apwalm,evecfv) deallocate(h,o,dlh,dlo) if (tevecsv) deallocate(evecsv) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writeepsinv.f900000644000000000000000000000013214061636517015623 xustar0030 mtime=1623670095.244102186 30 atime=1623670094.007103335 30 ctime=1623670095.244102186 elk-7.2.42/src/writeepsinv.f900000644002504400250440000000202414061636517017656 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeepsinv use modmain use modmpi implicit none ! local variables integer ik ! initialise global variables call init0 call init1 call init2 call init3 ! read density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! generate the inverse dielectric function and write to file call epsinv if (mp_mpi) then write(*,*) write(*,'("Info(writeepsinv):")') write(*,'(" inverse RPA dielectric function, eps^(-1)(G,G'',q,w), written to & &EPSINV.OUT")') end if end subroutine elk-7.2.42/src/PaxHeaders.21776/olprad.f900000644000000000000000000000013214061636517014525 xustar0030 mtime=1623670095.246102185 30 atime=1623670094.009103333 30 ctime=1623670095.246102185 elk-7.2.42/src/olprad.f900000644002504400250440000000330514061636517016563 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: olprad ! !INTERFACE: subroutine olprad ! !USES: use modmain ! !DESCRIPTION: ! Calculates the radial overlap integrals of the APW and local-orbital basis ! functions. In other words, for atom $\alpha$, it computes integrals of the ! form ! $$ o^{\alpha}_{qp}=\int_0^{R_i}u^{\alpha}_{q;l_p}(r)v^{\alpha}_p(r)r^2dr $$ ! and ! $$ o^{\alpha}_{pp'}=\int_0^{R_i}v^{\alpha}_p(r)v^{\alpha}_{p'}(r)r^2dr, ! \quad l_p=l_{p'} $$ ! where $u^{\alpha}_{q;l}$ is the $q$th APW radial function for angular ! momentum $l$; and $v^{\alpha}_p$ is the $p$th local-orbital radial function ! and has angular momentum $l_p$. ! ! !REVISION HISTORY: ! Created November 2003 (JKD) !EOP !BOC implicit none ! local variables integer is,ias,nr integer ilo,jlo,l,io do ias=1,natmtot is=idxis(ias) nr=nrmt(is) !-------------------------------------! ! APW-local-orbital integrals ! !-------------------------------------! do ilo=1,nlorb(is) l=lorbl(ilo,is) do io=1,apword(l,is) oalo(io,ilo,ias)=sum(apwfr(1:nr,1,io,l,ias)*lofr(1:nr,1,ilo,ias) & *wrmt(1:nr,is)) end do end do !-----------------------------------------------! ! local-orbital-local-orbital integrals ! !-----------------------------------------------! do ilo=1,nlorb(is) l=lorbl(ilo,is) do jlo=1,nlorb(is) if (lorbl(jlo,is).eq.l) then ololo(ilo,jlo,ias)=sum(lofr(1:nr,1,ilo,ias)*lofr(1:nr,1,jlo,ias) & *wrmt(1:nr,is)) end if end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/polark.f900000644000000000000000000000013214061636517014534 xustar0030 mtime=1623670095.247102184 30 atime=1623670094.011103331 30 ctime=1623670095.247102184 elk-7.2.42/src/polark.f900000644002504400250440000000346714061636517016603 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine polark(ik,l,expqmt,pl) use modmain implicit none ! arguments integer, intent(in) :: ik,l complex(8), intent(in) :: expqmt(npcmtmax,natmtot) real(8), intent(inout) :: pl ! local variables integer jk,nst,ist real(8) vkql(3) complex(8) z1 ! automatic arrays integer idx(nstsv),ngp(nspnfv) ! allocatable arrays integer, allocatable :: igpig(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfir(:,:,:) complex(8), allocatable :: wfmtq(:,:,:,:),wfgkq(:,:,:) complex(8), allocatable :: oq(:,:) ! external functions complex(8), external :: zmdet ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! find the adjacent k-point in lattice coordinates vkql(:)=vkl(:,ik) vkql(l)=vkql(l)+1.d0/dble(ngridk(l)) ! count and index the occupied states nst=0 do ist=1,nstsv if (evalsv(ist,jk).gt.efermi) cycle nst=nst+1 idx(nst)=ist end do allocate(igpig(ngkmax,nspnfv)) ! generate the wavefunctions for occupied states at k allocate(wfmt(npcmtmax,natmtot,nspinor,nst),wfir(ngtot,nspinor,nst)) call genwfsvp(.false.,.false.,nst,idx,ngridg,igfft,vkl(:,ik),ngp,igpig,wfmt, & ngtot,wfir) ! generate the wavefunctions for occupied states at k+q allocate(wfmtq(npcmtmax,natmtot,nspinor,nst),wfgkq(ngkmax,nspinor,nst)) call genwfsvp(.false.,.true.,nst,idx,ngridg,igfft,vkql,ngp,igpig,wfmtq,ngkmax, & wfgkq) ! determine the overlap matrix for all occupied states allocate(oq(nst,nst)) call genolpq(nst,expqmt,ngp,igpig,wfmt,wfir,wfmtq,wfgkq,oq) ! compute the determinant of the matrix z1=zmdet(nst,oq) ! determine the phase of the determinant and add to total polarisation pl=pl+atan2(aimag(z1),dble(z1)) deallocate(igpig,wfmt,wfir,wfmtq,wfgkq,oq) end subroutine elk-7.2.42/src/PaxHeaders.21776/zfmtinp.f900000644000000000000000000000013114061636517014732 xustar0030 mtime=1623670095.249102182 29 atime=1623670094.01210333 30 ctime=1623670095.249102182 elk-7.2.42/src/zfmtinp.f900000644002504400250440000000367114061636517016777 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zfmtinp ! !INTERFACE: complex(8) function zfmtinp(nr,nri,wr,zfmt1,zfmt2) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial mesh points (in,integer) ! nri : number of points on the inner part of the muffin-tin (in,integer) ! wr : weights for integration on radial mesh (in,real(nr)) ! zfmt1 : first complex muffin-tin function in spherical harmonics ! (in,complex(*)) ! zfmt2 : second complex muffin-tin function (in,complex(*)) ! !DESCRIPTION: ! Calculates the inner product of two complex fuctions in the muffin-tin. In ! other words, given two complex functions of the form ! $$ f({\bf r})=\sum_{l=0}^{l_{\rm max}}\sum_{m=-l}^{l}f_{lm}(r)Y_{lm} ! (\hat{\bf r}), $$ ! the function returns ! $$ I=\sum_{l=0}^{l_{\rm max}}\sum_{m=-l}^{l}\int f_{lm}^{1*}(r) ! f_{lm}^2(r)r^2\,dr\;. $$ ! ! !REVISION HISTORY: ! Created November 2003 (Sharma) ! Modified, September 2013 (JKD) ! Modified for packed functions, June 2016 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: wr(nr) complex(8), intent(in) :: zfmt1(*),zfmt2(*) ! local variables integer ir,i ! external functions complex(8), external :: zdotc ! compute the dot-products for each radial point and integrate over r zfmtinp=0.d0 i=1 if (lmaxi.eq.1) then do ir=1,nri zfmtinp=zfmtinp+wr(ir) & *(conjg(zfmt1(i))*zfmt2(i) & +conjg(zfmt1(i+1))*zfmt2(i+1) & +conjg(zfmt1(i+2))*zfmt2(i+2) & +conjg(zfmt1(i+3))*zfmt2(i+3)) i=i+4 end do else do ir=1,nri zfmtinp=zfmtinp+wr(ir)*zdotc(lmmaxi,zfmt1(i),1,zfmt2(i),1) i=i+lmmaxi end do end if do ir=nri+1,nr zfmtinp=zfmtinp+wr(ir)*zdotc(lmmaxo,zfmt1(i),1,zfmt2(i),1) i=i+lmmaxo end do end function !EOC elk-7.2.42/src/PaxHeaders.21776/hflocal.f900000644000000000000000000000013214061636517014654 xustar0030 mtime=1623670095.250102181 30 atime=1623670094.014103328 30 ctime=1623670095.250102181 elk-7.2.42/src/hflocal.f900000644002504400250440000000335414061636517016716 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine hflocal(vmt,vir,bmt,bir) use modmain implicit none ! arguments real(8), intent(out) :: vmt(npcmtmax,natmtot),vir(ngtot) real(8), intent(out) :: bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag) ! local variables integer idm,is,ias integer np,nrc,nrci ! automatic arrays real(8) rfmt1(npmtmax),rfmt2(npcmtmax) ! compute the Coulomb potential call potcoul ! convert to spherical coordinates and store in output arrays if (hybrid) then ! hybrid functional case call potxc(.true.,xctype,rhomt,rhoir,magmt,magir,taumt,tauir,exmt,exir,ecmt, & ecir,vxcmt,vxcir,bxcmt,bxcir,wxcmt,wxcir) do ias=1,natmtot is=idxis(ias) np=npmt(is) nrc=nrcmt(is) nrci=nrcmti(is) rfmt1(1:np)=vclmt(1:np,ias)+vxcmt(1:np,ias) call rfmtftoc(nrc,nrci,rfmt1,rfmt2) call rbsht(nrc,nrci,rfmt2,vmt(:,ias)) call rfcmtwr(nrc,nrci,wrcmt(:,is),vmt(:,ias)) end do vir(:)=(vclir(:)+vxcir(:))*cfunir(:) if (spinpol) then do idm=1,ndmag do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) call rfmtftoc(nrc,nrci,bxcmt(:,ias,idm),rfmt1) call rbsht(nrc,nrci,rfmt1,bmt(:,ias,idm)) call rfcmtwr(nrc,nrci,wrcmt(:,is),bmt(:,ias,idm)) end do bir(:,idm)=bxcir(:,idm)*cfunir(:) end do end if else ! normal Hartree-Fock case do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) call rfmtftoc(nrc,nrci,vclmt(:,ias),rfmt1) call rbsht(nrc,nrci,rfmt1,vmt(:,ias)) call rfcmtwr(nrc,nrci,wrcmt(:,is),vmt(:,ias)) end do vir(:)=vclir(:)*cfunir(:) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/mixbroyden.f900000644000000000000000000000013014061636517015422 xustar0029 mtime=1623670095.25110218 30 atime=1623670094.016103326 29 ctime=1623670095.25110218 elk-7.2.42/src/mixbroyden.f900000644002504400250440000000444214061636517017465 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine mixbroyden(iscl,n,msd,alpha,w0,nu,mu,f,df,u,a,d) use modomp implicit none ! arguments integer, intent(in) :: iscl,n,msd real(8), intent(in) :: alpha,w0 real(8), intent(inout) :: nu(n),mu(n,2) real(8), intent(inout) :: f(n,2),df(n,msd) real(8), intent(inout) :: u(n,msd) real(8), intent(inout) :: a(msd,msd) real(8), intent(out) :: d ! local variables integer jc,kp,kc integer k,l,m integer info,nthd real(8) t1 ! automatic arrays integer ipiv(msd) real(8) c(msd),beta(msd,msd),gamma(msd),work(msd) ! external functions real(8), external :: dnrm2 if (n.lt.1) then write(*,*) write(*,'("Error(mixbroyden): n < 1 : ",I8)') n write(*,*) stop end if if (msd.lt.2) then write(*,*) write(*,'("Error(mixbroyden): msd < 2 : ",I8)') msd write(*,*) stop end if ! initialise mixer if (iscl.le.0) then call dcopy(n,nu,1,mu,1) call dcopy(n,nu,1,mu(:,2),1) f(:,1)=0.d0 df(:,1)=0.d0 u(:,1)=0.d0 a(:,:)=0.d0 d=1.d0 return end if ! current subspace dimension m=min(iscl+1,msd) ! current index modulo m jc=mod(iscl,m)+1 ! previous index modulo 2 kp=mod(iscl-1,2)+1 ! current index modulo 2 kc=mod(iscl,2)+1 f(:,kc)=nu(:)-mu(:,kp) d=sum(f(:,kc)**2) d=sqrt(d/dble(n)) df(:,jc)=f(:,kc)-f(:,kp) t1=dnrm2(n,df(:,jc),1) if (t1.gt.1.d-8) t1=1.d0/t1 call dscal(n,t1,df(:,jc),1) u(:,jc)=alpha*df(:,jc)+t1*(mu(:,kp)-mu(:,kc)) call holdthd(m,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP DO do k=1,m c(k)=dot_product(df(:,k),f(:,kc)) end do !$OMP END DO NOWAIT !$OMP DO do k=1,m a(k,jc)=dot_product(df(:,jc),df(:,k)) a(jc,k)=a(k,jc) end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) beta(:,:)=a(:,:) do k=1,m beta(k,k)=beta(k,k)+w0**2 end do ! invert beta call dgetrf(m,m,beta,msd,ipiv,info) if (info.eq.0) call dgetri(m,beta,msd,ipiv,work,m,info) if (info.ne.0) then write(*,*) write(*,'("Error(mixbroyden): could not invert matrix")') write(*,*) stop end if do l=1,m gamma(l)=0.d0 do k=1,m gamma(l)=gamma(l)+c(k)*beta(k,l) end do end do nu(:)=mu(:,kp)+alpha*f(:,kc) do l=1,m call daxpy(n,-gamma(l),u(:,l),1,nu,1) end do call dcopy(n,nu,1,mu(:,kc),1) end subroutine elk-7.2.42/src/PaxHeaders.21776/zmdet.f900000644000000000000000000000013214061636517014367 xustar0030 mtime=1623670095.253102178 30 atime=1623670094.017103325 30 ctime=1623670095.253102178 elk-7.2.42/src/zmdet.f900000644002504400250440000000124414061636517016425 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. complex(8) function zmdet(n,a) implicit none ! arguments integer, intent(in) :: n complex(8), intent(in) :: a(n,n) ! local variables integer i,m,info ! automatic arrays integer ipiv(n) ! perform an LU factorisation of the input matrix call zgetrf(n,n,a,n,ipiv,info) ! multiply diagonal elements of U together zmdet=a(1,1) do i=2,n zmdet=zmdet*a(i,i) end do ! determine the sign from the number of row interchanges m=1 do i=1,n if (ipiv(i).ne.i) m=-m end do if (m.eq.-1) zmdet=-zmdet end function elk-7.2.42/src/PaxHeaders.21776/grad2rfmt.f900000644000000000000000000000013214061636517015134 xustar0030 mtime=1623670095.254102177 30 atime=1623670094.019103324 30 ctime=1623670095.254102177 elk-7.2.42/src/grad2rfmt.f900000644002504400250440000000301114061636517017164 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine grad2rfmt(nr,nri,ri,ri2,wcr,rfmt,g2rfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: ri(nr),ri2(nr),wcr(12,nr) real(8), intent(in) :: rfmt(*) real(8), intent(out) :: g2rfmt(*) ! local variables integer nro,iro,ir integer l,m,lm,npi,i real(8) t1 ! automatic arrays real(8) fr(nr),cf(3,nr) nro=nr-nri iro=nri+1 npi=lmmaxi*nri lm=0 do l=0,lmaxi t1=-dble(l*(l+1)) do m=-l,l lm=lm+1 ! use a cubic spline to compute radial derivatives i=lm do ir=1,nri fr(ir)=rfmt(i) i=i+lmmaxi end do do ir=iro,nr fr(ir)=rfmt(i) i=i+lmmaxo end do call splinew(nr,wcr,fr,cf) ! apply Laplacian i=lm do ir=1,nri g2rfmt(i)=2.d0*(ri(ir)*cf(1,ir)+cf(2,ir))+ri2(ir)*t1*rfmt(i) i=i+lmmaxi end do do ir=iro,nr g2rfmt(i)=2.d0*(ri(ir)*cf(1,ir)+cf(2,ir))+ri2(ir)*t1*rfmt(i) i=i+lmmaxo end do end do end do do l=lmaxi+1,lmaxo t1=-dble(l*(l+1)) do m=-l,l lm=lm+1 i=npi+lm do ir=iro,nr fr(ir)=rfmt(i) i=i+lmmaxo end do call splinew(nro,wcr(:,iro),fr(iro),cf(1,iro)) i=npi+lm do ir=iro,nr g2rfmt(i)=2.d0*(ri(ir)*cf(1,ir)+cf(2,ir))+ri2(ir)*t1*rfmt(i) i=i+lmmaxo end do end do end do ! apply smoothing if required call rfmtsm(msmooth,nr,nri,g2rfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/clebgor.f900000644000000000000000000000013214061636517014661 xustar0030 mtime=1623670095.256102175 30 atime=1623670094.021103322 30 ctime=1623670095.256102175 elk-7.2.42/src/clebgor.f900000644002504400250440000000331114061636517016714 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: clebgor ! !INTERFACE: real(8) function clebgor(j1,j2,j3,m1,m2,m3) ! !INPUT/OUTPUT PARAMETERS: ! j1, j2, j3 : angular momentum quantum numbers (in,integer) ! m1, m2, m3 : magnetic quantum numbers (in,integer) ! !DESCRIPTION: ! Returns the Clebsch-Gordon coefficients using the Wigner $3j$-symbols ! $$ C(J_1 J_2 J_3 | m_1 m_2 m_3)=(-1)^{J_1-J_2+m_3}\sqrt{2J_3+1} ! \begin{pmatrix} J_1 & J_2 & J_3 \\ m_1 & m_2 & -m_3 \end{pmatrix}. $$ ! Suitable for $J_i\le 50$. See {\tt wigner3j}. ! ! !REVISION HISTORY: ! Created September 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: j1,j2,j3 integer, intent(in) :: m1,m2,m3 ! external functions real(8), external :: wigner3j if ((j1.lt.0).or.(j2.lt.0).or.(j3.lt.0).or.(abs(m1).gt.j1).or.(abs(m2).gt.j2) & .or.(abs(m2).gt.j2).or.(abs(m3).gt.j3)) then write(*,*) write(*,'("Error(clebgor): non-physical arguments :")') write(*,'("j1 = ",I8," j2 = ",I8," j3 = ",I8)') j1,j2,j3 write(*,'("m1 = ",I8," m2 = ",I8," m3 = ",I8)') m1,m2,m3 write(*,*) stop end if if ((j1.eq.0).and.(j2.eq.0).and.(j3.eq.0)) then clebgor=1.d0 return end if if ((j1.gt.50).or.(j2.gt.50).or.(j3.gt.50)) then write(*,*) write(*,'("Error(clebgor): angular momenta out of range : ",3I8)') j1,j2,j3 write(*,*) stop end if if ((m1+m2.ne.m3).or.(j1+j2.lt.j3).or.(j2+j3.lt.j1).or.(j1+j3.lt.j2)) then clebgor=0.d0 return end if clebgor=sqrt(dble(2*j3+1))*wigner3j(j1,j2,j3,m1,m2,-m3) if (mod(j1-j2+m3,2).ne.0) clebgor=-clebgor end function !EOC elk-7.2.42/src/PaxHeaders.21776/rfirctof.f900000644000000000000000000000013214061636517015062 xustar0030 mtime=1623670095.257102174 30 atime=1623670094.022103321 30 ctime=1623670095.257102174 elk-7.2.42/src/rfirctof.f900000644002504400250440000000140514061636517017117 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rfirctof(rfirc,rfir) use modmain implicit none ! arguments real(8), intent(in) :: rfirc(ngtc) real(8), intent(out) :: rfir(ngtot) ! local variables integer ig ! allocatable arrays complex(8), allocatable :: zfftc(:),zfft(:) allocate(zfftc(ngtc),zfft(ngtot)) ! Fourier transform function on coarse grid to G-space zfftc(:)=rfirc(:) call zfftifc(3,ngdgc,-1,zfftc) ! Fourier transform to fine real-space grid zfft(:)=0.d0 do ig=1,ngvc zfft(igfft(ig))=zfftc(igfc(ig)) end do call zfftifc(3,ngridg,1,zfft) ! output real function rfir(:)=dble(zfft(:)) deallocate(zfftc,zfft) end subroutine elk-7.2.42/src/PaxHeaders.21776/effmass.f900000644000000000000000000000013214061636517014670 xustar0030 mtime=1623670095.258102174 30 atime=1623670094.024103319 30 ctime=1623670095.258102174 elk-7.2.42/src/effmass.f900000644002504400250440000001130114061636517016721 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine effmass use modmain use modomp use modtest implicit none ! local variables integer ik0,ik,ist,info integer i,j,k,l,m,n,nthd integer i1,i2,i3,j1,j2,j3 real(8) d(3,3),em(3,3) real(8) v1(3),v2(3) real(8) w(3),work(9) ! allocatable arrays integer, allocatable :: ipiv(:) real(8), allocatable :: a(:,:),b(:,:,:,:),c(:,:,:),evalfv(:,:) complex(8), allocatable :: evecfv(:,:,:),evecsv(:,:) ! initialise universal variables call init0 call init1 allocate(ipiv(nkpt)) allocate(a(nkpt,nkpt)) n=2*ndspem+1 allocate(b(0:n-1,0:n-1,0:n-1,nstsv)) allocate(c(0:n-1,0:n-1,0:n-1)) ! read density and potentials from file call readstate ! Fourier transform Kohn-Sham potential to G-space call genvsig ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! generate the spin-orbit coupling radial functions call gensocfr ik0=0 ! begin parallel loop over k-points call holdthd(nkpt,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evalfv,evecfv,evecsv) & !$OMP PRIVATE(i1,i2,i3,j1,j2,j3,ist) & !$OMP NUM_THREADS(nthd) allocate(evalfv(nstfv,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv)) allocate(evecsv(nstsv,nstsv)) !$OMP DO do ik=1,nkpt i1=ivk(1,ik); i2=ivk(2,ik); i3=ivk(3,ik) if ((i1.eq.0).and.(i2.eq.0).and.(i3.eq.0)) ik0=ik ! solve the first- and second-variational eigenvalue equations call eveqn(ik,evalfv,evecfv,evecsv) ! copy eigenvalues to new array j1=i1+ndspem; j2=i2+ndspem; j3=i3+ndspem do ist=1,nstsv b(j1,j2,j3,ist)=evalsv(ist,ik) end do end do !$OMP END DO deallocate(evalfv,evecfv,evecsv) !$OMP END PARALLEL call freethd(nthd) ! set up polynomial matrix i=0 do i3=-ndspem,ndspem do i2=-ndspem,ndspem do i1=-ndspem,ndspem i=i+1 v1(1)=dble(i1); v1(2)=dble(i2); v1(3)=dble(i3) v1(:)=v1(:)*deltaem j=0 v2(3)=1.d0 do j3=0,n-1 v2(2)=1.d0 do j2=0,n-1 v2(1)=1.d0 do j1=0,n-1 j=j+1 a(i,j)=v2(1)*v2(2)*v2(3) v2(1)=v2(1)*v1(1) end do v2(2)=v2(2)*v1(2) end do v2(3)=v2(3)*v1(3) end do end do end do end do ! solve for the polynomial coefficients call dgesv(nkpt,nstsv,a,nkpt,ipiv,b,nkpt,info) if (info.ne.0) then write(*,*) write(*,'("Error(effmass): could not determine polynomial coefficients")') write(*,'(" DGESV returned INFO = ",I8)') info write(*,*) stop end if open(50,file='EFFMASS.OUT',form='FORMATTED') write(50,*) write(50,'("(effective mass matrices are in Cartesian coordinates)")') write(50,*) write(50,'("k-point (lattice coordinates) :")') write(50,'(3G18.10)') vklem write(50,*) write(50,'("k-point (Cartesian coordinates) :")') call r3mv(bvec,vklem,v1) write(50,'(3G18.10)') v1 ! begin loop over states do ist=1,nstsv ! compute matrix of derivatives with respect to k-vector do k=1,3 do l=1,3 c(:,:,:)=b(:,:,:,ist) do i=1,2 if (i.eq.1) then m=k else m=l end if if (m.eq.1) then do j=0,n-2 c(j,:,:)=dble(j+1)*c(j+1,:,:) end do c(n-1,:,:)=0.d0 else if (m.eq.2) then do j=0,n-2 c(:,j,:)=dble(j+1)*c(:,j+1,:) end do c(:,n-1,:)=0.d0 else if (m.eq.3) then do j=0,n-2 c(:,:,j)=dble(j+1)*c(:,:,j+1) end do c(:,:,n-1)=0.d0 end if end do ! derivative evaluated at zero d(k,l)=c(0,0,0) end do end do write(50,*) write(50,*) write(50,'("State, eigenvalue : ",I6,G18.10)') ist,evalsv(ist,ik0) write(50,*) write(50,'(" matrix of eigenvalue derivatives with respect to k :")') do i=1,3 write(50,'(3G18.10)') (d(i,j),j=1,3) end do write(50,'(" trace : ",G18.10)') d(1,1)+d(2,2)+d(3,3) ! invert derivative matrix call r3minv(d,em) write(50,*) write(50,'(" effective mass tensor (inverse of derivative matrix) :")') do i=1,3 write(50,'(3G18.10)') (em(i,j),j=1,3) end do write(50,'(" trace : ",G18.10)') em(1,1)+em(2,2)+em(3,3) ! find the eigenvalues call dsyev('N','U',3,em,3,w,work,9,info) write(50,'(" eigenvalues :")') write(50,'(3G18.10)') w ! end loop over states end do close(50) write(*,*) write(*,'("Info(effmass):")') write(*,'(" Effective mass tensor for each state written to EFFMASS.OUT")') write(*,'(" for k-point (lattice) ",3G18.10)') vklem ! write the effective mass eigenvalues of the last state to test file call writetest(25,'effective mass',nv=3,tol=1.d-6,rva=w) deallocate(ipiv,a,b,c) end subroutine elk-7.2.42/src/PaxHeaders.21776/genffacgp.f900000644000000000000000000000013214061636517015164 xustar0030 mtime=1623670095.260102172 30 atime=1623670094.025103318 30 ctime=1623670095.260102172 elk-7.2.42/src/genffacgp.f900000644002504400250440000000116014061636517017217 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine genffacgp(is,gpc,ffacgp) use modmain implicit none ! arguments integer, intent(in) :: is real(8), intent(in) :: gpc(ngtot) real(8), intent(out) :: ffacgp(ngtot) ! local variables integer ig real(8) t1,t2 t1=fourpi/omega do ig=1,ngtot if (gpc(ig).gt.epslat) then t2=gpc(ig)*rmt(is) ffacgp(ig)=t1*(sin(t2)-t2*cos(t2))/(gpc(ig)**3) else ffacgp(ig)=(t1/3.d0)*rmt(is)**3 end if end do end subroutine elk-7.2.42/src/PaxHeaders.21776/zpotcoul.f900000644000000000000000000000013214061636517015123 xustar0030 mtime=1623670095.261102171 30 atime=1623670094.027103316 30 ctime=1623670095.261102171 elk-7.2.42/src/zpotcoul.f900000644002504400250440000002370214061636517017164 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zpotcoul ! !INTERFACE: subroutine zpotcoul(nr,nri,np,npi,ld1,rl,ngdg,igf,ngp,gpc,gclgp,ld2,jlgprmt, & ylmgp,sfacgp,zrhoir,ld3,zvclmt,zvclir) ! !USES: use modmain use modphonon ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial points for each species (in,integer(nspecies)) ! nri : number of radial points on inner part (in,integer(nspecies)) ! np : total number of points in muffin-tins (in,integer(nspecies)) ! npi : number of points on inner part (in,integer(nspecies)) ! ld1 : leading dimension (in,integer) ! rl : r^l on radial mesh for each species ! (in,real(ld1,-lmaxo-1:lmaxo+2,nspecies)) ! ngdg : G-vector grid sizes (in,integer(3)) ! igf : map from G-vector index to FFT array (in,integer(*)) ! ngp : number of G+p-vectors (in,integer) ! gpc : G+p-vector lengths (in,real(ngp)) ! gclgp : Coulomb Green's function in G+p-space (in,real(ngp)) ! ld2 : leading dimension (in,integer) ! jlgprmt : spherical Bessel functions for evergy G+p-vector and muffin-tin ! radius (in,real(0:lnpsd,ld2,nspecies)) ! ylmgp : spherical harmonics of the G+p-vectors (in,complex(lmmaxo,ngp)) ! sfacgp : structure factors of the G+p-vectors (in,complex(ld2,natmtot)) ! zrhoir : interstitial charge density (in,complex(*)) ! ld3 : leading dimension (in,integer) ! zvclmt : muffin-tin Coulomb potential, with the contribution from the ! isolated muffin-tin density precalculated and passed in ! (inout,complex(ld3,natmtot)) ! zvclir : interstitial Coulomb potential (out,complex(*)) ! !DESCRIPTION: ! Calculates the Coulomb potential of a complex charge density by solving ! Poisson's equation using the method of M. Weinert, {\it J. Math. Phys.} ! {\bf 22}, 2433 (1981). First, the multipole moments of the muffin-tin charge ! are determined for the $j$th atom of the $i$th species by ! $$ q_{ij;lm}^{\rm MT}=\int_0^{R_i}r^{l+2}\rho_{ij;lm}(r)dr+z_{ij}Y_{00} ! \,\delta_{l,0}\;, $$ ! where $R_i$ is the muffin-tin radius and $z_{ij}$ is a point charge located ! at the atom center (usually the nuclear charge, which should be taken as ! {\bf negative}). Next, the multipole moments of the continuation of the ! interstitial density, $\rho^{\rm I}$, into the muffin-tin are found with ! $$ q_{ij;lm}^{\rm I}=4\pi i^l R_i^{l+3}\sum_{\bf G}\frac{j_{l+1}(GR_i)} ! {GR_i}\rho^{\rm I}({\bf G})\exp(i{\bf G}\cdot{\bf r}_{ij})Y_{lm}^* ! (\hat{\bf G}), $$ ! remembering that ! $$ \lim_{x\rightarrow 0}\frac{j_{l+n}(x)}{x^n}=\frac{1}{(2n+1)!!} ! \delta_{l,0} $$ ! should be used for the case ${\bf G}=0$. A pseudocharge is now constructed ! which is equal to the real density in the interstitial region and whose ! multipoles are the difference between the real and interstitial muffin-tin ! multipoles. This pseudocharge density is smooth in the sense that it can be ! expanded in terms of the finite set of ${\bf G}$-vectors. In each muffin-tin ! the pseudocharge has the form ! $$ \rho_{ij}^{\rm P}({\bf r})=\rho^{\rm I}({\bf r}-{\bf r}_{ij})+\sum_{lm} ! \rho_{ij;lm}^{\rm P}\frac{1}{R_i^{l+3}}\left(\frac{r}{R_i}\right)^l\left(1- ! \frac{r^2}{R_i^2}\right)^{N_i}Y_{lm}(\hat{\bf r}) $$ ! where ! $$ \rho_{ij;lm}^{\rm P}=\frac{(2l+2N_i+3)!!}{2^N_iN_i!(2l+1)!!}\left( ! q_{ij;lm}^{\rm MT}-q_{ij;lm}^{\rm I}\right) $$ ! and $N_i\approx\frac{1}{4}R_iG_{\rm max}$ is generally a good choice. ! The pseudocharge in reciprocal space is given by ! $$ \rho^{\rm P}({\bf G})=\rho^{\rm I}({\bf G})+\sum_{ij;lm}2^{N_i}N_i! ! \frac{4\pi(-i)^l}{\Omega R_i^l}\frac{j_{l+N_i+1}(GR_i)}{(GR_i)^{N_i+1}} ! \rho_{ij;lm}^{\rm P}\exp(-i{\bf G}\cdot{\bf r}_{ij})Y_{lm}(\hat{\bf G}) $$ ! which may be used for solving Poisson's equation directly ! $$ V^{\rm P}({\bf G})=\begin{cases} ! 4\pi\frac{\rho^{\rm P}({\bf G})}{G^2} & G>0 \\ ! 0 & G=0 \end{cases}\;. $$ ! The usual Green's function approach is then employed to determine the ! potential in the muffin-tin sphere due to charge in the sphere. In other ! words ! $$ V_{ij;lm}^{\rm MT}(r)=\frac{4\pi}{2l+1}\left(\frac{1}{r^{l+1}}\int_0^r ! \rho_{ij;lm}^{\rm MT}(r'){r'}^{l+2}dr'+r^l\int_r^{R_i}\frac{ ! \rho_{ij;lm}^{\rm MT}(r')}{{r'}^{l-1}}dr'\right)+\frac{1}{Y_{00}} ! \frac{z_{ij}}{r}\delta_{l,0} $$ ! where the last term is the monopole arising from the point charge. All that ! remains is to add the homogenous solution of Poisson's equation, ! $$ V_{ij}^{\rm H}({\bf r})=\sum_{lm}V_{ij;lm}^{\rm H}\left(\frac{r} ! {R_i}\right)^lY_{lm}(\hat{\bf r}), $$ ! to the muffin-tin potential so that it is continuous at the muffin-tin ! boundary. Therefore the coefficients, $\rho_{ij;lm}^{\rm H}$, are given by ! $$ V_{ij;lm}^{\rm H}=4\pi i^l\sum_{\bf G}j_{l}(Gr)V^{\rm P}({\bf G}) ! \exp(i{\bf G}\cdot{\bf r}_{ij})Y_{lm}^*(\hat{\bf G})-V_{ij;lm}^{\rm MT} ! (R_i). $$ ! Finally note that the ${\bf G}$-vectors passed to the routine can represent ! vectors with a non-zero offset, ${\bf G}+{\bf p}$ say, which is required for ! calculating Coulomb matrix elements. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr(nspecies),nri(nspecies) integer, intent(in) :: np(nspecies),npi(nspecies) integer, intent(in) :: ld1 real(8), intent(in) :: rl(ld1,-lmaxo-1:lmaxo+2,nspecies) integer, intent(in) :: ngdg(3),igf(*),ngp real(8), intent(in) :: gpc(ngp),gclgp(ngp) integer, intent(in) :: ld2 real(8), intent(in) :: jlgprmt(0:lnpsd,ld2,nspecies) complex(8), intent(in) :: ylmgp(lmmaxo,ngp),sfacgp(ld2,natmtot) complex(8), intent(in) :: zrhoir(*) integer, intent(in) :: ld3 complex(8), intent(inout) :: zvclmt(ld3,natmtot) complex(8), intent(out) :: zvclir(*) ! local variables integer is,ia,ias integer ir,l,m,lm integer ig,jg,i,j real(8) t1,t2,t3 complex(8) z1,z2 ! automatic arrays real(8) rmtl(0:lmaxo+3,nspecies) complex(8) qlm(lmmaxo,natmtot) complex(8) zl(0:lmaxo),zlm(lmmaxo) complex(8) zhmt(ld3) ! external functions real(8), external :: factnm ! compute (R_mt)^l do is=1,nspecies rmtl(0,is)=1.d0 do l=1,lmaxo+3 rmtl(l,is)=rmtl(l-1,is)*rmt(is) end do end do ! compute the multipole moments from the muffin-tin potentials t1=1.d0/fourpi do ias=1,natmtot is=idxis(ias) i=np(is)-lmmaxo lm=0 do l=0,lmaxo t2=t1*dble(2*l+1)*rmtl(l+1,is) do m=-l,l lm=lm+1 i=i+1 qlm(lm,ias)=t2*zvclmt(i,ias) end do end do end do ! Fourier transform density to G-space and store in zvclir call zcopy(ngdg(1)*ngdg(2)*ngdg(3),zrhoir,1,zvclir,1) call zfftifc(3,ngdg,-1,zvclir) ! subtract the multipole moments of the interstitial charge density do is=1,nspecies do l=0,lmaxo zl(l)=fourpi*zil(l)*rmtl(l+2,is) end do do ia=1,natoms(is) ias=idxas(ia,is) zlm(:)=0.d0 do ig=1,ngp jg=igf(ig) if (gpc(ig).gt.epslat) then z1=zvclir(jg)*sfacgp(ig,ias)/gpc(ig) zlm(1)=zlm(1)+jlgprmt(1,ig,is)*z1*zl(0)*y00 lm=1 do l=1,lmaxo z2=jlgprmt(l+1,ig,is)*z1*zl(l) do m=-l,l lm=lm+1 zlm(lm)=zlm(lm)+z2*conjg(ylmgp(lm,ig)) end do end do else t1=(fourpi/3.d0)*rmtl(3,is)*y00 zlm(1)=zlm(1)+t1*zvclir(jg) end if end do qlm(:,ias)=qlm(:,ias)-zlm(:) end do end do ! find the smooth pseudocharge within the muffin-tin whose multipoles are the ! difference between the real muffin-tin and interstitial multipoles t1=(fourpi/omega)*factnm(2*lnpsd+1,2) do ias=1,natmtot is=idxis(ias) lm=0 do l=0,lmaxo t2=t1/(factnm(2*l+1,2)*rmtl(l,is)) z1=t2*zilc(l) do m=-l,l lm=lm+1 zlm(lm)=z1*qlm(lm,ias) end do end do ! add the pseudocharge and real interstitial densities in G-space do ig=1,ngp jg=igf(ig) if (gpc(ig).gt.epslat) then t2=gpc(ig)*rmt(is) t3=1.d0/t2**lnpsd z1=t3*zlm(1)*y00 lm=1 do l=1,lmaxo lm=lm+1 z2=zlm(lm)*ylmgp(lm,ig) do m=1-l,l lm=lm+1 z2=z2+zlm(lm)*ylmgp(lm,ig) end do t3=t3*t2 z1=z1+t3*z2 end do z2=jlgprmt(lnpsd,ig,is)*conjg(sfacgp(ig,ias)) zvclir(jg)=zvclir(jg)+z1*z2 else t2=y00/factnm(2*lnpsd+1,2) zvclir(jg)=zvclir(jg)+t2*zlm(1) end if end do end do ! solve Poisson's equation in G+p-space for the pseudocharge do ig=1,ngp jg=igf(ig) zvclir(jg)=gclgp(ig)*zvclir(jg) end do ! match potentials at muffin-tin boundary by adding homogeneous solution do ias=1,natmtot is=idxis(ias) ! find the spherical harmonic expansion of the interstitial potential at the ! muffin-tin radius zlm(:)=0.d0 do ig=1,ngp z1=fourpi*zvclir(igf(ig))*sfacgp(ig,ias) zlm(1)=zlm(1)+jlgprmt(0,ig,is)*z1*y00 lm=1 do l=1,lmaxo z2=jlgprmt(l,ig,is)*z1*zil(l) do m=-l,l lm=lm+1 zlm(lm)=zlm(lm)+z2*conjg(ylmgp(lm,ig)) end do end do end do ! calculate the homogenous solution i=np(is)-lmmaxo lm=0 do l=0,lmaxi t1=1.d0/rmtl(l,is) do m=-l,l lm=lm+1 i=i+1 z1=t1*(zlm(lm)-zvclmt(i,ias)) j=lm do ir=1,nri(is) zhmt(j)=z1*rl(ir,l,is) j=j+lmmaxi end do do ir=nri(is)+1,nr(is) zhmt(j)=z1*rl(ir,l,is) j=j+lmmaxo end do end do end do do l=lmaxi+1,lmaxo t1=1.d0/rmtl(l,is) do m=-l,l lm=lm+1 i=i+1 z1=t1*(zlm(lm)-zvclmt(i,ias)) j=npi(is)+lm do ir=nri(is)+1,nr(is) zhmt(j)=z1*rl(ir,l,is) j=j+lmmaxo end do end do end do zvclmt(1:np(is),ias)=zvclmt(1:np(is),ias)+zhmt(1:np(is)) ! store the nuclear potential without the self-term for the phonon dynamical ! matrix calculation if (tphdyn) then if (ias.eq.iasph) zvnmt(1:np(is))=zhmt(1:np(is)) end if end do ! Fourier transform interstitial potential to real-space call zfftifc(3,ngdg,1,zvclir) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/sfacmag.f900000644000000000000000000000013214061636517014645 xustar0030 mtime=1623670095.263102169 30 atime=1623670094.029103314 30 ctime=1623670095.263102169 elk-7.2.42/src/sfacmag.f900000644002504400250440000000550614061636517016710 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 A. I. Baranov and F. Wagner. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: sfacmag ! !INTERFACE: subroutine sfacmag ! !USES: use modmain use modpw use modtest ! !DESCRIPTION: ! Outputs magnetic structure factors, i.e. the Fourier transform coefficients ! of each component $j$ of magnetization ${\bf m}({\bf r})$, ! $$ F_j({\bf H})=\int_{\Omega}d^3r\,m_j({\bf r})e^{i{\bf H}\cdot{\bf r}}, $$ ! to the files {\tt SFACMAG\_j.OUT}. The lattice coordinates $(h,k,l)$ of ! $\bf H$-vectors in this file are transformed by the matrix {\tt vhmat}. See ! also routines {\tt zftrf} and {\tt genhvec}. ! ! !REVISION HISTORY: ! Created July 2010 (Alexey I. Baranov) ! Added multiplicity of the H-vectors, Oct. 2010 (Alexey I. Baranov) !EOP !BOC implicit none ! local variables integer idm,ih,iv(3) real(8) v(3),a,b,r character(256) fname ! allocatable arrays complex(8), allocatable :: zmagh(:) if (.not.spinpol) return ! initialise the structure factor specific variables call sfacinit ! generate the magnetic structure factors allocate(zmagh(nhvec)) do idm=1,ndmag call zftrf(nhvec,ivh,vhc,magmt(:,:,idm),magir(:,idm),zmagh) write(fname,'("SFACMAG_",I1.1,".OUT")') idm open(50,file=trim(fname),form='FORMATTED') write(50,*) write(50,'("h k l indices transformed by vhmat matrix:")') write(50,'(3G18.10)') vhmat(:,1) write(50,'(3G18.10)') vhmat(:,2) write(50,'(3G18.10)') vhmat(:,3) write(50,*) write(50,'(" h k l multipl. |H| Re(F)& & Im(F) |F|")') write(50,*) do ih=1,nhvec ! apply transformation matrix v(:)=vhmat(:,1)*dble(ivh(1,ih)) & +vhmat(:,2)*dble(ivh(2,ih)) & +vhmat(:,3)*dble(ivh(3,ih)) ! in crystallography the forward Fourier transform of real-space density is ! usually done with positive phase and without 1/omega prefactor a=dble(zmagh(ih))*omega b=-aimag(zmagh(ih))*omega r=abs(zmagh(ih))*omega iv(:)=nint(v(:)) if ((abs(v(1)-iv(1)).le.epslat).and. & (abs(v(2)-iv(2)).le.epslat).and. & (abs(v(3)-iv(3)).le.epslat)) then ! integer hkl write(50,'(4I7,4G16.8)') iv(:),mulh(ih),hc(ih),a,b,r else ! non-integer hkl write(50,'(3F7.2,I7,4G16.8)') v(:),mulh(ih),hc(ih),a,b,r end if end do close(50) end do write(*,*) write(*,'("Info(sfacmag): magnetic structure factors written to & &SFACMAG_j.OUT")') write(*,'(" for magnetic components j = ",3I2)') (idm,idm=1,ndmag) if (ndmag.eq.1) then write(*,'(" (this corresponds to the z-component of the magnetisation)")') end if write(*,*) write(*,'(" Energy window : ",2G18.10)') wsfac(:) ! write the structure factors to test file call writetest(196,'magnetic structure factors',nv=nhvec,tol=1.d-4,zva=zmagh(:)) deallocate(zmagh) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/polynm.f900000644000000000000000000000013214061636517014562 xustar0030 mtime=1623670095.264102168 30 atime=1623670094.031103312 30 ctime=1623670095.264102168 elk-7.2.42/src/polynm.f900000644002504400250440000000670014061636517016622 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: polynm ! !INTERFACE: pure real(8) function polynm(m,np,xa,ya,x) ! !INPUT/OUTPUT PARAMETERS: ! m : order of derivative (in,integer) ! np : number of points to fit (in,integer) ! xa : abscissa array (in,real(np)) ! ya : ordinate array (in,real(np)) ! x : evaluation abscissa (in,real) ! !DESCRIPTION: ! Fits a polynomial of order $n_p-1$ to a set of $n_p$ points. If $m\ge 0$ the ! function returns the $m$th derviative of the polynomial at $x$, while for ! $m<0$ the integral of the polynomial from the first point in the array to ! $x$ is returned. ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! argmuments integer, intent(in) :: m,np real(8), intent(in) :: xa(np),ya(np) real(8), intent(in) :: x ! local variables integer i,j,k real(8) x0,x1,x2,x3,y0,y1,y2,y3 real(8) t0,t1,t2,t3,t4,t5,t6 real(8) c1,c2,c3,sm ! automatic arrays real(8) c(np) ! fast evaluations for small np select case(np) case(1) select case(m) case(:-1) polynm=ya(1)*(x-xa(1)) case(0) polynm=ya(1) case default polynm=0.d0 end select return case(2) c1=(ya(2)-ya(1))/(xa(2)-xa(1)) t1=x-xa(1) select case(m) case(:-1) polynm=t1*(ya(1)+0.5d0*c1*t1) case(0) polynm=c1*t1+ya(1) case(1) polynm=c1 case default polynm=0.d0 end select return case(3) x0=xa(1) x1=xa(2)-x0; x2=xa(3)-x0 y0=ya(1) y1=ya(2)-y0; y2=ya(3)-y0 t0=1.d0/(x1*x2*(x2-x1)) t1=x1*y2; t2=x2*y1 c1=x2*t2-x1*t1 c2=t1-t2 t1=x-x0 select case(m) case(:-1) polynm=t1*(y0+t0*t1*(0.5d0*c1+0.3333333333333333333d0*c2*t1)) case(0) polynm=y0+t0*t1*(c1+c2*t1) case(1) polynm=t0*(2.d0*c2*t1+c1) case(2) polynm=t0*2.d0*c2 case default polynm=0.d0 end select return case(4) x0=xa(1) x1=xa(2)-x0; x2=xa(3)-x0; x3=xa(4)-x0 y0=ya(1) y1=ya(2)-y0; y2=ya(3)-y0; y3=ya(4)-y0 t4=x1-x2; t5=x1-x3; t6=x2-x3 t1=x1*x2*y3; t2=x2*x3*y1; t3=x1*x3 t0=1.d0/(x2*t3*t4*t5*t6) t3=t3*y2 c3=t1*t4+t2*t6-t3*t5 t4=x1**2; t5=x2**2; t6=x3**2 y1=t3*t6-t1*t5; y2=t1*t4-t2*t6; y3=t2*t5-t3*t4 c2=y1+y2+y3 c1=x1*y1+x2*y2+x3*y3 t1=x-x0 select case(m) case(:-1) polynm=t1*(y0+t0*t1*(0.5d0*c1+t1*(0.25d0*c3*t1-0.3333333333333333333d0*c2))) case(0) polynm=y0+t0*t1*(c1+t1*(c3*t1-c2)) case(1) polynm=t0*(c1+t1*(3.d0*c3*t1-2.d0*c2)) case(2) polynm=t0*(6.d0*c3*t1-2.d0*c2) case(3) polynm=t0*6.d0*c3 case default polynm=0.d0 end select return end select if ((np.le.0).or.(m.ge.np)) then polynm=0.d0 return end if ! find the polynomial coefficients in divided differences form c(:)=ya(:) do i=2,np do j=np,i,-1 c(j)=(c(j)-c(j-1))/(xa(j)-xa(j+1-i)) end do end do ! special case m=0 if (m.eq.0) then sm=c(1) t1=1.d0 do i=2,np t1=t1*(x-xa(i-1)) sm=sm+c(i)*t1 end do polynm=sm return end if x0=xa(1) ! convert to standard form do j=1,np-1 do i=1,np-j k=np-i c(k)=c(k)+(x0-xa(k-j+1))*c(k+1) end do end do if (m.gt.0) then ! take the m th derivative do j=1,m do i=m+1,np c(i)=c(i)*dble(i-j) end do end do t1=c(np) t2=x-x0 do i=np-1,m+1,-1 t1=t1*t2+c(i) end do polynm=t1 else ! find the integral t1=c(np)/dble(np) t2=x-x0 do i=np-1,1,-1 t1=t1*t2+c(i)/dble(i) end do polynm=t1*t2 end if end function !EOC elk-7.2.42/src/PaxHeaders.21776/epsinv.f900000644000000000000000000000013214061636517014550 xustar0030 mtime=1623670095.266102166 30 atime=1623670094.032103312 30 ctime=1623670095.266102166 elk-7.2.42/src/epsinv.f900000644002504400250440000000510614061636517016607 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine epsinv use modmain use modmpi use modomp implicit none ! local variables integer iq,ik,ig,iw integer n,nthd ! allocatable arrays integer(8), allocatable :: lock(:) real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqr(:,:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:),epsi(:,:,:) ! allocate local arrays allocate(vgqc(3,ngrf),gqc(ngrf),gclgq(ngrf)) allocate(jlgqr(njcmax,nspecies,ngrf)) allocate(ylmgq(lmmaxo,ngrf),sfacgq(ngrf,natmtot)) allocate(epsi(ngrf,ngrf,nwrf)) ! initialise the OpenMP locks allocate(lock(nwrf)) do iw=1,nwrf call omp_init_lock(lock(iw)) end do if (mp_mpi) write(*,*) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! loop over q-points do iq=1,nqpt if (mp_mpi) write(*,'("Info(epsinv): ",I6," of ",I6," q-points")') iq,nqpt ! generate the G+q-vectors and related functions call gengqf(ngrf,vqc(:,iq),vgqc,gqc,jlgqr,ylmgq,sfacgq) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.true.,iq,ngrf,gqc,gclgq) ! use the symmetric form gclgq(:)=sqrt(gclgq(:)) ! zero the response function (stored in epsi) epsi(:,:,:)=0.d0 call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! compute v^1/2 chi0 v^1/2 call genvchi0(.false.,ik,lock,0.d0,vql(:,iq),gclgq,jlgqr,ylmgq,sfacgq, & ngrf,epsi) end do !$OMP END PARALLEL DO call freethd(nthd) ! add epsi from each process and redistribute if (np_mpi.gt.1) then n=ngrf*ngrf*nwrf call mpi_allreduce(mpi_in_place,epsi,n,mpi_double_complex,mpi_sum,mpicom, & ierror) end if ! negate and add delta(G,G') epsi(:,:,:)=-epsi(:,:,:) do ig=1,ngrf epsi(ig,ig,:)=epsi(ig,ig,:)+1.d0 end do !-------------------------------------! ! invert epsilon over G-space ! !-------------------------------------! call holdthd(nwrf,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do iw=1,nwrf call zminv(ngrf,epsi(:,:,iw)) end do !$OMP END PARALLEL DO call freethd(nthd) ! write inverse RPA epsilon to EPSINV.OUT if (mp_mpi) call putepsinv(iq,epsi) ! end loop over q-points end do ! destroy the OpenMP locks do iw=1,nwrf call omp_destroy_lock(lock(iw)) end do deallocate(lock) deallocate(vgqc,gqc,gclgq,jlgqr) deallocate(ylmgq,sfacgq,epsi) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/rfinpc.f900000644000000000000000000000013114061636517014524 xustar0030 mtime=1623670095.267102165 29 atime=1623670094.03410331 30 ctime=1623670095.267102165 elk-7.2.42/src/rfinpc.f900000644002504400250440000000174314061636517016567 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. real(8) function rfinpc(ld,rfmt1,rfir1,rfmt2,rfir2) use modmain use modomp implicit none ! arguments integer, intent(in) :: ld real(8), intent(in) :: rfmt1(ld,natmtot),rfir1(ngtot) real(8), intent(in) :: rfmt2(ld,natmtot),rfir2(ngtot) ! local variables integer is,ias,ir,nthd ! external functions real(8), external :: rfmtinp ! interstitial contribution rfinpc=0.d0 do ir=1,ngtot rfinpc=rfinpc+rfir1(ir)*rfir2(ir)*cfunir(ir) end do rfinpc=rfinpc*omega/dble(ngtot) ! muffin-tin contribution call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) REDUCTION(+:rfinpc) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) rfinpc=rfinpc+rfmtinp(nrcmt(is),nrcmti(is),wrcmt(:,is),rfmt1(:,ias), & rfmt2(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) end function elk-7.2.42/src/PaxHeaders.21776/zmctmu.f900000644000000000000000000000013214061636517014563 xustar0030 mtime=1623670095.268102164 30 atime=1623670094.036103308 30 ctime=1623670095.268102164 elk-7.2.42/src/zmctmu.f900000644002504400250440000000205014061636517016615 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zmctmu(tcr,l,n,a,b,ld,c) use modomp implicit none ! arguments logical, intent(in) :: tcr integer, intent(in) :: l,n complex(8), intent(in) :: a(l,n),b(l,n) integer, intent(in) :: ld complex(8), intent(out) :: c(ld,*) ! local variables integer l2,i,j,nthd ! external functions real(8), external :: ddot complex(8), external :: zdotc call holdthd(n,nthd) if (tcr) then ! matrix c is real valued l2=2*l !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(i) & !$OMP NUM_THREADS(nthd) do j=1,n do i=1,j c(i,j)=c(i,j)+ddot(l2,a(:,i),1,b(:,j),1) end do end do !$OMP END PARALLEL DO else ! matrix c is complex valued !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(i) & !$OMP NUM_THREADS(nthd) do j=1,n do i=1,j c(i,j)=c(i,j)+zdotc(l,a(:,i),1,b(:,j),1) end do end do !$OMP END PARALLEL DO end if call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/zmctm.f900000644000000000000000000000013214061636517014376 xustar0030 mtime=1623670095.270102162 30 atime=1623670094.037103307 30 ctime=1623670095.270102162 elk-7.2.42/src/zmctm.f900000644002504400250440000000131314061636517016431 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zmctm(l,m,n,a,b,ld,c) use modomp implicit none ! arguments integer, intent(in) :: l,m,n complex(8), intent(in) :: a(l,m),b(l,n) integer, intent(in) :: ld complex(8), intent(out) :: c(ld,*) ! local variables integer i,j,nthd ! external functions complex(8), external :: zdotc call holdthd(n,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(i) & !$OMP NUM_THREADS(nthd) do j=1,n do i=1,m c(i,j)=c(i,j)+zdotc(l,a(:,i),1,b(:,j),1) end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/writeiad.f900000644000000000000000000000013214061636517015054 xustar0030 mtime=1623670095.271102161 30 atime=1623670094.039103305 30 ctime=1623670095.271102161 elk-7.2.42/src/writeiad.f900000644002504400250440000000254714061636517017121 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writeiad ! !INTERFACE: subroutine writeiad(fnum) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! fnum : file number for writing output (in,integer) ! !DESCRIPTION: ! Outputs the interatomic distances to file. ! ! !REVISION HISTORY: ! Created May 2005 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: fnum ! local variables integer is,js,ia,ja integer i1,i2,i3 real(8) d,dmin,v(3) do is=1,nspecies do ia=1,natoms(is) write(fnum,*) write(fnum,'("Distance between is = ",I4," (",A,"), ia = ",I4," and")') & is,trim(spsymb(is)),ia do js=1,nspecies do ja=1,natoms(js) dmin=1.d8 do i1=-1,1 do i2=-1,1 do i3=-1,1 v(:)=dble(i1)*avec(:,1) & +dble(i2)*avec(:,2) & +dble(i3)*avec(:,3)+atposc(:,ja,js) v(:)=v(:)-atposc(:,ia,is) d=sqrt(v(1)**2+v(2)**2+v(3)**2) dmin=min(d,dmin) end do end do end do write(fnum,'(" is = ",I4," (",A,"), ia = ",I4," : ",G18.10)') js, & trim(spsymb(js)),ja,dmin end do end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genapwfr.f900000644000000000000000000000013014061636517015053 xustar0029 mtime=1623670095.27310216 30 atime=1623670094.041103303 29 ctime=1623670095.27310216 elk-7.2.42/src/genapwfr.f900000644002504400250440000001001014061636517017102 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genapwfr ! !INTERFACE: subroutine genapwfr ! !USES: use modmain ! !DESCRIPTION: ! Generates the APW radial functions. This is done by integrating the scalar ! relativistic Schr\"{o}dinger equation (or its energy deriatives) at the ! current linearisation energies using the spherical part of the Kohn-Sham ! potential. The number of radial functions at each $l$-value is given by the ! variable {\tt apword} (at the muffin-tin boundary, the APW functions have ! continuous derivatives up to order ${\tt apword}-1$). Within each $l$, these ! functions are orthonormalised with the Gram-Schmidt method. The radial ! Hamiltonian is applied to the orthonormalised functions and the results are ! stored in the global array {\tt apwfr}. ! ! !REVISION HISTORY: ! Created March 2003 (JKD) ! Copied to equivalent atoms, February 2010 (A. Kozhevnikov and JKD) !EOP !BOC implicit none ! local variables integer is,ia,ja,ias,jas integer nr,nri,ir,i integer nn,l,io,jo real(8) e,t1 ! automatic arrays logical done(natmmax) real(8) vr(nrmtmax),fr(nrmtmax) real(8) p0(nrmtmax,apwordmax),p1(nrmtmax),p1s(apwordmax) real(8) q0(nrmtmax),q1(nrmtmax),ep0(nrmtmax,apwordmax) ! external functions real(8), external :: splint do is=1,nspecies nr=nrmt(is) nri=nrmti(is) done(:)=.false. do ia=1,natoms(is) if (done(ia)) cycle ias=idxas(ia,is) ! use spherical part of potential i=1 do ir=1,nri vr(ir)=vsmt(i,ias)*y00 i=i+lmmaxi end do do ir=nri+1,nr vr(ir)=vsmt(i,ias)*y00 i=i+lmmaxo end do do l=0,lmaxapw do io=1,apword(l,is) ! linearisation energy accounting for energy derivative e=apwe(io,l,ias)+dble(apwdm(io,l,is))*deapwlo ! integrate the radial Schrodinger equation call rschrodint(solsc,l,e,nr,rlmt(:,1,is),vr,nn,p0(:,io),p1,q0,q1) ! multiply by the linearisation energy ep0(1:nr,io)=e*p0(1:nr,io) ! normalise radial functions fr(1:nr)=p0(1:nr,io)**2 t1=splint(nr,rlmt(:,1,is),fr) t1=1.d0/sqrt(abs(t1)) call dscal(nr,t1,p0(:,io),1) p1s(io)=t1*p1(nr) call dscal(nr,t1,ep0(:,io),1) ! subtract linear combination of previous vectors do jo=1,io-1 fr(1:nr)=p0(1:nr,io)*p0(1:nr,jo) t1=-splint(nr,rlmt(:,1,is),fr) call daxpy(nr,t1,p0(:,jo),1,p0(:,io),1) p1s(io)=p1s(io)+t1*p1s(jo) call daxpy(nr,t1,ep0(:,jo),1,ep0(:,io),1) end do ! normalise radial functions again fr(1:nr)=p0(1:nr,io)**2 t1=splint(nr,rlmt(:,1,is),fr) t1=abs(t1) if (t1.lt.1.d-25) then write(*,*) write(*,'("Error(genapwfr): degenerate APW radial functions")') write(*,'(" for species ",I4)') is write(*,'(" atom ",I4)') ia write(*,'(" angular momentum ",I4)') l write(*,'(" and order ",I4)') io write(*,*) stop end if t1=1.d0/sqrt(t1) call dscal(nr,t1,p0(:,io),1) p1s(io)=t1*p1s(io) call dscal(nr,t1,ep0(:,io),1) ! divide by r and store in global array do ir=1,nr t1=rlmt(ir,-1,is) apwfr(ir,1,io,l,ias)=t1*p0(ir,io) apwfr(ir,2,io,l,ias)=t1*ep0(ir,io) end do ! derivative at the muffin-tin surface apwdfr(io,l,ias)=(p1s(io)-p0(nr,io)*t1)*t1 end do end do done(ia)=.true. ! copy to equivalent atoms do ja=1,natoms(is) if ((.not.done(ja)).and.(eqatoms(ia,ja,is))) then jas=idxas(ja,is) do l=0,lmaxapw do io=1,apword(l,is) call dcopy(nr,apwfr(:,1,io,l,ias),1,apwfr(:,1,io,l,jas),1) call dcopy(nr,apwfr(:,2,io,l,ias),1,apwfr(:,2,io,l,jas),1) apwdfr(io,l,jas)=apwdfr(io,l,ias) end do end do done(ja)=.true. end if end do ! end loop over atoms and species end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genws.f900000644000000000000000000000013214061636517014367 xustar0030 mtime=1623670095.274102159 30 atime=1623670094.042103302 30 ctime=1623670095.274102159 elk-7.2.42/src/genws.f900000644002504400250440000000156114061636517016427 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genws use modmain use modomp implicit none ! local variables integer is,ias,nthd integer nrc,nrci ! automatic arrays real(8) rfmt(npcmtmax) if (xcgrad.ne.4) return ! muffin-tin effective meta-GGA potential call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(rfmt,is,nrc,nrci) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) ! convert to coarse radial mesh and spherical coordinates call rfmtftoc(nrc,nrci,wxcmt(:,ias),rfmt) call rbsht(nrc,nrci,rfmt,wsmt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! interstitial meta-GGA potential wsir(1:ngtot)=wxcir(1:ngtot)*cfunir(1:ngtot) end subroutine elk-7.2.42/src/PaxHeaders.21776/gengclq.f900000644000000000000000000000013014061636517014662 xustar0030 mtime=1623670095.275102158 28 atime=1623670094.0441033 30 ctime=1623670095.275102158 elk-7.2.42/src/gengclq.f900000644002504400250440000000557514061636517016735 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: gengclq ! !INTERFACE: subroutine gengclq ! !USES: use modmain use modtest ! !DESCRIPTION: ! The Fock matrix elements ! $$ V_{ij{\bf k}}\equiv\sum_{l{\bf k'}}\int ! \frac{\Psi^{\dag}_{i{\bf k}}({\bf r})\cdot\Psi_{l{\bf k}'}({\bf r}) ! \Psi^{\dag}_{l{\bf k}'}({\bf r}')\cdot\Psi_{j{\bf k}}({\bf r}')} ! {|{\bf r}-{\bf r'}|}\,d^3r\,d^3r' $$ ! contain a divergent term in the sum over ${\bf k}'$ which behaves as ! $1/q^2$, where ${\bf q}\equiv{\bf k}-{\bf k}'$ is in the first Brillouin ! zone. The resulting convergence with respect to the number of discrete ! $q$-points, $N_q$, is very slow. This routine computes the regularised ! Coulomb Green's function ! \begin{align} ! g({\bf q}_i)=\frac{4\pi}{V}\int_{V_i}\frac{1}{q^2}\,d^3q, ! \end{align} ! where the integral is over the small parallelepiped with volume ! $V=\Omega_{\rm BZ}/N_q$ and centered on the discrete point ${\bf q}_i$. ! This dramatically increases the rate of convergence of methods which involve ! a summation over the $1/q^2$ part of the Coulomb interaction. The above ! integral is evaluated numerically on increasingly finer grids and then ! extrapolated to the continuum. ! ! !REVISION HISTORY: ! Created August 2004 (JKD,SS) ! Changed from genwiq2, July 2017 (JKD) !EOP !BOC implicit none ! local variables integer, parameter :: np=5 integer, parameter :: ns0=10,nss=20 integer ns,iq,i1,i2,i3,ip real(8) d(3),sm,t1,t2 real(8) v1(3),v2(3),v3(3) real(8) xa(np),ya(np) ! external functions real(8), external :: polynm ! allocate global gclq array if (allocated(gclq)) deallocate(gclq) allocate(gclq(nqpt)) ! begin loop over q-points, note that the vectors vqc are assumed to be in the ! first Brillouin zone do iq=1,nqpt ! loop over different subdivisions ns=ns0 do ip=1,np ! subdivision vectors in lattice coordinates d(:)=1.d0/dble(ngridq(:)*2*ns) ! compute the integral of 1/q^2 sm=0.d0 do i1=-ns,ns-1 t1=dble(i1)*d(1) v1(:)=vqc(:,iq)+t1*bvec(:,1) do i2=-ns,ns-1 t1=dble(i2)*d(2) v2(:)=v1(:)+t1*bvec(:,2) do i3=-ns,ns-1 t1=dble(i3)*d(3) v3(:)=v2(:)+t1*bvec(:,3) t2=v3(1)**2+v3(2)**2+v3(3)**2 if (t2.gt.1.d-14) sm=sm+1.d0/t2 end do end do end do t1=1.d0/dble(2*ns) xa(ip)=t1 ya(ip)=fourpi*sm*t1**3 ! increment number of subdivisions ns=ns+nss end do ! extrapolate the volume element to zero with a polynomial gclq(iq)=polynm(0,np,xa,ya,0.d0) end do ! zero the Green's function at q = 0 if required if (t0gclq0) gclq(1)=0.d0 ! write gclq to test file call writetest(800,"regularised Coulomb Green''s function (gclq)",nv=nqpt, & tol=1.d-8,rva=gclq) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/addbfsm.f900000644000000000000000000000013214061636517014644 xustar0030 mtime=1623670095.277102156 30 atime=1623670094.046103298 30 ctime=1623670095.277102156 elk-7.2.42/src/addbfsm.f900000644002504400250440000000163314061636517016704 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine addbfsm use modmain implicit none ! local variables integer idm,is,ias,npc real(8) t1 ! add the global fixed spin moment B-field to the Kohn-Sham field if ((abs(fsmtype).eq.1).or.(abs(fsmtype).eq.3)) then do idm=1,ndmag t1=bfsmc(idm) do ias=1,natmtot is=idxis(ias) npc=npcmt(is) bsmt(1:npc,ias,idm)=bsmt(1:npc,ias,idm)+t1 end do bsir(1:ngtot,idm)=bsir(1:ngtot,idm)+t1*cfunir(1:ngtot) end do end if ! add the muffin-tin fields if ((abs(fsmtype).eq.2).or.(abs(fsmtype).eq.3)) then do idm=1,ndmag do ias=1,natmtot is=idxis(ias) npc=npcmt(is) t1=bfsmcmt(idm,ias) bsmt(1:npc,ias,idm)=bsmt(1:npc,ias,idm)+t1 end do end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/genylmv.f900000644000000000000000000000013214061636517014725 xustar0030 mtime=1623670095.278102155 30 atime=1623670094.047103298 30 ctime=1623670095.278102155 elk-7.2.42/src/genylmv.f900000644002504400250440000000521114061636517016761 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: genylmv ! !INTERFACE: pure subroutine genylmv(lmax,v,ylm) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum angular momentum (in,integer) ! v : input vector (in,real(3)) ! ylm : array of spherical harmonics (out,complex((lmax+1)**2)) ! !DESCRIPTION: ! Generates a sequence of spherical harmonics, including the Condon-Shortley ! phase, evaluated at angles $(\theta,\phi)$ for $00}}(n-im) $$ ! for $n,\,m \ge 0$. $n$ should be less than 150. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n,m ! local variables integer i,j real(8), parameter :: f1(24)=[ & 1.d0, 2.d0, & 6.d0, 24.d0, & 120.d0, 720.d0, & 5040.d0, 40320.d0, & 362880.d0, 3628800.d0, & 39916800.d0, 479001600.d0, & 6227020800.d0, 87178291200.d0, & 1307674368000.d0, 20922789888000.d0, & 355687428096000.d0, 6402373705728000.d0, & 121645100408832000.d0, 2432902008176640000.d0, & 51090942171709440000.d0, 1124000727777607680000.d0, & 25852016738884976640000.d0, 620448401733239439360000.d0] real(8), parameter :: f2(38)=[ & 1.d0, 2.d0, & 3.d0, 8.d0, & 15.d0, 48.d0, & 105.d0, 384.d0, & 945.d0, 3840.d0, & 10395.d0, 46080.d0, & 135135.d0, 645120.d0, & 2027025.d0, 10321920.d0, & 34459425.d0, 185794560.d0, & 654729075.d0, 3715891200.d0, & 13749310575.d0, 81749606400.d0, & 316234143225.d0, 1961990553600.d0, & 7905853580625.d0, 51011754393600.d0, & 213458046676875.d0, 1428329123020800.d0, & 6190283353629375.d0, 42849873690624000.d0, & 191898783962510625.d0, 1371195958099968000.d0, & 6332659870762850625.d0, 46620662575398912000.d0, & 221643095476699771875.d0, 1678343852714360832000.d0, & 8200794532637891559375.d0, 63777066403145711616000.d0] ! fast return if possible if (n.le.1) then factnm=1.d0 return end if if (m.eq.1) then if (n.le.24) then factnm=f1(n) return end if factnm=f1(24) do i=25,n factnm=factnm*dble(i) end do return end if if (m.eq.2) then if (n.le.38) then factnm=f2(n) return end if end if ! return zero for invalid m if (m.le.0) then factnm=0.d0 return end if j=n/m if (mod(n,m).eq.0) j=j-1 factnm=dble(n) do i=1,j factnm=factnm*dble(n-i*m) end do end function !EOC elk-7.2.42/src/PaxHeaders.21776/sphcover.f900000644000000000000000000000013214061636517015075 xustar0030 mtime=1623670095.287102147 30 atime=1623670094.057103288 30 ctime=1623670095.287102147 elk-7.2.42/src/sphcover.f900000644002504400250440000000254614061636517017141 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: sphcover ! !INTERFACE: subroutine sphcover(n,tp) ! !INPUT/OUTPUT PARAMETERS: ! n : number of required points (in,integer) ! tp : (theta, phi) coordinates (out,real(2,n)) ! !DESCRIPTION: ! Produces a set of $N$ points which cover the unit sphere nearly optimally. ! The points in spherical $(\theta,\phi)$ coordinates are generated using the ! explicit `golden section' formula: ! \begin{align*} ! \theta_k&=\arccos\left[1-\left(k-\tfrac{1}{2}\right)\delta z\right] \\ ! \phi_k&=(k-1)\delta\phi, ! \end{align*} ! where $\delta z=2/n$ and $\delta\phi=\pi(1-\sqrt{5})$. ! ! !REVISION HISTORY: ! Created April 2008 (JKD) ! Improved covering, October 2009 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(out) :: tp(2,n) ! local variables integer k real(8), parameter :: pi=3.1415926535897932385d0 real(8) z,dz,p,dp if (n.le.0) then write(*,*) write(*,'("Error(sphcover): n <= 0 : ",I8)') n write(*,*) stop end if dz=2.d0/dble(n) z=1.d0-dz/2.d0 tp(1,1)=acos(z) dp=pi*(1.d0-sqrt(5.d0)) p=0.d0 tp(2,1)=p do k=2,n z=z-dz tp(1,k)=acos(z) p=p+dp tp(2,k)=mod(p,2.d0*pi) end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/sctovec.f900000644000000000000000000000013214061636517014712 xustar0030 mtime=1623670095.288102146 30 atime=1623670094.059103286 30 ctime=1623670095.288102146 elk-7.2.42/src/sctovec.f900000644002504400250440000000064214061636517016751 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine sctovec(tp,v) implicit none ! arguments real(8), intent(in) :: tp(2) real(8), intent(out) :: v(3) ! local variables real(8) t1 t1=sin(tp(1)) v(1)=t1*cos(tp(2)) v(2)=t1*sin(tp(2)) v(3)=cos(tp(1)) end subroutine elk-7.2.42/src/PaxHeaders.21776/genvmat.f900000644000000000000000000000013214061636517014705 xustar0030 mtime=1623670095.290102144 30 atime=1623670094.061103285 30 ctime=1623670095.290102144 elk-7.2.42/src/genvmat.f900000644002504400250440000000551514061636517016750 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genvmat(vmt,vir,vmat) ! generates potential matrix elements for all states and k-points use modmain use modmpi use modomp implicit none ! arguments real(8), intent(in) :: vmt(npmtmax,natmtot),vir(ngtot) complex(8), intent(out) :: vmat(nstsv,nstsv,nkpt) ! local variables integer ik,ist,ispn integer is,ias,nrc,nrci integer n,lp,nthd ! automatic arrays integer idx(nstsv) real(8) rfmt(npcmtmax) ! allocatable arrays real(8), allocatable :: vmt1(:,:),vir1(:) complex(8), allocatable :: apwalm(:,:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfgk(:,:,:) ! allocate local arrays allocate(vmt1(npcmtmax,natmtot),vir1(ngtot)) call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(rfmt,is,nrc,nrci) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) ! convert muffin-tin potential to a coarse radial mesg call rfmtftoc(nrc,nrci,vmt(:,ias),rfmt) ! convert potential to spherical coordinates call rbsht(nrc,nrci,rfmt,vmt1(:,ias)) ! multiply by the radial integration weights call rfcmtwr(nrc,nrci,wrcmt(:,is),vmt1(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! multiply interstitial potential by characteristic function vir1(:)=vir(:)*cfunir(:) ! index to all states do ist=1,nstsv idx(ist)=ist end do ! loop over k-points call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(apwalm,evecfv,evecsv) & !$OMP PRIVATE(wfmt,wfgk,ispn) & !$OMP NUM_THREADS(nthd) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) allocate(wfmt(npcmtmax,natmtot,nspinor,nstsv),wfgk(ngkmax,nspinor,nstsv)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! find the matching coefficients do ispn=1,nspnfv call match(ngk(ispn,ik),vgkc(:,:,ispn,ik),gkc(:,ispn,ik), & sfacgk(:,:,ispn,ik),apwalm(:,:,:,:,ispn)) end do ! get the eigenvectors from file call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! calculate the wavefunctions for all states of the input k-point call genwfsv(.false.,.true.,nstsv,idx,ngridg,igfft,ngk(:,ik),igkig(:,:,ik), & apwalm,evecfv,evecsv,wfmt,ngkmax,wfgk) call genvmatk(vmt1,vir1,ngk(:,ik),igkig(:,:,ik),wfmt,ngkmax,wfgk,vmat(:,:,ik)) end do !$OMP END DO deallocate(apwalm,evecfv,evecsv,wfmt,wfgk) !$OMP END PARALLEL call freethd(nthd) ! broadcast matrix elements to every process if (np_mpi.gt.1) then n=nstsv*nstsv do ik=1,nkpt lp=mod(ik-1,np_mpi) call mpi_bcast(vmat(:,:,ik),n,mpi_double_complex,lp,mpicom,ierror) end do end if deallocate(vmt1,vir1) end subroutine elk-7.2.42/src/PaxHeaders.21776/genppts.f900000644000000000000000000000013214061636517014724 xustar0030 mtime=1623670095.291102143 30 atime=1623670094.062103284 30 ctime=1623670095.291102143 elk-7.2.42/src/genppts.f900000644002504400250440000001367614061636517016776 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: genppts ! !INTERFACE: subroutine genppts(tfbz,nsym,sym,ngridp,npptnr,epslat,bvec,boxl,nppt,ipvip, & ipvipnr,ivp,vpl,vpc,wppt,wpptnr) ! !INPUT/OUTPUT PARAMETERS: ! tfbz : .true. if vpl and vpc should be mapped to the first Brillouin zone ! (in,logical) ! nsym : number of point group symmetries used for reduction, set to 1 for ! no reduction (in,integer) ! sym : symmetry matrices in lattice coordinates (in,integer(3,3,*)) ! ngridp : p-point grid sizes (in,integer(3)) ! npptnr : number of non-reduced p-points: ngridp(1)*ngridp(2)*ngridp(3) ! (in,integer) ! epslat : tolerance for determining identical vectors (in,real) ! bvec : reciprocal lattice vectors (in,real(3,3)) ! boxl : corners of box containing p-points in lattice coordinates, the ! zeroth vector is the origin (in,real(3,0:3)) ! nppt : total number of p-points (out,integer) ! ipvip : map from (i1,i2,i3) to reduced p-point index ! (out,integer(0:ngridp(1)-1,0:ngridp(2)-1,0:ngridp(3)-1)) ! ipvipnr : map from (i1,i2,i3) to non-reduced p-point index ! (out,integer(0:ngridp(1)-1,0:ngridp(2)-1,0:ngridp(3)-1)) ! ivp : integer coordinates of the p-points ! (out,integer(3,ngridp(1)*ngridp(2)*ngridp(3))) ! vpl : lattice coordinates of each p-point ! (out,real(3,ngridp(1)*ngridp(2)*ngridp(3))) ! vpc : Cartesian coordinates of each p-point ! (out,real(3,ngridp(1)*ngridp(2)*ngridp(3))) ! wppt : weights of each reduced p-point ! (out,real(ngridp(1)*ngridp(2)*ngridp(3))) ! wpptnr : weight of each non-reduced p-point (out,real) ! !DESCRIPTION: ! This routine is used for generating $k$-point or $q$-point sets. Since these ! are stored in global arrays, the points passed to this and other routines ! are referred to as $p$-points. In lattice coordinates, the ${\bf p}$ vectors ! are given by ! $$ {\bf p}=\left(\begin{matrix} & & \\ ! {\bf B}_2-{\bf B}_1 & {\bf B}_3-{\bf B}_1 & {\bf B}_4-{\bf B}_1 \\ ! & & \end{matrix}\right) ! \left(\begin{matrix}i_1/n_1 \\ i_2/n_2 \\ i_3/n_3 \end{matrix}\right) ! +{\bf B}_1 $$ ! where $i_j$ runs from 0 to $n_j-1$, and the ${\bf B}$ vectors define the ! corners of a box with ${\bf B}_1$ as the origin. If {\tt tfbz} is ! {\tt .true.} then each {\tt vpl} vector is mapped to the first Brillouin ! zone. If {\tt tfbz} is {\tt .false.} and then the coordinates of each ! {\tt vpl} are mapped to the $[0,1)$ interval. The $p$-point weights are ! stored in {\tt wppt} and the array {\tt ipvip} contains the map from the ! integer coordinates to the reduced index. ! ! !REVISION HISTORY: ! Created August 2002 (JKD) ! Updated April 2007 (JKD) ! Added mapping to the first Brillouin zone, September 2008 (JKD) ! Made independent of modmain, February 2010 (JKD) !EOP !BOC implicit none ! arguments logical, intent(in) :: tfbz integer, intent(in) :: nsym,sym(3,3,*) integer, intent(in) :: ngridp(3),npptnr real(8), intent(in) :: epslat real(8), intent(in) :: bvec(3,3),boxl(3,0:3) integer, intent(out) :: nppt integer, intent(out) :: ipvip(0:ngridp(1)-1,0:ngridp(2)-1,0:ngridp(3)-1) integer, intent(out) :: ipvipnr(0:ngridp(1)-1,0:ngridp(2)-1,0:ngridp(3)-1) integer, intent(out) :: ivp(3,npptnr) real(8), intent(out) :: vpl(3,npptnr),vpc(3,npptnr) real(8), intent(out) :: wppt(npptnr),wpptnr ! local variables integer i1,i2,i3,i integer isym,ip,jp real(8) v1(3),v2(3),v3(3) real(8) b(3,3),t1 if ((ngridp(1).le.0).or.(ngridp(2).le.0).or.(ngridp(3).le.0)) then write(*,*) write(*,'("Error(genppts): invalid ngridp : ",3I8)') ngridp write(*,*) stop end if if (npptnr.ne.ngridp(1)*ngridp(2)*ngridp(3)) then write(*,*) write(*,'("Error(genppts): mismatched npptnr and ngridp : ",4I8)') npptnr, & ngridp write(*,*) stop end if ! box vector matrix b(:,1)=boxl(:,1)-boxl(:,0) b(:,2)=boxl(:,2)-boxl(:,0) b(:,3)=boxl(:,3)-boxl(:,0) ! weight of each non-reduced p-point wpptnr=1.d0/dble(ngridp(1)*ngridp(2)*ngridp(3)) ip=0 jp=npptnr do i3=0,ngridp(3)-1 v1(3)=dble(i3)/dble(ngridp(3)) do i2=0,ngridp(2)-1 v1(2)=dble(i2)/dble(ngridp(2)) do i1=0,ngridp(1)-1 v1(1)=dble(i1)/dble(ngridp(1)) call r3mv(b,v1,v2) v2(:)=v2(:)+boxl(:,0) ! map vector components to [0,1) call r3frac(epslat,v2) if (nsym.gt.1) then ! determine if this point is equivalent to one already in the set do isym=1,nsym call i3mtrv(sym(:,:,isym),v2,v3) call r3frac(epslat,v3) do i=1,ip t1=abs(vpl(1,i)-v3(1))+abs(vpl(2,i)-v3(2))+abs(vpl(3,i)-v3(3)) if (t1.lt.epslat) then ! equivalent p-point found so add to existing weight ipvip(i1,i2,i3)=i wppt(i)=wppt(i)+wpptnr ! add new point to back of set ipvipnr(i1,i2,i3)=jp ivp(1,jp)=i1; ivp(2,jp)=i2; ivp(3,jp)=i3 vpl(:,jp)=v2(:) wppt(jp)=0.d0 jp=jp-1 goto 10 end if end do end do end if ! add new point to set ip=ip+1 ipvip(i1,i2,i3)=ip ipvipnr(i1,i2,i3)=ip ivp(1,ip)=i1; ivp(2,ip)=i2; ivp(3,ip)=i3 vpl(:,ip)=v2(:) wppt(ip)=wpptnr 10 continue end do end do end do nppt=ip do ip=1,npptnr ! map vpl to the first Brillouin zone if required if (tfbz) call vecfbz(epslat,bvec,vpl(:,ip)) ! determine the Cartesian coordinates of the p-points call r3mv(bvec,vpl(:,ip),vpc(:,ip)) end do return contains pure subroutine i3mtrv(a,x,y) implicit none ! arguments integer, intent(in) :: a(3,3) real(8), intent(in) :: x(3) real(8), intent(out) :: y(3) y(1)=a(1,1)*x(1)+a(2,1)*x(2)+a(3,1)*x(3) y(2)=a(1,2)*x(1)+a(2,2)*x(2)+a(3,2)*x(3) y(3)=a(1,3)*x(1)+a(2,3)*x(2)+a(3,3)*x(3) end subroutine end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/mtdmin.f900000644000000000000000000000013214061636517014534 xustar0030 mtime=1623670095.293102141 30 atime=1623670094.064103282 30 ctime=1623670095.293102141 elk-7.2.42/src/mtdmin.f900000644002504400250440000000324714061636517016577 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: mtdmin ! !INTERFACE: pure subroutine mtdmin(is,js,dmin) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! is, js : species numbers (out,integer) ! dmin : minimum distance between muffin-tin surfaces (out,real) ! !DESCRIPTION: ! Finds the atomic species pair for which the distance between the muffin-tin ! surfaces is a minimum. This distance may be negative if the muffin-tins ! overlap. ! ! !REVISION HISTORY: ! Created October 2011 (JKD) !EOP !BOC implicit none ! arguments integer, intent(out) :: is,js real(8), intent(out) :: dmin ! local variables integer i1,i2,i3,ks,ka,ls,la real(8) v1(3),v2(3),t1,t2,t3 is=1 js=1 dmin=1.d6 do i1=-1,1 do i2=-1,1 do i3=-1,1 v1(:)=dble(i1)*avec(:,1)+dble(i2)*avec(:,2)+dble(i3)*avec(:,3) do ks=1,nspecies do ka=1,natoms(ks) v2(:)=v1(:)+atposc(:,ka,ks) do ls=1,nspecies t1=rmt(ks)+rmt(ls) do la=1,natoms(ls) if ((i1.ne.0).or.(i2.ne.0).or.(i3.ne.0).or.(ks.ne.ls).or. & (ka.ne.la)) then t2=sqrt((v2(1)-atposc(1,la,ls))**2 & +(v2(2)-atposc(2,la,ls))**2 & +(v2(3)-atposc(3,la,ls))**2) t3=t2-t1 if (t3.lt.dmin-epslat) then is=ks js=ls dmin=t3 end if end if end do end do end do end do end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/eveqnzg.f900000644000000000000000000000012714061636517014727 xustar0029 mtime=1623670095.29410214 29 atime=1623670094.06610328 29 ctime=1623670095.29410214 elk-7.2.42/src/eveqnzg.f900000644002504400250440000000205214061636517016757 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine eveqnzg(n,ld,a,w) use modomp implicit none ! arguments integer, intent(in) :: n,ld complex(8), intent(inout) :: a(ld,n) complex(8), intent(out) :: w(n) ! local variables integer lwork,info integer nthd,nts ! allocatable arrays real(8), allocatable :: rwork(:) complex(8), allocatable :: vr(:,:),work(:) lwork=2*n allocate(rwork(2*n),vr(n,n),work(lwork)) ! enable MKL parallelism call holdthd(maxthdmkl,nthd) nts=mkl_set_num_threads_local(nthd) ! determine the eigenvalues and right eigenvectors call zgeev('N','V',n,a,ld,w,vr,1,vr,n,work,lwork,rwork,info) nts=mkl_set_num_threads_local(0) call freethd(nthd) if (info.ne.0) then write(*,*) write(*,'("Error(eveqnzg): diagonalisation failed")') write(*,'(" ZGEEV returned INFO = ",I8)') info write(*,*) stop end if ! copy right eigenvectors to output array a(1:n,1:n)=vr(1:n,1:n) deallocate(rwork,vr,work) end subroutine elk-7.2.42/src/PaxHeaders.21776/fderiv.f900000644000000000000000000000013214061636517014523 xustar0030 mtime=1623670095.296102138 30 atime=1623670094.067103279 30 ctime=1623670095.296102138 elk-7.2.42/src/fderiv.f900000644002504400250440000000324614061636517016565 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: fderiv ! !INTERFACE: subroutine fderiv(m,n,x,f,g) ! !INPUT/OUTPUT PARAMETERS: ! m : order of derivative (in,integer) ! n : number of points (in,integer) ! x : abscissa array (in,real(n)) ! f : function array (in,real(n)) ! g : (anti-)derivative of f (out,real(n)) ! !DESCRIPTION: ! Given function $f$ defined on a set of points $x_i$ then if $m\ge 0$ this ! routine computes the $m$th derivative of $f$ at each point. If $m=-1$ the ! anti-derivative of $f$ given by ! $$ g(x_i)=\int_{x_1}^{x_i} f(x)\,dx $$ ! is calculated. Both derivatives and integrals are computed by first fitting ! the function to a clamped cubic spline. ! ! !REVISION HISTORY: ! Created May 2002 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: m,n real(8), intent(in) :: x(n),f(n) real(8), intent(out) :: g(n) ! local variables integer i real(8) sm,dx ! automatic arrays real(8) cf(3,n) if (n.le.0) then write(*,*) write(*,'("Error(fderiv): invalid number of points : ",I8)') n write(*,*) stop end if ! high accuracy integration/differentiation from spline interpolation call spline(n,x,f,cf) select case(m) case(:-1) sm=0.d0 g(1)=0.d0 do i=1,n-1 dx=x(i+1)-x(i) sm=sm+dx*(f(i) & +dx*(0.5d0*cf(1,i) & +dx*(0.3333333333333333333d0*cf(2,i) & +dx*0.25d0*cf(3,i)))) g(i+1)=sm end do case(1) g(:)=cf(1,:) case(2) g(:)=2.d0*cf(2,:) case(3) g(:)=6.d0*cf(3,:) case(4:) g(:)=0.d0 end select end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genpmat.f900000644000000000000000000000013214061636517014677 xustar0030 mtime=1623670095.297102137 30 atime=1623670094.069103277 30 ctime=1623670095.297102137 elk-7.2.42/src/genpmat.f900000644002504400250440000000145714061636517016743 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genpmat use modmain use modmpi use modomp implicit none ! local variables integer ik,nthd if (mp_mpi) write(*,*) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(genpmat_) write(*,'("Info(genpmat): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(genpmat_) call putpmat(ik) end do !$OMP END PARALLEL DO call freethd(nthd) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/genexpmat.f900000644000000000000000000000013214061636517015234 xustar0030 mtime=1623670095.299102135 30 atime=1623670094.071103275 30 ctime=1623670095.299102135 elk-7.2.42/src/genexpmat.f900000644002504400250440000001250214061636517017271 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genexpmat(vpl,expmt,emat) use modmain implicit none ! arguments real(8), intent(in) :: vpl(3) complex(8), intent(in) :: expmt(npcmtmax,natmtot) complex(8), intent(out) :: emat(nstsv,nstsv) ! local variables integer ist,jst,ispn,i,j,k,l integer is,ia,ias,nrc,nrci integer npc,ngp,ngpq,igp,ifg real(8) vpc(3),vpql(3),vpqc(3),t1 complex(8) z1 ! allocatable arrays integer, allocatable :: igpig(:),igpqig(:) real(8), allocatable :: vgpl(:,:),vgpc(:,:),gpc(:) real(8), allocatable :: vgpql(:,:),vgpqc(:,:),gpqc(:) complex(8), allocatable :: sfacgp(:,:),sfacgpq(:,:) complex(8), allocatable :: apwalm1(:,:,:,:),apwalm2(:,:,:,:) complex(8), allocatable :: evecfv1(:,:),evecfv2(:,:) complex(8), allocatable :: evecsv1(:,:),evecsv2(:,:) complex(8), allocatable :: wfmt1(:),wfmt2(:,:) complex(8), allocatable :: zfir(:),x(:),em(:,:) ! external functions complex(8), external :: zfmtinp,zdotc ! check if q-vector is zero t1=abs(vecql(1))+abs(vecql(2))+abs(vecql(3)) if (t1.lt.epslat) then emat(:,:)=0.d0 do i=1,nstsv emat(i,i)=1.d0 end do return end if ! allocate local arrays allocate(igpig(ngkmax),igpqig(ngkmax)) allocate(vgpl(3,ngkmax),vgpc(3,ngkmax),gpc(ngkmax)) allocate(vgpql(3,ngkmax),vgpqc(3,ngkmax),gpqc(ngkmax)) allocate(sfacgp(ngkmax,natmtot),sfacgpq(ngkmax,natmtot)) allocate(apwalm1(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(apwalm2(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(evecfv1(nmatmax,nstfv),evecfv2(nmatmax,nstfv)) if (tevecsv) then allocate(evecsv1(nstsv,nstsv),evecsv2(nstsv,nstsv)) end if allocate(wfmt1(npcmtmax),wfmt2(npcmtmax,nstfv)) allocate(zfir(ngtot),x(ngkmax),em(nstfv,nstfv)) ! p-vector in Cartesian coordinates call r3mv(bvec,vpl,vpc) ! generate the G+p-vectors call gengkvec(ngvc,ivg,vgc,vpl,vpc,gkmax,ngkmax,ngp,igpig,vgpl,vgpc,gpc) ! generate the structure factors call gensfacgp(ngp,vgpc,ngkmax,sfacgp) ! find the matching coefficients for k-point p call match(ngp,vgpc,gpc,sfacgp,apwalm1) ! get the eigenvectors for k-point p call getevecfv(filext,0,vpl,vgpl,evecfv1) ! p+q-vector in lattice coordinates vpql(:)=vpl(:)+vecql(:) ! p+q-vector in Cartesian coordinates call r3mv(bvec,vpql,vpqc) ! generate the G+p+q-vectors call gengkvec(ngvc,ivg,vgc,vpql,vpqc,gkmax,ngkmax,ngpq,igpqig,vgpql,vgpqc,gpqc) ! generate the structure factors call gensfacgp(ngpq,vgpqc,ngkmax,sfacgpq) ! find the matching coefficients for k-point p+q call match(ngpq,vgpqc,gpqc,sfacgpq,apwalm2) ! get the eigenvectors for k-point p+q call getevecfv(filext,0,vpql,vgpql,evecfv2) ! set the first-variational matrix element array to zero em(:,:)=0.d0 !------------------------------------! ! muffin-tin matrix elements ! !------------------------------------! do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) do ist=1,nstfv ! calculate the wavefunction for k-point p+q call wavefmt(lradstp,ias,ngpq,apwalm2(:,:,:,ias),evecfv2(:,ist),wfmt1) ! convert from spherical harmonics to spherical coordinates call zbsht(nrc,nrci,wfmt1,wfmt2(:,ist)) ! multiply by exp(-iq.r) (conjugate because zfmtinp conjugates first function) wfmt1(1:npc)=conjg(expmt(1:npc,ias))*wfmt2(1:npc,ist) ! convert from spherical coordinates to spherical harmonics call zfsht(nrc,nrci,wfmt1,wfmt2(:,ist)) end do do jst=1,nstfv ! calculate the wavefunction for k-point p call wavefmt(lradstp,ias,ngp,apwalm1(:,:,:,ias),evecfv1(:,jst),wfmt1) do ist=1,nstfv em(ist,jst)=em(ist,jst)+zfmtinp(nrc,nrci,wrcmt(:,is),wfmt2(:,ist),wfmt1) end do end do ! end loops over atoms and species end do end do !--------------------------------------! ! interstitial matrix elements ! !--------------------------------------! ! compute interstitial wavefunctions for k-point p do jst=1,nstfv zfir(:)=0.d0 do igp=1,ngp ifg=igfft(igpig(igp)) zfir(ifg)=evecfv1(igp,jst) end do ! Fourier transform wavefunction to real-space call zfftifc(3,ngridg,1,zfir) ! multiply with the characteristic function zfir(:)=zfir(:)*cfunir(:) ! Fourier transform back to G-space call zfftifc(3,ngridg,-1,zfir) ! store as wavefunction with G+p+q index do igp=1,ngpq ifg=igfft(igpqig(igp)) x(igp)=zfir(ifg) end do ! add to the first-variational matrix elements do ist=1,nstfv em(ist,jst)=em(ist,jst)+zdotc(ngpq,evecfv2(:,ist),1,x,1) end do end do !-------------------------------------------! ! second-variational matrix elements ! !-------------------------------------------! if (tevecsv) then ! get the second-variational eigenvectors call getevecsv(filext,0,vpl,evecsv1) call getevecsv(filext,0,vpql,evecsv2) do i=1,nstsv do j=1,nstsv z1=0.d0 k=0 do ispn=1,nspinor do ist=1,nstfv k=k+1 l=(ispn-1)*nstfv do jst=1,nstfv l=l+1 z1=z1+em(ist,jst)*conjg(evecsv2(k,i))*evecsv1(l,j) end do end do end do emat(i,j)=z1 end do end do else emat(:,:)=em(:,:) end if deallocate(igpig,igpqig,vgpl,vgpc,gpc) deallocate(vgpql,vgpqc,gpqc,sfacgp,sfacgpq) deallocate(apwalm1,apwalm2,evecfv1,evecfv2) if (tevecsv) deallocate(evecsv1,evecsv2) deallocate(wfmt1,wfmt2,zfir,x,em) end subroutine elk-7.2.42/src/PaxHeaders.21776/writeforces.f900000644000000000000000000000013214061636517015600 xustar0030 mtime=1623670095.301102134 30 atime=1623670094.072103274 30 ctime=1623670095.301102134 elk-7.2.42/src/writeforces.f900000644002504400250440000000161514061636517017640 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2004-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeforces(fnum) use modmain implicit none ! arguments integer, intent(in) :: fnum ! local variables integer is,ia,ias real(8) t1 write(fnum,*) write(fnum,'("Forces :")') do is=1,nspecies write(fnum,'(" species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) ias=idxas(ia,is) write(fnum,'(" atom : ",I4)') ia write(fnum,'(" Hellmann-Feynman",T30,": ",3F14.8)') forcehf(:,ias) write(fnum,'(" IBS",T30,": ",3F14.8)') forceibs(:,ias) write(fnum,'(" total force",T30,": ",3F14.8)') forcetot(:,ias) t1=sqrt(forcetot(1,ias)**2+forcetot(2,ias)**2+forcetot(3,ias)**2) write(fnum,'(" total magnitude",T30,": ",F14.8)') t1 end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/r3cross.f900000644000000000000000000000013214061636517014642 xustar0030 mtime=1623670095.302102133 30 atime=1623670094.074103273 30 ctime=1623670095.302102133 elk-7.2.42/src/r3cross.f900000644002504400250440000000134214061636517016677 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3cross ! !INTERFACE: pure subroutine r3cross(x,y,z) ! !INPUT/OUTPUT PARAMETERS: ! x : input vector 1 (in,real(3)) ! y : input vector 2 (in,real(3)) ! z : output cross-product (out,real(3)) ! !DESCRIPTION: ! Returns the cross product of two real 3-vectors. ! ! !REVISION HISTORY: ! Created September 2002 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: x(3),y(3) real(8), intent(out) :: z(3) z(1)=x(2)*y(3)-x(3)*y(2) z(2)=x(3)*y(1)-x(1)*y(3) z(3)=x(1)*y(2)-x(2)*y(1) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/match.f900000644000000000000000000000013214061636517014340 xustar0030 mtime=1623670095.304102131 30 atime=1623670094.076103271 30 ctime=1623670095.304102131 elk-7.2.42/src/match.f900000644002504400250440000001177614061636517016411 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: match ! !INTERFACE: subroutine match(ngp,vgpc,gpc,sfacgp,apwalm) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ngp : number of G+p-vectors (in,integer) ! vgpc : G+p-vectors in Cartesian coordinates (in,real(3,ngkmax)) ! gpc : length of G+p-vectors (in,real(ngkmax)) ! sfacgp : structure factors of G+p-vectors (in,complex(ngkmax,natmtot)) ! apwalm : APW matching coefficients ! (out,complex(ngkmax,apwordmax,lmmaxapw,natmtot)) ! !DESCRIPTION: ! Computes the $({\bf G+p})$-dependent matching coefficients for the APW basis ! functions. Inside muffin-tin $\alpha$, the APW functions are given by ! $$ \phi^{\alpha}_{\bf G+p}({\bf r})=\sum_{l=0}^{l_{\rm max}} ! \sum_{m=-l}^{l}\sum_{j=1}^{M^{\alpha}_l}A^{\alpha}_{jlm}({\bf G+p}) ! u^{\alpha}_{jl}(r)Y_{lm}(\hat{{\bf r}}), $$ ! where $A^{\alpha}_{jlm}({\bf G+p})$ is the matching coefficient, ! $M^{\alpha}_l$ is the order of the APW and $u^{\alpha}_{jl}$ is the radial ! function. In the interstitial region, an APW function is a plane wave, ! $\exp(i({\bf G+p})\cdot{\bf r})/\sqrt{\Omega}$, where $\Omega$ is the unit ! cell volume. Ensuring continuity up to the $(M^{\alpha}_l-1)$th derivative ! across the muffin-tin boundary therefore requires that the matching ! coefficients satisfy ! $$ \sum_{j=1}^{M^{\alpha}_l}D_{ij}A^{\alpha}_{jlm}({\bf G+p})=b_i\;, $$ ! where ! $$ D_{ij}=\left.\frac{d^{i-1}u^{\alpha}_{jl}(r)}{dr^{i-1}} ! \right|_{r=R_{\alpha}} $$ ! and ! $$ b_i=\frac{4\pi i^l}{\sqrt{\Omega}}|{\bf G+p}|^{i-1}j^{(i-1)}_l ! (|{\bf G+p}|R_{\alpha})\exp(i({\bf G+p})\cdot{\bf r}_{\alpha})Y^*_{lm} ! (\widehat{{\bf G+p}}), $$ ! with ${\bf r}_{\alpha}$ the atomic position and $R_{\alpha}$ the muffin-tin ! radius. See routine {\tt wavefmt}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) ! Fixed documentation, June 2006 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: ngp real(8), intent(in) :: vgpc(3,ngkmax),gpc(ngkmax) complex(8), intent(in) :: sfacgp(ngkmax,natmtot) complex(8), intent(out) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot) ! local variables integer is,ia,ias integer omax,ord,info integer l,lma,lmb,lm,io,jo integer nr,ir,igp,i real(8) t0,t1 complex(8) z1,z2,z3 ! automatic arrays integer ipiv(apwordmax) real(8) djl(0:lmaxapw,apwordmax,ngp) complex(8) a(apwordmax,apwordmax),ylmgp(lmmaxapw,ngp) complex(8) b(apwordmax,ngp*(2*lmaxapw+1)) ! external functions real(8), external :: polynm ! compute the spherical harmonics of the G+p-vectors do igp=1,ngp call genylmv(lmaxapw,vgpc(:,igp),ylmgp(:,igp)) end do t0=fourpi/sqrt(omega) ! loop over species do is=1,nspecies nr=nrmt(is) ! maximum APW order for this species omax=maxval(apword(1:lmaxapw,is)) ! special case of omax=1 if (omax.eq.1) then do igp=1,ngp t1=gpc(igp)*rmt(is) call sbessel(lmaxapw,t1,djl(:,1,igp)) end do do ia=1,natoms(is) ias=idxas(ia,is) do l=0,lmaxapw z1=(t0/apwfr(nr,1,1,l,ias))*zil(l) lma=l**2+1; lmb=lma+2*l do igp=1,ngp z2=djl(l,1,igp)*z1*sfacgp(igp,ias) do lm=lma,lmb apwalm(igp,1,lm,ias)=z2*conjg(ylmgp(lm,igp)) end do end do end do end do cycle end if ! starting point on radial mesh for fitting polynomial of order npapw ir=nr-npapw+1 ! evaluate the spherical Bessel function derivatives for all G+p-vectors do igp=1,ngp t1=gpc(igp)*rmt(is) do io=1,omax call sbesseldm(io-1,lmaxapw,t1,djl(:,io,igp)) end do t1=1.d0 do io=2,omax t1=t1*gpc(igp) djl(:,io,igp)=t1*djl(:,io,igp) end do end do ! loop over atoms do ia=1,natoms(is) ias=idxas(ia,is) ! begin loop over l do l=0,lmaxapw ord=apword(l,is) z1=t0*zil(l) ! set up matrix of derivatives do jo=1,ord do io=1,ord a(io,jo)=polynm(io-1,npapw,rsp(ir,is),apwfr(ir,1,jo,l,ias),rmt(is)) end do end do lma=l**2+1; lmb=lma+2*l ! set up target vectors i=0 do igp=1,ngp z2=z1*sfacgp(igp,ias) do lm=lma,lmb i=i+1 z3=z2*conjg(ylmgp(lm,igp)) do io=1,ord b(io,i)=djl(l,io,igp)*z3 end do end do end do ! solve the general complex linear systems call zgesv(ord,i,a,apwordmax,ipiv,b,apwordmax,info) if (info.ne.0) then write(*,*) write(*,'("Error(match): could not find APW matching coefficients")') write(*,'(" for species ",I4," and atom ",I4)') is,ia write(*,'(" ZGESV returned INFO = ",I8)') info write(*,*) stop end if i=0 do igp=1,ngp do lm=lma,lmb i=i+1 do io=1,ord apwalm(igp,io,lm,ias)=b(io,i) end do end do end do ! end loop over l end do ! end loops over atoms and species end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genspchi0.f900000644000000000000000000000013014061636517015122 xustar0029 mtime=1623670095.30510213 30 atime=1623670094.078103269 29 ctime=1623670095.30510213 elk-7.2.42/src/genspchi0.f900000644002504400250440000001612514061636517017166 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genspchi0 ! !INTERFACE: subroutine genspchi0(ik,lock,ssr,vqpl,jlgqr,ylmgq,sfacgq,chi0) ! !USES: use modmain use modomp ! !INPUT/OUTPUT PARAMETERS: ! ik : k-point from non-reduced set (in,integer) ! lock : OpenMP locks for frequency index of chi0 (in,integer(nwrf)) ! ssr : scissor correction (in,real) ! vqpl : input q-point in lattice coordinates (in,real(3)) ! jlgqr : spherical Bessel functions evaluated on the coarse radial mesh for ! all species and G+q-vectors (in,real(njcmax,nspecies,ngrf)) ! ylmgq : spherical harmonics of the G+q-vectors (in,complex(lmmaxo,ngrf)) ! sfacgq : structure factors of G+q-vectors (in,complex(ngrf,natmtot)) ! chi0 : spin-dependent Kohn-Sham response function in G-space ! (out,complex(ngrf,4,ngrf,4,nwrf)) ! !DESCRIPTION: ! Computes the spin-dependent Kohn-Sham response function: ! \begin{align*} ! \chi_{\alpha\beta,\alpha'\beta'}({\bf r},{\bf r}',\omega) ! & \equiv\frac{\delta\rho_{\alpha\beta}({\bf r},\omega)} ! {\delta v_{\alpha'\beta'}({\bf r}',\omega)} \\ ! & =\frac{1}{N_k}\sum_{i{\bf k},j{\bf k}'}(f_{i{\bf k}}-f_{j{\bf k}'}) ! \frac{\langle i{\bf k}|\hat{\rho}_{\beta\alpha}({\bf r})|j{\bf k}'\rangle ! \langle j{\bf k}'|\hat{\rho}_{\alpha'\beta'}({\bf r}')|i{\bf k}\rangle} ! {w+(\varepsilon_{i{\bf k}}-\varepsilon_{j{\bf k}'})+i\eta}, ! \end{align*} ! where $\alpha$ and $\beta$ are spin-coordinates, $N_k$ is the number of ! $k$-points, $f_{i{\bf k}}$ are the occupancies, $v$ is the Kohn-Sham ! potential and $\hat{\rho}$ is the spin-density operator. With translational ! symmetry in mind, we adopt the following convention for its Fourier ! transform: ! $$ \chi_{\alpha\beta,\alpha'\beta'}({\bf G},{\bf G}',{\bf q},\omega)= ! \frac{1}{\Omega}\int d^3r\,d^3r'\,e^{-i({\bf G}+{\bf q})\cdot{\bf r}} ! e^{i({\bf G}'+{\bf q})\cdot{\bf r}'} ! \chi_{\alpha\beta,\alpha'\beta'}({\bf r},{\bf r}',\omega). $$ ! Let ! $$ Z_{i{\bf k},j{\bf k}+{\bf q}}^{\alpha\beta}({\bf G})\equiv ! \int d^3r\,e^{i({\bf G}+{\bf q})\cdot{\bf r}} ! \varphi_{j{\bf k}+{\bf q},\alpha}^*({\bf r}) ! \varphi_{i{\bf k},\beta}({\bf r}) $$ ! then the response function in $G$-space can be written ! $$ \chi_{\alpha\beta,\alpha'\beta'}({\bf G},{\bf G}',{\bf q},\omega)= ! \frac{1}{N_k\Omega}\sum_{i{\bf k},j{\bf k}+{\bf q}} ! (f_{i{\bf k}}-f_{j{\bf k}}) ! \frac{\left[Z_{i{\bf k},j{\bf k}+{\bf q}}^{\alpha\beta}({\bf G})\right]^* ! Z_{i{\bf k},j{\bf k}+{\bf q}}^{\alpha'\beta'}({\bf G}')} ! {w+(\varepsilon_{i{\bf k}}-\varepsilon_{j{\bf k}+{\bf q}})+i\eta}. $$ ! ! !REVISION HISTORY: ! Created March 2012 (SS and JKD) !EOP !BOC implicit none ! local variables integer, intent(in) :: ik integer(8), intent(in) :: lock(nwrf) real(8), intent(in) :: ssr,vqpl(3),jlgqr(njcmax,nspecies,ngrf) complex(8), intent(in) :: ylmgq(lmmaxo,ngrf),sfacgq(ngrf,natmtot) complex(8), intent(inout) :: chi0(ngrf,4,ngrf,4,nwrf) ! local variables logical tz(4),tssr integer isym,jk,jkq,iw integer nst,nstq,ist,jst,kst,lst integer ig,jg,a,b,i,j,nthd real(8) vkql(3),ei,ej,eij,t1 complex(8) z1 ! automatic arrays integer idx(nstsv),idxq(nstsv) integer ngp(nspnfv),ngpq(nspnfv) ! allocatable arrays integer, allocatable :: igpig(:,:),igpqig(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfir(:,:,:) complex(8), allocatable :: wfmtq(:,:,:,:),wfirq(:,:,:) complex(8), allocatable :: zrhomt(:,:),zrhoir(:),zrhoig(:,:) complex(8), allocatable :: zw(:),c(:,:,:,:) if (.not.spinpol) then write(*,*) write(*,'("Error(genspchi0): spin-unpolarised calculation")') write(*,*) stop end if ! k+q-vector in lattice coordinates vkql(:)=vkl(:,ik)+vqpl(:) ! equivalent reduced k-points for k and k+q jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) call findkpt(vkql,isym,jkq) ! count and index states at k and k+q in energy window nst=0 do ist=1,nstsv if (abs(evalsv(ist,jk)-efermi).lt.emaxrf) then nst=nst+1 idx(nst)=ist end if end do nstq=0 do jst=1,nstsv if (abs(evalsv(jst,jkq)-efermi).lt.emaxrf) then nstq=nstq+1 idxq(nstq)=jst end if end do ! set flag for scissor operator if (abs(ssr).gt.1.d-8) then tssr=.true. else tssr=.false. end if ! generate the wavefunctions for all states at k and k+q in energy window allocate(igpig(ngkmax,nspnfv)) allocate(wfmt(npcmtmax,natmtot,nspinor,nst),wfir(ngtc,nspinor,nst)) call genwfsvp(.false.,.false.,nst,idx,ngdgc,igfc,vkl(:,ik),ngp,igpig,wfmt,ngtc,& wfir) deallocate(igpig) allocate(igpqig(ngkmax,nspnfv)) allocate(wfmtq(npcmtmax,natmtot,nspinor,nstq),wfirq(ngtc,nspinor,nstq)) call genwfsvp(.false.,.false.,nstq,idxq,ngdgc,igfc,vkql,ngpq,igpqig,wfmtq,ngtc,& wfirq) deallocate(igpqig) call holdthd(nst,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zrhomt,zrhoir,zrhoig,zw,c) & !$OMP PRIVATE(jst,kst,lst,ei,ej,eij,t1) & !$OMP PRIVATE(iw,i,j,a,b,tz,ig,jg,z1) & !$OMP NUM_THREADS(nthd) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) allocate(zrhoig(ngrf,4),zw(nwrf),c(ngrf,4,ngrf,4)) !$OMP DO do ist=1,nst kst=idx(ist) ei=evalsv(kst,jk) do jst=1,nstq lst=idxq(jst) t1=wkptnr*omega*(occsv(kst,jk)-occsv(lst,jkq)) if (abs(t1).lt.1.d-8) cycle ej=evalsv(lst,jkq) eij=ei-ej ! scissor operator if (tssr) then if ((ei.gt.efermi).and.(ej.le.efermi)) then eij=eij+ssr else if ((ei.le.efermi).and.(ej.gt.efermi)) then eij=eij-ssr end if end if ! frequency-dependent part in response function formula for all frequencies do iw=1,nwrf zw(iw)=t1/(eij+wrf(iw)) end do ! compute the complex density in G+q-space i=0 do a=1,2 do b=1,2 i=i+1 ! find which contributions are zero for collinear case tz(i)=.false. if (.not.ncmag) then if (((a.eq.1).and.(kst.gt.nstfv)).or. & ((a.eq.2).and.(kst.le.nstfv)).or. & ((b.eq.1).and.(lst.gt.nstfv)).or. & ((b.eq.2).and.(lst.le.nstfv))) then tz(i)=.true. cycle end if end if call genzrho(.true.,.false.,ngtc,wfmt(:,:,a,ist),wfir(:,a,ist), & wfmtq(:,:,b,jst),wfirq(:,b,jst),zrhomt,zrhoir) call zftzf(ngrf,jlgqr,ylmgq,ngrf,sfacgq,zrhomt,zrhoir,zrhoig(:,i)) end do end do ! Hermitian part of matrix do j=1,4 if (tz(j)) cycle do jg=1,ngrf z1=conjg(zrhoig(jg,j)) do i=1,4 if (tz(i)) cycle do ig=1,ngrf c(ig,i,jg,j)=zrhoig(ig,i)*z1 end do end do end do end do do iw=1,nwrf z1=zw(iw) call omp_set_lock(lock(iw)) do j=1,4 if (tz(j)) cycle do jg=1,ngrf do i=1,4 if (tz(i)) cycle call zaxpy(ngrf,z1,c(:,i,jg,j),1,chi0(:,i,jg,j,iw),1) end do end do end do call omp_unset_lock(lock(iw)) end do ! end loop over jst end do ! end loop over ist end do !$OMP END DO deallocate(zrhomt,zrhoir,zrhoig,zw,c) !$OMP END PARALLEL call freethd(nthd) deallocate(wfmt,wfmtq,wfir,wfirq) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genzrho.f900000644000000000000000000000013214061636517014720 xustar0030 mtime=1623670095.307102128 30 atime=1623670094.079103268 30 ctime=1623670095.307102128 elk-7.2.42/src/genzrho.f900000644002504400250440000000630014061636517016754 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genzrho ! !INTERFACE: subroutine genzrho(tsh,tspc,ngt,wfmt1,wfir1,wfmt2,wfir2,zrhomt,zrhoir) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! tsh : .true. if the muffin-tin density is to be in spherical harmonics ! (in,logical) ! tspc : .true. if the density should be contracted over spin (in,logical) ! ngt : total number of interstitial grid points (in,integer) ! wfmt1 : muffin-tin part of wavefunction 1 in spherical coordinates ! (in,complex(npcmtmax,natmtot,*)) ! wfir1 : interstitial wavefunction 1 (in,complex(ngt,*)) ! wfmt2 : muffin-tin part of wavefunction 2 in spherical coordinates ! (in,complex(npcmtmax,natmtot,*)) ! wfir2 : interstitial wavefunction 2 (in,complex(ngt,*)) ! zrhomt : muffin-tin charge density in spherical harmonics/coordinates ! (out,complex(npcmtmax,natmtot)) ! zrhoir : interstitial charge density (out,complex(ngt)) ! !DESCRIPTION: ! Calculates the complex overlap charge density from two input wavefunctions: ! $$ \rho({\bf r})\equiv\Psi_1^{\dag}({\bf r})\cdot\Psi_2({\bf r}). $$ ! Note that the muffin-tin wavefunctions are provided in spherical coordinates ! and the returned density is either in terms of spherical harmonic ! coefficients or spherical coordinates when {\tt tsh} is {\tt .true.} or ! {\tt .false.}, respectively. ! ! !REVISION HISTORY: ! Created November 2004 (Sharma) !EOP !BOC implicit none ! arguments logical, intent(in) :: tsh,tspc integer, intent(in) :: ngt complex(8), intent(in) :: wfmt1(npcmtmax,natmtot,*),wfir1(ngt,*) complex(8), intent(in) :: wfmt2(npcmtmax,natmtot,*),wfir2(ngt,*) complex(8), intent(out) :: zrhomt(npcmtmax,natmtot),zrhoir(ngt) ! local variables integer is,ias ! automatic arrays complex(8) zfmt(npcmtmax) ! muffin-tin part do ias=1,natmtot is=idxis(ias) if (tsh) then if (tspc.and.spinpol) then ! contract over spin call zrho2(npcmt(is),wfmt1(:,ias,1),wfmt1(:,ias,2),wfmt2(:,ias,1), & wfmt2(:,ias,2),zfmt) else ! no spin contraction call zrho1(npcmt(is),wfmt1(:,ias,1),wfmt2(:,ias,1),zfmt) end if ! convert to spherical harmonics call zfsht(nrcmt(is),nrcmti(is),zfmt,zrhomt(:,ias)) else if (tspc.and.spinpol) then call zrho2(npcmt(is),wfmt1(:,ias,1),wfmt1(:,ias,2),wfmt2(:,ias,1), & wfmt2(:,ias,2),zrhomt(:,ias)) else call zrho1(npcmt(is),wfmt1(:,ias,1),wfmt2(:,ias,1),zrhomt(:,ias)) end if end if end do ! interstitial part if (tspc.and.spinpol) then call zrho2(ngt,wfir1,wfir1(:,2),wfir2,wfir2(:,2),zrhoir) else call zrho1(ngt,wfir1,wfir2,zrhoir) end if return contains pure subroutine zrho1(n,x,y,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x(n),y(n) complex(8), intent(out) :: z(n) z(:)=conjg(x(:))*y(:) end subroutine pure subroutine zrho2(n,x1,x2,y1,y2,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x1(n),x2(n),y1(n),y2(n) complex(8), intent(out) :: z(n) z(:)=conjg(x1(:))*y1(:)+conjg(x2(:))*y2(:) end subroutine end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/potefield.f900000644000000000000000000000013214061636517015217 xustar0030 mtime=1623670095.308102127 30 atime=1623670094.081103266 30 ctime=1623670095.308102127 elk-7.2.42/src/potefield.f900000644002504400250440000000320314061636517017252 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potefield use modmain implicit none ! local variables integer is,ia,ias integer nr,nri,ir integer i,i1,i2,i3 real(8) e,tp(2),r,t1 real(8) v0,e00,elm(-1:1) real(8) v1(3),v2(3) ! constant added to potential so that it is zero at the unit cell center v1(:)=0.5d0*(avec(:,1)+avec(:,2)+avec(:,3)) v0=dot_product(efieldc(:),v1(:)) ! determine the electric field vector in spherical coordinates call sphcrd(efieldc,e,tp) ! coefficients for real spherical harmonics R_1-1, R_10 and R_11 t1=e*sqrt(fourpi/3.d0) elm(-1)=t1*sin(tp(1))*sin(tp(2)) elm(0)=-t1*cos(tp(1)) elm(1)=t1*sin(tp(1))*cos(tp(2)) ! muffin-tin potential do is=1,nspecies nr=nrmt(is) nri=nrmti(is) do ia=1,natoms(is) ias=idxas(ia,is) ! coefficient for R_00 e00=v0-dot_product(efieldc(:),atposc(:,ia,is)) e00=e00/y00 i=1 do ir=1,nr r=rsp(ir,is) vclmt(i,ias)=vclmt(i,ias)+e00 vclmt(i+1,ias)=vclmt(i+1,ias)+elm(-1)*r vclmt(i+2,ias)=vclmt(i+2,ias)+elm(0)*r vclmt(i+3,ias)=vclmt(i+3,ias)+elm(1)*r if (ir.le.nri) then i=i+lmmaxi else i=i+lmmaxo end if end do end do end do ! interstitial potential ir=0 do i3=0,ngridg(3)-1 v1(3)=dble(i3)/dble(ngridg(3)) do i2=0,ngridg(2)-1 v1(2)=dble(i2)/dble(ngridg(2)) do i1=0,ngridg(1)-1 v1(1)=dble(i1)/dble(ngridg(1)) ir=ir+1 call r3mv(avec,v1,v2) vclir(ir)=vclir(ir)+v0-dot_product(efieldc(:),v2(:)) end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/rhoinit.f900000644000000000000000000000013214061636517014720 xustar0030 mtime=1623670095.310102125 30 atime=1623670094.083103264 30 ctime=1623670095.310102125 elk-7.2.42/src/rhoinit.f900000644002504400250440000000731114061636517016757 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rhoinit ! !INTERFACE: subroutine rhoinit ! !USES: use modmain use modomp ! !DESCRIPTION: ! Initialises the crystal charge density. Inside the muffin-tins it is set to ! the spherical atomic density. In the interstitial region it is taken to be ! constant such that the total charge is correct. Requires that the atomic ! densities have already been calculated. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) !EOP !BOC implicit none ! local variables integer lmax,is,ia,ias,i integer nr,nri,nro,nrs,ir integer nrc,nrci,irco,irc integer l,m,lm,ig,ifg,nthd real(8) x,sm,t1,t2 complex(8) z1,z2,z3 ! automatic arrays real(8) ffg(ngvc),wr(nrspmax),jl(0:lmaxi,nrcmtmax) complex(8) zfmt(npcmtmax) ! allocatable arrays complex(8), allocatable :: zfft(:) lmax=min(lmaxi,1) ! compute the superposition of all the atomic density tails allocate(zfft(ngtot)) zfft(:)=0.d0 call holdthd(nspecies,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ffg,wr,nr,nrs,nro,ig) & !$OMP PRIVATE(t1,t2,sm,ir,x,ia,ias,ifg) & !$OMP NUM_THREADS(nthd) do is=1,nspecies nr=nrmt(is) nrs=nrsp(is) nro=nrs-nr+1 ! determine the weights for the radial integral call wsplint(nro,rsp(nr,is),wr(nr)) do ig=1,ngvc t1=gc(ig) ! spherical bessel function j_0(x) times the atomic density tail if (t1.gt.epslat) then t2=1.d0/t1 sm=0.d0 do ir=nr,nrs x=t1*rsp(ir,is) sm=sm+t2*sin(x)*rhosp(ir,is)*rsp(ir,is)*wr(ir) end do else sm=sum(rhosp(nr:nrs,is)*(rsp(nr:nrs,is)**2)*wr(nr:nrs)) end if ! apply low-pass filter t1=sm*exp(-4.d0*(gc(ig)/gmaxvr)**2) ffg(ig)=(fourpi/omega)*t1 end do do ia=1,natoms(is) ias=idxas(ia,is) !$OMP CRITICAL(rhoinit_) do ig=1,ngvc ifg=igfft(ig) zfft(ifg)=zfft(ifg)+ffg(ig)*conjg(sfacg(ig,ias)) end do !$OMP END CRITICAL(rhoinit_) end do end do !$OMP END PARALLEL DO call freethd(nthd) ! compute the tails in each muffin-tin call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(jl,zfmt,is,nrc,nrci) & !$OMP PRIVATE(irco,ig,ifg,irc,x) & !$OMP PRIVATE(z1,z2,z3,lm,l,m,i) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) irco=nrci+1 zfmt(1:npcmt(is))=0.d0 do ig=1,ngvc ifg=igfft(ig) do irc=1,nrc x=gc(ig)*rcmt(irc,is) call sbessel(lmax,x,jl(:,irc)) end do z1=fourpi*zfft(ifg)*sfacg(ig,ias) lm=0 do l=0,lmax z2=z1*zil(l) do m=-l,l lm=lm+1 z3=z2*conjg(ylmg(lm,ig)) i=lm do irc=1,nrci zfmt(i)=zfmt(i)+jl(l,irc)*z3 i=i+lmmaxi end do do irc=irco,nrc zfmt(i)=zfmt(i)+jl(l,irc)*z3 i=i+lmmaxo end do end do end do end do call ztorfmt(nrc,nrci,zfmt,rhomt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! convert the density from a coarse to a fine radial mesh call rfmtctof(rhomt) ! add the atomic charge density and the excess charge in each muffin-tin t1=chgexs/omega do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) i=1 do ir=1,nri t2=(t1+rhosp(ir,is))/y00 rhomt(i,ias)=rhomt(i,ias)+t2 i=i+lmmaxi end do do ir=nri+1,nr t2=(t1+rhosp(ir,is))/y00 rhomt(i,ias)=rhomt(i,ias)+t2 i=i+lmmaxo end do end do ! interstitial density determined from the atomic tails and excess charge call zfftifc(3,ngridg,1,zfft) do ir=1,ngtot rhoir(ir)=dble(zfft(ir))+t1 ! make sure that the density is always positive if (rhoir(ir).lt.1.d-10) rhoir(ir)=1.d-10 end do deallocate(zfft) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/eveqnsv.f900000644000000000000000000000013214061636517014733 xustar0030 mtime=1623670095.311102124 30 atime=1623670094.084103263 30 ctime=1623670095.311102124 elk-7.2.42/src/eveqnsv.f900000644002504400250440000002757214061636517017005 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2010 J. K. Dewhurst, S. Sharma, C. Ambrosch-Draxl, ! F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine eveqnsv(ngp,igpig,vgpc,apwalm,evalfv,evecfv,evalsvp,evecsv) use modmain use moddftu use modomp implicit none ! arguments integer, intent(in) :: ngp,igpig(ngkmax) real(8), intent(in) :: vgpc(3,ngkmax) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot) real(8), intent(in) :: evalfv(nstfv) complex(8), intent(in) :: evecfv(nmatmax,nstfv) real(8), intent(out) :: evalsvp(nstsv) complex(8), intent(out) :: evecsv(nstsv,nstsv) ! local variables logical todsb,socz integer ld,ist,jst,ispn,is,ias integer nrc,nrci,nrco,irco,irc integer l,lm,nm,npc,npci,ipco integer igp,i,j,k,nthd real(8) a1,a2,a3,t1 real(8) ts0,ts1 complex(8) z1 ! automatic arrays complex(8) wfmt2(npcmtmax) complex(8) wfmt31(npcmtmax),wfmt32(npcmtmax),wfmt33(npcmtmax) complex(4) wfmt5(npcmtmax) complex(8) wfgp1(ngkmax),wfgp2(ngkmax),wfgp3(ngkmax) ! allocatable arrays complex(8), allocatable :: wfmt1(:,:),wfmt4(:,:) complex(4), allocatable :: wfmt6(:,:),gwfmt(:,:,:) complex(8), allocatable :: wfir1(:),wfir2(:),gwfgp(:,:) ! external functions complex(4), external :: cdotc complex(8), external :: zdotc ! no calculation of second-variational eigenvectors if (.not.tevecsv) then do i=1,nstsv evalsvp(i)=evalfv(i) end do evecsv(:,:)=0.d0 do i=1,nstsv evecsv(i,i)=1.d0 end do return end if call timesec(ts0) if (tafield) then ! coupling constant of the external A-field (-1/c) t1=-1.d0/solsc a1=t1*afieldc(1); a2=t1*afieldc(2); a3=t1*afieldc(3) end if ! check if the off-diagonal spin block of the Hamiltonian is required if (spinpol.and.(ncmag.or.spinorb)) then todsb=.true. else todsb=.false. end if ! special case of spin-orbit coupling and collinear magnetism if (spinorb.and.cmagz) then socz=.true. else socz=.false. end if ld=lmmaxdm*nspinor ! zero the second-variational Hamiltonian (stored in the eigenvector array) evecsv(:,:)=0.d0 !-------------------------! ! muffin-tin part ! !-------------------------! allocate(wfmt1(npcmtmax,nstfv),wfmt6(npcmtmax,nstfv)) if (xcgrad.eq.4) allocate(gwfmt(npcmtmax,3,nstfv)) call holdthd(nstfv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfmt2,wfmt31,wfmt32,wfmt33,wfmt4,wfmt5) & !$OMP PRIVATE(ias,is,nrc,nrci,nrco,irco) & !$OMP PRIVATE(npc,npci,ipco,ist,jst,i,j,k) & !$OMP PRIVATE(irc,t1,l,nm,lm,z1) & !$OMP NUM_THREADS(nthd) allocate(wfmt4(npcmtmax,3)) ! begin loop over atoms do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) nrco=nrc-nrci irco=nrci+1 npc=npcmt(is) npci=npcmti(is) ipco=npci+1 ! compute the first-variational wavefunctions !$OMP DO do ist=1,nstfv call wavefmt(lradstp,ias,ngp,apwalm(:,:,:,ias),evecfv(:,ist),wfmt1(:,ist)) ! make a single-precision copy of the wavefuntion wfmt6(1:npc,ist)=wfmt1(1:npc,ist) end do !$OMP END DO ! begin loop over states !$OMP DO do jst=1,nstfv if (spinpol) then ! convert wavefunction to spherical coordinates call zbsht(nrc,nrci,wfmt1(:,jst),wfmt2) ! apply Kohn-Sham effective magnetic field wfmt32(1:npc)=bsmt(1:npc,ias,ndmag)*wfmt2(1:npc) ! convert to spherical harmonics call zfsht(nrc,nrci,wfmt32,wfmt31) ! non-collinear magnetic field if (socz) then wfmt33(1:npc)=0.d0 else if (ncmag) then wfmt32(1:npc)=cmplx(bsmt(1:npc,ias,1),-bsmt(1:npc,ias,2),8)*wfmt2(1:npc) call zfsht(nrc,nrci,wfmt32,wfmt33) end if wfmt32(1:npc)=-wfmt31(1:npc) ! apply spin-orbit coupling if required if (spinorb) then call lopzflmn(lmaxi,nrci,lmmaxi,wfmt1(1,jst),wfmt4,wfmt4(1,2), & wfmt4(1,3)) call lopzflmn(lmaxo,nrco,lmmaxo,wfmt1(ipco,jst),wfmt4(ipco,1), & wfmt4(ipco,2),wfmt4(ipco,3)) i=1 ! inner part of muffin-tin do irc=1,nrci t1=socfr(irc,ias) do lm=1,lmmaxi wfmt31(i)=wfmt31(i)+t1*wfmt4(i,3) wfmt32(i)=wfmt32(i)-t1*wfmt4(i,3) wfmt33(i)=wfmt33(i)+t1*(wfmt4(i,1) & +cmplx(aimag(wfmt4(i,2)),-dble(wfmt4(i,2)),8)) i=i+1 end do end do ! outer part of muffin-tin do irc=irco,nrc t1=socfr(irc,ias) do lm=1,lmmaxo wfmt31(i)=wfmt31(i)+t1*wfmt4(i,3) wfmt32(i)=wfmt32(i)-t1*wfmt4(i,3) wfmt33(i)=wfmt33(i)+t1*(wfmt4(i,1) & +cmplx(aimag(wfmt4(i,2)),-dble(wfmt4(i,2)),8)) i=i+1 end do end do end if else wfmt31(1:npc)=0.d0 end if ! apply muffin-tin potential matrix if required if (tvmatmt) then do l=0,lmaxdm if (tvmmt(l,ias)) then nm=2*l+1 lm=l**2+1 i=npci+lm if (l.le.lmaxi) then call zgemm('N','N',nm,nrci,nm,zone,vmatmt(lm,1,lm,1,ias),ld, & wfmt1(lm,jst),lmmaxi,zone,wfmt31(lm),lmmaxi) end if call zgemm('N','N',nm,nrco,nm,zone,vmatmt(lm,1,lm,1,ias),ld, & wfmt1(i,jst),lmmaxo,zone,wfmt31(i),lmmaxo) if (spinpol) then if (l.le.lmaxi) then call zgemm('N','N',nm,nrci,nm,zone,vmatmt(lm,2,lm,2,ias),ld, & wfmt1(lm,jst),lmmaxi,zone,wfmt32(lm),lmmaxi) end if call zgemm('N','N',nm,nrco,nm,zone,vmatmt(lm,2,lm,2,ias),ld, & wfmt1(i,jst),lmmaxo,zone,wfmt32(i),lmmaxo) if (todsb) then if (l.le.lmaxi) then call zgemm('N','N',nm,nrci,nm,zone,vmatmt(lm,1,lm,2,ias),ld, & wfmt1(lm,jst),lmmaxi,zone,wfmt33(lm),lmmaxi) end if call zgemm('N','N',nm,nrco,nm,zone,vmatmt(lm,1,lm,2,ias),ld, & wfmt1(i,jst),lmmaxo,zone,wfmt33(i),lmmaxo) end if end if end if end do end if ! apply vector potential if required if (tafield) then call gradzfmt(nrc,nrci,rlcmt(:,-1,is),wcrcmt(:,:,is),wfmt1(:,jst), & npcmtmax,wfmt4) do i=1,npc z1=a1*wfmt4(i,1)+a2*wfmt4(i,2)+a3*wfmt4(i,3) z1=cmplx(aimag(z1),-dble(z1),8) wfmt31(i)=wfmt31(i)+z1 if (spinpol) wfmt32(i)=wfmt32(i)+z1 end do end if ! add to second-variational Hamiltonian matrix ! upper diagonal block call zcfmtwr(nrc,nrci,wrcmt(:,is),wfmt31,wfmt5) do ist=1,jst evecsv(ist,jst)=evecsv(ist,jst)+cdotc(npc,wfmt6(:,ist),1,wfmt5,1) end do if (spinpol) then j=jst+nstfv ! lower diagonal block call zcfmtwr(nrc,nrci,wrcmt(:,is),wfmt32,wfmt5) do ist=1,jst i=ist+nstfv evecsv(i,j)=evecsv(i,j)+cdotc(npc,wfmt6(:,ist),1,wfmt5,1) end do ! off-diagonal block if (todsb) then call zcfmtwr(nrc,nrci,wrcmt(:,is),wfmt33,wfmt5) do ist=1,nstfv evecsv(ist,j)=evecsv(ist,j)+cdotc(npc,wfmt6(:,ist),1,wfmt5,1) end do end if end if ! end loop over states end do !$OMP END DO ! apply meta-GGA non-multiplicative potential if required if (xcgrad.eq.4) then !$OMP DO do ist=1,nstfv ! compute gradient of wavefunction call gradzfmt(nrc,nrci,rlcmt(:,-1,is),wcrcmt(:,:,is),wfmt1(:,ist), & npcmtmax,wfmt4) ! store in single-precision array gwfmt(1:npc,:,ist)=wfmt4(1:npc,:) end do !$OMP END DO do k=1,3 !$OMP DO do jst=1,nstfv wfmt31(1:npc)=gwfmt(1:npc,k,jst) call zbsht(nrc,nrci,wfmt31,wfmt2) wfmt2(1:npc)=wsmt(1:npc,ias)*wfmt2(1:npc) call zfsht(nrc,nrci,wfmt2,wfmt31) call zcfmtwr(nrc,nrci,wrcmt(:,is),wfmt31,wfmt5) do ist=1,jst z1=cdotc(npc,gwfmt(:,k,ist),1,wfmt5,1) z1=0.5d0*z1 evecsv(ist,jst)=evecsv(ist,jst)+z1 if (spinpol) then i=ist+nstfv j=jst+nstfv evecsv(i,j)=evecsv(i,j)+z1 end if end do end do !$OMP END DO end do end if ! end loop over atoms end do deallocate(wfmt4) !$OMP END PARALLEL call freethd(nthd) deallocate(wfmt1,wfmt6) if (xcgrad.eq.4) deallocate(gwfmt) !---------------------------! ! interstitial part ! !---------------------------! if (spinpol.or.tafield.or.(xcgrad.eq.4)) then if (socz) todsb=.false. if (xcgrad.eq.4) allocate(gwfgp(ngkmax,nstfv)) call holdthd(nstfv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfir1,wfir2,wfgp1,wfgp2,wfgp3) & !$OMP PRIVATE(ist,jst,igp,t1,z1,i,j,k) & !$OMP NUM_THREADS(nthd) allocate(wfir1(ngtot),wfir2(ngtot)) ! begin loop over states !$OMP DO do jst=1,nstfv wfir1(:)=0.d0 do igp=1,ngp wfir1(igfft(igpig(igp)))=evecfv(igp,jst) end do ! Fourier transform wavefunction to real-space call zfftifc(3,ngridg,1,wfir1) ! multiply with magnetic field and transform to G-space if (spinpol) then wfir2(1:ngtot)=bsir(1:ngtot,ndmag)*wfir1(1:ngtot) call zfftifc(3,ngridg,-1,wfir2) do igp=1,ngp wfgp1(igp)=wfir2(igfft(igpig(igp))) end do wfgp2(1:ngp)=-wfgp1(1:ngp) if (ncmag) then wfir2(1:ngtot)=cmplx(bsir(1:ngtot,1),-bsir(1:ngtot,2),8)*wfir1(1:ngtot) call zfftifc(3,ngridg,-1,wfir2) do igp=1,ngp wfgp3(igp)=wfir2(igfft(igpig(igp))) end do end if else wfgp1(1:ngp)=0.d0 end if ! apply vector potential if required if (tafield) then wfir1(:)=0.d0 do igp=1,ngp t1=a1*vgpc(1,igp)+a2*vgpc(2,igp)+a3*vgpc(3,igp) wfir1(igfft(igpig(igp)))=t1*evecfv(igp,jst) end do call zfftifc(3,ngridg,1,wfir1) wfir1(1:ngtot)=wfir1(1:ngtot)*cfunir(1:ngtot) call zfftifc(3,ngridg,-1,wfir1) do igp=1,ngp z1=wfir1(igfft(igpig(igp))) wfgp1(igp)=wfgp1(igp)+z1 if (spinpol) wfgp2(igp)=wfgp2(igp)+z1 end do end if ! add to second-variational Hamiltonian matrix ! upper diagonal block do ist=1,jst evecsv(ist,jst)=evecsv(ist,jst)+zdotc(ngp,evecfv(:,ist),1,wfgp1,1) end do if (spinpol) then j=jst+nstfv ! lower diagonal block do ist=1,jst i=ist+nstfv evecsv(i,j)=evecsv(i,j)+zdotc(ngp,evecfv(:,ist),1,wfgp2,1) end do ! off-diagonal block if (todsb) then do ist=1,nstfv evecsv(ist,j)=evecsv(ist,j)+zdotc(ngp,evecfv(:,ist),1,wfgp3,1) end do end if end if ! end loop over states end do !$OMP END DO ! apply meta-GGA non-multiplicative potential if required if (xcgrad.eq.4) then do k=1,3 ! determine the gradient of the wavefunctions !$OMP DO do ist=1,nstfv do igp=1,ngp z1=evecfv(igp,ist) gwfgp(igp,ist)=vgpc(k,igp)*cmplx(-aimag(z1),dble(z1),8) end do end do !$OMP END DO !$OMP DO do jst=1,nstfv wfir1(:)=0.d0 do igp=1,ngp wfir1(igfft(igpig(igp)))=gwfgp(igp,jst) end do call zfftifc(3,ngridg,1,wfir1) wfir1(1:ngtot)=wsir(1:ngtot)*wfir1(1:ngtot) call zfftifc(3,ngridg,-1,wfir1) do igp=1,ngp wfgp1(igp)=wfir1(igfft(igpig(igp))) end do do ist=1,jst z1=0.5d0*zdotc(ngp,gwfgp(:,ist),1,wfgp1,1) evecsv(ist,jst)=evecsv(ist,jst)+z1 if (spinpol) then i=ist+nstfv j=jst+nstfv evecsv(i,j)=evecsv(i,j)+z1 end if end do end do !$OMP END DO end do end if deallocate(wfir1,wfir2) !$OMP END PARALLEL call freethd(nthd) if (xcgrad.eq.4) deallocate(gwfgp) end if ! add the diagonal first-variational part i=0 do ispn=1,nspinor do ist=1,nstfv i=i+1 evecsv(i,i)=evecsv(i,i)+evalfv(ist) end do end do if (spcpl.or.(.not.spinpol)) then ! spins are coupled; or spin-unpolarised: full diagonalisation call eveqnzh(nstsv,nstsv,evecsv,evalsvp) else ! spins not coupled: block diagonalise H call eveqnzh(nstfv,nstsv,evecsv,evalsvp) i=nstfv+1 call eveqnzh(nstfv,nstsv,evecsv(i,i),evalsvp(i)) do j=1,nstfv do i=1,nstfv evecsv(i,j+nstfv)=0.d0 evecsv(i+nstfv,j)=0.d0 end do end do end if call timesec(ts1) !$OMP ATOMIC timesv=timesv+ts1-ts0 end subroutine elk-7.2.42/src/PaxHeaders.21776/roteuler.f900000644000000000000000000000013214061636517015105 xustar0030 mtime=1623670095.313102122 30 atime=1623670094.086103261 30 ctime=1623670095.313102122 elk-7.2.42/src/roteuler.f900000644002504400250440000000537114061636517017150 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: roteuler ! !INTERFACE: subroutine roteuler(rot,ang) ! !INPUT/OUTPUT PARAMETERS: ! rot : rotation matrix (in,real(3,3)) ! ang : Euler angles (alpha, beta, gamma) (out,real(3)) ! !DESCRIPTION: ! Given a rotation matrix ! \begin{align*} ! &R(\alpha,\beta,\gamma)=\\ ! &\left(\begin{matrix} ! \cos\gamma\cos\beta\cos\alpha-\sin\gamma\sin\alpha & ! \cos\gamma\cos\beta\sin\alpha+\sin\gamma\cos\alpha & ! -\cos\gamma\sin\beta \\ ! -\sin\gamma\cos\beta\cos\alpha-\cos\gamma\sin\alpha & ! -\sin\gamma\cos\beta\sin\alpha+\cos\gamma\cos\alpha & ! \sin\gamma\sin\beta \\ ! \sin\beta\cos\alpha & ! \sin\beta\sin\alpha & ! \cos\beta ! \end{matrix}\right), ! \end{align*} ! this routine determines the Euler angles, $(\alpha,\beta,\gamma)$. This ! corresponds to the so-called `$y$-convention', which involves the following ! successive rotations of the coordinate system: ! \begin{itemize} ! \item[1.]{The $x_1$-, $x_2$-, $x_3$-axes are rotated anticlockwise through ! an angle $\alpha$ about the $x_3$ axis} ! \item[2.]{The $x_1'$-, $x_2'$-, $x_3'$-axes are rotated anticlockwise ! through an angle $\beta$ about the $x_2'$ axis} ! \item[3.]{The $x_1''$-, $x_2''$-, $x_3''$-axes are rotated anticlockwise ! through an angle $\gamma$ about the $x_3''$ axis} ! \end{itemize} ! Note that the Euler angles are not necessarily unique for a given rotation ! matrix. ! ! !REVISION HISTORY: ! Created May 2003 (JKD) ! Fixed problem thanks to Frank Wagner, June 2013 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: rot(3,3) real(8), intent(out) :: ang(3) ! local variables real(8), parameter :: eps=1.d-8 real(8), parameter :: pi=3.1415926535897932385d0 real(8) det ! find the determinant det=rot(1,1)*(rot(2,2)*rot(3,3)-rot(3,2)*rot(2,3)) & +rot(2,1)*(rot(3,2)*rot(1,3)-rot(1,2)*rot(3,3)) & +rot(3,1)*(rot(1,2)*rot(2,3)-rot(2,2)*rot(1,3)) if ((det.lt.1.d0-eps).or.(det.gt.1.d0+eps)) then write(*,*) write(*,'("Error(roteuler): matrix improper or not unitary")') write(*,'(" Determinant : ",G18.10)') det write(*,*) stop end if if ((abs(rot(3,1)).gt.eps).or.(abs(rot(3,2)).gt.eps)) then ang(1)=atan2(rot(3,2),rot(3,1)) if (abs(rot(3,1)).gt.abs(rot(3,2))) then ang(2)=atan2(rot(3,1)/cos(ang(1)),rot(3,3)) else ang(2)=atan2(rot(3,2)/sin(ang(1)),rot(3,3)) end if ang(3)=atan2(rot(2,3),-rot(1,3)) else ang(1)=atan2(rot(1,2),rot(1,1)) if (rot(3,3).gt.0.d0) then ang(2)=0.d0 ang(3)=0.d0 else ang(2)=pi ang(3)=pi end if end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genrmesh.f900000644000000000000000000000013214061636517015054 xustar0030 mtime=1623670095.315102121 30 atime=1623670094.088103259 30 ctime=1623670095.315102121 elk-7.2.42/src/genrmesh.f900000644002504400250440000000771214061636517017120 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genrmesh ! !INTERFACE: subroutine genrmesh ! !USES: use modmain use modvars ! !DESCRIPTION: ! Generates the coarse and fine radial meshes for each atomic species in the ! crystal. Also determines which points are in the inner part of the ! muffin-tin using the value of {\tt fracinr}. ! ! !REVISION HISTORY: ! Created September 2002 (JKD) !EOP !BOC implicit none ! local variables integer is,nr,nrc integer ir,irc,l real(8) t1 ! estimate the number of radial mesh points to infinity nrspmax=1 do is=1,nspecies ! logarithmic mesh t1=log(rmaxsp(is)/rminsp(is))/log(rmt(is)/rminsp(is)) t1=dble(nrmt(is)-1)*t1 nrsp(is)=nint(t1)+1 nrspmax=max(nrspmax,nrsp(is)) end do ! generate the radial meshes if (allocated(rsp)) deallocate(rsp) allocate(rsp(nrspmax,nspecies)) if (allocated(rlmt)) deallocate(rlmt) allocate(rlmt(nrmtmax,-lmaxo-1:lmaxo+2,nspecies)) if (allocated(wrmt)) deallocate(wrmt) allocate(wrmt(nrmtmax,nspecies)) if (allocated(wprmt)) deallocate(wprmt) allocate(wprmt(4,nrmtmax,nspecies)) if (allocated(wcrmt)) deallocate(wcrmt) allocate(wcrmt(12,nrmtmax,nspecies)) do is=1,nspecies t1=1.d0/dble(nrmt(is)-1) ! logarithmic mesh t1=t1*log(rmt(is)/rminsp(is)) do ir=1,nrsp(is) rsp(ir,is)=rminsp(is)*exp(dble(ir-1)*t1) end do ! calculate r^l on the fine radial mesh nr=nrmt(is) rlmt(1:nr,-1,is)=1.d0/rsp(1:nr,is) rlmt(1:nr,0,is)=1.d0 rlmt(1:nr,1,is)=rsp(1:nr,is) do l=-2,-lmaxo-1,-1 rlmt(1:nr,l,is)=rlmt(1:nr,l+1,is)*rlmt(1:nr,-1,is) end do do l=2,lmaxo+2 rlmt(1:nr,l,is)=rlmt(1:nr,l-1,is)*rlmt(1:nr,1,is) end do ! determine the weights for spline integration on the fine radial mesh call wsplint(nr,rsp(:,is),wrmt(:,is)) ! multiply by r^2 wrmt(1:nr,is)=wrmt(1:nr,is)*rlmt(1:nr,2,is) ! determine the weights for partial integration on fine radial mesh call wsplintp(nr,rsp(:,is),wprmt(:,:,is)) ! determine the weights for the spline coefficients call wspline(nr,rsp(:,is),wcrmt(:,:,is)) end do ! determine the fraction of the muffin-tin radius which defines the inner part if (fracinr.lt.0.d0) fracinr=sqrt(dble(lmmaxi)/dble(lmmaxo)) ! set up the coarse radial meshes and find the inner part of the muffin-tin ! where rho is calculated with lmaxi if (allocated(rcmt)) deallocate(rcmt) allocate(rcmt(nrcmtmax,nspecies)) if (allocated(rlcmt)) deallocate(rlcmt) allocate(rlcmt(nrcmtmax,-lmaxo-1:lmaxo+2,nspecies)) if (allocated(wrcmt)) deallocate(wrcmt) allocate(wrcmt(nrcmtmax,nspecies)) if (allocated(wprcmt)) deallocate(wprcmt) allocate(wprcmt(4,nrcmtmax,nspecies)) if (allocated(wcrcmt)) deallocate(wcrcmt) allocate(wcrcmt(12,nrcmtmax,nspecies)) do is=1,nspecies t1=fracinr*rmt(is) nrmti(is)=1 nrcmti(is)=1 irc=0 do ir=1,nrmt(is),lradstp irc=irc+1 rcmt(irc,is)=rsp(ir,is) if (rsp(ir,is).lt.t1) then nrmti(is)=ir nrcmti(is)=irc end if end do ! store r^l on the coarse radial mesh do l=-lmaxo-1,lmaxo+2 irc=0 do ir=1,nrmt(is),lradstp irc=irc+1 rlcmt(irc,l,is)=rlmt(ir,l,is) end do end do ! determine the weights for spline integration on the coarse radial mesh nrc=nrcmt(is) call wsplint(nrc,rcmt(:,is),wrcmt(:,is)) ! multiply by r^2 wrcmt(1:nrc,is)=wrcmt(1:nrc,is)*rlcmt(1:nrc,2,is) ! determine the weights for partial integration on coarse radial mesh call wsplintp(nrc,rcmt(:,is),wprcmt(:,:,is)) ! determine the weights for the spline coefficients call wspline(nrc,rcmt(:,is),wcrcmt(:,:,is)) end do ! write to VARIABLES.OUT call writevars('nrsp',nv=nspecies,iva=nrsp) call writevars('nrmt',nv=nspecies,iva=nrmt) call writevars('nrmti',nv=nspecies,iva=nrmti) call writevars('lradstp',iv=lradstp) call writevars('nrcmt',nv=nspecies,iva=nrcmt) call writevars('nrcmti',nv=nspecies,iva=nrcmti) do is=1,nspecies call writevars('rsp',nv=nrmt(is),rva=rsp(:,is)) end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/splint.f900000644000000000000000000000013014061636517014553 xustar0029 mtime=1623670095.31610212 30 atime=1623670094.090103258 29 ctime=1623670095.31610212 elk-7.2.42/src/splint.f900000644002504400250440000000340514061636517016614 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. real(8) function splint(n,x,f) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: x(n),f(n) ! local variables integer i real(8) x0,x1,x2,x3,y0,y1,y2,y3 real(8) t0,t1,t2,t3,t4,t5,t6,t7 ! external functions real(8), external :: polynm if (n.le.4) then splint=polynm(-1,n,x,f,x(n)) return end if ! fit piecewise cubic spline to data and integrate x0=x(1) x1=x(2)-x0; x2=x(3)-x0; x3=x(4)-x0 t4=x1-x2; t5=x1-x3; t6=x2-x3 y0=f(1) y1=f(2)-y0; y2=f(3)-y0; y3=f(4)-y0 t1=x1*x2*y3; t2=x2*x3*y1; t3=x1*x3 t0=0.5d0/(t3*t4*t5*t6) t3=t3*y2 t7=t1*t4+t2*t6-t3*t5 t4=x1**2; t5=x2**2; t6=x3**2 y1=t3*t6-t1*t5; y3=t2*t5-t3*t4; y2=t1*t4-t2*t6 t1=x1*y1+x2*y2+x3*y3 t2=y1+y2+y3 splint=x2*(y0+t0*(t1+x2*(0.5d0*t7*x2-0.6666666666666666667d0*t2))) do i=3,n-3 x0=x(i) x1=x(i-1)-x0; x2=x(i+1)-x0; x3=x(i+2)-x0 t4=x1-x2; t5=x1-x3; t6=x2-x3; t3=x1*x3 y0=f(i) y1=f(i-1)-y0; y2=f(i+1)-y0; y3=f(i+2)-y0 t1=x1*x2*y3; t2=x2*x3*y1 t0=0.5d0/(t3*t4*t5*t6) t3=t3*y2 t7=t1*t4+t2*t6-t3*t5 t4=x1**2; t5=x2**2; t6=x3**2 y1=t3*t6-t1*t5; y2=t1*t4-t2*t6; y3=t2*t5-t3*t4 t1=x1*y1+x2*y2+x3*y3 t2=y1+y2+y3 splint=splint+x2*(y0+t0*(t1+x2*(0.5d0*t7*x2-0.6666666666666666667d0*t2))) end do x0=x(n-2) x1=x(n-3)-x0; x2=x(n-1)-x0; x3=x(n)-x0 t4=x1-x2; t5=x1-x3; t6=x2-x3 y0=f(n-2) y1=f(n-3)-y0; y2=f(n-1)-y0; y3=f(n)-y0 t1=x1*x2; t2=x2*x3*y1; t3=x1*x3*y2 t0=0.5d0/(t1*t4*t5*t6) t1=t1*y3 t7=t1*t4+t2*t6-t3*t5 t4=x1**2; t5=x2**2; t6=x3**2 y1=t3*t6-t1*t5; y2=t1*t4-t2*t6; y3=t2*t5-t3*t4 t1=x1*y1+x2*y2+x3*y3 t2=y1+y2+y3 splint=splint+x3*(y0+t0*(t1+x3*(0.5d0*t7*x3-0.6666666666666666667d0*t2))) end function elk-7.2.42/src/PaxHeaders.21776/nfftifc.f900000644000000000000000000000013214061636517014663 xustar0030 mtime=1623670095.318102118 30 atime=1623670094.092103256 30 ctime=1623670095.318102118 elk-7.2.42/src/nfftifc.f900000644002504400250440000000233414061636517016722 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: nfftifc ! !INTERFACE: subroutine nfftifc(np,n) ! !INPUT/OUTPUT PARAMETERS: ! np : number of allowed primes (in,integer) ! n : required/avalable grid size (inout,integer) ! !DESCRIPTION: ! Interface to the grid requirements of the fast Fourier transform routine. ! Most routines restrict $n$ to specific prime factorisations. This routine ! returns the next largest grid size allowed by the FFT routine. ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: np integer, intent(inout) :: n ! local variables integer i,j integer, parameter :: p(10)=[2,3,5,7,11,13,17,19,23,29] if ((np.lt.1).or.(np.gt.10)) then write(*,*) write(*,'("Error(nfftifc): np out of range : ",I8)') np write(*,*) stop end if if (n.le.0) then write(*,*) write(*,'("Error(nfftifc): n <= 0 : ",I8)') n write(*,*) stop end if 10 continue i=n do j=1,np do while(mod(i,p(j)).eq.0) i=i/p(j) end do end do if (i.ne.1) then n=n+1 goto 10 end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/wavefcr.f900000644000000000000000000000013214061636517014701 xustar0030 mtime=1623670095.320102116 30 atime=1623670094.093103255 30 ctime=1623670095.320102116 elk-7.2.42/src/wavefcr.f900000644002504400250440000000551114061636517016740 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2011 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine wavefcr(tsh,lrstp,is,ia,ist,m,ld,wfcr) use modmain implicit none ! arguments logical, intent(in) :: tsh integer, intent(in) :: lrstp,is,ia,ist ! pass in m-1/2 integer, intent(in) :: m integer, intent(in) :: ld complex(8), intent(out) :: wfcr(ld,2) ! local variables integer ias,nr,nri,ir integer k,l,lm,lm1,lm2 integer i,i1,i2 real(8) c1,c2,t0,t1,t2 l=lsp(ist,is) k=ksp(ist,is) if (((k.ne.l+1).and.(k.ne.l)).or.(m.lt.-k).or.(m.gt.k-1)) then write(*,*) write(*,'("Error(wavefcr): mismatched l, k or m : ",3I4)') l,k,m write(*,'(" for species ",I4)') is write(*,'(" atom ",I4)') ia write(*,'(" and state ",I6)') ist write(*,*) stop end if if (l.gt.lmaxo) then wfcr(:,:)=0.d0 return end if ias=idxas(ia,is) ! calculate the Clebsch-Gordon coefficients t1=sqrt(dble(l+m+1)/dble(2*l+1)) t2=sqrt(dble(l-m)/dble(2*l+1)) if (k.eq.l+1) then c1=t1 c2=t2 else c1=t2 c2=-t1 end if if (abs(m).le.l) then lm1=l*(l+1)+m+1 else lm1=0 end if if (abs(m+1).le.l) then lm2=l*(l+1)+m+2 else lm2=0 end if nr=nrmt(is) nri=nrmti(is) ! zero the wavefunction if (lrstp.eq.1) then wfcr(1:npmt(is),:)=0.d0 else if (lrstp.eq.lradstp) then wfcr(1:npcmt(is),:)=0.d0 else write(*,*) write(*,'("Error(wavefcr): invalid lrstp : ",I8)') lrstp write(*,*) stop end if !----------------------------------! ! inner part of muffin-tin ! !----------------------------------! if (l.gt.lmaxi) goto 10 if (tsh) then i1=lm1 i2=lm2 else i=0 end if do ir=1,nri,lrstp ! major component of radial wavefunction t0=rwfcr(ir,1,ist,ias)*rlmt(ir,-1,is) if (tsh) then if (lm1.gt.0) wfcr(i1,1)=t0*c1 if (lm2.gt.0) wfcr(i2,2)=t0*c2 i1=i1+lmmaxi i2=i2+lmmaxi else t1=t0*c1 t2=t0*c2 if (lm1.gt.0) then do lm=1,lmmaxi wfcr(i+lm,1)=t1*zbshti(lm,lm1) end do end if if (lm2.gt.0) then do lm=1,lmmaxi wfcr(i+lm,2)=t2*zbshti(lm,lm2) end do end if i=i+lmmaxi end if end do !----------------------------------! ! outer part of muffin-tin ! !----------------------------------! 10 continue if (lrstp.eq.1) then i=lmmaxi*nrmti(is) else i=lmmaxi*nrcmti(is) end if if (tsh) then i1=i+lm1 i2=i+lm2 end if do ir=nri+lrstp,nr,lrstp t0=rwfcr(ir,1,ist,ias)*rlmt(ir,-1,is) if (tsh) then if (lm1.gt.0) wfcr(i1,1)=t0*c1 if (lm2.gt.0) wfcr(i2,2)=t0*c2 i1=i1+lmmaxo i2=i2+lmmaxo else t1=t0*c1 t2=t0*c2 if (lm1.gt.0) then do lm=1,lmmaxo wfcr(i+lm,1)=t1*zbshto(lm,lm1) end do end if if (lm2.gt.0) then do lm=1,lmmaxo wfcr(i+lm,2)=t2*zbshto(lm,lm2) end do end if i=i+lmmaxo end if end do end subroutine elk-7.2.42/src/PaxHeaders.21776/lopzflm.f900000644000000000000000000000013214061636517014727 xustar0030 mtime=1623670095.321102115 30 atime=1623670094.095103253 30 ctime=1623670095.321102115 elk-7.2.42/src/lopzflm.f900000644002504400250440000000357314061636517016774 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: lopzflm ! !INTERFACE: pure subroutine lopzflm(lmax,zflm,ld,zlflm) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum angular momentum (in,integer) ! zflm : coefficients of input spherical harmonic expansion ! (in,complex((lmax+1)**2)) ! ld : leading dimension (in,integer) ! zlflm : coefficients of output spherical harmonic expansion ! (out,complex(ld,3)) ! !DESCRIPTION: ! Applies the angular momentum operator $\hat{\bf L}$ to a function expanded ! in terms of complex spherical harmonics. This makes use of the identities ! \begin{align*} ! (L_x+iL_y)Y_{lm}(\theta,\phi)&=\sqrt{(l-m)(l+m+1)}Y_{lm+1}(\theta,\phi)\\ ! (L_x-iL_y)Y_{lm}(\theta,\phi)&=\sqrt{(l+m)(l-m+1)}Y_{lm-1}(\theta,\phi)\\ ! L_zY_{lm}(\theta,\phi)&=mY_{lm}(\theta,\phi). ! \end{align*} ! ! !REVISION HISTORY: ! Created March 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: lmax complex(8), intent(in) :: zflm(*) integer, intent(in) :: ld complex(8), intent(out) :: zlflm(ld,3) ! local variables integer l,m,lm real(8) t1 complex(8) z1 lm=0 do l=0,lmax do m=-l,l lm=lm+1 if (m.eq.-l) then zlflm(lm,1)=0.d0 zlflm(lm,2)=0.d0 end if if (m.lt.l) then t1=0.5d0*sqrt(dble((l-m)*(l+m+1))) z1=t1*zflm(lm) zlflm(lm+1,1)=z1 zlflm(lm+1,2)=cmplx(aimag(z1),-dble(z1),8) end if if (m.gt.-l) then t1=0.5d0*sqrt(dble((l+m)*(l-m+1))) z1=t1*zflm(lm) zlflm(lm-1,1)=zlflm(lm-1,1)+z1 zlflm(lm-1,2)=zlflm(lm-1,2)+cmplx(-aimag(z1),dble(z1),8) end if if (m.ne.0) then zlflm(lm,3)=dble(m)*zflm(lm) else zlflm(lm,3)=0.d0 end if end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/potks.f900000644000000000000000000000013214061636517014404 xustar0030 mtime=1623670095.323102113 30 atime=1623670094.097103251 30 ctime=1623670095.323102113 elk-7.2.42/src/potks.f900000644002504400250440000000362614061636517016450 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: potks ! !INTERFACE: subroutine potks(txc) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! txc : .true. if the exchange-correlation energy density and potentials ! should be calculated (in,logical) ! !DESCRIPTION: ! Computes the Kohn-Sham effective potential by adding together the Coulomb ! and exchange-correlation potentials. Also computes the effective magnetic ! field. See routines {\tt potcoul} and {\tt potxc}. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments logical, intent(in) :: txc ! local variables integer is,ias,np real(8) ts0,ts1 call timesec(ts0) ! compute the Coulomb potential call potcoul ! meta-GGA variables if required if ((xcgrad.eq.3).or.(xcgrad.eq.4)) then ! generate the kinetic energy density call gentau ! compute the Tran-Blaha '09 constant if required call xc_c_tb09 end if ! compute the exchange-correlation potential and fields if (txc) call potxc(.true.,xctype,rhomt,rhoir,magmt,magir,taumt,tauir,exmt, & exir,ecmt,ecir,vxcmt,vxcir,bxcmt,bxcir,wxcmt,wxcir) ! optimised effective potential exchange potential if (xctype(1).lt.0) call oepmain ! remove the source term of the exchange-correlation magnetic field if required if (spinpol.and.nosource) call projsbf ! effective potential from sum of Coulomb and exchange-correlation potentials do ias=1,natmtot is=idxis(ias) np=npmt(is) vsmt(1:np,ias)=vclmt(1:np,ias)+vxcmt(1:np,ias) end do vsir(1:ngtot)=vclir(1:ngtot)+vxcir(1:ngtot) ! smooth the interstitial potential if required call rfirsm(msmooth,vsir) ! generate the effective magnetic fields call genbs ! generate the meta-GGA effective potential call genws call timesec(ts1) timepot=timepot+ts1-ts0 end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/brzint.f900000644000000000000000000000013114061636517014553 xustar0030 mtime=1623670095.324102112 29 atime=1623670094.09810325 30 ctime=1623670095.324102112 elk-7.2.42/src/brzint.f900000644002504400250440000001154614061636517016620 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: brzint ! !INTERFACE: subroutine brzint(nsm,ngridk,nsk,ivkik,nw,wint,n,ld,e,f,g) ! !USES: use modomp ! !INPUT/OUTPUT PARAMETERS: ! nsm : level of smoothing for output function (in,integer) ! ngridk : k-point grid size (in,integer(3)) ! nsk : k-point subdivision grid size (in,integer(3)) ! ivkik : map from (i1,i2,i3) to k-point index ! (in,integer(0:ngridk(1)-1,0:ngridk(2)-1,0:ngridk(3)-1)) ! nw : number of energy divisions (in,integer) ! wint : energy interval (in,real(2)) ! n : number of functions to integrate (in,integer) ! ld : leading dimension (in,integer) ! e : array of energies as a function of k-points (in,real(ld,*)) ! f : array of weights as a function of k-points (in,real(ld,*)) ! g : output function (out,real(nw)) ! !DESCRIPTION: ! Given energy and weight functions, $e$ and $f$, on the Brillouin zone and a ! set of equidistant energies $\omega_i$, this routine computes the integrals ! $$ g(\omega_i)=\frac{\Omega}{(2\pi)^3}\int_{\rm BZ} f({\bf k}) ! \delta(\omega_i-e({\bf k}))d{\bf k}, $$ ! where $\Omega$ is the unit cell volume. This is done by first interpolating ! $e$ and $f$ on a finer $k$-point grid using the trilinear method. Then for ! each $e({\bf k})$ on the finer grid the nearest $\omega_i$ is found and ! $f({\bf k})$ is accumulated in $g(\omega_i)$. If the output function is ! noisy then either {\tt nsk} should be increased or {\tt nw} decreased. ! Alternatively, the output function can be artificially smoothed up to a ! level given by {\tt nsm}. See routine {\tt fsmooth}. ! ! !REVISION HISTORY: ! Created October 2003 (JKD) ! Improved efficiency, May 2007 (Sebastian Lebegue) ! Added parallelism, March 2020 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nsm,ngridk(3),nsk(3) integer, intent(in) :: ivkik(0:ngridk(1)-1,0:ngridk(2)-1,0:ngridk(3)-1) integer, intent(in) :: nw real(8), intent(in) :: wint(2) integer, intent(in) :: n,ld real(8), intent(in) :: e(ld,*),f(ld,*) real(8), intent(out) :: g(nw) ! local variables integer nk,i1,i2,i3,j1,j2,j3,k1,k2,k3,i,iw,nthd integer i000,i001,i010,i011,i100,i101,i110,i111 real(8) wd,dw,dwi,w1,t1,t2 ! automatic arrays real(8) f0(n),f1(n),e0(n),e1(n) real(8) f00(n),f01(n),f10(n),f11(n) real(8) e00(n),e01(n),e10(n),e11(n) if ((ngridk(1).lt.1).or.(ngridk(2).lt.1).or.(ngridk(3).lt.1)) then write(*,*) write(*,'("Error(brzint): ngridk < 1 : ",3I8)') ngridk write(*,*) stop end if if ((nsk(1).lt.1).or.(nsk(2).lt.1).or.(nsk(3).lt.1)) then write(*,*) write(*,'("Error(brzint): nsk < 1 : ",3I8)') nsk write(*,*) stop end if ! total number of k-points nk=ngridk(1)*ngridk(2)*ngridk(3) ! length of interval wd=wint(2)-wint(1) ! energy step size dw=wd/dble(nw) dwi=1.d0/dw w1=wint(1)*dwi g(:)=0.d0 call holdthd(nk,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(f0,f1,e0,e1) & !$OMP PRIVATE(f00,f01,f10,f11) & !$OMP PRIVATE(e00,e01,e10,e11) & !$OMP PRIVATE(k1,k2,k3,i1,i2,i3) & !$OMP PRIVATE(i000,i001,i010,i011) & !$OMP PRIVATE(i100,i101,i110,i111) & !$OMP PRIVATE(t1,t2,i,iw) & !$OMP REDUCTION(+:g) & !$OMP NUM_THREADS(nthd) !$OMP DO COLLAPSE(3) do j1=0,ngridk(1)-1 do j2=0,ngridk(2)-1 do j3=0,ngridk(3)-1 k1=mod(j1+1,ngridk(1)) k2=mod(j2+1,ngridk(2)) k3=mod(j3+1,ngridk(3)) i000=ivkik(j1,j2,j3); i001=ivkik(j1,j2,k3) i010=ivkik(j1,k2,j3); i011=ivkik(j1,k2,k3) i100=ivkik(k1,j2,j3); i101=ivkik(k1,j2,k3) i110=ivkik(k1,k2,j3); i111=ivkik(k1,k2,k3) do i1=0,nsk(1)-1 t2=dble(i1)/dble(nsk(1)) t1=1.d0-t2 f00(:)=f(:,i000)*t1+f(:,i100)*t2 f01(:)=f(:,i001)*t1+f(:,i101)*t2 f10(:)=f(:,i010)*t1+f(:,i110)*t2 f11(:)=f(:,i011)*t1+f(:,i111)*t2 t1=t1*dwi t2=t2*dwi e00(:)=e(:,i000)*t1+e(:,i100)*t2-w1 e01(:)=e(:,i001)*t1+e(:,i101)*t2-w1 e10(:)=e(:,i010)*t1+e(:,i110)*t2-w1 e11(:)=e(:,i011)*t1+e(:,i111)*t2-w1 do i2=0,nsk(2)-1 t2=dble(i2)/dble(nsk(2)) t1=1.d0-t2 f0(:)=f00(:)*t1+f10(:)*t2 f1(:)=f01(:)*t1+f11(:)*t2 e0(:)=e00(:)*t1+e10(:)*t2 e1(:)=e01(:)*t1+e11(:)*t2 do i3=0,nsk(3)-1 t2=dble(i3)/dble(nsk(3)) t1=1.d0-t2 do i=1,n iw=nint(e0(i)*t1+e1(i)*t2)+1 if ((iw.ge.1).and.(iw.le.nw)) g(iw)=g(iw)+f0(i)*t1+f1(i)*t2 end do end do end do end do end do end do end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) ! normalise function t1=dw*dble(nk)*dble(nsk(1)*nsk(2)*nsk(3)) t1=1.d0/t1 g(:)=t1*g(:) ! smooth output function if required if (nsm.gt.0) call fsmooth(nsm,nw,g) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rotdmat.f900000644000000000000000000000013014061636517014714 xustar0029 mtime=1623670095.32610211 30 atime=1623670094.100103248 29 ctime=1623670095.32610211 elk-7.2.42/src/rotdmat.f900000644002504400250440000000472414061636517016762 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rotdmat(rspl,rspn,lmax,nspinor,ld,dmat1,dmat2) implicit none ! arguments real(8), intent(in) :: rspl(3,3),rspn(3,3) integer, intent(in) :: lmax,nspinor integer, intent(in) :: ld complex(8), intent(in) :: dmat1(ld,nspinor,ld,nspinor) complex(8), intent(inout) :: dmat2(ld,nspinor,ld,nspinor) ! local variables integer lds,ispn,jspn,p integer lmmax,l,lm1,lm2,nm real(8), parameter :: eps=1.d-8 real(8) ang(3),angi(3) real(8) rot(3,3),det,v(3),th complex(8), parameter :: zzero=(0.d0,0.d0),zone=(1.d0,0.d0) complex(8) su2(2,2),a(2,2),b(2,2) ! allocatable arrays complex(8), allocatable :: dm(:,:,:,:),c(:,:),d(:,:) ! external functions real(8), external :: r3mdet lmmax=(lmax+1)**2 allocate(dm(ld,nspinor,ld,nspinor)) allocate(c(lmmax,lmmax),d(lmmax,lmmax)) ! find the determinant of the spatial rotation matrix det=r3mdet(rspl) if (det.gt.0.d0) then p=1 else p=-1 end if ! make the rotation matrix proper rot(:,:)=dble(p)*rspl(:,:) ! compute the Euler angles of the spatial rotation call roteuler(rot,ang) ! inverse rotation: the matrix is to be rotated, not the spherical harmonics angi(1)=-ang(3) angi(2)=-ang(2) angi(3)=-ang(1) ! determine the rotation matrix for complex spherical harmonics call ylmrot(p,angi,lmax,lmmax,d) ! apply (l,m) rotation matrix as U*D*conjg(U') lds=ld*nspinor do ispn=1,nspinor do jspn=1,nspinor lm1=1 do l=0,lmax nm=2*l+1 call zgemm('N','N',nm,lmmax,nm,zone,d(lm1,lm1),lmmax, & dmat1(lm1,ispn,1,jspn),lds,zzero,c(lm1,1),lmmax) lm1=lm1+nm end do lm1=1 do l=0,lmax nm=2*l+1 call zgemm('N','C',lmmax,nm,nm,zone,c(1,lm1),lmmax,d(lm1,lm1),lmmax, & zzero,dm(1,ispn,lm1,jspn),lds) lm1=lm1+nm end do end do end do ! spin rotation if required if (nspinor.eq.2) then ! convert spin rotation matrix to axis-angle form call rotaxang(eps,rspn,det,v,th) ! find the SU(2) representation of the rotation matrix call axangsu2(v,th,su2) ! apply SU(2) symmetry matrix as U*D*conjg(U*) andd add to dmat2 do lm1=1,lmmax do lm2=1,lmmax a(:,:)=dm(lm1,:,lm2,:) call z2mm(su2,a,b) call z2mmct(b,su2,a) dmat2(lm1,:,lm2,:)=dmat2(lm1,:,lm2,:)+a(:,:) end do end do else dmat2(1:lmmax,1,1:lmmax,1)=dmat2(1:lmmax,1,1:lmmax,1)+dm(1:lmmax,1,1:lmmax,1) end if deallocate(dm,c,d) end subroutine elk-7.2.42/src/PaxHeaders.21776/genylmg.f900000644000000000000000000000013214061636517014706 xustar0030 mtime=1623670095.327102109 30 atime=1623670094.102103246 30 ctime=1623670095.327102109 elk-7.2.42/src/genylmg.f900000644002504400250440000000135214061636517016744 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genylmg ! !INTERFACE: subroutine genylmg ! !USES: use modmain ! !DESCRIPTION: ! Generates a set of spherical harmonics, $Y_{lm}(\hat{\bf G})$, with angular ! momenta up to {\tt lmaxo} for the set of ${\bf G}$-vectors. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! local variables integer ig ! allocate global G-vector spherical harmonic array if (allocated(ylmg)) deallocate(ylmg) allocate(ylmg(lmmaxo,ngvec)) do ig=1,ngvec call genylmv(lmaxo,vgc(:,ig),ylmg(:,ig)) end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gentaucr.f900000644000000000000000000000013214061636517015054 xustar0030 mtime=1623670095.329102108 30 atime=1623670094.103103246 30 ctime=1623670095.329102108 elk-7.2.42/src/gentaucr.f900000644002504400250440000000360214061636517017112 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gentaucr use modmain use modomp implicit none ! local variables integer ist,ispn,jspn integer is,ia,ias,nthd integer nr,nri,np,i,m ! automatic arrays real(8) rfmt(npmtmax) ! allocatable arrays complex(8), allocatable :: wfcr(:,:),gzfmt(:,:),zfmt(:) taucr(:,:,:)=0.d0 call holdthd(natmtot,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfcr,gzfmt,zfmt) & !$OMP PRIVATE(is,ia,nr,nri,np) & !$OMP PRIVATE(ist,m,ispn,jspn,i) & !$OMP NUM_THREADS(nthd) allocate(wfcr(npmtmax,2),gzfmt(npmtmax,3),zfmt(npmtmax)) !$OMP DO do ias=1,natmtot is=idxis(ias) ia=idxia(ias) nr=nrmt(is) nri=nrmti(is) np=npmt(is) do ist=1,nstsp(is) if (spcore(ist,is)) then do m=-ksp(ist,is),ksp(ist,is)-1 ! generate the core wavefunction in spherical harmonics (pass in m-1/2) call wavefcr(.true.,1,is,ia,ist,m,npmtmax,wfcr) do ispn=1,2 if (spinpol) then jspn=ispn else jspn=1 end if ! compute the gradient call gradzfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),wfcr(:,ispn), & npmtmax,gzfmt) do i=1,3 ! convert gradient to spherical coordinates call zbsht(nr,nri,gzfmt(:,i),zfmt) ! add to total in muffin-tin taucr(1:np,ias,jspn)=taucr(1:np,ias,jspn) & +0.5d0*(dble(zfmt(1:np))**2+aimag(zfmt(1:np))**2) end do end do end do end if end do end do !$OMP END DO deallocate(wfcr,gzfmt,zfmt) !$OMP END PARALLEL call freethd(nthd) ! convert core tau to spherical harmonics do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) call dcopy(npmt(is),taucr(:,ias,ispn),1,rfmt,1) call rfsht(nrmt(is),nrmti(is),rfmt,taucr(:,ias,ispn)) end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/readinput.f900000644000000000000000000000013214061636517015237 xustar0030 mtime=1623670095.330102107 30 atime=1623670094.105103244 30 ctime=1623670095.330102107 elk-7.2.42/src/readinput.f900000644002504400250440000013662714061636517017313 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: readinput ! !INTERFACE: subroutine readinput ! !USES: use modmain use moddftu use modrdm use modphonon use modtest use modrandom use modpw use modtddft use modulr use modvars use modgw use modbog use modw90 use modmpi use modomp use modramdisk ! !DESCRIPTION: ! Reads in the input parameters from the file {\tt elk.in}. Also sets default ! values for the input parameters. ! ! !REVISION HISTORY: ! Created September 2002 (JKD) !EOP !BOC implicit none ! local variables logical lv integer is,ia,ias,ios integer i,j,k,l,n,p real(8) sc,sc1,sc2,sc3 real(8) scx,scy,scz real(8) scu,scu1,scu2,scu3 real(8) solscf,zn,a,b real(8) axang(4),rot(3,3) real(8) v1(3),v2(3),t1 character(256) block,symb,str !------------------------! ! default values ! !------------------------! ntasks=0 avec(:,:)=0.d0 avec(1,1)=1.d0 avec(2,2)=1.d0 avec(3,3)=1.d0 sc=1.d0 sc1=1.d0 sc2=1.d0 sc3=1.d0 scx=1.d0 scy=1.d0 scz=1.d0 epslat=1.d-6 primcell=.false. tshift=.true. ngridk(:)=1 vkloff(:)=0.d0 autokpt=.false. radkpt=40.d0 reducek=1 ngridq(:)=-1 reduceq=1 rgkmax=7.d0 gmaxvr=12.d0 lmaxapw=8 lmaxo=6 lmaxi=1 fracinr=0.01d0 trhonorm=.true. xctype(1)=3 xctype(2:3)=0 xctsp(1)=3 xctsp(2:3)=0 stype=3 swidth=0.001d0 autoswidth=.false. mstar=10.d0 epsocc=1.d-8 epschg=1.d-3 nempty0=4.d0 maxscl=200 mixtype=3 amixpm(1)=0.05d0 amixpm(2)=1.d0 ! Broyden parameters recommended by M. Meinert mixsdb=5 broydpm(1)=0.4d0 broydpm(2)=0.15d0 epspot=1.d-6 epsengy=1.d-4 epsforce=5.d-3 epsstress=1.d-3 molecule=.false. nspecies=0 natoms(:)=0 atposl(:,:,:)=0.d0 atposc(:,:,:)=0.d0 bfcmt0(:,:,:)=0.d0 sppath='' scrpath='' nvp1d=2 if (allocated(vvlp1d)) deallocate(vvlp1d) allocate(vvlp1d(3,nvp1d)) vvlp1d(:,1)=0.d0 vvlp1d(:,2)=1.d0 npp1d=200 vclp2d(:,:)=0.d0 vclp2d(1,1)=1.d0 vclp2d(2,2)=1.d0 np2d(:)=40 vclp3d(:,:)=0.d0 vclp3d(1,1)=1.d0 vclp3d(2,2)=1.d0 vclp3d(3,3)=1.d0 np3d(:)=20 nwplot=500 ngrkf=100 nswplot=1 wplot(1)=-0.5d0 wplot(2)=0.5d0 dosocc=.false. dosmsum=.false. dosssum=.false. lmirep=.true. spinpol=.false. spinorb=.false. socscf=1.d0 atpopt=1 maxatpstp=200 tau0atp=0.25d0 deltast=0.005d0 latvopt=0 maxlatvstp=30 tau0latv=0.2d0 lradstp=4 chgexs=0.d0 scissor=0.d0 noptcomp=1 optcomp(:,1)=1 intraband=.false. evaltol=-1.d0 epsband=1.d-12 demaxbnd=2.5d0 autolinengy=.false. dlefe=-0.1d0 deapwlo=0.05d0 bfieldc0(:)=0.d0 efieldc(:)=0.d0 afieldc(:)=0.d0 fsmtype=0 momfix(:)=0.d0 mommtfix(:,:,:)=1.d6 taufsm=0.01d0 rmtdelta=0.05d0 isgkmax=-1 symtype=1 deltaph=0.01d0 nphwrt=1 if (allocated(vqlwrt)) deallocate(vqlwrt) allocate(vqlwrt(3,nphwrt)) vqlwrt(:,:)=0.d0 notelns=0 tforce=.false. maxitoep=300 tauoep(1)=0.05d0 tauoep(2)=0.95d0 nkstlist=1 kstlist(:,1)=1 vklem(:)=0.d0 deltaem=0.025d0 ndspem=1 nosource=.false. spinsprl=.false. ssdph=.true. vqlss(:)=0.d0 nwrite=0 dftu=0 inpdftu=1 ndftu=0 ujdu(:,:)=0.d0 fdu(:,:)=0.d0 edu(:,:)=0.d0 lambdadu(:)=0.d0 udufix(:)=0.d0 lambdadu0(:)=0.d0 tmwrite=.false. readadu=.false. rdmxctype=2 rdmmaxscl=2 maxitn=200 maxitc=0 taurdmn=0.5d0 taurdmc=0.25d0 rdmalpha=0.565d0 rdmtemp=0.d0 reducebf=1.d0 ptnucl=.true. tefvr=.true. tefvit=.false. minitefv=6 maxitefv=4 befvit=0.25d0 epsefvit=1.d-5 vecql(:)=0.d0 mustar=0.15d0 sqados(1:2)=0.d0 sqados(3)=1.d0 test=.false. spincore=.false. solscf=1.d0 emaxelnes=-1.2d0 wsfac(1)=-1.d6; wsfac(2)=1.d6 vhmat(:,:)=0.d0 vhmat(1,1)=1.d0 vhmat(2,2)=1.d0 vhmat(3,3)=1.d0 reduceh=.true. hybrid0=.false. hybridc=1.d0 ecvcut=-3.5d0 esccut=-0.4d0 gmaxrf=3.d0 emaxrf=1.d6 ntemp=40 nvbse0=2 ncbse0=3 nvxbse=0 ncxbse=0 bsefull=.false. hxbse=.true. hdbse=.true. fxctype=-1 fxclrc(1)=0.d0 fxclrc(2)=0.d0 rndatposc=0.d0 rndbfcmt=0.d0 rndavec=0.d0 c_tb09=0.d0 tc_tb09=.false. hmaxvr=20.d0 hkmax=12.d0 lorbcnd=.false. lorbordc=3 nrmtscf=1.d0 lmaxdos=3 epsdev=0.005d0 msmooth=0 npmae0=-1 wrtvars=.false. ftmtype=0 ntmfix=0 tauftm=0.5d0 ftmstep=1 cmagz=.false. axang(:)=0.d0 dncgga=1.d-8 tstime=1000.d0 dtimes=0.1d0 npulse=0 nramp=0 ntswrite(1)=500 ntswrite(2)=1 nxoapwlo=0 nxlo=0 tdrho1d=.false. tdrho2d=.false. tdrho3d=.false. tdmag1d=.false. tdmag2d=.false. tdmag3d=.false. tdjr1d=.false. tdjr2d=.false. tdjr3d=.false. tddos=.false. tdlsj=.false. rndevt0=0.d0 sxcscf=1.d0 avecu(:,:)=0.d0 avecu(1,1)=1.d0 avecu(2,2)=1.d0 avecu(3,3)=1.d0 scu=1.d0 scu1=1.d0 scu2=1.d0 scu3=1.d0 q0cut=0.d0 rndbfcu=0.d0 efielduc(:)=0.d0 tplotq0=.true. trdvclr=.false. wmaxgw=-10.d0 twdiag=.false. tsediag=.true. actype=10 npole=3 nspade=100 tfav0=.true. rmtall=-1.d0 maxthd=0 maxthd1=0 maxthdmkl=8 maxlvl=4 taudft=.false. t0tdlr=0.d0 tdphi=0.d0 thetamld=45.d0*pi/180.d0 ntsbackup=0 ! Wannier90 variables seedname='wannier' num_wann=0 num_bands=0 num_iter=400 trial_step=1.d-3 nxlwin=0 tbdip=.false. tjr=.false. tauefm=0.01d0 epsefm=1.d-6 ehfb=1.d0 t0gclq0=.false. tafindt=.false. afindscf=1.d0 nkspolar=4 ntsforce=10 wphcut=1.d-6 ephscf(1)=8.d0 ephscf(2)=0.02d0 anomalous=.false. tephde=.false. bdiag=.false. ramdisk=.false. !--------------------------! ! read from elk.in ! !--------------------------! open(50,file='elk.in',status='OLD',form='FORMATTED',iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readinput): error opening elk.in")') write(*,*) stop end if 10 continue read(50,*,end=30) block ! check for a comment if ((scan(trim(block),'!').eq.1).or.(scan(trim(block),'#').eq.1)) goto 10 select case(trim(block)) case('tasks') do i=1,maxtasks read(50,'(A256)',err=20) str if (trim(str).eq.'') then if (i.eq.1) then write(*,*) write(*,'("Error(readinput): no tasks to perform")') write(*,*) stop end if ntasks=i-1 goto 10 end if read(str,*,iostat=ios) tasks(i) if (ios.ne.0) then write(*,*) write(*,'("Error(readinput): error reading tasks")') write(*,'("(blank line required after tasks block)")') write(*,*) stop end if end do write(*,*) write(*,'("Error(readinput): too many tasks")') write(*,'("Adjust maxtasks in modmain and recompile code")') write(*,*) stop case('species') ! generate a species file call genspecies(50) case('fspecies') ! generate fractional species files do is=1,maxspecies read(50,'(A256)',err=20) str if (trim(str).eq.'') goto 10 read(str,*,iostat=ios) zn,symb if (zn.gt.-1.d0+epsocc) then write(*,*) write(*,'("Error(readinput): fractional nuclear Z > -1 : ",G18.10)') zn write(*,*) stop end if call genfspecies(zn,symb) end do write(*,*) write(*,'("Error(readinput): too many fractional nucleus species")') write(*,*) stop case('avec') read(50,*,err=20) avec(:,1) read(50,*,err=20) avec(:,2) read(50,*,err=20) avec(:,3) case('scale') read(50,*,err=20) sc case('scale1') read(50,*,err=20) sc1 case('scale2') read(50,*,err=20) sc2 case('scale3') read(50,*,err=20) sc3 case('scalex') read(50,*,err=20) scx case('scaley') read(50,*,err=20) scy case('scalez') read(50,*,err=20) scz case('epslat') read(50,*,err=20) epslat if (epslat.le.0.d0) then write(*,*) write(*,'("Error(readinput): epslat <= 0 : ",G18.10)') epslat write(*,*) stop end if case('primcell') read(50,*,err=20) primcell case('tshift') read(50,*,err=20) tshift case('autokpt') read(50,*,err=20) autokpt case('radkpt') read(50,*,err=20) radkpt if (radkpt.le.0.d0) then write(*,*) write(*,'("Error(readinput): radkpt <= 0 : ",G18.10)') radkpt write(*,*) stop end if case('ngridk') read(50,*,err=20) ngridk(:) if (any(ngridk(:).le.0)) then write(*,*) write(*,'("Error(readinput): invalid ngridk : ",3I8)') ngridk write(*,*) stop end if autokpt=.false. case('vkloff') read(50,*,err=20) vkloff(:) if (any(vkloff(:).lt.0.d0).or.any(vkloff(:).ge.1.d0)) then write(*,*) write(*,'("Error(readinput): vkloff components should be in [0,1) : ",& &3G18.10)') vkloff write(*,*) stop end if case('reducek') read(50,*,err=20) reducek case('ngridq') read(50,*,err=20) ngridq(:) if (any(ngridq(:).le.0)) then write(*,*) write(*,'("Error(readinput): invalid ngridq : ",3I8)') ngridq write(*,*) stop end if case('reduceq') read(50,*,err=20) reduceq case('rgkmax') read(50,*,err=20) rgkmax if (rgkmax.le.0.d0) then write(*,*) write(*,'("Error(readinput): rgkmax <= 0 : ",G18.10)') rgkmax write(*,*) stop end if case('gmaxvr') read(50,*,err=20) gmaxvr case('lmaxapw') read(50,*,err=20) lmaxapw if (lmaxapw.lt.0) then write(*,*) write(*,'("Error(readinput): lmaxapw < 0 : ",I8)') lmaxapw write(*,*) stop end if if (lmaxapw.ge.maxlapw) then write(*,*) write(*,'("Error(readinput): lmaxapw too large : ",I8)') lmaxapw write(*,'("Adjust maxlapw in modmain and recompile code")') write(*,*) stop end if case('lmaxo','lmaxvr') read(50,*,err=20) lmaxo if (lmaxo.lt.3) then write(*,*) write(*,'("Error(readinput): lmaxo < 3 : ",I8)') lmaxo write(*,*) stop end if case('lmaxi','lmaxinr') read(50,*,err=20) lmaxi if (lmaxi.lt.1) then write(*,*) write(*,'("Error(readinput): lmaxi < 1 : ",I8)') lmaxi write(*,*) stop end if case('lmaxmat') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''lmaxmat'' is no longer used")') case('fracinr') read(50,*,err=20) fracinr case('trhonorm') read(50,*,err=20) trhonorm case('spinpol') read(50,*,err=20) spinpol case('spinorb') read(50,*,err=20) spinorb case('socscf') read(50,*,err=20) socscf if (socscf.lt.0.d0) then write(*,*) write(*,'("Error(readinput): socscf < 0 : ",G18.10)') socscf write(*,*) stop end if case('xctype') read(50,'(A256)',err=20) str str=trim(str)//' 0 0' read(str,*,err=20) xctype case('xctsp') read(50,'(A256)',err=20) str str=trim(str)//' 0 0' read(str,*,err=20) xctsp case('stype') read(50,*,err=20) stype case('swidth') read(50,*,err=20) swidth if (swidth.lt.1.d-9) then write(*,*) write(*,'("Error(readinput): swidth too small or negative : ",G18.10)') & swidth write(*,*) stop end if case('autoswidth') read(50,*,err=20) autoswidth case('mstar') read(50,*,err=20) mstar if (mstar.le.0.d0) then write(*,*) write(*,'("Error(readinput): mstar <= 0 : ",G18.10)') mstar write(*,*) stop end if case('epsocc') read(50,*,err=20) epsocc if (epsocc.le.0.d0) then write(*,*) write(*,'("Error(readinput): epsocc <= 0 : ",G18.10)') epsocc write(*,*) stop end if case('epschg') read(50,*,err=20) epschg if (epschg.le.0.d0) then write(*,*) write(*,'("Error(readinput): epschg <= 0 : ",G18.10)') epschg write(*,*) stop end if case('nempty','nempty0') read(50,*,err=20) nempty0 if (nempty0.le.0.d0) then write(*,*) write(*,'("Error(readinput): nempty <= 0 : ",G18.10)') nempty0 write(*,*) stop end if case('mixtype') read(50,*,err=20) mixtype case('amixpm','beta0','betamax') if (trim(block).eq.'amixpm') then read(50,*,err=20) amixpm(:) else if (trim(block).eq.'beta0') then read(50,*,err=20) amixpm(1) else read(50,*,err=20) amixpm(2) end if if (amixpm(1).lt.0.d0) then write(*,*) write(*,'("Error(readinput): beta0 [amixpm(1)] < 0 : ",G18.10)') amixpm(1) write(*,*) stop end if if ((amixpm(2).lt.0.d0).or.(amixpm(2).gt.1.d0)) then write(*,*) write(*,'("Error(readinput): betamax [amixpm(2)] not in [0,1] : ",G18.10)')& amixpm(2) write(*,*) stop end if case('mixsdb') read(50,*,err=20) mixsdb if (mixsdb.lt.2) then write(*,*) write(*,'("Error(readinput): mixsdb < 2 : ",I8)') mixsdb write(*,*) stop end if case('broydpm') read(50,*,err=20) broydpm(:) if ((broydpm(1).lt.0.d0).or.(broydpm(1).gt.1.d0).or. & (broydpm(2).lt.0.d0).or.(broydpm(2).gt.1.d0)) then write(*,*) write(*,'("Error(readinput): invalid Broyden mixing parameters : ",& &2G18.10)') broydpm write(*,*) stop end if case('maxscl') read(50,*,err=20) maxscl if (maxscl.lt.0) then write(*,*) write(*,'("Error(readinput): maxscl < 0 : ",I8)') maxscl write(*,*) stop end if case('epspot') read(50,*,err=20) epspot case('epsengy') read(50,*,err=20) epsengy case('epsforce') read(50,*,err=20) epsforce case('epsstress') read(50,*,err=20) epsstress case('sppath') read(50,*,err=20) sppath sppath=adjustl(sppath) case('scrpath') read(50,*,err=20) scrpath case('molecule') read(50,*,err=20) molecule case('atoms') read(50,*,err=20) nspecies if (nspecies.le.0) then write(*,*) write(*,'("Error(readinput): nspecies <= 0 : ",I8)') nspecies write(*,*) stop end if if (nspecies.gt.maxspecies) then write(*,*) write(*,'("Error(readinput): nspecies too large : ",I8)') nspecies write(*,'("Adjust maxspecies in modmain and recompile code")') write(*,*) stop end if do is=1,nspecies read(50,*,err=20) spfname(is) spfname(is)=adjustl(spfname(is)) read(50,*,err=20) natoms(is) if (natoms(is).le.0) then write(*,*) write(*,'("Error(readinput): natoms <= 0 : ",I8)') natoms(is) write(*,'(" for species ",I4)') is write(*,*) stop end if if (natoms(is).gt.maxatoms) then write(*,*) write(*,'("Error(readinput): natoms too large : ",I8)') natoms(is) write(*,'(" for species ",I4)') is write(*,'("Adjust maxatoms in modmain and recompile code")') write(*,*) stop end if do ia=1,natoms(is) read(50,'(A256)',err=20) str str=trim(str)//' 0.0 0.0 0.0' read(str,*,err=20) atposl(:,ia,is),bfcmt0(:,ia,is) end do end do case('plot1d') read(50,*,err=20) nvp1d,npp1d if (nvp1d.lt.1) then write(*,*) write(*,'("Error(readinput): nvp1d < 1 : ",I8)') nvp1d write(*,*) stop end if if (npp1d.lt.nvp1d) then write(*,*) write(*,'("Error(readinput): npp1d < nvp1d : ",2I8)') npp1d,nvp1d write(*,*) stop end if if (allocated(vvlp1d)) deallocate(vvlp1d) allocate(vvlp1d(3,nvp1d)) do i=1,nvp1d read(50,*,err=20) vvlp1d(:,i) end do case('plot2d') read(50,*,err=20) vclp2d(:,0) read(50,*,err=20) vclp2d(:,1) read(50,*,err=20) vclp2d(:,2) read(50,*,err=20) np2d(:) if ((np2d(1).lt.1).or.(np2d(2).lt.1)) then write(*,*) write(*,'("Error(readinput): np2d < 1 : ",2I8)') np2d write(*,*) stop end if case('plot3d') read(50,*,err=20) vclp3d(:,0) read(50,*,err=20) vclp3d(:,1) read(50,*,err=20) vclp3d(:,2) read(50,*,err=20) vclp3d(:,3) read(50,*,err=20) np3d(:) if ((np3d(1).lt.1).or.(np3d(2).lt.1).or.(np3d(3).lt.1)) then write(*,*) write(*,'("Error(readinput): np3d < 1 : ",3I8)') np3d write(*,*) stop end if case('wplot','dos') read(50,*,err=20) nwplot,ngrkf,nswplot if (nwplot.lt.2) then write(*,*) write(*,'("Error(readinput): nwplot < 2 : ",I8)') nwplot write(*,*) stop end if if (ngrkf.lt.1) then write(*,*) write(*,'("Error(readinput): ngrkf < 1 : ",I8)') ngrkf write(*,*) stop end if if (nswplot.lt.0) then write(*,*) write(*,'("Error(readinput): nswplot < 0 : ",I8)') nswplot write(*,*) stop end if read(50,*,err=20) wplot(:) if (wplot(1).gt.wplot(2)) then write(*,*) write(*,'("Error(readinput): wplot(1) > wplot(2) : ",2G18.10)') wplot write(*,*) stop end if case('dosocc') read(50,*,err=20) dosocc case('dosmsum') read(50,*,err=20) dosmsum case('dosssum') read(50,*,err=20) dosssum case('lmirep') read(50,*,err=20) lmirep case('atpopt') read(50,*,err=20) atpopt case('maxatpstp','maxatmstp') read(50,*,err=20) maxatpstp if (maxatpstp.le.0) then write(*,*) write(*,'("Error(readinput): maxatpstp <= 0 : ",I8)') maxatpstp write(*,*) stop end if case('tau0atp','tau0atm') read(50,*,err=20) tau0atp case('deltast') read(50,*,err=20) deltast if (deltast.le.0.d0) then write(*,*) write(*,'("Error(readinput): deltast <= 0 : ",G18.10)') deltast write(*,*) stop end if case('latvopt') read(50,*,err=20) latvopt case('maxlatvstp') read(50,*,err=20) maxlatvstp if (maxlatvstp.le.0) then write(*,*) write(*,'("Error(readinput): maxlatvstp <= 0 : ",I8)') maxlatvstp write(*,*) stop end if case('tau0latv') read(50,*,err=20) tau0latv case('nstfsp') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''nstfsp'' is no longer used")') case('lradstp') read(50,*,err=20) lradstp if (lradstp.le.0) then write(*,*) write(*,'("Error(readinput): lradstp <= 0 : ",I8)') lradstp write(*,*) stop end if case('chgexs') read(50,*,err=20) chgexs case('nprad') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''nprad'' is no longer used")') case('scissor') read(50,*,err=20) scissor case('optcomp') do i=1,27 read(50,'(A256)',err=20) str if (trim(str).eq.'') then if (i.eq.1) then write(*,*) write(*,'("Error(readinput): empty optical component list")') write(*,*) stop end if noptcomp=i-1 goto 10 end if str=trim(str)//' 1 1' read(str,*,iostat=ios) optcomp(:,i) if (ios.ne.0) then write(*,*) write(*,'("Error(readinput): error reading optical component list")') write(*,'("(blank line required after optcomp block)")') write(*,*) stop end if if (any(optcomp(:,i).lt.1).or.any(optcomp(:,i).gt.3)) then write(*,*) write(*,'("Error(readinput): invalid optcomp : ",3I8)') optcomp(:,i) write(*,*) stop end if end do write(*,*) write(*,'("Error(readinput): optical component list too long")') write(*,*) stop case('intraband') read(50,*,err=20) intraband case('evaltol') read(50,*,err=20) evaltol case('deband') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''deband'' is no longer used")') case('epsband') read(50,*,err=20) epsband if (epsband.le.0.d0) then write(*,*) write(*,'("Error(readinput): epsband <= 0 : ",G18.10)') epsband write(*,*) stop end if case('demaxbnd') read(50,*,err=20) demaxbnd if (demaxbnd.le.0.d0) then write(*,*) write(*,'("Error(readinput): demaxbnd <= 0 : ",G18.10)') demaxbnd write(*,*) stop end if case('autolinengy') read(50,*,err=20) autolinengy case('dlefe') read(50,*,err=20) dlefe case('deapwlo') read(50,*,err=20) deapwlo if (abs(deapwlo).lt.1.d-8) then write(*,*) write(*,'("Error(readinput): invalid deapwlo : ",G18.10)') deapwlo write(*,*) stop end if case('bfieldc') read(50,*,err=20) bfieldc0 case('efieldc') read(50,*,err=20) efieldc case('afieldc') read(50,*,err=20) afieldc case('fsmtype','fixspin') read(50,*,err=20) fsmtype case('momfix') read(50,*,err=20) momfix case('mommtfix') do ias=1,maxspecies*maxatoms read(50,'(A256)',err=20) str if (trim(str).eq.'') goto 10 read(str,*,iostat=ios) is,ia,mommtfix(:,ia,is) if (ios.ne.0) then write(*,*) write(*,'("Error(readinput): error reading muffin-tin fixed spin & &moments")') write(*,'("(blank line required after mommtfix block")') write(*,*) stop end if end do case('taufsm') read(50,*,err=20) taufsm if (taufsm.lt.0.d0) then write(*,*) write(*,'("Error(readinput): taufsm < 0 : ",G18.10)') taufsm write(*,*) stop end if case('autormt') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''autormt'' is no longer used")') case('rmtdelta') read(50,*,err=20) rmtdelta if (rmtdelta.lt.0.d0) then write(*,*) write(*,'("Warning(readinput): rmtdelta < 0 : ",G18.10)') rmtdelta end if case('isgkmax') read(50,*,err=20) isgkmax case('nosym') read(50,*,err=20) lv if (lv) symtype=0 case('symtype') read(50,*,err=20) symtype if ((symtype.lt.0).or.(symtype.gt.2)) then write(*,*) write(*,'("Error(readinput): symtype not defined : ",I8)') symtype write(*,*) stop end if case('deltaph') read(50,*,err=20) deltaph if (deltaph.le.0.d0) then write(*,*) write(*,'("Error(readinput): deltaph <= 0 : ",G18.10)') deltaph write(*,*) stop end if case('phwrite') read(50,*,err=20) nphwrt if (nphwrt.le.0) then write(*,*) write(*,'("Error(readinput): nphwrt <= 0 : ",I8)') nphwrt write(*,*) stop end if if (allocated(vqlwrt)) deallocate(vqlwrt) allocate(vqlwrt(3,nphwrt)) do i=1,nphwrt read(50,*,err=20) vqlwrt(:,i) end do case('notes') if (allocated(notes)) deallocate(notes) allocate(notes(0)) notelns=0 do read(50,'(A80)') str if (trim(str).eq.'') goto 10 notelns=notelns+1 call addstr(notes) end do case('tforce') read(50,*,err=20) tforce case('tfibs') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''tfibs'' is no longer used")') case('maxitoep') read(50,*,err=20) maxitoep if (maxitoep.lt.1) then write(*,*) write(*,'("Error(readinput): maxitoep < 1 : ",I8)') maxitoep write(*,*) stop end if case('tauoep') read(50,*,err=20) tauoep(:) if ((tauoep(1).lt.0.d0).or.(tauoep(2).lt.0.d0)) then write(*,*) write(*,'("Error(readinput): tauoep < 0 : ",3G18.10)') tauoep write(*,*) stop end if case('kstlist') do i=1,maxkst read(50,'(A256)',err=20) str if (trim(str).eq.'') then if (i.eq.1) then write(*,*) write(*,'("Error(readinput): empty k-point and state list")') write(*,*) stop end if nkstlist=i-1 goto 10 end if read(str,*,iostat=ios) kstlist(:,i) if (ios.ne.0) then write(*,*) write(*,'("Error(readinput): error reading k-point and state list")') write(*,'("(blank line required after kstlist block)")') write(*,*) stop end if end do write(*,*) write(*,'("Error(readinput): k-point and state list too long")') write(*,*) stop case('vklem') read(50,*,err=20) vklem case('deltaem') read(50,*,err=20) deltaem case('ndspem') read(50,*,err=20) ndspem if ((ndspem.lt.1).or.(ndspem.gt.4)) then write(*,*) write(*,'("Error(readinput): ndspem out of range : ",I8)') ndspem write(*,*) stop end if case('nosource') read(50,*,err=20) nosource case('spinsprl') read(50,*,err=20) spinsprl case('ssdph') read(50,*,err=20) ssdph case('vqlss') read(50,*,err=20) vqlss case('nwrite') read(50,*,err=20) nwrite case('DFT+U','dft+u','lda+u') read(50,*,err=20) dftu,inpdftu do i=1,maxdftu read(50,'(A256)',err=20) str if (trim(str).eq.'') then ndftu=i-1 goto 10 end if select case(inpdftu) case(1) read(str,*,iostat=ios) is,l,ujdu(1:2,i) case(2) read(str,*,iostat=ios) is,l,(fdu(k,i),k=0,2*l,2) case(3) read(str,*,iostat=ios) is,l,(edu(k,i),k=0,l) case(4) read(str,*,iostat=ios) is,l,lambdadu(i) case(5) read(str,*,iostat=ios) is,l,udufix(i) case default write(*,*) write(*,'("Error(readinput): invalid inpdftu : ",I8)') inpdftu write(*,*) stop end select if (ios.ne.0) then write(*,*) write(*,'("Error(readinput): error reading DFT+U parameters")') write(*,'("(blank line required after dft+u block)")') write(*,*) stop end if if ((is.le.0).or.(is.ge.maxspecies)) then write(*,*) write(*,'("Error(readinput): invalid species number in dft+u block : ", & &I8)') is write(*,*) stop end if if (l.lt.0) then write(*,*) write(*,'("Error(readinput): l < 0 in dft+u block : ",I8)') l write(*,*) stop end if if (l.gt.lmaxdm) then write(*,*) write(*,'("Error(readinput): l > lmaxdm in dft+u block : ",2I8)') l,lmaxdm write(*,*) stop end if ! check for repeated entries do j=1,i-1 if ((is.eq.idftu(1,j)).and.(l.eq.idftu(2,j))) then write(*,*) write(*,'("Error(readinput): repeated entry in DFT+U block")') write(*,*) stop end if end do idftu(1,i)=is idftu(2,i)=l end do write(*,*) write(*,'("Error(readinput): too many DFT+U entries")') write(*,'("Adjust maxdftu in modmain and recompile code")') write(*,*) stop case('tmwrite','tmomlu') read(50,*,err=20) tmwrite case('readadu','readalu') read(50,*,err=20) readadu case('rdmxctype') read(50,*,err=20) rdmxctype case('rdmmaxscl') read(50,*,err=20) rdmmaxscl if (rdmmaxscl.lt.0) then write(*,*) write(*,'("Error(readinput): rdmmaxscl < 0 : ",I8)') rdmmaxscl write(*,*) end if case('maxitn') read(50,*,err=20) maxitn if (maxitn.lt.1) then write(*,*) write(*,'("Error(readinput): maxitn < 1 : ",I8)') maxitn write(*,*) stop end if case('maxitc') read(50,*,err=20) maxitc case('taurdmn') read(50,*,err=20) taurdmn if (taurdmn.lt.0.d0) then write(*,*) write(*,'("Error(readinput): taurdmn < 0 : ",G18.10)') taurdmn write(*,*) stop end if case('taurdmc') read(50,*,err=20) taurdmc if (taurdmc.lt.0.d0) then write(*,*) write(*,'("Error(readinput): taurdmc < 0 : ",G18.10)') taurdmc write(*,*) stop end if case('rdmalpha') read(50,*,err=20) rdmalpha if ((rdmalpha.le.0.d0).or.(rdmalpha.ge.1.d0)) then write(*,*) write(*,'("Error(readinput): rdmalpha not in (0,1) : ",G18.10)') rdmalpha write(*,*) stop end if case('rdmtemp') read(50,*,err=20) rdmtemp if (rdmtemp.lt.0.d0) then write(*,*) write(*,'("Error(readinput): rdmtemp < 0 : ",G18.10)') rdmtemp write(*,*) stop end if case('reducebf') read(50,*,err=20) reducebf if ((reducebf.lt.0.49d0).or.(reducebf.gt.1.d0)) then write(*,*) write(*,'("Error(readinput): reducebf not in [0.5,1] : ",G18.10)') reducebf write(*,*) stop end if case('ptnucl') read(50,*,err=20) ptnucl case('tefvr','tseqr') read(50,*,err=20) tefvr case('tefvit','tseqit') read(50,*,err=20) tefvit case('minitefv','minseqit') read(50,*,err=20) minitefv if (minitefv.lt.1) then write(*,*) write(*,'("Error(readinput): minitefv < 1 : ",I8)') minitefv write(*,*) stop end if case('maxitefv','maxseqit') read(50,*,err=20) maxitefv if (maxitefv.lt.1) then write(*,*) write(*,'("Error(readinput): maxitefv < 1 : ",I8)') maxitefv write(*,*) stop end if case('befvit','bseqit') read(50,*,err=20) befvit if (befvit.le.0.d0) then write(*,*) write(*,'("Error(readinput): befvit <= 0 : ",G18.10)') befvit write(*,*) stop end if case('epsefvit','epsseqit') read(50,*,err=20) epsefvit if (epsefvit.lt.0.d0) then write(*,*) write(*,'("Error(readinput): epsefvit < 0 : ",G18.10)') epsefvit write(*,*) stop end if case('nseqit') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''nseqit'' is no longer used")') case('tauseq') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''tauseq'' is no longer used")') case('vecql') read(50,*,err=20) vecql(:) case('mustar') read(50,*,err=20) mustar case('sqados') read(50,*,err=20) sqados(:) case('test') read(50,*,err=20) test case('frozencr') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''frozencr'' is no longer used")') case('spincore') read(50,*,err=20) spincore case('solscf') read(50,*,err=20) solscf if (solscf.lt.0.d0) then write(*,*) write(*,'("Error(readinput): solscf < 0 : ",G18.10)') solscf write(*,*) stop end if case('emaxelnes') read(50,*,err=20) emaxelnes case('wsfac') read(50,*,err=20) wsfac(:) case('vhmat') read(50,*,err=20) vhmat(1,:) read(50,*,err=20) vhmat(2,:) read(50,*,err=20) vhmat(3,:) case('reduceh') read(50,*,err=20) reduceh case('hybrid') read(50,*,err=20) hybrid0 case('hybridc','hybmix') read(50,*,err=20) hybridc if ((hybridc.lt.0.d0).or.(hybridc.gt.1.d0)) then write(*,*) write(*,'("Error(readinput): invalid hybridc : ",G18.10)') hybridc write(*,*) stop end if case('ecvcut') read(50,*,err=20) ecvcut case('esccut') read(50,*,err=20) esccut case('nvbse') read(50,*,err=20) nvbse0 if (nvbse0.lt.0) then write(*,*) write(*,'("Error(readinput): nvbse < 0 : ",I8)') nvbse0 write(*,*) stop end if case('ncbse') read(50,*,err=20) ncbse0 if (ncbse0.lt.0) then write(*,*) write(*,'("Error(readinput): ncbse < 0 : ",I8)') ncbse0 write(*,*) stop end if case('istxbse') do i=1,maxxbse read(50,'(A256)',err=20) str if (trim(str).eq.'') then if (i.eq.1) then write(*,*) write(*,'("Error(readinput): empty BSE extra valence state list")') write(*,*) stop end if nvxbse=i-1 goto 10 end if read(str,*,iostat=ios) istxbse(i) if (ios.ne.0) then write(*,*) write(*,'("Error(readinput): error reading BSE valence state list")') write(*,'("(blank line required after istxbse block)")') write(*,*) stop end if end do write(*,*) write(*,'("Error(readinput): BSE extra valence state list too long")') write(*,*) stop case('jstxbse') do i=1,maxxbse read(50,'(A256)',err=20) str if (trim(str).eq.'') then if (i.eq.1) then write(*,*) write(*,'("Error(readinput): empty BSE extra conduction state list")') write(*,*) stop end if ncxbse=i-1 goto 10 end if read(str,*,iostat=ios) jstxbse(i) if (ios.ne.0) then write(*,*) write(*,'("Error(readinput): error reading BSE conduction state list")') write(*,'("(blank line required after jstxbse block)")') write(*,*) stop end if end do write(*,*) write(*,'("Error(readinput): BSE extra conduction state list too long")') write(*,*) stop case('bsefull') read(50,*,err=20) bsefull case('hxbse') read(50,*,err=20) hxbse case('hdbse') read(50,*,err=20) hdbse case('gmaxrf','gmaxrpa') read(50,*,err=20) gmaxrf if (gmaxrf.lt.0.d0) then write(*,*) write(*,'("Error(readinput): gmaxrf < 0 : ",G18.10)') gmaxrf write(*,*) stop end if case('emaxrf') read(50,*,err=20) emaxrf if (emaxrf.lt.0.d0) then write(*,*) write(*,'("Error(readinput): emaxrf < 0 : ",G18.10)') emaxrf write(*,*) stop end if case('fxctype') read(50,'(A256)',err=20) str str=trim(str)//' 0 0' read(str,*,err=20) fxctype case('fxclrc') read(50,'(A256)',err=20) str str=trim(str)//' 0.0' read(str,*,err=20) fxclrc(:) case('ntemp') read(50,*,err=20) ntemp if (ntemp.lt.1) then write(*,*) write(*,'("Error(readinput): ntemp < 1 : ",I8)') ntemp write(*,*) stop end if case('trimvg') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''trimvg'' is no longer used")') write(*,'(" setting msmooth=4 instead")') msmooth=4 case('rndstate','rndseed') read(50,*,err=20) rndstate(0) rndstate(0)=abs(rndstate(0)) case('rndatposc') read(50,*,err=20) rndatposc case('rndbfcmt') read(50,*,err=20) rndbfcmt case('rndavec') read(50,*,err=20) rndavec case('c_tb09') read(50,*,err=20) c_tb09 ! set flag to indicate Tran-Blaha constant has been read in tc_tb09=.true. case('lowq','highq','vhighq','uhighq') read(50,*,err=20) lv if (lv) then if (trim(block).eq.'lowq') then rgkmax=6.5d0 gmaxvr=10.d0 lmaxapw=7 lmaxo=5 nxlo=2 lorbcnd=.true. radkpt=25.d0 autokpt=.true. vkloff(:)=0.5d0 nempty0=4.d0 epspot=1.d-5 epsengy=5.d-4 epsforce=1.d-2 autolinengy=.true. gmaxrf=2.5d0 lradstp=5 else if (trim(block).eq.'highq') then ! parameter set for high quality calculation rgkmax=max(rgkmax,8.d0) gmaxvr=max(gmaxvr,16.d0) msmooth=max(msmooth,4) lmaxapw=max(lmaxapw,9) lmaxo=max(lmaxo,7) nrmtscf=max(nrmtscf,1.5d0) nxlo=max(nxlo,2) lorbcnd=.true. radkpt=max(radkpt,50.d0) autokpt=.true. vkloff(:)=0.d0 nempty0=max(nempty0,10.d0) epspot=min(epspot,1.d-7) epsengy=min(epsengy,1.d-5) epsforce=min(epsforce,1.d-4) autolinengy=.true. gmaxrf=max(gmaxrf,4.d0) else if (trim(block).eq.'vhighq') then ! parameter set for very high quality calculation rgkmax=max(rgkmax,9.d0) gmaxvr=max(gmaxvr,18.d0) msmooth=max(msmooth,4) lmaxapw=max(lmaxapw,10) lmaxo=max(lmaxo,8) nrmtscf=max(nrmtscf,2.d0) nxlo=max(nxlo,3) lorbcnd=.true. radkpt=max(radkpt,90.d0) autokpt=.true. vkloff(:)=0.d0 nempty0=max(nempty0,20.d0) epspot=min(epspot,1.d-7) epsengy=min(epsengy,1.d-6) epsforce=min(epsforce,1.d-4) autolinengy=.true. gmaxrf=max(gmaxrf,5.d0) else ! parameter set for ultra high quality calculation rgkmax=max(rgkmax,10.d0) gmaxvr=max(gmaxvr,20.d0) msmooth=max(msmooth,4) lmaxapw=max(lmaxapw,11) lmaxo=max(lmaxo,9) nrmtscf=max(nrmtscf,4.d0) nxlo=max(nxlo,3) lorbcnd=.true. radkpt=max(radkpt,120.d0) autokpt=.true. vkloff(:)=0.d0 nempty0=max(nempty0,40.d0) epspot=min(epspot,1.d-7) epsengy=min(epsengy,1.d-6) epsforce=min(epsforce,1.d-4) autolinengy=.true. gmaxrf=max(gmaxrf,6.d0) end if if (mp_mpi) then write(*,*) write(*,'("Info(readinput): parameters set by ",A," option")') trim(block) write(*,'(" rgkmax : ",G18.10)') rgkmax write(*,'(" gmaxvr : ",G18.10)') gmaxvr write(*,'(" msmooth : ",I4)') msmooth write(*,'(" lmaxapw : ",I4)') lmaxapw write(*,'(" lmaxo : ",I4)') lmaxo write(*,'(" nrmtscf : ",G18.10)') nrmtscf write(*,'(" nxlo : ",I4)') nxlo write(*,'(" lorbcnd : ",L1)') lorbcnd write(*,'(" radkpt : ",G18.10)') radkpt write(*,'(" autokpt : ",L1)') autokpt write(*,'(" vkloff : ",3G18.10)') vkloff write(*,'(" nempty0 : ",G18.10)') nempty0 write(*,'(" epspot : ",G18.10)') epspot write(*,'(" epsengy : ",G18.10)') epsengy write(*,'(" epsforce : ",G18.10)') epsforce write(*,'(" autolinengy : ",L1)') autolinengy write(*,'(" gmaxrf : ",G18.10)') gmaxrf if (trim(block).eq.'lowq') then write(*,'(" lradstp : ",I4)') lradstp end if end if end if case('hmaxvr') read(50,*,err=20) hmaxvr if (hmaxvr.lt.0.d0) then write(*,*) write(*,'("Error(readinput): hmaxvr < 0 : ",G18.10)') hmaxvr write(*,*) stop end if case('hkmax') read(50,*,err=20) hkmax if (hkmax.le.0.d0) then write(*,*) write(*,'("Error(readinput): hkmax <= 0 : ",G18.10)') hkmax write(*,*) stop end if case('lorbcnd') read(50,*,err=20) lorbcnd case('lorbordc') read(50,*,err=20) lorbordc if (lorbordc.lt.2) then write(*,*) write(*,'("Error(readinput): lorbordc < 2 : ",I8)') lorbordc write(*,*) stop end if if (lorbordc.gt.maxlorbord) then write(*,*) write(*,'("Error(readinput): lorbordc too large : ",I8)') lorbordc write(*,'("Adjust maxlorbord in modmain and recompile code")') write(*,*) stop end if case('nrmtscf') read(50,*,err=20) nrmtscf if (nrmtscf.lt.0.5d0) then write(*,*) write(*,'("Error(readinput): nrmtscf < 0.5 : ",G18.10)') nrmtscf write(*,*) stop end if case('lmaxdos') read(50,*,err=20) lmaxdos if (lmaxdos.lt.0) then write(*,*) write(*,'("Error(readinput): lmaxdos < 0 : ",I8)') lmaxdos write(*,*) stop end if case('epsdev') read(50,*,err=20) epsdev if (epsdev.le.0.d0) then write(*,*) write(*,'("Error(readinput): epsdev <= 0 : ",G18.10)') epsdev write(*,*) stop end if case('msmooth') read(50,*,err=20) msmooth if (msmooth.lt.0) then write(*,*) write(*,'("Error(readinput): msmooth < 0 : ",I8)') msmooth write(*,*) stop end if case('npmae') read(50,*,err=20) npmae0 case('wrtvars') read(50,*,err=20) wrtvars case('ftmtype') read(50,*,err=20) ftmtype case('tmomfix') read(50,*,err=20) ntmfix if (ntmfix.le.0) then write(*,*) write(*,'("Error(readinput): ntmfix <= 0 : ",I8)') ntmfix write(*,*) stop end if if (allocated(itmfix)) deallocate(itmfix) allocate(itmfix(8,ntmfix)) if (allocated(tmfix)) deallocate(tmfix) allocate(tmfix(ntmfix)) if (allocated(rtmfix)) deallocate(rtmfix) allocate(rtmfix(3,3,2,ntmfix)) do i=1,ntmfix read(50,*,err=20) is,ia,l,n if ((is.le.0).or.(ia.le.0).or.(l.lt.0).or.((n.ne.2).and.(n.ne.3))) then write(*,*) write(*,'("Error(readinput): invalid is, ia, l or n in tmomfix block : ",& &4I8)') is,ia,l,n write(*,*) stop end if itmfix(1,i)=is itmfix(2,i)=ia itmfix(3,i)=l itmfix(4,i)=n ! read k, p, x, y for the 2-index tensor or k, p, r, t for the 3-index tensor read(50,*,err=20) itmfix(5:8,i) ! read tensor component read(50,*,err=20) a,b tmfix(i)=cmplx(a,b,8) ! read parity and Euler angles of spatial and spin rotation matrices read(50,'(A256)',err=20) str str=trim(str)//' 0.0 0.0 0.0' read(str,*,err=20) p,v1(:),v2(:) if (abs(p).ne.1) then write(*,*) write(*,'("Error(readinput): parity should be -1 or 1 in tmomfix & &block : ",I8)') p write(*,*) stop end if ! convert Euler angles from degrees to radians v1(:)=v1(:)*pi/180.d0 v2(:)=v2(:)*pi/180.d0 ! compute the spatial and spin 3x3 rotation matrices from the Euler angles call eulerrot(v1,rtmfix(:,:,1,i)) call eulerrot(v2,rtmfix(:,:,2,i)) ! multiply the spatial rotation matrix by the parity rtmfix(:,:,1,i)=dble(p)*rtmfix(:,:,1,i) end do case('tauftm') read(50,*,err=20) tauftm if (tauftm.lt.0.d0) then write(*,*) write(*,'("Error(readinput): tauftm < 0 : ",G18.10)') tauftm write(*,*) stop end if case('ftmstep') read(50,*,err=20) ftmstep if (ftmstep.lt.1) then write(*,*) write(*,'("Error(readinput): ftmstep < 1 : ",I8)') ftmstep write(*,*) stop end if case('cmagz','forcecmag') read(50,*,err=20) cmagz case('rotavec') read(50,*,err=20) axang(:) case('tstime') read(50,*,err=20) tstime if (tstime.lt.0.d0) then write(*,*) write(*,'("Error(readinput): tstime <= 0 : ",G18.10)') tstime write(*,*) stop end if case('dtimes') read(50,*,err=20) dtimes if (dtimes.le.0.d0) then write(*,*) write(*,'("Error(readinput): dtimes <= 0 : ",G18.10)') dtimes write(*,*) stop end if case('pulse') read(50,*,err=20) npulse if (npulse.lt.1) then write(*,*) write(*,'("Error(readinput): npulse < 1 : ",I8)') npulse write(*,*) stop end if if (allocated(pulse)) deallocate(pulse) allocate(pulse(8,npulse)) do i=1,npulse read(50,*,err=20) pulse(:,i) end do case('ramp') read(50,*,err=20) nramp if (nramp.lt.1) then write(*,*) write(*,'("Error(readinput): nramp < 1 : ",I8)') nramp write(*,*) stop end if if (allocated(ramp)) deallocate(ramp) allocate(ramp(8,nramp)) do i=1,nramp read(50,'(A256)',err=20) str str=trim(str)//' 0.0 0.0' read(str,*,err=20) ramp(:,i) end do case('ncgga') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''ncgga'' is no longer used")') case('dncgga') read(50,*,err=20) dncgga if (dncgga.lt.0.d0) then write(*,*) write(*,'("Error(readinput): dncgga < 0 : ",G18.10)') dncgga write(*,*) stop end if case('ntswrite') read(50,'(A256)',err=20) str str=trim(str)//' 1' read(str,*,err=20) ntswrite(:) case('nxoapwlo','nxapwlo') read(50,*,err=20) nxoapwlo if (nxoapwlo.lt.0) then write(*,*) write(*,'("Error(readinput): nxoapwlo < 0 : ",I8)') nxoapwlo write(*,*) stop end if case('nxlo') read(50,*,err=20) nxlo if (nxlo.lt.0) then write(*,*) write(*,'("Error(readinput): nxlo < 0 : ",I8)') nxlo write(*,*) stop end if case('tdrho1d') read(50,*,err=20) tdrho1d case('tdrho2d') read(50,*,err=20) tdrho2d case('tdrho3d') read(50,*,err=20) tdrho3d case('tdmag1d') read(50,*,err=20) tdmag1d case('tdmag2d') read(50,*,err=20) tdmag2d case('tdmag3d') read(50,*,err=20) tdmag3d case('tdjr1d','tdcd1d') read(50,*,err=20) tdjr1d case('tdjr2d','tdcd2d') read(50,*,err=20) tdjr2d case('tdjr3d','tdcd3d') read(50,*,err=20) tdjr3d case('tddos') read(50,*,err=20) tddos case('tdlsj') read(50,*,err=20) tdlsj case('epseph') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''epseph'' is no longer used")') case('rndevt0') read(50,*,err=20) rndevt0 case('sxcscf','ssxc','rstsf') read(50,*,err=20) sxcscf case('tempk') read(50,*,err=20) tempk if (tempk.le.0.d0) then write(*,*) write(*,'("Error(readinput): tempk <= 0 : ",G18.10)') tempk write(*,*) stop end if ! set Fermi-Dirac smearing stype=3 ! set the smearing width swidth=kboltz*tempk case('avecu') read(50,*,err=20) avecu(:,1) read(50,*,err=20) avecu(:,2) read(50,*,err=20) avecu(:,3) case('scaleu') read(50,*,err=20) scu case('scaleu1') read(50,*,err=20) scu1 case('scaleu2') read(50,*,err=20) scu2 case('scaleu3') read(50,*,err=20) scu3 case('q0cut') read(50,*,err=20) q0cut if (q0cut.lt.0.d0) then write(*,*) write(*,'("Error(readinput): q0cut < 0 : ",G18.10)') q0cut write(*,*) stop end if case('rndbfcu') read(50,*,err=20) rndbfcu case('efielduc') read(50,*,err=20) efielduc case('tplotq0') read(50,*,err=20) tplotq0 case('trdvclr') read(50,*,err=20) trdvclr case('evtype') read(50,*,err=20) write(*,*) write(*,'("Info(readinput): variable ''evtype'' is no longer used")') case('wmaxgw') read(50,*,err=20) wmaxgw case('twdiag') read(50,*,err=20) twdiag case('tsediag') read(50,*,err=20) tsediag case('actype') read(50,*,err=20) actype case('npole') read(50,*,err=20) npole if (npole.le.0) then write(*,*) write(*,'("Error(readinput): npole <= 0 : ",I8)') npole write(*,*) stop end if case('nspade') read(50,*,err=20) nspade if (nspade.le.0) then write(*,*) write(*,'("Error(readinput): nspade <= 0 : ",I8)') nspade write(*,*) stop end if case('tfav0') read(50,*,err=20) tfav0 case('rmtall') read(50,*,err=20) rmtall case('maxthd','omp_num_threads','OMP_NUM_THREADS') read(50,*,err=20) maxthd case('maxthd1') read(50,*,err=20) maxthd1 case('maxthdmkl') read(50,*,err=20) maxthdmkl case('maxlvl','omp_max_active_levels','OMP_MAX_ACTIVE_LEVELS') read(50,*,err=20) maxlvl if (maxlvl.lt.1) then write(*,*) write(*,'("Error(readinput): maxlvl < 1 : ",I8)') maxlvl write(*,*) stop end if case('stable') read(50,*,err=20) lv if (lv) then mixtype=3 broydpm(1)=min(broydpm(1),0.04d0) broydpm(2)=min(broydpm(2),0.01d0) msmooth=max(msmooth,8) isgkmax=-4 if (mp_mpi) then write(*,*) write(*,'("Info(readinput): parameters set by stable option")') write(*,'(" mixtype : ",I4)') mixtype write(*,'(" broydpm : ",2G18.10)') broydpm write(*,'(" msmooth : ",I4)') msmooth write(*,'(" isgkmax : ",I4)') isgkmax end if end if case('metagga') read(50,*,err=20) lv if (lv) then nempty0=max(nempty0,10.d0) lradstp=1 nrmtscf=max(nrmtscf,2.d0) msmooth=max(msmooth,4) if (mp_mpi) then write(*,*) write(*,'("Info(readinput): parameters set by metagga option")') write(*,'(" nempty0 : ",G18.10)') nempty0 write(*,'(" lradstp : ",I4)') lradstp write(*,'(" nrmtscf : ",G18.10)') nrmtscf write(*,'(" msmooth : ",I4)') msmooth end if end if case('taudft') read(50,*,err=20) taudft case('t0tdlr') read(50,*,err=20) t0tdlr if (t0tdlr.le.0.d0) then write(*,*) write(*,'("Error(readinput): t0tdlr <= 0 : ",G18.10)') t0tdlr write(*,*) stop end if case('tdphi') read(50,*,err=20) tdphi ! convert phase from degrees to radians tdphi=tdphi*pi/180.d0 case('thetamld') read(50,*,err=20) thetamld ! convert MLD angle from degrees to radians thetamld=thetamld*pi/180.d0 case('ntsbackup') read(50,*,err=20) ntsbackup case('seedname') read(50,*,err=20) seedname seedname=adjustl(seedname) case('num_wann') read(50,*,err=20) num_wann case('idxw90','wann_bands') read(50,'(A256)',err=20) str num_bands=1024 if (allocated(idxw90)) deallocate(idxw90) allocate(idxw90(num_bands)) call numlist(str,num_bands,idxw90) case('num_iter') read(50,*,err=20) num_iter case('trial_step') read(50,*,err=20) trial_step case('xlwin','wannierExtra') if (allocated(xlwin)) deallocate(xlwin) allocate(xlwin(0)) nxlwin=0 do read(50,'(A256)',err=20) str if (trim(str).eq.'') goto 10 nxlwin=nxlwin+1 call addstr(xlwin) end do case('tbdip') read(50,*,err=20) tbdip case('tjr','tcden') read(50,*,err=20) tjr case('tauefm') read(50,*,err=20) tauefm case('epsefm') read(50,*,err=20) epsefm case('ehfb') read(50,*,err=20) ehfb case('t0gclq0') read(50,*,err=20) t0gclq0 case('tafindt') read(50,*,err=20) tafindt case('afindscf') read(50,*,err=20) afindscf case('nkspolar') read(50,*,err=20) nkspolar if (nkspolar.lt.1) then write(*,*) write(*,'("Error(readinput): nkspolar < 1 : ",I8)') nkspolar write(*,*) stop end if case('ntsforce') read(50,*,err=20) ntsforce if (ntsforce.lt.1) then write(*,*) write(*,'("Error(readinput): ntsforce < 1 : ",I8)') ntsforce write(*,*) stop end if case('wphcut') read(50,*,err=20) wphcut if (wphcut.le.0.d0) then write(*,*) write(*,'("Error(readinput): wphcut <= 0 : ",G18.10)') wphcut write(*,*) stop end if case('ephscf') read(50,*,err=20) ephscf(:) case('anomalous') read(50,*,err=20) anomalous case('tephde') read(50,*,err=20) tephde case('bdiag') read(50,*,err=20) bdiag case('ramdisk') read(50,*,err=20) ramdisk case('') goto 10 case default write(*,*) write(*,'("Error(readinput): invalid block name : ",A)') trim(block) write(*,*) stop end select goto 10 20 continue write(*,*) write(*,'("Error(readinput): error reading from elk.in")') write(*,'("Problem occurred in ''",A,"'' block")') trim(block) write(*,'("Check input convention in manual")') write(*,*) stop 30 continue close(50) ! scale the speed of light solsc=sol*solscf ! scale and rotate the lattice vectors (not referenced again in code) avec(:,:)=sc*avec(:,:) avec(:,1)=sc1*avec(:,1) avec(:,2)=sc2*avec(:,2) avec(:,3)=sc3*avec(:,3) avec(1,:)=scx*avec(1,:) avec(2,:)=scy*avec(2,:) avec(3,:)=scz*avec(3,:) t1=axang(4) if (t1.ne.0.d0) then t1=t1*pi/180.d0 call axangrot(axang(:),t1,rot) do i=1,3 v1(:)=avec(:,i) call r3mv(rot,v1,avec(:,i)) end do end if ! randomise lattice vectors if required if (rndavec.gt.0.d0) then do i=1,3 do j=1,3 t1=rndavec*(randomu()-0.5d0) avec(i,j)=avec(i,j)+t1 end do end do end if ! case of isolated molecule if (molecule) then ! convert atomic positions from Cartesian to lattice coordinates call r3minv(avec,ainv) do is=1,nspecies do ia=1,natoms(is) call r3mv(ainv,atposl(:,ia,is),v1) atposl(:,ia,is)=v1(:) end do end do end if ! randomise atomic positions if required if (rndatposc.gt.0.d0) then call r3minv(avec,ainv) do is=1,nspecies do ia=1,natoms(is) call r3mv(avec,atposl(:,ia,is),v1) do i=1,3 t1=rndatposc*(randomu()-0.5d0) v1(i)=v1(i)+t1 end do call r3mv(ainv,v1,atposl(:,ia,is)) end do end do end if ! randomise the muffin-tin magnetic fields if required if (rndbfcmt.gt.0.d0) then do is=1,nspecies do ia=1,natoms(is) do i=1,3 t1=rndbfcmt*(randomu()-0.5d0) bfcmt0(i,ia,is)=bfcmt0(i,ia,is)+t1 end do end do end do end if ! set fxctype to fxctype if required if (fxctype(1).eq.-1) fxctype(:)=xctype(:) ! find primitive cell if required if (primcell) call findprimcell ! scale the ultracell vectors if required avecu(:,1)=scu1*avecu(:,1) avecu(:,2)=scu2*avecu(:,2) avecu(:,3)=scu3*avecu(:,3) avecu(:,:)=scu*avecu(:,:) ! read in atomic species data call readspecies return contains subroutine addstr(slist) implicit none ! arguments character(256), intent(inout), allocatable :: slist(:) ! allocatable arrays character(256), allocatable :: stmp(:) n=size(slist) allocate(stmp(n)) stmp(1:n)=slist(1:n) deallocate(slist) allocate(slist(n+1)) slist(1:n)=stmp(1:n) slist(n+1)=str deallocate(stmp) end subroutine end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/numlist.f900000644000000000000000000000013214061636517014737 xustar0030 mtime=1623670095.333102104 30 atime=1623670094.108103241 30 ctime=1623670095.333102104 elk-7.2.42/src/numlist.f900000644002504400250440000000156514061636517017003 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 Manh Duc Le, 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin, ! Lars Nordstrom and J. K. Dewhurst. This file is distributed under the terms of ! the GNU General Public License. See the file COPYING for license details. subroutine numlist(str,n,list) implicit none ! arguments character(256), intent(in) :: str integer, intent(inout) :: n integer, intent(out) :: list(n) ! local variables integer i0,i1,i,j,m,ios ! automatic arrays integer l(n) i=0 i0=1 do m=index(str(i0:),'-') if (m.eq.0) then i1=256 else i1=i0+m-2 end if l(:)=0 read(str(i0:i1),*,iostat=ios) l if (i.gt.0) then do j=list(i)+1,l(1)-1 if (i.eq.n) goto 10 i=i+1 list(i)=j end do end if do j=1,n if (l(j).eq.0) exit if (i.eq.n) goto 10 i=i+1 list(i)=l(j) end do if (m.eq.0) exit i0=i0+m end do 10 continue n=i end subroutine elk-7.2.42/src/PaxHeaders.21776/hermite.f900000644000000000000000000000013114061636517014700 xustar0030 mtime=1623670095.334102103 29 atime=1623670094.10910324 30 ctime=1623670095.334102103 elk-7.2.42/src/hermite.f900000644002504400250440000000266414061636517016746 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: hermite ! !INTERFACE: real(8) function hermite(n,x) ! !INPUT/OUTPUT PARAMETERS: ! n : order of Hermite polynomial (in,integer) ! x : real argument (in,real) ! !DESCRIPTION: ! Returns the $n$th Hermite polynomial. The recurrence relation ! $$ H_i(x)=2xH_{i-1}(x)-2nH_{i-2}(x), $$ ! with $H_0=1$ and $H_1=2x$, is used. This procedure is numerically stable ! and accurate to near machine precision for $n\le 20$. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: x ! local variables integer i real(8) h1,h2,ht ! fast return if possible if (n.eq.0) then hermite=1.d0 return else if (n.eq.1) then hermite=2.d0*x return else if (n.eq.2) then hermite=4.d0*x**2-2.d0 return end if if (n.lt.0) then write(*,*) write(*,'("Error(hermite): n < 0 : ",I8)') n write(*,*) stop end if if (n.gt.20) then write(*,*) write(*,'("Error(hermite): n out of range : ",I8)') n write(*,*) stop end if if (abs(x).gt.1.d15) then write(*,*) write(*,'("Error(hermite): x out of range : ",G18.10)') x write(*,*) stop end if h1=2.d0*x h2=1.d0 do i=2,n ht=2.d0*(x*h1-dble(i-1)*h2) h2=h1 h1=ht end do hermite=h1 end function !EOC elk-7.2.42/src/PaxHeaders.21776/genfspecies.f900000644000000000000000000000013214061636517015537 xustar0030 mtime=1623670095.336102101 30 atime=1623670094.111103238 30 ctime=1623670095.336102101 elk-7.2.42/src/genfspecies.f900000644002504400250440000000645214061636517017603 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genfspecies(zn,symb) use modmain use modmpi implicit none ! arguments real(8), intent(in) :: zn character(*), intent(in) :: symb ! local variables integer, parameter :: nit=4 integer nst,ist,jst integer nmax,in,il,ik integer nrm,nr,ir,it integer n(maxstsp),l(maxstsp),k(maxstsp) integer idx(maxstsp),iv(maxstsp) real(8) rm,rmin,rmax real(8) mass,t1,t2,t3 real(8) occ(maxstsp),eval(maxstsp),rv(maxstsp) character(256) name ! allocatable arrays real(8), allocatable :: r(:),rho(:),vr(:),rwf(:,:,:) ! external functions real(8), external :: massnucl name='Fractional species' ! set up the initial occupancies occ(:)=0.d0 t1=abs(zn) nmax=1 ist=0 do in=1,maxstsp do il=0,in-1 do ik=max(il,1),il+1 t2=dble(2*ik) t2=min(t2,t1) ist=ist+1 n(ist)=in l(ist)=il k(ist)=ik occ(ist)=t2 if (t2.gt.epsocc) nmax=in t1=t1-t2 if (ist.eq.maxstsp) then if (t1.gt.epsocc) then write(*,*) write(*,'("Error(genfspecies): too many states for fractional & &species ",A)') trim(symb) write(*,*) stop else goto 10 end if end if end do end do end do 10 continue ! minimum radius rmin=2.d-6/sqrt(abs(zn)) ! initial maximum radius rmax=100.d0 ! initial muffin-tin radius rm=2.d0 ! number of points to muffin-tin radius nrm=100*(nmax+1) ! iterate the solution but not to self-consistency do it=1,nit ! number of points to effective infinity t1=log(rm/rmin) t2=log(rmax/rmin) t3=dble(nrm)*t2/t1 nr=int(t3) allocate(r(nr),rho(nr),vr(nr),rwf(nr,2,maxstsp)) ! generate logarithmic radial mesh t2=t1/dble(nrm-1) do ir=1,nr r(ir)=rmin*exp(dble(ir-1)*t2) end do ! solve the Kohn-Sham-Dirac equation for the atom call atom(sol,.true.,zn,maxstsp,n,l,k,occ,3,0,nr,r,eval,rho,vr,rwf) ! check for spurious eigenvalues do ist=2,maxstsp if (eval(ist).lt.eval(1)) eval(ist)=1.d6 end do ! recompute the effective infinity do ir=nr,1,-1 if (rho(ir).gt.1.d-20) then rmax=1.75d0*r(ir) exit end if end do ! estimate the muffin-tin radius do ir=nr,1,-1 if (rho(ir).gt.2.d-2) then rm=r(ir) exit end if end do if (rm.lt.1.d0) rm=1.d0 if (rm.gt.3.2d0) rm=3.2d0 ! sort the eigenvalues call sortidx(maxstsp,eval,idx) ! recompute the occupancies occ(:)=0.d0 t1=abs(zn) do ist=1,maxstsp jst=idx(ist) ik=k(jst) t2=dble(2*ik) t2=min(t2,t1) occ(jst)=t2 t1=t1-t2 end do deallocate(r,rho,vr,rwf) end do ! rearrange the arrays iv(:)=n(:) n(:)=iv(idx(:)) iv(:)=l(:) l(:)=iv(idx(:)) iv(:)=k(:) k(:)=iv(idx(:)) rv(:)=occ(:) occ(:)=rv(idx(:)) rv(:)=eval(:) eval(:)=rv(idx(:)) ! find the number of occupied states nst=0 do ist=1,maxstsp if (occ(ist).lt.epsocc) then nst=ist exit end if end do ! estimate the nuclear mass mass=massnucl(zn) ! convert from 'atomic mass units' to atomic units mass=mass*amu ! write the species file call writespecies(symb,name,zn,mass,rmin,rm,rmax,nrm,nst,n,l,k,occ,eval) if (mp_mpi) then write(*,*) write(*,'("Info(genfspecies): wrote fractional species file ",A,".in")') & trim(symb) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/atpstep.f900000644000000000000000000000012614061636517014727 xustar0028 mtime=1623670095.3371021 30 atime=1623670094.113103236 28 ctime=1623670095.3371021 elk-7.2.42/src/atpstep.f900000644002504400250440000000352414061636517016765 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: atpstep ! !INTERFACE: subroutine atpstep ! !USES: use modmain use modmpi ! !DESCRIPTION: ! Makes a geometry optimisation step and updates the current atomic positions ! according to the force on each atom. If ${\bf r}_{ij}^m$ is the position and ! ${\bf F}_{ij}^m$ is the force acting on it for atom $j$ of species $i$ and ! after time step $m$, then the new position is calculated by ! $$ {\bf r}_{ij}^{m+1}={\bf r}_{ij}^m+\tau_{ij}^m\left({\bf F}_{ij}^m ! +{\bf F}_{ij}^{m-1}\right), $$ ! where $\tau_{ij}^m$ is a parameter governing the size of the displacement. ! If ${\bf F}_{ij}^m\cdot{\bf F}_{ij}^{m-1}>0$ then $\tau_{ij}^m$ is ! increased, otherwise it is decreased. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! local variables integer is,ia,ias,n real(8) t1 do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) ! compute the dot-product between the current and previous total force t1=dot_product(forcetot(1:3,ias),forcetotp(1:3,ias)) ! if the force is in the same direction then increase step size parameter if (t1.gt.0.d0) then tauatp(ias)=tauatp(ias)+tau0atp else tauatp(ias)=tau0atp end if ! make atomic position step atposc(1:3,ia,is)=atposc(1:3,ia,is)+tauatp(ias)*(forcetot(1:3,ias) & +forcetotp(1:3,ias)) end do end do ! each MPI process should have identical atomic positions n=3*maxatoms*maxspecies call mpi_bcast(atposc,n,mpi_double_precision,0,mpicom,ierror) do is=1,nspecies do ia=1,natoms(is) ! compute the lattice coordinates of the atomic positions call r3mv(ainv,atposc(:,ia,is),atposl(:,ia,is)) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/dmatls.f900000644000000000000000000000013214061636517014530 xustar0030 mtime=1623670095.339102098 30 atime=1623670094.114103235 30 ctime=1623670095.339102098 elk-7.2.42/src/dmatls.f900000644002504400250440000000162114061636517016565 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dmatls(dmat,xl,xs) use modmain implicit none ! arguments complex(8), intent(in) :: dmat(lmmaxo,nspinor,lmmaxo,nspinor) real(8), intent(out) :: xl(3),xs(3) ! local variables integer ispn,lm ! automatic arrays complex(8) zlflm(lmmaxo,3) ! compute tr(LD) xl(:)=0.d0 do ispn=1,nspinor do lm=1,lmmaxo call lopzflm(lmaxo,dmat(:,ispn,lm,ispn),lmmaxo,zlflm) xl(:)=xl(:)+dble(zlflm(lm,:)) end do end do ! compute tr(sigma D) xs(:)=0.d0 if (spinpol) then do lm=1,lmmaxo xs(1)=xs(1)+dble(dmat(lm,2,lm,1)+dmat(lm,1,lm,2)) xs(2)=xs(2)+dble(-zi*dmat(lm,2,lm,1)+zi*dmat(lm,1,lm,2)) xs(3)=xs(3)+dble(dmat(lm,1,lm,1)-dmat(lm,2,lm,2)) end do ! S = 1/2 sigma xs(:)=0.5d0*xs(:) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/writeengy.f900000644000000000000000000000013214061636517015261 xustar0030 mtime=1623670095.340102097 30 atime=1623670094.116103234 30 ctime=1623670095.340102097 elk-7.2.42/src/writeengy.f900000644002504400250440000000305014061636517017314 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine writeengy(fnum) use modmain use moddftu implicit none ! arguments integer, intent(in) :: fnum write(fnum,*) write(fnum,'("Energies :")') write(fnum,'(" Fermi",T30,": ",G22.12)') efermi write(fnum,'(" sum of eigenvalues",T30,": ",G22.12)') evalsum write(fnum,'(" electron kinetic",T30,": ",G22.12)') engykn write(fnum,'(" core electron kinetic",T30,": ",G22.12)') engykncr write(fnum,'(" Coulomb",T30,": ",G22.12)') engycl write(fnum,'(" Coulomb potential",T30,": ",G22.12)') engyvcl write(fnum,'(" nuclear-nuclear",T30,": ",G22.12)') engynn write(fnum,'(" electron-nuclear",T30,": ",G22.12)') engyen write(fnum,'(" Hartree",T30,": ",G22.12)') engyhar write(fnum,'(" Madelung",T30,": ",G22.12)') engymad write(fnum,'(" xc potential",T30,": ",G22.12)') engyvxc if (spinpol) then write(fnum,'(" xc effective B-field",T30,": ",G22.12)') engybxc write(fnum,'(" external B-field",T30,": ",G22.12)') engybext end if write(fnum,'(" exchange",T30,": ",G22.12)') engyx write(fnum,'(" correlation",T30,": ",G22.12)') engyc if (dftu.ne.0) then write(fnum,'(" DFT+U",T30,": ",G22.12)') engydu end if if (stype.eq.3) then write(fnum,'(" electron entropic",T30,": ",G22.12)') engyts end if write(fnum,'(" total energy",T30,": ",G22.12)') engytot if (spinpol) then write(fnum,'(" (external B-field energy excluded from total)")') end if flush(fnum) end subroutine elk-7.2.42/src/PaxHeaders.21776/writechg.f900000644000000000000000000000013214061636517015060 xustar0030 mtime=1623670095.342102095 30 atime=1623670094.118103232 30 ctime=1623670095.342102095 elk-7.2.42/src/writechg.f900000644002504400250440000000225114061636517017115 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine writechg(fnum) use modmain implicit none ! arguments integer, intent(in) :: fnum ! local variables integer is,ia,ias ! write charges write(fnum,*) write(fnum,'("Charges :")') write(fnum,'(" core",T30,": ",G18.10)') chgcrtot write(fnum,'(" valence",T30,": ",G18.10)') chgval write(fnum,'(" interstitial",T30,": ",G18.10)') chgir write(fnum,'(" muffin-tins (core leakage)")') do is=1,nspecies write(fnum,'(" species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) ias=idxas(ia,is) write(fnum,'(" atom ",I4,T30,": ",G18.10," (",G18.10,")")') ia, & chgmt(ias),chgcrlk(ias) end do end do write(fnum,'(" total in muffin-tins",T30,": ",G18.10)') chgmttot if (chgexs.ne.0.d0) then write(fnum,'(" excess",T30,": ",G18.10)') chgexs end if write(fnum,'(" total calculated charge",T30,": ",G18.10)') chgcalc write(fnum,'(" total charge",T30,": ",G18.10)') chgtot write(fnum,'(" error",T30,": ",G18.10)') abs(chgtot-chgcalc) flush(fnum) end subroutine elk-7.2.42/src/PaxHeaders.21776/rbsht.f900000644000000000000000000000013214061636517014366 xustar0030 mtime=1623670095.343102095 30 atime=1623670094.119103231 30 ctime=1623670095.343102095 elk-7.2.42/src/rbsht.f900000644002504400250440000000127714061636517016432 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rbsht(nr,nri,rfmt1,rfmt2) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: rfmt1(*) real(8), intent(out) :: rfmt2(*) ! local variables integer i ! transform the inner part of the muffin-tin call dgemm('N','N',lmmaxi,nri,lmmaxi,1.d0,rbshti,lmmaxi,rfmt1,lmmaxi,0.d0, & rfmt2,lmmaxi) ! transform the outer part of the muffin-tin i=lmmaxi*nri+1 call dgemm('N','N',lmmaxo,nr-nri,lmmaxo,1.d0,rbshto,lmmaxo,rfmt1(i),lmmaxo, & 0.d0,rfmt2(i),lmmaxo) end subroutine elk-7.2.42/src/PaxHeaders.21776/rfsht.f900000644000000000000000000000013214061636517014372 xustar0030 mtime=1623670095.345102093 30 atime=1623670094.121103229 30 ctime=1623670095.345102093 elk-7.2.42/src/rfsht.f900000644002504400250440000000127714061636517016436 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rfsht(nr,nri,rfmt1,rfmt2) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: rfmt1(*) real(8), intent(out) :: rfmt2(*) ! local variables integer i ! transform the inner part of the muffin-tin call dgemm('N','N',lmmaxi,nri,lmmaxi,1.d0,rfshti,lmmaxi,rfmt1,lmmaxi,0.d0, & rfmt2,lmmaxi) ! transform the outer part of the muffin-tin i=lmmaxi*nri+1 call dgemm('N','N',lmmaxo,nr-nri,lmmaxo,1.d0,rfshto,lmmaxo,rfmt1(i),lmmaxo, & 0.d0,rfmt2(i),lmmaxo) end subroutine elk-7.2.42/src/PaxHeaders.21776/genlofr.f900000644000000000000000000000013214061636517014700 xustar0030 mtime=1623670095.346102092 30 atime=1623670094.122103228 30 ctime=1623670095.346102092 elk-7.2.42/src/genlofr.f900000644002504400250440000001122314061636517016734 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genlofr ! !INTERFACE: subroutine genlofr ! !USES: use modmain ! !DESCRIPTION: ! Generates the local-orbital radial functions. This is done by integrating ! the scalar relativistic Schr\"{o}dinger equation (or its energy deriatives) ! at the current linearisation energies using the spherical part of the ! Kohn-Sham potential. For each local-orbital, a linear combination of ! {\tt lorbord} radial functions is constructed such that its radial ! derivatives up to order ${\tt lorbord}-1$ are zero at the muffin-tin radius. ! This function is normalised and the radial Hamiltonian applied to it. The ! results are stored in the global array {\tt lofr}. ! ! !REVISION HISTORY: ! Created March 2003 (JKD) ! Copied to equivalent atoms, February 2010 (A. Kozhevnikov and JKD) !EOP !BOC implicit none ! local variables integer is,ia,ja,ias,jas integer nr,nri,ir,i integer ilo,jlo,io,jo integer nn,l,info real(8) e,t1 ! automatic arrays logical done(natmmax) integer ipiv(nplorb) real(8) vr(nrmtmax),fr(nrmtmax) real(8) p0(nrmtmax,lorbordmax),p1(nrmtmax) real(8) q0(nrmtmax),q1(nrmtmax),ep0(nrmtmax,lorbordmax) real(8) p0s(nrmtmax,nlomax),ep0s(nrmtmax,nlomax) real(8) xa(nplorb),ya(nplorb) real(8) a(nplorb,nplorb),b(nplorb) ! external functions real(8), external :: splint,polynm do is=1,nspecies nr=nrmt(is) nri=nrmti(is) done(:)=.false. do ia=1,natoms(is) if (done(ia)) cycle ias=idxas(ia,is) ! use spherical part of potential i=1 do ir=1,nri vr(ir)=vsmt(i,ias)*y00 i=i+lmmaxi end do do ir=nri+1,nr vr(ir)=vsmt(i,ias)*y00 i=i+lmmaxo end do do ilo=1,nlorb(is) l=lorbl(ilo,is) do jo=1,lorbord(ilo,is) ! linearisation energy accounting for energy derivative e=lorbe(jo,ilo,ias)+dble(lorbdm(jo,ilo,is))*deapwlo ! integrate the radial Schrodinger equation call rschrodint(solsc,l,e,nr,rlmt(:,1,is),vr,nn,p0(:,jo),p1,q0,q1) ep0(1:nr,jo)=e*p0(1:nr,jo) ! normalise radial functions fr(1:nr)=p0(1:nr,jo)**2 t1=splint(nr,rlmt(:,1,is),fr) t1=1.d0/sqrt(abs(t1)) call dscal(nr,t1,p0(:,jo),1) call dscal(nr,t1,ep0(:,jo),1) ! set up the matrix of radial derivatives do i=1,nplorb ir=nr-nplorb+i xa(i)=rlmt(ir,1,is) ya(i)=p0(ir,jo)*rlmt(ir,-1,is) end do do io=1,lorbord(ilo,is) a(io,jo)=polynm(io-1,nplorb,xa,ya,rmt(is)) end do end do ! set up the target vector b(:)=0.d0 b(lorbord(ilo,is))=1.d0 call dgesv(lorbord(ilo,is),1,a,nplorb,ipiv,b,nplorb,info) if (info.ne.0) goto 10 ! generate linear superposition of radial functions p0s(:,ilo)=0.d0 ep0s(:,ilo)=0.d0 do io=1,lorbord(ilo,is) t1=b(io) call daxpy(nr,t1,p0(:,io),1,p0s(:,ilo),1) call daxpy(nr,t1,ep0(:,io),1,ep0s(:,ilo),1) end do ! normalise radial functions fr(1:nr)=p0s(1:nr,ilo)**2 t1=splint(nr,rlmt(:,1,is),fr) t1=1.d0/sqrt(abs(t1)) call dscal(nr,t1,p0s(:,ilo),1) call dscal(nr,t1,ep0s(:,ilo),1) ! subtract linear combination of previous local-orbitals with same l do jlo=1,ilo-1 if (lorbl(jlo,is).eq.l) then fr(1:nr)=p0s(1:nr,ilo)*p0s(1:nr,jlo) t1=-splint(nr,rlmt(:,1,is),fr) call daxpy(nr,t1,p0s(:,jlo),1,p0s(:,ilo),1) call daxpy(nr,t1,ep0s(:,jlo),1,ep0s(:,ilo),1) end if end do ! normalise radial functions again fr(1:nr)=p0s(1:nr,ilo)**2 t1=splint(nr,rlmt(:,1,is),fr) t1=abs(t1) if (t1.lt.1.d-25) goto 10 t1=1.d0/sqrt(t1) call dscal(nr,t1,p0s(:,ilo),1) call dscal(nr,t1,ep0s(:,ilo),1) ! divide by r and store in global array do ir=1,nr t1=rlmt(ir,-1,is) lofr(ir,1,ilo,ias)=t1*p0s(ir,ilo) lofr(ir,2,ilo,ias)=t1*ep0s(ir,ilo) end do end do done(ia)=.true. ! copy to equivalent atoms do ja=1,natoms(is) if ((.not.done(ja)).and.(eqatoms(ia,ja,is))) then jas=idxas(ja,is) do ilo=1,nlorb(is) call dcopy(nr,lofr(:,1,ilo,ias),1,lofr(:,1,ilo,jas),1) call dcopy(nr,lofr(:,2,ilo,ias),1,lofr(:,2,ilo,jas),1) end do done(ja)=.true. end if end do ! end loop over atoms and species end do end do return 10 continue write(*,*) write(*,'("Error(genlofr): degenerate local-orbital radial functions")') write(*,'(" for species ",I4)') is write(*,'(" atom ",I4)') ia write(*,'(" and local-orbital ",I4)') ilo write(*,*) stop end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rotrfmt.f900000644000000000000000000000013014061636517014737 xustar0029 mtime=1623670095.34810209 30 atime=1623670094.124103226 29 ctime=1623670095.34810209 elk-7.2.42/src/rotrfmt.f900000644002504400250440000001443114061636517017001 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rotrfmt(rot,nr,nri,rfmt1,rfmt2) use modmain implicit none ! arguments real(8), intent(in) :: rot(3,3) integer, intent(in) :: nr,nri real(8), intent(in) :: rfmt1(*) real(8), intent(out) :: rfmt2(*) ! local variables integer i ! inner part of muffin-tin call rotrflm(rot,lmaxi,nri,lmmaxi,rfmt1,rfmt2) ! outer part of muffin-tin i=lmmaxi*nri+1 call rotrflm(rot,lmaxo,nr-nri,lmmaxo,rfmt1(i),rfmt2(i)) return contains !BOP ! !ROUTINE: rotrflm ! !INTERFACE: subroutine rotrflm(rot,lmax,n,ld,rflm1,rflm2) ! !INPUT/OUTPUT PARAMETERS: ! rot : rotation matrix (in,real(3,3)) ! lmax : maximum angular momentum (in,integer) ! n : number of functions to rotate (in,integer) ! ld : leading dimension (in,integer) ! rflm1 : coefficients of the real spherical harmonic expansion for each ! function (in,real(ld,n)) ! rflm2 : coefficients of rotated functions (out,complex(ld,n)) ! !DESCRIPTION: ! Rotates a set of real functions ! $$ f_i({\bf r})=\sum_{lm}f_{lm}^iR_{lm}(\hat{\bf r}) $$ ! for all $i$, given the coefficients $f_{lm}^i$ and a rotation matrix $R$. ! This is done by first the computing the Euler angles $(\alpha,\beta,\gamma)$ ! of $R^{-1}$ (see routine {\tt roteuler}) and then applying the spherical ! harmonic rotation matrix generated by the routine {\tt rlmrot}. ! ! !REVISION HISTORY: ! Created December 2008 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: rot(3,3) integer, intent(in) :: lmax,n,ld real(8), intent(in) :: rflm1(ld,*) real(8), intent(out) :: rflm2(ld,*) ! local variables integer l,lm,nm,p real(8) det,rotp(3,3) real(8) ang(3),angi(3) ! automatic arrays real(8) d(ld,ld) if (lmax.lt.0) then write(*,*) write(*,'("Error(rotrflm): lmax < 0 : ",I8)') lmax write(*,*) stop end if if (n.eq.0) return if (n.lt.0) then write(*,*) write(*,'("Error(rotrflm): n < 0 : ",I8)') n write(*,*) stop end if ! find the determinant det=rot(1,1)*(rot(2,2)*rot(3,3)-rot(3,2)*rot(2,3)) & +rot(2,1)*(rot(3,2)*rot(1,3)-rot(1,2)*rot(3,3)) & +rot(3,1)*(rot(1,2)*rot(2,3)-rot(2,2)*rot(1,3)) ! make the rotation proper p=1 if (det.lt.0.d0) p=-1 rotp(:,:)=dble(p)*rot(:,:) ! compute the Euler angles of the rotation matrix call roteuler(rotp,ang) ! inverse rotation: the function is to be rotated, not the spherical harmonics angi(1)=-ang(3) angi(2)=-ang(2) angi(3)=-ang(1) ! determine the rotation matrix for real spherical harmonics call rlmrot(p,angi,lmax,ld,d) ! apply rotation matrix do l=0,lmax nm=2*l+1 lm=l**2+1 call dgemm('N','N',nm,n,nm,1.d0,d(lm,lm),ld,rflm1(lm,1),ld,0.d0,rflm2(lm,1), & ld) end do end subroutine !EOC !BOP ! !ROUTINE: rlmrot ! !INTERFACE: subroutine rlmrot(p,ang,lmax,ld,d) ! !INPUT/OUTPUT PARAMETERS: ! p : if p=-1 then the rotation matrix is improper (in,integer) ! ang : Euler angles; alpha, beta, gamma (in,real(3)) ! lmax : maximum angular momentum (in,integer) ! ld : leading dimension (in,integer) ! d : real spherical harmonic rotation matrix (out,real(ld,*)) ! !DESCRIPTION: ! Returns the rotation matrix in the basis of real spherical harmonics given ! the three Euler angles, $(\alpha,\beta,\gamma)$, and the parity, $p$, of the ! rotation. The matrix is determined using the formula of V. V. Nechaev, ! [{\it J. Struct. Chem.} {\bf 35}, 115 (1994)], suitably modified for our ! definition of the real spherical harmonics ($m_1>0$, $m_2>0$): ! \begin{align*} ! &\Delta^l_{00}=d^l_{00}, \\ ! &\Delta^l_{m_10}=\sqrt{2}\,(-1)^{m_1}d^l_{0m_1}\cos(m_1\alpha), \\ ! &\Delta^l_{0m_2}=\sqrt{2}\,(-1)^{m_2}d^l_{m_20}\cos(m_2\gamma), \\ ! &\Delta^l_{-m_10}=-\sqrt{2}\,d^l_{0m_1}\sin(m_1\alpha), \\ ! &\Delta^l_{0-m_2}=\sqrt{2}\,d^l_{m_20}\sin(m_2\gamma), \\ ! &\Delta^l_{m_1m_2}=(-1)^{m_1}(-1)^{m_2}\{\cos(m_1\alpha)\cos(m_2\gamma) ! [d_A+d_B]-\sin(m_1\alpha)\sin(m_2\gamma)[d_A-d_B]\}, \\ ! &\Delta^l_{m_1-m_2}=(-1)^{m_1}\{\sin(m_1\alpha)\cos(m_2\gamma) ! [d_A-d_B]+\cos(m_1\alpha)\sin(m_2\gamma)[d_A+d_B]\}, \\ ! &\Delta^l_{-m_1m_2}=-(-1)^{m_2}\{\sin(m_1\alpha)\cos(m_2\gamma) ! [d_A+d_B]+\cos(m_1\alpha)\sin(m_2\gamma)[d_A-d_B]\}, \\ ! &\Delta^l_{-m_1-m_2}=\cos(m_1\alpha)\cos(m_2\gamma) ! [d_A-d_B]-\sin(m_1\alpha)\sin(m_2\gamma)[d_A+d_B], ! \end{align*} ! where $d_A\equiv d^l_{-m_1-m_2}$, $d_B\equiv(-1)^{m_1}d^l_{m_1-m_2}$ and ! $d$ is the rotation matrix about the $y$-axis for complex spherical ! harmonics. See the routines {\tt genrlm}, {\tt roteuler} and {\tt ylmroty}. ! ! !REVISION HISTORY: ! Created December 2008 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: p real(8), intent(in) :: ang(3) integer, intent(in) :: lmax,ld real(8), intent(out) :: d(ld,*) ! local variables integer l,m1,m2,lm0,lm1,lm2 real(8), parameter :: sqtwo=1.4142135623730950488d0 real(8) s1,s2,t1,t2,t3,t4,t5,t6,t7,t8 ! automatic arrays integer lmi(-lmax:lmax) real(8) ca(lmax),sa(lmax) real(8) cg(lmax),sg(lmax) real(8) dy(ld,ld) ! generate the complex spherical harmonic rotation matrix about the y-axis call ylmroty(ang(2),lmax,ld,dy) do m1=1,lmax ca(m1)=cos(m1*ang(1)) sa(m1)=sin(m1*ang(1)) cg(m1)=cos(m1*ang(3)) sg(m1)=sin(m1*ang(3)) end do lm1=0 do l=0,lmax do m1=-l,l lm1=lm1+1 lmi(m1)=lm1 end do lm0=lmi(0) d(lm0,lm0)=dy(lm0,lm0) do m1=1,l if (mod(m1,2).eq.0) then s1=1.d0 else s1=-1.d0 end if t1=sqtwo*dy(lm0,lmi(m1)) t2=sqtwo*dy(lmi(m1),lm0) d(lmi(m1),lm0)=s1*t1*ca(m1) d(lm0,lmi(m1))=s1*t2*cg(m1) d(lmi(-m1),lm0)=-t1*sa(m1) d(lm0,lmi(-m1))=t2*sg(m1) do m2=1,l if (mod(m2,2).eq.0) then s2=1.d0 else s2=-1.d0 end if t1=ca(m1)*cg(m2) t2=sa(m1)*sg(m2) t3=sa(m1)*cg(m2) t4=ca(m1)*sg(m2) t5=dy(lmi(-m1),lmi(-m2)) t6=s1*dy(lmi(m1),lmi(-m2)) t7=t5+t6 t8=t5-t6 d(lmi(m1),lmi(m2))=s1*s2*(t1*t7-t2*t8) d(lmi(m1),lmi(-m2))=s1*(t3*t8+t4*t7) d(lmi(-m1),lmi(m2))=-s2*(t3*t7+t4*t8) d(lmi(-m1),lmi(-m2))=t1*t8-t2*t7 end do end do end do ! apply inversion if required if (p.eq.-1) then do l=1,lmax,2 lm1=l**2+1 lm2=lm1+2*l d(lm1:lm2,lm1:lm2)=-d(lm1:lm2,lm1:lm2) end do end if end subroutine !EOC end subroutine elk-7.2.42/src/PaxHeaders.21776/zfmtint.f900000644000000000000000000000013214061636517014737 xustar0030 mtime=1623670095.349102089 30 atime=1623670094.126103224 30 ctime=1623670095.349102089 elk-7.2.42/src/zfmtint.f900000644002504400250440000000112214061636517016770 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure complex(8) function zfmtint(nr,nri,wr,zfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: wr(nr) complex(8), intent(in) :: zfmt(*) ! local variables integer ir,i zfmtint=0.d0 i=1 do ir=1,nri zfmtint=zfmtint+wr(ir)*zfmt(i) i=i+lmmaxi end do do ir=nri+1,nr zfmtint=zfmtint+wr(ir)*zfmt(i) i=i+lmmaxo end do zfmtint=fourpi*y00*zfmtint end function elk-7.2.42/src/PaxHeaders.21776/zftzf.f900000644000000000000000000000013214061636517014407 xustar0030 mtime=1623670095.351102087 30 atime=1623670094.128103222 30 ctime=1623670095.351102087 elk-7.2.42/src/zftzf.f900000644002504400250440000000526714061636517016456 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zftzf(ngp,jlgpr,ylmgp,ld,sfacgp,zfmt,zfir,zfgp) use modmain implicit none ! arguments integer, intent(in) :: ngp real(8), intent(in) :: jlgpr(njcmax,nspecies,ngp) complex(8), intent(in) :: ylmgp(lmmaxo,ngp) integer, intent(in) :: ld complex(8), intent(in) :: sfacgp(ld,natmtot) complex(8), intent(in) :: zfmt(npcmtmax,natmtot),zfir(ngtc) complex(8), intent(out) :: zfgp(ngp) ! local variables integer is,ia,ias,ig integer nrc,nrci,irco,irc integer l,m,lm,i,j real(8) t0,y0 complex(8) zsm,z1,z2 ! automatic arrays complex(8) ylm(lmmaxo),zfft(ngtc) !-----------------------------------! ! interstitial contribution ! !-----------------------------------! ! multiply by coarse characteristic function zfft(:)=zfir(:)*cfrc(:) ! Fourier transform to coarse G-grid call zfftifc(3,ngdgc,-1,zfft) zfgp(1:ngp)=zfft(igfc(1:ngp)) !---------------------------------! ! muffin-tin contribution ! !---------------------------------! t0=fourpi/omega y0=t0*y00 do ig=1,ngp lm=1 do l=1,lmaxo z1=t0*zilc(l) do m=-l,l lm=lm+1 ylm(lm)=z1*ylmgp(lm,ig) end do end do do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) irco=nrci+1 do ia=1,natoms(is) ias=idxas(ia,is) zsm=0.d0 i=1 j=1 ! inner part of muffin-tin if (lmaxi.eq.1) then do irc=1,nrci zsm=zsm+wrcmt(irc,is)*(jlgpr(j,is,ig)*zfmt(i,ias)*y0+jlgpr(j+1,is,ig)& *(zfmt(i+1,ias)*ylm(2)+zfmt(i+2,ias)*ylm(3)+zfmt(i+3,ias)*ylm(4))) i=i+4 j=j+2 end do else do irc=1,nrci z1=jlgpr(j,is,ig)*zfmt(i,ias)*y0 i=i+1 j=j+1 lm=1 do l=1,lmaxi lm=lm+1 z2=zfmt(i,ias)*ylm(lm) i=i+1 do m=1-l,l lm=lm+1 z2=z2+zfmt(i,ias)*ylm(lm) i=i+1 end do z1=z1+jlgpr(j,is,ig)*z2 j=j+1 end do zsm=zsm+wrcmt(irc,is)*z1 end do end if ! outer part of muffin-tin do irc=irco,nrc z1=jlgpr(j,is,ig)*zfmt(i,ias)*y0 i=i+1 j=j+1 lm=1 do l=1,lmaxo lm=lm+1 z2=zfmt(i,ias)*ylm(lm) i=i+1 do m=1-l,l lm=lm+1 z2=z2+zfmt(i,ias)*ylm(lm) i=i+1 end do z1=z1+jlgpr(j,is,ig)*z2 j=j+1 end do zsm=zsm+wrcmt(irc,is)*z1 end do zfgp(ig)=zfgp(ig)+conjg(sfacgp(ig,ias))*zsm end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/genpmatk.f900000644000000000000000000000013214061636517015052 xustar0030 mtime=1623670095.352102086 30 atime=1623670094.129103221 30 ctime=1623670095.352102086 elk-7.2.42/src/genpmatk.f900000644002504400250440000001352014061636517017110 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genpmatk ! !INTERFACE: subroutine genpmatk(ngp,igpig,vgpc,wfmt,wfgp,pmat) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ngp : number of G+p-vectors (in,integer(nspnfv)) ! igpig : index from G+p-vectors to G-vectors (in,integer(ngkmax,nspnfv)) ! vgpc : G+p-vectors in Cartesian coordinates (in,real(3,ngkmax,nspnfv)) ! wfmt : muffin-tin wavefunction in spherical harmonics ! (in,complex(npcmtmax,natmtot,nspinor,nstsv)) ! wfgp : interstitial wavefunction in plane wave basis ! (in,complex(ngkmax,nspinor,nstsv)) ! pmat : momentum matrix elements (out,complex(nstsv,nstsv,3)) ! !DESCRIPTION: ! Calculates the momentum matrix elements ! $$ P_{ij}=\int d^3r\,\Psi_{i{\bf k}}^*({\bf r})\left(-i\nabla ! +\frac{1}{4c^2}\left[\vec{\sigma}\times\nabla V_s({\bf r})\right]\right) ! \Psi_{j{\bf k}}({\bf r}), $$ ! where $V_s$ is the Kohn-Sham effective potential. The second term in the ! brackets is only calculated if spin-orbit coupling is enabled. See Rathgen ! and Katsnelson, {\it Physica Scripta} {\bf T109}, 170 (2004). ! ! !REVISION HISTORY: ! Created November 2003 (Sharma) ! Fixed bug found by Juergen Spitaler, September 2006 (JKD) ! Added spin-orbit correction, July 2010 (JKD) ! Fixed bug found by Koichi Kitahara, January 2014 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: ngp(nspnfv),igpig(ngkmax,nspnfv) real(8), intent(in) :: vgpc(3,ngkmax,nspnfv) complex(8), intent(in) :: wfmt(npcmtmax,natmtot,nspinor,nstsv) complex(8), intent(in) :: wfgp(ngkmax,nspinor,nstsv) complex(8), intent(out) :: pmat(nstsv,nstsv,3) ! local variables integer ist,jst,ispn,jspn integer is,ia,ias integer nrc,nrci,npc integer igp,ifg,i real(8) cso complex(8) z1,z2,z11,z12,z21,z22,z31,z32 ! automatic arrays real(8) rfmt(npcmtmax) complex(8) gwfmt(npcmtmax,3,nspinor),gvmt(npcmtmax,3) complex(8) zfmt1(npcmtmax,nspinor),zfmt2(npcmtmax,3,nspinor) complex(8) z(ngkmax) ! allocatable arrays complex(8), allocatable :: gwfir(:,:) ! external functions complex(8), external :: zdotc ! coefficient of spin-orbit coupling cso=1.d0/(4.d0*solsc**2) ! zero the momentum matrix elements array pmat(:,:,:)=0.d0 !---------------------------------! ! muffin-tin contribution ! !---------------------------------! do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) ! compute gradient of potential for spin-orbit correction if required if (spinorb) then call rfmtftoc(nrc,nrci,vsmt(:,ias),rfmt) !********** out of k-loop call rtozfmt(nrc,nrci,rfmt,zfmt1) call gradzfmt(nrc,nrci,rlcmt(:,-1,is),wcrcmt(:,:,is),zfmt1,npcmtmax,gvmt) ! convert to spherical coordinates do i=1,3 zfmt1(1:npc,1)=gvmt(1:npc,i) call zbsht(nrc,nrci,zfmt1,gvmt(:,i)) end do end if do jst=1,nstsv do ispn=1,nspinor ! compute the gradient of the wavefunction call gradzfmt(nrc,nrci,rlcmt(:,-1,is),wcrcmt(:,:,is), & wfmt(:,ias,ispn,jst),npcmtmax,gwfmt(:,:,ispn)) end do ! add spin-orbit correction if required if (spinorb) then do ispn=1,nspinor ! convert wavefunction to spherical coordinates call zbsht(nrc,nrci,wfmt(:,ias,ispn,jst),zfmt1(:,ispn)) end do ! compute i σ x (grad V(r)) φ(r) do i=1,npc z1=zfmt1(i,1) z1=cmplx(-aimag(z1),dble(z1),8) z2=zfmt1(i,2) z2=cmplx(-aimag(z2),dble(z2),8) z11=gvmt(i,1)*z1; z12=gvmt(i,1)*z2 z21=gvmt(i,2)*z1; z22=gvmt(i,2)*z2 z31=gvmt(i,3)*z1; z32=gvmt(i,3)*z2 zfmt2(i,1,1)=cmplx(aimag(z32),-dble(z32),8)-z21 zfmt2(i,1,2)=cmplx(-aimag(z31),dble(z31),8)+z22 zfmt2(i,2,1)=z11-z32 zfmt2(i,2,2)=-z12-z31 zfmt2(i,3,1)=cmplx(-aimag(z12),dble(z12),8)+z22 zfmt2(i,3,2)=cmplx(aimag(z11),-dble(z11),8)+z21 end do ! convert to spherical harmonics and add to wavefunction gradient do ispn=1,nspinor do i=1,3 call zfsht(nrc,nrci,zfmt2(:,i,ispn),zfmt1) gwfmt(1:npc,i,ispn)=gwfmt(1:npc,i,ispn)+cso*zfmt1(1:npc,1) end do end do end if do i=1,3 do ispn=1,nspinor ! apply the radial integral weights call zfmtwr(nrc,nrci,wrcmt(:,is),gwfmt(:,i,ispn)) ! compute the overlaps do ist=1,jst pmat(ist,jst,i)=pmat(ist,jst,i)+zdotc(npc,wfmt(:,ias,ispn,ist),1, & gwfmt(:,i,ispn),1) end do end do end do end do end do end do !-----------------------------------! ! interstitial contribution ! !-----------------------------------! allocate(gwfir(ngtot,3)) do jst=1,nstsv do ispn=1,nspinor jspn=jspnfv(ispn) ! compute the gradient gwfir(:,:)=0.d0 do igp=1,ngp(jspn) ifg=igfft(igpig(igp,jspn)) z1=wfgp(igp,ispn,jst) gwfir(ifg,1:3)=vgpc(1:3,igp,jspn)*cmplx(-aimag(z1),dble(z1),8) end do do i=1,3 ! Fourier transform to real-space call zfftifc(3,ngridg,1,gwfir(:,i)) ! multiply by characteristic function gwfir(:,i)=gwfir(:,i)*cfunir(:) ! Fourier transform back to G-space call zfftifc(3,ngridg,-1,gwfir(:,i)) end do ! find the overlaps do i=1,3 do igp=1,ngp(jspn) ifg=igfft(igpig(igp,jspn)) z(igp)=gwfir(ifg,i) end do do ist=1,jst pmat(ist,jst,i)=pmat(ist,jst,i)+zdotc(ngp(jspn),wfgp(:,ispn,ist),1,z,1) end do end do end do end do deallocate(gwfir) ! multiply by -i and set lower triangular part do i=1,3 do jst=1,nstsv do ist=1,jst z1=pmat(ist,jst,i) z1=cmplx(aimag(z1),-dble(z1),8) pmat(ist,jst,i)=z1 pmat(jst,ist,i)=conjg(z1) end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rvfcross.f900000644000000000000000000000013114061636517015112 xustar0030 mtime=1623670095.354102084 29 atime=1623670094.13110322 30 ctime=1623670095.354102084 elk-7.2.42/src/rvfcross.f900000644002504400250440000000420614061636517017152 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rvfcross ! !INTERFACE: subroutine rvfcross(rvfmt1,rvfir1,rvfmt2,rvfir2,rvfmt3,rvfir3) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! rvfmt1 : first input muffin-tin field (in,real(npmtmax,natmtot,3)) ! rvfir1 : first input interstitial field (in,real(ngtot,3)) ! rvfmt2 : second input muffin-tin field (in,real(npmtmax,natmtot,3)) ! rvfir2 : second input interstitial field (in,real(ngtot,3)) ! rvfmt3 : output muffin-tin field (out,real(npmtmax,natmtot,3)) ! rvfir3 : output interstitial field (out,real(ngtot,3)) ! !DESCRIPTION: ! Given two real vector fields, ${\bf f}_1$ and ${\bf f}_2$, defined over the ! entire unit cell, this routine computes the local cross product ! $$ {\bf f}_3({\bf r})\equiv{\bf f}_1({\bf r})\times{\bf f}_2({\bf r}). $$ ! ! !REVISION HISTORY: ! Created February 2007 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: rvfmt1(npmtmax,natmtot,3),rvfir1(ngtot,3) real(8), intent(in) :: rvfmt2(npmtmax,natmtot,3),rvfir2(ngtot,3) real(8), intent(out) :: rvfmt3(npmtmax,natmtot,3),rvfir3(ngtot,3) ! local variables integer is,ias,nr,nri,ir,i real(8) v1(3),v2(3),v3(3) ! allocatable arrays real(8), allocatable :: rvfmt4(:,:),rvfmt5(:,:) !---------------------------! ! muffin-tin region ! !---------------------------! allocate(rvfmt4(npmtmax,3),rvfmt5(npmtmax,3)) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) do i=1,3 call rbsht(nr,nri,rvfmt1(:,ias,i),rvfmt4(:,i)) call rbsht(nr,nri,rvfmt2(:,ias,i),rvfmt5(:,i)) end do do i=1,npmt(is) v1(:)=rvfmt4(i,:) v2(:)=rvfmt5(i,:) call r3cross(v1,v2,v3) rvfmt4(i,:)=v3(:) end do do i=1,3 call rfsht(nr,nri,rvfmt4(:,i),rvfmt3(:,ias,i)) end do end do deallocate(rvfmt4,rvfmt5) !-----------------------------! ! interstitial region ! !-----------------------------! do ir=1,ngtot v1(:)=rvfir1(ir,:) v2(:)=rvfir2(ir,:) call r3cross(v1,v2,v3) rvfir3(ir,:)=v3(:) end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writeinfo.f900000644000000000000000000000013214061636517015252 xustar0030 mtime=1623670095.355102083 30 atime=1623670094.133103218 30 ctime=1623670095.355102083 elk-7.2.42/src/writeinfo.f900000644002504400250440000003271714061636517017321 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2009 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writeinfo ! !INTERFACE: subroutine writeinfo(fnum) ! !USES: use modmain use moddftu use modrdm use modxcifc use modmpi ! !INPUT/OUTPUT PARAMETERS: ! fnum : unit specifier for INFO.OUT file (in,integer) ! !DESCRIPTION: ! Outputs basic information about the run to the file {\tt INFO.OUT}. Does not ! close the file afterwards. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) ! Updated with DFT+U quantities July 2009 (FC) !EOP !BOC implicit none ! arguments integer fnum ! local variables integer i,is,ia,k,l character(10) dat,tim write(fnum,'("+----------------------------+")') write(fnum,'("| Elk version ",I1.1,".",I1.1,".",I2.2," started |")') version write(fnum,'("+----------------------------+")') call date_and_time(date=dat,time=tim) write(fnum,*) write(fnum,'("Date (YYYY-MM-DD) : ",A4,"-",A2,"-",A2)') dat(1:4),dat(5:6), & dat(7:8) write(fnum,'("Time (hh:mm:ss) : ",A2,":",A2,":",A2)') tim(1:2),tim(3:4), & tim(5:6) if (np_mpi.gt.1) then write(fnum,*) write(fnum,'("Using MPI, number of processes : ",I8)') np_mpi end if if (notelns.gt.0) then write(fnum,*) write(fnum,'("Notes :")') do i=1,notelns write(fnum,'(A)') trim(notes(i)) end do end if write(fnum,*) write(fnum,'("All units are atomic (Hartree, Bohr, etc.)")') write(fnum,*) select case(task) case(2,3) if (trdstate) then write(fnum,'("+---------------------------------------------------+")') write(fnum,'("| Geometry optimisation run resuming from STATE.OUT |")') write(fnum,'("+---------------------------------------------------+")') else write(fnum,'("+------------------------------------------------------+")') write(fnum,'("| Geometry optimisation starting from atomic densities |")') write(fnum,'("+------------------------------------------------------+")') end if case(5) write(fnum,'("+-------------------------------+")') write(fnum,'("| Ground-state Hartree-Fock run |")') write(fnum,'("+-------------------------------+")') case(300) write(fnum,'("+----------------------------------------------+")') write(fnum,'("| Reduced density matrix functional theory run |")') write(fnum,'("+----------------------------------------------+")') case default if (trdstate) then write(fnum,'("+------------------------------------------+")') write(fnum,'("| Ground-state run resuming from STATE.OUT |")') write(fnum,'("+------------------------------------------+")') else write(fnum,'("+-------------------------------------------------+")') write(fnum,'("| Ground-state run starting from atomic densities |")') write(fnum,'("+-------------------------------------------------+")') end if end select write(fnum,*) write(fnum,'("Lattice vectors :")') write(fnum,'(3G18.10)') avec(1,1),avec(2,1),avec(3,1) write(fnum,'(3G18.10)') avec(1,2),avec(2,2),avec(3,2) write(fnum,'(3G18.10)') avec(1,3),avec(2,3),avec(3,3) write(fnum,*) write(fnum,'("Reciprocal lattice vectors :")') write(fnum,'(3G18.10)') bvec(1,1),bvec(2,1),bvec(3,1) write(fnum,'(3G18.10)') bvec(1,2),bvec(2,2),bvec(3,2) write(fnum,'(3G18.10)') bvec(1,3),bvec(2,3),bvec(3,3) write(fnum,*) write(fnum,'("Unit cell volume : ",G18.10)') omega write(fnum,'("Brillouin zone volume : ",G18.10)') omegabz write(fnum,*) write(fnum,'("Muffin-tin inner radius fraction : ",G18.10)') fracinr do is=1,nspecies write(fnum,*) write(fnum,'("Species : ",I4," (",A,")")') is,trim(spsymb(is)) write(fnum,'(" parameters loaded from : ",A)') trim(spfname(is)) write(fnum,'(" name : ",A)') trim(spname(is)) write(fnum,'(" nuclear charge : ",G18.10)') spzn(is) write(fnum,'(" electronic charge : ",G18.10)') spze(is) write(fnum,'(" atomic mass : ",G18.10)') spmass(is) write(fnum,'(" muffin-tin radius : ",G18.10)') rmt(is) write(fnum,'(" number of radial points in muffin-tin : ",I6)') nrmt(is) write(fnum,'(" number on inner part of muffin-tin : ",I6)') nrmti(is) write(fnum,'(" atomic positions (lattice), magnetic fields (Cartesian) :")') do ia=1,natoms(is) write(fnum,'(I4," : ",3F12.8," ",3F12.8)') ia,atposl(:,ia,is), & bfcmt(:,ia,is) end do end do write(fnum,*) write(fnum,'("Total number of atoms per unit cell : ",I4)') natmtot write(fnum,*) write(fnum,'("Spin treatment :")') if (spinpol) then write(fnum,'(" spin-polarised")') else write(fnum,'(" spin-unpolarised")') end if if (spinorb) then write(fnum,'(" spin-orbit coupling")') end if if (spincore) then write(fnum,'(" spin-polarised core states")') end if if (spinpol) then write(fnum,'(" global magnetic field (Cartesian) : ",3G18.10)') bfieldc if (ncmag) then write(fnum,'(" non-collinear magnetisation")') else write(fnum,'(" collinear magnetisation in z-direction")') end if end if if (spinsprl) then write(fnum,'(" spin-spiral state assumed")') write(fnum,'(" q-vector (lattice) : ",3G18.10)') vqlss write(fnum,'(" q-vector (Cartesian) : ",3G18.10)') vqcss write(fnum,'(" q-vector length : ",G18.10)') sqrt(vqcss(1)**2 & +vqcss(2)**2+vqcss(3)**2) end if if (fsmtype.ne.0) then write(fnum,'(" fixed spin moment (FSM) calculation, type : ",I4)') fsmtype if (fsmtype.lt.0) then write(fnum,'(" only moment direction is fixed")') end if end if if ((abs(fsmtype).eq.1).or.(abs(fsmtype).eq.3)) then write(fnum,'(" fixing total moment to (Cartesian) :")') write(fnum,'(" ",3G18.10)') momfix end if if ((abs(fsmtype).eq.2).or.(abs(fsmtype).eq.3)) then write(fnum,'(" fixing local muffin-tin moments to (Cartesian) :")') do is=1,nspecies write(fnum,'(" species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) write(fnum,'(" ",I4,3G18.10)') ia,mommtfix(:,ia,is) end do end do end if if (tssxc) then write(fnum,'(" scaled spin exchange-correlation enabled")') write(fnum,'(" scaling factor : ",G18.10)') sxcscf end if if (ftmtype.ne.0) then write(fnum,*) write(fnum,'(" fixed tensor moment (FTM) calculation, type : ",I4)') ftmtype end if if (tefield) then write(fnum,*) write(fnum,'("Constant electric field applied across unit cell")') write(fnum,'(" field strength : ",3G18.10)') efieldc end if if (tafield) then write(fnum,*) write(fnum,'("Constant A-field applied across unit cell")') write(fnum,'(" field strength : ",3G18.10)') afieldc end if write(fnum,*) write(fnum,'("Number of Bravais lattice symmetries : ",I4)') nsymlat write(fnum,'("Number of crystal symmetries : ",I4)') nsymcrys if (tsyminv) then write(fnum,'("Crystal has inversion symmetry")') else write(fnum,'("Crystal has no inversion symmetry")') end if if (tefvr) then write(fnum,'("Real symmetric eigensolver will be used")') else write(fnum,'("Complex Hermitian eigensolver will be used")') end if write(fnum,*) if (autokpt) then write(fnum,'("Radius of sphere used to determine k-point grid density : ",& &G18.10)') radkpt end if write(fnum,'("k-point grid : ",3I6)') ngridk write(fnum,'("k-point offset : ",3G18.10)') vkloff if (reducek.eq.0) then write(fnum,'("k-point set is not reduced")') else if (reducek.eq.1) then write(fnum,'("k-point set is reduced with full crystal symmetry group")') else if (reducek.eq.2) then write(fnum,'("k-point set is reduced with symmorphic symmetries only")') else write(*,*) write(*,'("Error(writeinfo): undefined k-point reduction type : ",I8)') & reducek write(*,*) stop end if write(fnum,'("Total number of k-points : ",I8)') nkpt write(fnum,*) write(fnum,'("Muffin-tin radius times maximum |G+k| : ",G18.10)') rgkmax select case(isgkmax) case(:-4) write(fnum,'(" using largest radius")') case(-3) write(fnum,'(" using smallest radius")') case(-2) write(fnum,'(" using gkmax = rgkmax / 2")') case(-1) write(fnum,'(" using average radius")') case(1:) if (isgkmax.le.nspecies) then write(fnum,'(" using radius of species ",I4," (",A,")")') isgkmax, & trim(spsymb(isgkmax)) else write(*,*) write(*,'("Error(writeinfo): isgkmax > nspecies : ",2I8)') isgkmax,nspecies write(*,*) stop end if end select write(fnum,'("Maximum |G+k| for APW functions : ",G18.10)') gkmax write(fnum,'("Maximum (1/2)|G+k|² : ",G18.10)') 0.5d0*gkmax**2 write(fnum,'("Maximum |G| for potential and density : ",G18.10)') gmaxvr write(fnum,'("Constant for pseudocharge density : ",I4)') npsd write(fnum,'("Radial integration step length : ",I4)') lradstp write(fnum,*) write(fnum,'("G-vector grid sizes : ",3I6)') ngridg(:) write(fnum,'("Number of G-vectors : ",I8)') ngvec write(fnum,*) write(fnum,'("Maximum angular momentum used for")') write(fnum,'(" APW functions : ",I4)') lmaxapw write(fnum,'(" outer part of muffin-tin : ",I4)') lmaxo write(fnum,'(" inner part of muffin-tin : ",I4)') lmaxi write(fnum,*) write(fnum,'("Total nuclear charge : ",G18.10)') chgzn write(fnum,'("Total core charge : ",G18.10)') chgcrtot write(fnum,'("Total valence charge : ",G18.10)') chgval write(fnum,'("Total excess charge : ",G18.10)') chgexs write(fnum,'("Total electronic charge : ",G18.10)') chgtot write(fnum,*) write(fnum,'("Effective Wigner radius, rₛ : ",G18.10)') rwigner write(fnum,*) write(fnum,'("Number of empty states : ",I4)') nempty write(fnum,'("Total number of valence states : ",I4)') nstsv write(fnum,'("Total number of core states : ",I4)') nstcr write(fnum,*) if (lorbcnd) then write(fnum,'("Conduction state local-orbitals added automatically")') end if write(fnum,'("Total number of local-orbitals : ",I4)') nlotot if (tefvit) then write(fnum,*) write(fnum,'("Using iterative diagonalisation for the first-variational & &eigenvalue equation")') end if write(fnum,*) if (task.eq.5) then write(fnum,'("Hartree-Fock calculation using Kohn-Sham states")') if (hybrid) then write(fnum,'(" hybrid functional, coefficient : ",G18.10)') hybridc end if end if if (xctype(1).eq.100) then write(fnum,'("Using Libxc version ",I2.2,".",I2.2,".",I2.2)') libxcv(:) end if if (xctype(1).lt.0) then write(fnum,'("Optimised effective potential (OEP) and exact exchange (EXX)")') write(fnum,'(" Phys. Rev. B 53, 7024 (1996)")') write(fnum,'("Correlation functional : ",3I6)') abs(xctype(1)),xctype(2:3) write(fnum,'(" ",A)') trim(xcdescr) else write(fnum,'("Exchange-correlation functional : ",3I6)') xctype(:) write(fnum,'(" ",A)') trim(xcdescr) end if if (xcgrad.eq.0) then write(fnum,'(" Local density approximation (LDA)")') else if ((xcgrad.eq.1).or.(xcgrad.eq.2)) then write(fnum,'(" Generalised gradient approximation (GGA)")') else if (xcgrad.eq.3) then write(fnum,'(" meta-GGA; using kinetic energy density")') end if if (dftu.ne.0) then write(fnum,*) write(fnum,'("DFT+U calculation")') if (dftu.eq.1) then write(fnum,'(" fully localised limit (FLL)")') write(fnum,'(" see Phys. Rev. B 52, R5467 (1995)")') else if (dftu.eq.2) then write(fnum,'(" around mean field (AMF)")') write(fnum,'(" see Phys. Rev. B 49, 14211 (1994)")') else if (dftu.eq.3) then write(fnum,'(" interpolation between FLL and AMF")') write(fnum,'(" see Phys. Rev. B 67, 153106 (2003)")') else write(*,*) write(*,'("Error(writeinfo): dftu not defined : ",I8)') dftu write(*,*) stop end if do i=1,ndftu is=idftu(1,i) l=idftu(2,i) if (inpdftu.eq.1) then write(fnum,'(" species : ",I4," (",A,")",", l = ",I2,", U = ",F12.8, & &", J = ",F12.8)') is,trim(spsymb(is)),l,ujdu(1,i),ujdu(2,i) else if (inpdftu.eq.2) then write(fnum,'(" species : ",I4," (",A,")",", l = ",I2)') is, & trim(spsymb(is)),l write(fnum,'(" Slater integrals are provided as input")') do k=0,2*l,2 write(fnum,'(" F^(",I1,") = ",F12.8)') k,fdu(k,i) end do else if (inpdftu.eq.3) then write(fnum,'(" species : ",I4," (",A,")",", l = ",I2)') is, & trim(spsymb(is)),l write(fnum,'(" Racah parameters are provided as input")') do k=0,l write(fnum,'(" E^(",I1,") = ",F12.8)') k,edu(k,i) end do else if (inpdftu.eq.4) then write(fnum,'(" species : ",I4," (",A,")",", l = ",I2)') is, & trim(spsymb(is)),l write(fnum,'(" Slater integrals are calculated by means of Yukawa & &potential")') write(fnum,'(" Yukawa potential screening length (a.u^-1) : ",F12.8)') & lambdadu(i) else if(inpdftu.eq.5) then write(fnum,'(" species : ",I4," (",A,")",", l = ",I2)') is, & trim(spsymb(is)),l write(fnum,'(" Slater integrals are calculated by means of Yukawa & &potential")') write(fnum,'(" Yukawa potential screening length corresponds to U = ",& &F12.8)') udufix(i) end if end do end if if (task.eq.300) then write(fnum,*) write(fnum,'("RDMFT calculation")') write(fnum,'(" see arXiv:0801.3787v1 [cond-mat.mtrl-sci]")') write(fnum,'(" RDMFT exchange-correlation type : ",I4)') rdmxctype if (rdmxctype.eq.1) then write(fnum,'(" Hartree-Fock functional")') else if (rdmxctype.eq.2) then write(fnum,'(" Power functional, exponent : ",G18.10)') rdmalpha end if end if write(fnum,*) write(fnum,'("Smearing type : ",I4)') stype write(fnum,'(" ",A)') trim(sdescr) if (autoswidth) then write(fnum,'("Automatic determination of smearing width")') else write(fnum,'("Smearing width : ",G18.10)') swidth write(fnum,'("Effective electronic temperature (K) : ",G18.10)') tempk end if write(fnum,*) write(fnum,'("Mixing type : ",I4)') mixtype write(fnum,'(" ",A)') trim(mixdescr) flush(fnum) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/mossbauer.f900000644000000000000000000000013214061636517015244 xustar0030 mtime=1623670095.357102082 30 atime=1623670094.135103216 30 ctime=1623670095.357102082 elk-7.2.42/src/mossbauer.f900000644002504400250440000001117714061636517017310 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: mossbauer ! !INTERFACE: subroutine mossbauer ! !USES: use modmain use modmpi use modtest ! !DESCRIPTION: ! Computes the contact charge density and magnetic hyperfine field for each ! atom and outputs the data to the file {\tt MOSSBAUER.OUT}. ! See S. Bl\"{u}gel, H. Akai, R. Zeller, and P. H. Dederichs, ! {\it Phys. Rev. B} {\bf 35}, 3271 (1987). ! ! !REVISION HISTORY: ! Created May 2004 (JKD) ! Contact hyperfine field evaluated at the nuclear radius rather than averaged ! over the Thomson sphere, June 2019 (JKD) ! Added spin and orbital dipole terms, July 2019 (JKD) !EOP !BOC implicit none ! local variables integer ik,idm integer is,ia,ias integer nr,nri,nrn real(8) mc(3),bc(3),bd(3) real(8) rho0,rhon,rhoa real(8) cb,t1 ! allocatable arrays real(8), allocatable :: fr(:) ! spin dipole field prefactor cb=gfacte/(4.d0*solsc) ! initialise universal variables call init0 call init1 ! read density and potentials from file call readstate ! generate the core wavefunctions and densities call gencore ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! calculate the density call rhomag ! calculate the dipole magnetic field if required if (tbdip) call bdipole ! allocate local arrays allocate(fr(nrmtmax)) if (mp_mpi) then open(50,file='MOSSBAUER.OUT',form='FORMATTED') end if ! loop over species do is=1,nspecies nr=nrmt(is) nri=nrmti(is) nrn=nrnucl(is) ! loop over atoms do ia=1,natoms(is) ias=idxas(ia,is) if (mp_mpi) then write(50,*) write(50,*) write(50,'("Species : ",I4," (",A,"), atom : ",I4)') is,trim(spsymb(is)),& ia write(50,*) write(50,'(" approximate nuclear radius : ",G18.10)') rnucl(is) write(50,'(" number of mesh points to nuclear radius : ",I6)') nrn end if !--------------------------------! ! contact charge density ! !--------------------------------! ! extract the l=m=0 component of the muffin-tin density call rfmtlm(1,nr,nri,rhomt(:,ias),fr) rho0=fr(1)*y00 rhon=fr(nrn)*y00 t1=dot_product(wrmt(1:nrn,is),fr(1:nrn)) rhoa=fourpi*y00*t1/volnucl(is) if (mp_mpi) then write(50,*) write(50,'(" density at nuclear center : ",G18.10)') rho0 write(50,'(" density at nuclear surface : ",G18.10)') rhon write(50,'(" average contact charge density : ",G18.10)') rhoa end if !----------------------------------! ! magnetic hyperfine field ! !----------------------------------! if (spinpol) then ! contact term do idm=1,ndmag ! extract the l=m=0 component of the muffin-tin magnetisation call rfmtlm(1,nr,nri,magmt(:,ias,idm),fr) t1=dot_product(wrmt(1:nrn,is),fr(1:nrn)) mc(idm)=fourpi*y00*t1/volnucl(is) end do t1=8.d0*pi*cb/(3.d0*solsc) bc(1:ndmag)=t1*mc(1:ndmag) if (mp_mpi) then write(50,*) write(50,'(" contact magnetic moment (mu_B) : ",3G18.10)') mc(1:ndmag) write(50,'(" contact field : ",3G18.10)') bc(1:ndmag) write(50,'(" tesla : ",3G18.10)') b_si*bc(1:ndmag) end if ! spin and orbital dipole term if (tbdip) then ! extract the l=m=0 component of the dipole field do idm=1,3 call rfmtlm(1,nr,nri,bdmt(:,ias,idm),fr) t1=dot_product(wrmt(1:nrn,is),fr(1:nrn)) bd(idm)=fourpi*y00*t1/(volnucl(is)*solsc) end do if (mp_mpi) then write(50,*) if (tjr) then write(50,'(" spin and orbital dipole field : ",3G18.10)') bd else write(50,'(" spin dipole field : ",3G18.10)') bd end if write(50,'(" tesla : ",3G18.10)') b_si*bd end if ! write to test file if required call writetest(110,'hyperfine field',nv=3,tol=1.d-4,rva=bd) end if end if end do end do if (mp_mpi) then if (spinpol.and.tbdip) then write(50,*) write(50,'("Note that the contact term is implicitly included in the & &spin dipole field")') write(50,'(" but may not match exactly with the directly & &calculated value.")') end if close(50) write(*,*) write(*,'("Info(mossbauer):")') write(*,'(" Mossbauer parameters written to MOSSBAUER.OUT")') end if deallocate(fr) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/initoep.f900000644000000000000000000000013014061636517014711 xustar0029 mtime=1623670095.35910208 30 atime=1623670094.137103214 29 ctime=1623670095.35910208 elk-7.2.42/src/initoep.f900000644002504400250440000000201114061636517016742 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine initoep use modmain implicit none ! local variables integer is,ic,ist,m ! find maximum core states over all species ncrmax=0 do is=1,nspecies ic=0 do ist=1,nstsp(is) if (spcore(ist,is)) then do m=-ksp(ist,is),ksp(ist,is)-1 ic=ic+1 end do end if end do ncrmax=max(ncrmax,ic) end do ! allocate the exchange potential and magnetic field if (allocated(vxmt)) deallocate(vxmt) allocate(vxmt(npcmtmax,natmtot)) if (allocated(vxir)) deallocate(vxir) allocate(vxir(ngtot)) if (spinpol) then if (allocated(bxmt)) deallocate(bxmt) allocate(bxmt(npcmtmax,natmtot,ndmag)) if (allocated(bxir)) deallocate(bxir) allocate(bxir(ngtot,ndmag)) end if ! zero the exchange potential and magnetic field vxmt(:,:)=0.d0 vxir(:)=0.d0 if (spinpol) then bxmt(:,:,:)=0.d0 bxir(:,:)=0.d0 end if end subroutine elk-7.2.42/src/PaxHeaders.21776/i3minv.f900000644000000000000000000000013214061636517014451 xustar0030 mtime=1623670095.360102079 30 atime=1623670094.138103213 30 ctime=1623670095.360102079 elk-7.2.42/src/i3minv.f900000644002504400250440000000242114061636517016505 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2003-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: i3minv ! !INTERFACE: subroutine i3minv(a,b) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix (in,integer(3,3)) ! b : output matrix (in,integer(3,3)) ! !DESCRIPTION: ! Computes the inverse of a integer $3\times 3$ matrix: $B=A^{-1}$. ! ! !REVISION HISTORY: ! Created November 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: a(3,3) integer, intent(out) :: b(3,3) ! local variables integer m m=a(1,1)*(a(2,2)*a(3,3)-a(3,2)*a(2,3)) & +a(2,1)*(a(3,2)*a(1,3)-a(1,2)*a(3,3)) & +a(3,1)*(a(1,2)*a(2,3)-a(2,2)*a(1,3)) if ((m.ne.1).and.(m.ne.-1)) then write(*,*) write(*,'("Error(i3minv): cannot invert matrix")') write(*,'(" Determinant : ",I8)') m write(*,*) stop end if b(1,1)=m*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) b(2,1)=m*(a(2,3)*a(3,1)-a(2,1)*a(3,3)) b(3,1)=m*(a(2,1)*a(3,2)-a(2,2)*a(3,1)) b(1,2)=m*(a(1,3)*a(3,2)-a(1,2)*a(3,3)) b(2,2)=m*(a(1,1)*a(3,3)-a(1,3)*a(3,1)) b(3,2)=m*(a(1,2)*a(3,1)-a(1,1)*a(3,2)) b(1,3)=m*(a(1,2)*a(2,3)-a(1,3)*a(2,2)) b(2,3)=m*(a(1,3)*a(2,1)-a(1,1)*a(2,3)) b(3,3)=m*(a(1,1)*a(2,2)-a(1,2)*a(2,1)) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/r3mv.f900000644000000000000000000000013214061636517014133 xustar0030 mtime=1623670095.362102077 30 atime=1623670094.140103211 30 ctime=1623670095.362102077 elk-7.2.42/src/r3mv.f900000644002504400250440000000140614061636517016171 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3mv ! !INTERFACE: pure subroutine r3mv(a,x,y) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix (in,real(3,3)) ! x : input vector (in,real(3)) ! y : output vector (out,real(3)) ! !DESCRIPTION: ! Multiplies a real $3\times 3$ matrix with a vector. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: a(3,3),x(3) real(8), intent(out) :: y(3) y(1)=a(1,1)*x(1)+a(1,2)*x(2)+a(1,3)*x(3) y(2)=a(2,1)*x(1)+a(2,2)*x(2)+a(2,3)*x(3) y(3)=a(3,1)*x(1)+a(3,2)*x(2)+a(3,3)*x(3) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genidxlo.f900000644000000000000000000000013214061636517015055 xustar0030 mtime=1623670095.363102076 30 atime=1623670094.142103209 30 ctime=1623670095.363102076 elk-7.2.42/src/genidxlo.f900000644002504400250440000000164114061636517017114 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genidxlo ! !INTERFACE: subroutine genidxlo ! !USES: use modmain ! !DESCRIPTION: ! Generates an index array which maps the local-orbitals in each atom to their ! locations in the overlap or Hamiltonian matrices. Also finds the total ! number of local-orbitals. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! local variables integer is,ias,i,ilo,l,m,lm ! allocate global local-orbital index if (allocated(idxlo)) deallocate(idxlo) allocate(idxlo(lolmmax,nlomax,natmtot)) i=0 do ias=1,natmtot is=idxis(ias) do ilo=1,nlorb(is) l=lorbl(ilo,is) do m=-l,l i=i+1 lm=l*(l+1)+m+1 idxlo(lm,ilo,ias)=i end do end do end do nlotot=i end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/nuclei.f900000644000000000000000000000013214061636517014523 xustar0030 mtime=1623670095.365102074 30 atime=1623670094.143103209 30 ctime=1623670095.365102074 elk-7.2.42/src/nuclei.f900000644002504400250440000000120714061636517016560 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine nuclei use modmain implicit none ! local variables integer is,ir ! external functions real(8), external :: radnucl do is=1,nspecies ! approximate nuclear radius rnucl(is)=radnucl(spzn(is)) ! nuclear volume volnucl(is)=(4.d0/3.d0)*pi*rnucl(is)**3 ! number of radial mesh points to nuclear radius nrnucl(is)=1 do ir=1,nrmt(is) if (rsp(ir,is).gt.rnucl(is)) then nrnucl(is)=ir exit end if end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/writeefg.f900000644000000000000000000000013214061636517015060 xustar0030 mtime=1623670095.366102073 30 atime=1623670094.145103207 30 ctime=1623670095.366102073 elk-7.2.42/src/writeefg.f900000644002504400250440000000623214061636517017120 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writeefg ! !INTERFACE: subroutine writeefg ! !USES: use modmain use modtest ! !DESCRIPTION: ! Computes the electric field gradient (EFG) tensor for each atom, $\alpha$, ! and writes it to the file {\tt EFG.OUT} along with its eigenvalues. The EFG ! is defined by ! $$ V^{\alpha}_{ij}\equiv\left.\frac{\partial^2 V'_{\rm C}({\bf r})} ! {\partial{\bf r}_i\partial{\bf r}_j}\right|_{{\bf r}={\bf r}_{\alpha}}, $$ ! where $V'_{\rm C}$ is the Coulomb potential with the $l=m=0$ component ! removed in each muffin-tin. The derivatives are computed explicitly using ! the routine {\tt gradrfmt}. ! ! !REVISION HISTORY: ! Created May 2004 (JKD) ! Fixed serious problem, November 2006 (JKD) !EOP !BOC implicit none ! local variables integer, parameter :: lwork=10 integer is,ia,ias integer nr,nri,ir integer np,i,j,info real(8) efg(3,3),a(3,3) real(8) w(3),work(lwork) ! allocatable arrays real(8), allocatable :: rfmt(:),grfmt1(:,:),grfmt2(:,:) if (lmaxi.lt.2) then write(*,*) write(*,'("Error(writeefg): lmaxi too small for calculating the EFG : ",& &I4)') lmaxi write(*,'(" Run the ground-state calculation again with lmaxi >= 2")') write(*,*) stop end if ! initialise universal variables call init0 ! read density and potentials from file call readstate ! allocate local arrays allocate(rfmt(npmtmax),grfmt1(npmtmax,3),grfmt2(npmtmax,3)) open(50,file='EFG.OUT',form='FORMATTED') write(50,*) write(50,'("(electric field gradient tensor is in Cartesian coordinates)")') do is=1,nspecies nr=nrmt(is) nri=nrmti(is) np=npmt(is) do ia=1,natoms(is) ias=idxas(ia,is) write(50,*) write(50,*) write(50,'("Species : ",I4," (",A,"), atom : ",I4)') is,trim(spsymb(is)),ia ! remove the l=m=0 part of the potential rfmt(1:np)=vclmt(1:np,ias) i=1 do ir=1,nri rfmt(i)=0.d0 i=i+lmmaxi end do do ir=nri+1,nr rfmt(i)=0.d0 i=i+lmmaxo end do ! compute the gradient of the Coulomb potential call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt,npmtmax,grfmt1) do i=1,3 ! compute the gradient of the gradient call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),grfmt1(:,i),npmtmax, & grfmt2) do j=1,3 efg(i,j)=grfmt2(1,j)*y00 end do end do ! symmetrise the EFG do i=1,3 do j=i+1,3 efg(i,j)=0.5d0*(efg(i,j)+efg(j,i)) efg(j,i)=efg(i,j) end do end do write(50,*) write(50,'(" EFG tensor :")') do i=1,3 write(50,'(3G18.10)') (efg(i,j),j=1,3) end do write(50,'(" trace : ",G18.10)') efg(1,1)+efg(2,2)+efg(3,3) ! diagonalise the EFG a(:,:)=efg(:,:) call dsyev('N','U',3,a,3,w,work,lwork,info) write(50,'(" eigenvalues :")') write(50,'(3G18.10)') w end do end do close(50) write(*,*) write(*,'("Info(writeefg): electric field gradient written to EFG.OUT")') deallocate(rfmt,grfmt1,grfmt2) ! write EFG of last atom to test file call writetest(115,'electric field gradient',nv=9,tol=1.d-3,rva=efg) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writeevsp.f900000644000000000000000000000013214061636517015274 xustar0030 mtime=1623670095.368102071 30 atime=1623670094.147103205 30 ctime=1623670095.368102071 elk-7.2.42/src/writeevsp.f900000644002504400250440000000177114061636517017337 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeevsp use modmain implicit none ! local variables integer is,ist ! solve the atomic Dirac-Kohn-Sham ground-state for all species call init0 ! write out the atomic eigenvalues for each species open(50,file='EVALSP.OUT',form='FORMATTED') write(50,*) write(50,'("Kohn-Sham-Dirac eigenvalues for all atomic species")') write(50,*) write(50,'("Exchange-correlation functional : ",3I6)') xctsp(:) do is=1,nspecies write(50,*) write(50,'("Species : ",I4," (",A,")",I4)') is,trim(spsymb(is)) do ist=1,nstsp(is) write(50,'(" n = ",I2,", l = ",I2,", k = ",I2," : ",G18.10)') nsp(ist,is), & lsp(ist,is),ksp(ist,is),evalsp(ist,is) end do end do close(50) write(*,*) write(*,'("Info(writeevsp)")') write(*,'(" Kohn-Sham-Dirac eigenvalues written to EVALSP.OUT for all atomic & &species")') end subroutine elk-7.2.42/src/PaxHeaders.21776/gencore.f900000644000000000000000000000013014061636517014664 xustar0029 mtime=1623670095.36910207 30 atime=1623670094.148103204 29 ctime=1623670095.36910207 elk-7.2.42/src/gencore.f900000644002504400250440000001114314061636517016723 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: gencore ! !INTERFACE: subroutine gencore ! !USES: use modmain use modomp ! !DESCRIPTION: ! Computes the core radial wavefunctions, eigenvalues and densities. The ! radial Dirac equation is solved in the spherical part of the Kohn-Sham ! potential to which the atomic potential has been appended for ! $r>R_{\rm MT}$. In the case of spin-polarised calculations, and when ! {\tt spincore} is set to {\tt .true.}, the Dirac equation is solved in the ! spin-up and -down potentials created from the Kohn-Sham scalar potential and ! magnetic field magnitude, with the occupancy divided equally between up and ! down. The up and down densities determined in this way are added to both the ! scalar density and the magnetisation in the routine {\tt rhocore}. Note ! that this procedure is a simple, but inexact, approach to solving the radial ! Dirac equation in a magnetic field. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) ! Added polarised cores, November 2009 (JKD) !EOP !BOC implicit none ! local variables integer ist,ispn,idm,nthd integer is,ia,ja,ias,jas integer nr,nri,nrs,ir real(8) v(ndmag),t1 ! automatic arrays logical done(natmmax) real(8) vr(nrspmax),br(nrmtmax),fr(nrmtmax) real(8) eval(nstspmax) ! external functions real(8), external :: rfmtint ! loop over species and atoms do is=1,nspecies nr=nrmt(is) nri=nrmti(is) nrs=nrsp(is) done(:)=.false. do ia=1,natoms(is) if (done(ia)) cycle ias=idxas(ia,is) ! Kohn-Sham magnetic field for spin-polarised core if (spincore) then ! compute the averaged direction of the exchange-correlation magnetic field do idm=1,ndmag v(idm)=rfmtint(nr,nri,wrmt(:,is),bxcmt(:,ias,idm)) end do ! normalise if (ncmag) then t1=sqrt(v(1)**2+v(2)**2+v(3)**2) else t1=abs(v(1)) end if if (t1.gt.1.d-10) v(:)=v(:)/t1 ! determine the component of the field along the averaged direction br(1:nr)=0.d0 do idm=1,ndmag ! extract the spherical (l=m=0) component of B_xc call rfmtlm(1,nr,nri,bxcmt(:,ias,idm),fr) t1=v(idm)*y00 call daxpy(nr,t1,fr,1,br,1) end do end if ! loop over spin channels do ispn=1,nspncr ! use the spherical part of the crystal Kohn-Sham potential call rfmtlm(1,nr,nri,vsmt(:,ias),vr) vr(1:nr)=vr(1:nr)*y00 ! spin-up and -down potentials for polarised core if (spincore) then if (ispn.eq.1) then vr(1:nr)=vr(1:nr)-br(1:nr) else vr(1:nr)=vr(1:nr)+br(1:nr) end if end if ! append the Kohn-Sham potential from the atomic calculation for r > R_MT t1=vr(nr)-vrsp(nr,is) do ir=nr+1,nrs vr(ir)=vrsp(ir,is)+t1 end do rhocr(:,ias,ispn)=0.d0 call holdthd(nstsp(is),nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(t1,ir) SHARED(is) & !$OMP NUM_THREADS(nthd) do ist=1,nstsp(is) if (spcore(ist,is)) then ! solve the Dirac equation eval(ist)=evalcr(ist,ias) call rdirac(solsc,nsp(ist,is),lsp(ist,is),ksp(ist,is),nrs,rsp(:,is), & vr,eval(ist),rwfcr(:,1,ist,ias),rwfcr(:,2,ist,ias)) if (spincore) then ! use the spin-averaged eigenvalue for the polarised core if (ispn.eq.1) then evalcr(ist,ias)=eval(ist) else evalcr(ist,ias)=0.5d0*(evalcr(ist,ias)+eval(ist)) end if t1=0.5d0*occcr(ist,ias) else evalcr(ist,ias)=eval(ist) t1=occcr(ist,ias) end if ! add to the core density !$OMP CRITICAL(gencore_) do ir=1,nr rhocr(ir,ias,ispn)=rhocr(ir,ias,ispn) & +t1*(rwfcr(ir,1,ist,ias)**2+rwfcr(ir,2,ist,ias)**2) end do !$OMP END CRITICAL(gencore_) end if end do !$OMP END PARALLEL DO call freethd(nthd) do ir=1,nr rhocr(ir,ias,ispn)=rhocr(ir,ias,ispn)*rlmt(ir,-2,is)*y00 end do ! end loop over spin channels end do done(ia)=.true. ! copy to equivalent atoms do ja=1,natoms(is) if ((.not.done(ja)).and.(eqatoms(ia,ja,is))) then jas=idxas(ja,is) do ist=1,nstsp(is) if (spcore(ist,is)) then evalcr(ist,jas)=evalcr(ist,ias) rwfcr(1:nrs,:,ist,jas)=rwfcr(1:nrs,:,ist,ias) end if end do rhocr(1:nr,jas,:)=rhocr(1:nr,ias,:) done(ja)=.true. end if end do ! end loop over species and atoms end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/r3mtv.f900000644000000000000000000000013214061636517014317 xustar0030 mtime=1623670095.371102069 30 atime=1623670094.150103202 30 ctime=1623670095.371102069 elk-7.2.42/src/r3mtv.f900000644002504400250440000000143114061636517016353 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3mtv ! !INTERFACE: pure subroutine r3mtv(a,x,y) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix (in,real(3,3)) ! x : input vector (in,real(3)) ! y : output vector (out,real(3)) ! !DESCRIPTION: ! Multiplies the transpose of a real $3\times 3$ matrix with a vector. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: a(3,3),x(3) real(8), intent(out) :: y(3) y(1)=a(1,1)*x(1)+a(2,1)*x(2)+a(3,1)*x(3) y(2)=a(1,2)*x(1)+a(2,2)*x(2)+a(3,2)*x(3) y(3)=a(1,3)*x(1)+a(2,3)*x(2)+a(3,3)*x(3) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/r3minv.f900000644000000000000000000000013014061636517014460 xustar0030 mtime=1623670095.372102068 28 atime=1623670094.1521032 30 ctime=1623670095.372102068 elk-7.2.42/src/r3minv.f900000644002504400250440000000235414061636517016523 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3minv ! !INTERFACE: subroutine r3minv(a,b) ! !INPUT/OUTPUT PARAMETERS: ! a : input matrix (in,real(3,3)) ! b : output matrix (out,real(3,3)) ! !DESCRIPTION: ! Computes the inverse of a real $3\times 3$ matrix. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: a(3,3) real(8), intent(out) :: b(3,3) ! local variables real(8) t1 t1=a(1,2)*a(2,3)*a(3,1)-a(1,3)*a(2,2)*a(3,1)+a(1,3)*a(2,1)*a(3,2) & -a(1,1)*a(2,3)*a(3,2)+a(1,1)*a(2,2)*a(3,3)-a(1,2)*a(2,1)*a(3,3) if (abs(t1).lt.1.d-40) then write(*,*) write(*,'("Error(r3minv): singular matrix")') write(*,*) stop end if t1=1.d0/t1 b(1,1)=t1*(a(2,2)*a(3,3)-a(2,3)*a(3,2)) b(2,1)=t1*(a(2,3)*a(3,1)-a(2,1)*a(3,3)) b(3,1)=t1*(a(2,1)*a(3,2)-a(2,2)*a(3,1)) b(1,2)=t1*(a(1,3)*a(3,2)-a(1,2)*a(3,3)) b(2,2)=t1*(a(1,1)*a(3,3)-a(1,3)*a(3,1)) b(3,2)=t1*(a(1,2)*a(3,1)-a(1,1)*a(3,2)) b(1,3)=t1*(a(1,2)*a(2,3)-a(1,3)*a(2,2)) b(2,3)=t1*(a(1,3)*a(2,1)-a(1,1)*a(2,3)) b(3,3)=t1*(a(1,1)*a(2,2)-a(1,2)*a(2,1)) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/r3frac.f900000644000000000000000000000013214061636517014424 xustar0030 mtime=1623670095.374102066 30 atime=1623670094.154103198 30 ctime=1623670095.374102066 elk-7.2.42/src/r3frac.f900000644002504400250440000000222714061636517016464 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: r3frac ! !INTERFACE: pure subroutine r3frac(eps,v) ! !INPUT/OUTPUT PARAMETERS: ! eps : zero component tolerance (in,real) ! v : input vector (inout,real(3)) ! !DESCRIPTION: ! Finds the fractional part of each component of a real 3-vector using the ! function ${\rm frac}\,(x)=x-\lfloor x\rfloor$. A component is taken to be ! zero if it lies within the intervals $[0,\epsilon)$ or $(1-\epsilon,1]$. ! ! !REVISION HISTORY: ! Created January 2003 (JKD) ! Removed iv, September 2011 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: eps real(8), intent(inout) :: v(3) ! local variables real(8) t1 t1=1.d0-eps v(1)=v(1)-int(v(1)) if (v(1).lt.0.d0) v(1)=v(1)+1.d0 if ((v(1).lt.eps).or.(v(1).gt.t1)) v(1)=0.d0 v(2)=v(2)-int(v(2)) if (v(2).lt.0.d0) v(2)=v(2)+1.d0 if ((v(2).lt.eps).or.(v(2).gt.t1)) v(2)=0.d0 v(3)=v(3)-int(v(3)) if (v(3).lt.0.d0) v(3)=v(3)+1.d0 if ((v(3).lt.eps).or.(v(3).gt.t1)) v(3)=0.d0 end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genapwlofr.f900000644000000000000000000000013214061636517015410 xustar0030 mtime=1623670095.375102065 30 atime=1623670094.155103197 30 ctime=1623670095.375102065 elk-7.2.42/src/genapwlofr.f900000644002504400250440000000134414061636517017447 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genapwlofr use modomp implicit none ! local variables integer nthd call holdthd(2,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP SECTIONS !$OMP SECTION ! generate the APW radial functions call genapwfr !$OMP SECTION ! generate the local-orbital radial functions call genlofr !$OMP END SECTIONS !$OMP SECTIONS !$OMP SECTION ! compute the overlap radial integrals call olprad !$OMP SECTION ! compute the Hamiltonian radial integrals call hmlrad !$OMP END SECTIONS !$OMP END PARALLEL call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/gridsize.f900000644000000000000000000000013214061636517015064 xustar0030 mtime=1623670095.377102063 30 atime=1623670094.157103195 30 ctime=1623670095.377102063 elk-7.2.42/src/gridsize.f900000644002504400250440000000342014061636517017120 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: gridsize ! !INTERFACE: subroutine gridsize(avec,gmaxvr,ngridg,ngtot,intgv) ! !INPUT/OUTPUT PARAMETERS: ! avec : lattice vectors (in,real(3,3)) ! gmaxvr : G-vector cut-off (in,real) ! ngridg : G-vector grid sizes (out,integer(3)) ! ngtot : total number of G-vectors (out,integer) ! intgv : integer grid intervals for each direction (out,integer(2,3)) ! !DESCRIPTION: ! Finds the ${\bf G}$-vector grid which completely contains the vectors with ! $G1/2 \end{array}\right. $$ ! ! !REVISION HISTORY: ! Created July 2008 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: x if (abs(x).le.0.5d0) then sdelta_sq=1.d0 else sdelta_sq=0.d0 end if end function !EOC elk-7.2.42/src/PaxHeaders.21776/potxcir.f900000644000000000000000000000013214061636517014734 xustar0030 mtime=1623670095.390102051 30 atime=1623670094.171103182 30 ctime=1623670095.390102051 elk-7.2.42/src/potxcir.f900000644002504400250440000002044314061636517016774 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potxcir(xctype_,rhoir_,magir_,tauir_,exir_,ecir_,vxcir_,bxcir_, & wxcir_) use modmain use modxcifc implicit none ! arguments integer, intent(in) :: xctype_(3) real(8), intent(in) :: rhoir_(ngtot),magir_(ngtot,ndmag),tauir_(ngtot,nspinor) real(8), intent(out) :: exir_(ngtot),ecir_(ngtot) real(8), intent(out) :: vxcir_(ngtot),bxcir_(ngtot,ndmag),wxcir_(ngtot) ! local variables integer n,i real(8) t0,t1,t2,t3,t4 ! allocatable arrays real(8), allocatable :: rhoup(:),rhodn(:) real(8), allocatable :: gvrho(:,:),gvup(:,:),gvdn(:,:) real(8), allocatable :: grho(:),gup(:),gdn(:) real(8), allocatable :: g2rho(:),g2up(:),g2dn(:) real(8), allocatable :: g3rho(:),g3up(:),g3dn(:) real(8), allocatable :: grho2(:),gup2(:),gdn2(:),gupdn(:) real(8), allocatable :: vx(:),vxup(:),vxdn(:) real(8), allocatable :: vc(:),vcup(:),vcdn(:) real(8), allocatable :: dxdgr2(:),dxdgu2(:),dxdgd2(:),dxdgud(:) real(8), allocatable :: dcdgr2(:),dcdgu2(:),dcdgd2(:),dcdgud(:) real(8), allocatable :: dxdg2r(:),dxdg2u(:),dxdg2d(:) real(8), allocatable :: dcdg2r(:),dcdg2u(:),dcdg2d(:) real(8), allocatable :: wx(:),wxup(:),wxdn(:) real(8), allocatable :: wc(:),wcup(:),wcdn(:) n=ngtot if (spinpol) then allocate(rhoup(n),rhodn(n)) allocate(vxup(n),vxdn(n),vcup(n),vcdn(n)) if (xcgrad.eq.1) then allocate(grho(n),gup(n),gdn(n)) allocate(g2up(n),g2dn(n)) allocate(g3rho(n),g3up(n),g3dn(n)) else if (xcgrad.eq.2) then allocate(g2up(n),g2dn(n)) allocate(gvup(n,3),gvdn(n,3)) allocate(gup2(n),gdn2(n),gupdn(n)) allocate(dxdgu2(n),dxdgd2(n),dxdgud(n)) allocate(dcdgu2(n),dcdgd2(n),dcdgud(n)) else if (xcgrad.eq.3) then allocate(g2up(n),g2dn(n)) allocate(gvup(n,3),gvdn(n,3)) allocate(gup2(n),gdn2(n),gupdn(n)) else if (xcgrad.eq.4) then allocate(g2up(n),g2dn(n)) allocate(gvup(n,3),gvdn(n,3)) allocate(gup2(n),gdn2(n),gupdn(n)) allocate(dxdgu2(n),dxdgd2(n),dxdgud(n)) allocate(dcdgu2(n),dcdgd2(n),dcdgud(n)) allocate(dxdg2u(n),dxdg2d(n)) allocate(dcdg2u(n),dcdg2d(n)) allocate(wxup(n),wxdn(n),wcup(n),wcdn(n)) end if else allocate(vx(n),vc(n)) if (xcgrad.eq.1) then allocate(grho(n),g2rho(n),g3rho(n)) else if (xcgrad.eq.2) then allocate(g2rho(n),gvrho(n,3),grho2(n)) allocate(dxdgr2(n),dcdgr2(n)) else if (xcgrad.eq.3) then allocate(g2rho(n),gvrho(n,3),grho2(n)) else if (xcgrad.eq.4) then allocate(g2rho(n),gvrho(n,3),grho2(n)) allocate(dxdgr2(n),dcdgr2(n)) allocate(dxdg2r(n),dcdg2r(n)) allocate(wx(n),wc(n)) end if end if if (spinpol) then !------------------------! ! spin-polarised ! !------------------------! if (ncmag) then ! non-collinear if (xcgrad.eq.0) then ! LSDA do i=1,n t0=rhoir_(i) t1=sqrt(magir_(i,1)**2+magir_(i,2)**2+magir_(i,3)**2)*sxcscf rhoup(i)=0.5d0*(t0+t1) rhodn(i)=0.5d0*(t0-t1) end do else ! functionals which require gradients do i=1,n t0=rhoir_(i) t1=sqrt(magir_(i,1)**2+magir_(i,2)**2+magir_(i,3)**2+dncgga)*sxcscf rhoup(i)=0.5d0*(t0+t1) rhodn(i)=0.5d0*(t0-t1) end do end if else ! collinear do i=1,n t0=rhoir_(i) t1=magir_(i,1)*sxcscf rhoup(i)=0.5d0*(t0+t1) rhodn(i)=0.5d0*(t0-t1) end do end if if (xcgrad.le.0) then call xcifc(xctype_,n,tempa=swidth,rhoup=rhoup,rhodn=rhodn,ex=exir_, & ec=ecir_,vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn) else if (xcgrad.eq.1) then call ggair_sp_1(rhoup,rhodn,grho,gup,gdn,g2up,g2dn,g3rho,g3up,g3dn) call xcifc(xctype_,n,rhoup=rhoup,rhodn=rhodn,grho=grho,gup=gup,gdn=gdn, & g2up=g2up,g2dn=g2dn,g3rho=g3rho,g3up=g3up,g3dn=g3dn,ex=exir_,ec=ecir_, & vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn) else if (xcgrad.eq.2) then call ggair_sp_2a(rhoup,rhodn,g2up,g2dn,gvup,gvdn,gup2,gdn2,gupdn) call xcifc(xctype_,n,rhoup=rhoup,rhodn=rhodn,gup2=gup2,gdn2=gdn2, & gupdn=gupdn,ex=exir_,ec=ecir_,vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn, & dxdgu2=dxdgu2,dxdgd2=dxdgd2,dxdgud=dxdgud,dcdgu2=dcdgu2,dcdgd2=dcdgd2, & dcdgud=dcdgud) call ggair_sp_2b(g2up,g2dn,gvup,gvdn,vxup,vxdn,vcup,vcdn,dxdgu2,dxdgd2, & dxdgud,dcdgu2,dcdgd2,dcdgud) else if (xcgrad.eq.3) then call ggair_sp_2a(rhoup,rhodn,g2up,g2dn,gvup,gvdn,gup2,gdn2,gupdn) call xcifc(xctype_,n,c_tb09=c_tb09,rhoup=rhoup,rhodn=rhodn,g2up=g2up, & g2dn=g2dn,gup2=gup2,gdn2=gdn2,gupdn=gupdn,tauup=tauir_(:,1), & taudn=tauir_(:,2),vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn) exir_(:)=0.d0; ecir_(:)=0.d0 else if (xcgrad.eq.4) then call ggair_sp_2a(rhoup,rhodn,g2up,g2dn,gvup,gvdn,gup2,gdn2,gupdn) call xcifc(xctype_,n,rhoup=rhoup,rhodn=rhodn,g2up=g2up,g2dn=g2dn, & gup2=gup2,gdn2=gdn2,gupdn=gupdn,tauup=tauir_(:,1),taudn=tauir_(:,2), & ex=exir_,ec=ecir_,vxup=vxup,vxdn=vxdn,vcup=vcup,vcdn=vcdn,dxdgu2=dxdgu2, & dxdgd2=dxdgd2,dxdgud=dxdgud,dcdgu2=dcdgu2,dcdgd2=dcdgd2,dcdgud=dcdgud, & dxdg2u=dxdg2u,dxdg2d=dxdg2d,dcdg2u=dcdg2u,dcdg2d=dcdg2d,wxup=wxup, & wxdn=wxdn,wcup=wcup,wcdn=wcdn) call ggair_sp_2b(g2up,g2dn,gvup,gvdn,vxup,vxdn,vcup,vcdn,dxdgu2,dxdgd2, & dxdgud,dcdgu2,dcdgd2,dcdgud) wxcir_(:)=0.5d0*(wxup(:)+wxdn(:)+wcup(:)+wcdn(:)) end if ! hybrid functionals if (hybrid) then t1=1.d0-hybridc ! scale exchange part of energy exir_(:)=t1*exir_(:) ! scale exchange part of potential vxup(:)=t1*vxup(:) vxdn(:)=t1*vxdn(:) end if if (ncmag) then ! non-collinear: spin rotate the local exchange potential do i=1,n t1=vxup(i)+vcup(i) t2=vxdn(i)+vcdn(i) vxcir_(i)=0.5d0*(t1+t2) ! determine the exchange-correlation magnetic field t3=0.5d0*(t1-t2) t4=rhoup(i)-rhodn(i) if (abs(t4).gt.1.d-8) t4=t3/t4 bxcir_(i,:)=magir_(i,:)*t4 end do else ! collinear do i=1,n t1=vxup(i)+vcup(i) t2=vxdn(i)+vcdn(i) vxcir_(i)=0.5d0*(t1+t2) bxcir_(i,1)=0.5d0*(t1-t2) end do end if ! scale field if required if (tssxc) bxcir_(:,1:ndmag)=bxcir_(:,1:ndmag)*sxcscf else !--------------------------! ! spin-unpolarised ! !--------------------------! if (xcgrad.le.0) then call xcifc(xctype_,n,tempa=swidth,rho=rhoir_,ex=exir_,ec=ecir_,vx=vx,vc=vc) else if (xcgrad.eq.1) then call ggair_1(rhoir_,grho,g2rho,g3rho) call xcifc(xctype_,n,rho=rhoir_,grho=grho,g2rho=g2rho,g3rho=g3rho,ex=exir_,& ec=ecir_,vx=vx,vc=vc) else if (xcgrad.eq.2) then call ggair_2a(rhoir_,g2rho,gvrho,grho2) call xcifc(xctype_,n,rho=rhoir_,grho2=grho2,ex=exir_,ec=ecir_,vx=vx,vc=vc, & dxdgr2=dxdgr2,dcdgr2=dcdgr2) call ggair_2b(g2rho,gvrho,vx,vc,dxdgr2,dcdgr2) else if (xcgrad.eq.3) then call ggair_2a(rhoir_,g2rho,gvrho,grho2) call xcifc(xctype_,n,c_tb09=c_tb09,rho=rhoir_,g2rho=g2rho,grho2=grho2, & tau=tauir_,vx=vx,vc=vc) exir_(:)=0.d0; ecir_(:)=0.d0 else if (xcgrad.eq.4) then call ggair_2a(rhoir_,g2rho,gvrho,grho2) call xcifc(xctype_,n,rho=rhoir_,g2rho=g2rho,grho2=grho2,tau=tauir_, & ex=exir_,ec=ecir_,vx=vx,vc=vc,dxdgr2=dxdgr2,dcdgr2=dcdgr2,dxdg2r=dxdg2r, & dcdg2r=dcdg2r,wx=wx,wc=wc) call ggair_2b(g2rho,gvrho,vx,vc,dxdgr2,dcdgr2) wxcir_(:)=wx(:)+wc(:) end if ! hybrid functionals if (hybrid) then t1=1.d0-hybridc ! scale exchange part of energy exir_(:)=t1*exir_(:) ! scale exchange part of potential vxcir_(:)=t1*vx(:)+vc(:) else vxcir_(:)=vx(:)+vc(:) end if end if if (spinpol) then deallocate(rhoup,rhodn,vxup,vxdn,vcup,vcdn) if (xcgrad.eq.1) then deallocate(grho,gup,gdn,g2up,g2dn,g3rho,g3up,g3dn) else if (xcgrad.eq.2) then deallocate(g2up,g2dn) deallocate(gvup,gvdn) deallocate(gup2,gdn2,gupdn) deallocate(dxdgu2,dxdgd2,dxdgud) deallocate(dcdgu2,dcdgd2,dcdgud) else if (xcgrad.eq.3) then deallocate(g2up,g2dn) deallocate(gvup,gvdn) deallocate(gup2,gdn2,gupdn) end if else deallocate(vx,vc) if (xcgrad.eq.1) then deallocate(grho,g2rho,g3rho) else if (xcgrad.eq.2) then deallocate(g2rho,gvrho,grho2) deallocate(dxdgr2,dcdgr2) else if (xcgrad.eq.3) then deallocate(g2rho,gvrho,grho2) else if (xcgrad.eq.4) then deallocate(g2rho,gvrho,grho2) deallocate(dxdgr2,dcdgr2,dxdg2r,dcdg2r) deallocate(wx,wc) end if end if end subroutine elk-7.2.42/src/PaxHeaders.21776/potxc.f900000644000000000000000000000013214061636517014401 xustar0030 mtime=1623670095.392102049 30 atime=1623670094.173103181 30 ctime=1623670095.392102049 elk-7.2.42/src/potxc.f900000644002504400250440000000501314061636517016435 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: potxc ! !INTERFACE: subroutine potxc(tsh,xctype_,rhomt_,rhoir_,magmt_,magir_,taumt_,tauir_,exmt_, & exir_,ecmt_,ecir_,vxcmt_,vxcir_,bxcmt_,bxcir_,wxcmt_,wxcir_) ! !USES: use modmain use modomp ! !DESCRIPTION: ! Computes the exchange-correlation potential and energy density. In the ! muffin-tin, the density is transformed from spherical harmonic coefficients ! $\rho_{lm}$ to spherical coordinates $(\theta,\phi)$ with a backward ! spherical harmonic transformation (SHT). Once calculated, the ! exchange-correlation potential and energy density are transformed with a ! forward SHT. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) !EOP !BOC implicit none ! arguments logical, intent(in) :: tsh integer, intent(in) :: xctype_(3) real(8), intent(in) :: rhomt_(npmtmax,natmtot),rhoir_(ngtot) real(8), intent(in) :: magmt_(npmtmax,natmtot,ndmag),magir_(ngtot,ndmag) real(8), intent(in) :: taumt_(npmtmax,natmtot,nspinor),tauir_(ngtot,nspinor) real(8), intent(out) :: exmt_(npmtmax,natmtot),exir_(ngtot) real(8), intent(out) :: ecmt_(npmtmax,natmtot),ecir_(ngtot) real(8), intent(out) :: vxcmt_(npmtmax,natmtot),vxcir_(ngtot) real(8), intent(out) :: bxcmt_(npmtmax,natmtot,ndmag),bxcir_(ngtot,ndmag) real(8), intent(out) :: wxcmt_(npmtmax,natmtot),wxcir_(ngtot) ! local variables integer ias,nthd1,nthd2 call holdthd(2,nthd1) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(nthd2,ias) & !$OMP NUM_THREADS(nthd1) !$OMP SECTIONS !$OMP SECTION ! muffin-tin exchange-correlation potential, field and energy density call holdthd(natmtot,nthd2) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd2) do ias=1,natmtot call potxcmt(tsh,ias,xctype_,rhomt_,magmt_,taumt_,exmt_,ecmt_,vxcmt_,bxcmt_, & wxcmt_) end do !$OMP END PARALLEL DO call freethd(nthd2) !$OMP SECTION ! interstitial exchange-correlation potential, field and energy density call potxcir(xctype_,rhoir_,magir_,tauir_,exir_,ecir_,vxcir_,bxcir_,wxcir_) !$OMP END SECTIONS ! symmetrise the exchange-correlation potential and magnetic field if (tsh) then !$OMP SECTIONS !$OMP SECTION call symrf(nrmt,nrmti,npmt,ngridg,ngtot,ngvec,igfft,npmtmax,vxcmt_,vxcir_) !$OMP SECTION if (spinpol) call symrvf(.true.,ncmag,nrmt,nrmti,npmt,ngridg,ngtot,ngvec, & igfft,npmtmax,bxcmt_,ngtot,bxcir_) !$OMP END SECTIONS end if !$OMP END PARALLEL call freethd(nthd1) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rzfmtinp.f900000644000000000000000000000013214061636517015115 xustar0030 mtime=1623670095.393102048 30 atime=1623670094.175103179 30 ctime=1623670095.393102048 elk-7.2.42/src/rzfmtinp.f900000644002504400250440000000202014061636517017144 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure complex(8) function rzfmtinp(nr,nri,wr,rfmt,zfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: wr(nr) real(8), intent(in) :: rfmt(*) complex(8), intent(in) :: zfmt(*) ! local variables integer n,ir,i complex(8) z1,z2 ! compute the dot-products for each radial point and integrate over r z1=0.d0 i=1 if (lmaxi.eq.1) then do ir=1,nri z1=z1+wr(ir) & *(rfmt(i)*zfmt(i) & +rfmt(i+1)*zfmt(i+1) & +rfmt(i+2)*zfmt(i+2) & +rfmt(i+3)*zfmt(i+3)) i=i+4 end do z1=pi*z1 else n=lmmaxi-1 do ir=1,nri z1=z1+wr(ir)*dot_product(rfmt(i:i+n),zfmt(i:i+n)) i=i+lmmaxi end do z1=(fourpi/dble(lmmaxi))*z1 end if z2=0.d0 n=lmmaxo-1 do ir=nri+1,nr z2=z2+wr(ir)*dot_product(rfmt(i:i+n),zfmt(i:i+n)) i=i+lmmaxo end do rzfmtinp=z1+(fourpi/dble(lmmaxo))*z2 end function elk-7.2.42/src/PaxHeaders.21776/rhoplot.f900000644000000000000000000000013214061636517014733 xustar0030 mtime=1623670095.395102046 30 atime=1623670094.177103177 30 ctime=1623670095.395102046 elk-7.2.42/src/rhoplot.f900000644002504400250440000000254614061636517016777 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rhoplot ! !INTERFACE: subroutine rhoplot ! !USES: use modmain ! !DESCRIPTION: ! Outputs the charge density, read in from {\tt STATE.OUT}, for 1D, 2D or 3D ! plotting. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! initialise universal variables call init0 ! read density from file call readstate ! write the density plot to file select case(task) case(31) open(50,file='RHO1D.OUT',form='FORMATTED',action='WRITE') open(51,file='RHOLINES.OUT',form='FORMATTED',action='WRITE') call plot1d(50,51,1,rhomt,rhoir) close(50) close(51) write(*,*) write(*,'("Info(rhoplot):")') write(*,'(" 1D density plot written to RHO1D.OUT")') write(*,'(" vertex location lines written to RHOLINES.OUT")') case(32) open(50,file='RHO2D.OUT',form='FORMATTED',action='WRITE') call plot2d(.false.,50,1,rhomt,rhoir) close(50) write(*,*) write(*,'("Info(rhoplot): 2D density plot written to RHO2D.OUT")') case(33) open(50,file='RHO3D.OUT',form='FORMATTED',action='WRITE') call plot3d(50,1,rhomt,rhoir) close(50) write(*,*) write(*,'("Info(rhoplot): 3D density plot written to RHO3D.OUT")') end select end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/occupy.f900000644000000000000000000000013214061636517014546 xustar0030 mtime=1623670095.396102045 30 atime=1623670094.178103176 30 ctime=1623670095.396102045 elk-7.2.42/src/occupy.f900000644002504400250440000000633614061636517016613 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: occupy ! !INTERFACE: subroutine occupy ! !USES: use modmain use modtest ! !DESCRIPTION: ! Finds the Fermi energy and sets the occupation numbers for the ! second-variational states using the routine {\tt fermi}. ! ! !REVISION HISTORY: ! Created February 2004 (JKD) ! Added gap estimation, November 2009 (F. Cricchio) ! Added adaptive smearing width, April 2010 (T. Bjorkman) !EOP !BOC implicit none ! local variables integer, parameter :: maxit=1000 integer ik,ist,it real(8) e0,e1,e real(8) chg,w,x,t1 ! external functions real(8), external :: sdelta,stheta ! determine the smearing width automatically if required if ((autoswidth).and.(iscl.gt.1)) call findswidth ! find minimum and maximum eigenvalues e0=evalsv(1,1) e1=e0 do ik=1,nkpt do ist=1,nstsv e=evalsv(ist,ik) if (e.lt.e0) e0=e if (e.gt.e1) e1=e end do end do if (e0.lt.e0min) then write(*,*) write(*,'("Warning(occupy): minimum eigenvalue less than minimum & &linearisation energy : ",2G18.10)') e0,e0min write(*,'(" for s.c. loop ",I5)') iscl end if t1=1.d0/swidth ! determine the Fermi energy using the bisection method do it=1,maxit efermi=0.5d0*(e0+e1) chg=0.d0 do ik=1,nkpt w=wkpt(ik) do ist=1,nstsv e=evalsv(ist,ik) if (e.lt.e0min) then occsv(ist,ik)=0.d0 else x=(efermi-e)*t1 occsv(ist,ik)=occmax*stheta(stype,x) chg=chg+w*occsv(ist,ik) end if end do end do if (chg.lt.chgval) then e0=efermi else e1=efermi end if if ((e1-e0).lt.1.d-12) goto 10 end do write(*,*) write(*,'("Warning(occupy): could not find Fermi energy")') 10 continue ! find the density of states at the Fermi surface in units of ! states/Hartree/unit cell fermidos=0.d0 do ik=1,nkpt w=wkpt(ik) do ist=1,nstsv x=(evalsv(ist,ik)-efermi)*t1 fermidos=fermidos+w*sdelta(stype,x)*t1 end do if (abs(occsv(nstsv,ik)).gt.epsocc) then write(*,*) write(*,'("Warning(occupy): not enough empty states for k-point ",I6)') ik write(*,'(" and s.c. loop ",I5)') iscl end if end do fermidos=fermidos*occmax ! write Fermi density of states to test file call writetest(500,'DOS at Fermi energy',tol=5.d-3,rv=fermidos) ! estimate the indirect band gap (FC) e0=-1.d8 e1=1.d8 ikgap(1)=1 ikgap(2)=1 ! these loops are inefficiently ordered to fix a bug in versions 17 and 18 of ! the Intel compiler do ist=1,nstsv do ik=1,nkpt e=evalsv(ist,ik) if (e.lt.efermi) then if (e.gt.e0) then e0=e ikgap(1)=ik end if else if (e.lt.e1) then e1=e ikgap(2)=ik end if end if end do end do bandgap(1)=e1-e0 ! write band gap to test file call writetest(510,'estimated indirect band gap',tol=2.d-2,rv=bandgap(1)) ! estimate the direct band gap e=1.d8 ikgap(3)=1 do ik=1,nkpt e0=-1.d8 e1=1.d8 do ist=1,nstsv t1=evalsv(ist,ik) if (t1.le.efermi) then if (t1.gt.e0) e0=t1 else if (t1.lt.e1) e1=t1 end if end do t1=e1-e0 if (t1.lt.e) then e=t1 ikgap(3)=ik end if end do bandgap(2)=e end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/symveca.f900000644000000000000000000000013214061636517014713 xustar0030 mtime=1623670095.398102044 30 atime=1623670094.180103174 30 ctime=1623670095.398102044 elk-7.2.42/src/symveca.f900000644002504400250440000000224114061636517016747 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: symveca ! !INTERFACE: subroutine symveca(vca) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! vca : vectors in Cartesian coordinates for all atoms (in,real(3,natmtot)) ! !DESCRIPTION: ! Symmetrises a 3-vector at each atomic site by rotating and averaging over ! equivalent atoms. Only the spatial part of each crystal symmetry is used. ! ! !REVISION HISTORY: ! Created June 2004 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(inout) :: vca(3,natmtot) ! local variables integer is,ia,ja,ias,jas integer isym,lspl real(8) v(3),t1 ! automatic arrays real(8) vs(3,natmtot) ! make symmetric average vs(:,:)=0.d0 do isym=1,nsymcrys lspl=lsplsymc(isym) do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) ja=ieqatom(ia,is,isym) jas=idxas(ja,is) call r3mv(symlatc(:,:,lspl),vca(:,jas),v) vs(:,ias)=vs(:,ias)+v(:) end do end do end do ! normalise t1=1.d0/dble(nsymcrys) vca(:,:)=t1*vs(:,:) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/jprplot.f900000644000000000000000000000013214061636517014736 xustar0030 mtime=1623670095.399102043 30 atime=1623670094.182103172 30 ctime=1623670095.399102043 elk-7.2.42/src/jprplot.f900000644002504400250440000000334414061636517016777 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine jprplot use modmain use modmpi implicit none ! local variables integer ik ! initialise universal variables call init0 call init1 ! read density and potentials from file call readstate ! generate the core wavefunctions and densities call gencore ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the occupancies from file do ik=1,nkpt call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! compute the paramagnetic current density call genjpr ! plot the current density (master process only) if (mp_mpi) then write(*,*) write(*,'("Info(jprplot):")') select case(task) case(371) open(50,file='JPR1D.OUT',form='FORMATTED') open(51,file='JPRLINES.OUT',form='FORMATTED') call plot1d(50,51,3,jrmt,jrir) close(50) write(*,'(" 1D paramagnetic current density written to JPR1D.OUT")') write(*,'(" vertex location lines written to JPRLINES.OUT")') case(372) open(50,file='JPR2D.OUT',form='FORMATTED') call plot2d(.true.,50,3,jrmt,jrir) close(50) write(*,'(" 2D paramagnetic current density written to JPR2D.OUT")') write(*,'(" Note that the 3D vector field has been locally projected")') write(*,'(" onto the 2D plotting plane axes")') case(373) open(50,file='JPR3D.OUT',form='FORMATTED') call plot3d(50,3,jrmt,jrir) close(50) write(*,'(" 3D paramagnetic current density written to JPR3D.OUT")') end select end if end subroutine elk-7.2.42/src/PaxHeaders.21776/genvmatk.f900000644000000000000000000000013214061636517015060 xustar0030 mtime=1623670095.401102041 30 atime=1623670094.183103171 30 ctime=1623670095.401102041 elk-7.2.42/src/genvmatk.f900000644002504400250440000000522414061636517017120 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genvmatk(vmt,vir,ngp,igpig,wfmt,ld,wfgp,vmat) use modmain use modomp implicit none ! arguments ! the potential is multiplied by the radial integration weights in the ! muffin-tin and by the characteristic function in the interstitial region real(8), intent(in) :: vmt(npcmtmax,natmtot),vir(ngtot) integer, intent(in) :: ngp(nspnfv),igpig(ngkmax,nspnfv) complex(8), intent(in) :: wfmt(npcmtmax,natmtot,nspinor,nstsv) integer, intent(in) :: ld complex(8), intent(in) :: wfgp(ld,nspinor,nstsv) complex(8), intent(out) :: vmat(nstsv,nstsv) ! local variables integer ist,jst,ispn,jspn integer is,ias,npc,igp,nthd ! automatic arrays complex(8) wfmt1(npcmtmax),z(ngkmax) ! allocatable arrays complex(8), allocatable :: wfir(:) ! external functions complex(8), external :: zdotc ! zero the matrix elements vmat(:,:)=0.d0 !-------------------------! ! muffin-tin part ! !-------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(wfmt1,ispn,ias) & !$OMP PRIVATE(is,npc,ist) & !$OMP NUM_THREADS(nthd) do jst=1,nstsv do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) npc=npcmt(is) ! apply potential to wavefunction wfmt1(1:npc)=vmt(1:npc,ias)*wfmt(1:npc,ias,ispn,jst) ! compute the inner products do ist=1,jst vmat(ist,jst)=vmat(ist,jst)+zdotc(npc,wfmt(:,ias,ispn,ist),1,wfmt1,1) end do end do end do end do !$OMP END PARALLEL DO call freethd(nthd) !---------------------------! ! interstitial part ! !---------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfir,z,ispn,jspn) & !$OMP PRIVATE(igp,ist) & !$OMP NUM_THREADS(nthd) allocate(wfir(ngtot)) !$OMP DO do jst=1,nstsv do ispn=1,nspinor jspn=jspnfv(ispn) ! Fourier transform wavefunction to real-space wfir(:)=0.d0 do igp=1,ngp(jspn) wfir(igfft(igpig(igp,jspn)))=wfgp(igp,ispn,jst) end do call zfftifc(3,ngridg,1,wfir) ! apply potential to wavefunction wfir(1:ngtot)=vir(1:ngtot)*wfir(1:ngtot) ! Fourier transform to G+p-space call zfftifc(3,ngridg,-1,wfir) do igp=1,ngp(jspn) z(igp)=wfir(igfft(igpig(igp,jspn))) end do do ist=1,jst ! compute inner product vmat(ist,jst)=vmat(ist,jst)+zdotc(ngp(jspn),wfgp(:,ispn,ist),1,z,1) end do end do end do !$OMP END DO deallocate(wfir) !$OMP END PARALLEL call freethd(nthd) ! lower triangular part do ist=1,nstsv do jst=1,ist-1 vmat(ist,jst)=conjg(vmat(jst,ist)) end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/geomopt.f900000644000000000000000000000012714061636517014722 xustar0029 mtime=1623670095.40210204 29 atime=1623670094.18510317 29 ctime=1623670095.40210204 elk-7.2.42/src/geomopt.f900000644002504400250440000001377314061636517016766 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine geomopt use modmain use modmpi use modstore use moddelf implicit none ! local variables integer istp,jstp,i real(8) ds ! initialise global variables (and the muffin-tin radii) call init0 call init1 ! smooth the exchange-correlation potentials and fields msmooth_=msmooth msmooth=4 ! store orginal volume omega_=omega ! atomic forces are required tforce=.true. if (task.eq.3) then trdstate=.true. else trdstate=.false. end if ! initial atomic step sizes if (allocated(tauatp)) deallocate(tauatp) allocate(tauatp(natmtot)) tauatp(:)=tau0atp ! initialise the previous total force on each atom if (allocated(forcetotp)) deallocate(forcetotp) allocate(forcetotp(3,natmtot)) forcetotp(:,:)=0.d0 ! initial lattice optimisation step size taulatv(:)=tau0latv ! initialise previous stress tensor stressp(:)=0.d0 if (mp_mpi) then ! open TOTENERGY.OUT open(71,file='TOTENERGY_OPT.OUT',form='FORMATTED') ! open FORCEMAX.OUT open(72,file='FORCEMAX.OUT',form='FORMATTED') ! open GEOMETRY_OPT.OUT open(73,file='GEOMETRY_OPT.OUT',form='FORMATTED') ! open IADIST_OPT.OUT open(74,file='IADIST_OPT.OUT',form='FORMATTED') ! open FORCES_OPT.OUT open(75,file='FORCES_OPT.OUT',form='FORMATTED') ! open MOMENTM_OPT.OUT if (spinpol) then open(78,file='MOMENTM_OPT.OUT',form='FORMATTED') end if ! open STRESSMAX.OUT and STRESS_OPT.OUT if required if (latvopt.ne.0) then open(86,file='STRESSMAX.OUT',form='FORMATTED') open(87,file='STRESS_OPT.OUT',form='FORMATTED') open(88,file='OMEGA_OPT.OUT',form='FORMATTED') end if end if if (mp_mpi) write(*,*) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) do istp=1,maxlatvstp do jstp=1,maxatpstp if (atpopt.eq.0) exit if (mp_mpi) then write(*,'("Info(geomopt): Atomic position optimisation step : ",I6)') jstp end if ! ground-state and forces calculation call gndstate ! check for stop signal if (tstop) goto 10 ! subsequent calculations will read in the potential from STATE.OUT trdstate=.true. ! update the atomic positions call atpstep ! write total energy, forces, atomic positions, interatomic distances to file if (mp_mpi) then write(71,'(G22.12)') engytot flush(71) write(72,'(G18.10)') forcemax flush(72) write(73,*); write(73,*) write(73,'("! Atomic position optimisation step : ",I6)') jstp call writegeom(73) flush(73) write(74,*); write(74,*) write(74,'("Atomic position optimisation step : ",I6)') jstp call writeiad(74) flush(74) write(75,*); write(75,*) write(75,'("Atomic position optimisation step : ",I6)') jstp call writeforces(75) write(75,*) write(75,'("Maximum force magnitude over all atoms (target) : ",G18.10,& &" (",G18.10,")")') forcemax,epsforce flush(75) if (spinpol) then write(78,'(G22.12)') momtotm flush(78) end if end if ! broadcast forcemax from master process to all other processes call mpi_bcast(forcemax,1,mpi_double_precision,0,mpicom,ierror) ! check force convergence if (forcemax.le.epsforce) then if (mp_mpi) then write(75,*) write(75,'("Force convergence target achieved")') end if exit end if if (mp_mpi.and.(jstp.eq.maxatpstp)) then write(*,*) write(*,'("Warning(geomopt): atomic position optimisation failed to & &converge in ",I6," steps")') maxatpstp end if ! store the current forces array forcetotp(:,:)=forcetot(:,:) ! end loop over atomic position optimisation end do ! exit lattice optimisation loop if required if (latvopt.eq.0) exit if (mp_mpi) then write(*,'("Info(geomopt): Lattice optimisation step : ",I6)') istp end if ! generate the stress tensor call genstress ! take average of current and previous stress tensors stress(:)=0.5d0*(stress(:)+stressp(:)) ! check for stop signal if (tstop) goto 10 ! update the lattice vectors call latvstep ! write stress tensor components and maximum magnitude to file if (mp_mpi) then write(71,'(G22.12)') engytot flush(71) write(73,*); write(73,*) write(73,'("! Lattice optimisation step : ",I6)') istp call writegeom(73) flush(73) write(74,*); write(74,*) write(74,'("Lattice optimisation step : ",I6)') istp call writeiad(74) flush(74) if (spinpol) then write(78,'(G22.12)') momtotm flush(78) end if write(86,'(G18.10)') stressmax flush(86) write(87,*) write(87,'("Lattice optimisation step : ",I6)') istp write(87,'("Derivative of total energy w.r.t. strain tensors :")') do i=1,nstrain write(87,'(G18.10)') stress(i) end do flush(87) write(88,'(G18.10)') omega flush(88) end if ! check for stress convergence if (latvopt.eq.1) then ds=sum(abs(stress(:))) else ! stress may be non-zero because of volume constraint; check change in stress ! tensor instead ds=sum(abs(stress(:)-stressp(:))) end if ! broadcase ds from master process to all other processes call mpi_bcast(ds,1,mpi_double_precision,0,mpicom,ierror) if ((istp.ge.3).and.(ds.le.epsstress*tau0latv)) then if (mp_mpi) then write(87,*) write(87,'("Stress convergence target achieved")') end if exit end if if (mp_mpi.and.(istp.eq.maxlatvstp)) then write(*,*) write(*,'("Warning(geomopt): lattice optimisation failed to converge in ",& &I6," steps")') maxlatvstp end if stressp(1:nstrain)=stress(1:nstrain) ! delete the eigenvector files call delfiles(evec=.true.) ! end loop over lattice optimisation end do 10 continue if (mp_mpi) then close(71); close(72); close(73); close(74); close(75) if (spinpol) close(78) if (latvopt.ne.0) then close(86); close(87); close(88) end if end if ! ground-state should be run again after lattice optimisation if (latvopt.ne.0) call gndstate ! restore original parameters msmooth=msmooth_ end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqnss.f900000644000000000000000000000013214061636517014730 xustar0030 mtime=1623670095.404102038 30 atime=1623670094.187103168 30 ctime=1623670095.404102038 elk-7.2.42/src/eveqnss.f900000644002504400250440000001472014061636517016771 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine eveqnss(ngp,igpig,apwalm,evalfv,evecfv,evalsvp,evecsv) use modmain use moddftu use modomp implicit none ! arguments integer, intent(in) :: ngp(nspnfv),igpig(ngkmax,nspnfv) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv) real(8), intent(in) :: evalfv(nstfv,nspnfv) complex(8), intent(in) :: evecfv(nmatmax,nstfv,nspnfv) real(8), intent(out) :: evalsvp(nstsv) complex(8), intent(out) :: evecsv(nstsv,nstsv) ! local variables integer ist,jst,ispn integer is,ias,i,j,k integer nrc,nrci,nrco integer l,lm,nm,npc,npci integer igp,ld,nthd real(8) ts0,ts1 complex(8) zq ! automatic arrays complex(8) wfmt2(npcmtmax,nspnfv),wfmt4(npcmtmax) complex(8) wfmt31(npcmtmax),wfmt32(npcmtmax),wfmt33(npcmtmax) complex(8) wfgp1(ngkmax),wfgp2(ngkmax),wfgp3(ngkmax) ! allocatable arrays complex(8), allocatable :: wfmt1(:,:,:),wfir1(:,:),wfir2(:) ! external functions complex(8), external :: zdotc if (.not.spinpol) then write(*,*) write(*,'("Error(eveqnss): spin-unpolarised calculation")') write(*,*) stop end if call timesec(ts0) ld=lmmaxdm*nspinor ! zero the second-variational Hamiltonian (stored in the eigenvector array) evecsv(:,:)=0.d0 !-------------------------! ! muffin-tin part ! !-------------------------! allocate(wfmt1(npcmtmax,nstfv,nspnfv)) call holdthd(nstfv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfmt2,wfmt31,wfmt32,wfmt33,wfmt4) & !$OMP PRIVATE(ias,is,nrc,nrci,nrco) & !$OMP PRIVATE(npc,npci,zq,ispn) & !$OMP PRIVATE(ist,jst,l,nm,lm,i,j,k) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) nrco=nrc-nrci npc=npcmt(is) npci=npcmti(is) ! de-phasing factor (FC, FB & LN) if (ssdph) zq=zqss(ias) ! compute the first-variational wavefunctions do ispn=1,nspnfv if (ssdph.and.(ispn.eq.2)) zq=conjg(zq) !$OMP DO do ist=1,nstfv call wavefmt(lradstp,ias,ngp(ispn),apwalm(:,:,:,ias,ispn), & evecfv(:,ist,ispn),wfmt1(:,ist,ispn)) ! de-phase if required if (ssdph) wfmt1(1:npc,ist,ispn)=zq*wfmt1(1:npc,ist,ispn) end do !$OMP END DO end do !$OMP DO do jst=1,nstfv ! convert wavefunction to spherical coordinates do ispn=1,nspnfv call zbsht(nrc,nrci,wfmt1(:,jst,ispn),wfmt2(:,ispn)) end do ! apply effective magnetic field and convert to spherical harmonics wfmt4(1:npc)=bsmt(1:npc,ias,3)*wfmt2(1:npc,1) call zfsht(nrc,nrci,wfmt4,wfmt31) wfmt4(1:npc)=-bsmt(1:npc,ias,3)*wfmt2(1:npc,2) call zfsht(nrc,nrci,wfmt4,wfmt32) wfmt4(1:npc)=cmplx(bsmt(1:npc,ias,1),-bsmt(1:npc,ias,2),8)*wfmt2(1:npc,2) call zfsht(nrc,nrci,wfmt4,wfmt33) ! apply muffin-tin potential matrix if required if (tvmatmt) then do l=0,lmaxdm if (tvmmt(l,ias)) then nm=2*l+1 lm=l**2+1 i=npci+lm if (l.le.lmaxi) then call zgemm('N','N',nm,nrci,nm,zone,vmatmt(lm,1,lm,1,ias),ld, & wfmt1(lm,jst,1),lmmaxi,zone,wfmt31(lm),lmmaxi) end if call zgemm('N','N',nm,nrco,nm,zone,vmatmt(lm,1,lm,1,ias),ld, & wfmt1(i,jst,1),lmmaxo,zone,wfmt31(i),lmmaxo) if (l.le.lmaxi) then call zgemm('N','N',nm,nrci,nm,zone,vmatmt(lm,2,lm,2,ias),ld, & wfmt1(lm,jst,2),lmmaxi,zone,wfmt32(lm),lmmaxi) end if call zgemm('N','N',nm,nrco,nm,zone,vmatmt(lm,2,lm,2,ias),ld, & wfmt1(i,jst,2),lmmaxo,zone,wfmt32(i),lmmaxo) if (l.le.lmaxi) then call zgemm('N','N',nm,nrci,nm,zone,vmatmt(lm,1,lm,2,ias),ld, & wfmt1(lm,jst,2),lmmaxi,zone,wfmt33(lm),lmmaxi) end if call zgemm('N','N',nm,nrco,nm,zone,vmatmt(lm,1,lm,2,ias),ld, & wfmt1(i,jst,2),lmmaxo,zone,wfmt33(i),lmmaxo) end if end do end if ! add to second-variational Hamiltonian matrix ! upper diagonal block call zfmtwr(nrc,nrci,wrcmt(:,is),wfmt31) do ist=1,jst evecsv(ist,jst)=evecsv(ist,jst)+zdotc(npc,wfmt1(:,ist,1),1,wfmt31,1) end do j=jst+nstfv ! lower diagonal block call zfmtwr(nrc,nrci,wrcmt(:,is),wfmt32) do ist=1,jst i=ist+nstfv evecsv(i,j)=evecsv(i,j)+zdotc(npc,wfmt1(:,ist,2),1,wfmt32,1) end do ! off-diagonal block call zfmtwr(nrc,nrci,wrcmt(:,is),wfmt33) do ist=1,nstfv evecsv(ist,j)=evecsv(ist,j)+zdotc(npc,wfmt1(:,ist,1),1,wfmt33,1) end do end do !$OMP END DO ! end loop over atoms end do !$OMP END PARALLEL call freethd(nthd) deallocate(wfmt1) !---------------------------! ! interstitial part ! !---------------------------! call holdthd(nstfv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfir1,wfir2,wfgp1,wfgp2,wfgp3) & !$OMP PRIVATE(ispn,igp,ist,i,j) & !$OMP NUM_THREADS(nthd) allocate(wfir1(ngtot,nspnfv),wfir2(ngtot)) ! begin loop over states !$OMP DO do jst=1,nstfv do ispn=1,nspnfv wfir1(:,ispn)=0.d0 do igp=1,ngp(ispn) wfir1(igfft(igpig(igp,ispn)),ispn)=evecfv(igp,jst,ispn) end do ! Fourier transform wavefunction to real-space call zfftifc(3,ngridg,1,wfir1(:,ispn)) end do ! multiply with magnetic field and transform to G-space wfir2(1:ngtot)=bsir(1:ngtot,3)*wfir1(1:ngtot,1) call zfftifc(3,ngridg,-1,wfir2) do igp=1,ngp(1) wfgp1(igp)=wfir2(igfft(igpig(igp,1))) end do wfir2(1:ngtot)=-bsir(1:ngtot,3)*wfir1(1:ngtot,2) call zfftifc(3,ngridg,-1,wfir2) do igp=1,ngp(2) wfgp2(igp)=wfir2(igfft(igpig(igp,2))) end do wfir2(1:ngtot)=cmplx(bsir(1:ngtot,1),-bsir(1:ngtot,2),8)*wfir1(1:ngtot,2) call zfftifc(3,ngridg,-1,wfir2) do igp=1,ngp(1) wfgp3(igp)=wfir2(igfft(igpig(igp,1))) end do ! add to second-variational Hamiltonian matrix ! upper diagonal block do ist=1,jst evecsv(ist,jst)=evecsv(ist,jst)+zdotc(ngp(1),evecfv(:,ist,1),1,wfgp1,1) end do ! lower diagonal block j=jst+nstfv do ist=1,jst i=ist+nstfv evecsv(i,j)=evecsv(i,j)+zdotc(ngp(2),evecfv(:,ist,2),1,wfgp2,1) end do ! off-diagonal block do ist=1,nstfv evecsv(ist,j)=evecsv(ist,j)+zdotc(ngp(1),evecfv(:,ist,1),1,wfgp3,1) end do end do !$OMP END DO deallocate(wfir1,wfir2) !$OMP END PARALLEL call freethd(nthd) ! add the diagonal first-variational part i=0 do ispn=1,nspinor do ist=1,nstfv i=i+1 evecsv(i,i)=evecsv(i,i)+evalfv(ist,ispn) end do end do ! diagonalise the second-variational Hamiltonian call eveqnzh(nstsv,nstsv,evecsv,evalsvp) call timesec(ts1) !$OMP ATOMIC timesv=timesv+ts1-ts0 end subroutine elk-7.2.42/src/PaxHeaders.21776/hartfock.f900000644000000000000000000000013214061636517015045 xustar0030 mtime=1623670095.405102037 30 atime=1623670094.189103166 30 ctime=1623670095.405102037 elk-7.2.42/src/hartfock.f900000644002504400250440000001575614061636517017120 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine hartfock use modmain use modmpi use modomp implicit none ! local variables integer ik,lp,nthd real(8) etp,de ! allocatable arrays real(8), allocatable :: vmt(:,:),vir(:) real(8), allocatable :: bmt(:,:,:),bir(:,:) complex(8), allocatable :: evecsv(:,:) ! initialise universal variables call init0 call init1 call init2 ! read the charge density from file call readstate ! Fourier transform Kohn-Sham potential to G-space call genvsig ! generate the core wavefunctions and densities call gencore ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! generate the spin-orbit coupling radial functions call gensocfr ! generate the first- and second-variational eigenvectors and eigenvalues call genevfsv ! find the occupation numbers and Fermi energy call occupy ! generate the kinetic matrix elements in the first-variational basis call genkmat(.true.,.true.) ! allocate local arrays allocate(vmt(npcmtmax,natmtot),vir(ngtot)) if (hybrid.and.spinpol) then allocate(bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag)) end if ! only the MPI master process should write files if (mp_mpi) then ! open HF_INFO.OUT file open(60,file='HF_INFO'//trim(filext),form='FORMATTED') ! open TOTENERGY.OUT open(61,file='TOTENERGY'//trim(filext),form='FORMATTED') ! open FERMIDOS.OUT open(62,file='FERMIDOS'//trim(filext),form='FORMATTED') ! open MOMENT.OUT if required if (spinpol) open(63,file='MOMENT'//trim(filext),form='FORMATTED') ! open GAP.OUT open(64,file='GAP'//trim(filext),form='FORMATTED') ! open DTOTENERGY.OUT open(66,file='DTOTENERGY'//trim(filext),form='FORMATTED') ! open MOMENTM.OUT if (spinpol) open(68,file='MOMENTM'//trim(filext),form='FORMATTED') ! write out general information to HF_INFO.OUT call writeinfo(60) end if ! set last self-consistent loop flag tlast=.false. etp=0.d0 ! begin the self-consistent loop if (mp_mpi) then write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop started |")') write(60,'("+------------------------------+")') end if do iscl=1,maxscl if (mp_mpi) then write(60,*) write(60,'("+--------------------+")') write(60,'("| Loop number : ",I4," |")') iscl write(60,'("+--------------------+")') flush(60) write(*,*) write(*,'("Info(hartfock): self-consistent loop number : ",I4)') iscl end if if (iscl.ge.maxscl) then if (mp_mpi) then write(60,*) write(60,'("Reached self-consistent loops maximum")') end if tlast=.true. end if ! reset the OpenMP thread variables call omp_reset ! compute the Hartree-Fock local potentials call hflocal(vmt,vir,bmt,bir) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evecsv) & !$OMP NUM_THREADS(nthd) allocate(evecsv(nstsv,nstsv)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call getevecsv(filext,ik,vkl(:,ik),evecsv) ! solve the Hartree-Fock eigenvalue equation call eveqnhf(ik,vmt,vir,bmt,bir,evecsv) ! write the eigenvalues/vectors to file call putevalsv(filext,ik,evalsv(:,ik)) call putevecsv(filext,ik,evecsv) end do !$OMP END DO deallocate(evecsv) !$OMP END PARALLEL call freethd(nthd) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! broadcast eigenvalue array to every process do ik=1,nkpt lp=mod(ik-1,np_mpi) call mpi_bcast(evalsv(:,ik),nstsv,mpi_double_precision,lp,mpicom,ierror) end do ! find the occupation numbers and Fermi energy call occupy if (mp_mpi) then ! write the occupation numbers to file do ik=1,nkpt call putoccsv(filext,ik,occsv(:,ik)) end do ! write out the eigenvalues and occupation numbers call writeeval ! write the Fermi energy to file call writefermi end if ! generate the density and magnetisation call rhomag ! compute the energy components call energy if (mp_mpi) then ! output energy components call writeengy(60) write(60,*) write(60,'("Density of states at Fermi energy : ",G18.10)') fermidos write(60,'(" (states/Hartree/unit cell)")') write(60,*) write(60,'("Estimated indirect band gap : ",G18.10)') bandgap(1) write(60,'(" from k-point ",I6," to k-point ",I6)') ikgap(1),ikgap(2) write(60,'("Estimated direct band gap : ",G18.10)') bandgap(2) write(60,'(" at k-point ",I6)') ikgap(3) ! write total energy to TOTENERGY.OUT write(61,'(G22.12)') engytot flush(61) ! write DOS at Fermi energy to FERMIDOS.OUT write(62,'(G18.10)') fermidos flush(62) ! output charges and moments call writechg(60) if (spinpol) then call writemom(60) ! write total moment to MOMENT.OUT write(63,'(3G18.10)') momtot(1:ndmag) flush(63) ! write total moment magnitude to MOMENTM.OUT write(68,'(G18.10)') momtotm flush(68) end if ! write estimated Hartree-Fock indirect band gap write(64,'(G22.12)') bandgap(1) flush(64) end if if (tlast) goto 10 ! compute the change in total energy and check for convergence if (iscl.ge.2) then de=abs(engytot-etp) if (mp_mpi) then write(60,*) write(60,'("Absolute change in total energy (target) : ",G18.10," (",& &G18.10,")")') de,epsengy end if if (de.lt.epsengy) then if (mp_mpi) then write(60,*) write(60,'("Energy convergence target achieved")') end if tlast=.true. end if if (mp_mpi) then write(66,'(G18.10)') de flush(66) end if end if etp=engytot ! check for STOP file call checkstop if (tstop) tlast=.true. ! broadcast tlast from master process to all other processes call mpi_bcast(tlast,1,mpi_logical,0,mpicom,ierror) end do 10 continue if (mp_mpi) then write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop stopped |")') write(60,'("+------------------------------+")') if (maxscl.gt.1) then call writestate write(60,*) write(60,'("Wrote STATE.OUT")') end if end if !-----------------------! ! compute forces ! !-----------------------! if (tforce) then call force ! output forces to HF_INFO.OUT if (mp_mpi) call writeforces(60) end if if (mp_mpi) then write(60,*) write(60,'("+----------------------------+")') write(60,'("| Elk version ",I1.1,".",I1.1,".",I2.2," stopped |")') version write(60,'("+----------------------------+")') ! close the HF_INFO.OUT file close(60) ! close the TOTENERGY.OUT file close(61) ! close the FERMIDOS.OUT file close(62) ! close the MOMENT.OUT and MOMENTM.OUT files if (spinpol) then close(63); close(68) end if ! close the GAP.OUT file close(64) ! close the DTOTENERGY.OUT file close(66) end if deallocate(vmt,vir) if (hybrid.and.spinpol) deallocate(bmt,bir) end subroutine elk-7.2.42/src/PaxHeaders.21776/potplot.f900000644000000000000000000000013214061636517014745 xustar0030 mtime=1623670095.407102035 30 atime=1623670094.190103165 30 ctime=1623670095.407102035 elk-7.2.42/src/potplot.f900000644002504400250440000000411614061636517017004 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: potplot ! !INTERFACE: subroutine potplot ! !USES: use modmain ! !DESCRIPTION: ! Outputs the exchange, correlation and Coulomb potentials, read in from ! {\tt STATE.OUT}, for 1D, 2D or 3D plotting. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! initialise universal variables call init0 ! read the density and potentials from file call readstate ! write the potential plots to file select case(task) case(41) open(50,file='VCL1D.OUT',form='FORMATTED',action='WRITE') open(51,file='VLINES.OUT',form='FORMATTED',action='WRITE') call plot1d(50,51,1,vclmt,vclir) close(50) close(51) open(50,file='VXC1D.OUT',form='FORMATTED',action='WRITE') open(51,file='VLINES.OUT',form='FORMATTED',action='WRITE') call plot1d(50,51,1,vxcmt,vxcir) close(50) close(51) write(*,*) write(*,'("Info(potplot):")') write(*,'(" 1D Coulomb potential plot written to VCL1D.OUT")') write(*,'(" 1D exchange-correlation potential plot written to VXC1D.OUT")') write(*,'(" vertex location lines written to VLINES.OUT")') case(42) open(50,file='VCL2D.OUT',form='FORMATTED',action='WRITE') call plot2d(.false.,50,1,vclmt,vclir) close(50) open(50,file='VXC2D.OUT',form='FORMATTED',action='WRITE') call plot2d(.false.,50,1,vxcmt,vxcir) close(50) write(*,*) write(*,'("Info(potplot):")') write(*,'(" 2D Coulomb potential plot written to VCL2D.OUT")') write(*,'(" 2D exchange-correlation potential plot written to VXC2D.OUT")') case(43) open(50,file='VCL3D.OUT',form='FORMATTED',action='WRITE') call plot3d(50,1,vclmt,vclir) close(50) open(50,file='VXC3D.OUT',form='FORMATTED',action='WRITE') call plot3d(50,1,vxcmt,vxcir) close(50) write(*,*) write(*,'("Info(potplot):")') write(*,'(" 3D Coulomb potential plot written to VCL3D.OUT")') write(*,'(" 3D exchange-correlation potential plot written to VXC3D.OUT")') end select end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genwfpw.f900000644000000000000000000000013214061636517014721 xustar0030 mtime=1623670095.409102033 30 atime=1623670094.192103163 30 ctime=1623670095.409102033 elk-7.2.42/src/genwfpw.f900000644002504400250440000001350714061636517016764 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genwfpw(vpl,ngp,igpig,vgpl,vgpc,gpc,sfacgp,nhp,vhpc,hpc,sfachp,wfpw) use modmain use modpw implicit none ! arguments real(8), intent(in) :: vpl(3) integer, intent(in) :: ngp(nspnfv),igpig(ngkmax,nspnfv) real(8), intent(in) :: vgpl(3,ngkmax,nspnfv),vgpc(3,ngkmax,nspnfv) real(8), intent(in) :: gpc(ngkmax,nspnfv) complex(8), intent(in) :: sfacgp(ngkmax,natmtot,nspnfv) integer, intent(in) :: nhp(nspnfv) real(8), intent(in) :: vhpc(3,nhkmax,nspnfv),hpc(nhkmax,nspnfv) complex(8), intent(in) :: sfachp(nhkmax,natmtot,nspnfv) complex(8), intent(out) :: wfpw(nhkmax,nspinor,nstsv) ! local variables integer ispn0,ispn1,ispn,jspn integer ist,is,ia,ias integer nrc,nrci,irco,irc integer lmax,l,m,lm integer npci,i,igp,ihp real(8) t0,t1 complex(8) zsm,z1,z2,z3,z4 ! automatic arrays integer idx(nstsv) complex(8) ylm(lmmaxo) ! allocatable arrays real(8), allocatable :: jl(:,:) complex(8), allocatable :: apwalm(:,:,:,:,:),evecfv(:,:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfgp(:,:,:) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv),evecsv(nstsv,nstsv)) allocate(wfmt(npcmtmax,natmtot,nspinor,nstsv)) allocate(wfgp(ngkmax,nspinor,nstsv)) ! get the eigenvectors from file call getevecfv(filext,0,vpl,vgpl,evecfv) call getevecsv(filext,0,vpl,evecsv) ! find the matching coefficients do ispn=1,nspnfv call match(ngp(ispn),vgpc(:,:,ispn),gpc(:,ispn),sfacgp(:,:,ispn), & apwalm(:,:,:,:,ispn)) end do ! index to all states do ist=1,nstsv idx(ist)=ist end do ! calculate the second-variational wavefunctions for all states call genwfsv(.true.,.true.,nstsv,idx,ngridg,igfft,ngp,igpig,apwalm,evecfv, & evecsv,wfmt,ngkmax,wfgp) deallocate(apwalm,evecfv,evecsv) ! zero the plane wave coefficients wfpw(:,:,:)=0.d0 !---------------------------! ! interstitial part ! !---------------------------! do jspn=1,nspnfv if (spinsprl) then ispn0=jspn; ispn1=jspn else ispn0=1; ispn1=nspinor end if i=1 do ihp=1,nhp(jspn) do igp=i,ngp(jspn) t1=abs(vhpc(1,ihp,jspn)-vgpc(1,igp,jspn)) & +abs(vhpc(2,ihp,jspn)-vgpc(2,igp,jspn)) & +abs(vhpc(3,ihp,jspn)-vgpc(3,igp,jspn)) if (t1.lt.epslat) then do ist=1,nstsv do ispn=ispn0,ispn1 wfpw(ihp,ispn,ist)=wfgp(igp,ispn,ist) end do end do if (igp.eq.i) i=i+1 exit end if end do end do end do !-------------------------! ! muffin-tin part ! !-------------------------! allocate(jl(0:lmaxo,nrcmtmax)) t0=fourpi/sqrt(omega) ! remove continuation of interstitial function into muffin-tin do jspn=1,nspnfv if (spinsprl) then ispn0=jspn; ispn1=jspn else ispn0=1; ispn1=nspinor end if ! loop over G+p-vectors do igp=1,ngp(jspn) ! generate the conjugate spherical harmonics Y_lm*(G+p) call genylmv(lmaxo,vgpc(:,igp,jspn),ylm) ylm(:)=conjg(ylm(:)) do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) irco=nrci+1 npci=npcmti(is) ! generate spherical Bessel functions lmax=lmaxi do irc=1,nrc t1=gpc(igp,jspn)*rcmt(irc,is) call sbessel(lmax,t1,jl(:,irc)) if (irc.eq.nrci) lmax=lmaxo end do ! loop over atoms do ia=1,natoms(is) ias=idxas(ia,is) z1=t0*sfacgp(igp,ias,jspn) do ist=1,nstsv do ispn=ispn0,ispn1 z2=z1*wfgp(igp,ispn,ist) lm=0 do l=0,lmaxi z3=z2*zil(l) do m=-l,l lm=lm+1 z4=z3*ylm(lm) i=lm do irc=1,nrci wfmt(i,ias,ispn,ist)=wfmt(i,ias,ispn,ist)-z4*jl(l,irc) i=i+lmmaxi end do end do end do lm=0 do l=0,lmaxo z3=z2*zil(l) do m=-l,l lm=lm+1 z4=z3*ylm(lm) i=npci+lm do irc=irco,nrc wfmt(i,ias,ispn,ist)=wfmt(i,ias,ispn,ist)-z4*jl(l,irc) i=i+lmmaxo end do end do end do end do end do end do end do end do end do ! Fourier transform the muffin-tin wavefunctions do jspn=1,nspnfv if (spinsprl) then ispn0=jspn; ispn1=jspn else ispn0=1; ispn1=nspinor end if ! loop over H+p-vectors do ihp=1,nhp(jspn) ! generate the spherical harmonics Y_lm(H+p) call genylmv(lmaxo,vhpc(:,ihp,jspn),ylm) do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) ! generate spherical Bessel functions lmax=lmaxi do irc=1,nrc t1=hpc(ihp,jspn)*rcmt(irc,is) call sbessel(lmax,t1,jl(:,irc)) if (irc.eq.nrci) lmax=lmaxo end do do ia=1,natoms(is) ias=idxas(ia,is) ! conjugate structure factor z3=t0*conjg(sfachp(ihp,ias,jspn)) ! loop over states do ist=1,nstsv do ispn=ispn0,ispn1 zsm=0.d0 lmax=lmaxi i=0 do irc=1,nrc i=i+1 z1=jl(0,irc)*wfmt(i,ias,ispn,ist)*ylm(1) lm=1 do l=1,lmax lm=lm+1 i=i+1 z2=wfmt(i,ias,ispn,ist)*ylm(lm) do m=1-l,l lm=lm+1 i=i+1 z2=z2+wfmt(i,ias,ispn,ist)*ylm(lm) end do z1=z1+jl(l,irc)*zilc(l)*z2 end do zsm=zsm+wrcmt(irc,is)*z1 if (irc.eq.nrci) lmax=lmaxo end do ! add to the H+p wavefunction wfpw(ihp,ispn,ist)=wfpw(ihp,ispn,ist)+z3*zsm end do end do end do end do end do end do deallocate(jl,wfmt,wfgp) end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlxbse.f900000644000000000000000000000013214061636517014706 xustar0030 mtime=1623670095.410102032 30 atime=1623670094.194103161 30 ctime=1623670095.410102032 elk-7.2.42/src/hmlxbse.f900000644002504400250440000000125414061636517016745 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine hmlxbse use modmain use modmpi use modomp implicit none ! local variables integer ik2,nthd call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik2=1,nkptnr ! distribute among MPI processes if (mod(ik2-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(hmlxbse_) write(*,'("Info(hmlxbse): ",I6," of ",I6," k-points")') ik2,nkptnr !$OMP END CRITICAL(hmlxbse_) call hmlxbsek(ik2) end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlxbsek.f900000644000000000000000000000013114061636517015060 xustar0030 mtime=1623670095.412102031 29 atime=1623670094.19510316 30 ctime=1623670095.412102031 elk-7.2.42/src/hmlxbsek.f900000644002504400250440000000671614061636517017130 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine hmlxbsek(ik2) use modmain implicit none ! arguments integer, intent(in) :: ik2 ! local variables integer ik1,ist1,ist2,jst1,jst2 integer i1,i2,j1,j2,a1,a2,b1,b2 integer is,ias,l real(8) t0 complex(8) z1 ! automatic arrays integer idx(nstsv),ngp(nspnfv) ! allocatable arrays integer, allocatable :: igpig(:,:) complex(8), allocatable :: wfmt1(:,:,:,:),wfir1(:,:,:) complex(8), allocatable :: wfmt2(:,:,:,:),wfir2(:,:,:) complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: zvclmt(:,:,:),zvclir(:,:) complex(8), allocatable :: zfmt(:) ! external functions complex(8), external :: zfinp ! allocate local arrays allocate(igpig(ngkmax,nspnfv)) allocate(wfmt1(npcmtmax,natmtot,nspinor,nstsv),wfir1(ngtc,nspinor,nstsv)) allocate(wfmt2(npcmtmax,natmtot,nspinor,nstsv),wfir2(ngtc,nspinor,nstsv)) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) allocate(zvclmt(npcmtmax,natmtot,nvcbse),zvclir(ngtc,nvcbse)) allocate(zfmt(npcmtmax)) ! index to all states do ist1=1,nstsv idx(ist1)=ist1 end do ! calculate the wavefunctions for all states of k-point ik2 call genwfsvp(.false.,.false.,nstsv,idx,ngdgc,igfc,vkl(:,ik2),ngp,igpig,wfmt2, & ngtc,wfir2) l=0 do i2=1,nvbse ist2=istbse(i2,ik2) do j2=1,ncbse jst2=jstbse(j2,ik2) a2=ijkbse(i2,j2,ik2) l=l+1 ! calculate the complex overlap density call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,ist2),wfir2(:,:,ist2), & wfmt2(:,:,:,jst2),wfir2(:,:,jst2),zrhomt,zrhoir) ! compute the Coulomb potential call genzvclmt(nrcmt,nrcmti,nrcmtmax,rlcmt,wprcmt,npcmtmax,zrhomt, & zvclmt(:,:,l)) call zpotcoul(nrcmt,nrcmti,npcmt,npcmti,nrcmtmax,rlcmt,ngdgc,igfc,ngvc,gc, & gclg,ngvec,jlgrmt,ylmg,sfacg,zrhoir,npcmtmax,zvclmt(:,:,l),zvclir(:,l)) zvclir(:,l)=zvclir(:,l)*cfrc(:) end do end do t0=occmax*wkptnr ! start loop over ik1 do ik1=1,nkptnr if (ik1.eq.ik2) then wfmt1(:,:,:,:)=wfmt2(:,:,:,:) wfir1(:,:,:)=wfir2(:,:,:) else call genwfsvp(.false.,.false.,nstsv,idx,ngdgc,igfc,vkl(:,ik1),ngp,igpig, & wfmt1,ngtc,wfir1) end if do i1=1,nvbse ist1=istbse(i1,ik1) do j1=1,ncbse jst1=jstbse(j1,ik1) a1=ijkbse(i1,j1,ik1) ! calculate the complex overlap density call genzrho(.true.,.true.,ngtc,wfmt1(:,:,:,ist1),wfir1(:,:,ist1), & wfmt1(:,:,:,jst1),wfir1(:,:,jst1),zrhomt,zrhoir) l=0 do i2=1,nvbse ist2=istbse(i2,ik2) do j2=1,ncbse jst2=jstbse(j2,ik2) a2=ijkbse(i2,j2,ik2) l=l+1 ! compute the matrix element z1=t0*zfinp(zrhomt,zrhoir,zvclmt(:,:,l),zvclir(:,l)) hmlbse(a1,a2)=hmlbse(a1,a2)+z1 ! compute off-diagonal blocks if required if (bsefull) then b1=a1+nbbse b2=a2+nbbse hmlbse(b1,b2)=hmlbse(b1,b2)-conjg(z1) ! conjugate the potential do ias=1,natmtot is=idxis(ias) call zfmtconj(nrcmt(is),nrcmti(is),npcmt(is),zvclmt(:,ias,l)) end do zvclir(:,l)=conjg(zvclir(:,l)) z1=t0*zfinp(zrhomt,zrhoir,zvclmt(:,:,l),zvclir(:,l)) hmlbse(a1,b2)=hmlbse(a1,b2)+z1 hmlbse(b1,a2)=hmlbse(b1,a2)-conjg(z1) end if end do end do end do end do end do deallocate(igpig,wfmt1,wfmt2,wfir1,wfir2) deallocate(zrhomt,zrhoir,zvclmt,zvclir,zfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/hmldbse.f900000644000000000000000000000013014061636517014660 xustar0029 mtime=1623670095.41310203 30 atime=1623670094.197103158 29 ctime=1623670095.41310203 elk-7.2.42/src/hmldbse.f900000644002504400250440000000125414061636517016721 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine hmldbse use modmain use modmpi use modomp implicit none ! local variables integer ik2,nthd call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik2=1,nkptnr ! distribute among MPI processes if (mod(ik2-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(hmldbse_) write(*,'("Info(hmldbse): ",I6," of ",I6," k-points")') ik2,nkptnr !$OMP END CRITICAL(hmldbse_) call hmldbsek(ik2) end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/hmldbsek.f900000644000000000000000000000013214061636517015035 xustar0030 mtime=1623670095.415102028 30 atime=1623670094.199103157 30 ctime=1623670095.415102028 elk-7.2.42/src/hmldbsek.f900000644002504400250440000001434514061636517017101 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine hmldbsek(ik2) use modmain use modomp implicit none ! arguments integer, intent(in) :: ik2 ! local variables integer ik1,ist1,ist2,jst1,jst2 integer i1,i2,j1,j2,a1,a2,b1,b2 integer iv(3),iq,ig,jg,nthd real(8) vl(3),vc(3),t0,t1,t2 complex(8) z1 ! automatic arrays integer idx(nstsv),ngp(nspnfv) ! allocatable arrays integer, allocatable :: igpig(:,:) real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqr(:,:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: wfmt1(:,:,:,:),wfir1(:,:,:) complex(8), allocatable :: wfmt2(:,:,:,:),wfir2(:,:,:) complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: zvv(:,:,:),zcc(:,:,:) complex(8), allocatable :: zvc(:,:,:),zcv(:,:,:) complex(8), allocatable :: epsi(:,:,:) allocate(igpig(ngkmax,nspnfv)) allocate(vgqc(3,ngrf),gqc(ngrf),gclgq(ngrf)) allocate(jlgqr(njcmax,nspecies,ngrf)) allocate(ylmgq(lmmaxo,ngrf),sfacgq(ngrf,natmtot)) allocate(wfmt1(npcmtmax,natmtot,nspinor,nstsv),wfir1(ngtc,nspinor,nstsv)) allocate(wfmt2(npcmtmax,natmtot,nspinor,nstsv),wfir2(ngtc,nspinor,nstsv)) allocate(zvv(ngrf,nvbse,nvbse),zcc(ngrf,ncbse,ncbse)) allocate(epsi(ngrf,ngrf,nwrf)) if (bsefull) then allocate(zvc(ngrf,nvbse,ncbse)) allocate(zcv(ngrf,ncbse,nvbse)) end if ! index to all states do ist1=1,nstsv idx(ist1)=ist1 end do ! generate the wavefunctions for all states of k-point ik2 call genwfsvp(.false.,.false.,nstsv,idx,ngdgc,igfc,vkl(:,ik2),ngp,igpig,wfmt2, & ngtc,wfir2) ! begin loop over ik1 do ik1=1,nkptnr ! generate the wavefunctions for all states of k-point ik1 call genwfsvp(.false.,.false.,nstsv,idx,ngdgc,igfc,vkl(:,ik1),ngp,igpig, & wfmt1,ngtc,wfir1) ! determine equivalent q-vector in first Brillouin zone iv(:)=ivk(:,ik1)-ivk(:,ik2) iv(:)=modulo(iv(:),ngridk(:)) iq=ivqiq(iv(1),iv(2),iv(3)) ! q-vector in lattice and Cartesian coordinates vl(:)=vkl(:,ik1)-vkl(:,ik2) vc(:)=vkc(:,ik1)-vkc(:,ik2) ! generate the G+q-vectors and related functions call gengqf(ngrf,vc,vgqc,gqc,jlgqr,ylmgq,sfacgq) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.true.,iq,ngrf,gqc,gclgq) ! symmetrise the Coulomb Green's function gclgq(:)=sqrt(gclgq(:)) ! compute the matrix elements call holdthd(nvbse,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zrhomt,zrhoir,ist1,ist2,i2) & !$OMP NUM_THREADS(nthd) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) !$OMP DO do i1=1,nvbse ist1=istbse(i1,ik1) do i2=1,nvbse ist2=istbse(i2,ik2) call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,ist2),wfir2(:,:,ist2), & wfmt1(:,:,:,ist1),wfir1(:,:,ist1),zrhomt,zrhoir) call zftzf(ngrf,jlgqr,ylmgq,ngrf,sfacgq,zrhomt,zrhoir,zvv(:,i1,i2)) end do end do !$OMP END DO deallocate(zrhomt,zrhoir) !$OMP END PARALLEL call freethd(nthd) ! compute the matrix elements call holdthd(ncbse,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zrhomt,zrhoir,jst1,jst2,j2) & !$OMP NUM_THREADS(nthd) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) !$OMP DO do j1=1,ncbse jst1=jstbse(j1,ik1) do j2=1,ncbse jst2=jstbse(j2,ik2) call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,jst2),wfir2(:,:,jst2), & wfmt1(:,:,:,jst1),wfir1(:,:,jst1),zrhomt,zrhoir) call zftzf(ngrf,jlgqr,ylmgq,ngrf,sfacgq,zrhomt,zrhoir,zcc(:,j1,j2)) end do end do !$OMP END DO deallocate(zrhomt,zrhoir) !$OMP END PARALLEL call freethd(nthd) ! matrix elements for full BSE kernel if required if (bsefull) then ! compute the matrix elements call holdthd(nvbse,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zrhomt,zrhoir,ist1,jst2,j2) & !$OMP NUM_THREADS(nthd) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) !$OMP DO do i1=1,nvbse ist1=istbse(i1,ik1) do j2=1,ncbse jst2=jstbse(j2,ik2) call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,jst2),wfir2(:,:,jst2), & wfmt1(:,:,:,ist1),wfir1(:,:,ist1),zrhomt,zrhoir) call zftzf(ngrf,jlgqr,ylmgq,ngrf,sfacgq,zrhomt,zrhoir,zvc(:,i1,j2)) end do end do !$OMP END DO deallocate(zrhomt,zrhoir) !$OMP END PARALLEL call freethd(nthd) ! compute the matrix elements call holdthd(ncbse,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zrhomt,zrhoir,jst1,ist2,i2) & !$OMP NUM_THREADS(nthd) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) !$OMP DO do j1=1,ncbse jst1=jstbse(j1,ik1) do i2=1,nvbse ist2=istbse(i2,ik2) call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,ist2),wfir2(:,:,ist2), & wfmt1(:,:,:,jst1),wfir1(:,:,jst1),zrhomt,zrhoir) call zftzf(ngrf,jlgqr,ylmgq,ngrf,sfacgq,zrhomt,zrhoir,zcv(:,j1,i2)) end do end do !$OMP END DO deallocate(zrhomt,zrhoir) !$OMP END PARALLEL call freethd(nthd) end if ! get RPA inverse epsilon from file call getcfgq('EPSINV.OUT',vl,ngrf,nwrf,epsi) t0=wkptnr*omega do i1=1,nvbse do j1=1,ncbse a1=ijkbse(i1,j1,ik1) do i2=1,nvbse do j2=1,ncbse a2=ijkbse(i2,j2,ik2) z1=0.d0 do ig=1,ngrf t1=t0*gclgq(ig) do jg=1,ngrf t2=t1*gclgq(jg) z1=z1+t2*epsi(ig,jg,1)*conjg(zcc(ig,j1,j2))*zvv(jg,i1,i2) end do end do hmlbse(a1,a2)=hmlbse(a1,a2)-z1 ! compute off-diagonal blocks if required if (bsefull) then b1=a1+nbbse b2=a2+nbbse hmlbse(b1,b2)=hmlbse(b1,b2)+conjg(z1) z1=0.d0 do ig=1,ngrf t1=t0*gclgq(ig) do jg=1,ngrf t2=t1*gclgq(jg) z1=z1+t2*epsi(ig,jg,1)*conjg(zcv(ig,j1,i2))*zvc(jg,i1,j2) end do end do hmlbse(a1,b2)=hmlbse(a1,b2)-z1 hmlbse(b1,a2)=hmlbse(b1,a2)+conjg(z1) end if ! end loop over i2 and j2 end do end do ! end loop over i1 and j1 end do end do ! end loop over ik1 end do deallocate(igpig,vgqc,gqc,gclgq,jlgqr) deallocate(ylmgq,sfacgq) deallocate(wfmt1,wfmt2,wfir1,wfir2) deallocate(zvv,zcc,epsi) if (bsefull) deallocate(zvc,zcv) end subroutine elk-7.2.42/src/PaxHeaders.21776/gradwfcr2.f900000644000000000000000000000013214061636517015125 xustar0030 mtime=1623670095.416102027 30 atime=1623670094.200103156 30 ctime=1623670095.416102027 elk-7.2.42/src/gradwfcr2.f900000644002504400250440000000255014061636517017164 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gradwfcr2(gwf2mt) use modmain implicit none ! arguments real(8), intent(inout) :: gwf2mt(npmtmax,natmtot) ! local variables integer ist,is,ias integer nr,nri,iro,ir integer np,l,lm,i ! allocatable arrays complex(8), allocatable :: wfmt(:),gwfmt(:,:),zfmt(:) allocate(wfmt(npmtmax),gwfmt(npmtmax,3),zfmt(npmtmax)) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) iro=nri+1 np=npmt(is) do ist=1,nstsp(is) if (spcore(ist,is).and.(ksp(ist,is).eq.lsp(ist,is)+1)) then l=lsp(ist,is) do lm=l**2+1,(l+1)**2 wfmt(1:np)=0.d0 i=lm do ir=1,nri wfmt(i)=rwfcr(ir,1,ist,ias)/rsp(ir,is) i=i+lmmaxi end do do ir=iro,nr wfmt(i)=rwfcr(ir,1,ist,ias)/rsp(ir,is) i=i+lmmaxo end do call gradzfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),wfmt,npmtmax,gwfmt) do i=1,3 call zbsht(nr,nri,gwfmt(:,i),zfmt) ! factor of 2 from spin gwf2mt(1:np,ias)=gwf2mt(1:np,ias) & +2.d0*(dble(zfmt(1:np))**2+aimag(zfmt(1:np))**2) end do end do end if end do ! end loops over atoms end do deallocate(wfmt,gwfmt,zfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/oepresk.f900000644000000000000000000000013214061636517014714 xustar0030 mtime=1623670095.418102025 30 atime=1623670094.202103154 30 ctime=1623670095.418102025 elk-7.2.42/src/oepresk.f900000644002504400250440000001402714061636517016755 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine oepresk(ik,vclcv,vclvv,dvxmt,dvxir,dbxmt,dbxir) use modmain implicit none ! arguments integer, intent(in) :: ik complex(8), intent(in) :: vclcv(ncrmax,natmtot,nstsv,nkpt) complex(8), intent(in) :: vclvv(nstsv,nstsv,nkpt) real(8), intent(inout) :: dvxmt(npcmtmax,natmtot),dvxir(ngtot) real(8), intent(inout) :: dbxmt(npcmtmax,natmtot,ndmag),dbxir(ngtot,ndmag) ! local variables integer ist,jst,idm integer is,ia,ias,ic,m integer nrc,nrci,npc real(8) de complex(8) z1,z2 ! automatic arrays integer idx(nstsv) ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfir(:,:,:),wfcr(:,:) complex(8), allocatable :: zfmt1(:),zvfmt1(:,:) complex(8), allocatable :: zfmt2(:,:),zfir2(:) complex(8), allocatable :: zvfmt2(:,:,:),zvfir2(:,:) ! external functions complex(8), external :: rzfinp,rzfmtinp ! get the eigenvalues/vectors from file for input k-point allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! find the matching coefficients allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! index to all states do ist=1,nstsv idx(ist)=ist end do ! calculate the wavefunctions for all states allocate(wfmt(npcmtmax,natmtot,nspinor,nstsv),wfir(ngtot,nspinor,nstsv)) call genwfsv(.false.,.false.,nstsv,idx,ngridg,igfft,ngk(1,ik),igkig(:,1,ik), & apwalm,evecfv,evecsv,wfmt,ngtot,wfir) deallocate(apwalm,evecfv,evecsv) !-----------------------------------------------------------! ! core-conduction overlap density and magnetisation ! !-----------------------------------------------------------! allocate(wfcr(npcmtmax,2),zfmt1(npcmtmax)) if (spinpol) allocate(zvfmt1(npcmtmax,ndmag)) do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) ic=0 do ist=1,nstsp(is) if (spcore(ist,is)) then do m=-ksp(ist,is),ksp(ist,is)-1 ic=ic+1 ! pass in m-1/2 to wavefcr call wavefcr(.false.,lradstp,is,ia,ist,m,npcmtmax,wfcr) do jst=1,nstsv if (evalsv(jst,ik).gt.efermi) then if (spinpol) then ! compute the complex density and magnetisation call genzrm(npc,wfcr,wfcr(:,2),wfmt(:,ias,1,jst), & wfmt(:,ias,2,jst),zfmt1,npcmtmax,zvfmt1) else ! compute the complex density zfmt1(1:npc)=conjg(wfcr(1:npc,1))*wfmt(1:npc,ias,1,jst) end if z1=conjg(vclcv(ic,ias,jst,ik)) z2=rzfmtinp(nrc,nrci,wrcmt(:,is),vxmt(:,ias),zfmt1) z1=z1-conjg(z2) do idm=1,ndmag z2=rzfmtinp(nrc,nrci,wrcmt(:,is),bxmt(:,ias,idm),zvfmt1(:,idm)) z1=z1-conjg(z2) end do de=evalcr(ist,ias)-evalsv(jst,ik) z1=z1*occmax*wkpt(ik)/(de+zi*swidth) ! residuals for exchange potential and field !$OMP CRITICAL(oepresk_) call rzadd(npc,z1,zfmt1,dvxmt(:,ias)) do idm=1,ndmag call rzadd(npc,z1,zvfmt1(:,idm),dbxmt(:,ias,idm)) end do !$OMP END CRITICAL(oepresk_) ! end loop over jst end if end do end do ! end loop over ist end if end do ! end loops over atoms and species end do end do deallocate(wfcr,zfmt1) if (spinpol) deallocate(zvfmt1) !--------------------------------------------------------------! ! valence-conduction overlap density and magnetisation ! !--------------------------------------------------------------! allocate(zfmt2(npcmtmax,natmtot),zfir2(ngtot)) if (spinpol) then allocate(zvfmt2(npcmtmax,natmtot,ndmag),zvfir2(ngtot,ndmag)) end if do ist=1,nstsv if (evalsv(ist,ik).lt.efermi) then do jst=1,nstsv if (evalsv(jst,ik).gt.efermi) then if (spinpol) then ! compute the complex density and magnetisation call genzfrm(wfmt(:,:,1,ist),wfmt(:,:,2,ist),wfir(:,1,ist), & wfir(:,2,ist),wfmt(:,:,1,jst),wfmt(:,:,2,jst),wfir(:,1,jst), & wfir(:,2,jst),zfmt2,zfir2,zvfmt2,zvfir2) else ! compute the complex density call genzrho(.false.,.true.,ngtot,wfmt(:,:,:,ist),wfir(:,:,ist), & wfmt(:,:,:,jst),wfir(:,:,jst),zfmt2,zfir2) end if z1=conjg(vclvv(ist,jst,ik)) z2=rzfinp(vxmt,vxir,zfmt2,zfir2) z1=z1-conjg(z2) do idm=1,ndmag z2=rzfinp(bxmt(:,:,idm),bxir(:,idm),zvfmt2(:,:,idm),zvfir2(:,idm)) z1=z1-conjg(z2) end do de=evalsv(ist,ik)-evalsv(jst,ik) z1=z1*occmax*wkpt(ik)/(de+zi*swidth) ! add to residuals for exchange potential and field !$OMP CRITICAL(oepresk_) call rzfadd(z1,zfmt2,zfir2,dvxmt,dvxir) do idm=1,ndmag call rzfadd(z1,zvfmt2(:,:,idm),zvfir2(:,idm),dbxmt(:,:,idm), & dbxir(:,idm)) end do !$OMP END CRITICAL(oepresk_) ! end loop over jst end if end do ! end loop over ist end if end do deallocate(wfmt,wfir,zfmt2,zfir2) if (spinpol) deallocate(zvfmt2,zvfir2) end subroutine subroutine rzadd(n,za,zv,rv) implicit none ! arguments integer, intent(in) :: n complex(8), intent(in) :: za real(8), intent(in) :: zv(2*n) real(8), intent(out) :: rv(n) ! local variables real(8) t1 t1=dble(za) if (abs(t1).gt.1.d-12) call daxpy(n,t1,zv,2,rv,1) t1=-aimag(za) if (abs(t1).gt.1.d-12) call daxpy(n,t1,zv(2),2,rv,1) end subroutine subroutine rzfadd(za,zfmt,zfir,rfmt,rfir) use modmain implicit none ! arguments complex(8), intent(in) :: za complex(8), intent(in) :: zfmt(npcmtmax,natmtot),zfir(ngtot) real(8), intent(inout) :: rfmt(npcmtmax,natmtot),rfir(ngtot) ! local variables integer is,ias do ias=1,natmtot is=idxis(ias) call rzadd(npcmt(is),za,zfmt(:,ias),rfmt(:,ias)) end do call rzadd(ngtot,za,zfir,rfir) end subroutine elk-7.2.42/src/PaxHeaders.21776/addlorbcnd.f900000644000000000000000000000013214061636517015340 xustar0030 mtime=1623670095.419102024 30 atime=1623670094.204103152 30 ctime=1623670095.419102024 elk-7.2.42/src/addlorbcnd.f900000644002504400250440000000157214061636517017402 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine addlorbcnd use modmain implicit none ! local variables integer is,nlo,l,io if (.not.lorbcnd) return ! add conduction local-orbitals to each species do is=1,nspecies nlo=nlorb(is) do l=0,lmaxo nlo=nlo+1 if (nlo.gt.maxlorb) then write(*,*) write(*,'("Error(addlorbcnd): nlorb too large : ",I8)') nlo write(*,'(" for species ",I4)') is write(*,'("Adjust maxlorb in modmain and recompile code")') write(*,*) stop end if lorbl(nlo,is)=l lorbord(nlo,is)=lorbordc do io=1,lorbordc lorbe0(io,nlo,is)=0.15d0 lorbdm(io,nlo,is)=io-1 lorbve(io,nlo,is)=.true. end do end do nlorb(is)=nlo end do end subroutine elk-7.2.42/src/PaxHeaders.21776/energy.f900000644000000000000000000000013114061636517014534 xustar0030 mtime=1623670095.421102022 29 atime=1623670094.20610315 30 ctime=1623670095.421102022 elk-7.2.42/src/energy.f900000644002504400250440000002127614061636517016602 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: energy ! !INTERFACE: subroutine energy ! !USES: use modmain use moddftu use modtest ! !DESCRIPTION: ! Computes the total energy and its individual contributions. The kinetic ! energy is given by ! $$ T_s=\sum_i n_i\epsilon_i-\int\rho({\bf r})[v_{\rm C}({\bf r}) ! +v_{\rm xc}({\bf r})]d{\bf r}-\int {\bf m}({\bf r})\cdot ! ({\bf B}_{\rm xc}({\bf r})+{\bf B}_{\rm ext}({\bf r}))d{\bf r}, $$ ! where $n_i$ are the occupancies and $\epsilon_i$ are the eigenvalues of both ! the core and valence states; $\rho$ is the density; ${\bf m}$ is the ! magnetisation density; $v_{\rm C}$ is the Coulomb potential; $v_{\rm xc}$ ! and ${\bf B}_{\rm xc}$ are the exchange-correlation potential and magnetic ! field, respectively; and ${\bf B}_{\rm ext}$ is the external magnetic field. ! The Hartree, electron-nuclear and nuclear-nuclear electrostatic energies are ! combined into the Coulomb energy: ! \begin{align*} ! E_{\rm C}&=E_{\rm H}+E_{\rm en}+E_{\rm nn} \\ ! &=\frac{1}{2}V_{\rm C}+E_{\rm Mad}, ! \end{align*} ! where ! $$ V_{\rm C}=\int\rho({\bf r})v_{\rm C}({\bf r})d{\bf r} $$ ! is the Coulomb potential energy. The Madelung energy is given by ! $$ E_{\rm Mad}=\frac{1}{2}\sum_{\alpha}z_{\alpha}R_{\alpha}, $$ ! where ! $$ R_{\alpha}=\lim_{r\rightarrow 0}\left(v^{\rm C}_{\alpha;00}(r)Y_{00} ! +\frac{z_{\alpha}}{r}\right) $$ ! for atom $\alpha$, with $v^{\rm C}_{\alpha;00}$ being the $l=0$ component of ! the spherical harmonic expansion of $v_{\rm C}$ in the muffin-tin, and ! $z_{\alpha}$ is the nuclear charge. Using the nuclear-nuclear energy ! determined at the start of the calculation, the electron-nuclear and Hartree ! energies can be isolated with ! $$ E_{\rm en}=2\left(E_{\rm Mad}-E_{\rm nn}\right) $$ ! and ! $$ E_{\rm H}=\frac{1}{2}(E_{\rm C}-E_{\rm en}). $$ ! Finally, the total energy is ! $$ E=T_s+E_{\rm C}+E_{\rm xc}, $$ ! where $E_{\rm xc}$ is obtained either by integrating the ! exchange-correlation energy density, or in the case of exact exchange, the ! explicit calculation of the Fock exchange integral. The energy from the ! external magnetic fields in the muffin-tins, {\tt bfcmt}, is always removed ! from the total since these fields are non-physical: their field lines do not ! close. The energy of the physical external field, {\tt bfieldc}, is also not ! included in the total because this field, like those in the muffin-tins, is ! used for breaking spin symmetry and taken to be infintesimal. If this field ! is intended to be finite, then the associated energy, {\tt engybext}, should ! be added to the total by hand. See {\tt potxc}, {\tt exxengy} and related ! subroutines. ! ! !REVISION HISTORY: ! Created May 2003 (JKD) !EOP !BOC implicit none ! local variables integer ik,ist,ispn,idm,jdm integer is,ia,ias,np,n2,i real(8) cb,sm,w,f complex(8) z1 ! allocatable arrays real(8), allocatable :: rfmt(:,:) complex(8), allocatable :: evecsv(:,:),kmat(:,:),c(:,:) ! external functions real(8), external :: rfinp complex(8), external :: zdotc ! coupling constant of the external field (g_e/4c) cb=gfacte/(4.d0*solsc) !-----------------------------------------------! ! exchange-correlation potential energy ! !-----------------------------------------------! engyvxc=rfinp(rhomt,rhoir,vxcmt,vxcir) !-----------------------------------------------------! ! exchange-correlation effective field energy ! !-----------------------------------------------------! engybxc=0.d0 do idm=1,ndmag engybxc=engybxc+rfinp(magmt(:,:,idm),magir(:,idm),bxcmt(:,:,idm),bxcir(:,idm)) end do !------------------------------------------! ! external magnetic field energies ! !------------------------------------------! engybext=0.d0 do idm=1,ndmag if (ncmag) then jdm=idm else jdm=3 end if ! energy of physical global field engybext=engybext+cb*momtot(idm)*bfieldc(jdm) end do !----------------------------------! ! Coulomb potential energy ! !----------------------------------! engyvcl=rfinp(rhomt,rhoir,vclmt,vclir) !-----------------------! ! Madelung term ! !-----------------------! engymad=0.d0 do ias=1,natmtot is=idxis(ias) engymad=engymad+0.5d0*spzn(is)*(vclmt(1,ias)-vcln(1,is))*y00 end do !---------------------------------------------! ! electron-nuclear interaction energy ! !---------------------------------------------! engyen=2.d0*(engymad-engynn) !------------------------! ! Hartree energy ! !------------------------! engyhar=0.5d0*(engyvcl-engyen) !------------------------! ! Coulomb energy ! !------------------------! engycl=engynn+engyen+engyhar !-------------------------! ! exchange energy ! !-------------------------! if ((xctype(1).lt.0).or.(task.eq.5)) then ! exact exchange for OEP-EXX or Hartree-Fock on last self-consistent loop if (tlast) then call exxengy ! mix exact and DFT exchange energies for hybrid functionals if (hybrid) then engyx=engyx*hybridc engyx=engyx+rfinp(rhomt,rhoir,exmt,exir) end if else engyx=0.d0 end if else ! exchange energy from the density engyx=rfinp(rhomt,rhoir,exmt,exir) end if !----------------------------! ! correlation energy ! !----------------------------! if (task.eq.5) then if (hybrid) then ! fraction of DFT correlation energy for hybrid functionals engyc=rfinp(rhomt,rhoir,ecmt,ecir) else ! zero correlation energy for pure Hartree-Fock engyc=0.d0 end if else ! correlation energy from the density engyc=rfinp(rhomt,rhoir,ecmt,ecir) end if !----------------------! ! DFT+U energy ! !----------------------! engydu=0.d0 if (dftu.ne.0) then do i=1,ndftu is=idftu(1,i) do ia=1,natoms(is) engydu=engydu+engyadu(ia,i) end do end do end if !----------------------------! ! sum of eigenvalues ! !----------------------------! ! core eigenvalues evalsum=0.d0 do ias=1,natmtot is=idxis(ias) do ist=1,nstsp(is) if (spcore(ist,is)) evalsum=evalsum+occcr(ist,ias)*evalcr(ist,ias) end do end do ! valence eigenvalues do ik=1,nkpt w=wkpt(ik) do ist=1,nstsv evalsum=evalsum+w*occsv(ist,ik)*evalsv(ist,ik) end do end do !------------------------! ! kinetic energy ! !------------------------! ! core electron kinetic energy call energykncr ! total electron kinetic energy if (task.eq.5) then ! Hartree-Fock case engykn=engykncr ! kinetic energy from valence states allocate(evecsv(nstsv,nstsv),kmat(nstsv,nstsv),c(nstsv,nstsv)) do ik=1,nkpt w=wkpt(ik) call getevecsv(filext,ik,vkl(:,ik),evecsv) call getkmat(ik,kmat) call zgemm('N','N',nstsv,nstsv,nstsv,zone,kmat,nstsv,evecsv,nstsv,zzero,c, & nstsv) do ist=1,nstsv z1=zdotc(nstsv,evecsv(:,ist),1,c(:,ist),1) engykn=engykn+w*occsv(ist,ik)*dble(z1) end do end do deallocate(evecsv,kmat,c) else ! Kohn-Sham case allocate(rfmt(npmtmax,natmtot)) ! remove magnetic field contribution sm=0.d0 do idm=1,ndmag do ias=1,natmtot is=idxis(ias) call rfsht(nrcmt(is),nrcmti(is),bsmt(:,ias,idm),rfmt(:,ias)) end do call rfmtctof(rfmt) sm=sm+rfinp(magmt(:,:,idm),magir(:,idm),rfmt,bsir(:,idm)) end do ! remove integral of w_xc times tau for generalised Kohn-Sham meta-GGA if (xcgrad.eq.4) then do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) np=npmt(is) rfmt(1:np,ias)=taumt(1:np,ias,ispn)-taucr(1:np,ias,ispn) end do sm=sm+rfinp(rfmt,tauir,wxcmt,wxcir) end do end if ! remove fixed tensor moment potential matrix contribution if (ftmtype.ne.0) then n2=(lmmaxdm*nspinor)**2 do ias=1,natmtot z1=zdotc(n2,dmatmt(:,:,:,:,ias),1,vmftm(:,:,:,:,ias),1) sm=sm+dble(z1) end do end if engykn=evalsum-engyvcl-engyvxc-sm deallocate(rfmt) end if !-------------------------------! ! entropic contribution ! !-------------------------------! entrpy=0.d0 engyts=0.d0 ! non-zero only for the Fermi-Dirac smearing function if (stype.eq.3) then sm=0.d0 do ik=1,nkpt w=wkpt(ik) do ist=1,nstsv f=occsv(ist,ik)/occmax if ((f.gt.0.d0).and.(f.lt.1.d0)) then sm=sm+w*(f*log(f)+(1.d0-f)*log(1.d0-f)) end if end do end do ! entropy entrpy=-occmax*kboltz*sm ! contribution to free energy engyts=-swidth*entrpy/kboltz end if !----------------------! ! total energy ! !----------------------! engytot=engykn+0.5d0*engyvcl+engymad+engyx+engyc+engyts ! add the DFT+U correction if required if (dftu.ne.0) engytot=engytot+engydu ! write total energy to test file call writetest(0,'total energy',tol=1.d-4,rv=engytot) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/wfplot.f900000644000000000000000000000013214061636517014557 xustar0030 mtime=1623670095.422102021 30 atime=1623670094.208103148 30 ctime=1623670095.422102021 elk-7.2.42/src/wfplot.f900000644002504400250440000000563614061636517016626 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine wfplot use modmain use modmpi use modomp implicit none ! local variables integer ik,ist real(8) x,t1 ! external functions real(8), external :: sdelta ! initialise universal variables call init0 call init1 ! read the density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! set the occupancies if ((task.eq.61).or.(task.eq.62).or.(task.eq.63)) then ! plot of wavefunction modulus squared ik=kstlist(1,1) ist=kstlist(2,1) if ((ik.lt.1).or.(ik.gt.nkpt)) then write(*,*) write(*,'("Error(wfplot): k-point out of range : ",I8)') ik write(*,*) stop end if if ((ist.lt.1).or.(ist.gt.nstsv)) then write(*,*) write(*,'("Error(wfplot): state out of range : ",I8)') ist write(*,*) stop end if ! select a particular wavefunction using its occupancy occsv(:,:)=0.d0 occsv(ist,ik)=1.d0/wkpt(ik) ! no symmetrisation required nsymcrys=1 else ! plotting an STM image by setting occupancies to be a delta function at the ! Fermi energy t1=1.d0/swidth do ik=1,nkpt ! get the eigenvalues from file call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) do ist=1,nstsv x=(efermi-evalsv(ist,ik))*t1 occsv(ist,ik)=occmax*wkpt(ik)*sdelta(stype,x)*t1 end do end do end if ! compute the valence charge density with the new occupancies call rhomagv ! write the wavefunction modulus squared plot to file if (mp_mpi) then select case(task) case(61) open(50,file='WF1D.OUT',form='FORMATTED') open(51,file='WFLINES.OUT',form='FORMATTED') call plot1d(50,51,1,rhomt,rhoir) close(50) close(51) write(*,*) write(*,'("Info(wfplot):")') write(*,'(" 1D wavefunction modulus squared written to WF1D.OUT")') write(*,'(" vertex location lines written to WFLINES.OUT")') case(62) open(50,file='WF2D.OUT',form='FORMATTED') call plot2d(.false.,50,1,rhomt,rhoir) close(50) write(*,*) write(*,'("Info(wfplot):")') write(*,'(" 2D wavefunction modulus squared written to WF2D.OUT")') case(162) open(50,file='STM2D.OUT',form='FORMATTED') call plot2d(.false.,50,1,rhomt,rhoir) close(50) write(*,*) write(*,'("Info(wfplot):")') write(*,'(" 2D STM image written to STM2D.OUT")') case(63) open(50,file='WF3D.OUT',form='FORMATTED') call plot3d(50,1,rhomt,rhoir) close(50) write(*,*) write(*,'("Info(wfplot):")') write(*,'(" 3D wavefunction modulus squared written to WF3D.OUT")') end select if (task.ne.162) then write(*,'(" for k-point ",I8," and state ",I6)') kstlist(1,1),kstlist(2,1) end if end if end subroutine elk-7.2.42/src/PaxHeaders.21776/oepvcl.f900000644000000000000000000000013214061636517014534 xustar0030 mtime=1623670095.424102019 30 atime=1623670094.210103146 30 ctime=1623670095.424102019 elk-7.2.42/src/oepvcl.f900000644002504400250440000000216514061636517016575 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine oepvcl(vclcv,vclvv) use modmain use modmpi use modomp implicit none ! arguments complex(8), intent(out) :: vclcv(ncrmax,natmtot,nstsv,nkpt) complex(8), intent(out) :: vclvv(nstsv,nstsv,nkpt) ! local variables integer ik,ncv,nvv integer lp,nthd call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(oepvcl_) write(*,'("Info(oepvcl): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(oepvcl_) call oepvclk(ik,vclcv(:,:,:,ik),vclvv(:,:,ik)) end do !$OMP END PARALLEL DO call freethd(nthd) ! broadcast matrix elements to all other processes ncv=ncrmax*natmtot*nstsv nvv=nstsv*nstsv do ik=1,nkpt lp=mod(ik-1,np_mpi) call mpi_bcast(vclcv(:,:,:,ik),ncv,mpi_double_complex,lp,mpicom,ierror) call mpi_bcast(vclvv(:,:,ik),nvv,mpi_double_complex,lp,mpicom,ierror) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/oepvclk.f900000644000000000000000000000013214061636517014707 xustar0030 mtime=1623670095.425102019 30 atime=1623670094.211103145 30 ctime=1623670095.425102019 elk-7.2.42/src/oepvclk.f900000644002504400250440000002336114061636517016751 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine oepvclk(ikp,vclcv,vclvv) use modmain implicit none ! arguments integer, intent(in) :: ikp complex(8), intent(out) :: vclcv(ncrmax,natmtot,nstsv) complex(8), intent(out) :: vclvv(nstsv,nstsv) ! local variables integer ik,jk,nst,ist1,ist2,ist3 integer is,ia,ias,nrc,nrci,npc integer iv(3),ig,iq integer ic,jc,m1,m2 real(8) vc(3) complex(8) z1 ! automatic arrays integer idx(nstsv) ! allocatable arrays real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqrmt(:,:,:) complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: wfmt1(:,:,:,:),wfmt2(:,:,:,:) complex(8), allocatable :: wfir1(:,:,:),wfir2(:,:,:) complex(8), allocatable :: wfcr1(:,:),wfcr2(:,:) complex(8), allocatable :: zrhomt1(:,:,:),zrhomt2(:,:),zrhoir1(:,:) complex(8), allocatable :: zvclmt(:,:),zvclir(:),zfmt(:) ! external functions complex(8), external :: zfinp,zfmtinp ! allocate local arrays allocate(vgqc(3,ngvc),gqc(ngvc),gclgq(ngvc)) allocate(jlgqrmt(0:lnpsd,ngvc,nspecies)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) allocate(ylmgq(lmmaxo,ngvc),sfacgq(ngvc,natmtot)) allocate(wfmt1(npcmtmax,natmtot,nspinor,nstsv)) allocate(wfmt2(npcmtmax,natmtot,nspinor,nstsv)) allocate(wfir1(ngtc,nspinor,nstsv),wfir2(ngtc,nspinor,nstsv)) allocate(wfcr1(npcmtmax,2),wfcr2(npcmtmax,2)) allocate(zrhomt1(npcmtmax,natmtot,nstsv),zrhoir1(ngtc,nstsv)) allocate(zrhomt2(npcmtmax,nstcr),zfmt(npcmtmax)) allocate(zvclmt(npcmtmax,natmtot),zvclir(ngtc)) ! zero the Coulomb matrix elements vclcv(:,:,:)=0.d0 vclvv(:,:)=0.d0 ! get the eigenvectors from file for input reduced k-point call getevecfv(filext,ikp,vkl(:,ikp),vgkl(:,:,:,ikp),evecfv) call getevecsv(filext,ikp,vkl(:,ikp),evecsv) ! find the matching coefficients call match(ngk(1,ikp),vgkc(:,:,1,ikp),gkc(:,1,ikp),sfacgk(:,:,1,ikp),apwalm) ! index to all states do ist1=1,nstsv idx(ist1)=ist1 end do ! calculate the wavefunctions for all states of the input k-point call genwfsv(.false.,.false.,nstsv,idx,ngdgc,igfc,ngk(1,ikp),igkig(:,1,ikp), & apwalm,evecfv,evecsv,wfmt1,ngtc,wfir1) ! loop over non-reduced k-point set do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! determine the q-vector iv(:)=ivk(:,ikp)-ivk(:,ik) iv(:)=modulo(iv(:),ngridk(:)) ! check if the q-point is in user-defined set iv(:)=iv(:)*ngridq(:) if (any(modulo(iv(:),ngridk(:)).ne.0)) cycle iv(:)=iv(:)/ngridk(:) iq=ivqiq(iv(1),iv(2),iv(3)) vc(:)=vkc(:,ikp)-vkc(:,ik) do ig=1,ngvc ! determine the G+q-vectors vgqc(:,ig)=vgc(:,ig)+vc(:) ! G+q-vector length gqc(ig)=sqrt(vgqc(1,ig)**2+vgqc(2,ig)**2+vgqc(3,ig)**2) ! spherical harmonics for G+q-vectors call genylmv(lmaxo,vgqc(:,ig),ylmgq(:,ig)) end do ! structure factors for G+q call gensfacgp(ngvc,vgqc,ngvc,sfacgq) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.true.,iq,ngvc,gqc,gclgq) ! compute the required spherical Bessel functions call genjlgprmt(lnpsd,ngvc,gqc,ngvc,jlgqrmt) ! find the matching coefficients call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! get the eigenvectors from file for non-reduced k-points call getevecfv(filext,0,vkl(:,ik),vgkl(:,:,1,ik),evecfv) call getevecsv(filext,0,vkl(:,ik),evecsv) ! count and index occupied states nst=0 do ist3=1,nstsv if (evalsv(ist3,jk).lt.efermi) then nst=nst+1 idx(nst)=ist3 end if end do ! calculate the wavefunctions for occupied states call genwfsv(.false.,.false.,nst,idx,ngdgc,igfc,ngk(1,ik),igkig(:,1,ik), & apwalm,evecfv,evecsv,wfmt2,ngtc,wfir2) do ist3=1,nst ! compute the complex overlap densities for all valence-valence states do ist1=1,nstsv call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,ist3),wfir2(:,:,ist3), & wfmt1(:,:,:,ist1),wfir1(:,:,ist1),zrhomt1(:,:,ist1),zrhoir1(:,ist1)) end do ! compute the complex overlap densities for all valence-core states jc=0 do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) do ist1=1,nstsp(is) if (spcore(ist1,is)) then do m1=-ksp(ist1,is),ksp(ist1,is)-1 jc=jc+1 ! generate the core wavefunction in spherical coordinates (pass in m-1/2) call wavefcr(.false.,lradstp,is,ia,ist1,m1,npcmtmax,wfcr1) if (spinpol) then call zrho2(npc,wfmt2(:,ias,1,ist3),wfmt2(:,ias,2,ist3),wfcr1, & wfcr1(:,2),zfmt) else call zrho1(npc,wfmt2(:,ias,1,ist3),wfcr1,zfmt) end if ! convert to spherical harmonics call zfsht(nrc,nrci,zfmt,zrhomt2(:,jc)) end do end if end do end do end do do ist2=1,nstsv if (evalsv(ist2,ikp).gt.efermi) then ! calculate the Coulomb potential call genzvclmt(nrcmt,nrcmti,nrcmtmax,rlcmt,wprcmt,npcmtmax, & zrhomt1(:,:,ist2),zvclmt) call zpotcoul(nrcmt,nrcmti,npcmt,npcmti,nrcmtmax,rlcmt,ngdgc,igfc,ngvc,& gqc,gclgq,ngvc,jlgqrmt,ylmgq,sfacgq,zrhoir1(:,ist2),npcmtmax,zvclmt, & zvclir) zvclir(:)=zvclir(:)*cfrc(:) !----------------------------------------------! ! valence-valence-valence contribution ! !----------------------------------------------! do ist1=1,nstsv if (evalsv(ist1,ikp).lt.efermi) then z1=zfinp(zrhomt1(:,:,ist1),zrhoir1(:,ist1),zvclmt,zvclir) vclvv(ist1,ist2)=vclvv(ist1,ist2)-wqptnr*z1 end if end do !-------------------------------------------! ! core-valence-valence contribution ! !-------------------------------------------! jc=0 do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) do ia=1,natoms(is) ias=idxas(ia,is) ic=0 do ist1=1,nstsp(is) if (spcore(ist1,is)) then do m1=-ksp(ist1,is),ksp(ist1,is)-1 ic=ic+1 jc=jc+1 z1=zfmtinp(nrc,nrci,wrcmt(:,is),zrhomt2(:,jc),zvclmt(:,ias)) vclcv(ic,ias,ist2)=vclcv(ic,ias,ist2)-wqptnr*z1 end do ! end loop over ist1 end if end do ! end loops over atoms and species end do end do ! end loop over ist2 end if end do ! end loop over ist3 end do ! end loop over non-reduced k-point set end do ! begin loops over atoms and species do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) do ist3=1,nstsp(is) if (spcore(ist3,is)) then do m1=-ksp(ist3,is),ksp(ist3,is)-1 ! generate the core wavefunction in spherical coordinates (pass in m-1/2) call wavefcr(.false.,lradstp,is,ia,ist3,m1,npcmtmax,wfcr1) ! compute the complex overlap densities for the core-valence states do ist1=1,nstsv if (spinpol) then call zrho2(npc,wfcr1,wfcr1(:,2),wfmt1(:,ias,1,ist1), & wfmt1(:,ias,2,ist1),zfmt) else call zrho1(npc,wfcr1,wfmt1(:,ias,1,ist1),zfmt) end if call zfsht(nrc,nrci,zfmt,zrhomt1(:,ias,ist1)) end do ! compute the complex overlap densities for the core-core states ic=0 do ist1=1,nstsp(is) if (spcore(ist1,is)) then do m2=-ksp(ist1,is),ksp(ist1,is)-1 ic=ic+1 call wavefcr(.false.,lradstp,is,ia,ist1,m2,npcmtmax,wfcr2) call zrho2(npc,wfcr1,wfcr1(:,2),wfcr2,wfcr2(:,2),zfmt) call zfsht(nrc,nrci,zfmt,zrhomt2(:,ic)) end do end if end do do ist2=1,nstsv if (evalsv(ist2,ikp).gt.efermi) then ! calculate the Coulomb potential call zpotclmt(nrc,nrci,nrcmtmax,rlcmt(:,:,is),wprcmt(:,:,is), & zrhomt1(:,ias,ist2),zvclmt) !-------------------------------------------! ! valence-core-valence contribution ! !-------------------------------------------! do ist1=1,nstsv if (evalsv(ist1,ikp).lt.efermi) then z1=zfmtinp(nrc,nrci,wrcmt(:,is),zrhomt1(:,ias,ist1),zvclmt) vclvv(ist1,ist2)=vclvv(ist1,ist2)-z1 end if end do !----------------------------------------! ! core-core-valence contribution ! !----------------------------------------! ic=0 do ist1=1,nstsp(is) if (spcore(ist1,is)) then do m2=-ksp(ist1,is),ksp(ist1,is)-1 ic=ic+1 z1=zfmtinp(nrc,nrci,wrcmt(:,is),zrhomt2(:,ic),zvclmt) vclcv(ic,ias,ist2)=vclcv(ic,ias,ist2)-z1 end do ! end loop over ist1 end if end do ! end loop over ist2 end if end do ! end loops over ist3 and m1 end do end if end do ! end loops over atoms and species end do end do deallocate(vgqc,gqc,gclgq,jlgqrmt) deallocate(apwalm,evecfv,evecsv,ylmgq,sfacgq) deallocate(wfmt1,wfmt2,wfir1,wfir2,wfcr1,wfcr2) deallocate(zrhomt1,zrhomt2,zrhoir1) deallocate(zvclmt,zvclir,zfmt) return contains pure subroutine zrho1(n,x,y,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x(n),y(n) complex(8), intent(out) :: z(n) z(:)=conjg(x(:))*y(:) end subroutine pure subroutine zrho2(n,x1,x2,y1,y2,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x1(n),x2(n),y1(n),y2(n) complex(8), intent(out) :: z(n) z(:)=conjg(x1(:))*y1(:)+conjg(x2(:))*y2(:) end subroutine end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/polar.f900000644000000000000000000000013214061636517014361 xustar0030 mtime=1623670095.427102017 30 atime=1623670094.213103143 30 ctime=1623670095.427102017 elk-7.2.42/src/polar.f900000644002504400250440000000501014061636517016412 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: polar ! !INTERFACE: subroutine polar(pvl) ! !USES: use modmain use modstore use modmpi use modomp ! !INPUT/OUTPUT PARAMETERS: ! pvl : polarisation vector modulo $2\pi$ (out,real(8)) ! !DESCRIPTION: ! Calculates the polarisation vector modulo $2\pi$ in lattice coordinates ! using the formula of R. D. King-Smith and David Vanderbilt [Phys. Rev. B ! {\bf 47}, 1651(R) (1993)], namely ! $$ P_l=\sum_{\bf k}{\rm Im}\ln\det\left(\langle ! u_{i{\bf k}+\Delta{\bf k}_l}|u_{j{\bf k}}\rangle\right),$$ ! where $\Delta{\bf k}_l=(1/n_l){\bf B}_l$ and ${\bf B}_l$ is a reciprocal ! lattice vector. The number of points $n_l$ is equal to that of the original ! $k$-point grid in direction of ${\bf B}_l$, multiplied by {\tt nskpolar}. ! See also the routines {\tt polark} and {\tt bornechg}. ! ! !REVISION HISTORY: ! Created May 2020 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(out) :: pvl(3) ! local variables integer ik,l,nthd real(8) vc(3),vgqc(3),gqc,pl ! allocatable arrays real(8), allocatable :: jlgqr(:,:) complex(8), allocatable :: ylmgq(:),sfacgq(:),expqmt(:,:) ! allocate local arrays allocate(jlgqr(njcmax,nspecies)) allocate(ylmgq(lmmaxo),sfacgq(natmtot)) allocate(expqmt(npcmtmax,natmtot)) maxscl=1 ! loop over reciprocal lattice vectors do l=1,3 ! create fine k-point grid in direction l ngridk(:)=ngridk_(:) ngridk(l)=nkspolar*ngridk(l) ! run one loop of the ground-state calculation call gndstate ! difference between adjacent k-vectors in this reciprocal lattice direction vc(:)=bvec(:,l)/dble(ngridk(l)) ! calculate the phase factor function exp(iq.r) call gengqf(1,vc,vgqc,gqc,jlgqr,ylmgq,sfacgq) call genexpmt(1,jlgqr,ylmgq,1,sfacgq,expqmt) pl=0.d0 ! parallel loop over non-reduced k-points call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP REDUCTION(+:pl) & !$OMP NUM_THREADS(nthd) do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call polark(ik,l,expqmt,pl) end do !$OMP END PARALLEL DO call freethd(nthd) ! add polarisation from each process and redistribute if (np_mpi.gt.1) then call mpi_allreduce(mpi_in_place,pl,1,mpi_double_precision,mpi_sum,mpicom, & ierror) end if pvl(l)=pl end do ! restore original input parameters ngridk(:)=ngridk_(:) maxscl=maxscl_ deallocate(jlgqr,ylmgq,sfacgq,expqmt) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/dbxcplot.f900000644000000000000000000000013214061636517015063 xustar0030 mtime=1623670095.429102015 30 atime=1623670094.215103142 30 ctime=1623670095.429102015 elk-7.2.42/src/dbxcplot.f900000644002504400250440000000416114061636517017122 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dbxcplot use modmain implicit none ! local variables integer idm,is,ias,np ! allocatable arrays real(8), allocatable :: rvfmt(:,:,:),rvfir(:,:) real(8), allocatable :: rfmt(:,:),rfir(:) real(8), allocatable :: grfmt(:,:,:),grfir(:,:) ! initialise universal variables call init0 if (.not.spinpol) then write(*,*) write(*,'("Error(dbxcplot): spin-unpolarised magnetic field is zero")') write(*,*) stop end if ! read magnetisation from file call readstate allocate(rvfmt(npmtmax,natmtot,3),rvfir(ngtot,3)) allocate(rfmt(npmtmax,natmtot),rfir(ngtot)) allocate(grfmt(npmtmax,natmtot,3),grfir(ngtot,3)) if (ncmag) then ! non-collinear rvfmt(:,:,:)=bxcmt(:,:,:) rvfir(:,:)=bxcir(:,:) else ! collinear rvfmt(:,:,1:2)=0.d0 rvfir(:,1:2)=0.d0 rvfmt(:,:,3)=bxcmt(:,:,1) rvfir(:,3)=bxcir(:,1) end if rfmt(:,:)=0.d0 rfir(:)=0.d0 do idm=1,3 call gradrf(rvfmt(:,:,idm),rvfir(:,idm),grfmt,grfir) do ias=1,natmtot is=idxis(ias) np=npmt(is) rfmt(1:np,ias)=rfmt(1:np,ias)+grfmt(1:np,ias,idm) end do rfir(:)=rfir(:)+grfir(:,idm) end do select case(task) case(91) open(50,file='DBXC1D.OUT',form='FORMATTED') open(51,file='DBXCLINES.OUT',form='FORMATTED') call plot1d(50,51,1,rfmt,rfir) close(50) close(51) write(*,*) write(*,'("Info(dbxcplot):")') write(*,'(" 1D divergence of exchange-correlation field written to & &DBXC1D.OUT")') write(*,'(" vertex location lines written to DBXCLINES.OUT")') case(92) open(50,file='DBXC2D.OUT',form='FORMATTED') call plot2d(.false.,50,1,rfmt,rfir) close(50) write(*,'("Info(dbxcplot):")') write(*,'(" 2D divergence of exchange-correlation field written to & &DBXC2D.OUT")') case(93) open(50,file='DBXC3D.OUT',form='FORMATTED') call plot3d(50,1,rfmt,rfir) close(50) write(*,'("Info(dbxcplot):")') write(*,'(" 3D divergence of exchange-correlation field written to & &DBXC3D.OUT")') end select deallocate(rvfmt,rvfir,rfmt,rfir,grfmt,grfir) end subroutine elk-7.2.42/src/PaxHeaders.21776/sbesseldm.f900000644000000000000000000000013114061636517015224 xustar0030 mtime=1623670095.430102014 29 atime=1623670094.21710314 30 ctime=1623670095.430102014 elk-7.2.42/src/sbesseldm.f900000644002504400250440000000603614061636517017267 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: sbesseldm ! !INTERFACE: subroutine sbesseldm(m,lmax,x,djl) ! !INPUT/OUTPUT PARAMETERS: ! m : order of derivatve (in,integer) ! lmax : maximum order of Bessel function (in,integer) ! x : real argument (in,real) ! djl : array of returned values (out,real(0:lmax)) ! !DESCRIPTION: ! Computes the $m$th derivative of the spherical Bessel function of the first ! kind, $j_l(x)$, for argument $x$ and $l=0,1,\ldots,l_{\rm max}$. For ! $x\ge 1$ this is done by repeatedly using the relations ! \begin{align*} ! \frac{d}{dx}j_l(x)&=\frac{l}{x}j_l(x)-j_{l+1}(x) \\ ! j_{l+1}(x)&=\frac{2l+1}{x}j_l(x)-j_{l-1}(x). ! \end{align*} ! While for $x<1$ the series expansion of the Bessel function is used ! $$ \frac{d^m}{dx^m}j_l(x)=\sum_{i=0}^{\infty} ! \frac{(2i+l)!}{(-2)^ii!(2i+l-m)!(2i+2l+1)!!}x^{2i+l-m}. $$ ! This procedure is numerically stable and accurate to near machine precision ! for $l\le 30$ and $m\le 6$. ! ! !REVISION HISTORY: ! Created March 2003 (JKD) ! Modified to return an array of values, October 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: m,lmax real(8), intent(in) :: x real(8), intent(out) :: djl(0:lmax) ! local variables integer, parameter :: maxm=6,maxns=20 integer i,j,l,i0 real(8) t1,sm,x2 ! automatic arrays integer a(0:maxm+1),a1(0:maxm+1) integer b(0:maxm+1),b1(0:maxm+1) real(8) jl(0:lmax+1) ! external functions real(8), external :: factnm,factr if (m.eq.0) then call sbessel(lmax,x,djl) return end if if ((m.lt.0).or.(m.gt.maxm)) then write(*,*) write(*,'("Error(sbesseldm): m out of range : ",I8)') m write(*,*) stop end if if ((lmax.lt.0).or.(lmax.gt.30)) then write(*,*) write(*,'("Error(sbesseldm): lmax out of range : ",I8)') lmax write(*,*) stop end if if ((x.lt.0.d0).or.(x.gt.1.d5)) then write(*,*) write(*,'("Error(sbesseldm): x out of range : ",G18.10)') x write(*,*) stop end if if (x.gt.1.d0) then call sbessel(lmax+1,x,jl) do l=0,lmax a(1:m+1)=0 a(0)=1 a1(0:m+1)=0 do i=1,m b(0)=0 b1(0)=0 do j=0,i b(j+1)=a(j)*(l-j) b1(j+1)=-a1(j)*(j+l+2) end do do j=0,i b1(j)=b1(j)-a(j) b(j)=b(j)+a1(j) end do a(0:i+1)=b(0:i+1) a1(0:i+1)=b1(0:i+1) end do t1=1.d0 sm=dble(a(0))*jl(l)+dble(a1(0))*jl(l+1) do i=1,m+1 t1=t1*x sm=sm+(dble(a(i))*jl(l)+dble(a1(i))*jl(l+1))/t1 end do djl(l)=sm end do else x2=x**2 do l=0,lmax i0=max((m-l+1)/2,0) j=2*i0+l-m if (j.eq.0) then t1=1.d0 else t1=x**j end if t1=factr(j+m,j)*t1/(factnm(i0,1)*factnm(j+l+m+1,2)*dble((-2)**i0)) sm=t1 do i=i0+1,maxns j=2*i+l t1=-t1*dble((j-1)*j)*x2/dble((j-l)*(j-m-1)*(j-m)*(j+l+1)) if (abs(t1).le.1.d-40) exit sm=sm+t1 end do djl(l)=sm end do end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writehmlbse.f900000644000000000000000000000013214061636517015571 xustar0030 mtime=1623670095.432102012 30 atime=1623670094.218103139 30 ctime=1623670095.432102012 elk-7.2.42/src/writehmlbse.f900000644002504400250440000000533114061636517017630 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writehmlbse use modmain use modmpi ! sets up the BSE matrix and writes it to file implicit none ! local variables integer ik,jk,ist,jst integer a,b,i,j,m,n real(8) t1 ! initialise global variables call init0 call init1 call init2 call init3 ! read density and potentials from file call readstate ! read Fermi energy from a file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! check if system is metallic t1=minval(abs(0.5d0-occsv(:,:)/occmax)) if (abs(t1-0.5d0).gt.0.01d0) then write(*,*) write(*,'("Warning(writehmlbse): system is metallic, the BSE may fail")') write(*,'("Try using a different vkloff or reducing swidth")') end if ! generate the BSE state index arrays call genidxbse if (allocated(hmlbse)) deallocate(hmlbse) allocate(hmlbse(nmbse,nmbse)) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) if (mp_mpi) then write(*,*) write(*,'("Info(writehmlbse): setting up BSE Hamiltonian matrix")') end if ! zero the BSE Hamiltonian hmlbse(:,:)=0.d0 ! compute diagonal matrix elements do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) do i=1,nvbse ist=istbse(i,ik) do j=1,ncbse jst=jstbse(j,ik) a=ijkbse(i,j,ik) hmlbse(a,a)=(evalsv(jst,jk)+scissor)-evalsv(ist,jk) if (bsefull) then b=a+nbbse hmlbse(b,b)=-hmlbse(a,a) end if end do end do end do ! add the exchange matrix elements if (hxbse) call hmlxbse ! add the direct matrix elements if (hdbse) call hmldbse ! add matrices from all processes and redistribute if (np_mpi.gt.1) then ! ensure that the number of elements transmitted by MPI is not larger than the ! maximum packet size (assumed to be 1024³ bytes) m=67108864/nmbse do b=1,nmbse,m n=min(nmbse-b+1,m) n=nmbse*n call mpi_allreduce(mpi_in_place,hmlbse(1,b),n,mpi_double_complex,mpi_sum, & mpicom,ierror) end do end if ! write the BSE matrix to HMLBSE.OUT if (mp_mpi) then open(140,file='HMLBSE.OUT',form='UNFORMATTED',action='WRITE') write(140) nmbse write(140) hmlbse close(140) write(*,*) write(*,'("Info(writehmlbse): BSE Hamiltonian matrix written to HMLBSE.OUT")') end if ! deallocate global BSE arrays deallocate(istbse,jstbse,ijkbse,hmlbse) end subroutine elk-7.2.42/src/PaxHeaders.21776/dielectric_bse.f900000644000000000000000000000013214061636517016204 xustar0030 mtime=1623670095.433102011 30 atime=1623670094.220103137 30 ctime=1623670095.433102011 elk-7.2.42/src/dielectric_bse.f900000644002504400250440000000654514061636517020253 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dielectric_bse use modmain use modtest implicit none ! local variables integer a1,a2,ik1,jk1 integer i1,j1,ist1,jst1 integer iw,i,j,l integer ios,nmbse_ real(8) e,eji,t1,t2 complex(8) eta,zv(3),z1 character(256) fname ! allocatable arrays real(8), allocatable :: w(:) complex(8), allocatable :: pmat(:,:,:),sigma(:,:,:) ! initialise global variables call init0 call init1 ! read Fermi energy from a file call readfermi ! get the eigenvalues from file do ik1=1,nkpt call getevalsv(filext,ik1,vkl(:,ik1),evalsv(:,ik1)) end do ! generate the BSE state index arrays call genidxbse ! allocate global BSE arrays if (allocated(evalbse)) deallocate(evalbse) allocate(evalbse(nmbse)) if (allocated(hmlbse)) deallocate(hmlbse) allocate(hmlbse(nmbse,nmbse)) ! read in the BSE eigenvectors and eigenvalues open(140,file='EVBSE.OUT',form='UNFORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(dielectric_bse): error opening EVBSE.OUT")') write(*,*) stop end if read(140) nmbse_ if (nmbse.ne.nmbse_) then write(*,*) write(*,'("Error(dielectric_bse): differing nmbse")') write(*,'(" current : ",I6)') nmbse write(*,'(" EVBSE.OUT : ",I6)') nmbse_ stop end if read(140) evalbse read(140) hmlbse close(140) ! allocate local arrays allocate(w(nwplot)) allocate(pmat(nstsv,nstsv,3)) allocate(sigma(3,3,nwplot)) ! set up the frequency grid (starting from zero) t1=wplot(2)/dble(nwplot) do iw=1,nwplot w(iw)=t1*dble(iw-1) end do ! i divided by the complex relaxation time eta=cmplx(0.d0,swidth,8) sigma(:,:,:)=0.d0 do a2=1,nmbse e=evalbse(a2) zv(:)=0.d0 ! loop over non-reduced k-points do ik1=1,nkptnr ! equivalent reduced k-point jk1=ivkik(ivk(1,ik1),ivk(2,ik1),ivk(3,ik1)) ! read the momentum matrix elements from file call getpmat(vkl(:,ik1),pmat) do i1=1,nvbse ist1=istbse(i1,ik1) do j1=1,ncbse jst1=jstbse(j1,ik1) a1=ijkbse(i1,j1,ik1) eji=evalsv(jst1,jk1)-evalsv(ist1,jk1) z1=(e/eji)*hmlbse(a1,a2) zv(:)=zv(:)+z1*pmat(ist1,jst1,:) end do end do end do if (abs(e).gt.1.d-8) then do i=1,3 do j=1,3 z1=zv(i)*conjg(zv(j))/e sigma(i,j,:)=sigma(i,j,:)+z1/(w(:)-e+eta)+conjg(z1)/(w(:)+e+eta) end do end do end if end do z1=zi*occmax*wkptnr/omega sigma(:,:,:)=z1*sigma(:,:,:) ! loop over tensor components do l=1,noptcomp i=optcomp(1,l) j=optcomp(2,l) t1=0.d0 if (i.eq.j) t1=1.d0 write(fname,'("EPSILON_BSE_",2I1,".OUT")') i,j open(50,file=trim(fname),form='FORMATTED') do iw=1,nwplot t2=t1-fourpi*aimag(sigma(i,j,iw)/(w(iw)+eta)) write(50,'(2G18.10)') w(iw),t2 end do write(50,*) do iw=1,nwplot t2=fourpi*dble(sigma(i,j,iw)/(w(iw)+eta)) write(50,'(2G18.10)') w(iw),t2 end do close(50) end do write(*,*) write(*,'("Info(dielectric_bse):")') write(*,'(" dielectric tensor written to EPSILON_BSE_ij.OUT")') write(*,'(" for components")') do l=1,noptcomp write(*,'(" i = ",I1,", j = ",I1)') optcomp(1:2,l) end do ! write sigma to test file call writetest(187,'BSE optical conductivity',nv=nwplot,tol=1.d-3,zva=sigma) deallocate(w,pmat,sigma) ! deallocate global BSE arrays deallocate(evalbse,hmlbse) end subroutine elk-7.2.42/src/PaxHeaders.21776/vecplot.f900000644000000000000000000000013214061636517014720 xustar0030 mtime=1623670095.435102009 30 atime=1623670094.222103135 30 ctime=1623670095.435102009 elk-7.2.42/src/vecplot.f900000644002504400250440000001241514061636517016760 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: vecplot ! !INTERFACE: subroutine vecplot ! !DESCRIPTION: ! Outputs a 2D or 3D vector field for plotting. The vector field can be the ! magnetisation vector field, ${\bf m}$; the exchange-correlation magnetic ! field, ${\bf B}_{\rm xc}$; or the electric field ! ${\bf E}\equiv-\nabla V_{\rm C}$. The magnetisation is obtained from the ! spin density matrix, $\rho_{\alpha\beta}$, by solving ! $$ \rho_{\alpha\beta}({\bf r})=\frac{1}{2}\left(n({\bf r}) ! \delta_{\alpha\beta}+\sigma\cdot {\bf m}({\bf r})\right), $$ ! where $n\equiv\tr\rho_{\alpha\beta}$ is the total density. In the case of 2D ! plots, the magnetisation vectors are still 3D, but are in the coordinate ! system of the plane. ! ! !REVISION HISTORY: ! Created August 2004 (JKD) ! Included electric field plots, August 2006 (JKD) !EOP !BOC use modmain implicit none ! allocatable arrays real(8), allocatable :: rvfmt(:,:,:),rvfir(:,:) ! initialise universal variables call init0 if ((task.eq.72).or.(task.eq.73).or.(task.eq.82).or.(task.eq.83)) then if (.not.spinpol) then write(*,*) write(*,'("Error(vecplot): spin-unpolarised magnetisation/field is zero")') write(*,*) stop end if end if ! read magnetisation and exchange-correlation magnetic field from file call readstate allocate(rvfmt(npmtmax,natmtot,3),rvfir(ngtot,3)) select case(task) case(71,72,73) ! magnetisation if (ncmag) then ! non-collinear rvfmt(:,:,:)=magmt(:,:,:) rvfir(:,:)=magir(:,:) else ! collinear rvfmt(:,:,1:2)=0.d0 rvfir(:,1:2)=0.d0 rvfmt(:,:,3)=magmt(:,:,1) rvfir(:,3)=magir(:,1) end if case(81,82,83) ! exchange-correlation magnetic field if (ncmag) then ! non-collinear rvfmt(:,:,:)=bxcmt(:,:,:) rvfir(:,:)=bxcir(:,:) else ! collinear rvfmt(:,:,1:2)=0.d0 rvfir(:,1:2)=0.d0 rvfmt(:,:,3)=bxcmt(:,:,1) rvfir(:,3)=bxcir(:,1) end if case(141,142,143) ! electric field call gradrf(vclmt,vclir,rvfmt,rvfir) ! use the negative of the gradient rvfmt(:,:,:)=-rvfmt(:,:,:) rvfir(:,:)=-rvfir(:,:) case(151,152,153) if (.not.ncmag) then write(*,*) write(*,'("Error(vecplot): collinear m(r) x B_xc(r) is zero")') write(*,*) stop end if call rvfcross(magmt,magir,bxcmt,bxcir,rvfmt,rvfir) end select select case(task) case(71,81,141,151) if (task.eq.71) then open(50,file='MAG1D.OUT',form='FORMATTED') open(51,file='MAGLINES.OUT',form='FORMATTED') else if (task.eq.81) then open(50,file='BXC1D.OUT',form='FORMATTED') open(51,file='BXCLINES.OUT',form='FORMATTED') else if (task.eq.141) then open(50,file='EF1D.OUT',form='FORMATTED') open(51,file='EFLINES.OUT',form='FORMATTED') else open(50,file='MCBXC1D.OUT',form='FORMATTED') open(51,file='MCBXCLINES.OUT',form='FORMATTED') end if call plot1d(50,51,3,rvfmt,rvfir) close(50) write(*,*) write(*,'("Info(vecplot):")') if (task.eq.71) then write(*,'(" 1D magnetisation density written to MAG1D.OUT")') write(*,'(" vertex location lines written to MAGLINES.OUT")') else if (task.eq.81) then write(*,'(" 1D exchange-correlation field written to BXC1D.OUT")') write(*,'(" vertex location lines written to BXCLINES.OUT")') else if (task.eq.141) then write(*,'(" 1D electric field written to EF1D.OUT")') write(*,'(" vertex location lines written to EFLINES.OUT")') else write(*,'(" 1D m(r) x B_xc(r) written to MCBXC1D.OUT")') write(*,'(" vertex location lines written to MCBXCLINES.OUT")') end if case(72,82,142,152) if (task.eq.72) then open(50,file='MAG2D.OUT',form='FORMATTED') else if (task.eq.82) then open(50,file='BXC2D.OUT',form='FORMATTED') else if (task.eq.142) then open(50,file='EF2D.OUT',form='FORMATTED') else open(50,file='MCBXC2D.OUT',form='FORMATTED') end if call plot2d(.true.,50,3,rvfmt,rvfir) close(50) write(*,*) write(*,'("Info(vecplot):")') if (task.eq.72) then write(*,'(" 2D magnetisation density written to MAG2D.OUT")') else if (task.eq.82) then write(*,'(" 2D exchange-correlation field written to BXC2D.OUT")') else if (task.eq.142) then write(*,'(" 2D electric field written to EF2D.OUT")') else write(*,'(" 2D m(r) x B_xc(r) written to MCBXC2D.OUT")') end if write(*,'(" Note that the 3D vector field has been locally projected")') write(*,'(" onto the 2D plotting plane axes")') case(73,83,143,153) if (task.eq.73) then open(50,file='MAG3D.OUT',form='FORMATTED') else if (task.eq.83) then open(50,file='BXC3D.OUT',form='FORMATTED') else if (task.eq.143) then open(50,file='EF3D.OUT',form='FORMATTED') else open(50,file='MCBXC3D.OUT',form='FORMATTED') end if call plot3d(50,3,rvfmt,rvfir) close(50) write(*,*) write(*,'("Info(vecplot):")') if (task.eq.73) then write(*,'(" 3D magnetisation density written to MAG3D.OUT")') else if (task.eq.83) then write(*,'(" 3D exchange-correlation field written to BXC3D.OUT")') else if (task.eq.143) then write(*,'(" 3D electric field written to EF3D.OUT")') else write(*,'(" 3D m(r) x B_xc(r) written to MCBXC3D.OUT")') end if end select deallocate(rvfmt,rvfir) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/nesting.f900000644000000000000000000000013214061636517014713 xustar0030 mtime=1623670095.436102008 30 atime=1623670094.223103134 30 ctime=1623670095.436102008 elk-7.2.42/src/nesting.f900000644002504400250440000000441714061636517016756 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine nesting use modmain use modomp implicit none ! local variables integer iq,ik,jk,jkq,ivkq(3) integer ist,i1,i2,i3,nthd real(8) sm0,sm1,sm2,sm3 real(8) vl(3),vc(3),x,t1 ! allocatable arrays real(8), allocatable :: nq(:) ! external functions real(8), external :: sdelta ! initialise universal variables call init0 call init1 call init2 ! read Fermi energy from file call readfermi ! get the eigenvalues from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) end do allocate(nq(nqpt)) t1=1.d0/swidth sm0=0.d0 call holdthd(nqpt,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(sm1,sm2,sm3,ik,jk) & !$OMP PRIVATE(ivkq,jkq,ist,x) & !$OMP REDUCTION(+:sm0) & !$OMP NUM_THREADS(nthd) do iq=1,nqpt !$OMP CRITICAL(nesting_) write(*,'("Info(nesting): ",I6," of ",I6," q-points")') iq,nqpt !$OMP END CRITICAL(nesting_) sm1=0.d0 do ik=1,nkptnr jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ivkq(:)=ivk(:,ik)+ivq(:,iq) ivkq(:)=mod(ivkq(:),ngridk(:)) jkq=ivkik(ivkq(1),ivkq(2),ivkq(3)) sm2=0.d0 do ist=1,nstsv x=(efermi-evalsv(ist,jk))*t1 sm2=sm2+sdelta(stype,x)*t1 end do sm3=0.d0 do ist=1,nstsv x=(efermi-evalsv(ist,jkq))*t1 sm3=sm3+sdelta(stype,x)*t1 end do sm1=sm1+sm2*sm3 end do nq(iq)=occmax*omegabz*wkptnr*sm1 sm0=sm0+omegabz*wqpt(iq)*nq(iq) end do !$OMP END PARALLEL DO call freethd(nthd) open(50,file='NEST3D.OUT',form='FORMATTED') write(50,'(3I6," : grid size")') ngridq(:) do i3=0,ngridq(3)-1 vl(3)=dble(i3)/dble(ngridq(3)) do i2=0,ngridq(2)-1 vl(2)=dble(i2)/dble(ngridq(2)) do i1=0,ngridq(1)-1 vl(1)=dble(i1)/dble(ngridq(1)) vc(:)=bvec(:,1)*vl(1)+bvec(:,2)*vl(2)+bvec(:,3)*vl(3) iq=ivqiq(i1,i2,i3) write(50,'(4G18.10)') vc(:),nq(iq) end do end do end do close(50) open(50,file='NESTING.OUT',form='FORMATTED') write(50,'(G18.10)') sm0 close(50) write(*,*) write(*,'("Info(nesting):")') write(*,'(" Nesting function N(q) written to NEST3D.OUT for plotting")') write(*,*) write(*,'(" Total integrated nesting per unit volume written to NESTING.OUT")') deallocate(nq) end subroutine elk-7.2.42/src/PaxHeaders.21776/writeevbse.f900000644000000000000000000000013214061636517015423 xustar0030 mtime=1623670095.438102006 30 atime=1623670094.225103132 30 ctime=1623670095.438102006 elk-7.2.42/src/writeevbse.f900000644002504400250440000000437714061636517017473 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeevbse use modmain implicit none ! local variables integer ik,a integer ios,nmbse_ ! allocatable arrays complex(8), allocatable :: w(:) ! initialise global variables call init0 call init1 ! read Fermi energy from a file call readfermi ! get the eigenvalues from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) end do ! generate the BSE state index arrays call genidxbse ! allocate global BSE arrays if (allocated(evalbse)) deallocate(evalbse) allocate(evalbse(nmbse)) if (allocated(hmlbse)) deallocate(hmlbse) allocate(hmlbse(nmbse,nmbse)) ! read in BSE Hamiltonian matrix open(140,file='HMLBSE.OUT',form='UNFORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(writeevbse): error opening HMLBSE.OUT")') write(*,*) stop end if read(140) nmbse_ if (nmbse.ne.nmbse_) then write(*,*) write(*,'("Error(writeevbse): differing nmbse")') write(*,'(" current : ",I6)') nmbse write(*,'(" HMLBSE.OUT : ",I6)') nmbse_ write(*,*) stop end if read(140) hmlbse close(140) write(*,*) write(*,'("Info(writeevbse): diagonalising the BSE Hamiltonian matrix")') if (bsefull) then ! full non-Hermitian matrix allocate(w(nmbse)) call eveqnzg(nmbse,nmbse,hmlbse,w) evalbse(:)=dble(w(:)) else ! Hermitian block only call eveqnzh(nmbse,nmbse,hmlbse,evalbse) end if ! write the BSE eigenvectors and eigenvalues to file open(140,file='EVBSE.OUT',form='UNFORMATTED',action='WRITE') write(140) nmbse write(140) evalbse write(140) hmlbse close(140) ! write the BSE eigenvalues to file open(50,file='EIGVAL_BSE.OUT',form='FORMATTED',action='WRITE') write(50,'(I6," : nmbse")') nmbse if (bsefull) then do a=1,nmbse write(50,'(I6,2G18.10)') a,dble(w(a)),aimag(w(a)) end do deallocate(w) else do a=1,nmbse write(50,'(I6,G18.10)') a,evalbse(a) end do end if close(50) write(*,*) write(*,'("Info(writeevbse):")') write(*,'(" BSE eigenvectors and eigenvalues written to EVBSE.OUT")') write(*,'(" BSE eigenvalues written to EIGVAL_BSE.OUT")') ! deallocate global BSE arrays deallocate(evalbse,hmlbse) end subroutine elk-7.2.42/src/PaxHeaders.21776/emdplot3d.f900000644000000000000000000000013114061636517015136 xustar0030 mtime=1623670095.439102006 29 atime=1623670094.22710313 30 ctime=1623670095.439102006 elk-7.2.42/src/emdplot3d.f900000644002504400250440000000202514061636517017173 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 D. Ernsting, S. Dugdale and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine emdplot3d(emds) use modmain use modpw use modomp implicit none ! arguments real(4), intent(in) :: emds(nhkmax,nkpt) ! local variables integer np,ip,nthd real(8) v1(3),t1 ! allocatable arrays real(8), allocatable :: vpl(:,:) ! external functions real(8), external :: rfhkintp ! total number of plot points np=np3d(1)*np3d(2)*np3d(3) ! generate the 3D plotting points allocate(vpl(3,np)) call plotpt3d(vpl) open(50,file='EMD3D.OUT',form='FORMATTED') write(50,'(3I6," : grid size")') np3d(:) call holdthd(np,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(t1,v1) & !$OMP NUM_THREADS(nthd) !$OMP DO ORDERED do ip=1,np t1=rfhkintp(vpl(:,ip),emds) call r3mv(bvec,vpl(:,ip),v1) !$OMP ORDERED write(50,'(4G18.10)') v1(:),t1 !$OMP END ORDERED end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) close(50) deallocate(vpl) end subroutine elk-7.2.42/src/PaxHeaders.21776/emdplot2d.f900000644000000000000000000000013214061636517015136 xustar0030 mtime=1623670095.441102004 30 atime=1623670094.229103129 30 ctime=1623670095.441102004 elk-7.2.42/src/emdplot2d.f900000644002504400250440000000311314061636517017171 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 D. Ernsting, S. Dugdale and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine emdplot2d(emds) use modmain use modpw use modomp implicit none ! arguments real(4), intent(in) :: emds(nhkmax,nkpt) ! local variables integer nh(3),np,ip,n,i,nthd real(8) vpnl(3),v1(3),t1 ! allocatable arrays real(8), allocatable :: vpl(:,:),vppc(:,:) real(8), allocatable :: x(:),wx(:),f(:) ! external functions real(8), external :: rfhkintp ! allocate local arrays np=np2d(1)*np2d(2) allocate(vpl(3,np),vppc(2,np)) ! generate the 2D plotting points call plotpt2d(bvec,binv,vpnl,vpl,vppc) ! determine the number of integration points nh(:)=int(hkmax*sqrt(avec(1,:)**2+avec(2,:)**2+avec(3,:)**2)/pi)+1 n=2*maxval(nh(:)*ngridk(:)) allocate(x(n),wx(n)) do i=1,n t1=2.d0*dble(i-1)/dble(n-1)-1.d0 x(i)=t1*hkmax end do ! determine the weights for spline integration call wsplint(n,x,wx) open(50,file='EMD2D.OUT',form='FORMATTED') write(50,'(2I6," : grid size")') np2d(:) ! loop over plotting points in the 2D plane call holdthd(np,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(f,i,v1,t1) & !$OMP NUM_THREADS(nthd) allocate(f(n)) !$OMP DO ORDERED do ip=1,np ! integrate along normal to plane do i=1,n v1(:)=vpl(:,ip)+x(i)*vpnl(:) f(i)=rfhkintp(v1,emds) end do t1=dot_product(wx(:),f(:)) !$OMP ORDERED write(50,'(3G18.10)') vppc(1,ip),vppc(2,ip),t1 !$OMP END ORDERED end do !$OMP END DO deallocate(f) !$OMP END PARALLEL call freethd(nthd) close(50) deallocate(vpl,vppc,x,wx) end subroutine elk-7.2.42/src/PaxHeaders.21776/emdplot1d.f900000644000000000000000000000013214061636517015135 xustar0030 mtime=1623670095.442102003 30 atime=1623670094.230103128 30 ctime=1623670095.442102003 elk-7.2.42/src/emdplot1d.f900000644002504400250440000000470414061636517017177 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 D. Ernsting, S. Dugdale and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine emdplot1d(emds) use modmain use modpw use modomp use modtest implicit none ! arguments real(4), intent(in) :: emds(nhkmax,nkpt) ! local variables integer nh(3),ip,n,i,j,nthd real(8) vl1(3),vl2(3),vl3(3) real(8) vc1(3),vc2(3),vc3(3),t1 ! allocatable arrays real(8), allocatable :: x(:),wx(:),f1(:),f2(:) ! external functions real(8), external :: rfhkintp ! generate the 1D plotting points: use only the first segment call plotpt1d(bvec,2,npp1d,vvlp1d,vplp1d,dvp1d,dpp1d) ! compute two vectors orthogonal to each other and the plotting vector; these ! are the directions to be used for integration vl1(:)=vvlp1d(:,2)-vvlp1d(:,1) call r3mv(bvec,vl1,vc1) t1=sqrt(vc1(1)**2+vc1(2)**2+vc1(3)**2) if (t1.lt.epslat) then write(*,*) write(*,'("Error(emdplot1d): zero length plotting vector")') write(*,*) stop end if vc1(:)=vc1(:)/t1 i=1 do j=2,3 if (abs(vc1(j)).lt.abs(vc1(i))) i=j end do vc2(:)=0.d0 vc2(i)=1.d0 t1=dot_product(vc1,vc2) vc2(:)=vc2(:)-t1*vc1(:) t1=sqrt(vc2(1)**2+vc2(2)**2+vc2(3)**2) vc2(:)=vc2(:)/t1 call r3cross(vc1,vc2,vc3) ! integration directions in lattice coordinates call r3mv(binv,vc2,vl2) call r3mv(binv,vc3,vl3) ! determine the number of integration points nh(:)=int(hkmax*sqrt(avec(1,:)**2+avec(2,:)**2+avec(3,:)**2)/pi)+1 n=2*maxval(nh(:)*ngridk(:)) allocate(x(n),wx(n)) do i=1,n t1=2.d0*dble(i-1)/dble(n-1)-1.d0 x(i)=t1*hkmax end do ! determine the weights for spline integration call wsplint(n,x,wx) open(50,file='EMD1D.OUT',form='FORMATTED') write(*,*) ! loop over plotting points along 1D line call holdthd(npp1d,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(f1,f2,i,j,vl1,t1) & !$OMP NUM_THREADS(nthd) allocate(f1(n),f2(n)) !$OMP DO ORDERED do ip=1,npp1d do i=1,n do j=1,n vl1(:)=vplp1d(:,ip)+x(i)*vl2(:)+x(j)*vl3(:) f1(j)=rfhkintp(vl1,emds) end do f2(i)=dot_product(wx(:),f1(:)) end do t1=dot_product(wx(:),f2(:)) !$OMP ORDERED write(*,'("Info(emdplot1d): done ",I6," of ",I6," points")') ip,npp1d write(50,'(2G18.10)') dpp1d(ip),t1 flush(50) !$OMP END ORDERED ! write to test file if required if (test.and.(ip.eq.1)) then call writetest(171,'integrated EMD',nv=n,tol=1.d-4,rva=f2) end if end do !$OMP END DO deallocate(f1,f2) !$OMP END PARALLEL call freethd(nthd) close(50) deallocate(x,wx) end subroutine elk-7.2.42/src/PaxHeaders.21776/rfhkintp.f900000644000000000000000000000013214061636517015071 xustar0030 mtime=1623670095.444102001 30 atime=1623670094.232103126 30 ctime=1623670095.444102001 elk-7.2.42/src/rfhkintp.f900000644002504400250440000000461314061636517017132 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 D. Ernsting, S. Dugdale and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. real(8) function rfhkintp(vhpl,rfhk) use modmain use modpw implicit none ! arguments real(8), intent(in) :: vhpl(3) real(4), intent(in) :: rfhk(nhkmax,nkpt) ! local variables integer ivh0(3),ivk0(3),ihk integer ivhb(3,0:1,0:1,0:1) integer ivkb(3,0:1,0:1,0:1) integer isym,lspl,ik,jk,i,j,k real(8) vpl(3),fb(0:1,0:1,0:1) real(8) f00,f01,f10,f11,f0,f1 real(8) v0(3),v1(3),v2(3),t1,t2 ! find the H-vector and k-vector corresponding to the input H+p-vector ivh0(:)=floor(vhpl(:)) vpl(:)=vhpl(:)-dble(ivh0(:)) v1(:)=vpl(:)*dble(ngridk(:)) ivk0(:)=floor(v1(:)) ! determine the corners of the box containing the input point do i=0,1; do j=0,1; do k=0,1 ivkb(1,i,j,k)=ivk0(1)+i ivkb(2,i,j,k)=ivk0(2)+j ivkb(3,i,j,k)=ivk0(3)+k ivhb(:,i,j,k)=ivh0(:)+ivkb(:,i,j,k)/ngridk(:) ivkb(:,i,j,k)=modulo(ivkb(:,i,j,k),ngridk(:)) end do; end do; end do ! determine the function at each corner of the box do i=0,1; do j=0,1; do k=0,1 fb(i,j,k)=0.d0 ! non-reduced k-point index jk=ivkiknr(ivkb(1,i,j,k),ivkb(2,i,j,k),ivkb(3,i,j,k)) ! H+k-vector at corner of box v1(:)=dble(ivhb(:,i,j,k))+vkl(:,jk) ! store the origin of the box if ((i.eq.0).and.(j.eq.0).and.(k.eq.0)) v0(:)=v1(:) ! vector in Cartesian coordinates v2(:)=bvec(:,1)*v1(1)+bvec(:,2)*v1(2)+bvec(:,3)*v1(3) ! check length is within range t1=sqrt(v2(1)**2+v2(2)**2+v2(3)**2) if (t1.gt.hkmax) cycle ! find the lattice symmetry which maps the non-reduced to reduced k-point call findkpt(vkl(:,jk),isym,ik) ! index to spatial rotation in lattice point group lspl=lsplsymc(isym) v2(:)=symlat(1,:,lspl)*v1(1)+symlat(2,:,lspl)*v1(2)+symlat(3,:,lspl)*v1(3) ! find the H+k-vector for the reduced k-point do ihk=1,nhk(1,ik) t1=abs(v2(1)-vhkl(1,ihk,1,ik)) & +abs(v2(2)-vhkl(2,ihk,1,ik)) & +abs(v2(3)-vhkl(3,ihk,1,ik)) if (t1.lt.epslat) then fb(i,j,k)=rfhk(ihk,ik) exit end if end do end do; end do; end do ! interpolate function t2=(vhpl(1)-v0(1))*dble(ngridk(1)) t1=1.d0-t2 f00=fb(0,0,0)*t1+fb(1,0,0)*t2 f01=fb(0,0,1)*t1+fb(1,0,1)*t2 f10=fb(0,1,0)*t1+fb(1,1,0)*t2 f11=fb(0,1,1)*t1+fb(1,1,1)*t2 t2=(vhpl(2)-v0(2))*dble(ngridk(2)) t1=1.d0-t2 f0=f00*t1+f10*t2 f1=f01*t1+f11*t2 t2=(vhpl(3)-v0(3))*dble(ngridk(3)) t1=1.d0-t2 rfhkintp=f0*t1+f1*t2 end function elk-7.2.42/src/PaxHeaders.21776/writewfpw.f900000644000000000000000000000012414061636517015303 xustar0027 mtime=1623670095.445102 30 atime=1623670094.233103125 27 ctime=1623670095.445102 elk-7.2.42/src/writewfpw.f900000644002504400250440000000415114061636517017340 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writewfpw use modmain use modpw use modmpi use modomp implicit none ! local variables integer ik,recl,nthd ! allocatable arrays complex(8), allocatable :: wfpw(:,:,:) ! initialise global variables call init0 call init1 call init4 ! read density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! delete existing WFPW.OUT if (mp_mpi) then open(270,file='WFPW.OUT') close(270,status='DELETE') end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! determine the record length and open WFPW.OUT allocate(wfpw(nhkmax,nspinor,nstsv)) inquire(iolength=recl) vkl(:,1),nhkmax,nspinor,nstsv,wfpw deallocate(wfpw) open(270,file='WFPW.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) ! begin parallel loop over k-points call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfpw) & !$OMP NUM_THREADS(nthd) allocate(wfpw(nhkmax,nspinor,nstsv)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(writewfpw_) write(*,'("Info(writewfpw): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(writewfpw_) ! generate the plane wave wavefunctions call genwfpw(vkl(:,ik),ngk(:,ik),igkig(:,:,ik),vgkl(:,:,:,ik), & vgkc(:,:,:,ik),gkc(:,:,ik),sfacgk(:,:,:,ik),nhk(:,ik),vhkc(:,:,:,ik), & hkc(:,:,ik),sfachk(:,:,:,ik),wfpw) !$OMP CRITICAL(u270) write(270,rec=ik) vkl(:,ik),nhkmax,nspinor,nstsv,wfpw !$OMP END CRITICAL(u270) end do !$OMP END DO deallocate(wfpw) !$OMP END PARALLEL call freethd(nthd) close(270) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) if (mp_mpi) then write(*,*) write(*,'("Info(writewfpw): plane wave wavefunctions written to WFPW.OUT")') write(*,'(" for all H+k-vectors up to |H+k| < hkmax")') end if end subroutine elk-7.2.42/src/PaxHeaders.21776/vblocal.f900000644000000000000000000000013214061636517014666 xustar0030 mtime=1623670095.447101998 30 atime=1623670094.235103123 30 ctime=1623670095.447101998 elk-7.2.42/src/vblocal.f900000644002504400250440000000273414061636517016731 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine vblocal(vmt,vir,bmt) use modmain use modomp implicit none ! arguments real(8), intent(out) :: vmt(npcmtmax,natmtot),vir(ngtot) real(8), intent(out) :: bmt(npcmtmax,natmtot,ndmag) ! local variables integer idm,is,ias,nthd integer nrc,nrci,npc ! automatic arrays real(8) rfmt(npcmtmax) call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(rfmt,is,nrc,nrci) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) ! convert muffin-tin Kohn-Sham potential to spherical coordinates call rfmtftoc(nrc,nrci,vsmt(:,ias),rfmt) call rbsht(nrc,nrci,rfmt,vmt(:,ias)) ! multiply by radial integration weights call rfcmtwr(nrc,nrci,wrcmt(:,is),vmt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! multiply interstitial Kohn-Sham potential by characteristic function vir(:)=vsir(:)*cfunir(:) if (.not.spinpol) return ! repeat for the Kohn-Sham magnetic field call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is,nrc,nrci,npc,idm) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do idm=1,ndmag bmt(1:npc,ias,idm)=bsmt(1:npc,ias,idm) call rfcmtwr(nrc,nrci,wrcmt(:,is),bmt(:,ias,idm)) end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/writefsm.f900000644000000000000000000000013214061636517015104 xustar0030 mtime=1623670095.448101997 30 atime=1623670094.237103121 30 ctime=1623670095.448101997 elk-7.2.42/src/writefsm.f900000644002504400250440000000154114061636517017142 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writefsm(fnum) use modmain implicit none ! arguments integer, intent(in) :: fnum ! local variables integer is,ia,ias if (fsmtype.eq.0) return write(fnum,*) if ((abs(fsmtype).eq.1).or.(abs(fsmtype).eq.3)) then write(fnum,'("FSM global effective field",T30,": ",3G18.10)') bfsmc(1:ndmag) end if if ((abs(fsmtype).eq.2).or.(abs(fsmtype).eq.3)) then write(fnum,'("FSM local muffin-tin effective fields :")') do is=1,nspecies write(fnum,'(" species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) ias=idxas(ia,is) write(fnum,'(" atom ",I4,T30,": ",3G18.10)') ia,bfsmcmt(1:ndmag,ias) end do end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/getwfpw.f900000644000000000000000000000013114061636517014726 xustar0030 mtime=1623670095.450101995 29 atime=1623670094.23810312 30 ctime=1623670095.450101995 elk-7.2.42/src/getwfpw.f900000644002504400250440000001177014061636517016772 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine getwfpw(vpl,vhpl,wfpw) use modmain use modpw implicit none ! arguments real(8), intent(in) :: vpl(3) real(8), intent(in) :: vhpl(3,nhkmax,nspnfv) complex(8), intent(out) :: wfpw(nhkmax,nspinor,nstsv) ! local variables integer isym,lspl,ilspl,lspn integer ik,ist,ihk,ihp,jhp,ig integer ispn0,ispn1,jspn,i integer recl,nhkmax_,nspinor_,nstsv_ real(8) vkl_(3),si(3,3) real(8) v(3),det,th,t1 complex(8) su2(2,2),z1,z2 ! automatic arrays logical done(nhkmax) ! allocatable arrays complex(8), allocatable :: wfpw_(:,:,:) ! find the equivalent k-point number and symmetry which rotates vkl to vpl call findkpt(vpl,isym,ik) ! index to spatial rotation in lattice point group lspl=lsplsymc(isym) ! find the record length inquire(iolength=recl) vkl_,nhkmax_,nspinor_,nstsv_,wfpw !$OMP CRITICAL(u270) open(270,file='WFPW.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(270,rec=ik) vkl_,nhkmax_,nspinor_,nstsv_,wfpw !$OMP END CRITICAL(u270) t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getwfpw): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" WFPW.OUT : ",3G18.10)') vkl_ write(*,*) stop end if if (nhkmax.ne.nhkmax_) then write(*,*) write(*,'("Error(getwfpw): differing nhkmax for k-point ",I8)') ik write(*,'(" current : ",I8)') nhkmax write(*,'(" WFPW.OUT : ",I8)') nhkmax_ write(*,*) stop end if if (nspinor.ne.nspinor_) then write(*,*) write(*,'("Error(getwfpw): differing nspinor for k-point ",I8)') ik write(*,'(" current : ",I8)') nspinor write(*,'(" WFPW.OUT : ",I8)') nspinor_ write(*,*) stop end if if (nstsv.ne.nstsv_) then write(*,*) write(*,'("Error(getwfpw): differing nstsv for k-point ",I8)') ik write(*,'(" current : ",I8)') nstsv write(*,'(" WFPW.OUT : ",I8)') nstsv_ write(*,*) stop end if ! if p = k then return t1=abs(vpl(1)-vkl(1,ik))+abs(vpl(2)-vkl(2,ik))+abs(vpl(3)-vkl(3,ik)) if (t1.lt.epslat) return !--------------------------------------------------------! ! translate and rotate wavefunction coefficients ! !--------------------------------------------------------! ! allocate temporary copy of wavefunction allocate(wfpw_(nhkmax,nspinor,nstsv)) ! the inverse of the spatial symmetry ilspl=isymlat(lspl) si(:,:)=dble(symlat(:,:,ilspl)) ! loop over first-variational spins do jspn=1,nspnfv if (spinsprl) then ispn0=jspn; ispn1=jspn else ispn0=1; ispn1=nspinor end if ! apply translation operation if required if (tv0symc(isym)) then ! translation vector is zero do ihk=1,nhk(jspn,ik) wfpw_(ihk,ispn0:ispn1,:)=wfpw(ihk,ispn0:ispn1,:) end do else ! non-zero translation vector gives a phase factor v(:)=vtcsymc(:,isym) do ihk=1,nhk(jspn,ik) ig=ihkig(ihk,jspn,ik) t1=-(vgc(1,ig)*v(1)+vgc(2,ig)*v(2)+vgc(3,ig)*v(3)) z1=cmplx(cos(t1),sin(t1),8) wfpw_(ihk,ispn0:ispn1,:)=z1*wfpw(ihk,ispn0:ispn1,:) end do end if ! apply spatial rotation operation (passive transformation) done(1:nhk(jspn,ik))=.false. i=1 do ihk=1,nhk(jspn,ik) call r3mtv(si,vhkl(:,ihk,jspn,ik),v) do ihp=i,nhk(jspn,ik) if (done(ihp)) cycle t1=abs(v(1)-vhpl(1,ihp,jspn)) & +abs(v(2)-vhpl(2,ihp,jspn)) & +abs(v(3)-vhpl(3,ihp,jspn)) if (t1.lt.epslat) then wfpw(ihp,ispn0:ispn1,:)=wfpw_(ihk,ispn0:ispn1,:) done(ihp)=.true. exit end if end do do ihp=i,nhk(jspn,ik) if (.not.done(ihp)) then i=ihp exit end if end do end do end do ! apply spin rotation if required if (spinpol) then ! index to global spin rotation in lattice point group lspn=lspnsymc(isym) ! if symmetry element is the identity return if (lspn.eq.1) return ! find the SU(2) representation of the spin rotation matrix call rotaxang(epslat,symlatc(:,:,lspn),det,v,th) call axangsu2(v,th,su2) ! apply SU(2) matrix to spinor wavefunctions (active transformation) if (spinsprl) then ! spin-spiral case wfpw(:,2,:)=0.d0 i=1 do ihp=1,nhk(1,ik) v(:)=vhpl(:,ihp,1)-vqlss(:) do jhp=i,nhk(2,ik) t1=abs(v(1)-vhpl(1,jhp,2)) & +abs(v(2)-vhpl(2,jhp,2)) & +abs(v(3)-vhpl(3,jhp,2)) if (t1.lt.epslat) then do ist=1,nstsv z1=wfpw(ihp,1,ist) z2=wfpw(jhp,2,ist) wfpw(ihp,1,ist)=su2(1,1)*z1+su2(1,2)*z2 wfpw(jhp,2,ist)=su2(2,1)*z1+su2(2,2)*z2 end do if (jhp.eq.i) i=i+1 goto 10 end if end do wfpw(ihp,1,:)=0.d0 10 continue end do else ! normal spin case do ist=1,nstsv do ihp=1,nhk(1,ik) z1=wfpw(ihp,1,ist) z2=wfpw(ihp,2,ist) wfpw(ihp,1,ist)=su2(1,1)*z1+su2(1,2)*z2 wfpw(ihp,2,ist)=su2(2,1)*z1+su2(2,2)*z2 end do end do end if end if deallocate(wfpw_) end subroutine elk-7.2.42/src/PaxHeaders.21776/plotpt1d.f900000644000000000000000000000013214061636517015013 xustar0030 mtime=1623670095.451101994 30 atime=1623670094.240103118 30 ctime=1623670095.451101994 elk-7.2.42/src/plotpt1d.f900000644002504400250440000000523414061636517017054 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: plotpt1d ! !INTERFACE: subroutine plotpt1d(cvec,nv,np,vvl,vpl,dv,dp) ! !INPUT/OUTPUT PARAMETERS: ! cvec : matrix of (reciprocal) lattice vectors stored column-wise ! (in,real(3,3)) ! nv : number of vertices (in,integer) ! np : number of connecting points (in,integer) ! vvl : vertex vectors in lattice coordinates (in,real(3,nv)) ! vpl : connecting point vectors in lattice coordinates (out,real(3,np)) ! dv : cummulative distance to each vertex (out,real(nv)) ! dp : cummulative distance to each connecting point (out,real(np)) ! !DESCRIPTION: ! Generates a set of points which interpolate between a given set of vertices. ! Vertex points are supplied in lattice coordinates in the array {\tt vvl} and ! converted to Cartesian coordinates with the matrix {\tt cvec}. Interpolating ! points are stored in the array {\tt vpl}. The cummulative distances to the ! vertices and points along the path are stored in arrays {\tt dv} and ! {\tt dp}, respectively. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) ! Improved September 2007 (JKD) ! Improved again, July 2010 (T. McQueen and JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: cvec(3,3) integer, intent(in) :: nv,np real(8), intent(in) :: vvl(3,nv) real(8), intent(out) :: vpl(3,np),dv(nv),dp(np) ! local variables integer i,j,k,m,n real(8) vl(3),vc(3) real(8) dt,f,t1 ! alloctable arrays real(8), allocatable :: seg(:) if (nv.lt.1) then write(*,*) write(*,'("Error(plotpt1d): nv < 1 : ",I8)') nv write(*,*) stop end if if (np.lt.nv) then write(*,*) write(*,'("Error(plotpt1d): np < nv : ",2I8)') np,nv write(*,*) stop end if ! special case of 1 vertex if (nv.eq.1) then dv(1)=0.d0 dp(:)=0.d0 do i=1,np vpl(:,i)=vvl(:,1) end do return end if allocate(seg(nv)) ! find the length of each segment and total distance dt=0.d0 do i=1,nv-1 dv(i)=dt vl(:)=vvl(:,i+1)-vvl(:,i) call r3mv(cvec,vl,vc) seg(i)=sqrt(vc(1)**2+vc(2)**2+vc(3)**2) dt=dt+seg(i) end do dv(nv)=dt ! add small amount to total distance to avoid 0/0 condition dt=dt+1.d-8 ! number of points to use between vertices n=np-nv ! construct the interpolating path k=0 do i=1,nv-1 t1=dble(n)*seg(i)/dt m=nint(t1) if ((m.gt.n).or.(i.eq.(nv-1))) m=n do j=1,m+1 k=k+1 f=dble(j-1)/dble(m+1) dp(k)=dv(i)+f*seg(i) vpl(:,k)=vvl(:,i)*(1.d0-f)+vvl(:,i+1)*f end do dt=dt-seg(i) n=n-m end do dp(np)=dv(nv) vpl(:,np)=vvl(:,nv) deallocate(seg) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/init1.f900000644000000000000000000000013214061636517014270 xustar0030 mtime=1623670095.453101992 30 atime=1623670094.242103116 30 ctime=1623670095.453101992 elk-7.2.42/src/init1.f900000644002504400250440000002516714061636517016340 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: init1 ! !INTERFACE: subroutine init1 ! !USES: use modmain use moddftu use modulr use modtddft use modtest use modvars use modstore ! !DESCRIPTION: ! Generates the $k$-point set and then allocates and initialises global ! variables which depend on the $k$-point set. ! ! !REVISION HISTORY: ! Created January 2004 (JKD) !EOP !BOC implicit none ! local variables logical lsym(48) integer is,ia,ias,nppt integer io,ilo,i1,i2,i3 integer ik,isym,jspn integer l1,l2,l3,m1,m2,m3 integer lm1,lm2,lm3,n real(8) vl(3),vc(3),t1 real(8) boxl(3,0:3) real(8) ts0,ts1 ! external functions complex(8), external :: gauntyry call timesec(ts0) !---------------------! ! k-point set ! !---------------------! ! check if the system is an isolated molecule if (molecule) then ngridk(:)=1 vkloff(:)=0.d0 autokpt=.false. end if ! store the point group symmetries for reducing the k-point set if (reducek.eq.0) then nsymkpt=1 symkpt(:,:,1)=symlat(:,:,1) else lsym(:)=.false. do isym=1,nsymcrys if (reducek.eq.2) then ! check symmetry is symmorphic if (.not.tv0symc(isym)) goto 10 ! check also that the spin rotation is the same as the spatial rotation if (spinpol) then if (lspnsymc(isym).ne.lsplsymc(isym)) goto 10 end if end if lsym(lsplsymc(isym))=.true. 10 continue end do nsymkpt=0 do isym=1,nsymlat if (lsym(isym)) then nsymkpt=nsymkpt+1 symkpt(:,:,nsymkpt)=symlat(:,:,isym) end if end do end if if (any(task.eq.[20,21,22,23])) then ! generate k-points along a path for band structure plots call plotpt1d(bvec,nvp1d,npp1d,vvlp1d,vplp1d,dvp1d,dpp1d) nkpt=npp1d if (allocated(vkl)) deallocate(vkl) allocate(vkl(3,nkpt)) if (allocated(vkc)) deallocate(vkc) allocate(vkc(3,nkpt)) do ik=1,nkpt vkl(:,ik)=vplp1d(:,ik) call r3mv(bvec,vkl(:,ik),vkc(:,ik)) end do nkptnr=nkpt else if (task.eq.25) then ! effective mass calculation nkpt=(2*ndspem+1)**3 if (allocated(ivk)) deallocate(ivk) allocate(ivk(3,nkpt)) if (allocated(vkl)) deallocate(vkl) allocate(vkl(3,nkpt)) if (allocated(vkc)) deallocate(vkc) allocate(vkc(3,nkpt)) ! map vector to [0,1) call r3frac(epslat,vklem) ik=0 do i3=-ndspem,ndspem do i2=-ndspem,ndspem do i1=-ndspem,ndspem ik=ik+1 ivk(1,ik)=i1; ivk(2,ik)=i2; ivk(3,ik)=i3 vc(1)=dble(i1); vc(2)=dble(i2); vc(3)=dble(i3) vc(:)=vc(:)*deltaem call r3mv(binv,vc,vl) vkl(:,ik)=vklem(:)+vl(:) call r3mv(bvec,vkl(:,ik),vkc(:,ik)) end do end do end do nkptnr=nkpt else ! determine the k-point grid automatically from radkpt if required if (autokpt) then t1=radkpt/twopi ngridk(:)=int(t1*sqrt(bvec(1,:)**2+bvec(2,:)**2+bvec(3,:)**2))+1 end if ! set up the default k-point box boxl(:,0)=vkloff(:)/dble(ngridk(:)) if (task.eq.102) boxl(:,0)=0.d0 boxl(:,1)=boxl(:,0) boxl(:,2)=boxl(:,0) boxl(:,3)=boxl(:,0) boxl(1,1)=boxl(1,1)+1.d0 boxl(2,2)=boxl(2,2)+1.d0 boxl(3,3)=boxl(3,3)+1.d0 ! k-point set and box for Fermi surface plots if (any(task.eq.[100,101,102])) then ngridk(:)=np3d(:) if (task.ne.102) boxl(:,:)=vclp3d(:,:) end if ! allocate the k-point set arrays if (allocated(ivkik)) deallocate(ivkik) allocate(ivkik(0:ngridk(1)-1,0:ngridk(2)-1,0:ngridk(3)-1)) if (allocated(ivkiknr)) deallocate(ivkiknr) allocate(ivkiknr(0:ngridk(1)-1,0:ngridk(2)-1,0:ngridk(3)-1)) nkptnr=ngridk(1)*ngridk(2)*ngridk(3) if (allocated(ivk)) deallocate(ivk) allocate(ivk(3,nkptnr)) if (allocated(vkl)) deallocate(vkl) allocate(vkl(3,nkptnr)) if (allocated(vkc)) deallocate(vkc) allocate(vkc(3,nkptnr)) if (allocated(wkpt)) deallocate(wkpt) allocate(wkpt(nkptnr)) ! generate the k-point set call genppts(.false.,nsymkpt,symkpt,ngridk,nkptnr,epslat,bvec,boxl,nkpt, & ivkik,ivkiknr,ivk,vkl,vkc,wkpt,wkptnr) ! write to VARIABLES.OUT call writevars('nsymkpt',iv=nsymkpt) call writevars('symkpt',nv=9*nsymkpt,iva=symkpt) call writevars('ngridk',nv=3,iva=ngridk) call writevars('vkloff',nv=3,rva=vkloff) call writevars('nkpt',iv=nkpt) call writevars('ivkik',nv=nkptnr,iva=ivkik) call writevars('ivk',nv=3*nkptnr,iva=ivk) call writevars('vkl',nv=3*nkptnr,rva=vkl) call writevars('wkpt',nv=nkpt,rva=wkpt) end if if (any(task.eq.[700,701,731,732,733,741,742,743,771,772,773])) then ! generate ultracell reciprocal lattice vectors if required call reciplat(avecu,bvecu,omegau,omegabzu) ! generate the kappa, k+kappa and Q-points if required call genkpakq end if ! write the k-points to test file call writetest(910,'k-points (Cartesian)',nv=3*nkpt,tol=1.d-8,rva=vkc) !---------------------! ! G+k-vectors ! !---------------------! if ((xctype(1).lt.0).or.tddos.or. & (any(task.eq.[5,10,205,300,600,620,630,800,801]))) then nppt=nkptnr else nppt=nkpt end if ! find the maximum number of G+k-vectors call findngkmax(nkpt,vkc,nspnfv,vqcss,ngvc,vgc,gkmax,ngkmax) ! allocate the G+k-vector arrays if (allocated(ngk)) deallocate(ngk) allocate(ngk(nspnfv,nppt)) if (allocated(igkig)) deallocate(igkig) allocate(igkig(ngkmax,nspnfv,nppt)) if (allocated(vgkl)) deallocate(vgkl) allocate(vgkl(3,ngkmax,nspnfv,nppt)) if (allocated(vgkc)) deallocate(vgkc) allocate(vgkc(3,ngkmax,nspnfv,nppt)) if (allocated(gkc)) deallocate(gkc) allocate(gkc(ngkmax,nspnfv,nppt)) if (allocated(sfacgk)) deallocate(sfacgk) allocate(sfacgk(ngkmax,natmtot,nspnfv,nppt)) do ik=1,nppt do jspn=1,nspnfv vl(:)=vkl(:,ik) vc(:)=vkc(:,ik) ! spin-spiral case if (spinsprl) then if (jspn.eq.1) then vl(:)=vl(:)+0.5d0*vqlss(:) vc(:)=vc(:)+0.5d0*vqcss(:) else vl(:)=vl(:)-0.5d0*vqlss(:) vc(:)=vc(:)-0.5d0*vqcss(:) end if end if ! generate the G+k-vectors call gengkvec(ngvc,ivg,vgc,vl,vc,gkmax,ngkmax,ngk(jspn,ik), & igkig(:,jspn,ik),vgkl(:,:,jspn,ik),vgkc(:,:,jspn,ik),gkc(:,jspn,ik)) ! generate structure factors for G+k-vectors call gensfacgp(ngk(jspn,ik),vgkc(:,:,jspn,ik),ngkmax,sfacgk(:,:,jspn,ik)) end do end do ! write to VARIABLES.OUT call writevars('nspnfv',iv=nspnfv) call writevars('ngk',nv=nspnfv*nkpt,iva=ngk) do ik=1,nkpt do jspn=1,nspnfv call writevars('igkig',l=jspn,m=ik,nv=ngk(jspn,ik),iva=igkig(:,jspn,ik)) end do end do !---------------------------------! ! APWs and local-orbitals ! !---------------------------------! apwordmax=0 lorbordmax=0 nlomax=0 lolmax=0 do is=1,nspecies lmoapw(is)=0 do l1=0,lmaxapw ! find the maximum APW order apwordmax=max(apwordmax,apword(l1,is)) ! find total number of APW coefficients (l, m and order) lmoapw(is)=lmoapw(is)+(2*l1+1)*apword(l1,is) end do ! find the maximum number of local-orbitals nlomax=max(nlomax,nlorb(is)) ! find the maximum local-orbital order and angular momentum do ilo=1,nlorb(is) lolmax=max(lolmax,lorbl(ilo,is)) lorbordmax=max(lorbordmax,lorbord(ilo,is)) end do end do lolmmax=(lolmax+1)**2 ! polynomial order used for APW and local-orbital radial derivatives npapw=max(apwordmax+1,4) nplorb=max(lorbordmax+1,4) ! set the APW and local-orbital linearisation energies to the default if (allocated(apwe)) deallocate(apwe) allocate(apwe(apwordmax,0:lmaxapw,natmtot)) if (allocated(lorbe)) deallocate(lorbe) allocate(lorbe(lorbordmax,maxlorb,natmtot)) do is=1,nspecies do l1=0,lmaxapw do io=1,apword(l1,is) do ia=1,natoms(is) ias=idxas(ia,is) apwe(io,l1,ias)=apwe0(io,l1,is) end do end do end do do ilo=1,nlorb(is) do io=1,lorbord(ilo,is) do ia=1,natoms(is) ias=idxas(ia,is) lorbe(io,ilo,ias)=lorbe0(io,ilo,is) end do end do end do end do ! generate the local-orbital index call genidxlo ! allocate radial function arrays if (allocated(apwfr)) deallocate(apwfr) allocate(apwfr(nrmtmax,2,apwordmax,0:lmaxapw,natmtot)) if (allocated(apwdfr)) deallocate(apwdfr) allocate(apwdfr(apwordmax,0:lmaxapw,natmtot)) if (allocated(lofr)) deallocate(lofr) allocate(lofr(nrmtmax,2,nlomax,natmtot)) !-------------------------! ! DFT+U variables ! !-------------------------! if (dftu.ne.0) then ! allocate energy arrays to calculate Slater integrals with Yukawa potential if (allocated(fdue)) deallocate(fdue) allocate(fdue(0:lmaxdm,natmtot)) ! allocate radial functions to calculate Slater integrals with Yukawa potential if (allocated(fdufr)) deallocate(fdufr) allocate(fdufr(nrmtmax,0:lmaxdm,natmtot)) end if !---------------------------------------! ! eigenvalue equation variables ! !---------------------------------------! ! total number of empty states (M. Meinert) nempty=nint(nempty0*max(natmtot,1)) if (nempty.lt.1) nempty=1 ! number of first-variational states nstfv=int(chgval/2.d0)+nempty+1 ! overlap and Hamiltonian matrix sizes if (allocated(nmat)) deallocate(nmat) allocate(nmat(nspnfv,nkpt)) nmatmax=0 do ik=1,nkpt do jspn=1,nspnfv n=ngk(jspn,ik)+nlotot if (nstfv.gt.n) then write(*,*) write(*,'("Error(init1): number of first-variational states larger than & &matrix size")') write(*,'("Increase rgkmax or decrease nempty")') write(*,*) stop end if nmat(jspn,ik)=n nmatmax=max(nmatmax,n) end do end do ! number of second-variational states nstsv=nstfv*nspinor ! allocate second-variational arrays if (allocated(evalsv)) deallocate(evalsv) allocate(evalsv(nstsv,nkpt)) if (allocated(occsv)) deallocate(occsv) allocate(occsv(nstsv,nkpt)) occsv(:,:)=0.d0 ! allocate overlap and Hamiltonian integral arrays if (allocated(oalo)) deallocate(oalo) allocate(oalo(apwordmax,nlomax,natmtot)) if (allocated(ololo)) deallocate(ololo) allocate(ololo(nlomax,nlomax,natmtot)) if (allocated(haa)) deallocate(haa) allocate(haa(lmmaxo,apwordmax,0:lmaxapw,apwordmax,0:lmaxapw,natmtot)) if (allocated(hloa)) deallocate(hloa) allocate(hloa(lmmaxo,apwordmax,0:lmaxapw,nlomax,natmtot)) if (allocated(hlolo)) deallocate(hlolo) allocate(hlolo(lmmaxo,nlomax,nlomax,natmtot)) ! allocate and generate complex Gaunt coefficient array if (allocated(gntyry)) deallocate(gntyry) allocate(gntyry(lmmaxo,lmmaxapw,lmmaxapw)) do l1=0,lmaxapw do m1=-l1,l1 lm1=l1*(l1+1)+m1+1 do l3=0,lmaxapw do m3=-l3,l3 lm3=l3*(l3+1)+m3+1 do l2=0,lmaxo do m2=-l2,l2 lm2=l2*(l2+1)+m2+1 gntyry(lm2,lm3,lm1)=gauntyry(l1,l2,l3,m1,m2,m3) end do end do end do end do end do end do ! write to VARIABLES.OUT call writevars('nempty',iv=nempty) call writevars('nstfv',iv=nstfv) call writevars('nlotot',iv=nlotot) call writevars('nstsv',iv=nstsv) call timesec(ts1) timeinit=timeinit+ts1-ts0 end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/init2.f900000644000000000000000000000013214061636517014271 xustar0030 mtime=1623670095.454101992 30 atime=1623670094.244103115 30 ctime=1623670095.454101992 elk-7.2.42/src/init2.f900000644002504400250440000000775414061636517016343 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine init2 use modmain use modrdm use modphonon use modvars use modmpi implicit none ! local variables logical lsym(48) integer isym,iv(3) real(8) boxl(3,0:3) real(8) ts0,ts1 call timesec(ts0) !---------------------! ! q-point set ! !---------------------! ! check if the system is an isolated molecule if (molecule) ngridq(:)=1 ! store the point group symmetries for reducing the q-point set if (reduceq.eq.0) then nsymqpt=1 symqpt(:,:,1)=symlat(:,:,1) else lsym(:)=.false. do isym=1,nsymcrys lsym(lsplsymc(isym))=.true. end do nsymqpt=0 do isym=1,nsymlat if (lsym(isym)) then nsymqpt=nsymqpt+1 symqpt(:,:,nsymqpt)=symlat(:,:,isym) end if end do end if if (any(task.eq.[105,180,185,320,330,331])) then ! equal k- and q-point grids for nesting function, BSE and linear-reposnse TDDFT ngridq(:)=ngridk(:) else if ((xctype(1).lt.0).or.(any(task.eq.[5,300,600,620,630,800,801]))) then ! allow the q-point grid to be smaller than the k-point grid for OEP, ! Hartree-Fock, RDMFT and GW if (any(ngridq(:).le.0)) ngridq(:)=ngridk(:) else ngridq(:)=abs(ngridq(:)) end if ! check that the q-point and k-point grids are commensurate for some tasks if ((xctype(1).lt.0).or.(any(task.eq.[5,205,240,241,300,600,620,630, & 800,801]))) then iv(:)=mod(ngridk(:),ngridq(:)) if ((iv(1).ne.0).or.(iv(2).ne.0).or.(iv(3).ne.0)) then write(*,*) write(*,'("Error(init2): k-point grid incommensurate with q-point grid")') write(*,'(" ngridk : ",3I6)') ngridk write(*,'(" ngridq : ",3I6)') ngridq write(*,*) stop end if end if ! allocate the q-point arrays if (allocated(ivqiq)) deallocate(ivqiq) allocate(ivqiq(0:ngridq(1)-1,0:ngridq(2)-1,0:ngridq(3)-1)) if (allocated(ivqiqnr)) deallocate(ivqiqnr) allocate(ivqiqnr(0:ngridq(1)-1,0:ngridq(2)-1,0:ngridq(3)-1)) nqptnr=ngridq(1)*ngridq(2)*ngridq(3) if (allocated(ivq)) deallocate(ivq) allocate(ivq(3,nqptnr)) if (allocated(vql)) deallocate(vql) allocate(vql(3,nqptnr)) if (allocated(vqc)) deallocate(vqc) allocate(vqc(3,nqptnr)) if (allocated(wqpt)) deallocate(wqpt) allocate(wqpt(nqptnr)) ! set up the q-point box (offset should always be zero) boxl(:,:)=0.d0 boxl(1,1)=1.d0; boxl(2,2)=1.d0; boxl(3,3)=1.d0 ! generate the q-point set ! (note that the vectors vql and vqc are in the first Brillouin zone) call genppts(.true.,nsymqpt,symqpt,ngridq,nqptnr,epslat,bvec,boxl,nqpt,ivqiq, & ivqiqnr,ivq,vql,vqc,wqpt,wqptnr) ! write the q-points to QPOINTS.OUT if (mp_mpi) call writeqpts ! write to VARIABLES.OUT call writevars('nsymqpt',iv=nsymqpt) call writevars('symqpt',nv=9*nsymqpt,iva=symqpt) call writevars('ngridq',nv=3,iva=ngridq) call writevars('nqpt',iv=nqpt) call writevars('ivqiq',nv=nqptnr,iva=ivqiq) call writevars('ivq',nv=3*nqptnr,iva=ivq) call writevars('vql',nv=3*nqptnr,rva=vql) call writevars('wqpt',nv=nqpt,rva=wqpt) !--------------------------------------------------------! ! OEP, Hartree-Fock, RDMFT, BSE and GW variables ! !--------------------------------------------------------! if ((xctype(1).lt.0).or.(any(task.eq.[5,180,185,188,205,300,320,330,331,600, & 620,630,800,801]))) then ! determine the regularised Coulomb Green's function for small q call gengclq ! output the Coulomb Green's function to GCLQ.OUT if (mp_mpi) call writegclq ! initialise OEP variables if (xctype(1).lt.0) call initoep end if if (task.eq.300) then if (allocated(vclmat)) deallocate(vclmat) allocate(vclmat(nstsv,nstsv,nkpt)) if (allocated(dkdc)) deallocate(dkdc) allocate(dkdc(nstsv,nstsv,nkpt)) end if !-------------------------! ! phonon variables ! !-------------------------! if (allocated(wphq)) deallocate(wphq) if (task.eq.220) then allocate(wphq(nbph,npp1d)) end if if (any(task.eq.[240,241,250,270,271,280,285])) then allocate(wphq(nbph,nqpt)) end if call timesec(ts1) timeinit=timeinit+ts1-ts0 end subroutine elk-7.2.42/src/PaxHeaders.21776/findsymcrys.f900000644000000000000000000000013014061636517015614 xustar0029 mtime=1623670095.45610199 30 atime=1623670094.245103114 29 ctime=1623670095.45610199 elk-7.2.42/src/findsymcrys.f900000644002504400250440000001475114061636517017663 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: findsymcrys ! !INTERFACE: subroutine findsymcrys ! !USES: use modmain use modmpi use modtest ! !DESCRIPTION: ! Finds the complete set of symmetries which leave the crystal structure ! (including the magnetic fields) invariant. A crystal symmetry is of the form ! $\{\alpha_S|\alpha_R|{\bf t}\}$, where ${\bf t}$ is a translation vector, ! $\alpha_R$ is a spatial rotation operation and $\alpha_S$ is a global spin ! rotation. Note that the order of operations is important and defined to be ! from right to left, i.e. translation followed by spatial rotation followed ! by spin rotation. In the case of spin-orbit coupling $\alpha_S=\alpha_R$. In ! order to determine the translation vectors, the entire atomic basis is ! shifted so that the first atom in the smallest set of atoms of the same ! species is at the origin. Then all displacement vectors between atoms in ! this set are checked as possible symmetry translations. If the global ! variable {\tt tshift} is set to {\tt .false.} then the shift is not ! performed. See L. M. Sandratskii and P. G. Guletskii, {\it J. Phys. F: Met. ! Phys.} {\bf 16}, L43 (1986) and the routine {\tt findsym}. ! ! !REVISION HISTORY: ! Created April 2007 (JKD) !EOP !BOC implicit none ! local variables integer ia,ja,is,js integer isym,nsym,i,n integer lspl(48),lspn(48),ilspl real(8) v0(3),v1(3),v2(3),t1 real(8) apl(3,maxatoms,maxspecies) ! automatic arrays integer iea(natmmax,nspecies,48) real(8) vtl(3,natmmax**2+1) ! allocate global equivalent atom arrays if (allocated(ieqatom)) deallocate(ieqatom) allocate(ieqatom(natmmax,nspecies,maxsymcrys)) if (allocated(eqatoms)) deallocate(eqatoms) allocate(eqatoms(natmmax,natmmax,nspecies)) ! store position of first atom if (natmtot.gt.0) v0(:)=atposl(:,1,1) ! find the smallest set of atoms is=1 do js=1,nspecies if (natoms(js).lt.natoms(is)) is=js end do if ((tshift).and.(natmtot.gt.0)) then ! shift basis so that the first atom in the smallest atom set is at the origin v1(:)=atposl(:,1,is) do js=1,nspecies do ia=1,natoms(js) ! shift atom atposl(:,ia,js)=atposl(:,ia,js)-v1(:) ! map lattice coordinates back to [0,1) call r3frac(epslat,atposl(:,ia,js)) ! determine the new Cartesian coordinates call r3mv(avec,atposl(:,ia,js),atposc(:,ia,js)) end do end do end if ! determine possible translation vectors from smallest set of atoms n=1 vtl(:,1)=0.d0 do ia=1,natoms(is) do ja=2,natoms(is) ! compute difference between two atom vectors v1(:)=atposl(:,ia,is)-atposl(:,ja,is) ! map lattice coordinates to [0,1) call r3frac(epslat,v1) ! check if vector has any component along electric field if (tefield) then call r3mv(avec,v1,v2) t1=efieldc(1)*v2(1)+efieldc(2)*v2(2)+efieldc(3)*v2(3) if (abs(t1).gt.epslat) goto 10 end if do i=1,n t1=abs(vtl(1,i)-v1(1))+abs(vtl(2,i)-v1(2))+abs(vtl(3,i)-v1(3)) if (t1.lt.epslat) goto 10 end do n=n+1 vtl(:,n)=v1(:) 10 continue end do end do ! no translations required when symtype=0,2 (F. Cricchio) if (symtype.ne.1) n=1 eqatoms(:,:,:)=.false. nsymcrys=0 ! loop over all possible translations do i=1,n ! construct new array with translated positions do is=1,nspecies do ia=1,natoms(is) apl(:,ia,is)=atposl(:,ia,is)+vtl(:,i) end do end do ! find the symmetries for current translation call findsym(atposl,apl,nsym,lspl,lspn,iea) do isym=1,nsym nsymcrys=nsymcrys+1 if (nsymcrys.gt.maxsymcrys) then write(*,*) write(*,'("Error(findsymcrys): too many crystal symmetries")') write(*,'(" Adjust maxsymcrys in modmain and recompile code")') write(*,*) stop end if vtlsymc(:,nsymcrys)=vtl(:,i) lsplsymc(nsymcrys)=lspl(isym) lspnsymc(nsymcrys)=lspn(isym) do is=1,nspecies do ia=1,natoms(is) ja=iea(ia,is,isym) ieqatom(ia,is,nsymcrys)=ja eqatoms(ia,ja,is)=.true. eqatoms(ja,ia,is)=.true. end do end do end do end do tsyminv=.false. do isym=1,nsymcrys ! check if inversion symmetry is present i=lsplsymc(isym) if (all(symlat(:,:,i).eq.-symlat(:,:,1))) then tsyminv=.true. ! make inversion the second symmetry element (the identity is the first) v1(:)=vtlsymc(:,isym); vtlsymc(:,isym)=vtlsymc(:,2); vtlsymc(:,2)=v1(:) i=lsplsymc(isym); lsplsymc(isym)=lsplsymc(2); lsplsymc(2)=i i=lspnsymc(isym); lspnsymc(isym)=lspnsymc(2); lspnsymc(2)=i do is=1,nspecies do ia=1,natoms(is) i=ieqatom(ia,is,isym) ieqatom(ia,is,isym)=ieqatom(ia,is,2) ieqatom(ia,is,2)=i end do end do exit end if end do ! if inversion exists then shift basis so that inversion center is at origin if (tsyminv.and.tshift) then v1(:)=v1(:)/2.d0 do is=1,nspecies do ia=1,natoms(is) ! shift atom atposl(:,ia,is)=atposl(:,ia,is)+v1(:) ! map lattice coordinates back to [0,1) call r3frac(epslat,atposl(:,ia,is)) ! map lattice coordinates to [-0.5,0.5) do i=1,3 if (atposl(i,ia,is).gt.0.5d0) atposl(i,ia,is)=atposl(i,ia,is)-1.d0 end do ! determine the new Cartesian coordinates call r3mv(avec,atposl(:,ia,is),atposc(:,ia,is)) end do end do ! recalculate crystal symmetry translation vectors do isym=1,nsymcrys ilspl=isymlat(lsplsymc(isym)) v2(:)=symlat(:,1,ilspl)*v1(1) & +symlat(:,2,ilspl)*v1(2) & +symlat(:,3,ilspl)*v1(3) vtlsymc(:,isym)=vtlsymc(:,isym)-v1(:)+v2(:) call r3frac(epslat,vtlsymc(:,isym)) end do end if ! translation vector in Cartesian coordinates do isym=1,nsymcrys call r3mv(avec,vtlsymc(:,isym),vtcsymc(:,isym)) end do ! set flag for zero translation vector do isym=1,nsymcrys t1=abs(vtlsymc(1,isym))+abs(vtlsymc(2,isym))+abs(vtlsymc(3,isym)) if (t1.lt.epslat) then tv0symc(isym)=.true. else tv0symc(isym)=.false. end if end do ! check inversion does not include a translation if (tsyminv) then if (.not.tv0symc(2)) tsyminv=.false. end if if (natmtot.gt.0) then v1(:)=atposl(:,1,1)-v0(:) t1=abs(v1(1))+abs(v1(2))+abs(v1(3)) if (mp_mpi.and.(t1.gt.epslat)) then write(*,*) write(*,'("Info(findsymcrys): atomic basis shift (lattice) :")') write(*,'(3G18.10)') v1(:) write(*,'("See GEOMETRY.OUT for new atomic positions")') end if end if ! write number of crystal symmetries to test file call writetest(705,'number of crystal symmetries',iv=nsymcrys) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/plotpt3d.f900000644000000000000000000000013214061636517015015 xustar0030 mtime=1623670095.457101989 30 atime=1623670094.247103112 30 ctime=1623670095.457101989 elk-7.2.42/src/plotpt3d.f900000644002504400250440000000142714061636517017056 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine plotpt3d(vpl) use modmain implicit none ! arguments real(8), intent(out) :: vpl(3,np3d(1)*np3d(2)*np3d(3)) ! local variables integer ip,i1,i2,i3 real(8) v1(3),v2(3),v3(3) real(8) t1,t2,t3 ! generate 3D grid from corner vectors v1(:)=vclp3d(:,1)-vclp3d(:,0) v2(:)=vclp3d(:,2)-vclp3d(:,0) v3(:)=vclp3d(:,3)-vclp3d(:,0) ip=0 do i3=0,np3d(3)-1 t3=dble(i3)/dble(np3d(3)) do i2=0,np3d(2)-1 t2=dble(i2)/dble(np3d(2)) do i1=0,np3d(1)-1 t1=dble(i1)/dble(np3d(1)) ip=ip+1 vpl(:,ip)=t1*v1(:)+t2*v2(:)+t3*v3(:)+vclp3d(:,0) end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/elnes.f900000644000000000000000000000013114061636517014351 xustar0030 mtime=1623670095.459101987 29 atime=1623670094.24910311 30 ctime=1623670095.459101987 elk-7.2.42/src/elnes.f900000644002504400250440000000717314061636517016417 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine elnes use modmain use modomp use modtest implicit none ! local variables integer ik,jk,ikq,isym,nsk(3) integer ist,jst,iw,n,nthd real(8) vgqc(3),gqc real(8) vkql(3),v(3) real(8) q,wd,dw,w,t1 ! allocatable arrays real(8), allocatable :: jlgqr(:,:),ddcs(:) real(8), allocatable :: e(:,:,:),f(:,:,:) complex(8), allocatable :: ylmgq(:),sfacgq(:) complex(8), allocatable :: expmt(:,:),emat(:,:) ! initialise universal variables call init0 call init1 call init2 ! check q-vector is commensurate with k-point grid v(:)=dble(ngridk(:))*vecql(:) v(:)=abs(v(:)-nint(v(:))) if ((v(1).gt.epslat).or.(v(2).gt.epslat).or.(v(3).gt.epslat)) then write(*,*) write(*,'("Error(elnes): q-vector incommensurate with k-point grid")') write(*,'(" ngridk : ",3I6)') ngridk write(*,'(" vecql : ",3G18.10)') vecql write(*,*) stop end if ! read in the density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the second-variational eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! generate the phase factor function exp(iq.r) in the muffin-tins allocate(jlgqr(njcmax,nspecies)) allocate(ylmgq(lmmaxo),sfacgq(natmtot)) allocate(expmt(npcmtmax,natmtot)) call gengqf(1,vecqc,vgqc,gqc,jlgqr,ylmgq,sfacgq) call genexpmt(1,jlgqr,ylmgq,1,sfacgq,expmt) deallocate(jlgqr,ylmgq,sfacgq) allocate(e(nstsv,nstsv,nkptnr),f(nstsv,nstsv,nkptnr)) e(:,:,:)=0.d0 f(:,:,:)=0.d0 ! begin parallel loop over non-reduced k-points call holdthd(nkptnr,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(emat,jk,vkql,isym) & !$OMP PRIVATE(ikq,ist,jst,t1) & !$OMP NUM_THREADS(nthd) allocate(emat(nstsv,nstsv)) !$OMP DO do ik=1,nkptnr !$OMP CRITICAL(elnes_) write(*,'("Info(elnes): ",I6," of ",I6," k-points")') ik,nkptnr !$OMP END CRITICAL(elnes_) ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! k+q-vector in lattice coordinates vkql(:)=vkl(:,ik)+vecql(:) ! index to k+q-vector call findkpt(vkql,isym,ikq) ! compute < i,k+q | exp(iq.r) | j,k > matrix elements call genexpmat(vkl(:,ik),expmt,emat) ! add to the double differential scattering cross-section do jst=1,nstsv if (evalsv(jst,jk).lt.emaxelnes) then do ist=1,nstsv e(ist,jst,ik)=evalsv(ist,ikq)-evalsv(jst,jk) t1=dble(emat(ist,jst))**2+aimag(emat(ist,jst))**2 f(ist,jst,ik)=t1*occsv(jst,jk)*(occmax-occsv(ist,ikq)) end do end if end do end do !$OMP END DO deallocate(emat) !$OMP END PARALLEL call freethd(nthd) ! number of subdivisions used for interpolation nsk(:)=max(ngrkf/ngridk(:),1) n=nstsv*nstsv ! integrate over the Brillouin zone allocate(ddcs(nwplot)) call brzint(nswplot,ngridk,nsk,ivkiknr,nwplot,wplot,n,n,e,f,ddcs) q=sqrt(vecqc(1)**2+vecqc(2)**2+vecqc(3)**2) t1=2.d0/(omega*occmax) if (q.gt.epslat) t1=t1/q**4 ddcs(:)=t1*ddcs(:) open(50,file='ELNES.OUT',form='FORMATTED') wd=wplot(2)-wplot(1) dw=wd/dble(nwplot) do iw=1,nwplot w=dw*dble(iw-1)+wplot(1) write(50,'(2G18.10)') w,ddcs(iw) end do close(50) write(*,*) write(*,'("Info(elnes):")') write(*,'(" ELNES double differential cross-section written to ELNES.OUT")') ! write ELNES distribution to test file call writetest(140,'ELNES cross-section',nv=nwplot,tol=1.d-2,rva=ddcs) deallocate(e,f,ddcs,expmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/fermisurfbxsf.f900000644000000000000000000000013214061636517016131 xustar0030 mtime=1623670095.460101986 30 atime=1623670094.250103109 30 ctime=1623670095.460101986 elk-7.2.42/src/fermisurfbxsf.f900000644002504400250440000001011514061636517020164 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 F. Cricchio, F. Bultmark and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine fermisurfbxsf use modmain use modomp implicit none ! local variables integer ik,nst,ist integer ist0,ist1,jst0,jst1 integer i1,i2,i3,j1,j2,j3 integer nf,f,i,nthd real(8) e0,e1 ! allocatable arrays integer, allocatable :: idx(:) real(8), allocatable :: evalfv(:,:),e(:) complex(8), allocatable :: evecfv(:,:,:) complex(8), allocatable :: evecsv(:,:) ! initialise universal variables call init0 call init1 ! read density and potentials from file call readstate ! Fourier transform Kohn-Sham potential to G-space call genvsig ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! generate the spin-orbit coupling radial functions call gensocfr ! begin parallel loop over reduced k-points set call holdthd(nkpt,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evalfv,evecfv,evecsv) & !$OMP NUM_THREADS(nthd) allocate(evalfv(nstfv,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv)) allocate(evecsv(nstsv,nstsv)) !$OMP DO do ik=1,nkpt !$OMP CRITICAL(fermisurfbxsf_) write(*,'("Info(fermisurfbxsf): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(fermisurfbxsf_) ! solve the first- and second-variational eigenvalue equations call eveqn(ik,evalfv,evecfv,evecsv) ! end loop over reduced k-points set end do !$OMP END DO deallocate(evalfv,evecfv,evecsv) !$OMP END PARALLEL call freethd(nthd) ! if iterative diagonalisation is used the eigenvalues must be reordered if (tefvit.and.(.not.spinpol)) then allocate(idx(nstsv),e(nstsv)) do ik=1,nkpt e(:)=evalsv(:,ik) call sortidx(nstsv,e,idx) do ist=1,nstsv evalsv(ist,ik)=e(idx(ist)) end do end do deallocate(idx,e) end if ! number of files to plot (2 for collinear magnetism, 1 otherwise) if (ndmag.eq.1) then nf=2 else nf=1 end if do f=1,nf if (nf.eq.2) then if (f.eq.1) then open(50,file='FERMISURF_UP.bxsf',form='FORMATTED') jst0=1; jst1=nstfv else open(50,file='FERMISURF_DN.bxsf',form='FORMATTED') jst0=nstfv+1; jst1=2*nstfv end if else open(50,file='FERMISURF.bxsf',form='FORMATTED') jst0=1; jst1=nstsv end if ! find the range of eigenvalues which contribute to the Fermi surface (Lars) ist0=jst1; ist1=jst0 do ist=jst0,jst1 e0=minval(evalsv(ist,:)); e1=maxval(evalsv(ist,:)) ! determine if the band crosses the Fermi energy if ((e0.lt.efermi).and.(e1.gt.efermi)) then ist0=min(ist0,ist); ist1=max(ist1,ist) end if end do nst=ist1-ist0+1 write(50,'(" BEGIN_INFO")') write(50,'(" # Band-XCRYSDEN-Structure-File for Fermi surface plotting")') write(50,'(" # created by Elk version ",I1.1,".",I1.1,".",I2.2)') version write(50,'(" # Launch as: xcrysden --bxsf FERMISURF(_UP/_DN).bxsf")') write(50,'(" Fermi Energy: ",G18.10)') 0.d0 write(50,'(" END_INFO")') write(50,'(" BEGIN_BLOCK_BANDGRID_3D")') write(50, '(" band_energies")') write(50,'(" BANDGRID_3D_BANDS")') write(50,'(I4)') nst write(50,'(3I6)') ngridk(:)+1 write(50,'(3G18.10)') 0.d0,0.d0,0.d0 do i=1,3 write(50,'(3G18.10)') bvec(:,i) end do do ist=ist0,ist1 write(50,'(" BAND: ",I4)') ist do i1=0,ngridk(1) j1=mod(i1,ngridk(1)) do i2=0,ngridk(2) j2=mod(i2,ngridk(2)) do i3=0,ngridk(3) j3=mod(i3,ngridk(3)) ik=ivkik(j1,j2,j3) write(50,'(G18.10)') evalsv(ist,ik)-efermi end do end do end do end do write(50,'(" END_BANDGRID_3D")') write(50,'(" END_BLOCK_BANDGRID_3D")') close(50) end do write(*,*) write(*,'("Info(fermisurfbxsf):")') if (ndmag.eq.1) then write(*,'(" 3D Fermi surface data written to FERMISURF_UP.bxsf and & &FERMISURF_DN.bxsf")') else write(*,'(" 3D Fermi surface data written to FERMISURF.bxsf")') end if write(*,'(" for plotting with XCrysDen (Fermi energy set to zero)")') write(*,*) write(*,'(" Launch as: xcrysden --bxsf FERMISURF(_UP/_DN).bxsf")') end subroutine elk-7.2.42/src/PaxHeaders.21776/genspecies.f900000644000000000000000000000013214061636517015371 xustar0030 mtime=1623670095.462101984 30 atime=1623670094.252103107 30 ctime=1623670095.462101984 elk-7.2.42/src/genspecies.f900000644002504400250440000000467514061636517017442 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genspecies(fnum) use modmain use modmpi implicit none ! arguments integer, intent(in) :: fnum ! local variables integer nz,nmax,nst,ist integer ne,nrm,nr,ir,it,i integer n(maxstsp),l(maxstsp),k(maxstsp) real(8) mass,zn,t1,t2,t3 real(8) rm,rmin,rmax real(8) occ(maxstsp),eval(maxstsp) character(256) symb,name ! allocatable arrays real(8), allocatable :: r(:),rho(:),vr(:),rwf(:,:,:) read(fnum,*,err=20) nz if (nz.le.0) then write(*,*) write(*,'("Error(genspecies): atomic number negative : ",I8)') nz write(*,*) stop end if read(fnum,*,err=20) symb,name read(fnum,*,err=20) mass ! convert from 'atomic mass units' to atomic units mass=mass*amu read(fnum,*,err=20) rm read(fnum,*,err=20) nst if ((nst.le.0).or.(nst.gt.maxstsp)) then write(*,*) write(*,'("Error(genspecies): nst out of range : ",I8)') nst write(*,'(" for species ",A)') trim(name) write(*,*) stop end if ne=0 nmax=1 do ist=1,nst read(fnum,*,err=20) n(ist),l(ist),k(ist),i ne=ne+i occ(ist)=i nmax=max(nmax,n(ist)) end do if (mp_mpi) then write(*,'("Info(genspecies): running Z = ",I4,", (",A,")")') nz,trim(name) if (ne.ne.nz) then write(*,*) write(*,'("Warning(genspecies): atom not neutral, electron number : ",& &I4)') ne end if end if ! nuclear charge in units of e zn=-dble(nz) ! minimum radial mesh point proportional to 1/sqrt(Z) rmin=2.d-6/sqrt(dble(nz)) ! default effective infinity rmax=100.d0 ! set the number of radial mesh points proportional to number of nodes nrm=100*(nmax+1) do it=1,2 ! number of points to effective infinity t1=log(rm/rmin) t2=log(rmax/rmin) t3=dble(nrm)*t2/t1 nr=int(t3) allocate(r(nr),rho(nr),vr(nr),rwf(nr,2,nst)) ! generate logarithmic radial mesh t2=t1/dble(nrm-1) do ir=1,nr r(ir)=rmin*exp(dble(ir-1)*t2) end do ! solve the Kohn-Sham-Dirac equation for the atom call atom(sol,.true.,zn,nst,n,l,k,occ,3,0,nr,r,eval,rho,vr,rwf) ! recompute the effective infinity do ir=nr,1,-1 if (rho(ir).gt.1.d-20) then rmax=1.75d0*r(ir) exit end if end do deallocate(r,rho,vr,rwf) end do ! write the species file call writespecies(symb,name,zn,mass,rmin,rm,rmax,nrm,nst,n,l,k,occ,eval) return 20 continue write(*,*) write(*,'("Error(genspecies): error reading species data")') write(*,*) stop end subroutine elk-7.2.42/src/PaxHeaders.21776/writeexpmat.f900000644000000000000000000000013214061636517015615 xustar0030 mtime=1623670095.464101982 30 atime=1623670094.254103105 30 ctime=1623670095.464101982 elk-7.2.42/src/writeexpmat.f900000644002504400250440000000501114061636517017647 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeexpmat use modmain implicit none ! local variables integer nk,ik,jk,i,j real(8) vgqc(3),gqc real(8) a,b ! allocatable arrays real(8), allocatable :: jlgqr(:,:) complex(8), allocatable :: ylmgq(:),sfacgq(:) complex(8), allocatable :: expmt(:,:),emat(:,:) ! initialise universal variables call init0 call init1 call init2 ! read in the density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! generate the phase factor function exp(iq.r) in the muffin-tins allocate(jlgqr(njcmax,nspecies)) allocate(ylmgq(lmmaxo),sfacgq(natmtot)) allocate(expmt(npcmtmax,natmtot)) call gengqf(1,vecqc,vgqc,gqc,jlgqr,ylmgq,sfacgq) call genexpmt(1,jlgqr,ylmgq,1,sfacgq,expmt) expmt(:,:)=omega*expmt(:,:) deallocate(jlgqr,ylmgq,sfacgq) ! number of k-points to write out if (kstlist(1,1).le.0) then nk=nkpt else nk=nkstlist end if open(50,file='EXPIQR.OUT',form='FORMATTED') write(50,*) write(50,'("q-vector (lattice coordinates) :")') write(50,'(3G18.10)') vecql write(50,'("q-vector (Cartesian coordinates) :")') write(50,'(3G18.10)') vecqc write(50,*) write(50,'(I8," : number of k-points")') nk write(50,'(I6," : number of states per k-point")') nstsv allocate(emat(nstsv,nstsv)) do jk=1,nk if (kstlist(1,1).le.0) then ik=jk else ik=kstlist(1,jk) end if if ((ik.le.0).or.(ik.gt.nkpt)) then write(*,*) write(*,'("Error(writeexpiqr): k-point out of range : ",I8)') ik write(*,*) stop end if write(50,*) write(50,'(" k-point (lattice coordinates) :")') write(50,'(3G18.10)') vkl(:,ik) write(50,*) write(50,'(" k-point (Cartesian coordinates) :")') write(50,'(3G18.10)') vkc(:,ik) call genexpmat(vkl(:,ik),expmt,emat) do i=1,nstsv write(50,*) write(50,'(I6," : state i; state j, <...>, |<...>|² below")') i do j=1,nstsv a=dble(emat(i,j)) b=aimag(emat(i,j)) write(50,'(I6,3G18.10)') j,a,b,a**2+b**2 end do end do ! end loop over k-points end do close(50) write(*,*) write(*,'("Info(writeexpmat)")') write(*,'(" < i,k+q | exp(iq.r) | j,k > matrix elements written to & &EXPIQR.OUT")') write(*,'(" for the q-vector in vecql and all k-points in kstlist")') deallocate(expmt,emat) end subroutine elk-7.2.42/src/PaxHeaders.21776/writekpts.f900000644000000000000000000000013214061636517015300 xustar0030 mtime=1623670095.465101981 30 atime=1623670094.255103104 30 ctime=1623670095.465101981 elk-7.2.42/src/writekpts.f900000644002504400250440000000137314061636517017341 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writekpts ! !INTERFACE: subroutine writekpts ! !USES: use modmain ! !DESCRIPTION: ! Writes the $k$-points in lattice coordinates, weights and number of ! ${\bf G+k}$-vectors to the file {\tt KPOINTS.OUT}. ! ! !REVISION HISTORY: ! Created June 2003 (JKD) !EOP !BOC implicit none ! local variables integer ik open(50,file='KPOINTS'//trim(filext),form='FORMATTED') write(50,'(I6," : nkpt; k-point, vkl, wkpt, nmat below")') nkpt do ik=1,nkpt write(50,'(I6,4G18.10,2I8)') ik,vkl(:,ik),wkpt(ik),nmat(:,ik) end do close(50) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/wfcrplot.f900000644000000000000000000000013014061636517015102 xustar0029 mtime=1623670095.46610198 30 atime=1623670094.257103103 29 ctime=1623670095.46610198 elk-7.2.42/src/wfcrplot.f900000644002504400250440000000177114061636517017147 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine wfcrplot use modmain implicit none ! local variables integer ist,is,ia,ias,ir character(256) fname ! initialise universal variables call init0 ! read density and potentials from file call readstate ! generate the core wavefunctions call gencore do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) write(fname,'("WFCORE_S",I2.2,"_A",I4.4,".OUT")') is,ia open(50,file=trim(fname),form='FORMATTED') do ist=1,nstsp(is) if (spcore(ist,is)) then do ir=1,nrsp(is) write(50,'(2G18.10)') rsp(ir,is),rwfcr(ir,1,ist,ias) end do write(50,*) end if end do close(50) end do end do write(*,*) write(*,'("Info(wfcrplot):")') write(*,'(" Core state wavefunctions written to WFCORE_Sss_Aaaaa.OUT")') write(*,'(" for all species and atoms")') end subroutine elk-7.2.42/src/PaxHeaders.21776/writedos.f900000644000000000000000000000013214061636517015104 xustar0030 mtime=1623670095.468101979 30 atime=1623670094.259103101 30 ctime=1623670095.468101979 elk-7.2.42/src/writedos.f900000644002504400250440000000344614061636517017150 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writedos use modmain implicit none ! local variables integer ik ! initialise universal variables call init0 call init1 ! read density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) if (dosocc) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! generate the partial and total DOS and write to file call dos('.OUT',dosocc,occsv) write(*,*) write(*,'("Info(writedos):")') write(*,'(" Total density of states written to TDOS.OUT")') write(*,*) write(*,'(" Partial density of states written to PDOS_Sss_Aaaaa.OUT")') write(*,'(" for all species and atoms")') if (dosmsum) then write(*,'(" PDOS summed over m")') end if if (dosssum) then write(*,'(" PDOS summed over spin")') end if write(*,*) write(*,'(" Spin-quantisation axis : ",3G18.10)') sqados(:) if (lmirep) then write(*,*) write(*,'(" Eigenvalues of a random matrix in the (l,m) basis symmetrised")') write(*,'(" with the site symmetries written to ELMIREP.OUT for all")') write(*,'(" species and atoms. Degenerate eigenvalues correspond to")') write(*,'(" irreducible representations of each site symmetry group")') end if write(*,*) write(*,'(" Interstitial density of states written to IDOS.OUT")') write(*,*) write(*,'(" Fermi energy is at zero in plots")') write(*,*) write(*,'(" DOS units are states/Hartree/unit cell")') end subroutine elk-7.2.42/src/PaxHeaders.21776/energykncr.f900000644000000000000000000000013014061636517015411 xustar0030 mtime=1623670095.470101977 28 atime=1623670094.2601031 30 ctime=1623670095.470101977 elk-7.2.42/src/energykncr.f900000644002504400250440000000223714061636517017454 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine energykncr use modmain implicit none integer ist,is,ias integer nr,nri,ir,i ! automatic arrays real(8) rfmt(npmtmax) ! external functions real(8), external :: rfmtinp ! calculate the kinetic energy for core states engykncr=0.d0 do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) ! sum of core eigenvalues do ist=1,nstsp(is) if (spcore(ist,is)) engykncr=engykncr+occcr(ist,ias)*evalcr(ist,ias) end do ! core density rfmt(1:npmt(is))=0.d0 i=1 if (spincore) then ! spin-polarised core do ir=1,nri rfmt(i)=rhocr(ir,ias,1)+rhocr(ir,ias,2) i=i+lmmaxi end do do ir=nri+1,nr rfmt(i)=rhocr(ir,ias,1)+rhocr(ir,ias,2) i=i+lmmaxo end do else ! spin-unpolarised core do ir=1,nri rfmt(i)=rhocr(ir,ias,1) i=i+lmmaxi end do do ir=nri+1,nr rfmt(i)=rhocr(ir,ias,1) i=i+lmmaxo end do end if engykncr=engykncr-rfmtinp(nr,nri,wrmt(:,is),rfmt,vsmt(:,ias)) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/ggamt_1.f900000644000000000000000000000013214061636517014563 xustar0030 mtime=1623670095.471101976 30 atime=1623670094.262103098 30 ctime=1623670095.471101976 elk-7.2.42/src/ggamt_1.f900000644002504400250440000000327514061636517016627 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggamt_1 ! !INTERFACE: subroutine ggamt_1(tsh,is,np,rho,grho,g2rho,g3rho) ! !USES: use modmain ! !DESCRIPTION: ! Spin-unpolarised version of {\tt ggamt\_sp\_1}. ! ! !REVISION HISTORY: ! Created November 2009 (JKD) !EOP !BOC implicit none ! arguments logical, intent(in) :: tsh integer, intent(in) :: is,np real(8), intent(in) :: rho(np) real(8), intent(out) :: grho(np),g2rho(np),g3rho(np) ! local variables integer nr,nri,i ! allocatable arrays real(8), allocatable :: grfmt(:,:),gvrho(:,:),rfmt1(:),rfmt2(:) allocate(grfmt(np,3),gvrho(np,3),rfmt2(np)) nr=nrmt(is) nri=nrmti(is) ! |grad rho| if (tsh) then call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rho,np,grfmt) else allocate(rfmt1(np)) call rfsht(nr,nri,rho,rfmt1) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) end if do i=1,3 call rbsht(nr,nri,grfmt(:,i),gvrho(:,i)) end do grho(1:np)=sqrt(gvrho(1:np,1)**2+gvrho(1:np,2)**2+gvrho(1:np,3)**2) ! grad^2 rho in spherical coordinates if (tsh) then call grad2rfmt(nr,nri,rlmt(:,-1,is),rlmt(:,-2,is),wcrmt(:,:,is),rho,rfmt2) else call grad2rfmt(nr,nri,rlmt(:,-1,is),rlmt(:,-2,is),wcrmt(:,:,is),rfmt1,rfmt2) end if call rbsht(nr,nri,rfmt2,g2rho) ! (grad rho).(grad |grad rho|) call rfsht(nr,nri,grho,rfmt2) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt2,np,grfmt) g3rho(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt2) g3rho(1:np)=g3rho(1:np)+gvrho(1:np,i)*rfmt2(1:np) end do deallocate(grfmt,gvrho,rfmt2) if (.not.tsh) deallocate(rfmt1) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggair_1.f900000644000000000000000000000013214061636517014555 xustar0030 mtime=1623670095.473101974 30 atime=1623670094.264103096 30 ctime=1623670095.473101974 elk-7.2.42/src/ggair_1.f900000644002504400250440000000307014061636517016612 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggair_1 ! !INTERFACE: subroutine ggair_1(rho,grho,g2rho,g3rho) ! !USES: use modmain ! !DESCRIPTION: ! Spin-unpolarised version of {\tt ggair\_sp\_1}. ! ! !REVISION HISTORY: ! Created November 2009 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: rho(ngtot) real(8), intent(out) :: grho(ngtot),g2rho(ngtot),g3rho(ngtot) ! local variables integer i,ig,ifg ! allocatable arrays real(8), allocatable :: gvrho(:,:) complex(8), allocatable :: zfft1(:),zfft2(:) allocate(gvrho(ngtot,3)) allocate(zfft1(ngtot),zfft2(ngtot)) zfft1(:)=rho(:) call zfftifc(3,ngridg,-1,zfft1) ! |grad rho| do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) gvrho(:,i)=dble(zfft2(:)) end do grho(:)=sqrt(gvrho(:,1)**2+gvrho(:,2)**2+gvrho(:,3)**2) ! grad^2 rho zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=-(gc(ig)**2)*zfft1(ifg) end do call zfftifc(3,ngridg,1,zfft2) g2rho(:)=dble(zfft2(:)) ! (grad rho).(grad |grad rho|) zfft1(:)=grho(:) call zfftifc(3,ngridg,-1,zfft1) g3rho(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) g3rho(:)=g3rho(:)+gvrho(:,i)*dble(zfft2(:)) end do deallocate(gvrho,zfft1,zfft2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggamt_sp_1.f900000644000000000000000000000013214061636517015265 xustar0030 mtime=1623670095.474101973 30 atime=1623670094.265103095 30 ctime=1623670095.474101973 elk-7.2.42/src/ggamt_sp_1.f900000644002504400250440000001017214061636517017323 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggamt_sp_1 ! !INTERFACE: subroutine ggamt_sp_1(is,np,rhoup,rhodn,grho,gup,gdn,g2up,g2dn,g3rho,g3up,g3dn) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! is : species number (in,integer) ! np : number of muffin-tin points (in,integer) ! rhoup : spin-up density in spherical coordinates (in,real(np)) ! rhodn : spin-down density (in,real(np)) ! grho : |grad rho| (out,real(np)) ! gup : |grad rhoup| (out,real(np)) ! gdn : |grad rhodn| (out,real(np)) ! g2up : grad^2 rhoup (out,real(np)) ! g2dn : grad^2 rhodn (out,real(np)) ! g3rho : (grad rho).(grad |grad rho|) (out,real(np)) ! g3up : (grad rhoup).(grad |grad rhoup|) (out,real(np)) ! g3dn : (grad rhodn).(grad |grad rhodn|) (out,real(np)) ! !DESCRIPTION: ! Computes $|\nabla\rho|$, $|\nabla\rho^{\uparrow}|$, ! $|\nabla\rho^{\downarrow}|$, $\nabla^2\rho^{\uparrow}$, ! $\nabla^2\rho^{\downarrow}$, $\nabla\rho\cdot(\nabla|\nabla\rho|)$, ! $\nabla\rho^{\uparrow}\cdot(\nabla|\nabla\rho^{\uparrow}|)$ and ! $\nabla\rho^{\downarrow}\cdot(\nabla|\nabla\rho^{\downarrow}|)$ ! for a muffin-tin charge density, as required by the generalised gradient ! approximation functionals of type 1 for spin-polarised densities. The input ! densities and output gradients are in terms of spherical coordinates. See ! routines {\tt potxc} and {\tt modxcifc}. ! ! !REVISION HISTORY: ! Created April 2004 (JKD) ! Simplified and improved, October 2009 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: is,np real(8), intent(in) :: rhoup(np),rhodn(np) real(8), intent(out) :: grho(np),gup(np),gdn(np) real(8), intent(out) :: g2up(np),g2dn(np) real(8), intent(out) :: g3rho(np),g3up(np),g3dn(np) ! local variables integer nr,nri,i ! allocatable arrays real(8), allocatable :: gvup(:,:),gvdn(:,:),grfmt(:,:) real(8), allocatable :: rfmt1(:),rfmt2(:) allocate(grfmt(np,3),gvup(np,3),gvdn(np,3)) allocate(rfmt1(np),rfmt2(np)) nr=nrmt(is) nri=nrmti(is) !----------------! ! rho up ! !----------------! ! convert rhoup to spherical harmonics call rfsht(nr,nri,rhoup,rfmt1) ! grad rhoup in spherical coordinates call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) do i=1,3 call rbsht(nr,nri,grfmt(:,i),gvup(:,i)) end do ! |grad rhoup| gup(1:np)=sqrt(gvup(1:np,1)**2+gvup(1:np,2)**2+gvup(1:np,3)**2) ! grad^2 rhoup in spherical coordinates call grad2rfmt(nr,nri,rlmt(:,-1,is),rlmt(:,-2,is),wcrmt(:,:,is),rfmt1,rfmt2) call rbsht(nr,nri,rfmt2,g2up) ! (grad rhoup).(grad |grad rhoup|) call rfsht(nr,nri,gup,rfmt1) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) g3up(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt1) g3up(1:np)=g3up(1:np)+gvup(1:np,i)*rfmt1(1:np) end do !------------------! ! rho down ! !------------------! ! convert rhodn to spherical harmonics call rfsht(nr,nri,rhodn,rfmt1) ! grad rhodn in spherical coordinates call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) do i=1,3 call rbsht(nr,nri,grfmt(:,i),gvdn(:,i)) end do gdn(1:np)=sqrt(gvdn(1:np,1)**2+gvdn(1:np,2)**2+gvdn(1:np,3)**2) ! grad^2 rhodn in spherical coordinates call grad2rfmt(nr,nri,rlmt(:,-1,is),rlmt(:,-2,is),wcrmt(:,:,is),rfmt1,rfmt2) call rbsht(nr,nri,rfmt2,g2dn) ! (grad rhodn).(grad |grad rhodn|) call rfsht(nr,nri,gdn,rfmt1) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) g3dn(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt1) g3dn(1:np)=g3dn(1:np)+gvdn(1:np,i)*rfmt1(1:np) end do !-------------! ! rho ! !-------------! ! |grad rho| grho(1:np)=sqrt((gvup(1:np,1)+gvdn(1:np,1))**2 & +(gvup(1:np,2)+gvdn(1:np,2))**2 & +(gvup(1:np,3)+gvdn(1:np,3))**2) ! (grad rho).(grad |grad rho|) call rfsht(nr,nri,grho,rfmt1) call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) g3rho(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt1) g3rho(1:np)=g3rho(1:np)+(gvup(1:np,i)+gvdn(1:np,i))*rfmt1(1:np) end do deallocate(rfmt1,rfmt2,grfmt,gvup,gvdn) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggair_sp_1.f900000644000000000000000000000013214061636517015257 xustar0030 mtime=1623670095.476101971 30 atime=1623670094.267103093 30 ctime=1623670095.476101971 elk-7.2.42/src/ggair_sp_1.f900000644002504400250440000001021214061636517017310 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggair_sp_1 ! !INTERFACE: subroutine ggair_sp_1(rhoup,rhodn,grho,gup,gdn,g2up,g2dn,g3rho,g3up,g3dn) ! !INPUT/OUTPUT PARAMETERS: ! rhoup : spin-up density (in,real(ngtot)) ! rhodn : spin-down density (in,real(ngtot)) ! grho : |grad rho| (out,real(ngtot)) ! gup : |grad rhoup| (out,real(ngtot)) ! gdn : |grad rhodn| (out,real(ngtot)) ! g2up : grad^2 rhoup (out,real(ngtot)) ! g2dn : grad^2 rhodn (out,real(ngtot)) ! g3rho : (grad rho).(grad |grad rho|) (out,real(ngtot)) ! g3up : (grad rhoup).(grad |grad rhoup|) (out,real(ngtot)) ! g3dn : (grad rhodn).(grad |grad rhodn|) (out,real(ngtot)) ! !DESCRIPTION: ! Computes $|\nabla\rho|$, $|\nabla\rho^{\uparrow}|$, ! $|\nabla\rho^{\downarrow}|$, $\nabla^2\rho^{\uparrow}$, ! $\nabla^2\rho^{\downarrow}$, $\nabla\rho\cdot(\nabla|\nabla\rho|)$, ! $\nabla\rho^{\uparrow}\cdot(\nabla|\nabla\rho^{\uparrow}|)$ and ! $\nabla\rho^{\downarrow}\cdot(\nabla|\nabla\rho^{\downarrow}|)$ for the ! interstitial charge density, as required by the generalised gradient ! approximation functionals of type 1 for spin-polarised densities. See ! routines {\tt potxc} and {\tt modxcifc}. ! ! !REVISION HISTORY: ! Created October 2004 (JKD) ! Simplified and improved, October 2009 (JKD) !EOP !BOC use modmain implicit none ! arguments real(8), intent(in) :: rhoup(ngtot),rhodn(ngtot) real(8), intent(out) :: grho(ngtot),gup(ngtot),gdn(ngtot) real(8), intent(out) :: g2up(ngtot),g2dn(ngtot) real(8), intent(out) :: g3rho(ngtot),g3up(ngtot),g3dn(ngtot) ! local variables integer ig,ifg,i ! allocatable arrays real(8), allocatable :: gvup(:,:),gvdn(:,:) complex(8), allocatable :: zfft1(:),zfft2(:) allocate(gvup(ngtot,3),gvdn(ngtot,3)) allocate(zfft1(ngtot),zfft2(ngtot)) !----------------! ! rho up ! !----------------! zfft1(:)=rhoup(:) call zfftifc(3,ngridg,-1,zfft1) ! |grad rhoup| do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) gvup(:,i)=dble(zfft2(:)) end do gup(:)=sqrt(gvup(:,1)**2+gvup(:,2)**2+gvup(:,3)**2) ! grad^2 rhoup zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=-(gc(ig)**2)*zfft1(ifg) end do call zfftifc(3,ngridg,1,zfft2) g2up(:)=dble(zfft2(:)) ! (grad rhoup).(grad |grad rhoup|) zfft1(:)=gup(:) call zfftifc(3,ngridg,-1,zfft1) g3up(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) g3up(:)=g3up(:)+gvup(:,i)*dble(zfft2(:)) end do !------------------! ! rho down ! !------------------! zfft1(:)=rhodn(:) call zfftifc(3,ngridg,-1,zfft1) ! |grad rhodn| do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) gvdn(:,i)=dble(zfft2(:)) end do gdn(:)=sqrt(gvdn(:,1)**2+gvdn(:,2)**2+gvdn(:,3)**2) ! grad^2 rhodn zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=-(gc(ig)**2)*zfft1(ifg) end do call zfftifc(3,ngridg,1,zfft2) g2dn(:)=dble(zfft2(:)) ! (grad rhodn).(grad |grad rhodn|) zfft1(:)=gdn(:) call zfftifc(3,ngridg,-1,zfft1) g3dn(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) g3dn(:)=g3dn(:)+gvdn(:,i)*dble(zfft2(:)) end do !-------------! ! rho ! !-------------! ! |grad rho| grho(:)=sqrt((gvup(:,1)+gvdn(:,1))**2 & +(gvup(:,2)+gvdn(:,2))**2 & +(gvup(:,3)+gvdn(:,3))**2) ! (grad rho).(grad |grad rho|) zfft1(:)=grho(:) call zfftifc(3,ngridg,-1,zfft1) g3rho(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) g3rho(:)=g3rho(:)+(gvup(:,i)+gvdn(:,i))*dble(zfft2(:)) end do deallocate(gvup,gvdn,zfft1,zfft2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggamt_2a.f900000644000000000000000000000013014061636517014723 xustar0029 mtime=1623670095.47710197 30 atime=1623670094.269103091 29 ctime=1623670095.47710197 elk-7.2.42/src/ggamt_2a.f900000644002504400250440000000273114061636517016765 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggamt_2a ! !INTERFACE: subroutine ggamt_2a(tsh,is,np,rho,g2rho,gvrho,grho2) ! !USES: use modmain ! !DESCRIPTION: ! Spin-unpolarised version of {\tt ggamt\_sp\_2a}. ! ! !REVISION HISTORY: ! Created November 2009 (JKD and TMcQ) !EOP !BOC implicit none ! arguments logical, intent(in) :: tsh integer, intent(in) :: is,np real(8), intent(in) :: rho(np) real(8), intent(out) :: g2rho(np),gvrho(np,3),grho2(np) ! local variables integer nr,nri,i ! allocatable arrays real(8), allocatable :: grfmt(:,:),rfmt1(:),rfmt2(:) allocate(grfmt(np,3),rfmt2(np)) nr=nrmt(is) nri=nrmti(is) ! compute grad^2 rho in spherical coordinates if (tsh) then call grad2rfmt(nr,nri,rlmt(:,-1,is),rlmt(:,-2,is),wcrmt(:,:,is),rho,rfmt2) else allocate(rfmt1(np)) call rfsht(nr,nri,rho,rfmt1) call grad2rfmt(nr,nri,rlmt(:,-1,is),rlmt(:,-2,is),wcrmt(:,:,is),rfmt1,rfmt2) end if call rbsht(nr,nri,rfmt2,g2rho) ! compute grad rho in spherical coordinates if (tsh) then call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rho,np,grfmt) else call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) end if do i=1,3 call rbsht(nr,nri,grfmt(:,i),gvrho(:,i)) end do ! (grad rho)^2 grho2(1:np)=gvrho(1:np,1)**2+gvrho(1:np,2)**2+gvrho(1:np,3)**2 deallocate(rfmt2,grfmt) if (.not.tsh) deallocate(rfmt1) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggair_2a.f900000644000000000000000000000013214061636517014717 xustar0030 mtime=1623670095.478101969 30 atime=1623670094.270103091 30 ctime=1623670095.478101969 elk-7.2.42/src/ggair_2a.f900000644002504400250440000000235014061636517016754 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggair_2a ! !INTERFACE: subroutine ggair_2a(rho,g2rho,gvrho,grho2) ! !USES: use modmain ! !DESCRIPTION: ! Spin-unpolarised version of {\tt ggair\_sp\_2a}. ! ! !REVISION HISTORY: ! Created November 2009 (JKD and TMcQ) !EOP !BOC implicit none ! arguments real(8), intent(in) :: rho(ngtot) real(8), intent(out) :: g2rho(ngtot),gvrho(ngtot,3),grho2(ngtot) ! local variables integer i,ig,ifg ! allocatable arrays complex(8), allocatable :: zfft1(:),zfft2(:) allocate(zfft1(ngtot),zfft2(ngtot)) ! Fourier transform density to G-space zfft1(:)=rho(:) call zfftifc(3,ngridg,-1,zfft1) ! grad^2 rho zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=-(gc(ig)**2)*zfft1(ifg) end do call zfftifc(3,ngridg,1,zfft2) g2rho(:)=dble(zfft2(:)) ! grad rho do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) gvrho(:,i)=dble(zfft2(:)) end do ! (grad rho)^2 grho2(:)=gvrho(:,1)**2+gvrho(:,2)**2+gvrho(:,3)**2 deallocate(zfft1,zfft2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggamt_2b.f900000644000000000000000000000013214061636517014726 xustar0030 mtime=1623670095.480101967 30 atime=1623670094.272103089 30 ctime=1623670095.480101967 elk-7.2.42/src/ggamt_2b.f900000644002504400250440000000336314061636517016770 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggamt_2b ! !INTERFACE: subroutine ggamt_2b(is,np,g2rho,gvrho,vx,vc,dxdgr2,dcdgr2) ! !USES: use modmain ! !DESCRIPTION: ! Spin-unpolarised version of {\tt ggamt\_sp\_2b}. ! ! !REVISION HISTORY: ! Created November 2009 (JKD and TMcQ) !EOP !BOC implicit none ! arguments integer, intent(in) :: is,np real(8), intent(in) :: g2rho(np),gvrho(np,3) real(8), intent(inout) :: vx(np),vc(np) real(8), intent(in) :: dxdgr2(np),dcdgr2(np) ! local variables integer nr,nri,i ! allocatable arrays real(8), allocatable :: rfmt1(:),rfmt2(:),grfmt(:,:) allocate(rfmt1(np),rfmt2(np),grfmt(np,3)) nr=nrmt(is) nri=nrmti(is) !------------------! ! exchange ! !------------------! ! convert dxdgr2 to spherical harmonics call rfsht(nr,nri,dxdgr2,rfmt1) ! compute grad dxdgr2 call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) ! (grad dxdgr2).(grad rho) in spherical coordinates rfmt1(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt2) rfmt1(1:np)=rfmt1(1:np)+rfmt2(1:np)*gvrho(1:np,i) end do vx(1:np)=vx(1:np)-2.d0*(rfmt1(1:np)+dxdgr2(1:np)*g2rho(1:np)) !---------------------! ! correlation ! !---------------------! ! convert dcdgr2 to spherical harmonics call rfsht(nr,nri,dcdgr2,rfmt1) ! compute grad dcdgr2 call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) ! (grad dcdgr2).(grad rho) in spherical coordinates rfmt1(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt2) rfmt1(1:np)=rfmt1(1:np)+rfmt2(1:np)*gvrho(1:np,i) end do vc(1:np)=vc(1:np)-2.d0*(rfmt1(1:np)+dcdgr2(1:np)*g2rho(1:np)) deallocate(rfmt1,rfmt2,grfmt) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggair_2b.f900000644000000000000000000000013214061636517014720 xustar0030 mtime=1623670095.481101967 30 atime=1623670094.274103087 30 ctime=1623670095.481101967 elk-7.2.42/src/ggair_2b.f900000644002504400250440000000332114061636517016754 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggair_2b ! !INTERFACE: subroutine ggair_2b(g2rho,gvrho,vx,vc,dxdgr2,dcdgr2) ! !USES: use modmain ! !DESCRIPTION: ! Spin-unpolarised version of {\tt ggair\_sp\_2b}. ! ! !REVISION HISTORY: ! Created November 2009 (JKD and TMcQ) !EOP !BOC implicit none ! arguments real(8), intent(in) :: g2rho(ngtot),gvrho(ngtot,3) real(8), intent(inout) :: vx(ngtot),vc(ngtot) real(8), intent(in) :: dxdgr2(ngtot),dcdgr2(ngtot) ! local variables integer ig,ifg,i ! allocatable arrays real(8), allocatable :: rfir(:) complex(8), allocatable :: zfft1(:),zfft2(:) allocate(rfir(ngtot)) allocate(zfft1(ngtot),zfft2(ngtot)) !------------------! ! exchange ! !------------------! ! compute grad dxdgr2 zfft1(:)=dxdgr2(:) call zfftifc(3,ngridg,-1,zfft1) ! (grad dxdgr2).(grad rho) rfir(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) rfir(:)=rfir(:)+dble(zfft2(:))*gvrho(:,i) end do vx(:)=vx(:)-2.d0*(rfir(:)+dxdgr2(:)*g2rho(:)) !---------------------! ! correlation ! !---------------------! ! compute grad dcdgr2 zfft1(:)=dcdgr2(:) call zfftifc(3,ngridg,-1,zfft1) ! (grad dcdgr2).(grad rho) rfir(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) rfir(:)=rfir(:)+dble(zfft2(:))*gvrho(:,i) end do vc(:)=vc(:)-2.d0*(rfir(:)+dcdgr2(:)*g2rho(:)) deallocate(rfir,zfft1,zfft2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggamt_sp_2a.f900000644000000000000000000000013214061636517015427 xustar0030 mtime=1623670095.483101965 30 atime=1623670094.275103086 30 ctime=1623670095.483101965 elk-7.2.42/src/ggamt_sp_2a.f900000644002504400250440000001032214061636517017462 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggamt_sp_2a ! !INTERFACE: subroutine ggamt_sp_2a(is,np,rhoup,rhodn,g2up,g2dn,gvup,gvdn,gup2,gdn2,gupdn) ! !USES: use modmain ! !DESCRIPTION: ! Computes the muffin-tin gradients $\nabla^2\rho^{\uparrow}$, ! $\nabla^2\rho^{\downarrow}$, $\nabla\rho^{\uparrow}$, ! $\nabla\rho^{\downarrow}$, $(\nabla\rho^{\uparrow})^2$, ! $(\nabla\rho^{\downarrow})^2$ and ! $\nabla\rho^{\uparrow}\cdot\nabla\rho^{\downarrow}$, which are passed in to ! GGA functional subroutines of type 2. The exchange-correlation energy in ! these routines has the functional form ! $$ E_{xc}[\rho^{\uparrow},\rho^{\downarrow}]=\int d^3r\,\hat{\epsilon}_{xc} ! \bigl(\rho^{\uparrow}({\bf r}),\rho^{\downarrow}({\bf r}), ! (\nabla\rho^{\uparrow}({\bf r}))^2,(\nabla\rho^{\downarrow}({\bf r}))^2, ! \nabla\rho^{\uparrow}({\bf r}) ! \cdot\nabla\rho^{\downarrow}({\bf r})\bigr), $$ ! where $\hat{\epsilon}_{xc}({\bf r})=\epsilon_{xc}({\bf r})\rho({\bf r})$ is ! the xc energy per unit volume, with $\epsilon_{xc}$ being the xc energy per ! electron, and $\rho=\rho^{\uparrow}+\rho^{\downarrow}$. From the gradients ! above, type 2 GGA routines return $\epsilon_{xc}$, but not directly the xc ! potentials. Instead they generate the derivatives ! $\partial\hat{\epsilon}_{xc}/\partial\rho^{\uparrow}({\bf r})$, ! $\partial\hat{\epsilon}_{xc}/\partial(\nabla\rho^{\uparrow}({\bf r}))^2$, ! and the same for down spin, as well as ! $\partial\hat{\epsilon}_{xc}/\partial(\nabla\rho^{\uparrow}({\bf r}) ! \cdot\nabla\rho^{\downarrow}({\bf r}))$. In a post-processing step invoked ! by {\tt ggamt\_sp\_2b}, integration by parts is used to obtain the xc ! potential explicitly with ! \begin{align*} ! V_{xc}^{\uparrow}({\bf r})=&\frac{\partial\hat{\epsilon}_{xc}}{\partial ! \rho^{\uparrow}({\bf r})}-2\left(\nabla\frac{\partial\hat{\epsilon}_{xc}} ! {\partial(\nabla\rho^{\uparrow})^2}\right)\cdot\nabla\rho^{\uparrow} ! -2\frac{\hat{\epsilon}_{xc}}{\partial(\nabla\rho^{\uparrow})^2}\nabla^2 ! \rho^{\uparrow}\\ ! &-\left(\nabla\frac{\hat{\epsilon}_{xc}}{\partial(\nabla\rho^{\uparrow} ! \cdot\nabla\rho^{\downarrow})}\right)\cdot\nabla\rho^{\downarrow} ! -\frac{\partial\hat{\epsilon}_{xc}}{\partial(\nabla\rho^{\uparrow}\cdot ! \nabla\rho^{\downarrow})}\nabla^2\rho^{\downarrow}, ! \end{align*} ! and similarly for $V_{xc}^{\downarrow}$. ! ! !REVISION HISTORY: ! Created November 2009 (JKD and TMcQ) !EOP !BOC implicit none ! arguments integer, intent(in) :: is,np real(8), intent(in) :: rhoup(np),rhodn(np) real(8), intent(out) :: g2up(np),g2dn(np) real(8), intent(out) :: gvup(np,3),gvdn(np,3) real(8), intent(out) :: gup2(np),gdn2(np),gupdn(np) ! local variables integer nr,nri,i ! allocatable arrays real(8), allocatable :: rfmt1(:),rfmt2(:),grfmt(:,:) allocate(rfmt1(np),rfmt2(np),grfmt(np,3)) nr=nrmt(is) nri=nrmti(is) !----------------! ! rho up ! !----------------! ! convert rhoup to spherical harmonics call rfsht(nr,nri,rhoup,rfmt1) ! compute grad^2 rhoup in spherical coordinates call grad2rfmt(nr,nri,rlmt(:,-1,is),rlmt(:,-2,is),wcrmt(:,:,is),rfmt1,rfmt2) call rbsht(nr,nri,rfmt2,g2up) ! grad rhoup in spherical coordinates call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) do i=1,3 call rbsht(nr,nri,grfmt(:,i),gvup(:,i)) end do ! (grad rhoup)^2 gup2(1:np)=gvup(1:np,1)**2+gvup(1:np,2)**2+gvup(1:np,3)**2 !------------------! ! rho down ! !------------------! ! convert rhodn to spherical harmonics call rfsht(nr,nri,rhodn,rfmt1) ! compute grad^2 rhodn in spherical coordinates call grad2rfmt(nr,nri,rlmt(:,-1,is),rlmt(:,-2,is),wcrmt(:,:,is),rfmt1,rfmt2) call rbsht(nr,nri,rfmt2,g2dn) ! grad rhodn in spherical coordinates call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) do i=1,3 call rbsht(nr,nri,grfmt(:,i),gvdn(:,i)) end do ! (grad rhodn)^2 gdn2(1:np)=gvdn(1:np,1)**2+gvdn(1:np,2)**2+gvdn(1:np,3)**2 ! (grad rhoup).(grad rhodn) gupdn(1:np)=gvup(1:np,1)*gvdn(1:np,1) & +gvup(1:np,2)*gvdn(1:np,2) & +gvup(1:np,3)*gvdn(1:np,3) deallocate(rfmt1,rfmt2,grfmt) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggair_sp_2a.f900000644000000000000000000000013214061636517015421 xustar0030 mtime=1623670095.484101964 30 atime=1623670094.277103084 30 ctime=1623670095.484101964 elk-7.2.42/src/ggair_sp_2a.f900000644002504400250440000000455314061636517017465 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggair_sp_2a ! !INTERFACE: subroutine ggair_sp_2a(rhoup,rhodn,g2up,g2dn,gvup,gvdn,gup2,gdn2,gupdn) ! !USES: use modmain ! !DESCRIPTION: ! Computes the interstitial gradients $\nabla^2\rho^{\uparrow}$, ! $\nabla^2\rho^{\downarrow}$, $\nabla\rho^{\uparrow}$, ! $\nabla\rho^{\downarrow}$, $(\nabla\rho^{\uparrow})^2$, ! $(\nabla\rho^{\downarrow})^2$ and ! $\nabla\rho^{\uparrow}\cdot\nabla\rho^{\downarrow}$. These are used for GGA ! functionals of type 2 and meta-GGA. See {\tt ggamt\_sp\_2a} for details. ! ! !REVISION HISTORY: ! Created November 2009 (JKD and TMcQ) !EOP !BOC implicit none ! arguments real(8), intent(in) :: rhoup(ngtot),rhodn(ngtot) real(8), intent(out) :: g2up(ngtot),g2dn(ngtot) real(8), intent(out) :: gvup(ngtot,3),gvdn(ngtot,3) real(8), intent(out) :: gup2(ngtot),gdn2(ngtot),gupdn(ngtot) ! local variables integer ig,ifg,i ! allocatable arrays complex(8), allocatable :: zfft1(:),zfft2(:) allocate(zfft1(ngtot),zfft2(ngtot)) !----------------! ! rho up ! !----------------! zfft1(:)=rhoup(:) call zfftifc(3,ngridg,-1,zfft1) ! compute grad^2 rhoup zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=-(gc(ig)**2)*zfft1(ifg) end do call zfftifc(3,ngridg,1,zfft2) g2up(:)=dble(zfft2(:)) ! grad rhoup do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) gvup(:,i)=dble(zfft2(:)) end do ! (grad rhoup)^2 gup2(:)=gvup(:,1)**2+gvup(:,2)**2+gvup(:,3)**2 !------------------! ! rho down ! !------------------! zfft1(:)=rhodn(:) call zfftifc(3,ngridg,-1,zfft1) ! compute grad^2 rhodn zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=-(gc(ig)**2)*zfft1(ifg) end do call zfftifc(3,ngridg,1,zfft2) g2dn(:)=dble(zfft2(:)) ! grad rhodn do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) gvdn(:,i)=dble(zfft2(:)) end do ! (grad rhodn)^2 gdn2(:)=gvdn(:,1)**2+gvdn(:,2)**2+gvdn(:,3)**2 ! (grad rhoup).(grad rhodn) gupdn(:)=gvup(:,1)*gvdn(:,1)+gvup(:,2)*gvdn(:,2)+gvup(:,3)*gvdn(:,3) deallocate(zfft1,zfft2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggamt_sp_2b.f900000644000000000000000000000013214061636517015430 xustar0030 mtime=1623670095.486101962 30 atime=1623670094.279103082 30 ctime=1623670095.486101962 elk-7.2.42/src/ggamt_sp_2b.f900000644002504400250440000000721314061636517017470 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggamt_sp_2b ! !INTERFACE: subroutine ggamt_sp_2b(is,np,g2up,g2dn,gvup,gvdn,vxup,vxdn,vcup,vcdn,dxdgu2, & dxdgd2,dxdgud,dcdgu2,dcdgd2,dcdgud) ! !USES: use modmain ! !DESCRIPTION: ! Post processing step of muffin-tin gradients for GGA type 2. See routine ! {\tt ggamt\_sp\_2a} for full details. ! ! !REVISION HISTORY: ! Created November 2009 (JKD and TMcQ) !EOP !BOC implicit none ! arguments integer, intent(in) :: is,np real(8), intent(in) :: g2up(np),g2dn(np) real(8), intent(in) :: gvup(np,3),gvdn(np,3) real(8), intent(inout) :: vxup(np),vxdn(np) real(8), intent(inout) :: vcup(np),vcdn(np) real(8), intent(in) :: dxdgu2(np),dxdgd2(np),dxdgud(np) real(8), intent(in) :: dcdgu2(np),dcdgd2(np),dcdgud(np) ! local variables integer nr,nri,i ! allocatable arrays real(8), allocatable :: rfmt1(:),rfmt2(:),grfmt(:,:) allocate(rfmt1(np),rfmt2(np),grfmt(np,3)) nr=nrmt(is) nri=nrmti(is) !------------------! ! exchange ! !------------------! ! convert dxdgu2 to spherical harmonics call rfsht(nr,nri,dxdgu2,rfmt1) ! compute grad dxdgu2 call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) ! (grad dxdgu2).(grad rhoup) in spherical coordinates rfmt1(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt2) rfmt1(1:np)=rfmt1(1:np)+rfmt2(1:np)*gvup(1:np,i) end do vxup(1:np)=vxup(1:np)-2.d0*(rfmt1(1:np)+dxdgu2(1:np)*g2up(1:np)) & -dxdgud(1:np)*g2dn(1:np) ! convert dxdgd2 to spherical harmonics call rfsht(nr,nri,dxdgd2,rfmt1) ! compute grad dxdgd2 call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) ! (grad dxdgd2).(grad rhodn) in spherical coordinates rfmt1(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt2) rfmt1(1:np)=rfmt1(1:np)+rfmt2(1:np)*gvdn(1:np,i) end do vxdn(1:np)=vxdn(1:np)-2.d0*(rfmt1(1:np)+dxdgd2(1:np)*g2dn(1:np)) & -dxdgud(1:np)*g2up(1:np) ! convert dxdgud to spherical harmonics call rfsht(nr,nri,dxdgud,rfmt1) ! compute grad dxdgud call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) ! (grad dxdgud).(grad rhodn) and (grad dxdgud).(grad rhoup) do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt1) vxup(1:np)=vxup(1:np)-rfmt1(1:np)*gvdn(1:np,i) vxdn(1:np)=vxdn(1:np)-rfmt1(1:np)*gvup(1:np,i) end do !---------------------! ! correlation ! !---------------------! ! convert dcdgu2 to spherical harmonics call rfsht(nr,nri,dcdgu2,rfmt1) ! compute grad dcdgu2 call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) ! (grad dcdgu2).(grad rhoup) in spherical coordinates rfmt1(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt2) rfmt1(1:np)=rfmt1(1:np)+rfmt2(1:np)*gvup(1:np,i) end do vcup(1:np)=vcup(1:np)-2.d0*(rfmt1(1:np)+dcdgu2(1:np)*g2up(1:np)) & -dcdgud(1:np)*g2dn(1:np) ! convert dcdgd2 to spherical harmonics call rfsht(nr,nri,dcdgd2,rfmt1) ! compute grad dcdgd2 call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) ! (grad dcdgd2).(grad rhodn) in spherical coordinates rfmt1(1:np)=0.d0 do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt2) rfmt1(1:np)=rfmt1(1:np)+rfmt2(1:np)*gvdn(1:np,i) end do vcdn(1:np)=vcdn(1:np)-2.d0*(rfmt1(1:np)+dcdgd2(1:np)*g2dn(1:np)) & -dcdgud(1:np)*g2up(1:np) ! convert dcdgud to spherical harmonics call rfsht(nr,nri,dcdgud,rfmt1) ! compute grad dcdgud call gradrfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),rfmt1,np,grfmt) ! (grad dcdgud).(grad rhodn) and (grad dcdgud).(grad rhoup) do i=1,3 call rbsht(nr,nri,grfmt(:,i),rfmt1) vcup(1:np)=vcup(1:np)-rfmt1(1:np)*gvdn(1:np,i) vcdn(1:np)=vcdn(1:np)-rfmt1(1:np)*gvup(1:np,i) end do deallocate(rfmt1,rfmt2,grfmt) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/ggair_sp_2b.f900000644000000000000000000000013114061636517015421 xustar0030 mtime=1623670095.487101961 29 atime=1623670094.28110308 30 ctime=1623670095.487101961 elk-7.2.42/src/ggair_sp_2b.f900000644002504400250440000000714514061636517017466 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: ggair_sp_2b ! !INTERFACE: subroutine ggair_sp_2b(g2up,g2dn,gvup,gvdn,vxup,vxdn,vcup,vcdn,dxdgu2,dxdgd2, & dxdgud,dcdgu2,dcdgd2,dcdgud) ! !USES: use modmain ! !DESCRIPTION: ! Post processing step of interstitial gradients for GGA type 2. See routine ! {\tt ggamt\_sp\_2a} for full details. ! ! !REVISION HISTORY: ! Created November 2009 (JKD and TMcQ) !EOP !BOC implicit none real(8), intent(in) :: g2up(ngtot),g2dn(ngtot) real(8), intent(in) :: gvup(ngtot,3),gvdn(ngtot,3) real(8), intent(inout) :: vxup(ngtot),vxdn(ngtot) real(8), intent(inout) :: vcup(ngtot),vcdn(ngtot) real(8), intent(in) :: dxdgu2(ngtot),dxdgd2(ngtot),dxdgud(ngtot) real(8), intent(in) :: dcdgu2(ngtot),dcdgd2(ngtot),dcdgud(ngtot) ! local variables integer ig,ifg,i ! allocatable arrays real(8), allocatable :: rfir(:) complex(8), allocatable :: zfft1(:),zfft2(:) allocate(rfir(ngtot)) allocate(zfft1(ngtot),zfft2(ngtot)) !------------------! ! exchange ! !------------------! ! compute grad dxdgu2 zfft1(:)=dxdgu2(:) call zfftifc(3,ngridg,-1,zfft1) ! (grad dxdgu2).(grad rhoup) rfir(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) rfir(:)=rfir(:)+dble(zfft2(:))*gvup(:,i) end do vxup(:)=vxup(:)-2.d0*(rfir(:)+dxdgu2(:)*g2up(:))-dxdgud(:)*g2dn(:) ! compute grad dxdgd2 zfft1(:)=dxdgd2(:) call zfftifc(3,ngridg,-1,zfft1) ! (grad dxdgd2).(grad rhodn) rfir(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) rfir(:)=rfir(:)+dble(zfft2(:))*gvdn(:,i) end do vxdn(:)=vxdn(:)-2.d0*(rfir(:)+dxdgd2(:)*g2dn(:))-dxdgud(:)*g2up(:) ! compute grad dxdgud zfft1(:)=dxdgud(:) call zfftifc(3,ngridg,-1,zfft1) ! (grad dxdgud).(grad rhodn) and (grad dxdgud).(grad rhoup) do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) vxup(:)=vxup(:)-dble(zfft2(:))*gvdn(:,i) vxdn(:)=vxdn(:)-dble(zfft2(:))*gvup(:,i) end do !---------------------! ! correlation ! !---------------------! ! compute grad dcdgu2 zfft1(:)=dcdgu2(:) call zfftifc(3,ngridg,-1,zfft1) ! (grad dcdgu2).(grad rhoup) rfir(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) rfir(:)=rfir(:)+dble(zfft2(:))*gvup(:,i) end do vcup(:)=vcup(:)-2.d0*(rfir(:)+dcdgu2(:)*g2up(:))-dcdgud(:)*g2dn(:) ! compute grad dcdgd2 zfft1(:)=dcdgd2(:) call zfftifc(3,ngridg,-1,zfft1) ! (grad dcdgd2).(grad rhodn) rfir(:)=0.d0 do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) rfir(:)=rfir(:)+dble(zfft2(:))*gvdn(:,i) end do vcdn(:)=vcdn(:)-2.d0*(rfir(:)+dcdgd2(:)*g2dn(:))-dcdgud(:)*g2up(:) ! compute grad dcdgud zfft1(:)=dcdgud(:) call zfftifc(3,ngridg,-1,zfft1) ! (grad dcdgud).(grad rhodn) and (grad dcdgud).(grad rhoup) do i=1,3 zfft2(:)=0.d0 do ig=1,ngvec ifg=igfft(ig) zfft2(ifg)=vgc(i,ig)*cmplx(-aimag(zfft1(ifg)),dble(zfft1(ifg)),8) end do call zfftifc(3,ngridg,1,zfft2) vcup(:)=vcup(:)-dble(zfft2(:))*gvdn(:,i) vcdn(:)=vcdn(:)-dble(zfft2(:))*gvup(:,i) end do deallocate(rfir,zfft1,zfft2) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writeemd.f900000644000000000000000000000013214061636517015064 xustar0030 mtime=1623670095.489101959 30 atime=1623670094.282103079 30 ctime=1623670095.489101959 elk-7.2.42/src/writeemd.f900000644002504400250440000000524114061636517017123 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 S. Dugdale, D. Ernsting and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeemd use modmain use modpw use modmpi use modomp implicit none ! local variables integer ik,ihk,recl integer ist,ispn,nthd real(8) sm,t1 complex(8) z1 ! allocatable arrays real(8), allocatable :: emd(:) complex(8), allocatable :: wfpw(:,:,:) if (spinsprl) then write(*,*) write(*,'("Error(writeemd): electron momentum density not available for & &spin-spirals")') write(*,*) stop end if ! initialise universal variables call init0 call init1 call init4 ! read density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the occupancies from file do ik=1,nkpt call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! delete existing EMD.OUT if (mp_mpi) then open(250,file='EMD.OUT') close(250,status='DELETE') end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) allocate(emd(nhkmax)) inquire(iolength=recl) vkl(:,1),nhkmax,emd deallocate(emd) open(250,file='EMD.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) ! loop over k-points call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(emd,wfpw,ihk,sm) & !$OMP PRIVATE(ist,ispn,z1,t1) & !$OMP NUM_THREADS(nthd) allocate(emd(nhkmax),wfpw(nhkmax,nspinor,nstsv)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(writeemd_) write(*,'("Info(writeemd): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(writeemd_) ! Fourier transform the wavefunctions call genwfpw(vkl(:,ik),ngk(1,ik),igkig(:,1,ik),vgkl(:,:,1,ik), & vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),nhk(1,ik),vhkc(:,:,1,ik), & hkc(:,1,ik),sfachk(:,:,1,ik),wfpw) ! loop over all H+k-vectors do ihk=1,nhk(1,ik) ! sum over occupied states and spins sm=0.d0 do ist=1,nstsv do ispn=1,nspinor z1=wfpw(ihk,ispn,ist) t1=dble(z1)**2+aimag(z1)**2 sm=sm+occsv(ist,ik)*t1 end do end do emd(ihk)=sm end do !$OMP CRITICAL(u250) write(250,rec=ik) vkl(:,ik),nhk(1,ik),emd !$OMP END CRITICAL(u250) end do !$OMP END DO deallocate(emd,wfpw) !$OMP END PARALLEL call freethd(nthd) close(250) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) if (mp_mpi) then write(*,*) write(*,'("Info(writeemd): electron momentum density written to EMD.OUT")') write(*,'(" for all H+k-vectors up to |H+k| < hkmax")') end if end subroutine elk-7.2.42/src/PaxHeaders.21776/reademd.f900000644000000000000000000000013214061636517014645 xustar0030 mtime=1623670095.493101955 30 atime=1623670094.284103078 30 ctime=1623670095.493101955 elk-7.2.42/src/reademd.f900000644002504400250440000000262714061636517016711 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 D. Ernsting, S. Dugdale and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine reademd(emds) use modmain use modpw use modtest implicit none ! arguments real(4), intent(out) :: emds(nhkmax,nkpt) ! local variables integer ik,recl,nhk_ real(8) vkl_(3),t1 ! allocatable arrays real(8), allocatable :: emd(:) allocate(emd(nhkmax)) ! find the record length inquire(iolength=recl) vkl_,nhk_,emd open(250,file='EMD.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) do ik=1,nkpt read(250,rec=ik) vkl_,nhk_,emd t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(reademd): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" EMD.OUT : ",3G18.10)') vkl_ write(*,*) stop end if if (nhk(1,ik).ne.nhk_) then write(*,*) write(*,'("Error(reademd): differing nhk for k-point ",I8)') ik write(*,'(" current : ",I8)') nhk(1,ik) write(*,'(" EMD.OUT : ",I8)') nhk_ write(*,*) stop end if ! store momentum density in single-precision array emds(:,ik)=real(emd(:)) end do close(250) ! write the EMD of the last k-point to test file if required call writetest(170,'electron momentum density',nv=nhkmax,tol=1.d-4,rva=emd) deallocate(emd) end subroutine elk-7.2.42/src/PaxHeaders.21776/emdplot.f900000644000000000000000000000013214061636517014710 xustar0030 mtime=1623670095.495101953 30 atime=1623670094.286103076 30 ctime=1623670095.495101953 elk-7.2.42/src/emdplot.f900000644002504400250440000000216114061636517016745 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 D. Ernsting, S. Dugdale and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine emdplot use modmain use modpw implicit none ! local variables real(8) t1 ! allocatable arrays real(4), allocatable :: emds(:,:) t1=sum(abs(vkloff(:))) if (t1.gt.epslat) then write(*,*) write(*,'("Error(emdplot): use vkloff = 0 for the ground-state run")') write(*,*) stop end if ! initialise universal variables call init0 call init1 call init4 ! read in the electron momentum density allocate(emds(nhkmax,nkpt)) call reademd(emds) ! write the density plot to file select case(task) case(171) call emdplot1d(emds) write(*,*) write(*,'("Info(emdplot): 1D electron momentum density written to & &EMD1D.OUT")') case(172) call emdplot2d(emds) write(*,*) write(*,'("Info(emdplot): 2D electron momentum density written to & &EMD2D.OUT")') case(173) call emdplot3d(emds) write(*,*) write(*,'("Info(emdplot): 3D electron momentum density written to & &EMD3D.OUT")') end select deallocate(emds) end subroutine elk-7.2.42/src/PaxHeaders.21776/init3.f900000644000000000000000000000013214061636517014272 xustar0030 mtime=1623670095.496101953 30 atime=1623670094.288103074 30 ctime=1623670095.496101953 elk-7.2.42/src/init3.f900000644002504400250440000000275214061636517016335 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine init3 use modmain use modgw use modtddft use modvars use modmpi implicit none ! local variables integer ig,iw real(8) w1,w2,t1,t2 !-------------------------------------------------------------! ! response function and perturbation theory variables ! !-------------------------------------------------------------! ! G-vectors for response functions ngrf=1 do ig=2,ngvec if (gc(ig).gt.gmaxrf) then ngrf=ig-1 exit end if end do ngrf=min(ngrf,ngvc) ! write the G-vectors to file if (mp_mpi) call writegvecrf ! frequencies for reponse functions nwrf=1 if (allocated(wrf)) deallocate(wrf) select case(task) case(188,320,330,331) nwrf=nwplot allocate(wrf(nwrf)) w1=wplot(1) w2=max(wplot(2),w1) t1=(w2-w1)/dble(nwplot) do iw=1,nwplot t2=w1+t1*dble(iw-1) wrf(iw)=cmplx(t2,swidth,8) end do ! set the first frequency to zero for the bootstrap functional if ((fxctype(1).eq.210).or.(fxctype(1).eq.211)) then wrf(1)=cmplx(0.d0,swidth,8) end if case(600,610,620,630,640) ! GW Matsubara frequencies call genwgw case default nwrf=1 allocate(wrf(nwrf)) wrf(1)=cmplx(0.d0,swidth,8) end select ! write to VARIABLES.OUT call writevars('gmaxrf',rv=gmaxrf) call writevars('ngrf',iv=ngrf) call writevars('nwrf',iv=nwrf) call writevars('wrf',nv=nwrf,zva=wrf) end subroutine elk-7.2.42/src/PaxHeaders.21776/init4.f900000644000000000000000000000013214061636517014273 xustar0030 mtime=1623670095.498101951 30 atime=1623670094.289103073 30 ctime=1623670095.498101951 elk-7.2.42/src/init4.f900000644002504400250440000001424314061636517016334 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine init4 use modmain use modphonon use modpw use modvars implicit none ! local variables integer ik,jspn,n,i integer l1,l2,l3,m1,m2,m3 integer lm1,lm2,lm3 real(8) vl(3),vc(3) ! external functions real(8), external :: gaunt !---------------------------! ! H+k-vector arrays ! !---------------------------! if (any(task.eq.[135,170,171,172,173])) then if (task.eq.135) hkmax=0.5d0*gmaxvr-epslat call findngkmax(nkpt,vkc,nspnfv,vqcss,ngvec,vgc,hkmax,nhkmax) ! allocate the H+k-vector arrays if (allocated(nhk)) deallocate(nhk) allocate(nhk(nspnfv,nkpt)) if (allocated(ihkig)) deallocate(ihkig) allocate(ihkig(nhkmax,nspnfv,nkpt)) if (allocated(vhkl)) deallocate(vhkl) allocate(vhkl(3,nhkmax,nspnfv,nkpt)) if (allocated(vhkc)) deallocate(vhkc) allocate(vhkc(3,nhkmax,nspnfv,nkpt)) if (allocated(hkc)) deallocate(hkc) allocate(hkc(nhkmax,nspnfv,nkpt)) if (allocated(sfachk)) deallocate(sfachk) allocate(sfachk(nhkmax,natmtot,nspnfv,nkpt)) ! initialise H+k-vectors arrays do ik=1,nkpt do jspn=1,nspnfv vl(:)=vkl(:,ik) vc(:)=vkc(:,ik) ! spin-spiral case if (spinsprl) then if (jspn.eq.1) then vl(:)=vl(:)+0.5d0*vqlss(:) vc(:)=vc(:)+0.5d0*vqcss(:) else vl(:)=vl(:)-0.5d0*vqlss(:) vc(:)=vc(:)-0.5d0*vqcss(:) end if end if ! generate the H+k-vectors call gengkvec(ngvec,ivg,vgc,vl,vc,hkmax,nhkmax,nhk(jspn,ik), & ihkig(:,jspn,ik),vhkl(:,:,jspn,ik),vhkc(:,:,jspn,ik),hkc(:,jspn,ik)) ! generate structure factors for H+k-vectors call gensfacgp(nhk(jspn,ik),vhkc(:,:,jspn,ik),nhkmax,sfachk(:,:,jspn,ik)) end do end do ! write to VARIABLES.OUT call writevars('hkmax',rv=hkmax) call writevars('nhk',nv=nspnfv*nkpt,iva=nhk) do ik=1,nkpt do jspn=1,nspnfv call writevars('ihkig',l=jspn,m=ik,nv=nhk(jspn,ik),iva=ihkig(:,jspn,ik)) end do end do end if !-----------------------------! ! G+k+q-vector arrays ! !-----------------------------! if (task.eq.205) then if (allocated(vkql)) deallocate(vkql) allocate(vkql(3,nkptnr)) if (allocated(vkqc)) deallocate(vkqc) allocate(vkqc(3,nkptnr)) if (allocated(ngkq)) deallocate(ngkq) allocate(ngkq(nspnfv,nkptnr)) if (allocated(igkqig)) deallocate(igkqig) allocate(igkqig(ngkmax,nspnfv,nkptnr)) if (allocated(vgkql)) deallocate(vgkql) allocate(vgkql(3,ngkmax,nspnfv,nkptnr)) if (allocated(vgkqc)) deallocate(vgkqc) allocate(vgkqc(3,ngkmax,nspnfv,nkptnr)) if (allocated(gkqc)) deallocate(gkqc) allocate(gkqc(ngkmax,nspnfv,nkptnr)) if (allocated(sfacgkq)) deallocate(sfacgkq) allocate(sfacgkq(ngkmax,natmtot,nspnfv,nkptnr)) end if !---------------------------! ! G+q-vector arrays ! !---------------------------! if (task.eq.205) then if (allocated(vgqc)) deallocate(vgqc) allocate(vgqc(3,ngtot)) if (allocated(gqc)) deallocate(gqc) allocate(gqc(ngtot)) if (allocated(gclgq)) deallocate(gclgq) allocate(gclgq(ngvec)) if (allocated(jlgqrmt)) deallocate(jlgqrmt) allocate(jlgqrmt(0:lnpsd,ngvec,nspecies)) if (allocated(ylmgq)) deallocate(ylmgq) allocate(ylmgq(lmmaxo,ngvec)) if (allocated(sfacgq)) deallocate(sfacgq) allocate(sfacgq(ngvec,natmtot)) if (allocated(ffacgq)) deallocate(ffacgq) allocate(ffacgq(ngtot,nspecies)) if (allocated(dcfunig)) deallocate(dcfunig) allocate(dcfunig(ngtot)) if (allocated(dcfunir)) deallocate(dcfunir) allocate(dcfunir(ngtot)) end if !-----------------------------------------------------------------! ! phonon density functional perturbation theory variables ! !-----------------------------------------------------------------! if (task.eq.205) then if (allocated(drhomt)) deallocate(drhomt) allocate(drhomt(npmtmax,natmtot)) if (allocated(drhoir)) deallocate(drhoir) allocate(drhoir(ngtot)) if (allocated(dmagmt)) deallocate(dmagmt) if (allocated(dmagir)) deallocate(dmagir) if (spinpol) then allocate(dmagmt(npmtmax,natmtot,ndmag)) allocate(dmagir(ngtot,ndmag)) end if if (allocated(dvclmt)) deallocate(dvclmt) allocate(dvclmt(npmtmax,natmtot)) if (allocated(dvclir)) deallocate(dvclir) allocate(dvclir(ngtot)) if (allocated(zvnmt)) deallocate(zvnmt) allocate(zvnmt(npmtmax)) if (allocated(gvsmt)) deallocate(gvsmt) allocate(gvsmt(npmtmax)) ! combined target array for Kohn-Sham potential and magnetic field derivative if (allocated(dvsbs)) deallocate(dvsbs) n=npmtmax*natmtot+ngtot if (spinpol) n=n+(npcmtmax*natmtot+ngtot)*ndmag allocate(dvsbs(n)) ! zero the array dvsbs(:)=0.d0 ! associate pointer arrays with target dvsmt(1:npmtmax,1:natmtot)=>dvsbs(1:) i=npmtmax*natmtot+1 dvsir(1:ngtot)=>dvsbs(i:) if (spinpol) then i=i+ngtot dbsmt(1:npcmtmax,1:natmtot,1:ndmag)=>dvsbs(i:) i=i+npcmtmax*natmtot*ndmag dbsir(1:ngtot,1:ndmag)=>dvsbs(i:) end if if (allocated(dvsig)) deallocate(dvsig) allocate(dvsig(ngtot)) if (allocated(dsocfr)) deallocate(dsocfr) if (spinorb) then allocate(dsocfr(nrcmtmax,natmtot)) end if if (allocated(dhaa)) deallocate(dhaa) allocate(dhaa(lmmaxo,apwordmax,0:lmaxapw,apwordmax,0:lmaxapw,natmtot)) if (allocated(dhloa)) deallocate(dhloa) allocate(dhloa(lmmaxo,apwordmax,0:lmaxapw,nlomax,natmtot)) if (allocated(dhlolo)) deallocate(dhlolo) allocate(dhlolo(lmmaxo,nlomax,nlomax,natmtot)) ! allocate and generate real Gaunt coefficient array if (allocated(gntyyy)) deallocate(gntyyy) allocate(gntyyy(lmmaxo,lmmaxapw,lmmaxapw)) do l1=0,lmaxapw do m1=-l1,l1 lm1=l1*(l1+1)+m1+1 do l3=0,lmaxapw do m3=-l3,l3 lm3=l3*(l3+1)+m3+1 do l2=0,lmaxo do m2=-l2,l2 lm2=l2*(l2+1)+m2+1 gntyyy(lm2,lm3,lm1)=gaunt(l1,l2,l3,m1,m2,m3) end do end do end do end do end do end do if (allocated(devalfv)) deallocate(devalfv) allocate(devalfv(nstfv,nspnfv,nkptnr)) if (allocated(devalsv)) deallocate(devalsv) allocate(devalsv(nstsv,nkptnr)) if (allocated(doccsv)) deallocate(doccsv) allocate(doccsv(nstsv,nkptnr)) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/fsmbfield.f900000644000000000000000000000013014061636517015175 xustar0029 mtime=1623670095.49910195 30 atime=1623670094.291103071 29 ctime=1623670095.49910195 elk-7.2.42/src/fsmbfield.f900000644002504400250440000000436514061636517017244 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: fsmbfield ! !INTERFACE: subroutine fsmbfield ! !USES: use modmain ! !DESCRIPTION: ! Updates the effective magnetic field, ${\bf B}_{\rm FSM}$, required for ! fixing the spin moment to a given value, ${\bf M}_{\rm FSM}$. This is done ! by adding a vector to the field which is proportional to the difference ! between the moment calculated in the $i$th self-consistent loop and the ! required moment: ! $$ {\bf B}_{\rm FSM}^{i+1}={\bf B}_{\rm FSM}^i+\lambda\left({\bf M}^i ! -{\bf M}_{\rm FSM}\right), $$ ! where $\lambda$ is a scaling factor. ! ! !REVISION HISTORY: ! Created March 2005 (JKD) !EOP !BOC implicit none ! local variables integer is,ia,ias real(8) v1(3),v2(3),t1 if ((.not.spinpol).or.(fsmtype.eq.0)) return ! fixed spin direction not valid for collinear magnetism if ((.not.ncmag).and.(fsmtype.lt.0)) return ! determine the global effective field if ((abs(fsmtype).eq.1).or.(abs(fsmtype).eq.3)) then if (ncmag) then v1(:)=momtot(:) else v1(:)=0.d0 v1(3)=momtot(1) end if v2(:)=v1(:)-momfix(:) if (ncmag) then bfsmc(:)=bfsmc(:)+taufsm*v2(:) else bfsmc(1)=bfsmc(1)+taufsm*v2(3) end if ! make sure that the constraining field is perpendicular to the fixed moment ! for fixed direction calculations (Y. Kvashnin and LN) if (fsmtype.lt.0) call r3vo(momfix,bfsmc) end if if ((abs(fsmtype).eq.2).or.(abs(fsmtype).eq.3)) then ! determine the muffin-tin fields for fixed local moments do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) ! if any component is >= 1000 then do not fix the moment t1=sum(abs(mommtfix(:,ia,is))) if (t1.ge.1000.d0) cycle if (ncmag) then v1(:)=mommt(:,ias) else v1(:)=0.d0 v1(3)=mommt(1,ias) end if v2(:)=v1(:)-mommtfix(:,ia,is) if (ncmag) then bfsmcmt(:,ias)=bfsmcmt(:,ias)+taufsm*v2(:) else bfsmcmt(1,ias)=bfsmcmt(1,ias)+taufsm*v2(3) end if ! fixed spin direction if (fsmtype.lt.0) call r3vo(mommtfix(:,ia,is),bfsmcmt(:,ias)) end do end do end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genvmmtsv.f900000644000000000000000000000013214061636517015272 xustar0030 mtime=1623670095.501101948 30 atime=1623670094.293103069 30 ctime=1623670095.501101948 elk-7.2.42/src/genvmmtsv.f900000644002504400250440000000401314061636517017325 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genvmmtsv(wfmt,vmat) use modmain use moddftu use modomp implicit none ! arguments complex(8), intent(in) :: wfmt(npcmtmax,natmtot,nspinor,nstsv) complex(8), intent(inout) :: vmat(nstsv,nstsv) ! local variables integer ist,jst,ispn,jspn integer is,ias,ld,nthd integer nrc,nrci,nrco,i integer nm,l,lm,npc,npci ! allocatable arrays complex(8), allocatable :: wfmt1(:,:,:),wfmt2(:) ! external functions complex(8), external :: zfmtinp if (.not.tvmatmt) return ld=lmmaxdm*nspinor allocate(wfmt1(npcmtmax,nspinor,nstsv),wfmt2(npcmtmax)) ! loop over atoms do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) nrco=nrc-nrci npc=npcmt(is) npci=npcmti(is) ! convert wavefunctions to spherical harmonics do ist=1,nstsv do ispn=1,nspinor call zfsht(nrc,nrci,wfmt(:,ias,ispn,ist),wfmt1(:,ispn,ist)) end do end do ! loop over second-variational states do jst=1,nstsv ! loop over spins do ispn=1,nspinor wfmt2(1:npc)=0.d0 do jspn=1,nspinor do l=0,lmaxdm if (tvmmt(l,ias)) then nm=2*l+1 lm=l**2+1 if (l.le.lmaxi) then call zgemm('N','N',nm,nrci,nm,zone,vmatmt(lm,ispn,lm,jspn,ias), & ld,wfmt1(lm,jspn,jst),lmmaxi,zone,wfmt2(lm),lmmaxi) end if i=npci+lm call zgemm('N','N',nm,nrco,nm,zone,vmatmt(lm,ispn,lm,jspn,ias),ld, & wfmt1(i,jspn,jst),lmmaxo,zone,wfmt2(i),lmmaxo) end if end do end do ! compute the matrix elements call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ist=1,nstsv vmat(ist,jst)=vmat(ist,jst)+zfmtinp(nrc,nrci,wrcmt(:,is), & wfmt1(:,ispn,ist),wfmt2) end do !$OMP END PARALLEL DO call freethd(nthd) end do end do end do deallocate(wfmt1,wfmt2) end subroutine elk-7.2.42/src/PaxHeaders.21776/testcheck.f900000644000000000000000000000013214061636517015221 xustar0030 mtime=1623670095.502101947 30 atime=1623670094.295103067 30 ctime=1623670095.502101947 elk-7.2.42/src/testcheck.f900000644002504400250440000001127714061636517017266 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine testcheck implicit none ! local variables logical exist integer i,j,k,n integer nv_,nv,vt_,vt,iv_,iv real(8) rv_,rv,a,b real(8) tol,t1,t2 complex(8) zv_,zv character(256) fname_,fname,descr n=0 do i=0,999 write(fname_,'("TEST_",I3.3,".OUT_")') i inquire(file=trim(fname_),exist=exist) if (exist) then write(fname,'("TEST_",I3.3,".OUT")') i inquire(file=trim(fname),exist=exist) if (.not.exist) then write(*,*) write(*,'("Error(testcheck): file ",A," does not exist")') trim(fname) write(*,*) error stop end if open(91,file=trim(fname_),form='FORMATTED') open(92,file=trim(fname),form='FORMATTED') read(91,*,err=10) descr read(92,*,err=20) descr read(91,*,err=10) vt_,nv_ read(92,*,err=20) vt,nv if (vt_.ne.vt) then write(*,*) write(*,'("Error(testcheck): differing variable type")') write(*,'(" for quantity ''",A,"''")') trim(descr) write(*,'(" ",A," : ",I8)') trim(fname_),vt_ write(*,'(" ",A," : ",I8)') trim(fname),vt write(*,*) error stop end if if (nv_.ne.nv) then write(*,*) write(*,'("Error(testcheck): differing number of variables")') write(*,'(" for quantity ''",A,"''")') trim(descr) write(*,'(" ",A," : ",I8)') trim(fname_),nv_ write(*,'(" ",A," : ",I8)') trim(fname),nv write(*,*) error stop end if if (nv.le.0) then write(*,*) write(*,'("Error(testcheck): nv <= 0 : ",I8)') nv write(*,*) error stop end if if (vt.eq.1) then ! integer variables do j=1,nv read(91,*,err=10) k,iv_ if (j.ne.k) goto 10 read(92,*,err=20) k,iv if (j.ne.k) goto 20 if (iv.ne.iv_) then write(*,*) write(*,'("Error(testcheck): variable ",I8," is different")') j write(*,'(" for quantity ''",A,"''")') trim(descr) write(*,'(" ",A," : ",I8)') trim(fname_),iv_ write(*,'(" ",A," : ",I8)') trim(fname),iv write(*,*) error stop end if end do else if (vt.eq.2) then ! real variables read(91,*,err=10) tol read(92,*,err=20) tol do j=1,nv read(91,*,err=10) k,rv_ if (j.ne.k) goto 10 read(92,*,err=20) k,rv if (j.ne.k) goto 20 t1=abs(rv_-rv) t2=abs(rv_)*tol if ((t1.gt.t2).and.(abs(rv_).gt.1.d-4)) then write(*,*) write(*,'("Error(testcheck): variable ",I8," outside tolerance")') j write(*,'(" for quantity ''",A,"''")') trim(descr) write(*,'(" ",A," (correct value)",T40," : ",G22.12)') trim(fname_), & rv_ write(*,'(" ",A,T40," : ",G22.12)') trim(fname),rv write(*,'(" absolute difference",T40," : ",G22.12)') t1 write(*,'(" required relative tolerance",T40," : ",G22.12)') tol write(*,'(" required absolute tolerance",T40," : ",G22.12)') t2 write(*,*) error stop end if end do else if (vt.eq.3) then ! complex variables read(91,*,err=10) tol read(92,*,err=20) tol do j=1,nv read(91,*,err=10) k,a,b zv_=cmplx(a,b,8) if (j.ne.k) goto 10 read(92,*,err=20) k,a,b zv=cmplx(a,b,8) if (j.ne.k) goto 20 t1=abs(zv_-zv) t2=abs(zv_)*tol if ((t1.gt.t2).and.(abs(zv_).gt.1.d-4)) then write(*,*) write(*,'("Error(testcheck): variable ",I8," outside tolerance")') j write(*,'(" for quantity ''",A,"''")') trim(descr) write(*,'(" ",A," (correct value)",T40," : ",2G22.12)') & trim(fname_),zv_ write(*,'(" ",A,T40," : ",2G22.12)') trim(fname),zv write(*,'(" difference",T40," : ",G22.12)') t1 write(*,'(" required relative tolerance",T40," : ",G22.12)') tol write(*,'(" required absolute tolerance",T40," : ",G22.12)') t2 write(*,*) error stop end if end do else write(*,*) write(*,'("Error(testcheck): variable type not defined : ",I8)') vt write(*,*) error stop end if close(91) close(92) n=n+1 end if end do if (n.eq.0) then write(*,*) write(*,'("Warning(testcheck): no tests found")') else write(*,*) write(*,'("Info(testcheck): passed all tests")') end if return 10 continue write(*,*) write(*,'("Error(testcheck): error reading from ",A)') trim(fname_) write(*,*) error stop 20 continue write(*,*) write(*,'("Error(testcheck): error reading from ",A)') trim(fname) write(*,*) error stop end subroutine elk-7.2.42/src/PaxHeaders.21776/pade.f900000644000000000000000000000013214061636517014155 xustar0030 mtime=1623670095.504101945 30 atime=1623670094.296103066 30 ctime=1623670095.504101945 elk-7.2.42/src/pade.f900000644002504400250440000000465014061636517016217 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) A. Sanna and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: pade ! !INTERFACE: subroutine pade(ni,zi,ui,no,zo,uo) ! !INPUT/OUTPUT PARAMETERS: ! ni : number of input points (in,integer) ! zi : input points (in,complex(ni)) ! ui : input function values (in,complex(ni)) ! no : number of output points (in,integer) ! zo : output points (in,complex(no)) ! uo : output function values (out,complex(no)) ! !DESCRIPTION: ! Calculates a Pad\'{e} approximant of a function, given the function ! evaluated on a set of points in the complex plane. The function is returned ! for a set of complex output points. The algorithm from H. J. Vidberg and ! J. W. Serene {\it J. Low Temp. Phys.} {\bf 29}, 179 (1977) is used. ! ! !REVISION HISTORY: ! Created December 2010 (Antonio Sanna) !EOP !BOC implicit none ! arguments integer, intent(in) :: ni complex(8), intent(in) :: zi(ni) complex(8), intent(in) :: ui(ni) integer, intent(in) :: no complex(8), intent(in) :: zo(no) complex(8), intent(out) :: uo(no) ! local variables integer i,j real(8) t1 complex(8) a0,a1,b0,b1,z1,z2 ! allocatable arrays complex(8), allocatable :: g(:,:) if ((ni.le.0).or.(no.le.0)) then write(*,*) write(*,'("Error(pade): invalid number of input or output points : ",2I8)') & ni,no write(*,*) stop end if allocate(g(ni,ni)) ! define the g functions using Eq. (A2) g(1,:)=ui(:) do i=2,ni do j=i,ni z1=(zi(j)-zi(i-1))*g(i-1,j) t1=abs(dble(z1))+abs(aimag(z1)) if (t1.gt.1.d-14) then g(i,j)=(g(i-1,i-1)-g(i-1,j))/z1 else g(i,j)=0.d0 end if end do end do ! loop over output points do i=1,no ! use recursive algorithm in Eq. (A3) to evaluate function a0=0.d0 a1=g(1,1) b0=1.d0 b1=1.d0 do j=2,ni z1=(zo(i)-zi(j-1))*g(j,j) z2=a1+z1*a0 a0=a1 a1=z2 z2=b1+z1*b0 b0=b1 b1=z2 ! check for overflow and rescale if ((abs(dble(a1)).gt.1.d100).or.(abs(aimag(a1)).gt.1.d100)) then t1=1.d0/abs(a1) a0=a0*t1 b0=b0*t1 a1=a1*t1 b1=b1*t1 end if if ((abs(dble(b1)).gt.1.d100).or.(abs(aimag(b1)).gt.1.d100)) then t1=1.d0/abs(b1) a0=a0*t1 b0=b0*t1 a1=a1*t1 b1=b1*t1 end if end do t1=abs(dble(b1))+abs(aimag(b1)) if (t1.ne.0.d0) then uo(i)=a1/b1 else uo(i)=0.d0 end if end do deallocate(g) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/wsplint.f900000644000000000000000000000013214061636517014744 xustar0030 mtime=1623670095.505101944 30 atime=1623670094.298103065 30 ctime=1623670095.505101944 elk-7.2.42/src/wsplint.f900000644002504400250440000000135714061636517017007 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine wsplint(n,x,w) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: x(n) real(8), intent(out) :: w(n) ! local variables integer i ! automatic arrays real(8) f(9) ! external functions real(8), external :: splint if (n.le.9) then do i=1,n f(:)=0.d0 f(i)=1.d0 w(i)=splint(n,x,f) end do return end if do i=1,4 f(:)=0.d0 f(i)=1.d0 w(i)=splint(9,x,f) end do f(:)=0.d0 f(5)=1.d0 do i=5,n-4 w(i)=splint(9,x(i-4),f) end do do i=1,4 f(:)=0.d0 f(i+5)=1.d0 w(n-4+i)=splint(9,x(n-8),f) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/gensocfr.f900000644000000000000000000000013214061636517015052 xustar0030 mtime=1623670095.507101942 30 atime=1623670094.300103063 30 ctime=1623670095.507101942 elk-7.2.42/src/gensocfr.f900000644002504400250440000000200314061636517017102 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine gensocfr use modmain use modomp implicit none ! local variables integer is,ias,nthd integer nr,nri,ir,irc real(8) cso,rm ! automatic arrays real(8) vr(nrmtmax),dvr(nrmtmax) if (.not.spinorb) return ! coefficient of spin-orbit coupling cso=y00*socscf/(4.d0*solsc**2) call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(vr,dvr,is,nr,nri) & !$OMP PRIVATE(irc,ir,rm) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) ! radial derivative of the spherical part of the Kohn-Sham potential call rfmtlm(1,nr,nri,vsmt(:,ias),vr) call splined(nr,wcrmt(:,:,is),vr,dvr) irc=0 do ir=1,nr,lradstp irc=irc+1 rm=1.d0-2.d0*cso*vr(ir) socfr(irc,ias)=cso*dvr(ir)/(rsp(ir,is)*rm**2) end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/pades.f900000644000000000000000000000013214061636517014340 xustar0030 mtime=1623670095.508101942 30 atime=1623670094.302103061 30 ctime=1623670095.508101942 elk-7.2.42/src/pades.f900000644002504400250440000000210614061636517016374 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine pades(ns,r,ni,zi,ui,no,zo,uo) implicit none ! arguments integer, intent(in) :: ns real(8), intent(in) :: r integer, intent(in) :: ni complex(8), intent(in) :: zi(ni) complex(8), intent(in) :: ui(ni) integer, intent(in) :: no complex(8), intent(in) :: zo(no) complex(8), intent(out) :: uo(no) ! local variables integer i real(8), parameter :: pi=3.1415926535897932385d0 real(8) t1,t2 complex(8) z1 ! allocatable arrays complex(8), allocatable :: u1(:),u2(:) if (ns.le.0) then write(*,*) write(*,'("Error(pades): ns <= 0 : ",I8)') ns write(*,*) stop end if if (ns.eq.1) then call pade(ni,zi,ui,no,zo,uo) return end if allocate(u1(ni),u2(no)) uo(:)=0.d0 do i=1,ns t1=dble(i-1)/dble(ns) t2=6.d0*pi*t1 z1=r*t1*cmplx(cos(t2),sin(t2),8) u1(:)=ui(:)+z1 call pade(ni,zi,u1,no,zo,u2) uo(:)=uo(:)+u2(:)-z1 end do t1=1.d0/dble(ns) uo(:)=t1*uo(:) deallocate(u1,u2) end subroutine elk-7.2.42/src/PaxHeaders.21776/genscss.f900000644000000000000000000000012714061636517014715 xustar0029 mtime=1623670095.51010194 29 atime=1623670094.30310306 29 ctime=1623670095.51010194 elk-7.2.42/src/genscss.f900000644002504400250440000000276014061636517016753 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genscss use modmain use modstore implicit none ! local variables integer is,ia,na,i real(8) vc(3),cs,sn,t1 ! automatic arrays real(8) vsc(3,nqptnr) ! find the smallest supercell which contains q-vector call findscq(iqss,avec_,nscss,vsc) ! construct supercell atomic positions and magnetic fields do is=1,nspecies na=0 do ia=1,natoms_(is) do i=1,nscss na=na+1 if (na.gt.maxatoms) then write(*,*) write(*,'("Error(genscss): too many atoms in supercell : ",I8)') na write(*,'(" for species ",I4)') is write(*,'("Adjust maxatoms in modmain and recompile code")') write(*,*) stop end if vc(:)=vsc(:,i)+atposc_(:,ia,is) ! new atomic position in lattice coordinates call r3mv(ainv,vc,atposl(:,na,is)) ! rotate external B-field and fixed spin moment vector by angle q.r t1=dot_product(vqc(:,iqss),vc(:)) cs=cos(t1); sn=sin(t1) bfcmt0(1,na,is)=cs*bfcmt0_(1,ia,is)-sn*bfcmt0_(2,ia,is) bfcmt0(2,na,is)=sn*bfcmt0_(1,ia,is)+cs*bfcmt0_(2,ia,is) bfcmt0(3,na,is)=bfcmt0_(3,ia,is) mommtfix(1,na,is)=cs*mommtfix_(1,ia,is)-sn*mommtfix_(2,ia,is) mommtfix(2,na,is)=sn*mommtfix_(1,ia,is)+cs*mommtfix_(2,ia,is) mommtfix(3,na,is)=mommtfix_(3,ia,is) end do end do natoms(is)=na end do end subroutine elk-7.2.42/src/PaxHeaders.21776/rfcmtwr.f900000644000000000000000000000013214061636517014730 xustar0030 mtime=1623670095.511101939 30 atime=1623670094.305103058 30 ctime=1623670095.511101939 elk-7.2.42/src/rfcmtwr.f900000644002504400250440000000134414061636517016767 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine rfcmtwr(nr,nri,wr,rfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: wr(nr) real(8), intent(inout) :: rfmt(*) ! local variables integer n,ir,i real(8) t1 i=1 if (lmaxi.eq.1) then do ir=1,nri rfmt(i:i+3)=(pi*wr(ir))*rfmt(i:i+3) i=i+4 end do else t1=fourpi/dble(lmmaxi) n=lmmaxi-1 do ir=1,nri rfmt(i:i+n)=(t1*wr(ir))*rfmt(i:i+n) i=i+lmmaxi end do end if t1=fourpi/dble(lmmaxo) n=lmmaxo-1 do ir=nri+1,nr rfmt(i:i+n)=(t1*wr(ir))*rfmt(i:i+n) i=i+lmmaxo end do end subroutine elk-7.2.42/src/PaxHeaders.21776/nonlinopt.f900000644000000000000000000000013214061636517015264 xustar0030 mtime=1623670095.513101937 30 atime=1623670094.307103056 30 ctime=1623670095.513101937 elk-7.2.42/src/nonlinopt.f900000644002504400250440000002100714061636517017321 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: nonlinopt ! !INTERFACE: subroutine nonlinopt ! !USES: use modmain use modtest use modomp ! !DESCRIPTION: ! Calculates susceptibility tensor for non-linear optical second-harmonic ! generation (SHG). The terms (ztm) are numbered according to Eqs. (49)-(51) ! of the article {\it Physica Scripta} {\bf T109}, 128 (2004). Other good ! references are {\it Phys. Rev. B} {\bf 48}, 11705 (1993) and ! {\it Phys. Rev. B} {\bf 53}, 10751 (1996). ! ! !REVISION HISTORY: ! Rewrote earlier version, June 2010 (Sharma) ! Improved parallelism, January 2020 (R. Cohen) !EOP !BOC implicit none ! local variables logical tssr integer ik,jk,ist,jst,kst integer iw,a,b,c,l,nthd ! smallest eigenvalue difference allowed in denominator real(8), parameter :: etol=1.d-4 real(8) ei,ej,ek,eji,eki,ekj,t1 complex(8) pii(3),dji(3),vji(3),vik(3),vkj(3) complex(8) eta,ztm(3,3),z1 character(256) fname ! allocatable arrays real(8), allocatable :: w(:) complex(8), allocatable :: pmat(:,:,:) complex(8), allocatable :: chiw(:,:),chi2w(:,:) ! initialise universal variables call init0 call init1 ! read Fermi energy from file call readfermi ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! generate energy grid (starting from zero) allocate(w(nwplot)) t1=wplot(2)/dble(nwplot) do iw=1,nwplot w(iw)=t1*dble(iw-1) end do ! allocate response function arrays allocate(chiw(nwplot,3)) allocate(chi2w(nwplot,2)) ! i divided by the complex relaxation time eta=cmplx(0.d0,swidth,8) ! set flag for scissor operator if (abs(scissor).gt.1.d-8) then tssr=.true. else tssr=.false. end if ! begin loop over components do l=1,noptcomp a=optcomp(1,l) b=optcomp(2,l) c=optcomp(3,l) chiw(:,:)=0.d0 chi2w(:,:)=0.d0 ! parallel loop over non-reduced k-points call holdthd(nkptnr,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(pmat,jk,ist,jst,kst) & !$OMP PRIVATE(ei,ej,ek,eji,eki,ekj,t1,z1) & !$OMP PRIVATE(pii,dji,vji,vik,vkj,ztm,iw) & !$OMP REDUCTION(+:chiw,chi2w) & !$OMP NUM_THREADS(nthd) allocate(pmat(nstsv,nstsv,3)) !$OMP DO do ik=1,nkptnr !$OMP CRITICAL(nonlinopt_) write(*,'("Info(nonlinopt): ",I6," of ",I6," k-points")') ik,nkptnr !$OMP END CRITICAL(nonlinopt_) ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! read momentum matrix elements from file call getpmat(vkl(:,ik),pmat) ! scissor correct the matrix elements if required if (tssr) then do ist=1,nstsv ei=evalsv(ist,jk) if (ei.lt.efermi) then do jst=1,nstsv ej=evalsv(jst,jk) if (ej.gt.efermi) then eji=ej-ei t1=(eji+scissor)/eji pmat(ist,jst,:)=t1*pmat(ist,jst,:) end if end do end if end do end if z1=(wkptnr*occmax/omega)*zi ! loop over valence states do ist=1,nstsv ei=evalsv(ist,jk) if (ei.lt.efermi) then pii(:)=pmat(ist,ist,:) ! loop over conduction states do jst=1,nstsv ej=evalsv(jst,jk) if (ej.gt.efermi) then eji=ej-ei+scissor dji(:)=pmat(jst,jst,:)-pii(:) vji(:)=pmat(jst,ist,:) ! loop over intermediate states do kst=1,nstsv ek=evalsv(kst,jk) if ((kst.ne.ist).and.(kst.ne.jst)) then eki=ek-ei ekj=ek-ej if (ek.gt.efermi) then eki=eki+scissor else ekj=ekj-scissor end if vik(:)=pmat(ist,kst,:) vkj(:)=pmat(kst,jst,:) ! interband terms t1=-eji*eki*(-ekj)*(eki+ekj) if (abs(t1).gt.etol) then t1=1.d0/t1 else t1=0.d0 end if ztm(1,1)=z1*conjg(vji(a))*(conjg(vkj(b))*conjg(vik(c)) & +conjg(vik(b))*conjg(vkj(c)))*t1 t1=eji*(-eki)*ekj*(-eki-eji) if (abs(t1).gt.etol) then t1=1.d0/t1 else t1=0.d0 end if ztm(1,2)=0.5d0*z1*vkj(c)*(vji(a)*vik(b)+vik(a)*vji(b))*t1 t1=eji*(-eki)*ekj*(ekj-eji) if (abs(t1).gt.etol) then t1=1.d0/t1 else t1=0.d0 end if ztm(1,3)=0.5d0*z1*vik(b)*(vkj(c)*vji(a)+vji(c)*vkj(a))*t1 ! intraband terms t1=(-eki)*ekj*eji**3 if (abs(t1).gt.etol) then t1=1.d0/t1 else t1=0.d0 end if ztm(2,1)=0.5d0*z1*(eki*vik(b)*(vkj(c)*vji(a)+vji(c)*vkj(a)) & +ekj*vkj(c)*(vji(a)*vik(b)+vik(a)*vji(b)))*t1 t1=((-eji)*eki*(-ekj)*eji**2)/(-ekj-eki) if (abs(t1).gt.etol) then t1=1.d0/t1 else t1=0.d0 end if ztm(2,3)=z1*conjg(vji(a))*(conjg(vkj(b))*conjg(vik(c)) & +conjg(vik(b))*conjg(vkj(c)))*t1 ! modulation terms t1=ekj*(-eki)*eji**3 if (abs(t1).gt.etol) then t1=1.d0/t1 else t1=0.d0 end if ztm(3,1)=0.25d0*z1*(-eki)*vkj(a)*(vji(b)*vik(c) & +vik(b)*vji(c))*t1 ztm(3,2)=0.25d0*z1*ekj*vik(a)*(vkj(b)*vji(c)+vji(b)*vkj(c))*t1 do iw=1,nwplot ! 2w interband chi2w(iw,1)=chi2w(iw,1)+ztm(1,1)/(eji-2.d0*w(iw)+eta) ! 2w intraband chi2w(iw,2)=chi2w(iw,2)+ztm(2,3)/(eji-2.d0*w(iw)+eta) ! w interband chiw(iw,1)=chiw(iw,1)-(ztm(1,2)-ztm(1,3))/(eji-w(iw)+eta) ! w intraband chiw(iw,2)=chiw(iw,2)+ztm(2,1)/(eji-w(iw)+eta) ! w modulation chiw(iw,3)=chiw(iw,3)+(ztm(3,1)-ztm(3,2))/(eji-w(iw)+eta) end do end if ! end loop over kst end do ztm(2,2)=4.d0*z1*conjg(vji(a))*(dji(b)*vji(c)+vji(b)*dji(c))/eji**4 ztm(3,3)=0.25d0*z1*vji(a)*(vji(b)*dji(c)+dji(b)*vji(c))/eji**4 do iw=1,nwplot ! 2w intraband chi2w(iw,2)=chi2w(iw,2)+ztm(2,2)/(eji-2.d0*w(iw)+eta) ! w modulation chiw(iw,3)=chiw(iw,3)+ztm(3,3)/(eji-w(iw)+eta) end do ! end loop over jst end if end do ! end loop over ist end if end do ! end loop over k-points end do !$OMP END DO deallocate(pmat) !$OMP END PARALLEL call freethd(nthd) ! write to files write(fname,'("CHI_INTER2w_",3I1,".OUT")') a,b,c open(51,file=trim(fname),form='FORMATTED') write(fname,'("CHI_INTRA2w_",3I1,".OUT")') a,b,c open(52,file=trim(fname),form='FORMATTED') write(fname,'("CHI_INTERw_",3I1,".OUT")') a,b,c open(53,file=trim(fname),form='FORMATTED') write(fname,'("CHI_INTRAw_",3I1,".OUT")') a,b,c open(54,file=trim(fname),form='FORMATTED') write(fname,'("CHI_",3I1,".OUT")') a,b,c open(55,file=trim(fname),form='FORMATTED') do iw=1,nwplot write(51,'(2G18.10)') w(iw),dble(chi2w(iw,1)) write(52,'(2G18.10)') w(iw),dble(chi2w(iw,2)) write(53,'(2G18.10)') w(iw),dble(chiw(iw,1)) write(54,'(2G18.10)') w(iw),dble(chiw(iw,2)) t1=dble(chi2w(iw,1)+chi2w(iw,2)+chiw(iw,1)+chiw(iw,2)+chiw(iw,3)) write(55,'(2G18.10)') w(iw),t1 end do write(51,*) write(52,*) write(53,*) write(54,*) write(55,*) do iw=1,nwplot write(51,'(2G18.10)') w(iw),aimag(chi2w(iw,1)) write(52,'(2G18.10)') w(iw),aimag(chi2w(iw,2)) write(53,'(2G18.10)') w(iw),aimag(chiw(iw,1)) write(54,'(2G18.10)') w(iw),aimag(chiw(iw,2)) t1=aimag(chi2w(iw,1)+chi2w(iw,2)+chiw(iw,1)+chiw(iw,2)+chiw(iw,3)) write(55,'(2G18.10)') w(iw),t1 end do close(51); close(52); close(53); close(54); close(55) ! end loop over components end do write(*,*) write(*,'("Info(nonlinopt):")') write(*,'(" susceptibility tensor written to CHI_abc.OUT")') write(*,'(" interband contributions written to CHI_INTERx_abc.OUT")') write(*,'(" intraband contributions written to CHI_INTRAx_abc.OUT")') write(*,'(" for components")') do l=1,noptcomp write(*,'(" a = ",I1,", b = ",I1,", c = ",I1)') optcomp(1:3,l) end do ! write chi2w to test file if required call writetest(125,'non-linear susceptibility',nv=nwplot*2,tol=1.d-2,zva=chi2w) deallocate(w,chiw,chi2w) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writelat.f900000644000000000000000000000013214061636517015077 xustar0030 mtime=1623670095.515101935 30 atime=1623670094.309103054 30 ctime=1623670095.515101935 elk-7.2.42/src/writelat.f900000644002504400250440000000325514061636517017141 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writelat use modmain implicit none open(50,file='LATTICE'//trim(filext),form='FORMATTED',action='WRITE') write(50,*) write(50,'("+----------------------------+")') write(50,'("| Real-space lattice vectors |")') write(50,'("+----------------------------+")') write(50,*) write(50,'("vector a1 : ",3G18.10)') avec(:,1) write(50,'("vector a2 : ",3G18.10)') avec(:,2) write(50,'("vector a3 : ",3G18.10)') avec(:,3) write(50,*) write(50,'("Stored column-wise as a matrix :")') write(50,'(3G18.10)') avec(1,:) write(50,'(3G18.10)') avec(2,:) write(50,'(3G18.10)') avec(3,:) write(50,*) write(50,'("Inverse of matrix :")') write(50,'(3G18.10)') ainv(1,:) write(50,'(3G18.10)') ainv(2,:) write(50,'(3G18.10)') ainv(3,:) write(50,*) write(50,'("Unit cell volume : ",G18.10)') omega write(50,*) write(50,*) write(50,'("+----------------------------------+")') write(50,'("| Reciprocal-space lattice vectors |")') write(50,'("+----------------------------------+")') write(50,*) write(50,'("vector b1 : ",3G18.10)') bvec(:,1) write(50,'("vector b2 : ",3G18.10)') bvec(:,2) write(50,'("vector b3 : ",3G18.10)') bvec(:,3) write(50,*) write(50,'("Stored column-wise as a matrix :")') write(50,'(3G18.10)') bvec(1,:) write(50,'(3G18.10)') bvec(2,:) write(50,'(3G18.10)') bvec(3,:) write(50,*) write(50,'("Inverse of matrix :")') write(50,'(3G18.10)') binv(1,:) write(50,'(3G18.10)') binv(2,:) write(50,'(3G18.10)') binv(3,:) write(50,*) write(50,'("Brillouin zone volume : ",G18.10)') omegabz close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/rhocore.f900000644000000000000000000000013214061636517014705 xustar0030 mtime=1623670095.516101934 30 atime=1623670094.311103052 30 ctime=1623670095.516101934 elk-7.2.42/src/rhocore.f900000644002504400250440000000374214061636517016750 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rhocore ! !INTERFACE: subroutine rhocore ! !USES: use modmain ! !DESCRIPTION: ! Adds the core density and magnetisation to the muffin-tin functions. Also ! computes the amount of leakage of core charge from the muffin-tin spheres ! into the interstitial. ! ! !REVISION HISTORY: ! Created April 2003 (JKD) ! Fixed core moment direction, October 2012 (M. Meinert) !EOP !BOC implicit none ! local variables integer ispn,idm,is,ias integer nr,nri,iro,ir,i real(8) v(ndmag),sm,t1 ! external functions real(8), external :: rfmtint do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) iro=nri+1 sm=0.d0 ! loop over spin channels do ispn=1,nspncr ! add the core density to the muffin-tin density i=1 do ir=1,nri rhomt(i,ias)=rhomt(i,ias)+rhocr(ir,ias,ispn) i=i+lmmaxi end do do ir=iro,nr rhomt(i,ias)=rhomt(i,ias)+rhocr(ir,ias,ispn) i=i+lmmaxo end do ! compute the core charge inside the muffin-tins t1=dot_product(wrmt(1:nr,is),rhocr(1:nr,ias,ispn)) sm=sm+fourpi*y00*t1 end do ! core leakage charge chgcrlk(ias)=chgcr(is)-sm ! add to the magnetisation in the case of a spin-polarised core if (spincore) then ! compute the moment in the muffin-tin do idm=1,ndmag v(idm)=rfmtint(nr,nri,wrmt(:,is),magmt(:,ias,idm)) end do ! normalise if (ncmag) then t1=sqrt(v(1)**2+v(2)**2+v(3)**2) else t1=abs(v(1)) end if if (t1.gt.1.d-10) v(:)=v(:)/t1 ! add the core magnetisation to the total i=1 do ir=1,nri t1=rhocr(ir,ias,1)-rhocr(ir,ias,2) magmt(i,ias,:)=magmt(i,ias,:)+t1*v(:) i=i+lmmaxi end do do ir=iro,nr t1=rhocr(ir,ias,1)-rhocr(ir,ias,2) magmt(i,ias,:)=magmt(i,ias,:)+t1*v(:) i=i+lmmaxo end do end if end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rzfinp.f900000644000000000000000000000013214061636517014554 xustar0030 mtime=1623670095.518101932 30 atime=1623670094.312103052 30 ctime=1623670095.518101932 elk-7.2.42/src/rzfinp.f900000644002504400250440000000172514061636517016616 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. complex(8) function rzfinp(rfmt,rfir,zfmt,zfir) use modmain use modomp implicit none ! arguments real(8), intent(in) :: rfmt(npcmtmax,natmtot),rfir(ngtot) complex(8), intent(in) :: zfmt(npcmtmax,natmtot),zfir(ngtot) ! local variables integer is,ias,ir,nthd ! external functions complex(8), external :: rzfmtinp ! interstitial contribution rzfinp=0.d0 do ir=1,ngtot rzfinp=rzfinp+(cfunir(ir)*rfir(ir))*zfir(ir) end do rzfinp=rzfinp*(omega/dble(ngtot)) ! muffin-tin contribution call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) REDUCTION(+:rzfinp) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) rzfinp=rzfinp+rzfmtinp(nrcmt(is),nrcmti(is),wrcmt(:,is),rfmt(:,ias), & zfmt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) end function elk-7.2.42/src/PaxHeaders.21776/readspecies.f900000644000000000000000000000013114061636517015532 xustar0030 mtime=1623670095.519101931 29 atime=1623670094.31410305 30 ctime=1623670095.519101931 elk-7.2.42/src/readspecies.f900000644002504400250440000002327614061636517017602 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readspecies use modmain implicit none ! local variables integer is,ist,ios integer nlx,ilx,lx,ilo integer io,jo,ko,l,i,j e0min=0.d0 do is=1,nspecies open(50,file=trim(sppath)//trim(spfname(is)),status='OLD',form='FORMATTED', & action='READ',iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readspecies): error opening species file ",A)') & trim(sppath)//trim(spfname(is)) write(*,*) stop end if read(50,*) spsymb(is) read(50,*) spname(is) read(50,*) spzn(is) read(50,*) spmass(is) read(50,*) rminsp(is),rmt(is),rmaxsp(is),nrmt(is) if (rminsp(is).le.0.d0) then write(*,*) write(*,'("Error(readspecies): rminsp <= 0 : ",G18.10)') rminsp(is) write(*,'(" for species ",I4)') is write(*,*) stop end if if (rmt(is).le.rminsp(is)) then write(*,*) write(*,'("Error(readspecies): rmt <= rminsp : ",2G18.10)') rmt(is), & rminsp(is) write(*,'(" for species ",I4)') is write(*,*) stop end if if (rmaxsp(is).lt.rmt(is)) then write(*,*) write(*,'("Error(readspecies): rmaxsp < rmt : ",2G18.10)') rmaxsp(is), & rmt(is) write(*,*) stop end if if (nrmt(is).lt.20) then write(*,*) write(*,'("Error(readspecies): nrmt too small : ",I8)') nrmt(is) write(*,'(" for species ",I4)') is write(*,*) stop end if ! multiply nrmt by the scale factor nrmt(is)=nint(dble(nrmt(is))*nrmtscf) ! reduce the minimum radial mesh point by the same factor rminsp(is)=rminsp(is)/nrmtscf read(50,*) nstsp(is) if ((nstsp(is).le.0).or.(nstsp(is).gt.maxstsp)) then write(*,*) write(*,'("Error(readspecies): nstsp out of range : ",I8)') nstsp(is) write(*,'(" for species ",I4)') is write(*,*) stop end if do ist=1,nstsp(is) read(50,*) nsp(ist,is),lsp(ist,is),ksp(ist,is),occsp(ist,is),spcore(ist,is) if (nsp(ist,is).lt.1) then write(*,*) write(*,'("Error(readspecies): nsp < 1 : ",I8)') nsp(ist,is) write(*,'(" for species ",I4)') is write(*,'(" and state ",I4)') ist write(*,*) stop end if if (lsp(ist,is).lt.0) then write(*,*) write(*,'("Error(readspecies): lsp < 0 : ",I8)') lsp(ist,is) write(*,'(" for species ",I4)') is write(*,'(" and state ",I4)') ist write(*,*) stop end if if (ksp(ist,is).lt.1) then write(*,*) write(*,'("Error(readspecies): ksp < 1 : ",I8)') ksp(ist,is) write(*,'(" for species ",I4)') is write(*,'(" and state ",I4)') ist write(*,*) stop end if if (occsp(ist,is).lt.0.d0) then write(*,*) write(*,'("Error(readspecies): occsp < 0 : ",G18.10)') occsp(ist,is) write(*,'(" for species ",I4)') is write(*,'(" and state ",I4)') ist write(*,*) stop end if end do read(50,*) apword(0,is) if (apword(0,is).le.0) then write(*,*) write(*,'("Error(readspecies): apword <= 0 : ",I8)') apword(0,is) write(*,'(" for species ",I4)') is write(*,*) stop end if if (apword(0,is).gt.maxapword) then write(*,*) write(*,'("Error(readspecies): apword too large : ",I8)') apword(0,is) write(*,'(" for species ",I4)') is write(*,'("Adjust maxapword in modmain and recompile code")') write(*,*) stop end if ! set the APW orders for l>0 apword(1:lmaxapw,is)=apword(0,is) do io=1,apword(0,is) read(50,*) apwe0(io,0,is),apwdm(io,0,is),apwve(io,0,is) if (apwdm(io,0,is).lt.0) then write(*,*) write(*,'("Error(readspecies): apwdm < 0 : ",I8)') apwdm(io,0,is) write(*,'(" for species ",I4)') is write(*,'(" and order ",I4)') io write(*,*) stop end if ! set the APW linearisation energies, derivative orders and variability for l>0 apwe0(io,1:lmaxapw,is)=apwe0(io,0,is) apwdm(io,1:lmaxapw,is)=apwdm(io,0,is) apwve(io,1:lmaxapw,is)=apwve(io,0,is) e0min=min(e0min,apwe0(io,0,is)) end do read(50,*) nlx if (nlx.lt.0) then write(*,*) write(*,'("Error(readspecies): nlx < 0 : ",I8)') nlx write(*,'(" for species ",I4)') is write(*,*) stop end if do ilx=1,nlx read(50,*) lx,io if (lx.lt.0) then write(*,*) write(*,'("Error(readspecies): lx < 0 : ",I8)') lx write(*,'(" for species ",I4)') is write(*,'(" and exception number ",I4)') ilx write(*,*) stop end if if (lx.gt.lmaxapw) then write(*,*) write(*,'("Error(readspecies): lx > lmaxapw : ",I8)') lx write(*,'(" for species ",I4)') is write(*,'(" and exception number ",I4)') ilx write(*,*) stop end if apword(lx,is)=io if (apword(lx,is).le.0) then write(*,*) write(*,'("Error(readspecies): apword <= 0 : ",I8)') apword(lx,is) write(*,'(" for species ",I4)') is write(*,'(" and exception number ",I4)') ilx write(*,*) stop end if if (apword(lx,is).gt.maxapword) then write(*,*) write(*,'("Error(readspecies): apword too large : ",I8)') apword(lx,is) write(*,'(" for species ",I4)') is write(*,'(" and exception number ",I4)') ilx write(*,'("Adjust maxapword in modmain and recompile code")') write(*,*) stop end if do io=1,apword(lx,is) read(50,*) apwe0(io,lx,is),apwdm(io,lx,is),apwve(io,lx,is) if (apwdm(io,lx,is).lt.0) then write(*,*) write(*,'("Error(readspecies): apwdm < 0 : ",I8)') apwdm(io,lx,is) write(*,'(" for species ",I4)') is write(*,'(" exception number ",I4)') ilx write(*,'(" and order ",I4)') io write(*,*) stop end if e0min=min(e0min,apwe0(io,lx,is)) end do end do ! add excess order to APW functions if required if (nxoapwlo.gt.0) then do l=0,lmaxapw jo=apword(l,is) ko=jo+nxoapwlo if (ko.gt.maxapword) ko=maxapword i=0 do io=jo+1,ko i=i+1 apwe0(io,l,is)=apwe0(jo,l,is) apwdm(io,l,is)=apwdm(jo,l,is)+i apwve(io,l,is)=apwve(jo,l,is) end do apword(l,is)=ko end do end if read(50,*) nlorb(is) if (nlorb(is).lt.0) then write(*,*) write(*,'("Error(readspecies): nlorb < 0 : ",I8)') nlorb(is) write(*,'(" for species ",I4)') is write(*,*) stop end if if (nlorb(is).gt.maxlorb) then write(*,*) write(*,'("Error(readspecies): nlorb too large : ",I8)') nlorb(is) write(*,'(" for species ",I4)') is write(*,'("Adjust maxlorb in modmain and recompile code")') write(*,*) stop end if do ilo=1,nlorb(is) read(50,*) lorbl(ilo,is),lorbord(ilo,is) if (lorbl(ilo,is).lt.0) then write(*,*) write(*,'("Error(readspecies): lorbl < 0 : ",I8)') lorbl(ilo,is) write(*,'(" for species ",I4)') is write(*,'(" and local-orbital ",I4)') ilo write(*,*) stop end if if (lorbl(ilo,is).gt.lmaxo) then write(*,*) write(*,'("Error(readspecies): lorbl > lmaxo : ",2I8)') lorbl(ilo,is), & lmaxo write(*,'(" for species ",I4)') is write(*,'(" and local-orbital ",I4)') ilo write(*,*) stop end if if (lorbord(ilo,is).lt.2) then write(*,*) write(*,'("Error(readspecies): lorbord < 2 : ",I8)') lorbord(ilo,is) write(*,'(" for species ",I4)') is write(*,'(" and local-orbital ",I4)') ilo write(*,*) stop end if if (lorbord(ilo,is).gt.maxlorbord) then write(*,*) write(*,'("Error(readspecies): lorbord too large : ",I8)') lorbord(ilo,is) write(*,'(" for species ",I4)') is write(*,'(" and local-orbital ",I4)') ilo write(*,'("Adjust maxlorbord in modmain and recompile code")') write(*,*) stop end if do io=1,lorbord(ilo,is) read(50,*) lorbe0(io,ilo,is),lorbdm(io,ilo,is),lorbve(io,ilo,is) if (lorbdm(io,ilo,is).lt.0) then write(*,*) write(*,'("Error(readspecies): lorbdm < 0 : ",I8)') lorbdm(io,ilo,is) write(*,'(" for species ",I4)') is write(*,'(" local-orbital ",I4)') ilo write(*,'(" and order ",I4)') io write(*,*) stop end if e0min=min(e0min,lorbe0(io,ilo,is)) end do end do ! add excess local-orbitals if required if (nxlo.gt.0) then lx=-1 do ilo=1,nlorb(is) do io=1,lorbord(ilo,is) if (lorbe0(io,ilo,is).lt.0.d0) goto 10 end do if (lorbl(ilo,is).gt.lx) lx=lorbl(ilo,is) 10 continue end do ilo=nlorb(is) do i=1,nxlo if (ilo.eq.maxlorb) exit l=lx+i if (l.gt.lmaxo) exit ilo=ilo+1 lorbl(ilo,is)=l lorbord(ilo,is)=apword(l,is)+1 do io=1,lorbord(ilo,is) lorbe0(io,ilo,is)=apwe0(1,l,is) lorbdm(io,ilo,is)=io-1 lorbve(io,ilo,is)=apwve(1,l,is) end do end do nlorb(is)=ilo end if ! add excess order to local-orbitals if required if (nxoapwlo.gt.0) then do ilo=1,nlorb(is) ! find the maximum energy derivative jo=1 j=lorbdm(jo,ilo,is) do io=1,lorbord(ilo,is) i=lorbdm(io,ilo,is) if (i.gt.j) then jo=io j=i end if end do ko=lorbord(ilo,is)+nxoapwlo if (ko.gt.maxlorbord) ko=maxlorbord i=0 do io=lorbord(ilo,is)+1,ko i=i+1 lorbe0(io,ilo,is)=lorbe0(jo,ilo,is) lorbdm(io,ilo,is)=lorbdm(jo,ilo,is)+i lorbve(io,ilo,is)=lorbve(jo,ilo,is) end do lorbord(ilo,is)=ko end do end if close(50) end do ! set all muffin-tin radii to single value if required if (rmtall.gt.0.d0) rmt(1:nspecies)=rmtall ! add conduction state local-orbitals if required call addlorbcnd ! subtract 2 Hartree from the minimum energy e0min=e0min-2.d0 end subroutine elk-7.2.42/src/PaxHeaders.21776/findband.f900000644000000000000000000000013214061636517015011 xustar0030 mtime=1623670095.521101929 30 atime=1623670094.316103048 30 ctime=1623670095.521101929 elk-7.2.42/src/findband.f900000644002504400250440000000631714061636517017055 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: findband ! !INTERFACE: subroutine findband(sol,l,nr,r,vr,eps,demax,e,fnd) ! !INPUT/OUTPUT PARAMETERS: ! sol : speed of light in atomic units (in,real) ! l : angular momentum quantum number (in,integer) ! nr : number of radial mesh points (in,integer) ! r : radial mesh (in,real(nr)) ! vr : potential on radial mesh (in,real(nr)) ! eps : energy search tolerance (in,real) ! demax : maximum allowed change from the input energy; enforced only if e < 0 ! (in,real) ! e : input energy and returned band energy (inout,real) ! fnd : set to .true. if the band energy is found (out,logical) ! !DESCRIPTION: ! Finds the band energies for a given radial potential and angular momentum. ! This is done by first searching upwards in energy, starting from the input ! energy plus the offset energy, until the radial wavefunction at the ! muffin-tin radius is zero. This is the energy at the top of the band, ! denoted $E_{\rm t}$. A downward search is now performed from $E_{\rm t}$ ! until the slope of the radial wavefunction at the muffin-tin radius is zero. ! This energy, $E_{\rm b}$, is at the bottom of the band. The band energy is ! taken as $(E_{\rm t}+E_{\rm b})/2$. If either $E_{\rm t}$ or $E_{\rm b}$ ! cannot be found then the band energy is set to the input value. ! ! !REVISION HISTORY: ! Created September 2004 (JKD) ! Added two-pass loop, October 2013 (JKD) !EOP !BOC implicit none ! arguments real(8), intent(in) :: sol integer, intent(in) :: l,nr real(8), intent(in) :: r(nr),vr(nr) real(8), intent(in) :: eps,demax real(8), intent(inout) :: e logical, intent(out) :: fnd ! local variables logical ft,fb ! maximum number of steps integer, parameter :: maxstp=250 integer ip,ie,nn ! initial step size real(8), parameter :: de0=0.001d0 real(8) de,et,eb,t,tp ! automatic arrays real(8) p0(nr),p1(nr),q0(nr),q1(nr) ft=.false. fb=.false. fnd=.false. et=e eb=e ! two-pass loop do ip=1,2 ! find the top of the band tp=0.d0 de=de0 do ie=1,maxstp et=et+de if (e.lt.0.d0) then if (et.gt.e+demax) exit end if call rschrodint(sol,l,et,nr,r,vr,nn,p0,p1,q0,q1) t=p0(nr) if (ie.gt.1) then if (t*tp.le.0.d0) then if (abs(de).lt.eps) then if (fb) goto 10 ft=.true. eb=et+5.d0*abs(de0) exit end if de=-0.5d0*de else de=1.5d0*de end if end if tp=t end do if (fb) return ! find the bottom of the band tp=0.d0 de=-de0 do ie=1,maxstp eb=eb+de if (eb.lt.e-demax) return call rschrodint(sol,l,eb,nr,r,vr,nn,p0,p1,q0,q1) t=p1(nr) if (ie.gt.1) then if (t*tp.le.0.d0) then if (abs(de).lt.eps) then if (ft) goto 10 fb=.true. et=eb-5.d0*abs(de0) exit end if de=-0.5d0*de else de=1.5d0*de end if end if tp=t end do end do return 10 continue ! set the band energy halfway between top and bottom e=(et+eb)/2.d0 fnd=.true. end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/exxengy.f900000644000000000000000000000013214061636517014733 xustar0030 mtime=1623670095.523101928 30 atime=1623670094.318103046 30 ctime=1623670095.523101928 elk-7.2.42/src/exxengy.f900000644002504400250440000000555014061636517016775 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2006 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine exxengy use modmain use modmpi use modomp implicit none ! local variables integer ik,ist,jst,is,ia integer nrc,nrci,npc integer m1,m2,nthd complex(8) z1 ! allocatable arrays complex(8), allocatable :: wfcr1(:,:),wfcr2(:,:) complex(8), allocatable :: zrhomt(:),zvclmt(:),zfmt(:) ! external functions complex(8), external :: zfmtinp allocate(wfcr1(npcmtmax,2),wfcr2(npcmtmax,2)) allocate(zrhomt(npcmtmax),zvclmt(npcmtmax),zfmt(npcmtmax)) ! zero the exchange energy engyx=0.d0 !--------------------------------------------------! ! val-val-val and val-cr-val contributions ! !--------------------------------------------------! call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(exxengy_) write(*,'("Info(exxengy): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(exxengy_) call exxengyk(ik) end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) ! add energies from each process and redistribute call mpi_allreduce(mpi_in_place,engyx,1,mpi_double_precision,mpi_sum,mpicom, & ierror) !-----------------------------------! ! core-core-core contribution ! !-----------------------------------! ! begin loops over atoms and species do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) do jst=1,nstsp(is) if (spcore(jst,is)) then do m2=-ksp(jst,is),ksp(jst,is)-1 ! generate the core wavefunction in spherical coordinates (pass in m-1/2) call wavefcr(.false.,lradstp,is,ia,jst,m2,npcmtmax,wfcr2) do ist=1,nstsp(is) if (spcore(ist,is)) then do m1=-ksp(ist,is),ksp(ist,is)-1 call wavefcr(.false.,lradstp,is,ia,ist,m1,npcmtmax,wfcr1) ! calculate the complex overlap density call zrho2(npc,wfcr1,wfcr1(:,2),wfcr2,wfcr2(:,2),zfmt) call zfsht(nrc,nrci,zfmt,zrhomt) ! calculate the Coulomb potential call zpotclmt(nrc,nrci,nrcmtmax,rlcmt(:,:,is),wprcmt(:,:,is), & zrhomt,zvclmt) z1=zfmtinp(nrc,nrci,wrcmt(:,is),zrhomt,zvclmt) engyx=engyx-0.5d0*dble(z1) end do ! end loop over ist end if end do end do ! end loop over jst end if end do ! end loops over atoms and species end do end do deallocate(wfcr1,wfcr2,zrhomt,zvclmt,zfmt) return contains pure subroutine zrho2(n,x1,x2,y1,y2,z) implicit none integer, intent(in) :: n complex(8), intent(in) :: x1(n),x2(n),y1(n),y2(n) complex(8), intent(out) :: z(n) z(:)=conjg(x1(:))*y1(:)+conjg(x2(:))*y2(:) end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/gentauk.f900000644000000000000000000000013214061636517014702 xustar0030 mtime=1623670095.524101927 30 atime=1623670094.320103044 30 ctime=1623670095.524101927 elk-7.2.42/src/gentauk.f900000644002504400250440000000554714061636517016752 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gentauk(ik) use modmain implicit none ! arguments integer, intent(in) :: ik ! local variables integer ispn,jspn,nst,ist,jst integer is,ias,nrc,nrci integer npc,igk,ifg,i real(8) wo complex(8) z1 ! automatic arrays integer idx(nstsv) ! automatic arrays complex(8) gzfmt(npcmtmax,3),zfmt(npcmtmax),zfft(ngtc) ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfgp(:,:,:) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) ! find the matching coefficients do ispn=1,nspnfv call match(ngk(ispn,ik),vgkc(:,:,ispn,ik),gkc(:,ispn,ik), & sfacgk(:,:,ispn,ik),apwalm(:,:,:,:,ispn)) end do ! get the eigenvectors from file call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! count and index the occupied states nst=0 do ist=1,nstsv if (abs(occsv(ist,ik)).lt.epsocc) cycle nst=nst+1 idx(nst)=ist end do ! calculate the second-variational wavefunctions for occupied states allocate(wfmt(npcmtmax,natmtot,nspinor,nst),wfgp(ngkmax,nspinor,nst)) call genwfsv(.true.,.true.,nst,idx,ngdgc,igfc,ngk(:,ik),igkig(:,:,ik),apwalm, & evecfv,evecsv,wfmt,ngkmax,wfgp) deallocate(apwalm,evecfv,evecsv) !-------------------------! ! muffin-tin part ! !-------------------------! do ist=1,nst jst=idx(ist) wo=0.5d0*wkpt(ik)*occsv(jst,ik) do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) ! compute the gradient of the wavefunction call gradzfmt(nrc,nrci,rlcmt(:,-1,is),wcrcmt(:,:,is), & wfmt(:,ias,ispn,ist),npcmtmax,gzfmt) do i=1,3 ! convert gradient to spherical coordinates call zbsht(nrc,nrci,gzfmt(:,i),zfmt) ! add to total in muffin-tin !$OMP CRITICAL(gentauk_1) taumt(1:npc,ias,ispn)=taumt(1:npc,ias,ispn) & +wo*(dble(zfmt(1:npc))**2+aimag(zfmt(1:npc))**2) !$OMP END CRITICAL(gentauk_1) end do end do end do end do deallocate(wfmt) !---------------------------! ! interstitial part ! !---------------------------! do ist=1,nst jst=idx(ist) wo=0.5d0*wkpt(ik)*occsv(jst,ik)/omega do ispn=1,nspinor jspn=jspnfv(ispn) do i=1,3 zfft(:)=0.d0 do igk=1,ngk(jspn,ik) ifg=igfc(igkig(igk,jspn,ik)) z1=wfgp(igk,ispn,ist) zfft(ifg)=vgkc(i,igk,jspn,ik)*cmplx(-aimag(z1),dble(z1),8) end do call zfftifc(3,ngdgc,1,zfft) !$OMP CRITICAL(gentauk_2) tauir(1:ngtc,ispn)=tauir(1:ngtc,ispn) & +wo*(dble(zfft(1:ngtc))**2+aimag(zfft(1:ngtc))**2) !$OMP END CRITICAL(gentauk_2) end do end do end do deallocate(wfgp) end subroutine elk-7.2.42/src/PaxHeaders.21776/gradrfmt.f900000644000000000000000000000013214061636517015052 xustar0030 mtime=1623670095.526101925 30 atime=1623670094.321103043 30 ctime=1623670095.526101925 elk-7.2.42/src/gradrfmt.f900000644002504400250440000000364514061636517017117 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: gradrfmt ! !INTERFACE: subroutine gradrfmt(nr,nri,ri,wcr,rfmt,ld,grfmt) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial mesh points (in,integer) ! nri : number of points on inner part of muffin-tin (in,integer) ! ri : 1/r on the radial mesh (in,real(nr)) ! wcr : weights for spline coefficients on radial mesh (in,real(12,nr)) ! rfmt : real muffin-tin function (in,real(*)) ! ld : leading dimension (in,integer) ! grfmt : gradient of rfmt (out,real(ld,3)) ! !DESCRIPTION: ! Calculates the gradient of a real muffin-tin function. In other words, given ! the real spherical harmonic expansion coefficients, $f_{lm}(r)$, of a ! function $f({\bf r})$, the routine returns ${\bf F}_{lm}$ where ! $$ \sum_{lm}{\bf F}_{lm}(r)R_{lm}(\hat{\bf r})=\nabla f({\bf r}), $$ ! and $R_{lm}$ is a real spherical harmonic function. This is done by first ! converting the function to a complex spherical harmonic expansion and then ! using the routine {\tt gradzfmt}. See routine {\tt genrlm}. ! ! !REVISION HISTORY: ! Created August 2003 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: ri(nr),wcr(12,nr) real(8), intent(in) :: rfmt(*) integer, intent(in) :: ld real(8), intent(out) :: grfmt(ld,3) ! local variables integer i ! automatic arrays complex(8) zfmt(ld),gzfmt(ld,3) ! convert real to complex spherical harmonic expansion call rtozfmt(nr,nri,rfmt,zfmt) ! compute the gradient call gradzfmt(nr,nri,ri,wcr,zfmt,ld,gzfmt) ! convert complex to real spherical harmonic expansion do i=1,3 call ztorfmt(nr,nri,gzfmt(:,i),grfmt(:,i)) ! apply smoothing if required call rfmtsm(msmooth,nr,nri,grfmt(:,i)) end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/symrf.f900000644000000000000000000000013214061636517014404 xustar0030 mtime=1623670095.527101924 30 atime=1623670094.323103041 30 ctime=1623670095.527101924 elk-7.2.42/src/symrf.f900000644002504400250440000000376114061636517016450 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: symrf ! !INTERFACE: subroutine symrf(nr,nri,np,ngdg,ngt,ngv,igf,ld,rfmt,rfir) ! !USES: use modmain use modomp ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial points for each species (in,integer(nspecies)) ! nri : number of radial points on the inner part (in,integer(nspecies)) ! np : total number of points in each muffin-tin (in,integer(nspecies)) ! ngdg : G-vector grid sizes (in,integer(3)) ! ngt : total number of G-vectors (in,integer) ! ngv : number of G-vectors within cut-off (in,integer) ! igf : map from G-vector index to FFT array (in,integer(ngv)) ! ld : leading dimension (in,integer) ! rfmt : real muffin-tin function (inout,real(ld,natmtot)) ! rfir : real intersitial function (inout,real(ngtot)) ! !DESCRIPTION: ! Symmetrises a real scalar function defined over the entire unit cell using ! the full set of crystal symmetries. In the muffin-tin of a particular atom ! the spherical harmonic coefficients of every equivlent atom are rotated and ! averaged. The interstitial part of the function is first Fourier transformed ! to $G$-space, and then averaged over each symmetry by rotating the Fourier ! coefficients and multiplying them by a phase factor corresponding to the ! symmetry translation. ! ! !REVISION HISTORY: ! Created May 2007 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr(nspecies),nri(nspecies),np(nspecies) integer, intent(in) :: ngdg(3),ngt,ngv,igf(ngv) integer, intent(in) :: ld real(8), intent(inout) :: rfmt(ld,natmtot),rfir(ngt) ! local variables integer nthd call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP SECTION call symrfmt(nr,nri,np,ld,rfmt) !$OMP SECTION call symrfir(ngdg,ngt,ngv,igf,rfir) !$OMP END PARALLEL SECTIONS call freethd(nthd) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rfmtinp.f900000644000000000000000000000013114061636517014722 xustar0030 mtime=1623670095.529101922 29 atime=1623670094.32510304 30 ctime=1623670095.529101922 elk-7.2.42/src/rfmtinp.f900000644002504400250440000000351114061636517016760 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2003-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rfmtinp ! !INTERFACE: pure real(8) function rfmtinp(nr,nri,wr,rfmt1,rfmt2) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! nr : number of radial mesh points (in,integer) ! nri : number of radial mesh points on the inner part of the muffin-tin ! (in,integer) ! wr : weights for integration on radial mesh (in,real(nr)) ! rfmt1 : first real function inside muffin-tin (in,real(*)) ! rfmt2 : second real function inside muffin-tin (in,real(*)) ! !DESCRIPTION: ! Calculates the inner product of two real functions in the muffin-tin. So ! given two real functions of the form ! $$ f({\bf r})=\sum_{l=0}^{l_{\rm max}}\sum_{m=-l}^{l}f_{lm}(r)R_{lm} ! (\hat{\bf r}) $$ ! where $R_{lm}$ are the real spherical harmonics, the function returns ! $$ I=\int\sum_{l=0}^{l_{\rm max}}\sum_{m=-l}^{l}f_{lm}^1(r)f_{lm}^2(r)r^2 ! dr\;. $$ ! ! !REVISION HISTORY: ! Created November 2003 (Sharma) !EOP !BOC implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: wr(nr) real(8), intent(in) :: rfmt1(*),rfmt2(*) ! local variables integer n,ir,i ! compute the dot-products for each radial point and integrate over r rfmtinp=0.d0 i=1 if (lmaxi.eq.1) then do ir=1,nri rfmtinp=rfmtinp+wr(ir) & *(rfmt1(i)*rfmt2(i) & +rfmt1(i+1)*rfmt2(i+1) & +rfmt1(i+2)*rfmt2(i+2) & +rfmt1(i+3)*rfmt2(i+3)) i=i+4 end do else n=lmmaxi-1 do ir=1,nri rfmtinp=rfmtinp+wr(ir)*dot_product(rfmt1(i:i+n),rfmt2(i:i+n)) i=i+lmmaxi end do end if n=lmmaxo-1 do ir=nri+1,nr rfmtinp=rfmtinp+wr(ir)*dot_product(rfmt1(i:i+n),rfmt2(i:i+n)) i=i+lmmaxo end do end function !EOC elk-7.2.42/src/PaxHeaders.21776/checkfsm.f900000644000000000000000000000013214061636517015027 xustar0030 mtime=1623670095.530101921 30 atime=1623670094.327103038 30 ctime=1623670095.530101921 elk-7.2.42/src/checkfsm.f900000644002504400250440000000304014061636517017061 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine checkfsm use modmain implicit none ! local variables integer isym,lspn integer is,ia,ja real(8) sc(3,3),v(3),t1 if (fsmtype.eq.0) return do isym=1,nsymcrys lspn=lspnsymc(isym) ! proper rotation matrix in Cartesian coordinates sc(:,:)=dble(symlatd(lspn))*symlatc(:,:,lspn) ! check invariance of global moment if ((abs(fsmtype).eq.1).or.(abs(fsmtype).eq.3)) then call r3mv(sc,momfix,v) t1=sum(abs(momfix(:)-v(:))) if (t1.gt.epslat) then write(*,*) write(*,'("Error(checkfsm): momfix not invariant under symmetry group")') write(*,*) stop end if end if ! check invariance of muffin-tin moments if ((abs(fsmtype).eq.2).or.(abs(fsmtype).eq.3)) then do is=1,nspecies do ia=1,natoms(is) ! if any component is >= 1000 then do not fix the moment t1=sum(abs(mommtfix(:,ia,is))) if (t1.ge.1000.d0) cycle ! equivalent atom ja=ieqatom(ia,is,isym) call r3mv(sc,mommtfix(:,ja,is),v) t1=sum(abs(mommtfix(:,ia,is)-v(:))) if (t1.gt.epslat) then write(*,*) write(*,'("Error(checkfsm): mommtfix not invariant under symmetry & &group")') write(*,'(" for species ",I4)') is write(*,'(" and equivalent atoms ",2I4)') ia,ja write(*,*) stop end if end do end do end if end do end subroutine elk-7.2.42/src/PaxHeaders.21776/genrlmv.f900000644000000000000000000000013214061636517014716 xustar0030 mtime=1623670095.532101919 30 atime=1623670094.328103037 30 ctime=1623670095.532101919 elk-7.2.42/src/genrlmv.f900000644002504400250440000000367514061636517016766 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: genrlmv ! !INTERFACE: subroutine genrlmv(lmax,v,rlm) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum angular momentum (in,integer) ! v : input vector (in,real(3)) ! rlm : array of real spherical harmonics (out,real((lmax+1)**2)) ! !DESCRIPTION: ! Generates a sequence of real spherical harmonics evaluated at angles ! $(\theta,\phi)$ for $00 \\ ! \sqrt{2}\,\Im\{Y_{lm}(\theta,\phi)\} & m<0 \\ ! \Re\{Y_{lm}(\theta,\phi)\} & m=0 ! \end{cases}, $$ ! where $Y_{lm}$ are the complex spherical harmonics. These functions are ! orthonormal and complete and may be used for expanding real-valued functions ! on the sphere. This routine is numerically stable and accurate to near ! machine precision for $l\le 50$. See routine {\tt genylmv}. ! ! !REVISION HISTORY: ! Created March 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: lmax real(8), intent(in) :: v(3) real(8), intent(out) :: rlm(*) ! local variables integer l,m,lm real(8), parameter :: sqtwo=1.4142135623730950488d0 ! automatic arrays complex(8) ylm((lmax+1)**2) if ((lmax.lt.0).or.(lmax.gt.50)) then write(*,*) write(*,'("Error(genrlmv): lmax out of range : ",I8)') lmax write(*,*) stop end if ! generate complex spherical harmonics call genylmv(lmax,v,ylm) ! convert to real spherical harmonics lm=0 do l=0,lmax do m=-l,-1 lm=lm+1 rlm(lm)=sqtwo*aimag(ylm(lm)) end do lm=lm+1 rlm(lm)=dble(ylm(lm)) do m=1,l lm=lm+1 rlm(lm)=sqtwo*dble(ylm(lm)) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/mae.f900000644000000000000000000000013214061636517014006 xustar0030 mtime=1623670095.533101918 30 atime=1623670094.330103035 30 ctime=1623670095.533101918 elk-7.2.42/src/mae.f900000644002504400250440000001007014061636517016041 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine mae use modmain use modmpi use modstore use moddelf implicit none ! local variables integer i,j,im(2) real(8) em(2),de real(8) v1(3),v2(3),th real(8) a(3,3),b(3,3) ! initialise global variables call init0 ! store original parameters avec_(:,:)=avec(:,:) spinpol_=spinpol spinorb_=spinorb cmagz_=cmagz bfieldc0_(:)=bfieldc0(:) reducebf_=reducebf fsmtype_=fsmtype vkloff_(:)=vkloff(:) ! enable spin-orbit coupling spinorb=.true. ! enforce collinear magnetism in the z-direction cmagz=.true. ! no fixed spin moment calculation: the crystal is rotated instead fsmtype=0 ! if task=28 then start from atomic densities; if task=29 read STATE.OUT if (task.eq.28) then trdstate=.false. else trdstate=.true. end if ! zero k-point offset vkloff(:)=0.d0 ! start with large magnetic field bfieldc0(1:2)=0.d0 bfieldc0(3)=-2.d0 ! reduce the external magnetic field after each s.c. loop reducebf=0.75d0 ! generate the spin moment directions in (theta,phi) coordinates call gentpmae ! open MAE_INFO.OUT if (mp_mpi) then open(71,file='MAE_INFO.OUT',form='FORMATTED') write(71,*) write(71,'("Scale factor of spin-orbit coupling term : ",G18.10)') socscf end if im(:)=1 em(1)=1.d8 em(2)=-1.d8 ! loop over points on sphere do i=1,npmae if (mp_mpi) then write(*,'("Info(mae): fixed spin moment direction ",I6," of ",I6)') i,npmae end if ! rotate lattice vectors instead of moment (thanks to J. Glasbrenner, ! K. Bussmann and I. Mazin) ! first by -phi around the z-axis v1(:)=0.d0 v1(3)=1.d0 th=-tpmae(2,i) call axangrot(v1,th,a) ! then by -theta around the y-axis v1(:)=0.d0 v1(2)=1.d0 th=-tpmae(1,i) call axangrot(v1,th,b) call r3mm(b,a,rotsht) call r3mm(rotsht,avec_,avec) ! find the corresponding moment direction vector call r3minv(rotsht,a) v1(:)=0.d0 v1(3)=1.d0 call r3mv(a,v1,v2) do j=1,3 if (abs(v2(j)).lt.epslat) v2(j)=0.d0 end do ! rotate the spherical cover used for the spherical harmonic transform trotsht=.true. ! run the ground-state calculation call gndstate ! subsequent calculations should read the previous density trdstate=.true. ! make external magnetic field small bfieldc0(3)=-0.01d0 if (mp_mpi) then write(71,*) write(71,'("Fixed spin moment direction point ",I6," of ",I6)') i,npmae write(71,'("Spherical coordinates of direction : ",2G18.10)') tpmae(:,i) write(71,'("Direction vector (Cartesian coordinates) : ",3G18.10)') v2 write(71,'("Calculated total moment magnitude : ",G18.10)') momtotm write(71,'("Total energy : ",G22.12)') engytot flush(71) end if ! check for minimum and maximum total energy if (engytot.lt.em(1)) then em(1)=engytot im(1)=i end if if (engytot.gt.em(2)) then em(2)=engytot im(2)=i end if ! delete the eigenvector files call delfiles(evec=.true.) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end do ! magnetic anisotropy energy de=em(2)-em(1) if (mp_mpi) then write(71,*) write(71,'("Minimum energy point : ",I6)') im(1) write(71,'("Maximum energy point : ",I6)') im(2) write(71,*) write(71,'("Estimated magnetic anisotropy energy (MAE) : ",G18.10)') de write(71,*) write(71,'("MAE per unit volume : ",G18.10)') de/omega close(71) open(50,file='MAE.OUT',form='FORMATTED') write(50,'(G18.10)') de close(50) open(50,file='MAEPUV.OUT',form='FORMATTED') write(50,'(G18.10)') de/omega close(50) write(*,*) write(*,'("Info(mae):")') write(*,'(" Estimated magnetic anisotropy energy written to MAE.OUT")') write(*,'(" MAE per unit volume written to MAEPUV.OUT")') write(*,*) write(*,'(" Number of fixed spin moment directions used : ",I6)') npmae write(*,*) write(*,'(" Additional information written to MAE_INFO.OUT")') end if ! restore original input parameters avec(:,:)=avec_(:,:) spinpol=spinpol_ spinorb=spinorb_ cmagz=cmagz_ fsmtype=fsmtype_ bfieldc0(:)=bfieldc0_(:) reducebf=reducebf_ vkloff(:)=vkloff_(:) trotsht=.false. end subroutine elk-7.2.42/src/PaxHeaders.21776/writegvecrf.f900000644000000000000000000000013214061636517015573 xustar0030 mtime=1623670095.535101916 30 atime=1623670094.332103033 30 ctime=1623670095.535101916 elk-7.2.42/src/writegvecrf.f900000644002504400250440000000077714061636517017643 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writegvecrf use modmain implicit none ! local variables integer ig open(50,file='GVECRF.OUT',form='FORMATTED',action='WRITE') write(50,'(G18.10," : gmaxrf")') gmaxrf write(50,'(I8," : ngrf; G-vector index, ivg below")') ngrf do ig=1,ngrf write(50,'(I8,3I6)') ig,ivg(1:3,ig) end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/zcfmtwr.f900000644000000000000000000000013214061636517014740 xustar0030 mtime=1623670095.536101915 30 atime=1623670094.333103032 30 ctime=1623670095.536101915 elk-7.2.42/src/zcfmtwr.f900000644002504400250440000000134714061636517017002 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine zcfmtwr(nr,nri,wr,zfmt,cfmt) use modmain implicit none ! arguments integer, intent(in) :: nr,nri real(8), intent(in) :: wr(nr) complex(8), intent(in) :: zfmt(*) complex(4), intent(out) :: cfmt(*) ! local variables integer n,ir,i i=1 if (lmaxi.eq.1) then do ir=1,nri cfmt(i:i+3)=cmplx(wr(ir)*zfmt(i:i+3)) i=i+4 end do else n=lmmaxi-1 do ir=1,nri cfmt(i:i+n)=cmplx(wr(ir)*zfmt(i:i+n)) i=i+lmmaxi end do end if n=lmmaxo-1 do ir=nri+1,nr cfmt(i:i+n)=cmplx(wr(ir)*zfmt(i:i+n)) i=i+lmmaxo end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dolpistl.f900000644000000000000000000000013114061636517015075 xustar0030 mtime=1623670095.538101914 29 atime=1623670094.33510303 30 ctime=1623670095.538101914 elk-7.2.42/src/dolpistl.f900000644002504400250440000000133614061636517017136 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine dolpistl(ngp,ngpq,igpig,igpqig,ld,od) use modmain use modphonon implicit none ! arguments integer, intent(in) :: ngp,ngpq integer, intent(in) :: igpig(ngkmax),igpqig(ngkmax) integer, intent(in) :: ld complex(8), intent(inout) :: od(ld,*) ! local variables integer i1,i2,i3,j1,j2,j3 integer ig,i,j do j=1,ngp ig=igpig(j) j1=ivg(1,ig); j2=ivg(2,ig); j3=ivg(3,ig) do i=1,ngpq ig=igpqig(i) i1=ivg(1,ig)-j1; i2=ivg(2,ig)-j2; i3=ivg(3,ig)-j3 od(i,j)=od(i,j)+dcfunig(ivgig(i1,i2,i3)) end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dhmlistl.f900000644000000000000000000000013214061636517015064 xustar0030 mtime=1623670095.539101913 30 atime=1623670094.336103029 30 ctime=1623670095.539101913 elk-7.2.42/src/dhmlistl.f900000644002504400250440000000162714061636517017127 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine dhmlistl(ngp,ngpq,igpig,igpqig,vgpc,vgpqc,ld,dh) use modmain use modphonon implicit none ! arguments integer, intent(in) :: ngp,ngpq integer, intent(in) :: igpig(ngkmax),igpqig(ngkmax) real(8), intent(in) :: vgpc(3,ngkmax),vgpqc(3,ngkmax) integer, intent(in) :: ld complex(8), intent(inout) :: dh(ld,*) ! local variables integer j1,j2,j3 integer ig,i,j real(8) v1,v2,v3,t1 do j=1,ngp ig=igpig(j) j1=ivg(1,ig); j2=ivg(2,ig); j3=ivg(3,ig) v1=0.5d0*vgpc(1,j); v2=0.5d0*vgpc(2,j); v3=0.5d0*vgpc(3,j) do i=1,ngpq ig=igpqig(i) ig=ivgig(ivg(1,ig)-j1,ivg(2,ig)-j2,ivg(3,ig)-j3) t1=vgpqc(1,i)*v1+vgpqc(2,i)*v2+vgpqc(3,i)*v3 dh(i,j)=dh(i,j)+dvsig(ig)+t1*dcfunig(ig) end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/olpaloq.f900000644000000000000000000000013214061636517014713 xustar0030 mtime=1623670095.541101911 30 atime=1623670094.338103027 30 ctime=1623670095.541101911 elk-7.2.42/src/olpaloq.f900000644002504400250440000000170514061636517016753 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine olpaloq(is,ias,ngp,ngpq,apwalm,apwalmq,ld,oq) use modmain implicit none ! arguments integer, intent(in) :: is,ias integer, intent(in) :: ngp,ngpq complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: oq(ld,*) ! local variables integer ilo,io,l,lm integer i0,j0,i,j real(8) t1 do ilo=1,nlorb(is) l=lorbl(ilo,is) do lm=l**2+1,(l+1)**2 i=idxlo(lm,ilo,ias) i0=ngpq+i j0=ngp+i do io=1,apword(l,is) t1=oalo(io,ilo,ias) do i=1,ngpq oq(i,j0)=oq(i,j0)+t1*conjg(apwalmq(i,io,lm)) end do do j=1,ngp oq(i0,j)=oq(i0,j)+t1*apwalm(j,io,lm) end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlaloq.f900000644000000000000000000000013014061636517014677 xustar0029 mtime=1623670095.54210191 30 atime=1623670094.340103026 29 ctime=1623670095.54210191 elk-7.2.42/src/hmlaloq.f900000644002504400250440000000262014061636517016736 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine hmlaloq(is,ias,ngp,ngpq,apwalm,apwalmq,ld,hq) use modmain implicit none ! arguments integer, intent(in) :: is,ias integer, intent(in) :: ngp,ngpq complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: hq(ld,*) ! local variables integer io,ilo integer l1,l2,l3 integer lm1,lm2,lm3 integer i0,j0,i,j complex(8) z1 do ilo=1,nlorb(is) l1=lorbl(ilo,is) do lm1=l1**2+1,(l1+1)**2 i=idxlo(lm1,ilo,ias) i0=ngpq+i j0=ngp+i do l3=0,lmaxapw do lm3=l3**2+1,(l3+1)**2 do io=1,apword(l3,is) z1=0.d0 do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyry(lm2,lm3,lm1)*hloa(lm2,io,l3,ilo,ias) end do end if end do if (abs(dble(z1))+abs(aimag(z1)).gt.1.d-14) then do i=1,ngpq hq(i,j0)=hq(i,j0)+conjg(z1*apwalmq(i,io,lm3)) end do do j=1,ngp hq(i0,j)=hq(i0,j)+z1*apwalm(j,io,lm3) end do end if end do end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dolpalo.f900000644000000000000000000000013214061636517014676 xustar0030 mtime=1623670095.544101908 30 atime=1623670094.341103025 30 ctime=1623670095.544101908 elk-7.2.42/src/dolpalo.f900000644002504400250440000000174014061636517016735 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine dolpalo(is,ias,ngp,ngpq,dapwalm,dapwalmq,ld,od) use modmain use modphonon implicit none ! arguments integer, intent(in) :: is,ias,ngp,ngpq complex(8), intent(in) :: dapwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalmq(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: od(ld,*) ! local variables integer ilo,io,l,lm integer i0,j0,i,j real(8) t1 if (ias.ne.iasph) return do ilo=1,nlorb(is) l=lorbl(ilo,is) do lm=l**2+1,(l+1)**2 i=idxlo(lm,ilo,ias) i0=ngpq+i j0=ngp+i do io=1,apword(l,is) t1=oalo(io,ilo,ias) do i=1,ngpq od(i,j0)=od(i,j0)+t1*conjg(dapwalmq(i,io,lm)) end do do j=1,ngp od(i0,j)=od(i0,j)+t1*dapwalm(j,io,lm) end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dhmlalo.f900000644000000000000000000000013214061636517014664 xustar0030 mtime=1623670095.545101907 30 atime=1623670094.343103023 30 ctime=1623670095.545101907 elk-7.2.42/src/dhmlalo.f900000644002504400250440000000435514061636517016730 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine dhmlalo(is,ias,ngp,ngpq,apwalm,apwalmq,dapwalm,dapwalmq,ld,dh) use modmain use modphonon implicit none ! arguments integer, intent(in) :: is,ias,ngp,ngpq complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalmq(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: dh(ld,*) ! local variables integer io,ilo integer l1,l2,l3 integer lm1,lm2,lm3 integer i0,j0,i,j complex(8) z1 do ilo=1,nlorb(is) l1=lorbl(ilo,is) do lm1=l1**2+1,(l1+1)**2 i=idxlo(lm1,ilo,ias) i0=ngpq+i j0=ngp+i do l3=0,lmaxapw do lm3=l3**2+1,(l3+1)**2 do io=1,apword(l3,is) z1=0.d0 do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyyy(lm2,lm3,lm1)*dhloa(lm2,io,l3,ilo,ias) end do end if end do if (abs(dble(z1))+abs(aimag(z1)).gt.1.d-14) then do i=1,ngpq dh(i,j0)=dh(i,j0)+conjg(z1*apwalmq(i,io,lm3)) end do do j=1,ngp dh(i0,j)=dh(i0,j)+z1*apwalm(j,io,lm3) end do end if end do end do end do if (ias.eq.iasph) then do l3=0,lmaxapw do lm3=l3**2+1,(l3+1)**2 do io=1,apword(l3,is) z1=0.d0 do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyry(lm2,lm3,lm1)*hloa(lm2,io,l3,ilo,ias) end do end if end do if (abs(dble(z1))+abs(aimag(z1)).gt.1.d-14) then do i=1,ngpq dh(i,j0)=dh(i,j0)+conjg(z1*dapwalmq(i,io,lm3)) end do do j=1,ngp dh(i0,j)=dh(i0,j)+z1*dapwalm(j,io,lm3) end do end if end do end do end do end if end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dhmllolo.f900000644000000000000000000000013214061636517015056 xustar0030 mtime=1623670095.547101905 30 atime=1623670094.345103021 30 ctime=1623670095.547101905 elk-7.2.42/src/dhmllolo.f900000644002504400250440000000200114061636517017104 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine dhmllolo(is,ias,ngp,ngpq,ld,dh) use modmain use modphonon implicit none ! arguments integer, intent(in) :: is,ias integer, intent(in) :: ngp,ngpq integer, intent(in) :: ld complex(8), intent(inout) :: dh(ld,*) ! local variables integer ilo,jlo,i,j integer l1,l2,l3 integer lm1,lm2,lm3 complex(8) z1 do jlo=1,nlorb(is) l3=lorbl(jlo,is) do lm3=l3**2+1,(l3+1)**2 j=ngp+idxlo(lm3,jlo,ias) do ilo=1,nlorb(is) l1=lorbl(ilo,is) do lm1=l1**2+1,(l1+1)**2 i=ngpq+idxlo(lm1,ilo,ias) z1=0.d0 do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyyy(lm2,lm3,lm1)*dhlolo(lm2,jlo,ilo,ias) end do end if end do dh(i,j)=dh(i,j)+z1 end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/olpaaq.f900000644000000000000000000000013114061636517014520 xustar0030 mtime=1623670095.548101904 29 atime=1623670094.34610302 30 ctime=1623670095.548101904 elk-7.2.42/src/olpaaq.f900000644002504400250440000000151314061636517016556 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine olpaaq(is,ngp,ngpq,apwalm,apwalmq,ld,oq) use modmain implicit none ! arguments integer, intent(in) :: is,ngp,ngpq complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: oq(*) ! local variables integer io,l,lm,i ! automatic arrays complex(8) a(lmoapw(is),ngpq),b(lmoapw(is),ngp) i=0 do l=0,lmaxapw do lm=l**2+1,(l+1)**2 do io=1,apword(l,is) i=i+1 a(i,1:ngpq)=apwalmq(1:ngpq,io,lm) b(i,1:ngp)=apwalm(1:ngp,io,lm) end do end do end do call zmctm(lmoapw(is),ngpq,ngp,a,b,ld,oq) end subroutine elk-7.2.42/src/PaxHeaders.21776/dolpaa.f900000644000000000000000000000013214061636517014504 xustar0030 mtime=1623670095.550101903 30 atime=1623670094.348103018 30 ctime=1623670095.550101903 elk-7.2.42/src/dolpaa.f900000644002504400250440000000240614061636517016543 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dolpaa(is,ias,ngp,ngpq,apwalm,apwalmq,dapwalm,dapwalmq,ld,od) use modmain use modphonon implicit none ! arguments integer, intent(in) :: is,ias integer, intent(in) :: ngp,ngpq complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalmq(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: od(*) ! local variables integer lmo,io,l,lm,i ! automatic arrays complex(8) a(lmoapw(is),ngpq),b(lmoapw(is),ngp) if (ias.ne.iasph) return lmo=lmoapw(is) i=0 do l=0,lmaxapw do lm=l**2+1,(l+1)**2 do io=1,apword(l,is) i=i+1 a(i,1:ngpq)=apwalmq(1:ngpq,io,lm) b(i,1:ngp)=dapwalm(1:ngp,io,lm) end do end do end do call zmctm(lmo,ngpq,ngp,a,b,ld,od) i=0 do l=0,lmaxapw do lm=l**2+1,(l+1)**2 do io=1,apword(l,is) i=i+1 a(i,1:ngpq)=dapwalmq(1:ngpq,io,lm) b(i,1:ngp)=apwalm(1:ngp,io,lm) end do end do end do call zmctm(lmo,ngpq,ngp,a,b,ld,od) end subroutine elk-7.2.42/src/PaxHeaders.21776/dhmlaa.f900000644000000000000000000000013214061636517014472 xustar0030 mtime=1623670095.551101901 30 atime=1623670094.349103017 30 ctime=1623670095.551101901 elk-7.2.42/src/dhmlaa.f900000644002504400250440000000517014061636517016532 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dhmlaa(is,ias,ngp,ngpq,apwalm,apwalmq,dapwalm,dapwalmq,ld,dh) use modmain use modphonon implicit none ! arguments integer, intent(in) :: is,ias integer, intent(in) :: ngp,ngpq complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalmq(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: dh(*) ! local variables integer lmo,io,jo,i integer l1,l2,l3 integer lm1,lm2,lm3 real(8) t0 complex(8) z1 ! automatic arrays complex(8) a1(lmoapw(is),ngpq),b1(lmoapw(is),ngp) complex(8) a2(lmoapw(is),ngpq),b2(lmoapw(is),ngp) lmo=lmoapw(is) t0=0.5d0*rmt(is)**2 i=0 do l1=0,lmaxapw do lm1=l1**2+1,(l1+1)**2 do io=1,apword(l1,is) i=i+1 b1(i,:)=0.d0 do l3=0,lmaxapw do lm3=l3**2+1,(l3+1)**2 do jo=1,apword(l3,is) z1=0.d0 do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyyy(lm2,lm3,lm1)*dhaa(lm2,jo,l3,io,l1,ias) end do end if end do if (abs(dble(z1))+abs(aimag(z1)).gt.1.d-14) then call zaxpy(ngp,z1,apwalm(:,jo,lm3),1,b1(i,1),lmo) end if end do end do end do if (ias.eq.iasph) then b2(i,:)=0.d0 do l3=0,lmaxapw do lm3=l3**2+1,(l3+1)**2 do jo=1,apword(l3,is) z1=0.d0 do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyry(lm2,lm3,lm1)*haa(lm2,jo,l3,io,l1,ias) end do end if end do ! kinetic surface contribution if (lm1.eq.lm3) then z1=z1+t0*apwfr(nrmt(is),1,io,l1,ias)*apwdfr(jo,l1,ias) end if if (abs(dble(z1))+abs(aimag(z1)).gt.1.d-14) then call zaxpy(ngp,z1,dapwalm(:,jo,lm3),1,b1(i,1),lmo) call zaxpy(ngp,z1,apwalm(:,jo,lm3),1,b2(i,1),lmo) end if end do end do end do a2(i,1:ngpq)=dapwalmq(1:ngpq,io,lm1) end if a1(i,1:ngpq)=apwalmq(1:ngpq,io,lm1) end do end do end do call zmctm(lmo,ngpq,ngp,a1,b1,ld,dh) if (ias.eq.iasph) then call zmctm(lmo,ngpq,ngp,a2,b2,ld,dh) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlaaq.f900000644000000000000000000000012614061636517014512 xustar0028 mtime=1623670095.5531019 30 atime=1623670094.351103015 28 ctime=1623670095.5531019 elk-7.2.42/src/hmlaaq.f900000644002504400250440000000315614061636517016551 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine hmlaaq(is,ias,ngp,ngpq,apwalm,apwalmq,ld,hq) use modmain implicit none integer, intent(in) :: is,ias,ngp,ngpq complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw) integer, intent(in) :: ld complex(8), intent(inout) :: hq(*) ! local variables integer lmo,io,jo,i integer l1,l2,l3 integer lm1,lm2,lm3 real(8) t0 complex(8) z1 ! automatic arrays complex(8) a(lmoapw(is),ngpq),b(lmoapw(is),ngp) lmo=lmoapw(is) t0=0.5d0*rmt(is)**2 i=0 do l1=0,lmaxapw do lm1=l1**2+1,(l1+1)**2 do io=1,apword(l1,is) i=i+1 b(i,:)=0.d0 do l3=0,lmaxapw do lm3=l3**2+1,(l3+1)**2 do jo=1,apword(l3,is) z1=0.d0 ! kinetic and potential contribution do l2=0,lmaxo if (mod(l1+l2+l3,2).eq.0) then do lm2=l2**2+1,(l2+1)**2 z1=z1+gntyry(lm2,lm3,lm1)*haa(lm2,jo,l3,io,l1,ias) end do end if end do ! kinetic surface contribution if (lm1.eq.lm3) then z1=z1+t0*apwfr(nrmt(is),1,io,l1,ias)*apwdfr(jo,l1,ias) end if if (abs(dble(z1))+abs(aimag(z1)).gt.1.d-14) then call zaxpy(ngp,z1,apwalm(:,jo,lm3),1,b(i,1),lmo) end if end do end do end do a(i,1:ngpq)=apwalmq(1:ngpq,io,lm1) end do end do end do call zmctm(lmo,ngpq,ngp,a,b,ld,hq) end subroutine elk-7.2.42/src/PaxHeaders.21776/initeph.f900000644000000000000000000000013214061636517014704 xustar0030 mtime=1623670095.554101899 30 atime=1623670094.353103013 30 ctime=1623670095.554101899 elk-7.2.42/src/initeph.f900000644002504400250440000000627614061636517016754 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine initeph use modmain use modphonon use modbog implicit none ! local variables integer iq,ik,n,i ! automatic arrays complex(8) u(nstsv,nstsv),v(nstsv,nstsv) complex(8) w(nbph,nbph),x(nbph,nbph),y(nbph) ! allocatable arrays complex(8), allocatable :: dynq(:,:,:),ev(:,:) complex(8), allocatable :: ephmat(:,:,:) ! combined target array for fermionic and bosonic density matrices if (allocated(duvwx)) deallocate(duvwx) n=2*nstsv*nstsv*nkpt+2*nbph*nbph*nqpt allocate(duvwx(n)) !------------------------------! ! electronic variables ! !------------------------------! if (allocated(evaluv)) deallocate(evaluv) allocate(evaluv(nstsv,nkpt)) if (allocated(vnorm)) deallocate(vnorm) allocate(vnorm(nstsv,nkpt)) ! associate the electronic density matrices with target dvv(1:nstsv,1:nstsv,1:nkpt)=>duvwx(1:) i=nstsv*nstsv*nkpt+1 duv(1:nstsv,1:nstsv,1:nkpt)=>duvwx(i:) i=i+nstsv*nstsv*nkpt if (task.eq.270) then ! initialise the density matrices to random numbers dvv(:,:,:)=0.d0 duv(:,:,:)=0.d0 do ik=1,nkpt call rndevsv(1.d-8,dvv(:,:,ik)) call rndevsv(1.d-8,duv(:,:,ik)) end do else do ik=1,nkpt ! get the eigenvalues from file call getevaluv(ik,evaluv(:,ik)) ! get the eigenvectors from file call getevecuv(ik,vkl(:,ik),u,v) ! calculate the density matrices call dmatuv(nstsv,efermi,evalsv(:,ik),u,v,dvv(:,:,ik),duv(:,:,ik)) end do end if !----------------------------! ! phononic variables ! !----------------------------! allocate(dynq(nbph,nbph,nqpt),ev(nbph,nbph)) ! read in the dynamical matrices call readdyn(dynq) ! apply the acoustic sum rule call sumrule(dynq) ! find the eigenvalues of the dynamical matrices and store in global array do iq=1,nqpt call dynev(dynq(:,:,iq),wphq(:,iq),ev) end do deallocate(dynq,ev) if (allocated(evalwx)) deallocate(evalwx) allocate(evalwx(nbph,nqpt)) ! associate the phononic density matrices with target dxx(1:nbph,1:nbph,1:nqpt)=>duvwx(i:) i=i+nbph*nbph*nqpt dwx(1:nbph,1:nbph,1:nqpt)=>duvwx(i:) if (task.eq.270) then ! zero the density matrices dxx(:,:,:)=0.d0 dwx(:,:,:)=0.d0 else do iq=1,nqpt ! get the eigenvalues from file call getevalwx(iq,evalwx(:,iq)) ! get the eigenvectors from file call getevecwxy(iq,w,x,y) ! calculate the density matrices call dmatwx(nbph,w,x,dxx(:,:,iq),dwx(:,:,iq)) end do end if !-----------------------------------! ! electron-phonon variables ! !-----------------------------------! if (any(task.eq.[270,271])) then ! allocate the electron-phonon matrix elements array if (allocated(ephmkq)) deallocate(ephmkq) allocate(ephmkq(nstsv,nstsv,nbph,nkptnr,nqpt)) ! read the matrix elements from file and store in global array allocate(ephmat(nstsv,nstsv,nbph)) do iq=1,nqpt do ik=1,nkptnr call getephmat(iq,ik,ephmat) ephmkq(:,:,:,ik,iq)=ephmat(:,:,:) end do ! zero the electron-phonon coupling for phonon small phonon frequencies do i=1,nbph if (wphq(i,iq).lt.wphcut) ephmkq(:,:,i,:,iq)=0.d0 end do end do deallocate(ephmat) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/dengyeph.f900000644000000000000000000000013214061636517015047 xustar0030 mtime=1623670095.556101897 30 atime=1623670094.355103012 30 ctime=1623670095.556101897 elk-7.2.42/src/dengyeph.f900000644002504400250440000000134314061636517017105 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine dengyeph use modmain use modphonon use modbog implicit none ! local variables integer ik,iq,i real(8) w ! change in electron energy per unit cell dengye=0.d0 do ik=1,nkpt w=wkpt(ik) do i=1,nstsv dengye=dengye+w*abs((evalsv(i,ik)-efermi)*dble(dvv(i,i,ik))) end do end do dengye=abs(occmax*dengye) ! change in phonon energy per unit cell dengyph=0.d0 do iq=1,nqpt w=wqpt(iq) do i=1,nbph dengyph=dengyph+w*abs(wphq(i,iq)*dble(dxx(i,i,iq))) end do end do ! sum of both dengy=dengye+dengyph end subroutine elk-7.2.42/src/PaxHeaders.21776/gndsteph.f900000644000000000000000000000013214061636517015060 xustar0030 mtime=1623670095.557101896 30 atime=1623670094.356103011 30 ctime=1623670095.557101896 elk-7.2.42/src/gndsteph.f900000644002504400250440000001103414061636517017114 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine gndsteph use modmain use modphonon use modbog use modmpi use modomp use modstore implicit none ! local variables integer nmix,nwork real(8) dv ! allocatable arrays real(8), allocatable :: work(:) ! initialise universal variables call init0 call init1 call init2 call readstate call genvsig call gencore call readfermi call linengy call genapwlofr call gensocfr call genevfsv ! precise determination of the Fermi energy swidth_=swidth swidth=1.d-5 call occupy swidth=swidth_ ! initialise electron-phonon variables call initeph ! size of mixing vector for electron and phonon density matrices (complex array) nmix=2*size(duvwx) ! determine the size of the mixer work array nwork=-1 call mixerifc(mixtype,nmix,duvwx,dv,nwork,duvwx) allocate(work(nwork)) ! initialise the mixer iscl=0 call mixerifc(mixtype,nmix,duvwx,dv,nwork,work) ! set the stop signal to .false. tstop=.false. ! set last self-consistent loop flag tlast=.false. ! only the MPI master process should write files if (mp_mpi) then ! open EPH_INFO.OUT file open(60,file='EPH_INFO.OUT',form='FORMATTED') write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop started |")') write(60,'("+------------------------------+")') ! open EPHGAP.OUT open(64,file='EPHGAP.OUT',form='FORMATTED') ! open RMSDVS.OUT open(65,file='RMSDVS.OUT',form='FORMATTED') ! open FACE.OUT open(67,file='FACE.OUT',form='FORMATTED') end if if (mp_mpi) write(*,*) ! begin the self-consistent loop do iscl=1,maxscl if (mp_mpi) then write(60,*) write(60,'("+--------------------+")') write(60,'("| Loop number : ",I4," |")') iscl write(60,'("+--------------------+")') flush(60) write(*,'("Info(gndsteph): self-consistent loop number : ",I4)') iscl end if if (iscl.ge.maxscl) then if (mp_mpi) then write(60,*) write(60,'("Reached self-consistent loops maximum")') end if tlast=.true. end if ! determine change in electron and phonon energies call dengyeph ! solve the electron and phonon eigenvalue equations call eveqneph ! update the Fermi energy call occupyuv if (mp_mpi) then ! write the electronic eigenvalues to file call writeevaluv ! write the Fermi energy to file call writefermi write(60,*) write(60,'("Energies :")') write(60,'(" Fermi",T30,": ",G22.12)') efermi write(60,'(" electronic change",T30,": ",G22.12)') dengye write(60,'(" phononic change",T30,": ",G22.12)') dengyph write(60,'(" sum of changes",T30,": ",G22.12)') dengy write(60,*) write(60,'("Estimated indirect band gap : ",G18.10)') bandgap(1) write(60,'(" from k-point ",I6," to k-point ",I6)') ikgap(1),ikgap(2) write(60,*) write(60,'("Fermionic anomalous correlation entropy : ",G18.10)') face write(60,*) write(60,'("Electron-phonon scaling factor : ",G18.10)') ephscf(1) ! write estimated indirect band gap write(64,'(G22.12)') bandgap(1) flush(64) ! write the fermionic anomalous correlation entropy write(67,'(G18.10)') face flush(67) end if ! mix the old and new electron and phonon density matrices call mixerifc(mixtype,nmix,duvwx,dv,nwork,work) ! adjust the electron-phonon term scale factor towards 1 ephscf(1)=(1.d0-ephscf(2))*ephscf(1)+ephscf(2) ! exit self-consistent loop if required if (tlast) goto 10 ! check for convergence if (iscl.ge.2) then if (mp_mpi) then write(60,*) write(60,'("RMS change in density matrices (target) : ",G18.10," (",& &G18.10,")")') dv,epspot write(65,'(G18.10)') dv flush(65) if (dv.lt.epspot) then write(60,*) write(60,'("Convergence targets achieved")') tlast=.true. end if end if end if ! check for STOP file call checkstop if (tstop) tlast=.true. ! broadcast tlast from master process to all other processes call mpi_bcast(tlast,1,mpi_logical,0,mpicom,ierror) ! reset the OpenMP thread variables call omp_reset end do 10 continue if (mp_mpi) then write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop stopped |")') write(60,'("+------------------------------+")') ! close the EPH_INFO.OUT file close(60) ! close the EPHGAP.OUT file close(64) ! close the RMSDVS.OUT file close(65) ! close the FACE.OUT file close(67) end if deallocate(work) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqneph.f900000644000000000000000000000013214061636517015057 xustar0030 mtime=1623670095.559101894 30 atime=1623670094.358103009 30 ctime=1623670095.559101894 elk-7.2.42/src/eveqneph.f900000644002504400250440000000721314061636517017117 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine eveqneph use modmain use modphonon use modbog use modmpi use modomp implicit none ! local variables integer iq,ik,ist integer n,lp,nthd ! automatic arrays real(8) xnorm(nbph) ! allocatable arrays complex(8), allocatable :: dw(:,:,:),ex(:,:,:),fy(:,:) complex(8), allocatable :: au(:,:,:),bv(:,:,:) !------------------------------------! ! phonon eigenvalue equation ! !------------------------------------! allocate(dw(nbph,nbph,nqpt),ex(nbph,nbph,nqpt),fy(nbph,nqpt)) ! parallel loop over reduced q-point set call holdthd(nqpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(xnorm) & !$OMP NUM_THREADS(nthd) !$OMP DO do iq=1,nqpt ! distribute among MPI processes if (mod(iq-1,np_mpi).ne.lp_mpi) cycle ! generate the matrices D and E call hmlephde(iq,dw(:,:,iq),ex(:,:,iq)) ! zero the vector F fy(:,iq)=0.d0 ! solve the phononic Bogoliubov equation call eveqnwxy(nbph,dw(:,:,iq),ex(:,:,iq),fy(:,iq),evalwx(:,iq),xnorm) ! write the eigenvalues and eigenvectors to file if (tlast) then call putevalwx(iq,evalwx(:,iq)) call putevecwxy(iq,dw(:,:,iq),ex(:,:,iq),fy(:,iq)) call putxnorm(iq,xnorm) end if end do !$OMP END DO !$OMP DO do iq=1,nqpt ! distribute among MPI processes if (mod(iq-1,np_mpi).ne.lp_mpi) cycle ! update the density matrices call dmatwx(nbph,dw(:,:,iq),ex(:,:,iq),dxx(:,:,iq),dwx(:,:,iq)) end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) deallocate(dw,ex,fy) ! broadcast arrays to every MPI process if (np_mpi.gt.1) then n=nbph*nbph do iq=1,nqpt lp=mod(iq-1,np_mpi) call mpi_bcast(evalwx(:,iq),nbph,mpi_double_precision,lp,mpicom,ierror) call mpi_bcast(dxx(:,:,iq),n,mpi_double_complex,lp,mpicom,ierror) call mpi_bcast(dwx(:,:,iq),n,mpi_double_complex,lp,mpicom,ierror) end do end if !--------------------------------------! ! electron eigenvalue equation ! !--------------------------------------! allocate(au(nstsv,nstsv,nkpt),bv(nstsv,nstsv,nkpt)) ! parallel loop over reduced k-point set call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(ist) & !$OMP NUM_THREADS(nthd) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! generate the matrix A call hmlepha(ik,au(:,:,ik)) ! generate the matrix B call hmlephb(ik,bv(:,:,ik)) ! solve the electronic Bogoliubov equation call eveqnuv(nstsv,au(:,:,ik),bv(:,:,ik),evaluv(:,ik),vnorm(:,ik)) ! negate eigenvalues corresponding to V-norm > 1/2 do ist=1,nstsv if (vnorm(ist,ik).gt.0.5d0) evaluv(ist,ik)=-evaluv(ist,ik) end do ! write the eigenvalues and eigenvectors to file if (tlast) then call putevaluv(ik,evaluv(:,ik)) call putevecuv(ik,au(:,:,ik),bv(:,:,ik)) call putvnorm(ik,vnorm(:,ik)) end if end do !$OMP END DO !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! update the density matrices call dmatuv(nstsv,efermi,evalsv(:,ik),au(:,:,ik),bv(:,:,ik),dvv(:,:,ik), & duv(:,:,ik)) end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) deallocate(au,bv) ! broadcast arrays to every MPI process if (np_mpi.gt.1) then n=nstsv*nstsv do ik=1,nkpt lp=mod(ik-1,np_mpi) call mpi_bcast(evaluv(:,ik),nstsv,mpi_double_precision,lp,mpicom,ierror) call mpi_bcast(vnorm(:,ik),nstsv,mpi_double_precision,lp,mpicom,ierror) call mpi_bcast(dvv(:,:,ik),n,mpi_double_complex,lp,mpicom,ierror) call mpi_bcast(duv(:,:,ik),n,mpi_double_complex,lp,mpicom,ierror) end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlepha.f900000644000000000000000000000013214061636517014662 xustar0030 mtime=1623670095.560101893 30 atime=1623670094.359103008 30 ctime=1623670095.560101893 elk-7.2.42/src/hmlepha.f900000644002504400250440000000371714061636517016727 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine hmlepha(ik,a) use modmain use modphonon use modbog use modomp implicit none ! arguments integer, intent(in) :: ik complex(8), intent(out) :: a(nstsv,nstsv) ! local variables integer iq,jq,ikq,isym,nthd integer i1,i2,j1,j2,l1,l2 real(8) vl(3),t0,t1 complex(8) z1 ! automatic arrays complex(4) ephmat(nstsv,nstsv,nbph) complex(8) x(nbph,nstsv),y(nstsv,nbph) ! prefactor t0=-2.d0*wqptnr*ephscf(1)**2/dengy a(:,:)=0.d0 ! parallel loop over non-reduced q-points call holdthd(nqptnr,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ephmat,x,y,jq,vl,isym,ikq) & !$OMP PRIVATE(i1,i2,j1,j2,l1,l2,z1,t1) & !$OMP REDUCTION(+:a) & !$OMP NUM_THREADS(nthd) do iq=1,nqptnr ! equivalent reduced q-point jq=ivqiq(ivq(1,iq),ivq(2,iq),ivq(3,iq)) ! k+q-vector in lattice coordinates vl(:)=vkl(:,ik)+vql(:,iq) ! index to reduced k+q-vector call findkpt(vl,isym,ikq) ! read in the electron-phonon matrix elements from file call getephmkq(iq,ik,ephmat) ! perform the contraction do i2=1,nstsv do j2=1,nstsv do l2=1,nbph z1=0.d0 do j1=1,nstsv z1=z1+ephmat(j1,i2,l2)*dvv(j1,j2,ikq) end do x(l2,j2)=z1 end do end do do l1=1,nbph do j2=1,nstsv z1=0.d0 do l2=1,nbph t1=dble(dxx(l1,l2,jq))+dble(dwx(l2,l1,jq)) z1=z1+t1*x(l2,j2) end do y(j2,l1)=z1 end do end do do i1=1,i2 z1=0.d0 do l1=1,nbph do j2=1,nstsv z1=z1+conjg(ephmat(j2,i1,l1))*y(j2,l1) end do end do a(i1,i2)=a(i1,i2)+t0*z1 end do end do end do !$OMP END PARALLEL DO call freethd(nthd) 10 continue ! add the second-variational eigenvalues minus the Fermi energy do i1=1,nstsv a(i1,i1)=a(i1,i1)+evalsv(i1,ik)-efermi end do end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlephb.f900000644000000000000000000000013214061636517014663 xustar0030 mtime=1623670095.562101891 30 atime=1623670094.361103006 30 ctime=1623670095.562101891 elk-7.2.42/src/hmlephb.f900000644002504400250440000000361114061636517016721 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine hmlephb(ik,b) use modmain use modphonon use modbog use modomp implicit none ! arguments integer, intent(in) :: ik complex(8), intent(out) :: b(nstsv,nstsv) ! local variables integer iq,jq,ikq,isym,nthd integer i1,i2,j1,j2,l1,l2 real(8) vl(3),t0,t1 complex(8) z1 ! automatic arrays complex(4) ephmat(nstsv,nstsv,nbph) complex(8) x(nbph,nstsv),y(nstsv,nbph) ! prefactor t0=-2.d0*wqptnr*ephscf(1)**2/dengy b(:,:)=0.d0 if (.not.anomalous) return ! parallel loop over non-reduced q-points call holdthd(nqptnr,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ephmat,x,y,jq,vl,isym,ikq) & !$OMP PRIVATE(i1,i2,j1,j2,l1,l2,z1,t1) & !$OMP REDUCTION(+:b) & !$OMP NUM_THREADS(nthd) do iq=1,nqptnr ! equivalent reduced q-point jq=ivqiq(ivq(1,iq),ivq(2,iq),ivq(3,iq)) ! k+q-vector in lattice coordinates vl(:)=vkl(:,ik)+vql(:,iq) ! index to reduced k+q-vector call findkpt(vl,isym,ikq) ! read in the electron-phonon matrix elements from file call getephmkq(iq,ik,ephmat) ! perform the contraction do i2=1,nstsv do j1=1,nstsv do l2=1,nbph z1=0.d0 do j2=1,nstsv z1=z1+ephmat(j2,i2,l2)*duv(j1,j2,ikq) end do x(l2,j1)=z1 end do end do do l1=1,nbph do j1=1,nstsv z1=0.d0 do l2=1,nbph t1=dble(dxx(l1,l2,jq))+dble(dwx(l2,l1,jq)) z1=z1+t1*x(l2,j1) end do y(j1,l1)=z1 end do end do do i1=1,nstsv if (bdiag.and.(i1.ne.i2)) cycle z1=0.d0 do l1=1,nbph do j1=1,nstsv z1=z1+conjg(ephmat(j1,i1,l1))*y(j1,l1) end do end do b(i1,i2)=b(i1,i2)+t0*z1 end do end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/hmlephde.f900000644000000000000000000000013014061636517015030 xustar0029 mtime=1623670095.56310189 30 atime=1623670094.363103004 29 ctime=1623670095.56310189 elk-7.2.42/src/hmlephde.f900000644002504400250440000000544314061636517017075 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine hmlephde(iq,d,e) use modmain use modphonon use modbog use modomp implicit none ! arguments integer, intent(in) :: iq complex(8), intent(out) :: d(nbph,nbph),e(nbph,nbph) ! local variables integer ik,jk,ikq,isym,nthd integer i1,i2,j1,j2,l1,l2 real(8) vl(3),t0 complex(8) z1 ! automatic arrays complex(4) ephmat(nstsv,nstsv,nbph) complex(8) x(nstsv,nstsv),y(nstsv,nstsv) ! prefactor t0=-occmax*wkptnr*ephscf(1)**2/dengy e(:,:)=0.d0 ! parallel loop over non-reduced k-points call holdthd(nkptnr,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ephmat,x,y,jk,vl,isym,ikq) & !$OMP PRIVATE(l1,l2,j1,j2,i1,i2,z1) & !$OMP REDUCTION(+:e) & !$OMP NUM_THREADS(nthd) do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! k+q-vector in lattice coordinates vl(:)=vkl(:,ik)+vql(:,iq) ! index to reduced k+q-vector call findkpt(vl,isym,ikq) ! read in the electron-phonon matrix elements from file call getephmkq(iq,ik,ephmat) ! perform the contraction if (anomalous) then do l2=1,nbph do j1=1,nstsv do i2=1,nstsv z1=0.d0 do j2=1,nstsv z1=z1+ephmat(j2,i2,l2)*duv(j1,j2,ikq) end do x(i2,j1)=z1 end do end do do i1=1,nstsv do j1=1,nstsv z1=0.d0 do i2=1,nstsv z1=z1-conjg(duv(i1,i2,jk))*x(i2,j1) end do y(j1,i1)=z1 end do end do do l1=1,l2 z1=0.d0 do i1=1,nstsv do j1=1,nstsv z1=z1+conjg(ephmat(j1,i1,l1))*y(j1,i1) end do end do e(l1,l2)=e(l1,l2)+t0*z1 end do end do else do l2=1,nbph do j2=1,nstsv do i2=1,nstsv z1=0.d0 do j1=1,nstsv z1=z1+ephmat(j1,i2,l2)*dvv(j1,j2,ikq) end do x(i2,j2)=z1 end do end do do j2=1,nstsv do i1=1,nstsv z1=0.d0 do i2=1,nstsv z1=z1+dvv(i1,i2,jk)*x(i2,j2) end do y(i1,j2)=z1 end do end do do l1=1,l2 z1=0.d0 do j2=1,nstsv do i1=1,nstsv z1=z1+conjg(ephmat(j2,i1,l1))*y(i1,j2) end do end do e(l1,l2)=e(l1,l2)+t0*z1 end do end do end if end do !$OMP END PARALLEL DO call freethd(nthd) ! set the lower triangular part of the Hermitian matrix E do l1=1,nbph do l2=1,l1-1 e(l1,l2)=conjg(e(l2,l1)) end do end do ! determine the matrix D = D0 or D = D0 + E if (tephde) then d(:,:)=e(:,:) else d(:,:)=0.d0 end if do l1=1,nbph d(l1,l1)=d(l1,l1)+wphq(l1,iq) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/getephmkq.f900000644000000000000000000000013214061636517015231 xustar0030 mtime=1623670095.565101889 30 atime=1623670094.364103003 30 ctime=1623670095.565101889 elk-7.2.42/src/getephmkq.f900000644002504400250440000000135314061636517017270 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine getephmkq(iqp,ikp,ephmat) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iqp,ikp complex(4), intent(out) :: ephmat(nstsv,nstsv,nbph) ! local variables integer isym,lspl,iq,ik,iv(3) if (iqp.le.nqpt) then ! q-point is in the reduced set iq=iqp ik=ikp else ! q-point is not in the reduced set call findqpt(vql(:,iqp),isym,iq) lspl=lsplsymc(isym) call i3mtv(symlat(:,:,lspl),ivk(:,ikp),iv) iv(:)=modulo(iv(:),ngridk(:)) ik=ivkiknr(iv(1),iv(2),iv(3)) end if ephmat(:,:,:)=ephmkq(:,:,:,ik,iq) end subroutine elk-7.2.42/src/PaxHeaders.21776/ephdos.f900000644000000000000000000000013214061636517014526 xustar0030 mtime=1623670095.566101888 30 atime=1623670094.366103001 30 ctime=1623670095.566101888 elk-7.2.42/src/ephdos.f900000644002504400250440000000443414061636517016570 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine ephdos use modmain use modphonon use modbog implicit none ! local variables integer nsk(3),ik,ist,iw real(8) dw,vn,t1 ! allocatable arrays integer, allocatable :: idx(:) real(8), allocatable :: w(:),f(:,:),g(:) ! initialise universal variables call init0 call init1 call init2 call initeph allocate(idx(nstsv),w(nstsv)) do ik=1,nkpt ! get the eigenvalues from file call getevaluv(ik,evaluv(:,ik)) ! arrange in ascending order w(:)=evaluv(:,ik) call sortidx(nstsv,w,idx) evaluv(:,ik)=w(idx(:)) ! get the V-norm from file and put in the same order as the eigenvalues call getvnorm(ik,vnorm(:,ik)) w(:)=vnorm(:,ik) vnorm(:,ik)=w(idx(:)) end do deallocate(idx,w) ! generate the partial and total DOS and write to file allocate(w(nwplot),f(nstsv,nkptnr),g(nwplot)) ! generate frequency grid dw=(wplot(2)-wplot(1))/dble(nwplot) do iw=1,nwplot w(iw)=dw*dble(iw-1)+wplot(1) end do ! number of subdivisions used for interpolation in the Brillouin zone nsk(:)=max(ngrkf/ngridk(:),1) ! set the weight array f(:,:)=occmax ! integrate over the Brillouin zone call brzint(nswplot,ngridk,nsk,ivkik,nwplot,wplot,nstsv,nstsv,evaluv,f,g) ! output the electronic DOS to file open(50,file='EPHDOS.OUT',form='FORMATTED',action='WRITE') do iw=1,nwplot write(50,'(2G18.10)') w(iw),g(iw) end do close(50) ! output the FACE vs energy histogram to file open(50,file='FACEEH.OUT',form='FORMATTED',action='WRITE') do ik=1,nkpt do ist=1,nstsv vn=vnorm(ist,ik) if ((vn.gt.0.d0).and.(vn.lt.1.d0)) then t1=-(vn*log(vn)+(1.d0-vn)*log(1.d0-vn)) else t1=0.d0 end if if (t1.lt.1.d-4) cycle write(50,'(2G18.10)') evaluv(ist,ik),t1 end do end do close(50) write(*,*) write(*,'("Info(ephdos):")') write(*,'(" Electronic density of states for the electron-phonon system")') write(*,'(" written to EPHDOS.OUT")') write(*,*) write(*,'(" Fermionic anomalous correlation entropy vs energy histogram")') write(*,'(" written to FACEEH.OUT")') write(*,*) write(*,'(" Fermi energy is at zero in plots")') write(*,*) write(*,'(" DOS units are states/Hartree/unit cell")') deallocate(w,f,g) end subroutine elk-7.2.42/src/PaxHeaders.21776/gradrhomt.f900000644000000000000000000000012714061636517015237 xustar0030 mtime=1623670095.568101886 27 atime=1623670094.368103 30 ctime=1623670095.568101886 elk-7.2.42/src/gradrhomt.f900000644002504400250440000000137114061636517017272 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gradrhomt use modmain use modphonon implicit none ! local variables integer nr,nri,np ! automatic arrays complex(8) zfmt(npmtmax),gzfmt(npmtmax,3) ! add gradient contribution from rigid shift of muffin-tin nr=nrmt(isph) nri=nrmti(isph) np=npmt(isph) ! convert the density to complex spherical harmonic expansion call rtozfmt(nr,nri,rhomt(:,iasph),zfmt) ! compute the gradient call gradzfmt(nr,nri,rlmt(:,-1,isph),wcrmt(:,:,isph),zfmt,npmtmax,gzfmt) ! subtract from the density derivative drhomt(1:np,iasph)=drhomt(1:np,iasph)-gzfmt(1:np,ipph) end subroutine elk-7.2.42/src/PaxHeaders.21776/gendcfun.f900000644000000000000000000000013214061636517015035 xustar0030 mtime=1623670095.569101885 30 atime=1623670094.369102999 30 ctime=1623670095.569101885 elk-7.2.42/src/gendcfun.f900000644002504400250440000000114414061636517017072 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gendcfun use modmain use modphonon implicit none ! local variables integer ig real(8) v1,v2,v3,t1,t2 complex(8) z1 v1=atposc(1,iaph,isph) v2=atposc(2,iaph,isph) v3=atposc(3,iaph,isph) do ig=1,ngtot t1=vgqc(1,ig)*v1+vgqc(2,ig)*v2+vgqc(3,ig)*v3 t2=ffacgq(ig,isph)*vgqc(ipph,ig) z1=t2*cmplx(sin(t1),cos(t1),8) dcfunig(ig)=z1 dcfunir(igfft(ig))=z1 end do call zfftifc(3,ngridg,1,dcfunir) end subroutine elk-7.2.42/src/PaxHeaders.21776/gendvsig.f900000644000000000000000000000013214061636517015052 xustar0030 mtime=1623670095.571101883 30 atime=1623670094.371102997 30 ctime=1623670095.571101883 elk-7.2.42/src/gendvsig.f900000644002504400250440000000102414061636517017104 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gendvsig use modmain use modphonon implicit none ! allocatable arrays complex(8), allocatable :: zfft(:) allocate(zfft(ngtot)) zfft(:)=dvsir(:)*cfunir(:)+vsir(:)*dcfunir(:) ! Fourier transform to G+q-space call zfftifc(3,ngridg,-1,zfft) ! store in global array dvsig(1:ngvec)=zfft(igfft(1:ngvec)) deallocate(zfft) end subroutine elk-7.2.42/src/PaxHeaders.21776/drhomagsh.f900000644000000000000000000000013214061636517015220 xustar0030 mtime=1623670095.572101882 30 atime=1623670094.373102995 30 ctime=1623670095.572101882 elk-7.2.42/src/drhomagsh.f900000644002504400250440000000210614061636517017254 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine drhomagsh use modmain use modphonon use modomp implicit none ! local variables integer idm,is,ias,nthd integer nrc,nrci,npc ! automatic arrays complex(8) zfmt(npcmtmax) call holdthd(natmtot,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zfmt,is,nrc,nrci,npc,idm) & !$OMP NUM_THREADS(nthd) !$OMP DO do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) ! convert the density derivative to spherical harmonics zfmt(1:npc)=drhomt(1:npc,ias) call zfsht(nrc,nrci,zfmt,drhomt(:,ias)) end do !$OMP END DO NOWAIT do idm=1,ndmag !$OMP DO do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) ! convert the magnetisation derivative to spherical harmonics zfmt(1:npc)=dmagmt(1:npc,ias,idm) call zfsht(nrc,nrci,zfmt,dmagmt(:,ias,idm)) end do !$OMP END DO end do !$OMP END PARALLEL call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/doccupy.f900000644000000000000000000000013214061636517014712 xustar0030 mtime=1623670095.573101881 30 atime=1623670094.374102994 30 ctime=1623670095.573101881 elk-7.2.42/src/doccupy.f900000644002504400250440000000213214061636517016745 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine doccupy use modmain use modphonon implicit none ! local variables integer, parameter :: maxit=1000 integer ik,jk,ist,it real(8) de0,de1,de real(8) dchg,x,dx,t1 ! external functions real(8), external :: sdelta if (.not.tphq0) return de0=1.d6 de1=-1.d6 do ik=1,nkptnr do ist=1,nstsv de=devalsv(ist,ik) if (de.lt.de0) de0=de if (de.gt.de1) de1=de end do end do t1=1.d0/swidth do it=1,maxit defermi=0.5d0*(de0+de1) dchg=0.d0 do ik=1,nkptnr jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) do ist=1,nstsv x=(efermi-evalsv(ist,jk))*t1 dx=(defermi-devalsv(ist,ik))*t1 doccsv(ist,ik)=occmax*sdelta(stype,x)*dx dchg=dchg+wkptnr*doccsv(ist,ik) end do end do if (dchg.lt.0.d0) then de0=defermi else de1=defermi end if if ((de1-de0).lt.1.d-12) return end do write(*,*) write(*,'("Warning(doccupy): could not find Fermi energy derivative")') end subroutine elk-7.2.42/src/PaxHeaders.21776/dhmlrad.f900000644000000000000000000000013214061636517014657 xustar0030 mtime=1623670095.575101879 30 atime=1623670094.376102992 30 ctime=1623670095.575101879 elk-7.2.42/src/dhmlrad.f900000644002504400250440000000772014061636517016722 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dhmlrad use modmain use modphonon implicit none ! local variables integer is,ias integer nr,nri,iro integer ir,npi,i integer l1,l2,l3,m2,lm2 integer io,jo,ilo,jlo real(8) t1 complex(8) zsm ! begin loops over atoms and species do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) iro=nri+1 npi=npmti(is) !---------------------------! ! APW-APW integrals ! !---------------------------! do l1=0,lmaxapw do io=1,apword(l1,is) do l3=0,lmaxapw do jo=1,apword(l3,is) lm2=0 do l2=0,lmaxi do m2=-l2,l2 lm2=lm2+1 zsm=0.d0 i=lm2 do ir=1,nri t1=apwfr(ir,1,io,l1,ias)*apwfr(ir,1,jo,l3,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxi end do do ir=iro,nr t1=apwfr(ir,1,io,l1,ias)*apwfr(ir,1,jo,l3,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxo end do dhaa(lm2,jo,l3,io,l1,ias)=zsm end do end do do l2=lmaxi+1,lmaxo do m2=-l2,l2 lm2=lm2+1 zsm=0.d0 i=npi+lm2 do ir=iro,nr t1=apwfr(ir,1,io,l1,ias)*apwfr(ir,1,jo,l3,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxo end do dhaa(lm2,jo,l3,io,l1,ias)=zsm end do end do end do end do end do end do !-------------------------------------! ! local-orbital-APW integrals ! !-------------------------------------! do ilo=1,nlorb(is) l1=lorbl(ilo,is) do l3=0,lmaxapw do io=1,apword(l3,is) lm2=0 do l2=0,lmaxi do m2=-l2,l2 lm2=lm2+1 zsm=0.d0 i=lm2 do ir=1,nri t1=lofr(ir,1,ilo,ias)*apwfr(ir,1,io,l3,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxi end do do ir=iro,nr t1=lofr(ir,1,ilo,ias)*apwfr(ir,1,io,l3,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxo end do dhloa(lm2,io,l3,ilo,ias)=zsm end do end do do l2=lmaxi+1,lmaxo do m2=-l2,l2 lm2=lm2+1 zsm=0.d0 i=npi+lm2 do ir=iro,nr t1=lofr(ir,1,ilo,ias)*apwfr(ir,1,io,l3,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxo end do dhloa(lm2,io,l3,ilo,ias)=zsm end do end do end do end do end do !-----------------------------------------------! ! local-orbital-local-orbital integrals ! !-----------------------------------------------! do ilo=1,nlorb(is) l1=lorbl(ilo,is) do jlo=1,nlorb(is) l3=lorbl(jlo,is) lm2=0 do l2=0,lmaxi do m2=-l2,l2 lm2=lm2+1 zsm=0.d0 i=lm2 do ir=1,nri t1=lofr(ir,1,ilo,ias)*lofr(ir,1,jlo,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxi end do do ir=iro,nr t1=lofr(ir,1,ilo,ias)*lofr(ir,1,jlo,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxo end do dhlolo(lm2,jlo,ilo,ias)=zsm end do end do do l2=lmaxi+1,lmaxo do m2=-l2,l2 lm2=lm2+1 zsm=0.d0 i=npi+lm2 do ir=iro,nr t1=lofr(ir,1,ilo,ias)*lofr(ir,1,jlo,ias)*wrmt(ir,is) zsm=zsm+t1*dvsmt(i,ias) i=i+lmmaxo end do dhlolo(lm2,jlo,ilo,ias)=zsm end do end do end do end do ! end loops over atoms and species end do end subroutine elk-7.2.42/src/PaxHeaders.21776/gendwfsv.f900000644000000000000000000000013114061636517015066 xustar0030 mtime=1623670095.576101878 29 atime=1623670094.37810299 30 ctime=1623670095.576101878 elk-7.2.42/src/gendwfsv.f900000644002504400250440000001255614061636517017135 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gendwfsv(tsh,tgp,nst,idx,ngp,ngpq,igpqig,apwalmq,dapwalm,evecfv, & devecfv,evecsv,devecsv,dwfmt,ld,dwfir) use modmain implicit none ! arguments logical, intent(in) :: tsh,tgp integer, intent(in) :: nst,idx(nst) integer, intent(in) :: ngp(nspnfv),ngpq(nspnfv) integer, intent(in) :: igpqig(ngkmax,nspnfv) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv) complex(8), intent(in) :: dapwalm(ngkmax,apwordmax,lmmaxapw,nspnfv) complex(8), intent(in) :: evecfv(nmatmax,nstfv,nspnfv) complex(8), intent(in) :: devecfv(nmatmax,nstfv,nspnfv) complex(8), intent(in) :: evecsv(nstsv,nstsv),devecsv(nstsv,nstsv) complex(8), intent(out) :: dwfmt(npcmtmax,natmtot,nspinor,nst) integer, intent(in) :: ld complex(8), intent(out) :: dwfir(ld,nspinor,nst) ! local variables integer ist,ispn,jspn integer is,ia,ias,nrc,nrci integer npc,igp,ifg,i,j,k real(8) t1 complex(8) z1 ! automatic arrays logical done(nstfv),ddone(nstfv) ! allocatable arrays complex(8), allocatable :: wfmt1(:,:),wfmt2(:),dwfmt1(:,:) !---------------------------------------------! ! muffin-tin wavefunction derivatives ! !---------------------------------------------! if (tevecsv) then allocate(wfmt1(npcmtmax,nstfv),dwfmt1(npcmtmax,nstfv)) end if if (.not.tsh) allocate(wfmt2(npcmtmax)) do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) do ia=1,natoms(is) ias=idxas(ia,is) done(:)=.false. do j=1,nst k=idx(j) if (tevecsv) then i=0 do ispn=1,nspinor jspn=jspnfv(ispn) dwfmt(1:npc,ias,ispn,j)=0.d0 do ist=1,nstfv i=i+1 z1=devecsv(i,k) !***** check if tq0 is needed here if (abs(dble(z1))+abs(aimag(z1)).gt.epsocc) then if (.not.done(ist)) then if (tsh) then call wavefmt(lradstp,ias,ngp(jspn),apwalmq(:,:,:,ias,jspn), & evecfv(:,ist,jspn),wfmt1(:,ist)) else call wavefmt(lradstp,ias,ngp(jspn),apwalmq(:,:,:,ias,jspn), & evecfv(:,ist,jspn),wfmt2) call zbsht(nrc,nrci,wfmt2,wfmt1(:,ist)) end if done(ist)=.true. end if call zaxpy(npc,z1,wfmt1(:,ist),1,dwfmt(:,ias,ispn,j),1) end if z1=evecsv(i,k) if (abs(dble(z1))+abs(aimag(z1)).gt.epsocc) then if (.not.ddone(ist)) then if (tsh) then call dwavefmt(lradstp,ias,ngp(jspn),ngpq(jspn), & apwalmq(:,:,:,ias,jspn),dapwalm(:,:,:,jspn), & evecfv(:,ist,jspn),devecfv(:,ist,jspn),dwfmt1(:,ist)) else call dwavefmt(lradstp,ias,ngp(jspn),ngpq(jspn), & apwalmq(:,:,:,ias,jspn),dapwalm(:,:,:,jspn), & evecfv(:,ist,jspn),devecfv(:,ist,jspn),wfmt2) call zbsht(nrc,nrci,wfmt2,dwfmt1(:,ist)) end if ddone(ist)=.true. end if call zaxpy(npc,z1,dwfmt1(:,ist),1,dwfmt(:,ias,ispn,j),1) end if end do end do else if (tsh) then call dwavefmt(lradstp,ias,ngp,ngpq,apwalmq(:,:,:,ias,1),dapwalm, & evecfv(:,k,1),devecfv(:,k,1),dwfmt(:,ias,1,j)) else call dwavefmt(lradstp,ias,ngp,ngpq,apwalmq(:,:,:,ias,1),dapwalm, & evecfv(:,k,1),devecfv(:,k,1),wfmt2) call zbsht(nrc,nrci,wfmt2,dwfmt(:,ias,1,j)) end if end if end do end do end do if (tevecsv) deallocate(wfmt1,dwfmt1) if (.not.tsh) deallocate(wfmt2) !-----------------------------------------------! ! interstitial wavefunction derivatives ! !-----------------------------------------------! t1=1.d0/sqrt(omega) do j=1,nst k=idx(j) dwfir(:,:,j)=0.d0 if (tevecsv) then i=0 do ispn=1,nspinor jspn=jspnfv(ispn) do ist=1,nstfv i=i+1 z1=devecsv(i,k) if (abs(dble(z1))+abs(aimag(z1)).gt.epsocc) then if (tgp) then do igp=1,ngp(jspn) dwfir(igp,ispn,j)=dwfir(igp,ispn,j)+z1*evecfv(igp,ist,jspn) end do else z1=t1*z1 do igp=1,ngp(jspn) ifg=igfft(igpqig(igp,jspn)) dwfir(ifg,ispn,j)=dwfir(ifg,ispn,j)+z1*evecfv(igp,ist,jspn) end do end if end if z1=evecsv(i,k) if (abs(dble(z1))+abs(aimag(z1)).gt.epsocc) then if (tgp) then do igp=1,ngpq(jspn) dwfir(igp,ispn,j)=dwfir(igp,ispn,j)+z1*devecfv(igp,ist,jspn) end do else z1=t1*z1 do igp=1,ngpq(jspn) ifg=igfft(igpqig(igp,jspn)) dwfir(ifg,ispn,j)=dwfir(ifg,ispn,j)+z1*devecfv(igp,ist,jspn) end do end if end if end do end do else if (tgp) then do igp=1,ngpq(1) dwfir(igp,1,j)=devecfv(igp,k,1) end do else do igp=1,ngpq(1) ifg=igfft(igpqig(igp,1)) dwfir(ifg,1,j)=t1*devecfv(igp,k,1) end do end if end if if (.not.tgp) then do ispn=1,nspinor call zfftifc(3,ngridg,1,dwfir(:,ispn,j)) end do end if end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dwavefmt.f900000644000000000000000000000013214061636517015061 xustar0030 mtime=1623670095.578101876 30 atime=1623670094.379102989 30 ctime=1623670095.578101876 elk-7.2.42/src/dwavefmt.f900000644002504400250440000000504114061636517017116 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dwavefmt(lrstp,ias,ngp,ngpq,apwalmq,dapwalm,evecfv,devecfv,dwfmt) use modmain use modphonon implicit none ! arguments integer, intent(in) :: lrstp,ias,ngp,ngpq complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: evecfv(nmatmax),devecfv(nmatmax) real(8), intent(out) :: dwfmt(2,*) ! local variables integer is,ldi,ldo,io,ilo integer nrc,nrci,nrco,iro integer l,lm,npc,npci,i complex(8) z1 ! external functions complex(8), external :: zdotu is=idxis(ias) ldi=2*lmmaxi ldo=2*lmmaxo iro=nrmti(is)+lrstp if (lrstp.eq.1) then nrc=nrmt(is) nrci=nrmti(is) npc=npmt(is) npci=npmti(is) else nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) npci=npcmti(is) end if nrco=nrc-nrci ! zero the wavefunction derivative dwfmt(:,1:npc)=0.d0 !-----------------------! ! APW functions ! !-----------------------! do l=0,lmaxo do lm=l**2+1,(l+1)**2 i=npci+lm do io=1,apword(l,is) z1=zdotu(ngpq,devecfv,1,apwalmq(:,io,lm),1) if (ias.eq.iasph) then z1=z1+zdotu(ngp,evecfv,1,dapwalm(:,io,lm),1) end if if (abs(dble(z1)).gt.1.d-14) then if (l.le.lmaxi) then call daxpy(nrci,dble(z1),apwfr(1,1,io,l,ias),lrstp,dwfmt(1,lm),ldi) end if call daxpy(nrco,dble(z1),apwfr(iro,1,io,l,ias),lrstp,dwfmt(1,i),ldo) end if if (abs(aimag(z1)).gt.1.d-14) then if (l.le.lmaxi) then call daxpy(nrci,aimag(z1),apwfr(1,1,io,l,ias),lrstp,dwfmt(2,lm),ldi) end if call daxpy(nrco,aimag(z1),apwfr(iro,1,io,l,ias),lrstp,dwfmt(2,i),ldo) end if end do end do end do !---------------------------------! ! local-orbital functions ! !---------------------------------! do ilo=1,nlorb(is) l=lorbl(ilo,is) do lm=l**2+1,(l+1)**2 i=npci+lm z1=devecfv(ngpq+idxlo(lm,ilo,ias)) if (abs(dble(z1)).gt.1.d-14) then if (l.le.lmaxi) then call daxpy(nrci,dble(z1),lofr(1,1,ilo,ias),lrstp,dwfmt(1,lm),ldi) end if call daxpy(nrco,dble(z1),lofr(iro,1,ilo,ias),lrstp,dwfmt(1,i),ldo) end if if (abs(aimag(z1)).gt.1.d-14) then if (l.le.lmaxi) then call daxpy(nrci,aimag(z1),lofr(1,1,ilo,ias),lrstp,dwfmt(2,lm),ldi) end if call daxpy(nrco,aimag(z1),lofr(iro,1,ilo,ias),lrstp,dwfmt(2,i),ldo) end if end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/gengqvec.f900000644000000000000000000000013214061636517015043 xustar0030 mtime=1623670095.579101876 30 atime=1623670094.381102988 30 ctime=1623670095.579101876 elk-7.2.42/src/gengqvec.f900000644002504400250440000000161714061636517017105 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gengqvec(iq) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq ! local variables integer is,ig do ig=1,ngtot ! G+q-vector in Cartesian coordinates vgqc(1:3,ig)=vgc(1:3,ig)+vqc(1:3,iq) ! G+q-vector length gqc(ig)=sqrt(vgqc(1,ig)**2+vgqc(2,ig)**2+vgqc(3,ig)**2) end do ! spherical harmonics for G+q-vectors do ig=1,ngvec call genylmv(lmaxo,vgqc(:,ig),ylmgq(:,ig)) end do ! compute the spherical Bessel functions j_l(|G+q|R_mt) call genjlgprmt(lnpsd,ngvec,gqc,ngvec,jlgqrmt) ! structure factors for G+q call gensfacgp(ngvec,vgqc,ngvec,sfacgq) ! generate the smooth step function form factors for G+q do is=1,nspecies call genffacgp(is,gqc,ffacgq(:,is)) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dmatch.f900000644000000000000000000000013214061636517014504 xustar0030 mtime=1623670095.581101874 30 atime=1623670094.396102974 30 ctime=1623670095.581101874 elk-7.2.42/src/dmatch.f900000644002504400250440000000152214061636517016541 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine dmatch(ias,ip,ngp,vgpc,apwalm,dapwalm) use modmain implicit none ! arguments integer, intent(in) :: ias,ip,ngp real(8), intent(in) :: vgpc(3,ngkmax) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot) complex(8), intent(out) :: dapwalm(ngkmax,apwordmax,lmmaxapw) ! local variables integer is,l,lm,io,igp complex(8) z1 ! take derivative with respect to atomic displacement is=idxis(ias) do l=0,lmaxapw do lm=l**2+1,(l+1)**2 do io=1,apword(l,is) do igp=1,ngp z1=apwalm(igp,io,lm,ias) dapwalm(igp,io,lm)=vgpc(ip,igp)*cmplx(-aimag(z1),dble(z1),8) end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/writedvs.f900000644000000000000000000000013214061636517015113 xustar0030 mtime=1623670095.582101873 30 atime=1623670094.398102972 30 ctime=1623670095.582101873 elk-7.2.42/src/writedvs.f900000644002504400250440000000147214061636517017154 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writedvs(fext) use modmain use modphonon implicit none ! arguments character(*), intent(in) :: fext ! local variables integer is,ias ! allocatable arrays complex(8), allocatable :: zfmt(:,:,:) allocate(zfmt(lmmaxo,nrmtmax,natmtot)) open(150,file='DVS'//trim(fext),form='UNFORMATTED',action='WRITE') write(150) version write(150) nspecies write(150) lmmaxo do is=1,nspecies write(150) natoms(is) write(150) nrmt(is) end do write(150) ngridg do ias=1,natmtot is=idxis(ias) call zfmtpack(.false.,nrmt(is),nrmti(is),dvsmt(:,ias),zfmt(:,:,ias)) end do write(150) zfmt,dvsir close(150) deallocate(zfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/readdyn.f900000644000000000000000000000013114061636517014671 xustar0030 mtime=1623670095.584101871 29 atime=1623670094.40010297 30 ctime=1623670095.584101871 elk-7.2.42/src/readdyn.f900000644002504400250440000000244714061636517016736 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readdyn(dynq) use modmain use modphonon implicit none ! arguments complex(8), intent(out) :: dynq(nbph,nbph,nqpt) ! local variables logical exist integer iq,is,js,ia,ja integer ip,jp,i,j real(8) a,b character(256) fext do iq=1,nqpt i=0 do is=1,nspecies do ia=1,natoms(is) do ip=1,3 i=i+1 call dynfext(iq,is,ia,ip,fext) inquire(file='DYN'//trim(fext),exist=exist) if (.not.exist) then write(*,*) write(*,'("Error(readdyn): file not found :")') write(*,'(A)') ' DYN'//trim(fext) write(*,*) stop end if open(50,file='DYN'//trim(fext),status='OLD',form='FORMATTED') j=0 do js=1,nspecies do ja=1,natoms(js) do jp=1,3 j=j+1 read(50,*) a,b dynq(i,j,iq)=cmplx(a,b,8) end do end do end do close(50) end do ! end loops over atoms and species end do end do ! symmetrise the dynamical matrix call dynsym(vql(:,iq),dynq(:,:,iq)) ! end loop over q-vectors end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dyntask.f900000644000000000000000000000013014061636517014717 xustar0029 mtime=1623670095.58510187 30 atime=1623670094.401102969 29 ctime=1623670095.58510187 elk-7.2.42/src/dyntask.f900000644002504400250440000000276714061636517016772 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dyntask(fnum,fext) use modmain use modphonon use modmpi implicit none ! arguments integer, intent(in) :: fnum character(*), intent(out) :: fext ! local variables logical exist ! only master process should search for file if (.not.mp_mpi) goto 10 do ipph=1,3 do isph=1,nspecies do iaph=1,natoms(isph) do iqph=1,nqpt ! construct the dynamical matrix file extension call dynfext(iqph,isph,iaph,ipph,fext) ! determine if the DYN file with this extension exists inquire(file='DYN'//trim(fext),exist=exist) if (.not.exist) then open(fnum,file='DYN'//trim(fext),form='FORMATTED') iasph=idxas(iaph,isph) goto 10 end if end do end do end do end do iqph=0; isph=0; iaph=0; iasph=0; ipph=0 write(*,*) write(*,'("Info(dyntask): nothing more to do")') 10 continue ! broadcast to all other MPI processes call mpi_bcast(iqph,1,mpi_integer,0,mpicom,ierror) call mpi_bcast(isph,1,mpi_integer,0,mpicom,ierror) call mpi_bcast(iaph,1,mpi_integer,0,mpicom,ierror) call mpi_bcast(iasph,1,mpi_integer,0,mpicom,ierror) call mpi_bcast(ipph,1,mpi_integer,0,mpicom,ierror) if (iqph.eq.0) then fext='.OUT' else call dynfext(iqph,isph,iaph,ipph,fext) end if ! set the q=0 flag if (iqph.eq.1) then tphq0=.true. else tphq0=.false. end if end subroutine elk-7.2.42/src/PaxHeaders.21776/dpotks.f900000644000000000000000000000013214061636517014550 xustar0030 mtime=1623670095.587101868 30 atime=1623670094.403102967 30 ctime=1623670095.587101868 elk-7.2.42/src/dpotks.f900000644002504400250440000000305314061636517016606 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dpotks use modmain use modphonon use modomp implicit none ! local variables integer is,ias,nthd integer nr,nri,np ! automatic arrays complex(8) zfmt(npmtmax) ! convert density derivative to spherical coordinates call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(zfmt,is,nr,nri,np) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) np=npmt(is) zfmt(1:np)=drhomt(1:np,ias) call zbsht(nr,nri,zfmt,drhomt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! compute the exchange-correlation potential derivative call dpotxc ! convert density derivative to spherical harmonics call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(zfmt,is,nr,nri,np) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) np=npmt(is) zfmt(1:np)=drhomt(1:np,ias) call zfsht(nr,nri,zfmt,drhomt(:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! generate the Coulomb potential derivative call dpotcoul ! add to the Kohn-Sham potential derivative do ias=1,natmtot is=idxis(ias) np=npmt(is) dvsmt(1:np,ias)=dvsmt(1:np,ias)+dvclmt(1:np,ias) end do dvsir(1:ngtot)=dvsir(1:ngtot)+dvclir(1:ngtot) ! remove the gradient part of the potential derivative for displaced muffin-tin np=npmt(isph) dvsmt(1:np,iasph)=dvsmt(1:np,iasph)+gvsmt(1:np) end subroutine elk-7.2.42/src/PaxHeaders.21776/dpotxc.f900000644000000000000000000000013214061636517014545 xustar0030 mtime=1623670095.588101867 30 atime=1623670094.405102965 30 ctime=1623670095.588101867 elk-7.2.42/src/dpotxc.f900000644002504400250440000001110614061636517016601 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dpotxc use modmain use modphonon implicit none ! local variables integer idm,is,ias integer nr,nri,nrc,nrci integer ir,np ! allocatable arrays real(8), allocatable :: fxcmt(:,:,:,:),fxcir(:,:,:) complex(8), allocatable :: dvmt(:),dbmt(:,:),zfmt(:) ! compute the exchange-correlation kernel if (spinpol) then allocate(fxcmt(npmtmax,natmtot,4,4),fxcir(ngtot,4,4)) call genspfxcr(.false.,fxcmt,fxcir) else allocate(fxcmt(npmtmax,natmtot,1,1),fxcir(ngtot,1,1)) call genfxcr(.false.,fxcmt,fxcir) end if allocate(dvmt(npmtmax)) if (spinpol) allocate(dbmt(npmtmax,3),zfmt(npcmtmax)) !---------------------------------------! ! muffin-tin potential and field ! !---------------------------------------! ! note: muffin-tin functions are in spherical coordinates do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) nrc=nrcmt(is) nrci=nrcmti(is) np=npmt(is) ! charge-charge contribution to potential derivative dvmt(1:np)=fxcmt(1:np,ias,1,1)*drhomt(1:np,ias) ! spin-polarised case if (spinpol) then if (ncmag) then ! non-collinear ! add charge-spin contribution to potential derivative dvmt(1:np)=dvmt(1:np) & +fxcmt(1:np,ias,1,2)*dmagmt(1:np,ias,1) & +fxcmt(1:np,ias,1,3)*dmagmt(1:np,ias,2) & +fxcmt(1:np,ias,1,4)*dmagmt(1:np,ias,3) ! spin-charge contribution to B-field derivative dbmt(1:np,1)=fxcmt(1:np,ias,1,2)*drhomt(1:np,ias) dbmt(1:np,2)=fxcmt(1:np,ias,1,3)*drhomt(1:np,ias) dbmt(1:np,3)=fxcmt(1:np,ias,1,4)*drhomt(1:np,ias) ! add spin-spin contribution to B-field derivative ! (note: fxc is stored as an upper triangular matrix) dbmt(1:np,1)=dbmt(1:np,1) & +fxcmt(1:np,ias,2,2)*dmagmt(1:np,ias,1) & +fxcmt(1:np,ias,2,3)*dmagmt(1:np,ias,2) & +fxcmt(1:np,ias,2,4)*dmagmt(1:np,ias,3) dbmt(1:np,2)=dbmt(1:np,2) & +fxcmt(1:np,ias,2,3)*dmagmt(1:np,ias,1) & +fxcmt(1:np,ias,3,3)*dmagmt(1:np,ias,2) & +fxcmt(1:np,ias,3,4)*dmagmt(1:np,ias,3) dbmt(1:np,3)=dbmt(1:np,3) & +fxcmt(1:np,ias,2,4)*dmagmt(1:np,ias,1) & +fxcmt(1:np,ias,3,4)*dmagmt(1:np,ias,2) & +fxcmt(1:np,ias,4,4)*dmagmt(1:np,ias,3) else ! collinear ! add charge-spin contribution to potential derivative dvmt(1:np)=dvmt(1:np)+fxcmt(1:np,ias,1,4)*dmagmt(1:np,ias,1) ! spin-charge contribution to B-field derivative dbmt(1:np,1)=fxcmt(1:np,ias,1,4)*drhomt(1:np,ias) ! add spin-spin contribution to B-field derivative dbmt(1:np,1)=dbmt(1:np,1)+fxcmt(1:np,ias,4,4)*dmagmt(1:np,ias,1) end if end if ! convert potential derivative to spherical harmonics call zfsht(nr,nri,dvmt,dvsmt(:,ias)) ! convert magnetic field derivative to spherical harmonics on coarse mesh do idm=1,ndmag call zfmtftoc(nrc,nrci,dbmt(:,idm),zfmt) call zfsht(nrc,nrci,zfmt,dbsmt(:,ias,idm)) end do end do !------------------------------------------! ! interstitial potential and field ! !------------------------------------------! ! charge-charge contribution to potential derivative do ir=1,ngtot dvsir(ir)=fxcir(ir,1,1)*drhoir(ir) end do ! spin-polarised case if (spinpol) then if (ncmag) then ! non-collinear do ir=1,ngtot ! add charge-spin contribution to potential derivative dvsir(ir)=dvsir(ir) & +fxcir(ir,1,2)*dmagir(ir,1) & +fxcir(ir,1,3)*dmagir(ir,2) & +fxcir(ir,1,4)*dmagir(ir,3) ! spin-charge contribution to B-field derivative dbsir(ir,1)=fxcir(ir,1,2)*drhoir(ir) dbsir(ir,2)=fxcir(ir,1,3)*drhoir(ir) dbsir(ir,3)=fxcir(ir,1,4)*drhoir(ir) ! add spin-spin contribution to B-field derivative dbsir(ir,1)=dbsir(ir,1) & +fxcir(ir,2,2)*dmagir(ir,1) & +fxcir(ir,2,3)*dmagir(ir,2) & +fxcir(ir,2,4)*dmagir(ir,3) dbsir(ir,2)=dbsir(ir,2) & +fxcir(ir,2,3)*dmagir(ir,1) & +fxcir(ir,3,3)*dmagir(ir,2) & +fxcir(ir,3,4)*dmagir(ir,3) dbsir(ir,3)=dbsir(ir,3) & +fxcir(ir,2,4)*dmagir(ir,1) & +fxcir(ir,3,4)*dmagir(ir,2) & +fxcir(ir,4,4)*dmagir(ir,3) end do else ! collinear do ir=1,ngtot ! add charge-spin contribution to potential derivative dvsir(ir)=dvsir(ir)+fxcir(ir,1,4)*dmagir(ir,1) ! spin-charge contribution to B-field derivative dbsir(ir,1)=fxcir(ir,1,4)*drhoir(ir) ! add spin-spin contribution to B-field derivative dbsir(ir,1)=dbsir(ir,1)+fxcir(ir,4,4)*dmagir(ir,1) end do end if end if deallocate(fxcmt,fxcir,dvmt) if (spinpol) deallocate(dbmt,zfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/deveqnfv.f900000644000000000000000000000013214061636517015062 xustar0030 mtime=1623670095.590101865 30 atime=1623670094.406102964 30 ctime=1623670095.590101865 elk-7.2.42/src/deveqnfv.f900000644002504400250440000000712614061636517017125 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine deveqnfv(ngp,ngpq,igpig,igpqig,vgpc,vgpqc,evalfv,apwalm,apwalmq, & dapwalm,dapwalmq,evecfv,devalfvp,devecfv) use modmain use modphonon use modomp implicit none ! arguments integer, intent(in) :: ngp,ngpq integer, intent(in) :: igpig(ngkmax),igpqig(ngkmax) real(8), intent(in) :: vgpc(3,ngkmax),vgpqc(3,ngkmax) real(8), intent(in) :: evalfv(nstfv) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw,natmtot) complex(8), intent(in) :: dapwalm(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: dapwalmq(ngkmax,apwordmax,lmmaxapw) complex(8), intent(in) :: evecfv(nmatmax,nstfv) real(8), intent(out) :: devalfvp(nstfv) complex(8), intent(out) :: devecfv(nmatmax,nstfv) ! local variables integer nm,nmq,is,ias,jst,i integer lwork,info,nthd real(8) t1 complex(8) z1 ! allocatable arrays real(8), allocatable :: w(:),rwork(:) complex(8), allocatable :: h(:,:),o(:,:),dh(:,:),od(:,:) complex(8), allocatable :: x(:),y(:),work(:) ! external functions complex(8), external :: zdotc ! matrix sizes for k and k+q nm=ngp+nlotot nmq=ngpq+nlotot allocate(h(nmq,nmq),o(nmq,nmq)) ! compute the Hamiltonian and overlap matrices at p+q call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP SECTION call hmlfv(nmq,ngpq,igpqig,vgpqc,apwalmq,h) !$OMP SECTION call olpfv(nmq,ngpq,igpqig,apwalmq,o) !$OMP END PARALLEL SECTIONS call freethd(nthd) ! solve the generalised eigenvalue problem (H - e_j O)|v_j> = 0 ! (note: these are also the eigenvalues/vectors of O^(-1)H ) lwork=2*nmq allocate(w(nmq),rwork(3*nmq),work(lwork)) call zhegv(1,'V','U',nmq,h,nmq,o,nmq,w,work,lwork,rwork,info) if (info.ne.0) then write(*,*) write(*,'("Error(deveqnfv): diagonalisation failed")') write(*,'(" ZHEGV returned INFO = ",I8)') info write(*,*) stop end if deallocate(rwork,o,work) ! compute the Hamiltonian and overlap matrix derivatives allocate(dh(nmq,nm),od(nmq,nm)) call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP PRIVATE(ias,is) & !$OMP NUM_THREADS(nthd) !$OMP SECTION dh(:,:)=0.d0 do ias=1,natmtot is=idxis(ias) call dhmlaa(is,ias,ngp,ngpq,apwalm(:,:,:,ias),apwalmq(:,:,:,ias),dapwalm, & dapwalmq,nmq,dh) call dhmlalo(is,ias,ngp,ngpq,apwalm(:,:,:,ias),apwalmq(:,:,:,ias),dapwalm, & dapwalmq,nmq,dh) call dhmllolo(is,ias,ngp,ngpq,nmq,dh) end do call dhmlistl(ngp,ngpq,igpig,igpqig,vgpc,vgpqc,nmq,dh) !$OMP SECTION od(:,:)=0.d0 do ias=1,natmtot is=idxis(ias) call dolpaa(is,ias,ngp,ngpq,apwalm(:,:,:,ias),apwalmq(:,:,:,ias),dapwalm, & dapwalmq,nmq,od) call dolpalo(is,ias,ngp,ngpq,dapwalm,dapwalmq,nmq,od) end do call dolpistl(ngp,ngpq,igpig,igpqig,nmq,od) !$OMP END PARALLEL SECTIONS call freethd(nthd) allocate(x(nmq),y(nmq)) ! loop over states do jst=1,nstfv ! compute |dv_j> = V(e_j - D)^(-1)V† (dH - e_j dO)|v_j> z1=-evalfv(jst) call zgemv('N',nmq,nm,z1,od,nmq,evecfv(:,jst),1,zzero,x,1) call zgemv('N',nmq,nm,zone,dh,nmq,evecfv(:,jst),1,zone,x,1) ! compute the first-order change in eigenvalue if (tphq0) then z1=zdotc(nmq,evecfv(:,jst),1,x,1) devalfvp(jst)=dble(z1) else devalfvp(jst)=0.d0 end if call zgemv('C',nmq,nmq,zone,h,nmq,x,1,zzero,y,1) do i=1,nmq t1=evalfv(jst)-w(i) if (abs(t1).gt.epsdev) then y(i)=y(i)/t1 else y(i)=0.d0 end if end do call zgemv('N',nmq,nmq,zone,h,nmq,y,1,zzero,devecfv(:,jst),1) end do deallocate(w,h,dh,od,x,y) end subroutine elk-7.2.42/src/PaxHeaders.21776/dpotcoul.f900000644000000000000000000000013214061636517015075 xustar0030 mtime=1623670095.591101864 30 atime=1623670094.408102963 30 ctime=1623670095.591101864 elk-7.2.42/src/dpotcoul.f900000644002504400250440000000155414061636517017137 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dpotcoul use modmain use modphonon implicit none ! local variables integer np ! automatic arrays complex(8) gzfmt(npmtmax,3) ! solve the complex Poisson's equation in the muffin-tins call genzvclmt(nrmt,nrmti,nrmtmax,rlmt,wprmt,npmtmax,drhomt,dvclmt) ! calculate the gradient of the nuclear potential call gradzvcln(isph,gzfmt) ! subtract gradient component corresponding to the phonon polarisation np=npmt(isph) dvclmt(1:np,iasph)=dvclmt(1:np,iasph)-gzfmt(1:np,ipph) ! solve Poisson's equation in the entire unit cell call zpotcoul(nrmt,nrmti,npmt,npmti,nrmtmax,rlmt,ngridg,igfft,ngvec,gqc,gclgq, & ngvec,jlgqrmt,ylmgq,sfacgq,drhoir,npmtmax,dvclmt,dvclir) end subroutine elk-7.2.42/src/PaxHeaders.21776/drhomagk.f900000644000000000000000000000013214061636517015040 xustar0030 mtime=1623670095.593101863 30 atime=1623670094.410102961 30 ctime=1623670095.593101863 elk-7.2.42/src/drhomagk.f900000644002504400250440000001533114061636517017100 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine drhomagk(ngp,ngpq,igpig,igpqig,occsvp,doccsvp,apwalm,apwalmq, & dapwalm,evecfv,devecfv,evecsv,devecsv) use modmain use modphonon implicit none ! arguments integer, intent(in) :: ngp(nspnfv),ngpq(nspnfv) integer, intent(in) :: igpig(ngkmax,nspnfv),igpqig(ngkmax,nspnfv) real(8), intent(in) :: occsvp(nstsv),doccsvp(nstsv) complex(8), intent(in) :: apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv) complex(8), intent(in) :: apwalmq(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv) complex(8), intent(in) :: dapwalm(ngkmax,apwordmax,lmmaxapw,nspnfv) complex(8), intent(in) :: evecfv(nmatmax,nstfv,nspnfv) complex(8), intent(in) :: devecfv(nmatmax,nstfv,nspnfv) complex(8), intent(in) :: evecsv(nstsv,nstsv),devecsv(nstsv,nstsv) ! local variables integer nst,ist,jst integer is,ias,npc real(8) wo,dwo ! automatic arrays integer idx(nstsv) ! allocatable arrays complex(8), allocatable :: wfmt(:,:,:,:),wfir(:,:,:) complex(8), allocatable :: dwfmt(:,:,:,:),dwfir(:,:,:) ! count and index the occupied states nst=0 do ist=1,nstsv if (abs(occsvp(ist)).gt.epsocc) then nst=nst+1 idx(nst)=ist end if end do ! generate the wavefunctions allocate(wfmt(npcmtmax,natmtot,nspinor,nst),wfir(ngtot,nspinor,nst)) call genwfsv(.false.,.false.,nst,idx,ngridg,igfft,ngp,igpig,apwalm,evecfv, & evecsv,wfmt,ngtot,wfir) ! generate the wavefunction derivatives allocate(dwfmt(npcmtmax,natmtot,nspinor,nst),dwfir(ngtot,nspinor,nst)) call gendwfsv(.false.,.false.,nst,idx,ngp,ngpq,igpqig,apwalmq,dapwalm,evecfv, & devecfv,evecsv,devecsv,dwfmt,ngtot,dwfir) ! loop over occupied states do ist=1,nst jst=idx(ist) wo=2.d0*wkptnr*occsvp(jst) dwo=wkptnr*doccsvp(jst) !----------------------------------------------! ! muffin-tin density and magnetisation ! !----------------------------------------------! do ias=1,natmtot is=idxis(ias) npc=npcmt(is) !$OMP CRITICAL(drhomagk_1) if (spinpol) then ! spin-polarised if (ncmag) then ! non-collinear call drmk1(npc,wo,wfmt(:,ias,1,jst),wfmt(:,ias,2,jst), & dwfmt(:,ias,1,jst),dwfmt(:,ias,2,jst),drhomt(:,ias),dmagmt(:,ias,1), & dmagmt(:,ias,2),dmagmt(:,ias,3)) if (tphq0) then call drmk01(npc,dwo,wfmt(:,ias,1,jst),wfmt(:,ias,2,jst), & drhomt(:,ias),dmagmt(:,ias,1),dmagmt(:,ias,2),dmagmt(:,ias,3)) end if else ! collinear call drmk2(npc,wo,wfmt(:,ias,1,jst),wfmt(:,ias,2,jst), & dwfmt(:,ias,1,jst),dwfmt(:,ias,2,jst),drhomt(:,ias),dmagmt(:,ias,1)) if (tphq0) then call drmk02(npc,dwo,wfmt(:,ias,1,jst),wfmt(:,ias,2,jst), & drhomt(:,ias),dmagmt(:,ias,1)) end if end if else ! spin-unpolarised call drmk3(npc,wo,wfmt(:,ias,1,jst),dwfmt(:,ias,1,jst),drhomt(:,ias)) if (tphq0) then call drmk03(npc,dwo,wfmt(:,ias,1,jst),drhomt(:,ias)) end if end if !$OMP END CRITICAL(drhomagk_1) !****** use lock end do !------------------------------------------------! ! interstitial density and magnetisation ! !------------------------------------------------! !$OMP CRITICAL(drhomagk_2) if (spinpol) then ! spin-polarised if (ncmag) then call drmk1(ngtot,wo,wfir(:,1,jst),wfir(:,2,jst),dwfir(:,1,jst), & dwfir(:,2,jst),drhoir,dmagir,dmagir(:,2),dmagir(:,3)) if (tphq0) then call drmk01(ngtot,dwo,wfir(:,1,jst),wfir(:,2,jst),drhoir,dmagir, & dmagir(:,2),dmagir(:,3)) end if else ! collinear call drmk2(ngtot,wo,wfir(:,1,jst),wfir(:,2,jst),dwfir(:,1,jst), & dwfir(:,2,jst),drhoir,dmagir) if (tphq0) then call drmk02(ngtot,dwo,wfir(:,1,jst),wfir(:,2,jst),drhoir,dmagir) end if end if else ! spin-unpolarised call drmk3(ngtot,wo,wfir(:,1,jst),dwfir(:,1,jst),drhoir) if (tphq0) then call drmk03(ngtot,dwo,wfir(:,1,jst),drhoir) end if end if !$OMP END CRITICAL(drhomagk_2) ! end loop over states end do deallocate(wfmt,wfir,dwfmt,dwfir) return contains pure subroutine drmk1(n,wo,wf1,wf2,dwf1,dwf2,drho,dmag1,dmag2,dmag3) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf1(n),wf2(n) complex(8), intent(in) :: dwf1(n),dwf2(n) complex(8), intent(inout) :: drho(n) complex(8), intent(inout) :: dmag1(n),dmag2(n),dmag3(n) ! local variables integer i complex(8) z1,z2,z3,z4,z5,z6 do i=1,n z1=conjg(wf1(i)) z2=conjg(wf2(i)) z3=dwf1(i) z4=dwf2(i) z5=z1*z3 z6=z2*z4 drho(i)=drho(i)+wo*(z5+z6) dmag3(i)=dmag3(i)+wo*(z5-z6) z5=z1*z4 z6=z2*z3 dmag1(i)=dmag1(i)+wo*(z5+z6) z5=z5-z6 dmag2(i)=dmag2(i)+wo*cmplx(aimag(z5),-dble(z5),8) end do end subroutine pure subroutine drmk01(n,dwo,wf1,wf2,drho,dmag1,dmag2,dmag3) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: dwo complex(8), intent(in) :: wf1(n),wf2(n) complex(8), intent(inout) :: drho(n) complex(8), intent(inout) :: dmag1(n),dmag2(n),dmag3(n) ! local variables integer i real(8) t1,t2 complex(8) z1,z2 do i=1,n z1=wf1(i) z2=wf2(i) t1=dble(z1)**2+aimag(z1)**2 t2=dble(z2)**2+aimag(z2)**2 z1=conjg(z1)*z2 drho(i)=drho(i)+dwo*(t1+t2) dmag1(i)=dmag1(i)+dwo*2.d0*dble(z1) dmag2(i)=dmag2(i)+dwo*2.d0*aimag(z1) dmag3(i)=dmag3(i)+dwo*(t1-t2) end do !******* speed up: see rhomagk end subroutine pure subroutine drmk2(n,wo,wf1,wf2,dwf1,dwf2,drho,dmag) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf1(n),wf2(n) complex(8), intent(in) :: dwf1(n),dwf2(n) complex(8), intent(inout) :: drho(n),dmag(n) ! local variables integer i complex(8) z1,z2 do i=1,n z1=conjg(wf1(i))*dwf1(i) z2=conjg(wf2(i))*dwf2(i) drho(i)=drho(i)+wo*(z1+z2) dmag(i)=dmag(i)+wo*(z1-z2) end do end subroutine pure subroutine drmk02(n,dwo,wf1,wf2,drho,dmag) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: dwo complex(8), intent(in) :: wf1(n),wf2(n) complex(8), intent(inout) :: drho(n),dmag(n) ! local variables integer i real(8) t1,t2 do i=1,n t1=dble(wf1(i))**2+aimag(wf1(i))**2 t2=dble(wf2(i))**2+aimag(wf2(i))**2 drho(i)=drho(i)+dwo*(t1+t2) dmag(i)=dmag(i)+dwo*(t1-t2) end do end subroutine pure subroutine drmk3(n,wo,wf,dwf,drho) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf(n),dwf(n) complex(8), intent(inout) :: drho(n) drho(:)=drho(:)+wo*conjg(wf(:))*dwf(:) end subroutine pure subroutine drmk03(n,dwo,wf,drho) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: dwo complex(8), intent(in) :: wf(n) complex(8), intent(inout) :: drho(n) drho(:)=drho(:)+dwo*(dble(wf(:))**2+aimag(wf(:))**2) end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/gengvsmt.f900000644000000000000000000000013114061636517015075 xustar0030 mtime=1623670095.594101862 29 atime=1623670094.41110296 30 ctime=1623670095.594101862 elk-7.2.42/src/gengvsmt.f900000644002504400250440000000135614061636517017140 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gengvsmt use modmain use modphonon implicit none ! local variables integer nr,nri,np ! allocatable arrays complex(8), allocatable :: zfmt(:),gzfmt(:,:) allocate(zfmt(npmtmax),gzfmt(npmtmax,3)) nr=nrmt(isph) nri=nrmti(isph) np=npmt(isph) ! convert potential to complex spherical harmonics call rtozfmt(nr,nri,vsmt(:,iasph),zfmt) ! calculate the gradient call gradzfmt(nr,nri,rlmt(:,-1,isph),wcrmt(:,:,isph),zfmt,npmtmax,gzfmt) ! copy current polarisation component to global array gvsmt(1:np)=gzfmt(1:np,ipph) deallocate(zfmt,gzfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/dforce.f900000644000000000000000000000013014061636517014504 xustar0029 mtime=1623670095.59610186 30 atime=1623670094.413102958 29 ctime=1623670095.59610186 elk-7.2.42/src/dforce.f900000644002504400250440000001150614061636517016546 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dforce(dyn) use modmain use modphonon use modomp implicit none ! arguments complex(8), intent(out) :: dyn(3,natmtot) ! local variables integer ik,is,ias,nthd integer nr,nri,ir,np,i complex(8) z1 ! allocatable arrays complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: grhomt(:,:,:),grhoir(:,:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) complex(8), allocatable :: gvclmt(:,:,:),gvclir(:,:) complex(8), allocatable :: zfmt(:),gzfmt(:,:) ! external functions complex(8), external :: zfmtinp allocate(zrhomt(npmtmax,natmtot),zrhoir(ngtot)) allocate(grhomt(npmtmax,natmtot,3),grhoir(ngtot,3)) allocate(zvclmt(npmtmax,natmtot),zvclir(ngtot)) allocate(gvclmt(npmtmax,natmtot,3),gvclir(ngtot,3)) allocate(zfmt(npmtmax),gzfmt(npmtmax,3)) ! make complex copy of the density do ias=1,natmtot is=idxis(ias) call rtozfmt(nrmt(is),nrmti(is),rhomt(:,ias),zrhomt(:,ias)) end do zrhoir(:)=rhoir(:) ! compute the gradient of the density call gradzf(zrhomt,zrhoir,grhomt,grhoir) !--------------------------------------------------------------! ! Hellmann-Feynman force derivative for displaced atom ! !--------------------------------------------------------------! nr=nrmt(isph) nri=nrmti(isph) np=npmt(isph) ! calculate the gradient of the nuclear potential call gradzvcln(isph,gzfmt) ! compute the q-dependent nuclear Coulomb potential derivative zvclmt(:,:)=0.d0 zvclmt(1:np,iasph)=gzfmt(1:np,ipph) tphdyn=.true. ! zero the interstitial density zrhoir(:)=0.d0 call zpotcoul(nrmt,nrmti,npmt,npmti,nrmtmax,rlmt,ngridg,igfft,ngvec,gqc,gclgq, & ngvec,jlgqrmt,ylmgq,sfacgq,zrhoir,npmtmax,zvclmt,zvclir) zfmt(1:np)=zvnmt(1:np) ! multiply with density derivative and integrate z1=0.d0 do ir=1,ngtot z1=z1+cfunir(ir)*conjg(zvclir(ir))*drhoir(ir) end do z1=z1*omega/dble(ngtot) do ias=1,natmtot is=idxis(ias) z1=z1+zfmtinp(nrmt(is),nrmti(is),wrmt(:,is),zvclmt(:,ias),drhomt(:,ias)) end do dyn(ipph,iasph)=-z1 ! compute the lattice-periodic nuclear Coulomb potential derivative zvclmt(:,:)=0.d0 zvclmt(1:np,iasph)=gzfmt(1:np,ipph) call zpotcoul(nrmt,nrmti,npmt,npmti,nrmtmax,rlmt,ngridg,igfft,ngvec,gc,gclg, & ngvec,jlgrmt,ylmg,sfacg,zrhoir,npmtmax,zvclmt,zvclir) tphdyn=.false. ! multiply with density gradient and integrate z1=0.d0 do ir=1,ngtot z1=z1+cfunir(ir)*zvclir(ir)*grhoir(ir,ipph) end do z1=z1*omega/dble(ngtot) do ias=1,natmtot is=idxis(ias) z1=z1+zfmtinp(nrmt(is),nrmti(is),wrmt(:,is),zvclmt(:,ias),grhomt(:,ias,ipph)) end do dyn(ipph,iasph)=dyn(ipph,iasph)-z1 ! nuclear-nuclear term zvclmt(1:np,iasph)=zvnmt(1:np)-zfmt(1:np) call gradzf(zvclmt,zvclir,gvclmt,gvclir) do ias=1,natmtot is=idxis(ias) z1=spzn(is)*gvclmt(1,ias,ipph)*y00 dyn(ipph,iasph)=dyn(ipph,iasph)+z1 end do !-------------------------------------------------------------------! ! Hellmann-Feynman force derivative for non-displaced atoms ! !-------------------------------------------------------------------! do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) np=npmt(is) ! remove the gradient part of the Coulomb potential for displaced muffin-tin if (ias.eq.iasph) then call rtozfmt(nr,nri,vclmt(:,ias),zfmt) call gradzfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),zfmt,npmtmax,gzfmt) dvclmt(1:np,ias)=dvclmt(1:np,ias)+gzfmt(1:np,ipph) end if ! compute the gradient of the Coulomb potential derivative at the nucleus call gradzfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),dvclmt(:,ias),npmtmax,gzfmt) do i=1,3 if ((ias.eq.iasph).and.(i.eq.ipph)) cycle dyn(i,ias)=spzn(is)*gzfmt(1,i)*y00 end do end do !--------------------------------------------! ! IBS correction to force derivative ! !--------------------------------------------! ! k-point dependent part call holdthd(nkptnr,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkptnr call dforcek(ik,dyn) end do !$OMP END PARALLEL DO call freethd(nthd) ! k-point independent part do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) np=npmt(is) do i=1,3 z1=zfmtinp(nr,nri,wrmt(:,is),grhomt(:,ias,i),dvsmt(:,ias)) dyn(i,ias)=dyn(i,ias)-z1 end do ! remove the gradient part from the density derivative for displaced muffin-tin if (ias.eq.iasph) then drhomt(1:np,ias)=drhomt(1:np,ias)+grhomt(1:np,ias,ipph) end if ! compute the gradient of the density derivative call gradzfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),drhomt(:,ias),npmtmax,gzfmt) ! convert Kohn-Sham potential to complex spherical harmonics call rtozfmt(nr,nri,vsmt(:,ias),zfmt) do i=1,3 z1=zfmtinp(nr,nri,wrmt(:,is),zfmt,gzfmt(:,i)) dyn(i,ias)=dyn(i,ias)-z1 end do end do deallocate(zrhomt,zrhoir,grhomt,grhoir) deallocate(zvclmt,zvclir,gvclmt,gvclir,zfmt,gzfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/dforcek.f900000644000000000000000000000013214061636517014661 xustar0030 mtime=1623670095.597101859 30 atime=1623670094.415102956 30 ctime=1623670095.597101859 elk-7.2.42/src/dforcek.f900000644002504400250440000002400014061636517016712 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dforcek(ik,dyn) use modmain use modphonon use modpw implicit none ! arguments integer, intent(in) :: ik complex(8), intent(inout) :: dyn(3,natmtot) ! local variables integer ispn0,ispn1,ispn,jspn integer n,nq,nm,nmq,nm2 integer is,ias,ist,jst,jk integer iv(3),ig,i,j,k,l real(8) t1 complex(8) z1,z2,dt1,dz1,dz2 ! automatic arrays real(8) evalfv(nstfv,nspnfv) complex(8) vh(nmatmax),vo(nmatmax),dvh(nmatmax),dvo(nmatmax) complex(8) ffv(nstfv,nstfv),dffv(nstfv,nstfv),y(nstfv),dy(nstfv) ! allocatable arrays integer, allocatable :: ijg(:,:),ijgq(:,:) real(8), allocatable :: dp(:,:),dpq(:,:) complex(8), allocatable :: apwalm(:,:,:,:),apwalmq(:,:,:,:),dapwalm(:,:,:) complex(8), allocatable :: evecfv(:,:,:),devecfv(:,:,:) complex(8), allocatable :: evecsv(:,:),devecsv(:,:) complex(8), allocatable :: h(:),o(:),dlh(:),dlo(:) complex(8), allocatable :: hq(:,:),oq(:,:),dh(:,:),od(:,:) complex(8), allocatable :: dlhq(:,:),dloq(:,:),ddlh(:,:),ddlo(:,:) ! external functions complex(8), external :: zdotc nm2=nmatmax**2 ! allocate local arrays allocate(ijg(nmatmax,nmatmax),ijgq(nmatmax,nmatmax)) allocate(dp(nmatmax,nmatmax),dpq(nmatmax,nmatmax)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(apwalmq(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(dapwalm(ngkmax,apwordmax,lmmaxapw)) allocate(evecfv(nmatmax,nstfv,nspnfv)) allocate(devecfv(nmatmax,nstfv,nspnfv)) allocate(h(nm2),o(nm2),dlh(nm2),dlo(nm2)) allocate(hq(nmatmax,nmatmax),oq(nmatmax,nmatmax)) allocate(dh(nmatmax,nmatmax),od(nmatmax,nmatmax)) allocate(dlhq(nmatmax,nmatmax),dloq(nmatmax,nmatmax)) allocate(ddlh(nmatmax,nmatmax),ddlo(nmatmax,nmatmax)) ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! get the eigenvalues/vectors from file call getevalfv(filext,0,vkl(:,ik),evalfv) call getevecfv(filext,0,vkl(:,ik),vgkl(:,:,:,ik),evecfv) ! get the eigenvalue/vector derivatives from file call getdevecfv(ik,iqph,isph,iaph,ipph,devecfv) if (tevecsv) then allocate(evecsv(nstsv,nstsv),devecsv(nstsv,nstsv)) call getevecsv(filext,0,vkl(:,ik),evecsv) call getdevecsv(ik,iqph,isph,iaph,ipph,devecsv) end if ! loop over first-variational spin components do jspn=1,nspnfv if (spinsprl) then ispn0=jspn; ispn1=jspn else ispn0=1; ispn1=nspinor end if n=ngk(jspn,ik) nq=ngkq(jspn,ik) nm=n+nlotot nmq=nq+nlotot do j=1,n do i=1,n iv(:)=ivg(:,igkig(i,jspn,ik))-ivg(:,igkig(j,jspn,ik)) iv(:)=modulo(iv(:)-intgv(1,:),ngridg(:))+intgv(1,:) ijg(i,j)=ivgig(iv(1),iv(2),iv(3)) dp(i,j)=0.5d0*dot_product(vgkc(1:3,i,jspn,ik),vgkc(1:3,j,jspn,ik)) end do end do do j=1,n do i=1,nq iv(:)=ivg(:,igkqig(i,jspn,ik))-ivg(:,igkig(j,jspn,ik)) iv(:)=modulo(iv(:)-intgv(1,:),ngridg(:))+intgv(1,:) ijgq(i,j)=ivgig(iv(1),iv(2),iv(3)) dpq(i,j)=0.5d0*dot_product(vgkqc(1:3,i,jspn,ik),vgkc(1:3,j,jspn,ik)) end do end do ! find the matching coefficients call match(n,vgkc(:,:,jspn,ik),gkc(:,jspn,ik),sfacgk(:,:,jspn,ik),apwalm) call match(nq,vgkqc(:,:,jspn,ik),gkqc(:,jspn,ik),sfacgkq(:,:,jspn,ik), & apwalmq) ! find the matching coefficient derivatives call dmatch(iasph,ipph,n,vgkc(:,:,jspn,ik),apwalm,dapwalm) ! loop over species and atoms do ias=1,natmtot is=idxis(ias) ! Hamiltonian and overlap matrices h(:)=0.d0 call hmlaa(.false.,is,ias,n,apwalm(:,:,:,ias),nm,h) call hmlalo(is,ias,n,apwalm(:,:,:,ias),nm,h) o(:)=0.d0 call olpaa(.false.,is,n,apwalm(:,:,:,ias),nm,o) call olpalo(is,ias,n,apwalm(:,:,:,ias),nm,o) hq(:,:)=0.d0 call hmlaaq(is,ias,n,nq,apwalm(:,:,:,ias),apwalmq(:,:,:,ias),nmatmax,hq) call hmlaloq(is,ias,n,nq,apwalm(:,:,:,ias),apwalmq(:,:,:,ias),nmatmax,hq) oq(:,:)=0.d0 call olpaaq(is,n,nq,apwalm(:,:,:,ias),apwalmq(:,:,:,ias),nmatmax,oq) call olpaloq(is,ias,n,nq,apwalm(:,:,:,ias),apwalmq(:,:,:,ias),nmatmax,oq) ! Hamiltonian and overlap derivatives dh(:,:)=0.d0 call dhmlaa(is,ias,n,n,apwalm(:,:,:,ias),apwalm(:,:,:,ias),dapwalm,dapwalm,& nmatmax,dh) call dhmlalo(is,ias,n,n,apwalm(:,:,:,ias),apwalm(:,:,:,ias),dapwalm, & dapwalm,nmatmax,dh) od(:,:)=0.d0 call dolpaa(is,ias,n,n,apwalm(:,:,:,ias),apwalm(:,:,:,ias),dapwalm,dapwalm,& nmatmax,od) call dolpalo(is,ias,n,n,dapwalm,dapwalm,nmatmax,od) ! loop over Cartesian directions do l=1,3 ! APW-APW contribution do j=1,n k=(j-1)*nm do i=1,j k=k+1 ig=ijg(i,j) t1=vgc(l,ig) z1=-ffacg(ig,is)*conjg(sfacg(ig,ias)) z2=t1*(dp(i,j)*z1+h(k)) dlh(k)=cmplx(-aimag(z2),dble(z2),8) z2=t1*(z1+o(k)) dlo(k)=cmplx(-aimag(z2),dble(z2),8) end do end do do j=n+1,nm k=(j-1)*nm ! APW-local-orbital contribution do i=1,n k=k+1 t1=vgkc(l,i,jspn,ik) z1=t1*h(k) dlh(k)=cmplx(-aimag(z1),dble(z1),8) z1=t1*o(k) dlo(k)=cmplx(-aimag(z1),dble(z1),8) end do ! zero the local-orbital-local-orbital contribution do i=n+1,j k=k+1 dlh(k)=0.d0 dlo(k)=0.d0 end do end do ! non-square H/O(G+k+q,G'+k) matrices ! APW-APW contribution do j=1,n do i=1,nq ig=ijgq(i,j) t1=vgqc(l,ig) z1=-ffacgq(ig,is)*conjg(sfacgq(ig,ias)) z2=t1*(dpq(i,j)*z1+hq(i,j)) dlhq(i,j)=cmplx(-aimag(z2),dble(z2),8) z2=t1*(z1+oq(i,j)) dloq(i,j)=cmplx(-aimag(z2),dble(z2),8) end do ! local-orbital-APW derivative t1=-vgkc(l,j,jspn,ik) do i=nq+1,nmq z1=t1*hq(i,j) dlhq(i,j)=cmplx(-aimag(z1),dble(z1),8) z1=t1*oq(i,j) dloq(i,j)=cmplx(-aimag(z1),dble(z1),8) end do end do do j=n+1,nm ! APW-local-orbital contribution do i=1,nq t1=vgkqc(l,i,jspn,ik) z1=t1*hq(i,j) dlhq(i,j)=cmplx(-aimag(z1),dble(z1),8) z1=t1*oq(i,j) dloq(i,j)=cmplx(-aimag(z1),dble(z1),8) end do ! zero the local-orbital-local-orbital contribution do i=nq+1,nmq dlhq(i,j)=0.d0 dloq(i,j)=0.d0 end do end do ! APW-APW derivative do j=1,n do i=1,n ig=ijg(i,j) t1=vgc(l,ig) if (ias.eq.iasph) then z1=-ffacg(ig,is)*conjg(sfacg(ig,ias)) dz1=vgc(ipph,ig)*cmplx(aimag(z1),-dble(z1),8) else dz1=0.d0 end if z2=t1*(dp(i,j)*dz1+dh(i,j)) ddlh(i,j)=cmplx(-aimag(z2),dble(z2),8) z2=t1*(dz1+od(i,j)) ddlo(i,j)=cmplx(-aimag(z2),dble(z2),8) end do ! local-orbital-APW derivative t1=-vgkc(l,j,jspn,ik) do i=n+1,nm z1=t1*dh(i,j) ddlh(i,j)=cmplx(-aimag(z1),dble(z1),8) z1=t1*od(i,j) ddlo(i,j)=cmplx(-aimag(z1),dble(z1),8) end do end do ! APW-local-orbital derivative do j=n+1,nm do i=1,n t1=vgkc(l,i,jspn,ik) z1=t1*dh(i,j) ddlh(i,j)=cmplx(-aimag(z1),dble(z1),8) z1=t1*od(i,j) ddlo(i,j)=cmplx(-aimag(z1),dble(z1),8) end do ! zero the local-orbital-local-orbital derivative do i=n+1,nm ddlh(i,j)=0.d0 ddlo(i,j)=0.d0 end do end do if (tphq0) then ! compute the force matrix elements in the first-variational basis do jst=1,nstfv call zhemv('U',nm,zone,dlh,nm,evecfv(:,jst,jspn),1,zzero,vh,1) call zhemv('U',nm,zone,dlo,nm,evecfv(:,jst,jspn),1,zzero,vo,1) t1=evalfv(jst,jspn) do ist=1,nstfv z1=zdotc(nm,evecfv(:,ist,jspn),1,vh,1) z2=zdotc(nm,evecfv(:,ist,jspn),1,vo,1) ffv(ist,jst)=z1-t1*z2 end do end do end if ! compute the force derivative matrix elements in the first-variational basis dffv(:,:)=0.d0 do jst=1,nstfv call zhemv('U',nm,zone,dlo,nm,evecfv(:,jst,jspn),1,zzero,vo,1) call zgemv('N',nm,nm,zone,ddlh,nmatmax,evecfv(:,jst,jspn),1,zzero,dvh,1) call zgemv('N',nm,nm,zone,ddlo,nmatmax,evecfv(:,jst,jspn),1,zzero,dvo,1) t1=evalfv(jst,jspn) dt1=devalfv(jst,jspn,ik) do ist=1,nstfv z2=zdotc(nm,evecfv(:,ist,jspn),1,vo,1) dz1=zdotc(nm,evecfv(:,ist,jspn),1,dvh,1) dz2=zdotc(nm,evecfv(:,ist,jspn),1,dvo,1) dffv(ist,jst)=dffv(ist,jst)+dz1-dt1*z2-t1*dz2 end do call zgemv('C',nmq,nm,zone,dlhq,nmatmax,devecfv(:,jst,jspn),1,zzero, & dvh,1) call zgemv('C',nmq,nm,zone,dloq,nmatmax,devecfv(:,jst,jspn),1,zzero, & dvo,1) do ist=1,nstfv dz1=2.d0*zdotc(nm,evecfv(:,ist,jspn),1,dvh,1) dz2=2.d0*zdotc(nm,evecfv(:,ist,jspn),1,dvo,1) dffv(ist,jst)=dffv(ist,jst)+dz1-t1*dz2 end do end do z1=0.d0 if (tevecsv) then ! spin-polarised case do j=1,nstsv do ispn=ispn0,ispn1 i=(ispn-1)*nstfv+1 call zgemv('N',nstfv,nstfv,zone,ffv,nstfv,evecsv(i,j),1,zzero,y,1) call zgemv('N',nstfv,nstfv,zone,dffv,nstfv,evecsv(i,j),1,zzero,dy,1) call zgemv('N',nstfv,nstfv,zone,ffv,nstfv,devecsv(i,j),1,zone,dy,1) dz1=zdotc(nstfv,evecsv(i,j),1,dy,1) dz1=dz1+zdotc(nstfv,devecsv(i,j),1,y,1) z1=z1+occsv(j,jk)*dz1 !******** doccsv end do end do else ! spin-unpolarised case do j=1,nstsv z1=z1+occsv(j,jk)*dffv(j,j) if (tphq0) then z1=z1+doccsv(j,ik)*dble(ffv(j,j)) end if end do end if !$OMP ATOMIC dyn(l,ias)=dyn(l,ias)-wkptnr*z1 ! end loop over Cartesian components end do ! end loop over atoms and species end do ! end loop over first-variational spins end do deallocate(ijg,ijgq,dp,dpq) deallocate(apwalm,apwalmq,dapwalm) deallocate(evecfv,devecfv) deallocate(h,o,dlh,dlo,hq,oq,dh,od) deallocate(dlhq,dloq,ddlh,ddlo) if (tevecsv) deallocate(evecsv,devecsv) end subroutine elk-7.2.42/src/PaxHeaders.21776/dynqtor.f900000644000000000000000000000013214061636517014744 xustar0030 mtime=1623670095.599101857 30 atime=1623670094.417102954 30 ctime=1623670095.599101857 elk-7.2.42/src/dynqtor.f900000644002504400250440000000426214061636517017005 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dynqtor(dynq,dynr) use modmain use modphonon implicit none ! arguments complex(8), intent(in) :: dynq(nbph,nbph,nqpt) complex(8), intent(out) :: dynr(nbph,nbph,nqptnr) ! local variables integer ir,iq,i,j,n integer isym,lspl,intr(2,3) integer i1,i2,i3,j1,j2,j3 real(8) v1(3),v2(3),v3(3) real(8) s(3,3),t1 complex(8) z1 ! automatic arrays complex(8) dyns(nbph,nbph) intr(2,:)=ngridq(:)/2 intr(1,:)=intr(2,:)-ngridq(:)+1 dynr(:,:,:)=0.d0 ! loop over q-vectors do j1=0,ngridq(1)-1 v1(1)=dble(j1)/dble(ngridq(1)) do j2=0,ngridq(2)-1 v1(2)=dble(j2)/dble(ngridq(2)) do j3=0,ngridq(3)-1 v1(3)=dble(j3)/dble(ngridq(3)) iq=ivqiq(j1,j2,j3) ! map v1 to the first Brillouin zone v2(:)=v1(:) call vecfbz(epslat,bvec,v2) ! rotate and add the dynamical matrix of the reduced q-point with all symmetries n=0 dyns(:,:)=0.d0 do isym=1,nsymcrys lspl=lsplsymc(isym) s(:,:)=dble(symlat(:,:,lspl)) call r3mtv(s,vql(:,iq),v3) call vecfbz(epslat,bvec,v3) t1=abs(v2(1)-v3(1))+abs(v2(2)-v3(2))+abs(v2(3)-v3(3)) if (t1.lt.epslat) then call dynsymapp(isym,vql(:,iq),dynq(:,:,iq),dyns) n=n+1 end if end do if (n.eq.0) then write(*,*) write(*,'("Error(dynqtor): vector ",3G18.10)') v1 write(*,'(" cannot be mapped to reduced q-point set")') write(*,*) stop end if t1=1.d0/dble(n) dyns(:,:)=t1*dyns(:,:) ! loop over R-vectors ir=0 do i3=intr(1,3),intr(2,3) do i2=intr(1,2),intr(2,2) do i1=intr(1,1),intr(2,1) ir=ir+1 t1=twopi*(v1(1)*dble(i1)+v1(2)*dble(i2)+v1(3)*dble(i3)) z1=cmplx(cos(t1),sin(t1),8) do i=1,nbph do j=1,nbph dynr(i,j,ir)=dynr(i,j,ir)+z1*dyns(i,j) end do end do end do end do end do end do end do end do t1=1.d0/dble(nqptnr) dynr(:,:,:)=t1*dynr(:,:,:) end subroutine elk-7.2.42/src/PaxHeaders.21776/dynevs.f900000644000000000000000000000013214061636517014554 xustar0030 mtime=1623670095.600101856 30 atime=1623670094.418102953 30 ctime=1623670095.600101856 elk-7.2.42/src/dynevs.f900000644002504400250440000000152614061636517016615 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dynevs(ev,a,w) use modmain use modphonon implicit none ! arguments complex(8), intent(in) :: ev(nbph,nbph) complex(8), intent(in) :: a(nbph,nbph) real(8), intent(out) :: w(nbph) ! local variables integer i,j,k real(8) t1,t2 complex(8) z1 ! automatic arrays real(8) wt(nbph) ! find the eigenvalues and eigenvectors of the matrix a call eveqnzh(nbph,nbph,a,w) ! reorder eigenvalues so that the eigenvectors maximally overlap with ev wt(:)=w(:) do i=1,nbph j=1 t1=0.d0 do k=1,nbph z1=dot_product(ev(:,i),a(:,k)) t2=dble(z1)**2+aimag(z1)**2 if (t2.gt.t1) then j=k t1=t2 end if end do w(i)=wt(j) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/phonon.f900000644000000000000000000000013214061636517014545 xustar0030 mtime=1623670095.602101854 30 atime=1623670094.420102951 30 ctime=1623670095.602101854 elk-7.2.42/src/phonon.f900000644002504400250440000002267714061636517016620 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine phonon use modmain use modphonon use modpw use modmpi use modomp use moddelf implicit none ! local variables integer ik,jk,iv(3),jspn,idm integer is,ia,ias,ip,nthd integer nmix,nwork,n,lp ! use Broyden mixing only integer, parameter :: mtype=3 real(8) ddv,a,b character(256) fext ! allocatable arrays real(8), allocatable :: evalfv(:,:),work(:) complex(8), allocatable :: dyn(:,:) complex(8), allocatable :: apwalm(:,:,:,:,:),apwalmq(:,:,:,:,:) complex(8), allocatable :: dapwalm(:,:,:,:),dapwalmq(:,:,:,:) complex(8), allocatable :: evecfv(:,:,:),devecfv(:,:,:) complex(8), allocatable :: evecsv(:,:),devecsv(:,:) ! initialise universal variables call init0 call init1 call init2 call init4 ! check k-point grid is commensurate with q-point grid iv(:)=mod(ngridk(:),ngridq(:)) if ((iv(1).ne.0).or.(iv(2).ne.0).or.(iv(3).ne.0)) then write(*,*) write(*,'("Error(phonon): k-point grid incommensurate with q-point grid")') write(*,'(" ngridk : ",3I6)') ngridk write(*,'(" ngridq : ",3I6)') ngridq write(*,*) stop end if if (spinpol) then write(*,*) write(*,'("Error(phonon): spin-polarised phonons not yet available")') write(*,*) stop end if ! check spin-spiral de-phasing is not used if (ssdph) then write(*,*) write(*,'("Error(phonon): ssdph should be .false. for DFPT phonons")') write(*,*) stop end if ! check for zero atoms if (natmtot.eq.0) return ! read in the density and potentials call readstate ! Fourier transform Kohn-Sham potential to G-space call genvsig ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! generate the spin-orbit coupling radial functions call gensocfr ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! size of mixing vector (complex array) nmix=2*size(dvsbs) ! determine the size of the mixer work array nwork=-1 call mixerifc(mtype,nmix,dvsbs,ddv,nwork,dvsbs) allocate(work(nwork)) ! allocate dynamical matrix column allocate(dyn(3,natmtot)) ! begin new dynamical matrix task 10 continue call dyntask(80,fext) ! if nothing more to do then return if (iqph.eq.0) return if (mp_mpi) then write(*,'("Info(phonon): working on ",A)') 'DYN'//trim(fext) ! open RMSDDVS.OUT open(65,file='RMSDDVS'//trim(fext),form='FORMATTED') end if ! zero the dynamical matrix row dyn(:,:)=0.d0 ! check to see if mass is considered infinite if (spmass(isph).le.0.d0) goto 20 ! generate the G+k+q-vectors and related quantities call gengkqvec(iqph) ! generate the G+q-vectors and related quantities call gengqvec(iqph) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.false.,iqph,ngvec,gqc,gclgq) ! generate the characteristic function derivative call gendcfun ! generate the gradient of the Kohn-Sham potential call gengvsmt ! initialise the potential derivative drhomt(:,:)=0.d0 drhoir(:)=0.d0 if (spinpol) then dmagmt(:,:,:)=0.d0 dmagir(:,:)=0.d0 end if call dpotks call gendvsig ! initialise the mixer iscl=0 call mixerifc(mtype,nmix,dvsbs,ddv,nwork,work) ! initialise the Fermi energy and occupancy derivatives defermi=0.d0 doccsv(:,:)=0.d0 ! set last self-consistent loop flag tlast=.false. ! begin the self-consistent loop do iscl=1,maxscl ! compute the Hamiltonian radial integral derivatives call dhmlrad ! zero the density and magnetisation derivatives drhomt(:,:)=0.d0 drhoir(:)=0.d0 if (spinpol) then dmagmt(:,:,:)=0.d0 dmagir(:,:)=0.d0 end if ! parallel loop over k-points call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evalfv,apwalm,apwalmq,dapwalm,dapwalmq) & !$OMP PRIVATE(evecfv,devecfv,evecsv,devecsv,jk,jspn) & !$OMP NUM_THREADS(nthd) allocate(evalfv(nstfv,nspnfv)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(apwalmq(ngkmax,apwordmax,lmmaxapw,natmtot,nspnfv)) allocate(dapwalm(ngkmax,apwordmax,lmmaxapw,nspnfv)) allocate(dapwalmq(ngkmax,apwordmax,lmmaxapw,nspnfv)) allocate(evecfv(nmatmax,nstfv,nspnfv),devecfv(nmatmax,nstfv,nspnfv)) allocate(evecsv(nstsv,nstsv),devecsv(nstsv,nstsv)) !$OMP DO do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! compute the matching coefficients and derivatives do jspn=1,nspnfv call match(ngk(jspn,ik),vgkc(:,:,jspn,ik),gkc(:,jspn,ik), & sfacgk(:,:,jspn,ik),apwalm(:,:,:,:,jspn)) call dmatch(iasph,ipph,ngk(jspn,ik),vgkc(:,:,jspn,ik), & apwalm(:,:,:,:,jspn),dapwalm(:,:,:,jspn)) call match(ngkq(jspn,ik),vgkqc(:,:,jspn,ik),gkqc(:,jspn,ik), & sfacgkq(:,:,jspn,ik),apwalmq(:,:,:,:,jspn)) call dmatch(iasph,ipph,ngkq(jspn,ik),vgkqc(:,:,jspn,ik), & apwalmq(:,:,:,:,jspn),dapwalmq(:,:,:,jspn)) end do ! get the first- and second-variational eigenvalues and eigenvectors from file call getevalfv(filext,0,vkl(:,ik),evalfv) call getevecfv(filext,0,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,0,vkl(:,ik),evecsv) ! solve the first-variational eigenvalue equation derivative do jspn=1,nspnfv call deveqnfv(ngk(jspn,ik),ngkq(jspn,ik),igkig(:,jspn,ik), & igkqig(:,jspn,ik),vgkc(:,:,jspn,ik),vgkqc(:,:,jspn,ik),evalfv(:,jspn), & apwalm(:,:,:,:,jspn),apwalmq(:,:,:,:,jspn),dapwalm(:,:,:,jspn), & dapwalmq(:,:,:,jspn),evecfv(:,:,jspn),devalfv(:,jspn,ik), & devecfv(:,:,jspn)) end do if (spinsprl) then ! solve the spin-spiral second-variational eigenvalue equation derivative ! call deveqnss(ngk(:,ik),ngkq(:,ik),igkig(:,:,ik),igkqig(:,:,ik),apwalm, & ! dapwalm,devalfv,evecfv,evecfvq,devecfv,evalsv(:,jk),evecsv,devecsv) else ! solve the second-variational eigenvalue equation derivative ! call deveqnsv(ngk(1,ik),ngkq(1,ik),igkig(:,1,ik),igkqig(:,1,ik), & ! vgkqc(:,:,1,ik),apwalm,dapwalm,devalfv,evecfv,evecfvq,devecfv, & ! evalsv(:,jk),evecsv,devecsv) end if !******* devalsv(:,ik)=devalfv(:,1,ik) !******* ! write the eigenvalue/vector derivatives to file call putdevecfv(ik,devecfv) if (tevecsv) call putdevecsv(ik,devecsv) ! add to the density and magnetisation derivatives call drhomagk(ngk(:,ik),ngkq(:,ik),igkig(:,:,ik),igkqig(:,:,ik), & occsv(:,jk),doccsv(:,ik),apwalm,apwalmq,dapwalm,evecfv,devecfv,evecsv, & devecsv) end do !$OMP END DO deallocate(evalfv,apwalm,apwalmq,dapwalm,dapwalmq) deallocate(evecfv,devecfv,evecsv,devecsv) !$OMP END PARALLEL call freethd(nthd) ! broadcast eigenvalue derivative arrays to every process n=nstfv*nspnfv do ik=1,nkptnr lp=mod(ik-1,np_mpi) call mpi_bcast(devalfv(:,:,ik),n,mpi_double_precision,lp,mpicom,ierror) call mpi_bcast(devalsv(:,ik),nstsv,mpi_double_precision,lp,mpicom,ierror) end do ! convert to spherical harmonic representation call drhomagsh ! convert from a coarse to a fine radial mesh call zfmtctof(drhomt) do idm=1,ndmag call zfmtctof(dmagmt(:,:,idm)) end do ! add densities from each process and redistribute if (np_mpi.gt.1) then n=npmtmax*natmtot call mpi_allreduce(mpi_in_place,drhomt,n,mpi_double_complex,mpi_sum, & mpicom,ierror) call mpi_allreduce(mpi_in_place,drhoir,ngtot,mpi_double_complex,mpi_sum, & mpicom,ierror) if (spinpol) then n=npmtmax*natmtot*ndmag call mpi_allreduce(mpi_in_place,dmagmt,n,mpi_double_complex,mpi_sum, & mpicom,ierror) n=ngtot*ndmag call mpi_allreduce(mpi_in_place,dmagir,n,mpi_double_complex,mpi_sum, & mpicom,ierror) end if end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! add gradient contribution to density derivative call gradrhomt ! compute the Kohn-Sham potential derivative call dpotks ! mix the old potential and field with the new call mixerifc(mtype,nmix,dvsbs,ddv,nwork,work) if (mp_mpi) then write(65,'(G18.10)') ddv flush(65) end if ! exit self-consistent loop if required if (tlast) goto 20 ! check for convergence if (iscl.ge.2) then if (ddv.lt.epspot) tlast=.true. end if ! broadcast tlast from master process to all other processes call mpi_bcast(tlast,1,mpi_logical,0,mpicom,ierror) ! Fourier transform Kohn-Sham potential derivative to G+q-space call gendvsig ! compute the occupation number derivatives call doccupy ! end the self-consistent loop end do write(*,*) write(*,'("Warning(phonon): failed to reach self-consistency after ",I4,& &" loops")') maxscl 20 continue ! close the RMSDDVS.OUT file if (mp_mpi) close(65) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! generate the dynamical matrix row from force derivatives call dforce(dyn) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! write dynamical matrix row to file if (mp_mpi) then do ias=1,natmtot is=idxis(ias) ia=idxia(ias) do ip=1,3 a=dble(dyn(ip,ias)) b=aimag(dyn(ip,ias)) if (abs(a).lt.1.d-12) a=0.d0 if (abs(b).lt.1.d-12) b=0.d0 write(80,'(2G18.10," : is = ",I4,", ia = ",I4,", ip = ",I4)') a,b,is,ia,ip end do end do close(80) ! write the complex Kohn-Sham potential derivative to file call writedvs(fext) end if ! delete the non-essential files call delfiles(devec=.true.) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) goto 10 end subroutine elk-7.2.42/src/PaxHeaders.21776/dynrtoq.f900000644000000000000000000000013214061636517014744 xustar0030 mtime=1623670095.604101852 30 atime=1623670094.422102949 30 ctime=1623670095.604101852 elk-7.2.42/src/dynrtoq.f900000644002504400250440000000171514061636517017005 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dynrtoq(vpl,dynr,dynp) use modmain use modphonon implicit none ! arguments real(8), intent(in) :: vpl(3) complex(8), intent(in) :: dynr(nbph,nbph,nqptnr) complex(8), intent(out) :: dynp(nbph,nbph) ! local variables integer i1,i2,i3,ir,i,j real(8) t1 complex(8) z1 dynp(:,:)=0.d0 ! loop over R-vectors ir=0 do i3=ngridq(3)/2-ngridq(3)+1,ngridq(3)/2 do i2=ngridq(2)/2-ngridq(2)+1,ngridq(2)/2 do i1=ngridq(1)/2-ngridq(1)+1,ngridq(1)/2 ir=ir+1 t1=-twopi*(vpl(1)*dble(i1)+vpl(2)*dble(i2)+vpl(3)*dble(i3)) z1=cmplx(cos(t1),sin(t1),8) do i=1,nbph do j=1,nbph dynp(i,j)=dynp(i,j)+z1*dynr(i,j,ir) end do end do end do end do end do ! symmetrise the dynamical matrix call dynsym(vpl,dynp) end subroutine elk-7.2.42/src/PaxHeaders.21776/mcmillan.f900000644000000000000000000000013214061636517015040 xustar0030 mtime=1623670095.605101851 30 atime=1623670094.424102948 30 ctime=1623670095.605101851 elk-7.2.42/src/mcmillan.f900000644002504400250440000000275114061636517017102 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, A. Sanna, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine mcmillan(w,a2f,lambda,wlog,wrms,tc) use modmain use modphonon implicit none ! arguments real(8), intent(in) :: w(nwplot),a2f(nwplot) real(8), intent(out) :: lambda,wlog,wrms,tc ! local variables integer iw real(8) l1,l2,f1,f2,t1 ! allocatable arrays real(8), allocatable :: f(:) ! external functions real(8), external :: splint allocate(f(nwplot)) ! compute the total lambda do iw=1,nwplot if (w(iw).gt.1.d-8) then f(iw)=a2f(iw)/w(iw) else f(iw)=0.d0 end if end do t1=splint(nwplot,w,f) lambda=2.d0*t1 ! compute the logarithmic average frequency do iw=1,nwplot if (w(iw).gt.1.d-8) then f(iw)=a2f(iw)*log(w(iw))/w(iw) else f(iw)=0.d0 end if end do t1=splint(nwplot,w,f) t1=(2.d0/lambda)*t1 wlog=exp(t1) ! compute < w^2 >^(1/2) do iw=1,nwplot if (w(iw).gt.1.d-8) then f(iw)=a2f(iw)*w(iw) else f(iw)=0.d0 end if end do t1=splint(nwplot,w,f) t1=(2.d0/lambda)*t1 wrms=sqrt(abs(t1)) ! compute McMillan-Allen-Dynes superconducting critical temperature t1=(-1.04d0*(1.d0+lambda))/(lambda-mustar-0.62d0*lambda*mustar) tc=(wlog/(1.2d0*kboltz))*exp(t1) l1=2.46d0*(1.d0+3.8d0*mustar) l2=1.82d0*(1.d0+6.3d0*mustar)*(wrms/wlog) f1=(1.d0+(lambda/l1)**(3.d0/2.d0))**(1.d0/3.d0) f2=1.d0+(wrms/wlog-1.d0)*(lambda**2)/(lambda**2+l2**2) tc=tc*f1*f2 deallocate(f) end subroutine elk-7.2.42/src/PaxHeaders.21776/genephmat.f900000644000000000000000000000013014061636517015212 xustar0029 mtime=1623670095.60710185 30 atime=1623670094.425102947 29 ctime=1623670095.60710185 elk-7.2.42/src/genephmat.f900000644002504400250440000000760714061636517017263 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genephmat(iq,ik,de,a,dvmt,dvir,ephmat) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq,ik real(8), intent(in) :: de complex(8), intent(in) :: a(nbph,nbph) complex(8), intent(in) :: dvmt(npcmtmax,natmtot,nbph),dvir(ngtot,nbph) complex(8), intent(out) :: ephmat(nstsv,nstsv,nbph) ! local variables integer jk,jkq,isym,ld integer nst,nstq,ist,jst integer ispn,jspn,is,ias integer nrc,nrci,npc,i,j,l integer igp,igpq,ifg real(8) vpql(3) ! automatic arrays integer idx(nstsv),idxq(nstsv) integer ngp(nspnfv),ngpq(nspnfv) complex(8) zfmt1(npcmtmax),zfmt2(npcmtmax) complex(8) z(ngkmax),x(nbph) ! allocatable arrays integer, allocatable :: igpig(:,:),igpqig(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfgp(:,:,:) complex(8), allocatable :: wfmtq(:,:,:,:),wfgpq(:,:,:) complex(8), allocatable :: wfir1(:),wfir2(:) ! external functions complex(8), external :: zdotc ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! k+q-vector in lattice coordinates vpql(:)=vkl(:,ik)+vql(:,iq) ! find reduced k-point index corresponding to k+q call findkpt(vpql,isym,jkq) ! index to states in energy window around Fermi energy nst=0 nstq=0 do ist=1,nstsv if (abs(evalsv(ist,jk)-efermi).lt.de) then nst=nst+1 idx(nst)=ist end if if (abs(evalsv(ist,jkq)-efermi).lt.de) then nstq=nstq+1 idxq(nstq)=ist end if end do ! generate the second-variational wavefunctions for all states at k and k+q allocate(igpig(ngkmax,nspnfv)) allocate(wfmt(npcmtmax,natmtot,nspinor,nst),wfgp(ngkmax,nspinor,nst)) call genwfsvp(.false.,.true.,nst,idx,ngridg,igfft,vkl(:,ik),ngp,igpig,wfmt, & ngkmax,wfgp) allocate(igpqig(ngkmax,nspnfv)) allocate(wfmtq(npcmtmax,natmtot,nspinor,nstq),wfgpq(ngkmax,nspinor,nstq)) call genwfsvp(.false.,.true.,nstq,idxq,ngridg,igfft,vpql,ngpq,igpqig,wfmtq, & ngkmax,wfgpq) ! zero the electron-phonon coupling matrix elements ephmat(:,:,:)=0.d0 !-------------------------! ! muffin-tin part ! !-------------------------! do j=1,nst jst=idx(j) do i=1,nstq ist=idxq(i) x(:)=0.d0 do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) if (spinpol) then zfmt1(1:npc)=wfmtq(1:npc,ias,1,i)*conjg(wfmt(1:npc,ias,1,j)) & +wfmtq(1:npc,ias,2,i)*conjg(wfmt(1:npc,ias,2,j)) else zfmt1(1:npc)=wfmtq(1:npc,ias,1,i)*conjg(wfmt(1:npc,ias,1,j)) end if call zfsht(nrc,nrci,zfmt1,zfmt2) do l=1,nbph x(l)=x(l)+zdotc(npc,zfmt2,1,dvmt(:,ias,l),1) end do end do ephmat(ist,jst,:)=x(:) end do end do deallocate(wfmt,wfmtq) !---------------------------! ! interstitial part ! !---------------------------! allocate(wfir1(ngtot),wfir2(ngtot)) do j=1,nst jst=idx(j) do ispn=1,nspinor jspn=jspnfv(ispn) ! Fourier transform wavefunction to real-space wfir1(:)=0.d0 do igp=1,ngp(jspn) ifg=igfft(igpig(igp,jspn)) wfir1(ifg)=wfgp(igp,ispn,j) end do call zfftifc(3,ngridg,1,wfir1) do l=1,nbph ! apply potential derivative to wavefunction wfir2(:)=dvir(:,l)*wfir1(:) ! Fourier transform to G+p+q-space call zfftifc(3,ngridg,-1,wfir2) do igpq=1,ngpq(jspn) ifg=igfft(igpqig(igpq,jspn)) z(igpq)=wfir2(ifg) end do do i=1,nstq ist=idxq(i) ! compute inner product ephmat(ist,jst,l)=ephmat(ist,jst,l)+zdotc(ngpq(jspn),wfgpq(:,ispn,i), & 1,z,1) end do end do end do end do deallocate(wfir1,wfir2) ! convert to phonon coordinates ld=nstsv**2 do i=1,nstq ist=idxq(i) do j=1,nst jst=idx(j) x(:)=ephmat(ist,jst,:) call zgemv('T',nbph,nbph,zone,a,nbph,x,1,zzero,ephmat(ist,jst,1),ld) end do end do deallocate(igpig,igpqig,wfgp,wfgpq) end subroutine elk-7.2.42/src/PaxHeaders.21776/gengkqvec.f900000644000000000000000000000013214061636517015216 xustar0030 mtime=1623670095.608101849 30 atime=1623670094.427102945 30 ctime=1623670095.608101849 elk-7.2.42/src/gengkqvec.f900000644002504400250440000000222314061636517017252 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gengkqvec(iq) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq ! local variables integer ik,jspn real(8) vl(3),vc(3) ! loop over non-reduced k-point set do ik=1,nkptnr ! k+q-vectors in lattice and Cartesian coordinates vkql(1:3,ik)=vkl(1:3,ik)+vql(1:3,iq) vkqc(1:3,ik)=vkc(1:3,ik)+vqc(1:3,iq) do jspn=1,nspnfv vl(:)=vkql(:,ik) vc(:)=vkqc(:,ik) ! spin-spiral case if (spinsprl) then if (jspn.eq.1) then vl(:)=vl(:)+0.5d0*vqlss(:) vc(:)=vc(:)+0.5d0*vqcss(:) else vl(:)=vl(:)-0.5d0*vqlss(:) vc(:)=vc(:)-0.5d0*vqcss(:) end if end if ! generate the G+k+q-vectors call gengkvec(ngvec,ivg,vgc,vl,vc,gkmax,ngkmax,ngkq(jspn,ik), & igkqig(:,jspn,ik),vgkql(:,:,jspn,ik),vgkqc(:,:,jspn,ik),gkqc(:,jspn,ik)) ! generate structure factors for the G+k+q-vectors call gensfacgp(ngkq(jspn,ik),vgkqc(:,:,jspn,ik),ngkmax,sfacgkq(:,:,jspn,ik)) end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/genmcph.f900000644000000000000000000000013214061636517014665 xustar0030 mtime=1623670095.609101848 30 atime=1623670094.429102943 30 ctime=1623670095.609101848 elk-7.2.42/src/genmcph.f900000644002504400250440000000131714061636517016724 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure subroutine genmcph(w,ev,a) use modmain use modphonon implicit none ! arguments real(8), intent(in) :: w(nbph) complex(8), intent(in) :: ev(nbph,nbph) complex(8), intent(out) :: a(nbph,nbph) ! local variables integer is,ia,ip,i,j real(8) t1 do j=1,nbph i=0 do is=1,nspecies t1=2.d0*spmass(is)*w(j) if (t1.gt.1.d-8) then t1=1.d0/sqrt(t1) else t1=0.d0 end if do ia=1,natoms(is) do ip=1,3 i=i+1 a(i,j)=t1*ev(i,j) end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/putdevecfv.f900000644000000000000000000000013214061636517015417 xustar0030 mtime=1623670095.611101846 30 atime=1623670094.430102942 30 ctime=1623670095.611101846 elk-7.2.42/src/putdevecfv.f900000644002504400250440000000200714061636517017453 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine putdevecfv(ik,devecfv) use modmain use modphonon use modramdisk implicit none ! arguments integer, intent(in) :: ik complex(8), intent(in) :: devecfv(nmatmax,nstfv,nspnfv) ! local variables integer recl character(256) fext,fname ! construct the dynamical matrix file extension call dynfext(iqph,isph,iaph,ipph,fext) ! construct filename fname=trim(scrpath)//'DEVECFV'//trim(fext) ! find the record length inquire(iolength=recl) vkl(:,ik),nmatmax,nstfv,nspnfv,devecfv !$OMP CRITICAL(u222) open(222,file=fname,form='UNFORMATTED',access='DIRECT',recl=recl) write(222,rec=ik) vkl(:,ik),nmatmax,nstfv,nspnfv,devecfv close(222) ! write to RAM disk if required if (ramdisk) then call putrd(fname,ik,v1=vkl(:,ik),n1=nmatmax,n2=nstfv,n3=nspnfv, & nzv=nmatmax*nstfv*nspnfv,zva=devecfv) end if !$OMP END CRITICAL(u222) end subroutine elk-7.2.42/src/PaxHeaders.21776/getdevecfv.f900000644000000000000000000000013114061636517015365 xustar0030 mtime=1623670095.612101845 29 atime=1623670094.43210294 30 ctime=1623670095.612101845 elk-7.2.42/src/getdevecfv.f900000644002504400250440000000410314061636517017421 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine getdevecfv(ik,iq,is,ia,ip,devecfv) use modmain use modphonon use modramdisk implicit none ! arguments integer, intent(in) :: ik,iq,is,ia,ip complex(8), intent(out) :: devecfv(nmatmax,nstfv,nspnfv) ! local variables logical tgs integer recl,nmatmax_,nstfv_,nspnfv_ real(8) vkl_(3),t1 character(256) fext,fname ! construct the dynamical matrix file extension call dynfext(iq,is,ia,ip,fext) ! construct filename fname=trim(scrpath)//'DEVECFV'//trim(fext) ! find the record length inquire(iolength=recl) vkl_,nmatmax_,nstfv_,nspnfv_,devecfv !$OMP CRITICAL(u222) ! read from RAM disk if required if (ramdisk) then call getrd(fname,ik,tgs,v1=vkl_,n1=nmatmax_,n2=nstfv_,n3=nspnfv_, & nzv=nmatmax*nstfv*nspnfv,zva=devecfv) if (tgs) goto 10 end if open(222,file=fname,form='UNFORMATTED',access='DIRECT',recl=recl) read(222,rec=ik) vkl_,nmatmax_,nstfv_,nspnfv_,devecfv 10 continue !$OMP END CRITICAL(u222) t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getdevecfv): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" ",A," : ",3G18.10)') trim(fname),vkl_ write(*,*) stop end if if (nmatmax.ne.nmatmax_) then write(*,*) write(*,'("Error(getdevecfv): differing nmatmax for k-point ",I8)') ik write(*,'(" current : ",I8)') nmatmax write(*,'(" ",A," : ",I8)') trim(fname),nmatmax_ write(*,*) stop end if if (nstfv.ne.nstfv_) then write(*,*) write(*,'("Error(getdevecfv): differing nstfv for k-point ",I8)') ik write(*,'(" current : ",I8)') nstfv write(*,'(" ",A," : ",I8)') trim(fname),nstfv_ write(*,*) stop end if if (nspnfv.ne.nspnfv_) then write(*,*) write(*,'("Error(getdevecfv): differing nspnfv for k-point ",I8)') ik write(*,'(" current : ",I8)') nspnfv write(*,'(" ",A," : ",I8)') trim(fname),nspnfv_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/putdevecsv.f900000644000000000000000000000013214061636517015434 xustar0030 mtime=1623670095.614101843 30 atime=1623670094.434102938 30 ctime=1623670095.614101843 elk-7.2.42/src/putdevecsv.f900000644002504400250440000000167414061636517017501 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine putdevecsv(ik,devecsv) use modmain use modphonon use modramdisk implicit none ! arguments integer, intent(in) :: ik complex(8), intent(in) :: devecsv(nstsv,nstsv) ! local variables integer recl character(256) fext,fname ! construct the dynamical matrix file extension call dynfext(iqph,isph,iaph,ipph,fext) ! construct filename fname=trim(scrpath)//'DEVECSV'//trim(fext) ! find the record length inquire(iolength=recl) vkl(:,ik),nstsv,devecsv !$OMP CRITICAL(u226) open(226,file=fname,form='UNFORMATTED',access='DIRECT',recl=recl) write(226,rec=ik) vkl(:,ik),nstsv,devecsv close(226) ! write to RAM disk if required if (ramdisk) then call putrd(fname,ik,v1=vkl(:,ik),n1=nstsv,nzv=nstsv*nstsv,zva=devecsv) end if !$OMP END CRITICAL(u226) end subroutine elk-7.2.42/src/PaxHeaders.21776/getdevecsv.f900000644000000000000000000000013214061636517015403 xustar0030 mtime=1623670095.615101842 30 atime=1623670094.435102937 30 ctime=1623670095.615101842 elk-7.2.42/src/getdevecsv.f900000644002504400250440000000302214061636517017435 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine getdevecsv(ik,iq,is,ia,ip,devecsv) use modmain use modphonon use modramdisk implicit none ! arguments integer, intent(in) :: ik,iq,is,ia,ip complex(8), intent(out) :: devecsv(nstsv,nstsv) ! local variables logical tgs integer recl,nstsv_ real(8) vkl_(3),t1 character(256) fext,fname ! construct the dynamical matrix file extension call dynfext(iq,is,ia,ip,fext) ! construct filename fname=trim(scrpath)//'DEVECSV'//trim(fext) ! find the record length inquire(iolength=recl) vkl_,nstsv_,devecsv !$OMP CRITICAL(u226) ! read from RAM disk if required if (ramdisk) then call getrd(fname,ik,tgs,v1=vkl_,n1=nstsv_,nzv=nstsv*nstsv,zva=devecsv) if (tgs) goto 10 end if open(226,file=fname,form='UNFORMATTED',access='DIRECT',recl=recl) read(226,rec=ik) vkl_,nstsv_,devecsv 10 continue !$OMP END CRITICAL(u226) t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getdevecsv): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" ",A," : ",3G18.10)') trim(fname),vkl_ write(*,*) stop end if if (nstsv.ne.nstsv_) then write(*,*) write(*,'("Error(getdevecsv): differing nstsv for k-point ",I8)') ik write(*,'(" current : ",I8)') nstsv write(*,'(" ",A," : ",I8)') trim(fname),nstsv_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/phononsc.f900000644000000000000000000000013014061636517015071 xustar0029 mtime=1623670095.61710184 30 atime=1623670094.437102936 29 ctime=1623670095.61710184 elk-7.2.42/src/phononsc.f900000644002504400250440000001171614061636517017136 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine phononsc use modmain use modphonon use modstore use modmpi use moddelf implicit none ! local variables integer is,ia,ja,ias,jas integer ip,nph,p,n,i real(8) a,b,t1 real(8) ft(3,maxatoms*maxspecies) complex(8) z1,z2 ! allocatable arrays real(8), allocatable :: vsmt_(:,:),vsir_(:) complex(8), allocatable :: dyn(:,:) ! store original parameters natoms_(:)=natoms(:) avec_(:,:)=avec(:,:) atposl_(:,:,:)=atposl(:,:,:) bfcmt0_(:,:,:)=bfcmt0(:,:,:) mommtfix_(:,:,:)=mommtfix(:,:,:) tshift_=tshift tforce_=tforce autokpt_=autokpt primcell_=primcell ngridk_(:)=ngridk(:) ! no shifting of atomic basis allowed tshift=.false. ! require forces tforce=.true. ! determine k-point grid size from radkpt autokpt=.true. ! no reduction to primitive cell primcell=.false. ! initialise universal variables call init0 ! initialise q-point dependent variables call init2 ! store original parameters natmtot_=natmtot idxis_(1:natmtot)=idxis(1:natmtot) bvec_(:,:)=bvec(:,:) binv_(:,:)=binv(:,:) atposc_(:,:,:)=atposc(:,:,:) ngridg_(:)=ngridg(:) ngtot_=ngtot if (allocated(ivg_)) deallocate(ivg_) allocate(ivg_(3,ngtot_)) ivg_(:,:)=ivg(:,:) if (allocated(igfft_)) deallocate(igfft_) allocate(igfft_(ngtot_)) igfft_(:)=igfft(:) ! allocate the Kohn-Sham potential derivative arrays if (allocated(dvsbs)) deallocate(dvsbs) n=npmtmax*natmtot+ngtot allocate(dvsbs(n)) dvsmt(1:npmtmax,1:natmtot)=>dvsbs(1:) i=npmtmax*natmtot+1 dvsir(1:ngtot)=>dvsbs(i:) ! allocate supercell offset vector array if (allocated(vscph)) deallocate(vscph) allocate(vscph(3,nqptnr)) ! allocate dynamical matrix column allocate(dyn(3,natmtot)) ! begin new phonon task 10 continue natoms(:)=natoms_(:) ! find a dynamical matrix to calculate call dyntask(80,filext) ! if nothing more to do then restore original input parameters and return if (iqph.eq.0) then filext='.OUT' natoms(:)=natoms_(:) avec(:,:)=avec_(:,:) atposl(:,:,:)=atposl_(:,:,:) bfcmt0(:,:,:)=bfcmt0_(:,:,:) mommtfix(:,:,:)=mommtfix_(:,:,:) tshift=tshift_ tforce=tforce_ autokpt=autokpt_ primcell=primcell_ ngridk(:)=ngridk_(:) deallocate(ivg_,igfft_) return end if if (mp_mpi) write(*,'("Info(phononsc): working on ",A)') 'DYN'//trim(filext) ! dry run: just generate empty DYN files if (task.eq.202) goto 10 ! zero the dynamical matrix row dyn(:,:)=0.d0 ! zero the Kohn-Sham potential derivative dvsmt(:,:)=0.d0 dvsir(:)=0.d0 ! check to see if mass is considered infinite if (spmass(isph).le.0.d0) goto 20 ! loop over phases: 0 = cos and 1 = sin displacements if ((ivq(1,iqph).eq.0).and.(ivq(2,iqph).eq.0).and.(ivq(3,iqph).eq.0)) then nph=0 else nph=1 end if ! initialise or read the charge density and potentials from file if (task.eq.200) then trdstate=.false. else trdstate=.true. end if ! loop over cos and sin displacements do p=0,nph ! generate the supercell with negative displacement call genscph(p,-0.5d0*deltaph) ! run the ground-state calculation call gndstate ! subsequent calculations will read in this supercell potential trdstate=.true. ! store the total force for this displacement do ias=1,natmtot ft(:,ias)=forcetot(:,ias) end do ! store the Kohn-Sham potential for this displacement allocate(vsmt_(npmtmax,natmtot),vsir_(ngtot)) vsmt_(:,:)=vsmt(:,:) vsir_(:)=vsir(:) ! generate the supercell again with positive displacement call genscph(p,0.5d0*deltaph) ! run the ground-state calculation again call gndstate ! compute the complex Kohn-Sham potential derivative with implicit q-phase call phscdvs(p,vsmt_,vsir_) deallocate(vsmt_,vsir_) ! Fourier transform the force differences to obtain the dynamical matrix z1=1.d0/(dble(nscph)*deltaph) ! multiply by i for sin-like displacement if (p.eq.1) z1=z1*zi ias=0 jas=0 do is=1,nspecies ja=0 do ia=1,natoms_(is) ias=ias+1 do i=1,nscph ja=ja+1 jas=jas+1 t1=-dot_product(vqc(:,iqph),vscph(:,i)) z2=z1*cmplx(cos(t1),sin(t1),8) do ip=1,3 t1=-(forcetot(ip,jas)-ft(ip,jas)) dyn(ip,ias)=dyn(ip,ias)+z2*t1 end do end do end do end do end do 20 continue ! write dynamical matrix row to file if (mp_mpi) then ias=0 do is=1,nspecies do ia=1,natoms_(is) ias=ias+1 do ip=1,3 a=dble(dyn(ip,ias)) b=aimag(dyn(ip,ias)) if (abs(a).lt.1.d-12) a=0.d0 if (abs(b).lt.1.d-12) b=0.d0 write(80,'(2G18.10," : is = ",I4,", ia = ",I4,", ip = ",I4)') a,b,is, & ia,ip end do end do end do close(80) ! write the complex Kohn-Sham potential derivative to file natoms(:)=natoms_(:) natmtot=natmtot_ idxis(1:natmtot)=idxis_(1:natmtot) ngridg(:)=ngridg_(:) call writedvs(filext) end if ! delete the non-essential files call delfiles(evec=.true.,eval=.true.,occ=.true.) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) goto 10 end subroutine elk-7.2.42/src/PaxHeaders.21776/genscph.f900000644000000000000000000000013214061636517014673 xustar0030 mtime=1623670095.618101839 30 atime=1623670094.439102934 30 ctime=1623670095.618101839 elk-7.2.42/src/genscph.f900000644002504400250440000000327414061636517016736 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genscph(p,dph) use modmain use modphonon use modstore implicit none ! arguments integer, intent(in) :: p real(8), intent(in) :: dph ! local variables integer is,ia,na,i real(8) vc(3),t1 if ((p.ne.0).and.(p.ne.1)) then write(*,*) write(*,'("Error(genscph): phase (p) should be 0 or 1 : ",I8)') p write(*,*) stop end if ! find the smallest supercell which contains the q-vector call findscq(iqph,avec_,nscph,vscph) ! construct supercell atomic positions and magnetic fields do is=1,nspecies na=0 do ia=1,natoms_(is) do i=1,nscph na=na+1 if (na.gt.maxatoms) then write(*,*) write(*,'("Error(genscph): too many atoms in supercell : ",I8)') na write(*,'(" for species ",I4)') is write(*,'("Adjust maxatoms in modmain and recompile code")') write(*,*) stop end if vc(:)=vscph(:,i)+atposc_(:,ia,is) ! add small periodic displacement if ((isph.eq.is).and.(iaph.eq.ia)) then t1=dot_product(vqc(:,iqph),vscph(:,i)) if (p.eq.0) then vc(ipph)=vc(ipph)+dph*cos(t1) else vc(ipph)=vc(ipph)+dph*sin(t1) end if end if ! convert to new lattice coordinates call r3mv(ainv,vc,atposl(:,na,is)) call r3frac(epslat,atposl(:,na,is)) ! set muffin-tin fields and fixed spin moments if required if (spinpol) then bfcmt0(:,na,is)=bfcmt0_(:,ia,is) mommtfix(:,na,is)=mommtfix_(:,ia,is) end if end do end do natoms(is)=na end do end subroutine elk-7.2.42/src/PaxHeaders.21776/phdisp.f900000644000000000000000000000013214061636517014533 xustar0030 mtime=1623670095.620101837 30 atime=1623670094.440102933 30 ctime=1623670095.620101837 elk-7.2.42/src/phdisp.f900000644002504400250440000000356514061636517016601 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine phdisp use modmain use modphonon implicit none ! local variables integer iq,i,iv real(8) wmin,wmax ! allocatable arrays complex(8), allocatable :: dynq(:,:,:),dynr(:,:,:) complex(8), allocatable :: dynp(:,:),ev(:,:) ! initialise universal variables call init0 call init2 ! allocate local arrays allocate(dynq(nbph,nbph,nqpt)) allocate(dynr(nbph,nbph,nqptnr)) allocate(dynp(nbph,nbph)) allocate(ev(nbph,nbph)) ! read in the dynamical matrices call readdyn(dynq) ! apply the acoustic sum rule call sumrule(dynq) ! Fourier transform the dynamical matrices to real-space call dynqtor(dynq,dynr) ! generate a set of q-point vectors along a path in the Brillouin zone call plotpt1d(bvec,nvp1d,npp1d,vvlp1d,vplp1d,dvp1d,dpp1d) wmin=0.d0 wmax=0.d0 ! compute the phonon frequencies along the path do iq=1,npp1d ! compute the dynamical matrix at this particular q-point call dynrtoq(vplp1d(:,iq),dynr,dynp) ! find the phonon frequencies and eigenvectors call dynev(dynp,wphq(:,iq),ev) wmin=min(wmin,wphq(1,iq)) wmax=max(wmax,wphq(nbph,iq)) end do wmax=wmax+(wmax-wmin)*0.5d0 wmin=wmin-(wmax-wmin)*0.5d0 ! output the vertex location lines open(50,file='PHDLINES.OUT',form='FORMATTED') do iv=1,nvp1d write(50,'(2G18.10)') dvp1d(iv),wmin write(50,'(2G18.10)') dvp1d(iv),wmax write(50,*) end do close(50) ! output the phonon dispersion open(50,file='PHDISP.OUT',form='FORMATTED') do i=1,nbph do iq=1,npp1d write(50,'(2G18.10)') dpp1d(iq),wphq(i,iq) end do write(50,*) end do close(50) write(*,*) write(*,'("Info(phdisp):")') write(*,'(" phonon dispersion written to PHDISP.OUT")') write(*,'(" vertex location lines written to PHDLINES.OUT")') deallocate(dynq,dynr,dynp,ev) end subroutine elk-7.2.42/src/PaxHeaders.21776/dynsymapp.f900000644000000000000000000000013214061636517015270 xustar0030 mtime=1623670095.621101837 30 atime=1623670094.442102931 30 ctime=1623670095.621101837 elk-7.2.42/src/dynsymapp.f900000644002504400250440000000360114061636517017325 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2005-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dynsymapp(isym,vpl,dyn,dyns) use modmain use modphonon implicit none ! arguments integer, intent(in) :: isym real(8), intent(in) :: vpl(3) complex(8), intent(in) :: dyn(nbph,nbph) complex(8), intent(inout) :: dyns(nbph,nbph) ! local variables integer is,ia,ja,ias,jas integer lspl,ilspl,i,j,k,l,m,n real(8) sl(3,3),sic(3,3),v(3),t1 real(8) a(3,3),b(3,3),c(3,3) complex(8) z1 ! automatic arrays integer map(natmtot) complex(8) zph(natmtot) ! index to spatial rotation in lattice point group lspl=lsplsymc(isym) ! the inverse of the spatial symmetry ilspl=isymlat(lspl) ! symmetry matrix in lattice coordinates sl(:,:)=dble(symlat(:,:,lspl)) ! inverse symmetry matrix in Cartesian coordinates sic(:,:)=symlatc(:,:,ilspl) ! operate with symmetry matrix on vpl call r3mtv(sl,vpl,v) do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) ! equivalent atom with this symmetry ja=ieqatom(ia,is,isym) jas=idxas(ja,is) map(ias)=jas ! phase factor t1=twopi*dot_product(vpl(:),atposl(:,ia,is)) z1=cmplx(cos(t1),sin(t1),8) zph(ias)=z1 t1=-twopi*dot_product(v(:),atposl(:,ja,is)) zph(ias)=z1*cmplx(cos(t1),sin(t1),8) end do end do ! rotate and phase-shift dynamical matrix with symmetry do ias=1,natmtot i=3*(ias-1) k=3*(map(ias)-1) do jas=1,natmtot j=3*(jas-1) l=3*(map(jas)-1) do m=1,3 do n=1,3 a(m,n)=dble(dyn(i+m,j+n)) b(m,n)=aimag(dyn(i+m,j+n)) end do end do call r3mm(sic,a,c) call r3mmt(c,sic,a) call r3mm(sic,b,c) call r3mmt(c,sic,b) z1=zph(ias)*conjg(zph(jas)) do m=1,3 do n=1,3 dyns(k+m,l+n)=dyns(k+m,l+n)+z1*cmplx(a(m,n),b(m,n),8) end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dynsym.f900000644000000000000000000000013214061636517014567 xustar0030 mtime=1623670095.623101835 30 atime=1623670094.444102929 30 ctime=1623670095.623101835 elk-7.2.42/src/dynsym.f900000644002504400250440000000234114061636517016624 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006-2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dynsym(vpl,dynp) use modmain use modphonon implicit none ! arguments real(8), intent(in) :: vpl(3) complex(8), intent(inout) :: dynp(nbph,nbph) ! local variables integer isym,lspl,i,j,n real(8) v1(3),v2(3),s(3,3),t1 ! automatic arrays complex(8) dyns(nbph,nbph) ! map input vector to first Brillouin zone v1(:)=vpl(:) call vecfbz(epslat,bvec,v1) n=0 dyns(:,:)=0.d0 ! use the symmetries which leave vpl invariant do isym=1,nsymcrys if (.not.tv0symc(isym)) cycle lspl=lsplsymc(isym) s(:,:)=dble(symlat(:,:,lspl)) call r3mtv(s,v1,v2) t1=abs(v1(1)-v2(1))+abs(v1(2)-v2(2))+abs(v1(3)-v2(3)) if (t1.lt.epslat) then call dynsymapp(isym,v1,dynp,dyns) n=n+1 end if end do if (n.eq.0) then write(*,*) write(*,'("Error(dynsym): no symmetries leave vpl invariant")') write(*,*) stop end if t1=1.d0/dble(n) dynp(:,:)=t1*dyns(:,:) ! make the matrix Hermitian do j=1,nbph do i=1,j-1 dynp(i,j)=0.5d0*(dynp(i,j)+conjg(dynp(j,i))) dynp(j,i)=conjg(dynp(i,j)) end do dynp(j,j)=dble(dynp(j,j)) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/dynev.f900000644000000000000000000000013214061636517014371 xustar0030 mtime=1623670095.624101834 30 atime=1623670094.445102928 30 ctime=1623670095.624101834 elk-7.2.42/src/dynev.f900000644002504400250440000000236014061636517016427 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dynev(dynp,w,ev) use modmain use modphonon implicit none ! arguments complex(8), intent(in) :: dynp(nbph,nbph) real(8), intent(out) :: w(nbph) complex(8), intent(out) :: ev(nbph,nbph) ! local variables integer is,ia,js,ja integer ip,jp,i,j real(8) t1 ev(:,:)=0.d0 i=0 do is=1,nspecies do ia=1,natoms(is) do ip=1,3 i=i+1 j=0 do js=1,nspecies ! mass factor if ((spmass(is).le.0.d0).or.(spmass(js).le.0.d0)) then ! infinite mass t1=0.d0 else t1=1.d0/sqrt(spmass(is)*spmass(js)) end if do ja=1,natoms(js) do jp=1,3 j=j+1 if (i.le.j) then ! use Hermitian average of dynamical matrix ev(i,j)=0.5d0*t1*(dynp(i,j)+conjg(dynp(j,i))) end if end do end do end do end do end do end do ! find the eigenvalues and eigenvectors of the dynamical matrix call eveqnzh(nbph,nbph,ev,w) do i=1,nbph if (w(i).ge.0.d0) then w(i)=sqrt(w(i)) else w(i)=-sqrt(abs(w(i))) end if end do end subroutine elk-7.2.42/src/PaxHeaders.21776/phdos.f900000644000000000000000000000013214061636517014361 xustar0030 mtime=1623670095.626101832 30 atime=1623670094.447102926 30 ctime=1623670095.626101832 elk-7.2.42/src/phdos.f900000644002504400250440000001011514061636517016414 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine phdos use modmain use modphonon use modtest implicit none ! local variables integer iq,i,iw integer i1,i2,i3 real(8) wmin,wmax,wd,dw real(8) tmax,temp(ntemp),s(ntemp) real(8) v(3),t1,t2 ! allocatable arrays real(8), allocatable :: wp(:),w(:),gw(:),f(:) complex(8), allocatable :: dynq(:,:,:),dynr(:,:,:) complex(8), allocatable :: dynp(:,:),ev(:,:) ! external functions real(8), external :: splint ! initialise universal variables call init0 call init2 allocate(wp(nbph),w(nwplot),gw(nwplot),f(nwplot)) allocate(dynq(nbph,nbph,nqpt),dynr(nbph,nbph,nqptnr)) allocate(dynp(nbph,nbph),ev(nbph,nbph)) ! read in the dynamical matrices call readdyn(dynq) ! apply the acoustic sum rule call sumrule(dynq) ! Fourier transform the dynamical matrices to real-space call dynqtor(dynq,dynr) ! find the minimum and maximum frequencies wmin=0.d0 wmax=0.d0 do iq=1,nqpt call dynev(dynq(:,:,iq),wp,ev) wmin=min(wmin,wp(1)) wmax=max(wmax,wp(nbph)) end do wmax=wmax+(wmax-wmin)*0.1d0 wmin=wmin-(wmax-wmin)*0.1d0 wd=wmax-wmin if (wd.lt.1.d-8) wd=1.d0 dw=wd/dble(nwplot) ! generate energy grid do iw=1,nwplot w(iw)=dw*dble(iw-1)+wmin end do gw(:)=0.d0 do i1=0,ngrkf-1 v(1)=dble(i1)/dble(ngrkf) do i2=0,ngrkf-1 v(2)=dble(i2)/dble(ngrkf) do i3=0,ngrkf-1 v(3)=dble(i3)/dble(ngrkf) ! compute the dynamical matrix at this particular q-point call dynrtoq(v,dynr,dynp) ! find the phonon frequencies call dynev(dynp,wp,ev) do i=1,nbph t1=(wp(i)-wmin)/dw+1.d0 iw=nint(t1) if ((iw.ge.1).and.(iw.le.nwplot)) then gw(iw)=gw(iw)+1.d0 end if end do end do end do end do t1=1.d0/(dw*dble(ngrkf)**3) gw(:)=t1*gw(:) ! smooth phonon DOS if required if (nswplot.gt.0) call fsmooth(nswplot,nwplot,gw) ! write phonon DOS to file open(50,file='PHDOS.OUT',form='FORMATTED') do iw=1,nwplot write(50,'(2G18.10)') w(iw),gw(iw) end do close(50) write(*,*) write(*,'("Info(phdos):")') write(*,'(" phonon density of states written to PHDOS.OUT")') !-------------------------------------------! ! thermodynamic properties from DOS ! !-------------------------------------------! ! maximum temperature tmax=wmax/kboltz ! temperature grid do i=1,ntemp temp(i)=tmax*dble(i)/dble(ntemp) end do open(50,file='THERMO.OUT',form='FORMATTED') write(50,*) write(50,'("(All quantities are per unit cell)")') ! zero point energy do iw=1,nwplot f(iw)=gw(iw)*w(iw) end do t1=splint(nwplot,w,f) t1=0.5d0*t1 write(50,*) write(50,'("Zero-point energy : ",G18.10)') t1 ! vibrational energy write(50,*) write(50,'("Vibrational energy vs. temperature :")') do i=1,ntemp do iw=1,nwplot t1=w(iw)/(2.d0*kboltz*temp(i)) if (t1.gt.0.d0) then f(iw)=gw(iw)*w(iw)*cosh(t1)/sinh(t1) else f(iw)=0.d0 end if end do t1=splint(nwplot,w,f) t1=0.5d0*t1 write(50,'(2G18.10)') temp(i),t1 s(i)=t1 end do ! free energy write(50,*) write(50,'("Free energy vs. temperature :")') do i=1,ntemp do iw=1,nwplot t1=2.d0*sinh(w(iw)/(2.d0*kboltz*temp(i))) if (t1.gt.0.d0) then f(iw)=gw(iw)*log(t1) else f(iw)=0.d0 end if end do t1=splint(nwplot,w,f) t1=kboltz*temp(i)*t1 write(50,'(2G18.10)') temp(i),t1 ! compute entropy from S = (F-E)/T s(i)=(s(i)-t1)/temp(i) end do ! entropy write(50,*) write(50,'("Entropy vs. temperature :")') do i=1,ntemp write(50,'(2G18.10)') temp(i),s(i) end do ! heat capacity write(50,*) write(50,'("Heat capacity vs. temperature :")') do i=1,ntemp do iw=1,nwplot t1=w(iw)/(kboltz*temp(i)) t2=exp(t1)-1.d0 if (abs(t2).gt.1.d-14) then f(iw)=gw(iw)*(t1**2)*(t2+1.d0)/t2**2 else f(iw)=0.d0 end if end do t1=splint(nwplot,w,f) t1=kboltz*t1 write(50,'(2G18.10)') temp(i),t1 end do close(50) write(*,'(" thermodynamic properties written to THERMO.OUT")') ! write phonon DOS to test file call writetest(210,'phonon DOS',nv=nwplot,tol=1.d-2,rva=gw) deallocate(wp,w,gw,f,dynq,dynr,dynp,ev) end subroutine elk-7.2.42/src/PaxHeaders.21776/sumrule.f900000644000000000000000000000013214061636517014740 xustar0030 mtime=1623670095.627101831 30 atime=1623670094.449102924 30 ctime=1623670095.627101831 elk-7.2.42/src/sumrule.f900000644002504400250440000000337614061636517017006 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: sumrule ! !INTERFACE: subroutine sumrule(dynq) ! !INPUT/OUTPUT PARAMETERS: ! dynq : dynamical matrices on q-point set (in,real(nbph,nbph,nqpt)) ! !DESCRIPTION: ! Applies the same correction to all the dynamical matrices such that the ! matrix for ${\bf q}=0$ satisfies the acoustic sum rule. In other words, the ! matrices are updated with ! $$ D_{ij}^{\bf q}\rightarrow D_{ij}^{\bf q}-\sum_{k=1}^3 \omega_k^0 ! v_{k;i}^0 v_{k;j}^0 $$ ! for all ${\bf q}$, where $\omega_k^0$ is the $k$th eigenvalue of the ! ${\bf q}=0$ dynamical matrix and $v_{k;i}^0$ the $i$th component of its ! eigenvector. The eigenvalues are assumed to be arranged in ascending order. ! This ensures that the ${\bf q}=0$ dynamical matrix has 3 zero eigenvalues, ! which the uncorrected matrix may not have due to the finite ! exchange-correlation grid. ! ! !REVISION HISTORY: ! Created May 2005 (JKD) !EOP !BOC use modmain use modphonon implicit none ! arguments complex(8), intent(inout) :: dynq(nbph,nbph,nqpt) ! local variables integer iq,i,j,k ! automatic arrays real(8) w(nbph) complex(8) ev(nbph,nbph) ! compute the eigenvalues and vectors of the q = 0 dynamical matrix do i=1,nbph do j=i,nbph ev(i,j)=0.5d0*(dynq(i,j,1)+conjg(dynq(j,i,1))) end do end do call eveqnzh(nbph,nbph,ev,w) ! subtract outer products of 3 lowest eigenvectors for q = 0 from all the ! dynamical matrices do iq=1,nqpt do i=1,nbph do j=1,nbph do k=1,3 dynq(i,j,iq)=dynq(i,j,iq)-w(k)*ev(i,k)*conjg(ev(j,k)) end do end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writephn.f900000644000000000000000000000013214061636517015104 xustar0030 mtime=1623670095.629101829 30 atime=1623670094.450102924 30 ctime=1623670095.629101829 elk-7.2.42/src/writephn.f900000644002504400250440000000325214061636517017143 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writephn use modmain use modphonon implicit none ! local variables integer iq,i,j,is,ia,ip ! allocatable arrays real(8), allocatable :: w(:) complex(8), allocatable :: dynq(:,:,:),dynr(:,:,:) complex(8), allocatable :: dynp(:,:),ev(:,:) ! initialise universal variables call init0 call init2 allocate(w(nbph)) allocate(dynq(nbph,nbph,nqpt)) allocate(dynr(nbph,nbph,nqptnr)) allocate(dynp(nbph,nbph)) allocate(ev(nbph,nbph)) ! read in the dynamical matrices call readdyn(dynq) ! apply the acoustic sum rule call sumrule(dynq) ! Fourier transform the dynamical matrices to real-space call dynqtor(dynq,dynr) open(50,file='PHONON.OUT',form='FORMATTED') do iq=1,nphwrt call dynrtoq(vqlwrt(:,iq),dynr,dynp) call dynev(dynp,w,ev) write(50,*) write(50,'(I6,3G18.10," : q-point, vqlwrt")') iq,vqlwrt(:,iq) do j=1,nbph write(50,*) write(50,'(I6,G18.10," : mode, frequency")') j,w(j) i=0 do is=1,nspecies do ia=1,natoms(is) do ip=1,3 i=i+1 if (i.eq.1) then write(50,'(3I4,2G18.10," : species, atom, polarisation, & &eigenvector")') is,ia,ip,ev(i,j) else write(50,'(3I4,2G18.10)') is,ia,ip,ev(i,j) end if end do end do end do end do write(50,*) end do close(50) write(*,*) write(*,'("Info(writephn): phonon frequencies and eigenvectors written to & &PHONON.OUT")') write(*,'(" for all q-vectors in the phwrite list")') deallocate(w,dynq,dynr,dynp,ev) end subroutine elk-7.2.42/src/PaxHeaders.21776/dynfext.f900000644000000000000000000000013214061636517014725 xustar0030 mtime=1623670095.630101828 30 atime=1623670094.452102922 30 ctime=1623670095.630101828 elk-7.2.42/src/dynfext.f900000644002504400250440000000132414061636517016762 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dynfext(iq,is,ia,ip,fext) use modmain implicit none ! arguments integer, intent(in) :: iq,is,ia,ip character(*), intent(out) :: fext ! local variables integer i,j,m(3),n(3) ! external functions integer, external :: gcd do i=1,3 if (ivq(i,iq).ne.0) then j=gcd(ivq(i,iq),ngridq(i)) m(i)=ivq(i,iq)/j n(i)=ngridq(i)/j else m(i)=0 n(i)=0 end if end do write(fext,'("_Q",2I2.2,"_",2I2.2,"_",2I2.2,"_S",I2.2,"_A",I3.3,"_P",I1,& &".OUT")') m(1),n(1),m(2),n(2),m(3),n(3),is,ia,ip end subroutine elk-7.2.42/src/PaxHeaders.21776/writegamma.f900000644000000000000000000000013114061636517015400 xustar0030 mtime=1623670095.632101826 29 atime=1623670094.45410292 30 ctime=1623670095.632101826 elk-7.2.42/src/writegamma.f900000644002504400250440000000164714061636517017446 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writegamma(gq) use modmain use modphonon implicit none ! arguments real(8), intent(in) :: gq(nbph,nqpt) ! local variables integer iq,i open(50,file='GAMMAQ.OUT',form='FORMATTED',action='WRITE') write(50,*) write(50,'(I4," : total number of atoms")') natmtot write(50,'(I6," : number of q-points")') nqpt write(50,*) do iq=1,nqpt write(50,'(I6," : q-point")') iq write(50,'(3G18.10," : q-vector (lattice coordinates)")') vql(:,iq) write(50,'(3G18.10," : q-vector (Cartesian coordinates)")') vqc(:,iq) do i=1,nbph write(50,'(I4,G18.10)') i,gq(i,iq) end do write(50,*) end do close(50) write(*,*) write(*,'("Info(writegamma):")') write(*,'(" wrote phonon linewidths for all q-points to GAMMAQ.OUT")') end subroutine elk-7.2.42/src/PaxHeaders.21776/readgamma.f900000644000000000000000000000013214061636517015162 xustar0030 mtime=1623670095.633101825 30 atime=1623670094.455102919 30 ctime=1623670095.633101825 elk-7.2.42/src/readgamma.f900000644002504400250440000000401314061636517017215 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readgamma(gq) use modmain use modphonon implicit none ! arguments real(8), intent(out) :: gq(nbph,nqpt) ! local variables integer iq,i integer natmtot_,nqpt_,iq_,i_ real(8) vql_(3),vqc_(3),t1 open(50,file='GAMMAQ.OUT',form='FORMATTED',status='OLD') read(50,*) read(50,*) natmtot_ if (natmtot.ne.natmtot_) then write(*,*) write(*,'("Error(readgamma): differing natmtot")') write(*,'(" current : ",I4)') natmtot write(*,'(" GAMMAQ.OUT : ",I4)') natmtot_ write(*,*) stop end if read(50,*) nqpt_ if (nqpt.ne.nqpt_) then write(*,*) write(*,'("Error(readgamma): differing nqpt")') write(*,'(" current : ",I6)') nqpt write(*,'(" GAMMAQ.OUT : ",I6)') nqpt_ write(*,*) stop end if read(50,*) do iq=1,nqpt read(50,*) iq_ if (iq.ne.iq_) then write(*,*) write(*,'("Error(readgamma): incorrect q-point index in GAMMAQ.OUT for & &q-point ",I6)') iq write(*,*) stop end if read(50,*) vql_ t1=sum(abs(vql(:,iq)-vql_(:))) if (t1.gt.epslat) then write(*,*) write(*,'("Error(readgamma): differing q-vectors in lattice coordinates & &for q-point ",I6)') iq write(*,'(" current : ",3G18.10)') vql(:,iq) write(*,'(" GAMMAQ.OUT : ",3G18.10)') vql_ write(*,*) stop end if read(50,*) vqc_ t1=sum(abs(vqc(:,iq)-vqc_(:))) if (t1.gt.epslat) then write(*,*) write(*,'("Error(readgamma): differing q-vectors in Cartesian coordinates & &for q-point ",I6)') iq write(*,'(" current : ",3G18.10)') vqc(:,iq) write(*,'(" GAMMAQ.OUT : ",3G18.10)') vqc_ write(*,*) stop end if do i=1,nbph read(50,*) i_,gq(i,iq) if (i.ne.i_) then write(*,*) write(*,'("Error(readgamma): incorrect mode index in GAMMAQ.OUT for & &q-point ",I6)') iq write(*,*) stop end if end do read(50,*) end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/phlwidth.f900000644000000000000000000000013214061636517015067 xustar0030 mtime=1623670095.635101824 30 atime=1623670094.457102917 30 ctime=1623670095.635101824 elk-7.2.42/src/phlwidth.f900000644002504400250440000000507514061636517017133 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine phlwidth use modmain use modphonon implicit none ! local variables integer i,j,iq,iv real(8) gmin,gmax,t1 ! allocatable arrays real(8), allocatable :: wq(:),gq(:,:),gp(:,:) complex(8), allocatable :: dynq(:,:,:),ev(:,:),b(:,:) complex(8), allocatable :: gmq(:,:,:),gmr(:,:,:),gmp(:,:) ! initialise universal variables call init0 call init2 allocate(wq(nbph),gq(nbph,nqpt),gp(nbph,npp1d)) allocate(dynq(nbph,nbph,nqpt)) allocate(ev(nbph,nbph),b(nbph,nbph)) allocate(gmq(nbph,nbph,nqpt)) allocate(gmr(nbph,nbph,nqptnr)) allocate(gmp(nbph,nbph)) ! read in the dynamical matrices call readdyn(dynq) ! apply the acoustic sum rule call sumrule(dynq) ! read in the phonon linewidths for each q-point call readgamma(gq) ! loop over phonon q-points do iq=1,nqpt ! diagonalise the dynamical matrix call dynev(dynq(:,:,iq),wq,ev) ! construct a complex matrix from the phonon eigenvectors such that its ! eigenvalues squared are the phonon linewidths do i=1,nbph t1=sqrt(abs(gq(i,iq))) do j=1,nbph b(i,j)=t1*conjg(ev(j,i)) end do end do call zgemm('N','N',nbph,nbph,nbph,zone,ev,nbph,b,nbph,zzero,gmq(:,:,iq),nbph) end do ! Fourier transform the gamma matrices to real-space call dynqtor(gmq,gmr) ! generate a set of q-point vectors along a path in the Brillouin zone call plotpt1d(bvec,nvp1d,npp1d,vvlp1d,vplp1d,dvp1d,dpp1d) gmin=1.d8 gmax=0.d0 ! compute the linewidths along the path do iq=1,npp1d ! compute the gamma matrix at this particular q-point call dynrtoq(vplp1d(:,iq),gmr,gmp) ! diagonalise the gamma matrix call eveqnzh(nbph,nbph,gmp,gp(:,iq)) ! square the eigenvalues to recover the linewidths gp(:,iq)=gp(:,iq)**2 gmin=min(gmin,gp(1,iq)) gmax=max(gmax,gp(nbph,iq)) end do gmax=gmax+(gmax-gmin)*0.5d0 gmin=gmin-(gmax-gmin)*0.5d0 ! output the vertex location lines open(50,file='PHLWLINES.OUT',form='FORMATTED') do iv=1,nvp1d write(50,'(2G18.10)') dvp1d(iv),gmin write(50,'(2G18.10)') dvp1d(iv),gmax write(50,*) end do close(50) ! output the phonon linewidth dispersion open(50,file='PHLWIDTH.OUT',form='FORMATTED') do i=1,nbph do iq=1,npp1d write(50,'(2G18.10)') dpp1d(iq),gp(i,iq) end do write(50,*) end do close(50) write(*,*) write(*,'("Info(phlwidth):")') write(*,'(" phonon linewidth dispersion written to PHLWIDTH.OUT")') write(*,'(" vertex location lines written to PHLWLINES.OUT")') deallocate(wq,gq,gp,dynq) deallocate(ev,b,gmq,gmr,gmp) end subroutine elk-7.2.42/src/PaxHeaders.21776/alpha2f.f900000644000000000000000000000013214061636517014561 xustar0030 mtime=1623670095.636101823 30 atime=1623670094.459102915 30 ctime=1623670095.636101823 elk-7.2.42/src/alpha2f.f900000644002504400250440000001155114061636517016621 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine alpha2f use modmain use modphonon use modtest implicit none ! local variables integer ik,iq,i,j integer i1,i2,i3,iw real(8) wmin,wmax,wd,dw real(8) wlog,wrms,lambda,tc real(8) v(3),t1 ! allocatable arrays real(8), allocatable :: gq(:,:),wp(:),a2fp(:),w(:),a2f(:) complex(8), allocatable :: dynq(:,:,:),dynr(:,:,:) complex(8), allocatable :: dynp(:,:),ev(:,:),b(:,:) complex(8), allocatable :: a2fmq(:,:,:),a2fmr(:,:,:),a2fmp(:,:) ! initialise universal variables call init0 call init1 call init2 ! allocate local arrays allocate(gq(nbph,nqpt),wp(nbph),a2fp(nbph)) allocate(w(nwplot),a2f(nwplot)) allocate(dynq(nbph,nbph,nqpt)) allocate(dynr(nbph,nbph,nqptnr)) allocate(dynp(nbph,nbph)) allocate(ev(nbph,nbph),b(nbph,nbph)) allocate(a2fmq(nbph,nbph,nqpt)) allocate(a2fmr(nbph,nbph,nqptnr)) allocate(a2fmp(nbph,nbph)) ! get the eigenvalues from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) end do ! compute the density of states at the Fermi energy call occupy ! read in the dynamical matrices call readdyn(dynq) ! apply the acoustic sum rule call sumrule(dynq) ! Fourier transform the dynamical matrices to real-space call dynqtor(dynq,dynr) ! read in the phonon linewidths for each q-point call readgamma(gq) ! loop over phonon q-points do iq=1,nqpt ! find the eigenvalues and eigenvectors of the dynamical matrix call dynev(dynq(:,:,iq),wphq(:,iq),ev) ! construct a complex matrix from the phonon eigenvectors such that its ! eigenvalues squared are the phonon linewidths divided by the frequency do i=1,nbph if (wphq(i,iq).gt.1.d-8) then t1=sqrt(abs(gq(i,iq)/wphq(i,iq))) else t1=0.d0 end if do j=1,nbph b(i,j)=t1*conjg(ev(j,i)) end do end do call zgemm('N','N',nbph,nbph,nbph,zone,ev,nbph,b,nbph,zzero,a2fmq(:,:,iq), & nbph) end do ! Fourier transform the matrices to real-space call dynqtor(a2fmq,a2fmr) ! find the minimum and maximum frequencies wmin=0.d0 wmax=0.d0 do iq=1,nqpt wmin=min(wmin,wphq(1,iq)) wmax=max(wmax,wphq(nbph,iq)) end do wmax=wmax+(wmax-wmin)*0.1d0 wmin=wmin-(wmax-wmin)*0.1d0 wd=wmax-wmin if (wd.lt.1.d-8) wd=1.d0 dw=wd/dble(nwplot) ! generate energy grid do iw=1,nwplot w(iw)=dw*dble(iw-1)+wmin end do a2f(:)=0.d0 do i1=0,ngrkf-1 v(1)=dble(i1)/dble(ngrkf) do i2=0,ngrkf-1 v(2)=dble(i2)/dble(ngrkf) do i3=0,ngrkf-1 v(3)=dble(i3)/dble(ngrkf) ! compute the dynamical matrix at this particular q-point call dynrtoq(v,dynr,dynp) ! find the phonon eigenvalues and eigenvectors call dynev(dynp,wp,ev) ! compute the α²F matrix at this particular q-point call dynrtoq(v,a2fmr,a2fmp) ! diagonalise the α²F matrix simultaneously with the dynamical matrix ! (thanks to Matthieu Verstraete and Ryotaro Arita for correcting this) call dynevs(ev,a2fmp,a2fp) ! square the eigenvalues to recover the linewidths divided by the frequency a2fp(:)=a2fp(:)**2 do i=1,nbph t1=(wp(i)-wmin)/dw+1.d0 iw=nint(t1) if ((iw.ge.1).and.(iw.le.nwplot)) then a2f(iw)=a2f(iw)+a2fp(i) end if end do end do end do end do t1=twopi*(fermidos/2.d0)*dw*dble(ngrkf)**3 if (t1.gt.1.d-8) then t1=1.d0/t1 else t1=0.d0 end if a2f(:)=t1*a2f(:) ! smooth Eliashberg function if required if (nswplot.gt.0) call fsmooth(nswplot,nwplot,a2f) ! write Eliashberg function to file open(50,file='ALPHA2F.OUT',form='FORMATTED') do iw=1,nwplot write(50,'(2G18.10)') w(iw),a2f(iw) end do close(50) write(*,*) write(*,'("Info(alpha2f):")') write(*,'(" Eliashberg function α²F written to ALPHA2F.OUT")') ! compute lambda, logarithmic average frequency, RMS average frequency and ! McMillan-Allen-Dynes superconducting critical temperature call mcmillan(w,a2f,lambda,wlog,wrms,tc) open(50,file='MCMILLAN.OUT',form='FORMATTED') write(50,*) write(50,'("Electron-phonon coupling constant, λ : ",G18.10)') lambda write(50,*) write(50,'("Logarithmic average frequency : ",G18.10)') wlog write(50,*) write(50,'("RMS average frequency : ",G18.10)') wrms write(50,*) write(50,'("Coulomb pseudopotential, μ* : ",G18.10)') mustar write(50,*) write(50,'("McMillan-Allen-Dynes superconducting critical temperature")') write(50,'(" [Eq. 34, Phys. Rev. B 12, 905 (1975)] (kelvin) : ",G18.10)') tc write(50,*) close(50) write(*,*) write(*,'("Info(alpha2f):")') write(*,'(" Electron-phonon coupling constant, λ,")') write(*,'(" logarithmic and RMS average frequencies,")') write(*,'(" and McMillan-Allen-Dynes superconducting critical temperature")') write(*,'(" written to MCMILLAN.OUT")') ! write lambda to test file call writetest(251,'electron-phonon coupling constant, lambda',tol=5.d-2, & rv=lambda) deallocate(wp,gq,a2fp,w,a2f) deallocate(dynq,dynr,dynp,ev,b) deallocate(a2fmq,a2fmr,a2fmp) end subroutine elk-7.2.42/src/PaxHeaders.21776/writelambda.f900000644000000000000000000000013214061636517015537 xustar0030 mtime=1623670095.637101822 30 atime=1623670094.460102914 30 ctime=1623670095.637101822 elk-7.2.42/src/writelambda.f900000644002504400250440000000205014061636517017571 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writelambda(gq) use modmain use modphonon implicit none ! arguments real(8), intent(in) :: gq(nbph,nqpt) ! local variables integer iq,i real(8) t1,t2 open(50,file='LAMBDAQ.OUT',form='FORMATTED') write(50,*) write(50,'(I4," : total number of atoms")') natmtot write(50,'(I6," : number of q-points")') nqpt write(50,*) do iq=1,nqpt write(50,'(I6," : q-point")') iq write(50,'(3G18.10," : q-vector (lattice coordinates)")') vql(:,iq) write(50,'(3G18.10," : q-vector (Cartesian coordinates)")') vqc(:,iq) do i=1,nbph t1=pi*fermidos*wphq(i,iq)**2 if (t1.gt.1.d-8) then t2=gq(i,iq)/t1 else t2=0.d0 end if write(50,'(I4,G18.10)') i,t2 end do write(50,*) end do close(50) write(*,*) write(*,'("Info(writelambda):")') write(*,'(" wrote electron-phonon coupling constants for all q-points to & &LAMBDAQ.OUT")') end subroutine elk-7.2.42/src/PaxHeaders.21776/ephcouple.f900000644000000000000000000000013014061636517015226 xustar0029 mtime=1623670095.63910182 30 atime=1623670094.462102912 29 ctime=1623670095.63910182 elk-7.2.42/src/ephcouple.f900000644002504400250440000001271014061636517017266 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine ephcouple use modmain use modphonon use modmpi use modomp use modstore implicit none ! local variables integer iq,ik,jk,jkq integer ist,jst,isym,ip integer is,ia,ias,js,jas integer nr,nri,np,i,n,nthd real(8) vl(3),de,x real(8) t1,t2,t3,t4 ! allocatable arrays real(8), allocatable :: gq(:,:) complex(8), allocatable :: dynq(:,:,:),ev(:,:),a(:,:) complex(8), allocatable :: dvmt(:,:,:),dvir(:,:) complex(8), allocatable :: zfmt(:),gzfmt(:,:,:) complex(8), allocatable :: ephmat(:,:,:) ! external functions real(8), external :: sdelta ! increase the angular momentum cut-off on the inner part of the muffin-tin lmaxi_=lmaxi lmaxi=max(lmaxi,4) ! initialise universal variables call init0 call init1 call init2 ! allocate global arrays if (allocated(dvsbs)) deallocate(dvsbs) n=npmtmax*natmtot+ngtot allocate(dvsbs(n)) dvsmt(1:npmtmax,1:natmtot)=>dvsbs(1:) i=npmtmax*natmtot+1 dvsir(1:ngtot)=>dvsbs(i:) ! allocate local arrays allocate(gq(nbph,nqpt)) allocate(dynq(nbph,nbph,nqpt),ev(nbph,nbph),a(nbph,nbph)) allocate(dvmt(npcmtmax,natmtot,nbph),dvir(ngtot,nbph)) allocate(zfmt(npmtmax),gzfmt(npmtmax,3,natmtot)) ! read in the density and potentials from file call readstate ! Fourier transform Kohn-Sham potential to G-space call genvsig ! read Fermi energy from file call readfermi ! set the speed of light >> 1 (non-relativistic approximation) solsc=sol*100.d0 ! new file extension for eigenvector files with c >> 1 filext='_EPH.OUT' ! generate the first- and second-variational eigenvectors and eigenvalues call linengy call genapwlofr call gensocfr call genevfsv ! precise determination of the Fermi energy swidth_=swidth swidth=1.d-5 call occupy swidth=swidth_ ! restore the speed of light solsc=sol ! read in the dynamical matrices call readdyn(dynq) ! apply the acoustic sum rule call sumrule(dynq) ! compute the gradients of the Kohn-Sham potential for the rigid-ion term do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) call rtozfmt(nr,nri,vsmt(:,ias),zfmt) call gradzfmt(nr,nri,rlmt(:,-1,is),wcrmt(:,:,is),zfmt,npmtmax,gzfmt(:,:,ias)) end do ! energy window for calculating the electron-phonon matrix elements if (task.eq.240) then de=4.d0*swidth else de=1.d6 end if ! loop over phonon q-points do iq=1,nqpt if (mp_mpi) write(*,'("Info(ephcouple): ",I6," of ",I6," q-points")') iq,nqpt ! diagonalise the dynamical matrix call dynev(dynq(:,:,iq),wphq(:,iq),ev) ! generate the matrix for converting between Cartesian and phonon coordinates call genmcph(wphq(:,iq),ev,a) i=0 do is=1,nspecies nr=nrmt(is) nri=nrmti(is) np=npmt(is) do ia=1,natoms(is) ias=idxas(ia,is) do ip=1,3 i=i+1 ! read in the Cartesian change in Kohn-Sham potential call readdvs(iq,is,ia,ip,dvsmt,dvsir) ! add the rigid-ion term dvsmt(1:np,ias)=dvsmt(1:np,ias)-gzfmt(1:np,ip,ias) do jas=1,natmtot js=idxis(jas) ! convert to coarse radial mesh call zfmtftoc(nrcmt(js),nrcmti(js),dvsmt(:,jas),dvmt(:,jas,i)) ! apply the radial integration weights call zfmtwr(nrcmt(js),nrcmti(js),wrcmt(:,js),dvmt(:,jas,i)) end do ! multiply the interstitial potential with the characteristic function dvir(:,i)=dvsir(:)*cfunir(:) end do end do end do ! zero the phonon linewidths array gq(:,iq)=0.d0 call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(ephmat,jk,vl,isym,jkq) & !$OMP PRIVATE(t1,t2,t3,t4,ist,jst,x,i) & !$OMP NUM_THREADS(nthd) allocate(ephmat(nstsv,nstsv,nbph)) !$OMP DO do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! compute the electron-phonon coupling matrix elements call genephmat(iq,ik,de,a,dvmt,dvir,ephmat) ! write the matrix elements to file if required if (task.eq.241) call putephmat(iq,ik,ephmat) ! k+q-vector in lattice coordinates vl(:)=vkl(:,ik)+vql(:,iq) ! index to k+q-vector call findkpt(vl,isym,jkq) t1=pi*wkptnr*occmax ! loop over second-variational states do ist=1,nstsv x=(evalsv(ist,jkq)-efermi)/swidth t2=t1*sdelta(stype,x)/swidth do jst=1,nstsv ! loop over phonon branches do i=1,nbph x=(wphq(i,iq)+evalsv(jst,jk)-evalsv(ist,jkq))/swidth t3=t2*sdelta(stype,x)/swidth t4=dble(ephmat(ist,jst,i))**2+aimag(ephmat(ist,jst,i))**2 !$OMP ATOMIC gq(i,iq)=gq(i,iq)+wphq(i,iq)*t3*t4 end do end do end do ! end loop over k-points end do !$OMP END DO deallocate(ephmat) !$OMP END PARALLEL call freethd(nthd) ! end loop over phonon q-points end do ! add gq from each MPI process if (np_mpi.gt.1) then n=nbph*nqpt call mpi_allreduce(mpi_in_place,gq,n,mpi_double_precision,mpi_sum,mpicom, & ierror) end if ! restore the default file extension filext='.OUT' if (mp_mpi) then ! write the phonon linewidths to file call writegamma(gq) ! write electron-phonon coupling constants to file call writelambda(gq) if (task.eq.241) then write(*,*) write(*,'("Info(ephcouple):")') write(*,'(" wrote electron-phonon matrix elements to EPHMAT.OUT")') end if end if ! deallocate global arrays deallocate(dvsbs) ! deallocate local arrays deallocate(gq,dynq,ev,a) deallocate(dvmt,dvir,zfmt,gzfmt) ! restore original input parameters lmaxi=lmaxi_ end subroutine elk-7.2.42/src/PaxHeaders.21776/eliashberg.f900000644000000000000000000000013214061636517015351 xustar0030 mtime=1623670095.640101819 30 atime=1623670094.464102911 30 ctime=1623670095.640101819 elk-7.2.42/src/eliashberg.f900000644002504400250440000001447214061636517017416 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 A. Sanna and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: eliashberg ! !INTERFACE: subroutine eliashberg ! !USES: use modmain use modphonon use modomp ! !DESCRIPTION: ! Calculates the superconducting gap within Eliashberg theory. This ! implementation is isotropic and assumes a flat density of states. The ! Eliashberg function $\alpha^2F$ is required as input for this calculation. ! ! !REVISION HISTORY: ! Created December 2010 (Antonio Sanna) ! Modified, June 2011 (JKD) !EOP !BOC implicit none ! local variables ! maximum allowed number of Matsubara frequencies integer, parameter :: maxwf=40000 ! maximum number of iterations integer, parameter :: maxit=1000 integer nwf,nwfcl,nin,nout integer itemp,it,i,m,n,nthd ! convergence tolerance real(8), parameter :: eps=1.d-12 ! mixing paramter real(8), parameter :: beta=0.5d0 real(8) lambda,wlog,wrms,tc real(8) wfmax,tmin,tmax,dtemp,temp real(8) dw,dmu,sm,a,b,t0,t1 ! allocatable arrays real(8), allocatable :: w(:),a2f(:),wf(:),l(:) real(8), allocatable :: d0(:),d(:),z0(:),z(:),r(:) complex(8), allocatable :: zin(:),uin(:),zout(:),uout(:) ! initialise universal variables call init0 call init1 allocate(w(nwplot),a2f(nwplot)) ! read in the Eliashberg function call readalpha2f(w,a2f) dw=(w(nwplot)-w(1))/dble(nwplot) ! compute the McMillan parameters call mcmillan(w,a2f,lambda,wlog,wrms,tc) ! Matsubara frequency cut-off wfmax=20.d0*wrms ! minumum temperature tmin=tc/6.d0 if (tmin.lt.1.d-2) tmin=0.1d0 ! maximum temperature tmax=5.d0*tc if (tmax.lt.1.d0) tmax=1.d0 ! temperature step size dtemp=(tmax-tmin)/dble(ntemp) ! maximum number of fermionic Matsubara frequencies nwf=nint(wfmax/(twopi*kboltz*dtemp)) if (nwf.lt.1) nwf=1 if (nwf.gt.maxwf) nwf=maxwf allocate(wf(-nwf:nwf)) allocate(l(-2*nwf:2*nwf)) allocate(d0(0:nwf),d(0:nwf)) allocate(z0(0:nwf),z(0:nwf)) allocate(r(0:nwf)) allocate(zin(0:nwf),uin(0:nwf)) ! generate output points for continuation on the real axis nout=4*nwplot allocate(zout(nout),uout(nout)) do i=1,nout zout(i)=cmplx(2.d0*dble(i-1)*dw,0.d0,8) end do ! open files for writing open(62,file='ELIASHBERG.OUT',form='FORMATTED') open(63,file='ELIASHBERG_IA.OUT',form='FORMATTED') open(64,file='ELIASHBERG_GAP_T.OUT',form='FORMATTED') open(65,file='ELIASHBERG_GAP_RA.OUT',form='FORMATTED') open(66,file='ELIASHBERG_Z_RA.OUT',form='FORMATTED') write(62,'("+------------------------------+")') write(62,'("| Eliashberg equations |")') write(62,'("+------------------------------+")') write(62,*) write(62,'("Temperature range : ",2G18.10)') tmin,tmax write(62,'("Number of temperature steps : ",I6)') ntemp write(62,'("Number of output frequencies : ",I8)') nout write(62,'("Fermionic Matsubara frequency cut-off")') write(62,'(" phonons : ",G18.10)') wfmax write(62,'(" Coulomb : ",G18.10)') 2.d0*wrms flush(62) d0(:)=1.d-4 z0(:)=1.d0 ! main loop over temperature do itemp=1,ntemp write(*,'("Info(eliashberg): temperature step ",I6," of ",I6)') itemp,ntemp temp=dble(itemp)*dtemp+tmin write(62,*) write(62,'("Temperature (kelvin) : ",G18.10)') temp t0=pi*kboltz*temp ! number of Matsubara frequencies nwf=nint(wfmax/(2.d0*t0)) if (nwf.gt.maxwf) nwf=maxwf nwfcl=nint(2.d0*wrms/(2.d0*t0)) if (nwfcl.lt.1) nwfcl=1 if (nwfcl.gt.nwf) nwfcl=nwf write(62,'("Number of Matsubara frequencies")') write(62,'(" phonons : ",I8)') nwf write(62,'(" Coulomb : ",I8)') nwfcl ! make Pade approximant input points same as Matsubara frequencies nin=nwf ! generate fermionic Matsubara frequencies do m=-nwf,nwf wf(m)=t0*dble(2*m+1) end do ! compute lambda call holdthd(4*nwf+1,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(t1,sm,i) & !$OMP NUM_THREADS(nthd) do m=-2*nwf,2*nwf t1=(t0*dble(2*m))**2 sm=0.d0 do i=1,nwplot sm=sm+w(i)*a2f(i)/(w(i)**2+t1) end do l(m)=2.d0*sm*dw end do !$OMP END PARALLEL DO call freethd(nthd) ! begin iteration loop do it=1,maxit do m=0,nwf r(m)=sqrt((wf(m)**2+d0(m)**2)*z0(m)**2) end do do n=0,nwf sm=0.d0 do m=0,nwf-1 sm=sm+(l(n-m)-l(n+m+1))*z0(m)*wf(m)/r(m) end do z(n)=t0*sm/wf(n) end do z(0:nwf)=z(0:nwf)+1.d0 z0(0:nwf)=z(0:nwf) ! Coulomb part of summation dmu=0.d0 do n=0,nwfcl dmu=dmu+mustar*d0(n)*z(n)/r(n) end do dmu=dmu*2.d0 ! Gap do n=0,nwf sm=0.d0 do m=0,nwf-1 sm=sm+(l(n-m)+l(n+m+1))*d0(m)*z(m)/r(m) end do d(n)=t0*(sm-dmu)/z(n) end do ! mix old and new gap functions d(0:nwf)=beta*d(0:nwf)+(1.d0-beta)*d0(0:nwf) sm=0.d0 do m=0,nwf sm=sm+abs(d0(m)-d(m)) end do sm=sm/dble(2*nwf) d0(0:nwf)=d(0:nwf) if (sm.le.eps) then write(62,'("Eliashberg equations converged in ",I6," iterations")') it goto 10 end if ! end iteration loop end do write(*,*) write(*,'("Warning(eliashberg): failed to converge: possibly close to T_c")') write(62,'("Failed to converge: possibly close to T_c")') 10 continue flush(62) do n=-nwf,nwf if (n.ge.0) then m=n else m=-n-1 end if write(63,'(3G18.10)') wf(n),d(m),z(m) end do write(63,*) flush(63) write(64,'(3G18.10)') temp,d(0),z(0) flush(64) ! analytic continuation to real axis do m=0,nin zin(m)=cmplx(0.d0,wf(m),8) uin(m)=cmplx(d(m),0.d0,8) end do call pade(nin,zin,uin,nout,zout,uout) do i=1,nout a=dble(uout(i)) b=aimag(uout(i)) write(65,'(3G18.10)') dble(zout(i)),a,b end do write(65,*) flush(65) do m=0,nin uin(m)=cmplx(z(m),0.d0,8) end do call pade(nin,zin,uin,nout,zout,uout) do i=1,nout a=dble(uout(i)) b=aimag(uout(i)) write(66,'(3G18.10)') dble(zout(i)),a,b end do write(66,*) flush(66) ! end loop over temperatures end do close(62); close(63); close(64); close(65); close(66) write(*,*) write(*,'("Info(eliashberg):")') write(*,'(" calculation information written to ELIASHBERG.OUT")') write(*,'(" gap and Z functions on the imaginary axis written to & &ELIASHBERG_IA.OUT")') write(*,'(" gap vs. temperature written to ELIASHBERG_GAP_T.OUT")') write(*,'(" gap function on the real axis written to ELIASHBERG_GAP_RA.OUT")') write(*,'(" Z function on the real axis written to ELIASHBERG_Z_RA.OUT")') deallocate(w,a2f,wf,l) deallocate(d0,d,z0,z,r) deallocate(zin,uin,zout,uout) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/phscdvs.f900000644000000000000000000000013214061636517014716 xustar0030 mtime=1623670095.642101817 30 atime=1623670094.466102909 30 ctime=1623670095.642101817 elk-7.2.42/src/phscdvs.f900000644002504400250440000000453014061636517016755 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine phscdvs(p,vsmt_,vsir_) use modmain use modphonon use modstore implicit none ! arguments integer, intent(in) :: p real(8), intent(in) :: vsmt_(npmtmax,natmtot),vsir_(ngtot) ! local variables integer is,ia,ja,ias,jas integer nr,nri,np,i integer iv(3),ig_,ifg_,ifg real(8) vl(3),vc(3),t1 complex(8) z0,z1,z2 ! allocatable arrays real(8), allocatable :: rfmt(:) complex(8), allocatable :: zfmt(:),zfir(:) ! prefactor z0=1.d0/deltaph ! multiply by i for sin-like displacement if (p.eq.1) z0=z0*zi !------------------------------! ! muffin-tin potential ! !------------------------------! allocate(rfmt(npmtmax),zfmt(npmtmax)) z1=z0/dble(nscph) ias=0 jas=0 do is=1,nspecies nr=nrmt(is) nri=nrmti(is) np=npmt(is) ja=0 do ia=1,natoms_(is) ias=ias+1 do i=1,nscph ja=ja+1 jas=jas+1 ! compute the difference between the perturbed and unperturbed potentials rfmt(1:np)=vsmt(1:np,jas)-vsmt_(1:np,jas) ! convert real potential difference to a complex spherical harmonic expansion call rtozfmt(nr,nri,rfmt,zfmt) ! the muffin-tin potential should have an *explicit* phase exp(iq.r) t1=-dot_product(vqc(:,iqph),vscph(:,i)) z2=z1*cmplx(cos(t1),sin(t1),8) ! add to total dvsmt(1:np,ias)=dvsmt(1:np,ias)+z2*zfmt(1:np) end do ! end loop over atoms and species end do end do deallocate(rfmt,zfmt) !--------------------------------! ! interstitial potential ! !--------------------------------! ! Fourier transform interstitial potential derivative to G-space allocate(zfir(ngtot)) zfir(:)=z0*(vsir(:)-vsir_(:)) call zfftifc(3,ngridg,-1,zfir) ! convert to G+q-space do ig_=1,ngtot_ ifg_=igfft_(ig_) vl(:)=dble(ivg_(:,ig_))+vql(:,iqph) call r3mv(bvec_,vl,vc) call r3mv(binv,vc,vl) iv(:)=nint(vl(:)) if ((iv(1).ge.intgv(1,1)).and.(iv(1).le.intgv(2,1)).and. & (iv(2).ge.intgv(1,2)).and.(iv(2).le.intgv(2,2)).and. & (iv(3).ge.intgv(1,3)).and.(iv(3).le.intgv(2,3))) then ifg=igfft(ivgig(iv(1),iv(2),iv(3))) dvsir(ifg_)=dvsir(ifg_)+zfir(ifg) else dvsir(ifg_)=0.d0 end if end do ! Fourier transform back to real-space if (p.eq.1) call zfftifc(3,ngridg_,1,dvsir) deallocate(zfir) end subroutine elk-7.2.42/src/PaxHeaders.21776/readdvs.f900000644000000000000000000000013214061636517014674 xustar0030 mtime=1623670095.644101815 30 atime=1623670094.467102908 30 ctime=1623670095.644101815 elk-7.2.42/src/readdvs.f900000644002504400250440000000550314061636517016734 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readdvs(iq,is,ia,ip,dvsmt,dvsir) use modmain implicit none ! arguments integer, intent(in) :: iq,is,ia,ip complex(8), intent(out) :: dvsmt(npmtmax,natmtot),dvsir(ngtot) ! local variables integer js,jas,ios integer version_(3),nspecies_ integer lmmaxo_,natoms_ integer nrmt_,ngridg_(3) character(256) fext,fname ! allocatable arrays complex(8), allocatable :: zfmt(:,:,:) allocate(zfmt(lmmaxo,nrmtmax,natmtot)) call dynfext(iq,is,ia,ip,fext) fname='DVS'//trim(fext) open(150,file=trim(fname),form='UNFORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readdvs): error opening ",A)') trim(fname) write(*,*) stop end if read(150) version_ if ((version(1).ne.version_(1)).or.(version(2).ne.version_(2)) & .or.(version(3).ne.version_(3))) then write(*,*) write(*,'("Warning(readdvs): different versions")') write(*,'(" current : ",I3.3,".",I3.3,".",I3.3)') version write(*,'(" file : ",I3.3,".",I3.3,".",I3.3)') version_ write(*,'(" in file ",A)') trim(fname) end if read(150) nspecies_ if (nspecies.ne.nspecies_) then write(*,*) write(*,'("Error(readdvs): differing nspecies")') write(*,'(" current : ",I4)') nspecies write(*,'(" file : ",I4)') nspecies_ write(*,'(" in file ",A)') trim(fname) write(*,*) stop end if read(150) lmmaxo_ if (lmmaxo.ne.lmmaxo_) then write(*,*) write(*,'("Error(readdvs): differing lmmaxo")') write(*,'(" current : ",I4)') lmmaxo write(*,'(" file : ",I4)') lmmaxo_ write(*,'(" in file ",A)') trim(fname) write(*,*) stop end if do js=1,nspecies read(150) natoms_ if (natoms(js).ne.natoms_) then write(*,*) write(*,'("Error(readdvs): differing natoms for species ",I4)') js write(*,'(" current : ",I4)') natoms(js) write(*,'(" file : ",I4)') natoms_ write(*,'(" in file ",A)') trim(fname) write(*,*) stop end if read(150) nrmt_ if (nrmt(js).ne.nrmt_) then write(*,*) write(*,'("Error(readdvs): differing nrmt for species ",I4)') js write(*,'(" current : ",I6)') nrmt(js) write(*,'(" file : ",I6)') nrmt_ write(*,'(" in file ",A)') trim(fname) write(*,*) stop end if end do read(150) ngridg_ if ((ngridg(1).ne.ngridg_(1)).or.(ngridg(2).ne.ngridg_(2)).or. & (ngridg(3).ne.ngridg_(3))) then write(*,*) write(*,'("Error(readdvs): differing ngridg")') write(*,'(" current : ",3I6)') ngridg write(*,'(" file : ",3I6)') ngridg_ write(*,'(" in file ",A)') trim(fname) write(*,*) stop end if read(150) zfmt,dvsir do jas=1,natmtot js=idxis(jas) call zfmtpack(.true.,nrmt(js),nrmti(js),zfmt(:,:,jas),dvsmt(:,jas)) end do close(150) deallocate(zfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/readalpha2f.f900000644000000000000000000000013214061636517015415 xustar0030 mtime=1623670095.645101814 30 atime=1623670094.469102906 30 ctime=1623670095.645101814 elk-7.2.42/src/readalpha2f.f900000644002504400250440000000146314061636517017456 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 A. Sanna and E. K. U. Gross ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readalpha2f(w,a2f) use modmain implicit none ! arguments real(8), intent(out) :: w(nwplot) real(8), intent(out) :: a2f(nwplot) ! local variables integer iw,ios open(50,file='ALPHA2F.OUT',form='FORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readalpha2f): error opening ALPHA2F.OUT")') write(*,*) stop end if do iw=1,nwplot read(50,*,iostat=ios) w(iw),a2f(iw) if (ios.ne.0) then write(*,*) write(*,'("Error(readalpha2f): error reading from ALPHA2F.OUT")') write(*,'(" for frequency ",I6)') iw write(*,*) stop end if end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/gendsocfr.f900000644000000000000000000000013214061636517015216 xustar0030 mtime=1623670095.647101812 30 atime=1623670094.471102904 30 ctime=1623670095.647101812 elk-7.2.42/src/gendsocfr.f900000644002504400250440000000214614061636517017256 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 J. K. Dewhurst, S. Sharma and E. K. U. Gross ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine gendsocfr use modmain use modphonon implicit none integer is,ias,i integer nr,nri,ir,irc real(8) cso complex(8) z1 ! allocatable arrays real(8), allocatable :: vr1(:),vr2(:) real(8), allocatable :: dvr1(:),dvr2(:) if (.not.spinorb) return ! coefficient of spin-orbit coupling cso=y00*socscf/(4.d0*solsc**2) allocate(vr1(nrmtmax),vr2(nrmtmax)) allocate(dvr1(nrmtmax),dvr2(nrmtmax)) do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) i=1 do ir=1,nri vr1(ir)=dble(dvsmt(i,ias)) vr2(ir)=aimag(dvsmt(i,ias)) i=i+lmmaxi end do do ir=nri+1,nr vr1(ir)=dble(dvsmt(i,ias)) vr2(ir)=aimag(dvsmt(i,ias)) i=i+lmmaxo end do call splined(nr,wcrmt(:,:,is),vr1,dvr1) call splined(nr,wcrmt(:,:,is),vr2,dvr2) irc=0 do ir=1,nr,lradstp irc=irc+1 z1=cmplx(dvr1(ir),dvr2(ir),8) dsocfr(irc,ias)=(cso/rsp(ir,is))*z1 end do end do deallocate(vr1,vr2,dvr1,dvr2) end subroutine elk-7.2.42/src/PaxHeaders.21776/bornechg.f900000644000000000000000000000013214061636517015033 xustar0030 mtime=1623670095.648101812 30 atime=1623670094.472102903 30 ctime=1623670095.648101812 elk-7.2.42/src/bornechg.f900000644002504400250440000000534414061636517017076 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine bornechg use modmain use modphonon use modstore use modmpi use modtest implicit none ! local variables integer ip,l real(8) vc(3),pvl1(3),pvl2(3) real(8) becl(3),becc(3),t1 ! no shifting of the atomic basis tshift_=tshift tshift=.false. ! initialise universal variables call init0 call init1 ! store original parameters atposl_(:,:,:)=atposl(:,:,:) atposc_(:,:,:)=atposc(:,:,:) ngridk_(:)=ngridk(:) maxscl_=maxscl ! begin new Born effective charge task 10 continue call bectask(80,filext) ! if nothing more to do then restore original input parameters and return if (isph.eq.0) then filext='.OUT' tshift=tshift_ atposl(:,:,:)=atposl_(:,:,:) return end if if (mp_mpi) then write(*,'("Info(bornechg): working on ",A)') 'BEC'//trim(filext) end if ! dry run: just generate empty BEC files if (task.eq.209) goto 10 ! apply negative atomic displacement atposl(:,:,:)=atposl_(:,:,:) atposc(:,:,:)=atposc_(:,:,:) vc(:)=atposc(:,iaph,isph) vc(ipph)=vc(ipph)-0.5d0*deltaph call r3mv(ainv,vc,atposl(:,iaph,isph)) ! initial ground-state run should start from atomic densities trdstate=.false. ! run the ground-state calculation call gndstate ! subsequent calculations will read in the previous potential trdstate=.true. ! compute the first polarisation in lattice coordinates call polar(pvl1) ! apply positive atomic displacement atposl(:,:,:)=atposl_(:,:,:) atposc(:,:,:)=atposc_(:,:,:) vc(:)=atposc(:,iaph,isph) vc(ipph)=vc(ipph)+0.5d0*deltaph call r3mv(ainv,vc,atposl(:,iaph,isph)) ! run the ground-state calculation again call gndstate ! compute the second polarisation call polar(pvl2) do l=1,3 ! add multiple of 2*pi to bring polarisation vectors into coincidence pvl1(l)=modulo(pvl1(l),twopi) pvl2(l)=modulo(pvl2(l),twopi) t1=pvl1(l)-pvl2(l) if (abs(t1-twopi).lt.abs(t1)) then pvl1(l)=pvl1(l)-twopi else if (abs(t1+twopi).lt.abs(t1)) then pvl1(l)=pvl1(l)+twopi end if ! calculate the Born effective charge from the difference in polarisations t1=wkptnr*occmax*dble(nkspolar*ngridk(l))/(twopi*deltaph) becl(l)=t1*(pvl2(l)-pvl1(l)) end do ! convert from lattice to Cartesian coordinates call r3mv(avec,becl,becc) ! add the core and nuclear charge becc(ipph)=becc(ipph)+chgcr(isph)+spzn(isph) ! write Born effective charge matrix row to file if (mp_mpi) then do ip=1,3 write(80,'(G18.10," : ip = ",I4)') becc(ip),ip end do close(80) end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! write test file if required and return if (test) then call writetest(208,'Born effective charge',nv=3,tol=1.d-3,rva=becc) return end if goto 10 end subroutine elk-7.2.42/src/PaxHeaders.21776/bectask.f900000644000000000000000000000013014061636517014656 xustar0029 mtime=1623670095.65010181 30 atime=1623670094.474102901 29 ctime=1623670095.65010181 elk-7.2.42/src/bectask.f900000644002504400250440000000241714061636517016721 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine bectask(fnum,fext) use modmain use modphonon use modmpi implicit none ! arguments integer, intent(in) :: fnum character(*), intent(out) :: fext ! local variables logical exist ! only master process should search for file if (.not.mp_mpi) goto 10 do ipph=1,3 do isph=1,nspecies do iaph=1,natoms(isph) ! Born effective charge file extension call becfext(isph,iaph,ipph,fext) ! determine if the BEC file with this extension exists inquire(file='BEC'//trim(fext),exist=exist) if (.not.exist) then open(fnum,file='BEC'//trim(fext),form='FORMATTED') iasph=idxas(iaph,isph) goto 10 end if end do end do end do isph=0; iaph=0; iasph=0; ipph=0 write(*,*) write(*,'("Info(bectask): nothing more to do")') 10 continue ! broadcast to all other MPI processes call mpi_bcast(isph,1,mpi_integer,0,mpicom,ierror) call mpi_bcast(iaph,1,mpi_integer,0,mpicom,ierror) call mpi_bcast(iasph,1,mpi_integer,0,mpicom,ierror) call mpi_bcast(ipph,1,mpi_integer,0,mpicom,ierror) if (isph.eq.0) then fext='.OUT' else call becfext(isph,iaph,ipph,fext) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/becfext.f900000644000000000000000000000013214061636517014664 xustar0030 mtime=1623670095.651101809 30 atime=1623670094.476102899 30 ctime=1623670095.651101809 elk-7.2.42/src/becfext.f900000644002504400250440000000060514061636517016722 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine becfext(is,ia,ip,fext) use modmain implicit none ! arguments integer, intent(in) :: is,ia,ip character(*), intent(out) :: fext write(fext,'("_S",I2.2,"_A",I3.3,"_P",I1,".OUT")') is,ia,ip end subroutine elk-7.2.42/src/PaxHeaders.21776/putephmat.f900000644000000000000000000000013214061636517015253 xustar0030 mtime=1623670095.653101807 30 atime=1623670094.477102899 30 ctime=1623670095.653101807 elk-7.2.42/src/putephmat.f900000644002504400250440000000133514061636517017312 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine putephmat(iq,ik,ephmat) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq,ik complex(8), intent(in) :: ephmat(nstsv,nstsv,nbph) ! local variables integer recl,n ! determine the record length inquire(iolength=recl) vql(:,iq),vkl(:,ik),nstsv,nbph,ephmat ! record number n=(iq-1)*nkptnr+ik !$OMP CRITICAL(u240) open(240,file='EPHMAT.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(240,rec=n) vql(:,iq),vkl(:,ik),nstsv,nbph,ephmat close(240) !$OMP END CRITICAL(u240) end subroutine elk-7.2.42/src/PaxHeaders.21776/getephmat.f900000644000000000000000000000013214061636517015222 xustar0030 mtime=1623670095.654101806 30 atime=1623670094.479102897 30 ctime=1623670095.654101806 elk-7.2.42/src/getephmat.f900000644002504400250440000000412614061636517017262 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine getephmat(iqp,ikp,ephmat) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iqp,ikp complex(8), intent(out) :: ephmat(nstsv,nstsv,nbph) ! local variables integer isym,lspl,iq,ik,iv(3) integer recl,n,nstsv_,nbph_ real(8) vql_(3),vkl_(3),t1 if (iqp.le.nqpt) then ! q-point is in the reduced set iq=iqp ik=ikp else ! q-point is not in the reduced set call findqpt(vql(:,iqp),isym,iq) lspl=lsplsymc(isym) call i3mtv(symlat(:,:,lspl),ivk(:,ikp),iv) iv(:)=modulo(iv(:),ngridk(:)) ik=ivkiknr(iv(1),iv(2),iv(3)) end if ! find the record length inquire(iolength=recl) vql_,vkl_,nstsv_,nbph_,ephmat ! record number n=(iq-1)*nkptnr+ik !$OMP CRITICAL(u240) open(240,file='EPHMAT.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(240,rec=n) vql_,vkl_,nstsv_,nbph_,ephmat !$OMP END CRITICAL(u240) t1=abs(vql(1,iq)-vql_(1))+abs(vql(2,iq)-vql_(2))+abs(vql(3,iq)-vql_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getephmat): differing vectors for q-point ",I8)') iq write(*,'(" current : ",3G18.10)') vql(:,iq) write(*,'(" EPHMAT.OUT : ",3G18.10)') vql_ write(*,*) stop end if t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getephmat): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" EPHMAT.OUT : ",3G18.10)') vkl_ write(*,*) stop end if if (nstsv.ne.nstsv_) then write(*,*) write(*,'("Error(getephmat): differing nstsv for q-point, k-point ",2I8)') & iq,ik write(*,'(" current : ",I8)') nstsv write(*,'(" EPHMAT.OUT : ",I8)') nstsv_ write(*,*) stop end if if (nbph.ne.nbph_) then write(*,*) write(*,'("Error(getephmat): differing nbph for q-point, k-point ",2I8)') & iq,ik write(*,'(" current : ",I8)') nbph write(*,'(" EPHMAT.OUT : ",I8)') nbph_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/xc_pzca.f900000644000000000000000000000013214061636517014673 xustar0030 mtime=1623670095.656101804 30 atime=1623670094.481102895 30 ctime=1623670095.656101804 elk-7.2.42/src/xc_pzca.f900000644002504400250440000000376214061636517016740 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: xc_pzca ! !INTERFACE: subroutine xc_pzca(n,rho,ex,ec,vx,vc) ! !INPUT/OUTPUT PARAMETERS: ! n : number of density points (in,integer) ! rho : charge density (in,real(n)) ! ex : exchange energy density (out,real(n)) ! ec : correlation energy density (out,real(n)) ! vx : exchange potential (out,real(n)) ! vc : correlation potential (out,real(n)) ! !DESCRIPTION: ! Spin-unpolarised exchange-correlation potential and energy of the ! Perdew-Zunger parameterisation of Ceperley-Alder electron gas: {\it Phys. ! Rev. B} {\bf 23}, 5048 (1981) and {\it Phys. Rev. Lett.} {\bf 45}, 566 ! (1980). ! ! !REVISION HISTORY: ! Created October 2002 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: rho(n) real(8), intent(out) :: ex(n),ec(n),vx(n),vc(n) ! local variables integer i real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: thrd=1.d0/3.d0, thrd2=2.d0/3.d0, thrd4=4.d0/3.d0 real(8), parameter :: g=-0.1423d0,b1=1.0529d0,b2=0.3334d0 real(8), parameter :: a=0.0311d0,b=-0.048d0,c=0.0020d0,d=-0.0116d0 real(8) p1,p2,r,rs,t1 if (n.le.0) then write(*,*) write(*,'("Error(xc_pzca): invalid n : ",I8)') n write(*,*) stop end if ! prefactors t1=3.d0/(4.d0*pi) p1=t1**thrd p2=t1*(9.d0*pi/4.d0)**thrd do i=1,n r=rho(i) if (r.lt.1.d-12) then ex(i)=0.d0 ec(i)=0.d0 vx(i)=0.d0 vc(i)=0.d0 cycle end if rs=p1/r**thrd ! exchange energy and potential ex(i)=-p2/rs vx(i)=thrd4*ex(i) ! correlation energy and potential if (rs.ge.1.d0) then t1=sqrt(rs) ec(i)=g/(1.d0+b1*t1+b2*rs) vc(i)=ec(i)*(1.d0+(7.d0/6.d0)*b1*t1+thrd4*b2*rs)/(1.d0+b1*t1+b2*rs) else t1=dlog(rs) ec(i)=a*t1+b+c*rs*t1+d*rs vc(i)=a*t1+(b-thrd*a)+thrd2*c*rs*t1+thrd*(2.d0*d-c)*rs end if end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/xc_pwca.f900000644000000000000000000000013214061636517014670 xustar0030 mtime=1623670095.657101803 30 atime=1623670094.482102894 30 ctime=1623670095.657101803 elk-7.2.42/src/xc_pwca.f900000644002504400250440000001102214061636517016721 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2011 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: xc_pwca ! !INTERFACE: subroutine xc_pwca(n,rhoup,rhodn,ex,ec,vxup,vxdn,vcup,vcdn) ! !INPUT/OUTPUT PARAMETERS: ! n : number of density points (in,integer) ! rhoup : spin-up charge density (in,real(n)) ! rhodn : spin-down charge density (in,real(n)) ! ex : exchange energy density (out,real(n)) ! ec : correlation energy density (out,real(n)) ! vxup : spin-up exchange potential (out,real(n)) ! vxdn : spin-down exchange potential (out,real(n)) ! vcup : spin-up correlation potential (out,real(n)) ! vcdn : spin-down correlation potential (out,real(n)) ! !DESCRIPTION: ! Spin-polarised exchange-correlation potential and energy of the Perdew-Wang ! parameterisation of the Ceperley-Alder electron gas: {\it Phys. Rev. B} ! {\bf 45}, 13244 (1992) and {\it Phys. Rev. Lett.} {\bf 45}, 566 (1980). ! ! !REVISION HISTORY: ! Created January 2004 (JKD) ! Rewrote, October 2011 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: rhoup(n),rhodn(n) real(8), intent(out) :: ex(n),ec(n) real(8), intent(out) :: vxup(n),vxdn(n) real(8), intent(out) :: vcup(n),vcdn(n) ! local variables integer i real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: thrd=1.d0/3.d0, thrd4=4.d0/3.d0 real(8), parameter :: d2f0=1.709921d0 real(8), parameter :: a(3)=[ 0.0310907d0, 0.01554535d0, 0.0168869d0 ] real(8), parameter :: a1(3)=[ 0.21370d0, 0.20548d0, 0.11125d0 ] real(8), parameter :: b1(3)=[ 7.5957d0, 14.1189d0, 10.357d0 ] real(8), parameter :: b2(3)=[ 3.5876d0, 6.1977d0, 3.6231d0 ] real(8), parameter :: b3(3)=[ 1.6382d0, 3.3662d0, 0.88026d0 ] real(8), parameter :: b4(3)=[ 0.49294d0, 0.62517d0, 0.49671d0 ] real(8) p1,p2,p3,rup,rdn,r,ri,ri2 real(8) rs,rs2,rs12,rs32,rsi,rs12i real(8) mz,z,z3,z4,drs,dzu,dzd real(8) fz,dfz,ders,dez,deu,ded real(8) a2,ec0,dec0,ec1,dec1,ac,dac real(8) t1,t2,t3,t4,t5,t6,t7,dt1,dt2 if (n.le.0) then write(*,*) write(*,'("Error(xc_pwca): invalid n : ",I8)') n write(*,*) stop end if ! prefactors t1=3.d0/(4.d0*pi) p1=t1**thrd p2=t1*(9.d0*pi/4.d0)**thrd p3=1.d0/(2.d0**thrd4-2.d0) do i=1,n rup=rhoup(i); rdn=rhodn(i) ! total density r=rup+rdn if ((rup.lt.0.d0).or.(rdn.lt.0.d0).or.(r.lt.1.d-20)) then ex(i)=0.d0 ec(i)=0.d0 vxup(i)=0.d0 vxdn(i)=0.d0 vcup(i)=0.d0 vcdn(i)=0.d0 cycle end if ri=1.d0/r ri2=ri**2 rs=p1*ri**thrd rs2=rs**2 rs12=sqrt(rs) rs32=rs12*rs rsi=1.d0/rs rs12i=1.d0/rs12 mz=rup-rdn z=mz/r z3=z**3 z4=z3*z ! drs/drup = drs/drdn = drs/drho drs=-thrd*rs*ri ! dz/drup, dz/drdn t1=mz*ri2 dzu=ri-t1 dzd=-ri-t1 !------------------! ! exchange ! !------------------! t1=-p2*rsi/2.d0 t2=1.d0+z t3=1.d0-z t4=t2**thrd4 t5=t3**thrd4 t6=t4+t5 ! exchange energy density ex(i)=t1*t6 ! dex/drs ders=-ex(i)*rsi ! f(z) fz=p3*(t6-2.d0) ! dex/dz t4=t4/t2 t5=t5/t3 t6=t4-t5 t7=thrd4*t6 dez=t1*t7 ! df/dz dfz=p3*t7 ! dex/drup, dex/drdn t1=ders*drs deu=t1+dez*dzu ded=t1+dez*dzd ! exchange potential vxup(i)=ex(i)+r*deu vxdn(i)=ex(i)+r*ded !---------------------! ! correlation ! !---------------------! ! ec(rs,0) a2=2.d0*a(1) t1=a2*(b1(1)*rs12+b2(1)*rs+b3(1)*rs32+b4(1)*rs2) dt1=a2*(0.5d0*b1(1)*rs12i+b2(1)+1.5d0*b3(1)*rs12+2.d0*b4(1)*rs) t3=1.d0/t1 t2=1.d0+t3 dt2=-dt1*t3**2 t3=1.d0/t2 t4=1.d0+a1(1)*rs t5=log(t2) ec0=-a2*t4*t5 dec0=-a2*(a1(1)*t5+t4*t3*dt2) ! ec(rs,1) a2=2.d0*a(2) t1=a2*(b1(2)*rs12+b2(2)*rs+b3(2)*rs32+b4(2)*rs2) dt1=a2*(0.5d0*b1(2)*rs12i+b2(2)+1.5d0*b3(2)*rs12+2.d0*b4(2)*rs) t3=1.d0/t1 t2=1.d0+t3 dt2=-dt1*t3**2 t3=1.d0/t2 t4=1.d0+a1(2)*rs t5=log(t2) ec1=-a2*t4*t5 dec1=-a2*(a1(2)*t5+t4*t3*dt2) ! ac(rs) a2=2.d0*a(3) t1=a2*(b1(3)*rs12+b2(3)*rs+b3(3)*rs32+b4(3)*rs2) dt1=a2*(0.5d0*b1(3)*rs12i+b2(3)+1.5d0*b3(3)*rs12+2.d0*b4(3)*rs) t3=1.d0/t1 t2=1.d0+t3 dt2=-dt1*t3**2 t3=1.d0/t2 t4=1.d0+a1(3)*rs t5=log(t2) ac=a2*t4*t5 dac=a2*(a1(3)*t5+t4*t3*dt2) ! correlation energy density t1=1.d0-z4 t2=(fz/d2f0)*t1 t3=ec1-ec0 t4=fz*z4 ec(i)=ec0+ac*t2+t3*t4 ! dec/drs t5=dec1-dec0 ders=dec0+dac*t2+t5*t4 ! dec/dz t6=4.d0*fz*z3 dez=(ac/d2f0)*(dfz*t1-t6)+t3*(dfz*z4+t6) ! dec/drup, dec/drdn t1=ders*drs deu=t1+dez*dzu ded=t1+dez*dzd ! correlation potential vcup(i)=ec(i)+r*deu vcdn(i)=ec(i)+r*ded end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/xc_pbe.f900000644000000000000000000000013214061636517014504 xustar0030 mtime=1623670095.659101801 30 atime=1623670094.484102892 30 ctime=1623670095.659101801 elk-7.2.42/src/xc_pbe.f900000644002504400250440000000711314061636517016543 0ustar00dewhurstdewhurst00000000000000 ! This routine is based on code written by K. Burke. !BOP ! !ROUTINE: xc_pbe ! !INTERFACE: subroutine xc_pbe(n,kappa,mu,beta,rhoup,rhodn,grho,gup,gdn,g2up,g2dn,g3rho, & g3up,g3dn,ex,ec,vxup,vxdn,vcup,vcdn) ! !INPUT/OUTPUT PARAMETERS: ! n : number of density points (in,integer) ! kappa : parameter for large-gradient limit (in,real) ! mu : gradient expansion coefficient (in,real) ! beta : gradient expansion coefficient (in,real) ! rhoup : spin-up charge density (in,real(n)) ! rhodn : spin-down charge density (in,real(n)) ! grho : |grad rho| (in,real(n)) ! gup : |grad rhoup| (in,real(n)) ! gdn : |grad rhodn| (in,real(n)) ! g2up : grad^2 rhoup (in,real(n)) ! g2dn : grad^2 rhodn (in,real(n)) ! g3rho : (grad rho).(grad |grad rho|) (in,real(n)) ! g3up : (grad rhoup).(grad |grad rhoup|) (in,real(n)) ! g3dn : (grad rhodn).(grad |grad rhodn|) (in,real(n)) ! ex : exchange energy density (out,real(n)) ! ec : correlation energy density (out,real(n)) ! vxup : spin-up exchange potential (out,real(n)) ! vxdn : spin-down exchange potential (out,real(n)) ! vcup : spin-up correlation potential (out,real(n)) ! vcdn : spin-down correlation potential (out,real(n)) ! !DESCRIPTION: ! Spin-polarised exchange-correlation potential and energy of the generalised ! gradient approximation functional of J. P. Perdew, K. Burke and M. Ernzerhof ! {\it Phys. Rev. Lett.} {\bf 77}, 3865 (1996) and {\bf 78}, 1396(E) (1997). ! The parameter $\kappa$, which controls the large-gradient limit, can be set ! to $0.804$ or $1.245$ corresponding to the value in the original article or ! the revised version of Y. Zhang and W. Yang, {\it Phys. Rev. Lett.} ! {\bf 80}, 890 (1998). ! ! !REVISION HISTORY: ! Modified routines written by K. Burke, October 2004 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: kappa,mu,beta real(8), intent(in) :: rhoup(n),rhodn(n) real(8), intent(in) :: grho(n),gup(n),gdn(n) real(8), intent(in) :: g2up(n),g2dn(n) real(8), intent(in) :: g3rho(n),g3up(n),g3dn(n) real(8), intent(out) :: ex(n),ec(n) real(8), intent(out) :: vxup(n),vxdn(n) real(8), intent(out) :: vcup(n),vcdn(n) ! local variables integer i real(8), parameter :: thrd=1.d0/3.d0 real(8), parameter :: thrd2=2.d0/3.d0 real(8), parameter :: pi=3.1415926535897932385d0 real(8) rup,rdn,r,r2,kf,s,u,v real(8) rs,z,g,ks,ksg real(8) t,uu,vv,ww real(8) g2rho,exup,exdn do i=1,n rup=rhoup(i); rdn=rhodn(i) ! total density r=rup+rdn if ((rup.ge.0.d0).and.(rdn.ge.0.d0).and.(r.gt.1.d-12)) then ! exchange energy density and potential ! spin-up r2=2.d0*rup kf=(r2*3.d0*pi**2)**thrd s=gup(i)/(2.d0*kf*rup) u=g3up(i)/((rup**2)*(2.d0*kf)**3) v=g2up(i)/(rup*(2.d0*kf)**2) call x_pbe(kappa,mu,r2,s,u,v,exup,vxup(i)) ! spin-down r2=2.d0*rdn kf=(r2*3.d0*pi**2)**thrd s=gdn(i)/(2.d0*kf*rdn) u=g3dn(i)/((rdn**2)*(2.d0*kf)**3) v=g2dn(i)/(rdn*(2.d0*kf)**2) call x_pbe(kappa,mu,r2,s,u,v,exdn,vxdn(i)) ! average exchange energy density ex(i)=(exup*rhoup(i)+exdn*rhodn(i))/r ! correlation rs=(3.d0/(4.d0*pi*r))**thrd z=(rhoup(i)-rhodn(i))/r g=((1.d0+z)**thrd2+(1.d0-z)**thrd2)/2.d0 kf=(r*3.d0*pi**2)**thrd ks=sqrt(4.d0*kf/pi) ksg=2.d0*ks*g t=grho(i)/(ksg*r) uu=g3rho(i)/((r**2)*ksg**3) g2rho=g2up(i)+g2dn(i) vv=g2rho/(r*ksg**2) ww=(gup(i)**2-gdn(i)**2-z*grho(i)**2)/(r*r*ksg**2) call c_pbe(beta,rs,z,t,uu,vv,ww,ec(i),vcup(i),vcdn(i)) else ex(i)=0.d0 ec(i)=0.d0 vxup(i)=0.d0 vxdn(i)=0.d0 vcup(i)=0.d0 vcdn(i)=0.d0 end if end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/xc_am05.f900000644000000000000000000000012514061636517014502 xustar0028 mtime=1623670095.6601018 29 atime=1623670094.48610289 28 ctime=1623670095.6601018 elk-7.2.42/src/xc_am05.f900000644002504400250440000002323414061636517016541 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2004, 2005 Rickard Armiento ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: xc_am05 ! !INTERFACE: subroutine xc_am05(n,rho,grho,g2rho,g3rho,ex,ec,vx,vc) ! !INPUT/OUTPUT PARAMETERS: ! n : number of density points (in,integer) ! rho : charge density (in,real(n)) ! grho : |grad rho| (in,real(n)) ! g2rho : grad^2 rho (in,real(n)) ! g3rho : (grad rho).(grad |grad rho|) (in,real(n)) ! ex : exchange energy density (out,real(n)) ! ec : correlation energy density (out,real(n)) ! vx : spin-unpolarised exchange potential (out,real(n)) ! vc : spin-unpolarised correlation potential (out,real(n)) ! !DESCRIPTION: ! Spin-unpolarised exchange-correlation potential and energy functional of ! R. Armiento and A. E. Mattsson, {\it Phys. Rev. B} {\bf 72}, 085108 (2005). ! ! !REVISION HISTORY: ! Created April 2005 (RAR); based on xc_pbe !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: rho(n),grho(n),g2rho(n),g3rho(n) real(8), intent(out) :: ex(n),ec(n),vx(n),vc(n) ! local variables integer i real(8), parameter :: pi=3.1415926535897932385d0 real(8) r,kf,s,v,u real(8) grho_,g2rho_,g3rho_ do i=1,n r=rho(i) if (r.gt.1.d-12) then grho_=grho(i) g2rho_=g2rho(i) g3rho_=g3rho(i) ! exchange energy density and potential kf=(r*3.d0*pi**2)**(1.d0/3.d0) s=grho_/(2.d0*kf*r) v=g2rho_/(r*(2.d0*kf)**2) u=g3rho_/((r**2)*(2.d0*kf)**3) call xc_am05_point(r,s,u,v,ex(i),ec(i),vx(i),vc(i),1) else ex(i)=0.d0 ec(i)=0.d0 vx(i)=0.d0 vc(i)=0.d0 end if end do end subroutine !EOC !BOP ! !ROUTINE: xc_am05_point ! !INTERFACE: subroutine xc_am05_point(rho,s,u,v,ex,ec,vx,vc,pot) ! !INPUT/OUTPUT PARAMETERS: ! rho : electron density (in,real) ! s : gradient of n / (2 kF n) ! u : grad n * grad | grad n | / (n**2 (2 kF)**3) ! v : laplacian of density / (n**2 (2.d0*kf)**3) ! ex : exchange energy density (out,real) ! ec : correlation energy density (out,real) ! vx : spin-unpolarised exchange potential (out,real) ! vc : spin-unpolarised correlation potential (out,real) ! !DESCRIPTION: ! Calculate the spin-unpolarised exchange-correlation potential and energy for ! the Armiento-Mattsson 05 functional for a single point. ! ! !REVISION HISTORY: ! Created April 2005 (RAR) !EOP !BOC implicit none ! arguments real(8), intent(in) :: rho, s, u, v integer, intent(in) :: pot real(8), intent(out) :: ex, ec, vx, vc ! constants real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: g = 0.8098d0 real(8), parameter :: a = 2.804d0 real(8), parameter :: c = 0.7168d0 ! local variables real(8) s2,exlda, vxlda, eclda, vclda, X, Xs, Xss real(8) F, Fs, Fss, Hx, Hxs, Hxss, Hc, Hcs, Hcss real(8) zb, zbs, zbss, w real(8) n0b, n0bs, n0bss real(8) ln0b, ln0bs, ln0bss real(8) zbb, zbbc, zbbs, zbbss real(8) fxb, fxbs, fxbss ! cutoff if((rho .le. 1.0d-16)) then ex = 0.0d0 ec = 0.0d0 vx = 0.0d0 vc = 0.0d0 return endif s2 = s**2 ! LDA correlation call xc_am05_ldapwc(rho,eclda,vclda) ! LDA exchange call xc_am05_ldax(rho,exlda,vxlda) !------------------! ! exchange ! !------------------! ! interpolation index X = 1.0d0 - a*s2/(1.0d0 + a*s2) ! Airy LAA refinement function call xc_am05_labertw(s**(3.0d0/2.0d0)/sqrt(24.0d0),w) zb = (3.0d0/2.0d0*w)**(2.0d0/3.0d0) n0b = w/(2.0d0*pi**2*s**3) ln0b = -3.0d0/(2.0d0*pi)*(3.0d0*pi**2*n0b)**(1.0d0/3.0d0) zbbc = ((4.0d0/3.0d0)**(1.0d0/3.0d0)*2.0d0*pi/3.0d0)**4 zbb = (zbbc*zb**2 + zb**4)**(1.0d0/4.0d0) Fxb = -1.0d0/(ln0b*2.0d0*zbb) F = (c*s2 + 1.0d0)/(c*s2/Fxb + 1.0d0) ! exchange refinement function Hx = X + (1.0d0 - X)*F ! exchange energy per particle, Ex = Integrate[n*ex] ex = exlda*Hx !---------------------! ! correlation ! !---------------------! ! correlation refinement function Hc = X + g*(1.0d0 - X) ! correlation energy per particle, Ec = Integrate[rho*ec] ec = eclda*Hc if (pot .eq. 0) return !----------------------------! ! exchange potential ! !----------------------------! ! interpolation index derivatives, dX/ds Xs = -2.0d0*a*s/(1.0d0 + a*s2)**2 Xss = 2.0d0*a*(3.0d0*a*s2-1.0d0)/(1.0d0+a*s2)**3 ! airy LAA refinement function derivatives, dF/ds zbs = zb/(s + s*w) zbss = - zb*w*(5.0d0+2.0d0*w)/(2.0d0*s2*(1.0d0+w)**3) n0bs = sqrt(zb)*(-2.0d0*zb+s*zbs)/(2.0d0*pi**2*s2**2) n0bss = (16.0d0*zb**2+s**2*zbs**2+2.0d0*s*zb*(-6.0d0* & zbs+s*zbss))/(4.0d0*pi**2*s**5*sqrt(zb)) ln0bs = -(3.0d0/pi)**(1.0d0/3.0d0)*n0bs/ & (2.0d0*n0b**(2.0d0/3.0d0)) ln0bss = (2.0d0*n0bs**2-3.0d0*n0b*n0bss)/(2.0d0* & 3.0d0**(2.0d0/3.0d0)*pi**(1.0d0/3.0d0)*n0b**(5.0d0/3.0d0)) zbbs = zb*(zbbc+2*zb**2)*zbs/ & (2.0d0*(zb**2*(zbbc+zb**2))**(3.0d0/4.0d0)) zbbss = zb**2*(-zbbc*(zbbc-2.0d0*zb**2)*zbs**2+ & 2.0d0*zb*(zbbc+zb**2)*(zbbc+2.0d0*zb**2)*zbss)/ & (4.0d0*(zb**2*(zbbc+zb**2))**(7.0d0/4.0d0)) Fxbs = (zbb*ln0bs+ln0b*zbbs)/(2.0d0*ln0b**2*zbb**2) Fxbss = (-2.0d0*ln0b**2*zbbs**2+zbb**2*(-2.0d0*ln0bs**2 + & ln0b*ln0bss)+ln0b*zbb*(-2.0d0*ln0bs*zbbs+ln0b*zbbss))/ & (2.0d0*ln0b**3*zbb**3) Fs = (c*s*(2.0d0*(Fxb-1.0d0)*Fxb + s*(1.0d0+c*s2)*Fxbs))/ & (c*s2 + Fxb)**2 Fss = (c*(-2.0d0*(3.0d0*c*s2-Fxb)*(Fxb-1.0d0)*Fxb+ & 4.0d0*s*(-c*s2+Fxb+2.0d0*c*s2*Fxb)*Fxbs - & 2.0d0*s2*(1.0d0+c*s2)*Fxbs**2+s2*(1.0d0+c*s2)* & (c*s2 + Fxb)*Fxbss))/(c*s2+Fxb)**3 ! GGA refinement function derivatives, dF/ds Hxs = - (X - 1.0d0)*Fs - (F - 1.0d0)*Xs Hxss = - 2.0d0*Fs*Xs - (X - 1.0d0)*Fss - (F - 1.0d0)*Xss ! vx formula for gradient dependent functional, ! generalized form of Eq. (24) in PRB 33, 8800 (1986) vx = vxlda*(Hx - s*Hxs) + & exlda*((4.0d0/3.0d0*s-v/s)*Hxs - & (u-4.0d0/3.0d0*s**3)*(Hxss/s-Hxs/s2)) !-------------------------------! ! correlation potential ! !-------------------------------! ! correlation refinement function derivatives, dF/ds Hcs = Xs - g*Xs Hcss = Xss - g*Xss ! vc formula for gradient dependent functional, ! generalized form of Eq. (24) in Phys. Rev. B 33, 8800 (1986) vc = vclda*(Hc - s*Hcs) + & eclda*((4.0d0/3.0d0*s - v/s)*Hcs - & (u - 4.0d0/3.0d0*s**3)*(Hcss/s - Hcs/s2)) end subroutine !EOC !BOP ! !ROUTINE: xc_am05_ldax ! !INTERFACE: subroutine xc_am05_ldax(n,ex,vx) ! !INPUT/OUTPUT PARAMETERS: ! n : electron density (in,real) ! ex : exchange energy per electron (out,real) ! vx : exchange potential (out,real) ! !DESCRIPTION: ! Local density approximation exchange. ! ! !REVISION HISTORY: ! Created April 2005 (RAR) !EOP !BOC implicit none ! arguments real(8), intent(in) :: n real(8), intent(out) :: ex real(8), intent(out) :: vx ! constants real(8), parameter :: pi=3.1415926535897932385d0 vx=-(3.d0*n/pi)**(1.d0/3.d0) ex=(3.d0/4.d0)*vx end subroutine !EOC !BOP ! !ROUTINE: xc_am05_ldapwc ! !INTERFACE: subroutine xc_am05_ldapwc(n,ec,vc) ! !INPUT/OUTPUT PARAMETERS: ! n : electron density (in,real) ! ec : correlation energy per electron (out,real) ! vc : correlation potential (out,real) ! !DESCRIPTION: ! Correlation energy and potential of the Perdew-Wang parameterisation of ! the Ceperley-Alder electron gas {\it Phys. Rev. B} {\bf 45}, 13244 (1992) ! and {\it Phys. Rev. Lett.} {\bf 45}, 566 (1980). This is a clean-room ! implementation from paper. ! ! !REVISION HISTORY: ! Created April 2005 (RAR) !EOP !BOC implicit none ! arguments real(8), intent(in) :: n real(8), intent(out) :: ec real(8), intent(out) :: vc ! constants real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: a01 = 0.21370d0 real(8), parameter :: b01 = 7.5957d0 real(8), parameter :: b02 = 3.5876d0 real(8), parameter :: b03 = 1.6382d0 real(8), parameter :: b04 = 0.49294d0 ! paper actually use this: ! real(8), parameter (A0 = 0.031091d0) ! but routines now "defacto standard" was distributed using: real(8), parameter :: A0 = 0.0310907d0 ! local variables real(8) rsq real(8) Q0, Q1, Q1p, ecrs rsq = (3.0d0/(4.0d0*pi*n))**(1.0d0/6.0d0) ec = -2.0d0*A0*(1.0d0 + a01*rsq**2)* & log(1.0d0 + 1.0d0/ & (2.0d0*A0*rsq*(b01 + rsq*(b02 + rsq*(b03 + b04*rsq))))) Q0 = -2.0d0*A0*(1.0d0 + a01*rsq**2) Q1 = 2.0d0*A0*rsq*(b01 + rsq*(b02 + rsq*(b03 + b04*rsq))) Q1p = A0*(b01/rsq+2.0d0*b02+3.0d0*b03*rsq+4.0d0*b04*rsq**2) ecrs = -2.0d0*A0*a01*log(1.0d0 + 1.0d0/Q1)-Q0*Q1p/(Q1**2+Q1) vc = ec - rsq**2/3.0d0*ecrs end subroutine !EOC !BOP ! !ROUTINE: xc_am05_labertw ! !INTERFACE: subroutine xc_am05_labertw(z,val) ! !INPUT/OUTPUT PARAMETERS: ! z : function argument (in,real) ! val : value of lambert W function of z (out,real) ! !DESCRIPTION: ! Lambert $W$-function using the method of Corless, Gonnet, Hare, Jeffrey and ! Knuth, {\it Adv. Comp. Math.} {\bf 5}, 329 (1996). The approach is based ! loosely on that in GNU Octave by N. N. Schraudolph, but this implementation ! is for real values and the principal branch only. ! ! !REVISION HISTORY: ! Created April 2005 (RAR) !EOP !BOC implicit none ! arguments real(8), intent(in) :: z real(8), intent(out) :: val ! local variables real(8) e,t,p integer i ! if z too low, go with the first term of the power expansion, z if (z.lt.1.d-20) then val=z return end if e=exp(1.d0) ! inital guess if (abs(z+1.d0/e).gt.1.45d0) then ! asymptotic expansion at 0 and Inf val=log(z) val=val-log(val) else ! series expansion about -1/e to first order val=1.d0*sqrt(2.d0*e*z+2.d0)-1.d0 end if ! find val through iteration do i=1,10 p=exp(val) t=val*p-z if (val.ne.-1.d0) then t=t/(p*(val+1.d0)-0.5d0*(val+2.d0)*t/(val+1.d0)) else t=0.d0 end if val=val-t if (abs(t).lt.(2.48d0*1.d-14)*(1.d0+abs(val))) return end do ! this should never happen! write(*,*) write(*,'("Error(xc_am05_labertw): iteration limit reached")') write(*,'(" Likely cause: improper numbers (INFs, NaNs) in density")') write(*,*) stop end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/xc_xalpha.f900000644000000000000000000000013214061636517015213 xustar0030 mtime=1623670095.662101798 30 atime=1623670094.488102888 30 ctime=1623670095.662101798 elk-7.2.42/src/xc_xalpha.f900000644002504400250440000000244114061636517017251 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 1998-2006 ABINIT group (DCA, XG, GMR). ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: xc_xalpha ! !INTERFACE: subroutine xc_xalpha(n,rho,exc,vxc) ! !INPUT/OUTPUT PARAMETERS: ! n : number of density points (in,integer) ! rho : charge density (in,real(n)) ! exc : exchange-correlation energy density (out,real(n)) ! vxc : exchange-correlation potential (out,real(n)) ! !DESCRIPTION: ! $X_{\alpha}$ approximation to the exchange-correlation potential and energy ! density. See J. C. Slater, {\it Phys. Rev.} {\bf 81}, 385 (1951). ! ! !REVISION HISTORY: ! Modified an ABINIT routine, September 2006 (JKD) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: rho(n) real(8), intent(out) :: exc(n),vxc(n) ! local variables integer i real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: alpha=1.d0 real(8) r,efac,rs,rsm1,vfac vfac=(1.5d0/pi)**(2.d0/3.d0) efac=0.75d0*vfac ! loop over density points do i=1,n r=rho(i) if (r.gt.1.d-12) then rs=(3.d0/(4.d0*pi*r))**(1.d0/3.d0) rsm1=1.0d0/rs ! compute energy density exc(i)=-alpha*efac*rsm1 ! compute potential vxc(i)=-alpha*vfac*rsm1 end if end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/xc_wc06.f900000644000000000000000000000013214061636517014515 xustar0030 mtime=1623670095.663101798 30 atime=1623670094.490102886 30 ctime=1623670095.663101798 elk-7.2.42/src/xc_wc06.f900000644002504400250440000000242614061636517016556 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 Zhigang Wu and R. E. Cohen. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine xc_wc06(n,rho,grho,g2rho,g3rho,ex,ec,vx,vc) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: rho(n),grho(n),g2rho(n),g3rho(n) real(8), intent(out) :: ex(n),ec(n),vx(n),vc(n) ! local variables integer i real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: thrd=1.d0/3.d0 ! default PBE beta real(8), parameter :: beta=0.06672455060314922d0 real(8) r,grho_,g2rho_,g3rho_ real(8) kf,s,u,v,rs,z,g real(8) ks,ksg,t,uu,vv,ww do i=1,n r=rho(i) if (r.gt.1.d-12) then grho_=grho(i) g2rho_=g2rho(i) g3rho_=g3rho(i) kf=(r*3.d0*pi**2)**thrd s=grho_/(2.d0*kf*r) u=g3rho_/((r**2)*(2.d0*kf)**3) v=g2rho_/(r*(2.d0*kf)**2) ! Wu-Cohen exchange call x_wc06(r,s,u,v,ex(i),vx(i)) ! Perdew-Burke-Ernzerhof correlation rs=(3.d0/(4.d0*pi*r))**thrd z=0.d0 g=1.d0 ks=sqrt(4.d0*kf/pi) ksg=2.d0*ks*g t=grho_/(ksg*r) uu=g3rho_/((r**2)*ksg**3) vv=g2rho_/(r*ksg**2) ww=0.d0 call c_pbe(beta,rs,z,t,uu,vv,ww,ec(i),vc(i),vc(i)) else ex(i)=0.d0 ec(i)=0.d0 vx(i)=0.d0 vc(i)=0.d0 end if end do end subroutine elk-7.2.42/src/PaxHeaders.21776/x_wc06.f900000644000000000000000000000013214061636517014352 xustar0030 mtime=1623670095.664101797 30 atime=1623670094.491102885 30 ctime=1623670095.664101797 elk-7.2.42/src/x_wc06.f900000644002504400250440000000221314061636517016405 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2006 Zhigang Wu and R. E. Cohen. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. elemental subroutine x_wc06(rho,s,u,v,ex,vx) implicit none ! arguments real(8), intent(in) :: rho,s,u,v real(8), intent(out) :: ex,vx ! local variables real(8), parameter :: ax=-0.7385587663820224059d0 real(8), parameter :: mu=0.2195149727645171d0 real(8), parameter :: kappa=0.804d0 real(8), parameter :: b=10.d0/81.d0 real(8), parameter :: c=0.00793746933516d0 real(8), parameter :: thrd=1.d0/3.d0 real(8), parameter :: thrd4=4.d0/3.d0 real(8) dmu,exu real(8) s2,s4,es2,x,p0,fxwc real(8) fs,fss,t0,t1,t2,t3 ! lda exchange energy density exu=ax*rho**thrd s2=s**2 s4=s2**2 es2=exp(-s2) t0=1.d0+c*s4 dmu=mu-b x=b*s2+dmu*s2*es2+log(t0) p0=1.d0+x/kappa ! WC enhancement factor fxwc=1.d0+kappa-kappa/p0 ! exchange energy density ex=exu*fxwc t1=b+dmu*(1.d0-s2)*es2+2.d0*c*s2/t0 t2=dmu*s*(s2-2.d0)*es2+2.d0*c/t0-4.d0*(c**2)*s4/(t0**2) t3=1.d0/(p0**2) fs=2.d0*t1*t3 fss=t3*(4.d0*t2-8.d0*s*(t1**2)/(kappa*p0)) ! exchange potential vx=exu*(thrd4*fxwc-(u-thrd4*s2*s)*fss-v*fs) end subroutine elk-7.2.42/src/PaxHeaders.21776/x_pbe.f900000644000000000000000000000013214061636517014341 xustar0030 mtime=1623670095.666101795 30 atime=1623670094.493102884 30 ctime=1623670095.666101795 elk-7.2.42/src/x_pbe.f900000644002504400250440000000125714061636517016403 0ustar00dewhurstdewhurst00000000000000 ! This routine is based on code written by K. Burke. elemental subroutine x_pbe(kappa,mu,rho,s,u,v,ex,vx) implicit none ! arguments real(8), intent(in) :: kappa,mu real(8), intent(in) :: rho,s,u,v real(8), intent(out) :: ex,vx ! local variables real(8), parameter :: ax=-0.7385587663820224058d0 real(8), parameter :: thrd=1.d0/3.d0 real(8), parameter :: thrd4=4.d0/3.d0 real(8) ul,exu,s2,p0 real(8) fxpbe,fs,fss ul=mu/kappa ! LDA exchange energy density exu=ax*rho**thrd ! PBE enhancement factor s2=s**2 p0=1.d0+ul*s2 fxpbe=1.d0+kappa-kappa/p0 ex=exu*fxpbe fs=2.d0*kappa*ul/(p0*p0) fss=-4.d0*ul*s*fs/p0 ! exchange potential vx=exu*(thrd4*fxpbe-(u-thrd4*s2*s)*fss-v*fs) end subroutine elk-7.2.42/src/PaxHeaders.21776/c_pbe.f900000644000000000000000000000013214061636517014314 xustar0030 mtime=1623670095.667101794 30 atime=1623670094.495102882 30 ctime=1623670095.667101794 elk-7.2.42/src/c_pbe.f900000644002504400250440000000516414061636517016357 0ustar00dewhurstdewhurst00000000000000 ! This routine is based on code written by K. Burke. subroutine c_pbe(beta,rs,z,t,uu,vv,ww,ec,vcup,vcdn) implicit none ! arguments real(8), intent(in) :: beta,rs,z,t,uu,vv,ww real(8), intent(out) :: ec,vcup,vcdn ! local variables real(8), parameter :: thrd=1.d0/3.d0 real(8), parameter :: thrdm=-thrd real(8), parameter :: thrd2=2.d0*thrd real(8), parameter :: thrd4=4.d0*thrd real(8), parameter :: sixthm=thrdm/2.d0 real(8), parameter :: gam=0.5198420997897463295d0 real(8), parameter :: fzz=8.d0/(9.d0*gam) real(8), parameter :: gamma=0.0310906908696548950d0 real(8), parameter :: eta=1.d-12 real(8) rtrs,eu,eurs,ep,eprs,alfm,alfrsm,z4,f real(8) ecrs,fz,ecz,comm,g,g3,pon,b,b2,t2,t4 real(8) q4,q5,g4,t6,rsthrd,gz,fac,bg,bec,q8,q9 real(8) hb,hrs,fact0,fact1,hbt,hrst,hz,ht,hzt real(8) fact2,fact3,htt,pref,fact5,h,dvcup,dvcdn real(8) delt delt=beta/gamma rtrs=sqrt(rs) call c_pbe_gcor(0.0310907d0,0.21370d0,7.5957d0,3.5876d0,1.6382d0,0.49294d0, & rtrs,eu,eurs) call c_pbe_gcor(0.01554535d0,0.20548d0,14.1189d0,6.1977d0,3.3662d0,0.62517d0, & rtrs,ep,eprs) call c_pbe_gcor(0.0168869d0,0.11125d0,10.357d0,3.6231d0,0.88026d0,0.49671d0, & rtrs,alfm,alfrsm) z4=z**4 f=((1.d0+z)**thrd4+(1.d0-z)**thrd4-2.d0)/gam ! local contribution to correlation energy density ec=eu*(1.d0-f*z4)+ep*f*z4-alfm*f*(1.d0-z4)/fzz ecrs=eurs*(1.d0-f*z4)+eprs*f*z4-alfrsm*f*(1.d0-z4)/fzz fz=thrd4*((1.d0+z)**thrd-(1.d0-z)**thrd)/gam ecz=4.d0*(z**3)*f*(ep-eu+alfm/fzz)+fz*(z4*ep-z4*eu-(1.d0-z4)*alfm/fzz) comm=ec-rs*ecrs/3.d0-z*ecz ! local contribution to correlation potential vcup=comm+ecz vcdn=comm-ecz g=((1.d0+z)**thrd2+(1.d0-z)**thrd2)/2.d0 g3=g**3 pon=-ec/(g3*gamma) b=delt/(exp(pon)-1.d0) b2=b*b t2=t*t t4=t2*t2 q4=1.d0+b*t2 q5=1.d0+b*t2+b2*t4 ! gradient correction to energy density h=g3*(beta/delt)*log(1.d0+delt*q4*t2/q5) g4=g3*g t6=t4*t2 rsthrd=rs/3.d0 gz=(((1.d0+z)**2+eta)**sixthm-((1.d0-z)**2+eta)**sixthm)/3.d0 fac=delt/b+1.d0 bg=-3.d0*b2*ec*fac/(beta*g4) bec=b2*fac/(beta*g3) q8=q5*q5+delt*q4*q5*t2 q9=1.d0+2.d0*b*t2 hb=-beta*g3*b*t6*(2.d0+b*t2)/q8 hrs=-rsthrd*hb*bec*ecrs fact0=2.d0*delt-6.d0*b fact1=q5*q9+q4*q9*q9 hbt=2.d0*beta*g3*t4*((q4*q5*fact0-delt*fact1)/q8)/q8 hrst=rsthrd*t2*hbt*bec*ecrs hz=3.d0*gz*h/g+hb*(bg*gz+bec*ecz) ht=2.d0*beta*g3*q9/q8 hzt=3.d0*gz*ht/g+hbt*(bg*gz+bec*ecz) fact2=q4*q5+b*t2*(q4*q9+q5) fact3=2.d0*b*q5*q9+delt*fact2 htt=4.d0*beta*g3*t*(2.d0*b/q8-(q9*fact3/q8)/q8) comm=h+hrs+hrst+t2*ht/6.d0+7.d0*t2*t*htt/6.d0 pref=hz-gz*t2*ht/g fact5=gz*(2.d0*ht+t*htt)/g comm=comm-pref*z-uu*htt-vv*ht-ww*(hzt-fact5) ! gradient correction to potential dvcup=comm+pref dvcdn=comm-pref ! add gradient corrections ec=ec+h vcup=vcup+dvcup vcdn=vcdn+dvcdn end subroutine elk-7.2.42/src/PaxHeaders.21776/c_pbe_gcor.f900000644000000000000000000000013214061636517015326 xustar0030 mtime=1623670095.669101792 30 atime=1623670094.496102881 30 ctime=1623670095.669101792 elk-7.2.42/src/c_pbe_gcor.f900000644002504400250440000000073314061636517017366 0ustar00dewhurstdewhurst00000000000000 ! This routine is based on code written by K. Burke. elemental subroutine c_pbe_gcor(a,a1,b1,b2,b3,b4,rtrs,gg,ggrs) implicit none ! arguments real(8), intent(in) :: a,a1,b1,b2,b3,b4,rtrs real(8), intent(out) :: gg,ggrs ! local variables real(8) q0,q1,q2,q3 q0=-2.d0*a*(1.d0+a1*rtrs*rtrs) q1=2.d0*a*rtrs*(b1+rtrs*(b2+rtrs*(b3+b4*rtrs))) q2=log(1.d0+1.d0/q1) gg=q0*q2 q3=a*(b1/rtrs+2.d0*b2+rtrs*(3.d0*b3+4.d0*b4*rtrs)) ggrs=-2.d0*a*a1*q2-q0*q3/(q1*(1.d0+q1)) end subroutine elk-7.2.42/src/PaxHeaders.21776/xc_vbh.f900000644000000000000000000000013214061636517014515 xustar0030 mtime=1623670095.670101791 30 atime=1623670094.498102879 30 ctime=1623670095.670101791 elk-7.2.42/src/xc_vbh.f900000644002504400250440000000620214061636517016552 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 F. Cricchio, J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: xc_vbh ! !INTERFACE: subroutine xc_vbh(n,rhoup,rhodn,ex,ec,vxup,vxdn,vcup,vcdn) ! !INPUT/OUTPUT PARAMETERS: ! n : number of density points (in,integer) ! rhoup : spin-up charge density (in,real(n)) ! rhodn : spin-down charge density (in,real(n)) ! ex : exchange energy density (out,real(n)) ! ec : correlation energy density (out,real(n)) ! vxup : spin-up exchange potential (out,real(n)) ! vxdn : spin-down exchange potential (out,real(n)) ! vcup : spin-up correlation potential (out,real(n)) ! vcdn : spin-down correlation potential (out,real(n)) ! !DESCRIPTION: ! Spin-polarised exchange-correlation potential and energy functional of ! von Barth and Hedin: {\it J. Phys. C} {\bf 5}, 1629 (1972). Note that the ! implementation is in Rydbergs in order to follow the paper step by step, at ! the end the potential and energy are converted to Hartree. ! ! !REVISION HISTORY: ! Created September 2007 (F. Cricchio) !EOP !BOC implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: rhoup(n),rhodn(n) real(8), intent(out) :: ex(n),ec(n) real(8), intent(out) :: vxup(n),vxdn(n) real(8), intent(out) :: vcup(n),vcdn(n) ! local variables integer i real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: cp=0.0504d0 real(8), parameter :: cf=0.0254d0 real(8), parameter :: rp=30.d0 real(8), parameter :: rf=75.d0 real(8) alpha0,eps0_x,a,gamma real(8) rup,rdn,r,rs,x,zf,zp real(8) fx,fp,ff,epsp_x,mup_x real(8) epsp_c,epsf_c,mup_c,muf_c,vc,tau_c alpha0=(4.d0/(9.d0*pi))**(1.d0/3.d0) eps0_x=(3.d0/2.d0)/(pi*alpha0) a=2.d0**(-1.d0/3.d0) gamma=(4.d0/3.d0)*a/(1.d0-a) do i=1,n rup=rhoup(i); rdn=rhodn(i) ! total density r=rup+rdn if ((rup.ge.0.d0).and.(rdn.ge.0.d0).and.(r.gt.1.d-12)) then ! Wigner-Seitz radius in atomic units (a0=1) rs=(3.d0/(4.d0*pi*r))**(1.d0/3.d0) x=rup/r fx=(1.d0/(1.d0-a))*(x**(4.d0/3.d0)+(1.d0-x)**(4.d0/3.d0)-a) epsp_x=-eps0_x/rs mup_x=(4.d0/3.d0)*epsp_x ! exchange energy ex(i)=epsp_x+(1.d0/gamma)*mup_x*fx zp=rs/rp fp=(1.d0+zp**3)*log(1.d0+1.d0/zp)+0.5d0*zp-zp**2-1.d0/3.d0 zf=rs/rf ff=(1.d0+zf**3)*log(1.d0+1.d0/zf)+0.5d0*zf-zf**2-1.d0/3.d0 epsp_c=-cp*fp epsf_c=-cf*ff vc=gamma*(epsf_c-epsp_c) ! correlation energy ec(i)=epsp_c+(1.d0/gamma)*vc*fx mup_c=-cp*log(1.d0+rp/rs) muf_c=-cf*log(1.d0+rf/rs) tau_c=muf_c-mup_c-(4.d0/3.d0)*(epsf_c-epsp_c) ! exchange potential vxup(i)=mup_x*(2.d0*x)**(1.d0/3.d0) vxdn(i)=mup_x*(2.d0*(1.d0-x))**(1.d0/3.d0) ! correlation potential vcup(i)=vc*(2.d0*x)**(1.d0/3.d0)+mup_c-vc+tau_c*fx vcdn(i)=vc*(2.d0*(1.d0-x))**(1.d0/3.d0)+mup_c-vc+tau_c*fx ! convert from Rybergs to Hartree ex(i)=0.5d0*ex(i) ec(i)=0.5d0*ec(i) vxup(i)=0.5d0*vxup(i) vxdn(i)=0.5d0*vxdn(i) vcup(i)=0.5d0*vcup(i) vcdn(i)=0.5d0*vcdn(i) else ex(i)=0.d0 ec(i)=0.d0 vxup(i)=0.d0 vxdn(i)=0.d0 vcup(i)=0.d0 vcdn(i)=0.d0 end if end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/fxc_pwca.f900000644000000000000000000000013214061636517015036 xustar0030 mtime=1623670095.672101789 30 atime=1623670094.500102877 30 ctime=1623670095.672101789 elk-7.2.42/src/fxc_pwca.f900000644002504400250440000001251714061636517017101 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine fxc_pwca(n,rhoup,rhodn,fxcuu,fxcud,fxcdd) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: rhoup(n) real(8), intent(in) :: rhodn(n) real(8), intent(out) :: fxcuu(n) real(8), intent(out) :: fxcud(n) real(8), intent(out) :: fxcdd(n) ! local variables integer i real(8), parameter :: pi=3.1415926535897932385d0 real(8), parameter :: thrd=1.d0/3.d0, thrd4=4.d0/3.d0 real(8), parameter :: d2f0=1.709921d0 real(8), parameter :: a(3)=[ 0.0310907d0, 0.01554535d0, 0.0168869d0 ] real(8), parameter :: a1(3)=[ 0.21370d0, 0.20548d0, 0.11125d0 ] real(8), parameter :: b1(3)=[ 7.5957d0, 14.1189d0, 10.357d0 ] real(8), parameter :: b2(3)=[ 3.5876d0, 6.1977d0, 3.6231d0 ] real(8), parameter :: b3(3)=[ 1.6382d0, 3.3662d0, 0.88026d0 ] real(8), parameter :: b4(3)=[ 0.49294d0, 0.62517d0, 0.49671d0 ] real(8) p1,p2,p3,rup,rdn,r,ri,ri2,ri3 real(8) rs,rs2,rs12,rs32,rsi,rs12i,rs32i real(8) mz,z,z2,z3,z4,fz,dfz,d2fz real(8) drs,d2rs,dzu,d2zu,dzd,d2zd,d2zud real(8) ders,d2ers,dez,d2ez,d2ersz real(8) deu,d2eu,ded,d2ed,d2eud,ex real(8) ec0,dec0,d2ec0,ec1,dec1,d2ec1 real(8) ac,dac,d2ac,a2,dt1,d2t1,dt2,d2t2 real(8) t1,t2,t3,t4,t5,t6,t7,t8 if (n.le.0) then write(*,*) write(*,'("Error(xc_pwca): invalid n : ",I8)') n write(*,*) stop end if ! prefactors t1=3.d0/(4.d0*pi) p1=t1**thrd p2=t1*(9.d0*pi/4.d0)**thrd p3=1.d0/(2.d0**thrd4-2.d0) do i=1,n rup=rhoup(i); rdn=rhodn(i) ! total density r=rup+rdn if ((rup.lt.0.d0).or.(rdn.lt.0.d0).or.(r.lt.1.d-20)) then fxcuu(i)=0.d0 fxcud(i)=0.d0 fxcdd(i)=0.d0 cycle end if ri=1.d0/r ri2=ri**2 ri3=ri2*ri rs=p1*ri**thrd rs2=rs**2 rs12=sqrt(rs) rs32=rs12*rs rsi=1.d0/rs rs12i=1.d0/rs12 rs32i=1.d0/rs32 mz=rup-rdn z=mz/r z2=z**2 z3=z2*z z4=z3*z ! drs/drup = drs/drdn = drs/drho drs=-thrd*rs*ri ! d2rs/drup^2 = d^2rs/drn^2 = d^2rs/drho^2 d2rs=-thrd4*drs*ri ! dz/drup, dz/drdn t1=mz*ri2 dzu=ri-t1 dzd=-ri-t1 ! d^2z/drup^2, d^2z/drdn^2, d^2z/drup*drdn t1=2.d0*mz*ri3 t2=2.d0*ri2 d2zu=t1-t2 d2zd=t1+t2 d2zud=t1 !------------------! ! exchange ! !------------------! t1=-p2*rsi/2.d0 t2=1.d0+z t3=1.d0-z t4=t2**thrd4 t5=t3**thrd4 t6=t4+t5 ! exchange energy density ex=t1*t6 ! dex/drs ders=-ex*rsi ! d^2ex/drs^2 d2ers=-2.d0*ders*rsi ! f(z) fz=p3*(t6-2.d0) ! dex/dz t4=t4/t2 t5=t5/t3 t6=t4-t5 t7=thrd4*t6 dez=t1*t7 ! df/dz dfz=p3*t7 ! d^2ex/dz^2 t4=t4/t2 t5=t5/t3 t6=t4+t5 t7=thrd4*thrd*t6 d2ez=t1*t7 ! d^2f/dz^2 d2fz=p3*t7 ! d^2ex/drs*dz d2ersz=-dez*rsi ! dex/drup, dex/drdn t1=ders*drs deu=t1+dez*dzu ded=t1+dez*dzd ! d^2ex/drup^2 t1=d2ers*drs t2=d2ersz*drs t3=ders*d2rs t4=(t1+d2ersz*dzu)*drs+t3 t5=t2+d2ez*dzu d2eu=t4+t5*dzu+dez*d2zu ! d^2ex/drdn^2 d2ed=(t1+d2ersz*dzd)*drs+t3+(t2+d2ez*dzd)*dzd+dez*d2zd ! d^2ex/drup*drdn d2eud=t4+t5*dzd+dez*d2zud ! calculate fxc fxcuu(i)=2.d0*deu+r*d2eu fxcud(i)=deu+ded+r*d2eud fxcdd(i)=2.d0*ded+r*d2ed !---------------------! ! correlation ! !---------------------! ! ec(rs,0) a2=2.d0*a(1) t1=a2*(b1(1)*rs12+b2(1)*rs+b3(1)*rs32+b4(1)*rs2) dt1=a2*(0.5d0*b1(1)*rs12i+b2(1)+1.5d0*b3(1)*rs12+2.d0*b4(1)*rs) d2t1=a2*(-0.25d0*b1(1)*rs32i+0.75d0*b3(1)*rs12i+2.d0*b4(1)) t3=1.d0/t1 t4=t3**2 t2=1.d0+t3 dt2=-dt1*t4 d2t2=t4*(2.d0*t3*dt1**2-d2t1) t3=1.d0/t2 t4=1.d0+a1(1)*rs t5=log(t2) ec0=-a2*t4*t5 dec0=-a2*(a1(1)*t5+t4*t3*dt2) d2ec0=-a2*(2.d0*a1(1)*t3*dt2+t4*t3*(d2t2-t3*dt2**2)) ! ec(rs,1) a2=2.d0*a(2) t1=a2*(b1(2)*rs12+b2(2)*rs+b3(2)*rs32+b4(2)*rs2) dt1=a2*(0.5d0*b1(2)*rs12i+b2(2)+1.5d0*b3(2)*rs12+2.d0*b4(2)*rs) d2t1=a2*(-0.25d0*b1(2)*rs32i+0.75d0*b3(2)*rs12i+2.d0*b4(2)) t3=1.d0/t1 t4=t3**2 t2=1.d0+t3 dt2=-dt1*t4 d2t2=t4*(2.d0*t3*dt1**2-d2t1) t3=1.d0/t2 t4=1.d0+a1(2)*rs t5=log(t2) ec1=-a2*t4*t5 dec1=-a2*(a1(2)*t5+t4*t3*dt2) d2ec1=-a2*(2.d0*a1(2)*t3*dt2+t4*t3*(d2t2-t3*dt2**2)) ! ac(rs) a2=2.d0*a(3) t1=a2*(b1(3)*rs12+b2(3)*rs+b3(3)*rs32+b4(3)*rs2) dt1=a2*(0.5d0*b1(3)*rs12i+b2(3)+1.5d0*b3(3)*rs12+2.d0*b4(3)*rs) d2t1=a2*(-0.25d0*b1(3)*rs32i+0.75d0*b3(3)*rs12i+2.d0*b4(3)) t3=1.d0/t1 t4=t3**2 t2=1.d0+t3 dt2=-dt1*t4 d2t2=t4*(2.d0*t3*dt1**2-d2t1) t3=1.d0/t2 t4=1.d0+a1(3)*rs t5=log(t2) ac=a2*t4*t5 dac=a2*(a1(3)*t5+t4*t3*dt2) d2ac=a2*(2.d0*a1(3)*t3*dt2+t4*t3*(d2t2-t3*dt2**2)) ! correlation energy density derivatives t1=1.d0-z4 t2=(fz/d2f0)*t1 t3=ec1-ec0 t4=fz*z4 ! dec/drs t5=dec1-dec0 ders=dec0+dac*t2+t5*t4 ! d^2ec/drs^2 t6=d2ec1-d2ec0 d2ers=d2ec0+d2ac*t2+t6*t4 ! dec/dz t4=ac/d2f0 t6=4.d0*fz*z3 t7=dfz*t1-t6 t8=dfz*z4+t6 dez=t4*t7+t3*t8 ! d^2ec/drs*dz d2ersz=(dac/d2f0)*t7+t5*t8 ! d^2ec/dz^2 t7=8.d0*dfz*z3 t8=12.d0*fz*z2 d2ez=t4*(d2fz*t1-t7-t8)+t3*(d2fz*z4+t7+t8) ! dec/drup, dec/drdn t1=ders*drs deu=t1+dez*dzu ded=t1+dez*dzd ! d^2ec/drup^2 t1=d2ers*drs t2=d2ersz*drs t3=ders*d2rs t4=(t1+d2ersz*dzu)*drs+t3 t5=t2+d2ez*dzu d2eu=t4+t5*dzu+dez*d2zu ! d^2ec/drdn^2 d2ed=(t1+d2ersz*dzd)*drs+t3+(t2+d2ez*dzd)*dzd+dez*d2zd ! d^2ec/drup*drdn d2eud=t4+t5*dzd+dez*d2zud ! calculate fxc fxcuu(i)=fxcuu(i)+2.d0*deu+r*d2eu fxcud(i)=fxcud(i)+deu+ded+r*d2eud fxcdd(i)=fxcdd(i)+2.d0*ded+r*d2ed end do end subroutine elk-7.2.42/src/PaxHeaders.21776/gendmatmt.f900000644000000000000000000000013214061636517015224 xustar0030 mtime=1623670095.673101788 30 atime=1623670094.501102876 30 ctime=1623670095.673101788 elk-7.2.42/src/gendmatmt.f900000644002504400250440000000107714061636517017266 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gendmatmt use modmain use moddftu implicit none ! generate the density matrix in each muffin-tin call gendmat(.false.,.false.,0,lmaxdm,lmmaxdm,dmatmt) ! initialise with symmetry-breaking tensor moments if (ftmtype.lt.0) then dmftm=dmftm*reducebf dmatmt=dmatmt+dmftm endif ! symmetrise the density matrix call symdmat(lmaxdm,lmmaxdm,dmatmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/genveedu.f900000644000000000000000000000013214061636517015046 xustar0030 mtime=1623670095.675101786 30 atime=1623670094.503102874 30 ctime=1623670095.675101786 elk-7.2.42/src/genveedu.f900000644002504400250440000000316114061636517017104 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genveedu ! !INTERFACE: subroutine genveedu(i,u,j,vee) ! !USES: use modmain use moddftu ! !INPUT/OUTPUT PARAMETERS: ! i : DFT+U entry (in,integer) ! u : parameter U (out,real) ! j : parameter J (out,real) ! vee : Coulomb matrix elements (out,real(-lmaxdm:lmaxdm,-lmaxdm:lmaxdm, ! -lmaxdm:lmaxdm,-lmaxdm:lmaxdm)) ! !DESCRIPTION: ! Calculates the Coulomb matrix elements used in DFT+U calculations. See ! {\it Phys. Rev. B} {\bf 52}, 5467 (1995). ! ! !REVISION HISTORY: ! Created November 2007 (FC,JKD,FB,LN) ! Modified July 2009 (FC) !EOP !BOC implicit none ! arguments integer, intent(in) :: i real(8), intent(out) :: u,j real(8), intent(out) :: vee(-lmaxdm:lmaxdm,-lmaxdm:lmaxdm,-lmaxdm:lmaxdm, & -lmaxdm:lmaxdm) ! local variables integer l,m1,m2,m3,m4,k,q real(8) sm1,sm2,t1 ! automatic arrays real(8) :: f(0:2*lmaxdm) ! external functions real(8), external :: gaunt l=idftu(2,i) ! calculate Slater integrals call genfdu(i,u,j,f) do m1=-l,l do m2=-l,l do m3=-l,l do m4=-l,l sm1=0.d0 do k=0,2*l,2 sm2=0.d0 do q=-k,k t1=gaunt(l,k,l,m1,q,m2)*gaunt(l,k,l,m3,-q,m4) if (mod(q,2).eq.0) then sm2=sm2+t1 else sm2=sm2-t1 end if end do sm1=sm1+f(k)*sm2/dble(2*k+1) end do vee(m1,m3,m2,m4)=fourpi*sm1 end do end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genvmatmt.f900000644000000000000000000000013214061636517015246 xustar0030 mtime=1623670095.676101785 30 atime=1623670094.505102872 30 ctime=1623670095.676101785 elk-7.2.42/src/genvmatmt.f900000644002504400250440000002000714061636517017302 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genvmatmt !INTERFACE: subroutine genvmatmt ! !USES: use modmain use moddftu ! !DESCRIPTION: ! Calculate the DFT+U potential matrix to be used in the second-variational ! step. See {\it Phys. Rev. B} {\bf 52}, 5467 (1995) and {\it Phys. Rev. B} ! {\bf 80}, 035121 (2009). ! ! !REVISION HISTORY: ! Created November 2007 (FC,FB,LN,JKD) ! Fixed bug for dftu=3, January 2021 (JKD) !EOP !BOC ! local variables integer is,ia,ias,i integer l,lma,lmb,lm1,lm2 real(8) t1,t2 ! allocatable arrays real(8), allocatable :: enfll(:,:) complex(8), allocatable :: vmfll(:,:,:,:,:) select case(dftu) case(0) vmatmt(:,:,:,:,:)=0.d0 case(1,2) ! fully localised limit (FLL) or around mean field (AFM) call genvmatmt_12 case(3) ! interpolation between the two [PRB 67, 153106 (2003)] allocate(enfll(natmmax,ndftu)) allocate(vmfll(lmmaxdm,nspinor,lmmaxdm,nspinor,natmtot)) dftu=1 call genvmatmt_12 vmfll(:,:,:,:,:)=vmatmt(:,:,:,:,:) enfll(:,:)=engyadu(:,:) dftu=2 call genvmatmt_12 ! read in the interpolation constant (alpha) if required if (readadu) call readalphadu ! reset dftu value dftu=3 do i=1,ndftu is=idftu(1,i) l=idftu(2,i) lma=l**2+1; lmb=lma+2*l do ia=1,natoms(is) ias=idxas(ia,is) t1=alphadu(ia,i) t2=1.d0-t1 do lm1=lma,lmb do lm2=lma,lmb vmatmt(lm1,:,lm2,:,ias)=t1*vmfll(lm1,:,lm2,:,ias) & +t2*vmatmt(lm1,:,lm2,:,ias) end do end do engyadu(ia,i)=t1*enfll(ia,i)+t2*engyadu(ia,i) end do end do deallocate(enfll,vmfll) case default write(*,*) write(*,'("Error(genvmatmt): invalid dftu : ",I8)') dftu write(*,*) stop end select ! add the fixed tensor moment field if required call ftmfield end subroutine subroutine genvmatmt_12 use modmain use moddftu use modtest implicit none ! local variables integer ispn,jspn integer is,ia,ias,i integer l,m1,m2,m3,m4 integer ll,nm,lma,lmb integer lm1,lm2,lm3,lm4 real(8) u,j,n,n0 real(8) mg(3),mg0(3),mg2 real(8) edc,sm1,sm2 complex(8) z1,z2 ! automatic arrays real(8) vee(-lmaxdm:lmaxdm,-lmaxdm:lmaxdm,-lmaxdm:lmaxdm,-lmaxdm:lmaxdm) complex(8) dm(lmmaxdm,nspinor,lmmaxdm,nspinor) complex(8) dms(nspinor,nspinor) ! zero the DFT+U potential for each atom vmatmt(:,:,:,:,:)=0.d0 ! zero the DFT+U energy for each atom engyadu(:,:)=0.d0 ! zero the interpolation constants alphadu(:,:)=0.d0 ! loop over DFT+U entries do i=1,ndftu is=idftu(1,i) l=idftu(2,i) ll=l*(l+1)+1 nm=2*l+1 lma=l**2+1; lmb=lma+2*l ! calculate u, v and the Coulomb matrix elements call genveedu(i,u,j,vee) if ((abs(u).lt.1.d-10).and.(abs(j).lt.1.d-10)) cycle ! begin loop over atoms do ia=1,natoms(is) ias=idxas(ia,is) ! copy the density matrix for this atom dm(:,:,:,:)=dmatmt(:,:,:,:,ias) ! trace of density matrix for each spin dms(:,:)=0.d0 do ispn=1,nspinor do jspn=1,nspinor do lm1=lma,lmb dms(ispn,jspn)=dms(ispn,jspn)+dm(lm1,ispn,lm1,jspn) end do end do end do ! trace over spin n=dble(dms(1,1)) if (spinpol) n=n+dble(dms(2,2)) n0=n/dble(nspinor*nm) ! magnetisation if (spinpol) then mg(:)=0.d0 mg(3)=dble(dms(1,1)-dms(2,2)) ! non-collinear terms if (ncmag) then mg(1)=dble(dms(1,2)+dms(2,1)) mg(2)=dble(zi*(dms(1,2)-dms(2,1))) end if mg0(:)=mg(:)/dble(nspinor*nm) end if ! around mean field (AFM) approach if (dftu.eq.2) then ! modify density matrices do lm1=lma,lmb if (spinpol) then dm(lm1,1,lm1,1)=dm(lm1,1,lm1,1)-(n0+mg0(3)) dm(lm1,2,lm1,2)=dm(lm1,2,lm1,2)-(n0-mg0(3)) ! non-collinear terms if (ncmag) then dm(lm1,1,lm1,2)=dm(lm1,1,lm1,2)-(mg0(1)-zi*mg0(2)) dm(lm1,2,lm1,1)=dm(lm1,2,lm1,1)-(mg0(1)+zi*mg0(2)) end if else ! spin-unpolarised case dm(lm1,1,lm1,1)=dm(lm1,1,lm1,1)-n0 end if end do ! determine alpha [PRB 67,153106 (2003)] sm1=0.d0 do ispn=1,nspinor do lm1=lma,lmb do jspn=1,nspinor do lm2=lma,lmb sm1=sm1+dble(dm(lm1,ispn,lm2,jspn)*dm(lm2,jspn,lm1,ispn)) end do end do end do end do if (spinpol) then mg2=mg(3)**2 if (ncmag) mg2=mg2+mg(1)**2+mg(2)**2 else mg2=0.d0 end if sm2=n*(1.d0-0.5d0*n/dble(nm))-0.5d0*mg2/dble(nm) if (abs(sm2).gt.1.d-14) then alphadu(ia,i)=sm1/sm2 else alphadu(ia,i)=0.d0 end if end if ! calculation of DFT+U potential and energy ! begin loops over m1 and m2 do m1=-l,l lm1=ll+m1 do m2=-l,l lm2=ll+m2 ! begin loops over m3 and m4 do m3=-l,l lm3=ll+m3 do m4=-l,l lm4=ll+m4 do ispn=1,nspinor do jspn=1,nspinor z1=dm(lm2,ispn,lm1,ispn)*dm(lm4,jspn,lm3,jspn) z2=dm(lm4,jspn,lm1,ispn)*dm(lm2,ispn,lm3,jspn) engyadu(ia,i)=engyadu(ia,i)+dble(z1-z2)*vee(m1,m3,m2,m4) vmatmt(lm1,ispn,lm2,ispn,ias)=vmatmt(lm1,ispn,lm2,ispn,ias) & +dm(lm4,jspn,lm3,jspn)*vee(m1,m3,m2,m4) vmatmt(lm1,ispn,lm4,jspn,ias)=vmatmt(lm1,ispn,lm4,jspn,ias) & -dm(lm2,ispn,lm3,jspn)*vee(m1,m3,m2,m4) end do end do ! end loops over m3 and m4 end do end do ! end loops over m1 and m2 end do end do ! multiply energy by factor 1/2 engyadu(ia,i)=0.5d0*engyadu(ia,i) ! fully localised limit (FLL) approach: double counting corrections if (dftu.eq.1) then if (spinpol) then ! spin-polarised if (ncmag) then ! non-collinear case ! correction to the energy edc=0.5d0*u*n*(n-1.d0) edc=edc-0.5d0*j*dble(dms(1,1)*(dms(1,1)-1.d0)) edc=edc-0.5d0*j*dble(dms(2,2)*(dms(2,2)-1.d0)) edc=edc-0.5d0*j*dble(dms(1,2)*dms(2,1)) edc=edc-0.5d0*j*dble(dms(2,1)*dms(1,2)) ! correction to the potential do lm1=lma,lmb vmatmt(lm1,1,lm1,1,ias)=vmatmt(lm1,1,lm1,1,ias) & -u*(n-0.5d0)+j*(dms(1,1)-0.5d0) vmatmt(lm1,2,lm1,2,ias)=vmatmt(lm1,2,lm1,2,ias) & -u*(n-0.5d0)+j*(dms(2,2)-0.5d0) vmatmt(lm1,1,lm1,2,ias)=vmatmt(lm1,1,lm1,2,ias)+j*dms(1,2) vmatmt(lm1,2,lm1,1,ias)=vmatmt(lm1,2,lm1,1,ias)+j*dms(2,1) end do else ! collinear case ! correction to the energy edc=0.5d0*u*n*(n-1.d0) edc=edc-0.5d0*j*dble(dms(1,1)*(dms(1,1)-1.d0)) edc=edc-0.5d0*j*dble(dms(2,2)*(dms(2,2)-1.d0)) ! correction to the potential do lm1=lma,lmb vmatmt(lm1,1,lm1,1,ias)=vmatmt(lm1,1,lm1,1,ias) & -u*(n-0.5d0)+j*(dms(1,1)-0.5d0) vmatmt(lm1,2,lm1,2,ias)=vmatmt(lm1,2,lm1,2,ias) & -u*(n-0.5d0)+j*(dms(2,2)-0.5d0) end do end if else ! spin-unpolarised ! correction to the energy edc=0.5d0*u*n*(n-1.d0) edc=edc-0.5d0*j*n*(n-1.d0) ! correction to the potential do lm1=lma,lmb vmatmt(lm1,1,lm1,1,ias)=vmatmt(lm1,1,lm1,1,ias)-u*(n-0.5d0) & +j*(n-0.5d0) end do end if engyadu(ia,i)=engyadu(ia,i)-edc end if ! trace of dmatmt times vmatmt sm1=0.d0 do ispn=1,nspinor do lm1=lma,lmb do jspn=1,nspinor do lm2=lma,lmb sm1=sm1+dble(dm(lm1,ispn,lm2,jspn)*vmatmt(lm2,jspn,lm1,ispn,ias)) end do end do end do end do ! subtract contribution to the energy of DFT+U potential engyadu(ia,i)=engyadu(ia,i)-sm1 ! end loop over atoms end do ! end loop over species end do ! symmetrise the potential call symdmat(lmaxdm,lmmaxdm,vmatmt) ! write potential matrix to test file call writetest(800,'DFT+U energy for each atom',nv=natmmax*ndftu,tol=1.d-4, & rva=engyadu) ! write U and J parameters to test file call writetest(810,'U and J parameters',nv=2*maxdftu,tol=1.d-4,rva=ujdu) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writedftu.f900000644000000000000000000000013214061636517015261 xustar0030 mtime=1623670095.678101784 30 atime=1623670094.507102871 30 ctime=1623670095.678101784 elk-7.2.42/src/writedftu.f900000644002504400250440000000477214061636517017330 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine writedftu use modmain use moddftu implicit none ! local variables integer ispn,jspn,is,ia,ias integer i,k,l,ll,m1,m2,lm1,lm2 if (dftu.eq.0) return ! machine readable density matrix file open(50,file='DMATMT'//trim(filext),form='FORMATTED',action='WRITE') do i=1,ndftu is=idftu(1,i) l=idftu(2,i) ll=l*(l+1)+1 do ia=1,natoms(is) ias=idxas(ia,is) write(50,*) write(50,*) write(50,'(3I4," : species, atom, l")') is,ia,l do ispn=1,nspinor do jspn=1,nspinor write(50,*) write(50,'(2I4," : ispn, jspn; m1, m2, dmatmt below")') ispn,jspn do m1=-l,l lm1=ll+m1 do m2=-l,l lm2=ll+m2 write(50,'(2I6," ",2G18.10)') m1,m2,dmatmt(lm1,ispn,lm2,jspn,ias) end do end do end do end do end do end do close(50) ! machine readable potential matrix file open(50,file='VMATMT'//trim(filext),form='FORMATTED',action='WRITE') do i=1,ndftu is=idftu(1,i) l=idftu(2,i) ll=l*(l+1)+1 do ia=1,natoms(is) ias=idxas(ia,is) write(50,*) write(50,*) write(50,'(3I4," : species, atom, l")') is,ia,l do ispn=1,nspinor do jspn=1,nspinor write(50,*) write(50,'(2I4," : ispn, jspn; m1, m2, vmatmt below")') ispn,jspn do m1=-l,l lm1=ll+m1 do m2=-l,l lm2=ll+m2 write(50,'(2I6," ",2G18.10)') m1,m2,vmatmt(lm1,ispn,lm2,jspn,ias) end do end do end do end do end do end do close(50) ! machine readable alpha parameters if ((dftu.eq.3).and.(.not.readadu)) then open(50,file='ALPHADU'//trim(filext),form='FORMATTED',action='WRITE') do i=1,ndftu is=idftu(1,i) l=idftu(2,i) do ia=1,natoms(is) ias=idxas(ia,is) write(50,*) write(50,'(3I4," : species, atom, l")') is,ia,l write(50,'(G18.10," : alpha")') alphadu(ia,i) end do end do close(50) end if ! Slater parameters open(50,file='FDU'//trim(filext),form='FORMATTED',action='WRITE') do i=1,ndftu is=idftu(1,i) l=idftu(2,i) write(50,*) write(50,'(3I4," : species, l")') is,l do k=0,2*l,2 write(50,'(G18.10," : F^(",I1,")")') fdu(k,i),k end do write(50,'(G18.10," : U")') ujdu(1,i) write(50,'(G18.10," : J")') ujdu(2,i) if (inpdftu.ge.4) write(50,'(G18.10," : lambdadu")') lambdadu(i) end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/readalphadu.f900000644000000000000000000000013114061636517015515 xustar0030 mtime=1623670095.679101783 29 atime=1623670094.50810287 30 ctime=1623670095.679101783 elk-7.2.42/src/readalphadu.f900000644002504400250440000000151214061636517017552 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. subroutine readalphadu use modmain use moddftu implicit none ! local variables integer is,ia,i,l integer is_,ia_,l_ if (.not.readadu) return open(50,file='ALPHADU'//trim(filext),form='FORMATTED') do i=1,ndftu is=idftu(1,i) l=idftu(2,i) do ia=1,natoms(is) read(50,*) read(50,*) is_,ia_,l_ if ((is.ne.is_).or.(ia.ne.ia_).or.(l.ne.l_)) then write(*,*) write(*,'("Error(readalphadu): differing is, ia or l")') write(*,'(" current : ",3I8)') is,ia,l write(*,'(" ALPHADU.OUT : ",3I8)') is_,ia_,l_ write(*,*) stop end if read(50,*) alphadu(ia,i) end do end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/fyukawa.f900000644000000000000000000000013214061636517014713 xustar0030 mtime=1623670095.681101781 30 atime=1623670094.510102868 30 ctime=1623670095.681101781 elk-7.2.42/src/fyukawa.f900000644002504400250440000000452014061636517016751 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: fyukawa ! !INTERFACE: real(8) function fyukawa(is,l,k,lambda) ! !USES: use modmain use moddftu ! !INPUT/OUTPUT PARAMETERS: ! is : species type (in,integer) ! l : an angular momentum (in,integer) ! k : order of Slater parameter (in,integer) ! lambda : screening length of Yukawa potential (in,real) ! !DESCRIPTION: ! Calculates the Slater parameters using a screened Yukawa potential. See ! {\it Phys. Rev. B} {\bf 52}, 1421 (1995) and {\it Phys. Rev. B} {\bf 80}, ! 035121 (2009). ! ! !REVISION HISTORY: ! Created April 2008 (Lars Nordstrom) ! Modified and tested July 2008 (LN and FC) !EOP !BOC implicit none ! arguments integer, intent(in) :: is integer, intent(in) :: l,k real(8), intent(in) :: lambda ! local variables integer ias,nr,ir integer nr1,nr2,ir1,ir2 real(8) r2,x,t1 ! automatic arrays real(8) clow(nrmtmax),chigh(nrmtmax) real(8) blow(nrmtmax),bhigh(nrmtmax),fint(nrmtmax) real(8) bint(nrmtmax),cint(nrmtmax) ! allocatable arrays real(8), allocatable :: a(:,:),b(:,:) ias=idxas(1,is) nr=nrmt(is) ! (-1)**k factor takes care of the additional (-1)**k introduced by zbessela(b) t1=lambda*dble((2*k+1)*(-1)**(k+1)) ! allocate Bessel and Hankel functions allocate(a(0:2*l,nr),b(0:2*l,nr)) ! zero all quantities a(:,:)=0.d0 b(:,:)=0.d0 bint(:)=0.d0 blow(:)=0.d0 bhigh(:)=0.d0 clow(:)=0.d0 chigh(:)=0.d0 ! calculate Slater parameters do ir=1,nr r2=rlmt(ir,2,is) bint(ir)=fdufr(ir,l,ias)*fdufr(ir,l,ias)*r2 ! argument of Bessel and Hankel functions divided by i x=rsp(ir,is)*lambda ! calculate Bessel and Hankel functions divided by i call zbessela(2*l,x,a(:,ir)) call zbesselb(2*l,x,b(:,ir)) end do do ir=1,nr nr1=ir nr2=nr-ir+1 ! 1st term: r1 < r do ir1=1,nr1 ir2=ir1 blow(ir1)=bint(ir2)*a(k,ir2) end do ! integrate 1st term call fderiv(-1,nr1,rsp(1,is),blow,clow) ! 2nd term : r2 > r do ir1=1,nr2 ir2=ir1+ir-1 bhigh(ir1)=bint(ir2)*b(k,ir2) end do ! integrate 2nd term call fderiv(-1,nr2,rsp(ir,is),bhigh,chigh) ! sum of the two terms cint(ir)=bint(ir)*(b(k,ir)*clow(nr1)+a(k,ir)*chigh(nr2)) end do call fderiv(-1,nr,rsp(1,is),cint,fint) fyukawa=t1*fint(nr) deallocate(a,b) end function !EOC elk-7.2.42/src/PaxHeaders.21776/fyukawa0.f900000644000000000000000000000013014061636517014771 xustar0029 mtime=1623670095.68210178 30 atime=1623670094.512102866 29 ctime=1623670095.68210178 elk-7.2.42/src/fyukawa0.f900000644002504400250440000000354214061636517017034 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: fyukawa0 ! !INTERFACE: real(8) function fyukawa0(is,l1,k) ! !USES: use modmain use moddftu ! !INPUT/OUTPUT PARAMETERS: ! is : species type (in,integer) ! l : an angular momentum (in,integer) ! k : order of Slater parameter (in,integer) ! !DESCRIPTION: ! Calculates the Slater parameters in the unscreened case. See {\it Phys. Rev. ! B} {\bf 52}, 1421 (1995) and {\it Phys. Rev. B} {\bf 80}, 035121 (2009). ! ! !REVISION HISTORY: ! Created April 2008 (LN) ! Modified and tested July 2008 (LN and FC) !EOP !BOC implicit none ! arguments integer, intent(in) :: is integer, intent(in) :: l1 integer, intent(in) :: k ! local variables integer, parameter :: nstart=1 integer ir,nr,ias integer ir1,ir2,nr1,nr2 real(8) r2,x ! automatic arrays real(8) clow(nrmtmax),chigh(nrmtmax) real(8) blow(nrmtmax),bhigh(nrmtmax),fint(nrmtmax) real(8) bint(nrmtmax),cint(nrmtmax) ! allocatable arrays real(8), allocatable :: a(:,:),b(:,:) ias=idxas(1,is) nr=nrmt(is) allocate(a(0:k,nr),b(0:k,nr)) a(:,:)=0.d0 b(:,:)=0.d0 ! calculate unscreened Slater parameters do ir=1,nr r2=rlmt(ir,2,is) bint(ir)=fdufr(ir,l1,ias)*fdufr(ir,l1,ias)*r2 x=rsp(ir,is)**k a(k,ir)=x b(k,ir)=1.d0/(x*rsp(ir,is)) end do do ir=nstart,nr nr1=ir-nstart+1 nr2=nr-ir+1 do ir1=1,nr1 ir2=ir1+nstart-1 blow(ir1)=bint(ir2)*a(k,ir2) end do call fderiv(-1,nr1,rsp(nstart,is),blow,clow) do ir1=1,nr2 ir2=ir1+ir-1 bhigh(ir1)=bint(ir2)*b(k,ir2) end do call fderiv(-1,nr2,rsp(ir,is),bhigh,chigh) cint(ir-nstart+1)=bint(ir)*(b(k,ir)*clow(nr1)+a(k,ir)*chigh(nr2)) end do nr1=nr-nstart+1 call fderiv(-1,nr1,rsp(nstart,is),cint,fint) fyukawa0=fint(nr1) deallocate(a,b) end function !EOC elk-7.2.42/src/PaxHeaders.21776/genfdufr.f900000644000000000000000000000013214061636517015044 xustar0030 mtime=1623670095.684101778 30 atime=1623670094.513102865 30 ctime=1623670095.684101778 elk-7.2.42/src/genfdufr.f900000644002504400250440000000312614061636517017103 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genfdufr ! !INTERFACE: subroutine genfdufr ! !USES: use modmain use moddftu ! !DESCRIPTION: ! Generates the radial functions used to calculate the Slater integrals ! through a Yukawa potential. ! ! !REVISION HISTORY: ! Created April 2008 from genapwfr (Francesco Cricchio) !EOP !BOC implicit none ! local variables integer is,ia,ias integer nr,nri,ir integer nn,i,l real(8) t1 ! automatic arrays real(8) vr(nrmtmax),fr(nrmtmax) real(8) p0(nrmtmax),p1(nrmtmax),q0(nrmtmax),q1(nrmtmax) ! external functions real(8), external :: splint do i=1,ndftu is=idftu(1,i) l=idftu(2,i) nr=nrmt(is) nri=nrmti(is) do ia=1,natoms(is) ias=idxas(ia,is) call rfmtlm(1,nr,nri,vsmt(:,ias),vr) vr(1:nr)=vr(1:nr)*y00 ! integrate the radial Schrodinger equation call rschrodint(solsc,l,fdue(l,ias),nr,rlmt(:,1,is),vr,nn,p0,p1,q0,q1) ! normalise radial functions fr(1:nr)=p0(1:nr)**2 t1=splint(nr,rlmt(:,1,is),fr) if (t1.lt.1.d-20) then write(*,*) write(*,'("Error(genfdufr): degenerate APW radial functions")') write(*,'(" for species ",I4)') is write(*,'(" atom ",I4)') ia write(*,'(" and angular momentum ",I4)') l write(*,*) stop end if t1=1.d0/sqrt(abs(t1)) p0(1:nr)=t1*p0(1:nr) ! divide by r and store in global array do ir=1,nr fdufr(ir,l,ias)=p0(ir)/rsp(ir,is) end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/energyfdu.f900000644000000000000000000000013214061636517015234 xustar0030 mtime=1623670095.685101777 30 atime=1623670094.515102863 30 ctime=1623670095.685101777 elk-7.2.42/src/energyfdu.f900000644002504400250440000000311214061636517017266 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: energyfdu ! !INTERFACE: subroutine energyfdu ! !USES: use modmain use moddftu use modmpi ! !DESCRIPTION: ! Calculates the energies of radial functions to be used to calculate the ! Slater integrals. By convention those energies are chosen to be the ones at ! the center of the band. ! ! !REVISION HISTORY: ! Created April 2008 (F. Cricchio) !EOP !BOC implicit none ! local variables integer is,ia,ja,ias,jas integer nr,nri,nnf,i,l logical fnd ! automatic arrays logical done(natmmax) real(8) vr(nrmtmax) nnf=0 ! loop over DFT+U entries do i=1,ndftu is=idftu(1,i) l=idftu(2,i) nr=nrmt(is) nri=nrmti(is) done(:)=.false. do ia=1,natoms(is) if (done(ia)) cycle ias=idxas(ia,is) call rfmtlm(1,nr,nri,vsmt(:,ias),vr) vr(1:nr)=vr(1:nr)*y00 ! find the center of the band starting from -0.5 Ha fdue(l,ias)=-0.5d0 call findband(solsc,l,nrmt(is),rsp(1,is),vr,epsband,demaxbnd,fdue(l,ias), & fnd) if (.not.fnd) nnf=nnf+1 done(ia)=.true. ! copy to equivalent atoms do ja=1,natoms(is) if ((.not.done(ja)).and.(eqatoms(ia,ja,is))) then jas=idxas(ja,is) fdue(l,jas)=fdue(l,ias) done(ja)=.true. end if end do ! end loops over atoms and species end do end do if (mp_mpi.and.(nnf.gt.0)) then write(*,*) write(*,'("Warning(energyfdu): could not find ",I3," energies")') nnf end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writeefdu.f900000644000000000000000000000013214061636517015242 xustar0030 mtime=1623670095.687101775 30 atime=1623670094.517102861 30 ctime=1623670095.687101775 elk-7.2.42/src/writeefdu.f900000644002504400250440000000174414061636517017305 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writeefdu ! !INTERFACE: subroutine writeefdu ! !USES: use modmain use moddftu ! !DESCRIPTION: ! Writes to file the linearisation energies for all radial functions used to ! calculate the Slater integrals through a Yukawa potential. ! ! !REVISION HISTORY: ! Created July 2008 (Francesco Cricchio) !EOP !BOC implicit none ! local variables integer is,ia,ias,i,l open(50,file='ENGYFDU'//trim(filext),form='FORMATTED') do i=1,ndftu is=idftu(1,i) l=idftu(2,i) do ia=1,natoms(is) ias=idxas(ia,is) write(50,*) write(50,'("Species : ",I4," (",A,"), atom : ",I4)') is,trim(spsymb(is)),ia write(50,'(" Radial functions used for Slater parameters :")') write(50,'(" l = ",I2," : ",G18.10)') l,fdue(l,ias) end do end do close(50) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/zbessela.f900000644000000000000000000000013114061636517015053 xustar0030 mtime=1623670095.688101774 29 atime=1623670094.51810286 30 ctime=1623670095.688101774 elk-7.2.42/src/zbessela.f900000644002504400250440000000364614061636517017122 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zbessela ! !INTERFACE: subroutine zbessela(lmax,x,a) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum order of Bessel function (in,integer) ! x : real argument (in,real) ! a : array of returned values (out,real(0:lmax)) ! !DESCRIPTION: ! Computes variations of the spherical Bessel function, $a_l(x)=i^lj_l(ix)$, ! for real argument $x$ and $l=0,1,\ldots,l_{\rm max}$. The recursion relation ! $$ j_{l+1}(x)=\frac{2l+1}{x}j_l(x)+j_{l-1}(x) $$ ! is used upwards. For starting values there are ! $$ a_0(x)=\frac{\sinh(x)}{x};\qquad a_1(x)=\frac{a_0(x)-\cosh(x)}{x} $$. ! For $x\ll 1$ the asymtotic forms ! $$ a_l(x)\approx\frac{(-x)^l}{(2l+1)!!} $$ ! are used. ! ! !REVISION HISTORY: ! Created April 2008 from sbessel routine (Lars Nordstrom) !EOP !BOC implicit none ! arguments integer, intent(in) :: lmax real(8), intent(in) :: x real(8), intent(out) :: a(0:lmax) ! local variables integer l real(8) xi,a0,a1,at,t1,t2,xmin if ((lmax.lt.0).or.(lmax.gt.50)) then write(*,*) write(*,'("Error(zbessela): lmax out of range : ",I8)') lmax write(*,*) stop end if if ((x.lt.0.d0).or.(x.gt.1.d8)) then write(*,*) write(*,'("Error(zbessela): x out of range : ",G18.10)') x write(*,*) stop end if xi=1.d0/x xmin=1.d-7 select case (lmax) case(0) xmin=1.d-6 case(1:2) xmin=1.d-4 case(3:4) xmin=1.d-2 case(5:) xmin=1.d0 end select ! treat x << 1 if (x.lt.xmin) then a(0)=1.d0 t1=1.d0 t2=1.d0 do l=1,lmax t1=t1/dble(2*l+1) t2=-t2*x a(l)=t2*t1 end do return end if ! recurse up a(0)=xi*(sinh(x)) if (lmax.eq.0) return a(1)=xi*(a(0)-cosh(x)) if (lmax.eq.1) return a0=a(0) a1=a(1) do l=2,lmax at=dble(2*l-1)*a1*xi+a0 a0=a1 a1=at a(l)=a1 end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/zbesselb.f900000644000000000000000000000013214061636517015055 xustar0030 mtime=1623670095.690101773 30 atime=1623670094.520102858 30 ctime=1623670095.690101773 elk-7.2.42/src/zbesselb.f900000644002504400250440000000345714061636517017123 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: zbesselb ! !INTERFACE: subroutine zbesselb(lmax,x,b) ! !INPUT/OUTPUT PARAMETERS: ! lmax : maximum order of Bessel function (in,integer) ! x : real argument (in,real) ! b : array of returned values (out,real(0:lmax)) ! !DESCRIPTION: ! Computes variations of the spherical Bessel function ! $b_l(x)=i^lh^{(1)}_l(ix)$, for real argument $x$ and ! $l=0,1,\ldots,l_{\rm max}$. The recursion relation ! $$ j_{l+1}(x)=\frac{2l+1}{x}j_l(x)+j_{l-1}(x) $$ ! is used upwards. For starting values there are ! $$ b_0(x)=-\frac{e^{-x}}{x};\qquad b_1(x)=b_0(x)\left\{1+\frac{1}{x} ! \right\}. $$ ! For $x\ll 1$ the asymtotic forms ! $$ b_l(x)\approx\frac{-(2l-1)!!}{(-x)^{l+1}} $$ ! are used. ! ! !REVISION HISTORY: ! Created April 2008 from sbessel routine (Lars Nordstrom) !EOP !BOC implicit none ! arguments integer, intent(in) :: lmax real(8), intent(in) :: x real(8), intent(out) :: b(0:lmax) ! local variables integer l real(8) xi,b0,b1,bt,t3,t4 if ((lmax.lt.0).or.(lmax.gt.50)) then write(*,*) write(*,'("Error(zbesselb): lmax out of range : ",I8)') lmax write(*,*) stop end if if ((x.lt.0.d0).or.(x.gt.1.d8)) then write(*,*) write(*,'("Error(zbesselb): x out of range : ",G18.10)') x write(*,*) stop end if xi=1.d0/x ! treat x << 1 if (x.lt.1.d-7) then b(0)=-xi t3=-1.d0 t4=xi do l=1,lmax t3=t3*dble(2*l-1) t4=t4*xi b(l)=t4*t3 end do return end if ! recurse up b(0)=-xi*exp(-x) if (lmax.eq.0) return b(1)=b(0)*(1.d0+xi) if (lmax.eq.1) return b0=b(0) b1=b(1) do l=2,lmax bt=dble(2*l-1)*b1*xi+b0 b0=b1 b1=bt b(l)=b1 end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/readdmatmt.f900000644000000000000000000000013214061636517015366 xustar0030 mtime=1623670095.691101772 30 atime=1623670094.522102857 30 ctime=1623670095.691101772 elk-7.2.42/src/readdmatmt.f900000644002504400250440000000353414061636517017430 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readdmatmt use modmain use moddftu implicit none ! local variables integer is,ia,ias,ispn,jspn integer is_,ia_,ispn_,jspn_ integer i,l,ll,m1,m2,lm1,lm2 integer l_,m1_,m2_ real(8) a,b ! read density matrix from DMATMT.OUT open(50,file='DMATMT'//trim(filext),form='FORMATTED') do i=1,ndftu is=idftu(1,i) l=idftu(2,i) ll=l*(l+1)+1 do ia=1,natoms(is) ias=idxas(ia,is) read(50,*) read(50,*) read(50,*) is_,ia_,l_ if ((is.ne.is_).or.(ia.ne.ia_).or.(l.ne.l_)) then write(*,*) write(*,'("Error(readdmatmt): differing is, ia or l")') write(*,'(" current : ",3I4)') is,ia,l write(*,'(" DMATMT.OUT : ",3I4)') is_,ia_,l_ write(*,*) stop end if do ispn=1,nspinor do jspn=1,nspinor read(50,*) read(50,*) ispn_,jspn_ if ((ispn.ne.ispn_).or.(jspn.ne.jspn_)) then write(*,*) write(*,'("Error(readdmatmt): differing ispn or jspn")') write(*,'(" current : ",2I4)') ispn,jspn write(*,'(" DMATMT.OUT : ",2I4)') ispn_,jspn_ write(*,*) stop end if do m1=-l,l lm1=ll+m1 do m2=-l,l lm2=ll+m2 read(50,*) m1_,m2_,a,b if ((m1.ne.m1_).or.(m2.ne.m2_)) then write(*,*) write(*,'("Error(readdmatmt): differing m1 or m2")') write(*,'(" current : ",2I6)') m1,m2 write(*,'(" DMATMT.OUT : ",2I6)') m1_,m2_ write(*,*) stop end if dmatmt(lm1,ispn,lm2,jspn,ias)=cmplx(a,b,8) end do end do end do end do end do end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/genfdu.f900000644000000000000000000000013014061636517014512 xustar0029 mtime=1623670095.69310177 30 atime=1623670094.523102856 29 ctime=1623670095.69310177 elk-7.2.42/src/genfdu.f900000644002504400250440000001201414061636517016547 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genfdu ! !INTERFACE: subroutine genfdu(i,u,j,f) ! !USES: use moddftu use modmpi ! !INPUT/OUTPUT PARAMETERS: ! i : DFT+U entry (in,integer) ! u : parameter U (inout,real) ! j : parameter J (inout,real) ! f : Slater parameters (inout,real) ! !DESCRIPTION: ! Calculate the Slater parameters for DFT+$U$ calculation with different ! approaches, see {\it Phys. Rev. B} {\bf 80}, 035121 (2009). The relations ! among Slater and Racah parameters are from E. U. Condon and G. H. Shortley, ! {\it The Theory of Atomic Spectra}, The University Press, Cambridge (1935). ! ! !REVISION HISTORY: ! Created July 2008 (Francesco Cricchio) !EOP !BOC implicit none ! arguments integer, intent(in) :: i real(8), intent(inout) :: u,j real(8), intent(inout) :: f(0:2*lmaxdm) ! local variables integer is,l,k,q real(8) r1,r2 real(8) lambda,ufix ! automatic arrays real(8) :: e(0:lmaxdm) real(8) :: a(3,3),v1(3),v2(3) ! external functions real(8), external :: fyukawa,fyukawa0 is=idftu(1,i) l=idftu(2,i) ! load input parameters to calculate Slater integrals u=ujdu(1,i) j=ujdu(2,i) f(:)=fdu(:,i) e(:)=edu(:,i) lambda=lambdadu(i) if (inpdftu.lt.4) then ! F(0) = U for any l-shell if (inpdftu.eq.1) f(0)=u select case(l) case(0) ! s electrons only f(0)=u if (inpdftu.eq.3) then f(0)=e(0) u=f(0) end if case(1) ! p electrons if (inpdftu.eq.1) then ! F(2) = 5.0 * J f(2)=5.d0*j else if (inpdftu.eq.3) then ! F(0) = E(0) + J= E(0) + 5/3 * E(1) f(0)=e(0)+(5.d0/3.d0)*e(1) ! F(2) = 5 * J = 25/3 * E1, Eq. 101 f(2)=(25.d0/3.d0)*e(1) end if case(2) ! d electrons if (inpdftu.eq.1) then ! r1 = F(4)/F(2), see PRB 52, R5467 (1995) r1=0.625d0 f(2)=(14.d0*j)/(1.d0+r1) f(4)=f(2)*r1 else if (inpdftu.eq.3) then ! copy Racah parameters v1(1:3)=e(0:2) ! transformation matrix from Racah to Slater parameters ! obtained from inversion of Eq. 110-112, LN Notes 29-12-08 a(1,1)=1.d0 a(1,2)=1.4d0 a(1,3)=0.d0 a(2,1)=0.d0 a(2,2)=0.1428571428571428d0 a(2,3)=1.285714285714286d0 a(3,1)=0.d0 a(3,2)=2.8571428571428571d-2 a(3,3)=-0.1428571428571428d0 ! multiply transformation matrix by Racah parameters call r3mv(a,v1,v2) ! Slater parameters, Eq. 104-105, LN Notes 29-12-08 f(0)=v2(1) f(2)=49.d0*v2(2) f(4)=441.d0*v2(3) end if case(3) ! f electrons if (inpdftu.eq.1) then ! r2 = F(6)/F(2), r1 = F(4)/F(2), see PRB 50, 16861 (1994) r1=451.d0/675.d0 r2=1001.d0/2025.d0 f(2)=6435.d0*j/(286.d0+195.d0*r1+250.d0*r2) f(4)=f(2)*r1 f(6)=f(2)*r2 else if (inpdftu.eq.3) then ! F(0) = E(0) + 9/7 * E(1) , Eq. 119, LN Notes 29-12-08 f(0)=e(0)+(9.d0/7.d0)*e(1) ! copy Racah parameters v1(1:3)=e(1:3) ! transformation matrix from Racah to Slater parameters ! obtained from inversion of Eq. 120-122, LN Notes 29-12-08 a(1,1)=2.3809523809523808d-2 a(1,2)=3.404761904761904d0 a(1,3)=0.2619047619047619d0 a(2,1)=1.2987012987012984d-2 a(2,2)=-1.688311688311688d0 a(2,3)=5.1948051948051951d-2 a(3,1)=2.1645021645021645d-3 a(3,2)=7.5757575757575760d-2 a(3,3)=-1.5151515151515152d-2 ! multiply transformation matrix by Racah parameters call r3mv(a,v1,v2) ! Slater parameters, Eq. 115-117, LN Notes 29-12-08 f(2)=225.d0*v2(1) f(4)=1089.d0*v2(2) f(6)=(184041.d0/25.d0)*v2(3) end if case default write(*,*) write(*,'("Error(genfdu): invalid l : ",I8)') l write(*,*) stop end select else if (inpdftu.ge.4) then ! define energies for Slater parameters call energyfdu ! write energies for Slater parameters to a file if (mp_mpi) call writeefdu ! calculate radial functions for Slater parameters call genfdufr if (inpdftu.eq.5) then ufix=udufix(i) ! calculate the lambda corresponding to udufix ! lambdadu0 is in/out and is initialized to 0 in readinput call findlambdadu(is,l,ufix,lambdadu0(i),lambda) end if do q=0,l k=2*q if (lambda.lt.1.d-2) then ! unscreened Slater parameters f(k)=fyukawa0(is,l,k) else ! screened Slater parameters f(k)=fyukawa(is,l,k,lambda) end if end do end if ! calculate U and J from Slater integrals if (inpdftu.ne.1) then u=f(0) select case(l) case(0) j=0.d0 case(1) ! J = 1/5 * F(2) j=(1.d0/5.d0)*f(2) case(2) ! J = 1/14 * ( F(2) + F(4) ), Eq. 106, LN Notes 29-12-08 j=(1.d0/14.d0)*(f(2)+f(4)) case(3) ! J= 2/45 * F(2) + 1/33 * F(4) + 50/1287 * F(6), Eq. 118, LN Notes 29-12-08 j=(2.d0/45.d0)*f(2)+(1.d0/33.d0)*f(4)+(50.d0/1287.d0)*f(6) case default write(*,*) write(*,'("Error(genfdu): invalid l : ",I8)') l write(*,*) stop end select end if ! save calculated parameters ! (except Racah parameters that are provided only as input) ujdu(1,i)=u ujdu(2,i)=j fdu(:,i)=f(:) lambdadu(i)=lambda end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/findlambdadu.f900000644000000000000000000000013214061636517015656 xustar0030 mtime=1623670095.694101769 30 atime=1623670094.525102854 30 ctime=1623670095.694101769 elk-7.2.42/src/findlambdadu.f900000644002504400250440000000726314061636517017723 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: findlambdadu ! !INTERFACE: subroutine findlambdadu(is,l,ufix,lambda0,lambda) use modmpi ! !INPUT/OUTPUT PARAMETERS: ! is : species type (in,integer) ! l : angular momentum (in,integer) ! ufix : fixed U (in,integer) ! lambda0 : starting value for screening length (inout,real) ! lambda : screening length corresponding to fixed U (out,real) ! !DESCRIPTION: ! Find the screening length corresponding to a fixed value of $U$ by using the ! half-interval method in the first few steps and then the more efficient ! secant method. For $U=0$ the code automatically sets the screening length to ! ${\rm lambdamax}=50$. This value is enough to get $F^{(k)}\sim 10^{-3}$ ! corresponding to $U\sim 0$ (that perfectly mimics a bare DFT calculation). ! However the code is stable up to ${\rm lambdamax}\sim 200$ thanks to ! improvement of {\tt spline}. ! ! !REVISION HISTORY: ! Created July 2009 (Francesco Cricchio) !EOP !BOC implicit none ! arguments integer, intent(in) :: is integer, intent(in) :: l real(8), intent(in) :: ufix real(8), intent(inout) :: lambda0 real(8), intent(out) :: lambda ! local variables ! max iterations in secant algorithm integer, parameter :: maxit=100 integer it,nit ! if ufix 2*l : ",2I8)') k,2*l write(*,*) stop end if if ((p.lt.0).or.(p.gt.1)) then write(*,*) write(*,'("Error(dmtotm2): p should be 0 or 1 : ",I8)') p write(*,*) stop end if ! calculate the 2-index tensor moment; see Eq. (23) in article nlk=factnm(2*l,1)/sqrt(factnm(2*l-k,1)*factnm(2*l+k+1,1)) nsp=1.d0/sqrt(factnm(2+p,1)) t1=dble((-1)**(l))/(nlk*nsp) tm2(:,:)=0.d0 do x=-k,k do y=-p,p do ispn=1,nspinor do jspn=1,nspinor t2=t1*wigner3jf(1,2*p,1,2*jspn-3,2*y,3-2*ispn) if (abs(t2).gt.1.d-10) then lm1=l**2 do m1=-l,l lm1=lm1+1 lm2=l**2 do m2=-l,l lm2=lm2+1 t3=t2*dble((-1)**(1+jspn-m2))*wigner3j(l,k,l,-m2,x,m1) tm2(x,y)=tm2(x,y)+t3*dmat(lm1,ispn,lm2,jspn) end do end do end if end do end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/dmtotm3.f900000644000000000000000000000013014061636517014631 xustar0029 mtime=1623670095.70310176 30 atime=1623670094.535102845 29 ctime=1623670095.70310176 elk-7.2.42/src/dmtotm3.f900000644002504400250440000000643214061636517016675 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! !ROUTINE: dmtotm3 ! !INTERFACE: subroutine dmtotm3(l,nspinor,k,p,r,ld,dmat,tm3) ! !INPUT/OUTPUT PARAMETERS: ! l : angular momentum (in,integer) ! nspinor : number of spinor components (in,integer) ! k : k-index of tensor moment (in,integer) ! p : p-index of tensor moment (in,integer) ! r : r-index of tensor moment (in,integer) ! ld : leading dimension (in,integer) ! dmat : density matrix (in,complex(ld,nspinor,ld,nspinor)) ! tm3 : 3-index spherical tensor moment (out,complex(-ld:ld)) ! !DESCRIPTION: ! Transform the density matrix to a 3-index spherical tensor moment ! representation, see {\it Phys. Rev. B} {\bf 80}, 035121 (2009). ! ! !REVISION HISTORY: ! Created April 2008 (F. Cricchio and L. Nordstrom) ! Modified, January 2014 (JKD) !EOP !BOC implicit none integer, intent(in) :: l,nspinor integer, intent(in) :: k,p,r integer, intent(in) :: ld complex(8), intent(in) :: dmat(ld,nspinor,ld,nspinor) complex(8), intent(out) :: tm3(-ld:ld) ! local variables integer ispn,jspn,g,t,x,y integer m1,m2,lm1,lm2 real(8) nlk,nsp,t1,t2,t3 complex(8), parameter :: zi=(0.d0,1.d0) complex(8) z1 ! external functions real(8), external :: wigner3j,wigner3jf,factnm,factr if (l.lt.0) then write(*,*) write(*,'("Error(dmtotm3): l < 0 : ",I8)') l write(*,*) stop end if if ((nspinor.lt.1).or.(nspinor.gt.2)) then write(*,*) write(*,'("Error(dmtotm3): nspinor should be 1 or 2 : ",I8)') nspinor write(*,*) stop end if if (k.lt.0) then write(*,*) write(*,'("Error(dmtotm3): k < 0 : ",I8)') k write(*,*) stop end if if (k.gt.2*l) then write(*,*) write(*,'("Error(dmtotm3): k > 2*l : ",2I8)') k,2*l write(*,*) stop end if if ((p.lt.0).or.(p.gt.1)) then write(*,*) write(*,'("Error(dmtotm3): p should be 0 or 1 : ",I8)') p write(*,*) stop end if if (r.lt.abs(k-p)) then write(*,*) write(*,'("Error(dmtotm3): r < |k-p| : ",2I8)') r,abs(k-p) write(*,*) stop end if if (r.gt.(k+p)) then write(*,*) write(*,'("Error(dmtotm3): r > k+p : ",2I8)') r,k+p write(*,*) stop end if ! calculate the 3-index tensor moment; see Eqs. (23), (26), (27) in article g=k+p+r if (mod(g,2).eq.0) then z1=1.d0/wigner3j(k,p,r,0,0,0) else t1=sqrt(factr(g+1,g-2*k)/(factnm(g-2*p,1)*factnm(g-2*r,1))) t1=t1*factnm(g-2*k,2)*factnm(g-2*p,2)*factnm(g-2*r,2)/factnm(g,2) z1=t1*zi**(-g) end if nlk=factnm(2*l,1)/sqrt(factnm(2*l-k,1)*factnm(2*l+k+1,1)) nsp=1.d0/sqrt(factnm(2+p,1)) z1=z1*dble((-1)**(k+p+l))/(nlk*nsp) tm3(:)=0.d0 do t=-r,r do x=-k,k do y=-p,p t1=dble((-1)**(x+y))*wigner3j(k,r,p,-x,t,-y) do ispn=1,nspinor do jspn=1,nspinor t2=t1*wigner3jf(1,2*p,1,2*jspn-3,2*y,3-2*ispn) if (abs(t2).gt.1.d-10) then lm1=l**2 do m1=-l,l lm1=lm1+1 lm2=l**2 do m2=-l,l lm2=lm2+1 t3=t2*dble((-1)**(1+jspn-m2))*wigner3j(l,k,l,-m2,x,m1) tm3(t)=tm3(t)+t3*z1*dmat(lm1,ispn,lm2,jspn) end do end do end if end do end do end do end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/tm2todm.f900000644000000000000000000000013214061636517014632 xustar0030 mtime=1623670095.705101759 30 atime=1623670094.536102844 30 ctime=1623670095.705101759 elk-7.2.42/src/tm2todm.f900000644002504400250440000000361014061636517016667 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tm2todm(l,nspinor,k,p,ld,tm2,dmat) implicit none ! arguments integer, intent(in) :: l,nspinor integer, intent(in) :: k,p integer, intent(in) :: ld complex(8), intent(in) :: tm2(-ld:ld,-1:1) complex(8), intent(out) :: dmat(ld,nspinor,ld,nspinor) ! local variables integer ispn,jspn,x,y integer m1,m2,lm1,lm2 real(8) nlk,nsp,t1,t2,t3 ! external functions real(8), external :: wigner3j,wigner3jf,factnm if (l.lt.0) then write(*,*) write(*,'("Error(tm2todm): l < 0 : ",I8)') l write(*,*) stop end if if ((nspinor.lt.1).or.(nspinor.gt.2)) then write(*,*) write(*,'("Error(tm2todm): nspinor should be 1 or 2 : ",I8)') nspinor write(*,*) stop end if if (k.lt.0) then write(*,*) write(*,'("Error(tm2todm): k < 0 : ",I8)') k write(*,*) stop end if if (k.gt.2*l) then write(*,*) write(*,'("Error(tm2todm): k > 2*l : ",2I8)') k,2*l write(*,*) stop end if if ((p.lt.0).or.(p.gt.1)) then write(*,*) write(*,'("Error(tm2todm): p should be 0 or 1 : ",I8)') p write(*,*) stop end if ! factors n_lk and n_sp; Eq. (21) in article nlk=factnm(2*l,1)/sqrt(factnm(2*l-k,1)*factnm(2*l+k+1,1)) nsp=1.d0/sqrt(factnm(2+p,1)) t1=dble((2*k+1)*(2*p+1))*nlk*nsp ! compute density matrix from 2-index tensor moment dmat(:,:,:,:)=0.d0 do x=-k,k do y=-p,p do ispn=1,nspinor do jspn=1,nspinor t2=t1*wigner3jf(1,2*p,1,2*jspn-3,2*y,3-2*ispn) lm1=l**2 do m1=-l,l lm1=lm1+1 lm2=l**2 do m2=-l,l lm2=lm2+1 t3=t2*dble((-1)**(m2-l+jspn-1))*wigner3j(l,k,l,-m2,x,m1) dmat(lm1,ispn,lm2,jspn)=dmat(lm1,ispn,lm2,jspn)+t3*tm2(x,y) end do end do end do end do end do end do end subroutine elk-7.2.42/src/PaxHeaders.21776/tm3todm.f900000644000000000000000000000013214061636517014633 xustar0030 mtime=1623670095.706101758 30 atime=1623670094.538102842 30 ctime=1623670095.706101758 elk-7.2.42/src/tm3todm.f900000644002504400250440000000422514061636517016673 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tm3todm(l,nspinor,k,p,r,ld,tm3,dmat) implicit none ! arguments integer, intent(in) :: l,nspinor integer, intent(in) :: k,p,r integer, intent(in) :: ld complex(8), intent(in) :: tm3(-ld:ld) complex(8), intent(out) :: dmat(ld,nspinor,ld,nspinor) ! parameters complex(8), parameter :: zi=(0.d0,1.d0) ! local variables integer x,y,g,t real(8) t1,t2 complex(8) z1 ! allocatable arrays complex(8), allocatable :: tm2(:,:) ! external functions real(8), external :: wigner3j,factnm,factr if (l.lt.0) then write(*,*) write(*,'("Error(tm3todm): l < 0 : ",I8)') l write(*,*) stop end if if ((nspinor.lt.1).or.(nspinor.gt.2)) then write(*,*) write(*,'("Error(tm3todm): nspinor should be 1 or 2 : ",I8)') nspinor write(*,*) stop end if if (k.lt.0) then write(*,*) write(*,'("Error(tm3todm): k < 0 : ",I8)') k write(*,*) stop end if if (k.gt.2*l) then write(*,*) write(*,'("Error(tm3todm): k > 2*l : ",2I8)') k,2*l write(*,*) stop end if if ((p.lt.0).or.(p.gt.1)) then write(*,*) write(*,'("Error(tm3todm): p should be 0 or 1 : ",I8)') p write(*,*) stop end if if (r.lt.abs(k-p)) then write(*,*) write(*,'("Error(tm3todm): r < |k-p| : ",2I8)') r,abs(k-p) write(*,*) stop end if if (r.gt.(k+p)) then write(*,*) write(*,'("Error(tm3todm): r > k+p : ",2I8)') r,k+p write(*,*) stop end if ! compute 2-index tensor moment from 3-index tensor moment allocate(tm2(-ld:ld,-1:1)) tm2(:,:)=0.d0 do x=-k,k do y=-p,p t1=dble((-1)**(x+y-k-p)) g=k+p+r if (mod(g,2).eq.0) then z1=t1*wigner3j(k,p,r,0,0,0) else t1=t1*sqrt(factr(g-2*k,g+1)*factnm(g-2*p,1)*factnm(g-2*r,1)) t1=t1*factnm(g,2)/(factnm(g-2*k,2)*factnm(g-2*p,2)*factnm(g-2*r,2)) z1=t1*zi**g end if do t=-r,r t2=wigner3j(k,r,p,-x,t,-y)*(2*r+1) tm2(x,y)=tm2(x,y)+t2*z1*tm3(t) end do end do end do ! compute the density matrix from the 2-index tensor moment call tm2todm(l,nspinor,k,p,ld,tm2,dmat) deallocate(tm2) end subroutine elk-7.2.42/src/PaxHeaders.21776/pottm2.f900000644000000000000000000000013114061636517014470 xustar0030 mtime=1623670095.707101757 29 atime=1623670094.54010284 30 ctime=1623670095.707101757 elk-7.2.42/src/pottm2.f900000644002504400250440000000246114061636517016531 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: pottm2 ! !INTERFACE: subroutine pottm2(i,k1,p,vh,vx) ! !USES: use moddftu ! !INPUT/OUTPUT PARAMETERS: ! i : DFT+U entry (in,integer) ! k1 : k-index of tensor moment (in,integer) ! p : p-index of tensor moment (in,integer) ! vh : Hartree potential energy (out,real) ! vx : exchange potential energy (out,real) ! !DESCRIPTION: ! Calculates the DFT+$U$ Hartree and exchange potential energies for a 2-index ! tensor moment component. See {\tt pottm3}. ! ! !REVISION HISTORY: ! Created April 2008 (F. Cricchio and L. Nordstrom) ! Modified, January 2014 (JKD) !EOP !BOC implicit none integer, intent(in) :: i integer, intent(in) :: k1,p real(8), intent(out) :: vh,vx ! local variables integer l,k real(8) nlk,t1,t2 ! external functions real(8), external :: wigner3j,wigner6j,factnm l=idftu(2,i) nlk=factnm(2*l,1)/sqrt(factnm(2*l-k1,1)*factnm(2*l+k1+1,1)) vh=0.d0 vx=0.d0 do k=0,2*l,2 t1=0.5d0*(dble(2*l+1)*nlk*wigner3j(l,k,l,0,0,0))**2 t2=0.5d0*dble((2*k1+1)*(-1)**k1)*wigner6j(l,l,k1,l,l,k) if (k.eq.k1) then if (p.eq.0) vh=t1*fdu(k1,i) end if vx=vx-t1*t2*fdu(k,i) end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/pottm3.f900000644000000000000000000000013214061636517014472 xustar0030 mtime=1623670095.709101755 30 atime=1623670094.541102839 30 ctime=1623670095.709101755 elk-7.2.42/src/pottm3.f900000644002504400250440000000332014061636517016525 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: pottm3 ! !INTERFACE: subroutine pottm3(i,k1,p,r,vh,vx) ! !USES: use moddftu ! !INPUT/OUTPUT PARAMETERS: ! i : DFT+U entry (in,integer) ! k1 : k-index of tensor moment (in,integer) ! p : p-index of tensor moment (in,integer) ! r : r-index of tensor moment (in,integer) ! vh : Hartree potential energy (out,real) ! vx : exchange potential energy (out,real) ! !DESCRIPTION: ! Calculates the DFT+$U$ Hartree and exchange potential energies for a 3-index ! tensor moment component. See Eq. (28) in {\it Phys. Rev. B} {\bf 80}, 035121 ! (2009); and Eqs. (3), (4) in {\it Phys. Rev. B} {\bf 78}, 100404 (2008). ! ! !REVISION HISTORY: ! Created April 2008 (F. Cricchio and L. Nordstrom) ! Modified and fixed bug, January 2014 (JKD) !EOP !BOC implicit none integer, intent(in) :: i integer, intent(in) :: k1,p,r real(8), intent(out) :: vh,vx ! local variables integer l,k,g real(8) nlk,t1,t2,t3 ! external functions real(8), external :: wigner3j,wigner6j,factnm,factr l=idftu(2,i) g=k1+p+r if (mod(g,2).eq.0) then t1=wigner3j(k1,p,r,0,0,0) else t1=sqrt(factr(g-2*k1,g+1)*factnm(g-2*p,1)*factnm(g-2*r,1)) t1=t1*factnm(g,2)/(factnm(g-2*k1,2)*factnm(g-2*p,2)*factnm(g-2*r,2)) end if t3=dble(2*r+1)*t1**2 nlk=factnm(2*l,1)/sqrt(factnm(2*l-k1,1)*factnm(2*l+k1+1,1)) vh=0.d0 vx=0.d0 do k=0,2*l,2 t1=0.5d0*(dble(2*l+1)*nlk*wigner3j(l,k,l,0,0,0))**2 t2=0.5d0*dble((2*k1+1)*(-1)**k1)*wigner6j(l,l,k1,l,l,k)*t3 if (k.eq.k1) then if (p.eq.0) vh=t1*fdu(k1,i) end if vx=vx-t1*t2*fdu(k,i) end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/tm2pol.f900000644000000000000000000000013214061636517014461 xustar0030 mtime=1623670095.711101753 30 atime=1623670094.543102837 30 ctime=1623670095.711101753 elk-7.2.42/src/tm2pol.f900000644002504400250440000000176314061636517016525 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tm2pol(l,k,w2,tm2p) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! l : angular momentum (in,integer) ! k : k-index of tensor moment (in,integer) ! w2 : modulus square of k-p tensmom (in,real) ! tm2p : polarisation (out,real) ! !DESCRIPTION: ! Calculate the polarisation of each 2-index tensor component of the density ! matrix, see {\it Phys. Rev. B} {\bf 80}, 035121 (2009). ! ! !REVISION HISTORY: ! Created April 2008 (F. Cricchio and L. Nordstrom) !EOP !BOC implicit none ! input variables integer, intent(in) :: l,k real(8),intent(in) :: w2 real(8),intent(out) :: tm2p ! local variables real(8) nlk ! external functions real(8), external :: factnm nlk=factnm(2*l,1)/sqrt(factnm(2*l-k,1)*factnm(2*l+k+1,1)) tm2p=dble((2*k+1)*(2*l+1))*(nlk**2)*w2 end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/tm3pol.f900000644000000000000000000000013214061636517014462 xustar0030 mtime=1623670095.712101752 30 atime=1623670094.545102835 30 ctime=1623670095.712101752 elk-7.2.42/src/tm3pol.f900000644002504400250440000000266314061636517016526 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 F. Bultmark, F. Cricchio, L. Nordstrom and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tm3pol(l,k,p,r,w2,tm3p) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! l : angular momentum (in,integer) ! k : k-index of tensor moment (in,integer) ! p : p-index of tensor moment (in,integer) ! r : r-index of tensor moment (in,integer) ! w2 : modulus square of k-p-r tensor moment (in,real) ! tm3p : polarisation (out,real) ! !DESCRIPTION: ! Calculate the polarisation of each 3-index tensor component of the density ! matrix, see {\it Phys. Rev. B} {\bf 80}, 035121 (2009). ! ! !REVISION HISTORY: ! Created April 2008 (F. Cricchio and L. Nordstrom) !EOP !BOC implicit none ! input variables integer, intent(in) :: l,k,p,r real(8), intent(in) :: w2 real(8), intent(out) :: tm3p ! local variables integer g real(8) nlk,t1 ! external functions real(8), external :: wigner3j,factnm,factr g=k+p+r if (g.eq.0) then t1=sqrt(w2) tm3p=t1*(dble(2*(2*l+1))-t1) else if (mod(g,2).eq.0) then t1=wigner3j(k,p,r,0,0,0) else t1=sqrt(factnm(g-2*p,1)*factnm(g-2*r,1)*factr(g-2*k,g+1)) t1=t1*factnm(g,2)/(factnm(g-2*k,2)*factnm(g-2*p,2)*factnm(g-2*r,2)) end if nlk=factnm(2*l,1)/sqrt(factnm(2*l-k,1)*factnm(2*l+k+1,1)) tm3p=dble((2*k+1)*(2*r+1)*(2*l+1))*((t1*nlk)**2)*w2 end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gendmftm.f900000644000000000000000000000013014061636517015043 xustar0029 mtime=1623670095.71410175 30 atime=1623670094.546102834 29 ctime=1623670095.71410175 elk-7.2.42/src/gendmftm.f900000644002504400250440000000474514061636517017114 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma, E. K. U. Gross and L. Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gendmftm use modmain use moddftu implicit none ! local variables integer is,ia,ias,i integer l,n,k,p,r,t,x,y ! allocatable arrays complex(8), allocatable :: tm2(:,:),tm3(:) complex(8), allocatable :: dmat(:,:,:,:) ! external functions real(8), external :: dznrm2 if (ftmtype.eq.0) return ! allocate global array if (allocated(dmftm)) deallocate(dmftm) allocate(dmftm(lmmaxdm,nspinor,lmmaxdm,nspinor,natmtot)) ! allocate local arrays allocate(tm2(-lmmaxdm:lmmaxdm,-1:1),tm3(-lmmaxdm:lmmaxdm)) allocate(dmat(lmmaxdm,nspinor,lmmaxdm,nspinor)) ! zero the fixed tensor moment density matrices dmftm(:,:,:,:,:)=0.d0 do i=1,ntmfix is=itmfix(1,i) if (is.gt.nspecies) then write(*,*) write(*,'("Error(gendmftm): invalid species number : ",I8)') is write(*,*) stop end if ia=itmfix(2,i) if (ia.gt.natoms(is)) then write(*,*) write(*,'("Error(gendmftm): invalid atom number : ",I8)') ia write(*,'(" for species ",I4)') is write(*,*) stop end if ias=idxas(ia,is) l=itmfix(3,i) if (l.gt.lmaxdm) then write(*,*) write(*,'("Error(gendmftm): l > lmaxdm ",2I8)') l,lmaxdm write(*,'(" for species ",I4," and atom ",I4)') is,ia write(*,*) stop end if n=itmfix(4,i) k=itmfix(5,i) p=itmfix(6,i) if (n.eq.2) then ! generate the 2-index density matrix x=itmfix(7,i) y=itmfix(8,i) if ((abs(x).gt.lmmaxdm).or.(abs(y).gt.1)) then write(*,*) write(*,'("Error(gendmftm): invalid x or y : ",2I8)') x,y write(*,'(" for tensor moment entry ",I3)') i write(*,*) stop end if tm2(:,:)=0.d0 tm2(x,y)=tmfix(i) call tm2todm(l,nspinor,k,p,lmmaxdm,tm2,dmat) else ! generate the 3-index density matrix r=itmfix(7,i) t=itmfix(8,i) if (abs(t).gt.lmmaxdm) then write(*,*) write(*,'("Error(gendmftm): invalid t : ",I8)') t write(*,'(" for tensor moment entry ",I3)') i write(*,*) stop end if tm3(:)=0.d0 tm3(t)=tmfix(i) call tm3todm(l,nspinor,k,p,r,lmmaxdm,tm3,dmat) end if ! make density matrix Hermitian call hrmdmat(lmmaxdm*nspinor,dmat) ! apply rotation matrices and add to density matrix global array call rotdmat(rtmfix(:,:,1,i),rtmfix(:,:,2,i),lmaxdm,nspinor,lmmaxdm,dmat, & dmftm(:,:,:,:,ias)) end do deallocate(tm2,tm3,dmat) end subroutine elk-7.2.42/src/PaxHeaders.21776/ftmfield.f900000644000000000000000000000013214061636517015036 xustar0030 mtime=1623670095.715101749 30 atime=1623670094.548102833 30 ctime=1623670095.715101749 elk-7.2.42/src/ftmfield.f900000644002504400250440000000354714061636517017104 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 L. Nordstrom, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine ftmfield use modmain use moddftu implicit none ! local variables integer is,ia,ias,n2,i integer l,n,k,p,r,t,x,y complex(8) z1 ! allocatable arrays complex(8), allocatable :: tm2(:,:),tm3(:) complex(8), allocatable :: dmat(:,:,:,:) if (ftmtype.le.0) return if (mod(iscl,ftmstep).ne.1) return allocate(tm2(-lmmaxdm:lmmaxdm,-1:1),tm3(-lmmaxdm:lmmaxdm)) allocate(dmat(lmmaxdm,nspinor,lmmaxdm,nspinor)) n2=(lmmaxdm*nspinor)**2 ! loop over FTM entries do i=1,ntmfix is=itmfix(1,i) ia=itmfix(2,i) ias=idxas(ia,is) l=itmfix(3,i) n=itmfix(4,i) k=itmfix(5,i) p=itmfix(6,i) if (n.eq.2) then x=itmfix(7,i) y=itmfix(8,i) ! decompose density matrix in 2-index tensor moment components call dmtotm2(l,nspinor,k,p,lmmaxdm,dmatmt(:,:,:,:,ias),tm2) ! take difference between current and target moment z1=tm2(x,y)-tmfix(i) tm2(:,:)=0.d0 tm2(x,y)=tauftm*z1 ! compute new density matrix call tm2todm(l,nspinor,k,p,lmmaxdm,tm2,dmat) else r=itmfix(7,i) t=itmfix(8,i) ! decompose density matrix in 3-index tensor moment components call dmtotm3(l,nspinor,k,p,r,lmmaxdm,dmatmt(:,:,:,:,ias),tm3) ! take difference between current and target moment z1=tm3(t)-tmfix(i) tm3(:)=0.d0 tm3(t)=tauftm*z1 ! compute new density matrix call tm3todm(l,nspinor,k,p,r,lmmaxdm,tm3,dmat) end if ! make density matrix Hermitian call hrmdmat(lmmaxdm*nspinor,dmat) ! apply rotation matrices and add to potential matrix global arrays call rotdmat(rtmfix(:,:,1,i),rtmfix(:,:,2,i),lmaxdm,nspinor,lmmaxdm,dmat, & vmftm(:,:,:,:,ias)) call zaxpy(n2,zone,vmftm(:,:,:,:,ias),1,vmatmt(:,:,:,:,ias),1) end do deallocate(tm2,tm3,dmat) end subroutine elk-7.2.42/src/PaxHeaders.21776/writeftm.f900000644000000000000000000000013214061636517015105 xustar0030 mtime=1623670095.717101748 30 atime=1623670094.549102832 30 ctime=1623670095.717101748 elk-7.2.42/src/writeftm.f900000644002504400250440000000306214061636517017143 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeftm use modmain use moddftu implicit none ! local variables integer is,ia,ias,i integer l,n,k,p,r,t,x,y ! allocatable arrays complex(8), allocatable :: tm2(:,:),tm3(:) allocate(tm2(-lmmaxdm:lmmaxdm,-1:1),tm3(-lmmaxdm:lmmaxdm)) ! open FTM.OUT open(50,file='FTM.OUT',form='FORMATTED') do i=1,ntmfix is=itmfix(1,i) ia=itmfix(2,i) ias=idxas(ia,is) l=itmfix(3,i) n=itmfix(4,i) k=itmfix(5,i) p=itmfix(6,i) write(50,*) write(50,'("Species : ",I4," (",A,"), atom : ",I4)') is,trim(spsymb(is)),ia write(50,'(" l = ",I2,", n = ",I2)') l,n if (n.eq.2) then x=itmfix(7,i) y=itmfix(8,i) write(50,'(" k = ",I2,", p = ",I2,", x = ",I2,", y = ",I2)') k,p,x,y ! decompose density matrix in 2-index tensor moment components call dmtotm2(l,nspinor,k,p,lmmaxdm,dmatmt(:,:,:,:,ias),tm2) write(50,'(" tensor moment")') write(50,'(" current : ",2G18.10)') tm2(x,y) write(50,'(" target : ",2G18.10)') tmfix(i) else r=itmfix(7,i) t=itmfix(8,i) write(50,'(" k = ",I2,", p = ",I2,", r = ",I2,", t = ",I2)') k,p,r,t ! decompose density matrix in 3-index tensor moment components call dmtotm3(l,nspinor,k,p,r,lmmaxdm,dmatmt(:,:,:,:,ias),tm3) write(50,'(" tensor moment")') write(50,'(" current : ",2G18.10)') tm3(t) write(50,'(" target : ",2G18.10)') tmfix(i) end if end do close(50) deallocate(tm2,tm3) end subroutine elk-7.2.42/src/PaxHeaders.21776/genvclijji.f900000644000000000000000000000013114061636517015367 xustar0030 mtime=1623670095.718101746 29 atime=1623670094.55110283 30 ctime=1623670095.718101746 elk-7.2.42/src/genvclijji.f900000644002504400250440000001107514061636517017431 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genvclijji ! !INTERFACE: subroutine genvclijji(ikp,vclijji) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ikp : k-point from non-reduced set (in,integer) ! vclijji : Coulomb matrix elements (out,real(nstsv,nstsv,nkpt)) ! !DESCRIPTION: ! Calculates the Coulomb matrix elements of the type $(i-jj-i)$. ! ! !REVISION HISTORY: ! Created June 2008 (Sharma) !EOP !BOC implicit none ! arguments integer, intent(in) :: ikp real(8), intent(out) :: vclijji(nstsv,nstsv,nkpt) ! local variables integer ik,ist1,ist2 integer iv(3),iq,ig real(8) vc(3) complex(8) z1 ! automatic arrays integer idx(nstsv) ! allocatable arrays real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqrmt(:,:,:) complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: wfmt2(:,:,:,:),wfir2(:,:,:) complex(8), allocatable :: wfmt1(:,:,:,:),wfir1(:,:,:) complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) ! external functions complex(8), external :: zfinp ! allocate local arrays allocate(vgqc(3,ngvc),gqc(ngvc),gclgq(ngvc)) allocate(jlgqrmt(0:lnpsd,ngvc,nspecies)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) allocate(ylmgq(lmmaxo,ngvc),sfacgq(ngvc,natmtot)) allocate(wfmt1(npcmtmax,natmtot,nspinor,nstsv),wfir1(ngtc,nspinor,nstsv)) allocate(wfmt2(npcmtmax,natmtot,nspinor,nstsv),wfir2(ngtc,nspinor,nstsv)) allocate(zrhomt(npcmtmax,natmtot),zrhoir(ngtc)) allocate(zvclmt(npcmtmax,natmtot),zvclir(ngtc)) ! get the eigenvectors from file for non-reduced k-point ikp call getevecfv(filext,0,vkl(:,ikp),vgkl(:,:,1,ikp),evecfv) call getevecsv(filext,0,vkl(:,ikp),evecsv) ! find the matching coefficients call match(ngk(1,ikp),vgkc(:,:,1,ikp),gkc(:,1,ikp),sfacgk(:,:,1,ikp),apwalm) ! index to all states do ist1=1,nstsv idx(ist1)=ist1 end do ! calculate the wavefunctions for all states of passed non-reduced k-point ikp call genwfsv(.false.,.false.,nstsv,idx,ngdgc,igfc,ngk(1,ikp),igkig(:,1,ikp), & apwalm,evecfv,evecsv,wfmt2,ngtc,wfir2) ! start loop over reduced k-point set do ik=1,nkpt ! determine the q-vector iv(:)=ivk(:,ik)-ivk(:,ikp) iv(:)=modulo(iv(:),ngridk(:)) ! check if the q-point is in user-defined set iv(:)=iv(:)*ngridq(:) if (any(modulo(iv(:),ngridk(:)).ne.0)) cycle iv(:)=iv(:)/ngridk(:) iq=ivqiq(iv(1),iv(2),iv(3)) vc(:)=vkc(:,ik)-vkc(:,ikp) do ig=1,ngvc ! determine the G+q-vectors vgqc(:,ig)=vgc(:,ig)+vc(:) ! G+q-vector length gqc(ig)=sqrt(vgqc(1,ig)**2+vgqc(2,ig)**2+vgqc(3,ig)**2) ! spherical harmonics for G+q-vectors call genylmv(lmaxo,vgqc(:,ig),ylmgq(:,ig)) end do ! structure factors for G+q call gensfacgp(ngvc,vgqc,ngvc,sfacgq) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.true.,iq,ngvc,gqc,gclgq) ! compute the required spherical Bessel functions call genjlgprmt(lnpsd,ngvc,gqc,ngvc,jlgqrmt) ! find the matching coefficients call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! get the eigenvectors from file call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! calculate the wavefunctions for all states of the reduced k-point call genwfsv(.false.,.false.,nstsv,idx,ngdgc,igfc,ngk(1,ik),igkig(:,1,ik), & apwalm,evecfv,evecsv,wfmt1,ngtc,wfir1) !----------------------------------------------! ! valence-valence-valence contribution ! !----------------------------------------------! do ist1=1,nstsv do ist2=1,nstsv ! calculate the complex overlap density call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,ist2),wfir2(:,:,ist2), & wfmt1(:,:,:,ist1),wfir1(:,:,ist1),zrhomt,zrhoir) ! compute the potential and G=0 coefficient of the density call genzvclmt(nrcmt,nrcmti,nrcmtmax,rlcmt,wprcmt,npcmtmax,zrhomt,zvclmt) call zpotcoul(nrcmt,nrcmti,npcmt,npcmti,nrcmtmax,rlcmt,ngdgc,igfc,ngvc, & gqc,gclgq,ngvc,jlgqrmt,ylmgq,sfacgq,zrhoir,npcmtmax,zvclmt,zvclir) zvclir(:)=zvclir(:)*cfrc(:) z1=zfinp(zrhomt,zrhoir,zvclmt,zvclir) vclijji(ist1,ist2,ik)=wqptnr*dble(z1) ! end loop over ist2 end do ! end loop over ist1 end do ! end loop over reduced k-point set end do deallocate(vgqc,gqc,gclgq,jlgqrmt) deallocate(apwalm,evecfv,evecsv,ylmgq,sfacgq) deallocate(wfmt1,wfmt2,wfir1,wfir2) deallocate(zrhomt,zrhoir,zvclmt,zvclir) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmft.f900000644000000000000000000000013214061636517014360 xustar0030 mtime=1623670095.720101745 30 atime=1623670094.553102828 30 ctime=1623670095.720101745 elk-7.2.42/src/rdmft.f900000644002504400250440000000636414061636517016426 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmft ! !INTERFACE: subroutine rdmft ! !USES: use modmain use modrdm use modmpi ! !DESCRIPTION: ! Main routine for one-body reduced density matrix functional theory (RDMFT). ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! initialise global variables call init0 call init1 ! generate q-point set and gclq array call init2 ! read density and potentials from file call readstate ! Fourier transform Kohn-Sham potential to G-space call genvsig ! generate the core wavefunctions and densities call gencore ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! generate the spin-orbit coupling radial functions call gensocfr ! compute the kinetic energy of the core call energykncr ! generate the first- and second-variational eigenvectors and eigenvalues call genevfsv ! find the occupation numbers call occupy ! generate the kinetic matrix elements in the first-variational basis call genkmat(.true.,.false.) ! open information files (MPI master process only) if (mp_mpi) then open(60,file='RDM_INFO.OUT',form='FORMATTED') open(61,file='RDMN_ENERGY.OUT',form='FORMATTED') open(62,file='RDMC_ENERGY.OUT',form='FORMATTED') if (spinpol) then open(63,file='RDMN_MOMENT.OUT',form='FORMATTED') open(64,file='RDMC_MOMENT.OUT',form='FORMATTED') end if open(65,file='RDM_ENERGY.OUT',form='FORMATTED') ! write out general information to RDM_INFO.OUT call writeinfo(60) write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop started |")') write(60,'("+------------------------------+")') end if ! begin main RDMFT self-consistent loop do iscl=1,rdmmaxscl if (mp_mpi) then write(60,*) write(60,'("+--------------------+")') write(60,'("| Loop number : ",I4," |")') iscl write(60,'("+--------------------+")') flush(60) write(*,*) write(*,'("Info(rdmft): self-consistent loop number : ",I4)') iscl end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! minimisation over natural orbitals call rdmminc ! minimisation over occupation number call rdmminn ! compute the RDMFT 'eigenvalues' call rdmeval if (mp_mpi) then call rdmwriteengy(60) call writechg(60) if (spinpol) call writemom(60) call writeeval ! write out the total energy write(65,'(G18.10)') engytot flush(65) end if end do if (mp_mpi) then write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop stopped |")') write(60,'("+------------------------------+")') ! write density to STATE.OUT call writestate write(60,*) write(60,'("Wrote STATE.OUT")') write(60,*) write(60,'("+----------------------------+")') write(60,'("| Elk version ",I1.1,".",I1.1,".",I2.2," stopped |")') version write(60,'("+----------------------------+")') ! close information files close(60) close(61) close(62) if (spinpol) then close(63) close(64) end if close(65) end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmdkdc.f900000644000000000000000000000013214061636517014654 xustar0030 mtime=1623670095.721101744 30 atime=1623670094.554102827 30 ctime=1623670095.721101744 elk-7.2.42/src/rdmdkdc.f900000644002504400250440000000203614061636517016712 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmdkdc ! !INTERFACE: subroutine rdmdkdc ! !USES: use modmain use modrdm use modomp ! !DESCRIPTION: ! Calculates the derivative of kinetic energy w.r.t. the second-variational ! coefficients {\tt evecsv}. ! ! !REVISION HISTORY: ! Created October 2008 (Sharma) !EOP !BOC implicit none ! local variables integer ik,nthd ! allocatable arrays complex(8), allocatable :: evecsv(:,:),kmat(:,:) call holdthd(nkpt,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evecsv,kmat) & !$OMP NUM_THREADS(nthd) allocate(evecsv(nstsv,nstsv),kmat(nstsv,nstsv)) !$OMP DO do ik=1,nkpt call getevecsv(filext,ik,vkl(:,ik),evecsv) call getkmat(ik,kmat) call zgemm('N','N',nstsv,nstsv,nstsv,zone,kmat,nstsv,evecsv,nstsv,zzero, & dkdc(:,:,ik),nstsv) end do !$OMP END DO deallocate(evecsv,kmat) !$OMP END PARALLEL call freethd(nthd) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmminc.f900000644000000000000000000000013214061636517014675 xustar0030 mtime=1623670095.722101743 30 atime=1623670094.556102825 30 ctime=1623670095.722101743 elk-7.2.42/src/rdmminc.f900000644002504400250440000000275514061636517016743 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmminc ! !INTERFACE: subroutine rdmminc ! !USES: use modmain use modrdm use modmpi ! !DESCRIPTION: ! Minimizes the total energy with respect to the second-variational ! coefficients {\tt evecsv}. The steepest-descent algorithm is used. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! local variables integer it if (maxitc.lt.1) return ! begin iteration loop do it=1,maxitc if (mp_mpi) then write(*,'("Info(rdmminc): iteration ",I4," of ",I4)') it,maxitc end if ! generate the density and magnetisation call rhomag ! calculate the Coulomb potential call potcoul ! calculate Coulomb potential matrix elements call genvmat(vclmt,vclir,vclmat) ! calculate derivative of kinetic energy w.r.t. evecsv call rdmdkdc ! write the Coulomb matrix elements to file call writevclijjk ! update evecsv, orthogonalise and write to file (MPI master process only) if (mp_mpi) call rdmvaryc ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! calculate the energy call rdmenergy ! write energy to file if (mp_mpi) then write(62,'(I6,G18.10)') it,engytot flush(62) end if ! end iteration loop end do if (mp_mpi) then write(60,*) write(60,'("Natural orbital minimisation done")') write(62,*) if (spinpol) write(64,*) end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmvaryc.f900000644000000000000000000000013214061636517015073 xustar0030 mtime=1623670095.724101741 30 atime=1623670094.557102824 30 ctime=1623670095.724101741 elk-7.2.42/src/rdmvaryc.f900000644002504400250440000000211314061636517017125 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmvaryc ! !INTERFACE: subroutine rdmvaryc ! !USES: use modmain use modrdm ! !DESCRIPTION: ! Calculates new {\tt evecsv} from old by using the derivatives of the total ! energy w.r.t. {\tt evecsv}. A single step of steepest-descent is made. ! ! !REVISION HISTORY: ! Created 2009 (Sharma) !EOP !BOC implicit none ! local variables integer ik ! allocatable arrays complex(8), allocatable :: dedc(:,:,:),evecsv(:,:) ! compute the derivative w.r.t. evecsv allocate(dedc(nstsv,nstsv,nkpt)) call rdmdedc(dedc) allocate(evecsv(nstsv,nstsv)) do ik=1,nkpt ! get the eigenvectors from file call getevecsv(filext,ik,vkl(:,ik),evecsv) ! calculate new evecsv evecsv(:,:)=evecsv(:,:)-taurdmc*dedc(:,:,ik) ! othogonalise evecsv call unitary(nstsv,evecsv) ! write new evecsv to file call putevecsv(filext,ik,evecsv) ! end loop over k-points end do deallocate(dedc,evecsv) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmdedc.f900000644000000000000000000000013014061636517014644 xustar0029 mtime=1623670095.72510174 30 atime=1623670094.559102822 29 ctime=1623670095.72510174 elk-7.2.42/src/rdmdedc.f900000644002504400250440000000256414061636517016712 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmdedc ! !INTERFACE: subroutine rdmdedc(dedc) ! !USES: use modmain use modrdm use modomp ! !INPUT/OUTPUT PARAMETERS: ! dedc : energy derivative (out,complex(nstsv,nstsv,nkpt)) ! !DESCRIPTION: ! Calculates the derivative of the total energy w.r.t. the second-variational ! coefficients {\tt evecsv}. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! arguments complex(8), intent(out) :: dedc(nstsv,nstsv,nkpt) ! local variables integer ik,ist,nthd ! allocatable arrays complex(8), allocatable :: evecsv(:,:),c(:,:) call holdthd(nkpt,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evecsv,c,ist) & !$OMP NUM_THREADS(nthd) allocate(evecsv(nstsv,nstsv),c(nstsv,nstsv)) !$OMP DO do ik=1,nkpt ! get the eigenvectors from file call getevecsv(filext,ik,vkl(:,ik),evecsv) ! kinetic and Coulomb potential contribution call zgemm('N','N',nstsv,nstsv,nstsv,zone,evecsv,nstsv,vclmat(:,:,ik),nstsv, & zzero,c,nstsv) do ist=1,nstsv dedc(:,ist,ik)=occsv(ist,ik)*(dkdc(:,ist,ik)+c(:,ist)) end do end do !$OMP END DO deallocate(evecsv,c) !$OMP END PARALLEL call freethd(nthd) ! exchange-correlation contribution call rdmdexcdc(dedc) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmenergy.f900000644000000000000000000000013114061636517015237 xustar0030 mtime=1623670095.727101738 29 atime=1623670094.56110282 30 ctime=1623670095.727101738 elk-7.2.42/src/rdmenergy.f900000644002504400250440000000433114061636517017276 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2005-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmenergy ! !INTERFACE: subroutine rdmenergy ! !USES: use modmain use modrdm use modtest ! !DESCRIPTION: ! Calculates RDMFT total energy (free energy for finite temperatures). ! ! !REVISION HISTORY: ! Created 2008 (Sharma) ! Updated for free energy 2009 (Baldsiefen) !EOP !BOC implicit none ! local variables integer ik,ist,is,ias integer nr,nri,ir,i real(8) wo complex(8) z1 ! allocatable arrays real(8), allocatable :: rfmt(:) complex(8), allocatable :: evecsv(:,:) ! external functions real(8), external :: rfmtinp complex(8), external :: zdotc allocate(rfmt(npmtmax)) ! Coulomb energy from core states engyvcl=0.d0 do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) rfmt(1:npmt(is))=0.d0 i=1 if (spincore) then ! spin-polarised core do ir=1,nri rfmt(i)=rhocr(ir,ias,1)+rhocr(ir,ias,2) i=i+lmmaxi end do do ir=nri+1,nr rfmt(i)=rhocr(ir,ias,1)+rhocr(ir,ias,2) i=i+lmmaxo end do else ! spin-unpolarised core do ir=1,nri rfmt(i)=rhocr(ir,ias,1) i=i+lmmaxi end do do ir=nri+1,nr rfmt(i)=rhocr(ir,ias,1) i=i+lmmaxo end do end if engyvcl=engyvcl+rfmtinp(nr,nri,wrmt(:,is),rfmt,vclmt(:,ias)) end do deallocate(rfmt) engykn=engykncr allocate(evecsv(nstsv,nstsv)) do ik=1,nkpt call getevecsv(filext,ik,vkl(:,ik),evecsv) do ist=1,nstsv wo=wkpt(ik)*occsv(ist,ik) ! Coulomb energy from valence states engyvcl=engyvcl+wo*dble(vclmat(ist,ist,ik)) ! kinetic energy from valence states z1=zdotc(nstsv,evecsv(:,ist),1,dkdc(:,ist,ik),1) engykn=engykn+wo*dble(z1) end do end do deallocate(evecsv) ! Madelung term engymad=0.d0 do ias=1,natmtot is=idxis(ias) engymad=engymad+0.5d0*spzn(is)*(vclmt(1,ias)-vcln(1,is))*y00 end do ! exchange-correlation energy call rdmengyxc ! total energy engytot=0.5d0*engyvcl+engymad+engykn+engyx if (rdmtemp.gt.0.d0) then call rdmentropy engytot=engytot-rdmtemp*rdmentrpy end if ! write total energy to test file call writetest(300,'RDMFT total energy',tol=1.d-6,rv=engytot) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmengyxc.f900000644000000000000000000000013114061636517015243 xustar0030 mtime=1623670095.728101737 29 atime=1623670094.56210282 30 ctime=1623670095.728101737 elk-7.2.42/src/rdmengyxc.f900000644002504400250440000000353214061636517017304 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rdmengyxc ! !INTERFACE: subroutine rdmengyxc ! !USES: use modmain use modrdm ! !DESCRIPTION: ! Calculates RDMFT exchange-correlation energy. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! local variables integer ik1,ik2,jk,iv(3) integer ist1,ist2 real(8) t1,t2,t3,t4 ! allocatable arays real(8), allocatable :: vclijji(:,:,:) ! calculate the prefactor if (rdmxctype.eq.0) then engyx=0.d0 return else if (rdmxctype.eq.1) then ! Hartree-Fock functional t1=0.5d0/occmax else if (rdmxctype.eq.2) then ! Power functional if (spinpol) then t1=0.5d0 else t1=(0.25d0)**rdmalpha end if else write(*,*) write(*,'("Error(rdmengyxc): rdmxctype not defined : ",I8)') rdmxctype write(*,*) stop end if ! exchange-correlation energy engyx=0.d0 allocate(vclijji(nstsv,nstsv,nkpt)) ! start loop over non-reduced k-points do ik1=1,nkptnr call getvclijji(ik1,vclijji) ! find the equivalent reduced k-point iv(:)=ivk(:,ik1) jk=ivkik(iv(1),iv(2),iv(3)) do ist1=1,nstsv ! start loop over reduced k-points do ik2=1,nkpt do ist2=1,nstsv ! Hartree-Fock functional if (rdmxctype.eq.1) then t2=t1*wkpt(ik2)*occsv(ist2,ik2)*occsv(ist1,jk) ! Power functional else if (rdmxctype.eq.2) then t3=occsv(ist2,ik2)*occsv(ist1,jk) t4=sum(abs(vkl(:,ik2)-vkl(:,ik1))) if ((ist2.eq.ist1).and.(t4.lt.epslat)) then t2=(0.5d0/occmax)*wkpt(ik2)*t3 else t2=t1*wkpt(ik2)*(t3**rdmalpha) end if end if engyx=engyx-t2*vclijji(ist2,ist1,ik2) end do end do end do end do deallocate(vclijji) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmwritededn.f900000644000000000000000000000013214061636517015734 xustar0030 mtime=1623670095.730101735 30 atime=1623670094.564102818 30 ctime=1623670095.730101735 elk-7.2.42/src/rdmwritededn.f900000644002504400250440000000203714061636517017773 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rdmwritededn ! !INTERFACE: subroutine rdmwritededn(dedn) ! !USES: use modmain use modrdm ! !INPUT/OUTPUT PARAMETERS: ! dedn : derivative of energy (in,real(nstsv,nkpt)) ! !DESCRIPTION: ! Writes the derivative of total energy with respect to occupation numbers to ! file {\tt RDM\_DEDN.OUT}. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! arguments real(8), intent(in) :: dedn(nstsv,nkpt) ! local variables integer ik,ist open(50,file='RDM_DEDN.OUT',form='FORMATTED') write(50,'(I6," : nkpt")') nkpt write(50,'(I6," : nstsv")') nstsv do ik=1,nkpt write(50,*) write(50,'(I6,3G18.10," : k-point, vkl")') ik,vkl(:,ik) write(50,'(" (state, occupancy and derivative below)")') do ist=1,nstsv write(50,'(I6,4G18.10)') ist,occsv(ist,ik),-dedn(ist,ik) end do end do close(50) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmwriteengy.f900000644000000000000000000000013214061636517015764 xustar0030 mtime=1623670095.731101734 30 atime=1623670094.566102816 30 ctime=1623670095.731101734 elk-7.2.42/src/rdmwriteengy.f900000644002504400250440000000206714061636517020026 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmwriteengy ! !INTERFACE: subroutine rdmwriteengy(fnum) ! !USES: use modmain use modrdm ! !INPUT/OUTPUT PARAMETERS: ! fnum : file number for writing output (in,integer) ! !DESCRIPTION: ! Writes all contributions to the total energy to file. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! arguments integer, intent(in) :: fnum write(fnum,*) write(fnum,'("Energies :")') write(fnum,'(" electronic kinetic",T30,": ",G18.10)') engykn write(fnum,'(" core electron kinetic",T30,": ",G18.10)') engykncr write(fnum,'(" Coulomb",T30,": ",G18.10)') engyvcl write(fnum,'(" Madelung",T30,": ",G18.10)') engymad write(fnum,'(" exchange-correlation",T30,": ",G18.10)') engyx if (rdmtemp.gt.0.d0) then write(fnum,'(" entropy",T30,": ",G18.10)') rdmentrpy end if write(fnum,'(" total energy",T30,": ",G18.10)') engytot flush(fnum) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmminn.f900000644000000000000000000000013214061636517014710 xustar0030 mtime=1623670095.733101733 30 atime=1623670094.567102815 30 ctime=1623670095.733101733 elk-7.2.42/src/rdmminn.f900000644002504400250440000000307114061636517016746 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmminn ! !INTERFACE: subroutine rdmminn ! !USES: use modmain use modrdm use modmpi ! !DESCRIPTION: ! Minimizes the total energy w.r.t. occupation numbers. The steepest-descent ! algorithm is used. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! local variables integer it,n if (maxitn.lt.1) return ! write the Coulomb matrix elements to file call writevclijji ! calculate derivative of kinetic energy w.r.t. evecsv call rdmdkdc ! begin iteration loop do it=1,maxitn if (mp_mpi) then if (mod(it,10).eq.0) then write(*,'("Info(rdmminn): iteration ",I4," of ",I4)') it,maxitn end if end if ! generate the density and magnetisation call rhomag ! calculate the Coulomb potential call potcoul ! calculate Coulomb potential matrix elements call genvmat(vclmt,vclir,vclmat) ! update occupation numbers and write to file (MPI master process only) if (mp_mpi) call rdmvaryn ! broadcast occupation numbers to all other processes n=nstsv*nkpt call mpi_bcast(occsv,n,mpi_double_precision,0,mpicom,ierror) ! calculate the energy call rdmenergy ! write energy to file if (mp_mpi) then write(61,'(I6,G18.10)') it,engytot flush(61) end if ! end iteration loop end do if (mp_mpi) then write(60,*) write(60,'("Occupation number minimisation done")') write(61,*) if (spinpol) write(63,*) end if end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmvaryn.f900000644000000000000000000000013214061636517015106 xustar0030 mtime=1623670095.734101732 30 atime=1623670094.569102813 30 ctime=1623670095.734101732 elk-7.2.42/src/rdmvaryn.f900000644002504400250440000000732614061636517017153 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rdmvaryn ! !INTERFACE: subroutine rdmvaryn ! !USES: use modmain use modrdm use modmpi ! !DESCRIPTION: ! Calculates new occupation numbers from old by using the derivatives of the ! total energy: $n_i^{\rm new} = n_i^{\rm old}-\tau \gamma_i$, where $\tau$ is ! chosen such that $0 \le n_i \le n_{\rm max}$ with ! $$ \gamma_i=\begin{cases} ! g_i(n_{\rm max}-n_i) & g_i > 0 \\ ! g_i n_i & g_i\le 0 \end{cases} $$ ! where $g_i=\partial E/\partial n_i-\kappa$, and $\kappa$ is chosen such that ! $\sum_i\gamma_i=0$. ! ! !REVISION HISTORY: ! Created 2009 (JKD,Sharma) !EOP !BOC implicit none ! local variables integer, parameter :: maxit=10000 integer it,ik,ist real(8), parameter :: eps=1.d-12 real(8) tau,sm,gs,gsp,dgs real(8) kapa,dkapa,t1 ! allocatable arrays real(8), allocatable :: dedn(:,:),gamma(:,:) ! add constant to occupancies for charge conservation sm=0.d0 do ik=1,nkpt do ist=1,nstsv sm=sm+wkpt(ik)*occsv(ist,ik) end do end do t1=(chgval-sm)/dble(nstsv) occsv(:,:)=occsv(:,:)+t1 ! redistribute charge so that occupancies are in the interval [0,occmax] sm=0.d0 do ik=1,nkpt do ist=1,nstsv if (occsv(ist,ik).gt.occmax) then sm=sm+wkpt(ik)*(occsv(ist,ik)-occmax) occsv(ist,ik)=occmax end if if (occsv(ist,ik).lt.0.d0) then sm=sm+wkpt(ik)*occsv(ist,ik) occsv(ist,ik)=0.d0 end if end do end do do ist=1,nstsv do ik=1,nkpt if (sm.gt.0.d0) then t1=wkpt(ik)*(occmax-occsv(ist,ik)) t1=min(t1,sm) occsv(ist,ik)=occsv(ist,ik)+t1/wkpt(ik) sm=sm-t1 else t1=wkpt(ik)*occsv(ist,ik) t1=min(t1,-sm) occsv(ist,ik)=occsv(ist,ik)-t1/wkpt(ik) sm=sm+t1 end if end do end do allocate(dedn(nstsv,nkpt)) allocate(gamma(nstsv,nkpt)) ! get the derivatives call rdmdedn(dedn) ! find suitable value of kapa such that sum of gamma is 0 gsp=0.d0 kapa=0.d0 dkapa=0.1d0 do it=1,maxit gs=0.d0 sm=0.d0 do ik=1,nkpt do ist=1,nstsv t1=dedn(ist,ik)-kapa if (t1.gt.0.d0) then gamma(ist,ik)=t1*(occmax-occsv(ist,ik)) else gamma(ist,ik)=t1*occsv(ist,ik) end if gs=gs+wkpt(ik)*gamma(ist,ik) sm=sm+wkpt(ik)*gamma(ist,ik)**2 end do end do sm=sqrt(sm) sm=max(sm,1.d0) t1=abs(gs)/sm if (t1.lt.eps) goto 10 if (it.ge.2) then dgs=gs-gsp if (gs*dgs.gt.0.d0) dkapa=-dkapa if (gs*gsp.lt.0.d0) then dkapa=0.5d0*dkapa else dkapa=1.1d0*dkapa end if end if gsp=gs kapa=kapa+dkapa end do write(*,*) write(*,'("Error(rdmvaryn): could not find offset")') write(*,*) stop 10 continue ! write derivatives and occupancies to file call rdmwritededn(dedn) deallocate(dedn) ! normalize gamma if sum of squares is greater than 1 sm=0.d0 do ik=1,nkpt do ist=1,nstsv sm=sm+wkpt(ik)*gamma(ist,ik)**2 end do end do if (sm.gt.1.d0) then t1=1.d0/sqrt(sm) gamma(:,:)=t1*gamma(:,:) end if ! find step size which keeps occupancies in the interval [0,occmax] tau=taurdmn 20 continue if (abs(tau).lt.eps) goto 30 do ik=1,nkpt do ist=1,nstsv t1=occsv(ist,ik)+tau*gamma(ist,ik) if (gamma(ist,ik).gt.0.d0) then if (t1.gt.occmax+eps) then tau=0.75d0*tau goto 20 end if end if if (gamma(ist,ik).lt.0.d0) then if (t1.lt.-eps) then tau=0.75d0*tau goto 20 end if end if end do end do 30 continue ! update occupancies and write to file do ik=1,nkpt do ist=1,nstsv occsv(ist,ik)=occsv(ist,ik)+tau*gamma(ist,ik) end do call putoccsv(filext,ik,occsv(:,ik)) end do deallocate(gamma) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmdedn.f900000644000000000000000000000013014061636517014657 xustar0029 mtime=1623670095.73610173 30 atime=1623670094.571102811 29 ctime=1623670095.73610173 elk-7.2.42/src/rdmdedn.f900000644002504400250440000000265714061636517016730 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmdedn ! !INTERFACE: subroutine rdmdedn(dedn) ! !USES: use modmain use modrdm use modomp ! !INPUT/OUTPUT PARAMETERS: ! dedn : free energy derivative (out,real(nstsv,nkpt)) ! !DESCRIPTION: ! Calculates the negative of the derivative of total free energy w.r.t. ! occupation numbers. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! arguments real(8), intent(out) :: dedn(nstsv,nkpt) ! local variables integer ik,ist,nthd ! allocatable arrays complex(8), allocatable :: evecsv(:,:),c(:,:) call holdthd(nkpt,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evecsv,c,ist) & !$OMP NUM_THREADS(nthd) allocate(evecsv(nstsv,nstsv),c(nstsv,nstsv)) !$OMP DO do ik=1,nkpt ! get eigenvectors from file call getevecsv(filext,ik,vkl(:,ik),evecsv) ! kinetic and Coulomb potential contribution call zgemm('C','N',nstsv,nstsv,nstsv,zone,evecsv,nstsv,dkdc(:,:,ik),nstsv, & zzero,c,nstsv) do ist=1,nstsv dedn(ist,ik)=-(dble(c(ist,ist))+dble(vclmat(ist,ist,ik))) end do end do !$OMP END DO deallocate(evecsv,c) !$OMP END PARALLEL call freethd(nthd) ! add exchange correlation contribution call rdmdexcdn(dedn) ! add entropic contribution if needed if (rdmtemp.gt.0.d0) call rdmdtsdn(dedn) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmdexcdn.f900000644000000000000000000000013114061636517015213 xustar0030 mtime=1623670095.737101729 29 atime=1623670094.57210281 30 ctime=1623670095.737101729 elk-7.2.42/src/rdmdexcdn.f900000644002504400250440000000420414061636517017251 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmdexcdn ! !INTERFACE: subroutine rdmdexcdn(dedn) ! !USES: use modmain use modrdm ! !INPUT/OUTPUT PARAMETERS: ! dedn : energy derivative (inout,real(nstsv,nkpt)) ! !DESCRIPTION: ! Calculates the derivative of the exchange-correlation energy w.r.t. ! occupation numbers and adds the result to the total. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! arguments real(8), intent(inout) :: dedn(nstsv,nkpt) ! local variables integer ik1,ik2,jk,iv(3) integer ist1,ist2 ! parameter for calculating the functional derivatives real(8), parameter :: eps=1.d-12 real(8) t1,t2,t3,t4 ! allocatable arays real(8), allocatable :: vclijji(:,:,:) if (rdmxctype.eq.0) return ! calculate the prefactor if (rdmxctype.eq.1) then t1=1.d0/occmax ! power functional else if (rdmxctype.eq.2) then if (spinpol) then t1=rdmalpha else t1=2.d0*rdmalpha*(0.25d0)**rdmalpha end if else write(*,*) write(*,'("Error(rdmdexcdn): rdmxctype not defined : ",I8)') rdmxctype write(*,*) stop end if allocate(vclijji(nstsv,nstsv,nkpt)) ! start loop over non-reduced k-points do ik1=1,nkptnr ! get the Coulomb matrix elements call getvclijji(ik1,vclijji) ! find the equivalent reduced k-point iv(:)=ivk(:,ik1) jk=ivkik(iv(1),iv(2),iv(3)) ! loop over reduced k-points do ik2=1,nkpt do ist1=1,nstsv do ist2=1,nstsv ! Hartree-Fock functional if (rdmxctype.eq.1) then t2=t1*occsv(ist1,jk) ! power functional else if (rdmxctype.eq.2) then t3=sum(abs(vkl(:,ik2)-vkl(:,ik1))) if ((ist2.eq.ist1).and.(t3.lt.epslat)) then t2=(1.d0/occmax)*occsv(ist1,jk) else t3=max(occsv(ist2,ik2),eps) t4=max(occsv(ist1,jk),eps) t2=t1*(t4**rdmalpha)/(t3**(1.d0-rdmalpha)) end if end if dedn(ist2,ik2)=dedn(ist2,ik2)+t2*vclijji(ist2,ist1,ik2) end do end do end do end do deallocate(vclijji) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/genvclijjk.f900000644000000000000000000000013214061636517015372 xustar0030 mtime=1623670095.739101727 30 atime=1623670094.574102808 30 ctime=1623670095.739101727 elk-7.2.42/src/genvclijjk.f900000644002504400250440000001151614061636517017433 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genvclijjk ! !INTERFACE: subroutine genvclijjk(ikp,vclijjk) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ikp : k-point from non-reduced set (in,integer) ! vclijjk : Coulomb matrix elements (out,complex(nstsv,nstsv,nstsv,nkpt)) ! !DESCRIPTION: ! Calculates Coulomb matrix elements of the type $(i-jj-k)$. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! arguments integer, intent(in) :: ikp complex(8), intent(out) :: vclijjk(nstsv,nstsv,nstsv,nkpt) ! local variables integer ik,ist1,ist2,ist3 integer iv(3),iq,ig real(8) vc(3) complex(8) z1 ! automatic arrays integer idx(nstsv) ! allocatable arrays real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqrmt(:,:,:) complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: wfmt1(:,:,:,:),wfir1(:,:,:) complex(8), allocatable :: wfmt2(:,:,:,:),wfir2(:,:,:) complex(8), allocatable :: zrhomt(:,:,:),zrhoir(:,:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) ! external functions complex(8), external :: zfinp ! allocate local arrays allocate(vgqc(3,ngvc),gqc(ngvc),gclgq(ngvc)) allocate(jlgqrmt(0:lnpsd,ngvc,nspecies)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) allocate(ylmgq(lmmaxo,ngvc),sfacgq(ngvc,natmtot)) allocate(wfmt1(npcmtmax,natmtot,nspinor,nstsv),wfir1(ngtc,nspinor,nstsv)) allocate(wfmt2(npcmtmax,natmtot,nspinor,nstsv),wfir2(ngtc,nspinor,nstsv)) allocate(zrhomt(npcmtmax,natmtot,nstsv),zrhoir(ngtc,nstsv)) allocate(zvclmt(npcmtmax,natmtot),zvclir(ngtc)) ! get the eigenvectors from file for non-reduced k-point ikp call getevecfv(filext,0,vkl(:,ikp),vgkl(:,:,1,ikp),evecfv) call getevecsv(filext,0,vkl(:,ikp),evecsv) ! find the matching coefficients call match(ngk(1,ikp),vgkc(:,:,1,ikp),gkc(:,1,ikp),sfacgk(:,:,1,ikp),apwalm) ! index to all states do ist1=1,nstsv idx(ist1)=ist1 end do ! calculate the wavefunctions for all states of passed non-reduced k-point ikp call genwfsv(.false.,.false.,nstsv,idx,ngdgc,igfc,ngk(1,ikp),igkig(:,1,ikp), & apwalm,evecfv,evecsv,wfmt2,ngtc,wfir2) ! start loop over reduced k-point set do ik=1,nkpt ! determine the q-vector iv(:)=ivk(:,ik)-ivk(:,ikp) iv(:)=modulo(iv(:),ngridk(:)) ! check if the q-point is in user-defined set iv(:)=iv(:)*ngridq(:) if (any(modulo(iv(:),ngridk(:)).ne.0)) cycle iv(:)=iv(:)/ngridk(:) iq=ivqiq(iv(1),iv(2),iv(3)) vc(:)=vkc(:,ik)-vkc(:,ikp) do ig=1,ngvc ! determine the G+q-vectors vgqc(:,ig)=vgc(:,ig)+vc(:) ! G+q-vector length gqc(ig)=sqrt(vgqc(1,ig)**2+vgqc(2,ig)**2+vgqc(3,ig)**2) ! spherical harmonics for G+q-vectors call genylmv(lmaxo,vgqc(:,ig),ylmgq(:,ig)) end do ! structure factors for G+q call gensfacgp(ngvc,vgqc,ngvc,sfacgq) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.true.,iq,ngvc,gqc,gclgq) ! compute the required spherical Bessel functions call genjlgprmt(lnpsd,ngvc,gqc,ngvc,jlgqrmt) ! find the matching coefficients call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! get the eigenvectors from file call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! calculate the wavefunctions for all states of the reduced k-point call genwfsv(.false.,.false.,nstsv,idx,ngdgc,igfc,ngk(1,ik),igkig(:,1,ik), & apwalm,evecfv,evecsv,wfmt1,ngtc,wfir1) !----------------------------------------------! ! valence-valence-valence contribution ! !----------------------------------------------! do ist2=1,nstsv do ist1=1,nstsv ! calculate the complex overlap density for all states call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,ist2),wfir2(:,:,ist2), & wfmt1(:,:,:,ist1),wfir1(:,:,ist1),zrhomt(:,:,ist1),zrhoir(:,ist1)) end do do ist1=1,nstsv ! compute the Coulomb potential call genzvclmt(nrcmt,nrcmti,nrcmtmax,rlcmt,wprcmt,npcmtmax, & zrhomt(:,:,ist1),zvclmt) call zpotcoul(nrcmt,nrcmti,npcmt,npcmti,nrcmtmax,rlcmt,ngdgc,igfc,ngvc, & gqc,gclgq,ngvc,jlgqrmt,ylmgq,sfacgq,zrhoir(:,ist1),npcmtmax,zvclmt, & zvclir) zvclir(:)=zvclir(:)*cfrc(:) do ist3=ist1,nstsv z1=zfinp(zrhomt(:,:,ist3),zrhoir(:,ist3),zvclmt,zvclir) vclijjk(ist3,ist1,ist2,ik)=wqptnr*z1 end do end do end do ! calculate the lower diagonal do ist1=1,nstsv do ist3=1,ist1-1 vclijjk(ist3,ist1,:,ik)=conjg(vclijjk(ist1,ist3,:,ik)) end do end do ! end loop over reduced k-point set end do deallocate(vgqc,gqc,gclgq,jlgqrmt) deallocate(apwalm,evecfv,evecsv,ylmgq,sfacgq) deallocate(wfmt1,wfmt2,wfir1,wfir2) deallocate(zrhomt,zrhoir,zvclmt,zvclir) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/getvclijji.f900000644000000000000000000000013214061636517015376 xustar0030 mtime=1623670095.740101726 30 atime=1623670094.576102806 30 ctime=1623670095.740101726 elk-7.2.42/src/getvclijji.f900000644002504400250440000000172014061636517017433 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: getvclijji ! !INTERFACE: subroutine getvclijji(ikp,vclijji) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ikp : k-point from non-reduced set (in,integer) ! vclijji : Coulomb matrix elements (out,real(nstsv,nstsv,nkpt)) ! !DESCRIPTION: ! Retrieves Coulomb matrix elements of the type $(i-jj-i)$ from the file ! {\tt VCLIJJI.OUT}. ! ! !REVISION HISTORY: ! Created 2009 (Sharma) !EOP !BOC implicit none ! arguments integer, intent(in) :: ikp real(8), intent(out) :: vclijji(nstsv,nstsv,nkpt) ! local variables integer recl ! determine record length inquire(iolength=recl) vclijji !$OMP CRITICAL(u260) open(260,file='VCLIJJI.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(260,rec=ikp) vclijji !$OMP END CRITICAL(u260) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/getvclijjk.f900000644000000000000000000000013214061636517015400 xustar0030 mtime=1623670095.742101724 30 atime=1623670094.577102806 30 ctime=1623670095.742101724 elk-7.2.42/src/getvclijjk.f900000644002504400250440000000174214061636517017441 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: getvclijjk ! !INTERFACE: subroutine getvclijjk(ikp,vclijjk) ! !USES: use modmain ! !INPUT/OUTPUT PARAMETERS: ! ikp : k-point from non-reduced set (in,integer) ! vclijjk : Coulomb matrix elements (out,complex(nstsv,nstsv,nstsv,nkpt)) ! !DESCRIPTION: ! Retrieves Coulomb matrix elements of the type $(i-jj-k)$ from the file ! {\tt VCLIJJK.OUT}. ! ! !REVISION HISTORY: ! Created 2009 (Sharma) !EOP !BOC implicit none ! arguments integer, intent(in) :: ikp complex(8), intent(out) :: vclijjk(nstsv,nstsv,nstsv,nkpt) ! local variables integer recl ! determine record length inquire(iolength=recl) vclijjk !$OMP CRITICAL(u262) open(262,file='VCLIJJK.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(262,rec=ikp) vclijjk !$OMP END CRITICAL(u262) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writevclijji.f900000644000000000000000000000013214061636517015751 xustar0030 mtime=1623670095.743101723 30 atime=1623670094.579102804 30 ctime=1623670095.743101723 elk-7.2.42/src/writevclijji.f900000644002504400250440000000275714061636517020021 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writevclijji ! !INTERFACE: subroutine writevclijji ! !USES: use modmain use modmpi use modomp ! !DESCRIPTION: ! Generates Coulomb matrix elements of the type $(i-jj-i)$ and outputs them to ! the file {\tt VCLIJJI.OUT}. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! allocatable arrays real(8), allocatable :: vclijji(:,:,:) integer recl,ik,nthd ! determine record length for vclijji and open file allocate(vclijji(nstsv,nstsv,nkpt)) inquire(iolength=recl) vclijji deallocate(vclijji) open(260,file='VCLIJJI.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(vclijji) & !$OMP NUM_THREADS(nthd) allocate(vclijji(nstsv,nstsv,nkpt)) !$OMP DO do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(writevclijji_) write(*,'("Info(writevclijji): ",I6," of ",I6," k-points")') ik,nkptnr !$OMP END CRITICAL(writevclijji_) ! calculate Coulomb matrix elements of the type (i-jj-i) call genvclijji(ik,vclijji) !$OMP CRITICAL(u260) write(260,rec=ik) vclijji !$OMP END CRITICAL(u260) end do !$OMP END DO deallocate(vclijji) !$OMP END PARALLEL call freethd(nthd) close(260) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writevclijjk.f900000644000000000000000000000013214061636517015753 xustar0030 mtime=1623670095.745101721 30 atime=1623670094.581102802 30 ctime=1623670095.745101721 elk-7.2.42/src/writevclijjk.f900000644002504400250440000000414314061636517020012 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: writevclijjk ! !INTERFACE: subroutine writevclijjk ! !USES: use modmain use modmpi use modomp ! !DESCRIPTION: ! Generates Coulomb matrix elements of the type $(i-jj-k)$ and outputs them to ! the file {\tt VCLIJJK.OUT}. Also writes the real diagonal of this matrix, ! $(i-jj-i)$, to {\tt VCLIJJI.OUT}. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! local variables integer ik,ist,recl,nthd ! allocatable arrays real(8), allocatable :: vclijji(:,:,:) complex(8), allocatable :: vclijjk(:,:,:,:) ! determine record length for vclijji and open file allocate(vclijji(nstsv,nstsv,nkpt)) inquire(iolength=recl) vclijji deallocate(vclijji) open(260,file='VCLIJJI.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) ! determine record length for vclijjk and open file allocate(vclijjk(nstsv,nstsv,nstsv,nkpt)) inquire(iolength=recl) vclijjk deallocate(vclijjk) open(262,file='VCLIJJK.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(vclijji,vclijjk,ist) & !$OMP NUM_THREADS(nthd) allocate(vclijji(nstsv,nstsv,nkpt),vclijjk(nstsv,nstsv,nstsv,nkpt)) !$OMP DO do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(writevclijjk_) write(*,'("Info(writevclijjk): ",I6," of ",I6," k-points")') ik,nkptnr !$OMP END CRITICAL(writevclijjk_) ! calculate Coulomb matrix elements of the type (i-jj-k) call genvclijjk(ik,vclijjk) ! make a copy of the diagonal elements (i-jj-i) do ist=1,nstsv vclijji(ist,:,:)=dble(vclijjk(ist,ist,:,:)) end do !$OMP CRITICAL(u260) write(260,rec=ik) vclijji !$OMP END CRITICAL(u260) !$OMP CRITICAL(u262) write(262,rec=ik) vclijjk !$OMP END CRITICAL(u262) end do !$OMP END DO deallocate(vclijji,vclijjk) !$OMP END PARALLEL call freethd(nthd) close(260) close(262) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmdexcdc.f900000644000000000000000000000013214061636517015201 xustar0030 mtime=1623670095.746101721 30 atime=1623670094.582102801 30 ctime=1623670095.746101721 elk-7.2.42/src/rdmdexcdc.f900000644002504400250440000000464014061636517017242 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmdexcdc ! !INTERFACE: subroutine rdmdexcdc(dedc) ! !USES: use modmain use modrdm ! !INPUT/OUTPUT PARAMETERS: ! dedc : energy derivative (inout,complex(nstsv,nstsv,nkpt)) ! !DESCRIPTION: ! Calculates the derivative of the exchange-correlation energy w.r.t. ! {\tt evecsv} and adds the result to the total. ! ! !REVISION HISTORY: ! Created 2008 (Sharma) !EOP !BOC implicit none ! arguments complex(8), intent(inout) :: dedc(nstsv,nstsv,nkpt) ! local variables integer ik1,ik2,jk,iv(3) integer ist1,ist2,ist3,ist4 real(8) t1,t2,t3 ! allocatable arrays complex(8), allocatable :: vclijjk(:,:,:,:),evecsv(:,:) if (rdmxctype.eq.0) return ! calculate the prefactor if (rdmxctype.eq.1) then ! Hartree-Fock functional t1=1.d0/occmax else if (rdmxctype.eq.2) then ! power functional if (spinpol) then t1=1.d0 else t1=2.d0*(0.25d0)**rdmalpha end if else write(*,*) write(*,'("Error(rdmdexcdc): rdmxctype not defined : ",I8)') rdmxctype write(*,*) stop end if allocate(vclijjk(nstsv,nstsv,nstsv,nkpt)) allocate(evecsv(nstsv,nstsv)) ! start loop over non-reduced k-points do ik1=1,nkptnr ! get the Coulomb matrix elements call getvclijjk(ik1,vclijjk) ! find the equivalent reduced k-point iv(:)=ivk(:,ik1) jk=ivkik(iv(1),iv(2),iv(3)) ! start loop over reduced k-points do ik2=1,nkpt ! get the eigenvectors from file call getevecsv(filext,ik2,vkl(:,ik2),evecsv) do ist4=1,nstsv do ist3=1,nstsv do ist2=1,nstsv do ist1=1,nstsv if (rdmxctype.eq.1) then ! Hartree-Fock functional t2=t1*occsv(ist3,ik2)*occsv(ist4,jk) else if (rdmxctype.eq.2) then ! power functional t3=sum(abs(vkl(:,ik2)-vkl(:,ik1))) if ((ist3.eq.ist4).and.(t3.lt.epslat)) then t2=(1.d0/occmax)*occsv(ist4,jk)**2 else t2=t1*(occsv(ist3,ik2)*occsv(ist4,jk))**rdmalpha end if end if dedc(ist2,ist3,ik2)=dedc(ist2,ist3,ik2)-t2*evecsv(ist2,ist1)* & vclijjk(ist1,ist3,ist4,ik2) end do end do end do end do ! end loop over reduced k-points end do ! end loop over non-reduced k-points end do deallocate(vclijjk,evecsv) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmdtsdn.f900000644000000000000000000000013014061636517015061 xustar0029 mtime=1623670095.74710172 30 atime=1623670094.584102799 29 ctime=1623670095.74710172 elk-7.2.42/src/rdmdtsdn.f900000644002504400250440000000162414061636517017123 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 T. Baldsiefen, S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU Lesser General Public ! License. See the file COPYING for license details. !BOP ! !ROUTINE: rdmdtsdn ! !INTERFACE: subroutine rdmdtsdn(dedn) ! !USES: use modmain use modrdm ! !INPUT/OUTPUT PARAMETERS: ! dedn : energy derivative (inout,real(nstsv,nkpt)) ! !DESCRIPTION: ! Calculates the derivative of the entropic contribution to the free energy ! w.r.t. occupation numbers and adds it to the total. ! ! !REVISION HISTORY: ! Created 2008 (Baldsiefen) !EOP !BOC implicit none ! arguments real(8), intent(inout) :: dedn(nstsv,nkpt) ! local variables integer ik,ist real(8) t1 do ik=1,nkpt do ist=1,nstsv t1=max(occsv(ist,ik),epsocc) t1=min(t1,occmax-epsocc) dedn(ist,ik)=dedn(ist,ik)-rdmtemp*kboltz*log(t1/(occmax-t1)) end do end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmentropy.f900000644000000000000000000000013214061636517015447 xustar0030 mtime=1623670095.749101718 30 atime=1623670094.586102797 30 ctime=1623670095.749101718 elk-7.2.42/src/rdmentropy.f900000644002504400250440000000156014061636517017506 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2008 T. Baldsiefen, S. Sharma, J. K. Dewhurst and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. !BOP ! !ROUTINE: rdmentropy ! !INTERFACE: subroutine rdmentropy ! !USES: use modmain use modrdm ! !DESCRIPTION: ! Calculates RDMFT entropy $S=-\sum_i n_i\log(n_i/n_{\rm max}) ! +(n_{\rm max}-n_i)\log(1-n_i/n_{\rm max})$, where $n_{\rm max}$ is the ! maximum allowed occupancy (1 or 2). ! ! !REVISION HISTORY: ! Created 2008 (Baldsiefen) !EOP !BOC implicit none ! local variables integer ik,ist real(8) t1 rdmentrpy=0.d0 do ik=1,nkpt do ist=1,nstsv t1=max(occsv(ist,ik),epsocc) t1=min(t1,occmax-epsocc) rdmentrpy=rdmentrpy-wkpt(ik)*(t1*log(t1/occmax) & +(occmax-t1)*log(1.d0-t1/occmax)) end do end do rdmentrpy=kboltz*rdmentrpy end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/rdmeval.f900000644000000000000000000000013214061636517014676 xustar0030 mtime=1623670095.750101717 30 atime=1623670094.587102796 30 ctime=1623670095.750101717 elk-7.2.42/src/rdmeval.f900000644002504400250440000000165014061636517016735 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007-2008 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: rdmeval ! !INTERFACE: subroutine rdmeval ! !USES: use modmain use modrdm ! !DESCRIPTION: ! RDMFT eigenvalues are determined by calculating the derivative of the total ! energy with respect to the occupation number at half the maximum occupancy ! ($n_{\rm max}/2$). ! ! !REVISION HISTORY: ! Created 2009 (Sharma) !EOP !BOC implicit none ! local variables integer ik,ist real(8) t1 ! allocatable arrays real(8), allocatable :: dedn(:,:) allocate(dedn(nstsv,nkpt)) do ik=1,nkpt do ist=1,nstsv t1=occsv(ist,ik) occsv(ist,ik)=occmax/2.d0 call rdmdedn(dedn) evalsv(ist,ik)=-dedn(ist,ik) occsv(ist,ik)=t1 end do call putevalsv(filext,ik,evalsv(:,ik)) end do deallocate(dedn) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/gwdmat.f900000644000000000000000000000013214061636517014527 xustar0030 mtime=1623670095.752101715 30 atime=1623670094.589102794 30 ctime=1623670095.752101715 elk-7.2.42/src/gwdmat.f900000644002504400250440000000231214061636517016562 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gwdmat use modmain use modgw use modmpi use modomp implicit none ! local variables integer ik,nthd ! initialise universal variables call init0 call init1 call init3 ! read Fermi energy from file call readfermi ! get the eigenvalues from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) end do ! determine the GW Fermi energy call gwefermi ! compute the GW density matrices and write the natural orbitals and occupation ! numbers to EVECSV.OUT and OCCSV.OUT, respectively call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call gwdmatk(ik) end do !$OMP END PARALLEL DO call freethd(nthd) if (mp_mpi) then write(*,*) write(*,'("Info(gwdmat):")') write(*,'(" GW density matrices determined for each k-point")') write(*,*) write(*,'(" Natural orbitals and occupation numbers written to")') write(*,'(" EVECSV.OUT and OCCSV.OUT, respectively")') end if end subroutine elk-7.2.42/src/PaxHeaders.21776/gwlocal.f900000644000000000000000000000013214061636517014674 xustar0030 mtime=1623670095.753101714 30 atime=1623670094.591102793 30 ctime=1623670095.753101714 elk-7.2.42/src/gwlocal.f900000644002504400250440000000301314061636517016726 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine gwlocal(vmt,vir,bmt,bir) use modmain implicit none ! arguments real(8), intent(out) :: vmt(npcmtmax,natmtot),vir(ngtot) real(8), intent(out) :: bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag) ! local variables integer idm,is,ias integer nrc,nrci,npc ! automatic arrays real(8) rfmt(npcmtmax) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) ! convert exchange-correlation potential to a coarse radial mesh call rfmtftoc(nrc,nrci,vxcmt(:,ias),rfmt) ! negate because V_xc should be removed from the self-energy rfmt(1:npc)=-rfmt(1:npc) ! convert to spherical coordinates call rbsht(nrc,nrci,rfmt,vmt(:,ias)) ! multiply by radial integration weights call rfcmtwr(nrc,nrci,wrcmt(:,is),vmt(:,ias)) end do ! negate and multiply the interstitial V_xc by the characteristic function vir(:)=-vxcir(:)*cfunir(:) ! do the same for B_xc in the spin-polarised case if (spinpol) then do idm=1,ndmag do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) call rfmtftoc(nrc,nrci,bxcmt(:,ias,idm),rfmt) rfmt(1:npc)=-rfmt(1:npc) call rbsht(nrc,nrci,rfmt,bmt(:,ias,idm)) call rfcmtwr(nrc,nrci,wrcmt(:,is),bmt(:,ias,idm)) end do end do do idm=1,ndmag bir(:,idm)=-bxcir(:,idm)*cfunir(:) end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/genwgw.f900000644000000000000000000000013214061636517014542 xustar0030 mtime=1623670095.755101712 30 atime=1623670094.592102792 30 ctime=1623670095.755101712 elk-7.2.42/src/genwgw.f900000644002504400250440000000326414061636517016604 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine genwgw use modmain use modgw implicit none ! local variables integer ik,iw,jw,n real(8) de,t0,t1 t0=kboltz*tempk if (wmaxgw.le.0.d0) then ! read the Fermi energy from file call readfermi ! find the maximum eigenvalue range over all k-points do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) end do de=maxval(abs(evalsv(:,:)-efermi)) wmaxgw=abs(wmaxgw)*de end if ! number of Matsubara frequencies t1=pi*t0 nwgw=2*nint(wmaxgw/t1) nwgw=max(nwgw,2) call nfftifc(3,nwgw) ! determine integer ranges for grid intwgw(1)=nwgw/2-nwgw+1 intwgw(2)=nwgw/2 if (allocated(iwfft)) deallocate(iwfft) allocate(iwfft(intwgw(1):intwgw(2))) if (allocated(wgw)) deallocate(wgw) allocate(wgw(intwgw(1):intwgw(2))) do iw=intwgw(1),intwgw(2) if (iw.ge.0) then jw=iw else jw=nwgw+iw end if iwfft(iw)=jw+1 wgw(iw)=dble(iw)*t1 end do n=minval(abs(intwgw(:))) if (n.eq.0) then write(*,*) write(*,'("Error(genwgw): not enough Matsubara frequencies")') write(*,'("Increase wmaxgw")') write(*,*) stop end if if (mod(n,2).eq.0) then nwbs=n nwfm=n-1 else nwfm=n nwbs=n-1 end if ! store the complex fermionic frequencies if (allocated(wfm)) deallocate(wfm) allocate(wfm(0:nwfm)) do iw=-nwfm,nwfm,2 jw=(iw+nwfm)/2 wfm(jw)=cmplx(0.d0,wgw(iw),8) end do ! store the complex response function frequencies nwrf=nwbs+1 if (allocated(wrf)) deallocate(wrf) allocate(wrf(nwrf)) do iw=-nwbs,nwbs,2 jw=(iw+nwbs)/2+1 wrf(jw)=cmplx(0.d0,wgw(iw),8) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/ksinvert.f900000644000000000000000000000013114061636517015110 xustar0030 mtime=1623670095.756101711 29 atime=1623670094.59410279 30 ctime=1623670095.756101711 elk-7.2.42/src/ksinvert.f900000644002504400250440000000505014061636517017146 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 P. Elliott, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine ksinvert use modmain use modmpi implicit none ! local variables integer idm,it real(8) tau ! allocatable arrays real(8), allocatable :: rhomt_(:,:),rhoir_(:) real(8), allocatable :: magmt_(:,:,:),magir_(:,:) real(8), allocatable :: rfmt(:,:),rfir(:) ! copy the existing density and magnetisation allocate(rhomt_(npmtmax,natmtot),rhoir_(ngtot)) call rfcopy(rhomt,rhoir,rhomt_,rhoir_) allocate(rfmt(npmtmax,natmtot),rfir(ngtot)) if (spinpol) then allocate(magmt_(npmtmax,natmtot,ndmag),magir_(ngtot,ndmag)) do idm=1,ndmag call rfcopy(magmt(:,:,idm),magir(:,idm),magmt_(:,:,idm),magir_(:,idm)) end do end if ! initialise the exchange-correlation potential and magnetic field tau=tauoep(2) vxcmt(:,:)=tau*vxcmt(:,:) vxcir(:)=tau*vxcir(:) if (spinpol) then bxcmt(:,:,:)=tau*bxcmt(:,:,:) bxcir(:,:)=tau*bxcir(:,:) end if ! iterative method step size tau=tauoep(1) if (mp_mpi) then write(*,*) write(*,'("Info(ksinvert): inverting the Kohn-Sham equations")') end if do it=1,maxitoep if (mp_mpi.and.(mod(it,10).eq.0)) then write(*,'("Info(ksinvert): done ",I4," iterations of ",I4)') it,maxitoep end if call hmlrad call genevfsv call occupy call rhomag ! determine the residual and add it to the exchange-correlation potential call residual ! set the constant part of V_xc equal to zero call rfint0(0.d0,vxcmt,vxcir) ! add the external and Hartree potentials call potks(.false.) call genvsig end do deallocate(rhomt_,rhoir_,rfmt,rfir) if (spinpol) deallocate(magmt_,magir_) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) return contains subroutine residual implicit none ! local variables integer is,ias,np ! external functions real(8), external :: rfinp do ias=1,natmtot is=idxis(ias) np=npmt(is) rfmt(1:np,ias)=rhomt(1:np,ias)-rhomt_(1:np,ias) call daxpy(np,tau,rfmt(:,ias),1,vxcmt(:,ias),1) end do rfir(:)=rhoir(:)-rhoir_(:) call daxpy(ngtot,tau,rfir,1,vxcir,1) resoep=rfinp(rfmt,rfir,rfmt,rfir) if (spinpol) then do idm=1,ndmag do ias=1,natmtot is=idxis(ias) np=npmt(is) rfmt(1:np,ias)=magmt(1:np,ias,idm)-magmt_(1:np,ias,idm) call daxpy(np,tau,rfmt(:,ias),1,bxcmt(:,ias,idm),1) end do rfir(:)=magir(:,idm)-magir_(:,idm) call daxpy(ngtot,tau,rfir,1,bxcir(:,idm),1) resoep=resoep+rfinp(rfmt,rfir,rfmt,rfir) end do end if resoep=sqrt(resoep)/omega end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/gtwsum.f900000644000000000000000000000013214061636517014572 xustar0030 mtime=1623670095.758101709 30 atime=1623670094.596102788 30 ctime=1623670095.758101709 elk-7.2.42/src/gtwsum.f900000644002504400250440000000105014061636517016623 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 A. Davydov, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure complex(8) function gtwsum(gf,gl) use modmain use modgw implicit none ! arguments complex(8), intent(in) :: gf,gl ! local variables integer iw real(8) b complex(8) a1,a2,z1 z1=wfm(0) a1=0.5d0*(gf-gl)*z1 a2=0.5d0*(gf+gl)*z1**2 b=1.d0/(kboltz*tempk) gtwsum=b*(0.5d0*a1-0.25d0*b*a2) do iw=0,nwfm gtwsum=gtwsum-a2/wfm(iw)**2 end do end function elk-7.2.42/src/PaxHeaders.21776/minf_nm.f900000644000000000000000000000013214061636517014667 xustar0030 mtime=1623670095.759101709 30 atime=1623670094.598102786 30 ctime=1623670095.759101709 elk-7.2.42/src/minf_nm.f900000644002504400250440000000403414061636517016725 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2007 J. K. Dewhurst and D. W. H. Rankin. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine minf_nm(id,rd,n,x,maxit,iter,eps) implicit none ! arguments integer, intent(in) :: id(*) real(8), intent(in) :: rd(*) integer, intent(in) :: n real(8), intent(inout) :: x(n,n+1) integer, intent(in) :: maxit integer, intent(out) :: iter real(8), intent(in) :: eps ! local variables integer i,j,il,iu ! Nelder-Mead parmeters real(8), parameter :: alpha=1.d0,gamma=2.d0 real(8), parameter :: beta=0.5d0,sigma=0.5d0 real(8) fr,fe,fc,sm,t1 ! automatic arrays real(8) f(n+1),xm(n),xr(n),xe(n),xc(n) ! external functions real(8), external :: fmin_nm if (n.lt.0) then write(*,*) write(*,'("Error(minf_nm): n <= 0 : ",I8)') n write(*,*) stop end if ! evaluate the function at each vertex do i=1,n+1 f(i)=fmin_nm(id,rd,x(:,i)) end do iter=0 10 continue iter=iter+1 if (iter.ge.maxit) return ! find the lowest and highest vertex il=1 iu=1 do i=2,n+1 if (f(i).lt.f(il)) il=i if (f(i).gt.f(iu)) iu=i end do ! check for convergence if ((f(iu)-f(il)).lt.eps) return ! compute the mean of the n lowest vertices t1=1.d0/dble(n) do i=1,n sm=0.d0 do j=1,iu-1 sm=sm+x(i,j) end do do j=iu+1,n+1 sm=sm+x(i,j) end do xm(i)=t1*sm end do xr(:)=xm(:)+alpha*(xm(:)-x(:,iu)) fr=fmin_nm(id,rd,xr) if (f(il).gt.fr) goto 30 if ((f(il).le.fr).and.(fr.lt.f(iu))) then ! reflection x(:,iu)=xr(:) f(iu)=fr goto 10 else goto 40 end if 30 continue xe(:)=xm(:)+gamma*(xr(:)-xm(:)) fe=fmin_nm(id,rd,xe) if (fr.gt.fe) then ! expansion x(:,iu)=xe(:) f(iu)=fe else ! reflection x(:,iu)=xr(:) f(iu)=fr end if goto 10 40 continue xc(:)=xm(:)+beta*(x(:,iu)-xm(:)) fc=fmin_nm(id,rd,xc) if (fc.lt.f(iu)) then ! contraction x(:,iu)=xc(:) f(iu)=fc goto 10 end if ! shrinkage do j=1,il-1 x(:,j)=x(:,il)+sigma*(x(:,j)-x(:,il)) f(j)=fmin_nm(id,rd,x(1,j)) end do do j=il+1,n+1 x(:,j)=x(:,il)+sigma*(x(:,j)-x(:,il)) f(j)=fmin_nm(id,rd,x(1,j)) end do goto 10 end subroutine elk-7.2.42/src/PaxHeaders.21776/acpole.f900000644000000000000000000000013214061636517014507 xustar0030 mtime=1623670095.761101707 30 atime=1623670094.599102785 30 ctime=1623670095.761101707 elk-7.2.42/src/acpole.f900000644002504400250440000000263014061636517016545 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine acpole(zm,zwr,zr) use modmain use modgw implicit none ! arguments complex(8), intent(in) :: zm(0:nwfm),zwr(nwplot) complex(8), intent(out) :: zr(nwplot) ! local variables integer, parameter :: maxit=1000 integer iter,iw integer n,n2,i,j real(8), parameter :: eps=1.d-5 ! allocatable arrays real(8), allocatable :: x(:,:) ! external functions complex(8), external :: zfpole n=2*npole+1 n2=2*n allocate(x(n2,n2+1)) ! intialise simplex x(:,:)=0.d0 ! fit the constant x(1,2)=0.5d0 x(2,3)=0.5d0 call minf_nm(1,zm,n2,x,maxit,iter,eps) ! fit the constant and the first pole x(3,1)=1.d0 do i=1,6 x(i,i+1)=x(i,1)+0.1d0 end do call minf_nm(1,zm,n2,x,maxit,iter,eps) ! fit the remaining poles one-by-one i=7 do j=2,npole x(i,1)=1.d0 x(i,i+1)=x(i,1)+0.1d0 i=i+1 x(i,i+1)=0.1d0 i=i+1 x(i,i+1)=0.1d0 i=i+1 x(i,i+1)=0.1d0 i=i+1 call minf_nm(1,zm,n2,x,maxit,iter,eps) end do ! fit the constant and the first pole again do i=1,6 x(i,i+1)=x(i,1)+0.1d0 end do call minf_nm(1,zm,n2,x,maxit,iter,eps) ! fit everything together if (npole.gt.1) then do i=1,n2 x(i,i+1)=x(i,1)+0.1d0 end do call minf_nm(1,zm,n2,x,maxit,iter,eps) end if do iw=1,nwplot zr(iw)=zfpole(x(:,1),zwr(iw)) end do deallocate(x) end subroutine elk-7.2.42/src/PaxHeaders.21776/gwrhomag.f900000644000000000000000000000013214061636517015057 xustar0030 mtime=1623670095.762101706 30 atime=1623670094.601102783 30 ctime=1623670095.762101706 elk-7.2.42/src/gwrhomag.f900000644002504400250440000000152014061636517017112 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine gwrhomag use modmain use modgw use modmpi use modomp implicit none ! local variables integer ik,nthd ! compute the GW density matrices and write the natural orbitals and occupation ! numbers to EVECSV.OUT and OCCSV.OUT, respectively call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call gwdmatk(ik) end do !$OMP END PARALLEL DO call freethd(nthd) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! determine the density and magnetisation in the usual way call rhomag end subroutine elk-7.2.42/src/PaxHeaders.21776/gwdmatk.f900000644000000000000000000000013214061636517014702 xustar0030 mtime=1623670095.763101705 30 atime=1623670094.603102781 30 ctime=1623670095.763101705 elk-7.2.42/src/gwdmatk.f900000644002504400250440000000452414061636517016744 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gwdmatk(ik) use modmain use modgw implicit none ! arguments integer, intent(in) :: ik ! local variables integer ist,jst,iw real(8) e,t1 complex(8) z1 ! allocatable arrays complex(8), allocatable :: evecsv(:,:),se(:,:,:) complex(8), allocatable :: gs(:),g(:,:),gf(:,:),gl(:,:) complex(8), allocatable :: d(:,:),a(:,:) ! external functions complex(8), external :: gtwsum ! read the self-energy from file allocate(se(nstsv,nstsv,0:nwfm)) call getgwsefm(ik,se) ! allocate local arrays allocate(gs(nstsv),g(nstsv,nstsv)) allocate(gf(nstsv,nstsv),gl(nstsv,nstsv)) allocate(d(nstsv,nstsv)) ! zero the density matrix d(:,:)=0.d0 ! loop over fermionic Matsubara frequencies do iw=0,nwfm ! compute the diagonal matrix G_s do ist=1,nstsv e=evalsv(ist,ik)-efermi gs(ist)=1.d0/(wfm(iw)-e) end do ! compute 1 - G_s Sigma do ist=1,nstsv z1=-gs(ist) g(ist,:)=z1*se(ist,:,iw) g(ist,ist)=g(ist,ist)+1.d0 end do ! invert this matrix call zminv(nstsv,g) ! compute G = (1 - G_s Sigma)^(-1) G_s do jst=1,nstsv z1=gs(jst) g(:,jst)=g(:,jst)*z1 end do ! add to the density matrix d(:,:)=d(:,:)+g(:,:) ! store the Green's function at the first and last frequencies if (iw.eq.0) gf(:,:)=g(:,:) if (iw.eq.nwfm) gl(:,:)=g(:,:) end do ! add the Matsubara tails analytically do jst=1,nstsv do ist=1,nstsv d(ist,jst)=d(ist,jst)+gtwsum(gf(ist,jst),gl(ist,jst)) end do end do ! multiply by 1/beta t1=kboltz*tempk d(:,:)=t1*d(:,:) deallocate(se,gs,g,gf,gl) ! diagonalise the density matrix for the natural orbitals and occupation numbers call eveqnzh(nstsv,nstsv,d,occsv(:,ik)) occsv(:,ik)=occsv(:,ik)*occmax ! write the occupation numbers to file call putoccsv(filext,ik,occsv(:,ik)) ! get the second-variational eigenvectors from file allocate(evecsv(nstsv,nstsv)) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! apply unitary transformation to the third-variational states so that they ! refer to the first-variational basis allocate(a(nstsv,nstsv)) call zgemm('N','N',nstsv,nstsv,nstsv,zone,evecsv,nstsv,d,nstsv,zzero,a,nstsv) ! write the density matrix to file as second-variational eigenvectors call putevecsv(filext,ik,a) deallocate(evecsv,d,a) end subroutine elk-7.2.42/src/PaxHeaders.21776/gwefermi.f900000644000000000000000000000013114061636517015050 xustar0030 mtime=1623670095.765101703 29 atime=1623670094.60510278 30 ctime=1623670095.765101703 elk-7.2.42/src/gwefermi.f900000644002504400250440000000301014061636517017100 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 P. Elliott, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gwefermi use modmain use modgw use modmpi use modomp implicit none ! local variables integer, parameter :: maxit=1000 integer ik,ist,it,nthd real(8) e0,e1,e real(8) chg,chgk if (mp_mpi) then write(*,*) write(*,'("Info(gwefermi): finding the GW Fermi energy")') end if ! find minimum and maximum eigenvalues e0=evalsv(1,1) e1=e0 do ik=1,nkpt do ist=1,nstsv e=evalsv(ist,ik) if (e.lt.e0) e0=e if (e.gt.e1) e1=e end do end do do it=1,maxit if (mp_mpi.and.(mod(it,10).eq.0)) then write(*,'("Info(gwefermi): done ",I4," iterations")') it end if efermi=0.5d0*(e0+e1) chg=0.d0 ! begin parallel loop over k-points call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(chgk) REDUCTION(+:chg) & !$OMP NUM_THREADS(nthd) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call gwchgk(ik,chgk) chg=chg+chgk end do !$OMP END PARALLEL DO call freethd(nthd) ! add charge from each process and redistribute if (np_mpi.gt.1) then call mpi_allreduce(mpi_in_place,chg,1,mpi_double_precision,mpi_sum,mpicom, & ierror) end if if (chg.lt.chgval) then e0=efermi else e1=efermi end if if ((e1-e0).lt.1.d-12) return end do write(*,*) write(*,'("Warning(gwefermi): could not find GW Fermi energy")') end subroutine elk-7.2.42/src/PaxHeaders.21776/dysonr.f900000644000000000000000000000013214061636517014562 xustar0030 mtime=1623670095.766101702 30 atime=1623670094.606102779 30 ctime=1623670095.766101702 elk-7.2.42/src/dysonr.f900000644002504400250440000000355514061636517016627 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine dysonr(ik,wr,sem,sf) use modmain use modgw use modomp implicit none ! arguments integer, intent(in) :: ik real(8), intent(in) :: wr(nwplot) complex(8), intent(in) :: sem(nstsv,nstsv,0:nwfm) real(8), intent(out) :: sf(nwplot) ! local variables integer ist,jst,iw integer nthd real(8) w,e,sm,t1 complex(8) z1 ! allocatable arrays complex(8), allocatable :: ser(:,:,:),gs(:),g(:,:) allocate(ser(nstsv,nstsv,nwplot)) ser(:,:,:)=0.d0 call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ist) & !$OMP NUM_THREADS(nthd) do jst=1,nstsv do ist=1,nstsv if (tsediag.and.(ist.ne.jst)) cycle ! perform analytic continuation from the imaginary to the real axis call acgwse(ist,jst,sem,wr,ser) end do end do !$OMP END PARALLEL DO call freethd(nthd) ! solve the Dyson equation for each frequency call holdthd(nwplot,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(gs,g,w,ist,jst) & !$OMP PRIVATE(e,t1,z1,sm) & !$OMP NUM_THREADS(nthd) allocate(gs(nstsv),g(nstsv,nstsv)) !$OMP DO do iw=1,nwplot w=wr(iw) ! compute the diagonal matrix G_s do ist=1,nstsv e=evalsv(ist,ik)-efermi t1=sign(swidth,e) gs(ist)=1.d0/cmplx(w-e,t1,8) end do ! compute 1 - G_s Sigma do ist=1,nstsv z1=-gs(ist) g(ist,:)=z1*ser(ist,:,iw) g(ist,ist)=g(ist,ist)+1.d0 end do ! invert this matrix call zminv(nstsv,g) ! compute G = (1 - G_s Sigma)^(-1) G_s do jst=1,nstsv z1=gs(jst) g(:,jst)=g(:,jst)*z1 end do ! determine the spectral function sm=0.d0 do ist=1,nstsv sm=sm+abs(aimag(g(ist,ist))) end do sf(iw)=sm*occmax/pi end do !$OMP END DO deallocate(gs,g) !$OMP END PARALLEL call freethd(nthd) deallocate(ser) end subroutine elk-7.2.42/src/PaxHeaders.21776/gwsefm.f900000644000000000000000000000012614061636517014537 xustar0028 mtime=1623670095.7681017 30 atime=1623670094.608102777 28 ctime=1623670095.7681017 elk-7.2.42/src/gwsefm.f900000644002504400250440000000441714061636517016577 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine gwsefm use modmain use modgw use modmpi use modomp implicit none ! local variables integer ik,nthd ! allocatable arrays real(8), allocatable :: vmt(:,:),vir(:) real(8), allocatable :: bmt(:,:,:),bir(:,:) complex(8), allocatable :: se(:,:,:) ! initialise universal variables call init0 call init1 call init2 call init3 ! read density and potentials from file call readstate ! generate the core wavefunctions and densities call gencore ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! write the momentum matrix elements in the second-variational basis to file call genpmat ! generate the inverse dielectric function and write to file call epsinv ! compute the matrix elements of -V_xc and -B_xc allocate(vmt(npcmtmax,natmtot),vir(ngtot)) if (spinpol) then allocate(bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag)) end if call gwlocal(vmt,vir,bmt,bir) if (mp_mpi) write(*,*) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! loop over reduced k-point set call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(se) & !$OMP NUM_THREADS(nthd) allocate(se(nstsv,nstsv,0:nwfm)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(gwsefm_) write(*,'("Info(gwsefm): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(gwsefm_) ! determine the self-energy at the fermionic frequencies for current k-point call gwsefmk(ik,vmt,vir,bmt,bir,se) ! write the self-energy to file call putgwsefm(ik,se) end do !$OMP END DO deallocate(se) !$OMP END PARALLEL call freethd(nthd) if (mp_mpi) then write(*,*) write(*,'("Info(gwsefm): GW self-energy at the fermionic frequencies & &written to GWSEFM.OUT")') end if deallocate(vmt,vir) if (spinpol) deallocate(bmt,bir) end subroutine elk-7.2.42/src/PaxHeaders.21776/putgwsefm.f900000644000000000000000000000013214061636517015265 xustar0030 mtime=1623670095.769101699 30 atime=1623670094.609102776 30 ctime=1623670095.769101699 elk-7.2.42/src/putgwsefm.f900000644002504400250440000000121714061636517017323 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine putgwsefm(ik,se) use modmain use modgw implicit none ! arguments integer, intent(in) :: ik complex(8), intent(in) :: se(nstsv,nstsv,0:nwfm) ! local variables integer recl ! find the record length inquire(iolength=recl) vkl(:,ik),nstsv,nwfm,se !$OMP CRITICAL(u280) open(280,file='GWSEFM.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(280,rec=ik) vkl(:,ik),nstsv,nwfm,se close(280) !$OMP END CRITICAL(u280) end subroutine elk-7.2.42/src/PaxHeaders.21776/getgwsefm.f900000644000000000000000000000013214061636517015234 xustar0030 mtime=1623670095.771101697 30 atime=1623670094.611102774 30 ctime=1623670095.771101697 elk-7.2.42/src/getgwsefm.f900000644002504400250440000000257514061636517017302 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine getgwsefm(ik,se) use modmain use modgw implicit none ! arguments integer, intent(in) :: ik complex(8), intent(out) :: se(nstsv,nstsv,0:nwfm) ! local variables integer recl,nstsv_,nwfm_ real(8) vkl_(3),t1 ! find the record length inquire(iolength=recl) vkl_,nstsv_,nwfm_,se !$OMP CRITICAL(u280) open(280,file='GWSEFM.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(280,rec=ik) vkl_,nstsv_,nwfm_,se !$OMP END CRITICAL(u280) t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getgwsefm): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" GWSEFM.OUT : ",3G18.10)') vkl_ write(*,*) stop end if if (nstsv.ne.nstsv_) then write(*,*) write(*,'("Error(getgwsefm): differing nstsv for k-point ",I8)') ik write(*,'(" current : ",I8)') nstsv write(*,'(" GWSEFM.OUT : ",I8)') nstsv_ write(*,*) stop end if if (nwfm.ne.nwfm_) then write(*,*) write(*,'("Error(getgwsefm): differing nwfm for k-point ",I8)') ik write(*,'(" current : ",I8)') nwfm write(*,'(" GWSEFM.OUT : ",I8)') nwfm_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/writeigw.f900000644000000000000000000000013214061636517015105 xustar0030 mtime=1623670095.772101696 30 atime=1623670094.613102772 30 ctime=1623670095.772101696 elk-7.2.42/src/writeigw.f900000644002504400250440000000151114061636517017140 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeigw(fnum) use modmain use modgw implicit none ! arguments integer fnum write(fnum,'("+----------------------------------------|")') write(fnum,'("| Self-consistent density GW calculation |")') write(fnum,'("+----------------------------------------|")') write(fnum,*) write(fnum,'("Temperature (K) : ",G18.10)') tempk write(fnum,*) write(fnum,'("Matsubara frequency cut-off : ",G18.10)') wmaxgw write(fnum,'("Number of Matsubara frequencies : ",I6)') nwgw write(fnum,*) write(fnum,'("Maximum |G| for response function : ",G18.10)') gmaxrf write(fnum,'("Number of response-function G-vectors : ",I8)') ngrf flush(fnum) end subroutine elk-7.2.42/src/PaxHeaders.21776/polefit.f900000644000000000000000000000013214061636517014706 xustar0030 mtime=1623670095.774101695 30 atime=1623670094.614102771 30 ctime=1623670095.774101695 elk-7.2.42/src/polefit.f900000644002504400250440000000101614061636517016741 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. real(8) function polefit(zfm,c) use modgw implicit none ! arguments complex(8), intent(in) :: zfm(0:nwfm),c(2*npole+1) ! local variables integer iw complex(8) z1 ! external functions complex(8), external :: zfpole polefit=0.d0 do iw=0,nwfm z1=zfm(iw)-zfpole(c,wfm(iw)) polefit=polefit+dble(z1)**2+aimag(z1)**2 end do end function elk-7.2.42/src/PaxHeaders.21776/gwchgk.f900000644000000000000000000000013214061636517014516 xustar0030 mtime=1623670095.775101694 30 atime=1623670094.616102769 30 ctime=1623670095.775101694 elk-7.2.42/src/gwchgk.f900000644002504400250440000000310314061636517016550 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 P. Elliott, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gwchgk(ik,chgk) use modmain use modgw implicit none ! arguments integer, intent(in) :: ik real(8), intent(out) :: chgk ! local variables integer ist,iw real(8) e complex(8) z1 ! allocatable arrays complex(8), allocatable :: gs(:),g(:,:),gf(:),gl(:) complex(8), allocatable :: se(:,:,:) ! external functions complex(8), external :: gtwsum ! read the self-energy from file allocate(se(nstsv,nstsv,0:nwfm)) call getgwsefm(ik,se) ! allocate local arrays allocate(gs(nstsv),g(nstsv,nstsv)) allocate(gf(nstsv),gl(nstsv)) chgk=0.d0 do iw=0,nwfm ! compute the diagonal matrix G_s do ist=1,nstsv e=evalsv(ist,ik)-efermi gs(ist)=1.d0/(wfm(iw)-e) end do ! compute 1 - G_s Sigma do ist=1,nstsv z1=-gs(ist) g(ist,:)=z1*se(ist,:,iw) g(ist,ist)=g(ist,ist)+1.d0 end do ! invert this matrix call zminv(nstsv,g) ! take the trace of G = (1 - G_s Sigma)^(-1) G_s do ist=1,nstsv g(ist,ist)=g(ist,ist)*gs(ist) chgk=chgk+dble(g(ist,ist)) end do ! store the Green's function at the first and last frequencies if (iw.eq.0) then do ist=1,nstsv gf(ist)=g(ist,ist) end do end if if (iw.eq.nwfm) then do ist=1,nstsv gl(ist)=g(ist,ist) end do end if end do ! add the Matsubara tails analytically do ist=1,nstsv chgk=chgk+dble(gtwsum(gf(ist),gl(ist))) end do chgk=chgk*wkpt(ik)*occmax*kboltz*tempk deallocate(se,gs,g,gf,gl) end subroutine elk-7.2.42/src/PaxHeaders.21776/gwsefmk.f900000644000000000000000000000013214061636517014707 xustar0030 mtime=1623670095.777101692 30 atime=1623670094.618102767 30 ctime=1623670095.777101692 elk-7.2.42/src/gwsefmk.f900000644002504400250440000002334214061636517016750 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine gwsefmk(ikp,vmt,vir,bmt,bir,se) use modmain use modgw use modomp implicit none ! arguments integer, intent(in) :: ikp real(8), intent(in) :: vmt(npcmtmax,natmtot),vir(ngtot) real(8), intent(in) :: bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag) complex(8), intent(out) :: se(nstsv,nstsv,0:nwfm) ! local variables integer ik,jk,ist1,ist2,ist3 integer iv(3),iq,ig,jg integer iw,jw,it,nthd real(8) vl(3),vc(3),t1,t2 complex(8) z1,z2 ! automatic arrays integer idx(nstsv) ! allocatable arrays integer(8), allocatable :: lock(:) real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:) real(8), allocatable :: jlgqr(:,:,:),jlgqrmt(:,:,:) complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: wfmt1(:,:,:,:),wfir1(:,:,:) complex(8), allocatable :: wfmt2(:,:,:,:),wfir2(:,:,:) complex(8), allocatable :: zrhomt(:,:,:),zrhoir(:,:) complex(8), allocatable :: zvclmt(:,:),zvclir(:) complex(8), allocatable :: zfgq(:),zrho(:,:,:),epsi(:,:,:) complex(8), allocatable :: v(:,:),stau(:,:,:) complex(8), allocatable :: gs(:,:),wc(:,:),zv(:) ! external functions complex(8), external :: zfinp ! allocate local arrays allocate(vgqc(3,ngvc),gqc(ngvc),gclgq(ngvc)) allocate(jlgqr(njcmax,nspecies,ngrf),jlgqrmt(0:lnpsd,ngvc,nspecies)) allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) allocate(ylmgq(lmmaxo,ngvc),sfacgq(ngvc,natmtot)) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) allocate(wfmt1(npcmtmax,natmtot,nspinor,nstsv),wfir1(ngtc,nspinor,nstsv)) allocate(wfmt2(npcmtmax,natmtot,nspinor,nstsv),wfir2(ngtc,nspinor,nstsv)) allocate(zrhomt(npcmtmax,natmtot,nstsv),zrhoir(ngtc,nstsv)) allocate(zrho(nstsv,ngrf,nstsv),epsi(ngrf,ngrf,nwrf)) allocate(v(nstsv,nstsv),stau(nstsv,nstsv,nwgw),gs(nwgw,nstsv)) ! initialise the OpenMP locks allocate(lock(nwgw)) do it=1,nwgw call omp_init_lock(lock(it)) end do ! get the eigenvectors from file for input reduced k-point call getevecfv(filext,ikp,vkl(:,ikp),vgkl(:,:,:,ikp),evecfv) call getevecsv(filext,ikp,vkl(:,ikp),evecsv) ! find the matching coefficients call match(ngk(1,ikp),vgkc(:,:,1,ikp),gkc(:,1,ikp),sfacgk(:,:,1,ikp),apwalm) ! index to all states do ist1=1,nstsv idx(ist1)=ist1 end do ! calculate the wavefunctions for all states of the input k-point call genwfsv(.false.,.true.,nstsv,idx,ngdgc,igfc,ngk(1,ikp),igkig(:,1,ikp), & apwalm,evecfv,evecsv,wfmt1,ngtc,wfir1) ! local -V_xc and -B_xc matrix elements if (spinpol) then call genvbmatk(vmt,vir,bmt,bir,ngk(1,ikp),igkig(:,1,ikp),wfmt1,ngtc,wfir1,v) else call genvmatk(vmt,vir,ngk(1,ikp),igkig(:,1,ikp),wfmt1,ngtc,wfir1,v) end if ! Fourier transform wavefunctions to real-space call zftwfir(ngk(1,ikp),igkig(:,1,ikp),wfir1) ! add the core Fock matrix elements call vclcore(wfmt1,v) ! zero the self-energy matrix elements in tau-space stau(:,:,:)=0.d0 ! loop over non-reduced k-point set do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) ! determine the q-vector iv(:)=ivk(:,ikp)-ivk(:,ik) iv(:)=modulo(iv(:),ngridk(:)) ! check if the q-point is in user-defined set iv(:)=iv(:)*ngridq(:) if (any(modulo(iv(:),ngridk(:)).ne.0)) cycle iv(:)=iv(:)/ngridk(:) iq=ivqiq(iv(1),iv(2),iv(3)) vl(:)=vkl(:,ikp)-vkl(:,ik) vc(:)=vkc(:,ikp)-vkc(:,ik) do ig=1,ngvc ! determine the G+q-vectors vgqc(:,ig)=vgc(:,ig)+vc(:) ! G+q-vector length gqc(ig)=sqrt(vgqc(1,ig)**2+vgqc(2,ig)**2+vgqc(3,ig)**2) ! spherical harmonics for G+q-vectors call genylmv(lmaxo,vgqc(:,ig),ylmgq(:,ig)) end do ! structure factors for G+q call gensfacgp(ngvc,vgqc,ngvc,sfacgq) ! generate the regularised Coulomb Green's function in G+q-space call gengclgq(.true.,iq,ngvc,gqc,gclgq) ! compute the required spherical Bessel functions call genjlgprmt(lnpsd,ngvc,gqc,ngvc,jlgqrmt) call genjlgpr(ngrf,gqc,jlgqr) ! find the matching coefficients call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! get the eigenvectors from file for non-reduced k-point call getevecfv(filext,0,vkl(:,ik),vgkl(:,:,1,ik),evecfv) call getevecsv(filext,0,vkl(:,ik),evecsv) ! calculate the wavefunctions for all states call genwfsv(.false.,.false.,nstsv,idx,ngdgc,igfc,ngk(1,ik),igkig(:,1,ik), & apwalm,evecfv,evecsv,wfmt2,ngtc,wfir2) ! determine the complex densities and Fourier transform to G+q-space do ist3=1,nstsv call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zfgq) & !$OMP NUM_THREADS(nthd) allocate(zfgq(ngrf)) !$OMP DO do ist1=1,nstsv call genzrho(.true.,.true.,ngtc,wfmt2(:,:,:,ist3),wfir2(:,:,ist3), & wfmt1(:,:,:,ist1),wfir1(:,:,ist1),zrhomt(:,:,ist1),zrhoir(:,ist1)) call zftzf(ngrf,jlgqr,ylmgq,ngvc,sfacgq,zrhomt(:,:,ist1),zrhoir(:,ist1), & zfgq) zrho(ist1,:,ist3)=conjg(zfgq(:)) end do !$OMP END DO deallocate(zfgq) !$OMP END PARALLEL call freethd(nthd) !--------------------------------------! ! valence Fock matrix elements ! !--------------------------------------! t1=wqptnr*occsv(ist3,jk)/occmax if (abs(t1).lt.epsocc) cycle call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zvclmt,zvclir) & !$OMP PRIVATE(ist1,z1) & !$OMP NUM_THREADS(nthd) allocate(zvclmt(npcmtmax,natmtot),zvclir(ngtc)) !$OMP DO do ist2=1,nstsv ! calculate the Coulomb potential call genzvclmt(nrcmt,nrcmti,nrcmtmax,rlcmt,wprcmt,npcmtmax, & zrhomt(:,:,ist2),zvclmt) call zpotcoul(nrcmt,nrcmti,npcmt,npcmti,nrcmtmax,rlcmt,ngdgc,igfc,ngvc, & gqc,gclgq,ngvc,jlgqrmt,ylmgq,sfacgq,zrhoir(:,ist2),npcmtmax,zvclmt, & zvclir) zvclir(:)=zvclir(:)*cfrc(:) do ist1=1,ist2 z1=zfinp(zrhomt(:,:,ist1),zrhoir(:,ist1),zvclmt,zvclir) v(ist1,ist2)=v(ist1,ist2)-t1*z1 end do end do !$OMP END DO deallocate(zvclmt,zvclir) !$OMP END PARALLEL call freethd(nthd) end do !-------------------------------------! ! correlation matrix elements ! !-------------------------------------! ! symmetrise the Coulomb Green's function gclgq(1:ngrf)=sqrt(gclgq(1:ngrf)) ! generate G_s in tau-space call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(t1,iw) & !$OMP NUM_THREADS(nthd) do ist1=1,nstsv t1=efermi-evalsv(ist1,jk) gs(:,ist1)=0.d0 do iw=-nwfm,nwfm,2 gs(iwfft(iw),ist1)=1.d0/cmplx(t1,wgw(iw),8) end do call zfftifc(1,nwgw,1,gs(:,ist1)) end do !$OMP END PARALLEL DO call freethd(nthd) ! get RPA inverse epsilon from file call getcfgq('EPSINV.OUT',vl,ngrf,nwrf,epsi) call holdthd(ngrf,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wc,zv,t1,t2,ig,iw,jw) & !$OMP PRIVATE(it,ist2,ist3,z1,z2) & !$OMP NUM_THREADS(nthd) allocate(wc(nwgw,ngrf),zv(nstsv)) !$OMP DO do jg=1,ngrf ! if epsi is exactly zero then there is no entry for this particular G'+q-vector ! so we cycle to the next if (abs(epsi(jg,jg,1)).eq.0.d0) cycle ! subtract one from inverse epsilon to leave just the correlation part epsi(jg,jg,:)=epsi(jg,jg,:)-1.d0 ! compute the correlation part of the screened interaction W_c t1=gclgq(jg) do ig=1,ngrf t2=t1*gclgq(ig) wc(:,ig)=0.d0 do iw=-nwbs,nwbs,2 jw=(iw+nwbs)/2+1 wc(iwfft(iw),ig)=t2*epsi(ig,jg,jw) end do ! Fourier transform W_c to tau-space call zfftifc(1,nwgw,1,wc(:,ig)) end do do it=1,nwgw do ist3=1,nstsv z1=gs(it,ist3) zv(1:nstsv)=0.d0 if (twdiag) then ! use only the diagonal elements of W_c z2=z1*wc(it,jg) call zaxpy(nstsv,z2,zrho(:,jg,ist3),1,zv,1) else ! use the full W_c do ig=1,ngrf z2=z1*wc(it,ig) call zaxpy(nstsv,z2,zrho(:,ig,ist3),1,zv,1) end do end if call omp_set_lock(lock(it)) if (tsediag) then ! compute only the diagonal elements of the self-energy do ist2=1,nstsv z2=conjg(zrho(ist2,jg,ist3)) stau(ist2,ist2,it)=stau(ist2,ist2,it)+z2*zv(ist2) end do else ! compute the full self-energy matrix do ist2=1,nstsv z2=conjg(zrho(ist2,jg,ist3)) call zaxpy(nstsv,z2,zv,1,stau(:,ist2,it),1) end do end if call omp_unset_lock(lock(it)) end do end do end do !$OMP END DO deallocate(wc,zv) !$OMP END PARALLEL call freethd(nthd) ! end loop over k-points end do ! destroy the OpenMP locks do it=1,nwgw call omp_destroy_lock(lock(it)) end do deallocate(lock) ! Fourier transform the self-energy to frequency space, multiply by GW diagram ! prefactor and store in output array t1=-wqptnr*omega*kboltz*tempk call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zv,ist1,iw,jw) & !$OMP NUM_THREADS(nthd) allocate(zv(nwgw)) !$OMP DO do ist2=1,nstsv do ist1=1,nstsv zv(1:nwgw)=stau(ist1,ist2,1:nwgw) call zfftifc(1,nwgw,-1,zv) do iw=-nwfm,nwfm,2 jw=(iw+nwfm)/2 se(ist1,ist2,jw)=t1*zv(iwfft(iw)) end do end do end do !$OMP END DO deallocate(zv) !$OMP END PARALLEL call freethd(nthd) ! add the local potential and Fock matrix elements to the self-energy for each ! Matsubara frequency call holdthd(nwfm+1,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ist1,ist2) & !$OMP NUM_THREADS(nthd) do iw=0,nwfm do ist2=1,nstsv do ist1=1,ist2 se(ist1,ist2,iw)=se(ist1,ist2,iw)+v(ist1,ist2) end do do ist1=ist2+1,nstsv se(ist1,ist2,iw)=se(ist1,ist2,iw)+conjg(v(ist2,ist1)) end do end do end do !$OMP END PARALLEL DO call freethd(nthd) deallocate(vgqc,gqc,gclgq,jlgqr,jlgqrmt) deallocate(ylmgq,sfacgq,apwalm,evecfv,evecsv) deallocate(wfmt1,wfir1,wfmt2,wfir2) deallocate(zrhomt,zrhoir,zrho) deallocate(epsi,v,gs) end subroutine elk-7.2.42/src/PaxHeaders.21776/gwspecf.f900000644000000000000000000000013214061636517014702 xustar0030 mtime=1623670095.778101691 30 atime=1623670094.620102766 30 ctime=1623670095.778101691 elk-7.2.42/src/gwspecf.f900000644002504400250440000000574514061636517016752 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine gwspecf use modmain use modgw use modmpi use modomp use modtest implicit none ! local variables integer ik,iw,nthd real(8) dw,w ! allocatable arrays real(8), allocatable :: wr(:),sft(:),sf(:) complex(8), allocatable :: se(:,:,:) ! initialise universal variables call init0 call init1 call init2 call init3 ! read Fermi energy from file call readfermi ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! real axis frequencies allocate(wr(nwplot)) dw=(wplot(2)-wplot(1))/dble(nwplot) do iw=1,nwplot wr(iw)=dw*dble(iw-1)+wplot(1) end do ! allocate and zero the total spectral function allocate(sft(nwplot)) sft(:)=0.d0 if (mp_mpi) write(*,*) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! loop over reduced k-point set call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(sf,se) & !$OMP NUM_THREADS(nthd) allocate(sf(nwplot),se(nstsv,nstsv,0:nwfm)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(gwspecf_1) write(*,'("Info(gwspecf): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(gwspecf_1) ! get the self-energy at the fermionic frequencies from file call getgwsefm(ik,se) ! solve the Dyson equation on the real axis call dysonr(ik,wr,se,sf) ! write the spectral function to file !$OMP CRITICAL(gwspecf_2) call writegwsf(ik,sf) !$OMP END CRITICAL(gwspecf_2) ! add to the total spectral function !$OMP CRITICAL(gwspecf_3) sft(:)=sft(:)+wkpt(ik)*sf(:) !$OMP END CRITICAL(gwspecf_3) end do !$OMP END DO deallocate(sf,se) !$OMP END PARALLEL call freethd(nthd) ! add total spectral function from each process if (np_mpi.gt.1) then call mpi_allreduce(mpi_in_place,sft,nwplot,mpi_double_precision,mpi_sum, & mpicom,ierror) end if ! write the total spectral function to file (MPI master process only) if (mp_mpi) then open(50,file='GWTSF.OUT',form='FORMATTED') dw=(wplot(2)-wplot(1))/dble(nwplot) do iw=1,nwplot w=dw*dble(iw-1)+wplot(1) write(50,'(2G18.10)') w,sft(iw) end do close(50) write(*,*) write(*,'("Info(gw):")') write(*,'(" GW spectral functions and Kohn-Sham eigenvalues written to & &GWSF_Kkkkkkk.OUT")') write(*,'(" for all k-points")') write(*,*) write(*,'(" Total GW spectral function written to GWTSF.OUT")') write(*,*) write(*,'(" Fermi energy for the Kohn-Sham eigenvalues is at zero in plots")') write(*,'(" Fermi energy for the GW spectral function is undetermined")') write(*,*) write(*,'(" Spectral function units are states/Hartree/unit cell")') end if ! write the total GW spectral function to test file call writetest(610,'total GW spectral function',nv=nwplot,tol=5.d-2,rva=sft) deallocate(wr,sft) end subroutine elk-7.2.42/src/PaxHeaders.21776/writegwsf.f900000644000000000000000000000013214061636517015265 xustar0030 mtime=1623670095.780101689 30 atime=1623670094.621102765 30 ctime=1623670095.780101689 elk-7.2.42/src/writegwsf.f900000644002504400250440000000154614061636517017330 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 A. Davydov, A. Sanna, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine writegwsf(ik,sf) use modmain use modgw implicit none ! arguments integer, intent(in) :: ik real(8), intent(in) :: sf(nwplot) ! local variables integer iw,ist real(8) dw,w,e character(256) fname write(fname,'("GWSF_K",I6.6,".OUT")') ik open(50,file=trim(fname),form='FORMATTED') ! write the GW spectral function dw=(wplot(2)-wplot(1))/dble(nwplot) do iw=1,nwplot w=dw*dble(iw-1)+wplot(1) write(50,'(2G18.10)') w,sf(iw) end do write(50,*) ! write the Kohn-Sham eigenvalues for reference do ist=1,nstsv e=evalsv(ist,ik)-efermi write(50,'(2G18.10)') e,0.d0 write(50,'(2G18.10)') e,1.d0/swidth write(50,*) end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/acgwse.f900000644000000000000000000000013214061636517014515 xustar0030 mtime=1623670095.781101688 30 atime=1623670094.623102763 30 ctime=1623670095.781101688 elk-7.2.42/src/acgwse.f900000644002504400250440000000163514061636517016557 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine acgwse(ist,jst,sem,wr,ser) use modmain use modgw implicit none ! arguments integer ist,jst complex(8), intent(in) :: sem(nstsv,nstsv,0:nwfm) real(8), intent(in) :: wr(nwplot) complex(8), intent(out) :: ser(nstsv,nstsv,nwplot) ! allocatable arrays complex(8), allocatable :: zm(:),zwr(:),zr(:) allocate(zm(0:nwfm),zwr(nwplot),zr(nwplot)) zm(:)=sem(ist,jst,:) zwr(:)=wr(:) select case(actype) case(1) ! fit a multipole model call acpole(zm,zwr,zr) case(10) ! stabilised Pade approximant call pades(nspade,swidth,nwfm+1,wfm,zm,nwplot,zwr,zr) case default write(*,*) write(*,'("Error(acgwse): actype not defined : ",I8)') actype write(*,*) stop end select ser(ist,jst,:)=zr(:) deallocate(zm,zwr,zr) end subroutine elk-7.2.42/src/PaxHeaders.21776/fmin_nm.f900000644000000000000000000000013214061636517014667 xustar0030 mtime=1623670095.783101686 30 atime=1623670094.625102761 30 ctime=1623670095.783101686 elk-7.2.42/src/fmin_nm.f900000644002504400250440000000106514061636517016726 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2007 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. real(8) function fmin_nm(id,rd,x) implicit none ! arguments integer, intent(in) :: id(*) real(8), intent(in) :: rd(*),x(*) ! external functions real(8), external :: polefit select case(id(1)) case(1) fmin_nm=polefit(rd,x) case default write(*,*) write(*,'("Error(fmin_nm): function type not defined : ",I8)') id(1) write(*,*) stop end select end function elk-7.2.42/src/PaxHeaders.21776/zfpole.f900000644000000000000000000000013114061636517014542 xustar0030 mtime=1623670095.784101685 29 atime=1623670094.62610276 30 ctime=1623670095.784101685 elk-7.2.42/src/zfpole.f900000644002504400250440000000076314061636517016606 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. pure complex(8) function zfpole(c,z) use modgw implicit none ! arguments complex(8), intent(in) :: c(*),z ! local variables integer i,j real(8) t1 complex(8) z1 zfpole=c(1) i=2 do j=1,npole z1=c(i)+z t1=abs(dble(z1))+abs(aimag(z1)) if (t1.gt.1.d-8) zfpole=zfpole+c(i+1)/z1 i=i+2 end do end function elk-7.2.42/src/PaxHeaders.21776/gwbandstr.f900000644000000000000000000000013214061636517015237 xustar0030 mtime=1623670095.786101684 30 atime=1623670094.628102758 30 ctime=1623670095.786101684 elk-7.2.42/src/gwbandstr.f900000644002504400250440000000554314061636517017303 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gwbandstr use modmain use modgw use modstore use modmpi use modomp implicit none ! local variables integer ip,iw real(8) dw ! allocatable arrays real(8), allocatable :: vmt(:,:),vir(:) real(8), allocatable :: bmt(:,:,:),bir(:,:) real(8), allocatable :: wr(:),sf(:) complex(8), allocatable :: se(:,:,:) ! store original parameters vkloff_(:)=vkloff(:) ! initialise universal variables call init0 call init1 call init2 call init3 ! read density and potentials from file call readstate ! generate the core wavefunctions and densities call gencore ! Fourier transform Kohn-Sham potential to G-space call genvsig ! read Fermi energy from file call readfermi ! generate k-points along a path for band structure plots call plotpt1d(bvec,nvp1d,npp1d,vvlp1d,vplp1d,dvp1d,dpp1d) ! compute the matrix elements of -V_xc and -B_xc allocate(vmt(npcmtmax,natmtot),vir(ngtot)) if (spinpol) then allocate(bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag)) end if call gwlocal(vmt,vir,bmt,bir) ! real axis frequencies allocate(wr(nwplot)) dw=(wplot(2)-wplot(1))/dble(nwplot) do iw=1,nwplot wr(iw)=dw*dble(iw-1)+wplot(1) end do allocate(sf(nwplot),se(nstsv,nstsv,0:nwfm)) if (mp_mpi) then open(85,file='GWBAND.OUT',form='FORMATTED',action='WRITE') write(85,'(2I6," : grid size")') nwplot,npp1d end if ! loop over plot points along path do ip=1,npp1d if (mp_mpi) then write(*,*) write(*,'("Info(gwbandstr): ",I6," of ",I6," plot points")') ip,npp1d end if ! reset the OpenMP thread variables call omp_reset ! change the k-point offset vkloff(:)=vplp1d(:,ip)*ngridk(:) ! generate the new k-point set call init1 ! determine the Kohn-Sham ground-state for this k-point offset call linengy call genapwlofr call gensocfr call genevfsv call occupy ! write the momentum matrix elements to file call genpmat ! generate the inverse dielectric function and write to file call epsinv ! determine the self-energy for the first k-point if (mp_mpi) then write(*,*) write(*,'("Info(gwbandstr): calculating self-energy for first k-point")') end if call gwsefmk(1,vmt,vir,bmt,bir,se) ! solve the Dyson equation on the real axis call dysonr(1,wr,se,sf) if (mp_mpi) then do iw=1,nwplot write(85,'(3G18.10)') dpp1d(ip),wr(iw),sf(iw) end do flush(85) end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end do deallocate(vmt,vir,wr,sf,se) if (spinpol) deallocate(bmt,bir) if (mp_mpi) then close(85) write(*,*) write(*,'("Info(gwbandstr):")') write(*,'(" GW spectral function band structure written to GWBAND.OUT")') end if ! restore original input parameters vkloff(:)=vkloff_(:) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/gwscrho.f900000644000000000000000000000013214061636517014720 xustar0030 mtime=1623670095.787101682 30 atime=1623670094.630102756 30 ctime=1623670095.787101682 elk-7.2.42/src/gwscrho.f900000644002504400250440000001466114061636517016765 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 A. Davydov, P. Elliott, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine gwscrho use modmain use modgw use modmpi use modomp implicit none ! local variables integer ik,nthd integer nmix,nwork real(8) dv ! allocatable arrays real(8), allocatable :: vmt(:,:),vir(:) real(8), allocatable :: bmt(:,:,:),bir(:,:) real(8), allocatable :: work(:) complex(8), allocatable :: se(:,:,:) ! initialise universal variables call init0 call init1 call init2 call init3 ! read density and potentials from file call readstate call genvsig ! read the Fermi energy call readfermi ! zero the exchange-correlation potential and magnetic field vxcmt(:,:)=0.d0 vxcir(:)=0.d0 if (spinpol) then bxcmt(:,:,:)=0.d0 bxcir(:,:)=0.d0 end if ! re-calculate the ground-state call gencore call linengy call genapwlofr call gensocfr call genevfsv call occupy allocate(vmt(npcmtmax,natmtot),vir(ngtot)) if (spinpol) then allocate(bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag)) end if if (mp_mpi) then ! open GW_INFO.OUT file open(60,file='GW_INFO.OUT',form='FORMATTED') ! open FERMIDOS.OUT open(62,file='FERMIDOS.OUT',form='FORMATTED') ! open MOMENT.OUT if required if (spinpol) open(63,file='MOMENT.OUT',form='FORMATTED') ! open GAP.OUT open(64,file='GAP.OUT',form='FORMATTED') ! open RMSDVS.OUT open(65,file='RMSDVS.OUT',form='FORMATTED') ! open MOMENTM.OUT if (spinpol) open(68,file='MOMENTM.OUT',form='FORMATTED') ! open RESIDUAL.OUT open(69,file='RESIDUAL.OUT',form='FORMATTED') ! write out general information to GW_INFO.OUT call writeigw(60) write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop started |")') write(60,'("+------------------------------+")') end if ! size of mixing vector nmix=size(vsbs) ! determine the size of the mixer work array nwork=-1 call mixerifc(mixtype,nmix,vsbs,dv,nwork,vsbs) allocate(work(nwork)) ! initialise the mixer iscl=0 call mixerifc(mixtype,nmix,vsbs,dv,nwork,work) ! set the stop signal to .false. tstop=.false. ! set last self-consistent loop flag tlast=.false. do iscl=1,maxscl if (mp_mpi) then write(60,*) write(60,'("+--------------------+")') write(60,'("| Loop number : ",I4," |")') iscl write(60,'("+--------------------+")') end if call genpmat call epsinv ! compute the matrix elements of -V_xc and -B_xc call gwlocal(vmt,vir,bmt,bir) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) if (mp_mpi) write(*,*) ! loop over reduced k-point set call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(se) & !$OMP NUM_THREADS(nthd) allocate(se(nstsv,nstsv,0:nwfm)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(gwscrho_) write(*,'("Info(gwscrho): ",I6," of ",I6," k-points")') ik,nkpt !$OMP END CRITICAL(gwscrho_) ! determine the self-energy at the fermionic frequencies for current k-point call gwsefmk(ik,vmt,vir,bmt,bir,se) ! write the self-energy to file call putgwsefm(ik,se) end do !$OMP END DO deallocate(se) !$OMP END PARALLEL call freethd(nthd) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) if (mp_mpi) then write(60,*) write(60,'("Kohn-Sham Fermi energy : ",G18.10)') efermi end if ! determine the GW Fermi energy call gwefermi if (mp_mpi) then write(60,'("GW Fermi energy : ",G18.10)') efermi flush(60) end if ! determine the density and magnetisation call gwrhomag ! invert the Kohn-Sham equations to find V_s and B_s call ksinvert ! mix the old effective potential and field with the new call mixerifc(mixtype,nmix,vsbs,dv,nwork,work) ! Fourier transform Kohn-Sham potential to G-space call genvsig if (mp_mpi) then ! write the Kohn-Sham occupation numbers to file do ik=1,nkpt call putoccsv(filext,ik,occsv(:,ik)) end do call writeeval call writefermi ! write STATE.OUT file call writestate write(60,*) write(60,'("Density of states at Fermi energy : ",G18.10)') fermidos write(60,'(" (states/Hartree/unit cell)")') write(60,*) write(60,'("Estimated indirect band gap : ",G18.10)') bandgap(1) write(60,'(" from k-point ",I6," to k-point ",I6)') ikgap(1),ikgap(2) write(60,'("Estimated direct band gap : ",G18.10)') bandgap(2) write(60,'(" at k-point ",I6)') ikgap(3) ! output charges and moments call writechg(60) if (spinpol) call writemom(60) write(60,*) write(60,'("Magnitude of residual : ",G18.10)') resoep flush(60) ! write DOS at Fermi energy to FERMIDOS.OUT write(62,'(G18.10)') fermidos flush(62) if (spinpol) then ! write total moment to MOMENT.OUT write(63,'(3G18.10)') momtot(1:ndmag) flush(63) ! write total moment magnitude to MOMENTM.OUT write(68,'(G18.10)') momtotm flush(68) end if ! write estimated Kohn-Sham indirect band gap write(64,'(G22.12)') bandgap(1) flush(64) ! write residual to RESIDUAL.OUT write(69,'(G18.10)') resoep flush(69) end if ! exit self-consistent loop if required if (tlast) goto 10 ! check for convergence if (iscl.ge.2) then if (mp_mpi) then write(60,*) write(60,'("RMS change in Kohn-Sham potential (target) : ",G18.10," (",& &G18.10,")")') dv,epspot flush(60) write(65,'(G18.10)') dv flush(65) end if if (dv.lt.epspot) then if (mp_mpi) then write(60,*) write(60,'("Convergence targets achieved")') end if tlast=.true. end if end if ! check for STOP file call checkstop if (tstop) tlast=.true. ! broadcast tlast from master process to all other processes call mpi_bcast(tlast,1,mpi_logical,0,mpicom,ierror) ! reset the OpenMP thread variables call omp_reset ! end the self-consistent loop end do 10 continue ! synchronise MPI processes call mpi_barrier(mpicom,ierror) if (mp_mpi) then write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop stopped |")') write(60,'("+------------------------------+")') ! close the GW_INFO.OUT file close(60) ! close the FERMIDOS.OUT file close(62) ! close the MOMENT.OUT and MOMENTM.OUT files if (spinpol) then close(63); close(68) end if ! close the GAP.OUT file close(64) ! close the RMSDVS.OUT file close(65) ! close the RESIDUAL.OUT file close(69) end if deallocate(vmt,vir) if (spinpol) deallocate(bmt,bir) end subroutine elk-7.2.42/src/PaxHeaders.21776/atptstep.f900000644000000000000000000000013214061636517015110 xustar0030 mtime=1623670095.789101681 30 atime=1623670094.632102755 30 ctime=1623670095.789101681 elk-7.2.42/src/atptstep.f900000644002504400250440000000134214061636517017145 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine atptstep use modmain use modtddft use modmpi implicit none ! local variables integer is,ia,ias real(8) dt,t1 ! time step length dt=times(itimes+1)-times(itimes) do is=1,nspecies t1=dt/spmass(is) do ia=1,natoms(is) ias=idxas(ia,is) ! add to the atomic velocities datposc(:,1,ia,is)=datposc(:,1,ia,is)+t1*forcet(:,ias,itimes) ! add to the atomic displacements datposc(:,0,ia,is)=datposc(:,0,ia,is)+datposc(:,1,ia,is)*dt end do end do ! write the atomic displacements and velocities to file if (mp_mpi) call writedatposc end subroutine elk-7.2.42/src/PaxHeaders.21776/potkst.f900000644000000000000000000000013014061636517014566 xustar0029 mtime=1623670095.79010168 30 atime=1623670094.633102754 29 ctime=1623670095.79010168 elk-7.2.42/src/potkst.f900000644002504400250440000000053314061636517016626 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potkst use modmain use modtddft implicit none ! adiabatic approximation to the exchange-correlation potential call potks(.true.) end subroutine elk-7.2.42/src/PaxHeaders.21776/tdbackup.f900000644000000000000000000000013214061636517015041 xustar0030 mtime=1623670095.792101678 30 atime=1623670094.635102752 30 ctime=1623670095.792101678 elk-7.2.42/src/tdbackup.f900000644002504400250440000000173314061636517017102 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tdbackup use modmain use modtddft use modmpi implicit none ! local variables integer ik ! allocatable arrays complex(8), allocatable :: evecsvt(:,:) if (ntsbackup.le.0) return if (mod(itimes-1,ntsbackup).ne.0) return allocate(evecsvt(nstsv,nstsv)) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! read in time-dependent Kohn-Sham eigenvectors call getevecsv(filext,ik,vkl(:,ik),evecsvt) ! write eigenvectors to backup file call putevecsv('_TD_BACKUP.OUT',ik,evecsvt) end do deallocate(evecsvt) ! write the time step backup file if (mp_mpi) then open(50,file='TIMESTEP_BACKUP.OUT',form='FORMATTED') write(50,'(I8,G18.10)') itimes,times(itimes) close(50) end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/writetimes.f900000644000000000000000000000013214061636517015440 xustar0030 mtime=1623670095.793101677 30 atime=1623670094.636102751 30 ctime=1623670095.793101677 elk-7.2.42/src/writetimes.f900000644002504400250440000000057514061636517017504 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writetimes use modmain use modtddft implicit none open(50,file='TIMESTEP.OUT',form='FORMATTED') write(50,'(I8,G18.10)') itimes,times(itimes) close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/readtimes.f900000644000000000000000000000013214061636517015221 xustar0030 mtime=1623670095.795101675 30 atime=1623670094.638102749 30 ctime=1623670095.795101675 elk-7.2.42/src/readtimes.f900000644002504400250440000000220514061636517017255 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readtimes(itimes0) use modmain use modtddft implicit none ! arguments integer, intent(out) :: itimes0 ! local variables integer ios real(8) times_,t1 open(50,file='TIMESTEP.OUT',form='FORMATTED',status='OLD',iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readtimes): error opening TIMESTEP.OUT")') write(*,*) stop end if read(50,*,iostat=ios) itimes0,times_ if (ios.ne.0) then write(*,*) write(*,'("Error(readtimes): error reading time step from TIMESTEP.OUT")') write(*,*) stop end if if ((itimes0.lt.1).or.(itimes0.gt.ntimes)) then write(*,*) write(*,'("Error(readtimes): invalid itimes : ",I8)') itimes0 write(*,*) stop end if t1=abs(times(itimes0)-times_) if (t1.gt.1.d-8) then write(*,*) write(*,'("Error(readtimes): differing time step")') write(*,'(" current : ",G18.10)') times(itimes0) write(*,'(" TIMESTEP.OUT : ",G18.10)') times_ write(*,*) stop end if close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/gentimes.f900000644000000000000000000000013214061636517015057 xustar0030 mtime=1623670095.796101674 30 atime=1623670094.640102747 30 ctime=1623670095.796101674 elk-7.2.42/src/gentimes.f900000644002504400250440000000120014061636517017105 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gentimes use modmain use modtddft implicit none ! local variables integer its if (tstime.lt.dtimes) then write(*,*) write(*,'("Error(gentimes): tstime < dtimes : ",2G18.10)') tstime,dtimes write(*,*) stop end if ! number of time steps ntimes=nint(tstime/dtimes)+1 ! generate the time step array if (allocated(times)) deallocate(times) allocate(times(ntimes)) do its=1,ntimes times(its)=dble(its-1)*dtimes end do end subroutine elk-7.2.42/src/PaxHeaders.21776/readafieldt.f900000644000000000000000000000013214061636517015510 xustar0030 mtime=1623670095.798101672 30 atime=1623670094.641102746 30 ctime=1623670095.798101672 elk-7.2.42/src/readafieldt.f900000644002504400250440000000266614061636517017557 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readafieldt use modmain use modtddft implicit none ! local variables integer ios,ntimes_,its,its_ real(8) times_,t1 ! generate the time step grid call gentimes ! read in the time-dependent vector potential open(50,file='AFIELDT.OUT',form='FORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readafieldt): error opening AFIELDT.OUT")') write(*,*) stop end if read(50,*) ntimes_ if (ntimes_.le.0) then write(*,*) write(*,'("Error(readafieldt): ntimes <= 0 : ",I8)') ntimes_ write(*,*) stop end if ntimes=min(ntimes,ntimes_) if (allocated(afieldt)) deallocate(afieldt) allocate(afieldt(3,ntimes)) do its=1,ntimes read(50,*) its_,times_,afieldt(:,its) if (its.ne.its_) then write(*,*) write(*,'("Error(readafieldt): time step number mismatch")') write(*,'(" internal : ",I8)') its write(*,'(" AFIELDT.OUT : ",I8)') its_ write(*,*) stop end if t1=abs(times(its)-times_) if (t1.gt.1.d-10) then write(*,*) write(*,'("Error(readafieldt): time step mismatch for step number ",& &I8)') its write(*,'(" internal : ",G18.10)') times(its) write(*,'(" AFIELDT.OUT : ",G18.10)') times_ stop end if end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/genjr.f900000644000000000000000000000013214061636517014351 xustar0030 mtime=1623670095.799101671 30 atime=1623670094.643102744 30 ctime=1623670095.799101671 elk-7.2.42/src/genjr.f900000644002504400250440000000151114061636517016404 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genjr use modmain use modtddft implicit none ! local variables integer is,ias,np,l real(8) ca,t1 ! generate the paramagnetic current call genjpr ! add the diamagnetic term if a time-dependent A-field is present if (tafieldt) then ! coupling constant of the external A-field (-1/c) ca=-1.d0/solsc ! muffin-tin part do l=1,3 t1=ca*afieldt(l,itimes) do ias=1,natmtot is=idxis(ias) np=npmt(is) jrmt(1:np,ias,l)=jrmt(1:np,ias,l)+t1*(rhomt(1:np,ias)-rhosmt(1:np,ias,l)) end do end do ! interstitial part do l=1,3 t1=ca*afieldt(l,itimes) jrir(:,l)=jrir(:,l)+t1*(rhoir(:)-rhosir(:,l)) end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/tddft.f900000644000000000000000000000013014061636517014347 xustar0029 mtime=1623670095.80010167 30 atime=1623670094.645102742 29 ctime=1623670095.80010167 elk-7.2.42/src/tddft.f900000644002504400250440000001142314061636517016407 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tddft use modmain use modtddft use moddftu use modmpi use modomp use modstore use modtest implicit none ! local variables integer ik,itimes0 ! allocatable arrays real(8), allocatable :: evalfv(:,:) complex(8), allocatable :: evecfv(:,:,:),evecsv(:,:) if (tshift) then write(*,*) write(*,'("Error(tddft): use tshift = .false. for the ground-state run")') write(*,*) stop end if ! average force can be non-zero (allow for translation of atomic basis) tfav0_=tfav0 tfav0=.false. tforce_=tforce ! determine the static density and charge call rhostatic ! Ehrenfest dynamics if (any(task.eq.[462,463])) then ! forces should not be calculated tforce=.false. ! enable small amplitude displacements tdatpos=.true. ! zero the displacements and velocities datposc(:,:,:,:)=0.d0 ! generate the gradient of the nucleus and static density Coulomb potential call gengvclns end if ! currents should be calculated with forces if (tforce) tjr=.true. ! deallocate the static density if not required if (.not.tjr) deallocate(rhosmt,rhosir) ! initialise global variables call init0 call init1 ! read the charge density and potentials from file call readstate ! generate the first- and second-variational eigenvectors and eigenvalues for ! the k-point set reduced with the symmetries which leave A(t) invariant for all ! time steps call genvsig call gencore call energykncr call readfermi call linengy call genapwlofr call gensocfr call genevfsv call occupy ! DFT+U if (dftu.ne.0) then call gendmatmt call genvmatmt end if ! generate the kinetic matrix elements in the second-variational basis call genkmat(.false.,.false.) ! write the momentum matrix elements in the second-variational basis call genpmat ! write the power density to file if (mp_mpi) call writeafpdt ! copy EVALFV.OUT, EVECFV.OUT, OCCSV.OUT and EVECSV.OUT to _TD.OUT extension if ((task.eq.460).or.(task.eq.462)) then allocate(evalfv(nstfv,nspnfv),evecfv(nmatmax,nstfv,nspnfv)) allocate(evecsv(nstsv,nstsv)) do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle call getevalfv('.OUT',ik,vkl(:,ik),evalfv) call putevalfv('_TD.OUT',ik,evalfv) call getevecfv('.OUT',ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call putevecfv('_TD.OUT',ik,evecfv) call putoccsv('_TD.OUT',ik,occsv(:,ik)) call getevecsv('.OUT',ik,vkl(:,ik),evecsv) ! randomise eigenvectors at t=0 if required call rndevsv(rndevt0,evecsv) call putevecsv('_TD.OUT',ik,evecsv) end do deallocate(evalfv,evecfv,evecsv) end if ! set global file extension filext='_TD.OUT' ! output the new k-point set to file if (mp_mpi) call writekpts ! synchronise MPI processes call mpi_barrier(mpicom,ierror) if (any(task.eq.[461,463])) then ! restart if required call tdrestart(itimes0) else ! start from t=0 itimes0=1 end if ! read the forces calculated during the previous TDDFT run if (tdatpos) call readforcet ! read the atomic displacements and velocities if (trddatpos) call readdatposc ! set the stop signal to .false. tstop=.false. !---------------------------------! ! main loop over time steps ! !---------------------------------! if (mp_mpi) write(*,*) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) do itimes=itimes0,ntimes-1 if (mp_mpi) then write(*,'("Info(tddft): time step ",I8," of ",I8,", t = ",G18.10)') & itimes,ntimes-1,times(itimes) end if ! reset the OpenMP thread variables call omp_reset ! evolve the wavefunctions across a single time step call timestep ! generate the density and magnetisation at current time step call rhomag ! compute the gauge-invariant current j(r) if required if (tjr) call genjr ! time step the induced A-field if (tafindt) call afindtstep ! calculate the electric field call genefieldt ! compute the time-dependent Kohn-Sham potentials and magnetic fields call potkst ! DFT+U if (dftu.ne.0) then call gendmatmt call genvmatmt end if ! compute the total energy call energytd ! write muffin-tin L, S and J if required if (tdlsj) call writetdlsj ! calculate the atomic forces if required if (tforce) then if ((itimes.eq.itimes0).or.(mod(itimes-1,ntsforce).eq.0)) then call force end if end if ! time step the atomic positions for Ehrenfest dynamics using forces calculated ! during the previous TDDFT run if (tdatpos) call atptstep ! write TDDFT output if (mp_mpi) call writetddft ! check for STOP file call checkstop if (tstop) exit end do filext='.OUT' tfav0=tfav0_ tforce=tforce_ tdatpos=.false. ! write the total current of the last step to test file call writetest(460,'total current of last time step',nv=3,tol=1.d-4,rva=jtot) end subroutine elk-7.2.42/src/PaxHeaders.21776/tddftlr.f900000644000000000000000000000013214061636517014707 xustar0030 mtime=1623670095.802101669 30 atime=1623670094.646102742 30 ctime=1623670095.802101669 elk-7.2.42/src/tddftlr.f900000644002504400250440000002022414061636517016744 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2010 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tddftlr use modmain use modtddft use modtest use modmpi use modomp implicit none ! local variables logical tq0 integer, parameter :: maxit=500 integer iq,ik,isym integer nm,i,j,l,n integer iw,it,nthd real(8) v(3),t1,t2 complex(8) vfxcp,z1 character(256) fname ! allocatable arrays integer(8), allocatable :: lock(:) real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqr(:,:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: vchi0(:,:,:),vfxc(:,:,:) complex(8), allocatable :: eps0(:,:,:),epsi(:,:,:),epsm(:,:,:) complex(8), allocatable :: zw(:),a(:,:) ! initialise global variables call init0 call init1 call init2 call init3 ! check q-vector is commensurate with k-point grid v(:)=dble(ngridk(:))*vecql(:) v(:)=abs(v(:)-nint(v(:))) if ((v(1).gt.epslat).or.(v(2).gt.epslat).or.(v(3).gt.epslat)) then write(*,*) write(*,'("Error(tddftlr): q-vector incommensurate with k-point grid")') write(*,'(" ngridk : ",3I6)') ngridk write(*,'(" vecql : ",3G18.10)') vecql write(*,*) stop end if ! find the equivalent reduced q-point call findqpt(vecql,isym,iq) ! check if q=0 tq0=.false. if (sum(abs(vecql(:))).lt.epslat) tq0=.true. ! read density and potentials from file call readstate ! read Fermi energy from a file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! generate the G+q-vectors and related functions allocate(vgqc(3,ngrf),gqc(ngrf),jlgqr(njcmax,nspecies,ngrf)) allocate(ylmgq(lmmaxo,ngrf),sfacgq(ngrf,natmtot)) call gengqf(ngrf,vecqc,vgqc,gqc,jlgqr,ylmgq,sfacgq) deallocate(vgqc) ! generate the regularised Coulomb Green's function in G+q-space allocate(gclgq(ngrf)) call gengclgq(.true.,iq,ngrf,gqc,gclgq) gclgq(:)=sqrt(gclgq(:)) ! matrix sizes if (tq0) then nm=ngrf+2 else nm=ngrf end if ! allocate local arrays allocate(vchi0(nm,nm,nwrf),vfxc(nm,nm,nwrf)) allocate(eps0(nm,nm,nwrf),epsi(nm,nm,nwrf)) ! initialise the OpenMP locks allocate(lock(nwrf)) do iw=1,nwrf call omp_init_lock(lock(iw)) end do ! compute v^1/2 chi0 v^1/2 (the symmetric version of v chi0) vchi0(:,:,:)=0.d0 call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP DO do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(tddftlr_) write(*,'("Info(tddftlr): ",I6," of ",I6," k-points")') ik,nkptnr !$OMP END CRITICAL(tddftlr_) ! compute v^1/2 chi0 v^1/2 call genvchi0(.true.,ik,lock,scissor,vecql,gclgq,jlgqr,ylmgq,sfacgq,nm,vchi0) end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) ! destroy the OpenMP locks do iw=1,nwrf call omp_destroy_lock(lock(iw)) end do deallocate(lock) ! add vchi0 from each process and redistribute if (np_mpi.gt.1) then n=nm*nm*nwrf call mpi_allreduce(mpi_in_place,vchi0,n,mpi_double_complex,mpi_sum,mpicom, & ierror) end if ! calculate symmetric epsilon = 1 - v^1/2 chi0 v^1/2 do i=1,nm do j=1,nm eps0(i,j,:)=-vchi0(i,j,:) epsi(i,j,:)=vchi0(i,j,:) end do eps0(i,i,:)=eps0(i,i,:)+1.d0 epsi(i,i,:)=epsi(i,i,:)+1.d0 end do allocate(a(nm,nm)) vfxcp=0.d0 it=0 10 continue ! compute vchi0 v^(-1/2) f_xc v^(-1/2) vchi0 call genvfxc(tq0,.true.,gclgq,nm,vchi0,eps0,epsi,vfxc) ! begin loop over frequencies do iw=1,nwrf ! compute 1 - v^1/2 chi0 v^1/2 - v^(-1/2) f_xc v^(-1/2) vchi0 a(:,:)=eps0(:,:,iw)-vfxc(:,:,iw) ! invert this matrix call zminv(nm,a) ! left multiply by v^1/2 chi0 v^1/2 call zgemm('N','N',nm,nm,nm,zone,vchi0(:,:,iw),nm,a,nm,zzero,epsi(:,:,iw),nm) ! compute epsilon^(-1) = 1 + v^1/2 chi v^1/2 do i=1,nm epsi(i,i,iw)=1.d0+epsi(i,i,iw) end do end do if (fxctype(1).eq.210) then ! self-consistent bootstrap f_xc it=it+1 if (it.gt.maxit) then write(*,*) write(*,'("Error(tddftlr): bootstrap kernel failed to converge")') write(*,*) stop end if if (mod(it,10).eq.0) then write(*,'("Info(tddftlr): done ",I4," bootstrap iterations")') it write(*,'(" head of matrix v.f_xc : ",2G18.10)') vfxc(1,1,1) end if ! check for convergence t1=abs(vfxcp)-abs(vfxc(1,1,1)) vfxcp=vfxc(1,1,1) if (abs(t1).gt.1.d-8) goto 10 else if (fxctype(1).eq.211) then ! single iteration bootstrap it=it+1 if (it.le.1) goto 10 end if deallocate(gclgq,jlgqr) deallocate(ylmgq,sfacgq) deallocate(vchi0,vfxc) ! invert epsilon^(-1) to find epsilon and store in array eps0 do iw=1,nwrf eps0(:,:,iw)=epsi(:,:,iw) call zminv(nm,eps0(:,:,iw)) end do ! write G = G' = 0 components to file if (mp_mpi) then do l=1,noptcomp i=optcomp(1,l) j=optcomp(2,l) write(fname,'("EPSILON_TDDFT_",2I1,".OUT")') i,j open(50,file=trim(fname),form='FORMATTED') write(fname,'("EPSINV_TDDFT_",2I1,".OUT")') i,j open(51,file=trim(fname),form='FORMATTED') do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(eps0(i,j,iw)) write(51,'(2G18.10)') dble(wrf(iw)),dble(epsi(i,j,iw)) end do write(50,*) write(51,*) do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(eps0(i,j,iw)) write(51,'(2G18.10)') dble(wrf(iw)),aimag(epsi(i,j,iw)) end do close(50) close(51) end do end if ! find the macroscopic part of epsilon by inverting the 3x3 head only if (mp_mpi.and.tq0) then allocate(epsm(3,3,nwrf)) do iw=1,nwrf epsm(1:3,1:3,iw)=epsi(1:3,1:3,iw) call zminv(3,epsm(:,:,iw)) end do ! write out the macroscopic components do l=1,noptcomp i=optcomp(1,l) j=optcomp(2,l) write(fname,'("EPSM_TDDFT_",2I1,".OUT")') i,j open(50,file=trim(fname),form='FORMATTED') do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(epsm(i,j,iw)) end do write(50,*) do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(epsm(i,j,iw)) end do close(50) end do allocate(zw(nwrf)) ! output the Faraday angle components Delta delta and Delta beta do iw=2,nwrf zw(iw)=0.5d0*zi*epsm(1,2,iw)/sqrt(epsm(1,1,iw)) end do open(50,file='FARADAY.OUT',form='FORMATTED') do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(zw(iw)) end do write(50,*) do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(zw(iw)) end do close(50) ! output the Kerr angle do iw=2,nwrf zw(iw)=-epsm(1,2,iw)/(sqrt(epsm(1,1,iw))*(epsm(1,1,iw)-1.d0)) end do open(50,file='KERR_TDDFT.OUT',form='FORMATTED') do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(zw(iw))*180.d0/pi end do write(50,*) do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(zw(iw))*180.d0/pi end do close(50) ! output magnetic linear dichroism (MLD) spectrum t1=sin(thetamld)**2 t2=sin(2.d0*thetamld) do iw=2,nwrf z1=epsm(1,1,iw) zw(iw)=t2*epsm(1,2,iw)/((z1-1.d0)*(z1-(t1*(z1+1.d0)))) end do open(50,file='MLD.OUT',form='FORMATTED') do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(zw(iw)) end do write(50,*) do iw=2,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(zw(iw)) end do close(50) deallocate(epsm,zw) end if ! write inverse epsilon to test file call writetest(320,'inverse epsilon',nv=nm*nm*nwrf,tol=1.d-2,zva=epsi) deallocate(eps0,epsi,a) if (mp_mpi) then write(*,*) write(*,'("Info(tddftlr):")') write(*,'(" Dielectric tensor written to EPSILON_TDDFT_ij.OUT")') write(*,'(" Inverse written to EPSINV_TDDFT_ij.OUT")') if (tq0) then write(*,'(" Macroscopic part written to EPSM_TDDFT_ij.OUT")') end if write(*,'(" for components")') do l=1,noptcomp write(*,'(" i = ",I1,", j = ",I1)') optcomp(1:2,l) end do write(*,'(" q-vector (lattice coordinates) : ")') write(*,'(3G18.10)') vecql write(*,'(" q-vector length : ",G18.10)') gqc(1) if (tq0) then write(*,*) write(*,'(" Faraday angle parameters Δδ and Δβ written to FARADAY.OUT")') write(*,'(" MOKE Kerr angle written to KERR_TDDFT.OUT")') write(*,'(" Magnetic linear dichroism (MLD) spectrum written to MLD.OUT")') end if end if deallocate(gqc) end subroutine elk-7.2.42/src/PaxHeaders.21776/genhmlt.f900000644000000000000000000000013114061636517014701 xustar0030 mtime=1623670095.803101668 29 atime=1623670094.64810274 30 ctime=1623670095.803101668 elk-7.2.42/src/genhmlt.f900000644002504400250440000000420114061636517016734 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genhmlt(ik,vmt,vir,bmt,bir,kmat,pmat,h) use modmain use modtddft use modmpi implicit none ! arguments integer, intent(in) :: ik real(8), intent(in) :: vmt(npcmtmax,natmtot),vir(ngtot) real(8), intent(in) :: bmt(npcmtmax,natmtot,ndmag),bir(ngtot,ndmag) complex(8), intent(in) :: kmat(nstsv,nstsv),pmat(nstsv,nstsv,3) complex(8), intent(out) :: h(nstsv,nstsv) ! local variables integer ist,i real(8) ca,t1 ! automatic arrays integer idx(nstsv) ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfgk(:,:,:) allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) ! get the ground-state eigenvectors from file for input k-point call getevecfv('.OUT',ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv('.OUT',ik,vkl(:,ik),evecsv) ! find the matching coefficients allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! index to all states do ist=1,nstsv idx(ist)=ist end do ! calculate the wavefunctions for all states of the input k-point allocate(wfmt(npcmtmax,natmtot,nspinor,nstsv),wfgk(ngkmax,nspinor,nstsv)) call genwfsv(.false.,.true.,nstsv,idx,ngridg,igfft,ngk(:,ik),igkig(:,:,ik), & apwalm,evecfv,evecsv,wfmt,ngkmax,wfgk) deallocate(apwalm,evecfv,evecsv) ! Kohn-Sham potential and magnetic field matrix elements if (spinpol) then call genvbmatk(vmt,vir,bmt,bir,ngk(:,ik),igkig(:,:,ik),wfmt,ngkmax,wfgk,h) else call genvmatk(vmt,vir,ngk(:,ik),igkig(:,:,ik),wfmt,ngkmax,wfgk,h) end if ! add the DFT+U matrix elements if required call genvmmtsv(wfmt,h) deallocate(wfmt,wfgk) ! add the kinetic matrix elements in the second-variational basis h(:,:)=h(:,:)+kmat(:,:) ! coupling constant of the external A-field (-1/c) ca=-1.d0/solsc ! add the A-field matrix elements in the second-variational basis do i=1,3 t1=ca*afieldt(i,itimes) if (abs(t1).gt.1.d-10) h(:,:)=h(:,:)+t1*pmat(:,:,i) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/timestep.f900000644000000000000000000000013214061636517015076 xustar0030 mtime=1623670095.805101666 30 atime=1623670094.650102738 30 ctime=1623670095.805101666 elk-7.2.42/src/timestep.f900000644002504400250440000001116114061636517017133 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine timestep use modmain use modtddft use modmpi use modomp implicit none ! local variables integer ik,i,j,nthd real(8) ca,dt,t1 complex(8) z1,z2 ! automatic arrays real(8) w(nstsv) ! allocatable arrays real(8), allocatable :: vmt(:,:),vir(:),bmt(:,:,:) complex(8), allocatable :: evecsv(:,:),evectv(:,:),evecsvt(:,:) complex(8), allocatable :: kmat(:,:),pmat(:,:,:) complex(8), allocatable :: a(:,:),b(:,:),c(:,:) if (itimes.ge.ntimes) then write(*,*) write(*,'("Error(timestep): itimes >= ntimes : ",2I8)') itimes,ntimes write(*,*) stop end if allocate(vmt(npcmtmax,natmtot),vir(ngtot)) if (spinpol) allocate(bmt(npcmtmax,natmtot,ndmag)) ! generate the Kohn-Sham potential and magnetic field in spherical coordinates ! and multiply by the radial integration weights; also multiply the interstitial ! potential with the characteristic function call vblocal(vmt,vir,bmt) ! backup existing time-dependent Kohn-Sham eigenvectors if required call tdbackup ! time step length dt=times(itimes+1)-times(itimes) ! zero the kinetic energy engykn=0.d0 ! zero the total current jtot(:)=0.d0 ! loop over k-points call holdthd(nkpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evecsv,evectv,evecsvt) & !$OMP PRIVATE(kmat,pmat,w,a,b,c) & !$OMP PRIVATE(i,j,t1,z1,z2) & !$OMP NUM_THREADS(nthd) allocate(evecsv(nstsv,nstsv),evectv(nstsv,nstsv),evecsvt(nstsv,nstsv)) allocate(kmat(nstsv,nstsv),pmat(nstsv,nstsv,3)) allocate(a(nstsv,nstsv),b(nstsv,nstsv),c(nstsv,nstsv)) !$OMP DO do ik=1,nkpt ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle ! get the kinetic matrix elements from file call getkmat(ik,kmat) ! get the momentum matrix elements from file call getpmat(vkl(:,ik),pmat) ! generate the Hamiltonian matrix in the ground-state second-variational basis call genhmlt(ik,vmt,vir,bmt,bsir,kmat,pmat,evectv) ! diagonalise the Hamiltonian to get third-variational eigenvectors if (spinpol.and.(.not.ncmag)) then ! collinear case requires block diagonalisation call eveqnzh(nstfv,nstsv,evectv,w) i=nstfv+1 call eveqnzh(nstfv,nstsv,evectv(i,i),w(i)) do i=1,nstfv do j=1,nstfv evectv(i,j+nstfv)=0.d0 evectv(i+nstfv,j)=0.d0 end do end do else ! non-collinear or spin-unpolarised: full diagonalisation call eveqnzh(nstsv,nstsv,evectv,w) end if ! read in ground-state eigenvectors call getevecsv('.OUT',ik,vkl(:,ik),evecsv) ! convert third-variational eigenvectors to first-variational basis call zgemm('N','N',nstsv,nstsv,nstsv,zone,evecsv,nstsv,evectv,nstsv,zzero,a, & nstsv) ! time propagate instantaneous eigenvectors across one time step if (tdphi.eq.0.d0) then ! real time evolution do i=1,nstsv t1=-w(i)*dt z1=cmplx(cos(t1),sin(t1),8) b(:,i)=z1*a(:,i) end do else ! complex time evolution z2=cmplx(sin(tdphi),cos(tdphi),8) do i=1,nstsv t1=-w(i)*dt z1=exp(t1*z2) b(:,i)=z1*a(:,i) end do end if ! read in time-dependent Kohn-Sham eigenvectors (first-variational basis) call getevecsv(filext,ik,vkl(:,ik),evecsvt) ! apply time evolution operator call zgemm('C','N',nstsv,nstsv,nstsv,zone,a,nstsv,evecsvt,nstsv,zzero,c,nstsv) call zgemm('N','N',nstsv,nstsv,nstsv,zone,b,nstsv,c,nstsv,zzero,evecsvt,nstsv) ! orthonormalise the eigenvectors if required if (tdphi.ne.0.d0) call unitary(nstsv,evecsvt) ! add to the kinetic energy call engyknk(ik,kmat,evecsv,evecsvt) ! add to the total current call jtotk(ik,pmat,evecsv,evecsvt) ! write the new eigenvectors to file call putevecsv(filext,ik,evecsvt) end do !$OMP END DO deallocate(evecsv,evectv,evecsvt) deallocate(kmat,pmat,a,b,c) !$OMP END PARALLEL call freethd(nthd) deallocate(vmt,vir) if (spinpol) deallocate(bmt) ! add the kinetic energy and total current from each process and redistribute if (np_mpi.gt.1) then call mpi_allreduce(mpi_in_place,engykn,1,mpi_double_precision,mpi_sum,mpicom,& ierror) call mpi_allreduce(mpi_in_place,jtot,3,mpi_double_precision,mpi_sum,mpicom, & ierror) end if ! add the core kinetic energy engykn=engykn+engykncr ! coupling constant of the external A-field (-1/c) ca=-1.d0/solsc ! add the diamagnetic current to total do i=1,3 jtot(i)=jtot(i)+ca*afieldt(i,itimes)*(chgtot-chgstot(i)) end do ! symmetrise the vector call symvec(jtot) ! total current magnitude jtotm=sqrt(jtot(1)**2+jtot(2)**2+jtot(3)**2) ! write the time step to file if (mp_mpi) call writetimes ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/writetddos.f900000644000000000000000000000013214061636517015434 xustar0030 mtime=1623670095.806101665 30 atime=1623670094.652102736 30 ctime=1623670095.806101665 elk-7.2.42/src/writetddos.f900000644002504400250440000000254614061636517017500 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writetddos(fext) use modmain use modtddft implicit none ! arguments character(*), intent(in) :: fext ! local variables integer ik,ist,jst real(8) sm,t1 complex(8) z1 ! allocatable arrays real(8), allocatable :: occsvp(:,:) complex(8), allocatable :: evecsv(:,:),evecsvt(:,:) ! external functions complex(8), external :: zdotc allocate(occsvp(nstsv,nkpt)) do ik=1,nkpt allocate(evecsv(nstsv,nstsv),evecsvt(nstsv,nstsv)) ! read in ground-state eigenvectors call getevecsv('.OUT',ik,vkl(:,ik),evecsv) ! read in the time evolving eigenvectors call getevecsv('_TD.OUT',ik,vkl(:,ik),evecsvt) ! determine the time-dependent projected occupancies do ist=1,nstsv sm=0.d0 do jst=1,nstsv t1=occsv(jst,ik) if (abs(t1).lt.epsocc) cycle z1=zdotc(nstsv,evecsv(:,ist),1,evecsvt(:,jst),1) sm=sm+t1*(dble(z1)**2+aimag(z1)**2) end do occsvp(ist,ik)=sm end do ! write projected occupancies to file call putoccsv('P'//trim(fext),ik,occsvp(:,ik)) deallocate(evecsv,evecsvt) end do ! compute the effective electronic temperature call tdtemp(occsvp) ! write the DOS to file call dos(fext,.true.,occsvp) deallocate(occsvp) end subroutine elk-7.2.42/src/PaxHeaders.21776/writeafpdt.f900000644000000000000000000000013214061636517015415 xustar0030 mtime=1623670095.808101663 30 atime=1623670094.653102735 30 ctime=1623670095.808101663 elk-7.2.42/src/writeafpdt.f900000644002504400250440000000255614061636517017462 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeafpdt use modmain use modtddft implicit none ! local variables integer its,i real(8) ed,t1 ! conversion factor of energy density to J/cm^2 real(8), parameter :: ced=ha_si/(100.d0*br_si)**2 ! allocatable arrays real(8), allocatable :: f(:),g(:),pd(:) ! external functions real(8), external :: splint ! allocate local arrays allocate(f(ntimes),g(ntimes),pd(ntimes)) ! compute the power density at each time step pd(:)=0.d0 do i=1,3 f(:)=afieldt(i,:) call fderiv(1,ntimes,times,f,g) pd(:)=pd(:)+g(:)**2 end do t1=1.d0/(8.d0*pi*solsc) pd(:)=t1*pd(:) ! write the power density to file open(50,file='AFPDT.OUT',form='FORMATTED') do its=1,ntimes write(50,'(2G18.10)') times(its),pd(its) end do close(50) ! integrate power density to find the total energy density ed=splint(ntimes,times,pd) open(50,file='AFTED.OUT',form='FORMATTED') write(50,*) write(50,'("Total energy density : ",G18.10)') ed write(50,'(" in J/cm² : ",G18.10)') ed*ced close(50) write(*,*) write(*,'("Info(writeafpdt):")') write(*,'(" Power density of A-field written to AFPDT.OUT")') write(*,'(" Total energy density of A-field written to AFTED.OUT")') deallocate(f,g,pd) end subroutine elk-7.2.42/src/PaxHeaders.21776/readafindt.f900000644000000000000000000000013214061636517015345 xustar0030 mtime=1623670095.809101662 30 atime=1623670094.655102733 30 ctime=1623670095.809101662 elk-7.2.42/src/readafindt.f900000644002504400250440000000101414061636517017376 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Peter Elliott, J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readafindt use modtddft implicit none ! local variables integer ios open(50,file='AFINDT.OUT',form='FORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readafindt): error opening AFINDT.OUT")') write(*,*) stop end if read(50,*) afindt(:,:) close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/genvfxc.f900000644000000000000000000000013014061636517014702 xustar0029 mtime=1623670095.81110166 30 atime=1623670094.657102731 29 ctime=1623670095.81110166 elk-7.2.42/src/genvfxc.f900000644002504400250440000000330114061636517016736 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2011 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genvfxc(tq0,t3hw,gclgq,nm,vchi0,eps0,epsi,vfxc) use modmain use modtddft implicit none ! arguments logical, intent(in) :: tq0,t3hw real(8), intent(in) :: gclgq(ngrf) integer, intent(in) :: nm complex(8), intent(in) :: vchi0(nm,nm,nwrf) complex(8), intent(in) :: eps0(nm,nm,nwrf) complex(8), intent(in) :: epsi(nm,nm,nwrf) complex(8), intent(out) :: vfxc(nm,nm,nwrf) ! local variables integer iw,i,j complex(8) z1 ! allocatable arrays complex(8), allocatable :: a(:,:) ! compute v^(-1/2) f_xc v^(-1/2) select case(fxctype(1)) case(0,1) ! RPA vfxc(:,:,:)=0.d0 return case(3) ! ALDA if (tq0.and.t3hw) then call genvfxcg(gclgq,nm,vfxc(3,3,1)) ! the head and wings are zero vfxc(1:3,:,:)=0.d0 vfxc(4:,1:3,:)=0.d0 else call genvfxcg(gclgq,nm,vfxc) end if case(200) ! long-range contribution with dynamic correlations vfxc(:,:,:)=0.d0 do i=1,nm vfxc(i,i,:)=-(fxclrc(1)+fxclrc(2)*dble(wrf(:))**2)/fourpi end do case(210,211) ! bootstrap vfxc(:,:,:)=0.d0 if (tq0.and.t3hw) then z1=(eps0(1,1,1)+eps0(2,2,1)+eps0(3,3,1))/3.d0 else z1=eps0(1,1,1) end if z1=-1.d0/(z1-1.d0) do i=1,nm do j=1,nm vfxc(i,j,:)=z1*epsi(i,j,1) end do end do case default write(*,*) write(*,'("Error(genvfxc): fxctype not defined : ",3I8)') fxctype write(*,*) stop end select ! right multiply by v^1/2 chi0 v^1/2 allocate(a(nm,nm)) do iw=1,nwrf a(:,:)=vfxc(:,:,iw) call zgemm('N','N',nm,nm,nm,zone,a,nm,vchi0(:,:,iw),nm,zzero,vfxc(:,:,iw),nm) end do deallocate(a) end subroutine elk-7.2.42/src/PaxHeaders.21776/genfxcr.f900000644000000000000000000000013114061636517014677 xustar0030 mtime=1623670095.812101659 29 atime=1623670094.65810273 30 ctime=1623670095.812101659 elk-7.2.42/src/genfxcr.f900000644002504400250440000000625414061636517016744 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genfxcr(tsh,fxcmt,fxcir) use modmain use modtddft use modfxcifc implicit none ! arguments logical, intent(in) :: tsh real(8), intent(out) :: fxcmt(npmtmax,natmtot),fxcir(ngtot) ! local variables integer idm,is,ias integer nr,nri,ir,np,i,n real(8) t1 real(8), allocatable :: rho(:),rhoup(:),rhodn(:),mag(:,:) real(8), allocatable :: fxc(:),fxcuu(:),fxcud(:),fxcdd(:) ! number of independent spin components n=npmtmax allocate(rho(n),fxc(n)) if (spinpol) then allocate(mag(n,3)) n=max(n,ngtot) allocate(rhoup(n),rhodn(n)) allocate(fxcuu(n),fxcud(n),fxcdd(n)) end if !---------------------------! ! muffin-tin kernel ! !---------------------------! do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) np=npmt(is) ! compute the density in spherical coordinates call rbsht(nr,nri,rhomt(:,ias),rho) if (spinpol) then !------------------------! ! spin-polarised ! !------------------------! ! magnetisation in spherical coordinates do idm=1,ndmag call rbsht(nr,nri,magmt(:,ias,idm),mag(:,idm)) end do if (ncmag) then ! non-collinear (use Kubler's trick) do i=1,np ! compute rhoup=(rho+|m|)/2 and rhodn=(rho-|m|)/2 t1=sqrt(mag(i,1)**2+mag(i,2)**2+mag(i,3)**2) rhoup(i)=0.5d0*(rho(i)+t1) rhodn(i)=0.5d0*(rho(i)-t1) end do else ! collinear do i=1,np ! compute rhoup=(rho+m_z)/2 and rhodn=(rho-m_z)/2 rhoup(i)=0.5d0*(rho(i)+mag(i,1)) rhodn(i)=0.5d0*(rho(i)-mag(i,1)) end do end if ! compute fxc call fxcifc(fxctype,n=np,rhoup=rhoup,rhodn=rhodn,fxcuu=fxcuu,fxcud=fxcud, & fxcdd=fxcdd) ! form the scalar quantity dv/drho do i=1,np fxc(i)=0.25d0*(fxcuu(i)+2.d0*fxcud(i)+fxcdd(i)) end do else !--------------------------! ! spin-unpolarised ! !--------------------------! call fxcifc(fxctype,n=np,rho=rho,fxc=fxc) end if if (tsh) then ! convert fxc to spherical harmonics if required call rfsht(nr,nri,fxc,fxcmt(:,ias)) else fxcmt(1:np,ias)=fxc(1:np) end if end do !-----------------------------! ! interstitial kernel ! !-----------------------------! if (spinpol) then !------------------------! ! spin-polarised ! !------------------------! if (ncmag) then ! non-collinear do ir=1,ngtot t1=sqrt(magir(ir,1)**2+magir(ir,2)**2+magir(ir,3)**2) rhoup(ir)=0.5d0*(rhoir(ir)+t1) rhodn(ir)=0.5d0*(rhoir(ir)-t1) end do else ! collinear do ir=1,ngtot rhoup(ir)=0.5d0*(rhoir(ir)+magir(ir,1)) rhodn(ir)=0.5d0*(rhoir(ir)-magir(ir,1)) end do end if ! compute fxc call fxcifc(fxctype,n=ngtot,rhoup=rhoup,rhodn=rhodn,fxcuu=fxcuu,fxcud=fxcud, & fxcdd=fxcdd) do ir=1,ngtot fxcir(ir)=0.25d0*(fxcuu(ir)+2.d0*fxcud(ir)+fxcdd(ir)) end do else !--------------------------! ! spin-unpolarised ! !--------------------------! call fxcifc(fxctype,n=ngtot,rho=rhoir,fxc=fxcir) end if deallocate(rho,fxc) if (spinpol) then deallocate(mag,rhoup,rhodn) deallocate(fxcuu,fxcud,fxcdd) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/tdtemp.f900000644000000000000000000000013214061636517014541 xustar0030 mtime=1623670095.814101657 30 atime=1623670094.660102729 30 ctime=1623670095.814101657 elk-7.2.42/src/tdtemp.f900000644002504400250440000000241414061636517016577 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tdtemp(occsvp) use modmain use modtddft implicit none ! arguments real(8), intent(in) :: occsvp(nstsv,nkpt) ! local variables integer, parameter :: maxit=1000 integer ik,ist,it real(8), parameter :: eps=1.d-6 real(8) sw,dsw,sm,sp real(8) x,t1,t2,t3 ! external functions real(8), external :: sdelta_fd,stheta_fd ! initial smearing width sw=1.d-6 ! initial smearing width step size dsw=1.d-6 sp=0.d0 do it=1,maxit t1=1.d0/sw sm=0.d0 do ik=1,nkpt do ist=1,nstsv x=(efermi-evalsv(ist,ik))*t1 t2=occmax*stheta_fd(x) t3=sdelta_fd(x)*x*t1 sm=sm+(occsvp(ist,ik)-t2)*t3 end do end do if ((sm*sp).lt.0.d0) then dsw=-0.5d0*dsw if (abs(dsw).lt.eps) goto 10 else dsw=1.5d0*dsw end if sp=sm sw=sw+dsw if ((sw.lt.0.d0).or.(sw.gt.1.d6)) exit end do write(*,*) write(*,'("Warning(tdtemp): could not estimate effective temperature")') return 10 continue ! write effective temperature to file t1=sw/kboltz open(50,file='TDTEMP.OUT',form='FORMATTED',position='APPEND') write(50,'(2G18.10)') times(itimes),t1 close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/writetdlsj.f900000644000000000000000000000013214061636517015437 xustar0030 mtime=1623670095.815101657 30 atime=1623670094.662102727 30 ctime=1623670095.815101657 elk-7.2.42/src/writetdlsj.f900000644002504400250440000000234614061636517017501 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writetdlsj use modmain use modtddft use modmpi implicit none ! local variables integer is,ia,ias real(8) xl(3),xs(3) character(256) fext ! allocatable arrays complex(8), allocatable :: dmat(:,:,:,:,:) if (ntswrite(1).le.0) return if (mod(itimes-1,ntswrite(1)).ne.0) return if ((itimes.gt.1).and.(itimes.lt.ntswrite(2))) return allocate(dmat(lmmaxo,nspinor,lmmaxo,nspinor,natmtot)) ! generate the density matrix in each muffin-tin call gendmat(.false.,.false.,0,lmaxo,lmmaxo,dmat) if (mp_mpi) then write(fext,'("_TS",I8.8,".OUT")') itimes open(50,file='LSJ'//trim(fext),form='FORMATTED') do is=1,nspecies write(50,*) write(50,'("Species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) ias=idxas(ia,is) ! calculate the expectation value of L and S call dmatls(dmat(:,:,:,:,ias),xl,xs) write(50,'(" atom : ",I4)') ia write(50,'(" L : ",3G18.10)') xl(:) write(50,'(" S : ",3G18.10)') xs(:) write(50,'(" J : ",3G18.10)') xl(:)+xs(:) end do end do close(50) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/genspfxcr.f900000644000000000000000000000013214061636517015243 xustar0030 mtime=1623670095.817101655 30 atime=1623670094.663102726 30 ctime=1623670095.817101655 elk-7.2.42/src/genspfxcr.f900000644002504400250440000001205614061636517017304 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genspfxcr(tsh,fxcmt,fxcir) use modmain use modtddft use modfxcifc implicit none ! arguments logical, intent(in) :: tsh real(8), intent(out) :: fxcmt(npmtmax,natmtot,4,4),fxcir(ngtot,4,4) ! local variables integer idm,is,ias integer nr,nri,ir,np,i,j,n real(8) t1 ! allocatable arrays real(8), allocatable :: rho(:),rhoup(:),rhodn(:) real(8), allocatable :: mag(:,:),magu(:,:),magm(:) real(8), allocatable :: bxc(:,:),bxcp(:) real(8), allocatable :: fxcuu(:),fxcud(:),fxcdd(:) real(8), allocatable :: fxc(:,:,:) if (.not.spinpol) then write(*,*) write(*,'("Error(genspfxcr): spin-unpolarised calculation")') write(*,*) stop end if ! allocate local arrays n=npmtmax allocate(rho(n),mag(n,ndmag)) allocate(bxc(n,ndmag),fxc(n,4,4)) n=max(n,ngtot) allocate(rhoup(n),rhodn(n)) allocate(magu(3,n),magm(n),bxcp(n)) allocate(fxcuu(n),fxcud(n),fxcdd(n)) !---------------------------! ! muffin-tin kernel ! !---------------------------! do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) np=npmt(is) ! compute the density in spherical coordinates call rbsht(nr,nri,rhomt(:,ias),rho) do idm=1,ndmag ! magnetisation in spherical coordinates call rbsht(nr,nri,magmt(:,ias,idm),mag(:,idm)) ! B_xc in spherical coordinates call rbsht(nr,nri,bxcmt(:,ias,idm),bxc(:,idm)) end do if (ncmag) then ! non-collinear (use Kubler's trick) do i=1,np ! compute |m| magm(i)=sqrt(mag(i,1)**2+mag(i,2)**2+mag(i,3)**2) ! compute rhoup=(rho+|m|)/2 and rhodn=(rho-|m|)/2 rhoup(i)=0.5d0*(rho(i)+magm(i)) rhodn(i)=0.5d0*(rho(i)-magm(i)) ! unit vector m/|m| t1=1.d0/(magm(i)+1.d-8) magu(1,i)=t1*mag(i,1) magu(2,i)=t1*mag(i,2) magu(3,i)=t1*mag(i,3) ! compute B_xc.(m/|m|) bxcp(i)=bxc(i,1)*magu(1,i)+bxc(i,2)*magu(2,i)+bxc(i,3)*magu(3,i) end do else ! collinear do i=1,np ! compute |m| = |m_z| magm(i)=abs(mag(i,1)) ! compute rhoup=(rho+|m|)/2 and rhodn=(rho-|m|)/2 rhoup(i)=0.5d0*(rho(i)+magm(i)) rhodn(i)=0.5d0*(rho(i)-magm(i)) ! unit vector m/|m| magu(1,i)=0.d0 magu(2,i)=0.d0 if (mag(i,1).gt.0.d0) then magu(3,i)=1.d0 else magu(3,i)=-1.d0 end if ! compute B_xc.(m/|m|) bxcp(i)=bxc(i,1)*magu(3,i) end do end if ! compute f_xc in U(2) x U(2) basis call fxcifc(fxctype,n=np,rhoup=rhoup,rhodn=rhodn,fxcuu=fxcuu,fxcud=fxcud, & fxcdd=fxcdd) ! transform f_xc to O(1) x O(3) basis (upper triangular part) call tfm2213(np,fxcuu,fxcud,fxcdd,magu,magm,bxcp,npmtmax,fxc) do i=1,4 do j=i,4 if (tsh) then ! convert to spherical harmonics if required call rfsht(nr,nri,fxc(:,i,j),fxcmt(:,ias,i,j)) else call dcopy(np,fxc(:,i,j),fxcmt(:,ias,i,j),1) end if end do end do end do !-----------------------------! ! interstitial kernel ! !-----------------------------! if (ncmag) then ! non-collinear do ir=1,ngtot magm(ir)=sqrt(magir(ir,1)**2+magir(ir,2)**2+magir(ir,3)**2) rhoup(ir)=0.5d0*(rhoir(ir)+magm(ir)) rhodn(ir)=0.5d0*(rhoir(ir)-magm(ir)) t1=1.d0/(magm(ir)+1.d-8) magu(1,ir)=t1*magir(ir,1) magu(2,ir)=t1*magir(ir,2) magu(3,ir)=t1*magir(ir,3) ! compute B_xc.(m/|m|) bxcp(ir)=bxcir(ir,1)*magu(1,ir) & +bxcir(ir,2)*magu(2,ir) & +bxcir(ir,3)*magu(3,ir) end do else ! collinear do ir=1,ngtot magm(ir)=abs(magir(ir,1)) rhoup(ir)=0.5d0*(rhoir(ir)+magm(ir)) rhodn(ir)=0.5d0*(rhoir(ir)-magm(ir)) magu(1,ir)=0.d0 magu(2,ir)=0.d0 if (magir(ir,1).gt.0.d0) then magu(3,ir)=1.d0 else magu(3,ir)=-1.d0 end if ! compute B_xc.(m/|m|) bxcp(ir)=bxcir(ir,1)*magu(3,ir) end do end if ! compute f_xc in U(2) x U(2) basis call fxcifc(fxctype,n=ngtot,rhoup=rhoup,rhodn=rhodn,fxcuu=fxcuu,fxcud=fxcud, & fxcdd=fxcdd) ! transform f_xc to O(1) x O(3) basis call tfm2213(ngtot,fxcuu,fxcud,fxcdd,magu,magm,bxcp,ngtot,fxcir) deallocate(rho,mag,bxc,fxc) deallocate(rhoup,rhodn) deallocate(magu,magm,bxcp) deallocate(fxcuu,fxcud,fxcdd) return contains pure subroutine tfm2213(n,fxcuu,fxcud,fxcdd,magu,magm,bxcp,ld,fxc) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: fxcuu(n),fxcud(n),fxcdd(n) real(8), intent(in) :: magu(3,n),magm(n),bxcp(n) integer, intent(in) :: ld real(8), intent(out) :: fxc(ld,4,4) ! local variables integer i real(8) t1,t2 do i=1,n ! charge-charge fxc(i,1,1)=0.25d0*(fxcuu(i)+2.d0*fxcud(i)+fxcdd(i)) ! charge-spin t1=0.25d0*(fxcuu(i)-fxcdd(i)) fxc(i,1,2)=t1*magu(1,i) fxc(i,1,3)=t1*magu(2,i) fxc(i,1,4)=t1*magu(3,i) ! spin-spin if (magm(i).gt.1.d-14) then t1=bxcp(i)/magm(i) else t1=0.d0 end if t2=0.25d0*(fxcuu(i)-2.d0*fxcud(i)+fxcdd(i))-t1 fxc(i,2,2)=t2*magu(1,i)*magu(1,i)+t1 fxc(i,2,3)=t2*magu(1,i)*magu(2,i) fxc(i,2,4)=t2*magu(1,i)*magu(3,i) fxc(i,3,3)=t2*magu(2,i)*magu(2,i)+t1 fxc(i,3,4)=t2*magu(2,i)*magu(3,i) fxc(i,4,4)=t2*magu(3,i)*magu(3,i)+t1 end do end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/genvfxcg.f900000644000000000000000000000013214061636517015053 xustar0030 mtime=1623670095.818101654 30 atime=1623670094.665102724 30 ctime=1623670095.818101654 elk-7.2.42/src/genvfxcg.f900000644002504400250440000000216414061636517017113 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2012 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genvfxcg(gclgq,nm,vfxc) use modmain implicit none ! arguments real(8), intent(in) :: gclgq(ngrf) integer, intent(in) :: nm complex(8), intent(out) :: vfxc(nm,nm,nwrf) ! local variables integer ig,jg,kg,iv(3) ! allocatable arrays real(8), allocatable :: fxcmt(:,:),fxcir(:) complex(8), allocatable :: fxcg(:) allocate(fxcmt(npmtmax,natmtot),fxcir(ngtot)) allocate(fxcg(ngtot)) ! generate the kernel f_xc in real-space call genfxcr(.true.,fxcmt,fxcir) ! Fourier transform the kernel to G-space call zftrf(ngtot,ivg,vgc,fxcmt,fxcir,fxcg) do ig=1,ngrf do jg=1,ngrf iv(:)=ivg(:,ig)-ivg(:,jg) if ((iv(1).ge.intgv(1,1)).and.(iv(1).le.intgv(2,1)).and. & (iv(2).ge.intgv(1,2)).and.(iv(2).le.intgv(2,2)).and. & (iv(3).ge.intgv(1,3)).and.(iv(3).le.intgv(2,3))) then kg=ivgig(iv(1),iv(2),iv(3)) vfxc(ig,jg,:)=fxcg(kg)/(gclgq(ig)*gclgq(jg)) end if end do end do deallocate(fxcmt,fxcir,fxcg) end subroutine elk-7.2.42/src/PaxHeaders.21776/tddftsplr.f900000644000000000000000000000013214061636517015252 xustar0030 mtime=1623670095.820101652 30 atime=1623670094.666102723 30 ctime=1623670095.820101652 elk-7.2.42/src/tddftsplr.f900000644002504400250440000002072114061636517017311 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tddftsplr use modmain use modtest use modmpi use modomp implicit none ! local variables integer ik,isym,iq,iw integer ig,jg,i,j,n integer nthd real(8) v(3) complex(8) a(4,4),b(4,4),z1 character(256) fname ! allocatable arrays integer(8), allocatable :: lock(:) real(8), allocatable :: vgqc(:,:),gqc(:),gclgq(:),jlgqr(:,:,:) complex(8), allocatable :: ylmgq(:,:),sfacgq(:,:) complex(8), allocatable :: chi(:,:,:,:,:),chit(:),fxc(:,:,:,:) complex(8), allocatable :: c(:,:),d(:,:,:,:) if (.not.spinpol) then write(*,*) write(*,'("Error(tddftsplr): spin-unpolarised calculation")') write(*,*) stop end if ! initialise global variables call init0 call init1 call init2 call init3 ! check q-vector is commensurate with k-point grid v(:)=dble(ngridk(:))*vecql(:) v(:)=abs(v(:)-nint(v(:))) if ((v(1).gt.epslat).or.(v(2).gt.epslat).or.(v(3).gt.epslat)) then write(*,*) write(*,'("Error(tddftsplr): q-vector incommensurate with k-point grid")') write(*,'(" ngridk : ",3I6)') ngridk write(*,'(" vecql : ",3G18.10)') vecql write(*,*) stop end if ! find the equivalent reduced q-point call findqpt(vecql,isym,iq) ! read density and potentials from file call readstate ! read Fermi energy from a file call readfermi ! find the new linearisation energies call linengy ! generate the APW radial functions call genapwfr ! generate the local-orbital radial functions call genlofr ! get the eigenvalues and occupancies from file do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) call getoccsv(filext,ik,vkl(:,ik),occsv(:,ik)) end do ! generate the G+q-vectors and related functions allocate(vgqc(3,ngrf),gqc(ngrf),jlgqr(njcmax,nspecies,ngrf)) allocate(ylmgq(lmmaxo,ngrf),sfacgq(ngrf,natmtot)) call gengqf(ngrf,vecqc,vgqc,gqc,jlgqr,ylmgq,sfacgq) deallocate(vgqc) ! initialise the OpenMP locks allocate(lock(nwrf)) do iw=1,nwrf call omp_init_lock(lock(iw)) end do ! compute chi0 allocate(chi(ngrf,4,ngrf,4,nwrf)) chi(:,:,:,:,:)=0.d0 call holdthd(nkptnr/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) !$OMP DO do ik=1,nkptnr ! distribute among MPI processes if (mod(ik-1,np_mpi).ne.lp_mpi) cycle !$OMP CRITICAL(tddftsplr_) write(*,'("Info(tddftsplr): ",I6," of ",I6," k-points")') ik,nkptnr !$OMP END CRITICAL(tddftsplr_) call genspchi0(ik,lock,scissor,vecql,jlgqr,ylmgq,sfacgq,chi) end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) ! destroy the OpenMP locks do iw=1,nwrf call omp_destroy_lock(lock(iw)) end do deallocate(lock) ! add chi0 from each process and redistribute if (np_mpi.gt.1) then n=ngrf*4*ngrf*4*nwrf call mpi_allreduce(mpi_in_place,chi,n,mpi_double_complex,mpi_sum,mpicom, & ierror) end if ! transform chi0 from 2x2 to 1x3 basis do iw=1,nwrf do ig=1,ngrf do jg=1,ngrf a(:,:)=chi(ig,:,jg,:,iw) call tfm2213(a,b) chi(ig,:,jg,:,iw)=b(:,:) end do end do end do ! generate transverse chi0 for the collinear case if (.not.ncmag) then allocate(chit(nwrf)) do iw=1,nwrf a(:,:)=chi(1,:,1,:,iw) call tfm13t(a,b) chit(iw)=b(2,2) end do end if ! write chi0 to file if (mp_mpi) then ! write chi0 to file in 1x3 basis do i=1,4 do j=1,4 write(fname,'("CHI0_",2I1,".OUT")') i-1,j-1 open(50,file=trim(fname),form='FORMATTED',action='WRITE') do iw=1,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(chi(1,i,1,j,iw)) end do write(50,*) do iw=1,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(chi(1,i,1,j,iw)) end do close(50) end do end do ! write transverse chi0 for collinear case if (.not.ncmag) then open(50,file='CHI0_T.OUT',form='FORMATTED',action='WRITE') do iw=1,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(chit(iw)) end do write(50,*) do iw=1,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(chit(iw)) end do close(50) end if end if ! compute f_xc in G-space allocate(fxc(ngrf,4,ngrf,4)) call genspfxcg(fxc) ! generate the Coulomb Green's function in G+q-space regularised for q=0 allocate(gclgq(ngrf)) call gengclgq(.true.,iq,ngrf,gqc,gclgq) ! add the regularised Coulomb interaction to f_xc to give f_Hxc do ig=1,ngrf fxc(ig,1,ig,1)=fxc(ig,1,ig,1)+gclgq(ig) end do deallocate(gclgq) ! matrix size n=4*ngrf allocate(c(n,n),d(ngrf,4,ngrf,4)) ! loop over frequencies do iw=1,nwrf ! multiply f_Hxc by -chi0 from the left z1=-1.d0 call zgemm('N','N',n,n,n,z1,chi(:,:,:,:,iw),n,fxc,n,zzero,c,n) ! add the identity do i=1,n c(i,i)=c(i,i)+1.d0 end do ! invert the matrix call zminv(n,c) ! multiply by chi0 on the right and store in chi call zgemm('N','N',n,n,n,zone,c,n,chi(:,:,:,:,iw),n,zzero,d,n) chi(:,:,:,:,iw)=d(:,:,:,:) end do deallocate(c,d) ! generate transverse chi for the collinear case if (.not.ncmag) then do iw=1,nwrf a(:,:)=chi(1,:,1,:,iw) call tfm13t(a,b) chit(iw)=b(2,2) end do end if if (mp_mpi) then ! write the complete chi matrix if required if (task.eq.331) then open(120,file='CHI.OUT',form='UNFORMATTED',action='WRITE') write(120) chi close(120) end if ! write chi for G = G' = 0 in the 1x3 basis do i=1,4 do j=1,4 write(fname,'("CHI_",2I1,".OUT")') i-1,j-1 open(50,file=trim(fname),form='FORMATTED',action='WRITE') do iw=1,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(chi(1,i,1,j,iw)) end do write(50,*) do iw=1,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(chi(1,i,1,j,iw)) end do close(50) end do end do ! write transverse chi for collinear case if (.not.ncmag) then open(50,file='CHI_T.OUT',form='FORMATTED',action='WRITE') do iw=1,nwrf write(50,'(2G18.10)') dble(wrf(iw)),dble(chit(iw)) end do write(50,*) do iw=1,nwrf write(50,'(2G18.10)') dble(wrf(iw)),aimag(chit(iw)) end do close(50) end if write(*,*) write(*,'("Info(tddftsplr):")') write(*,'(" Spin-dependent response function chi_ij(G,G'',q,w) written to & &CHI_ij.OUT")') write(*,'(" for i,j = 0-3; G = G'' = 0; and all wplot frequencies")') write(*,'(" q-vector (lattice coordinates) : ")') write(*,'(3G18.10)') vecql write(*,'(" q-vector length : ",G18.10)') gqc(1) write(*,*) write(*,'(" The elements of chi labeled by (i,j) form the 4x4 matrix :")') write(*,*) write(*,'(" (_|_ _ _)")') write(*,'(" chi(G,G'',q,w) = ( | )")') write(*,'(" ( | )")') write(*,'(" ( | )")') write(*,*) write(*,'(" (0,0) is the charge-charge response drho/dv")') write(*,'(" (0,1-3) is the charge-magnetisation response drho/dB")') write(*,'(" (1-3,0) is the magnetisation-charge response dm/v")') write(*,'(" (1-3,1-3) is the magnetisation-magnetisation response dm/dB")') write(*,*) write(*,'(" Non-interacting Kohn-Sham reponse function written to & &CHI0_ij.OUT")') if (.not.ncmag) then write(*,*) write(*,'(" Transverse components corresponding to m_+- = m_x +- im_y")') write(*,'(" written to CHI_T.OUT and CHI0_T.OUT")') end if if (task.eq.331) then write(*,*) write(*,'(" Complete response function for all G, G'' written to binary & &file CHI.OUT")') write(*,'(" (array index ordering changed from version 4.5.16 onwards)")') end if end if ! write transverse response to test file call writetest(330,'transverse response function',nv=nwrf,tol=1.d-2,zva=chit) deallocate(gqc,ylmgq,sfacgq,chi,fxc) if (.not.ncmag) deallocate(chit) return contains pure subroutine tfm2213(a,b) implicit none ! arguments complex(8), intent(in) :: a(4,4) complex(8), intent(out) :: b(4,4) ! local variables integer i,j complex(8) c(4,4),z1 do i=1,4 c(i,1)=a(i,1)+a(i,4) c(i,2)=a(i,2)+a(i,3) z1=a(i,2)-a(i,3) c(i,3)=cmplx(aimag(z1),-dble(z1),8) c(i,4)=a(i,1)-a(i,4) end do do j=1,4 b(1,j)=c(1,j)+c(4,j) b(2,j)=c(2,j)+c(3,j) z1=c(2,j)-c(3,j) b(3,j)=cmplx(-aimag(z1),dble(z1),8) b(4,j)=c(1,j)-c(4,j) end do end subroutine pure subroutine tfm13t(a,b) implicit none ! arguments complex(8), intent(in) :: a(4,4) complex(8), intent(out) :: b(4,4) ! local variables integer i,j complex(8) c(4,4),z1 do i=1,4 c(i,1)=a(i,1) z1=a(i,3) c(i,2)=a(i,2)+cmplx(aimag(z1),-dble(z1),8) c(i,3)=a(i,2)+cmplx(-aimag(z1),dble(z1),8) c(i,4)=a(i,4) end do do j=1,4 b(1,j)=c(1,j) z1=c(3,j) b(2,j)=c(2,j)+cmplx(-aimag(z1),dble(z1),8) b(3,j)=c(2,j)+cmplx(aimag(z1),-dble(z1),8) b(4,j)=c(4,j) end do end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/genspfxcg.f900000644000000000000000000000013014061636517015226 xustar0029 mtime=1623670095.82210165 30 atime=1623670094.668102721 29 ctime=1623670095.82210165 elk-7.2.42/src/genspfxcg.f900000644002504400250440000000233614061636517017271 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2013 S. Sharma, J. K. Dewhurst and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genspfxcg(fxc) use modmain implicit none ! arguments complex(8), intent(out) :: fxc(ngrf,4,ngrf,4) ! local variables integer ig,jg,kg integer iv(3),i,j complex(8) z1 ! allocatable arrays real(8), allocatable :: fxcmt(:,:,:,:),fxcir(:,:,:) complex(8), allocatable :: fxcg(:) allocate(fxcmt(npmtmax,natmtot,4,4),fxcir(ngtot,4,4)) allocate(fxcg(ngtot)) ! generate the kernel f_xc in real-space call genspfxcr(.true.,fxcmt,fxcir) ! Fourier transform the kernel to G-space do i=1,4 do j=i,4 call zftrf(ngtot,ivg,vgc,fxcmt(:,:,i,j),fxcir(:,i,j),fxcg) do ig=1,ngrf do jg=1,ngrf iv(:)=ivg(:,ig)-ivg(:,jg) if ((iv(1).ge.intgv(1,1)).and.(iv(1).le.intgv(2,1)).and. & (iv(2).ge.intgv(1,2)).and.(iv(2).le.intgv(2,2)).and. & (iv(3).ge.intgv(1,3)).and.(iv(3).le.intgv(2,3))) then kg=ivgig(iv(1),iv(2),iv(3)) z1=fxcg(kg) fxc(ig,i,jg,j)=z1 fxc(jg,j,ig,i)=conjg(z1) end if end do end do end do end do deallocate(fxcmt,fxcir,fxcg) end subroutine elk-7.2.42/src/PaxHeaders.21776/genafieldt.f900000644000000000000000000000013214061636517015346 xustar0030 mtime=1623670095.823101649 30 atime=1623670094.670102719 30 ctime=1623670095.823101649 elk-7.2.42/src/genafieldt.f900000644002504400250440000001114114061636517017401 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: genafieldt ! !INTERFACE: subroutine genafieldt ! !USES: use modmain use modtddft ! !DESCRIPTION: ! Generates a time-dependent vector potential, ${\bf A}(t)$, representing a ! laser pulse and stores it in {\tt AFIELDT.OUT}. The vector potential is ! constructed from a sum of sinusoidal waves, each modulated with a Gaussian ! envelope function: ! $$ {\bf A}(t)={\bf A}_0 ! \frac{e^{-(t-t_0)^2/2\sigma^2}}{\sigma\sqrt{2\pi}} ! \sin(\omega(t-t_0)+\phi). $$ ! Seven real numbers have to be specified for each pulse, namely the vector ! amplitude ${\bf A}_0$, peak time $t_0$, full-width at half-maximum ! $d=2\sqrt{2\ln 2}\sigma$, frequency $\omega$ and phase $\phi$. ! ! !REVISION HISTORY: ! Created May 2012 (K. Krieger) ! Modified, January 2014 (S. Sharma) ! Modified, February 2014 (JKD) !EOP !BOC implicit none ! local variables integer its,i real(8) a0(3),t0,d,w,phi,rc real(8) ft,ppd,s,t,t1,t2,t3,t4 ! conversion factor of power density to W/cm^2 real(8), parameter :: cpd=ha_si/(t_si*(100.d0*br_si)**2) ! generate the time step grid call gentimes open(50,file='TD_INFO.OUT',form='FORMATTED') write(50,*) write(50,'("(All units are atomic unless otherwise specified)")') write(50,*) write(50,'("1 atomic unit of time is ",G18.10," attoseconds")') t_si*1.d18 write(50,*) write(50,'("Total simulation time : ",G18.10)') tstime write(50,'(" in attoseconds : ",G18.10)') tstime*t_si*1.d18 write(50,*) write(50,'("Time step length : ",G18.10)') dtimes write(50,'(" in attoseconds : ",G18.10)') dtimes*t_si*1.d18 write(50,*) write(50,'("Number of time steps : ",I8)') ntimes write(50,*) write(50,'("Number of laser pulses : ",I6)') npulse write(50,'("Number of ramps : ",I6)') nramp ! allocate and zero time-dependent A-field array if (allocated(afieldt)) deallocate(afieldt) allocate(afieldt(3,ntimes)) afieldt(:,:)=0.d0 ! loop over laser pulses do i=1,npulse ! vector amplitude a0(1:3)=pulse(1:3,i) ! frequency w=pulse(4,i) ! phase phi=pulse(5,i) ! chirp rate rc=pulse(6,i) ! peak time t0=pulse(7,i) ! full-width at half-maximum d=pulse(8,i) ! sigma s=d/(2.d0*sqrt(2.d0*log(2.d0))) ! write information to TD_INFO.OUT write(50,*) write(50,'("Pulse : ",I6)') i write(50,'(" vector amplitude : ",3G18.10)') a0(:) write(50,'(" laser frequency : ",G18.10)') w write(50,'(" in eV : ",G18.10)') w*ha_ev write(50,'(" laser wavelength (Angstroms) : ",G18.10)') 1.d10/(w*ha_im) write(50,'(" phase (degrees) : ",G18.10)') phi write(50,'(" chirp rate : ",G18.10)') rc write(50,'(" peak time : ",G18.10)') t0 write(50,'(" full-width at half-maximum : ",G18.10)') d write(50,'(" Gaussian sigma = FWHM/2*sqrt(2*ln 2) : ",G18.10)') s t1=a0(1)**2+a0(2)**2+a0(3)**2 ppd=t1*(w**2)/(8.d0*pi*solsc) write(50,'(" peak laser power density : ",G18.10)') ppd write(50,'(" in W/cm² : ",G18.10)') ppd*cpd ! loop over time steps do its=1,ntimes t=times(its) t1=t-t0 t2=-0.5d0*(t1/s)**2 t3=w*t1+phi*pi/180.d0+0.5d0*rc*t**2 ft=exp(t2)*sin(t3) if (abs(ft).lt.1.d-20) ft=0.d0 afieldt(:,its)=afieldt(:,its)+a0(:)*ft end do end do ! loop over ramps do i=1,nramp ! vector amplitude a0(1:3)=ramp(1:3,i) ! ramp start time t0=ramp(4,i) ! linear coefficient t1=ramp(5,i) ! quadratic coefficient t2=ramp(6,i) ! cubic coefficient t3=ramp(7,i) ! quartic coefficient t4=ramp(8,i) ! write information to TD_INFO.OUT write(50,*) write(50,'("Ramp : ",I6)') i write(50,'(" vector amplitude : ",3G18.10)') a0(:) write(50,'(" ramp start time : ",G18.10)') t0 write(50,'(" coefficients : ",4G18.10)') t1,t2,t3,t4 ! loop over time steps do its=1,ntimes t=times(its)-t0 if (t.gt.0.d0) then ft=t*(t1+t*(t2+t*(t3+t*t4))) afieldt(:,its)=afieldt(:,its)+a0(:)*ft end if end do end do close(50) ! write the vector potential to AFIELDT.OUT open(50,file='AFIELDT.OUT',form='FORMATTED') write(50,'(I8," : number of time steps")') ntimes do its=1,ntimes write(50,'(I8,4G18.10)') its,times(its),afieldt(:,its) end do close(50) write(*,*) write(*,'("Info(genafieldt):")') write(*,'(" Time-dependent A-field written to AFIELDT.OUT")') write(*,'(" Laser pulse and ramp parameters written to TD_INFO.OUT")') write(*,*) write(*,'(" 1 atomic unit of time is ",G18.10," attoseconds")') t_si*1.d18 write(*,'(" Total simulation time : ",G18.10)') tstime write(*,'(" in attoseconds : ",G18.10)') tstime*t_si*1.d18 deallocate(times,afieldt) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writetddft.f900000644000000000000000000000013214061636517015424 xustar0030 mtime=1623670095.825101647 30 atime=1623670094.672102717 30 ctime=1623670095.825101647 elk-7.2.42/src/writetddft.f900000644002504400250440000001502114061636517017460 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2014 K. Krieger, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writetddft use modmain use modtddft use moddftu implicit none ! local variables integer is,ia,ias real(8) vc(3),vl(3) character(256) fext ! allocatable arrays real(8), allocatable :: rvfmt(:,:,:),rvfir(:,:) ! file extension write(fext,'("_TS",I8.8,".OUT")') itimes ! delete all files at first time step if (itimes.le.1) then open(50,file='CHARGEMT_TD.OUT') close(50,status='DELETE') open(50,file='CHARGEIR_TD.OUT') close(50,status='DELETE') open(50,file='MOMENT_TD.OUT') close(50,status='DELETE') open(50,file='MOMENTM_TD.OUT') close(50,status='DELETE') open(50,file='MOMENTMT_TD.OUT') close(50,status='DELETE') open(50,file='MOMENTIR_TD.OUT') close(50,status='DELETE') open(50,file='JTOT_TD.OUT') close(50,status='DELETE') open(50,file='JTOTM_TD.OUT') close(50,status='DELETE') open(50,file='TOTENERGY_TD.OUT') close(50,status='DELETE') if (tddos) then open(50,file='TDTEMP.OUT') close(50,status='DELETE') end if if (tdlsj) then open(50,file='TDLSJ.OUT') close(50,status='DELETE') end if if (tforce) then open(50,file='FORCETOT_TD.OUT') close(50,status='DELETE') end if if (tdatpos) then open(50,file='ATPOSL_TD.OUT') close(50,status='DELETE') end if if (tafindt) then open(50,file='AFIND_TD.OUT') close(50,status='DELETE') end if end if ! muffin-tin charges open(50,file='CHARGEMT_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(G18.10)') times(itimes) do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) write(50,'(2I4,G18.10)') is,ia,chgmt(ias) end do end do write(50,*) close(50) ! interstitial charge open(50,file='CHARGEIR_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(2G18.10)') times(itimes),chgir close(50) ! spin moment open(50,file='MOMENT_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(4G18.10)') times(itimes),momtot(1:ndmag) close(50) open(50,file='MOMENTM_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(2G18.10)') times(itimes),momtotm close(50) ! muffin-tin moments open(50,file='MOMENTMT_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(G18.10)') times(itimes) do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) write(50,'(2I4,3G18.10)') is,ia,mommt(1:ndmag,ias) end do end do write(50,*) close(50) ! interstitial moment open(50,file='MOMENTIR_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(4G18.10)') times(itimes),momir(1:ndmag) close(50) ! total current open(50,file='JTOT_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(4G18.10)') times(itimes),jtot(:) close(50) ! total current magnitude open(50,file='JTOTM_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(4G18.10)') times(itimes),jtotm close(50) ! total energy open(50,file='TOTENERGY_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(2G18.10)') times(itimes),engytot close(50) ! total force if (tforce) then open(50,file='FORCETOT_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(I8,G18.10)') itimes,times(itimes) do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) write(50,'(2I4,3G18.10)') is,ia,forcetot(:,ias) end do end do close(50) end if ! write the time-dependent atomic positions in lattice coordinates if (tdatpos) then open(50,file='ATPOSL_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(I8,G18.10)') itimes,times(itimes) do is=1,nspecies do ia=1,natoms(is) vc(:)=atposc(:,ia,is)+datposc(:,0,ia,is) call r3mv(ainv,vc,vl) write(50,'(2I4,3G18.10)') is,ia,vl(:) end do end do close(50) end if if (tafindt) then open(50,file='AFIND_TD.OUT',form='FORMATTED',position='APPEND') write(50,'(4G18.10)') times(itimes),afindt(:,0) close(50) end if ! write optional quantities if (ntswrite(1).le.0) return if (mod(itimes-1,ntswrite(1)).ne.0) return if ((itimes.gt.1).and.(itimes.lt.ntswrite(2))) return ! charge density in 1D if (tdrho1d) then open(50,file='RHO1D'//trim(fext),form='FORMATTED',action='WRITE') open(51,file='RHOLINES.OUT',form='FORMATTED',action='WRITE') call plot1d(50,51,1,rhomt,rhoir) close(50) close(51) end if ! charge density in 2D if (tdrho2d) then open(50,file='RHO2D'//trim(fext),form='FORMATTED',action='WRITE') call plot2d(.false.,50,1,rhomt,rhoir) close(50) end if ! charge density in 3D if (tdrho3d) then open(50,file='RHO3D'//trim(fext),form='FORMATTED',action='WRITE') call plot3d(50,1,rhomt,rhoir) close(50) end if ! magnetisation in 1D, 2D or 3D if ((tdmag1d.or.tdmag2d.or.tdmag3d).and.(spinpol)) then allocate(rvfmt(npmtmax,natmtot,3),rvfir(ngtot,3)) if (ncmag) then ! non-collinear rvfmt(:,:,:)=magmt(:,:,:) rvfir(:,:)=magir(:,:) else ! collinear rvfmt(:,:,1:2)=0.d0 rvfir(:,1:2)=0.d0 rvfmt(:,:,3)=magmt(:,:,1) rvfir(:,3)=magir(:,1) end if if (tdmag1d) then open(50,file='MAG1D'//trim(fext),form='FORMATTED',action='WRITE') open(51,file='MAGLINES.OUT',form='FORMATTED',action='WRITE') call plot1d(50,51,3,rvfmt,rvfir) close(50) close(51) end if if (tdmag2d) then open(50,file='MAG2D'//trim(fext),form='FORMATTED',action='WRITE') call plot2d(.true.,50,3,rvfmt,rvfir) close(50) end if if (tdmag3d) then open(50,file='MAG3D'//trim(fext),form='FORMATTED',action='WRITE') call plot3d(50,3,rvfmt,rvfir) close(50) end if deallocate(rvfmt,rvfir) end if ! gauge-invariant current density in 1D if (tdjr1d) then open(50,file='JR1D'//trim(fext),form='FORMATTED',action='WRITE') open(51,file='JRLINES.OUT',form='FORMATTED',action='WRITE') call plot1d(50,51,3,jrmt,jrir) close(50) close(51) end if ! gauge-invariant current density in 2D if (tdjr2d) then open(50,file='JR2D'//trim(fext),form='FORMATTED',action='WRITE') call plot2d(.true.,50,3,jrmt,jrir) close(50) end if ! gauge-invariant current density in 3D if (tdjr3d) then open(50,file='JR3D'//trim(fext),form='FORMATTED',action='WRITE') call plot3d(50,3,jrmt,jrir) close(50) end if ! calculate and write tensor moments if (dftu.ne.0) then if (tmwrite) then open(50,file='TMDFTU'//trim(fext),form='FORMATTED',action='WRITE') if (spinorb) then call writetm3du(50) else call writetm2du(50) end if close(50) end if end if ! write time-dependent DOS if (tddos) then call writetddos(fext) end if ! write the atomic forces if (tforce) then open(50,file='FORCES'//trim(fext),form='FORMATTED',action='WRITE') call writeforces(50) close(50) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/dielectric_tdrt.f900000644000000000000000000000013214061636517016410 xustar0030 mtime=1623670095.826101646 30 atime=1623670094.673102717 30 ctime=1623670095.826101646 elk-7.2.42/src/dielectric_tdrt.f900000644002504400250440000000717214061636517020454 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine dielectric_tdrt use modmain use modtddft implicit none ! local variables integer nts,its0,its integer iw,i,j real(8) w1,w2,a0,t0,t1,t2 complex(8) eta,z1,z2 character(256) fname ! allocatable arrays real(8), allocatable :: w(:),wt(:),jt(:,:) real(8), allocatable :: f1(:),f2(:),g(:) complex(8), allocatable :: ew(:,:),jw(:,:),eps(:) ! initialise global variables call init0 call init1 ! generate energy grid (always non-negative) allocate(w(nwplot)) w1=max(wplot(1),0.d0) w2=max(wplot(2),w1) t1=(w2-w1)/dble(nwplot) do iw=1,nwplot w(iw)=w1+t1*dble(iw-1) end do ! i divided by the complex relaxation time eta=cmplx(0.d0,swidth,8) ! find the starting time step for the Fourier transform its0=1 do its=2,ntimes if (times(its).gt.t0tdlr) then its0=its-1 exit end if end do nts=ntimes-its0+1 ! determine the weights for the spline integration allocate(wt(ntimes)) call wsplint(nts,times(its0),wt(its0)) ! compute the electric field from E = -1/c dA/dt and Fourier transform allocate(f1(ntimes),f2(ntimes),g(ntimes)) allocate(ew(nwplot,3)) t0=-1.d0/solsc do i=1,3 f1(:)=afieldt(i,:) call fderiv(1,ntimes,times,f1,g) ! constant term corresponding to instantaneous A-field at t=0 a0=f1(1) if (task.eq.480) then ! Fourier transform E(t) numerically do iw=1,nwplot do its=its0,ntimes t1=g(its) t2=w(iw)*times(its) f1(its)=t1*cos(t2) f2(its)=t1*sin(t2) end do t1=dot_product(wt(its0:ntimes),f1(its0:ntimes)) t2=dot_product(wt(its0:ntimes),f2(its0:ntimes)) ew(iw,i)=t0*cmplx(t1+a0,t2,8) end do else ! analytic Fourier transform of E(t) assumed to be a delta function at t=0 t1=t0*a0 ew(1:nwplot,i)=t1 end if end do ! read in the total current from file allocate(jt(3,ntimes)) call readjtot(jt) ! divide by the unit cell volume jt(:,:)=jt(:,:)/omega ! filter the high-frequency components from the current using an exponentially ! decaying function do its=its0,ntimes t1=times(its)-t0tdlr t1=exp(-swidth*t1) jt(:,its)=t1*jt(:,its) end do ! Fourier transform the current allocate(jw(nwplot,3)) do i=1,3 do iw=1,nwplot do its=its0,ntimes t1=jt(i,its) t2=w(iw)*times(its) f1(its)=t1*cos(t2) f2(its)=t1*sin(t2) end do t1=dot_product(wt(its0:ntimes),f1(its0:ntimes)) t2=dot_product(wt(its0:ntimes),f2(its0:ntimes)) jw(iw,i)=cmplx(t1,t2,8) end do end do deallocate(wt,f1,f2,g,jt) ! compute the dielectric function and write to file allocate(eps(nwplot)) do i=1,3 do j=1,3 do iw=1,nwplot z1=jw(iw,i) z2=ew(iw,j) t1=abs(dble(z2))+abs(aimag(z2)) if (t1.gt.1.d-8) then z1=z1/z2 else z1=0.d0 end if z1=fourpi*cmplx(-aimag(z1),dble(z1),8) z1=z1/(w(iw)+eta) if (i.eq.j) z1=z1+1.d0 eps(iw)=z1 end do write(fname,'("EPSILON_TDRT_",2I1,".OUT")') i,j open(50,file=trim(fname),form='FORMATTED') do iw=1,nwplot write(50,'(2G18.10)') w(iw),dble(eps(iw)) end do write(50,*) do iw=1,nwplot write(50,'(2G18.10)') w(iw),aimag(eps(iw)) end do close(50) end do end do write(*,*) write(*,'("Info(dielectric_tdrt):")') write(*,'(" dielectric tensor determined from real-time evolution")') write(*,'(" written to EPSILON_TDRT_ij.OUT for components i,j = 1,2,3")') write(*,*) write(*,'("(Note that only those components which are not orthogonal to the")') write(*,'(" applied A-field will be calculated correctly)")') deallocate(w,ew,jw,eps) end subroutine elk-7.2.42/src/PaxHeaders.21776/readjtot.f900000644000000000000000000000013214061636517015060 xustar0030 mtime=1623670095.828101644 30 atime=1623670094.675102715 30 ctime=1623670095.828101644 elk-7.2.42/src/readjtot.f900000644002504400250440000000173014061636517017116 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readjtot(jt) use modmain use modtddft implicit none ! arguments real(8), intent(out) :: jt(3,ntimes) ! local variables integer its,ios real(8) times_,t1 open(50,file='JTOT_TD.OUT',form='FORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readjtot): error opening JTOT_TD.OUT")') write(*,*) stop end if do its=1,ntimes-1 read(50,*) times_,jt(:,its) t1=abs(times(its)-times_) if (t1.gt.1.d-10) then write(*,*) write(*,'("Error(readjtot): time step mismatch for step number ",I8)') its write(*,'(" internal : ",G18.10)') times(its) write(*,'(" JTOT_TD.OUT : ",G18.10)') times_ write(*,*) stop end if end do close(50) ! set current at last time step jt(:,ntimes)=jt(:,ntimes-1) end subroutine elk-7.2.42/src/PaxHeaders.21776/afindtstep.f900000644000000000000000000000013214061636517015405 xustar0030 mtime=1623670095.829101643 30 atime=1623670094.677102713 30 ctime=1623670095.829101643 elk-7.2.42/src/afindtstep.f900000644002504400250440000000145014061636517017442 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Peter Elliott, J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine afindtstep use modmain use modtddft use modmpi implicit none ! local variables real(8) dt,t1 ! time step length dt=times(itimes+1)-times(itimes) ! add to the time derivative of the induced A-field t1=fourpi*solsc*afindscf*dt/omega afindt(:,1)=afindt(:,1)+t1*jtot(:) ! add to the induced A-field afindt(:,0)=afindt(:,0)+afindt(:,1)*dt ! add to the total A-field afieldt(:,itimes+1)=afieldt(:,itimes+1)+afindt(:,0) ! write the induced A-field and its time derivative to file if (mp_mpi) then open(50,file='AFINDT.OUT',form='FORMATTED') write(50,'(6G18.10)') afindt(:,:) close(50) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/genefieldt.f900000644000000000000000000000013214061636517015352 xustar0030 mtime=1623670095.831101642 30 atime=1623670094.679102711 30 ctime=1623670095.831101642 elk-7.2.42/src/genefieldt.f900000644002504400250440000000115414061636517017410 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Peter Elliott, J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genefieldt use modmain use modtddft implicit none ! local variables integer np,it,i,j real(8) t1 ! automatic arrays real(8) ya(4) ! external functions real(8), external :: polynm ! determine the electric field at the current time step t1=-1.d0/solsc np=min(4,itimes) it=itimes-np+1 do i=1,3 do j=1,np ya(j)=afieldt(i,it+j-1) end do efieldt(i)=t1*polynm(1,np,times(it),ya,times(itimes)) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/energytd.f900000644000000000000000000000013214061636517015065 xustar0030 mtime=1623670095.832101641 30 atime=1623670094.681102709 30 ctime=1623670095.832101641 elk-7.2.42/src/energytd.f900000644002504400250440000000147614061636517017132 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine energytd use modmain use modtddft implicit none ! local variables integer is,ias real(8) ca,engya ! external functions real(8), external :: rfinp ! Coulomb potential energy engyvcl=rfinp(rhomt,rhoir,vclmt,vclir) ! Madelung term engymad=0.d0 do ias=1,natmtot is=idxis(ias) engymad=engymad+0.5d0*spzn(is)*(vclmt(1,ias)-vcln(1,is))*y00 end do ! exchange and correlation energy engyx=rfinp(rhomt,rhoir,exmt,exir) engyc=rfinp(rhomt,rhoir,ecmt,ecir) ! external vector potential interaction energy ca=-1.d0/solsc engya=ca*dot_product(afieldt(:,itimes),jtot(:)) ! total energy engytot=engykn+0.5d0*engyvcl+engymad+engyx+engyc+engya end subroutine elk-7.2.42/src/PaxHeaders.21776/engyknk.f900000644000000000000000000000013214061636517014712 xustar0030 mtime=1623670095.834101639 30 atime=1623670094.682102708 30 ctime=1623670095.834101639 elk-7.2.42/src/engyknk.f900000644002504400250440000000221314061636517016745 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine engyknk(ik,kmat,evecsv,evecsvt) use modmain use modtddft implicit none ! arguments integer, intent(in) :: ik complex(8), intent(in) :: kmat(nstsv,nstsv) complex(8), intent(in) :: evecsv(nstsv,nstsv),evecsvt(nstsv,nstsv) ! local variables integer ist real(8) wo complex(8) z1 ! allocatable arrays complex(8), allocatable :: a(:,:),b(:,:) ! external functions complex(8), external :: zdotc allocate(a(nstsv,nstsv),b(nstsv,nstsv)) ! form the kinetic operator matrix elements in the first-variational basis call zgemm('N','C',nstsv,nstsv,nstsv,zone,kmat,nstsv,evecsv,nstsv,zzero,a,nstsv) call zgemm('N','N',nstsv,nstsv,nstsv,zone,evecsv,nstsv,a,nstsv,zzero,b,nstsv) ! add to the kinetic energy call zgemm('N','N',nstsv,nstsv,nstsv,zone,b,nstsv,evecsvt,nstsv,zzero,a,nstsv) do ist=1,nstsv wo=occsv(ist,ik) if (abs(wo).lt.epsocc) cycle wo=wo*wkpt(ik) z1=zdotc(nstsv,evecsvt(:,ist),1,a(:,ist),1) !$OMP ATOMIC engykn=engykn+wo*dble(z1) end do deallocate(a,b) end subroutine elk-7.2.42/src/PaxHeaders.21776/readforcet.f900000644000000000000000000000013214061636517015362 xustar0030 mtime=1623670095.835101638 30 atime=1623670094.684102706 30 ctime=1623670095.835101638 elk-7.2.42/src/readforcet.f900000644002504400250440000000335314061636517017423 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readforcet use modmain use modtddft implicit none ! local variables integer ios,its,its_ integer is,ia,ias,is_,ia_ real(8) times_,t1 if (allocated(forcet)) deallocate(forcet) allocate(forcet(3,natmtot,ntimes)) ! read in the time-dependent total atomic forces open(50,file='FORCETOT_TD.OUT',form='FORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readforcet): error opening FORCETOT_TD.OUT")') write(*,*) stop end if do its=1,ntimes-1 read(50,*) its_,times_ if (its.ne.its_) then write(*,*) write(*,'("Error(readforcet): time step number mismatch")') write(*,'(" internal : ",I8)') its write(*,'(" FORCETOT_TD.OUT : ",I8)') its_ write(*,*) stop end if t1=abs(times(its)-times_) if (t1.gt.1.d-10) then write(*,*) write(*,'("Error(readforcet): time step mismatch for step number ",I8)') its write(*,'(" internal : ",G18.10)') times(its) write(*,'(" FORCETOT_TD.OUT : ",G18.10)') times_ stop end if do is=1,nspecies do ia=1,natoms(is) ias=idxas(ia,is) read(50,*) is_,ia_,forcet(:,ias,its) if ((is.ne.is_).or.(ia.ne.ia_)) then write(*,*) write(*,'("Error(readforcet): species or atom number mismatch for time & &step number ",I8)') its write(*,'(" internal : ",2I4)') is,ia write(*,'(" FORCETOT_TD.OUT : ",2I4)') is_,ia_ write(*,*) stop end if end do end do end do close(50) ! set force at last time step forcet(:,:,ntimes)=forcet(:,:,ntimes-1) end subroutine elk-7.2.42/src/PaxHeaders.21776/tdrestart.f900000644000000000000000000000013214061636517015260 xustar0030 mtime=1623670095.837101636 30 atime=1623670094.686102705 30 ctime=1623670095.837101636 elk-7.2.42/src/tdrestart.f900000644002504400250440000000151414061636517017316 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Peter Elliott, J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine tdrestart(itimes0) use modmain use modtddft use moddftu implicit none ! arguments integer, intent(out) :: itimes0 ! last time step for which the eigenvectors were written to file call readtimes(itimes0) ! generate the density and magnetisation call rhomag ! compute the time-dependent Kohn-Sham potentials and magnetic fields call potkst ! DFT+U if (dftu.ne.0) then call gendmatmt call genvmatmt end if ! read in the induced A-field and its time derivative if (tafindt) call readafindt ! read in the atomic displacements and velocities if (tdatpos) trddatpos=.true. ! begin TDDFT loop with next time step itimes0=itimes0+1 end subroutine elk-7.2.42/src/PaxHeaders.21776/readdatposc.f900000644000000000000000000000013214061636517015535 xustar0030 mtime=1623670095.838101635 30 atime=1623670094.687102703 30 ctime=1623670095.838101635 elk-7.2.42/src/readdatposc.f900000644002504400250440000000154114061636517017573 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readdatposc use modmain implicit none ! local variables integer is,ia,is_,ia_,ios open(50,file='DATPOSC.OUT',form='FORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readdatposc): error opening DATPOSC.OUT")') write(*,*) stop end if do is=1,nspecies do ia=1,natoms(is) read(50,*) is_,ia_,datposc(:,:,ia,is) if ((is.ne.is_).or.(ia.ne.ia_)) then write(*,*) write(*,'("Error(readdatposc): species or atom number mismatch")') write(*,'(" internal : ",2I4)') is,ia write(*,'(" DATPOSC.OUT : ",2I4)') is_,ia_ write(*,*) stop end if end do end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/writedatposc.f900000644000000000000000000000013214061636517015754 xustar0030 mtime=1623670095.839101634 30 atime=1623670094.689102702 30 ctime=1623670095.839101634 elk-7.2.42/src/writedatposc.f900000644002504400250440000000077414061636517020021 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writedatposc use modmain implicit none ! local variables integer is,ia ! write the atomic displacements and velocities to file open(50,file='DATPOSC.OUT',form='FORMATTED',action='WRITE') do is=1,nspecies do ia=1,natoms(is) write(50,'(2I4,6G18.10)') is,ia,datposc(:,:,ia,is) end do end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/rhostatic.f900000644000000000000000000000013014061636517015242 xustar0030 mtime=1623670095.841101632 28 atime=1623670094.6911027 30 ctime=1623670095.841101632 elk-7.2.42/src/rhostatic.f900000644002504400250440000000410414061636517017300 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rhostatic use modmain use modtddft use modmpi use modstore implicit none ! local variables integer is,ias,np,i ! allocatable arrays real(8), allocatable :: jrmt0(:,:,:),jrir0(:,:) ! external functions real(8), external :: rfmtint,rfint ! store original parameters maxscl_=maxscl afieldc_(:)=afieldc(:) tjr_=tjr tforce_=tforce ! initialise global variables call init0 ! only one self-consistent loop required maxscl=1 ! read potential from STATE.OUT trdstate=.true. ! calculate current density with zero A-field tjr=.true. afieldc(:)=0.d0 ! switch off forces tforce=.false. ! run the ground-state calculation call gndstate ! store the current density allocate(jrmt0(npmtmax,natmtot,3),jrir0(ngtot,3)) do i=1,3 call rfcopy(jrmt(:,:,i),jrir(:,i),jrmt0(:,:,i),jrir0(:,i)) end do ! allocate static density global arrays if (allocated(rhosmt)) deallocate(rhosmt) allocate(rhosmt(npmtmax,natmtot,3)) if (allocated(rhosir)) deallocate(rhosir) allocate(rhosir(ngtot,3)) if (allocated(chgsmt)) deallocate(chgsmt) allocate(chgsmt(natmtot,3)) ! loop over three directions do i=1,3 afieldc(:)=0.d0 afieldc(i)=1.d0 ! run the ground-state calculation call gndstate ! muffin-tin static density do ias=1,natmtot is=idxis(ias) np=npmt(is) rhosmt(1:np,ias,i)=rhomt(1:np,ias) & -solsc*(jrmt(1:np,ias,i)-jrmt0(1:np,ias,i)) ! compute the muffin-tin static charge chgsmt(ias,i)=rfmtint(nrmt(is),nrmti(is),wrmt(:,is),rhosmt(:,ias,i)) end do ! interstitial static density rhosir(:,i)=rhoir(:)-solsc*(jrir(:,i)-jrir0(:,i)) ! compute the static charge chgstot(i)=rfint(rhosmt(:,:,i),rhosir(:,i)) end do ! write static charge to file if (mp_mpi) then open(50,file='CHGSTAT.OUT',form='FORMATTED',action='WRITE') write(50,'(3G18.10)') chgstot(:) close(50) end if deallocate(jrmt0,jrir0) ! restore original input parameters maxscl=maxscl_ afieldc(:)=afieldc_(:) tafield=.false. tjr=tjr_ tforce=tforce_ end subroutine elk-7.2.42/src/PaxHeaders.21776/jtotk.f900000644000000000000000000000013014061636517014375 xustar0029 mtime=1623670095.84310163 30 atime=1623670094.692102699 29 ctime=1623670095.84310163 elk-7.2.42/src/jtotk.f900000644002504400250440000000226314061636517016437 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine jtotk(ik,pmat,evecsv,evecsvt) use modmain implicit none ! arguments integer, intent(in) :: ik complex(8), intent(in) :: pmat(nstsv,nstsv,3) complex(8), intent(in) :: evecsv(nstsv,nstsv),evecsvt(nstsv,nstsv) ! local variables integer ist,l real(8) wo complex(8) z1 ! allocatable arrays complex(8), allocatable :: a(:,:),b(:,:) ! external functions complex(8), external :: zdotc allocate(a(nstsv,nstsv),b(nstsv,nstsv)) do l=1,3 ! form the momentum operator matrix elements in the first-variational basis call zgemm('N','C',nstsv,nstsv,nstsv,zone,pmat(:,:,l),nstsv,evecsv,nstsv, & zzero,a,nstsv) call zgemm('N','N',nstsv,nstsv,nstsv,zone,evecsv,nstsv,a,nstsv,zzero,b,nstsv) ! add to the total current call zgemm('N','N',nstsv,nstsv,nstsv,zone,b,nstsv,evecsvt,nstsv,zzero,a,nstsv) do ist=1,nstsv wo=occsv(ist,ik) if (abs(wo).lt.epsocc) cycle wo=wo*wkpt(ik) z1=zdotc(nstsv,evecsvt(:,ist),1,a(:,ist),1) !$OMP ATOMIC jtot(l)=jtot(l)+wo*dble(z1) end do end do deallocate(a,b) end subroutine elk-7.2.42/src/PaxHeaders.21776/rhosplot.f900000644000000000000000000000013014061636517015114 xustar0029 mtime=1623670095.84410163 30 atime=1623670094.694102697 29 ctime=1623670095.84410163 elk-7.2.42/src/rhosplot.f900000644002504400250440000000223114061636517017151 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rhosplot use modmain use modtddft implicit none ! local variables integer is,ias,ispn integer nr,nri,iro,ir,i ! determine the static density and charge call rhostatic ! remove the core charge density do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) iro=nri+1 do ispn=1,nspncr i=1 do ir=1,nri rhosmt(i,ias,:)=rhosmt(i,ias,:)-rhocr(ir,ias,ispn) i=i+lmmaxi end do do ir=iro,nr rhosmt(i,ias,:)=rhosmt(i,ias,:)-rhocr(ir,ias,ispn) i=i+lmmaxo end do end do end do ! produce 1D plot of the static density open(50,file='RHOS1D.OUT',form='FORMATTED',action='WRITE') open(51,file='RHOSLINES.OUT',form='FORMATTED',action='WRITE') call plot1d(50,51,3,rhosmt,rhosir) close(50) close(51) write(*,*) write(*,'("Info(rhosplot):")') write(*,'(" 1D static density plot written to RHOS1D.OUT")') write(*,'(" vertex location lines written to RHOSLINES.OUT")') write(*,*) write(*,'(" The core density is not included in the plot")') end subroutine elk-7.2.42/src/PaxHeaders.21776/bornectd.f900000644000000000000000000000013214061636517015044 xustar0030 mtime=1623670095.846101628 30 atime=1623670094.696102695 30 ctime=1623670095.846101628 elk-7.2.42/src/bornectd.f900000644002504400250440000000442714061636517017110 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine bornectd use modmain use modphonon use modtddft use modstore use modmpi implicit none ! local variables integer ip real(8) vc(3),bec(3),t1 character(256) fext ! allocatable arrays real(8), allocatable :: jt(:,:),f(:) ! external functions real(8), external :: splint ! store original parameters atposl_(:,:,:)=atposl(:,:,:) ! no shifting of atomic basis allowed tshift=.false. ! initialise universal variables call init0 atposc_(:,:,:)=atposc(:,:,:) ! generate a zero A-field npulse=0 nramp=0 if (mp_mpi) call genafieldt ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! initial ground-state run should start from atomic densities trdstate=.false. ! begin new Born effective charge task 10 continue call bectask(80,fext) ! if nothing more to do then restore original input parameters and return if (isph.eq.0) then filext='.OUT' atposl(:,:,:)=atposl_(:,:,:) tshift=tshift_ return end if if (mp_mpi) then write(*,'("Info(bornectd): working on ",A)') 'BEC'//trim(fext) end if ! dry run: just generate empty BEC files if (task.eq.209) goto 10 ! break the crystal symmetry for the displaced atom atposl(:,:,:)=atposl_(:,:,:) atposc(:,:,:)=atposc_(:,:,:) vc(:)=atposc(:,iaph,isph) vc(ipph)=vc(ipph)-0.5d0*deltaph call r3mv(ainv,vc,atposl(:,iaph,isph)) ! run the ground-state calculation call gndstate ! subsequent calculations will read in the previous potential trdstate=.true. ! write the atomic forces to file call becforce ! run the time evolution calculation with Ehrenfest dynamics task=462 call tddft task=478 ! read in the total current from file allocate(jt(3,ntimes),f(ntimes)) call readjtot(jt) ! calculate the Born effective charge from the integrated current do ip=1,3 f(:)=jt(ip,:) t1=splint(ntimes,times,f) bec(ip)=t1/(deltaph*cos(tdphi)) end do deallocate(jt,f) ! add the static and nuclear charge t1=sum(chgsmt(iasph,1:3))/3.d0 bec(ipph)=bec(ipph)+t1+spzn(isph) ! write Born effective charge matrix row to file if (mp_mpi) then do ip=1,3 write(80,'(G18.10," : ip = ",I4)') bec(ip),ip end do close(80) end if ! synchronise MPI processes call mpi_barrier(mpicom,ierror) goto 10 end subroutine elk-7.2.42/src/PaxHeaders.21776/becforce.f900000644000000000000000000000013214061636517015014 xustar0030 mtime=1623670095.847101627 30 atime=1623670094.697102694 30 ctime=1623670095.847101627 elk-7.2.42/src/becforce.f900000644002504400250440000000156514061636517017060 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine becforce use modmain use modphonon use modtddft implicit none integer its,is,ia real(8) ft(3) ! generate the time step grid call gentimes ! determine the force which gives the correct final displacement of the atom ft(:)=0.d0 ft(ipph)=12.d0*spmass(isph)*deltaph/tstime**4 ! write force to file for all time steps open(50,file='FORCETOT_TD.OUT',form='FORMATTED') do its=1,ntimes write(50,'(I8,G18.10)') its,times(its) do is=1,nspecies do ia=1,natoms(is) if ((is.eq.isph).and.(ia.eq.iaph)) then write(50,'(2I4,3G18.10)') is,ia,ft(:)*times(its)**2 else write(50,'(2I4,3G18.10)') is,ia,0.d0,0.d0,0.d0 end if end do end do end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/zfirctof.f900000644000000000000000000000013214061636517015072 xustar0030 mtime=1623670095.849101625 30 atime=1623670094.699102692 30 ctime=1623670095.849101625 elk-7.2.42/src/zfirctof.f900000644002504400250440000000121614061636517017127 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zfirctof(zfirc,zfir) use modmain implicit none ! arguments complex(8), intent(in) :: zfirc(ngtc) complex(8), intent(out) :: zfir(ngtot) ! local variables integer ig ! automatic arrays complex(8) zfftc(ngtc) ! Fourier transform function on coarse grid to G-space zfftc(:)=zfirc(:) call zfftifc(3,ngdgc,-1,zfftc) ! Fourier transform to fine real-space grid zfir(:)=0.d0 do ig=1,ngvc zfir(igfft(ig))=zfftc(igfc(ig)) end do call zfftifc(3,ngridg,1,zfir) end subroutine elk-7.2.42/src/PaxHeaders.21776/writeevalu.f900000644000000000000000000000013114061636517015432 xustar0030 mtime=1623670095.850101624 29 atime=1623670094.70110269 30 ctime=1623670095.850101624 elk-7.2.42/src/writeevalu.f900000644002504400250440000000136714061636517017477 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeevalu use modmain use modulr implicit none ! local variables integer ik0,ik,ist ! write out the valence eigenvalues open(50,file='EIGVALU.OUT',form='FORMATTED') write(50,'(I6," : nkpt0")') nkpt0 write(50,'(I6," : nstulr")') nstulr do ik0=1,nkpt0 ! central k-point ik=(ik0-1)*nkpa+1 write(50,*) write(50,'(I6,3G18.10," : k-point, vkl")') ik0,vkl(:,ik) write(50,'(" (state, eigenvalue and occupancy below)")') do ist=1,nstulr write(50,'(I6,2G18.10)') ist,evalu(ist,ik0),occulr(ist,ik0) end do end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/rhocoreu.f900000644000000000000000000000013114061636517015071 xustar0030 mtime=1623670095.852101622 29 atime=1623670094.70210269 30 ctime=1623670095.852101622 elk-7.2.42/src/rhocoreu.f900000644002504400250440000000225014061636517017126 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rhocoreu use modmain use modulr use modomp implicit none ! local variables integer is,ias,ir,i integer nrc,nrci,irc integer npc,n,nthd real(8) t1 ! allocatable arrays real(8), allocatable :: rfmt(:,:) ! generate the core density in spherical coordinates allocate(rfmt(npcmtmax,natmtot)) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) n=lmmaxi-1 ir=1 i=1 do irc=1,nrci t1=rhocr(ir,ias,1)*y00 rfmt(i:i+n,ias)=t1 ir=ir+lradstp i=i+lmmaxi end do n=lmmaxo-1 do irc=nrci+1,nrc t1=rhocr(ir,ias,1)*y00 rfmt(i:i+n,ias)=t1 ir=ir+lradstp i=i+lmmaxo end do end do ! add to the ultra long-range density call holdthd(nqpt,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ias,is,npc) & !$OMP NUM_THREADS(nthd) do ir=1,nqpt do ias=1,natmtot is=idxis(ias) npc=npcmt(is) rhormt(1:npc,ias,ir)=rhormt(1:npc,ias,ir)+rfmt(1:npc,ias) end do end do !$OMP END PARALLEL DO call freethd(nthd) deallocate(rfmt) end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqnulr.f900000644000000000000000000000013214061636517015105 xustar0030 mtime=1623670095.853101621 30 atime=1623670094.704102688 30 ctime=1623670095.853101621 elk-7.2.42/src/eveqnulr.f900000644002504400250440000000100014061636517017131 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2016 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine eveqnulr(ik0,evecu) use modmain use modulr implicit none ! arguments integer, intent(in) :: ik0 complex(8), intent(out) :: evecu(nstulr,nstulr) ! generate the ultra long-range Hamiltonian call genhmlu(ik0,evecu) ! find the eigenvalues and vectors call eveqnzh(nstulr,nstulr,evecu,evalu(:,ik0)) end subroutine elk-7.2.42/src/PaxHeaders.21776/rfzfftq.f900000644000000000000000000000013214061636517014726 xustar0030 mtime=1623670095.855101619 30 atime=1623670094.706102686 30 ctime=1623670095.855101619 elk-7.2.42/src/rfzfftq.f900000644002504400250440000000647714061636517017001 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rfzfftq(sgn,nf,ngt,rfmt,rfir,zfmt,zfir) use modmain use modmpi use modomp implicit none ! arguments integer, intent(in) :: sgn,nf,ngt real(8), intent(inout) :: rfmt(npcmtmax,natmtot,nf,nqpt) real(8), intent(inout) :: rfir(ngt,nf,nqpt) complex(8), intent(inout) :: zfmt(npcmtmax,natmtot,nf,nfqrz) complex(8), intent(inout) :: zfir(ngt,nf,nfqrz) ! local variables integer jf,is,ias,ir integer npc,i,n,nthd ! automatic arrays real(8) r(nqpt) complex(8) z(nfqrz) if (sgn.eq.-1) then ! loop over the number of functions do jf=1,nf ! Fourier transform the muffin-tin function do ias=1,natmtot is=idxis(ias) npc=npcmt(is) if (np_mpi.gt.1) zfmt(1:npc,ias,jf,:)=0.d0 call holdthd(npc/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(r,z) & !$OMP NUM_THREADS(nthd) do i=1,npc ! distribute among MPI processes if (mod(i-1,np_mpi).ne.lp_mpi) cycle r(1:nqpt)=rfmt(i,ias,jf,1:nqpt) call rzfftifc(3,ngridq,-1,r,z) zfmt(i,ias,jf,1:nfqrz)=z(1:nfqrz) end do !$OMP END PARALLEL DO call freethd(nthd) end do ! Fourier transform the interstitial function if (np_mpi.gt.1) zfir(:,jf,:)=0.d0 call holdthd(ngt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(r,z) & !$OMP NUM_THREADS(nthd) do ir=1,ngt ! distribute among MPI processes if (mod(ir-1,np_mpi).ne.lp_mpi) cycle r(1:nqpt)=rfir(ir,jf,1:nqpt) call rzfftifc(3,ngridq,-1,r,z) zfir(ir,jf,1:nfqrz)=z(1:nfqrz) end do !$OMP END PARALLEL DO call freethd(nthd) ! end loop over number of functions end do if (np_mpi.gt.1) then n=npcmtmax*natmtot*nf*nfqrz call mpi_allreduce(mpi_in_place,zfmt,n,mpi_double_complex,mpi_sum,mpicom, & ierror) n=ngt*nf*nfqrz call mpi_allreduce(mpi_in_place,zfir,n,mpi_double_complex,mpi_sum,mpicom, & ierror) end if else ! loop over the number of functions do jf=1,nf do ias=1,natmtot is=idxis(ias) npc=npcmt(is) if (np_mpi.gt.1) rfmt(1:npc,ias,jf,:)=0.d0 call holdthd(npc/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(z,r) & !$OMP NUM_THREADS(nthd) do i=1,npc ! distribute among MPI processes if (mod(i-1,np_mpi).ne.lp_mpi) cycle z(1:nfqrz)=zfmt(i,ias,jf,1:nfqrz) call rzfftifc(3,ngridq,1,r,z) rfmt(i,ias,jf,1:nqpt)=r(1:nqpt) end do !$OMP END PARALLEL DO call freethd(nthd) end do if (np_mpi.gt.1) rfir(:,jf,:)=0.d0 call holdthd(ngt/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(z,r) & !$OMP NUM_THREADS(nthd) do ir=1,ngt ! distribute among MPI processes if (mod(ir-1,np_mpi).ne.lp_mpi) cycle z(1:nfqrz)=zfir(ir,jf,1:nfqrz) call rzfftifc(3,ngridq,1,r,z) rfir(ir,jf,1:nqpt)=r(1:nqpt) end do !$OMP END PARALLEL DO call freethd(nthd) ! end loop over number of functions end do if (np_mpi.gt.1) then n=npcmtmax*natmtot*nf*nqpt call mpi_allreduce(mpi_in_place,rfmt,n,mpi_double_precision,mpi_sum, & mpicom,ierror) n=ngt*nf*nqpt call mpi_allreduce(mpi_in_place,rfir,n,mpi_double_precision,mpi_sum, & mpicom,ierror) end if end if end subroutine elk-7.2.42/src/PaxHeaders.21776/writekpa.f900000644000000000000000000000013214061636517015072 xustar0030 mtime=1623670095.856101618 30 atime=1623670094.707102685 30 ctime=1623670095.856101618 elk-7.2.42/src/writekpa.f900000644002504400250440000000077114061636517017134 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writekpa use modmain use modulr implicit none ! local variables integer ikpa open(50,file='KAPPA.OUT',form='FORMATTED') write(50,'(I6," : nkpa; kappa-point, vector in unit cell reciprocal lattice & &coordinates below")') nkpa do ikpa=1,nkpa write(50,'(I6,3G18.10)') ikpa,vql(:,ikpa) end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/rhomaguk.f900000644000000000000000000000013214061636517015061 xustar0030 mtime=1623670095.858101617 30 atime=1623670094.709102683 30 ctime=1623670095.858101617 elk-7.2.42/src/rhomaguk.f900000644002504400250440000001464614061636517017131 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rhomaguk(ik0,lock,evecu) use modmain use modulr use modomp implicit none ! arguments integer, intent(in) :: ik0 integer(8), intent(in) :: lock(nqpt) complex(8), intent(in) :: evecu(nstulr,nstulr) ! local variables integer ik,ikpa,ist,i,j integer ngk0,ispn,is,ias integer npc,ir,nthd real(8) wm,wi ! automatic arrays integer idx(nstsv) complex(8) zfft(nqpt),wfir(ngtc,nspinor) ! allocatable arrays integer(8), allocatable :: lockl(:) complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfgk(:,:,:) complex(8), allocatable :: wfrmt(:,:,:,:),wfrgk(:,:,:) ! central k-point ik=(ik0-1)*nkpa+1 ! number of G+k-vectors for central k-point ngk0=ngk(1,ik) ! initialise the local OpenMP locks allocate(lockl(nqpt)) do ir=1,nqpt call omp_init_lock(lockl(ir)) end do ! get the eigenvectors from file allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) call getevecfv(filext,ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv(filext,ik,vkl(:,ik),evecsv) ! find the matching coefficients allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) call match(ngk0,vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! index to all states do ist=1,nstsv idx(ist)=ist end do allocate(wfmt(npcmtmax,natmtot,nspinor,nstsv),wfgk(ngk0,nspinor,nstsv)) call genwfsv(.false.,.true.,nstsv,idx,ngdgc,igfc,ngk0,igkig(:,1,ik),apwalm, & evecfv,evecsv,wfmt,ngk0,wfgk) deallocate(apwalm,evecfv,evecsv) allocate(wfrmt(npcmtmax,natmtot,nspinor,nqpt),wfrgk(ngk0,nspinor,nqpt)) ! loop over ultra long-range states do j=1,nstulr wm=occulr(j,ik0) if (abs(wm).lt.epsocc) cycle wm=wm*wkpt(ik) wi=wm/omega ! zero the ultra long-range wavefunctions call holdthd(2,nthd) !$OMP PARALLEL SECTIONS DEFAULT(SHARED) & !$OMP PRIVATE(ir,ispn) & !$OMP NUM_THREADS(nthd) !$OMP SECTION do ir=1,nqpt do ispn=1,nspinor call wfmt0(wfrmt(:,:,ispn,ir)) end do end do !$OMP SECTION wfrgk(:,:,:)=0.d0 !$OMP END PARALLEL SECTIONS call freethd(nthd) ! parallel loop over second-variational states call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(zfft,ikpa,i,ir) & !$OMP NUM_THREADS(nthd) do ist=1,nstsv zfft(:)=0.d0 ! loop over kappa-points do ikpa=1,nkpa i=(ikpa-1)*nstsv+ist ! store the wavefunction in Q-space zfft(iqfft(ikpa))=evecu(i,j) end do ! Fourier transform to R-space call zfftifc(3,ngridq,1,zfft) ! loop over R-points do ir=1,nqpt call omp_set_lock(lockl(ir)) call wfadd(zfft(ir),wfmt(:,:,:,ist),wfgk(:,:,ist),wfrmt(:,:,:,ir), & wfrgk(:,:,ir)) call omp_unset_lock(lockl(ir)) end do end do !$OMP END PARALLEL DO call freethd(nthd) ! parallel loop over R-points call holdthd(nqpt,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(wfir,ispn,ias,is,npc) & !$OMP NUM_THREADS(nthd) do ir=1,nqpt do ispn=1,nspinor ! Fourier transform the interstitial part to real-space wfir(:,ispn)=0.d0 wfir(igfc(igkig(1:ngk0,1,ik)),ispn)=wfrgk(1:ngk0,ispn,ir) call zfftifc(3,ngdgc,1,wfir(:,ispn)) end do ! add to the density and magnetisation call omp_set_lock(lock(ir)) do ias=1,natmtot is=idxis(ias) npc=npcmt(is) if (spinpol) then if (ncmag) then call rmk1(npc,wm,wfrmt(:,ias,1,ir),wfrmt(:,ias,2,ir), & rhormt(:,ias,ir),magrmt(:,ias,1,ir),magrmt(:,ias,2,ir), & magrmt(:,ias,3,ir)) else call rmk2(npc,wm,wfrmt(:,ias,1,ir),wfrmt(:,ias,2,ir), & rhormt(:,ias,ir),magrmt(:,ias,1,ir)) end if else call rmk3(npc,wm,wfrmt(:,ias,1,ir),rhormt(:,ias,ir)) end if end do if (spinpol) then if (ncmag) then call rmk1(ngtc,wi,wfir,wfir(:,2),rhorir(:,ir),magrir(:,1,ir), & magrir(:,2,ir),magrir(:,3,ir)) else call rmk2(ngtc,wi,wfir,wfir(:,2),rhorir(:,ir),magrir(:,1,ir)) end if else call rmk3(ngtc,wi,wfir,rhorir(:,ir)) end if call omp_unset_lock(lock(ir)) ! end loop over R-points end do !$OMP END PARALLEL DO call freethd(nthd) ! end loop over long-range states end do ! destroy the local OpenMP locks do ir=1,nqpt call omp_destroy_lock(lockl(ir)) end do deallocate(lockl) deallocate(wfmt,wfgk,wfrmt,wfrgk) return contains pure subroutine wfmt0(wfmt) implicit none ! arguments complex(8), intent(out) :: wfmt(npcmtmax,natmtot) ! local variables integer is,ias do ias=1,natmtot is=idxis(ias) wfmt(1:npcmt(is),ias)=0.d0 end do end subroutine subroutine wfadd(za,wfmt1,wfgk1,wfmt2,wfgk2) implicit none ! arguments complex(8), intent(in) :: za complex(8), intent(in) :: wfmt1(npcmtmax,natmtot,nspinor) complex(8), intent(in) :: wfgk1(ngk0,nspinor) complex(8), intent(inout) :: wfmt2(npcmtmax,natmtot,nspinor) complex(8), intent(inout) :: wfgk2(ngk0,nspinor) ! local variables integer ispn,is,ias do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) call zaxpy(npcmt(is),za,wfmt1(:,ias,ispn),1,wfmt2(:,ias,ispn),1) end do end do call zaxpy(ngk0*nspinor,za,wfgk1,1,wfgk2,1) end subroutine pure subroutine rmk1(n,wo,wf1,wf2,rho,mag1,mag2,mag3) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf1(n),wf2(n) real(8), intent(inout) :: rho(n),mag1(n),mag2(n),mag3(n) ! local variables integer i real(8) wo2,t1,t2 real(8) a1,b1,a2,b2 wo2=2.d0*wo !$OMP SIMD PRIVATE(a1,b1,a2,b2,t1,t2) SIMDLEN(8) do i=1,n a1=dble(wf1(i)); b1=aimag(wf1(i)) a2=dble(wf2(i)); b2=aimag(wf2(i)) t1=a1**2+b1**2; t2=a2**2+b2**2 mag1(i)=mag1(i)+wo2*(a1*a2+b1*b2) mag2(i)=mag2(i)+wo2*(a1*b2-b1*a2) mag3(i)=mag3(i)+wo*(t1-t2) rho(i)=rho(i)+wo*(t1+t2) end do end subroutine pure subroutine rmk2(n,wo,wf1,wf2,rho,mag) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf1(n),wf2(n) real(8), intent(inout) :: rho(n),mag(n) ! local variables integer i real(8) t1,t2 !$OMP SIMD PRIVATE(t1,t2) SIMDLEN(8) do i=1,n t1=dble(wf1(i))**2+aimag(wf1(i))**2 t2=dble(wf2(i))**2+aimag(wf2(i))**2 mag(i)=mag(i)+wo*(t1-t2) rho(i)=rho(i)+wo*(t1+t2) end do end subroutine pure subroutine rmk3(n,wo,wf,rho) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: wo complex(8), intent(in) :: wf(n) real(8), intent(inout) :: rho(n) rho(:)=rho(:)+wo*(dble(wf(:))**2+aimag(wf(:))**2) end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/rhomagq.f900000644000000000000000000000013214061636517014702 xustar0030 mtime=1623670095.859101616 30 atime=1623670094.711102681 30 ctime=1623670095.859101616 elk-7.2.42/src/rhomagq.f900000644002504400250440000000262014061636517016737 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rhomagq use modmain use modulr use modomp implicit none ! local variables integer ifq,idm,is,ias,nthd ! automatic arrays complex(8) zfmt(npcmtmax) ! partial Fourier transform of density to Q-space call rfzfftq(-1,1,ngtc,rhormt,rhorir,rhoqmt,rhoqir) ! convert density to spherical harmonics call holdthd(nfqrz,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(zfmt,ias,is) & !$OMP NUM_THREADS(nthd) do ifq=1,nfqrz do ias=1,natmtot is=idxis(ias) call zcopy(npcmt(is),rhoqmt(:,ias,ifq),1,zfmt,1) call zfsht(nrcmt(is),nrcmti(is),zfmt,rhoqmt(:,ias,ifq)) end do end do !$OMP END PARALLEL DO call freethd(nthd) if (.not.spinpol) return ! partial Fourier transform of magnetisation to Q-space call rfzfftq(-1,ndmag,ngtc,magrmt,magrir,magqmt,magqir) ! convert magnetisation to spherical harmonics call holdthd(nfqrz,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(zfmt,idm,ias,is) & !$OMP NUM_THREADS(nthd) do ifq=1,nfqrz do idm=1,ndmag do ias=1,natmtot is=idxis(ias) call zcopy(npcmt(is),magqmt(:,ias,idm,ifq),1,zfmt,1) call zfsht(nrcmt(is),nrcmti(is),zfmt,magqmt(:,ias,idm,ifq)) end do end do end do !$OMP END PARALLEL DO call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/genhmlu.f900000644000000000000000000000013114061636517014702 xustar0030 mtime=1623670095.861101614 29 atime=1623670094.71210268 30 ctime=1623670095.861101614 elk-7.2.42/src/genhmlu.f900000644002504400250440000000727614061636517016754 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genhmlu(ik0,h) use modmain use modulr use modomp implicit none ! arguments integer, intent(in) :: ik0 complex(8), intent(out) :: h(nstulr,nstulr) ! local variables integer ik,ist,jst,ispn,nthd integer ikpa,jkpa,iq,ifq,ngk0,igk integer i1,i2,i3,j1,j2,j3,i,j ! automatic arrays integer idx(nstsv) complex(8) vmat(nstsv,nstsv) ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfir(:,:,:),wfgk(:,:,:) complex(8), allocatable :: hdb(:,:,:) ! central k-point ik=(ik0-1)*nkpa+1 ! number of G+k-vectors for central k-point ngk0=ngk(1,ik) ! get the ground-state eigenvectors from file for central k-point allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) call getevecfv('.OUT',ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv('.OUT',ik,vkl(:,ik),evecsv) ! find the matching coefficients allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) call match(ngk0,vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! index to all states do ist=1,nstsv idx(ist)=ist end do ! calculate the wavefunctions for all states of the central k-point allocate(wfmt(npcmtmax,natmtot,nspinor,nstsv),wfgk(ngk0,nspinor,nstsv)) call genwfsv(.false.,.true.,nstsv,idx,ngridg,igfft,ngk0,igkig(:,1,ik),apwalm, & evecfv,evecsv,wfmt,ngk0,wfgk) deallocate(apwalm,evecfv,evecsv) ! determine the interstitial wavefunctions in real-space (without 1/sqrt(omega)) allocate(wfir(ngtot,nspinor,nstsv)) call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(ispn,igk) & !$OMP NUM_THREADS(nthd) do ist=1,nstsv do ispn=1,nspinor wfir(:,ispn,ist)=0.d0 do igk=1,ngk0 wfir(igfft(igkig(igk,1,ik)),ispn,ist)=wfgk(igk,ispn,ist) end do call zfftifc(3,ngridg,1,wfir(:,ispn,ist)) end do end do !$OMP END PARALLEL DO call freethd(nthd) ! generate the matrix elements for all Q-vectors call holdthd(nfqrz,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(vmat,iq,i,j,ikpa,jkpa) & !$OMP PRIVATE(j1,j2,j3,ist,jst,i1,i2,i3) & !$OMP NUM_THREADS(nthd) do ifq=1,nfqrz iq=iqrzf(ifq) if (spinpol) then call genzvbmatk(vsqmt(:,:,ifq),vsqir(:,ifq),bsqmt(:,:,:,ifq), & bsqir(:,:,ifq),ngk0,igkig(:,1,ik),wfmt,wfir,wfgk,vmat) else call genzvmatk(vsqmt(:,:,ifq),vsqir(:,ifq),ngk0,igkig(:,1,ik),wfmt,wfir, & wfgk,vmat) end if j=0 do jkpa=1,nkpa j1=ivq(1,jkpa); j2=ivq(2,jkpa); j3=ivq(3,jkpa) do jst=1,nstsv j=j+1 do ikpa=1,jkpa-1 i=(ikpa-1)*nstsv+1 i1=ivq(1,ikpa)-j1; i2=ivq(2,ikpa)-j2; i3=ivq(3,ikpa)-j3 if (ivqiq(i1,i2,i3).eq.iq) then ! copy matrix elements for kappa_i - kappa_j in Q-point set call zcopy(nstsv,vmat(:,jst),1,h(i,j),1) else if (ivqiq(-i1,-i2,-i3).eq.iq) then ! otherwise use conjugate transpose do ist=1,nstsv h(i,j)=conjg(vmat(jst,ist)) i=i+1 end do end if end do ! copy only the upper triangular part for Q=0 if (ifq.eq.1) then i=(jkpa-1)*nstsv+1 call zcopy(jst,vmat(:,jst),1,h(i,j),1) end if end do end do end do !$OMP END PARALLEL DO call freethd(nthd) deallocate(wfmt,wfir,wfgk) ! add the second-variational eigenvalues of k+kappa to the diagonal but in the ! basis of the states at k do ist=1,nstsv h(ist,ist)=h(ist,ist)+evalsv(ist,ik) end do allocate(hdb(nstsv,nstsv,2:nkpa)) call gethdbulr(ik0,hdb) do ikpa=2,nkpa i=(ikpa-1)*nstsv do jst=1,nstsv j=i+jst do ist=1,jst h(i+ist,j)=h(i+ist,j)+hdb(ist,jst,ikpa) end do end do end do deallocate(hdb) end subroutine elk-7.2.42/src/PaxHeaders.21776/chargeu.f900000644000000000000000000000013214061636517014662 xustar0030 mtime=1623670095.862101613 30 atime=1623670094.714102678 30 ctime=1623670095.862101613 elk-7.2.42/src/chargeu.f900000644002504400250440000000166614061636517016730 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine chargeu use modmain use modulr implicit none ! local variables integer ifq,is,ias integer nrc,nrci real(8) t1 ! automatic arrays real(8) rfft(nqpt) complex(8) zfft(nfqrz) ! external functions real(8), external :: ddot complex(8), external :: zfmtint ! calculate muffin-tin charges chgmttot=0.d0 do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) do ifq=1,nfqrz zfft(ifq)=zfmtint(nrc,nrci,wrcmt(:,is),rhoqmt(:,ias,ifq)) end do chgmt(ias)=dble(zfft(1)) chgmttot=chgmttot+chgmt(ias) call rzfftifc(3,ngridq,1,rfft,zfft) chgmtru(ias,:)=rfft(:) end do ! calculate interstitial charge t1=ddot(ngtc,rhoqir(:,1),2,cfrc,1) chgir=t1*omega/dble(ngtc) ! total calculated charge chgcalc=chgmttot+chgir end subroutine elk-7.2.42/src/PaxHeaders.21776/momentu.f900000644000000000000000000000013214061636517014730 xustar0030 mtime=1623670095.864101611 30 atime=1623670094.716102677 30 ctime=1623670095.864101611 elk-7.2.42/src/momentu.f900000644002504400250440000000226414061636517016771 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine momentu use modmain use modulr implicit none ! local variables integer ifq,idm,is,ias integer nrc,nrci real(8) t1 ! automatic arrays real(8) rfft(nqpt) complex(8) zfft(nfqrz) ! external functions real(8), external :: ddot complex(8), external :: zfmtint if (.not.spinpol) return ! calculate muffin-tin moments mommttot(:)=0.d0 do idm=1,ndmag do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) do ifq=1,nfqrz zfft(ifq)=zfmtint(nrc,nrci,wrcmt(:,is),magqmt(:,ias,idm,ifq)) end do mommt(idm,ias)=dble(zfft(1)) mommttot(idm)=mommttot(idm)+mommt(idm,ias) call rzfftifc(3,ngridq,1,rfft,zfft) mommtru(idm,ias,:)=rfft(:) end do end do ! calculate interstitial moment do idm=1,ndmag t1=ddot(ngtc,magqir(:,idm,1),2,cfrc,1) momir(idm)=t1*omega/dble(ngtc) end do momtot(:)=mommttot(:)+momir(:) ! total moment magnitude if (ncmag) then momtotm=sqrt(momtot(1)**2+momtot(2)**2+momtot(3)**2) else momtotm=abs(momtot(1)) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/potxcu.f900000644000000000000000000000013014061636517014564 xustar0029 mtime=1623670095.86510161 30 atime=1623670094.717102676 29 ctime=1623670095.86510161 elk-7.2.42/src/potxcu.f900000644002504400250440000001143714061636517016631 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potxcu use modmain use modulr use modmpi use modomp implicit none ! local variables integer ifq,idm,is,ias integer ir,npc,n,lp,nthd complex(8) z1,z2 ! allocatable arrays real(8), allocatable :: vxcrmt(:,:,:),vxcrir(:,:) real(8), allocatable :: bxcrmt(:,:,:,:),bxcrir(:,:,:) real(8), allocatable :: rhomt_(:,:),rhoir_(:) real(8), allocatable :: magmt_(:,:,:),magir_(:,:) real(8), allocatable :: vxcmt_(:,:),bxcmt_(:,:,:) complex(8), allocatable :: vxcqmt(:,:,:),vxcqir(:,:) allocate(vxcrmt(npcmtmax,natmtot,nqpt),vxcrir(ngtot,nqpt)) if (spinpol) then allocate(bxcrmt(npcmtmax,natmtot,ndmag,nqpt)) allocate(bxcrir(ngtot,ndmag,nqpt)) end if call holdthd(nqpt/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(rhomt_,rhoir_,vxcmt_) & !$OMP PRIVATE(magmt_,magir_,bxcmt_) & !$OMP PRIVATE(ias,is,idm) & !$OMP NUM_THREADS(nthd) allocate(rhomt_(npmtmax,natmtot),rhoir_(ngtot)) allocate(vxcmt_(npmtmax,natmtot)) if (spinpol) then allocate(magmt_(npmtmax,natmtot,ndmag),magir_(ngtot,ndmag)) allocate(bxcmt_(npmtmax,natmtot,ndmag)) end if !$OMP DO do ir=1,nqpt ! distribute among MPI processes if (mod(ir-1,np_mpi).ne.lp_mpi) cycle ! convert muffin-tin density and magnetisation from coarse to fine radial mesh do ias=1,natmtot is=idxis(ias) call dcopy(npcmt(is),rhormt(:,ias,ir),1,rhomt_(:,ias),1) end do call rfmtctof(rhomt_) do idm=1,ndmag do ias=1,natmtot is=idxis(ias) call dcopy(npcmt(is),magrmt(:,ias,idm,ir),1,magmt_(:,ias,idm),1) end do call rfmtctof(magmt_(:,:,idm)) end do ! convert interstitial density and magnetisation from coarse to fine grid call rfirctof(rhorir(:,ir),rhoir_) do idm=1,ndmag call rfirctof(magrir(:,idm,ir),magir_(:,idm)) end do ! calculate the exchange-correlation potential and magnetic field call potxc(.false.,xctype,rhomt_,rhoir_,magmt_,magir_,taumt,tauir,exmt,exir, & ecmt,ecir,vxcmt_,vxcrir(:,ir),bxcmt_,bxcrir(:,:,ir),wxcmt,wxcir) ! convert muffin-tin potential and field from fine to coarse radial mesh do ias=1,natmtot is=idxis(ias) call rfmtftoc(nrcmt(is),nrcmti(is),vxcmt_(:,ias),vxcrmt(:,ias,ir)) end do do idm=1,ndmag do ias=1,natmtot is=idxis(ias) call rfmtftoc(nrcmt(is),nrcmti(is),bxcmt_(:,ias,idm),bxcrmt(:,ias,idm,ir)) end do end do end do !$OMP END DO deallocate(rhomt_,rhoir_,vxcmt_) if (spinpol) deallocate(magmt_,magir_,bxcmt_) !$OMP END PARALLEL call freethd(nthd) ! broadcast potentials and fields to every MPI process if (np_mpi.gt.1) then n=npcmtmax*natmtot do ir=1,nqpt lp=mod(ir-1,np_mpi) call mpi_bcast(vxcrmt(:,:,ir),n,mpi_double_precision,lp,mpicom,ierror) end do do ir=1,nqpt lp=mod(ir-1,np_mpi) call mpi_bcast(vxcrir(:,ir),ngtot,mpi_double_precision,lp,mpicom,ierror) end do if (spinpol) then n=npcmtmax*natmtot*ndmag do ir=1,nqpt lp=mod(ir-1,np_mpi) call mpi_bcast(bxcrmt(:,:,:,ir),n,mpi_double_precision,lp,mpicom,ierror) end do n=ngtot*ndmag do ir=1,nqpt lp=mod(ir-1,np_mpi) call mpi_bcast(bxcrir(:,:,ir),n,mpi_double_precision,lp,mpicom,ierror) end do end if end if allocate(vxcqmt(npcmtmax,natmtot,nfqrz),vxcqir(ngtot,nfqrz)) ! Fourier transform exchange-correlation potential to Q-space call rfzfftq(-1,1,ngtot,vxcrmt,vxcrir,vxcqmt,vxcqir) deallocate(vxcrmt,vxcrir) ! add V_xc and external Coulomb potential to Kohn-Sham potential call holdthd(nfqrz,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(z1,ias,is,npc) & !$OMP NUM_THREADS(nthd) !$OMP DO do ifq=1,nfqrz z1=vclq(ifq) do ias=1,natmtot is=idxis(ias) npc=npcmt(is) vsqmt(1:npc,ias,ifq)=vsqmt(1:npc,ias,ifq)+vxcqmt(1:npc,ias,ifq)+z1 end do end do !$OMP END DO NOWAIT !$OMP DO do ifq=1,nfqrz z1=vclq(ifq) vsqir(:,ifq)=vsqir(:,ifq)+vxcqir(:,ifq)+z1 end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) deallocate(vxcqmt,vxcqir) if (spinpol) then ! Fourier transform the exchange-correlation magnetic field to Q-space call rfzfftq(-1,ndmag,ngtot,bxcrmt,bxcrir,bsqmt,bsqir) deallocate(bxcrmt,bxcrir) ! add external magnetic fields call holdthd(nfqrz,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(idm,z1,z2,ias,is,npc) & !$OMP NUM_THREADS(nthd) !$OMP DO do ifq=1,nfqrz do idm=1,ndmag z1=bfcq(idm,ifq) do ias=1,natmtot is=idxis(ias) npc=npcmt(is) z2=z1+bfcmtq(ias,idm,ifq) bsqmt(1:npc,ias,idm,ifq)=bsqmt(1:npc,ias,idm,ifq)+z2 end do end do end do !$OMP END DO NOWAIT !$OMP DO do ifq=1,nfqrz do idm=1,ndmag z1=bfcq(idm,ifq) bsqir(:,idm,ifq)=bsqir(:,idm,ifq)+z1 end do end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/occupyulr.f900000644000000000000000000000013214061636517015271 xustar0030 mtime=1623670095.867101608 30 atime=1623670094.719102674 30 ctime=1623670095.867101608 elk-7.2.42/src/occupyulr.f900000644002504400250440000000261714061636517017334 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine occupyulr use modmain use modulr implicit none ! local variables integer, parameter :: maxit=1000 integer ik0,ik,ist,it real(8) e0,e1,e real(8) chg,x,t1 ! external functions real(8), external :: stheta ! find minimum and maximum eigenvalues e0=evalu(1,1) e1=e0 do ik0=1,nkpt0 do ist=1,nstulr e=evalu(ist,ik0) if (e.lt.e0) e0=e if (e.gt.e1) e1=e end do end do if (e0.lt.e0min) then write(*,*) write(*,'("Warning(occupyulr): minimum eigenvalue less than minimum & &linearisation energy : ",2G18.10)') e0,e0min write(*,'(" for s.c. loop ",I5)') iscl end if t1=1.d0/swidth ! determine the Fermi energy using the bisection method do it=1,maxit efermi=0.5d0*(e0+e1) chg=0.d0 do ik0=1,nkpt0 ! central k-point ik=(ik0-1)*nkpa+1 do ist=1,nstulr e=evalu(ist,ik0) if (e.lt.e0min) then occulr(ist,ik0)=0.d0 else x=(efermi-e)*t1 occulr(ist,ik0)=occmax*stheta(stype,x) chg=chg+wkpt(ik)*occulr(ist,ik0) end if end do end do if (chg.lt.chgval) then e0=efermi else e1=efermi end if if ((e1-e0).lt.1.d-12) return end do write(*,*) write(*,'("Warning(occupyulr): could not find Fermi energy")') end subroutine elk-7.2.42/src/PaxHeaders.21776/writeinfou.f900000644000000000000000000000013214061636517015437 xustar0030 mtime=1623670095.868101607 30 atime=1623670094.721102672 30 ctime=1623670095.868101607 elk-7.2.42/src/writeinfou.f900000644002504400250440000000336014061636517017476 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeinfou(fnum) use modmain use modulr implicit none ! arguments integer fnum ! local variables real(8) t1 write(fnum,'("+------------------------------+")') write(fnum,'("| Ultra long-range calculation |")') write(fnum,'("+------------------------------+")') write(fnum,*) write(fnum,'("Ultracell lattice vectors :")') write(fnum,'(3G18.10)') avecu(1,1),avecu(2,1),avecu(3,1) write(fnum,'(3G18.10)') avecu(1,2),avecu(2,2),avecu(3,2) write(fnum,'(3G18.10)') avecu(1,3),avecu(2,3),avecu(3,3) write(fnum,*) write(fnum,'("Ultracell reciprocal lattice vectors :")') write(fnum,'(3G18.10)') bvecu(1,1),bvecu(2,1),bvecu(3,1) write(fnum,'(3G18.10)') bvecu(1,2),bvecu(2,2),bvecu(3,2) write(fnum,'(3G18.10)') bvecu(1,3),bvecu(2,3),bvecu(3,3) write(fnum,*) write(fnum,'("Ultracell volume : ",G18.10)') omegau write(fnum,'("Ultracell Brillouin zone volume : ",G18.10)') omegabzu write(fnum,*) t1=omegau/omega write(fnum,'("Ratio of ultracell to unit cell volume : ",G18.10)') t1 t1=t1*dble(natmtot) write(fnum,'("Number of atoms in ultracell : ",I16)') nint(t1,8) write(fnum,*) write(fnum,'("kappa-point grid : ",3I6)') ngridkpa write(fnum,'("Q-point grid : ",3I6)') ngridq write(fnum,*) write(fnum,'("Small Q-vector cut-off : ",G18.10)') q0cut if (fsmtype.ne.0) then write(fnum,*) write(fnum,'("Fixed spin moment (FSM) calculation, type : ",I4)') fsmtype if (fsmtype.lt.0) then write(fnum,'(" only moment direction is fixed")') end if end if write(fnum,*) write(fnum,'("Hamiltonian matrix size : ",I8)') nstulr flush(fnum) end subroutine elk-7.2.42/src/PaxHeaders.21776/zfplot.f900000644000000000000000000000013214061636517014562 xustar0030 mtime=1623670095.870101605 30 atime=1623670094.722102671 30 ctime=1623670095.870101605 elk-7.2.42/src/zfplot.f900000644002504400250440000001000514061636517016613 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zfplot(np,vpl,zfmt,zfir,fp) use modmain use modomp implicit none ! arguments integer, intent(in) :: np real(8), intent(in) :: vpl(3,np) complex(8), intent(in) :: zfmt(npcmtmax,natmtot),zfir(ngtot) complex(8), intent(out) :: fp(np) ! local variables integer ias,is,ip,nthd ! allocatable arrays complex(8), allocatable :: zfmt1(:,:,:),zfft(:) ! unpack the muffin-tin function allocate(zfmt1(lmmaxo,nrcmtmax,natmtot)) call holdthd(natmtot,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(is) & !$OMP NUM_THREADS(nthd) do ias=1,natmtot is=idxis(ias) call zfmtpack(.false.,nrcmt(is),nrcmti(is),zfmt(:,ias),zfmt1(:,:,ias)) end do !$OMP END PARALLEL DO call freethd(nthd) ! Fourier transform rfir to G-space allocate(zfft(ngtot)) zfft(:)=zfir(:) call zfftifc(3,ngridg,-1,zfft) ! begin loop over all points call holdthd(np,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ip=1,np call zfip(ip) end do !$OMP END PARALLEL DO call freethd(nthd) deallocate(zfmt1,zfft) return contains subroutine zfip(ip) implicit none ! arguments integer, intent(in) :: ip ! local variables integer is,ia,ias,nrc,nrci integer irc0,irc,lmax,l,m,lm integer ig,ifg,i1,i2,i3,i,j real(8) rmt2,r,ya1(4),ya2(4),t1,t2 real(8) v1(3),v2(3),v3(3),v4(3),v5(3) complex(8) z1 ! automatic arrays complex(8) ylm(lmmaxo) v2(:)=vpl(:,ip) call r3frac(epslat,v2) ! convert point to Cartesian coordinates call r3mv(avec,v2,v1) ! check if point is in a muffin-tin do is=1,nspecies nrc=nrcmt(is) nrci=nrcmti(is) rmt2=rmt(is)**2 do ia=1,natoms(is) ias=idxas(ia,is) v2(:)=v1(:)-atposc(:,ia,is) do i1=-1,1 v3(:)=v2(:)+dble(i1)*avec(:,1) do i2=-1,1 v4(:)=v3(:)+dble(i2)*avec(:,2) do i3=-1,1 v5(:)=v4(:)+dble(i3)*avec(:,3) t1=v5(1)**2+v5(2)**2+v5(3)**2 if (t1.lt.rmt2) then r=sqrt(t1) call genylmv(lmaxo,v5,ylm) do irc=1,nrc if (rcmt(irc,is).ge.r) then if (irc.le.3) then irc0=1 else if (irc.gt.nrc-2) then irc0=nrc-3 else irc0=irc-2 end if r=max(r,rcmt(1,is)) if (irc0.le.nrci) then lmax=lmaxi else lmax=lmaxo end if z1=0.d0 lm=0 do l=0,lmax do m=-l,l lm=lm+1 do j=1,4 i=irc0+j-1 ya1(j)=dble(zfmt1(lm,i,ias)) ya2(j)=aimag(zfmt1(lm,i,ias)) end do t1=poly4(rcmt(irc0,is),ya1,r) t2=poly4(rcmt(irc0,is),ya2,r) z1=z1+cmplx(t1,t2,8)*ylm(lm) end do end do goto 10 end if end do end if end do end do end do end do end do ! otherwise use direct Fourier transform of interstitial function z1=0.d0 do ig=1,ngvec ifg=igfft(ig) t1=vgc(1,ig)*v1(1)+vgc(2,ig)*v1(2)+vgc(3,ig)*v1(3) z1=z1+zfft(ifg)*cmplx(cos(t1),sin(t1),8) end do 10 continue fp(ip)=z1 end subroutine pure real(8) function poly4(xa,ya,x) implicit none ! arguments real(8), intent(in) :: xa(4),ya(4),x ! local variables real(8) x0,x1,x2,x3,y0,y1,y2,y3 real(8) c1,c2,c3,t0,t1,t2,t3,t4,t5,t6 ! evaluate the polynomial coefficients x0=xa(1) x1=xa(2)-x0; x2=xa(3)-x0; x3=xa(4)-x0 t4=x1-x2; t5=x1-x3; t6=x2-x3 y0=ya(1) y1=ya(2)-y0; y2=ya(3)-y0; y3=ya(4)-y0 t1=x1*x2*y3; t2=x2*x3*y1; t3=x1*x3 t0=1.d0/(x2*t3*t4*t5*t6) t3=t3*y2 c3=t1*t4+t2*t6-t3*t5 t4=x1**2; t5=x2**2; t6=x3**2 c2=t1*(t5-t4)+t2*(t6-t5)+t3*(t4-t6) c1=t1*(x2*t4-x1*t5)+t2*(x3*t5-x2*t6)+t3*(x1*t6-x3*t4) t1=x-x0 ! evaluate the polynomial poly4=y0+t0*t1*(c1+t1*(c2+c3*t1)) end function end subroutine elk-7.2.42/src/PaxHeaders.21776/writeengyu.f900000644000000000000000000000013214061636517015446 xustar0030 mtime=1623670095.871101605 30 atime=1623670094.724102669 30 ctime=1623670095.871101605 elk-7.2.42/src/writeengyu.f900000644002504400250440000000063714061636517017511 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeengyu(fnum) use modmain use modulr implicit none ! arguments integer, intent(in) :: fnum write(fnum,*) write(fnum,'("Energies :")') write(fnum,'(" Fermi",T30,": ",G22.12)') efermi end subroutine elk-7.2.42/src/PaxHeaders.21776/writevclr.f900000644000000000000000000000013214061636517015265 xustar0030 mtime=1623670095.873101603 30 atime=1623670094.726102667 30 ctime=1623670095.873101603 elk-7.2.42/src/writevclr.f900000644002504400250440000000144414061636517017325 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writevclr use modmain use modulr implicit none ! local variables integer i1,i2,i3,ir ! allocatable arrays real(8), allocatable :: vclr(:) allocate(vclr(nqpt)) ! Fourier transform external Coulomb potential from Q-space to real-space call rzfftifc(3,ngridq,1,vclr,vclq) ! write the real-space potential to file open(50,file='VCLR.OUT',form='FORMATTED') write(50,'(3I6," : grid size")') ngridq ir=0 do i3=1,ngridq(3) do i2=1,ngridq(2) do i1=1,ngridq(1) ir=ir+1 write(50,'(3I6,G18.10)') i1,i2,i3,vclr(ir) end do end do end do close(50) deallocate(vclr) end subroutine elk-7.2.42/src/PaxHeaders.21776/vclqinit.f900000644000000000000000000000013214061636517015075 xustar0030 mtime=1623670095.874101602 30 atime=1623670094.727102666 30 ctime=1623670095.874101602 elk-7.2.42/src/vclqinit.f900000644002504400250440000000113214061636517017127 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine vclqinit use modmain use modulr implicit none ! zero the external Coulomb potential in Q-space vclq(:)=0.d0 if (trdvclr) then ! read the external Coulomb potential from file if required call readvclr else ! determine the external Coulomb potential from the constant electric field call potefieldu ! write the external Coulomb potential to file call writevclr end if end subroutine elk-7.2.42/src/PaxHeaders.21776/genhdbulr.f900000644000000000000000000000012614061636517015221 xustar0028 mtime=1623670095.8761016 30 atime=1623670094.729102665 28 ctime=1623670095.8761016 elk-7.2.42/src/genhdbulr.f900000644002504400250440000000133614061636517017256 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genhdbulr use modmain use modulr use modmpi use modomp implicit none ! local variables integer ik0,nthd ! loop over original k-points call holdthd(nkpt0/np_mpi,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ik0=1,nkpt0 ! distribute among MPI processes if (mod(ik0-1,np_mpi).ne.lp_mpi) cycle ! write the long-range Hamiltonian diagonal blocks to file call puthdbulr(ik0) end do !$OMP END PARALLEL DO call freethd(nthd) ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/addbfsmu.f900000644000000000000000000000013214061636517015031 xustar0030 mtime=1623670095.877101599 30 atime=1623670094.731102663 30 ctime=1623670095.877101599 elk-7.2.42/src/addbfsmu.f900000644002504400250440000000167514061636517017077 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine addbfsmu use modmain use modulr implicit none ! local variables integer idm,is,ias,npc real(8) t1 ! add the global fixed spin moment B-field to the Kohn-Sham field if ((abs(fsmtype).eq.1).or.(abs(fsmtype).eq.3)) then do idm=1,ndmag t1=bfsmc(idm) do ias=1,natmtot is=idxis(ias) npc=npcmt(is) bsqmt(1:npc,ias,idm,1)=bsqmt(1:npc,ias,idm,1)+t1 end do bsqir(1:ngtot,idm,1)=bsqir(1:ngtot,idm,1)+t1*cfunir(1:ngtot) end do end if ! add the muffin-tin fields if ((abs(fsmtype).eq.2).or.(abs(fsmtype).eq.3)) then do idm=1,ndmag do ias=1,natmtot is=idxis(ias) npc=npcmt(is) t1=bfsmcmt(idm,ias) bsqmt(1:npc,ias,idm,1)=bsqmt(1:npc,ias,idm,1)+t1 end do end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/writechgrmt.f900000644000000000000000000000013214061636517015603 xustar0030 mtime=1623670095.879101597 30 atime=1623670094.732102662 30 ctime=1623670095.879101597 elk-7.2.42/src/writechgrmt.f900000644002504400250440000000131314061636517017636 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writechgrmt use modmain use modulr implicit none ! local variables integer is,ia,ias,ir open(50,file='CHGMTRU.OUT',form='FORMATTED') do ir=1,nqpt write(50,*) write(50,'("R-point (Cartesian coordinates) :")') write(50,'(3G18.10)') vrcu(:,ir) do is=1,nspecies write(50,'(" species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) ias=idxas(ia,is) write(50,'(" atom ",I4,T30,": ",G18.10)') ia,chgmtru(ias,ir) end do end do end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/initulr.f900000644000000000000000000000013114061636517014731 xustar0030 mtime=1623670095.880101596 29 atime=1623670094.73410266 30 ctime=1623670095.880101596 elk-7.2.42/src/initulr.f900000644002504400250440000001166614061636517017001 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine initulr use modmain use modulr use modomp implicit none ! local variables integer ik0,ik,ist,jst integer iq,jq,ifq,ig integer n,i,i1,i2,i3,nthd real(8) t1 ! allocatable arrays integer, allocatable :: idx(:) real(8), allocatable :: jlgqr(:,:) ! allocate long-range density and magnetisation arrays if (allocated(rhormt)) deallocate(rhormt) allocate(rhormt(npcmtmax,natmtot,nqpt)) if (allocated(rhorir)) deallocate(rhorir) allocate(rhorir(ngtc,nqpt)) if (allocated(magrmt)) deallocate(magrmt) if (allocated(magrir)) deallocate(magrir) if (spinpol) then allocate(magrmt(npcmtmax,natmtot,ndmag,nqpt)) allocate(magrir(ngtc,ndmag,nqpt)) end if if (allocated(rhoqmt)) deallocate(rhoqmt) allocate(rhoqmt(npcmtmax,natmtot,nfqrz)) if (allocated(rhoqir)) deallocate(rhoqir) allocate(rhoqir(ngtc,nfqrz)) if (allocated(chgmtru)) deallocate(chgmtru) allocate(chgmtru(natmtot,nqpt)) if (allocated(magqmt)) deallocate(magqmt) if (allocated(magqir)) deallocate(magqir) if (allocated(mommtru)) deallocate(mommtru) if (spinpol) then allocate(magqmt(npcmtmax,natmtot,ndmag,nfqrz)) allocate(magqir(ngtc,ndmag,nfqrz)) allocate(mommtru(ndmag,natmtot,nqpt)) end if ! allocate potential and magnetic field arrays if (allocated(vclq)) deallocate(vclq) allocate(vclq(nfqrz)) if (allocated(bfcq)) deallocate(bfcq) if (allocated(bfcmtq)) deallocate(bfcmtq) if (spinpol) then allocate(bfcq(ndmag,nfqrz)) allocate(bfcmtq(natmtot,ndmag,nfqrz)) end if ! combined target array for Kohn-Sham potential and magnetic field if (allocated(vsbsq)) deallocate(vsbsq) n=(npcmtmax*natmtot+ngtot)*nfqrz if (spinpol) n=n*(1+ndmag) allocate(vsbsq(n)) ! zero the array vsbsq(:)=0.d0 ! associate pointer arrays with target vsqmt(1:npcmtmax,1:natmtot,1:nfqrz)=>vsbsq(1:) i=npcmtmax*natmtot*nfqrz+1 vsqir(1:ngtot,1:nfqrz)=>vsbsq(i:) if (spinpol) then i=i+ngtot*nfqrz bsqmt(1:npcmtmax,1:natmtot,1:ndmag,1:nfqrz)=>vsbsq(i:) i=i+npcmtmax*natmtot*ndmag*nfqrz bsqir(1:ngtot,1:ndmag,1:nfqrz)=>vsbsq(i:) end if ! G+Q-vector arrays if (allocated(vgqc)) deallocate(vgqc) allocate(vgqc(3,ngvec,nfqrz)) if (allocated(gqc)) deallocate(gqc) allocate(gqc(ngvec,nfqrz)) if (allocated(ylmgq)) deallocate(ylmgq) allocate(ylmgq(lmmaxo,ngvec,nfqrz)) if (allocated(sfacgq)) deallocate(sfacgq) allocate(sfacgq(ngvec,natmtot,nfqrz)) if (allocated(gclq)) deallocate(gclq) allocate(gclq(nqpt)) if (allocated(gclgq)) deallocate(gclgq) allocate(gclgq(ngvec,nfqrz)) if (allocated(jlgqrmt)) deallocate(jlgqrmt) allocate(jlgqrmt(0:lnpsd,ngvec,nspecies,nfqrz)) if (allocated(expqmt)) deallocate(expqmt) allocate(expqmt(npcmtmax,natmtot,nqpt)) call holdthd(nfqrz,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(jlgqr,iq,ig,t1) & !$OMP PRIVATE(i1,i2,i3,jq) & !$OMP NUM_THREADS(nthd) allocate(jlgqr(njcmax,nspecies)) !$OMP DO do ifq=1,nfqrz iq=iqrzf(ifq) do ig=1,ngvec ! determine the G+Q-vectors vgqc(:,ig,ifq)=vgc(:,ig)+vqc(:,iq) ! G+Q-vector length gqc(ig,ifq)=sqrt(vgqc(1,ig,ifq)**2+vgqc(2,ig,ifq)**2+vgqc(3,ig,ifq)**2) ! spherical harmonics for G+Q-vectors call genylmv(lmaxo,vgqc(:,ig,ifq),ylmgq(:,ig,ifq)) end do ! generate the spherical Bessel functions j_l(|G+Q|r) call genjlgpr(1,gqc(1,ifq),jlgqr) ! structure factors for G+Q-vectors call gensfacgp(ngvec,vgqc(:,:,ifq),ngvec,sfacgq(:,:,ifq)) ! generate the Coulomb Green's function in Q-space with small Q cut-off t1=sqrt(vqc(1,iq)**2+vqc(2,iq)**2+vqc(3,iq)**2) if (t1.gt.q0cut+epslat) then gclq(iq)=fourpi/t1**2 else gclq(iq)=0.d0 end if ! generate the Coulomb Green's function in G+Q-space call gengclgq(.true.,iq,ngvec,gqc(:,ifq),gclgq(:,ifq)) ! compute the spherical Bessel functions j_l(|G+Q|R_mt) call genjlgprmt(lnpsd,ngvec,gqc(:,ifq),ngvec,jlgqrmt(:,:,:,ifq)) ! generate phase factor functions exp(iQ.r) in each muffin-tin call genexpmt(1,jlgqr,ylmgq(:,:,ifq),ngvec,sfacgq(:,:,ifq),expqmt(:,:,iq)) ! store the phase factor function for -Q i1=-ivq(1,iq); i2=-ivq(2,iq); i3=-ivq(3,iq) if ((i1.ge.intq(1,1)).and.(i1.le.intq(2,1)).and. & (i2.ge.intq(1,2)).and.(i2.le.intq(2,2)).and. & (i3.ge.intq(1,3)).and.(i3.le.intq(2,3)).and.(ifq.gt.1)) then jq=ivqiq(i1,i2,i3) expqmt(:,:,jq)=conjg(expqmt(:,:,iq)) end if end do !$OMP END DO deallocate(jlgqr) !$OMP END PARALLEL call freethd(nthd) ! number of long-range states nstulr=nstsv*nkpa ! allocate eigenvalue array if (allocated(evalu)) deallocate(evalu) allocate(evalu(nstulr,nkpt0)) ! allocate the occupation number array if (allocated(occulr)) deallocate(occulr) allocate(occulr(nstulr,nkpt0)) ! initialise the occupation numbers allocate(idx(nstulr)) do ik0=1,nkpt0 ik=(ik0-1)*nkpa+1 call sortidx(nstulr,occsv(1,ik),idx) do ist=1,nstulr i=idx(nstulr-ist+1)-1 ik=(ik0-1)*nkpa+i/nstsv+1 jst=mod(i,nstsv)+1 occulr(ist,ik0)=occsv(jst,ik) end do end do deallocate(idx) end subroutine elk-7.2.42/src/PaxHeaders.21776/writemomrmt.f900000644000000000000000000000013214061636517015632 xustar0030 mtime=1623670095.882101594 30 atime=1623670094.736102658 30 ctime=1623670095.882101594 elk-7.2.42/src/writemomrmt.f900000644002504400250440000000132414061636517017667 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writemomrmt use modmain use modulr implicit none ! local variables integer is,ia,ias,ir open(50,file='MOMMTRU.OUT',form='FORMATTED') do ir=1,nqpt write(50,*) write(50,'("R-point (Cartesian coordinates) :")') write(50,'(3G18.10)') vrcu(:,ir) do is=1,nspecies write(50,'(" species : ",I4," (",A,")")') is,trim(spsymb(is)) do ia=1,natoms(is) ias=idxas(ia,is) write(50,'(" atom ",I4,T30,": ",3G18.10)') ia,mommtru(1:ndmag,ias,ir) end do end do end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/writestulr.f900000644000000000000000000000013214061636517015470 xustar0030 mtime=1623670095.883101593 30 atime=1623670094.737102657 30 ctime=1623670095.883101593 elk-7.2.42/src/writestulr.f900000644002504400250440000000307214061636517017527 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writestulr use modmain use modulr implicit none ! local variables integer ifq,idm open(100,file='STATE_ULR.OUT',form='UNFORMATTED',action='WRITE') write(100) version write(100) natmtot write(100) npcmtmax write(100) ngtc write(100) ngtot write(100) ndmag write(100) fsmtype write(100) nqpt write(100) nfqrz write(100) ivq write(100) iqrzf ! write the ultra long-range density in Q-space do ifq=1,nfqrz write(100) rhoqmt(:,:,ifq) write(100) rhoqir(:,ifq) end do ! write the Kohn-Sham effective potential in Q-space do ifq=1,nfqrz write(100) vsqmt(:,:,ifq) write(100) vsqir(:,ifq) end do ! write the external Coulomb potential in Q-space do ifq=1,nfqrz write(100) vclq(ifq) end do if (spinpol) then ! write the magnetisation in Q-space do ifq=1,nfqrz do idm=1,ndmag write(100) magqmt(:,:,idm,ifq) write(100) magqir(:,idm,ifq) end do end do ! write the Kohn-Sham effective magnetic field in Q-space do ifq=1,nfqrz do idm=1,ndmag write(100) bsqmt(:,:,idm,ifq) write(100) bsqir(:,idm,ifq) end do end do ! write the external magnetic fields in Q-space do ifq=1,nfqrz do idm=1,ndmag write(100) bfcq(idm,ifq) write(100) bfcmtq(:,idm,ifq) end do end do ! write fixed spin moment magnetic fields if (fsmtype.ne.0) then write(100) bfsmc write(100) bfsmcmt end if end if close(100) end subroutine elk-7.2.42/src/PaxHeaders.21776/readstulr.f900000644000000000000000000000013214061636517015251 xustar0030 mtime=1623670095.885101591 30 atime=1623670094.739102655 30 ctime=1623670095.885101591 elk-7.2.42/src/readstulr.f900000644002504400250440000001212114061636517017303 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readstulr use modmain use modulr implicit none ! local variables integer iq,jq,ifq,jfq integer idm,i1,i2,i3 integer version_(3),ios integer natmtot_,npcmtmax_,ngtc_,ngtot_ integer ndmag_,fsmtype_,nqpt_,nfqrz_ complex(8) z1 ! automatic arrays complex(8) zv(natmtot) ! allocatable arrays integer, allocatable :: ivq_(:,:),iqrzf_(:),map(:) complex(8), allocatable :: zfmt(:,:),zfir(:) open(100,file='STATE_ULR.OUT',form='UNFORMATTED',action='READ',status='OLD', & iostat=ios) if (ios.ne.0) then write(*,*) write(*,'("Error(readstulr): error opening STATE_ULR.OUT")') write(*,*) stop end if read(100) version_ if ((version(1).ne.version_(1)).or.(version(2).ne.version_(2)).or. & (version(3).ne.version_(3))) then write(*,*) write(*,'("Warning(readstulr): different versions")') write(*,'(" current : ",I3.3,".",I3.3,".",I3.3)') version write(*,'(" STATE_ULR.OUT : ",I3.3,".",I3.3,".",I3.3)') version_ end if read(100) natmtot_ if (natmtot.ne.natmtot_) then write(*,*) write(*,'("Error(readstulr): differing natmtot")') write(*,'(" current : ",I6)') natmtot write(*,'(" STATE_ULR.OUT : ",I6)') natmtot_ write(*,*) stop end if read(100) npcmtmax_ if (npcmtmax.ne.npcmtmax_) then write(*,*) write(*,'("Error(readstulr): differing npcmtmax")') write(*,'(" current : ",I6)') npcmtmax write(*,'(" STATE_ULR.OUT : ",I6)') npcmtmax_ write(*,*) stop end if read(100) ngtc_ if (ngtc.ne.ngtc_) then write(*,*) write(*,'("Error(readstulr): differing ngtc")') write(*,'(" current : ",I8)') ngtc write(*,'(" STATE_ULR.OUT : ",I8)') ngtc_ write(*,*) stop end if read(100) ngtot_ if (ngtot.ne.ngtot_) then write(*,*) write(*,'("Error(readstulr): differing ngtot")') write(*,'(" current : ",I8)') ngtot write(*,'(" STATE_ULR.OUT : ",I8)') ngtot_ write(*,*) stop end if read(100) ndmag_ if (ndmag.ne.ndmag_) then write(*,*) write(*,'("Error(readstulr): differing ndmag")') write(*,'(" current : ",I1)') ndmag write(*,'(" STATE_ULR.OUT : ",I1)') ndmag_ write(*,*) stop end if read(100) fsmtype_ if (fsmtype.ne.fsmtype_) then write(*,*) write(*,'("Error(readstulr): differing fsmtype")') write(*,'(" current : ",I4)') fsmtype write(*,'(" STATE_ULR.OUT : ",I4)') fsmtype_ write(*,*) stop end if read(100) nqpt_ if (nqpt_.le.0) then write(*,*) write(*,'("Error(readstulr): nqpt_ <= 0 : ",I8)') nqpt_ write(*,*) stop end if read(100) nfqrz_ if (nfqrz_.le.0) then write(*,*) write(*,'("Error(readstulr): nfqrz_ <= 0 : ",I8)') nfqrz_ write(*,*) stop end if allocate(ivq_(3,nqpt_),iqrzf_(nfqrz_),map(nfqrz_)) read(100) ivq_ read(100) iqrzf_ ! generate map from old Q-vector grid to new map(:)=0 do ifq=1,nfqrz_ iq=iqrzf_(ifq) i1=ivq_(1,iq); i2=ivq_(2,iq); i3=ivq_(3,iq) if ((i1.ge.intq(1,1)).and.(i1.le.intq(2,1)).and. & (i2.ge.intq(1,2)).and.(i2.le.intq(2,2)).and. & (i3.ge.intq(1,3)).and.(i3.le.intq(2,3))) then jq=ivqiq(i1,i2,i3) jfq=ifqrz(jq) map(ifq)=jfq end if end do deallocate(ivq_,iqrzf_) allocate(zfmt(npcmtmax,natmtot),zfir(ngtot)) ! read the Q-space density rhoqmt(:,:,:)=0.d0 rhoqir(:,:)=0.d0 do ifq=1,nfqrz_ jfq=map(ifq) if (jfq.gt.0) then read(100) rhoqmt(:,:,jfq) read(100) rhoqir(:,jfq) else read(100) zfmt read(100) zfir(1:ngtc) end if end do ! read the Q-space Kohn-Sham potential vsqmt(:,:,:)=0.d0 vsqir(:,:)=0.d0 do ifq=1,nfqrz_ jfq=map(ifq) if (jfq.gt.0) then read(100) vsqmt(:,:,jfq) read(100) vsqir(:,jfq) else read(100) zfmt read(100) zfir end if end do ! read the external Coulomb potential in Q-space vclq(:)=0.d0 do ifq=1,nfqrz_ jfq=map(ifq) if (jfq.gt.0) then read(100) vclq(jfq) else read(100) z1 end if end do if (spinpol) then ! read the Q-space magnetisation density magqmt(:,:,:,:)=0.d0 magqir(:,:,:)=0.d0 do ifq=1,nfqrz_ jfq=map(ifq) if (jfq.gt.0) then do idm=1,ndmag read(100) magqmt(:,:,idm,jfq) read(100) magqir(:,idm,jfq) end do else do idm=1,ndmag read(100) zfmt read(100) zfir(1:ngtc) end do end if end do bsqmt(:,:,:,:)=0.d0 bsqir(:,:,:)=0.d0 do ifq=1,nfqrz_ jfq=map(ifq) if (jfq.gt.0) then do idm=1,ndmag read(100) bsqmt(:,:,idm,jfq) read(100) bsqir(:,idm,jfq) end do else do idm=1,ndmag read(100) zfmt read(100) zfir end do end if end do ! read the external magnetic fields in Q-space bfcq(:,:)=0.d0 bfcmtq(:,:,:)=0.d0 do ifq=1,nfqrz_ jfq=map(ifq) if (jfq.gt.0) then do idm=1,ndmag read(100) bfcq(idm,jfq) read(100) bfcmtq(:,idm,jfq) end do else do idm=1,ndmag read(100) z1 read(100) zv end do end if end do ! read fixed spin moment effective fields if (fsmtype.ne.0) then read(100) bfsmc read(100) bfsmcmt end if end if close(100) deallocate(map,zfmt,zfir) end subroutine elk-7.2.42/src/PaxHeaders.21776/potefieldu.f900000644000000000000000000000013214061636517015404 xustar0030 mtime=1623670095.886101591 30 atime=1623670094.741102653 30 ctime=1623670095.886101591 elk-7.2.42/src/potefieldu.f900000644002504400250440000000142414061636517017442 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potefieldu use modmain use modulr implicit none ! local variables integer ir real(8) v0,v(3) ! allocatable arrays real(8), allocatable :: rfft(:) if (sum(abs(efielduc(:))).lt.epslat) return allocate(rfft(nqpt)) ! constant added to potential so that it is zero at the ultracell center v(:)=0.5d0*(avecu(:,1)+avecu(:,2)+avecu(:,3)) v0=dot_product(efielduc(:),v(:)) ! calculate the potential in real-space do ir=1,nqpt rfft(ir)=v0-dot_product(efielduc(:),vrcu(:,ir)) end do ! Fourier transform to Q-space call rzfftifc(3,ngridq,-1,rfft,vclq) deallocate(rfft) end subroutine elk-7.2.42/src/PaxHeaders.21776/puthdbulr.f900000644000000000000000000000013214061636517015255 xustar0030 mtime=1623670095.888101589 30 atime=1623670094.742102653 30 ctime=1623670095.888101589 elk-7.2.42/src/puthdbulr.f900000644002504400250440000000613114061636517017313 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine puthdbulr(ik0) use modmain use modulr use modramdisk implicit none ! arguments integer, intent(in) :: ik0 ! local variables integer ik,ikk,ikpa integer ist,recl real(8) t1 ! automatic arrays integer idx(nstsv) ! allocatable arrays complex(8), allocatable :: apwalm(:,:,:,:),evecfv(:,:),evecsv(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfir(:,:,:) complex(8), allocatable :: wfmtk(:,:,:,:),wfgkk(:,:,:) complex(8), allocatable :: hdb(:,:,:),ok(:,:),b(:,:) ! central k-point ik=(ik0-1)*nkpa+1 ! get the ground-state eigenvectors from file for central k-point allocate(evecfv(nmatmax,nstfv),evecsv(nstsv,nstsv)) call getevecfv('.OUT',ik,vkl(:,ik),vgkl(:,:,:,ik),evecfv) call getevecsv('.OUT',ik,vkl(:,ik),evecsv) ! find the matching coefficients allocate(apwalm(ngkmax,apwordmax,lmmaxapw,natmtot)) call match(ngk(1,ik),vgkc(:,:,1,ik),gkc(:,1,ik),sfacgk(:,:,1,ik),apwalm) ! index to all states do ist=1,nstsv idx(ist)=ist end do ! calculate the wavefunctions for all states of the central k-point allocate(wfmt(npcmtmax,natmtot,nspinor,nstsv),wfir(ngtot,nspinor,nstsv)) call genwfsv(.false.,.false.,nstsv,idx,ngridg,igfft,ngk(1,ik),igkig(:,1,ik), & apwalm,evecfv,evecsv,wfmt,ngtot,wfir) ! compute the diagonal blocks of the ultra long-range Hamiltonian in the basis ! of the states at the central k-point allocate(wfmtk(npcmtmax,natmtot,nspinor,nstsv),wfgkk(ngkmax,nspinor,nstsv)) allocate(hdb(nstsv,nstsv,2:nkpa),ok(nstsv,nstsv),b(nstsv,nstsv)) do ikpa=2,nkpa ikk=(ik0-1)*nkpa+ikpa call getevecfv('.OUT',ikk,vkl(:,ikk),vgkl(:,:,:,ikk),evecfv) call getevecsv('.OUT',ikk,vkl(:,ikk),evecsv) call match(ngk(1,ikk),vgkc(:,:,1,ikk),gkc(:,1,ikk),sfacgk(:,:,1,ikk),apwalm) call genwfsv(.false.,.true.,nstsv,idx,ngridg,igfft,ngk(:,ikk),igkig(:,:,ikk),& apwalm,evecfv,evecsv,wfmtk,ngkmax,wfgkk) ! compute the overlap matrix between the states at k and k+kappa call genolpq(nstsv,expqmt(:,:,ikpa),ngk(:,ikk),igkig(:,:,ikk),wfmt,wfir, & wfmtk,wfgkk,ok) ! use singular value decompostion to make the matrix strictly unitary call unitary(nstsv,ok) ! apply the overlap matrix from the right to the eigenvalues at k+kappa do ist=1,nstsv t1=evalsv(ist,ikk) b(ist,:)=t1*ok(ist,:) end do ! apply the conjugate transpose of the overlap matrix from the left to form the ! Hamiltonian matrix in the basis of states at k call zgemm('C','N',nstsv,nstsv,nstsv,zone,ok,nstsv,b,nstsv,zzero, & hdb(:,:,ikpa),nstsv) end do ! determine the record length inquire(iolength=recl) vkl(:,1),nstsv,nkpa,hdb !$OMP CRITICAL(u300) open(300,file='HDBULR.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(300,rec=ik0) vkl(:,ik),nstsv,nkpa,hdb close(300) ! write to RAM disk if required if (ramdisk) then call putrd('HDBULR.OUT',ik0,v1=vkl(:,ik),n1=nstsv,n2=nkpa, & nzv=nstsv*nstsv*(nkpa-1),zva=hdb) end if !$OMP END CRITICAL(u300) deallocate(apwalm,evecfv,evecsv) deallocate(wfmt,wfir,wfmtk,wfgkk) deallocate(hdb,ok,b) end subroutine elk-7.2.42/src/PaxHeaders.21776/gethdbulr.f900000644000000000000000000000013214061636517015224 xustar0030 mtime=1623670095.889101588 30 atime=1623670094.744102651 30 ctime=1623670095.889101588 elk-7.2.42/src/gethdbulr.f900000644002504400250440000000320614061636517017262 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gethdbulr(ik0,hdb) use modmain use modulr use modramdisk implicit none ! arguments integer, intent(in) :: ik0 complex(8), intent(out) :: hdb(nstsv,nstsv,2:nkpa) ! local variables logical tgs integer nstsv_,nkpa_ integer ik,recl real(8) vkl_(3),t1 ! find the record length inquire(iolength=recl) vkl_,nstsv_,nkpa_,hdb !$OMP CRITICAL(u300) ! read from RAM disk if required if (ramdisk) then call getrd('HDBULR.OUT',ik0,tgs,v1=vkl_,n1=nstsv_,n2=nkpa_, & nzv=nstsv*nstsv*(nkpa-1),zva=hdb) if (tgs) goto 10 end if open(300,file='HDBULR.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(300,rec=ik0) vkl_,nstsv_,nkpa_,hdb 10 continue !$OMP END CRITICAL(u300) ! central k-point ik=(ik0-1)*nkpa+1 t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(gethdbulr): differing vectors for k-point ",I8)') ik0 write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" HDBULR.OUT : ",3G18.10)') vkl_ write(*,*) stop end if if (nstsv.ne.nstsv_) then write(*,*) write(*,'("Error(gethdbulr): differing nstsv for k-point ",I8)') ik0 write(*,'(" current : ",I8)') nstsv write(*,'(" HDBULR.OUT : ",I8)') nstsv_ write(*,*) stop end if if (nkpa.ne.nkpa_) then write(*,*) write(*,'("Error(gethdbulr): differing nkpa for k-point ",I8)') ik0 write(*,'(" current : ",I8)') nkpa write(*,'(" HDBULR.OUT : ",I8)') nkpa_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/potuinit.f900000644000000000000000000000013214061636517015117 xustar0030 mtime=1623670095.891101586 30 atime=1623670094.746102649 30 ctime=1623670095.891101586 elk-7.2.42/src/potuinit.f900000644002504400250440000000350714061636517017161 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potuinit use modmain use modulr use modrandom use modomp implicit none ! local variables integer ifq,idm,is,ias integer nrc,nrci,npc real(8) cb,t1 ! automatic arrays real(8) rfmt1(npcmtmax),rfmt2(npcmtmax) ! set the Q=0 muffin-tin potential equal to that of the normal ground-state do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) call rfmtftoc(nrc,nrci,vsmt(:,ias),rfmt1) call rbsht(nrc,nrci,rfmt1,rfmt2) vsqmt(1:npc,ias,1)=rfmt2(1:npc) end do ! zero the muffin-tin potential for non-zero Q do ifq=2,nfqrz do ias=1,natmtot is=idxis(ias) vsqmt(1:npcmt(is),ias,ifq)=0.d0 end do end do ! repeat for the interstitial potential vsqir(:,1)=vsir(:) vsqir(:,2:nfqrz)=0.d0 if (.not.spinpol) return ! set the Q=0 muffin-tin magnetic field equal to that of the normal ground-state do idm=1,ndmag do ias=1,natmtot is=idxis(ias) npc=npcmt(is) bsqmt(1:npc,ias,idm,1)=bsmt(1:npc,ias,idm) end do end do ! zero the magnetic field for non-zero Q do ifq=2,nfqrz do idm=1,ndmag do ias=1,natmtot is=idxis(ias) bsqmt(1:npcmt(is),ias,idm,ifq)=0.d0 end do end do end do ! repeat for the interstitial magnetic field bsqir(:,:,1)=bsir(:,:) bsqir(:,:,2:nfqrz)=0.d0 ! coupling constant of the external field (g_e/4c) cb=gfacte/(4.d0*solsc) ! initialise the external magnetic fields t1=cb*rndbfcu do ifq=1,nfqrz do idm=1,ndmag bfcq(idm,ifq)=t1*cmplx(randomu()-0.5d0,randomu()-0.5d0,8) do ias=1,natmtot bfcmtq(ias,idm,ifq)=t1*cmplx(randomu()-0.5d0,randomu()-0.5d0,8) end do end do end do bfcq(:,1)=dble(bfcq(:,1)) bfcmtq(:,:,1)=dble(bfcmtq(:,:,1)) end subroutine elk-7.2.42/src/PaxHeaders.21776/readvclr.f900000644000000000000000000000013214061636517015046 xustar0030 mtime=1623670095.892101585 30 atime=1623670094.747102648 30 ctime=1623670095.892101585 elk-7.2.42/src/readvclr.f900000644002504400250440000000245314061636517017107 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine readvclr use modmain use modulr implicit none ! local variables integer i1,i2,i3,ir integer ngridq_(3),i1_,i2_,i3_ ! allocatable arrays real(8), allocatable :: vclr(:) allocate(vclr(nqpt)) ! read the real-space external Coulomb potential from file open(50,file='VCLR.OUT',form='FORMATTED') read(50,*) ngridq_(:) if (any(ngridq(:).ne.ngridq_(:))) then write(*,*) write(*,'("Error(readvclr): differing ngridq")') write(*,'(" current : ",3I6)') ngridq write(*,'(" VCLR.OUT : ",3I6)') ngridq_ write(*,*) stop end if ir=0 do i3=1,ngridq(3) do i2=1,ngridq(2) do i1=1,ngridq(1) ir=ir+1 read(50,*) i1_,i2_,i3_,vclr(ir) if ((i1.ne.i1_).or.(i2.ne.i2_).or.(i3.ne.i3_)) then write(*,*) write(*,'("Error(readvclr): differing i1, i2 or i3")') write(*,'(" current : ",3I6)') i1,i2,i3 write(*,'(" VCLR.OUT : ",3I6)') i1_,i2_,i3_ write(*,*) stop end if end do end do end do close(50) ! Fourier transform external Coulomb potential from real-space to Q-space call rzfftifc(3,ngridq,-1,vclr,vclq) deallocate(vclr) end subroutine elk-7.2.42/src/PaxHeaders.21776/genkpakq.f900000644000000000000000000000013214061636517015045 xustar0030 mtime=1623670095.894101583 30 atime=1623670094.749102646 30 ctime=1623670095.894101583 elk-7.2.42/src/genkpakq.f900000644002504400250440000001041114061636517017077 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genkpakq use modmain use modulr implicit none ! local variables integer i1,i2,i3,j1,j2,j3 integer ikpa,ik0,ik integer n1,iq,ifq,ir real(8) v(3) ! allocatable arrays real(8), allocatable :: vkl0(:,:),vkc0(:,:),wkpt0(:) ! find next largest FFT-compatible Q-point grid size (radices 2, 3, 5 and 7) call nfftifc(4,ngridq(1)) call nfftifc(4,ngridq(2)) call nfftifc(4,ngridq(3)) ! total number of Q-points nqpt=ngridq(1)*ngridq(2)*ngridq(3) ! number of complex FFT elements for real-complex transforms n1=ngridq(1)/2+1 nfqrz=n1*ngridq(2)*ngridq(3) ! integer grid intervals for the Q-points intq(1,:)=ngridq(:)/2-ngridq(:)+1 intq(2,:)=ngridq(:)/2 ! kappa-point grid should be half the Q-point grid ngridkpa(:)=(ngridq(:)+1)/2 ! number of kappa-points nkpa=ngridkpa(1)*ngridkpa(2)*ngridkpa(3) ! integer grid intervals for the kappa-points intkpa(1,:)=ngridkpa(:)/2-ngridkpa(:)+1 intkpa(2,:)=ngridkpa(:)/2 ! allocate global Q-point arrays if (allocated(ivq)) deallocate(ivq) allocate(ivq(3,nqpt)) if (allocated(ivqiq)) deallocate(ivqiq) allocate(ivqiq(intq(1,1):intq(2,1),intq(1,2):intq(2,2),intq(1,3):intq(2,3))) if (allocated(iqfft)) deallocate(iqfft) allocate(iqfft(nqpt)) if (allocated(ifqrz)) deallocate(ifqrz) allocate(ifqrz(nqpt)) if (allocated(iqrzf)) deallocate(iqrzf) allocate(iqrzf(nfqrz)) if (allocated(vql)) deallocate(vql) allocate(vql(3,nqpt)) if (allocated(vqc)) deallocate(vqc) allocate(vqc(3,nqpt)) ! store the kappa-points as the first nkpa entries in the Q-point arrays iq=0 do i1=intkpa(1,1),intkpa(2,1) do i2=intkpa(1,2),intkpa(2,2) do i3=intkpa(1,3),intkpa(2,3) iq=iq+1 ivq(1,iq)=i1 ivq(2,iq)=i2 ivq(3,iq)=i3 end do end do end do ! store the remaining Q-points do i1=intq(1,1),intq(2,1) do i2=intq(1,2),intq(2,2) do i3=intq(1,3),intq(2,3) if ((i1.lt.intkpa(1,1)).or.(i1.gt.intkpa(2,1)).or. & (i2.lt.intkpa(1,2)).or.(i2.gt.intkpa(2,2)).or. & (i3.lt.intkpa(1,3)).or.(i3.gt.intkpa(2,3))) then iq=iq+1 ivq(1,iq)=i1 ivq(2,iq)=i2 ivq(3,iq)=i3 end if end do end do end do ! ensure the first point is the zero vector do iq=1,nkpa if ((ivq(1,iq).eq.0).and.(ivq(2,iq).eq.0).and.(ivq(3,iq).eq.0)) then ivq(:,iq)=ivq(:,1) ivq(:,1)=0 exit end if end do do iq=1,nqpt i1=ivq(1,iq); i2=ivq(2,iq); i3=ivq(3,iq) ! map from (i1,i2,i3) to Q-vector index ivqiq(i1,i2,i3)=iq ! Q-vector in Cartesian coordinates vqc(:,iq)=dble(i1)*bvecu(:,1) & +dble(i2)*bvecu(:,2) & +dble(i3)*bvecu(:,3) ! Q-vector in (unit cell) lattice coordinates call r3mv(binv,vqc(:,iq),vql(:,iq)) where(abs(vql(:,iq)).lt.epslat) vql(:,iq)=0.d0 end do ! set up Fourier transform index do iq=1,nqpt i1=ivq(1,iq); i2=ivq(2,iq); i3=ivq(3,iq) if (i1.ge.0) then j1=i1 else j1=ngridq(1)+i1 end if if (i2.ge.0) then j2=i2 else j2=ngridq(2)+i2 end if if (i3.ge.0) then j3=i3 else j3=ngridq(3)+i3 end if iqfft(iq)=j3*ngridq(2)*ngridq(1)+j2*ngridq(1)+j1+1 ! map from q-point index to real-complex FFT index and vice versa if (i1.ge.0) then ifq=j3*ngridq(2)*n1+j2*n1+j1+1 ifqrz(iq)=ifq iqrzf(ifq)=iq end if end do ! store the R-vectors in Cartesian coordinates spanning the ultracell if (allocated(vrcu)) deallocate(vrcu) allocate(vrcu(3,nqpt)) ir=0 do i3=0,ngridq(3)-1 v(3)=dble(i3)/dble(ngridq(3)) do i2=0,ngridq(2)-1 v(2)=dble(i2)/dble(ngridq(2)) do i1=0,ngridq(1)-1 v(1)=dble(i1)/dble(ngridq(1)) ir=ir+1 call r3mv(avecu,v,vrcu(:,ir)) end do end do end do ! store the existing k-point and weight arrays allocate(vkl0(3,nkpt),vkc0(3,nkpt),wkpt0(nkpt)) vkl0(:,1:nkpt)=vkl(:,1:nkpt) vkc0(:,1:nkpt)=vkc(:,1:nkpt) wkpt0(1:nkpt)=wkpt(1:nkpt) ! number of k+kappa-points nkpt0=nkpt nkpt=nkpt0*nkpa ! deallocate and reallocate k-point and weight arrays deallocate(vkl,vkc,wkpt) allocate(vkl(3,nkpt),vkc(3,nkpt),wkpt(nkpt)) ik=0 do ik0=1,nkpt0 do ikpa=1,nkpa ik=ik+1 vkl(:,ik)=vkl0(:,ik0)+vql(:,ikpa) vkc(:,ik)=vkc0(:,ik0)+vqc(:,ikpa) wkpt(ik)=wkpt0(ik0)/dble(nkpa) end do end do deallocate(vkl0,vkc0,wkpt0) end subroutine elk-7.2.42/src/PaxHeaders.21776/genzvmatk.f900000644000000000000000000000013214061636517015252 xustar0030 mtime=1623670095.895101582 30 atime=1623670094.751102644 30 ctime=1623670095.895101582 elk-7.2.42/src/genzvmatk.f900000644002504400250440000000456714061636517017323 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genzvmatk(zvmt,zvir,ngp,igpig,wfmt,wfir,wfgp,vmat) use modmain use modomp implicit none ! arguments ! the potential is multiplied by the radial integration weights in the ! muffin-tin and by the characteristic function in the interstitial region complex(8), intent(in) :: zvmt(npcmtmax,natmtot),zvir(ngtot) integer, intent(in) :: ngp,igpig(ngp) complex(8), intent(in) :: wfmt(npcmtmax,natmtot,nspinor,nstsv) ! note that wfir does not have a 1/sqrt(omega) prefactor complex(8), intent(in) :: wfir(ngtot,nspinor,nstsv) complex(8), intent(in) :: wfgp(ngp,nspinor,nstsv) complex(8), intent(out) :: vmat(nstsv,nstsv) ! local variables integer ist,jst,ispn integer is,ias,npc,nthd ! automatic arrays complex(8) wfmt1(npcmtmax),z(ngp) ! allocatable arrays complex(8), allocatable :: wfir1(:) ! external functions complex(8), external :: zdotc ! zero the matrix elements vmat(:,:)=0.d0 !-------------------------! ! muffin-tin part ! !-------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(wfmt1,ispn,ias) & !$OMP PRIVATE(is,npc,ist) & !$OMP NUM_THREADS(nthd) do jst=1,nstsv do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) npc=npcmt(is) ! apply complex potential to wavefunction wfmt1(1:npc)=zvmt(1:npc,ias)*wfmt(1:npc,ias,ispn,jst) ! compute the inner products do ist=1,nstsv vmat(ist,jst)=vmat(ist,jst)+zdotc(npc,wfmt(:,ias,ispn,ist),1,wfmt1,1) end do end do end do end do !$OMP END PARALLEL DO call freethd(nthd) !---------------------------! ! interstitial part ! !---------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfir1,z,ispn,ist) & !$OMP NUM_THREADS(nthd) allocate(wfir1(ngtot)) !$OMP DO do jst=1,nstsv do ispn=1,nspinor ! apply potential to wavefunction wfir1(1:ngtot)=zvir(1:ngtot)*wfir(1:ngtot,ispn,jst) ! Fourier transform to G+p-space call zfftifc(3,ngridg,-1,wfir1) z(1:ngp)=wfir1(igfft(igpig(1:ngp))) do ist=1,nstsv ! compute inner product vmat(ist,jst)=vmat(ist,jst)+zdotc(ngp,wfgp(:,ispn,ist),1,z,1) end do end do end do !$OMP END DO deallocate(wfir1) !$OMP END PARALLEL call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/genzvbmatk.f900000644000000000000000000000013014061636517015412 xustar0029 mtime=1623670095.89710158 30 atime=1623670094.752102643 29 ctime=1623670095.89710158 elk-7.2.42/src/genzvbmatk.f900000644002504400250440000000746614061636517017466 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genzvbmatk(zvmt,zvir,zbmt,zbir,ngp,igpig,wfmt,wfir,wfgp,vbmat) use modmain use modomp implicit none ! arguments ! the potential and field are multiplied by the radial integration weights in ! the muffin-tin and by the characteristic function in the interstitial region complex(8), intent(in) :: zvmt(npcmtmax,natmtot),zvir(ngtot) complex(8), intent(in) :: zbmt(npcmtmax,natmtot,ndmag),zbir(ngtot,ndmag) integer, intent(in) :: ngp,igpig(ngp) complex(8), intent(in) :: wfmt(npcmtmax,natmtot,nspinor,nstsv) ! note that wfir does not have a 1/sqrt(omega) prefactor complex(8), intent(in) :: wfir(ngtot,nspinor,nstsv) complex(8), intent(in) :: wfgp(ngp,nspinor,nstsv) complex(8), intent(out) :: vbmat(nstsv,nstsv) ! local variables integer ist,jst,ispn integer is,ias,npc,nthd ! automatic arrays complex(8) wfmt2(npcmtmax,nspinor),z(ngp) ! allocatable arrays complex(8), allocatable :: wfir2(:,:) ! external functions complex(8), external :: zdotc ! zero the matrix elements vbmat(:,:)=0.d0 !-------------------------! ! muffin-tin part ! !-------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(wfmt2,ias,is,npc,ist) & !$OMP NUM_THREADS(nthd) do jst=1,nstsv do ias=1,natmtot is=idxis(ias) npc=npcmt(is) ! apply local potential and magnetic field to spinor wavefunction if (ncmag) then ! non-collinear case call zvbmk1(npc,zvmt(:,ias),zbmt(:,ias,1),zbmt(:,ias,2),zbmt(:,ias,3), & wfmt(:,ias,1,jst),wfmt(:,ias,2,jst),wfmt2,wfmt2(:,2)) else ! collinear case call zvbmk2(npc,zvmt(:,ias),zbmt(:,ias,1),wfmt(:,ias,1,jst), & wfmt(:,ias,2,jst),wfmt2,wfmt2(:,2)) end if ! compute the inner products do ist=1,nstsv vbmat(ist,jst)=vbmat(ist,jst) & +zdotc(npc,wfmt(:,ias,1,ist),1,wfmt2,1) & +zdotc(npc,wfmt(:,ias,2,ist),1,wfmt2(:,2),1) end do end do end do !$OMP END PARALLEL DO call freethd(nthd) !---------------------------! ! interstitial part ! !---------------------------! call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(wfir2,z,ispn,ist) & !$OMP NUM_THREADS(nthd) allocate(wfir2(ngtot,nspinor)) !$OMP DO do jst=1,nstsv ! apply local potential and magnetic field to spinor wavefunction if (ncmag) then ! non-collinear case call zvbmk1(ngtot,zvir,zbir,zbir(:,2),zbir(:,3),wfir(:,1,jst), & wfir(:,2,jst),wfir2,wfir2(:,2)) else ! collinear case call zvbmk2(ngtot,zvir,zbir,wfir(:,1,jst),wfir(:,2,jst),wfir2,wfir2(:,2)) end if do ispn=1,nspinor ! Fourier transform to G+p-space call zfftifc(3,ngridg,-1,wfir2(:,ispn)) z(1:ngp)=wfir2(igfft(igpig(1:ngp)),ispn) do ist=1,nstsv vbmat(ist,jst)=vbmat(ist,jst)+zdotc(ngp,wfgp(:,ispn,ist),1,z,1) end do end do end do !$OMP END DO deallocate(wfir2) !$OMP END PARALLEL call freethd(nthd) return contains pure subroutine zvbmk1(n,zv,zb1,zb2,zb3,wf11,wf12,wf21,wf22) implicit none ! arguments integer, intent(in) :: n complex(8), intent(in) :: zv(n),zb1(n),zb2(n),zb3(n) complex(8), intent(in) :: wf11(n),wf12(n) complex(8), intent(out) :: wf21(n),wf22(n) ! local variables integer i complex(8) z1 do i=1,n z1=cmplx(-aimag(zb2(i)),dble(zb2(i)),8) wf21(i)=(zv(i)+zb3(i))*wf11(i)+(zb1(i)-z1)*wf12(i) wf22(i)=(zv(i)-zb3(i))*wf12(i)+(zb1(i)+z1)*wf11(i) end do end subroutine pure subroutine zvbmk2(n,zv,zb,wf11,wf12,wf21,wf22) implicit none ! arguments integer, intent(in) :: n complex(8), intent(in) :: zv(n),zb(n) complex(8), intent(in) :: wf11(n),wf12(n) complex(8), intent(out) :: wf21(n),wf22(n) ! local variables integer i do i=1,n wf21(i)=(zv(i)+zb(i))*wf11(i) wf22(i)=(zv(i)-zb(i))*wf12(i) end do end subroutine end subroutine elk-7.2.42/src/PaxHeaders.21776/potksu.f900000644000000000000000000000013214061636517014571 xustar0030 mtime=1623670095.898101579 30 atime=1623670094.754102641 30 ctime=1623670095.898101579 elk-7.2.42/src/potksu.f900000644002504400250440000000107714061636517016633 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potksu use modmain use modulr implicit none ! compute the ultra long-range Coulomb potential call potcoulu ! compute the ultra long-range exchange-correlation potential and fields call potxcu ! reduce the external magnetic field if required if (reducebf.lt.1.d0) then bfcq(:,:)=bfcq(:,:)*reducebf bfcmtq(:,:,:)=bfcmtq(:,:,:)*reducebf end if end subroutine elk-7.2.42/src/PaxHeaders.21776/plotu1d.f900000644000000000000000000000013214061636517014634 xustar0030 mtime=1623670095.900101578 30 atime=1623670094.756102639 30 ctime=1623670095.900101578 elk-7.2.42/src/plotu1d.f900000644002504400250440000000233514061636517016674 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine plotu1d(fnum1,fnum2,nf,zfmt,zfir) use modmain implicit none ! arguments integer, intent(in) :: fnum1,fnum2,nf complex(8), intent(in) :: zfmt(npcmtmax,natmtot,nf,nfqrz) complex(8), intent(in) :: zfir(ngtot,nf,nfqrz) ! local variables integer jf,ip,iv real(8) fmin,fmax,t1 ! allocatable arrays real(8), allocatable :: fp(:,:) if ((nf.lt.1).or.(nf.gt.4)) then write(*,*) write(*,'("Error(plotu1d): invalid number of functions : ",I8)') nf write(*,*) stop end if allocate(fp(npp1d,nf)) ! connect the 1D plotting vertices call plotpt1d(avec,nvp1d,npp1d,vvlp1d,vplp1d,dvp1d,dpp1d) ! evaluate function at each point call plotulr(npp1d,vplp1d,nf,zfmt,zfir,fp) do ip=1,npp1d ! write the point distances and function to file write(fnum1,'(5G18.10)') dpp1d(ip),(fp(ip,jf),jf=1,nf) end do ! write the vertex location lines fmin=minval(fp(:,:)) fmax=maxval(fp(:,:)) t1=0.5d0*(fmax-fmin) do iv=1,nvp1d write(fnum2,'(2G18.10)') dvp1d(iv),fmax+t1 write(fnum2,'(2G18.10)') dvp1d(iv),fmin-t1 write(fnum2,*) end do deallocate(fp) end subroutine elk-7.2.42/src/PaxHeaders.21776/plotu2d.f900000644000000000000000000000013214061636517014635 xustar0030 mtime=1623670095.901101577 30 atime=1623670094.758102638 30 ctime=1623670095.901101577 elk-7.2.42/src/plotu2d.f900000644002504400250440000000236414061636517016677 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine plotu2d(tproj,fnum,nf,zfmt,zfir) use modmain implicit none ! arguments logical, intent(in) :: tproj integer, intent(in) :: fnum,nf complex(8), intent(in) :: zfmt(npcmtmax,natmtot,nf,nfqrz) complex(8), intent(in) :: zfir(ngtot,nf,nfqrz) ! local variables integer np,jf,ip real(8) vpnl(3) ! allocatable arrays real(8), allocatable :: vpl(:,:),vppc(:,:),fp(:,:) if ((nf.lt.1).or.(nf.gt.4)) then write(*,*) write(*,'("Error(plotu2d): invalid number of functions : ",I8)') nf write(*,*) stop end if ! allocate local arrays np=np2d(1)*np2d(2) allocate(vpl(3,np),vppc(2,np),fp(np,nf)) ! generate the 2D plotting points call plotpt2d(avec,ainv,vpnl,vpl,vppc) ! evaluate the functions at the grid points call plotulr(np,vpl,nf,zfmt,zfir,fp) ! project the vector function onto the 2D plotting plane if required if (tproj.and.(nf.eq.3)) then call proj2d(np,fp) end if ! write the functions to file write(fnum,'(2I6," : grid size")') np2d(:) do ip=1,np write(fnum,'(6G18.10)') vppc(1,ip),vppc(2,ip),(fp(ip,jf),jf=1,nf) end do deallocate(vpl,vppc,fp) end subroutine elk-7.2.42/src/PaxHeaders.21776/plotu3d.f900000644000000000000000000000013214061636517014636 xustar0030 mtime=1623670095.903101575 30 atime=1623670094.759102637 30 ctime=1623670095.903101575 elk-7.2.42/src/plotu3d.f900000644002504400250440000000212314061636517016671 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine plotu3d(fnum,nf,zfmt,zfir) use modmain implicit none ! arguments integer, intent(in) :: fnum,nf complex(8), intent(in) :: zfmt(npcmtmax,natmtot,nf,nfqrz) complex(8), intent(in) :: zfir(ngtot,nf,nfqrz) ! local variables integer np,jf,ip real(8) v1(3) ! allocatable arrays real(8), allocatable :: vpl(:,:),fp(:,:) if ((nf.lt.1).or.(nf.gt.4)) then write(*,*) write(*,'("Error(plotu3d): invalid number of functions : ",I8)') nf write(*,*) stop end if ! total number of plot points np=np3d(1)*np3d(2)*np3d(3) ! allocate local arrays allocate(vpl(3,np),fp(np,nf)) ! generate the 3D plotting points call plotpt3d(vpl) ! evaluate the functions at the grid points call plotulr(np,vpl,nf,zfmt,zfir,fp) ! write functions to file write(fnum,'(3I6," : grid size")') np3d(:) do ip=1,np call r3mv(avec,vpl(:,ip),v1) write(fnum,'(7G18.10)') v1(:),(fp(ip,jf),jf=1,nf) end do deallocate(vpl,fp) end subroutine elk-7.2.42/src/PaxHeaders.21776/gndstulr.f900000644000000000000000000000013214061636517015106 xustar0030 mtime=1623670095.904101574 30 atime=1623670094.761102635 30 ctime=1623670095.904101574 elk-7.2.42/src/gndstulr.f900000644002504400250440000001623414061636517017151 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine gndstulr use modmain use modulr use moddftu use modmpi use modomp use modstore implicit none ! local variables logical twrite integer ik0,ir,lp,nthd integer nmix,nwork,n real(8) dv ! allocatable arrays integer(8), allocatable :: lock(:) real(8), allocatable :: work(:) complex(8), allocatable :: evecu(:,:) if (xctype(1).lt.0) then write(*,*) write(*,'("Error(gndstulr): ultra long-range does not work with OEP")') write(*,*) stop end if if (spincore) then write(*,*) write(*,'("Error(gndstulr): ultra long-range does not work with & &spin-polarised cores")') write(*,*) stop end if ! no k-point reduction reducek_=reducek reducek=0 ! initialise global variables call init0 call init1 ! write the kappa-points to file call writekpa ! write the k+kappa-points to file call writekpts ! read the regular Kohn-Sham potential from file call readstate ! generate the first- and second-variational eigenvectors and eigenvalues for ! the k+kappa-point set call genvsig call gencore call readfermi call linengy call genapwlofr call gensocfr call genevfsv call occupy ! initialise the ultra long-range variables call initulr if (task.eq.700) then ! initialise the long-range Kohn-Sham potential and magnetic field call potuinit else ! read in the potential and density from STATE_ULR.OUT call readstulr end if ! initialise the external Coulomb potential call vclqinit ! write the long-range Hamiltonian diagonal blocks to file call genhdbulr ! size of mixing vector (complex array) nmix=2*size(vsbsq) ! determine the size of the mixer work array nwork=-1 call mixerifc(mixtype,nmix,vsbsq,dv,nwork,vsbsq) allocate(work(nwork)) ! initialise the mixer iscl=0 call mixerifc(mixtype,nmix,vsbsq,dv,nwork,work) ! initialise the OpenMP locks allocate(lock(nqpt)) do ir=1,nqpt call omp_init_lock(lock(ir)) end do ! set last self-consistent loop flag tlast=.false. ! begin the self-consistent loop if (mp_mpi) then ! open ULR_INFO.OUT file open(60,file='ULR_INFO.OUT',form='FORMATTED') ! open RMSDVS.OUT open(65,file='RMSDVS.OUT',form='FORMATTED') call writeinfou(60) write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop started |")') write(60,'("+------------------------------+")') end if do iscl=1,maxscl if (mp_mpi) then write(60,*) write(60,'("+--------------------+")') write(60,'("| Loop number : ",I4," |")') iscl write(60,'("+--------------------+")') end if if (iscl.ge.maxscl) then if (mp_mpi) then write(60,*) write(60,'("Reached self-consistent loops maximum")') end if write(*,*) write(*,'("Warning(gndstulr): failed to reach self-consistency after ",I4,& &" loops")') iscl tlast=.true. end if ! reset the OpenMP thread variables call omp_reset ! apply required local operations to the potential and magnetic field call vblocalu ! zero the density and magnetisation rhormt(:,:,:)=0.d0 rhorir(:,:)=0.d0 if (spinpol) then magrmt(:,:,:,:)=0.d0 magrir(:,:,:)=0.d0 end if ! loop over original k-points call holdthd(nkpt0/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(evecu) & !$OMP NUM_THREADS(nthd) allocate(evecu(nstulr,nstulr)) !$OMP DO do ik0=1,nkpt0 ! distribute among MPI processes if (mod(ik0-1,np_mpi).ne.lp_mpi) cycle ! solve the ultra long-range eigenvalue equation call eveqnulr(ik0,evecu) ! add to the density, magnetisation and current call rhomaguk(ik0,lock,evecu) end do !$OMP END DO deallocate(evecu) !$OMP END PARALLEL call freethd(nthd) if (np_mpi.gt.1) then ! broadcast eigenvalue array to every process do ik0=1,nkpt0 lp=mod(ik0-1,np_mpi) call mpi_bcast(evalu(:,ik0),nstulr,mpi_double_precision,lp,mpicom,ierror) end do ! add densities from each process and redistribute n=npcmtmax*natmtot*nqpt call mpi_allreduce(mpi_in_place,rhormt,n,mpi_double_precision,mpi_sum, & mpicom,ierror) n=ngtc*nqpt call mpi_allreduce(mpi_in_place,rhorir,n,mpi_double_precision,mpi_sum, & mpicom,ierror) if (spinpol) then n=npcmtmax*natmtot*ndmag*nqpt call mpi_allreduce(mpi_in_place,magrmt,n,mpi_double_precision,mpi_sum, & mpicom,ierror) n=ngtc*ndmag*nqpt call mpi_allreduce(mpi_in_place,magrir,n,mpi_double_precision,mpi_sum, & mpicom,ierror) end if end if ! find the occupation numbers and Fermi energy call occupyulr ! synchronise MPI processes call mpi_barrier(mpicom,ierror) ! add the core density call rhocoreu ! perform partial Fourier transform to Q-space call rhomagq ! determine the muffin-tin and interstitial charges and moments call chargeu call momentu ! compute the ultra long-range Kohn-Sham potential call potksu ! mix the old potential and field with the new call mixerifc(mixtype,nmix,vsbsq,dv,nwork,work) ! multiply the RMS change in potential by the number of Q-points dv=dv*dble(nfqrz) ! calculate and add the fixed spin moment effective field (after mixing) call fsmbfield call addbfsmu if (mp_mpi) then ! write eigenvalues to file call writeevalu ! output energy components call writeengyu(60) ! output charges call writechg(60) ! write muffin-tin charges for each R-vector call writechgrmt if (spinpol) then ! output moments call writemom(60) ! write muffin-tin moments for each R-vector call writemomrmt end if ! output effective fields for fixed spin moment calculations if (fsmtype.ne.0) call writefsm(60) ! check for WRITE file call checkwrite(twrite) ! write STATE_ULR.OUT file if required if (twrite.or.((nwrite.ge.1).and.(mod(iscl,nwrite).eq.0))) then call writestulr write(60,*) write(60,'("Wrote STATE_ULR.OUT")') end if end if ! exit self-consistent loop if required if (tlast) goto 10 ! check for convergence if (iscl.ge.2) then if (mp_mpi) then write(60,*) write(60,'("RMS change in Kohn-Sham potential (target) : ",G18.10," (",& &G18.10,")")') dv,epspot flush(60) write(65,'(G18.10)') dv flush(65) end if if (dv.lt.epspot) then if (mp_mpi) then write(60,*) write(60,'("Convergence targets achieved")') end if tlast=.true. end if end if ! check for STOP file call checkstop if (tstop) tlast=.true. ! broadcast tlast from master process to all other processes call mpi_bcast(tlast,1,mpi_logical,0,mpicom,ierror) ! reset the OpenMP thread variables call omp_reset end do 10 continue if (mp_mpi) then write(60,*) write(60,'("+------------------------------+")') write(60,'("| Self-consistent loop stopped |")') write(60,'("+------------------------------+")') if (maxscl.gt.1) then call writestulr write(60,*) write(60,'("Wrote STATE_ULR.OUT")') end if ! close the ULR_INFO.OUT file close(60) ! close the RMSDVS.OUT file close(65) end if ! destroy the OpenMP locks do ir=1,nqpt call omp_destroy_lock(lock(ir)) end do deallocate(lock,work) ! restore original parameters reducek=reducek_ ! synchronise MPI processes call mpi_barrier(mpicom,ierror) end subroutine elk-7.2.42/src/PaxHeaders.21776/vblocalu.f900000644000000000000000000000013214061636517015053 xustar0030 mtime=1623670095.906101572 30 atime=1623670094.762102634 30 ctime=1623670095.906101572 elk-7.2.42/src/vblocalu.f900000644002504400250440000000456114061636517017116 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine vblocalu use modmain use modulr use modomp implicit none ! local variables integer ifq,idm,is,ias integer nrc,nrci,npc,nthd ! automatic arrays real(8) rfmt1(npcmtmax),rfmt2(npcmtmax) ! subtract the normal Kohn-Sham potential for Q=0 do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) npc=npcmt(is) call rfmtftoc(nrc,nrci,vsmt(:,ias),rfmt1) call rbsht(nrc,nrci,rfmt1,rfmt2) vsqmt(1:npc,ias,1)=vsqmt(1:npc,ias,1)-rfmt2(1:npc) end do vsqir(1:ngtot,1)=vsqir(1:ngtot,1)-vsir(1:ngtot) call holdthd(nfqrz,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(ias,is,nrc,nrci) & !$OMP NUM_THREADS(nthd) !$OMP DO do ifq=1,nfqrz do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) ! multiply the muffin-tin potential by the radial integration weights call zfcmtwr(nrc,nrci,wrcmt(:,is),vsqmt(:,ias,ifq)) end do end do !$OMP END DO NOWAIT !$OMP DO do ifq=1,nfqrz ! multiply the interstitial potential by the characteristic function vsqir(1:ngtot,ifq)=vsqir(1:ngtot,ifq)*cfunir(1:ngtot) end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) if (.not.spinpol) return ! subtract the normal Kohn-Sham magnetic field for Q=0 in the muffin-tins do idm=1,ndmag do ias=1,natmtot is=idxis(ias) npc=npcmt(is) bsqmt(1:npc,ias,idm,1)=bsqmt(1:npc,ias,idm,1)-bsmt(1:npc,ias,idm) end do end do call holdthd(nfqrz,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(idm,ias,is,nrc,nrci) & !$OMP NUM_THREADS(nthd) !$OMP DO do ifq=1,nfqrz do idm=1,ndmag do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) ! multiply the muffin-tin field by the radial integration weights call zfcmtwr(nrc,nrci,wrcmt(:,is),bsqmt(:,ias,idm,ifq)) end do end do end do !$OMP END DO NOWAIT !$OMP DO do ifq=1,nfqrz do idm=1,ndmag ! multiply interstitial field by the characteristic function bsqir(1:ngtot,idm,ifq)=bsqir(1:ngtot,idm,ifq)*cfunir(1:ngtot) end do end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) ! subtract the normal Kohn-Sham magnetic field for Q=0 in the interstitial ! (this is already multiplied by the characteristic function) do idm=1,ndmag bsqir(1:ngtot,idm,1)=bsqir(1:ngtot,idm,1)-bsir(1:ngtot,idm) end do end subroutine elk-7.2.42/src/PaxHeaders.21776/plotulr.f900000644000000000000000000000013214061636517014745 xustar0030 mtime=1623670095.907101571 30 atime=1623670094.764102632 30 ctime=1623670095.907101571 elk-7.2.42/src/plotulr.f900000644002504400250440000000254314061636517017006 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine plotulr(np,vpl,nf,zfmt,zfir,fp) use modmain use modulr use modomp implicit none ! arguments integer, intent(in) :: np real(8), intent(in) :: vpl(3,np) integer, intent(in) :: nf complex(8), intent(in) :: zfmt(npcmtmax,natmtot,nf,nfqrz) complex(8), intent(in) :: zfir(ngtot,nf,nfqrz) real(8), intent(out) :: fp(np,nf) ! local variables integer iq,ifq0,ifq integer jf,ip real(8) sm,t1 complex(8) z1 ! allocatable arrays complex(8), allocatable :: fpq(:,:) allocate(fpq(np,nfqrz)) ! include or exclude the Q=0 component as required if (tplotq0) then ifq0=1 else ifq0=2 end if ! loop over the number of functions do jf=1,nf ! loop over real-complex FFT points do ifq=ifq0,nfqrz ! evaluate the complex function at all the plot points call zfplot(np,vpl,zfmt(:,:,jf,ifq),zfir(:,jf,ifq),fpq(:,ifq)) end do do ip=1,np sm=0.d0 do ifq=ifq0,nfqrz iq=iqrzf(ifq) ! multiply complex function by phase factor exp(iQ.r) t1=twopi*dot_product(vql(:,iq),vpl(:,ip)) z1=cmplx(cos(t1),sin(t1),8) t1=dble(fpq(ip,ifq)*z1) if (ifq.gt.1) t1=t1*2.d0 sm=sm+t1 end do fp(ip,jf)=sm end do end do deallocate(fpq) end subroutine elk-7.2.42/src/PaxHeaders.21776/potuplot.f900000644000000000000000000000013114061636517015131 xustar0030 mtime=1623670095.909101569 29 atime=1623670094.76610263 30 ctime=1623670095.909101569 elk-7.2.42/src/potuplot.f900000644002504400250440000000326014061636517017170 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potuplot use modmain use modulr implicit none ! local variables integer ifq,ias,is,npc ! allocatable arrays complex(8), allocatable :: zfmt(:) ! initialise universal variables call init0 call init1 ! initialise the ultra long-range variables call initulr ! read in the Kohn-Sham potential from STATE_ULR.OUT call readstulr ! convert potential to spherical harmonics allocate(zfmt(npcmtmax)) do ifq=1,nfqrz do ias=1,natmtot is=idxis(ias) npc=npcmt(is) zfmt(1:npc)=vsqmt(1:npc,ias,ifq) call zfsht(nrcmt(is),nrcmti(is),zfmt,vsqmt(:,ias,ifq)) end do end do deallocate(zfmt) ! write the density plot to file select case(task) case(741) open(50,file='VSU1D.OUT',form='FORMATTED') open(51,file='VSULINES.OUT',form='FORMATTED') call plotu1d(50,51,1,vsqmt,vsqir) close(50) close(51) write(*,*) write(*,'("Info(potuplot):")') write(*,'(" 1D ultra long-range Kohn-Sham potential plot written to & &VSU1D.OUT")') write(*,'(" vertex location lines written to VSULINES.OUT")') case(742) open(50,file='VSU2D.OUT',form='FORMATTED') call plotu2d(.false.,50,1,vsqmt,vsqir) open(50) write(*,*) write(*,'("Info(potuplot):")') write(*,'(" 2D ultra long-range Kohn-Sham potential plot written to & &VSU2D.OUT")') case(743) open(50,file='VSU3D.OUT',form='FORMATTED') call plotu3d(50,1,vsqmt,vsqir) close(50) write(*,*) write(*,'("Info(potuplot):")') write(*,'(" 3D ultra long-range Kohn-Sham potential plot written to & &VSU3D.OUT")') end select end subroutine elk-7.2.42/src/PaxHeaders.21776/potcoulu.f900000644000000000000000000000013214061636517015116 xustar0030 mtime=1623670095.910101568 30 atime=1623670094.767102629 30 ctime=1623670095.910101568 elk-7.2.42/src/potcoulu.f900000644002504400250440000000512614061636517017157 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2018 T. Mueller, J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine potcoulu use modmain use modulr use modmpi use modomp implicit none ! local variables integer ifq,is,ias integer nr,nri,ir integer nrc,nrci,i integer n,lp,nthd ! allocatable arrays complex(8), allocatable :: zrhomt(:,:),zrhoir(:) complex(8), allocatable :: zvclmt(:,:),zfmt(:) call holdthd(nfqrz/np_mpi,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(zrhomt,zrhoir,zvclmt,zfmt) & !$OMP PRIVATE(ias,is,nr,nri) & !$OMP PRIVATE(i,ir,nrc,nrci) & !$OMP NUM_THREADS(nthd) allocate(zrhomt(npmtmax,natmtot),zrhoir(ngtot)) allocate(zvclmt(npmtmax,natmtot),zfmt(npcmtmax)) !$OMP DO do ifq=1,nfqrz ! distribute among MPI processes if (mod(ifq-1,np_mpi).ne.lp_mpi) cycle ! convert the complex muffin-tin density from coarse to fine radial mesh do ias=1,natmtot is=idxis(ias) call zcopy(npcmt(is),rhoqmt(:,ias,ifq),1,zrhomt(:,ias),1) end do call zfmtctof(zrhomt) ! solve the complex Poisson's equation in the muffin-tins call genzvclmt(nrmt,nrmti,nrmtmax,rlmt,wprmt,npmtmax,zrhomt,zvclmt) ! add the nuclear monopole potentials for Q=0 if (ifq.eq.1) then do ias=1,natmtot is=idxis(ias) nr=nrmt(is) nri=nrmti(is) i=1 do ir=1,nri zvclmt(i,ias)=zvclmt(i,ias)+vcln(ir,is) i=i+lmmaxi end do do ir=nri+1,nr zvclmt(i,ias)=zvclmt(i,ias)+vcln(ir,is) i=i+lmmaxo end do end do end if ! convert the interstitial density from coarse to fine grid call zfirctof(rhoqir(:,ifq),zrhoir) ! solve Poisson's equation in the entire unit cell call zpotcoul(nrmt,nrmti,npmt,npmti,nrmtmax,rlmt,ngridg,igfft,ngvec, & gqc(:,ifq),gclgq(:,ifq),ngvec,jlgqrmt(:,:,:,ifq),ylmgq(:,:,ifq), & sfacgq(:,:,ifq),zrhoir,npmtmax,zvclmt,vsqir(:,ifq)) do ias=1,natmtot is=idxis(ias) nrc=nrcmt(is) nrci=nrcmti(is) ! convert from fine to coarse radial mesh call zfmtftoc(nrc,nrci,zvclmt(:,ias),zfmt) ! convert to spherical coordinates call zbsht(nrc,nrci,zfmt,vsqmt(:,ias,ifq)) end do end do !$OMP END DO deallocate(zrhomt,zrhoir,zvclmt,zfmt) !$OMP END PARALLEL call freethd(nthd) ! broadcast potentials to every MPI process if (np_mpi.gt.1) then n=npcmtmax*natmtot do ifq=1,nfqrz lp=mod(ifq-1,np_mpi) call mpi_bcast(vsqmt(:,:,ifq),n,mpi_double_complex,lp,mpicom,ierror) end do do ifq=1,nfqrz lp=mod(ifq-1,np_mpi) call mpi_bcast(vsqir(:,ifq),ngtot,mpi_double_complex,lp,mpicom,ierror) end do end if end subroutine elk-7.2.42/src/PaxHeaders.21776/rhouplot.f900000644000000000000000000000013214061636517015120 xustar0030 mtime=1623670095.912101566 30 atime=1623670094.769102627 30 ctime=1623670095.912101566 elk-7.2.42/src/rhouplot.f900000644002504400250440000000322414061636517017156 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine rhouplot use modmain use modulr use modomp implicit none ! local variables integer ifq,nthd ! allocatable arrays complex(8), allocatable :: rhoqir_(:,:) ! initialise universal variables call init0 call init1 ! initialise the ultra long-range variables call initulr ! read in the density from STATE_ULR.OUT call readstulr ! convert interstitial density from coarse to fine grid allocate(rhoqir_(ngtot,nfqrz)) call holdthd(nfqrz,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP NUM_THREADS(nthd) do ifq=1,nfqrz call zfirctof(rhoqir(:,ifq),rhoqir_(:,ifq)) end do !$OMP END PARALLEL DO call freethd(nthd) ! write the density plot to file select case(task) case(731) open(50,file='RHOU1D.OUT',form='FORMATTED') open(51,file='RHOULINES.OUT',form='FORMATTED') call plotu1d(50,51,1,rhoqmt,rhoqir_) close(50) close(51) write(*,*) write(*,'("Info(rhouplot):")') write(*,'(" 1D ultra long-range density plot written to RHOU1D.OUT")') write(*,'(" vertex location lines written to RHOULINES.OUT")') case(732) open(50,file='RHOU2D.OUT',form='FORMATTED') call plotu2d(.false.,50,1,rhoqmt,rhoqir_) close(50) write(*,*) write(*,'("Info(rhouplot): 2D ultra long-range density plot written to & &RHOU2D.OUT")') case(733) open(50,file='RHOU3D.OUT',form='FORMATTED') call plotu3d(50,1,rhoqmt,rhoqir_) close(50) write(*,*) write(*,'("Info(rhouplot): 3D ultra long-range density plot written to & &RHOU3D.OUT")') end select deallocate(rhoqir_) end subroutine elk-7.2.42/src/PaxHeaders.21776/maguplot.f900000644000000000000000000000013214061636517015074 xustar0030 mtime=1623670095.913101566 30 atime=1623670094.771102626 30 ctime=1623670095.913101566 elk-7.2.42/src/maguplot.f900000644002504400250440000000404714061636517017136 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine maguplot use modmain use modulr use modomp implicit none ! local variables integer ifq,idm,nthd ! allocatable arrays complex(8), allocatable :: magqir_(:,:,:) ! initialise universal variables call init0 call init1 if (.not.spinpol) then write(*,*) write(*,'("Error(maguplot): spin-unpolarised calculation")') write(*,*) stop end if ! initialise the ultra long-range variables call initulr ! read in the magnetisation from STATE_ULR.OUT call readstulr ! convert interstitial magnetisation from coarse to fine grid allocate(magqir_(ngtot,ndmag,nfqrz)) call holdthd(nfqrz,nthd) !$OMP PARALLEL DO DEFAULT(SHARED) & !$OMP PRIVATE(idm) & !$OMP NUM_THREADS(nthd) do ifq=1,nfqrz do idm=1,ndmag call zfirctof(magqir(:,idm,ifq),magqir_(:,idm,ifq)) end do end do !$OMP END PARALLEL DO call freethd(nthd) ! write the magnetisation plot to file select case(task) case(771) open(50,file='MAGU1D.OUT',form='FORMATTED') open(51,file='MAGULINES.OUT',form='FORMATTED') call plotu1d(50,51,ndmag,magqmt,magqir_) close(50) close(51) write(*,*) write(*,'("Info(maguplot):")') write(*,'(" 1D ultra long-range magnetisation plot written to MAGU1D.OUT")') write(*,'(" vertex location lines written to MAGULINES.OUT")') case(772) open(50,file='MAGU2D.OUT',form='FORMATTED') call plotu2d(.true.,50,ndmag,magqmt,magqir_) close(50) write(*,*) write(*,'("Info(maguplot): 2D ultra long-range magnetisation plot written to & &MAGU2D.OUT")') if (ndmag.eq.3) then write(*,'(" Note that the 3D vector field has been locally projected")') write(*,'(" onto the 2D plotting plane axes")') end if case(773) open(50,file='MAGU3D.OUT',form='FORMATTED') call plotu3d(50,ndmag,magqmt,magqir_) close(50) write(*,*) write(*,'("Info(maguplot): 3D ultra long-range magnetisation plot written to & &MAGU3D.OUT")') end select deallocate(magqir_) end subroutine elk-7.2.42/src/PaxHeaders.21776/initw90.f900000644000000000000000000000013214061636517014547 xustar0030 mtime=1623670095.915101564 30 atime=1623670094.772102625 30 ctime=1623670095.915101564 elk-7.2.42/src/initw90.f900000644002504400250440000000317314061636517016610 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin and Lars Nordstrom. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. !BOP ! !ROUTINE: initw90 ! !INTERFACE: subroutine initw90 ! !USES: use modmain use modw90 ! !DESCRIPTION: ! Initialises global variables for the Wannier90 interface. ! ! !REVISION HISTORY: ! Created November 2018 (Arsenii Gerasimov) !EOP !BOC implicit none ! local variables integer ik,ist,i ! initialise universal variables call init0 call init1 if (num_bands.gt.nstsv) then write(*,*) write(*,'("Error(initw90): num_bands > nstsv : ",2I8)') num_bands,nstsv write(*,*) stop end if ! if num_bands is not positive then assume all states are used if (num_bands.le.0) then if (allocated(idxw90)) deallocate(idxw90) allocate(idxw90(nstsv)) do ist=1,nstsv idxw90(ist)=ist end do num_bands=nstsv end if ! check that each state index is in range do i=1,num_bands ist=idxw90(i) if ((ist.lt.1).or.(ist.gt.nstsv)) then write(*,*) write(*,'("Error(initw90): state index out of range : ",I8)') ist write(*,*) stop end if end do ! set the number of Wannier functions equal to the number of states if required if (num_wann.le.0) num_wann=num_bands ! read density and potentials from file call readstate ! read Fermi energy from file call readfermi ! find the new linearisation energies call linengy ! generate the APW and local-orbital radial functions and integrals call genapwlofr ! read in the second-variational eigenvalues do ik=1,nkpt call getevalsv(filext,ik,vkl(:,ik),evalsv(:,ik)) end do end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writew90.f900000644000000000000000000000013214061636517014736 xustar0030 mtime=1623670095.916101563 30 atime=1623670094.774102623 30 ctime=1623670095.916101563 elk-7.2.42/src/writew90.f900000644002504400250440000000106114061636517016771 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 Manh Duc Le, 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin ! and Lars Nordstrom. This file is distributed under the terms of the GNU ! General Public License. See the file COPYING for license details. subroutine writew90 use modmain use modw90 implicit none ! initialise universal and Wannier90 variables call initw90 ! write the .win file call writew90win ! write the .eig file call writew90eig ! call the Wannier90 setup routine call setupw90 ! write the .mmn file call writew90mmn ! write the .spn file call writew90spn end subroutine elk-7.2.42/src/PaxHeaders.21776/writew90win.f900000644000000000000000000000013214061636517015454 xustar0030 mtime=1623670095.918101561 30 atime=1623670094.776102621 30 ctime=1623670095.918101561 elk-7.2.42/src/writew90win.f900000644002504400250440000000405214061636517017512 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 Manh Duc Le, 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin ! and Lars Nordstrom. This file is distributed under the terms of the GNU ! General Public License. See the file COPYING for license details. !BOP ! !ROUTINE: writew90win ! !INTERFACE: subroutine writew90win ! !USES: use modmain use modw90 ! !DESCRIPTION: ! Writes out a template {\tt seedname.win} file with the Wannier90 input ! parameters. Uses {\tt wannier} and {\tt wannierExtra} blocks. ! ! !REVISION HISTORY: ! Created January 2015 (Manh Duc Le) ! Modified, August 2018 (Arsenii Gerasimov) ! Modified, February 2019 (JKD) !EOP !BOC implicit none ! local variables integer ik,is,ia,i character(256) fname fname=trim(seedname)//'.win' open(50,file=trim(fname),action='WRITE',form='FORMATTED') ! write the number of Wannier functions and bands write(50,'("length_unit = bohr")') write(50,'("num_wann = ",I8)') num_wann write(50,'("num_bands = ",I8)') num_bands write(50,'("num_iter = ",I8)') num_iter write(50,*) write(50,'("trial_step = ",G18.10)') trial_step write(50,*) write(50,'("use_bloch_phases = true")') ! write spinors if required if (spinpol) then write(50,*) write(50,'("spinors = true")') write(50,'("spn_formatted = true")') end if ! write lattice vectors write(50,*) write(50,'("begin unit_cell_cart")') write(50,'("bohr")') write(50,'(3G18.10)') avec(:,1) write(50,'(3G18.10)') avec(:,2) write(50,'(3G18.10)') avec(:,3) write(50,'("end unit_cell_cart")') ! writes atomic positions write(50,*) write(50,'("begin atoms_frac")') do is=1,nspecies do ia=1,natoms(is) write(50,'(A5,3G18.10)') trim(spsymb(is)),atposl(:,ia,is) end do end do write(50,'("end atoms_frac")') ! write the list of k-points write(50,*) write(50,'("mp_grid = ",3I6)') ngridk write(50,*) write(50,'("begin kpoints")') do ik=1,nkptnr write(50,'(3G18.10)') vkl(:,ik) end do write(50,'("end kpoints")') write(50,*) ! write the extra lines do i=1,nxlwin write(50,'(A)') trim(xlwin(i)) end do close(50) write(*,*) write(*,'("Info(writew90win): created file ",A)') trim(fname) end subroutine !EOC elk-7.2.42/src/PaxHeaders.21776/writew90eig.f900000644000000000000000000000012714061636517015427 xustar0029 mtime=1623670095.91910156 29 atime=1623670094.77710262 29 ctime=1623670095.91910156 elk-7.2.42/src/writew90eig.f900000644002504400250440000000141714061636517017463 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 Manh Duc Le, 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin ! and Lars Nordstrom. This file is distributed under the terms of the GNU ! General Public License. See the file COPYING for license details. subroutine writew90eig use modmain use modw90 implicit none ! local variables integer ik,jk,ist,i real(8) t1 character(256) fname fname=trim(seedname)//'.eig' open(50,file=trim(fname),action='WRITE',form='FORMATTED') ! loop over non-reduced k-points do ik=1,nkptnr ! equivalent reduced k-point jk=ivkik(ivk(1,ik),ivk(2,ik),ivk(3,ik)) do i=1,num_bands ist=idxw90(i) t1=evalsv(ist,jk)-efermi write(50,'(2I6,G18.10)') i,ik,t1*ha_ev end do end do close(50) write(*,*) write(*,'("Info(writew90eig): created file ",A)') trim(fname) end subroutine elk-7.2.42/src/PaxHeaders.21776/setupw90.f900000644000000000000000000000013214061636517014744 xustar0030 mtime=1623670095.921101558 30 atime=1623670094.779102618 30 ctime=1623670095.921101558 elk-7.2.42/src/setupw90.f900000644002504400250440000000355714061636517017013 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 Manh Duc Le, 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin ! and Lars Nordstrom. This file is distributed under the terms of the GNU ! General Public License. See the file COPYING for license details. subroutine setupw90 use modmain use modw90 implicit none ! local variables integer is,ia,ias real(8) real_lattice(3,3),recip_lattice(3,3) ! allocatable arrays integer, allocatable :: proj_l(:),proj_m(:),proj_radial(:),proj_s(:) integer, allocatable :: exclude_bands(:) real(8), allocatable :: atoms_cart(:,:),proj_site(:,:) real(8), allocatable :: proj_z(:,:),proj_x(:,:) real(8), allocatable :: proj_zona(:),proj_s_qaxis(:,:) character(256), allocatable :: atom_symbols(:) ! allocate global arrays if (allocated(nnlist)) deallocate(nnlist) allocate(nnlist(nkptnr,num_nnmax)) if (allocated(nncell)) deallocate(nncell) allocate(nncell(3,nkptnr,num_nnmax)) ! allocate local arrays allocate(proj_l(num_bands),proj_m(num_bands)) allocate(proj_radial(num_bands),proj_s(num_bands)) allocate(exclude_bands(num_bands)) allocate(atoms_cart(3,natmtot),proj_site(3,num_bands)) allocate(proj_z(3,num_bands),proj_x(3,num_bands)) allocate(proj_zona(num_bands),proj_s_qaxis(3,num_bands)) allocate(atom_symbols(natmtot)) real_lattice=br_ang*transpose(avec) recip_lattice=(1.d0/br_ang)*transpose(bvec) do ias=1,natmtot is=idxis(ias) ia=idxia(ias) atom_symbols(ias)=trim(spsymb(is)) atoms_cart(:,ias)=br_ang*atposc(:,ia,is) end do call wannier_setup(seedname,ngridk,nkptnr,real_lattice,recip_lattice,vkl, & num_bands,natmtot,atom_symbols,atoms_cart,.false.,spinpol,nntot,nnlist, & nncell,num_bands,num_wann,proj_site,proj_l,proj_m,proj_radial,proj_z,proj_x, & proj_zona,exclude_bands,proj_s,proj_s_qaxis) deallocate(proj_l,proj_m) deallocate(proj_radial,proj_s,exclude_bands) deallocate(atoms_cart,proj_site,proj_z,proj_x) deallocate(proj_zona,proj_s_qaxis,atom_symbols) end subroutine elk-7.2.42/src/PaxHeaders.21776/writew90mmn.f900000644000000000000000000000013214061636517015446 xustar0030 mtime=1623670095.922101557 30 atime=1623670094.781102616 30 ctime=1623670095.922101557 elk-7.2.42/src/writew90mmn.f900000644002504400250440000000501614061636517017505 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 Manh Duc Le, 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin ! and Lars Nordstrom. This file is distributed under the terms of the GNU ! General Public License. See the file COPYING for license details. subroutine writew90mmn use modmain use modw90 implicit none ! local variables integer ik,jk,ist,jst,i integer ngp(nspnfv),ngpq(nspnfv) real(8) vl(3),vc(3),q,vkql(3) character(256) fname ! automatic arrays complex(8) ylmq(lmmaxo),sfacq(natmtot) ! allocatable arrays integer, allocatable :: igpig(:,:),igpqig(:,:) real(8), allocatable :: jlqr(:,:) complex(8), allocatable :: wfmt(:,:,:,:),wfir(:,:,:) complex(8), allocatable :: wfmtq(:,:,:,:),wfgpq(:,:,:) complex(8), allocatable :: expqmt(:,:),oq(:,:) ! allocate local arrays allocate(igpig(ngkmax,nspnfv),igpqig(ngkmax,nspnfv)) allocate(jlqr(njcmax,nspecies)) allocate(wfmt(npcmtmax,natmtot,nspinor,num_bands)) allocate(wfir(ngtot,nspinor,num_bands)) allocate(wfmtq(npcmtmax,natmtot,nspinor,num_bands)) allocate(wfgpq(ngkmax,nspinor,num_bands)) allocate(expqmt(npcmtmax,natmtot)) allocate(oq(num_bands,num_bands)) fname=trim(seedname)//'.mmn' open(50,file=trim(fname),action='WRITE',form='FORMATTED') write(50,'("Generated by Elk version ",I1.1,".",I1.1,".",I2.2)') version write(50,'(3I8)') num_bands,nkptnr,nntot do ik=1,nkptnr call genwfsvp(.false.,.false.,num_bands,idxw90,ngridg,igfft,vkl(:,ik),ngp, & igpig,wfmt,ngtot,wfir) do i=1,nntot jk=nnlist(ik,i) ! q-vector in lattice coordinates vl(:)=dble(nncell(:,ik,i))+vkl(:,jk)-vkl(:,ik) ! q-vector in Cartesian coordinates call r3mv(bvec,vl,vc) ! q-vector length q=sqrt(vc(1)**2+vc(2)**2+vc(3)**2) ! generate phase factor function exp(iq.r) in the muffin-tins call genjlgpr(1,q,jlqr) call genylmv(lmaxo,vc,ylmq) call gensfacgp(1,vc,1,sfacq) call genexpmt(1,jlqr,ylmq,1,sfacq,expqmt) ! k+q-vector in lattice coordinates vkql(:)=vkl(:,ik)+vl(:) ! generate the wavefunctions at k+q call genwfsvp(.false.,.true.,num_bands,idxw90,ngridg,igfft,vkql,ngpq, & igpqig,wfmtq,ngkmax,wfgpq) ! determine the overlap matrix call genolpq(num_bands,expqmt,ngpq,igpqig,wfmt,wfir,wfmtq,wfgpq,oq) ! write overlap matrix to file write(50,'(5I8)') ik,jk,nncell(:,ik,i) do jst=1,num_bands do ist=1,num_bands write(50,'(2G18.10)') dble(oq(jst,ist)),-aimag(oq(jst,ist)) end do end do end do end do close(50) write(*,*) write(*,'("Info(writew90mmn): created file ",A)') trim(fname) deallocate(igpig,igpqig,jlqr) deallocate(wfmt,wfir,wfmtq,wfgpq) deallocate(expqmt,oq) end subroutine elk-7.2.42/src/PaxHeaders.21776/writew90spn.f900000644000000000000000000000013214061636517015457 xustar0030 mtime=1623670095.924101555 30 atime=1623670094.782102615 30 ctime=1623670095.924101555 elk-7.2.42/src/writew90spn.f900000644002504400250440000000233414061636517017516 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 Manh Duc Le, 2017-18 Arsenii Gerasimov, Yaroslav Kvashnin ! and Lars Nordstrom. This file is distributed under the terms of the GNU ! General Public License. See the file COPYING for license details. subroutine writew90spn use modmain use modw90 implicit none ! local variables integer ik,ist,jst,i,j complex(8) z1 character(256) fname ! allocatable arrays complex(8), allocatable :: smat(:,:,:,:) if (.not.spinpol) return fname=trim(seedname)//'.spn' open(50,file=trim(fname),action='WRITE',form='FORMATTED') write(50,'("Generated by Elk version ",I1.1,".",I1.1,".",I2.2)') version write(50,'(3I8)') num_bands,nkptnr allocate(smat(2,2,nstsv,nstsv)) do ik=1,nkptnr ! generate the spin operator matrix elements call gensmatk(vkl(:,ik),smat) do j=1,num_bands jst=idxw90(j) do i=1,j ist=idxw90(i) z1=smat(1,2,ist,jst)+smat(2,1,ist,jst) write(50,'(2G18.10)') z1 z1=smat(2,1,ist,jst)-smat(1,2,ist,jst) z1=cmplx(-aimag(z1),dble(z1),8) write(50,'(2G18.10)') z1 z1=smat(1,1,ist,jst)-smat(2,2,ist,jst) write(50,'(2G18.10)') z1 end do end do end do deallocate(smat) close(50) write(*,*) write(*,'("Info(writew90spn): created file ",A)') trim(fname) end subroutine elk-7.2.42/src/PaxHeaders.21776/dmatuv.f900000644000000000000000000000013214061636517014544 xustar0030 mtime=1623670095.925101554 30 atime=1623670094.784102614 30 ctime=1623670095.925101554 elk-7.2.42/src/dmatuv.f900000644002504400250440000000136014061636517016601 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine dmatuv(n,ef,e,u,v,dvv,duv) implicit none ! arguments integer, intent(in) :: n real(8), intent(in) :: ef,e(n) complex(8), intent(in) :: u(n,n),v(n,n) complex(8), intent(out) :: dvv(n,n),duv(n,n) ! local variables integer i ! normal electronic density matrix VV† call zgemm('N','C',n,n,n,(1.d0,0.d0),v,n,v,n,(0.d0,0.d0),dvv,n) ! subtract unperturbed density matrix do i=1,n if (e(i).le.ef) dvv(i,i)=dvv(i,i)-1.d0 end do ! anomalous density matrix UV† call zgemm('N','C',n,n,n,(1.d0,0.d0),u,n,v,n,(0.d0,0.d0),duv,n) end subroutine elk-7.2.42/src/PaxHeaders.21776/dmatwx.f900000644000000000000000000000013214061636517014550 xustar0030 mtime=1623670095.926101554 30 atime=1623670094.786102612 30 ctime=1623670095.926101554 elk-7.2.42/src/dmatwx.f900000644002504400250440000000112014061636517016577 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine dmatwx(n,w,x,dxx,dwx) implicit none ! arguments integer, intent(in) :: n complex(8), intent(in) :: w(n,n),x(n,n) complex(8), intent(out) :: dxx(n,n),dwx(n,n) ! normal bosonic density matrix XX† call zgemm('N','C',n,n,n,(1.d0,0.d0),x,n,x,n,(0.d0,0.d0),dxx,n) ! anomalous density matrix -WX† call zgemm('N','C',n,n,n,(-1.d0,0.d0),w,n,x,n,(0.d0,0.d0),dwx,n) end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqnuv.f900000644000000000000000000000013214061636517014735 xustar0030 mtime=1623670095.928101552 30 atime=1623670094.787102611 30 ctime=1623670095.928101552 elk-7.2.42/src/eveqnuv.f900000644002504400250440000000177714061636517017006 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine eveqnuv(n,au,bv,w,vn) implicit none ! arguments integer, intent(in) :: n complex(8), intent(inout) :: au(n,n),bv(n,n) real(8), intent(out) :: w(n),vn(n) ! local variables integer n2,i,j ! allocatable arrays real(8), allocatable :: w2(:) complex(8), allocatable :: h(:,:) n2=2*n ! setup the fermionic Bogoliubov Hamiltonian allocate(w2(n2),h(n2,n2)) do j=1,n do i=1,j h(i,j)=au(i,j) h(n+i,n+j)=-au(i,j) end do end do do j=1,n do i=1,n h(i,n+j)=bv(i,j) end do end do ! find the eigenvalues and eigenvectors call eveqnzh(n2,n2,h,w2) ! copy to output arrays do i=1,n ! choose the positive eigenvalues j=n+i w(i)=w2(j) call zcopy(n,h(1,j),1,au(1,i),1) call zcopy(n,h(n+1,j),1,bv(1,i),1) ! store the V-norm vn(i)=dot_product(bv(:,i),bv(:,i)) end do deallocate(w2,h) end subroutine elk-7.2.42/src/PaxHeaders.21776/eveqnwxy.f900000644000000000000000000000013014061636517015130 xustar0029 mtime=1623670095.93010155 30 atime=1623670094.789102609 29 ctime=1623670095.93010155 elk-7.2.42/src/eveqnwxy.f900000644002504400250440000000316514061636517017174 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine eveqnwxy(n,dw,ex,fy,w,xn) implicit none ! arguments integer, intent(in) :: n complex(8), intent(inout) :: dw(n,n),ex(n,n),fy(n) real(8), intent(out) :: w(n),xn(n) ! local variables integer n2,i,j real(8) t1,t2 ! allocatable arrays integer, allocatable :: idx(:) real(8), allocatable :: r(:) complex(8), allocatable :: w2(:),h(:,:) complex(8), allocatable :: x(:),a(:,:) ! external functions real(8), external :: dznrm2 n2=2*n ! setup the bosonic Bogoliubov Hamiltonian allocate(w2(n2),h(n2,n2)) do j=1,n do i=1,n h(i,j)=dw(i,j) h(n+i,n+j)=-dw(i,j) h(i,n+j)=-ex(i,j) h(n+i,j)=ex(i,j) end do end do ! find the eigenvalues and right eigenvectors call eveqnzg(n2,n2,h,w2) ! select the eigenpairs corresponding to W†W - X†X = I allocate(idx(n2),r(n2)) do j=1,n2 t1=dznrm2(n,h(1,j),1)**2 t2=dznrm2(n,h(n+1,j),1)**2 r(j)=t1-t2 end do call sortidx(n2,r,idx) ! pseudo-normalise the eigenvectors and store in output arrays do i=1,n j=idx(n+i) t1=abs(r(j))+1.d-8 t1=(1.d0-(1.d0-t1)**4)/sqrt(t1) w(i)=dble(w2(j)) dw(1:n,i)=t1*h(1:n,j) ex(1:n,i)=t1*h(n+1:n2,j) ! compute the X-norm xn(i)=dznrm2(n,ex(:,i),1)**2 end do deallocate(idx,r,w2,h) ! solve for the vector y allocate(x(n),a(n,n)) a(:,:)=dw(:,:)-ex(:,:) x(:)=fy(:) call zgemv('T',n,n,(1.d0,0.d0),a,n,x,1,(0.d0,0.d0),fy,1) do i=1,n if (w(i).gt.1.d-6) then fy(i)=fy(i)/w(i) else fy(i)=0.d0 end if end do deallocate(x,a) end subroutine elk-7.2.42/src/PaxHeaders.21776/writeevaluv.f900000644000000000000000000000013214061636517015621 xustar0030 mtime=1623670095.931101549 30 atime=1623670094.791102607 30 ctime=1623670095.931101549 elk-7.2.42/src/writeevaluv.f900000644002504400250440000000130014061636517017650 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine writeevaluv use modmain use modbog implicit none ! local variables integer ik,ist ! write out the valence eigenvalues open(50,file='EIGVALUV.OUT',form='FORMATTED',action='WRITE') write(50,'(I6," : nkpt")') nkpt write(50,'(I6," : nstsv")') nstsv do ik=1,nkpt write(50,*) write(50,'(I6,3G18.10," : k-point, vkl")') ik,vkl(:,ik) write(50,'(" (state, eigenvalue, V-norm below)")') do ist=1,nstsv write(50,'(I6,3G18.10)') ist,evaluv(ist,ik),vnorm(ist,ik) end do write(50,*) end do close(50) end subroutine elk-7.2.42/src/PaxHeaders.21776/occupyuv.f900000644000000000000000000000013214061636517015121 xustar0030 mtime=1623670095.933101547 30 atime=1623670094.792102606 30 ctime=1623670095.933101547 elk-7.2.42/src/occupyuv.f900000644002504400250440000000226114061636517017157 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine occupyuv use modmain use modbog use modmpi implicit none integer ik,ist real(8) chg,w,vn real(8) e0,e1,e ! determine the total charge and fermionic anomalous correlation entropy chg=0.d0 face=0.d0 do ik=1,nkpt w=wkpt(ik) do ist=1,nstsv vn=vnorm(ist,ik) chg=chg+w*vn if ((vn.gt.0.d0).and.(vn.lt.1.d0)) then face=face+w*(vn*log(vn)+(1.d0-vn)*log(1.d0-vn)) end if end do end do chg=occmax*chg face=-occmax*face ! adjust the Fermi energy efermi=efermi+tauefm*(chgval-chg) if (mp_mpi) then if (abs(chg-chgval).gt.epschg) then write(*,*) write(*,'("Warning(occupyuv): incorrect charge : ",2G18.10)') chg,chgval end if end if ! estimate the indirect band gap e0=-1.d8 e1=1.d8 ikgap(1)=1 ikgap(2)=1 do ist=1,nstsv do ik=1,nkpt e=evaluv(ist,ik) if (e.lt.0.d0) then if (e.gt.e0) then e0=e ikgap(1)=ik end if else if (e.lt.e1) then e1=e ikgap(2)=ik end if end if end do end do bandgap(1)=e1-e0 end subroutine elk-7.2.42/src/PaxHeaders.21776/inithfb.f900000644000000000000000000000013214061636517014667 xustar0030 mtime=1623670095.934101546 30 atime=1623670094.794102604 30 ctime=1623670095.934101546 elk-7.2.42/src/inithfb.f900000644002504400250440000000200614061636517016722 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine inithfb use modmain use modbog use modrandom implicit none ! local variables integer ik,ist,jst real(8), parameter :: rndevv=0.01d0 ! allocatable arrays complex(8), allocatable :: evecu(:,:),evecv(:,:) ! initialise the Bogoliubov eigenvectors and write to file if (task.eq.800) then allocate(evecu(nstsv,nstsv),evecv(nstsv,nstsv)) evecu(:,:)=0.d0 do ist=1,nstsv evecu(ist,ist)=1.d0 end do do jst=1,nstsv do ist=1,nstsv evecv(ist,jst)=rndevv*cmplx(randomu()-0.5d0,randomu()-0.5d0,8) end do end do do ik=1,nkpt call putevecuv(ik,evecu,evecv) end do deallocate(evecu,evecv) end if ! allocate the Bogoliubov eigenvalue array if (allocated(evaluv)) deallocate(evaluv) allocate(evaluv(nstsv,nkpt)) ! allocate the V-norm array if (allocated(vnorm)) deallocate(vnorm) allocate(vnorm(nstsv,nkpt)) end subroutine elk-7.2.42/src/PaxHeaders.21776/genwfuv.f900000644000000000000000000000013214061636517014725 xustar0030 mtime=1623670095.936101544 30 atime=1623670094.796102602 30 ctime=1623670095.936101544 elk-7.2.42/src/genwfuv.f900000644002504400250440000000360114061636517016762 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine genwfuv(evecu,evecv,wfmt,wfir,wfumt,wfuir,wfvmt,wfvir) use modmain use modomp implicit none ! arguments complex(8), intent(in) :: evecu(nstsv,nstsv),evecv(nstsv,nstsv) complex(8), intent(in) :: wfmt(npcmtmax,natmtot,nspinor,nstsv) complex(8), intent(in) :: wfir(ngtc,nspinor,nstsv) complex(8), intent(out) :: wfumt(npcmtmax,natmtot,nspinor,nstsv) complex(8), intent(out) :: wfuir(ngtc,nspinor,nstsv) complex(8), intent(out) :: wfvmt(npcmtmax,natmtot,nspinor,nstsv) complex(8), intent(out) :: wfvir(ngtc,nspinor,nstsv) ! local variables integer ist,jst,ispn integer is,ias,npc,nthd complex(8) z1 call holdthd(nstsv,nthd) !$OMP PARALLEL DEFAULT(SHARED) & !$OMP PRIVATE(ist,z1,ispn) & !$OMP PRIVATE(ias,is,npc) & !$OMP NUM_THREADS(nthd) !$OMP DO do jst=1,nstsv wfumt(:,:,:,jst)=0.d0 wfuir(:,:,jst)=0.d0 do ist=1,nstsv z1=evecu(ist,jst) if (abs(dble(z1))+abs(aimag(z1)).gt.epsocc) then do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) npc=npcmt(is) call zaxpy(npc,z1,wfmt(:,ias,ispn,ist),1,wfumt(:,ias,ispn,jst),1) end do call zaxpy(ngtc,z1,wfir(:,ispn,ist),1,wfuir(:,ispn,jst),1) end do end if end do end do !$OMP END DO NOWAIT !$OMP DO do jst=1,nstsv wfvmt(:,:,:,jst)=0.d0 wfvir(:,:,jst)=0.d0 do ist=1,nstsv z1=evecv(ist,jst) if (abs(dble(z1))+abs(aimag(z1)).gt.epsocc) then do ispn=1,nspinor do ias=1,natmtot is=idxis(ias) npc=npcmt(is) call zaxpy(npc,z1,wfmt(:,ias,ispn,ist),1,wfvmt(:,ias,ispn,jst),1) end do call zaxpy(ngtc,z1,wfir(:,ispn,ist),1,wfvir(:,ispn,jst),1) end do end if end do end do !$OMP END DO !$OMP END PARALLEL call freethd(nthd) end subroutine elk-7.2.42/src/PaxHeaders.21776/putevaluv.f900000644000000000000000000000013214061636517015277 xustar0030 mtime=1623670095.937101543 30 atime=1623670094.797102601 30 ctime=1623670095.937101543 elk-7.2.42/src/putevaluv.f900000644002504400250440000000113114061636517017330 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine putevaluv(ik,evaluvp) use modmain implicit none ! arguments integer, intent(in) :: ik real(8), intent(in) :: evaluvp(nstsv) ! local variables integer recl ! find the record length inquire(iolength=recl) vkl(:,ik),nstsv,evaluvp !$OMP CRITICAL(u320) open(320,file='EVALUV.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(320,rec=ik) vkl(:,ik),nstsv,evaluvp close(320) !$OMP END CRITICAL(u320) end subroutine elk-7.2.42/src/PaxHeaders.21776/getevaluv.f900000644000000000000000000000013014061636517015244 xustar0030 mtime=1623670095.938101542 28 atime=1623670094.7991026 30 ctime=1623670095.938101542 elk-7.2.42/src/getevaluv.f900000644002504400250440000000215114061636517017302 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine getevaluv(ik,evaluvp) use modmain implicit none ! arguments integer, intent(in) :: ik real(8), intent(out) :: evaluvp(nstsv) ! local variables integer recl,nstsv_ real(8) vkl_(3),t1 ! find the record length inquire(iolength=recl) vkl_,nstsv_,evaluvp !$OMP CRITICAL(u320) open(320,file='EVALUV.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(320,rec=ik) vkl_,nstsv_,evaluvp !$OMP END CRITICAL(u320) t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getevaluv): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" EVALUV.OUT : ",3G18.10)') vkl_ write(*,*) stop end if if (nstsv.ne.nstsv_) then write(*,*) write(*,'("Error(getevaluv): differing nstsv for k-point ",I8)') ik write(*,'(" current : ",I8)') nstsv write(*,'(" EVALUV.OUT : ",I8)') nstsv_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/putevecuv.f900000644000000000000000000000013214061636517015272 xustar0030 mtime=1623670095.940101541 30 atime=1623670094.801102598 30 ctime=1623670095.940101541 elk-7.2.42/src/putevecuv.f900000644002504400250440000000117714061636517017335 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine putevecuv(ik,evecu,evecv) use modmain implicit none ! arguments integer, intent(in) :: ik complex(8), intent(in) :: evecu(nstsv,nstsv),evecv(nstsv,nstsv) ! local variables integer recl ! find the record length inquire(iolength=recl) vkl(:,ik),nstsv,evecu,evecv !$OMP CRITICAL(u322) open(322,file='EVECUV.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(322,rec=ik) vkl(:,ik),nstsv,evecu,evecv close(322) !$OMP END CRITICAL(u322) end subroutine elk-7.2.42/src/PaxHeaders.21776/getevecuv.f900000644000000000000000000000013014061636517015237 xustar0029 mtime=1623670095.94110154 30 atime=1623670094.802102597 29 ctime=1623670095.94110154 elk-7.2.42/src/getevecuv.f900000644002504400250440000000246214061636517017302 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2019 J. K. Dewhurst and S. Sharma. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine getevecuv(ikp,vpl,u,v) use modmain implicit none ! arguments integer, intent(in) :: ikp real(8), intent(in) :: vpl(3) complex(8), intent(out) :: u(nstsv,nstsv),v(nstsv,nstsv) ! local variables integer isym,ik integer recl,nstsv_ real(8) vkl_(3),t1 if (ikp.gt.0) then ik=ikp else ! find the equivalent k-point number and symmetry which rotates vkl to vpl call findkpt(vpl,isym,ik) end if ! find the record length inquire(iolength=recl) vkl_,nstsv_,u,v !$OMP CRITICAL(u322) open(322,file='EVECUV.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(322,rec=ik) vkl_,nstsv_,u,v !$OMP END CRITICAL(u322) t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getevecuv): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" EVECUV.OUT : ",3G18.10)') vkl_ write(*,*) stop end if if (nstsv.ne.nstsv_) then write(*,*) write(*,'("Error(getevecuv): differing nstsv for k-point ",I8)') ik write(*,'(" current : ",I8)') nstsv write(*,'(" EVECUV.OUT : ",I8)') nstsv_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/putevecwxy.f900000644000000000000000000000013214061636517015467 xustar0030 mtime=1623670095.943101538 30 atime=1623670094.804102595 30 ctime=1623670095.943101538 elk-7.2.42/src/putevecwxy.f900000644002504400250440000000122614061636517017525 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine putevecwxy(iq,w,x,y) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq complex(8), intent(in) :: w(nbph,nbph),x(nbph,nbph),y(nbph) ! local variables integer recl ! find the record length inquire(iolength=recl) vql(:,iq),nbph,w,x,y !$OMP CRITICAL(u332) open(332,file='EVECWXY.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(332,rec=iq) vql(:,iq),nbph,w,x,y close(332) !$OMP END CRITICAL(u332) end subroutine elk-7.2.42/src/PaxHeaders.21776/getevecwxy.f900000644000000000000000000000013214061636517015436 xustar0030 mtime=1623670095.944101537 30 atime=1623670094.806102593 30 ctime=1623670095.944101537 elk-7.2.42/src/getevecwxy.f900000644002504400250440000000224614061636517017477 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine getevecwxy(iq,w,x,y) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq complex(8), intent(out) :: w(nbph,nbph),x(nbph,nbph),y(nbph) ! local variables integer recl,nbph_ real(8) vql_(3),t1 ! find the record length inquire(iolength=recl) vql_,nbph_,w,x,y !$OMP CRITICAL(u332) open(332,file='EVECWXY.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(332,rec=iq) vql_,nbph_,w,x,y !$OMP END CRITICAL(u332) t1=abs(vql(1,iq)-vql_(1))+abs(vql(2,iq)-vql_(2))+abs(vql(3,iq)-vql_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getevecwxy): differing vectors for q-point ",I8)') iq write(*,'(" current : ",3G18.10)') vql(:,iq) write(*,'(" EVECWXY.OUT : ",3G18.10)') vql_ write(*,*) stop end if if (nbph.ne.nbph_) then write(*,*) write(*,'("Error(getevecwxy): differing nbph for q-point ",I8)') iq write(*,'(" current : ",I8)') nbph write(*,'(" EVECWXY.OUT : ",I8)') nbph_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/putevalwx.f900000644000000000000000000000013214061636517015303 xustar0030 mtime=1623670095.946101535 30 atime=1623670094.807102592 30 ctime=1623670095.946101535 elk-7.2.42/src/putevalwx.f900000644002504400250440000000120314061636517017334 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine putevalwx(iq,evalwxp) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq real(8), intent(in) :: evalwxp(nbph) ! local variables integer recl ! find the record length inquire(iolength=recl) vql(:,iq),nbph,evalwxp !$OMP CRITICAL(u330) open(330,file='EVALWX.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(330,rec=iq) vql(:,iq),nbph,evalwxp close(330) !$OMP END CRITICAL(u330) end subroutine elk-7.2.42/src/PaxHeaders.21776/getevalwx.f900000644000000000000000000000013114061636517015251 xustar0030 mtime=1623670095.947101534 29 atime=1623670094.80910259 30 ctime=1623670095.947101534 elk-7.2.42/src/getevalwx.f900000644002504400250440000000221514061636517017307 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2020 Chung-Yu Wang, J. K. Dewhurst, S. Sharma and ! E. K. U. Gross. This file is distributed under the terms of the GNU General ! Public License. See the file COPYING for license details. subroutine getevalwx(iq,evalwxp) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq real(8), intent(out) :: evalwxp(nbph) ! local variables integer recl,nbph_ real(8) vql_(3),t1 ! find the record length inquire(iolength=recl) vql_,nbph_,evalwxp !$OMP CRITICAL(u330) open(330,file='EVALWX.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(330,rec=iq) vql_,nbph_,evalwxp !$OMP END CRITICAL(u330) t1=abs(vql(1,iq)-vql_(1))+abs(vql(2,iq)-vql_(2))+abs(vql(3,iq)-vql_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getevalwx): differing vectors for q-point ",I8)') iq write(*,'(" current : ",3G18.10)') vql(:,iq) write(*,'(" EVALWX.OUT : ",3G18.10)') vql_ write(*,*) stop end if if (nbph.ne.nbph_) then write(*,*) write(*,'("Error(getevalwx): differing nbph for q-point ",I8)') iq write(*,'(" current : ",I8)') nbph write(*,'(" EVALWX.OUT : ",I8)') nbph_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/aceplot.f900000644000000000000000000000013214061636517014673 xustar0030 mtime=1623670095.949101532 30 atime=1623670094.811102589 30 ctime=1623670095.949101532 elk-7.2.42/src/aceplot.f900000644002504400250440000000426214061636517016734 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine aceplot use modmain use modphonon implicit none ! local variables integer ik,jk,iq,jq integer i1,i2,i3,ist,i real(8) ace,vn,xn ! allocatable arrays real(8), allocatable :: vnorm(:),xnorm(:) ! initialise universal variables call init0 call init1 call init2 call initeph !----------------------------------------------------------! ! plot the fermionic anomalous correlation entropy ! !----------------------------------------------------------! allocate(vnorm(nstsv)) open(50,file='FACE3D.OUT',form='FORMATTED',action='WRITE') write(50,'(3I6," : grid size")') ngridk(:) do i3=0,ngridk(3)-1 do i2=0,ngridk(2)-1 do i1=0,ngridk(1)-1 ik=ivkiknr(i1,i2,i3) jk=ivkik(i1,i2,i3) ! get the V-norm from file call getvnorm(jk,vnorm) ace=0.d0 do ist=1,nstsv vn=vnorm(ist) if ((vn.gt.0.d0).and.(vn.lt.1.d0)) then ace=ace+vn*log(vn)+(1.d0-vn)*log(1.d0-vn) end if end do ace=-occmax*ace write(50,'(4G18.10)') vkc(:,ik),ace end do end do end do close(50) deallocate(vnorm) !--------------------------------------------------------! ! plot the bosonic anomalous correlation entropy ! !--------------------------------------------------------! allocate(xnorm(nbph)) open(50,file='BACE3D.OUT',form='FORMATTED',action='WRITE') write(50,'(3I6," : grid size")') ngridq(:) do i3=0,ngridq(3)-1 do i2=0,ngridq(2)-1 do i1=0,ngridq(1)-1 iq=ivqiqnr(i1,i2,i3) jq=ivqiq(i1,i2,i3) ! get the X-norm from file call getxnorm(jq,xnorm) ace=0.d0 do i=1,nbph xn=xnorm(i) if (xn.gt.0.d0) then ace=ace+xn*log(xn)-(1.d0+xn)*log(1.d0+xn) end if end do ace=-ace write(50,'(4G18.10)') vqc(:,iq),ace end do end do end do close(50) deallocate(xnorm) write(*,*) write(*,'("Info(aceplot):")') write(*,'(" 3D fermionic anomalous correlation entropy written to FACE3D.OUT")') write(*,'(" 3D bosonic anomalous correlation entropy written to BACE3D.OUT")') end subroutine elk-7.2.42/src/PaxHeaders.21776/putxnorm.f900000644000000000000000000000013214061636517015140 xustar0030 mtime=1623670095.950101531 30 atime=1623670094.812102587 30 ctime=1623670095.950101531 elk-7.2.42/src/putxnorm.f900000644002504400250440000000115214061636517017174 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine putxnorm(iq,xnorm) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq real(8), intent(in) :: xnorm(nbph) ! local variables integer recl ! find the record length inquire(iolength=recl) vql(:,iq),nbph,xnorm !$OMP CRITICAL(u334) open(334,file='XNORM.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(334,rec=iq) vql(:,iq),nbph,xnorm close(334) !$OMP END CRITICAL(u334) end subroutine elk-7.2.42/src/PaxHeaders.21776/putvnorm.f900000644000000000000000000000013214061636517015136 xustar0030 mtime=1623670095.952101529 30 atime=1623670094.814102586 30 ctime=1623670095.952101529 elk-7.2.42/src/putvnorm.f900000644002504400250440000000115514061636517017175 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine putvnorm(ik,vnorm) use modmain use modphonon implicit none ! arguments integer, intent(in) :: ik real(8), intent(in) :: vnorm(nstsv) ! local variables integer recl ! find the record length inquire(iolength=recl) vkl(:,ik),nstsv,vnorm !$OMP CRITICAL(u324) open(324,file='VNORM.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) write(324,rec=ik) vkl(:,ik),nstsv,vnorm close(324) !$OMP END CRITICAL(u324) end subroutine elk-7.2.42/src/PaxHeaders.21776/getxnorm.f900000644000000000000000000000013214061636517015107 xustar0030 mtime=1623670095.953101528 30 atime=1623670094.816102584 30 ctime=1623670095.953101528 elk-7.2.42/src/getxnorm.f900000644002504400250440000000215614061636517017150 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine getxnorm(iq,xnorm) use modmain use modphonon implicit none ! arguments integer, intent(in) :: iq real(8), intent(out) :: xnorm(nbph) ! local variables integer recl,nbph_ real(8) vql_(3),t1 ! find the record length inquire(iolength=recl) vql_,nbph_,xnorm !$OMP CRITICAL(u334) open(334,file='XNORM.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(334,rec=iq) vql_,nbph_,xnorm !$OMP END CRITICAL(u334) t1=abs(vql(1,iq)-vql_(1))+abs(vql(2,iq)-vql_(2))+abs(vql(3,iq)-vql_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getxnorm): differing vectors for q-point ",I8)') iq write(*,'(" current : ",3G18.10)') vql(:,iq) write(*,'(" XNORM.OUT : ",3G18.10)') vql_ write(*,*) stop end if if (nbph.ne.nbph_) then write(*,*) write(*,'("Error(getxnorm): differing nbph for q-point ",I8)') iq write(*,'(" current : ",I8)') nbph write(*,'(" XNORM.OUT : ",I8)') nbph_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/getvnorm.f900000644000000000000000000000013214061636517015105 xustar0030 mtime=1623670095.955101527 30 atime=1623670094.817102583 30 ctime=1623670095.955101527 elk-7.2.42/src/getvnorm.f900000644002504400250440000000215114061636517017141 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2021 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine getvnorm(ik,vnorm) use modmain implicit none ! arguments integer, intent(in) :: ik real(8), intent(out) :: vnorm(nstsv) ! local variables integer recl,nstsv_ real(8) vkl_(3),t1 ! find the record length inquire(iolength=recl) vkl_,nstsv_,vnorm !$OMP CRITICAL(u324) open(324,file='VNORM.OUT',form='UNFORMATTED',access='DIRECT',recl=recl) read(324,rec=ik) vkl_,nstsv_,vnorm !$OMP END CRITICAL(u324) t1=abs(vkl(1,ik)-vkl_(1))+abs(vkl(2,ik)-vkl_(2))+abs(vkl(3,ik)-vkl_(3)) if (t1.gt.epslat) then write(*,*) write(*,'("Error(getvnorm): differing vectors for k-point ",I8)') ik write(*,'(" current : ",3G18.10)') vkl(:,ik) write(*,'(" VNORM.OUT : ",3G18.10)') vkl_ write(*,*) stop end if if (nstsv.ne.nstsv_) then write(*,*) write(*,'("Error(getvnorm): differing nstsv for k-point ",I8)') ik write(*,'(" current : ",I8)') nstsv write(*,'(" VNORM.OUT : ",I8)') nstsv_ write(*,*) stop end if end subroutine elk-7.2.42/src/PaxHeaders.21776/Makefile0000644000000000000000000000013014061636516014361 xustar0029 mtime=1623670094.82010258 30 atime=1623670094.819102581 29 ctime=1623670094.82010258 elk-7.2.42/src/Makefile0000644002504400250440000003300314061636516016417 0ustar00dewhurstdewhurst00000000000000 include ../make.inc # modules SRC_modules = modmain.f90 $(SRC_MPI) modmpi.f90 modramdisk.f90 $(SRC_libxc) \ modxcifc.f90 modfxcifc.f90 moddftu.f90 modrdm.f90 modphonon.f90 \ modtest.f90 modrandom.f90 modstore.f90 modpw.f90 modvars.f90 modtddft.f90 \ modgw.f90 modulr.f90 modbog.f90 moddelf.f90 $(SRC_OMP) \ modomp.f90 $(SRC_MKL) mkl_init.f90 $(SRC_OBLAS) oblas_init.f90 $(SRC_BLIS) \ blis_init.f90 $(SRC_W90S) modw90.f90 # Elk program SRC_elk = elk.f90 # main subroutines and functions SRC_main0 = \ olpistl.f90 hmlistl.f90 olpalo.f90 hmlalo.f90 olplolo.f90 hmllolo.f90 \ olpaa.f90 hmlaa.f90 gengclg.f90 rhomagsh.f90 charge.f90 moment.f90 rfint0.f90 \ potnucl.f90 r3mm.f90 r3mtm.f90 r3mmt.f90 r3vo.f90 gengvc.f90 gengvec.f90 \ r3mdet.f90 gencfrc.f90 checkstop.f90 genbs.f90 rfirsm.f90 rfmtsm.f90 \ rfint.f90 gradwf2.f90 closefiles.f90 writelinen.f90 rfmtlm.f90 putpmat.f90 \ getpmat.f90 rfmtpack.f90 zfmtpack.f90 rfmtint.f90 putevalfv.f90 getevalfv.f90 \ wavefmt.f90 putkmat.f90 getkmat.f90 putepsinv.f90 getcfgq.f90 putevalsv.f90 \ getevalsv.f90 getevecsv.f90 putevecsv.f90 genshtmat.f90 allatoms.f90 \ putevecfv.f90 getevecfv.f90 writesym.f90 putoccsv.f90 getoccsv.f90 torque.f90 \ findqpt.f90 findkpt.f90 genevfsv.f90 genwfsv.f90 SRC_main1 = \ sdelta.f90 stheta.f90 sortidx.f90 symmat.f90 radnucl.f90 hrmdmat.f90 \ wigner3j.f90 symrvf.f90 writeqpts.f90 rndevsv.f90 gengkvec.f90 \ mixlinear.f90 writesf.f90 gengqf.f90 genkmat.f90 genolpq.f90 genjlgprmt.f90 \ rfinterp.f90 fsmooth.f90 axangrot.f90 rotaxang.f90 wspline.f90 splined.f90 \ findswidth.f90 findsymlat.f90 writepmat.f90 genstrain.f90 symmetry.f90 \ linengy.f90 writestress.f90 eulerrot.f90 zftwfir.f90 rschrodint.f90 \ writegclq.f90 writegeom.f90 writemom.f90 gendmat.f90 curlrvf.f90 \ genzvclmt.f90 genjtot.f90 symvec.f90 checkwrite.f90 genjprk.f90 proj2d.f90 \ genidxbse.f90 symrvfir.f90 genjpr.f90 eveqnfvr.f90 gentau.f90 genjlgpr.f90 \ writestrain.f90 writefermi.f90 rfmtctof.f90 findsym.f90 zfsht.f90 rhonorm.f90 \ genvchi0.f90 zfmtconj.f90 stheta_sq.f90 sdelta_lr.f90 \ stheta_lr.f90 findsymsite.f90 genlmirep.f90 writespecies.f90 rhomagk.f90 \ symrvfmt.f90 wigner3jf.f90 wigner6j.f90 genhvec.f90 ylmrot.f90 wxcplot.f90 \ massnucl.f90 gendmatk.f90 rfplot.f90 straingkq.f90 \ eveqnit.f90 oepmain.f90 rdirac.f90 unitary.f90 bandstr.f90 sfacinit.f90 \ findscq.f90 plot1d.f90 plot2d.f90 plot3d.f90 init0.f90 readstate.f90 \ eveqnhf.f90 zbsht.f90 i3mtv.f90 spline.f90 gauntyry.f90 findnjcmax.f90 \ gndstate.f90 sstask.f90 fermisurf.f90 spiralsc.f90 atom.f90 maginit.f90 \ exxengyk.f90 xc_c_tb09.f90 moke.f90 hmlrad.f90 dos.f90 findprimcell.f90 \ plotpt2d.f90 sfacrho.f90 bdipole.f90 dielectric.f90 elfplot.f90 vclcore.f90 \ zfmtwr.f90 zvcldisp.f90 vecfbz.f90 gcd.f90 lopzflmn.f90 zpotclmt.f90 \ readfermi.f90 gensdmat.f90 symrfmt.f90 sphcrd.f90 potcoul.f90 genzrm.f90 \ rfmtftoc.f90 rminv.f90 zminv.f90 rtozfmt.f90 genwfsvp.f90 rdiracint.f90 \ findngkmax.f90 rotzflm.f90 zfinp.f90 latvstep.f90 gradzfmt.f90 eveqnfv.f90 \ symdmat.f90 z2mm.f90 z2mctm.f90 z2mmct.f90 axangsu2.f90 gradzvcln.f90 \ gentpmae.f90 zfcmtwr.f90 projsbf.f90 splinew.f90 gradzf.f90 mixerifc.f90 \ genvsig.f90 timesec.f90 zfmtftoc.f90 ztorfmt.f90 zfmtctof.f90 eveqnfvz.f90 \ energynn.f90 gaunt.f90 potxcmt.f90 sdelta_mp.f90 stheta_mp.f90 sdelta_fd.f90 \ stheta_fd.f90 writelsj.f90 eveqnzh.f90 gensmatk.f90 gensfacgp.f90 rhomag.f90 \ wsplintp.f90 checkmt.f90 rhomagv.f90 reciplat.f90 gradrf.f90 genzfrm.f90 \ mixadapt.f90 zftrf.f90 sbessel.f90 gengclgq.f90 gencfun.f90 writeeval.f90 \ factr.f90 genstress.f90 rfcopy.f90 force.f90 genvbmatk.f90 eveqn.f90 \ forcek.f90 writeepsinv.f90 olprad.f90 polark.f90 zfmtinp.f90 \ hflocal.f90 mixbroyden.f90 zmdet.f90 grad2rfmt.f90 clebgor.f90 rfirctof.f90 \ effmass.f90 genffacgp.f90 zpotcoul.f90 sfacmag.f90 polynm.f90 epsinv.f90 \ rfinpc.f90 zmctmu.f90 zmctm.f90 writeiad.f90 genapwfr.f90 genws.f90 \ gengclq.f90 addbfsm.f90 genylmv.f90 olpfv.f90 hmlfv.f90 \ genexpmt.f90 rfinp.f90 factnm.f90 sphcover.f90 sctovec.f90 \ genvmat.f90 genppts.f90 mtdmin.f90 eveqnzg.f90 fderiv.f90 genpmat.f90 \ genexpmat.f90 writeforces.f90 r3cross.f90 match.f90 genspchi0.f90 genzrho.f90 \ potefield.f90 rhoinit.f90 eveqnsv.f90 roteuler.f90 genrmesh.f90 \ splint.f90 nfftifc.f90 wavefcr.f90 lopzflm.f90 potks.f90 brzint.f90 \ rotdmat.f90 genylmg.f90 gentaucr.f90 readinput.f90 numlist.f90 hermite.f90 \ genfspecies.f90 atpstep.f90 dmatls.f90 writeengy.f90 writechg.f90 \ rbsht.f90 rfsht.f90 genlofr.f90 rotrfmt.f90 zfmtint.f90 zftzf.f90 \ genpmatk.f90 rvfcross.f90 writeinfo.f90 mossbauer.f90 initoep.f90 i3minv.f90 \ r3mv.f90 genidxlo.f90 nuclei.f90 writeefg.f90 writeevsp.f90 \ gencore.f90 r3mtv.f90 r3minv.f90 r3frac.f90 genapwlofr.f90 gridsize.f90 \ symrfir.f90 erf.f90 geomplot.f90 ylmroty.f90 gengvclns.f90 ssfext.f90 \ writestate.f90 sdelta_sq.f90 potxcir.f90 potxc.f90 rzfmtinp.f90 rhoplot.f90 \ occupy.f90 symveca.f90 jprplot.f90 genvmatk.f90 geomopt.f90 \ eveqnss.f90 hartfock.f90 potplot.f90 genwfpw.f90 hmlxbse.f90 hmlxbsek.f90 \ hmldbse.f90 hmldbsek.f90 gradwfcr2.f90 oepresk.f90 addlorbcnd.f90 energy.f90 \ wfplot.f90 oepvcl.f90 oepvclk.f90 polar.f90 dbxcplot.f90 sbesseldm.f90 \ writehmlbse.f90 dielectric_bse.f90 vecplot.f90 nesting.f90 writeevbse.f90 \ emdplot3d.f90 emdplot2d.f90 emdplot1d.f90 rfhkintp.f90 writewfpw.f90 \ vblocal.f90 writefsm.f90 getwfpw.f90 plotpt1d.f90 init1.f90 init2.f90 \ findsymcrys.f90 plotpt3d.f90 elnes.f90 fermisurfbxsf.f90 genspecies.f90 \ writeexpmat.f90 writekpts.f90 wfcrplot.f90 writedos.f90 energykncr.f90 \ ggamt_1.f90 ggair_1.f90 ggamt_sp_1.f90 ggair_sp_1.f90 ggamt_2a.f90 \ ggair_2a.f90 ggamt_2b.f90 ggair_2b.f90 ggamt_sp_2a.f90 ggair_sp_2a.f90 \ ggamt_sp_2b.f90 ggair_sp_2b.f90 writeemd.f90 reademd.f90 emdplot.f90 \ init3.f90 init4.f90 fsmbfield.f90 genvmmtsv.f90 testcheck.f90 pade.f90 \ wsplint.f90 gensocfr.f90 pades.f90 genscss.f90 rfcmtwr.f90 nonlinopt.f90 \ writelat.f90 rhocore.f90 rzfinp.f90 readspecies.f90 findband.f90 exxengy.f90 \ gentauk.f90 gradrfmt.f90 symrf.f90 rfmtinp.f90 checkfsm.f90 \ genrlmv.f90 mae.f90 writegvecrf.f90 zcfmtwr.f90 SRC_main = $(SRC_main0) $(SRC_main1) SRC_BOG0 = \ dmatuv.f90 dmatwx.f90 eveqnuv.f90 eveqnwxy.f90 SRC_BOG1 = \ writeevaluv.f90 occupyuv.f90 inithfb.f90 genwfuv.f90 putevaluv.f90 \ getevaluv.f90 putevecuv.f90 getevecuv.f90 putevecwxy.f90 \ getevecwxy.f90 putevalwx.f90 getevalwx.f90 aceplot.f90 putxnorm.f90 \ putvnorm.f90 getxnorm.f90 getvnorm.f90 SRC_BOG = $(SRC_BOG0) $(SRC_BOG1) SRC_phonon0 = \ dolpistl.f90 dhmlistl.f90 olpaloq.f90 hmlaloq.f90 dolpalo.f90 dhmlalo.f90 \ dhmllolo.f90 olpaaq.f90 dolpaa.f90 dhmlaa.f90 hmlaaq.f90 initeph.f90 \ dengyeph.f90 gndsteph.f90 eveqneph.f90 hmlepha.f90 hmlephb.f90 hmlephde.f90 \ getephmkq.f90 ephdos.f90 SRC_phonon1 = \ gradrhomt.f90 gendcfun.f90 gendvsig.f90 drhomagsh.f90 doccupy.f90 \ dhmlrad.f90 gendwfsv.f90 dwavefmt.f90 gengqvec.f90 dmatch.f90 \ writedvs.f90 readdyn.f90 dyntask.f90 dpotks.f90 dpotxc.f90 deveqnfv.f90 \ dpotcoul.f90 drhomagk.f90 gengvsmt.f90 dforce.f90 dforcek.f90 dynqtor.f90 \ dynevs.f90 phonon.f90 dynrtoq.f90 mcmillan.f90 genephmat.f90 gengkqvec.f90 \ genmcph.f90 putdevecfv.f90 getdevecfv.f90 putdevecsv.f90 getdevecsv.f90 \ phononsc.f90 genscph.f90 phdisp.f90 dynsymapp.f90 dynsym.f90 dynev.f90 \ phdos.f90 sumrule.f90 writephn.f90 dynfext.f90 writegamma.f90 readgamma.f90 \ phlwidth.f90 alpha2f.f90 writelambda.f90 ephcouple.f90 eliashberg.f90 \ phscdvs.f90 readdvs.f90 readalpha2f.f90 gendsocfr.f90 bornechg.f90 \ bectask.f90 becfext.f90 putephmat.f90 getephmat.f90 SRC_phonon = $(SRC_phonon0) $(SRC_phonon1) SRC_ULR0 = \ zfirctof.f90 SRC_ULR1 = \ writeevalu.f90 rhocoreu.f90 eveqnulr.f90 \ rfzfftq.f90 writekpa.f90 rhomaguk.f90 rhomagq.f90 genhmlu.f90 chargeu.f90 \ momentu.f90 potxcu.f90 occupyulr.f90 writeinfou.f90 zfplot.f90 writeengyu.f90 \ writevclr.f90 vclqinit.f90 genhdbulr.f90 addbfsmu.f90 writechgrmt.f90 \ initulr.f90 writemomrmt.f90 writestulr.f90 readstulr.f90 potefieldu.f90 \ puthdbulr.f90 gethdbulr.f90 potuinit.f90 readvclr.f90 genkpakq.f90 \ genzvmatk.f90 genzvbmatk.f90 potksu.f90 plotu1d.f90 plotu2d.f90 plotu3d.f90 \ gndstulr.f90 vblocalu.f90 plotulr.f90 potuplot.f90 potcoulu.f90 rhouplot.f90 \ maguplot.f90 SRC_ULR = $(SRC_ULR0) $(SRC_ULR1) SRC_DFTU = \ gendmatmt.f90 genveedu.f90 genvmatmt.f90 writedftu.f90 readalphadu.f90 \ fyukawa.f90 fyukawa0.f90 genfdufr.f90 energyfdu.f90 writeefdu.f90 \ zbessela.f90 zbesselb.f90 readdmatmt.f90 genfdu.f90 findlambdadu.f90 \ readfdu.f90 writetmdu.f90 writetm2du.f90 writetm3du.f90 dmtotm2.f90 \ dmtotm3.f90 tm2todm.f90 tm3todm.f90 pottm2.f90 pottm3.f90 tm2pol.f90 \ tm3pol.f90 gendmftm.f90 ftmfield.f90 writeftm.f90 SRC_RDMFT0 = \ genvclijji.f90 SRC_RDMFT1 = \ rdmft.f90 rdmdkdc.f90 rdmminc.f90 rdmvaryc.f90 rdmdedc.f90 rdmenergy.f90 \ rdmengyxc.f90 rdmwritededn.f90 rdmwriteengy.f90 rdmminn.f90 rdmvaryn.f90 \ rdmdedn.f90 rdmdexcdn.f90 genvclijjk.f90 getvclijji.f90 getvclijjk.f90 \ writevclijji.f90 writevclijjk.f90 rdmdexcdc.f90 rdmdtsdn.f90 rdmentropy.f90 \ rdmeval.f90 SRC_RDMFT = $(SRC_RDMFT0) $(SRC_RDMFT1) SRC_GW0 = \ gwdmat.f90 gwlocal.f90 genwgw.f90 ksinvert.f90 gtwsum.f90 minf_nm.f90 \ acpole.f90 SRC_GW1 = \ gwrhomag.f90 gwdmatk.f90 gwefermi.f90 dysonr.f90 gwsefm.f90 putgwsefm.f90 \ getgwsefm.f90 writeigw.f90 polefit.f90 gwchgk.f90 gwsefmk.f90 gwspecf.f90 \ writegwsf.f90 acgwse.f90 fmin_nm.f90 zfpole.f90 gwbandstr.f90 gwscrho.f90 SRC_GW = $(SRC_GW0) $(SRC_GW1) SRC_TDDFT0 = \ atptstep.f90 potkst.f90 tdbackup.f90 writetimes.f90 readtimes.f90 \ gentimes.f90 readafieldt.f90 genjr.f90 tddft.f90 SRC_TDDFT1 = \ tddftlr.f90 genhmlt.f90 timestep.f90 writetddos.f90 writeafpdt.f90 \ readafindt.f90 genvfxc.f90 genfxcr.f90 tdtemp.f90 writetdlsj.f90 \ genspfxcr.f90 genvfxcg.f90 tddftsplr.f90 genspfxcg.f90 genafieldt.f90 \ writetddft.f90 dielectric_tdrt.f90 readjtot.f90 afindtstep.f90 \ genefieldt.f90 energytd.f90 engyknk.f90 readforcet.f90 tdrestart.f90 \ readdatposc.f90 writedatposc.f90 rhostatic.f90 jtotk.f90 rhosplot.f90 \ bornectd.f90 becforce.f90 SRC_TDDFT = $(SRC_TDDFT0) $(SRC_TDDFT1) SRC_XC = \ xc_pzca.f90 xc_pwca.f90 xc_pbe.f90 xc_am05.f90 xc_xalpha.f90 xc_wc06.f90 \ x_wc06.f90 x_pbe.f90 c_pbe.f90 c_pbe_gcor.f90 xc_vbh.f90 fxc_pwca.f90 SRC_W90 = \ initw90.f90 writew90.f90 writew90win.f90 writew90eig.f90 setupw90.f90 \ writew90mmn.f90 writew90spn.f90 SRC = $(SRC_modules) $(SRC_FFT) $(SRC_elk) $(SRC_main) $(SRC_phonon) \ $(SRC_XC) $(SRC_DFTU) $(SRC_RDMFT) $(SRC_GW) $(SRC_TDDFT) \ $(SRC_ULR) $(SRC_W90) $(SRC_BOG) OBJ = $(SRC:.f90=.o) EXE = elk #------------------------------------------------------------------------------- # Suffix rules #------------------------------------------------------------------------------- .SUFFIXES: .o .f90 .f90.o: $(F90) $(F90_OPTS) -c $< #------------------------------------------------------------------------------- # Targets #------------------------------------------------------------------------------- elk: $(OBJ) $(F90) $(F90_OPTS) -o $(EXE) $(OBJ) $(LIB_W90) $(LIB_LPK) $(LIB_FFT) \ $(LIB_libxc) $(LIB_SYS) blas: cd BLAS; $(MAKE); cp blas.a .. lapack: cd LAPACK; $(MAKE); cp lapack.a .. fft: cd fftlib; $(MAKE); cp fftlib.a .. all: blas lapack fft elk clean: rm -f *.o *.mod *~ ifc* *.gcno gmon.out *.aux *.dvi *.log \ elk.pdf *.tex *.toc *.out $(EXE) cleanall: cd BLAS; $(MAKE) clean cd LAPACK; $(MAKE) clean cd fftlib; $(MAKE) clean $(MAKE) clean doc: rm -f elk.aux elk.bbl elk.blg elk.log elk.pdf elk.tex elk.toc elk.lst ls $(SRC_modules) $(SRC_main) $(SRC_XC) $(SRC_phonon) $(SRC_DFTU) \ $(SRC_RDMFT) $(SRC_TDDFT) > elk.lst ./protex -F -s $(SRC_elk) $$(cat elk.lst) > elk.tex pdflatex elk;pdflatex elk;pdflatex elk backup: tar -czf elk.tgz *.f90 fftlib eos spacegroup junk BLAS LAPACK \ Makefile notes.txt ../docs ../examples ../tests ../tests-libxc \ protex ../COPYING ../README elk_silhouette.pdf depend gentest \ genalltests checklist.txt rmspaces grepelk vimelk VERSION = $$(grep "version(3)" modmain.f90 | sed 's/.*\[\([^]]*\)\].*/\1/g' | sed 's/,/./g') NAME = elk-$(VERSION) RELEASE = ../release/$(NAME) version: echo $(VERSION) release: rm -rf $(RELEASE) mkdir $(RELEASE) cd BLAS; $(MAKE) clean cd LAPACK; $(MAKE) clean cd fftlib; $(MAKE) clean cd eos; $(MAKE) clean cd spacegroup; $(MAKE) clean cd ..; find . -type f -name *~ -exec rm -f {} \; cd ..; find . -type f -name gmon.out -exec rm -f {} \; cd ..; find . -type f -name RUNNING -exec rm -f {} \; mkdir $(RELEASE)/src cp -r BLAS $(RELEASE)/src cp -r LAPACK $(RELEASE)/src cp -r fftlib $(RELEASE)/src cp -r eos $(RELEASE)/src cp -r spacegroup $(RELEASE)/src cp $(SRC) Makefile protex elk_silhouette.pdf $(RELEASE)/src cp $(SRC) rmspaces grepelk vimelk $(RELEASE)/src cp mpi_stub.f90 omp_stub.f90 mkl_stub.f90 oblas_stub.f90 blis_stub.f90 w90_stub.f90 $(RELEASE)/src cp libxcf90.f90 libxcifc.f90 libxcifc_stub.f90 $(RELEASE)/src cp zfftifc.f90 zfftifc_fftw.f90 zfftifc_mkl.f90 $(RELEASE)/src cp -r ../examples $(RELEASE) cp -r ../tests $(RELEASE) cp -r ../tests-libxc $(RELEASE) mkdir $(RELEASE)/species cp ../species/*.in $(RELEASE)/species cp -r ../utilities $(RELEASE) cp ../COPYING $(RELEASE) cp ../README $(RELEASE) cp ../release_notes.txt $(RELEASE) cp ../Makefile $(RELEASE) cp ../setup $(RELEASE) cp ../make.def $(RELEASE) $(MAKE) doc cp elk.pdf ../docs cd spacegroup;$(MAKE) doc;cp spacegroup.pdf ../../docs;$(MAKE) clean cp -r ../docs $(RELEASE) mkdir $(RELEASE)/release tar -C ../release -czf ../release/$(NAME).tgz $(NAME) cp ../docs/elk.pdf ../release cp ../docs/spacegroup.pdf ../release echo $(NAME) lines: cat $(SRC) | wc -l spaces: ./rmspaces $(SRC) vim: ./vimelk elk-7.2.42/src/PaxHeaders.21776/protex0000644000000000000000000000013214061636516014167 xustar0030 mtime=1623670094.822102578 30 atime=1623670094.821102579 30 ctime=1623670094.822102578 elk-7.2.42/src/protex0000755002504400250440000011077514061636516016242 0ustar00dewhurstdewhurst00000000000000#!/usr/bin/perl # # $Id: protex,v 1.15 2004/06/03 23:49:46 eschwab Exp $ # #BOP # # !ROUTINE: ProTeX v. 2.00 - Translates DAO Prologues to LaTeX # # !INTERFACE: # protex [-hbACFS] ] [+-nlsxf] [src_file(s)] # # !DESCRIPTION: # Perl filter to produce a \LaTeX compatible document # from a DAO Fortran source code with standard Pro\TeX # prologues. If source files are not specified it # reads from stdin; output is always to stdout. # # \noindent # {\bf Command Line Switches:} \vspace{0.2cm} # # \begin{center} # \begin{tabular}{|c|l|} \hline \hline # -h & Help mode: list command line options \\ \hline # -b & Bare mode, meaning no preamble, etc. \\ \hline # -i & internal mode: omit prologues marked !BOPI \\ \hline # +/-n & New Page for each subsection (wastes paper) \\ \hline # +/-l & Listing mode, default is prologues only \\ \hline # +/-s & Shut-up mode, i.e., ignore any code from BOC to EOC \\ \hline # +/-x & No LaTeX mode, i.e., put !DESCRIPTION: in verbatim mode \\ \hline # +/-f & No source file info \\ \hline # -A & Ada code \\ \hline # -C & C++ code \\ \hline # -F & F90 code (default) \\ \hline # -S & Shell script \\ \hline \hline # \end{tabular} # \end{center} # # The options can appear in any order. The options, -h and -b, affect # the input from all files listed on command-line input. Each of the # remaining options effects only the input from the files listed after # the option and prior to any overriding option. The plus sign # turns off the option. For example, the command-line input, # \bv # protex -bnS File1 -F File2.f +n File3.f # \ev # will cause the option, {\tt -n} to affect the input from the files, # {\tt File} and {\tt File2.f}, but not from {\tt File3.f}. The # {\tt -S} option is implemented for {\tt File1} but is overridden by # the {\tt -F} for files {\tt File2.f} and {\tt File3.f}. # # # !SEE ALSO: # For a more detailed description of ProTeX functionality, # DAO Prologue and other conventions, consult: # # Sawyer, W., and A. da Silva, 1997: ProTeX: A Sample # Fortran 90 Source Code Documentation System. # DAO Office Note 97-11 # # # !REVISION HISTORY: # # 20Dec1995 da Silva First experimental version # 10Nov1996 da Silva First internal release (v1.01) # 28Jun1997 da Silva Modified so that !DESCRIPTION can appear after # !INTERFACE, and !INPUT PARAMETERS etc. changed to italics. # 02Jul1997 Sawyer Added shut-up mode # 20Oct1997 Sawyer Added support for shell scripts # 11Mar1998 Sawyer Added: file name, date in header, C, script support # 05Aug1998 Sawyer Fixed LPChang-bug-support-for-files-with-underscores # 10Oct1998 da Silva Introduced -f option for removing source file info # from subsection, etc. Added help (WS). # 06Dec1999 C. Redder Added LaTeX command "\label{sec:prologues}" just # after the beginning of the proglogue section. # 13Dec1999 C. Redder Increased flexbility in command-line # interface. The options can appear in any # order which will allow the user to implement # options for select files. # 01Feb1999 C. Redder Added \usepackage commands to preamble of latex # document to include the packages amsmath, epsfig # and hangcaption. # 10May2000 C. Redder Revised LaTeX command "\label{sec:prologues}" # to "\label{app:ProLogues}" # 10/10/2002 da Silva Introduced ARGUMENTS keyword, touch ups. # # 15Jan2003 R. Staufer Modified table of contents to print only section headers - no descriptions # # 25Feb2003 R. Staufer Added BOPI/EOPI and -i (internal) switch to provide the option of omitting prologue information from output files. # #EOP #---------------------------------------------------------------------------- # Keep this if you don't know what it does... # ------------------------------------------- ### $[ = 1; # set array base to 1 (removed to maintain Perl 5.30 compatibility) $, = ' '; # set output field separator $\ = "\n"; # set output record separator # Set valid options lists # ----------------------- $GlobOptions = 'hb'; # Global options (i.e for all files) $LangOptions = 'ACFS'; # Options for setting programming languages $SwOptions = 'flinsx'; # Options that can change for each input # file $RegOptions = "$GlobOptions$LangOptions"; # Scan for global options until first first # file is processed. # Scan for global options # ----------------------- $NFiles = 0; Arg: foreach $arg (@ARGV) { $option = &CheckOpts ( $arg, $RegOptions, $SwOptions ) + 1; if ( $option ) { $rc = &GetOpts ( $arg, $GlobOptions ); next Arg; } else { $NFiles++; }# end if }# end foreach # If all input arguments are options, then assume the # filename, "-", for the standard input # -------------------------------------------------- if ( $NFiles == 0 ) { push (@ARGV, "-"); } # Implement help option # --------------------- if ( $opt_h ) { &print_help(); exit(); }#end if # Optional Prologue Keywords # -------------------------- @keys = ( "!INTERFACE:", "!USES:", "!PUBLIC TYPES:", "!PRIVATE TYPES:", "!PUBLIC MEMBER FUNCTIONS:", "!PRIVATE MEMBER FUNCTIONS:", "!PUBLIC DATA MEMBERS:", "!PARAMETERS:", "!ARGUMENTS:", "!DEFINED PARAMETERS:", "!INPUT PARAMETERS:", "!INPUT/OUTPUT PARAMETERS:", "!OUTPUT PARAMETERS:", "!RETURN VALUE:", "!REVISION HISTORY:", "!BUGS:", "!SEE ALSO:", "!SYSTEM ROUTINES:", "!FILES USED:", "!REMARKS:", "!TO DO:", "!CALLING SEQUENCE:", "!AUTHOR:", "!CALLED FROM:", "!LOCAL VARIABLES:" ); # Initialize these for clarity # ---------------------------- $intro = 0; # doing introduction? $prologue = 0; # doing prologue? $first = 1; # first prologue? $source = 0; # source code mode? $verb = 0; # verbatim mode? $tpage = 0; # title page? $begdoc = 0; # has \begin{document} been written? # Initial LaTeX stuff # ------------------- &print_notice(); &print_preamble(); # \documentclass, text dimensions, etc. &print_macros(); # short-hand LaTeX macros # Main loop -- for each command-line argument # ------------------------------------------- ARG: foreach $arg (@ARGV) { # Scan for non-global command-line options # ---------------------------------------- $option = &CheckOpts ( $arg, $RegOptions, $SwOptions, "quiet" ) + 1; if ( $option ) { &GetOpts ( $arg, $SwOptions ); &SetOpt ( $arg, $LangOptions ); next ARG; }# end if # Determine the type of code, set corresponding search strings # ------------------------------------------------------------ # if ( $opt_F ) { # FORTRAN $comment_string = '!'; # ------- $boi_string = '!BOI'; $eoi_string = '!EOI'; $bop_string = '!BOP'; $eop_string = '!EOP'; $bopi_string = '!BOPI'; $eopi_string = '!EOPI'; $boc_string = '!BOC'; $eoc_string = '!EOC'; $boe_string = '!BOE'; $eoe_string = '!EOE'; #}# end if if ( $opt_A ) { # ADA $comment_string = '--'; # --- $boi_string = '--BOI'; $eoi_string = '--EOI'; $bop_string = '--BOP'; $eop_string = '--EOP'; $bopi_string = '--BOPI'; $eopi_string = '--EOPI'; $boc_string = '--BOC'; $eoc_string = '--EOC'; $boe_string = '--BOE'; $eoe_string = '--EOE'; }# end if if ( $opt_C ) { $comment_string = '//'; # C $boi_string = '//BOI'; # - $eoi_string = '//EOI'; $bop_string = '//BOP'; $eop_string = '//EOP'; $bopi_string = '//BOPI'; $eopi_string = '//EOPI'; $boc_string = '//BOC'; $eoc_string = '//EOC'; $boe_string = '//BOE'; $eoe_string = '//EOE'; }# end if if ( $opt_S ) { # Script $comment_string = '#'; # ------ $boi_string = '#BOI'; $eoi_string = '#EOI'; $bop_string = '#BOP'; $eop_string = '#EOP'; $bopi_string = '#BOPI'; $eopi_string = '#EOPI'; $boc_string = '#BOC'; $eoc_string = '#EOC'; $boe_string = '#BOE'; $eoe_string = '#EOE'; }# end if # Set file name parameters # ------------------------ $InputFile = $arg; @all_path_components = split( /\//, $InputFile ); $FileBaseName = pop ( @all_path_components ); $FileBaseName =~ s/_/\\_/g; if ( $InputFile eq "-" ) {$FileBaseName = "Standard Input";} # Set date # -------- $Date = `date`; # Open current file # ----------------- open ( InputFile, "$InputFile" ) or print STDERR "Unable to open $InputFile: $!"; # Print page header # ----------------- # printf "\n\\markboth{Left}{Source File: %s, Date: %s}\n\n", # $FileBaseName, $Date; LINE: # Inner loop --- for processing each line of the input file # --------------------------------------------------------- while ( ) { chop; # strip record separator # !PARAMETERS: really mean !ARGUMENTS: # ------------------------------------ # s/!PARAMETERS:/!ARGUMENTS:/g; @Fld = split(' ', $_, 9999); # Straight quote # -------------- if ($Fld[0] eq '!QUOTE:') { for ($i = 1; $i <= $#Fld - 1; $i++) { printf '%s ', $Fld[$i]; }# end for print " "; next LINE; }# end if # Handle optional Title Page and Introduction # ------------------------------------------- if ($Fld[0] eq $boi_string) { print ' '; $intro = 1; next LINE; }# end if if ($Fld[1] eq '!TITLE:') { if ( $intro ) { shift @Fld; shift @Fld; @title = @Fld; $tpage = 1; next LINE; }# end if }# end if if ($Fld[1] eq '!AUTHORS:') { if ( $intro ) { shift @Fld; shift @Fld; @author = @Fld; $tpage = 1; next LINE; }# end if }# end if if ($Fld[1] eq '!AFFILIATION:') { if ( $intro ) { shift @Fld; shift @Fld; @affiliation = @Fld; $tpage = 1; next LINE; }# end if }# end if if ($Fld[1] eq '!DATE:') { if ( $intro ) { shift @Fld; shift @Fld; @date = @Fld; $tpage = 1; next LINE; }# end if }# end if if ($Fld[1] eq '!INTRODUCTION:') { if ( $intro ) { &do_beg(); print ' '; print '%..............................................'; shift @Fld; shift @Fld; print "\\section{@Fld}"; next LINE; }# end if }# end if # End of introduction # ------------------- if ($Fld[0] eq $eoi_string) { print ' '; print '%/////////////////////////////////////////////////////////////'; print "\\newpage"; $intro = 0; next LINE; }# end if # Beginning of prologue # --------------------- if ($Fld[0] eq $bop_string) { if ( $source ) { &do_eoc(); } print ' '; print '%/////////////////////////////////////////////////////////////'; &do_beg(); if ($first == 0) { ### print "\\newpage"; print " "; print "\\mbox{}\\hrulefill\\ "; print " ";} else { unless($opt_b){print "\\section{Routine/Function Prologues} \\label{app:ProLogues}";} }# end if $first = 0; $prologue = 1; $verb = 0; $source = 0; &set_missing(); # no required keyword yet next LINE; }# end if # Beginning of internal prologue # ------------------------------ if ($Fld[0] eq $bopi_string) { if ($opt_i) {$prologue = 0;} else { if ($source) { &do_eoc(); } print ' '; print '%/////////////////////////////////////////////////////////////'; &do_beg(); if ($first ==0) { ### print "\\newpage"; print " "; print "\\mbox{}\\hrulefill\\"; print " ";} else { unless($opt_b){print "\\section{Routine/Function Prologues} \\label{app:ProLogues}";} }# endif $first = 0; $prologue = 1; $verb = 0; $source = 0; &set_missing(); # no required keyword yet next LINE; }# endelse }# endif # A new subroutine/function # ------------------------- if ($Fld[1] eq '!ROUTINE:' ) { if ($prologue) { shift @Fld; shift @Fld; $_ = join(' ', @Fld); $name_is = $_; s/_/\\_/g; # Replace "_" with "\_" if ( $opt_n && $not_first ) { printf "\\newpage\n"; } unless ($opt_f) {printf "\\subsection{%s (Source File: %s)}\n\n", $_, $FileBaseName;} else {printf "\\subsection{%s }\n\n", $_;} $have_name = 1; $not_first = 1; next LINE; }# end if }# end if # A new Module # ------------ if ($Fld[1] eq '!MODULE:' ) { if ($prologue) { shift @Fld; shift @Fld; $_ = join(' ', @Fld); $name_is = $_; s/_/\\_/g; # Replace "_" with "\_" if ( $opt_n && $not_first ) { printf "\\newpage\n"; } unless($opt_f) {printf "\\subsection{Fortran: Module Interface %s (Source File: %s)}\n\n", $_, $FileBaseName;} else {printf "\\subsection{Fortran: Module Interface %s }\n\n", $_;} $have_name = 1; $have_intf = 1; # fake it, it does not need one. $not_first = 1; next LINE; }# end if }# end if # A new include file # ------------------ if ($Fld[1] eq '!INCLUDE:' ) { if ($prologue) { shift @Fld; shift @Fld; $_ = join(' ', @Fld); $name_is = $_; s/_/\\_/g; # Replace "_" with "\_" if ( $opt_n && $not_first ) { printf "\\newpage\n"; } unless($opt_f) {printf "\\subsection{Include File %s (Source File: %s)}\n\n", $_, $FileBaseName;} else {printf "\\subsection{Include File %s }\n\n", $_;} $have_name = 1; $have_intf = 1; # fake it, it does not need one. $not_first = 1; next LINE; }# end if }# end if # A new INTERNAL subroutine/function # ---------------------------------- if ($Fld[1] eq '!IROUTINE:') { # Internal routine if ($prologue) { shift @Fld; shift @Fld; $_ = join(' ', @Fld); $name_is = $_; s/_/\\_/g; # Replace "_" with "\_" @words = split " ", $_; printf "\\subsection [$words[1]] {$_}\n\n"; $have_name = 1; next LINE; }# end if }# end if # A new CLASS # ------------ if ($Fld[1] eq '!CLASS:' ) { if ($prologue) { shift @Fld; shift @Fld; $_ = join(' ', @Fld); $name_is = $_; s/_/\\_/g; # Replace "_" with "\_" if ( $opt_n && $not_first ) { printf "\\newpage\n"; } unless($opt_f) {printf "\\subsection{C++: Class Interface %s (Source File: %s)}\n\n", $_, $FileBaseName;} else {printf "\\subsection{C++: Class Interface %s }\n\n", $_;} $have_name = 1; $have_intf = 1; # fake it, it does not need one. $not_first = 1; next LINE; }# end if }# end if # A new Method # ------------------------- if ($Fld[1] eq '!METHOD:' ) { if ($prologue) { shift @Fld; shift @Fld; $_ = join(' ', @Fld); $name_is = $_; s/_/\\_/g; # Replace "_" with "\_" if ( $opt_n && $not_first ) { printf "\\newpage\n"; } unless ($opt_f) {printf "\\subsection{%s (Source File: %s)}\n\n", $_, $FileBaseName;} else {printf "\\subsection{%s }\n\n", $_;} $have_name = 1; $not_first = 1; next LINE; }# end if }# end if # A new function # ------------------------- if ($Fld[1] eq '!FUNCTION:' ) { if ($prologue) { shift @Fld; shift @Fld; $_ = join(' ', @Fld); $name_is = $_; s/_/\\_/g; # Replace "_" with "\_" if ( $opt_n && $not_first ) { printf "\\newpage\n"; } unless ($opt_f) {printf "\\subsection{%s (Source File: %s)}\n\n", $_, $FileBaseName;} else {printf "\\subsection{%s }\n\n", $_;} $have_name = 1; $not_first = 1; next LINE; }# end if }# end if # Description: what follows will be regular LaTeX (no verbatim) # ------------------------------------------------------------- if (/!DESCRIPTION:/) { if ($prologue) { if ($verb) { printf "\\end{verbatim}"; printf "\n{\\sf DESCRIPTION:\\\\ }\n\n"; $verb = 0; } else { # probably never occurs }# end if if ($opt_x) { printf "\\begin{verbatim} "; $verb = 1; $first_verb = 1; } else { for ($i = 2; $i <= $#Fld - 1; $i++) { printf '%s ', $Fld[$i]; }# end for }# end if ### print " "; $have_desc = 1; next LINE; }# end if }# end if # Handle optional keywords (these will appear as verbatim) # -------------------------------------------------------- if ($prologue) { KEY: foreach $key ( @keys ) { if ( /$key/ ) { if ($verb) { printf "\\end{verbatim}"; $verb = 0; } else { printf "\n\\bigskip"; }# end if $k = sprintf('%s', $key); $ln = length($k); ###printf "\\subsection*{%s}\n", substr($k, 2, $ln - 1); ###printf "{\\Large \\em %s}\n", ucfirst lc substr($k, 2, $ln - 1); $_ = $key; if( /USES/ || /INPUT/ || /OUTPUT/ || /PARAMETERS/ || /VALUE/ || /ARGUMENTS/ ) { printf "{\\em %s}\n", substr($k, 1, $ln - 1); } # italics else { printf "{\\sf %s}\n", substr($k, 1, $ln - 1); # san serif }# end if printf "\\begin{verbatim} "; $verb = 1; $first_verb = 1; if ( $key eq "!INTERFACE:" ) { $have_intf = 1; } if ( $key eq "!CALLING SEQUENCE:" ) { $have_intf = 1; } if ( $key eq "!REVISION HISTORY:" ) { $have_hist = 1; } next LINE; }# end if }# end foreach }# end if # End of prologue # --------------- if ($Fld[0] eq $eop_string) { if ($verb) { print "\\end{verbatim}"; $verb = 0; }# end if $prologue = 0; # &check_if_all_there(); # check if all required keywords are there. if ( $opt_l ) { $Fld[0] = $boc_string;} else { next LINE; } }# end if unless ( $opt_s ) { # End of Internal Prologue # ------------------------ if ($Fld[0] eq $eopi_string) { if ($verb) { print "\\end{verbatim}"; $verb = 0; }# endif $prologue = 0; # &check_if_all_there(); # check if all required keywords are there. if ($opt_l) { $Fld[0] = $boc_string;} else { next LINE; } }# endif # # Beginning of source code section # -------------------------------- if ($Fld[0] eq $boc_string) { print ' '; print '%/////////////////////////////////////////////////////////////'; $first = 0; $prologue = 0; $source = 1; ### printf "\\subsection*{CONTENTS:}\n\n", $Fld[3]; ###printf "{\\sf CONTENTS:}"; printf "\n \\begin{verbatim}\n"; $verb = 1; next LINE; }# end if # End of source code # ------------------ if ($Fld[0] eq $eoc_string) { &do_eoc(); $prologue = 0; next LINE; }# end if # Beginning of example prologue # ----------------------------- if ($Fld[0] eq $boe_string) { if ( $source ) { &do_eoc(); } print ' '; print '%/////////////////////////////////////////////////////////////'; $first = 0; $prologue = 1; $verb = 0; $source = 0; next LINE; }# end if # End of example prologue # ----------------------- if ($Fld[0] eq $eoe_string) { if ($verb) { print "\\end{verbatim}"; $verb = 0; }# end if $prologue = 0; if ( $opt_l ) { $Fld[0] = $boc_string;} else { next LINE; } }# end if }# end unless # Prologue or Introduction, print regular line (except for !) # ----------------------------------------------------------- if ($prologue||$intro) { if ( $verb && $#Fld == 0 && ( $Fld[0] eq $comment_string ) ) { next LINE; # to eliminate excessive blanks }# end if if ( $Fld[1] eq "\\ev" ) { # special handling $_ = $comment_string . " \\end{verbatim}"; }# end if s/^$comment_string/ /; # replace comment string with blank # $line = sprintf('%s', $_); # not necessary -- comment str is absent # $ln = length($line); # not necessary -- comment str is absent unless ( $first_verb ) { printf "\n "; } printf '%s', $_; # printf '%s', substr($line, 1, $ln - 1); # comment str is absent $first_verb = 0; next LINE; }# end if # Source code: print the full line # -------------------------------- if ($source) { print $_; next LINE; }# end if }# end inner loop for processing each line of the input file # --------------------------------------------------------- }# end main loop for each command-line argument # -------------------------------------------- print $_; if ( $source ) { &do_eoc(); } print '%...............................................................'; # see comment above where these are originally set. #print "\\setlength{\\parskip}{\\oldparskip}"; #print "\\setlength{\\parindent}{\\oldparindent}"; #print "\\setlength{\\baselineskip}{\\oldbaselineskip}"; unless ( $opt_b ) { print "\\end{document}"; }#end unless #---------------------------------------------------------------------- sub CheckOpts # Checks options against a given list. Outputs error message # for any invalid option. # # Usage: # $rc = &CheckOpts ( options, valid_reg_options, # valid_sw_options, # quiet_mode ) # # character: options - options to be checked. (e.g. -df+x) The # list must begin with a positive or # negative sign. If no sign appears at the # beginning or by itself, then the argument # is not recognized as a list of options. # character: valid_reg_options - list of valid regular options. # (i.e. options that are associated only # eith negative sign.) # character: valid_sw_options - list of valid switch options. # (i.e. options that can be associated with # either a positive or negative sign. # logical: quiet mode (optional) If true then print no error # messages. # integer: rc - return code # = -1 if the arguement, options, is # not recognized as a list of options # = 0 if all options are valid. # > 0 for the number of invalid options. # { local($options, $valid_reg_options, $valid_sw_options, $quiet_mode ) = @_; if ( $options eq "+" || $options eq "-" ) {return -1} local(@Options) = split( / */, $options ); if ( $Options[ $[ ] ne "-" && $Options[ $[ ] ne "+" ) {return -1;} local($option, $option_sign, $valid_list, $pos); local($errs) = 0; foreach $option ( @Options ) { if ( $option eq "-" || $option eq "+" ) {$option_sign = $option;} else { if ( $option_sign eq "-" ) { $valid_list = $valid_reg_options . $valid_sw_options; } else { $valid_list = $valid_sw_options; } $pos = index ($valid_list,$option); if ( $pos < $[ && $quiet_mode ) { $errs++; print STDERR "Invalid option: $option_sign$option \n"; }# end if }# end if }# end foreach return $errs; }#end sub GetOpts sub GetOpts # Gets options. If an option is valid, then opt_[option] is # set to 0 or 1 as a side effect if the option is preceeded by # a positive or negative sign. # # Usage: # $rc = &GetOpts ( options, valid_options ) # # character: options - options to be checked. (e.g. -df+x) The # list must begin with a positive or # negative sign. If no sign appears at the # beginning or by itself, then the argument # is not recognized as a list of options. # character: valid_options - list of valid options (e.g. dfhx) # integer: rc - return code # = -1 if the arguement, options, is # not recognized as a list of options. # = 0 otherwise # { local($options,$valid_options) = @_; if ( $options eq "+" || $options eq "-" ) {return -1} local(@Options) = split( / */, $options ); if ( $Options[ $[ ] ne "-" && $Options[ $[ ] ne "+" ) {return -1;} local($option, $option_sign); foreach $option ( @Options ) { if ( $option eq "-" || $option eq "+" ) { $option_sign = $option; } else { if ( index ($valid_options,$option) >= $[ ) { if ( $option_sign eq "-" ) {${"opt_$option"} = 1;} if ( $option_sign eq "+" ) {${"opt_$option"} = 0;}; }# end if }# end if }# end foreach return 0; }#end sub GetOpts sub SetOpt # Sets option flags. For the last input option that is in a # list, the flag opt_[option] is set to 1 as a side effect. # For all other options in the list, opt_[option] is set to 0. # # Usage: # $rc = &SetOpt ( options, valid_options ) # # character: options - options to be checked. (e.g. -df+x) The # list must begin with a positive or # negative sign. If no sign appears at the # beginning or by itself, then the argument # is not recognized as a list of options. # character: valid_options - list of valid options (e.g. def ) # integer: rc - return code # = -1 if the arguement, options, is # not recognized as a list of options. # = 0 otherwise # Note: For the examples provided for the input arguments, # $opt_d = 0, $opt_e = 0, and $opt_f = 1, since the # input option, -f, was the last in the argument, # option. # { local($options,$valid_options) = @_; if ( $options eq "+" || $options eq "-" ) {return -1} local(@Options) = split( / */, $options ); local(@ValidOptions) = split( / */, $valid_options ); if ( $Options[ $[ ] ne "-" && $Options[ $[ ] ne "+" ) {return -1;} local($option, $option_sign); foreach $option ( @Options ) { if ( $option ne "-" && $option ne "+" ) { if ( index ($valid_options,$option) >= $[ ) { foreach $valid_option (@ValidOptions ) { ${"opt_$valid_option"} = 0; }# end foreach ${"opt_$option"} = 1; }# end if }# end if }# end foreach return 0; }#end sub SetOpt sub print_help { print "Usage: protex [-hbACFS] [+-nlsxf] [src_file(s)]"; print " "; print " Options:"; print " -h Help mode: list command line options"; print " -b Bare mode, meaning no preamble, etc."; print " +-n New Page for each subsection (wastes paper)"; print " +-l Listing mode, default is prologues only"; print " +-s Shut-up mode, i.e., ignore any code from BOC to EOC"; print " +-x No LaTeX mode, i.e., put !DESCRIPTION: in verbatim mode"; print " +-f No source file info"; print " -A Ada code"; print " -C C++ code"; print " -F F90 code"; print " -S Shell script"; print " "; print " The options can appear in any order. The options, -h and -b,"; print " affect the input from all files listed on command-line input."; print " Each of the remaining options effects only the input from the"; print " files listed after the option and prior to any overriding"; print " option. The plus sign turns off the option."; }# end sub print_help sub print_notice { print "% **** IMPORTANT NOTICE *****" ; print "% This LaTeX file has been automatically produced by ProTeX v. 1.1"; print "% Any changes made to this file will likely be lost next time"; print "% this file is regenerated from its source. Send questions "; print "% to Arlindo da Silva, dasilva\@gsfc.nasa.gov"; print " "; }# sub print_notice sub print_preamble { unless ( $opt_b ) { print "%------------------------ PREAMBLE --------------------------"; print "\\documentclass[a4paper,11pt]{article}"; print "\\usepackage{amsmath}"; print "\\usepackage{amssymb}"; print "\\usepackage{epsfig}"; print "\\usepackage{tabularx}"; print "\\usepackage{color}"; print "\\usepackage[linkbordercolor={0 0 1}]{hyperref}"; print "\\textheight 9in"; print "\\topmargin 0pt"; print "\\headsep 1cm"; print "\\headheight 0pt"; print "\\textwidth 6in"; print "\\oddsidemargin 0in"; print "\\evensidemargin 0in"; print "\\marginparpush 0pt"; print "\\pagestyle{plain}"; print "\\markboth{}{}"; print "%-------------------------------------------------------------"; }# end unless # in your main document before you include any protex-generated files # for the first time, if you define these three variables as length # settings (like this:) # \newlength{\oldparskip} # \newlength{\oldparindent} # \newlength{\oldbaselineskip} # then 1) comment in all the lines below, and 2) find the 3 reset lines # further down and comment in them as well. # then protex will override the paragraph and skip settings during # the source sections, but will restore the original document settings # at the end. if someone can figure out how to check to see if a # latex variable exists, and do a conditional section, we could make # this fully self-contained. # nsc feb 2003 #print "\\setlength{\\oldparskip}{\\parskip}"; print "\\setlength{\\parskip}{0pt}"; #print "\\setlength{\\oldparindent}{\\parindent}"; print "\\setlength{\\parindent}{0pt}"; #print "\\setlength{\\oldbaselineskip}{\\baselineskip}"; print "\\setlength{\\baselineskip}{11pt}"; }# end sub print_preamble sub print_macros { print " "; print "%--------------------- SHORT-HAND MACROS ----------------------"; print "\\def\\bv{\\begin{verbatim}}"; print "\\def\\ev\{\\end\{verbatim}}"; print "\\def\\be{\\begin{equation}}"; print "\\def\\ee{\\end{equation}}"; print "\\def\\bea{\\begin{eqnarray}}"; print "\\def\\eea{\\end{eqnarray}}"; print "\\def\\bi{\\begin{itemize}}"; print "\\def\\ei{\\end{itemize}}"; print "\\def\\bn{\\begin{enumerate}}"; print "\\def\\en{\\end{enumerate}}"; print "\\def\\bd{\\begin{description}}"; print "\\def\\ed{\\end{description}}"; print "\\def\\({\\left (}"; print "\\def\\){\\right )}"; print "\\def\\[{\\left [}"; print "\\def\\]{\\right ]}"; print "\\def\\<{\\left \\langle}"; print "\\def\\>{\\right \\rangle}"; print "\\def\\cI{{\\cal I}}"; print "\\def\\diag{\\mathop{\\rm diag}}"; print "\\def\\tr{\\mathop{\\rm tr}}"; print "%-------------------------------------------------------------"; print " "; print "%------------------------ Elk commands -----------------------"; print "\\newcommand{\\block}[2]{"; print "\\color{blue}\\subsection{\\tt #1}\\color{black}"; print "\\begin{tabularx}{\\textwidth}[h]{|l|X|c|c|}"; print "\\hline"; print "#2 \\\\"; print "\\hline"; print "\\end{tabularx}\\vskip 0.25cm"; print "}"; print "%-------------------------------------------------------------"; }# end sub print_macros sub do_beg { unless ( $opt_b ) { if ( $begdoc == 0 ) { if ( $tpage ) { print "\\title{@title}"; print "\\author{@author\\\\ {\\em @affiliation}}"; print "\\date{@date}"; } print "\\begin{document}"; if ( $tpage ) { print "\\pagecolor[rgb]{1,0.95,0.85}"; print "\\fcolorbox{black}{white}{\\fbox{"; print "\\begin{minipage}[t]{\\linewidth}"; print "\\maketitle"; print "\\end{minipage}}}"; print "\\thispagestyle{empty}"; print "\\newpage"; 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then rm -f ~/.vim/ftdetect/elk.vim rm -f ~/.vim/syntax/elk.vim echo echo "Syntax highlighting disabled for vim." echo exit fi rm -f elk.vim echo > elk.vim echo 'syn match elkComment "!.*$"' >> elk.vim echo 'syn match elkComment ":.*$"' >> elk.vim grep "case('" readinput.f90 | cut -d "'" -f2 | grep -v '^$' > vimelk.temp grep "case('" readinput.f90 | cut -d "'" -f4 | grep -v '^$' >> vimelk.temp grep "case('" readinput.f90 | cut -d "'" -f6 | grep -v '^$' >> vimelk.temp grep "case('" readinput.f90 | cut -d "'" -f8 | grep -v '^$' >> vimelk.temp awk '{print "syn match elkBlock '\''"$1"'\''";}' vimelk.temp >> elk.vim rm vimelk.temp echo >> elk.vim echo 'colorscheme zellner' >> elk.vim echo >> elk.vim echo 'hi link elkComment Comment' >> elk.vim echo 'hi link elkBlock Identifier' >> elk.vim mkdir -p ~/.vim/ftdetect mkdir -p ~/.vim/syntax echo "au BufRead,BufNewFile elk.in set filetype=elk" > ~/.vim/ftdetect/elk.vim mv elk.vim ~/.vim/syntax echo echo "Syntax highlighting enabled for vim." echo echo "To disable highlighting type:" echo " ./vimelk -d" echo elk-7.2.42/src/PaxHeaders.21776/omp_stub.f900000644000000000000000000000013214061636517015074 xustar0030 mtime=1623670095.969101514 30 atime=1623670095.969101514 30 ctime=1623670095.969101514 elk-7.2.42/src/omp_stub.f900000644002504400250440000000312314061636517017130 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2015 J. K. Dewhurst, S. Sharma and E. K. U. Gross. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. ! Stub routines for OpenMP. integer function omp_get_num_procs() implicit none omp_get_num_procs=1 end function integer function omp_get_max_threads() implicit none omp_get_max_threads=1 end function integer function omp_get_num_threads() implicit none omp_get_num_threads=1 end function integer function omp_get_thread_num() implicit none omp_get_thread_num=0 end function integer function omp_get_max_active_levels() implicit none omp_get_max_active_levels=1 end function logical function omp_get_dynamic() implicit none omp_get_dynamic=.false. end function integer function omp_get_level() implicit none omp_get_level=0 end function subroutine omp_set_num_threads(num_threads) implicit none integer, intent(in) :: num_threads end subroutine subroutine omp_set_nested(nested) implicit none logical, intent(in) :: nested end subroutine subroutine omp_set_max_active_levels(max_levels) implicit none integer, intent(in) :: max_levels end subroutine subroutine omp_set_dynamic(dynamic) implicit none logical, intent(in) :: dynamic end subroutine subroutine omp_init_lock(lock) implicit none integer(8), intent(in) :: lock end subroutine subroutine omp_destroy_lock(lock) implicit none integer(8), intent(in) :: lock end subroutine subroutine omp_set_lock(lock) implicit none integer(8), intent(in) :: lock end subroutine subroutine omp_unset_lock(lock) implicit none integer(8), intent(in) :: lock end subroutine elk-7.2.42/src/PaxHeaders.21776/libxcf90.f900000644000000000000000000000012614061636517014667 xustar0028 mtime=1623670095.9831015 30 atime=1623670095.982101502 28 ctime=1623670095.9831015 elk-7.2.42/src/libxcf90.f900000644002504400250440000036171314061636517016734 0ustar00dewhurstdewhurst00000000000000!! Copyright (C) 2016 Micael Oliveira !! 2020 Susi Lehtola !! All rights reserved. !! !! This Source Code Form is subject to the terms of the Mozilla Public !! License, v. 2.0. If a copy of the MPL was not distributed with this !! file, You can obtain one at mozilla.org/MPL/2.0/. module xc_f90_lib_m use, intrinsic :: iso_c_binding implicit none private public :: & ! version xc_f90_version, & xc_f90_version_string, & ! literature reference xc_f90_reference, & xc_f90_reference_doi, & ! func_info xc_f90_func_info_t, & xc_f90_func_info_get_number, & xc_f90_func_info_get_kind, & xc_f90_func_info_get_name, & xc_f90_func_info_get_family, & xc_f90_func_info_get_references, & xc_f90_func_info_get_flags, & xc_f90_func_info_get_n_ext_params, & xc_f90_func_info_get_ext_params_name, & xc_f90_func_info_get_ext_params_description, & xc_f90_func_info_get_ext_params_default_value, & ! func_reference xc_f90_func_reference_t, & xc_f90_func_reference_get_ref, & xc_f90_func_reference_get_doi, & xc_f90_func_reference_get_bibtex, & ! func xc_f90_func_t, & xc_f90_func_init, & xc_f90_func_end, & xc_f90_func_get_info, & xc_f90_functional_get_name, & xc_f90_functional_get_number, & xc_f90_family_from_id, & xc_f90_number_of_functionals, & xc_f90_maximum_name_length, & xc_f90_available_functional_numbers, & xc_f90_available_functional_names, & xc_f90_func_set_dens_threshold, & xc_f90_func_set_zeta_threshold, & xc_f90_func_set_sigma_threshold, & xc_f90_func_set_tau_threshold, & xc_f90_func_set_ext_params, & xc_f90_func_set_ext_params_name, & ! lda xc_f90_lda, & xc_f90_lda_exc, & xc_f90_lda_exc_vxc, & xc_f90_lda_exc_vxc_fxc, & xc_f90_lda_exc_vxc_fxc_kxc, & xc_f90_lda_vxc, & xc_f90_lda_vxc_fxc, & xc_f90_lda_vxc_fxc_kxc, & xc_f90_lda_fxc, & xc_f90_lda_kxc, & xc_f90_lda_lxc, & ! gga xc_f90_gga, & xc_f90_gga_exc, & xc_f90_gga_exc_vxc, & xc_f90_gga_exc_vxc_fxc, & xc_f90_gga_exc_vxc_fxc_kxc, & xc_f90_gga_vxc, & xc_f90_gga_vxc_fxc, & xc_f90_gga_vxc_fxc_kxc, & xc_f90_gga_fxc, & xc_f90_gga_kxc, & xc_f90_gga_lxc, & xc_f90_gga_ak13_get_asymptotic, & xc_f90_hyb_exx_coef, & xc_f90_hyb_cam_coef, & xc_f90_nlc_coef, & ! mgga xc_f90_mgga, & xc_f90_mgga_exc, & xc_f90_mgga_exc_vxc, & xc_f90_mgga_exc_vxc_fxc, & xc_f90_mgga_exc_vxc_fxc_kxc, & xc_f90_mgga_vxc, & xc_f90_mgga_vxc_fxc, & xc_f90_mgga_vxc_fxc_kxc, & xc_f90_mgga_fxc, & xc_f90_mgga_kxc, & xc_f90_mgga_lxc integer(c_int), parameter, public :: & XC_UNPOLARIZED = 1, & ! Spin unpolarized XC_POLARIZED = 2 ! Spin polarized integer(c_int), parameter, public :: & XC_NON_RELATIVISTIC = 0, & ! Functional includes or not relativistic XC_RELATIVISTIC = 1 ! corrections. Only available in some functionals. ! Kinds integer(c_int), parameter, public :: & XC_EXCHANGE = 0, & XC_CORRELATION = 1, & XC_EXCHANGE_CORRELATION = 2, & XC_KINETIC = 3 ! Families of xc functionals integer(c_int), parameter, public :: & XC_FAMILY_UNKNOWN = -1, & XC_FAMILY_NONE = 0, & XC_FAMILY_LDA = 1, & XC_FAMILY_GGA = 2, & XC_FAMILY_MGGA = 4, & XC_FAMILY_LCA = 8, & XC_FAMILY_OEP = 16, & XC_FAMILY_HYB_GGA = 32, & XC_FAMILY_HYB_MGGA = 64, & XC_FAMILY_HYB_LDA = 128 integer(c_int), parameter, public :: & XC_FLAGS_HAVE_EXC = 1, & XC_FLAGS_HAVE_VXC = 2, & XC_FLAGS_HAVE_FXC = 4, & XC_FLAGS_HAVE_KXC = 8, & XC_FLAGS_HAVE_LXC = 16, & XC_FLAGS_HAVE_ALL = 31, & ! The most common case XC_FLAGS_1D = 32, & XC_FLAGS_2D = 64, & XC_FLAGS_3D = 128, & XC_FLAGS_HYB_CAM = 256, & XC_FLAGS_HYB_CAMY = 512, & XC_FLAGS_VV10 = 1024, & XC_FLAGS_HYB_LC = 2048, & XC_FLAGS_HYB_LCY = 4096, & XC_FLAGS_STABLE = 8192, & XC_FLAGS_DEVELOPMENT = 16384, & XC_FLAGS_NEEDS_LAPLACIAN = 32768 integer(c_int), parameter, public :: & XC_TAU_EXPLICIT = 0, & XC_TAU_EXPANSION = 1 integer(c_int), parameter, public :: & XC_MAX_REFERENCES = 5 ! List of functionals integer(c_int), parameter, public :: XC_HYB_LDA_XC_LDA0 = 177 ! LDA0: hybrid LDA exchange integer(c_int), parameter, public :: XC_HYB_LDA_XC_CAM_LDA0 = 178 ! CAM version of LDA0 integer(c_int), parameter, public :: XC_LDA_X = 1 ! Exchange integer(c_int), parameter, public :: XC_LDA_C_WIGNER = 2 ! Wigner parametrization integer(c_int), parameter, public :: XC_LDA_C_RPA = 3 ! Random Phase Approximation integer(c_int), parameter, public :: XC_LDA_C_HL = 4 ! Hedin & Lundqvist integer(c_int), parameter, public :: XC_LDA_C_GL = 5 ! Gunnarson & Lundqvist integer(c_int), parameter, public :: XC_LDA_C_XALPHA = 6 ! Slater Xalpha integer(c_int), parameter, public :: XC_LDA_C_VWN = 7 ! Vosko, Wilk, & Nusair (5) integer(c_int), parameter, public :: XC_LDA_C_VWN_RPA = 8 ! Vosko, Wilk, & Nusair (RPA) integer(c_int), parameter, public :: XC_LDA_C_PZ = 9 ! Perdew & Zunger integer(c_int), parameter, public :: XC_LDA_C_PZ_MOD = 10 ! Perdew & Zunger (Modified) integer(c_int), parameter, public :: XC_LDA_C_OB_PZ = 11 ! Ortiz & Ballone (PZ) integer(c_int), parameter, public :: XC_LDA_C_PW = 12 ! Perdew & Wang integer(c_int), parameter, public :: XC_LDA_C_PW_MOD = 13 ! Perdew & Wang (Modified) integer(c_int), parameter, public :: XC_LDA_C_OB_PW = 14 ! Ortiz & Ballone (PW) integer(c_int), parameter, public :: XC_LDA_C_2D_AMGB = 15 ! Attaccalite et al integer(c_int), parameter, public :: XC_LDA_C_2D_PRM = 16 ! Pittalis, Rasanen & Marques correlation in 2D integer(c_int), parameter, public :: XC_LDA_C_VBH = 17 ! von Barth & Hedin integer(c_int), parameter, public :: XC_LDA_C_1D_CSC = 18 ! Casula, Sorella, and Senatore 1D correlation integer(c_int), parameter, public :: XC_LDA_X_2D = 19 ! Exchange in 2D integer(c_int), parameter, public :: XC_LDA_XC_TETER93 = 20 ! Teter 93 parametrization integer(c_int), parameter, public :: XC_LDA_X_1D_SOFT = 21 ! Exchange in 1D for a soft-Coulomb interaction integer(c_int), parameter, public :: XC_LDA_C_ML1 = 22 ! Modified LSD (version 1) of Proynov and Salahub integer(c_int), parameter, public :: XC_LDA_C_ML2 = 23 ! Modified LSD (version 2) of Proynov and Salahub integer(c_int), parameter, public :: XC_LDA_C_GOMBAS = 24 ! Gombas parametrization integer(c_int), parameter, public :: XC_LDA_C_PW_RPA = 25 ! Perdew & Wang fit of the RPA integer(c_int), parameter, public :: XC_LDA_C_1D_LOOS = 26 ! P-F Loos correlation LDA integer(c_int), parameter, public :: XC_LDA_C_RC04 = 27 ! Ragot-Cortona integer(c_int), parameter, public :: XC_LDA_C_VWN_1 = 28 ! Vosko, Wilk, & Nusair (1) integer(c_int), parameter, public :: XC_LDA_C_VWN_2 = 29 ! Vosko, Wilk, & Nusair (2) integer(c_int), parameter, public :: XC_LDA_C_VWN_3 = 30 ! Vosko, Wilk, & Nusair (3) integer(c_int), parameter, public :: XC_LDA_C_VWN_4 = 31 ! Vosko, Wilk, & Nusair (4) integer(c_int), parameter, public :: XC_LDA_XC_ZLP = 43 ! Zhao, Levy & Parr, Eq. (20) integer(c_int), parameter, public :: XC_LDA_K_TF = 50 ! Thomas-Fermi kinetic energy functional integer(c_int), parameter, public :: XC_LDA_K_LP = 51 ! Lee and Parr Gaussian ansatz integer(c_int), parameter, public :: XC_LDA_XC_KSDT = 259 ! Karasiev et al. parametrization integer(c_int), parameter, public :: XC_LDA_C_CHACHIYO = 287 ! Chachiyo simple 2 parameter correlation integer(c_int), parameter, public :: XC_LDA_C_LP96 = 289 ! Liu-Parr correlation integer(c_int), parameter, public :: XC_LDA_C_CHACHIYO_MOD = 307 ! Chachiyo simple 2 parameter correlation with modified scaling integer(c_int), parameter, public :: XC_LDA_C_KARASIEV_MOD = 308 ! Karasiev reparameterization of Chachiyo with modified scaling integer(c_int), parameter, public :: XC_LDA_X_REL = 532 ! Relativistic exchange integer(c_int), parameter, public :: XC_LDA_XC_1D_EHWLRG_1 = 536 ! LDA constructed from slab-like systems of 1 electron integer(c_int), parameter, public :: XC_LDA_XC_1D_EHWLRG_2 = 537 ! LDA constructed from slab-like systems of 2 electrons integer(c_int), parameter, public :: XC_LDA_XC_1D_EHWLRG_3 = 538 ! LDA constructed from slab-like systems of 3 electrons integer(c_int), parameter, public :: XC_LDA_X_ERF = 546 ! Attenuated exchange LDA (erf) integer(c_int), parameter, public :: XC_LDA_XC_LP_A = 547 ! Lee-Parr reparametrization A integer(c_int), parameter, public :: XC_LDA_XC_LP_B = 548 ! Lee-Parr reparametrization B integer(c_int), parameter, public :: XC_LDA_X_RAE = 549 ! Rae self-energy corrected exchange integer(c_int), parameter, public :: XC_LDA_K_ZLP = 550 ! kinetic energy version of ZLP integer(c_int), parameter, public :: XC_LDA_C_MCWEENY = 551 ! McWeeny 76 integer(c_int), parameter, public :: XC_LDA_C_BR78 = 552 ! Brual & Rothstein 78 integer(c_int), parameter, public :: XC_LDA_C_PK09 = 554 ! Proynov and Kong 2009 integer(c_int), parameter, public :: XC_LDA_C_OW_LYP = 573 ! Wigner with corresponding LYP parameters integer(c_int), parameter, public :: XC_LDA_C_OW = 574 ! Optimized Wigner integer(c_int), parameter, public :: XC_LDA_XC_GDSMFB = 577 ! Groth et al. parametrization integer(c_int), parameter, public :: XC_LDA_C_GK72 = 578 ! Gordon and Kim 1972 integer(c_int), parameter, public :: XC_LDA_C_KARASIEV = 579 ! Karasiev reparameterization of Chachiyo integer(c_int), parameter, public :: XC_LDA_K_LP96 = 580 ! Liu-Parr kinetic integer(c_int), parameter, public :: XC_LDA_XC_BN05 = 588 ! Baer and Neuhauser, gamma=1 integer(c_int), parameter, public :: XC_LDA_C_PMGB06 = 590 ! Long-range LDA correlation functional integer(c_int), parameter, public :: XC_LDA_XC_TIH = 599 ! Neural network LDA from Tozer et al integer(c_int), parameter, public :: XC_LDA_X_1D_EXPONENTIAL = 600 ! Exchange in 1D for an exponentially screened interaction integer(c_int), parameter, public :: XC_LDA_C_UPW92 = 683 ! Ruggeri, Rios, and Alavi unrestricted fit integer(c_int), parameter, public :: XC_LDA_C_RPW92 = 684 ! Ruggeri, Rios, and Alavi restricted fit integer(c_int), parameter, public :: XC_LDA_X_SLOC = 692 ! simple local model for Slater potential integer(c_int), parameter, public :: XC_HYB_GGA_X_N12_SX = 81 ! N12-SX functional from Minnesota integer(c_int), parameter, public :: XC_HYB_GGA_XC_B97_1P = 266 ! version of B97 by Cohen and Handy integer(c_int), parameter, public :: XC_HYB_GGA_XC_PBE_MOL0 = 273 ! PBEmol0 integer(c_int), parameter, public :: XC_HYB_GGA_XC_PBE_SOL0 = 274 ! PBEsol0 integer(c_int), parameter, public :: XC_HYB_GGA_XC_PBEB0 = 275 ! PBEbeta0 integer(c_int), parameter, public :: XC_HYB_GGA_XC_PBE_MOLB0 = 276 ! PBEmolbeta0 integer(c_int), parameter, public :: XC_HYB_GGA_XC_PBE50 = 290 ! PBE0 with 50% exx integer(c_int), parameter, public :: XC_HYB_GGA_XC_HFLYP = 314 ! Hartree-Fock + LYP correlation integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAM_O3LYP = 395 ! range separated hybrid based on the optx functional integer(c_int), parameter, public :: XC_HYB_GGA_XC_WB97X_D3 = 399 ! Lin et al integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_BLYP = 400 ! Long-range corrected BLYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_B3PW91 = 401 ! The original (ACM) hybrid of Becke integer(c_int), parameter, public :: XC_HYB_GGA_XC_B3LYP = 402 ! The (in)famous B3LYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_B3P86 = 403 ! Perdew 86 hybrid similar to B3PW91 integer(c_int), parameter, public :: XC_HYB_GGA_XC_O3LYP = 404 ! hybrid using the optx functional integer(c_int), parameter, public :: XC_HYB_GGA_XC_MPW1K = 405 ! mixture of mPW91 and PW91 optimized for kinetics integer(c_int), parameter, public :: XC_HYB_GGA_XC_PBEH = 406 ! aka PBE0 or PBE1PBE integer(c_int), parameter, public :: XC_HYB_GGA_XC_B97 = 407 ! Becke 97 integer(c_int), parameter, public :: XC_HYB_GGA_XC_B97_1 = 408 ! Becke 97-1 integer(c_int), parameter, public :: XC_HYB_GGA_XC_APF = 409 ! APF hybrid density functional integer(c_int), parameter, public :: XC_HYB_GGA_XC_B97_2 = 410 ! Becke 97-2 integer(c_int), parameter, public :: XC_HYB_GGA_XC_X3LYP = 411 ! hybrid by Xu and Goddard integer(c_int), parameter, public :: XC_HYB_GGA_XC_B1WC = 412 ! Becke 1-parameter mixture of WC and PBE integer(c_int), parameter, public :: XC_HYB_GGA_XC_B97_K = 413 ! Boese-Martin for Kinetics integer(c_int), parameter, public :: XC_HYB_GGA_XC_B97_3 = 414 ! Becke 97-3 integer(c_int), parameter, public :: XC_HYB_GGA_XC_MPW3PW = 415 ! mixture with the mPW functional integer(c_int), parameter, public :: XC_HYB_GGA_XC_B1LYP = 416 ! Becke 1-parameter mixture of B88 and LYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_B1PW91 = 417 ! Becke 1-parameter mixture of B88 and PW91 integer(c_int), parameter, public :: XC_HYB_GGA_XC_MPW1PW = 418 ! Becke 1-parameter mixture of mPW91 and PW91 integer(c_int), parameter, public :: XC_HYB_GGA_XC_MPW3LYP = 419 ! mixture of mPW and LYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_SB98_1A = 420 ! Schmider-Becke 98 parameterization 1a integer(c_int), parameter, public :: XC_HYB_GGA_XC_SB98_1B = 421 ! Schmider-Becke 98 parameterization 1b integer(c_int), parameter, public :: XC_HYB_GGA_XC_SB98_1C = 422 ! Schmider-Becke 98 parameterization 1c integer(c_int), parameter, public :: XC_HYB_GGA_XC_SB98_2A = 423 ! Schmider-Becke 98 parameterization 2a integer(c_int), parameter, public :: XC_HYB_GGA_XC_SB98_2B = 424 ! Schmider-Becke 98 parameterization 2b integer(c_int), parameter, public :: XC_HYB_GGA_XC_SB98_2C = 425 ! Schmider-Becke 98 parameterization 2c integer(c_int), parameter, public :: XC_HYB_GGA_X_SOGGA11_X = 426 ! Hybrid based on SOGGA11 form integer(c_int), parameter, public :: XC_HYB_GGA_XC_HSE03 = 427 ! the 2003 version of the screened hybrid HSE integer(c_int), parameter, public :: XC_HYB_GGA_XC_HSE06 = 428 ! the 2006 version of the screened hybrid HSE integer(c_int), parameter, public :: XC_HYB_GGA_XC_HJS_PBE = 429 ! HJS hybrid screened exchange PBE version integer(c_int), parameter, public :: XC_HYB_GGA_XC_HJS_PBE_SOL = 430 ! HJS hybrid screened exchange PBE_SOL version integer(c_int), parameter, public :: XC_HYB_GGA_XC_HJS_B88 = 431 ! HJS hybrid screened exchange B88 version integer(c_int), parameter, public :: XC_HYB_GGA_XC_HJS_B97X = 432 ! HJS hybrid screened exchange B97x version integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAM_B3LYP = 433 ! CAM version of B3LYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_TUNED_CAM_B3LYP = 434 ! CAM version of B3LYP tuned for excitations integer(c_int), parameter, public :: XC_HYB_GGA_XC_BHANDH = 435 ! Becke half-and-half or BHLYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_BHANDHLYP = 436 ! Becke half-and-half with B88 exchange integer(c_int), parameter, public :: XC_HYB_GGA_XC_MB3LYP_RC04 = 437 ! B3LYP with RC04 LDA integer(c_int), parameter, public :: XC_HYB_GGA_XC_MPWLYP1M = 453 ! MPW with 1 par. for metals/LYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_REVB3LYP = 454 ! Revised B3LYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAMY_BLYP = 455 ! BLYP with yukawa screening integer(c_int), parameter, public :: XC_HYB_GGA_XC_PBE0_13 = 456 ! PBE0-1/3 integer(c_int), parameter, public :: XC_HYB_GGA_XC_B3LYPS = 459 ! B3LYP* functional integer(c_int), parameter, public :: XC_HYB_GGA_XC_QTP17 = 460 ! global hybrid for vertical ionization potentials integer(c_int), parameter, public :: XC_HYB_GGA_XC_B3LYP_MCM1 = 461 ! B3LYP reoptimized in 6-31+G(2df,p) for enthalpies of formation integer(c_int), parameter, public :: XC_HYB_GGA_XC_B3LYP_MCM2 = 462 ! B3LYP reoptimized in 6-31+G(2df,p) for enthalpies of formation integer(c_int), parameter, public :: XC_HYB_GGA_XC_WB97 = 463 ! Chai and Head-Gordon integer(c_int), parameter, public :: XC_HYB_GGA_XC_WB97X = 464 ! Chai and Head-Gordon integer(c_int), parameter, public :: XC_HYB_GGA_XC_LRC_WPBEH = 465 ! Long-range corrected functional by Rorhdanz et al integer(c_int), parameter, public :: XC_HYB_GGA_XC_WB97X_V = 466 ! Mardirossian and Head-Gordon integer(c_int), parameter, public :: XC_HYB_GGA_XC_LCY_PBE = 467 ! PBE with yukawa screening integer(c_int), parameter, public :: XC_HYB_GGA_XC_LCY_BLYP = 468 ! BLYP with yukawa screening integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_VV10 = 469 ! Vydrov and Van Voorhis integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAMY_B3LYP = 470 ! B3LYP with Yukawa screening integer(c_int), parameter, public :: XC_HYB_GGA_XC_WB97X_D = 471 ! Chai and Head-Gordon integer(c_int), parameter, public :: XC_HYB_GGA_XC_HPBEINT = 472 ! hPBEint integer(c_int), parameter, public :: XC_HYB_GGA_XC_LRC_WPBE = 473 ! Long-range corrected functional by Rorhdanz et al integer(c_int), parameter, public :: XC_HYB_GGA_XC_B3LYP5 = 475 ! B3LYP with VWN functional 5 instead of RPA integer(c_int), parameter, public :: XC_HYB_GGA_XC_EDF2 = 476 ! Empirical functional from Lin, George and Gill integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAP0 = 477 ! Correct Asymptotic Potential hybrid integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_WPBE = 478 ! Long-range corrected functional by Vydrov and Scuseria integer(c_int), parameter, public :: XC_HYB_GGA_XC_HSE12 = 479 ! HSE12 by Moussa, Schultz and Chelikowsky integer(c_int), parameter, public :: XC_HYB_GGA_XC_HSE12S = 480 ! Short-range HSE12 by Moussa, Schultz, and Chelikowsky integer(c_int), parameter, public :: XC_HYB_GGA_XC_HSE_SOL = 481 ! HSEsol functional by Schimka, Harl, and Kresse integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAM_QTP_01 = 482 ! CAM-QTP-01 integer(c_int), parameter, public :: XC_HYB_GGA_XC_MPW1LYP = 483 ! Becke 1-parameter mixture of mPW91 and LYP integer(c_int), parameter, public :: XC_HYB_GGA_XC_MPW1PBE = 484 ! Becke 1-parameter mixture of mPW91 and PBE integer(c_int), parameter, public :: XC_HYB_GGA_XC_KMLYP = 485 ! Kang-Musgrave hybrid integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_WPBE_WHS = 486 ! Long-range corrected functional by Weintraub, Henderson and Scuseria integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_WPBEH_WHS = 487 ! Long-range corrected functional by Weintraub, Henderson and Scuseria integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_WPBE08_WHS = 488 ! Long-range corrected functional by Weintraub, Henderson and Scuseria integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_WPBESOL_WHS = 489 ! Long-range corrected functional by Weintraub, Henderson and Scuseria integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAM_QTP_00 = 490 ! CAM-QTP-00 integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAM_QTP_02 = 491 ! CAM-QTP-02 integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_QTP = 492 ! LC-QTP integer(c_int), parameter, public :: XC_HYB_GGA_X_S12H = 496 ! Swart 2012 GGA hybrid exchange integer(c_int), parameter, public :: XC_HYB_GGA_XC_BLYP35 = 499 ! Becke 1-parameter mixture for mixed-valence systems integer(c_int), parameter, public :: XC_HYB_GGA_XC_B5050LYP = 572 ! Like B3LYP but more exact exchange integer(c_int), parameter, public :: XC_HYB_GGA_XC_APBE0 = 607 ! Hybrid based on APBE integer(c_int), parameter, public :: XC_HYB_GGA_XC_HAPBE = 608 ! Hybrid based in APBE and zvPBEloc integer(c_int), parameter, public :: XC_HYB_GGA_XC_RCAM_B3LYP = 610 ! Similar to CAM-B3LYP, but trying to reduce the many-electron self-interaction integer(c_int), parameter, public :: XC_HYB_GGA_XC_WC04 = 611 ! hybrid fitted to carbon NMR shifts integer(c_int), parameter, public :: XC_HYB_GGA_XC_WP04 = 612 ! hybrid fitted to proton NMR shifts integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAMH_B3LYP = 614 ! CAM version of B3LYP tuned for tddft integer(c_int), parameter, public :: XC_HYB_GGA_XC_WHPBE0 = 615 ! Long-range corrected functional by Shao et al integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_BOP = 636 ! Long-range corrected B88 with B88OP correlation integer(c_int), parameter, public :: XC_HYB_GGA_XC_LC_PBEOP = 637 ! Long-range corrected PBE with PBEOP correlation integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAM_PBEH = 681 ! CAM version of PBEH integer(c_int), parameter, public :: XC_HYB_GGA_XC_CAMY_PBEH = 682 ! PBEH with Yukawa screening integer(c_int), parameter, public :: XC_GGA_X_GAM = 32 ! GAM functional from Minnesota integer(c_int), parameter, public :: XC_GGA_C_GAM = 33 ! GAM functional from Minnesota integer(c_int), parameter, public :: XC_GGA_X_HCTH_A = 34 ! HCTH-A integer(c_int), parameter, public :: XC_GGA_X_EV93 = 35 ! Engel and Vosko integer(c_int), parameter, public :: XC_GGA_X_BCGP = 38 ! Burke, Cancio, Gould, and Pittalis integer(c_int), parameter, public :: XC_GGA_C_ACGGA = 39 ! acGGA, asymptotically corrected GGA integer(c_int), parameter, public :: XC_GGA_X_LAMBDA_OC2_N = 40 ! lambda_OC2(N) version of PBE integer(c_int), parameter, public :: XC_GGA_X_B86_R = 41 ! Revised Becke 86 Xalpha,beta,gamma (with mod. grad. correction) integer(c_int), parameter, public :: XC_GGA_X_LAMBDA_CH_N = 44 ! lambda_CH(N) version of PBE integer(c_int), parameter, public :: XC_GGA_X_LAMBDA_LO_N = 45 ! lambda_LO(N) version of PBE integer(c_int), parameter, public :: XC_GGA_X_HJS_B88_V2 = 46 ! HJS screened exchange corrected B88 version integer(c_int), parameter, public :: XC_GGA_C_Q2D = 47 ! Chiodo et al integer(c_int), parameter, public :: XC_GGA_X_Q2D = 48 ! Chiodo et al integer(c_int), parameter, public :: XC_GGA_X_PBE_MOL = 49 ! Del Campo, Gazquez, Trickey and Vela (PBE-like) integer(c_int), parameter, public :: XC_GGA_K_TFVW = 52 ! Thomas-Fermi plus von Weiszaecker correction integer(c_int), parameter, public :: XC_GGA_K_REVAPBEINT = 53 ! interpolated version of REVAPBE integer(c_int), parameter, public :: XC_GGA_K_APBEINT = 54 ! interpolated version of APBE integer(c_int), parameter, public :: XC_GGA_K_REVAPBE = 55 ! revised APBE integer(c_int), parameter, public :: XC_GGA_X_AK13 = 56 ! Armiento & Kuemmel 2013 integer(c_int), parameter, public :: XC_GGA_K_MEYER = 57 ! Meyer, Wang, and Young integer(c_int), parameter, public :: XC_GGA_X_LV_RPW86 = 58 ! Berland and Hyldgaard integer(c_int), parameter, public :: XC_GGA_X_PBE_TCA = 59 ! PBE revised by Tognetti et al integer(c_int), parameter, public :: XC_GGA_X_PBEINT = 60 ! PBE for hybrid interfaces integer(c_int), parameter, public :: XC_GGA_C_ZPBEINT = 61 ! spin-dependent gradient correction to PBEint integer(c_int), parameter, public :: XC_GGA_C_PBEINT = 62 ! PBE for hybrid interfaces integer(c_int), parameter, public :: XC_GGA_C_ZPBESOL = 63 ! spin-dependent gradient correction to PBEsol integer(c_int), parameter, public :: XC_GGA_XC_OPBE_D = 65 ! oPBE_D functional of Goerigk and Grimme integer(c_int), parameter, public :: XC_GGA_XC_OPWLYP_D = 66 ! oPWLYP-D functional of Goerigk and Grimme integer(c_int), parameter, public :: XC_GGA_XC_OBLYP_D = 67 ! oBLYP-D functional of Goerigk and Grimme integer(c_int), parameter, public :: XC_GGA_X_VMT84_GE = 68 ! VMT{8,4} with constraint satisfaction with mu = mu_GE integer(c_int), parameter, public :: XC_GGA_X_VMT84_PBE = 69 ! VMT{8,4} with constraint satisfaction with mu = mu_PBE integer(c_int), parameter, public :: XC_GGA_X_VMT_GE = 70 ! Vela, Medel, and Trickey with mu = mu_GE integer(c_int), parameter, public :: XC_GGA_X_VMT_PBE = 71 ! Vela, Medel, and Trickey with mu = mu_PBE integer(c_int), parameter, public :: XC_GGA_C_N12_SX = 79 ! N12-SX functional from Minnesota integer(c_int), parameter, public :: XC_GGA_C_N12 = 80 ! N12 functional from Minnesota integer(c_int), parameter, public :: XC_GGA_X_N12 = 82 ! N12 functional from Minnesota integer(c_int), parameter, public :: XC_GGA_C_REGTPSS = 83 ! Regularized TPSS correlation (ex-VPBE) integer(c_int), parameter, public :: XC_GGA_C_OP_XALPHA = 84 ! one-parameter progressive functional (XALPHA version) integer(c_int), parameter, public :: XC_GGA_C_OP_G96 = 85 ! one-parameter progressive functional (G96 version) integer(c_int), parameter, public :: XC_GGA_C_OP_PBE = 86 ! one-parameter progressive functional (PBE version) integer(c_int), parameter, public :: XC_GGA_C_OP_B88 = 87 ! one-parameter progressive functional (B88 version) integer(c_int), parameter, public :: XC_GGA_C_FT97 = 88 ! Filatov & Thiel correlation integer(c_int), parameter, public :: XC_GGA_C_SPBE = 89 ! PBE correlation to be used with the SSB exchange integer(c_int), parameter, public :: XC_GGA_X_SSB_SW = 90 ! Swart, Sola and Bickelhaupt correction to PBE integer(c_int), parameter, public :: XC_GGA_X_SSB = 91 ! Swart, Sola and Bickelhaupt integer(c_int), parameter, public :: XC_GGA_X_SSB_D = 92 ! Swart, Sola and Bickelhaupt dispersion integer(c_int), parameter, public :: XC_GGA_XC_HCTH_407P = 93 ! HCTH/407+ integer(c_int), parameter, public :: XC_GGA_XC_HCTH_P76 = 94 ! HCTH p=7/6 integer(c_int), parameter, public :: XC_GGA_XC_HCTH_P14 = 95 ! HCTH p=1/4 integer(c_int), parameter, public :: XC_GGA_XC_B97_GGA1 = 96 ! Becke 97 GGA-1 integer(c_int), parameter, public :: XC_GGA_C_HCTH_A = 97 ! HCTH-A integer(c_int), parameter, public :: XC_GGA_X_BPCCAC = 98 ! BPCCAC (GRAC for the energy) integer(c_int), parameter, public :: XC_GGA_C_REVTCA = 99 ! Tognetti, Cortona, Adamo (revised) integer(c_int), parameter, public :: XC_GGA_C_TCA = 100 ! Tognetti, Cortona, Adamo integer(c_int), parameter, public :: XC_GGA_X_PBE = 101 ! Perdew, Burke & Ernzerhof exchange integer(c_int), parameter, public :: XC_GGA_X_PBE_R = 102 ! Perdew, Burke & Ernzerhof exchange (revised) integer(c_int), parameter, public :: XC_GGA_X_B86 = 103 ! Becke 86 Xalpha,beta,gamma integer(c_int), parameter, public :: XC_GGA_X_HERMAN = 104 ! Herman et al original GGA integer(c_int), parameter, public :: XC_GGA_X_B86_MGC = 105 ! Becke 86 Xalpha,beta,gamma (with mod. grad. correction) integer(c_int), parameter, public :: XC_GGA_X_B88 = 106 ! Becke 88 integer(c_int), parameter, public :: XC_GGA_X_G96 = 107 ! Gill 96 integer(c_int), parameter, public :: XC_GGA_X_PW86 = 108 ! Perdew & Wang 86 integer(c_int), parameter, public :: XC_GGA_X_PW91 = 109 ! Perdew & Wang 91 integer(c_int), parameter, public :: XC_GGA_X_OPTX = 110 ! Handy & Cohen OPTX 01 integer(c_int), parameter, public :: XC_GGA_X_DK87_R1 = 111 ! dePristo & Kress 87 (version R1) integer(c_int), parameter, public :: XC_GGA_X_DK87_R2 = 112 ! dePristo & Kress 87 (version R2) integer(c_int), parameter, public :: XC_GGA_X_LG93 = 113 ! Lacks & Gordon 93 integer(c_int), parameter, public :: XC_GGA_X_FT97_A = 114 ! Filatov & Thiel 97 (version A) integer(c_int), parameter, public :: XC_GGA_X_FT97_B = 115 ! Filatov & Thiel 97 (version B) integer(c_int), parameter, public :: XC_GGA_X_PBE_SOL = 116 ! Perdew, Burke & Ernzerhof exchange (solids) integer(c_int), parameter, public :: XC_GGA_X_RPBE = 117 ! Hammer, Hansen & Norskov (PBE-like) integer(c_int), parameter, public :: XC_GGA_X_WC = 118 ! Wu & Cohen integer(c_int), parameter, public :: XC_GGA_X_MPW91 = 119 ! Modified form of PW91 by Adamo & Barone integer(c_int), parameter, public :: XC_GGA_X_AM05 = 120 ! Armiento & Mattsson 05 exchange integer(c_int), parameter, public :: XC_GGA_X_PBEA = 121 ! Madsen (PBE-like) integer(c_int), parameter, public :: XC_GGA_X_MPBE = 122 ! Adamo & Barone modification to PBE integer(c_int), parameter, public :: XC_GGA_X_XPBE = 123 ! xPBE reparametrization by Xu & Goddard integer(c_int), parameter, public :: XC_GGA_X_2D_B86_MGC = 124 ! Becke 86 MGC for 2D systems integer(c_int), parameter, public :: XC_GGA_X_BAYESIAN = 125 ! Bayesian best fit for the enhancement factor integer(c_int), parameter, public :: XC_GGA_X_PBE_JSJR = 126 ! JSJR reparametrization by Pedroza, Silva & Capelle integer(c_int), parameter, public :: XC_GGA_X_2D_B88 = 127 ! Becke 88 in 2D integer(c_int), parameter, public :: XC_GGA_X_2D_B86 = 128 ! Becke 86 Xalpha, beta, gamma integer(c_int), parameter, public :: XC_GGA_X_2D_PBE = 129 ! Perdew, Burke & Ernzerhof exchange in 2D integer(c_int), parameter, public :: XC_GGA_C_PBE = 130 ! Perdew, Burke & Ernzerhof correlation integer(c_int), parameter, public :: XC_GGA_C_LYP = 131 ! Lee, Yang & Parr integer(c_int), parameter, public :: XC_GGA_C_P86 = 132 ! Perdew 86 integer(c_int), parameter, public :: XC_GGA_C_PBE_SOL = 133 ! Perdew, Burke & Ernzerhof correlation SOL integer(c_int), parameter, public :: XC_GGA_C_PW91 = 134 ! Perdew & Wang 91 integer(c_int), parameter, public :: XC_GGA_C_AM05 = 135 ! Armiento & Mattsson 05 correlation integer(c_int), parameter, public :: XC_GGA_C_XPBE = 136 ! xPBE reparametrization by Xu & Goddard integer(c_int), parameter, public :: XC_GGA_C_LM = 137 ! Langreth and Mehl correlation integer(c_int), parameter, public :: XC_GGA_C_PBE_JRGX = 138 ! JRGX reparametrization by Pedroza, Silva & Capelle integer(c_int), parameter, public :: XC_GGA_X_OPTB88_VDW = 139 ! Becke 88 reoptimized to be used with vdW functional of Dion et al integer(c_int), parameter, public :: XC_GGA_X_PBEK1_VDW = 140 ! PBE reparametrization for vdW integer(c_int), parameter, public :: XC_GGA_X_OPTPBE_VDW = 141 ! PBE reparametrization for vdW integer(c_int), parameter, public :: XC_GGA_X_RGE2 = 142 ! Regularized PBE integer(c_int), parameter, public :: XC_GGA_C_RGE2 = 143 ! Regularized PBE integer(c_int), parameter, public :: XC_GGA_X_RPW86 = 144 ! refitted Perdew & Wang 86 integer(c_int), parameter, public :: XC_GGA_X_KT1 = 145 ! Exchange part of Keal and Tozer version 1 integer(c_int), parameter, public :: XC_GGA_XC_KT2 = 146 ! Keal and Tozer version 2 integer(c_int), parameter, public :: XC_GGA_C_WL = 147 ! Wilson & Levy integer(c_int), parameter, public :: XC_GGA_C_WI = 148 ! Wilson & Ivanov integer(c_int), parameter, public :: XC_GGA_X_MB88 = 149 ! Modified Becke 88 for proton transfer integer(c_int), parameter, public :: XC_GGA_X_SOGGA = 150 ! Second-order generalized gradient approximation integer(c_int), parameter, public :: XC_GGA_X_SOGGA11 = 151 ! Second-order generalized gradient approximation 2011 integer(c_int), parameter, public :: XC_GGA_C_SOGGA11 = 152 ! SOGGA11 correlation integer(c_int), parameter, public :: XC_GGA_C_WI0 = 153 ! Wilson & Ivanov initial version integer(c_int), parameter, public :: XC_GGA_XC_TH1 = 154 ! Tozer and Handy v. 1 integer(c_int), parameter, public :: XC_GGA_XC_TH2 = 155 ! Tozer and Handy v. 2 integer(c_int), parameter, public :: XC_GGA_XC_TH3 = 156 ! Tozer and Handy v. 3 integer(c_int), parameter, public :: XC_GGA_XC_TH4 = 157 ! Tozer and Handy v. 4 integer(c_int), parameter, public :: XC_GGA_X_C09X = 158 ! C09x to be used with the VdW of Rutgers-Chalmers integer(c_int), parameter, public :: XC_GGA_C_SOGGA11_X = 159 ! SOGGA11-X correlation integer(c_int), parameter, public :: XC_GGA_X_LB = 160 ! van Leeuwen & Baerends integer(c_int), parameter, public :: XC_GGA_XC_HCTH_93 = 161 ! HCTH functional fitted to 93 molecules integer(c_int), parameter, public :: XC_GGA_XC_HCTH_120 = 162 ! HCTH functional fitted to 120 molecules integer(c_int), parameter, public :: XC_GGA_XC_HCTH_147 = 163 ! HCTH functional fitted to 147 molecules integer(c_int), parameter, public :: XC_GGA_XC_HCTH_407 = 164 ! HCTH functional fitted to 407 molecules integer(c_int), parameter, public :: XC_GGA_XC_EDF1 = 165 ! Empirical functionals from Adamson, Gill, and Pople integer(c_int), parameter, public :: XC_GGA_XC_XLYP = 166 ! XLYP functional integer(c_int), parameter, public :: XC_GGA_XC_KT1 = 167 ! Keal and Tozer version 1 integer(c_int), parameter, public :: XC_GGA_X_LSPBE = 168 ! PW91-like exchange with simple analytical form integer(c_int), parameter, public :: XC_GGA_X_LSRPBE = 169 ! PW91-like modification of RPBE integer(c_int), parameter, public :: XC_GGA_XC_B97_D = 170 ! Grimme functional to be used with C6 vdW term integer(c_int), parameter, public :: XC_GGA_X_OPTB86B_VDW = 171 ! Becke 86 reoptimized for use with vdW functional of Dion et al integer(c_int), parameter, public :: XC_GGA_XC_PBE1W = 173 ! Functionals fitted for water integer(c_int), parameter, public :: XC_GGA_XC_MPWLYP1W = 174 ! Functionals fitted for water integer(c_int), parameter, public :: XC_GGA_XC_PBELYP1W = 175 ! Functionals fitted for water integer(c_int), parameter, public :: XC_GGA_C_ACGGAP = 176 ! Asymptotically corrected GGA + integer(c_int), parameter, public :: XC_GGA_X_B88_6311G = 179 ! Becke 88 reoptimized with 6-311G** basis set integer(c_int), parameter, public :: XC_GGA_X_NCAP = 180 ! Nearly correct asymptotic potential integer(c_int), parameter, public :: XC_GGA_XC_NCAP = 181 ! Nearly correct asymptotic potential + P86 correlation integer(c_int), parameter, public :: XC_GGA_X_LBM = 182 ! van Leeuwen & Baerends modified integer(c_int), parameter, public :: XC_GGA_X_OL2 = 183 ! Exchange form based on Ou-Yang and Levy v.2 integer(c_int), parameter, public :: XC_GGA_X_APBE = 184 ! mu fixed from the semiclassical neutral atom integer(c_int), parameter, public :: XC_GGA_K_APBE = 185 ! mu fixed from the semiclassical neutral atom integer(c_int), parameter, public :: XC_GGA_C_APBE = 186 ! mu fixed from the semiclassical neutral atom integer(c_int), parameter, public :: XC_GGA_K_TW1 = 187 ! Tran and Wesolowski set 1 (Table II) integer(c_int), parameter, public :: XC_GGA_K_TW2 = 188 ! Tran and Wesolowski set 2 (Table II) integer(c_int), parameter, public :: XC_GGA_K_TW3 = 189 ! Tran and Wesolowski set 3 (Table II) integer(c_int), parameter, public :: XC_GGA_K_TW4 = 190 ! Tran and Wesolowski set 4 (Table II) integer(c_int), parameter, public :: XC_GGA_X_HTBS = 191 ! Haas, Tran, Blaha, and Schwarz integer(c_int), parameter, public :: XC_GGA_X_AIRY = 192 ! Constantin et al based on the Airy gas integer(c_int), parameter, public :: XC_GGA_X_LAG = 193 ! Local Airy Gas integer(c_int), parameter, public :: XC_GGA_XC_MOHLYP = 194 ! Functional for organometallic chemistry integer(c_int), parameter, public :: XC_GGA_XC_MOHLYP2 = 195 ! Functional for barrier heights integer(c_int), parameter, public :: XC_GGA_XC_TH_FL = 196 ! Tozer and Handy v. FL integer(c_int), parameter, public :: XC_GGA_XC_TH_FC = 197 ! Tozer and Handy v. FC integer(c_int), parameter, public :: XC_GGA_XC_TH_FCFO = 198 ! Tozer and Handy v. FCFO integer(c_int), parameter, public :: XC_GGA_XC_TH_FCO = 199 ! Tozer and Handy v. FCO integer(c_int), parameter, public :: XC_GGA_C_OPTC = 200 ! Optimized correlation functional of Cohen and Handy integer(c_int), parameter, public :: XC_GGA_X_ECMV92 = 215 ! Engel, Chevary, Macdonald, and Vosko integer(c_int), parameter, public :: XC_GGA_C_PBE_VWN = 216 ! Perdew, Burke & Ernzerhof correlation based on VWN LDA integer(c_int), parameter, public :: XC_GGA_C_P86_FT = 217 ! Perdew 86 with a more accurate value for ftilde integer(c_int), parameter, public :: XC_GGA_K_RATIONAL_P = 218 ! Lehtomaki and Lopez-Acevedo integer(c_int), parameter, public :: XC_GGA_K_PG1 = 219 ! PG1 functional by Constantin, Fabiano, and Della Sala integer(c_int), parameter, public :: XC_GGA_C_PBELOC = 246 ! Semilocal dynamical correlation integer(c_int), parameter, public :: XC_GGA_C_P86VWN = 252 ! Perdew 86 based on the VWN5 LDA integer(c_int), parameter, public :: XC_GGA_C_P86VWN_FT = 253 ! Perdew 86 based on the VWN5 LDA with a more accurate value for ftilde integer(c_int), parameter, public :: XC_GGA_XC_VV10 = 255 ! Vydrov and Van Voorhis integer(c_int), parameter, public :: XC_GGA_C_PBEFE = 258 ! PBE for formation energies integer(c_int), parameter, public :: XC_GGA_C_OP_PW91 = 262 ! one-parameter progressive functional (PW91 version) integer(c_int), parameter, public :: XC_GGA_X_PBEFE = 265 ! PBE for formation energies integer(c_int), parameter, public :: XC_GGA_X_CAP = 270 ! Correct Asymptotic Potential integer(c_int), parameter, public :: XC_GGA_X_EB88 = 271 ! Non-empirical (excogitated) B88 functional of Becke and Elliott integer(c_int), parameter, public :: XC_GGA_C_PBE_MOL = 272 ! Del Campo, Gazquez, Trickey and Vela (PBE-like) integer(c_int), parameter, public :: XC_GGA_K_ABSP3 = 277 ! gamma-TFvW form by Acharya et al [g = 1 - 1.513/N^0.35] integer(c_int), parameter, public :: XC_GGA_K_ABSP4 = 278 ! gamma-TFvW form by Acharya et al [g = l = 1/(1 + 1.332/N^(1/3))] integer(c_int), parameter, public :: XC_GGA_C_BMK = 280 ! Boese-Martin for kinetics integer(c_int), parameter, public :: XC_GGA_C_TAU_HCTH = 281 ! correlation part of tau-hcth integer(c_int), parameter, public :: XC_GGA_C_HYB_TAU_HCTH = 283 ! correlation part of hyb_tau-hcth integer(c_int), parameter, public :: XC_GGA_X_BEEFVDW = 285 ! BEEF-vdW exchange integer(c_int), parameter, public :: XC_GGA_XC_BEEFVDW = 286 ! BEEF-vdW exchange-correlation integer(c_int), parameter, public :: XC_GGA_X_PBETRANS = 291 ! Gradient-based interpolation between PBE and revPBE integer(c_int), parameter, public :: XC_GGA_X_CHACHIYO = 298 ! Chachiyo exchange integer(c_int), parameter, public :: XC_GGA_C_CHACHIYO = 309 ! Chachiyo simple GGA correlation integer(c_int), parameter, public :: XC_GGA_X_REVSSB_D = 312 ! Revised Swart, Sola and Bickelhaupt dispersion integer(c_int), parameter, public :: XC_GGA_C_CCDF = 313 ! ccDF, coupled-cluster based density functional integer(c_int), parameter, public :: XC_GGA_X_PW91_MOD = 316 ! Perdew & Wang 91, alternate version with more digits integer(c_int), parameter, public :: XC_GGA_X_S12G = 495 ! Swart 2012 GGA exchange integer(c_int), parameter, public :: XC_GGA_K_VW = 500 ! von Weiszaecker functional integer(c_int), parameter, public :: XC_GGA_K_GE2 = 501 ! Second-order gradient expansion (l = 1/9) integer(c_int), parameter, public :: XC_GGA_K_GOLDEN = 502 ! TF-lambda-vW form by Golden (l = 13/45) integer(c_int), parameter, public :: XC_GGA_K_YT65 = 503 ! TF-lambda-vW form by Yonei and Tomishima (l = 1/5) integer(c_int), parameter, public :: XC_GGA_K_BALTIN = 504 ! TF-lambda-vW form by Baltin (l = 5/9) integer(c_int), parameter, public :: XC_GGA_K_LIEB = 505 ! TF-lambda-vW form by Lieb (l = 0.185909191) integer(c_int), parameter, public :: XC_GGA_K_ABSP1 = 506 ! gamma-TFvW form by Acharya et al [g = 1 - 1.412/N^(1/3)] integer(c_int), parameter, public :: XC_GGA_K_ABSP2 = 507 ! gamma-TFvW form by Acharya et al [g = 1 - 1.332/N^(1/3)] integer(c_int), parameter, public :: XC_GGA_K_GR = 508 ! gamma-TFvW form by Gazquez and Robles integer(c_int), parameter, public :: XC_GGA_K_LUDENA = 509 ! gamma-TFvW form by Ludena integer(c_int), parameter, public :: XC_GGA_K_GP85 = 510 ! gamma-TFvW form by Ghosh and Parr integer(c_int), parameter, public :: XC_GGA_K_PEARSON = 511 ! Pearson integer(c_int), parameter, public :: XC_GGA_K_OL1 = 512 ! Ou-Yang and Levy v.1 integer(c_int), parameter, public :: XC_GGA_K_OL2 = 513 ! Ou-Yang and Levy v.2 integer(c_int), parameter, public :: XC_GGA_K_FR_B88 = 514 ! Fuentealba & Reyes (B88 version) integer(c_int), parameter, public :: XC_GGA_K_FR_PW86 = 515 ! Fuentealba & Reyes (PW86 version) integer(c_int), parameter, public :: XC_GGA_K_DK = 516 ! DePristo and Kress integer(c_int), parameter, public :: XC_GGA_K_PERDEW = 517 ! Perdew integer(c_int), parameter, public :: XC_GGA_K_VSK = 518 ! Vitos, Skriver, and Kollar integer(c_int), parameter, public :: XC_GGA_K_VJKS = 519 ! Vitos, Johansson, Kollar, and Skriver integer(c_int), parameter, public :: XC_GGA_K_ERNZERHOF = 520 ! Ernzerhof integer(c_int), parameter, public :: XC_GGA_K_LC94 = 521 ! Lembarki & Chermette integer(c_int), parameter, public :: XC_GGA_K_LLP = 522 ! Lee, Lee & Parr integer(c_int), parameter, public :: XC_GGA_K_THAKKAR = 523 ! Thakkar 1992 integer(c_int), parameter, public :: XC_GGA_X_WPBEH = 524 ! short-range version of the PBE integer(c_int), parameter, public :: XC_GGA_X_HJS_PBE = 525 ! HJS screened exchange PBE version integer(c_int), parameter, public :: XC_GGA_X_HJS_PBE_SOL = 526 ! HJS screened exchange PBE_SOL version integer(c_int), parameter, public :: XC_GGA_X_HJS_B88 = 527 ! HJS screened exchange B88 version integer(c_int), parameter, public :: XC_GGA_X_HJS_B97X = 528 ! HJS screened exchange B97x version integer(c_int), parameter, public :: XC_GGA_X_ITYH = 529 ! short-range recipe B88 functionals - erf integer(c_int), parameter, public :: XC_GGA_X_SFAT = 530 ! short-range recipe for PBE functional integer(c_int), parameter, public :: XC_GGA_X_SG4 = 533 ! Semiclassical GGA at fourth order integer(c_int), parameter, public :: XC_GGA_C_SG4 = 534 ! Semiclassical GGA at fourth order integer(c_int), parameter, public :: XC_GGA_X_GG99 = 535 ! Gilbert and Gill 1999 integer(c_int), parameter, public :: XC_GGA_X_PBEPOW = 539 ! PBE power integer(c_int), parameter, public :: XC_GGA_X_KGG99 = 544 ! Gilbert and Gill 1999 (mixed) integer(c_int), parameter, public :: XC_GGA_XC_HLE16 = 545 ! high local exchange 2016 integer(c_int), parameter, public :: XC_GGA_C_SCAN_E0 = 553 ! GGA component of SCAN integer(c_int), parameter, public :: XC_GGA_C_GAPC = 555 ! GapC integer(c_int), parameter, public :: XC_GGA_C_GAPLOC = 556 ! Gaploc integer(c_int), parameter, public :: XC_GGA_C_ZVPBEINT = 557 ! another spin-dependent correction to PBEint integer(c_int), parameter, public :: XC_GGA_C_ZVPBESOL = 558 ! another spin-dependent correction to PBEsol integer(c_int), parameter, public :: XC_GGA_C_TM_LYP = 559 ! Takkar and McCarthy reparametrization integer(c_int), parameter, public :: XC_GGA_C_TM_PBE = 560 ! Thakkar and McCarthy reparametrization integer(c_int), parameter, public :: XC_GGA_C_W94 = 561 ! Wilson 94 (Eq. 25) integer(c_int), parameter, public :: XC_GGA_C_CS1 = 565 ! A dynamical correlation functional integer(c_int), parameter, public :: XC_GGA_X_B88M = 570 ! Becke 88 reoptimized to be used with mgga_c_tau1 integer(c_int), parameter, public :: XC_GGA_XC_KT3 = 587 ! Keal and Tozer version 3 integer(c_int), parameter, public :: XC_GGA_XC_LB07 = 589 ! Livshits and Baer, empirical functional integer(c_int), parameter, public :: XC_GGA_K_GDS08 = 591 ! Combined analytical theory with Monte Carlo sampling integer(c_int), parameter, public :: XC_GGA_K_GHDS10 = 592 ! As GDS08 but for an electron gas with spin integer(c_int), parameter, public :: XC_GGA_K_GHDS10R = 593 ! Reparametrized GHDS10 integer(c_int), parameter, public :: XC_GGA_K_TKVLN = 594 ! Trickey, Karasiev, and Vela integer(c_int), parameter, public :: XC_GGA_K_PBE3 = 595 ! Three parameter PBE-like expansion integer(c_int), parameter, public :: XC_GGA_K_PBE4 = 596 ! Four parameter PBE-like expansion integer(c_int), parameter, public :: XC_GGA_K_EXP4 = 597 ! Intermediate form between PBE3 and PBE4 integer(c_int), parameter, public :: XC_GGA_X_SFAT_PBE = 601 ! short-range recipe for PBE functional integer(c_int), parameter, public :: XC_GGA_X_FD_LB94 = 604 ! Functional derivative recovered from the stray LB94 potential integer(c_int), parameter, public :: XC_GGA_X_FD_REVLB94 = 605 ! Revised FD_LB94 integer(c_int), parameter, public :: XC_GGA_C_ZVPBELOC = 606 ! PBEloc variation with enhanced compatibility with exact exchange integer(c_int), parameter, public :: XC_GGA_K_LKT = 613 ! Luo-Karasiev-Trickey kinetic GGA integer(c_int), parameter, public :: XC_GGA_K_PBE2 = 616 ! Two parameter PBE-like expansion integer(c_int), parameter, public :: XC_GGA_K_VT84F = 619 ! VT84F by Karasiev et al integer(c_int), parameter, public :: XC_GGA_K_LGAP = 620 ! LGAP by Constantin et al integer(c_int), parameter, public :: XC_GGA_X_ITYH_OPTX = 622 ! short-range OPTX functional integer(c_int), parameter, public :: XC_GGA_X_ITYH_PBE = 623 ! short-range PBE functional integer(c_int), parameter, public :: XC_GGA_K_LGAP_GE = 633 ! LGAP_GE by Constantin et al integer(c_int), parameter, public :: XC_GGA_K_TFVW_OPT = 635 ! empirically optimized gamma-TFvW form integer(c_int), parameter, public :: XC_GGA_C_MGGAC = 712 ! beta fitted to LC20 to be used with MGGAC integer(c_int), parameter, public :: XC_HYB_MGGA_X_DLDF = 36 ! Dispersionless Density Functional integer(c_int), parameter, public :: XC_HYB_MGGA_X_MS2H = 224 ! MS2 hybrid exchange of Sun, et al integer(c_int), parameter, public :: XC_HYB_MGGA_X_MN12_SX = 248 ! MN12-SX hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_SCAN0 = 264 ! SCAN hybrid exchange integer(c_int), parameter, public :: XC_HYB_MGGA_X_MN15 = 268 ! MN15 hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_BMK = 279 ! Boese-Martin for kinetics integer(c_int), parameter, public :: XC_HYB_MGGA_X_TAU_HCTH = 282 ! Hybrid version of tau-HCTH integer(c_int), parameter, public :: XC_HYB_MGGA_X_M08_HX = 295 ! M08-HX exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_M08_SO = 296 ! M08-SO exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_M11 = 297 ! M11 hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_REVM11 = 304 ! revM11 hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_REVM06 = 305 ! revised M06 hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_M06_SX = 310 ! M06-SX exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_XC_TPSS0 = 396 ! TPSS hybrid with 25% exact exchange integer(c_int), parameter, public :: XC_HYB_MGGA_XC_B94_HYB = 398 ! Hybrid meta-GGA by Becke integer(c_int), parameter, public :: XC_HYB_MGGA_X_M05 = 438 ! M05 hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_M05_2X = 439 ! M05-2X hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_XC_B88B95 = 440 ! Mixture of B88 with BC95 (B1B95) integer(c_int), parameter, public :: XC_HYB_MGGA_XC_B86B95 = 441 ! Mixture of B86 with BC95 integer(c_int), parameter, public :: XC_HYB_MGGA_XC_PW86B95 = 442 ! Mixture of PW86 with BC95 integer(c_int), parameter, public :: XC_HYB_MGGA_XC_BB1K = 443 ! Mixture of B88 with BC95 from Zhao and Truhlar integer(c_int), parameter, public :: XC_HYB_MGGA_X_M06_HF = 444 ! M06-HF hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_XC_MPW1B95 = 445 ! Mixture of mPW91 with BC95 from Zhao and Truhlar integer(c_int), parameter, public :: XC_HYB_MGGA_XC_MPWB1K = 446 ! Mixture of mPW91 with BC95 for kinetics integer(c_int), parameter, public :: XC_HYB_MGGA_XC_X1B95 = 447 ! Mixture of X with BC95 integer(c_int), parameter, public :: XC_HYB_MGGA_XC_XB1K = 448 ! Mixture of X with BC95 for kinetics integer(c_int), parameter, public :: XC_HYB_MGGA_X_M06 = 449 ! M06 hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_X_M06_2X = 450 ! M06-2X hybrid exchange functional from Minnesota integer(c_int), parameter, public :: XC_HYB_MGGA_XC_PW6B95 = 451 ! Mixture of PW91 with BC95 from Zhao and Truhlar integer(c_int), parameter, public :: XC_HYB_MGGA_XC_PWB6K = 452 ! Mixture of PW91 with BC95 from Zhao and Truhlar for kinetics integer(c_int), parameter, public :: XC_HYB_MGGA_XC_TPSSH = 457 ! TPSS hybrid integer(c_int), parameter, public :: XC_HYB_MGGA_XC_REVTPSSH = 458 ! revTPSS hybrid integer(c_int), parameter, public :: XC_HYB_MGGA_X_MVSH = 474 ! MVSh hybrid integer(c_int), parameter, public :: XC_HYB_MGGA_XC_WB97M_V = 531 ! Mardirossian and Head-Gordon integer(c_int), parameter, public :: XC_HYB_MGGA_XC_B0KCIS = 563 ! Hybrid based on KCIS integer(c_int), parameter, public :: XC_HYB_MGGA_XC_MPW1KCIS = 566 ! Modified Perdew-Wang + KCIS hybrid integer(c_int), parameter, public :: XC_HYB_MGGA_XC_MPWKCIS1K = 567 ! Modified Perdew-Wang + KCIS hybrid with more exact exchange integer(c_int), parameter, public :: XC_HYB_MGGA_XC_PBE1KCIS = 568 ! Perdew-Burke-Ernzerhof + KCIS hybrid integer(c_int), parameter, public :: XC_HYB_MGGA_XC_TPSS1KCIS = 569 ! TPSS hybrid with KCIS correlation integer(c_int), parameter, public :: XC_HYB_MGGA_X_REVSCAN0 = 583 ! revised SCAN hybrid exchange integer(c_int), parameter, public :: XC_HYB_MGGA_XC_B98 = 598 ! Becke 98 integer(c_int), parameter, public :: XC_HYB_MGGA_XC_EDMGGAH = 695 ! Tao 2001 hybrid integer(c_int), parameter, public :: XC_HYB_MGGA_X_JS18 = 705 ! a screened version of TM integer(c_int), parameter, public :: XC_HYB_MGGA_X_PJS18 = 706 ! a screened version of TM integer(c_int), parameter, public :: XC_MGGA_C_DLDF = 37 ! Dispersionless Density Functional integer(c_int), parameter, public :: XC_MGGA_XC_ZLP = 42 ! Zhao, Levy & Parr, Eq. (21) integer(c_int), parameter, public :: XC_MGGA_XC_OTPSS_D = 64 ! oTPSS_D functional of Goerigk and Grimme integer(c_int), parameter, public :: XC_MGGA_C_CS = 72 ! Colle and Salvetti integer(c_int), parameter, public :: XC_MGGA_C_MN12_SX = 73 ! MN12-SX correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_MN12_L = 74 ! MN12-L correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M11_L = 75 ! M11-L correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M11 = 76 ! M11 correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M08_SO = 77 ! M08-SO correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M08_HX = 78 ! M08-HX correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_REVM11 = 172 ! Revised M11 correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_X_LTA = 201 ! Local tau approximation of Ernzerhof & Scuseria integer(c_int), parameter, public :: XC_MGGA_X_TPSS = 202 ! Tao, Perdew, Staroverov & Scuseria exchange integer(c_int), parameter, public :: XC_MGGA_X_M06_L = 203 ! M06-L exchange functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_X_GVT4 = 204 ! GVT4 from Van Voorhis and Scuseria integer(c_int), parameter, public :: XC_MGGA_X_TAU_HCTH = 205 ! tau-HCTH from Boese and Handy integer(c_int), parameter, public :: XC_MGGA_X_BR89 = 206 ! Becke-Roussel 89, gamma = 0.8 integer(c_int), parameter, public :: XC_MGGA_X_BJ06 = 207 ! Becke & Johnson correction to Becke-Roussel 89 integer(c_int), parameter, public :: XC_MGGA_X_TB09 = 208 ! Tran & Blaha correction to Becke & Johnson integer(c_int), parameter, public :: XC_MGGA_X_RPP09 = 209 ! Rasanen, Pittalis, and Proetto correction to Becke & Johnson integer(c_int), parameter, public :: XC_MGGA_X_2D_PRHG07 = 210 ! Pittalis, Rasanen, Helbig, Gross Exchange Functional integer(c_int), parameter, public :: XC_MGGA_X_2D_PRHG07_PRP10 = 211 ! PRGH07 with PRP10 correction integer(c_int), parameter, public :: XC_MGGA_X_REVTPSS = 212 ! revised Tao, Perdew, Staroverov & Scuseria exchange integer(c_int), parameter, public :: XC_MGGA_X_PKZB = 213 ! Perdew, Kurth, Zupan, and Blaha integer(c_int), parameter, public :: XC_MGGA_X_BR89_1 = 214 ! Becke-Roussel 89, gamma = 1.0 integer(c_int), parameter, public :: XC_MGGA_K_PGSL025 = 220 ! PGSL0.25 functional by Constantin, Fabiano, and Della Sala integer(c_int), parameter, public :: XC_MGGA_X_MS0 = 221 ! MS exchange of Sun, Xiao, and Ruzsinszky integer(c_int), parameter, public :: XC_MGGA_X_MS1 = 222 ! MS1 exchange of Sun, et al integer(c_int), parameter, public :: XC_MGGA_X_MS2 = 223 ! MS2 exchange of Sun, et al integer(c_int), parameter, public :: XC_MGGA_X_TH = 225 ! Tsuneda and Hirao integer(c_int), parameter, public :: XC_MGGA_X_M11_L = 226 ! M11-L exchange functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_X_MN12_L = 227 ! MN12-L exchange functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_X_MS2_REV = 228 ! MS2 exchange of Sun, et al with a revised value for c integer(c_int), parameter, public :: XC_MGGA_XC_CC06 = 229 ! Cancio and Chou 2006 integer(c_int), parameter, public :: XC_MGGA_X_MK00 = 230 ! Exchange for accurate virtual orbital energies integer(c_int), parameter, public :: XC_MGGA_C_TPSS = 231 ! Tao, Perdew, Staroverov & Scuseria correlation integer(c_int), parameter, public :: XC_MGGA_C_VSXC = 232 ! VSxc from Van Voorhis and Scuseria (correlation part) integer(c_int), parameter, public :: XC_MGGA_C_M06_L = 233 ! M06-L correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M06_HF = 234 ! M06-HF correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M06 = 235 ! M06 correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M06_2X = 236 ! M06-2X correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M05 = 237 ! M05 correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M05_2X = 238 ! M05-2X correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_PKZB = 239 ! Perdew, Kurth, Zupan, and Blaha integer(c_int), parameter, public :: XC_MGGA_C_BC95 = 240 ! Becke correlation 95 integer(c_int), parameter, public :: XC_MGGA_C_REVTPSS = 241 ! revised TPSS correlation integer(c_int), parameter, public :: XC_MGGA_XC_TPSSLYP1W = 242 ! Functionals fitted for water integer(c_int), parameter, public :: XC_MGGA_X_MK00B = 243 ! Exchange for accurate virtual orbital energies (v. B) integer(c_int), parameter, public :: XC_MGGA_X_BLOC = 244 ! functional with balanced localization integer(c_int), parameter, public :: XC_MGGA_X_MODTPSS = 245 ! Modified Tao, Perdew, Staroverov & Scuseria exchange integer(c_int), parameter, public :: XC_MGGA_C_TPSSLOC = 247 ! Semilocal dynamical correlation integer(c_int), parameter, public :: XC_MGGA_X_MBEEF = 249 ! mBEEF exchange integer(c_int), parameter, public :: XC_MGGA_X_MBEEFVDW = 250 ! mBEEF-vdW exchange integer(c_int), parameter, public :: XC_MGGA_C_TM = 251 ! Tao and Mo 2016 correlation integer(c_int), parameter, public :: XC_MGGA_XC_B97M_V = 254 ! Mardirossian and Head-Gordon integer(c_int), parameter, public :: XC_MGGA_X_JK = 256 ! Jemmer-Knowles meta-GGA exchange integer(c_int), parameter, public :: XC_MGGA_X_MVS = 257 ! MVS exchange of Sun, Perdew, and Ruzsinszky integer(c_int), parameter, public :: XC_MGGA_X_MN15_L = 260 ! MN15-L exhange functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_MN15_L = 261 ! MN15-L correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_X_SCAN = 263 ! SCAN exchange of Sun, Ruzsinszky, and Perdew integer(c_int), parameter, public :: XC_MGGA_C_SCAN = 267 ! SCAN correlation integer(c_int), parameter, public :: XC_MGGA_C_MN15 = 269 ! MN15 correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_X_B00 = 284 ! Becke 2000 integer(c_int), parameter, public :: XC_MGGA_XC_HLE17 = 288 ! high local exchange 2017 integer(c_int), parameter, public :: XC_MGGA_C_SCAN_RVV10 = 292 ! SCAN correlation + rVV10 correlation integer(c_int), parameter, public :: XC_MGGA_X_REVM06_L = 293 ! revised M06-L exchange functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_REVM06_L = 294 ! Revised M06-L correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_X_RTPSS = 299 ! Revised TPSS exchange by Garza, Bell and Head-Gordon integer(c_int), parameter, public :: XC_MGGA_X_MS2B = 300 ! MS2beta exchange by Furness and Sun integer(c_int), parameter, public :: XC_MGGA_X_MS2BS = 301 ! MS2beta* exchange by Furness and Sun integer(c_int), parameter, public :: XC_MGGA_X_MVSB = 302 ! MVSBeta exchange of Furness and Sun integer(c_int), parameter, public :: XC_MGGA_X_MVSBS = 303 ! MVSBeta* exchange of Furness and Sun integer(c_int), parameter, public :: XC_MGGA_C_REVM06 = 306 ! Revised M06 correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_M06_SX = 311 ! M06-SX correlation functional from Minnesota integer(c_int), parameter, public :: XC_MGGA_C_B94 = 397 ! Meta-GGA correlation by Becke integer(c_int), parameter, public :: XC_MGGA_X_RSCAN = 493 ! Regularized SCAN exchange integer(c_int), parameter, public :: XC_MGGA_C_RSCAN = 494 ! Regularized SCAN correlation integer(c_int), parameter, public :: XC_MGGA_X_R2SCAN = 497 ! Re-regularized SCAN exchange integer(c_int), parameter, public :: XC_MGGA_C_R2SCAN = 498 ! Re-regularized SCAN correlation integer(c_int), parameter, public :: XC_MGGA_X_TM = 540 ! Tao and Mo 2016 exchange integer(c_int), parameter, public :: XC_MGGA_X_VT84 = 541 ! meta-GGA version of VT{8,4} GGA integer(c_int), parameter, public :: XC_MGGA_X_SA_TPSS = 542 ! TPSS with correct surface asymptotics integer(c_int), parameter, public :: XC_MGGA_K_PC07 = 543 ! Perdew and Constantin 2007 integer(c_int), parameter, public :: XC_MGGA_C_KCIS = 562 ! Krieger, Chen, Iafrate, and Savin integer(c_int), parameter, public :: XC_MGGA_XC_LP90 = 564 ! Lee & Parr, Eq. (56) integer(c_int), parameter, public :: XC_MGGA_C_B88 = 571 ! Meta-GGA correlation by Becke integer(c_int), parameter, public :: XC_MGGA_X_GX = 575 ! GX functional of Loos integer(c_int), parameter, public :: XC_MGGA_X_PBE_GX = 576 ! PBE-GX functional of Loos integer(c_int), parameter, public :: XC_MGGA_X_REVSCAN = 581 ! revised SCAN integer(c_int), parameter, public :: XC_MGGA_C_REVSCAN = 582 ! revised SCAN correlation integer(c_int), parameter, public :: XC_MGGA_C_SCAN_VV10 = 584 ! SCAN correlation + VV10 correlation integer(c_int), parameter, public :: XC_MGGA_C_REVSCAN_VV10 = 585 ! revised SCAN correlation integer(c_int), parameter, public :: XC_MGGA_X_BR89_EXPLICIT = 586 ! Becke-Roussel 89 with an explicit inversion of x(y), gamma = 0.8 integer(c_int), parameter, public :: XC_MGGA_X_BR89_EXPLICIT_1 = 602 ! Becke-Roussel 89 with an explicit inversion of x(y), gamma = 1.0 integer(c_int), parameter, public :: XC_MGGA_X_REGTPSS = 603 ! Regularized TPSS integer(c_int), parameter, public :: XC_MGGA_X_2D_JS17 = 609 ! JS17 meta-GGA for 2D integer(c_int), parameter, public :: XC_MGGA_K_L04 = 617 ! L0.4 by Laricchia et al integer(c_int), parameter, public :: XC_MGGA_K_L06 = 618 ! L0.6 by Laricchia et al integer(c_int), parameter, public :: XC_MGGA_K_RDA = 621 ! RDA by Karasiev et al integer(c_int), parameter, public :: XC_MGGA_K_GEA2 = 627 ! Second-order gradient expansion integer(c_int), parameter, public :: XC_MGGA_K_GEA4 = 628 ! Fourth-order gradient expansion integer(c_int), parameter, public :: XC_MGGA_K_CSK1 = 629 ! mGGA-rev functional by Cancio, Stewart, and Kuna (a=1) integer(c_int), parameter, public :: XC_MGGA_K_CSK4 = 630 ! mGGA-rev functional by Cancio, Stewart, and Kuna (a=4) integer(c_int), parameter, public :: XC_MGGA_K_CSK_LOC1 = 631 ! mGGAloc-rev functional by Cancio, Stewart, and Kuna (a=1) integer(c_int), parameter, public :: XC_MGGA_K_CSK_LOC4 = 632 ! mGGAloc-rev functional by Cancio, Stewart, and Kuna (a=4) integer(c_int), parameter, public :: XC_MGGA_K_PC07_OPT = 634 ! Reoptimized version by Mejia-Rodriguez and Trickey integer(c_int), parameter, public :: XC_MGGA_C_KCISK = 638 ! Krieger, Chen, and Kurth integer(c_int), parameter, public :: XC_MGGA_X_TLDA = 685 ! LDA-type exchange with tau-dependent potential integer(c_int), parameter, public :: XC_MGGA_X_EDMGGA = 686 ! Tao 2001 integer(c_int), parameter, public :: XC_MGGA_X_GDME_NV = 687 ! Generalized density-matrix with a=1/2 integer(c_int), parameter, public :: XC_MGGA_X_RLDA = 688 ! Reparametrized local-density approximation integer(c_int), parameter, public :: XC_MGGA_X_GDME_0 = 689 ! Generalized density-matrix with a=0 integer(c_int), parameter, public :: XC_MGGA_X_GDME_KOS = 690 ! Generalized density-matrix with a=0.00638 integer(c_int), parameter, public :: XC_MGGA_X_GDME_VT = 691 ! Varied-terms (VT) mGGA of Koehl, Odom, and Scuseria integer(c_int), parameter, public :: XC_MGGA_X_REVTM = 693 ! revised Tao and Mo 2016 exchange integer(c_int), parameter, public :: XC_MGGA_C_REVTM = 694 ! revised Tao and Mo 2016 correlation integer(c_int), parameter, public :: XC_MGGA_X_MBRXC_BG = 696 ! Modified Becke-Roussel for band gaps - cuspless hole integer(c_int), parameter, public :: XC_MGGA_X_MBRXH_BG = 697 ! Modified Becke-Roussel for band gaps - hydrogen hole integer(c_int), parameter, public :: XC_MGGA_X_HLTA = 698 ! Half-and-half by Lehtola and Marques integer(c_int), parameter, public :: XC_MGGA_C_HLTAPW = 699 ! Meta-GGAized PW integer(c_int), parameter, public :: XC_MGGA_X_SCANL = 700 ! Deorbitalized SCAN exchange integer(c_int), parameter, public :: XC_MGGA_X_REVSCANL = 701 ! Deorbitalized revSCAN exchange integer(c_int), parameter, public :: XC_MGGA_C_SCANL = 702 ! SCAN correlation integer(c_int), parameter, public :: XC_MGGA_C_SCANL_RVV10 = 703 ! SCAN correlation + rVV10 correlation integer(c_int), parameter, public :: XC_MGGA_C_SCANL_VV10 = 704 ! SCAN correlation + VV10 correlation integer(c_int), parameter, public :: XC_MGGA_X_TASK = 707 ! TASK exchange of Aschebrock and Kuemmel integer(c_int), parameter, public :: XC_MGGA_X_MGGAC = 711 ! MGGAC of Patras et al integer(c_int), parameter, public :: XC_MGGA_X_MBR = 716 ! modified Becke-Roussel by Patra et al integer(c_int), parameter, public :: XC_MGGA_X_R2SCANL = 718 ! Deorbitalized r^2SCAN exchange integer(c_int), parameter, public :: XC_MGGA_C_R2SCANL = 719 ! Deorbitalized r^2SCAN correlation ! These are old names kept for compatibility integer(c_int), parameter, public :: & XC_LDA_X_1D = 21, & XC_GGA_X_BGCP = 38, & XC_GGA_C_BGCP = 39, & XC_GGA_C_BCGP = 39, & XC_GGA_C_VPBE = 83, & XC_GGA_XC_LB = 160, & XC_MGGA_C_CC06 = 229, & XC_GGA_K_ABSR1 = 506, & XC_GGA_K_ABSR2 = 507, & XC_LDA_C_LP_A = 547, & XC_LDA_C_LP_B = 548, & XC_MGGA_C_LP90 = 564 !---------------------------------------------------------------- interface subroutine xc_version(major, minor, micro) bind(c) import integer(c_int), intent(out) :: major, minor, micro end subroutine xc_version type(c_ptr) function xc_version_string() bind(c) import end function xc_version_string type(c_ptr) function xc_reference() bind(c) import end function xc_reference type(c_ptr) function xc_reference_doi() bind(c) import end function xc_reference_doi end interface !---------------------------------------------------------------- type :: xc_f90_func_info_t private type(c_ptr) :: ptr = C_NULL_PTR end type xc_f90_func_info_t interface integer(c_int) function xc_func_info_get_number(info) bind(c) import type(c_ptr), value :: info end function xc_func_info_get_number integer(c_int) function xc_func_info_get_kind(info) bind(c) import type(c_ptr), value :: info end function xc_func_info_get_kind type(c_ptr) function xc_func_info_get_name(info) bind(c) import type(c_ptr), value :: info end function xc_func_info_get_name integer(c_int) function xc_func_info_get_family(info) bind(c) import type(c_ptr), value :: info end function xc_func_info_get_family integer(c_int) function xc_func_info_get_flags(info) bind(c) import type(c_ptr), value :: info end function xc_func_info_get_flags type(c_ptr) function xc_func_info_get_references(info, number) bind(c) import type(c_ptr), value :: info integer(c_int), value :: number end function xc_func_info_get_references integer(c_int) function xc_func_info_get_n_ext_params(info) bind(c) import type(c_ptr), value :: info end function xc_func_info_get_n_ext_params type(c_ptr) function xc_func_info_get_ext_params_name(info, number) bind(c) import type(c_ptr), value :: info integer(c_int), value :: number end function xc_func_info_get_ext_params_name type(c_ptr) function xc_func_info_get_ext_params_description(info, number) bind(c) import type(c_ptr), value :: info integer(c_int), value :: number end function xc_func_info_get_ext_params_description real(c_double) function xc_func_info_get_ext_params_default_value(info, number) bind(c) import type(c_ptr), value :: info integer(c_int), value :: number end function xc_func_info_get_ext_params_default_value end interface !---------------------------------------------------------------- type :: xc_f90_func_reference_t private type(c_ptr) :: ptr = C_NULL_PTR end type xc_f90_func_reference_t interface type(c_ptr) function xc_func_reference_get_ref(reference) bind(c) import type(c_ptr), value :: reference end function xc_func_reference_get_ref type(c_ptr) function xc_func_reference_get_doi(reference) bind(c) import type(c_ptr), value :: reference end function xc_func_reference_get_doi type(c_ptr) function xc_func_reference_get_bibtex(reference) bind(c) import type(c_ptr), value :: reference end function xc_func_reference_get_bibtex end interface !---------------------------------------------------------------- type :: xc_f90_func_t private type(c_ptr) :: ptr = C_NULL_PTR end type xc_f90_func_t interface type(c_ptr) function xc_func_alloc() bind(c) import end function xc_func_alloc integer(c_int) function xc_func_init(p, functional, nspin) bind(c) import type(c_ptr), value :: p integer(c_int), value :: functional, nspin end function xc_func_init subroutine xc_func_end(p) bind(c) import type(c_ptr), value :: p end subroutine xc_func_end subroutine xc_func_free(p) bind(c) import type(c_ptr), value :: p end subroutine xc_func_free type(c_ptr) function xc_func_get_info(p) bind(c) import type(c_ptr), value :: p end function xc_func_get_info type(c_ptr) function xc_functional_get_name(number) bind(c) import integer(c_int), value :: number end function xc_functional_get_name integer(c_int) function xc_functional_get_number(func_string) bind(c) import character(kind=c_char), intent(in) :: func_string(*) end function xc_functional_get_number integer(c_int) function xc_family_from_id(id, family, number) bind(c) import integer(c_int), value :: id type(c_ptr), value :: family, number end function xc_family_from_id integer(c_int) function xc_f90_number_of_functionals() bind(c, name="xc_number_of_functionals") import end function xc_f90_number_of_functionals integer(c_int) function xc_f90_maximum_name_length() bind(c, name="xc_maximum_name_length") import end function xc_f90_maximum_name_length subroutine xc_f90_available_functional_numbers(list) bind(c, name="xc_available_functional_numbers") import integer(c_int), intent(out) :: list(*) end subroutine xc_f90_available_functional_numbers subroutine xc_available_functional_names(list) bind(c) import type(c_ptr) :: list(*) end subroutine xc_available_functional_names subroutine xc_func_set_dens_threshold(p, dens_threshold) bind(c) import type(c_ptr), value :: p real(c_double), value :: dens_threshold end subroutine xc_func_set_dens_threshold subroutine xc_func_set_zeta_threshold(p, zeta_threshold) bind(c) import type(c_ptr), value :: p real(c_double), value :: zeta_threshold end subroutine xc_func_set_zeta_threshold subroutine xc_func_set_sigma_threshold(p, sigma_threshold) bind(c) import type(c_ptr), value :: p real(c_double), value :: sigma_threshold end subroutine xc_func_set_sigma_threshold subroutine xc_func_set_tau_threshold(p, tau_threshold) bind(c) import type(c_ptr), value :: p real(c_double), value :: tau_threshold end subroutine xc_func_set_tau_threshold subroutine xc_func_set_ext_params(p, ext_params) bind(c) import type(c_ptr), value :: p real(c_double), intent(in) :: ext_params(*) end subroutine xc_func_set_ext_params subroutine xc_func_set_ext_params_name(p, name, par) bind(c) import type(c_ptr), value :: p character(kind=c_char), intent(in) :: name(*) real(c_double), value :: par end subroutine xc_func_set_ext_params_name end interface ! LDAs !---------------------------------------------------------------- interface subroutine xc_lda(p, np, rho, zk, vrho, v2rho2, v3rho3, v4rho4) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*), vrho(*), v2rho2(*), v3rho3(*), v4rho4(*) end subroutine xc_lda subroutine xc_lda_exc(p, np, rho, zk) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*) end subroutine xc_lda_exc subroutine xc_lda_exc_vxc(p, np, rho, zk, vrho) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*), vrho(*) end subroutine xc_lda_exc_vxc subroutine xc_lda_exc_vxc_fxc(p, np, rho, zk, vrho, v2rho2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*), vrho(*), v2rho2(*) end subroutine xc_lda_exc_vxc_fxc subroutine xc_lda_exc_vxc_fxc_kxc(p, np, rho, zk, vrho, v2rho2, v3rho3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*), vrho(*), v2rho2(*), v3rho3(*) end subroutine xc_lda_exc_vxc_fxc_kxc subroutine xc_lda_vxc(p, np, rho, vrho) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: vrho(*) end subroutine xc_lda_vxc subroutine xc_lda_vxc_fxc(p, np, rho, vrho, v2rho2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: vrho(*), v2rho2(*) end subroutine xc_lda_vxc_fxc subroutine xc_lda_vxc_fxc_kxc(p, np, rho, vrho, v2rho2, v3rho3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: vrho(*), v2rho2(*), v3rho3(*) end subroutine xc_lda_vxc_fxc_kxc subroutine xc_lda_fxc(p, np, rho, v2rho2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: v2rho2(*) end subroutine xc_lda_fxc subroutine xc_lda_kxc(p, np, rho, v3rho3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: v3rho3(*) end subroutine xc_lda_kxc subroutine xc_lda_lxc(p, np, rho, v4rho4) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: v4rho4(*) end subroutine xc_lda_lxc end interface ! GGAs !---------------------------------------------------------------- interface subroutine xc_gga(p, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3, & v4rho4, v4rho3sigma, v4rho2sigma2, v4rhosigma3, v4sigma4 & ) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rhosigma2(*), v3sigma3(*) real(c_double), intent(out) :: v4rho4(*), v4rho3sigma(*), v4rho2sigma2(*), v4rhosigma3(*), v4sigma4(*) end subroutine xc_gga subroutine xc_gga_exc(p, np, rho, sigma, zk) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*) end subroutine xc_gga_exc subroutine xc_gga_exc_vxc(p, np, rho, sigma, zk, vrho, vsigma) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*) end subroutine xc_gga_exc_vxc subroutine xc_gga_exc_vxc_fxc(p, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) end subroutine xc_gga_exc_vxc_fxc subroutine xc_gga_exc_vxc_fxc_kxc(p, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rhosigma2(*), v3sigma3(*) end subroutine xc_gga_exc_vxc_fxc_kxc subroutine xc_gga_vxc(p, np, rho, sigma, vrho, vsigma) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: vrho(*), vsigma(*) end subroutine xc_gga_vxc subroutine xc_gga_vxc_fxc(p, np, rho, sigma, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) end subroutine xc_gga_vxc_fxc subroutine xc_gga_vxc_fxc_kxc(p, np, rho, sigma, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rhosigma2(*), v3sigma3(*) end subroutine xc_gga_vxc_fxc_kxc subroutine xc_gga_fxc(p, np, rho, sigma, v2rho2, v2rhosigma, v2sigma2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) end subroutine xc_gga_fxc subroutine xc_gga_kxc(p, np, rho, sigma, v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rhosigma2(*), v3sigma3(*) end subroutine xc_gga_kxc subroutine xc_gga_lxc(p, np, rho, sigma, v4rho4, v4rho3sigma, v4rho2sigma2, v4rhosigma3, v4sigma4) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: v4rho4(*), v4rho3sigma(*), v4rho2sigma2(*), v4rhosigma3(*), v4sigma4(*) end subroutine xc_gga_lxc end interface interface real(c_double) function xc_gga_ak13_get_asymptotic(homo) bind(c) import real(c_double), value :: homo end function xc_gga_ak13_get_asymptotic end interface interface real(c_double) function xc_hyb_exx_coef(p) bind(c) import type(c_ptr), value :: p end function xc_hyb_exx_coef subroutine xc_hyb_cam_coef(p, omega, alpha, beta) bind(c) import type(c_ptr), value :: p real(c_double), intent(out) :: omega, alpha, beta end subroutine xc_hyb_cam_coef subroutine xc_nlc_coef(p, nlc_b, nlc_c) bind(c) import type(c_ptr), value :: p real(c_double), intent(out) :: nlc_b, nlc_c end subroutine xc_nlc_coef end interface ! the meta-GGAs !---------------------------------------------------------------- interface subroutine xc_mgga(p, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3, & v4rho4, v4rho3sigma, v4rho3lapl, v4rho3tau, v4rho2sigma2, v4rho2sigmalapl, & v4rho2sigmatau, v4rho2lapl2, v4rho2lapltau, v4rho2tau2, v4rhosigma3, & v4rhosigma2lapl, v4rhosigma2tau, v4rhosigmalapl2, v4rhosigmalapltau, & v4rhosigmatau2, v4rholapl3, v4rholapl2tau, v4rholapltau2, v4rhotau3, v4sigma4, & v4sigma3lapl, v4sigma3tau, v4sigma2lapl2, v4sigma2lapltau, v4sigma2tau2, & v4sigmalapl3, v4sigmalapl2tau, v4sigmalapltau2, v4sigmatau3, v4lapl4, & v4lapl3tau, v4lapl2tau2, v4lapltau3, v4tau4 & ) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rho2lapl(*), v3rho2tau(*), & v3rhosigma2(*), v3rhosigmalapl(*), v3rhosigmatau(*), v3rholapl2(*), & v3rholapltau(*), v3rhotau2(*), v3sigma3(*), v3sigma2lapl(*), v3sigma2tau(*), & v3sigmalapl2(*), v3sigmalapltau(*), v3sigmatau2(*), v3lapl3(*), v3lapl2tau(*), & v3lapltau2(*), v3tau3(*) real(c_double), intent(out) :: & v4rho4(*), v4rho3sigma(*), v4rho3lapl(*), v4rho3tau(*), v4rho2sigma2(*), v4rho2sigmalapl(*), & v4rho2sigmatau(*), v4rho2lapl2(*), v4rho2lapltau(*), v4rho2tau2(*), v4rhosigma3(*), & v4rhosigma2lapl(*), v4rhosigma2tau(*), v4rhosigmalapl2(*), v4rhosigmalapltau(*), & v4rhosigmatau2(*), v4rholapl3(*), v4rholapl2tau(*), v4rholapltau2(*), v4rhotau3(*), v4sigma4(*), & v4sigma3lapl(*), v4sigma3tau(*), v4sigma2lapl2(*), v4sigma2lapltau(*), v4sigma2tau2(*), & v4sigmalapl3(*), v4sigmalapl2tau(*), v4sigmalapltau2(*), v4sigmatau3(*), v4lapl4(*), & v4lapl3tau(*), v4lapl2tau2(*), v4lapltau3(*), v4tau4(*) end subroutine xc_mgga subroutine xc_mgga_exc(p, np, rho, sigma, lapl, tau, zk) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*) end subroutine xc_mgga_exc subroutine xc_mgga_exc_vxc(p, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*), vlapl(*), vtau(*) end subroutine xc_mgga_exc_vxc subroutine xc_mgga_exc_vxc_fxc(p, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) end subroutine xc_mgga_exc_vxc_fxc subroutine xc_mgga_exc_vxc_fxc_kxc(p, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rho2lapl(*), v3rho2tau(*), & v3rhosigma2(*), v3rhosigmalapl(*), v3rhosigmatau(*), v3rholapl2(*), & v3rholapltau(*), v3rhotau2(*), v3sigma3(*), v3sigma2lapl(*), v3sigma2tau(*), & v3sigmalapl2(*), v3sigmalapltau(*), v3sigmatau2(*), v3lapl3(*), v3lapl2tau(*), & v3lapltau2(*), v3tau3(*) end subroutine xc_mgga_exc_vxc_fxc_kxc subroutine xc_mgga_vxc(p, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: vrho(*), vsigma(*), vlapl(*), vtau(*) end subroutine xc_mgga_vxc subroutine xc_mgga_vxc_fxc(p, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) end subroutine xc_mgga_vxc_fxc subroutine xc_mgga_vxc_fxc_kxc(p, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rho2lapl(*), v3rho2tau(*), & v3rhosigma2(*), v3rhosigmalapl(*), v3rhosigmatau(*), v3rholapl2(*), & v3rholapltau(*), v3rhotau2(*), v3sigma3(*), v3sigma2lapl(*), v3sigma2tau(*), & v3sigmalapl2(*), v3sigmalapltau(*), v3sigmatau2(*), v3lapl3(*), v3lapl2tau(*), & v3lapltau2(*), v3tau3(*) end subroutine xc_mgga_vxc_fxc_kxc subroutine xc_mgga_fxc(p, np, rho, sigma, lapl, tau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) end subroutine xc_mgga_fxc subroutine xc_mgga_kxc(p, np, rho, sigma, lapl, tau, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rho2lapl(*), v3rho2tau(*), & v3rhosigma2(*), v3rhosigmalapl(*), v3rhosigmatau(*), v3rholapl2(*), & v3rholapltau(*), v3rhotau2(*), v3sigma3(*), v3sigma2lapl(*), v3sigma2tau(*), & v3sigmalapl2(*), v3sigmalapltau(*), v3sigmatau2(*), v3lapl3(*), v3lapl2tau(*), & v3lapltau2(*), v3tau3(*) end subroutine xc_mgga_kxc subroutine xc_mgga_lxc(p, np, rho, sigma, lapl, tau, & v4rho4, v4rho3sigma, v4rho3lapl, v4rho3tau, v4rho2sigma2, v4rho2sigmalapl, & v4rho2sigmatau, v4rho2lapl2, v4rho2lapltau, v4rho2tau2, v4rhosigma3, & v4rhosigma2lapl, v4rhosigma2tau, v4rhosigmalapl2, v4rhosigmalapltau, & v4rhosigmatau2, v4rholapl3, v4rholapl2tau, v4rholapltau2, v4rhotau3, v4sigma4, & v4sigma3lapl, v4sigma3tau, v4sigma2lapl2, v4sigma2lapltau, v4sigma2tau2, & v4sigmalapl3, v4sigmalapl2tau, v4sigmalapltau2, v4sigmatau3, v4lapl4, & v4lapl3tau, v4lapl2tau2, v4lapltau3, v4tau4 & ) bind(c) import type(c_ptr), value :: p integer(c_size_t), value :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: & v4rho4(*), v4rho3sigma(*), v4rho3lapl(*), v4rho3tau(*), v4rho2sigma2(*), v4rho2sigmalapl(*), & v4rho2sigmatau(*), v4rho2lapl2(*), v4rho2lapltau(*), v4rho2tau2(*), v4rhosigma3(*), & v4rhosigma2lapl(*), v4rhosigma2tau(*), v4rhosigmalapl2(*), v4rhosigmalapltau(*), & v4rhosigmatau2(*), v4rholapl3(*), v4rholapl2tau(*), v4rholapltau2(*), v4rhotau3(*), v4sigma4(*), & v4sigma3lapl(*), v4sigma3tau(*), v4sigma2lapl2(*), v4sigma2lapltau(*), v4sigma2tau2(*), & v4sigmalapl3(*), v4sigmalapl2tau(*), v4sigmalapltau2(*), v4sigmatau3(*), v4lapl4(*), & v4lapl3tau(*), v4lapl2tau2(*), v4lapltau3(*), v4tau4(*) end subroutine xc_mgga_lxc end interface contains !---------------------------------------------------------------- subroutine xc_f90_version(major, minor, micro) integer(c_int), intent(out) :: major, minor, micro call xc_version(major, minor, micro) end subroutine xc_f90_version subroutine xc_f90_version_string(version) character(len=*), intent(out) :: version type(c_ptr) :: c_version c_version = xc_version_string() call c_to_f_string_ptr(c_version, version) end subroutine xc_f90_version_string subroutine xc_f90_reference(ref) character(len=*), intent(out) :: ref type(c_ptr) :: c_ref c_ref = xc_reference() call c_to_f_string_ptr(c_ref, ref) end subroutine xc_f90_reference subroutine xc_f90_reference_doi(doi) character(len=*), intent(out) :: doi type(c_ptr) :: c_doi c_doi = xc_reference_doi() call c_to_f_string_ptr(c_doi, doi) end subroutine xc_f90_reference_doi !---------------------------------------------------------------- integer(c_int) function xc_f90_func_info_get_number(info) result(number) type(xc_f90_func_info_t), intent(in) :: info number = xc_func_info_get_number(info%ptr) end function xc_f90_func_info_get_number integer(c_int) function xc_f90_func_info_get_kind(info) result(kind) type(xc_f90_func_info_t), intent(in) :: info kind = xc_func_info_get_kind(info%ptr) end function xc_f90_func_info_get_kind character(len=128) function xc_f90_func_info_get_name(info) result(name) type(xc_f90_func_info_t), intent(in) :: info call c_to_f_string_ptr(xc_func_info_get_name(info%ptr), name) end function xc_f90_func_info_get_name integer(c_int) function xc_f90_func_info_get_family(info) result(family) type(xc_f90_func_info_t), intent(in) :: info family = xc_func_info_get_family(info%ptr) end function xc_f90_func_info_get_family integer(c_int) function xc_f90_func_info_get_flags(info) result(flags) type(xc_f90_func_info_t), intent(in) :: info flags = xc_func_info_get_flags(info%ptr) end function xc_f90_func_info_get_flags type(xc_f90_func_reference_t) function xc_f90_func_info_get_references(info, number) result(reference) type(xc_f90_func_info_t), intent(in) :: info integer(c_int), intent(inout) :: number ! number of the reference. Must be 0 in the first call type(c_ptr) :: next_ref reference%ptr = xc_func_info_get_references(info%ptr, number) next_ref = xc_func_info_get_references(info%ptr, INT(number + 1, c_int)) if (c_associated(next_ref)) then number = number + 1 else number = -1 end if end function xc_f90_func_info_get_references integer(c_int) function xc_f90_func_info_get_n_ext_params(info) result(n_ext_params) type(xc_f90_func_info_t), intent(in) :: info n_ext_params = xc_func_info_get_n_ext_params(info%ptr) end function xc_f90_func_info_get_n_ext_params character(len=128) function xc_f90_func_info_get_ext_params_name(info, number) result(name) type(xc_f90_func_info_t), intent(in) :: info integer(c_int), intent(in) :: number call c_to_f_string_ptr(xc_func_info_get_ext_params_name(info%ptr, number), name) end function xc_f90_func_info_get_ext_params_name character(len=128) function xc_f90_func_info_get_ext_params_description(info, number) result(description) type(xc_f90_func_info_t), intent(in) :: info integer(c_int), intent(in) :: number call c_to_f_string_ptr(xc_func_info_get_ext_params_description(info%ptr, number), description) end function xc_f90_func_info_get_ext_params_description real(c_double) function xc_f90_func_info_get_ext_params_default_value(info, number) result(val) type(xc_f90_func_info_t), intent(in) :: info integer(c_int), intent(in) :: number val = xc_func_info_get_ext_params_default_value(info%ptr, number) end function xc_f90_func_info_get_ext_params_default_value !---------------------------------------------------------------- character(len=1024) function xc_f90_func_reference_get_ref(reference) result(ref) type(xc_f90_func_reference_t), intent(in) :: reference call c_to_f_string_ptr(xc_func_reference_get_ref(reference%ptr), ref) end function xc_f90_func_reference_get_ref character(len=1024) function xc_f90_func_reference_get_doi(reference) result(doi) type(xc_f90_func_reference_t), intent(in) :: reference call c_to_f_string_ptr(xc_func_reference_get_doi(reference%ptr), doi) end function xc_f90_func_reference_get_doi character(len=1024) function xc_f90_func_reference_get_bibtex(reference) result(bibtex) type(xc_f90_func_reference_t), intent(in) :: reference call c_to_f_string_ptr(xc_func_reference_get_bibtex(reference%ptr), bibtex) end function xc_f90_func_reference_get_bibtex !---------------------------------------------------------------- subroutine xc_f90_func_init(p, functional, nspin, err) type(xc_f90_func_t), intent(inout) :: p integer(c_int), intent(in) :: functional integer(c_int), intent(in) :: nspin integer(c_int), optional, intent(out) :: err integer(c_int) :: ierr p%ptr = xc_func_alloc() ierr = xc_func_init(p%ptr, functional, nspin) if(present(err)) err = ierr end subroutine xc_f90_func_init subroutine xc_f90_func_end(p) type(xc_f90_func_t), intent(inout) :: p call xc_func_end(p%ptr) call xc_func_free(p%ptr) end subroutine xc_f90_func_end type(xc_f90_func_info_t) function xc_f90_func_get_info(p) result(info) type(xc_f90_func_t), intent(in) :: p info%ptr = xc_func_get_info(p%ptr) end function xc_f90_func_get_info character(len=128) function xc_f90_functional_get_name(number) result(name) integer(c_int), intent(in) :: number call c_to_f_string_ptr(xc_functional_get_name(number), name) end function xc_f90_functional_get_name integer(c_int) function xc_f90_functional_get_number(func_string) result(number) character(len=*), intent(in) :: func_string number = xc_functional_get_number(f_to_c_string(func_string)) end function xc_f90_functional_get_number integer(c_int) function xc_f90_family_from_id(id, family, number) integer(c_int), intent(in) :: id integer(c_int), intent(out), optional, target :: family, number type(c_ptr) c_family, c_number integer(c_int), pointer :: f_family, f_number if (present(family)) then f_family => family call c_f_pointer(c_family, f_family) else c_family = C_NULL_PTR end if if (present(number)) then f_number => number call c_f_pointer(c_number, f_number) else c_number = C_NULL_PTR end if xc_f90_family_from_id = xc_family_from_id(id, c_family, c_number) end function xc_f90_family_from_id subroutine xc_f90_available_functional_names(list) character(len=*), intent(out) :: list(*) integer(c_int) :: n, i, maxlen character(kind=c_char), allocatable, target :: names(:,:) type(c_ptr), allocatable :: c_list(:) n = xc_f90_number_of_functionals() maxlen = xc_f90_maximum_name_length() allocate(names(maxlen, n)) allocate(c_list(n)) do i = 1, n c_list(i) = c_loc(names(1,i)) end do call xc_available_functional_names(c_list) do i = 1, n call c_to_f_string_ptr(c_list(i), list(i)) end do deallocate(c_list) deallocate(names) end subroutine xc_f90_available_functional_names subroutine xc_f90_func_set_dens_threshold(p, dens_threshold) type(xc_f90_func_t), intent(in) :: p real(c_double), intent(in) :: dens_threshold call xc_func_set_dens_threshold(p%ptr, dens_threshold) end subroutine xc_f90_func_set_dens_threshold subroutine xc_f90_func_set_zeta_threshold(p, zeta_threshold) type(xc_f90_func_t), intent(in) :: p real(c_double), intent(in) :: zeta_threshold call xc_func_set_zeta_threshold(p%ptr, zeta_threshold) end subroutine xc_f90_func_set_zeta_threshold subroutine xc_f90_func_set_sigma_threshold(p, sigma_threshold) type(xc_f90_func_t), intent(in) :: p real(c_double), intent(in) :: sigma_threshold call xc_func_set_sigma_threshold(p%ptr, sigma_threshold) end subroutine xc_f90_func_set_sigma_threshold subroutine xc_f90_func_set_tau_threshold(p, tau_threshold) type(xc_f90_func_t), intent(in) :: p real(c_double), intent(in) :: tau_threshold call xc_func_set_tau_threshold(p%ptr, tau_threshold) end subroutine xc_f90_func_set_tau_threshold subroutine xc_f90_func_set_ext_params(p, ext_params) type(xc_f90_func_t), intent(in) :: p real(c_double), intent(in) :: ext_params(*) call xc_func_set_ext_params(p%ptr, ext_params) end subroutine xc_f90_func_set_ext_params subroutine xc_f90_func_set_ext_params_name(p, name, par) type(xc_f90_func_t), intent(in) :: p character(len=*), intent(in) :: name real(c_double), intent(in) :: par call xc_func_set_ext_params_name(p%ptr, f_to_c_string(name), par) end subroutine xc_f90_func_set_ext_params_name ! LDAs !---------------------------------------------------------------- subroutine xc_f90_lda(p, np, rho, zk, vrho, v2rho2, v3rho3, v4rho4) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*), vrho(*), v2rho2(*), v3rho3(*), v4rho4(*) call xc_lda(p%ptr, np, rho, zk, vrho, v2rho2, v3rho3, v4rho4) end subroutine xc_f90_lda subroutine xc_f90_lda_exc(p, np, rho, zk) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*) call xc_lda_exc(p%ptr, np, rho, zk) end subroutine xc_f90_lda_exc subroutine xc_f90_lda_exc_vxc(p, np, rho, zk, vrho) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*), vrho(*) call xc_lda_exc_vxc(p%ptr, np, rho, zk, vrho) end subroutine xc_f90_lda_exc_vxc subroutine xc_f90_lda_exc_vxc_fxc(p, np, rho, zk, vrho, v2rho2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*), vrho(*), v2rho2(*) call xc_lda_exc_vxc_fxc(p%ptr, np, rho, zk, vrho, v2rho2) end subroutine xc_f90_lda_exc_vxc_fxc subroutine xc_f90_lda_exc_vxc_fxc_kxc(p, np, rho, zk, vrho, v2rho2, v3rho3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: zk(*), vrho(*), v2rho2(*), v3rho3(*) call xc_lda_exc_vxc_fxc_kxc(p%ptr, np, rho, zk, vrho, v2rho2, v3rho3) end subroutine xc_f90_lda_exc_vxc_fxc_kxc subroutine xc_f90_lda_vxc(p, np, rho, vrho) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: vrho(*) call xc_lda_vxc(p%ptr, np, rho, vrho) end subroutine xc_f90_lda_vxc subroutine xc_f90_lda_vxc_fxc(p, np, rho, vrho, v2rho2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: vrho(*), v2rho2(*) call xc_lda_vxc_fxc(p%ptr, np, rho, vrho, v2rho2) end subroutine xc_f90_lda_vxc_fxc subroutine xc_f90_lda_vxc_fxc_kxc(p, np, rho, vrho, v2rho2, v3rho3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: vrho(*), v2rho2(*), v3rho3(*) call xc_lda_vxc_fxc_kxc(p%ptr, np, rho, vrho, v2rho2, v3rho3) end subroutine xc_f90_lda_vxc_fxc_kxc subroutine xc_f90_lda_fxc(p, np, rho, v2rho2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: v2rho2(*) call xc_lda_fxc(p%ptr, np, rho, v2rho2) end subroutine xc_f90_lda_fxc subroutine xc_f90_lda_kxc(p, np, rho, v3rho3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: v3rho3(*) call xc_lda_kxc(p%ptr, np, rho, v3rho3) end subroutine xc_f90_lda_kxc subroutine xc_f90_lda_lxc(p, np, rho, v4rho4) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*) real(c_double), intent(out) :: v4rho4(*) call xc_lda_lxc(p%ptr, np, rho, v4rho4) end subroutine xc_f90_lda_lxc ! GGAs !---------------------------------------------------------------- subroutine xc_f90_gga(p, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3, & v4rho4, v4rho3sigma, v4rho2sigma2, v4rhosigma3, v4sigma4 & ) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rhosigma2(*), v3sigma3(*) real(c_double), intent(out) :: v4rho4(*), v4rho3sigma(*), v4rho2sigma2(*), v4rhosigma3(*), v4sigma4(*) call xc_gga(p%ptr, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3, & v4rho4, v4rho3sigma, v4rho2sigma2, v4rhosigma3, v4sigma4 & ) end subroutine xc_f90_gga subroutine xc_f90_gga_exc(p, np, rho, sigma, zk) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*) call xc_gga_exc(p%ptr, np, rho, sigma, zk) end subroutine xc_f90_gga_exc subroutine xc_f90_gga_exc_vxc(p, np, rho, sigma, zk, vrho, vsigma) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*) call xc_gga_exc_vxc(p%ptr, np, rho, sigma, zk, vrho, vsigma) end subroutine xc_f90_gga_exc_vxc subroutine xc_f90_gga_exc_vxc_fxc(p, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) call xc_gga_exc_vxc_fxc(p%ptr, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2) end subroutine xc_f90_gga_exc_vxc_fxc subroutine xc_f90_gga_exc_vxc_fxc_kxc(p, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rhosigma2(*), v3sigma3(*) call xc_gga_exc_vxc_fxc_kxc(p%ptr, np, rho, sigma, zk, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) end subroutine xc_f90_gga_exc_vxc_fxc_kxc subroutine xc_f90_gga_vxc(p, np, rho, sigma, vrho, vsigma) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: vrho(*), vsigma(*) call xc_gga_vxc(p%ptr, np, rho, sigma, vrho, vsigma) end subroutine xc_f90_gga_vxc subroutine xc_f90_gga_vxc_fxc(p, np, rho, sigma, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) call xc_gga_vxc_fxc(p%ptr, np, rho, sigma, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2) end subroutine xc_f90_gga_vxc_fxc subroutine xc_f90_gga_vxc_fxc_kxc(p, np, rho, sigma, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: vrho(*), vsigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rhosigma2(*), v3sigma3(*) call xc_gga_vxc_fxc_kxc(p%ptr, np, rho, sigma, vrho, vsigma, & v2rho2, v2rhosigma, v2sigma2, & v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) end subroutine xc_f90_gga_vxc_fxc_kxc subroutine xc_f90_gga_fxc(p, np, rho, sigma, v2rho2, v2rhosigma, v2sigma2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2sigma2(*) call xc_gga_fxc(p%ptr, np, rho, sigma, v2rho2, v2rhosigma, v2sigma2) end subroutine xc_f90_gga_fxc subroutine xc_f90_gga_kxc(p, np, rho, sigma, v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rhosigma2(*), v3sigma3(*) call xc_gga_kxc(p%ptr, np, rho, sigma, v3rho3, v3rho2sigma, v3rhosigma2, v3sigma3) end subroutine xc_f90_gga_kxc subroutine xc_f90_gga_lxc(p, np, rho, sigma, v4rho4, v4rho3sigma, v4rho2sigma2, v4rhosigma3, v4sigma4) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*) real(c_double), intent(out) :: v4rho4(*), v4rho3sigma(*), v4rho2sigma2(*), v4rhosigma3(*), v4sigma4(*) call xc_gga_lxc(p%ptr, np, rho, sigma, v4rho4, v4rho3sigma, v4rho2sigma2, v4rhosigma3, v4sigma4) end subroutine xc_f90_gga_lxc real(c_double) function xc_f90_gga_ak13_get_asymptotic(homo) result(asymptotic) real(c_double), intent(in) :: homo asymptotic = xc_gga_ak13_get_asymptotic(homo) end function xc_f90_gga_ak13_get_asymptotic real(c_double) function xc_f90_hyb_exx_coef(p) result(coef) type(xc_f90_func_t), intent(in) :: p coef = xc_hyb_exx_coef(p%ptr) end function xc_f90_hyb_exx_coef subroutine xc_f90_hyb_cam_coef(p, omega, alpha, beta) type(xc_f90_func_t), intent(in) :: p real(c_double), intent(out) :: omega, alpha, beta call xc_hyb_cam_coef(p%ptr, omega, alpha, beta) end subroutine xc_f90_hyb_cam_coef subroutine xc_f90_nlc_coef(p, nlc_b, nlc_c) type(xc_f90_func_t), intent(in) :: p real(c_double), intent(out) :: nlc_b, nlc_c call xc_nlc_coef(p%ptr, nlc_b, nlc_c) end subroutine xc_f90_nlc_coef ! the meta-GGAs !---------------------------------------------------------------- subroutine xc_f90_mgga(p, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3, & v4rho4, v4rho3sigma, v4rho3lapl, v4rho3tau, v4rho2sigma2, v4rho2sigmalapl, & v4rho2sigmatau, v4rho2lapl2, v4rho2lapltau, v4rho2tau2, v4rhosigma3, & v4rhosigma2lapl, v4rhosigma2tau, v4rhosigmalapl2, v4rhosigmalapltau, & v4rhosigmatau2, v4rholapl3, v4rholapl2tau, v4rholapltau2, v4rhotau3, v4sigma4, & v4sigma3lapl, v4sigma3tau, v4sigma2lapl2, v4sigma2lapltau, v4sigma2tau2, & v4sigmalapl3, v4sigmalapl2tau, v4sigmalapltau2, v4sigmatau3, v4lapl4, & v4lapl3tau, v4lapl2tau2, v4lapltau3, v4tau4 & ) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rho2lapl(*), v3rho2tau(*), & v3rhosigma2(*), v3rhosigmalapl(*), v3rhosigmatau(*), v3rholapl2(*), & v3rholapltau(*), v3rhotau2(*), v3sigma3(*), v3sigma2lapl(*), v3sigma2tau(*), & v3sigmalapl2(*), v3sigmalapltau(*), v3sigmatau2(*), v3lapl3(*), v3lapl2tau(*), & v3lapltau2(*), v3tau3(*) real(c_double), intent(out) :: & v4rho4(*), v4rho3sigma(*), v4rho3lapl(*), v4rho3tau(*), v4rho2sigma2(*), v4rho2sigmalapl(*), & v4rho2sigmatau(*), v4rho2lapl2(*), v4rho2lapltau(*), v4rho2tau2(*), v4rhosigma3(*), & v4rhosigma2lapl(*), v4rhosigma2tau(*), v4rhosigmalapl2(*), v4rhosigmalapltau(*), & v4rhosigmatau2(*), v4rholapl3(*), v4rholapl2tau(*), v4rholapltau2(*), v4rhotau3(*), v4sigma4(*), & v4sigma3lapl(*), v4sigma3tau(*), v4sigma2lapl2(*), v4sigma2lapltau(*), v4sigma2tau2(*), & v4sigmalapl3(*), v4sigmalapl2tau(*), v4sigmalapltau2(*), v4sigmatau3(*), v4lapl4(*), & v4lapl3tau(*), v4lapl2tau2(*), v4lapltau3(*), v4tau4(*) call xc_mgga(p%ptr, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3, & v4rho4, v4rho3sigma, v4rho3lapl, v4rho3tau, v4rho2sigma2, v4rho2sigmalapl, & v4rho2sigmatau, v4rho2lapl2, v4rho2lapltau, v4rho2tau2, v4rhosigma3, & v4rhosigma2lapl, v4rhosigma2tau, v4rhosigmalapl2, v4rhosigmalapltau, & v4rhosigmatau2, v4rholapl3, v4rholapl2tau, v4rholapltau2, v4rhotau3, v4sigma4, & v4sigma3lapl, v4sigma3tau, v4sigma2lapl2, v4sigma2lapltau, v4sigma2tau2, & v4sigmalapl3, v4sigmalapl2tau, v4sigmalapltau2, v4sigmatau3, v4lapl4, & v4lapl3tau, v4lapl2tau2, v4lapltau3, v4tau4 & ) end subroutine xc_f90_mgga subroutine xc_f90_mgga_exc(p, np, rho, sigma, lapl, tau, zk) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*) call xc_mgga_exc(p%ptr, np, rho, sigma, lapl, tau, zk) end subroutine xc_f90_mgga_exc subroutine xc_f90_mgga_exc_vxc(p, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*), vlapl(*), vtau(*) call xc_mgga_exc_vxc(p%ptr, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau) end subroutine xc_f90_mgga_exc_vxc subroutine xc_f90_mgga_exc_vxc_fxc(p, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) call xc_mgga_exc_vxc_fxc(p%ptr, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2) end subroutine xc_f90_mgga_exc_vxc_fxc subroutine xc_f90_mgga_exc_vxc_fxc_kxc(p, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: zk(*), vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rho2lapl(*), v3rho2tau(*), & v3rhosigma2(*), v3rhosigmalapl(*), v3rhosigmatau(*), v3rholapl2(*), & v3rholapltau(*), v3rhotau2(*), v3sigma3(*), v3sigma2lapl(*), v3sigma2tau(*), & v3sigmalapl2(*), v3sigmalapltau(*), v3sigmatau2(*), v3lapl3(*), v3lapl2tau(*), & v3lapltau2(*), v3tau3(*) call xc_mgga_exc_vxc_fxc_kxc(p%ptr, np, rho, sigma, lapl, tau, zk, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) end subroutine xc_f90_mgga_exc_vxc_fxc_kxc subroutine xc_f90_mgga_vxc(p, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: vrho(*), vsigma(*), vlapl(*), vtau(*) call xc_mgga_vxc(p%ptr, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau) end subroutine xc_f90_mgga_vxc subroutine xc_f90_mgga_vxc_fxc(p, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) call xc_mgga_vxc_fxc(p%ptr, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2) end subroutine xc_f90_mgga_vxc_fxc subroutine xc_f90_mgga_vxc_fxc_kxc(p, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: vrho(*), vsigma(*), vlapl(*), vtau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rho2lapl(*), v3rho2tau(*), & v3rhosigma2(*), v3rhosigmalapl(*), v3rhosigmatau(*), v3rholapl2(*), & v3rholapltau(*), v3rhotau2(*), v3sigma3(*), v3sigma2lapl(*), v3sigma2tau(*), & v3sigmalapl2(*), v3sigmalapltau(*), v3sigmatau2(*), v3lapl3(*), v3lapl2tau(*), & v3lapltau2(*), v3tau3(*) call xc_mgga_vxc_fxc_kxc(p%ptr, np, rho, sigma, lapl, tau, vrho, vsigma, vlapl, vtau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) end subroutine xc_f90_mgga_vxc_fxc_kxc subroutine xc_f90_mgga_fxc(p, np, rho, sigma, lapl, tau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, v2sigma2, v2sigmalapl, v2sigmatau, & v2lapl2, v2lapltau, v2tau2) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: v2rho2(*), v2rhosigma(*), v2rholapl(*), v2rhotau(*), & v2sigma2(*), v2sigmalapl(*), v2sigmatau(*), v2lapl2(*), v2lapltau(*), v2tau2(*) call xc_mgga_fxc(p%ptr, np, rho, sigma, lapl, tau, & v2rho2, v2rhosigma, v2rholapl, v2rhotau, & v2sigma2, v2sigmalapl, v2sigmatau, v2lapl2, v2lapltau, v2tau2) end subroutine xc_f90_mgga_fxc subroutine xc_f90_mgga_kxc(p, np, rho, sigma, lapl, tau, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: v3rho3(*), v3rho2sigma(*), v3rho2lapl(*), v3rho2tau(*), & v3rhosigma2(*), v3rhosigmalapl(*), v3rhosigmatau(*), v3rholapl2(*), & v3rholapltau(*), v3rhotau2(*), v3sigma3(*), v3sigma2lapl(*), v3sigma2tau(*), & v3sigmalapl2(*), v3sigmalapltau(*), v3sigmatau2(*), v3lapl3(*), v3lapl2tau(*), & v3lapltau2(*), v3tau3(*) call xc_mgga_kxc(p%ptr, np, rho, sigma, lapl, tau, & v3rho3, v3rho2sigma, v3rho2lapl, v3rho2tau, v3rhosigma2, v3rhosigmalapl, & v3rhosigmatau, v3rholapl2, v3rholapltau, v3rhotau2, v3sigma3, v3sigma2lapl, & v3sigma2tau, v3sigmalapl2, v3sigmalapltau, v3sigmatau2, v3lapl3, v3lapl2tau, & v3lapltau2, v3tau3) end subroutine xc_f90_mgga_kxc subroutine xc_f90_mgga_lxc(p, np, rho, sigma, lapl, tau, & v4rho4, v4rho3sigma, v4rho3lapl, v4rho3tau, v4rho2sigma2, v4rho2sigmalapl, & v4rho2sigmatau, v4rho2lapl2, v4rho2lapltau, v4rho2tau2, v4rhosigma3, & v4rhosigma2lapl, v4rhosigma2tau, v4rhosigmalapl2, v4rhosigmalapltau, & v4rhosigmatau2, v4rholapl3, v4rholapl2tau, v4rholapltau2, v4rhotau3, v4sigma4, & v4sigma3lapl, v4sigma3tau, v4sigma2lapl2, v4sigma2lapltau, v4sigma2tau2, & v4sigmalapl3, v4sigmalapl2tau, v4sigmalapltau2, v4sigmatau3, v4lapl4, & v4lapl3tau, v4lapl2tau2, v4lapltau3, v4tau4 & ) type(xc_f90_func_t), intent(in) :: p integer(c_size_t), intent(in) :: np real(c_double), intent(in) :: rho(*), sigma(*), lapl(*), tau(*) real(c_double), intent(out) :: & v4rho4(*), v4rho3sigma(*), v4rho3lapl(*), v4rho3tau(*), v4rho2sigma2(*), v4rho2sigmalapl(*), & v4rho2sigmatau(*), v4rho2lapl2(*), v4rho2lapltau(*), v4rho2tau2(*), v4rhosigma3(*), & v4rhosigma2lapl(*), v4rhosigma2tau(*), v4rhosigmalapl2(*), v4rhosigmalapltau(*), & v4rhosigmatau2(*), v4rholapl3(*), v4rholapl2tau(*), v4rholapltau2(*), v4rhotau3(*), v4sigma4(*), & v4sigma3lapl(*), v4sigma3tau(*), v4sigma2lapl2(*), v4sigma2lapltau(*), v4sigma2tau2(*), & v4sigmalapl3(*), v4sigmalapl2tau(*), v4sigmalapltau2(*), v4sigmatau3(*), v4lapl4(*), & v4lapl3tau(*), v4lapl2tau2(*), v4lapltau3(*), v4tau4(*) call xc_mgga_lxc(p%ptr, np, rho, sigma, lapl, tau, & v4rho4, v4rho3sigma, v4rho3lapl, v4rho3tau, v4rho2sigma2, v4rho2sigmalapl, & v4rho2sigmatau, v4rho2lapl2, v4rho2lapltau, v4rho2tau2, v4rhosigma3, & v4rhosigma2lapl, v4rhosigma2tau, v4rhosigmalapl2, v4rhosigmalapltau, & v4rhosigmatau2, v4rholapl3, v4rholapl2tau, v4rholapltau2, v4rhotau3, v4sigma4, & v4sigma3lapl, v4sigma3tau, v4sigma2lapl2, v4sigma2lapltau, v4sigma2tau2, & v4sigmalapl3, v4sigmalapl2tau, v4sigmalapltau2, v4sigmatau3, v4lapl4, & v4lapl3tau, v4lapl2tau2, v4lapltau3, v4tau4 & ) end subroutine xc_f90_mgga_lxc ! Helper functions to convert between C and Fortran strings ! Based on the routines by Joseph M. Krahn function f_to_c_string(f_string) result(c_string) character(len=*), intent(in) :: f_string character(kind=c_char,len=1) :: c_string(len_trim(f_string)+1) integer :: i, strlen strlen = len_trim(f_string) forall (i=1:strlen) c_string(i) = f_string(i:i) end forall c_string(strlen+1) = C_NULL_CHAR end function f_to_c_string subroutine c_to_f_string(c_string, f_string) character(kind=c_char,len=1), intent(in) :: c_string(*) character(len=*), intent(out) :: f_string integer :: i i = 1 do while(c_string(i) /= C_NULL_CHAR .and. i <= len(f_string)) f_string(i:i) = c_string(i) i = i + 1 end do if (i < len(f_string)) f_string(i:) = ' ' end subroutine c_to_f_string subroutine c_to_f_string_ptr(c_string, f_string) type(c_ptr), intent(in) :: c_string character(len=*), intent(out) :: f_string character(len=1, kind=c_char), pointer :: p_chars(:) integer :: i if (.not. c_associated(c_string)) then f_string = ' ' else call c_f_pointer(c_string, p_chars, [huge(0)]) i = 1 do while(p_chars(i) /= C_NULL_CHAR .and. i <= len(f_string)) f_string(i:i) = p_chars(i) i = i + 1 end do if (i < len(f_string)) f_string(i:) = ' ' end if end subroutine c_to_f_string_ptr end module xc_f90_lib_m !! Local Variables: !! mode: f90 !! coding: utf-8 !! End: elk-7.2.42/src/PaxHeaders.21776/libxcifc.f900000644000000000000000000000013214061636517015027 xustar0030 mtime=1623670095.985101499 30 atime=1623670095.985101499 30 ctime=1623670095.985101499 elk-7.2.42/src/libxcifc.f900000644002504400250440000004132514061636517017071 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2009 T. McQueen and J. K. Dewhurst. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. module libxcifc use xc_f90_lib_m ! libxc version number integer libxcv(3) contains !BOP ! !ROUTINE: xcifc_libxc ! !INTERFACE: subroutine xcifc_libxc(xctype,n,c_tb09,tempa,rho,rhoup,rhodn,g2rho,g2up,g2dn, & grho2,gup2,gdn2,gupdn,tau,tauup,taudn,ex,ec,vx,vc,vxup,vxdn,vcup,vcdn,dxdgr2, & dxdgu2,dxdgd2,dxdgud,dcdgr2,dcdgu2,dcdgd2,dcdgud,dxdg2r,dxdg2u,dxdg2d,dcdg2r, & dcdg2u,dcdg2d,wx,wxup,wxdn,wc,wcup,wcdn) ! !USES: use, intrinsic :: iso_c_binding ! !INPUT/OUTPUT PARAMETERS: ! xctype : type of exchange-correlation functional (in,integer(3)) ! n : number of density points (in,integer) ! c_tb09 : Tran-Blaha '09 constant c (in,real,optional) ! tempa : temperature in atomic units (in,real,optional) ! rho : spin-unpolarised charge density (in,real(n),optional) ! rhoup : spin-up charge density (in,real(n),optional) ! rhodn : spin-down charge density (in,real(n),optional) ! g2rho : grad^2 rho (in,real(n),optional) ! g2up : grad^2 rhoup (in,real(n),optional) ! g2dn : grad^2 rhodn (in,real(n),optional) ! grho2 : |grad rho|^2 (in,real(n),optional) ! gup2 : |grad rhoup|^2 (in,real(n),optional) ! gdn2 : |grad rhodn|^2 (in,real(n),optional) ! gupdn : (grad rhoup).(grad rhodn) (in,real(n),optional) ! tau : kinetic energy density (in,real(n),optional) ! tauup : spin-up kinetic energy density (in,real(n),optional) ! taudn : spin-down kinetic energy density (in,real(n),optional) ! ex : exchange energy density (out,real(n),optional) ! ec : correlation energy density (out,real(n),optional) ! vx : spin-unpolarised exchange potential (out,real(n),optional) ! vc : spin-unpolarised correlation potential (out,real(n),optional) ! vxup : spin-up exchange potential (out,real(n),optional) ! vxdn : spin-down exchange potential (out,real(n),optional) ! vcup : spin-up correlation potential (out,real(n),optional) ! vcdn : spin-down correlation potential (out,real(n),optional) ! dxdgr2 : de_x/d(|grad rho|^2) (out,real(n),optional) ! dxdgu2 : de_x/d(|grad rhoup|^2) (out,real(n),optional) ! dxdgd2 : de_x/d(|grad rhodn|^2) (out,real(n),optional) ! dxdgud : de_x/d((grad rhoup).(grad rhodn)) (out,real(n),optional) ! dcdgr2 : de_c/d(|grad rho|^2) (out,real(n),optional) ! dcdgu2 : de_c/d(|grad rhoup|^2) (out,real(n),optional) ! dcdgd2 : de_c/d(|grad rhodn|^2) (out,real(n),optional) ! dcdgud : de_c/d((grad rhoup).(grad rhodn)) (out,real(n),optional) ! dxdg2r : de_x/d(grad^2 rho) (out,real(n),optional) ! dxdg2u : de_x/d(grad^2 rhoup) (out,real(n),optional) ! dxdg2d : de_x/d(grad^2 rhodn) (out,real(n),optional) ! dcdg2r : de_c/d(grad^2 rho) (out,real(n),optional) ! dcdg2u : de_c/d(grad^2 rhoup) (out,real(n),optional) ! dcdg2d : de_c/d(grad^2 rhodn) (out,real(n),optional) ! wx : de_x/dtau (out,real(n),optional) ! wxup : de_x/dtauup (out,real(n),optional) ! wxdn : de_x/dtaudn (out,real(n),optional) ! wc : de_c/dtau (out,real(n),optional) ! wcup : de_c/dtauup (out,real(n),optional) ! wcdn : de_c/dtaudn (out,real(n),optional) ! !DESCRIPTION: ! Interface to the ETSF {\tt libxc} exchange-correlation functional library: ! \newline{\tt http://www.tddft.org/programs/octopus/wiki/index.php/Libxc}. ! The second and third integers in {\tt xctype} define the exchange and ! correlation functionals in {\tt libxc}, respectively. ! ! !REVISION HISTORY: ! Created April 2009 (Tyrel McQueen) ! Modified September 2009 (JKD and TMQ) ! Updated for Libxc 1, July 2010 (JKD) ! Updated for Libxc 4, March 2018 (JKD) ! Updated for Libxc 5, May 2020 (JKD) !EOP !BOC implicit none ! mandatory arguments integer, intent(in) :: xctype(3),n ! optional arguments real(8), optional, intent(in) :: c_tb09,tempa real(8), optional, intent(in) :: rho(n),rhoup(n),rhodn(n) real(8), optional, intent(in) :: g2rho(n),g2up(n),g2dn(n) real(8), optional, intent(in) :: grho2(n),gup2(n),gdn2(n),gupdn(n) real(8), optional, intent(in) :: tau(n),tauup(n),taudn(n) real(8), optional, intent(out) :: ex(n),ec(n),vx(n),vc(n) real(8), optional, intent(out) :: vxup(n),vxdn(n),vcup(n),vcdn(n) real(8), optional, intent(out) :: dxdgr2(n),dxdgu2(n),dxdgd2(n),dxdgud(n) real(8), optional, intent(out) :: dxdg2r(n),dxdg2u(n),dxdg2d(n) real(8), optional, intent(out) :: wx(n),wxup(n),wxdn(n) real(8), optional, intent(out) :: dcdgr2(n),dcdgu2(n),dcdgd2(n),dcdgud(n) real(8), optional, intent(out) :: dcdg2r(n),dcdg2u(n),dcdg2d(n) real(8), optional, intent(out) :: wc(n),wcup(n),wcdn(n) ! local variables integer nspin,fmly,id,k integer(c_size_t) np type(xc_f90_func_t) p real(8) ta ! allocatable arrays real(8), allocatable :: r(:,:),sigma(:,:),vrho(:,:),vsigma(:,:) real(8), allocatable :: lapl(:,:),t(:,:),vlapl(:,:),vtau(:,:) if (present(rho)) then nspin=XC_UNPOLARIZED else if (present(rhoup).and.present(rhodn)) then nspin=XC_POLARIZED else write(*,*) write(*,'("Error(xcifc_libxc): missing arguments")') write(*,*) stop end if if (xctype(2).ne.0) then if (xctype(2).eq.xctype(3)) then write(*,*) write(*,'("Error(xcifc_libxc): Libxc exchange and correlation & &functionals")') write(*,'(" are the same : ",2I8)') xctype(2:3) write(*,*) stop end if end if ! convert number of points to long integer np=n ! loop over functional kinds (exchange or correlation) do k=2,3 id=xctype(k) if (id.gt.0) then fmly=xc_f90_family_from_id(id) ! initialise functional call xc_f90_func_init(p,id,nspin) select case(fmly) case(XC_FAMILY_LDA) !-------------------------! ! LDA functionals ! !-------------------------! ! set temperature for free energy functional if ((id.eq.XC_LDA_XC_KSDT).or.(id.eq.XC_LDA_XC_GDSMFB)) then call xc_f90_func_set_ext_params(p,[tempa]) end if if (k.eq.2) then ! exchange if (present(rho)) then call xc_f90_lda_exc_vxc(p,np,rho(1),ex(1),vx(1)) else allocate(r(2,n),vrho(2,n)) r(1,:)=rhoup(:); r(2,:)=rhodn(:) call xc_f90_lda_exc_vxc(p,np,r(1,1),ex(1),vrho(1,1)) vxup(:)=vrho(1,:); vxdn(:)=vrho(2,:) deallocate(r,vrho) end if else ! correlation if (present(rho)) then call xc_f90_lda_exc_vxc(p,np,rho(1),ec(1),vc(1)) else allocate(r(2,n),vrho(2,n)) r(1,:)=rhoup(:); r(2,:)=rhodn(:) call xc_f90_lda_exc_vxc(p,np,r(1,1),ec(1),vrho(1,1)) vcup(:)=vrho(1,:); vcdn=vrho(2,:) deallocate(r,vrho) end if end if case(XC_FAMILY_GGA,XC_FAMILY_HYB_GGA) !-------------------------! ! GGA functionals ! !-------------------------! if (k.eq.2) then ! exchange if (present(rho)) then call xc_f90_gga_exc_vxc(p,np,rho(1),grho2(1),ex(1),vx(1),dxdgr2(1)) else allocate(r(2,n),sigma(3,n),vrho(2,n),vsigma(3,n)) r(1,:)=rhoup(:); r(2,:)=rhodn(:) sigma(1,:)=gup2(:); sigma(2,:)=gupdn(:); sigma(3,:)=gdn2(:) call xc_f90_gga_exc_vxc(p,np,r(1,1),sigma(1,1),ex(1),vrho(1,1), & vsigma(1,1)) vxup(:)=vrho(1,:); vxdn(:)=vrho(2,:) dxdgu2(:)=vsigma(1,:); dxdgud(:)=vsigma(2,:); dxdgd2(:)=vsigma(3,:) deallocate(r,sigma,vrho,vsigma) end if else ! correlation if (present(rho)) then call xc_f90_gga_exc_vxc(p,np,rho(1),grho2(1),ec(1),vc(1),dcdgr2(1)) else allocate(r(2,n),sigma(3,n),vrho(2,n),vsigma(3,n)) r(1,:)=rhoup(:); r(2,:)=rhodn(:) sigma(1,:)=gup2(:); sigma(2,:)=gupdn(:); sigma(3,:)=gdn2(:) call xc_f90_gga_exc_vxc(p,np,r(1,1),sigma(1,1),ec(1),vrho(1,1), & vsigma(1,1)) vcup(:)=vrho(1,:); vcdn(:)=vrho(2,:) dcdgu2(:)=vsigma(1,:); dcdgud(:)=vsigma(2,:); dcdgd2(:)=vsigma(3,:) deallocate(r,sigma,vrho,vsigma) end if end if case(XC_FAMILY_MGGA) !------------------------------! ! meta-GGA functionals ! !------------------------------! ! set Tran-Blaha '09 constant if required if (id.eq.XC_MGGA_X_TB09) then if (present(c_tb09)) call xc_f90_func_set_ext_params(p,[c_tb09]) end if if (k.eq.2) then ! exchange if (present(rho)) then if (present(ex)) then ! spin-unpolarised energy functional call xc_f90_mgga_exc_vxc(p,np,rho(1),grho2(1),g2rho(1),tau(1), & ex(1),vx(1),dxdgr2(1),dxdg2r(1),wx(1)) else ! spin-unpolarised potential-only functional allocate(vsigma(1,n),vlapl(1,n),vtau(1,n)) call xc_f90_mgga_vxc(p,np,rho(1),grho2(1),g2rho(1),tau(1),vx(1), & vsigma(1,1),vlapl(1,1),vtau(1,1)) deallocate(vsigma,vlapl,vtau) end if else allocate(r(2,n),sigma(3,n),lapl(2,n),t(2,n)) allocate(vrho(2,n),vsigma(3,n),vlapl(2,n),vtau(2,n)) r(1,:)=rhoup(:); r(2,:)=rhodn(:) sigma(1,:)=gup2(:); sigma(2,:)=gupdn(:); sigma(3,:)=gdn2(:) lapl(1,:)=g2up(:); lapl(2,:)=g2dn(:) t(1,:)=tauup(:); t(2,:)=taudn(:) if (present(ex)) then ! spin-polarised energy functional call xc_f90_mgga_exc_vxc(p,np,r(1,1),sigma(1,1),lapl(1,1),t(1,1), & ex(1),vrho(1,1),vsigma(1,1),vlapl(1,1),vtau(1,1)) dxdgu2(:)=vsigma(1,:); dxdgud(:)=vsigma(2,:); dxdgd2(:)=vsigma(3,:) dxdg2u(:)=vlapl(1,:); dxdg2d(:)=vlapl(2,:) wxup(:)=vtau(1,:); wxdn(:)=vtau(2,:) else ! spin-polarised potential-only functional call xc_f90_mgga_vxc(p,np,r(1,1),sigma(1,1),lapl(1,1),t(1,1), & vrho(1,1),vsigma(1,1),vlapl(1,1),vtau(1,1)) end if vxup(:)=vrho(1,:); vxdn(:)=vrho(2,:) deallocate(r,sigma,lapl,t) deallocate(vrho,vsigma,vlapl,vtau) end if else ! correlation if (present(rho)) then if (present(ec)) then call xc_f90_mgga_exc_vxc(p,np,rho(1),grho2(1),g2rho(1),tau(1), & ec(1),vc(1),dcdgr2(1),dcdg2r(1),wc(1)) else allocate(vsigma(1,n),vlapl(1,n),vtau(1,n)) call xc_f90_mgga_vxc(p,np,rho(1),grho2(1),g2rho(1),tau(1),vc(1), & vsigma(1,1),vlapl(1,1),vtau(1,1)) deallocate(vsigma,vlapl,vtau) end if else allocate(r(2,n),sigma(3,n),lapl(2,n),t(2,n)) allocate(vrho(2,n),vsigma(3,n),vlapl(2,n),vtau(2,n)) r(1,:)=rhoup(:); r(2,:)=rhodn(:) sigma(1,:)=gup2(:); sigma(2,:)=gupdn(:); sigma(3,:)=gdn2(:) lapl(1,:)=g2up(:); lapl(2,:)=g2dn(:) t(1,:)=tauup(:); t(2,:)=taudn(:) if (present(ec)) then call xc_f90_mgga_exc_vxc(p,np,r(1,1),sigma(1,1),lapl(1,1),t(1,1), & ec(1),vrho(1,1),vsigma(1,1),vlapl(1,1),vtau(1,1)) dcdgu2(:)=vsigma(1,:); dcdgud(:)=vsigma(2,:); dcdgd2(:)=vsigma(3,:) dcdg2u(:)=vlapl(1,:); dcdg2d(:)=vlapl(2,:) wcup(:)=vtau(1,:); wcdn(:)=vtau(2,:) else call xc_f90_mgga_vxc(p,np,r(1,1),sigma(1,1),lapl(1,1),t(1,1), & vrho(1,1),vsigma(1,1),vlapl(1,1),vtau(1,1)) end if vcup(:)=vrho(1,:); vcdn(:)=vrho(2,:) deallocate(r,sigma,lapl,t) deallocate(vrho,vsigma,vlapl,vtau) end if end if case default write(*,*) write(*,'("Error(xcifc_libxc): unsupported Libxc functional family : ",& &I8)') fmly write(*,*) stop end select ! destroy functional call xc_f90_func_end(p) else ! case when id=0 if (k.eq.2) then if (present(ex)) ex(:)=0.d0 if (present(vx)) vx(:)=0.d0 if (present(vxup)) vxup(:)=0.d0 if (present(vxdn)) vxdn(:)=0.d0 if (present(dxdgr2)) dxdgr2(:)=0.d0 if (present(dxdgu2)) dxdgu2(:)=0.d0 if (present(dxdgd2)) dxdgd2(:)=0.d0 if (present(dxdgud)) dxdgud(:)=0.d0 else if (present(ec)) ec(:)=0.d0 if (present(vc)) vc(:)=0.d0 if (present(vcup)) vcup(:)=0.d0 if (present(vcdn)) vcdn(:)=0.d0 if (present(dcdgr2)) dcdgr2(:)=0.d0 if (present(dcdgu2)) dcdgu2(:)=0.d0 if (present(dcdgd2)) dcdgd2(:)=0.d0 if (present(dcdgud)) dcdgud(:)=0.d0 end if end if end do end subroutine subroutine fxcifc_libxc(fxctype,n,rho,rhoup,rhodn,fxc,fxcuu,fxcud,fxcdd) use, intrinsic :: iso_c_binding implicit none ! mandatory arguments integer, intent(in) :: fxctype(3),n ! optional arguments real(8), optional, intent(in) :: rho(n),rhoup(n),rhodn(n) real(8), optional, intent(out) :: fxc(n),fxcuu(n),fxcud(n),fxcdd(n) ! local variables integer nspin,fmly,id,k integer(c_size_t) np type(xc_f90_func_t) p ! allocatable arrays real(8), allocatable :: r(:,:),f(:,:) np=n if (present(rho)) then nspin=XC_UNPOLARIZED else if (present(rhoup).and.present(rhodn)) then nspin=XC_POLARIZED else write(*,*) write(*,'("Error(fxcifc_libxc): missing arguments")') write(*,*) stop end if ! zero the kernel if (present(fxc)) fxc(:)=0.d0 if (present(fxcuu)) fxcuu(:)=0.d0 if (present(fxcud)) fxcud(:)=0.d0 if (present(fxcdd)) fxcdd(:)=0.d0 ! loop over functional kinds (exchange or correlation) do k=2,3 id=fxctype(k) if (id.le.0) cycle fmly=xc_f90_family_from_id(id) ! initialise functional call xc_f90_func_init(p,id,nspin) select case(fmly) case(XC_FAMILY_LDA) !-------------------------! ! LDA functionals ! !-------------------------! if (present(rho)) then allocate(f(1,n)) call xc_f90_lda_fxc(p,np,rho(1),f(1,1)) fxc(:)=fxc(:)+f(1,:) deallocate(f) else allocate(r(2,n),f(3,n)) r(1,:)=rhoup(:); r(2,:)=rhodn(:) call xc_f90_lda_fxc(p,np,r(1,1),f(1,1)) fxcuu(:)=fxcuu(:)+f(1,:) fxcud(:)=fxcud(:)+f(2,:) fxcdd(:)=fxcdd(:)+f(3,:) deallocate(r,f) end if case default write(*,*) write(*,'("Error(fxcifc_libxc): unsupported Libxc functional family : ",& &I8)') fmly write(*,*) stop end select ! destroy functional call xc_f90_func_end(p) end do end subroutine subroutine xcdata_libxc(xctype,xcdescr,xcspin,xcgrad,hybrid,hybridc) implicit none ! arguments integer, intent(in) :: xctype(3) character(512), intent(out) :: xcdescr integer, intent(out) :: xcspin integer, intent(out) :: xcgrad logical, intent(inout) :: hybrid real(8), intent(inout) :: hybridc ! local variables integer j,k,id integer fmly,flg character(128) name type(xc_f90_func_t) p type(xc_f90_func_info_t) info ! check version is compatible call xc_f90_version(libxcv(1),libxcv(2),libxcv(3)) if (libxcv(1).ne.5) then write(*,*) write(*,'("Error(xcdata_libxc): incompatible Libxc version : ",I2.2,".",& &I3.3,".",I3.3)') libxcv(:) write(*,*) stop end if ! unknown spin polarisation xcspin=-1 ! no gradients by default xcgrad=0 ! not hybrid by default hybrid=.false. do k=2,3 id=xctype(k) if (id.gt.0) then call xc_f90_func_init(p,id,XC_UNPOLARIZED) name=xc_f90_functional_get_name(id) fmly=xc_f90_family_from_id(id) info=xc_f90_func_get_info(p) if (fmly.eq.XC_FAMILY_HYB_GGA) then hybridc=xc_f90_hyb_exx_coef(p) hybrid=.true. end if ! hybrids should have only correlation part to avoid double-scaling with hybridc if ((fmly.eq.XC_FAMILY_HYB_GGA).and.(k.eq.2)) then write(*,*) write(*,'("Error(xcdata_libxc): set only correlation part of xctype for & &Libxc hybrids")') write(*,*) stop end if ! functional family if ((fmly.ne.XC_FAMILY_LDA).and.(fmly.ne.XC_FAMILY_GGA).and. & (fmly.ne.XC_FAMILY_HYB_GGA).and.(fmly.ne.XC_FAMILY_MGGA)) then write(*,*) write(*,'("Error(xcdata_libxc): unsupported Libxc family : ",I8)') fmly write(*,*) stop end if ! post-processed gradients required for GGA functionals if (fmly.eq.XC_FAMILY_GGA.or.fmly.eq.XC_FAMILY_HYB_GGA) xcgrad=2 ! kinetic energy density required for meta-GGA functionals if (fmly.eq.XC_FAMILY_MGGA) then flg=xc_f90_func_info_get_flags(info) if ((iand(flg,XC_FLAGS_HAVE_VXC).ne.0).and. & (iand(flg,XC_FLAGS_HAVE_EXC).eq.0)) then ! potential-only functional xcgrad=3 else if (iand(flg,XC_FLAGS_HAVE_EXC).ne.0) then ! energy functional xcgrad=4 else write(*,*) write(*,'("Error(xcdata_libxc): unsupported Libxc meta-GGA type")') write(*,*) stop end if ! check if the density laplacian is required if ((xcgrad.eq.4).and.(iand(flg,XC_FLAGS_NEEDS_LAPLACIAN).ne.0)) then write(*,*) write(*,'("Error(xcdata_libxc): energy meta-GGAs requiring the density & &laplacian are not supported")') write(*,*) stop end if end if ! destroy functional call xc_f90_func_end(p) else name='none' end if if (k.eq.2) then xcdescr='exchange: '//trim(name) else xcdescr=trim(xcdescr)//'; correlation: '//trim(name) end if end do end subroutine !EOC end module elk-7.2.42/src/PaxHeaders.21776/zfftifc_fftw.f900000644000000000000000000000013214061636517015725 xustar0030 mtime=1623670095.996101488 30 atime=1623670095.996101488 30 ctime=1623670095.996101488 elk-7.2.42/src/zfftifc_fftw.f900000644002504400250440000000266714061636517017775 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zfftifc(nd,n,sgn,z) implicit none ! arguments integer, intent(in) :: nd,n(nd),sgn complex(8), intent(inout) :: z(*) ! local variables integer, parameter :: FFTW_ESTIMATE=64 integer p integer(8) plan real(8) t1 ! interface to FFTW version 3 !$OMP CRITICAL(zfftifc_) call dfftw_plan_dft(plan,nd,n,z,z,sgn,FFTW_ESTIMATE) !$OMP END CRITICAL(zfftifc_) call dfftw_execute(plan) !$OMP CRITICAL(zfftifc_) call dfftw_destroy_plan(plan) !$OMP END CRITICAL(zfftifc_) if (sgn.eq.-1) then p=product(n(:)) t1=1.d0/dble(p) call zdscal(p,t1,z,1) end if end subroutine subroutine rzfftifc(nd,n,sgn,r,z) implicit none ! arguments integer, intent(in) :: nd,n(nd),sgn real(8), intent(inout) :: r(*) complex(8), intent(inout) :: z(*) ! local variables integer, parameter :: FFTW_ESTIMATE=64 integer p integer(8) plan real(8) t1 !$OMP CRITICAL(rzfftifc_) if (sgn.eq.-1) then call dfftw_plan_dft_r2c(plan,nd,n,r,z,FFTW_ESTIMATE) else call dfftw_plan_dft_c2r(plan,nd,n,z,r,FFTW_ESTIMATE) end if !$OMP END CRITICAL(rzfftifc_) call dfftw_execute(plan) !$OMP CRITICAL(rzfftifc_) call dfftw_destroy_plan(plan) !$OMP END CRITICAL(rzfftifc_) if (sgn.eq.-1) then p=product(n(:)) t1=1.d0/dble(p) p=p/n(1) p=p*(n(1)/2+1) call zdscal(p,t1,z,1) end if end subroutine elk-7.2.42/src/PaxHeaders.21776/zfftifc_mkl.f900000644000000000000000000000013214061636517015542 xustar0030 mtime=1623670095.998101487 30 atime=1623670095.997101488 30 ctime=1623670095.998101487 elk-7.2.42/src/zfftifc_mkl.f900000644002504400250440000000364314061636517017605 0ustar00dewhurstdewhurst00000000000000 ! Copyright (C) 2002-2005 J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl. ! This file is distributed under the terms of the GNU General Public License. ! See the file COPYING for license details. subroutine zfftifc(nd,n,sgn,z) use mkl_dfti implicit none ! arguments integer, intent(in) :: nd,n(nd),sgn complex(8), intent(inout) :: z(*) ! local variables integer status,p real(8) t1 type(DFTI_DESCRIPTOR), pointer :: handle ! interface to the Intel MKL advanced Discreet Fourier Transform (DFT) routines ! (with thanks to Torbjorn Bjorkman) p=product(n(:)) t1=1.d0/dble(p) status=DftiCreateDescriptor(handle,DFTI_DOUBLE,DFTI_COMPLEX,nd,n) status=DftiSetValue(handle,DFTI_FORWARD_SCALE,t1) status=DftiCommitDescriptor(handle) if (sgn.eq.-1) then status=DftiComputeForward(handle,z) else status=DftiComputeBackward(handle,z) end if status=DftiFreeDescriptor(handle) end subroutine subroutine rzfftifc(nd,n,sgn,r,z) use mkl_dfti implicit none ! arguments integer, intent(in) :: nd,n(nd),sgn real(8), intent(inout) :: r(*) complex(8), intent(inout) :: z(*) ! local variables integer status,p,i real(8) t1 type(DFTI_DESCRIPTOR), pointer :: handle ! automatic arrays integer strides(0:nd) p=product(n(:)) t1=1.d0/dble(p) status=DftiCreateDescriptor(handle,DFTI_DOUBLE,DFTI_REAL,nd,n) status=DftiSetValue(handle,DFTI_CONJUGATE_EVEN_STORAGE,DFTI_COMPLEX_COMPLEX) status=DftiSetValue(handle,DFTI_PLACEMENT,DFTI_NOT_INPLACE) status=DftiSetValue(handle,DFTI_FORWARD_SCALE,t1) strides(0)=0 strides(1)=1 if (nd.gt.1) then strides(2)=n(1)/2+1 do i=2,nd-1 strides(i+1)=strides(i)*n(i) end do end if if (sgn.eq.-1) then status=DftiSetValue(handle,DFTI_OUTPUT_STRIDES,strides) status=DftiCommitDescriptor(handle) status=DftiComputeForward(handle,r,z) else status=DftiSetValue(handle,DFTI_INPUT_STRIDES,strides) status=DftiCommitDescriptor(handle) status=DftiComputeBackward(handle,z,r) end if status=DftiFreeDescriptor(handle) end subroutine elk-7.2.42/PaxHeaders.21776/examples0000644000000000000000000000013214061636520013670 xustar0030 mtime=1623670096.496101024 30 atime=1623670096.003101482 30 ctime=1623670096.496101024 elk-7.2.42/examples/0000755002504400250440000000000014061636520016002 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/PaxHeaders.21776/BSE0000644000000000000000000000013114061636520014300 xustar0030 mtime=1623670096.019101467 29 atime=1623670096.00510148 30 ctime=1623670096.019101467 elk-7.2.42/examples/BSE/0000755002504400250440000000000014061636520016413 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0.9850000000 0.3633970964E-02 0.9862500000 0.3619153547E-02 0.9875000000 0.3604418385E-02 0.9887500000 0.3589764894E-02 0.9900000000 0.3575192493E-02 0.9912500000 0.3560700608E-02 0.9925000000 0.3546288670E-02 0.9937500000 0.3531956115E-02 0.9950000000 0.3517702383E-02 0.9962500000 0.3503526919E-02 0.9975000000 0.3489429174E-02 0.9987500000 0.3475408602E-02 elk-7.2.42/examples/BSE/Si/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016034 xustar0030 mtime=1623670096.013101473 30 atime=1623670096.012101474 30 ctime=1623670096.013101473 elk-7.2.42/examples/BSE/Si/elk.in0000644002504400250440000000330114061636520020066 0ustar00dewhurstdewhurst00000000000000 ! BSE optical spectrum of silicon. Note that the non-zero vkloff is needed to ! make the system non-metallic, i.e. all occupancies in EIGVAL.OUT should be ! either 0 or 1. If this is not the case, then the response function will be ! too large. This is quite a time-consuming calculation and should be run on ! a multi-processor system. ! Silicon is surprisingly difficult for a BSE calculation: it requires quite a ! large k-point set for good convergence, unlike the excitonic peak in LiF. tasks 0 ! ground-state calculation 120 ! compute momentum matrix elements 121 ! compute RPA dielectric function with no local field contributions 180 ! generate RPA dielectric function with local field contributions 185 ! write the BSE Hamiltonian matrix to file 186 ! diagonalise the BSE matrix 187 ! compute BSE dielectric function ! this should be small (but not so small that it affects the results!) for a ! fast calculation because the wavefunctions used in the construction of the BSE ! matrix elements are expanded to this angular momentum cut-off lmaxo 4 ! number of valence states to use in BSE Hamiltonian nvbse 3 ! number of conduction states ncbse 4 ! a scissor correction is required to match the gap to experiment scissor 0.0331 swidth 0.005 wplot 800 100 0 : nwplot, ngrkf, nswplot 0.0 1.0 : wplot avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 5 5 5 vkloff 0.25 0.5 0.625 elk-7.2.42/examples/BSE/PaxHeaders.21776/CaO-core0000644000000000000000000000013214061636520015671 xustar0030 mtime=1623670096.018101468 30 atime=1623670096.014101472 30 ctime=1623670096.018101468 elk-7.2.42/examples/BSE/CaO-core/0000755002504400250440000000000014061636520020003 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/BSE/CaO-core/PaxHeaders.21776/Ca_lo.in0000644000000000000000000000013014061636520017311 xustar0029 mtime=1623670096.01610147 30 atime=1623670096.015101471 29 ctime=1623670096.01610147 elk-7.2.42/examples/BSE/CaO-core/Ca_lo.in0000644002504400250440000000357314061636520021360 0ustar00dewhurstdewhurst00000000000000 'Ca_lo' : spsymb 'calcium' : spname -20.0000 : spzn 73057.72467 : spmass 0.447214E-06 2.2000 40.2509 500 : sprmin, rmt, sprmax, nrmt 8 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 T 2 1 1 2.00000 F 2 1 2 4.00000 F 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -12.300 0 T 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -1.9708 0 T 1 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -1.2735 0 T 2 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0.5000 0 T elk-7.2.42/examples/BSE/CaO-core/PaxHeaders.21776/O.in0000644000000000000000000000013214061636520016474 xustar0030 mtime=1623670096.017101469 30 atime=1623670096.017101469 30 ctime=1623670096.017101469 elk-7.2.42/examples/BSE/CaO-core/O.in0000644002504400250440000000222014061636520020525 0ustar00dewhurstdewhurst00000000000000 'O' : spsymb 'oxygen' : spname -8.00000 : spzn 29165.12202 : spmass 0.707107E-06 1.6000 22.7954 300 : sprmin, rmt, sprmax, nrmt 4 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 F 2 1 1 2.00000 F 2 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -1.1227 0 T elk-7.2.42/examples/BSE/CaO-core/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017051 xustar0030 mtime=1623670096.019101467 30 atime=1623670096.018101468 30 ctime=1623670096.019101467 elk-7.2.42/examples/BSE/CaO-core/elk.in0000644002504400250440000000506214061636520021111 0ustar00dewhurstdewhurst00000000000000 ! This example demonstrates the calculation of the Ca 2p 1/2 - 2p 3/2 (L2 / L3) ! x-ray absorption spectra in CaO. The Ca 2p states are treated as local ! orbitals in Ca_lo.in; additional local orbitals are added to allow an accurate ! description of the unoccupied 3d states (compare with the default version of Ca.in). ! Look at the imaginary part of the spectrum (EPSILON_BSE_11.OUT) in the range 11.8 to ! 12.5 Ha. Compare to the independent-particle calculation (EPSILON_11.OUT). ! Try switching off the exchange and the direct term in the BSE Hamiltonian ! individually (set hxbse/hdbse to .false.). ! For a converged spectrum a lot more k-points (6 x 6 x 6 or more) are needed. ! The numerical cut-offs are well converged, so the computation is quite time ! and memory consuming. Run with hybrid parallelization (MPI across nodes, OpenMP ! across cores) on a cluster for smaller memory footprint. Compare with calculations ! and experimental data in J. Phys. Condens. Matter 23, 145501 (2011). ! Example by Markus Meinert. tasks 0 ! ground-state calculation 120 ! compute momentum matrix elements 121 ! compute RPA dielectric function without local field contributions 180 ! generate RPA dielectric function with local field contributions 185 ! write the BSE Hamiltonian matrix to file 186 ! diagonalise BSE matrix 187 ! compute BSE dielectric function ! do not include valence bands right below E_F nvbse 0 ! additional valence bands for the BSE calculation - these are the six 2p states ! of Ca (check EIGVAL.OUT) istxbse 1 2 3 4 5 6 ! number of conduction band states for the BSE calculation ncbse 20 ! large number of empty states required nempty 20 ! enhanced G-vector cut-off of local contribution to RPA gmaxrf 5.0 ! the spectrum is very sensitive to the k-point mesh ngridk 2 2 2 ! use a symmetry breaking shift for more efficient use of the k-points vkloff 0.05 0.15 0.25 ! Broyden mixing for fast convergence mixtype 3 ! the energy window for the plot starts at zero by default; ! sufficient energy points needed wplot 5000 100 0 0.0 14.0 ! include spin-orbit coupling for the 2p 1/2 - 2p 3/2 splitting spinorb .true. ! about 0.27 eV Lorentzian broadening to simulate lifetime effects swidth 0.01 sppath './' avec 4.545 4.545 0.0 4.545 -4.545 0.0 4.545 0.0 4.545 atoms 2 : nspecies 'Ca_lo.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'O.in' 1 0.5 0.5 0.0 elk-7.2.42/examples/BSE/PaxHeaders.21776/LiF0000644000000000000000000000013214061636520014753 xustar0030 mtime=1623670096.020101466 30 atime=1623670096.019101467 30 ctime=1623670096.020101466 elk-7.2.42/examples/BSE/LiF/0000755002504400250440000000000014061636520017065 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/BSE/LiF/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016133 xustar0030 mtime=1623670096.021101465 30 atime=1623670096.021101465 30 ctime=1623670096.021101465 elk-7.2.42/examples/BSE/LiF/elk.in0000644002504400250440000000217614061636520020176 0ustar00dewhurstdewhurst00000000000000 ! BSE optical spectrum of lithium fluoride. This material has a prominent ! excitonic peak, which is absent in the usual RPA dielectric function. tasks 0 ! ground-state calculation 120 ! compute momentum matrix elements 121 ! compute RPA dielectric function with no local field contributions 180 ! generate RPA dielectric function with local field contributions 185 ! write BSE Hamiltonian matrix 186 ! diagonalise BSE matrix 187 ! generate BSE dielectric function scissor 0.21 ! number of BSE valence states nvbse 3 ! number of BSE conduction states ncbse 4 ! G-vector cut-off of local contribution to RPA gmaxrf 3.0 swidth 0.005 nempty 8 wplot 800 100 0 : nwplot, ngrkf, nswplot 0.0 1.5 : wplot avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 ngridk 4 4 4 elk-7.2.42/examples/PaxHeaders.21776/ELF0000644000000000000000000000013214061636520014276 xustar0030 mtime=1623670096.026101461 30 atime=1623670096.022101464 30 ctime=1623670096.026101461 elk-7.2.42/examples/ELF/0000755002504400250440000000000014061636520016410 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ELF/PaxHeaders.21776/BN0000644000000000000000000000013214061636520014575 xustar0030 mtime=1623670096.024101463 30 atime=1623670096.023101463 30 ctime=1623670096.024101463 elk-7.2.42/examples/ELF/BN/0000755002504400250440000000000014061636520016707 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ELF/BN/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015755 xustar0030 mtime=1623670096.024101463 30 atime=1623670096.024101463 30 ctime=1623670096.024101463 elk-7.2.42/examples/ELF/BN/elk.in0000644002504400250440000000105514061636520020013 0ustar00dewhurstdewhurst00000000000000 ! Electron localisation function (ELF) of cubic boron nitride. Note that the ELF ! is not continuous at the muffin-tin boundaries. To make it smooth increase ! several parameters such as rgkmax, gmaxvr, lmaxo and lmaxapw. Alternatively, ! run with highq=.true. tasks 0 51 plot1d 2 400 0.0 0.0 0.0 1.0 1.0 1.0 avec 3.4204 3.4204 0.0000 3.4204 0.0000 3.4204 0.0000 3.4204 3.4204 sppath '../../../species/' atoms 2 'B.in' 1 0.0 0.0 0.0 'N.in' 1 0.25 0.25 0.25 ngridk 2 2 2 vkloff 0.25 0.5 0.625 elk-7.2.42/examples/ELF/PaxHeaders.21776/Ru0000644000000000000000000000013214061636520014664 xustar0030 mtime=1623670096.028101459 30 atime=1623670096.026101461 30 ctime=1623670096.028101459 elk-7.2.42/examples/ELF/Ru/0000755002504400250440000000000014061636520016776 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ELF/Ru/PaxHeaders.21776/Ru.in0000644000000000000000000000012714061636520015663 xustar0029 mtime=1623670096.02710146 29 atime=1623670096.02710146 29 ctime=1623670096.02710146 elk-7.2.42/examples/ELF/Ru/Ru.in0000644002504400250440000000404114061636520017713 0ustar00dewhurstdewhurst00000000000000 'Ru' : spsymb 'ruthenium' : spname -44.0000 : spzn 184239.3392 : spmass 0.301511E-06 2.0000 43.5262 600 : sprmin, rmt, sprmax, nrmt 15 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 3.00000 F 5 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 1 : nlx 2 2 : lx, io 0.1500 0 F : apwe0, apwdm, apwve 0.1500 1 F 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0.1500 2 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -2.6548 0 T 1 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -1.6432 0 T elk-7.2.42/examples/ELF/Ru/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016044 xustar0030 mtime=1623670096.029101458 30 atime=1623670096.029101458 30 ctime=1623670096.029101458 elk-7.2.42/examples/ELF/Ru/elk.in0000644002504400250440000000150414061636520020101 0ustar00dewhurstdewhurst00000000000000 ! Example due to A. Baranov on how to obtain a very smooth electron localisation ! function (ELF). Since the ELF depends on derivatives of the density it can ! sometimes be mismatched at the muffin-tin boundaries. This can be corrected ! by using high cut-offs for angular momenta and APW functions. Note also that a ! modified species file Ru.in is used. tasks 0 31 51 avec 4.42816109463 -2.5566 0.0 0.0 5.1132 0.0 0.0 0.0 8.0901 atoms 1 'Ru.in' 2 0.3333333333 0.6666666667 0.25 0.6666666667 0.3333333333 0.75 ! this ensures that no radial points will be skipped when computing the density lradstp 1 rgkmax 11.0 gmaxvr 22.0 msmooth 4 lmaxapw 12 lmaxo 12 ngridk 2 2 1 vkloff 0.5 0.5 0.5 plot1d 2 1000 0.0 0.0 0.0 0.0 1.0 0.0 elk-7.2.42/examples/PaxHeaders.21776/Hartree-Fock0000644000000000000000000000013214061636520016142 xustar0030 mtime=1623670096.033101454 30 atime=1623670096.030101457 30 ctime=1623670096.033101454 elk-7.2.42/examples/Hartree-Fock/0000755002504400250440000000000014061636520020254 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Hartree-Fock/PaxHeaders.21776/HEG0000644000000000000000000000013214061636520016545 xustar0030 mtime=1623670096.032101455 30 atime=1623670096.031101456 30 ctime=1623670096.032101455 elk-7.2.42/examples/Hartree-Fock/HEG/0000755002504400250440000000000014061636520020657 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Hartree-Fock/HEG/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017725 xustar0030 mtime=1623670096.032101455 30 atime=1623670096.032101455 30 ctime=1623670096.032101455 elk-7.2.42/examples/Hartree-Fock/HEG/elk.in0000644002504400250440000000065214061636520021765 0ustar00dewhurstdewhurst00000000000000 ! Hartree-Fock ground state of the homogenous electron gas. The Wigner radius ! (r_s) is written to INFO.OUT. Note that the exact exchange energy is only ! computed during the last iteration. tasks 0 5 chgexs 10.0 ! use the unit cell of aluminium avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.75 ! note that low density gases require denser k-point grids! ngridk 2 2 2 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/Hartree-Fock/PaxHeaders.21776/Si0000644000000000000000000000013214061636520016515 xustar0030 mtime=1623670096.034101453 30 atime=1623670096.033101454 30 ctime=1623670096.034101453 elk-7.2.42/examples/Hartree-Fock/Si/0000755002504400250440000000000014061636520020627 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Hartree-Fock/Si/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017675 xustar0030 mtime=1623670096.035101452 30 atime=1623670096.034101453 30 ctime=1623670096.035101452 elk-7.2.42/examples/Hartree-Fock/Si/elk.in0000644002504400250440000000151214061636520021731 0ustar00dewhurstdewhurst00000000000000 ! Hartree-Fock calculation of silicon. Note that this is still an experimental ! feature in Elk. It is also quite slow and is best run using OpenMP on a ! multi-processor machine. ! Important: the exact exchange energy is only calculated on the last iteration. ! All previously calculated exchange energies are approximate. tasks 0 5 ! Hartree-Fock is treated as a second-variational correction to the Kohn-Sham ! problem. Thus a large number of empty states are required for convergence. nempty 8 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 2 2 2 vkloff 0.25 0.25 0.25 elk-7.2.42/examples/PaxHeaders.21776/TDDFT-magnetic-response0000644000000000000000000000013214061636520020156 xustar0030 mtime=1623670096.043101445 30 atime=1623670096.036101451 30 ctime=1623670096.043101445 elk-7.2.42/examples/TDDFT-magnetic-response/0000755002504400250440000000000014061636520022270 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-magnetic-response/PaxHeaders.21776/Ni-magnetic-response0000644000000000000000000000013114061636520024144 xustar0030 mtime=1623670096.041101447 29 atime=1623670096.03710145 30 ctime=1623670096.041101447 elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnetic-response/0000755002504400250440000000000014061636520026257 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnetic-response/PaxHeaders.21776/CHI0_T.OUT0000644000000000000000000000013114061636520025560 xustar0030 mtime=1623670096.039101449 29 atime=1623670096.03810145 30 ctime=1623670096.039101449 elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnetic-response/CHI0_T.OUT0000644002504400250440000001053214061636520027617 0ustar00dewhurstdewhurst00000000000000 0.000000000 -1.169399737 0.3333333333E-03 -1.180064743 0.6666666667E-03 -1.190839903 0.1000000000E-02 -1.201497740 0.1333333333E-02 -1.211893033 0.1666666667E-02 -1.222342874 0.2000000000E-02 -1.233315994 0.2333333333E-02 -1.245298205 0.2666666667E-02 -1.258562475 0.3000000000E-02 -1.273000392 0.3333333333E-02 -1.288383516 0.3666666667E-02 -1.304637755 0.4000000000E-02 -1.321833172 0.4333333333E-02 -1.340027347 0.4666666667E-02 -1.359238627 0.5000000000E-02 -1.379484422 0.5333333333E-02 -1.400824318 0.5666666667E-02 -1.423370803 0.6000000000E-02 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-0.1070291645 0.7333333333E-02 -0.1217502007 0.7666666667E-02 -0.1400093291 0.8000000000E-02 -0.1615460765 0.8333333333E-02 -0.1838532507 0.8666666667E-02 -0.2054415729 0.9000000000E-02 -0.2277103553 0.9333333333E-02 -0.2485751570 0.9666666667E-02 -0.2670959518 0.1000000000E-01 -0.2838540861 0.1033333333E-01 -0.2943655775 0.1066666667E-01 -0.2937976104 0.1100000000E-01 -0.2815054704 0.1133333333E-01 -0.2645243724 0.1166666667E-01 -0.2535438630 0.1200000000E-01 -0.2545997152 0.1233333333E-01 -0.2677295870 0.1266666667E-01 -0.2889050781 0.1300000000E-01 -0.3143707938 0.1333333333E-01 -0.3481122778 0.1366666667E-01 -0.3955258521 0.1400000000E-01 -0.4479752645 0.1433333333E-01 -0.4811172622 0.1466666667E-01 -0.4853855451 0.1500000000E-01 -0.4829100648 0.1533333333E-01 -0.4910656543 0.1566666667E-01 -0.5040959354 0.1600000000E-01 -0.5126483863 0.1633333333E-01 -0.5226747535 0.1666666667E-01 -0.5459798699 0.1700000000E-01 -0.5899690415 0.1733333333E-01 -0.6597397675 0.1766666667E-01 -0.7552227926 0.1800000000E-01 -0.8673797682 0.1833333333E-01 -0.9844396909 0.1866666667E-01 -1.102311376 0.1900000000E-01 -1.238407654 0.1933333333E-01 -1.423779339 0.1966666667E-01 -1.660370932 elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnetic-response/PaxHeaders.21776/CHI_T.OUT0000644000000000000000000000013214061636520025501 xustar0030 mtime=1623670096.040101448 30 atime=1623670096.040101448 30 ctime=1623670096.040101448 elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnetic-response/CHI_T.OUT0000644002504400250440000001053214061636520027537 0ustar00dewhurstdewhurst00000000000000 0.000000000 -7.947625401 0.3333333333E-03 -8.437765313 0.6666666667E-03 -8.964537558 0.1000000000E-02 -9.512772499 0.1333333333E-02 -10.07748384 0.1666666667E-02 -10.69051052 0.2000000000E-02 -11.39609507 0.2333333333E-02 -12.23183126 0.2666666667E-02 -13.15147742 0.3000000000E-02 -13.95607301 0.3333333333E-02 -14.26787677 0.3666666667E-02 -13.36053649 0.4000000000E-02 -9.771320013 0.4333333333E-02 -2.424589324 0.4666666667E-02 6.093511471 0.5000000000E-02 11.43418701 0.5333333333E-02 13.05307386 0.5666666667E-02 12.67045067 0.6000000000E-02 11.57071734 0.6333333333E-02 10.32941695 0.6666666667E-02 9.158722357 0.7000000000E-02 8.128141390 0.7333333333E-02 7.252062436 0.7666666667E-02 6.516791089 0.8000000000E-02 5.917830063 0.8333333333E-02 5.463322839 0.8666666667E-02 5.114826421 0.9000000000E-02 4.833042646 0.9333333333E-02 4.631614923 0.9666666667E-02 4.493575097 0.1000000000E-01 4.411970992 0.1033333333E-01 4.403105999 0.1066666667E-01 4.447642841 0.1100000000E-01 4.485349736 0.1133333333E-01 4.435113452 0.1166666667E-01 4.271194411 0.1200000000E-01 4.042496785 0.1233333333E-01 3.806813331 0.1266666667E-01 3.595745727 0.1300000000E-01 3.407989749 0.1333333333E-01 3.228114181 0.1366666667E-01 3.062801866 0.1400000000E-01 2.938586661 0.1433333333E-01 2.872491455 0.1466666667E-01 2.837604389 0.1500000000E-01 2.787366568 0.1533333333E-01 2.719670235 0.1566666667E-01 2.657991234 0.1600000000E-01 2.602456618 0.1633333333E-01 2.534386517 0.1666666667E-01 2.447813997 0.1700000000E-01 2.350605028 0.1733333333E-01 2.253322405 0.1766666667E-01 2.165368402 0.1800000000E-01 2.090486430 0.1833333333E-01 2.023927027 0.1866666667E-01 1.957906575 0.1900000000E-01 1.888382522 0.1933333333E-01 1.818930266 0.1966666667E-01 1.757425101 0.000000000 -1.580545278 0.3333333333E-03 -1.950668145 0.6666666667E-03 -2.415558754 0.1000000000E-02 -2.989251270 0.1333333333E-02 -3.666678700 0.1666666667E-02 -4.456243558 0.2000000000E-02 -5.412859379 0.2333333333E-02 -6.661497976 0.2666666667E-02 -8.417568557 0.3000000000E-02 -10.92675946 0.3333333333E-02 -14.41576173 0.3666666667E-02 -19.07814087 0.4000000000E-02 -24.45213244 0.4333333333E-02 -27.94948860 0.4666666667E-02 -26.36873493 0.5000000000E-02 -20.97036535 0.5333333333E-02 -15.38297753 0.5666666667E-02 -11.16759873 0.6000000000E-02 -8.290034133 0.6333333333E-02 -6.370392998 0.6666666667E-02 -5.092453311 0.7000000000E-02 -4.244113480 0.7333333333E-02 -3.682622714 0.7666666667E-02 -3.317876023 0.8000000000E-02 -3.100910340 0.8333333333E-02 -2.971031250 0.8666666667E-02 -2.867009256 0.9000000000E-02 -2.793713099 0.9333333333E-02 -2.744699557 0.9666666667E-02 -2.691555862 0.1000000000E-01 -2.640594933 0.1033333333E-01 -2.565924960 0.1066666667E-01 -2.419947718 0.1100000000E-01 -2.171690692 0.1133333333E-01 -1.849959957 0.1166666667E-01 -1.542994748 0.1200000000E-01 -1.312573298 0.1233333333E-01 -1.161818538 0.1266666667E-01 -1.063608651 0.1300000000E-01 -0.9891054435 0.1333333333E-01 -0.9365564833 0.1366666667E-01 -0.9202209036 0.1400000000E-01 -0.9363459151 0.1433333333E-01 -0.9501975250 0.1466666667E-01 -0.9218537854 0.1500000000E-01 -0.8612213124 0.1533333333E-01 -0.8045842577 0.1566666667E-01 -0.7554398023 0.1600000000E-01 -0.6953404972 0.1633333333E-01 -0.6238407621 0.1666666667E-01 -0.5572012273 0.1700000000E-01 -0.5066171962 0.1733333333E-01 -0.4748287160 0.1766666667E-01 -0.4578680894 0.1800000000E-01 -0.4463923863 0.1833333333E-01 -0.4325528159 0.1866666667E-01 -0.4159591229 0.1900000000E-01 -0.4025242244 0.1933333333E-01 -0.3987401259 0.1966666667E-01 -0.4042694944 elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnetic-response/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520025325 xustar0030 mtime=1623670096.042101446 30 atime=1623670096.041101447 30 ctime=1623670096.042101446 elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnetic-response/elk.in0000644002504400250440000000161014061636520027360 0ustar00dewhurstdewhurst00000000000000 ! Magnetic response of fcc nickel. Try plotting the transverse component as a ! function of frequency. Compare to B. Rousseau, A. Eiguren and A. Bergara, ! Phys. Rev. B 85, 054305 (2012) and references therein. tasks 0 330 ! energy cut-off for Kohn-Sham response function emaxrf 1.5 ! G-vector cut-off for response function gmaxrf 5.0 ! frequency plot range wplot 60 100 1 0 0.020 ! q-vector of response function vecql 0.1 0.1 0.0 spinpol .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ! dense k-point grid is required for response functions ngridk 10 10 10 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/TDDFT-magnetic-response/PaxHeaders.21776/Ni-magnon-spiral0000644000000000000000000000013214061636520023271 xustar0030 mtime=1623670096.044101444 30 atime=1623670096.043101445 30 ctime=1623670096.044101444 elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnon-spiral/0000755002504400250440000000000014061636520025403 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnon-spiral/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520024451 xustar0030 mtime=1623670096.044101444 30 atime=1623670096.044101444 30 ctime=1623670096.044101444 elk-7.2.42/examples/TDDFT-magnetic-response/Ni-magnon-spiral/elk.in0000644002504400250440000000334614061636520026514 0ustar00dewhurstdewhurst00000000000000 ! In this example, the frequency of a magnon at a particular q-vector in fcc Ni ! is determined. Computing a magnon frequency requires the energy difference, ! dE, between the ferromagnetic and a conical spin-spiral state with small polar ! angle theta. The following formula can then be used to compute the frequency: ! ! w(q) = (4/M) dE / sin^2(theta) ! ! where M is the total moment in the unit cell. See Q. Niu and L. Kleinman, ! Phys. Rev. Lett. 80, 2205 (1998). It is good practice to fix a q and then run ! two fixed spin direction calculations: one at theta=0, and the other at a ! finite theta (in this case 15 degrees). ! Note that the energy difference is very small (order of meV), and the ! calculation has to be very well converged in all parameters. As a result this ! example is best run on a multi-processor, and is still quite time-consuming. tasks 0 stype 1 taufsm 0.01 swidth 0.005 rgkmax 8.0 gmaxvr 14.0 lmaxapw 8 lmaxo 8 ! tight convergence required epspot 1.d-9 epsengy 1.d-6 ! use a fixed spin direction calculation fsmtype -1 ! use a polar angle of 15 degrees momfix 0.0 0.258819045 0.965925826 ! large global field in same direction as momfix bfieldc 0.0 0.258819045 0.965925826 spinsprl .true. ! spin-spiral q-vector in lattice coordinates vqlss 0.1 0.1 0.0 nempty 10 ! very fine k-point grid required for good convergence ngridk 20 20 20 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 ! experimental lattice parameter scale 3.325 sppath '../../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/examples/PaxHeaders.21776/basic0000644000000000000000000000013214061636520014751 xustar0030 mtime=1623670096.085101406 30 atime=1623670096.045101443 30 ctime=1623670096.085101406 elk-7.2.42/examples/basic/0000755002504400250440000000000014061636520017063 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/PaxHeaders.21776/Au0000644000000000000000000000013014061636520015314 xustar0029 mtime=1623670096.04810144 30 atime=1623670096.047101441 29 ctime=1623670096.04810144 elk-7.2.42/examples/basic/Au/0000755002504400250440000000000014061636520017430 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/Au/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520016502 xustar0029 mtime=1623670096.04810144 29 atime=1623670096.04810144 29 ctime=1623670096.04810144 elk-7.2.42/examples/basic/Au/elk.in0000644002504400250440000000125214061636520020533 0ustar00dewhurstdewhurst00000000000000 ! Example of spin-orbit coupling for Au. Try comparing the band structure ! without spin-orbit coupling. tasks 0 20 spinorb .true. avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.85 sppath '../../../species/' atoms 1 : nspecies 'Au.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 plot1d 7 100 : nvp1d, npp1d 0.0 0.0 1.0 : vlvp1d 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 elk-7.2.42/examples/basic/PaxHeaders.21776/HfSiO40000644000000000000000000000013214061636520016005 xustar0030 mtime=1623670096.051101438 30 atime=1623670096.049101439 30 ctime=1623670096.051101438 elk-7.2.42/examples/basic/HfSiO4/0000755002504400250440000000000014061636520020117 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/HfSiO4/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017165 xustar0030 mtime=1623670096.050101438 30 atime=1623670096.050101438 30 ctime=1623670096.050101438 elk-7.2.42/examples/basic/HfSiO4/elk.in0000644002504400250440000000454514061636520021232 0ustar00dewhurstdewhurst00000000000000 ! HfSiO4 generated with spacegroup data from Am. Mineral. 67, 804 (1982). tasks 0 ngridk 2 2 2 ! Atomic positions generated by spacegroup version 1.2.00 ! Hermann-Mauguin symbol : I41/amd:2 ! Hall symbol : -I 4bd 2 ! Schoenflies symbol : D4h^19 ! space group number : 141:2 ! lattice constants (a,b,c) : 12.42022400 12.42022400 11.26881400 ! angles in degrees (bc,ac,ab) : 90.00000000 90.00000000 90.00000000 ! number of conventional unit cells : 1 1 1 ! reduction to primitive cell : T ! Wyckoff positions : ! species : 1, Hf.in ! 0.000000000 0.7500000000 0.1250000000 ! species : 2, Si.in ! 0.000000000 0.7500000000 0.6250000000 ! species : 3, O.in ! 0.000000000 0.6550000000E-01 0.1948000000 avec 6.210112000 6.210112000 5.634407000 6.210112000 6.210112000 -5.634407000 6.210112000 -6.210112000 5.634407000 sppath '../../../species/' atoms 3 : nspecies 'Hf.in' : spfname 2 : natoms; atposl, bfcmt below 0.87500000 0.87500000 0.25000000 0.00000000 0.00000000 0.00000000 0.12500000 0.12500000 0.75000000 0.00000000 0.00000000 0.00000000 'Si.in' : spfname 2 : natoms; atposl, bfcmt below 0.37500000 0.37500000 0.25000000 0.00000000 0.00000000 0.00000000 0.62500000 0.62500000 0.75000000 0.00000000 0.00000000 0.00000000 'O.in' : spfname 8 : natoms; atposl, bfcmt below 0.26030000 0.80520000 0.93450000 0.00000000 0.00000000 0.00000000 0.73970000 0.19480000 0.06550000 0.00000000 0.00000000 0.00000000 0.19480000 0.73970000 0.43450000 0.00000000 0.00000000 0.00000000 0.80520000 0.26030000 0.56550000 0.00000000 0.00000000 0.00000000 0.62930000 0.80520000 0.56550000 0.00000000 0.00000000 0.00000000 0.37070000 0.19480000 0.43450000 0.00000000 0.00000000 0.00000000 0.19480000 0.37070000 0.06550000 0.00000000 0.00000000 0.00000000 0.80520000 0.62930000 0.93450000 0.00000000 0.00000000 0.00000000 elk-7.2.42/examples/basic/HfSiO4/PaxHeaders.21776/spacegroup.in0000644000000000000000000000013214061636520020562 xustar0030 mtime=1623670096.052101436 30 atime=1623670096.052101436 30 ctime=1623670096.052101436 elk-7.2.42/examples/basic/HfSiO4/spacegroup.in0000644002504400250440000000101414061636520022613 0ustar00dewhurstdewhurst00000000000000 'I41/amd:2' : hrmg 12.420224 12.420224 11.268814 : a, b, c 90.0 90.0 90.0 : ab, ac, bc 1 1 1 : ncell .true. : primcell 3 : nspecies 'Hf' 'Hf.in' : spsymb, spfname 1 : nwpos 0.0000 0.7500 0.1250 : wpos 'Si' 'Si.in' 1 0.0000 0.7500 0.6250 'O' 'O.in' 1 0.0000 0.0655 0.1948 elk-7.2.42/examples/basic/PaxHeaders.21776/Si0000644000000000000000000000013214061636520015324 xustar0030 mtime=1623670096.054101435 30 atime=1623670096.053101436 30 ctime=1623670096.054101435 elk-7.2.42/examples/basic/Si/0000755002504400250440000000000014061636520017436 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/Si/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016504 xustar0030 mtime=1623670096.055101434 30 atime=1623670096.054101435 30 ctime=1623670096.055101434 elk-7.2.42/examples/basic/Si/elk.in0000644002504400250440000000141714061636520020544 0ustar00dewhurstdewhurst00000000000000 ! Band structure of silicon. The points listed after plot1d below are the ! vertices joined in the band structure. tasks 0 20 ! use Broyden mixing mixtype 3 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 2 2 2 vkloff 0.25 0.5 0.625 ! These are the vertices to be joined for the band structure plot plot1d 7 200 : nvp1d, npp1d 0.0 0.0 1.0 : vlvp1d 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 elk-7.2.42/examples/basic/PaxHeaders.21776/graphene0000644000000000000000000000013214061636520016542 xustar0030 mtime=1623670096.056101433 30 atime=1623670096.055101434 30 ctime=1623670096.056101433 elk-7.2.42/examples/basic/graphene/0000755002504400250440000000000014061636520020654 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/graphene/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017722 xustar0030 mtime=1623670096.057101432 30 atime=1623670096.056101433 30 ctime=1623670096.057101432 elk-7.2.42/examples/basic/graphene/elk.in0000644002504400250440000000141514061636520021760 0ustar00dewhurstdewhurst00000000000000 ! Band structure of graphene. Observe the massless Dirac-like dispersion in the ! density of states. tasks 0 10 nempty 8 wplot 200 150 1 -0.5 0.5 plot1d 4 100 0.333333333 0.333333333 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.333333333 0.333333333 0.0 ! very high number of k-points required to resolve the linear dispersion ngridk 30 30 1 avec -0.5 0.866025403784 0.0 -1.0 0.0 0.0 0.0 0.0 3.2265697 scale 4.64890 sppath '../../../species/' atoms 1 : nspecies 'C.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.333333333333 0.333333333333 0.0 elk-7.2.42/examples/basic/PaxHeaders.21776/B120000644000000000000000000000013014061636520015273 xustar0029 mtime=1623670096.05910143 30 atime=1623670096.058101431 29 ctime=1623670096.05910143 elk-7.2.42/examples/basic/B12/0000755002504400250440000000000014061636520017407 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/B12/PaxHeaders.21776/elk.in0000644000000000000000000000013114061636520016454 xustar0030 mtime=1623670096.060101429 29 atime=1623670096.05910143 30 ctime=1623670096.060101429 elk-7.2.42/examples/basic/B12/elk.in0000644002504400250440000000137014061636520020513 0ustar00dewhurstdewhurst00000000000000 ! B12 ground state (Andrew Chizmeshya) tasks 0 10 rgkmax 6.0 scale 9.6376071 avec 0.55522 0.00000 0.82027 -0.27761 0.48083 0.82027 -0.27761 -0.48083 0.82027 sppath '../../../species/' atoms 1 : nspecies 'B.in' : spfname 12 : natoms; atposl below 0.77917 0.77917 0.36899 0.36899 0.77917 0.77914 0.77917 0.36899 0.77918 0.22082 0.22082 0.63108 0.22082 0.63100 0.22082 0.63100 0.22082 0.22086 0.98989 0.98989 0.34576 0.34579 0.98989 0.98986 0.98989 0.34579 0.98981 0.01010 0.01010 0.65424 0.01010 0.65420 0.01019 0.65420 0.01010 0.01014 ngridk 2 2 2 elk-7.2.42/examples/basic/PaxHeaders.21776/Nb-autoswidth0000644000000000000000000000013214061636520017501 xustar0030 mtime=1623670096.062101427 30 atime=1623670096.061101428 30 ctime=1623670096.062101427 elk-7.2.42/examples/basic/Nb-autoswidth/0000755002504400250440000000000014061636520021613 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/Nb-autoswidth/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020661 xustar0030 mtime=1623670096.062101427 30 atime=1623670096.062101427 30 ctime=1623670096.062101427 elk-7.2.42/examples/basic/Nb-autoswidth/elk.in0000644002504400250440000000100514061636520022712 0ustar00dewhurstdewhurst00000000000000 ! Example demonstrating the automatic determination of the smearing width. See ! 'autoswidth' in the manual for details. ! Example by T. Bjorkman and O. Granas. tasks 0 autoswidth .true. avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 3.118 sppath '../../../species/' atoms 1 : nspecies 'Nb.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 elk-7.2.42/examples/basic/PaxHeaders.21776/TiC-eg-t2g0000644000000000000000000000013214061636520016513 xustar0030 mtime=1623670096.064101425 30 atime=1623670096.063101426 30 ctime=1623670096.064101425 elk-7.2.42/examples/basic/TiC-eg-t2g/0000755002504400250440000000000014061636520020625 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/TiC-eg-t2g/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017673 xustar0030 mtime=1623670096.065101424 30 atime=1623670096.065101424 30 ctime=1623670096.065101424 elk-7.2.42/examples/basic/TiC-eg-t2g/elk.in0000644002504400250440000000213214061636520021726 0ustar00dewhurstdewhurst00000000000000 ! Density of states of TiC resolved into irreducible representations. When ! lmirep is set to .true., the Y_lm basis is transformed into one in which the ! site symmetries are block diagonal. The band characters determined from the ! density matrix expressed in this basis correspond therefore to irreducible ! representations (IR). ! In this example, we want the e_g and t_2g resolved DOS for the Ti atom. The ! ELMIREP.OUT file contains a set of eigenvalues, the degeneracies of which ! allow for easy identification of the IR. For l = 2, the 3-fold degeneracy is ! the t_2g IR, while the 2-fold is the e_g IR. Adding together curves 5, 6 and 7 ! in the file PDOS_S01_A0001.OUT will give the t_2g plot, and adding curves 8 ! and 9 will give the e_g plot. tasks 0 10 lmirep .true. avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 8.1787 sppath '../../../species/' atoms 2 : nspecies 'Ti.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'C.in' 1 0.5 0.5 0.5 ngridk 8 8 8 elk-7.2.42/examples/basic/PaxHeaders.21776/Al0000644000000000000000000000013214061636520015305 xustar0030 mtime=1623670096.066101424 30 atime=1623670096.065101424 30 ctime=1623670096.066101424 elk-7.2.42/examples/basic/Al/0000755002504400250440000000000014061636520017417 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/Al/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016465 xustar0030 mtime=1623670096.067101423 30 atime=1623670096.067101423 30 ctime=1623670096.067101423 elk-7.2.42/examples/basic/Al/elk.in0000644002504400250440000000127514061636520020527 0ustar00dewhurstdewhurst00000000000000 ! Ground state of aluminium. Try calculating the density of states by using ! tasks=10 tasks 0 ! You can add notes to the INFO.OUT file using the "notes" block notes Simple calculation of the ground state of aluminium. Must check convergence with respect to k-point set later. Run by H. Golightly avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.8267 ! this is the relative path to the species files sppath '../../../species/' atoms 1 : nspecies 'Al.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/basic/PaxHeaders.21776/Cu0000644000000000000000000000013214061636520015320 xustar0030 mtime=1623670096.069101421 30 atime=1623670096.068101422 30 ctime=1623670096.069101421 elk-7.2.42/examples/basic/Cu/0000755002504400250440000000000014061636520017432 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/Cu/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520016504 xustar0029 mtime=1623670096.07010142 29 atime=1623670096.07010142 29 ctime=1623670096.07010142 elk-7.2.42/examples/basic/Cu/elk.in0000644002504400250440000000144414061636520020540 0ustar00dewhurstdewhurst00000000000000 ! Try and find the equilibrium volume of fcc copper by adjusting the scale ! parameter. The individual lattice vectors can also be scaled separately using ! scale1, scale2 or scale3. Remember that a previously converged charge density ! can be used to begin a new calculation, even at a different volume. This is ! done by setting task=1. tasks 0 avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale1 6.83117 scale2 6.83117 scale3 6.83117 scale 0.96 ! large cut-off is required for Cu rgkmax 8.5 lmaxapw 10 gmaxvr 14.0 sppath '../../../species/' atoms 1 : nspecies 'Cu.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 8 8 8 elk-7.2.42/examples/basic/PaxHeaders.21776/Pb0000644000000000000000000000013214061636520015312 xustar0030 mtime=1623670096.072101418 30 atime=1623670096.071101419 30 ctime=1623670096.072101418 elk-7.2.42/examples/basic/Pb/0000755002504400250440000000000014061636520017424 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/Pb/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016472 xustar0030 mtime=1623670096.072101418 30 atime=1623670096.072101418 30 ctime=1623670096.072101418 elk-7.2.42/examples/basic/Pb/elk.in0000644002504400250440000000123614061636520020531 0ustar00dewhurstdewhurst00000000000000 ! Band structure of lead with spin-orbit coupling. tasks 0 20 spinpol .true. spinorb .true. nempty 8 rgkmax 8.0 avec 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 scale 9.3541 sppath '../../../species/' atoms 1 : nspecies 'Pb.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 8 8 8 plot1d 7 200 : nvp1d, npp1d 0.0 0.0 1.0 : vlvp1d 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 elk-7.2.42/examples/basic/PaxHeaders.21776/YBCO0000644000000000000000000000013214061636520015505 xustar0030 mtime=1623670096.074101416 30 atime=1623670096.073101417 30 ctime=1623670096.074101416 elk-7.2.42/examples/basic/YBCO/0000755002504400250440000000000014061636520017617 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/YBCO/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016665 xustar0030 mtime=1623670096.075101415 30 atime=1623670096.075101415 30 ctime=1623670096.075101415 elk-7.2.42/examples/basic/YBCO/elk.in0000644002504400250440000000147014061636520020724 0ustar00dewhurstdewhurst00000000000000 ! High T_c superconductor YBa2Cu3O7. Note that the code determines which atoms ! are equivalent, and lists them in EQATOMS.OUT. tasks 0 ! small cut-off for testing purposes rgkmax 6.0 ! use Broyden mixing mixtype 3 avec 7.2246 0.0 0.0 0.0 7.3442 0.0 0.0 0.0 22.0733 sppath '../../../species/' atoms 4 : nspecies 'Y.in' : spfname 1 : natoms; atposl below 0.5 0.5 0.5 'Ba.in' 2 0.5 0.5 0.1843 0.5 0.5 0.8157 'Cu.in' 3 0.0 0.0 0.0 0.0 0.0 0.3556 0.0 0.0 0.6444 'O.in' 7 0.0 0.5 0.0 0.5 0.0 0.3773 0.5 0.0 0.6227 0.0 0.5 0.3789 0.0 0.5 0.6211 0.0 0.0 0.1584 0.0 0.0 0.8416 ngridk 2 2 1 vkloff 0.25 0.5 0.5 elk-7.2.42/examples/basic/PaxHeaders.21776/AlAs-fatbands0000644000000000000000000000013214061636520017351 xustar0030 mtime=1623670096.078101412 30 atime=1623670096.075101415 30 ctime=1623670096.078101412 elk-7.2.42/examples/basic/AlAs-fatbands/0000755002504400250440000000000014061636520021463 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/AlAs-fatbands/PaxHeaders.21776/AlAs.par0000644000000000000000000000013214061636520020752 xustar0030 mtime=1623670096.077101413 30 atime=1623670096.077101413 30 ctime=1623670096.077101413 elk-7.2.42/examples/basic/AlAs-fatbands/AlAs.par0000644002504400250440000000551114061636520023011 0ustar00dewhurstdewhurst00000000000000 world 0.0, -0.25, 1.113445717, 0.5 title "AlAs band structure" subtitle "(atomic character of As)" xaxis tick off xaxis ticklabel off yaxis tick major 0.1 yaxis tick minor ticks 2 yaxis label "Energy (Hartree)" s0.y1=0.05*s0.y1 s1.y1=0.05*s1.y1 s2.y1=0.05*s2.y1 s3.y1=0.05*s3.y1 s4.y1=0.05*s4.y1 s5.y1=0.05*s5.y1 s6.y1=0.05*s6.y1 s7.y1=0.05*s7.y1 s8.y1=0.05*s8.y1 s9.y1=0.05*s9.y1 s10.y1=0.05*s10.y1 s11.y1=0.05*s11.y1 s12.y1=0.05*s12.y1 s13.y1=0.05*s13.y1 s14.y1=0.05*s14.y1 s15.y1=0.05*s15.y1 s16.y1=0.05*s16.y1 s17.y1=0.05*s17.y1 s18.y1=0.05*s18.y1 s19.y1=0.05*s19.y1 s20.y1=0.05*s20.y1 s21.y1=0.05*s21.y1 s22.y1=0.05*s22.y1 s0 line type 0 s1 line type 0 s2 line type 0 s3 line type 0 s4 line type 0 s5 line type 0 s6 line type 0 s7 line type 0 s8 line type 0 s9 line type 0 s10 line type 0 s11 line type 0 s12 line type 0 s13 line type 0 s14 line type 0 s15 line type 0 s16 line type 0 s17 line type 0 s18 line type 0 s19 line type 0 s20 line type 0 s21 line type 0 s22 line type 0 s0 errorbar linestyle 0 s1 errorbar linestyle 0 s2 errorbar linestyle 0 s3 errorbar linestyle 0 s4 errorbar linestyle 0 s5 errorbar linestyle 0 s6 errorbar linestyle 0 s7 errorbar linestyle 0 s8 errorbar linestyle 0 s9 errorbar linestyle 0 s10 errorbar linestyle 0 s11 errorbar linestyle 0 s12 errorbar linestyle 0 s13 errorbar linestyle 0 s14 errorbar linestyle 0 s15 errorbar linestyle 0 s16 errorbar linestyle 0 s17 errorbar linestyle 0 s18 errorbar linestyle 0 s19 errorbar linestyle 0 s20 errorbar linestyle 0 s21 errorbar linestyle 0 s22 errorbar linestyle 0 s0 errorbar riser linewidth 3.5 s1 errorbar riser linewidth 3.5 s2 errorbar riser linewidth 3.5 s3 errorbar riser linewidth 3.5 s4 errorbar riser linewidth 3.5 s5 errorbar riser linewidth 3.5 s6 errorbar riser linewidth 3.5 s7 errorbar riser linewidth 3.5 s8 errorbar riser linewidth 3.5 s9 errorbar riser linewidth 3.5 s10 errorbar riser linewidth 3.5 s11 errorbar riser linewidth 3.5 s12 errorbar riser linewidth 3.5 s13 errorbar riser linewidth 3.5 s14 errorbar riser linewidth 3.5 s15 errorbar riser linewidth 3.5 s16 errorbar riser linewidth 3.5 s17 errorbar riser linewidth 3.5 s18 errorbar riser linewidth 3.5 s19 errorbar riser linewidth 3.5 s20 errorbar riser linewidth 3.5 s21 errorbar riser linewidth 3.5 s22 errorbar riser linewidth 3.5 s0 errorbar color 1 s1 errorbar color 1 s2 errorbar color 1 s3 errorbar color 1 s4 errorbar color 1 s5 errorbar color 1 s6 errorbar color 1 s7 errorbar color 1 s8 errorbar color 1 s9 errorbar color 1 s10 errorbar color 1 s11 errorbar color 1 s12 errorbar color 1 s13 errorbar color 1 s14 errorbar color 1 s15 errorbar color 1 s16 errorbar color 1 s17 errorbar color 1 s18 errorbar color 1 s19 errorbar color 1 s20 errorbar color 1 s21 errorbar color 1 s22 errorbar color 1 s23 line color 1 s24 line color 1 s25 line color 1 s23 linewidth 2.0 s24 linewidth 2.0 s25 linewidth 2.0 elk-7.2.42/examples/basic/AlAs-fatbands/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020531 xustar0030 mtime=1623670096.078101412 30 atime=1623670096.078101412 30 ctime=1623670096.078101412 elk-7.2.42/examples/basic/AlAs-fatbands/elk.in0000644002504400250440000000146514061636520022574 0ustar00dewhurstdewhurst00000000000000 ! Band structure of AlAs which produces a band-structure with line thickness ! proportional to the atomic character. You can produce the plot by running ! ! xmgrace -settype xydy BAND_S02_A0001.OUT -settype xy BANDLINES.OUT -param AlAs.par ! ! You can change the graph appearance either in xmgrace or by editing AlAs.par tasks 0 21 nempty 8 plot1d 3 200 : nvp1d, npp1d 0.5 0.0 0.0 : vlvp1d 0.0 0.0 0.0 0.5 0.5 0.0 avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 10.53 sppath '../../../species/' atoms 2 : nspecies 'Al.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'As.in' 1 0.25 0.25 0.25 ngridk 4 4 4 elk-7.2.42/examples/basic/PaxHeaders.21776/CuFeS20000644000000000000000000000013014061636520015776 xustar0029 mtime=1623670096.08110141 30 atime=1623670096.080101411 29 ctime=1623670096.08110141 elk-7.2.42/examples/basic/CuFeS2/0000755002504400250440000000000014061636520020112 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/CuFeS2/PaxHeaders.21776/elk.in0000644000000000000000000000013114061636520017157 xustar0030 mtime=1623670096.082101409 29 atime=1623670096.08110141 30 ctime=1623670096.082101409 elk-7.2.42/examples/basic/CuFeS2/elk.in0000644002504400250440000000324714061636520021223 0ustar00dewhurstdewhurst00000000000000 ! An example of how Elk can automatically determine the primitive unit cell ! from the conventional one. The input chalcopyrite unit cell contains 16 atoms ! which is reduced to 8 by the code. tasks 0 ! large smearing width for better convergence swidth 0.01 ! automatic determination of the primitive unit cell primcell .true. avec 9.99476 0.00000 0.00000 0.00000 9.99476 0.00000 0.00000 0.00000 19.6966 sppath '../../../species/' atoms 3 : nspecies 'Cu.in' : spfname 4 : natoms; atposl, bfcmt below 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5000 0.2500 0.0000 0.0000 0.0000 0.5000 0.0000 0.7500 0.0000 0.0000 0.0000 0.5000 0.5000 0.5000 0.0000 0.0000 0.0000 'Fe.in' : spfname 4 : natoms; atposl, bfcmt below 0.0000 0.0000 0.5000 0.0000 0.0000 0.0000 0.0000 0.5000 0.7500 0.0000 0.0000 0.0000 0.5000 0.0000 0.2500 0.0000 0.0000 0.0000 0.5000 0.5000 0.0000 0.0000 0.0000 0.0000 'S.in' : spfname 8 : natoms; atposl, bfcmt below 0.2574 0.2500 0.1250 0.0000 0.0000 0.0000 0.7426 0.7500 0.1250 0.0000 0.0000 0.0000 0.2500 0.7426 0.8750 0.0000 0.0000 0.0000 0.7500 0.2574 0.8750 0.0000 0.0000 0.0000 0.7574 0.7500 0.6250 0.0000 0.0000 0.0000 0.2426 0.2500 0.6250 0.0000 0.0000 0.0000 0.7500 0.2426 0.3750 0.0000 0.0000 0.0000 0.2500 0.7574 0.3750 0.0000 0.0000 0.0000 ngridk 2 2 2 elk-7.2.42/examples/basic/PaxHeaders.21776/Si-PBEsol0000644000000000000000000000013214061636520016446 xustar0030 mtime=1623670096.083101408 30 atime=1623670096.082101409 30 ctime=1623670096.083101408 elk-7.2.42/examples/basic/Si-PBEsol/0000755002504400250440000000000014061636520020560 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/Si-PBEsol/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017626 xustar0030 mtime=1623670096.084101407 30 atime=1623670096.084101407 30 ctime=1623670096.084101407 elk-7.2.42/examples/basic/Si-PBEsol/elk.in0000644002504400250440000000136514061636520021670 0ustar00dewhurstdewhurst00000000000000 ! Band structure of silicon using the new PBEsol functional (xctype = 22) ! (http://arxiv.org/pdf/0711.0156). tasks 0 20 xctype 22 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 2 2 2 vkloff 0.25 0.5 0.625 ! These are the vertices to be joined for the band structure plot plot1d 7 200 : nvp1d, npp1d 0.0 0.0 1.0 : vlvp1d 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 elk-7.2.42/examples/basic/PaxHeaders.21776/diamond-rho3D0000644000000000000000000000013214061636520017341 xustar0030 mtime=1623670096.089101402 30 atime=1623670096.085101406 30 ctime=1623670096.089101402 elk-7.2.42/examples/basic/diamond-rho3D/0000755002504400250440000000000014061636520021453 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/basic/diamond-rho3D/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020521 xustar0030 mtime=1623670096.086101405 30 atime=1623670096.086101405 30 ctime=1623670096.086101405 elk-7.2.42/examples/basic/diamond-rho3D/elk.in0000644002504400250440000000112314061636520022553 0ustar00dewhurstdewhurst00000000000000 ! 3D plot of the charge density of diamond using OpenDX. tasks 0 33 ! define box corners and grid size for 3D plot, first point is the origin plot3d 0.0 0.0 0.0 : vclp3d 2.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 2.0 80 80 80 avec 3.3637 3.3637 0.0000 3.3637 0.0000 3.3637 0.0000 3.3637 3.3637 sppath '../../../species/' atoms 1 : nspecies 'C.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 2 2 2 vkloff 0.25 0.5 0.625 elk-7.2.42/examples/basic/diamond-rho3D/PaxHeaders.21776/rho3d.general0000644000000000000000000000013214061636520021774 xustar0030 mtime=1623670096.088101403 30 atime=1623670096.088101403 30 ctime=1623670096.088101403 elk-7.2.42/examples/basic/diamond-rho3D/rho3d.general0000644002504400250440000000027414061636520024034 0ustar00dewhurstdewhurst00000000000000file = RHO3D.OUT grid = 80 x 80 x 80 format = ascii interleaving = field majority = column header = lines 1 field = locations, field0 structure = 3-vector, scalar type = float, float end elk-7.2.42/examples/basic/diamond-rho3D/PaxHeaders.21776/rho3d.net0000644000000000000000000000013214061636520021145 xustar0030 mtime=1623670096.090101401 30 atime=1623670096.089101402 30 ctime=1623670096.090101401 elk-7.2.42/examples/basic/diamond-rho3D/rho3d.net0000644002504400250440000003450214061636520023206 0ustar00dewhurstdewhurst00000000000000// // time: Fri Sep 26 23:37:42 2008 // // version: 3.2.0 (format), 4.4.0 (DX) // // // MODULE main // workspace: width = 298, height = 472 // layout: snap = 0, width = 50, height = 50, align = NN // macro main( ) -> ( ) { // // node Import[1]: x = 56, y = 47, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "rho3d.general" // main_Import_1_out_1 = Import( main_Import_1_in_1, main_Import_1_in_2, main_Import_1_in_3, main_Import_1_in_4, main_Import_1_in_5, main_Import_1_in_6 ) [instance: 1, cache: 1]; // // node Isosurface[2]: x = 220, y = 121, inputs = 6, label = Isosurface // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.04 // main_Isosurface_2_out_1 = Isosurface( main_Import_1_out_1, main_Isosurface_2_in_2, main_Isosurface_2_in_3, main_Isosurface_2_in_4, main_Isosurface_2_in_5, main_Isosurface_2_in_6 ) [instance: 2, cache: 1]; // // node Color[1]: x = 72, y = 232, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "white" // input[4]: defaulting = 0, visible = 0, type = 32, value = "front colors" // main_Color_1_out_1 = Color( main_Isosurface_2_out_1, main_Color_1_in_2, main_Color_1_in_3, main_Color_1_in_4, main_Color_1_in_5 ) [instance: 1, cache: 1]; // // node Color[2]: x = 69, y = 316, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "orange" // input[4]: defaulting = 0, visible = 0, type = 32, value = "back colors" // main_Color_2_out_1 = Color( main_Color_1_out_1, main_Color_2_in_2, main_Color_2_in_3, main_Color_2_in_4, main_Color_2_in_5 ) [instance: 2, cache: 1]; // // node Image[4]: x = 223, y = 410, inputs = 49, label = Image // input[1]: defaulting = 0, visible = 0, type = 32, value = "Image_4" // input[4]: defaulting = 0, visible = 0, type = 1, value = 1 // input[5]: defaulting = 0, visible = 0, type = 8, value = [7.29024 7.29024 7.29024] // input[6]: defaulting = 0, visible = 0, type = 8, value = [-4.66221 51.8696 -4.66221] // input[7]: defaulting = 0, visible = 0, type = 5, value = 21.0859 // input[8]: defaulting = 0, visible = 0, type = 1, value = 640 // input[9]: defaulting = 0, visible = 0, type = 5, value = 0.75 // input[10]: defaulting = 0, visible = 0, type = 8, value = [0 0 -1] // input[11]: defaulting = 1, visible = 0, type = 5, value = 24.9389 // input[12]: defaulting = 0, visible = 0, type = 1, value = 0 // input[14]: defaulting = 0, visible = 0, type = 1, value = 1 // input[15]: defaulting = 1, visible = 0, type = 32, value = "none" // input[16]: defaulting = 1, visible = 0, type = 32, value = "none" // input[17]: defaulting = 1, visible = 0, type = 1, value = 1 // input[18]: defaulting = 1, visible = 0, type = 1, value = 1 // input[19]: defaulting = 0, visible = 0, type = 1, value = 0 // input[29]: defaulting = 1, visible = 0, type = 3, value = 0 // input[41]: defaulting = 0, visible = 0, type = 32, value = "zoom" // depth: value = 24 // window: position = (0.0104,0.0600), size = 0.4542x0.5800, screen = 0 // internal caching: 1 // main_Image_4_out_1, main_Image_4_out_2, main_Image_4_out_3 = Image( main_Image_4_in_1, main_Color_2_out_1, main_Image_4_in_3, main_Image_4_in_4, main_Image_4_in_5, main_Image_4_in_6, main_Image_4_in_7, main_Image_4_in_8, main_Image_4_in_9, main_Image_4_in_10, main_Image_4_in_11, main_Image_4_in_12, main_Image_4_in_13, main_Image_4_in_14, main_Image_4_in_15, main_Image_4_in_16, main_Image_4_in_17, main_Image_4_in_18, main_Image_4_in_19, main_Image_4_in_20, main_Image_4_in_21, main_Image_4_in_22, main_Image_4_in_23, main_Image_4_in_24, main_Image_4_in_25, main_Image_4_in_26, main_Image_4_in_27, main_Image_4_in_28, main_Image_4_in_29, main_Image_4_in_30, main_Image_4_in_31, main_Image_4_in_32, main_Image_4_in_33, main_Image_4_in_34, main_Image_4_in_35, main_Image_4_in_36, main_Image_4_in_37, main_Image_4_in_38, main_Image_4_in_39, main_Image_4_in_40, main_Image_4_in_41, main_Image_4_in_42, main_Image_4_in_43, main_Image_4_in_44, main_Image_4_in_45, main_Image_4_in_46, main_Image_4_in_47, main_Image_4_in_48, main_Image_4_in_49 ) [instance: 4, cache: 1]; // network: end of macro body CacheScene(main_Image_4_in_1, main_Image_4_out_1, main_Image_4_out_2); } main_Import_1_in_1 = "rho3d.general"; main_Import_1_in_2 = NULL; main_Import_1_in_3 = NULL; main_Import_1_in_4 = NULL; main_Import_1_in_5 = NULL; main_Import_1_in_6 = NULL; main_Import_1_out_1 = NULL; main_Isosurface_2_in_2 = 0.04; main_Isosurface_2_in_3 = NULL; main_Isosurface_2_in_4 = NULL; main_Isosurface_2_in_5 = NULL; main_Isosurface_2_in_6 = NULL; main_Isosurface_2_out_1 = NULL; main_Color_1_in_2 = "white"; main_Color_1_in_3 = NULL; main_Color_1_in_4 = "front colors"; main_Color_1_in_5 = NULL; main_Color_1_out_1 = NULL; main_Color_2_in_2 = "orange"; main_Color_2_in_3 = NULL; main_Color_2_in_4 = "back colors"; main_Color_2_in_5 = NULL; main_Color_2_out_1 = NULL; macro Image( id, object, where, useVector, to, from, width, resolution, aspect, up, viewAngle, perspective, options, buttonState = 1, buttonUpApprox = "none", buttonDownApprox = "none", buttonUpDensity = 1, buttonDownDensity = 1, renderMode = 0, defaultCamera, reset, backgroundColor, throttle, RECenable = 0, RECfile, RECformat, RECresolution, RECaspect, AAenable = 0, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, interactionMode, title, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels, webOptions) -> ( object, camera, where) { ImageMessage( id, backgroundColor, throttle, RECenable, RECfile, RECformat, RECresolution, RECaspect, AAenable, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels, interactionMode, title, renderMode, buttonUpApprox, buttonDownApprox, buttonUpDensity, buttonDownDensity) [instance: 1, cache: 1]; autoCamera = AutoCamera( object, "front", object, resolution, aspect, [0,1,0], perspective, viewAngle, backgroundColor) [instance: 1, cache: 1]; realCamera = Camera( to, from, width, resolution, aspect, up, perspective, viewAngle, backgroundColor) [instance: 1, cache: 1]; coloredDefaultCamera = UpdateCamera(defaultCamera, background=backgroundColor) [instance: 1, cache: 1]; nullDefaultCamera = Inquire(defaultCamera, "is null + 1") [instance: 1, cache: 1]; resetCamera = Switch( nullDefaultCamera, coloredDefaultCamera, autoCamera) [instance: 1, cache: 1]; resetNull = Inquire( reset, "is null + 1") [instance: 2, cache: 1]; reset = Switch( resetNull, reset, 0) [instance: 2, cache: 1]; whichCamera = Compute( "($0 != 0 || $1 == 0) ? 1 : 2", reset, useVector) [instance: 1, cache: 1]; camera = Switch( whichCamera, resetCamera, realCamera) [instance: 3, cache: 1]; AAobject = AutoAxes( object, camera, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels) [instance: 1, cache: 1]; switchAAenable = Compute("$0+1", AAenable) [instance: 2, cache: 1]; object = Switch( switchAAenable, object, AAobject) [instance:4, cache: 1]; SWapproximation_options = Switch( buttonState, buttonUpApprox, buttonDownApprox) [instance: 5, cache: 1]; SWdensity_options = Switch( buttonState, buttonUpDensity, buttonDownDensity) [instance: 6, cache: 1]; HWapproximation_options = Format( "%s,%s", buttonDownApprox, buttonUpApprox) [instance: 1, cache: 1]; HWdensity_options = Format( "%d,%d", buttonDownDensity, buttonUpDensity) [instance: 2, cache: 1]; switchRenderMode = Compute( "$0+1", renderMode) [instance: 3, cache: 1]; approximation_options = Switch( switchRenderMode, SWapproximation_options, HWapproximation_options) [instance: 7, cache: 1]; density_options = Switch( switchRenderMode, SWdensity_options, HWdensity_options) [instance: 8, cache: 1]; renderModeString = Switch( switchRenderMode, "software", "hardware")[instance: 9, cache: 1]; object_tag = Inquire( object, "object tag")[instance: 3, cache: 1]; annoted_object = Options( object, "send boxes", 0, "cache", 1, "object tag", object_tag, "ddcamera", whichCamera, "rendering approximation", approximation_options, "render every", density_options, "button state", buttonState, "rendering mode", renderModeString) [instance: 1, cache: 1]; RECresNull = Inquire( RECresolution, "is null + 1") [instance: 4, cache: 1]; ImageResolution = Inquire( camera, "camera resolution") [instance: 5, cache: 1]; RECresolution = Switch( RECresNull, RECresolution, ImageResolution) [instance: 10, cache: 1]; RECaspectNull = Inquire( RECaspect, "is null + 1") [instance: 6, cache: 1]; ImageAspect = Inquire( camera, "camera aspect") [instance: 7, cache: 1]; RECaspect = Switch( RECaspectNull, RECaspect, ImageAspect) [instance: 11, cache: 1]; switchRECenable = Compute( "$0 == 0 ? 1 : (($2 == $3) && ($4 == $5)) ? ($1 == 1 ? 2 : 3) : 4", RECenable, switchRenderMode, RECresolution, ImageResolution, RECaspect, ImageAspect) [instance: 4, cache: 1]; NoRECobject, RECNoRerenderObject, RECNoRerHW, RECRerenderObject = Route(switchRECenable, annoted_object); Display( NoRECobject, camera, where, throttle) [instance: 1, cache: 1]; image = Render( RECNoRerenderObject, camera) [instance: 1, cache: 1]; Display( image, NULL, where, throttle) [instance: 2, cache: 1]; WriteImage( image, RECfile, RECformat) [instance: 1, cache: 1]; rec_where = Display( RECNoRerHW, camera, where, throttle) [instance: 1, cache: 0]; rec_image = ReadImageWindow( rec_where) [instance: 1, cache: 1]; WriteImage( rec_image, RECfile, RECformat) [instance: 1, cache: 1]; RECupdateCamera = UpdateCamera( camera, resolution=RECresolution, aspect=RECaspect) [instance: 2, cache: 1]; Display( RECRerenderObject, camera, where, throttle) [instance: 1, cache: 1]; RECRerenderObject = ScaleScreen( RECRerenderObject, NULL, RECresolution, camera) [instance: 1, cache: 1]; image = Render( RECRerenderObject, RECupdateCamera) [instance: 2, cache: 1]; WriteImage( image, RECfile, RECformat) [instance: 2, cache: 1]; } main_Image_4_in_1 = "Image_4"; main_Image_4_in_3 = "X24,,"; main_Image_4_in_4 = 1; main_Image_4_in_5 = [7.29024 7.29024 7.29024]; main_Image_4_in_6 = [-4.66221 51.8696 -4.66221]; main_Image_4_in_7 = 21.0859; main_Image_4_in_8 = 640; main_Image_4_in_9 = 0.75; main_Image_4_in_10 = [0 0 -1]; main_Image_4_in_11 = NULL; main_Image_4_in_12 = 0; main_Image_4_in_13 = NULL; main_Image_4_in_14 = 1; main_Image_4_in_15 = NULL; main_Image_4_in_16 = NULL; main_Image_4_in_17 = NULL; main_Image_4_in_18 = NULL; main_Image_4_in_19 = 0; main_Image_4_in_20 = NULL; main_Image_4_in_21 = NULL; main_Image_4_in_22 = NULL; main_Image_4_in_23 = NULL; main_Image_4_in_25 = NULL; main_Image_4_in_26 = NULL; main_Image_4_in_27 = NULL; main_Image_4_in_28 = NULL; main_Image_4_in_29 = NULL; main_Image_4_in_30 = NULL; main_Image_4_in_31 = NULL; main_Image_4_in_32 = NULL; main_Image_4_in_33 = NULL; main_Image_4_in_34 = NULL; main_Image_4_in_35 = NULL; main_Image_4_in_36 = NULL; main_Image_4_in_37 = NULL; main_Image_4_in_38 = NULL; main_Image_4_in_39 = NULL; main_Image_4_in_40 = NULL; main_Image_4_in_41 = "zoom"; main_Image_4_in_42 = NULL; main_Image_4_in_43 = NULL; main_Image_4_in_44 = NULL; main_Image_4_in_45 = NULL; main_Image_4_in_46 = NULL; main_Image_4_in_47 = NULL; main_Image_4_in_48 = NULL; main_Image_4_in_49 = NULL; Executive("product version 4 4 0"); $sync main(); elk-7.2.42/examples/PaxHeaders.21776/magnetism-source-free0000644000000000000000000000013014061636520020067 xustar0030 mtime=1623670096.092101399 28 atime=1623670096.0911014 30 ctime=1623670096.092101399 elk-7.2.42/examples/magnetism-source-free/0000755002504400250440000000000014061636520022203 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism-source-free/PaxHeaders.21776/Ba1220000644000000000000000000000013214061636520020640 xustar0030 mtime=1623670096.098101394 30 atime=1623670096.092101399 30 ctime=1623670096.098101394 elk-7.2.42/examples/magnetism-source-free/Ba122/0000755002504400250440000000000014061636520022752 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism-source-free/Ba122/PaxHeaders.21776/Ba122-Bxc-field-lines.png0000644000000000000000000000013214061636520025075 xustar0030 mtime=1623670096.097101395 30 atime=1623670096.093101399 30 ctime=1623670096.097101395 elk-7.2.42/examples/magnetism-source-free/Ba122/Ba122-Bxc-field-lines.png0000644002504400250440000124625314061636520027147 0ustar00dewhurstdewhurst00000000000000PNG  IHDRyL] pHYs5ؗtIME 9} IDATxyeOU5wfr bS  VXq]Y*ʱ @A r rMIf&sOYzj{fz!$5:>_!ć;vnFTנQ?cƌVRJ۶Çϵ>|V:SUwwUɤ}և!zݰG5M===ޞ={3Çϵ>|v׏;|YYYSO=nnnϰу={L0AJ)(~+˲0x'׾v'N4?>|\hGWWرcmd2,_nݲen9sևA}E訩)ks<Ϻ=cJ ZЇϵ>|8`H$J+,+ ysc=v{P___>P(4`cצeYӧO1u]K.7j*ևbXEEE vm*RUջ4h4:a„mڵ-K'Jh(B**+++kEٰKJ9^0jjj.yY_>B"дa?h=A ujdooowww{{ԩS'MT¡s>>aض]P?TWWw'h,+W\hQgg(dλ+|\Ç ݊2, )e qGBG"cۿouYضgϞP(k}_"` wuud,+|(][nĉgcSUuԩq Cct'~,ˊD"9EGuuu9>|\ÇYfRӴn:.A*HR& և/D</fM!4Ѳ.uwaصx<u|m'?ٴiև#^|_|ѶbxζCYNKpG[sD"(p/^||\hkk #9_JHiN0*++իWϙ3+Wz7dm|Ga! e9>Rʁ,lH|1Kp ޽{ƌ^xW׿^v?(7nPܱx5?>|\[䚶mH cb$2M3-_~~@׶1cxނhtO?ST >|oG=qD߮Ga"0>zaYVWWWηb5T*o~`i9>T*Urd[[7`|! 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KKK׮]34ԩS!!![l@]CCCZZT*ݿ9W^QThZWƺ|ªJߏ޺u+ 0Bd3gt??p<?ڮ]V]]uVVNb-`Hrʓ'O}||d2DBrykkkmmmUUUGGL^r%DsZF2>_]]]UU%ɐHB1bZkkkkjjr9 ~OTX. M"LMM?tZD:;;ds 0Jdf.doogp8 `tKҞplvss?caabk4Zh4"bl.B@ 0V$...( D" 9՗!rIENDB`elk-7.2.42/examples/magnetism-source-free/Ba122/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520022020 xustar0030 mtime=1623670096.099101393 30 atime=1623670096.099101393 30 ctime=1623670096.099101393 elk-7.2.42/examples/magnetism-source-free/Ba122/elk.in0000644002504400250440000000474514061636520024067 0ustar00dewhurstdewhurst00000000000000 ! Magnetism in BaFe2As2 using the source-free version of LSDA. ! Source-Free Exchange-Correlation Magnetic Fields in Density Functional Theory ! S. Sharma, E. K. U. Gross, A. Sanna and J. K. Dewhurst ! Journal of Chemical Theory and Computation 14 (3), 1247 (2018) tasks 0 ! ground-state run 72 ! 2D plot of magnetisation 82 ! 2D plot of B_xc 83 ! 3D plot of B_xc 92 ! 2D plot of divergence of B_xc 152 ! 2D plot of m(r) x B_xc(r) ! enable source-free B_xc nosource .true. ! spin exchange-correlation scaling factor (see article) sxcscf 1.12 highq .true. ngridk 8 8 6 xctype 3 spinpol .true. spinorb .true. plot2d 0.0 0.0 0.5 1.0 0.0 0.5 0.0 1.0 0.5 600 600 plot3d 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 200 200 200 scale 9.8337 avec 1.078174 0.000000 0.000000 -0.000000 1.096817 0.000000 0.000000 0.000000 2.473656 primcell .true. sppath '../../../species/' atoms 3 "Ba.in" 4 0.00000 -0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 0.50000 0.50000 0.00000 0.00000 0.00000 0.50000 0.50000 -0.00000 0.00000 0.00000 0.00000 0.50000 -0.00000 0.50000 0.00000 0.00000 0.00000 "Fe.in" 8 0.75000 0.25000 0.25000 0.00000 0.00000 -0.01000 0.75000 0.75000 0.25000 0.00000 0.00000 0.01000 0.25000 0.25000 0.25000 0.00000 0.00000 -0.01000 0.25000 0.75000 0.25000 0.00000 0.00000 0.01000 0.75000 0.25000 0.75000 0.00000 0.00000 0.01000 0.75000 0.75000 0.75000 0.00000 0.00000 -0.01000 0.25000 0.25000 0.75000 0.00000 0.00000 0.01000 0.25000 0.75000 0.75000 0.00000 0.00000 -0.01000 "As.in" 8 0.00000 -0.00000 0.64970 0.00000 0.00000 0.00000 0.00000 -0.00000 0.35030 0.00000 0.00000 0.00000 0.50000 0.50000 0.64970 0.00000 0.00000 0.00000 0.50000 0.50000 0.35030 0.00000 0.00000 0.00000 0.00000 0.50000 0.14970 0.00000 0.00000 0.00000 0.00000 0.50000 0.85030 0.00000 0.00000 0.00000 0.50000 -0.00000 0.14970 0.00000 0.00000 0.00000 0.50000 -0.00000 0.85030 0.00000 0.00000 0.00000 elk-7.2.42/examples/PaxHeaders.21776/molecules0000644000000000000000000000013214061636520015660 xustar0030 mtime=1623670096.106101386 30 atime=1623670096.100101392 30 ctime=1623670096.106101386 elk-7.2.42/examples/molecules/0000755002504400250440000000000014061636520017772 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/molecules/PaxHeaders.21776/C600000644000000000000000000000013014061636520016206 xustar0029 mtime=1623670096.10210139 30 atime=1623670096.101101391 29 ctime=1623670096.10210139 elk-7.2.42/examples/molecules/C60/0000755002504400250440000000000014061636520020322 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/molecules/C60/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520017374 xustar0029 mtime=1623670096.10210139 29 atime=1623670096.10210139 29 ctime=1623670096.10210139 elk-7.2.42/examples/molecules/C60/elk.in0000644002504400250440000000550714061636520021434 0ustar00dewhurstdewhurst00000000000000 ! C60 buckyball example. This example has high memory and time requirements and ! employs iterative diagonalisation. tasks 0 ! use iterative diagonalisation for the first-variational step tefvit .true. ! molecule calculation molecule .true. ! use very small energy cut-off rgkmax 4.0 sppath '../../../species/' ! use an fcc box to contain the molecule avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 24.0 ! the atomic coordinates are Cartesian with molecule=.true. atoms 1 : nspecies 'C.in' : spfname 60 : natoms; atposc below 4.20790955 1.12423579 5.07240250 5.92255243 0.30577656 3.09053347 2.53625794 -0.58931105 6.15449739 5.89150423 -2.19125067 2.27598598 6.07911622 -2.76287388 -0.40300296 6.14208189 2.34350589 1.26288498 6.32168145 1.79658139 -1.30022597 6.28972619 -0.81331917 -2.15152863 -0.85451519 2.59699373 6.10424958 0.89249869 4.38777367 4.97351314 -0.05102260 0.16353689 6.68186323 3.36781297 3.66786366 4.46912637 4.56285678 4.42127851 2.11483015 -0.49930340 5.89307270 3.14654495 0.64416979 6.61402206 0.89416165 3.23137475 5.86189222 0.36707927 -4.04684820 -1.59965305 5.07597408 -4.88658574 0.94354019 4.47250898 -1.68274430 -1.98120762 6.15625484 -3.32578546 2.99557474 4.97542176 -3.10623709 5.03232141 3.14743312 -6.29775752 0.83554235 2.11927100 -6.08784676 2.78439786 0.37044299 -4.45682426 4.92933134 0.89618365 -0.95746747 -5.66581425 3.40868774 -3.42822750 -5.26727104 2.27991661 -0.10387824 -4.05947157 5.30402621 -4.93898784 -3.27912812 3.09521999 -6.32980727 -1.77424483 1.26783606 -3.23999190 -5.83991471 -0.39909123 -4.57094481 -4.40022696 -2.14742792 -6.15020772 -2.32243545 -1.29533158 4.14416909 -3.98220068 3.40634448 3.25204835 -5.66116553 1.42568487 2.50352789 -3.19913602 5.30279789 0.75764784 -6.48459473 1.42687540 -0.65282474 -6.59204455 -0.92630589 4.44820711 -4.90778847 -0.92840348 3.09860260 -5.01057066 -3.17986082 0.49168780 -5.87162431 -3.17872698 -4.21537397 -1.10412910 -5.10475461 -3.37499392 -3.64732234 -4.50151628 -0.89933950 -4.36660874 -5.00582745 -2.54410030 0.61009804 -6.18628259 -4.15359883 4.00310105 -3.43858320 -5.90029145 2.21167861 -2.30835699 -5.93067825 -0.28551870 -3.12307455 -2.51263637 3.22020647 -5.33473426 0.94767869 5.68830199 -3.44022726 -0.76728544 6.50657224 -1.45864170 -3.26164816 5.68270840 -1.45786691 0.09442961 4.08156247 -5.33543346 4.03843892 1.62287778 -5.10734353 4.93027621 3.30214499 -3.12685400 3.41902454 5.29011783 -2.31168290 1.67416495 2.00384654 -6.18737863 0.84756100 -2.57503512 -6.13588359 3.31858560 -2.97318149 -5.00728254 4.87893235 -0.92061781 -4.50446425 0.04346370 -0.14161607 -6.71310040 elk-7.2.42/examples/molecules/PaxHeaders.21776/H2O-iterative0000644000000000000000000000013214061636520020242 xustar0030 mtime=1623670096.104101388 30 atime=1623670096.103101389 30 ctime=1623670096.104101388 elk-7.2.42/examples/molecules/H2O-iterative/0000755002504400250440000000000014061636520022354 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/molecules/H2O-iterative/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021422 xustar0030 mtime=1623670096.105101387 30 atime=1623670096.104101388 30 ctime=1623670096.105101387 elk-7.2.42/examples/molecules/H2O-iterative/elk.in0000644002504400250440000000136314061636520023462 0ustar00dewhurstdewhurst00000000000000 ! Water molecule in a box. This example uses iterative diagonalisation which may ! be used for fine-grained parallelism. tasks 0 maxscl 30 lorbcnd .true. ! solve the first-variational eigenvalue equation iteratively tefvit .true. ! molecule calculation (atomic positions are in Cartesian coordinates) molecule .true. ! put molecule in a large box avec 6.0 0.0 0.0 0.0 6.0 0.0 0.0 0.0 6.0 sppath '../../../species/' ! atomic positions in Cartesian coordinates atoms 2 : nspecies 'O.in' : spfname 1 : natoms; atposc below 0.0 0.0 0.0 'H.in' 2 1.811 0.0 0.0 -0.451907959 1.753710409 0.0 elk-7.2.42/examples/molecules/PaxHeaders.21776/NaCl-monomer0000644000000000000000000000013214061636520020147 xustar0030 mtime=1623670096.107101385 30 atime=1623670096.106101386 30 ctime=1623670096.107101385 elk-7.2.42/examples/molecules/NaCl-monomer/0000755002504400250440000000000014061636520022261 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/molecules/NaCl-monomer/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021327 xustar0030 mtime=1623670096.108101384 30 atime=1623670096.107101385 30 ctime=1623670096.108101384 elk-7.2.42/examples/molecules/NaCl-monomer/elk.in0000644002504400250440000000163714061636520023373 0ustar00dewhurstdewhurst00000000000000 ! NaCl monomer in a large box. Note that with 'molecule=.true.' the atomic ! positions are supplied in Cartesian coordinates. Try plotting the 1D ! density along the molcular axis. You can also compute the vibrational ! frequency using task=200. tasks 0 molecule .true. ! large smearing width improves convergence for molecules swidth 0.05 rgkmax 6.0 ! large box containing the molecule avec 10.0 0.0 0.0 0.0 10.0 0.0 0.0 0.0 10.0 sppath '../../../species/' ! note that atomic positions are now in Cartesian coordinates atoms 2 : nspecies 'Na.in' : spfname 1 : natoms; atposc below 0.0 0.0 0.0 'Cl.in' : spfname 1 : natoms; atposc below 4.4121 0.0 0.0 plot1d 2 1000 0.0 0.0 0.0 1.0 0.0 0.0 elk-7.2.42/examples/PaxHeaders.21776/structure-factors0000644000000000000000000000013214061636520017367 xustar0030 mtime=1623670096.110101383 30 atime=1623670096.109101384 30 ctime=1623670096.110101383 elk-7.2.42/examples/structure-factors/0000755002504400250440000000000014061636520021501 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/structure-factors/PaxHeaders.21776/MnO0000644000000000000000000000013214061636520020060 xustar0030 mtime=1623670096.111101382 30 atime=1623670096.110101383 30 ctime=1623670096.111101382 elk-7.2.42/examples/structure-factors/MnO/0000755002504400250440000000000014061636520022172 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/structure-factors/MnO/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021240 xustar0030 mtime=1623670096.111101382 30 atime=1623670096.111101382 30 ctime=1623670096.111101382 elk-7.2.42/examples/structure-factors/MnO/elk.in0000644002504400250440000000455014061636520023301 0ustar00dewhurstdewhurst00000000000000 ! MnO in AFMII structure with LDA, in analogy with NiO example. Unit cell from ! Transactions and Journal of the British Ceramic Society (1984) 83, 5-9. ! ! This example illustrates the calculation of X-ray and magnetic structure ! factors which are the Fourier transforms of the electron density and ! magnetisation, respectively. ! ! The structure factors are calculated for the reflections whose diffraction ! vectors have lengths up to hmaxvr (given in a.u.). The connection to the ! traditional sin(theta)/lambda ratio is ! ! max|H| = 4*pi*max(sin(theta)/lambda) [wavelength also in a.u.!] ! ! Additionally, the hkl indices of the reflections are transformed by matrix ! vhmat. ! ! Since the primitive magnetic unit cell (given by avec) is bigger than the ! conventional crystallographic unit cell (cubic with a = 8.397946), a ! non-integer hkl indices appears when reflections are reindexed to the latter ! with vhmat. They have zero intensity for X-ray structure factors but are of ! non-zero intensity in case of magnetic structure factors. ! ! Example by Alexey I. Baranov. tasks 0 195 196 spinpol .true. scale 8.397946 avec 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 atoms 2 : nspecies 'Mn.in' : spfname 2 : natoms; atpos, bfcmt below 0.0 0.0 0.0 0.0 0.0 -0.01 0.5 0.5 0.5 0.0 0.0 0.01 'O.in' : spfname 2 : natoms; atpos, bfcmt below 0.25 0.25 0.25 0.0 0.0 0.0 0.75 0.75 0.75 0.0 0.0 0.0 ! fairly high number of empty states nempty 8 sppath '../../../species/' ! this grid is too small for accurate magnetic moment ngridk 4 4 4 ! maximum |H| hmaxvr 6.0 ! H-vectors are reduced by the symmorphic crystal symmetries reduceh .true. ! uncomment the following lines to define an energy window for which only the ! orbitals within this window will contribute to the structure factors !wsfac ! -1.0 -0.1 ! H-vector transformation matrix for the conventional cell (cubic, a=8.397946) ! in the usual matrix row-column setting and applied directly as H' = MH but ! only for the output of the structure factor files. vhmat 1.5 -0.5 -0.5 -0.5 1.5 -0.5 -0.5 -0.5 1.5 ! For accurate results fine radial mesh (lradstp=1) should be used. lradstp 1 elk-7.2.42/examples/PaxHeaders.21776/README0000644000000000000000000000013014061636520014623 xustar0029 mtime=1623670096.11310138 30 atime=1623670096.112101381 29 ctime=1623670096.11310138 elk-7.2.42/examples/README0000644002504400250440000000037714061636520016671 0ustar00dewhurstdewhurst00000000000000 Elk Code examples Please note that these examples are simply to demonstrate the features of the code. Any calculations used for production work must be thoroughly checked for convergence with respect to input parameters. elk-7.2.42/examples/PaxHeaders.21776/Compton-scattering0000644000000000000000000000013114061636520017447 xustar0030 mtime=1623670096.125101369 29 atime=1623670096.11310138 30 ctime=1623670096.125101369 elk-7.2.42/examples/Compton-scattering/0000755002504400250440000000000014061636520021562 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Compton-scattering/PaxHeaders.21776/Li0000644000000000000000000000013214061636520020014 xustar0030 mtime=1623670096.119101374 30 atime=1623670096.115101378 30 ctime=1623670096.119101374 elk-7.2.42/examples/Compton-scattering/Li/0000755002504400250440000000000014061636520022126 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Compton-scattering/Li/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021174 xustar0030 mtime=1623670096.117101376 30 atime=1623670096.116101377 30 ctime=1623670096.117101376 elk-7.2.42/examples/Compton-scattering/Li/elk.in0000644002504400250440000000163214061636520023233 0ustar00dewhurstdewhurst00000000000000 ! Once-integrated electron momentum density (EMD) plot for fcc Li. ! First the EMD is calculated on a regular H+k grid. This is then interpolated ! and integrated perpendicular to the plotting plane given by plot2d. The files ! required for plotting the EMD with OpenDX are included in this directory. ! Example by David Ernsting and Stephen Dugdale. tasks 0 170 172 ! the 2D plotting plane vertices are given in reciprocal lattice coordinates plot2d -2.0 -2.0 0.0 -2.0 2.0 0.0 2.0 -2.0 0.0 100 100 ! maximum length of H+k-vectors for the regular EMD grid hkmax 7.0 ! large k-point grid required ngridk 20 20 20 avec 0.5 0.5 -0.5 0.5 -0.5 0.5 -0.5 0.5 0.5 scale 6.6226 sppath '../../../species/' atoms 1 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 elk-7.2.42/examples/Compton-scattering/Li/PaxHeaders.21776/emd2d.general0000644000000000000000000000013214061636520022423 xustar0030 mtime=1623670096.118101375 30 atime=1623670096.118101375 30 ctime=1623670096.118101375 elk-7.2.42/examples/Compton-scattering/Li/emd2d.general0000644002504400250440000000027114061636520024460 0ustar00dewhurstdewhurst00000000000000file = EMD2D.OUT grid = 100 x 100 format = ascii interleaving = field majority = column header = lines 1 field = locations, field0 structure = 2-vector, scalar type = float, float end elk-7.2.42/examples/Compton-scattering/Li/PaxHeaders.21776/emd2d.net0000644000000000000000000000013214061636520021574 xustar0030 mtime=1623670096.120101373 30 atime=1623670096.120101373 30 ctime=1623670096.120101373 elk-7.2.42/examples/Compton-scattering/Li/emd2d.net0000644002504400250440000003741414061636520023642 0ustar00dewhurstdewhurst00000000000000// // time: Mon Jan 26 19:22:44 2015 // // version: 3.2.0 (format), 4.4.4 (DX) // // // MODULE main // workspace: width = 425, height = 581 // layout: snap = 0, width = 50, height = 50, align = NN // macro main( ) -> ( ) { // // node Import[2]: x = 199, y = 111, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "emd2d.general" // main_Import_2_out_1 = Import( main_Import_2_in_1, main_Import_2_in_2, main_Import_2_in_3, main_Import_2_in_4, main_Import_2_in_5, main_Import_2_in_6 ) [instance: 2, cache: 1]; // // node RubberSheet[2]: x = 138, y = 249, inputs = 4, label = RubberSheet // main_RubberSheet_2_out_1 = RubberSheet( main_Import_2_out_1, main_RubberSheet_2_in_2, main_RubberSheet_2_in_3, main_RubberSheet_2_in_4 ) [instance: 2, cache: 1]; // // node Colormap[3]: x = 351, y = 266, inputs = 19, label = Colormap // input[1]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 0.666667] [1.0 0.0] } // input[2]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[3]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[4]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[5]: defaulting = 0, visible = 0, type = 32, value = "Colormap_3" // input[7]: defaulting = 1, visible = 0, type = 5, value = 4.1046274e-06 // input[8]: defaulting = 1, visible = 0, type = 5, value = 0.014571383 // input[9]: defaulting = 1, visible = 0, type = 1, value = 20 // input[12]: defaulting = 0, visible = 0, type = 16777221, value = { 4.1046274e-06 0.014571383 } // input[17]: defaulting = 0, visible = 0, type = 5, value = 4.1046274e-06 // input[18]: defaulting = 0, visible = 0, type = 5, value = 0.014571383 // window: position = (17.0661,30.3398), size = 17.0661x30.3398 // main_Colormap_3_out_1[cache: 2], main_Colormap_3_out_2[cache: 2] = Colormap( main_Colormap_3_in_1, main_Colormap_3_in_2, main_Colormap_3_in_3, main_Colormap_3_in_4, main_Colormap_3_in_5, main_RubberSheet_2_out_1, main_Colormap_3_in_7, main_Colormap_3_in_8, main_Colormap_3_in_9, main_Colormap_3_in_10, main_Colormap_3_in_11, main_Colormap_3_in_12, main_Colormap_3_in_13, main_Colormap_3_in_14, main_Colormap_3_in_15, main_Colormap_3_in_16, main_Colormap_3_in_17, main_Colormap_3_in_18, main_Colormap_3_in_19 ) [instance: 3, cache: 1]; // // node Color[4]: x = 277, y = 387, inputs = 5, label = Color // main_Color_4_out_1 = Color( main_RubberSheet_2_out_1, main_Colormap_3_out_1, main_Color_4_in_3, main_Color_4_in_4, main_Color_4_in_5 ) [instance: 4, cache: 1]; // // node Image[4]: x = 226, y = 519, inputs = 49, label = Image // input[1]: defaulting = 0, visible = 0, type = 32, value = "Image_4" // input[4]: defaulting = 0, visible = 0, type = 1, value = 1 // input[5]: defaulting = 0, visible = 0, type = 8, value = [3.98495 2.30071 0.460402] // input[6]: defaulting = 0, visible = 0, type = 8, value = [3.98495 2.30071 23.7018] // input[7]: defaulting = 0, visible = 0, type = 5, value = 12.455 // input[8]: defaulting = 0, visible = 0, type = 1, value = 826 // input[9]: defaulting = 0, visible = 0, type = 5, value = 0.751 // input[10]: defaulting = 0, visible = 0, type = 8, value = [0 1 0] // input[11]: defaulting = 1, visible = 0, type = 5, value = 29.9999 // input[12]: defaulting = 0, visible = 0, type = 1, value = 0 // input[14]: defaulting = 0, visible = 0, type = 1, value = 1 // input[15]: defaulting = 1, visible = 0, type = 32, value = "none" // input[16]: defaulting = 1, visible = 0, type = 32, value = "none" // input[17]: defaulting = 1, visible = 0, type = 1, value = 1 // input[18]: defaulting = 1, visible = 0, type = 1, value = 1 // input[19]: defaulting = 0, visible = 0, type = 1, value = 0 // input[29]: defaulting = 1, visible = 0, type = 3, value = 0 // input[41]: defaulting = 0, visible = 0, type = 32, value = "rotate" // depth: value = 24 // window: position = (0.2953,0.1796), size = 0.4375x0.6120 // internal caching: 1 // main_Image_4_out_1, main_Image_4_out_2, main_Image_4_out_3 = Image( main_Image_4_in_1, main_Color_4_out_1, main_Image_4_in_3, main_Image_4_in_4, main_Image_4_in_5, main_Image_4_in_6, main_Image_4_in_7, main_Image_4_in_8, main_Image_4_in_9, main_Image_4_in_10, main_Image_4_in_11, main_Image_4_in_12, main_Image_4_in_13, main_Image_4_in_14, main_Image_4_in_15, main_Image_4_in_16, main_Image_4_in_17, main_Image_4_in_18, main_Image_4_in_19, main_Image_4_in_20, main_Image_4_in_21, main_Image_4_in_22, main_Image_4_in_23, main_Image_4_in_24, main_Image_4_in_25, main_Image_4_in_26, main_Image_4_in_27, main_Image_4_in_28, main_Image_4_in_29, main_Image_4_in_30, main_Image_4_in_31, main_Image_4_in_32, main_Image_4_in_33, main_Image_4_in_34, main_Image_4_in_35, main_Image_4_in_36, main_Image_4_in_37, main_Image_4_in_38, main_Image_4_in_39, main_Image_4_in_40, main_Image_4_in_41, main_Image_4_in_42, main_Image_4_in_43, main_Image_4_in_44, main_Image_4_in_45, main_Image_4_in_46, main_Image_4_in_47, main_Image_4_in_48, main_Image_4_in_49 ) [instance: 4, cache: 1]; // network: end of macro body CacheScene(main_Image_4_in_1, main_Image_4_out_1, main_Image_4_out_2); } main_Import_2_in_1 = "emd2d.general"; main_Import_2_in_2 = NULL; main_Import_2_in_3 = NULL; main_Import_2_in_4 = NULL; main_Import_2_in_5 = NULL; main_Import_2_in_6 = NULL; main_Import_2_out_1 = NULL; main_RubberSheet_2_in_2 = NULL; main_RubberSheet_2_in_3 = NULL; main_RubberSheet_2_in_4 = NULL; main_RubberSheet_2_out_1 = NULL; main_Colormap_3_in_1 = { [0.0 0.666667] [1.0 0.0] }; main_Colormap_3_in_2 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_3_in_3 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_3_in_4 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_3_in_5 = "Colormap_3"; main_Colormap_3_in_7 = NULL; main_Colormap_3_in_8 = NULL; main_Colormap_3_in_9 = NULL; main_Colormap_3_in_10 = NULL; main_Colormap_3_in_11 = NULL; main_Colormap_3_in_12 = { 4.1046274e-06 0.014571383 }; main_Colormap_3_in_13 = NULL; main_Colormap_3_in_14 = NULL; main_Colormap_3_in_15 = NULL; main_Colormap_3_in_16 = NULL; main_Colormap_3_in_17 = 4.1046274e-06; main_Colormap_3_in_18 = 0.014571383; main_Colormap_3_in_19 = NULL; main_Colormap_3_out_1 = NULL; main_Color_4_in_3 = NULL; main_Color_4_in_4 = NULL; main_Color_4_in_5 = NULL; main_Color_4_out_1 = NULL; macro Image( id, object, where, useVector, to, from, width, resolution, aspect, up, viewAngle, perspective, options, buttonState = 1, buttonUpApprox = "none", buttonDownApprox = "none", buttonUpDensity = 1, buttonDownDensity = 1, renderMode = 0, defaultCamera, reset, backgroundColor, throttle, RECenable = 0, RECfile, RECformat, RECresolution, RECaspect, AAenable = 0, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, interactionMode, title, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels, webOptions) -> ( object, camera, where) { ImageMessage( id, backgroundColor, throttle, RECenable, RECfile, RECformat, RECresolution, RECaspect, AAenable, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels, interactionMode, title, renderMode, buttonUpApprox, buttonDownApprox, buttonUpDensity, buttonDownDensity) [instance: 1, cache: 1]; autoCamera = AutoCamera( object, "front", object, resolution, aspect, [0,1,0], perspective, viewAngle, backgroundColor) [instance: 1, cache: 1]; realCamera = Camera( to, from, width, resolution, aspect, up, perspective, viewAngle, backgroundColor) [instance: 1, cache: 1]; coloredDefaultCamera = UpdateCamera(defaultCamera, background=backgroundColor) [instance: 1, cache: 1]; nullDefaultCamera = Inquire(defaultCamera, "is null + 1") [instance: 1, cache: 1]; resetCamera = Switch( nullDefaultCamera, coloredDefaultCamera, autoCamera) [instance: 1, cache: 1]; resetNull = Inquire( reset, "is null + 1") [instance: 2, cache: 1]; reset = Switch( resetNull, reset, 0) [instance: 2, cache: 1]; whichCamera = Compute( "($0 != 0 || $1 == 0) ? 1 : 2", reset, useVector) [instance: 1, cache: 1]; camera = Switch( whichCamera, resetCamera, realCamera) [instance: 3, cache: 1]; AAobject = AutoAxes( object, camera, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels) [instance: 1, cache: 1]; switchAAenable = Compute("$0+1", AAenable) [instance: 2, cache: 1]; object = Switch( switchAAenable, object, AAobject) [instance:4, cache: 1]; SWapproximation_options = Switch( buttonState, buttonUpApprox, buttonDownApprox) [instance: 5, cache: 1]; SWdensity_options = Switch( buttonState, buttonUpDensity, buttonDownDensity) [instance: 6, cache: 1]; HWapproximation_options = Format( "%s,%s", buttonDownApprox, buttonUpApprox) [instance: 1, cache: 1]; HWdensity_options = Format( "%d,%d", buttonDownDensity, buttonUpDensity) [instance: 2, cache: 1]; switchRenderMode = Compute( "$0+1", renderMode) [instance: 3, cache: 1]; approximation_options = Switch( switchRenderMode, SWapproximation_options, HWapproximation_options) [instance: 7, cache: 1]; density_options = Switch( switchRenderMode, SWdensity_options, HWdensity_options) [instance: 8, cache: 1]; renderModeString = Switch( switchRenderMode, "software", "hardware")[instance: 9, cache: 1]; object_tag = Inquire( object, "object tag")[instance: 3, cache: 1]; annoted_object = Options( object, "send boxes", 0, "cache", 1, "object tag", object_tag, "ddcamera", whichCamera, "rendering approximation", approximation_options, "render every", density_options, "button state", buttonState, "rendering mode", renderModeString) [instance: 1, cache: 1]; RECresNull = Inquire( RECresolution, "is null + 1") [instance: 4, cache: 1]; ImageResolution = Inquire( camera, "camera resolution") [instance: 5, cache: 1]; RECresolution = Switch( RECresNull, RECresolution, ImageResolution) [instance: 10, cache: 1]; RECaspectNull = Inquire( RECaspect, "is null + 1") [instance: 6, cache: 1]; ImageAspect = Inquire( camera, "camera aspect") [instance: 7, cache: 1]; RECaspect = Switch( RECaspectNull, RECaspect, ImageAspect) [instance: 11, cache: 1]; switchRECenable = Compute( "$0 == 0 ? 1 : (($2 == $3) && ($4 == $5)) ? ($1 == 1 ? 2 : 3) : 4", RECenable, switchRenderMode, RECresolution, ImageResolution, RECaspect, ImageAspect) [instance: 4, cache: 1]; NoRECobject, RECNoRerenderObject, RECNoRerHW, RECRerenderObject = Route(switchRECenable, annoted_object); Display( NoRECobject, camera, where, throttle) [instance: 1, cache: 1]; image = Render( RECNoRerenderObject, camera) [instance: 1, cache: 1]; Display( image, NULL, where, throttle) [instance: 2, cache: 1]; WriteImage( image, RECfile, RECformat) [instance: 1, cache: 1]; rec_where = Display( RECNoRerHW, camera, where, throttle) [instance: 1, cache: 0]; rec_image = ReadImageWindow( rec_where) [instance: 1, cache: 1]; WriteImage( rec_image, RECfile, RECformat) [instance: 1, cache: 1]; RECupdateCamera = UpdateCamera( camera, resolution=RECresolution, aspect=RECaspect) [instance: 2, cache: 1]; Display( RECRerenderObject, camera, where, throttle) [instance: 1, cache: 1]; RECRerenderObject = ScaleScreen( RECRerenderObject, NULL, RECresolution, camera) [instance: 1, cache: 1]; image = Render( RECRerenderObject, RECupdateCamera) [instance: 2, cache: 1]; WriteImage( image, RECfile, RECformat) [instance: 2, cache: 1]; } main_Image_4_in_1 = "Image_4"; main_Image_4_in_3 = "X24,,"; main_Image_4_in_4 = 1; main_Image_4_in_5 = [3.98495 2.30071 0.460402]; main_Image_4_in_6 = [3.98495 2.30071 23.7018]; main_Image_4_in_7 = 12.455; main_Image_4_in_8 = 826; main_Image_4_in_9 = 0.751; main_Image_4_in_10 = [0 1 0]; main_Image_4_in_11 = NULL; main_Image_4_in_12 = 0; main_Image_4_in_13 = NULL; main_Image_4_in_14 = 1; main_Image_4_in_15 = NULL; main_Image_4_in_16 = NULL; main_Image_4_in_17 = NULL; main_Image_4_in_18 = NULL; main_Image_4_in_19 = 0; main_Image_4_in_20 = NULL; main_Image_4_in_21 = NULL; main_Image_4_in_22 = NULL; main_Image_4_in_23 = NULL; main_Image_4_in_25 = NULL; main_Image_4_in_26 = NULL; main_Image_4_in_27 = NULL; main_Image_4_in_28 = NULL; main_Image_4_in_29 = NULL; main_Image_4_in_30 = NULL; main_Image_4_in_31 = NULL; main_Image_4_in_32 = NULL; main_Image_4_in_33 = NULL; main_Image_4_in_34 = NULL; main_Image_4_in_35 = NULL; main_Image_4_in_36 = NULL; main_Image_4_in_37 = NULL; main_Image_4_in_38 = NULL; main_Image_4_in_39 = NULL; main_Image_4_in_40 = NULL; main_Image_4_in_41 = "rotate"; main_Image_4_in_42 = NULL; main_Image_4_in_43 = NULL; main_Image_4_in_44 = NULL; main_Image_4_in_45 = NULL; main_Image_4_in_46 = NULL; main_Image_4_in_47 = NULL; main_Image_4_in_48 = NULL; main_Image_4_in_49 = NULL; Executive("product version 4 4 4"); $sync main(); elk-7.2.42/examples/Compton-scattering/PaxHeaders.21776/Ni0000644000000000000000000000013014061636520020014 xustar0029 mtime=1623670096.12410137 30 atime=1623670096.121101372 29 ctime=1623670096.12410137 elk-7.2.42/examples/Compton-scattering/Ni/0000755002504400250440000000000014061636520022130 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Compton-scattering/Ni/PaxHeaders.21776/EMD1D.OUT0000644000000000000000000000013214061636520021256 xustar0030 mtime=1623670096.123101371 30 atime=1623670096.122101372 30 ctime=1623670096.123101371 elk-7.2.42/examples/Compton-scattering/Ni/EMD1D.OUT0000644002504400250440000001265614061636520023325 0ustar00dewhurstdewhurst00000000000000 0.000000000 13.36944509 0.3808160347E-01 13.36242486 0.7616320694E-01 13.34713589 0.1142448104 13.32147908 0.1523264139 13.27585701 0.1904080173 13.20894159 0.2284896208 13.13144996 0.2665712243 13.05060461 0.3046528277 12.95891882 0.3427344312 12.85570551 0.3808160347 12.73724511 0.4188976382 12.58594259 0.4569792416 12.40646548 0.4950608451 12.20258717 0.5331424486 11.98203209 0.5712240520 11.74982301 0.6093056555 11.50397852 0.6473872590 11.25947488 0.6854688624 11.02068933 0.7235504659 10.79507807 0.7616320694 10.59602405 0.7997136728 10.41950030 0.8377952763 10.24830043 0.8758768798 10.07520866 0.9139584832 9.896749716 0.9520400867 9.714049752 0.9901216902 9.530473138 1.028203294 9.339954965 1.066284897 9.140787720 1.104366501 8.935569331 1.142448104 8.738411330 1.180529708 8.561515588 1.218611311 8.394655152 1.256692914 8.228303536 1.294774518 8.068561140 1.332856121 7.910297932 1.370937725 7.742682296 1.409019328 7.573756340 1.447100932 7.410641772 1.485182535 7.254345570 1.523264139 7.097871593 1.561345742 6.940479426 1.599427346 6.789792236 1.637508949 6.639704472 1.675590553 6.489502153 1.713672156 6.355455259 1.751753760 6.239973890 1.789835363 6.120954124 1.827916966 5.988027446 1.865998570 5.841258977 1.904080173 5.692287515 1.942161777 5.546780416 1.980243380 5.395408983 2.018324984 5.236678739 2.056406587 5.076396106 2.094488191 4.928660100 2.132569794 4.796921137 2.170651398 4.667976134 2.208733001 4.538842525 2.246814605 4.414996074 2.284896208 4.291667931 2.322977812 4.163871229 2.361059415 4.036540109 2.399141019 3.912284859 2.437222622 3.794245903 2.475304225 3.679202305 2.513385829 3.567232516 2.551467432 3.462760945 2.589549036 3.361378745 2.627630639 3.263495724 2.665712243 3.177204176 2.703793846 3.100418825 2.741875450 3.022089438 2.779957053 2.938390805 2.818038657 2.850146442 2.856120260 2.763888755 2.894201864 2.680168113 2.932283467 2.593537368 2.970365071 2.504035903 3.008446674 2.415061089 3.046528277 2.334230769 3.084609881 2.261386065 3.122691484 2.189648361 3.160773088 2.119272318 3.198854691 2.052492680 3.236936295 1.985614800 3.275017898 1.917490125 3.313099502 1.850589025 3.351181105 1.786127365 3.389262709 1.725223654 3.427344312 1.665586690 3.465425916 1.608161480 3.503507519 1.554434647 3.541589123 1.502060642 3.579670726 1.452381398 3.617752329 1.409522582 3.655833933 1.370733010 3.693915536 1.330727243 3.731997140 1.288452971 3.770078743 1.244733351 3.808160347 1.202922648 3.846241950 1.162416103 3.884323554 1.120802947 3.922405157 1.078265333 3.960486761 1.036333665 3.998568364 0.9988444237 4.036649968 0.9649956003 4.074731571 0.9318476569 4.112813175 0.8997748555 4.150894778 0.8695350725 4.188976382 0.8389903421 4.227057985 0.8083465603 4.265139588 0.7786091047 4.303221192 0.7499539424 4.341302795 0.7229939196 4.379384399 0.6965284364 4.417466002 0.6713876299 4.455547606 0.6479272515 4.493629209 0.6251312139 4.531710813 0.6041244525 4.569792416 0.5862059253 4.607874020 0.5694603533 4.645955623 0.5520693813 4.684037227 0.5339913846 4.722118830 0.5158421203 4.760200434 0.4990218240 4.798282037 0.4827316178 4.836363640 0.4659253487 4.874445244 0.4486479322 4.912526847 0.4318071797 4.950608451 0.4171274069 4.988690054 0.4040055540 5.026771658 0.3911671146 5.064853261 0.3788656153 5.102934865 0.3672275819 5.141016468 0.3553093866 5.179098072 0.3434334700 5.217179675 0.3319091178 5.255261279 0.3207857681 5.293342882 0.3100308349 5.331424486 0.2991821951 5.369506089 0.2888413378 5.407587693 0.2790769534 5.445669296 0.2695133828 5.483750899 0.2607814560 5.521832503 0.2533991562 5.559914106 0.2461602714 5.597995710 0.2385604544 5.636077313 0.2307868105 5.674158917 0.2231243759 elk-7.2.42/examples/Compton-scattering/Ni/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520021202 xustar0029 mtime=1623670096.12410137 29 atime=1623670096.12410137 29 ctime=1623670096.12410137 elk-7.2.42/examples/Compton-scattering/Ni/elk.in0000644002504400250440000000170214061636520023233 0ustar00dewhurstdewhurst00000000000000 ! Twice-integrated electron momentum density (EMD) plot for ferromagnetic Ni. ! First the EMD is calculated on a regular H+k grid. This is then interpolated ! and integrated in directions which are mutually orthogonal to each other and ! along the plotting line. This line is given by plot1d. ! Example by David Ernsting and Stephen Dugdale. tasks 0 170 171 ! define the plotting line in reciprocal lattice coordinates plot1d 2 150 0.0 0.0 0.0 3.0 3.0 0.0 ! maximum length of H+k-vectors for the EMD hkmax 8.d0 ! small swidth to give a sharp profile swidth 0.00016 ngridk 20 20 20 spinpol .true. bfieldc 0.0 0.0 -0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.322 sppath '../../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/examples/Compton-scattering/PaxHeaders.21776/Si-GW0000644000000000000000000000013214061636520020336 xustar0030 mtime=1623670096.126101368 30 atime=1623670096.125101369 30 ctime=1623670096.126101368 elk-7.2.42/examples/Compton-scattering/Si-GW/0000755002504400250440000000000014061636520022450 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Compton-scattering/Si-GW/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021516 xustar0030 mtime=1623670096.127101367 30 atime=1623670096.127101367 30 ctime=1623670096.127101367 elk-7.2.42/examples/Compton-scattering/Si-GW/elk.in0000644002504400250440000000244614061636520023561 0ustar00dewhurstdewhurst00000000000000 ! Compton profile determined for silicon from the GW approximation. ! The density matrices are calculated from the interacting Green's function at ! each k-point and the files EVECSV.OUT and OCCSV.OUT are updated. The electron ! momentum density (EMD) is then computed from these. tasks 0 : ground state calculation 600 : determined the GW self-energy 640 : write the natural orbitals and occupaction numbers 170 : write the EMD for each k-point 171 : produce the 1D EMD plot ! use LAPW nxoapwlo 1 ! Matsubara frequency cut-off wmaxgw 20.0 ! response function G-vector cut-off gmaxrf 3.0 ! temperature of many-body system (determines Matsubara frequency spacing) tempk 1000.0 ! define the plotting line in reciprocal lattice coordinates plot1d 2 150 0.0 0.0 0.0 3.0 3.0 0.0 ! maximum length of H+k-vectors for the EMD hkmax 8.d0 ngridk 8 8 8 ! q-point grid can be smaller than (but commensurate with) the k-point set ngridq 2 2 2 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 elk-7.2.42/examples/PaxHeaders.21776/ELNES0000644000000000000000000000013214061636520014536 xustar0030 mtime=1623670096.142101353 30 atime=1623670096.128101366 30 ctime=1623670096.142101353 elk-7.2.42/examples/ELNES/0000755002504400250440000000000014061636520016650 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ELNES/PaxHeaders.21776/Pu0000644000000000000000000000013214061636520015122 xustar0030 mtime=1623670096.132101362 30 atime=1623670096.129101365 30 ctime=1623670096.132101362 elk-7.2.42/examples/ELNES/Pu/0000755002504400250440000000000014061636520017234 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ELNES/Pu/PaxHeaders.21776/Pu+.in0000644000000000000000000000013214061636520016166 xustar0030 mtime=1623670096.131101363 30 atime=1623670096.130101364 30 ctime=1623670096.131101363 elk-7.2.42/examples/ELNES/Pu/Pu+.in0000644002504400250440000000472314061636520020231 0ustar00dewhurstdewhurst00000000000000 'Pu' : spsymb 'plutonium' : spname -94.0000 : spzn 444784.7903 : spmass 0.206284E-06 2.2000 42.3450 800 : sprmin, rmt, sprmax, nrmt 27 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 3.50000 T <---- 1/2 electron removed from next lowest state 4 2 2 4.00000 F 4 2 3 6.00000 F 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 3.00000 F 5 3 4 3.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.50000 F <---- and added to highest state 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -1.7999 0 T 1 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -0.7412 0 T 2 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -30.0000 0 T elk-7.2.42/examples/ELNES/Pu/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016302 xustar0030 mtime=1623670096.132101362 30 atime=1623670096.132101362 30 ctime=1623670096.132101362 elk-7.2.42/examples/ELNES/Pu/elk.in0000644002504400250440000000140114061636520020333 0ustar00dewhurstdewhurst00000000000000 ! Electron loss near-edge spectroscopy (ELNES) of spin-polarised fcc plutonium. ! Take note of the modified species file, 'Pu+.in', and the requirement of ! spin-orbit coupling. tasks 0 140 spinorb .true. ! maximum allowed energy for the initial state in the double differential ! cross-section formula emaxelnes -20.0 wplot 300 100 6 : nwplot, ngrkf, nswplot 28.0 32.0 : wplot nempty 20 ! q-vector in lattice coordinates vecql 0.0 0.0 0.25 avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 9.13730 atoms 1 : nspecies 'Pu+.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.01 : atposl, bfcmt ngridk 4 4 4 elk-7.2.42/examples/ELNES/PaxHeaders.21776/BN0000644000000000000000000000013214061636520015035 xustar0030 mtime=1623670096.140101355 30 atime=1623670096.133101361 30 ctime=1623670096.140101355 elk-7.2.42/examples/ELNES/BN/0000755002504400250440000000000014061636520017147 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ELNES/BN/PaxHeaders.21776/B.in0000644000000000000000000000013114061636520015622 xustar0030 mtime=1623670096.135101359 29 atime=1623670096.13410136 30 ctime=1623670096.135101359 elk-7.2.42/examples/ELNES/BN/B.in0000644002504400250440000000172214061636520017662 0ustar00dewhurstdewhurst00000000000000 'B' : spsymb 'boron' : spname -5.00000 : spzn 19707.24740 : spmass 0.894427E-06 1.8000 43.3288 300 : sprmin, rmt, sprmax, nrmt 3 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 F 2 1 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 2 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F elk-7.2.42/examples/ELNES/BN/PaxHeaders.21776/ELNES.OUT0000644000000000000000000000013214061636520016351 xustar0030 mtime=1623670096.136101359 30 atime=1623670096.136101359 30 ctime=1623670096.136101359 elk-7.2.42/examples/ELNES/BN/ELNES.OUT0000644002504400250440000002553414061636520020417 0ustar00dewhurstdewhurst00000000000000 18.00000000 0.000000000 18.01333333 0.000000000 18.02666667 0.000000000 18.04000000 0.000000000 18.05333333 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21.60000000 0.000000000 21.61333333 0.000000000 21.62666667 0.000000000 21.64000000 0.000000000 21.65333333 0.000000000 21.66666667 0.000000000 21.68000000 0.000000000 21.69333333 0.000000000 21.70666667 0.000000000 21.72000000 0.000000000 21.73333333 0.000000000 21.74666667 0.000000000 21.76000000 0.000000000 21.77333333 0.000000000 21.78666667 0.000000000 21.80000000 0.000000000 21.81333333 0.000000000 21.82666667 0.000000000 21.84000000 0.000000000 21.85333333 0.000000000 21.86666667 0.000000000 21.88000000 0.000000000 21.89333333 0.000000000 21.90666667 0.000000000 21.92000000 0.000000000 21.93333333 0.000000000 21.94666667 0.000000000 21.96000000 0.000000000 21.97333333 0.000000000 21.98666667 0.000000000 elk-7.2.42/examples/ELNES/BN/PaxHeaders.21776/N+.in0000644000000000000000000000013214061636520015712 xustar0030 mtime=1623670096.138101357 30 atime=1623670096.138101357 30 ctime=1623670096.138101357 elk-7.2.42/examples/ELNES/BN/N+.in0000644002504400250440000000253414061636520017753 0ustar00dewhurstdewhurst00000000000000 'N+' : spsymb 'nitrogen with pseudo core-hole' : spname -8.00000 : spzn 25532.72506 : spmass 0.755929E-06 1.4500 26.9237 300 : sprmin, rmt, sprmax, nrmt 4 : spnst 1 0 1 2.00000 F : spn, spl, spk, spocc, spcore 2 0 1 2.00000 F 2 1 1 1.00000 F 2 1 2 3.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -0.6020 0 T 0 3 0.1500 0 F 0.1500 1 F -20.0000 0 T elk-7.2.42/examples/ELNES/BN/PaxHeaders.21776/N.in0000644000000000000000000000013214061636520015637 xustar0030 mtime=1623670096.139101356 30 atime=1623670096.139101356 30 ctime=1623670096.139101356 elk-7.2.42/examples/ELNES/BN/N.in0000644002504400250440000000222014061636520017670 0ustar00dewhurstdewhurst00000000000000 'N' : spsymb 'nitrogen' : spname -7.00000 : spzn 25532.65213 : spmass 0.755929E-06 1.8000 33.2667 300 : sprmin, rmt, sprmax, nrmt 4 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 F 2 1 1 1.00000 F 2 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -0.6770 0 T elk-7.2.42/examples/ELNES/BN/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016215 xustar0030 mtime=1623670096.141101354 30 atime=1623670096.141101354 30 ctime=1623670096.141101354 elk-7.2.42/examples/ELNES/BN/elk.in0000644002504400250440000000356214061636520020260 0ustar00dewhurstdewhurst00000000000000 ! Calculation of the electron loss near-edge spectroscopy (ELNES) for boron ! nitride. Note that a 16 atom supercell has been constructed with a special ! N atom (defined in the species file 'N+.in') for which the nuclear and ! electronic charges have been increased by one, and the 1s core code state has ! been included as a valence state by adding a local-orbital at the appropriate ! energy. This approximates the local core-hole interation. Compare with Phys. ! Rev. B 64, 115107 (2001). ! This example is well converged and is of publication quality. However it is ! fairly time-consuming and is best run on a multi-processor machine. tasks 0 140 ! spin-orbit coupling required to obtain realistic 1s state in valence spinorb .true. ! ELNES q-vector in lattice coordinates vecql 0.0 0.0 0.125 ! energy range for ELNES plot wplot 300 150 3 : nwplot, ngrkf, nswplot 18.0 22.0 : wplot (for the nitrogen K-edge) ! maximum allowed energy for the initial state in the double differential ! cross-section formula emaxelnes -10.0 ! large number of empty states required nempty 30 ngridk 8 8 8 avec 9.674352 0.0 0.0 4.837176 8.378234597 0.0 4.837176 2.792744866 7.899075331 atoms 3 : nspecies 'B.in' : spfname 8 : natoms; atposl below 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.5 0.0 0.0 0.5 0.5 0.5 0.0 0.0 0.5 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 'N+.in' : spfname 1 : natoms; atposl below 0.125 0.125 0.125 'N.in' : spfname 7 0.125 0.125 0.625 0.125 0.625 0.125 0.125 0.625 0.625 0.625 0.125 0.125 0.625 0.125 0.625 0.625 0.625 0.125 0.625 0.625 0.625 elk-7.2.42/examples/ELNES/PaxHeaders.21776/Cu0000644000000000000000000000013014061636520015103 xustar0029 mtime=1623670096.14510135 30 atime=1623670096.142101353 29 ctime=1623670096.14510135 elk-7.2.42/examples/ELNES/Cu/0000755002504400250440000000000014061636520017217 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ELNES/Cu/PaxHeaders.21776/Cu+.in0000644000000000000000000000013214061636520016134 xustar0030 mtime=1623670096.144101351 30 atime=1623670096.143101352 30 ctime=1623670096.144101351 elk-7.2.42/examples/ELNES/Cu/Cu+.in0000644002504400250440000000373314061636520020177 0ustar00dewhurstdewhurst00000000000000 'Cu+' : spsymb 'copper with pseudo core-hole' : spname -29.0000 : spzn 115837.2717 : spmass 0.371391E-06 2.0000 37.1331 500 : sprmin, rmt, sprmax, nrmt 10 : spnst 1 0 1 1.50000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 F 2 1 1 2.00000 F 2 1 2 4.00000 F 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 1.50000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 8 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -2.6152 0 T 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -4.0000 0 T 1 3 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -34.0000 0 T 0 3 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -41.0000 0 T elk-7.2.42/examples/ELNES/Cu/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520016271 xustar0029 mtime=1623670096.14510135 29 atime=1623670096.14510135 29 ctime=1623670096.14510135 elk-7.2.42/examples/ELNES/Cu/elk.in0000644002504400250440000000225214061636520020323 0ustar00dewhurstdewhurst00000000000000 ! Electron loss near-edge spectroscopy for fcc Cu. Note that a special species ! file has been constructed to simulate dynamical core-hole effects by removing ! half an electron from the 1s core state (even though we are interested in the ! 2s and 2p transitions). This is a publication-quality calculation and may take ! some time to complete. ! No supercell is required because of the strong metallic screening of copper. ! Compare with Eur. Phys. J. B21, 363 (2001). tasks 0 140 ! spin-orbit coupling required for accurate description of deep valence states spinorb .true. ! maximum allowed energy for the initial state in the double differential ! cross-section formula emaxelnes -30.0 ! energy range for ELNES plot wplot 500 200 1 : nwplot, ngrkf, nswplot 33.0 37.5 : wplot (suitable for the Cu L3 edge) vecql 0.0 0.0 0.1 rgkmax 8.0 gmaxvr 14.0 nempty 20 ngridk 10 10 10 avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 6.83117 atoms 1 : nspecies 'Cu+.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/examples/PaxHeaders.21776/Mossbauer0000644000000000000000000000013214061636520015630 xustar0030 mtime=1623670096.163101333 30 atime=1623670096.146101349 30 ctime=1623670096.163101333 elk-7.2.42/examples/Mossbauer/0000755002504400250440000000000014061636520017742 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Mossbauer/PaxHeaders.21776/Mg2SiO40000644000000000000000000000013214061636520016754 xustar0030 mtime=1623670096.152101344 30 atime=1623670096.148101347 30 ctime=1623670096.152101344 elk-7.2.42/examples/Mossbauer/Mg2SiO4/0000755002504400250440000000000014061636520021066 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Mossbauer/Mg2SiO4/PaxHeaders.21776/EFG.OUT0000644000000000000000000000013214061636520020023 xustar0030 mtime=1623670096.149101347 30 atime=1623670096.149101347 30 ctime=1623670096.149101347 elk-7.2.42/examples/Mossbauer/Mg2SiO4/EFG.OUT0000644002504400250440000002127714061636520022071 0ustar00dewhurstdewhurst00000000000000 (electric field gradient tensor is in Cartesian coordinates) Species : 1 (Mg), atom : 1 EFG tensor : 0.4540892586E-01 -0.1763387239E-01 0.6360381772E-01 -0.1763387239E-01 -0.6707466662E-01 0.5324981887E-01 0.6360381772E-01 0.5324981887E-01 0.2166574076E-01 trace : 0.2255140519E-15 eigenvalues : -0.1057174610 0.4640486884E-02 0.1010769741 Species : 1 (Mg), atom : 2 EFG tensor : 0.4540892586E-01 -0.1763387239E-01 -0.6360381772E-01 -0.1763387239E-01 -0.6707466662E-01 -0.5324981887E-01 -0.6360381772E-01 -0.5324981887E-01 0.2166574076E-01 trace : -0.8673617380E-16 eigenvalues : -0.1057174610 0.4640486884E-02 0.1010769741 Species : 1 (Mg), atom : 3 EFG tensor : 0.4540892586E-01 0.1763387239E-01 -0.6360381772E-01 0.1763387239E-01 -0.6707466662E-01 0.5324981887E-01 -0.6360381772E-01 0.5324981887E-01 0.2166574076E-01 trace : -0.2324529458E-15 eigenvalues : -0.1057174610 0.4640486884E-02 0.1010769741 Species : 1 (Mg), atom : 4 EFG tensor : 0.4540892586E-01 0.1763387239E-01 0.6360381772E-01 0.1763387239E-01 -0.6707466662E-01 -0.5324981887E-01 0.6360381772E-01 -0.5324981887E-01 0.2166574076E-01 trace : -0.5204170428E-16 eigenvalues : -0.1057174610 0.4640486884E-02 0.1010769741 Species : 1 (Mg), atom : 5 EFG tensor : -0.8040555871E-01 -0.3650637845E-01 -0.3047653057E-16 -0.3650637845E-01 0.1498274433E-01 -0.1054253974E-15 -0.3047653057E-16 -0.1054253974E-15 0.6542281438E-01 trace : -0.7216449660E-15 eigenvalues : -0.9277343976E-01 0.2735062538E-01 0.6542281438E-01 Species : 1 (Mg), atom : 6 EFG tensor : -0.8040555871E-01 -0.3650637845E-01 -0.8533708916E-16 -0.3650637845E-01 0.1498274433E-01 -0.1268311785E-15 -0.8533708916E-16 -0.1268311785E-15 0.6542281438E-01 trace : 0.2775557562E-16 eigenvalues : -0.9277343976E-01 0.2735062538E-01 0.6542281438E-01 Species : 1 (Mg), atom : 7 EFG tensor : -0.8040555871E-01 0.3650637845E-01 0.6083835430E-16 0.3650637845E-01 0.1498274433E-01 0.8868811951E-16 0.6083835430E-16 0.8868811951E-16 0.6542281438E-01 trace : 0.4163336342E-16 eigenvalues : -0.9277343976E-01 0.2735062538E-01 0.6542281438E-01 Species : 1 (Mg), atom : 8 EFG tensor : -0.8040555871E-01 0.3650637845E-01 -0.2566982641E-16 0.3650637845E-01 0.1498274433E-01 0.1392643800E-15 -0.2566982641E-16 0.1392643800E-15 0.6542281438E-01 trace : 0.9714451465E-16 eigenvalues : -0.9277343976E-01 0.2735062538E-01 0.6542281438E-01 Species : 2 (Si), atom : 1 EFG tensor : 0.1998888880 0.3247854545E-01 0.9705954098E-16 0.3247854545E-01 -0.1762801640 -0.3077944466E-15 0.9705954098E-16 -0.3077944466E-15 -0.2360872399E-01 trace : -0.4787836794E-15 eigenvalues : -0.1790637727 -0.2360872399E-01 0.2026724967 Species : 2 (Si), atom : 2 EFG tensor : 0.1998888880 0.3247854545E-01 0.9050580257E-16 0.3247854545E-01 -0.1762801640 -0.3344693075E-15 0.9050580257E-16 -0.3344693075E-15 -0.2360872399E-01 trace : 0.4336808690E-15 eigenvalues : -0.1790637727 -0.2360872399E-01 0.2026724967 Species : 2 (Si), atom : 3 EFG tensor : 0.1998888880 -0.3247854545E-01 0.1056039611E-15 -0.3247854545E-01 -0.1762801640 0.8244420802E-16 0.1056039611E-15 0.8244420802E-16 -0.2360872399E-01 trace : 0.1151856388E-14 eigenvalues : -0.1790637727 -0.2360872399E-01 0.2026724967 Species : 2 (Si), atom : 4 EFG tensor : 0.1998888880 -0.3247854545E-01 0.1427804355E-16 -0.3247854545E-01 -0.1762801640 0.1160800898E-15 0.1427804355E-16 0.1160800898E-15 -0.2360872399E-01 trace : 0.2775557562E-16 eigenvalues : -0.1790637727 -0.2360872399E-01 0.2026724967 Species : 3 (O), atom : 1 EFG tensor : -0.4883142850 -0.4644265160E-01 -0.2893374241E-15 -0.4644265160E-01 0.1719771655 0.2307362823E-15 -0.2893374241E-15 0.2307362823E-15 0.3163371195 trace : -0.9436895709E-15 eigenvalues : -0.4915649001 0.1752277806 0.3163371195 Species : 3 (O), atom : 2 EFG tensor : -0.4883142850 -0.4644265160E-01 -0.8665332380E-16 -0.4644265160E-01 0.1719771655 0.1921692501E-15 -0.8665332380E-16 0.1921692501E-15 0.3163371195 trace : 0.7216449660E-15 eigenvalues : -0.4915649001 0.1752277806 0.3163371195 Species : 3 (O), atom : 3 EFG tensor : -0.4883142850 0.4644265160E-01 -0.1075299185E-15 0.4644265160E-01 0.1719771655 -0.4737739850E-15 -0.1075299185E-15 -0.4737739850E-15 0.3163371195 trace : 0.3330669074E-14 eigenvalues : -0.4915649001 0.1752277806 0.3163371195 Species : 3 (O), atom : 4 EFG tensor : -0.4883142850 0.4644265160E-01 -0.1908814821E-15 0.4644265160E-01 0.1719771655 -0.3512425491E-15 -0.1908814821E-15 -0.3512425491E-15 0.3163371195 trace : -0.2164934898E-14 eigenvalues : -0.4915649001 0.1752277806 0.3163371195 Species : 3 (O), atom : 5 EFG tensor : -0.5817198967E-01 0.2576542145 0.1269063876E-15 0.2576542145 -0.2568887445 -0.2865787890E-16 0.1269063876E-15 -0.2865787890E-16 0.3150607341 trace : 0.1165734176E-14 eigenvalues : -0.4336784820 0.1186177479 0.3150607341 Species : 3 (O), atom : 6 EFG tensor : -0.5817198967E-01 0.2576542145 0.1229734413E-15 0.2576542145 -0.2568887445 0.1684989048E-15 0.1229734413E-15 0.1684989048E-15 0.3150607341 trace : 0.5551115123E-16 eigenvalues : -0.4336784820 0.1186177479 0.3150607341 Species : 3 (O), atom : 7 EFG tensor : -0.5817198967E-01 -0.2576542145 -0.4353297598E-15 -0.2576542145 -0.2568887445 -0.8050984716E-15 -0.4353297598E-15 -0.8050984716E-15 0.3150607341 trace : -0.5551115123E-16 eigenvalues : -0.4336784820 0.1186177479 0.3150607341 Species : 3 (O), atom : 8 EFG tensor : -0.5817198967E-01 -0.2576542145 -0.3397294856E-15 -0.2576542145 -0.2568887445 -0.6887664005E-15 -0.3397294856E-15 -0.6887664005E-15 0.3150607341 trace : -0.1276756478E-14 eigenvalues : -0.4336784820 0.1186177479 0.3150607341 Species : 3 (O), atom : 9 EFG tensor : 0.3617984671E-01 -0.1046542712 -0.2284590635 -0.1046542712 0.1873139119 -0.1586476054 -0.2284590635 -0.1586476054 -0.2234937586 trace : 0.1165734176E-14 eigenvalues : -0.4161232705 0.1678290337 0.2482942368 Species : 3 (O), atom : 10 EFG tensor : 0.3617984671E-01 -0.1046542712 -0.2284590635 -0.1046542712 0.1873139119 -0.1586476054 -0.2284590635 -0.1586476054 -0.2234937586 trace : 0.3330669074E-15 eigenvalues : -0.4161232705 0.1678290337 0.2482942368 Species : 3 (O), atom : 11 EFG tensor : 0.3617984671E-01 -0.1046542712 0.2284590635 -0.1046542712 0.1873139119 0.1586476054 0.2284590635 0.1586476054 -0.2234937586 trace : 0.8049116929E-15 eigenvalues : -0.4161232705 0.1678290337 0.2482942368 Species : 3 (O), atom : 12 EFG tensor : 0.3617984671E-01 -0.1046542712 0.2284590635 -0.1046542712 0.1873139119 0.1586476054 0.2284590635 0.1586476054 -0.2234937586 trace : -0.4163336342E-15 eigenvalues : -0.4161232705 0.1678290337 0.2482942368 Species : 3 (O), atom : 13 EFG tensor : 0.3617984671E-01 0.1046542712 0.2284590635 0.1046542712 0.1873139119 -0.1586476054 0.2284590635 -0.1586476054 -0.2234937586 trace : -0.5273559367E-15 eigenvalues : -0.4161232705 0.1678290337 0.2482942368 Species : 3 (O), atom : 14 EFG tensor : 0.3617984671E-01 0.1046542712 0.2284590635 0.1046542712 0.1873139119 -0.1586476054 0.2284590635 -0.1586476054 -0.2234937586 trace : 0.9714451465E-15 eigenvalues : -0.4161232705 0.1678290337 0.2482942368 Species : 3 (O), atom : 15 EFG tensor : 0.3617984671E-01 0.1046542712 -0.2284590635 0.1046542712 0.1873139119 0.1586476054 -0.2284590635 0.1586476054 -0.2234937586 trace : 0.000000000 eigenvalues : -0.4161232705 0.1678290337 0.2482942368 Species : 3 (O), atom : 16 EFG tensor : 0.3617984671E-01 0.1046542712 -0.2284590635 0.1046542712 0.1873139119 0.1586476054 -0.2284590635 0.1586476054 -0.2234937586 trace : 0.1665334537E-15 eigenvalues : -0.4161232705 0.1678290337 0.2482942368 elk-7.2.42/examples/Mossbauer/Mg2SiO4/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020134 xustar0030 mtime=1623670096.151101345 30 atime=1623670096.151101345 30 ctime=1623670096.151101345 elk-7.2.42/examples/Mossbauer/Mg2SiO4/elk.in0000644002504400250440000000760214061636520022176 0ustar00dewhurstdewhurst00000000000000 ! Electric field gradient of Mg2SiO4. ! See: B. Winkler, P. Blaha and K. Schwarz, Am. Mineralog. 81, 545 (1996). tasks 0 115 lmaxi 2 xctype 20 ngridk 2 2 2 sppath '../../../species/' ! Atomic positions generated by spacegroup version 1.2.01 ! Hermann-Mauguin symbol : Pbnm ! Hall symbol : -P 2c 2ab ! Schoenflies symbol : D2h^16 ! space group number : 62:cab ! lattice constants (a,b,c) : 8.980000000 19.26010000 11.29680000 ! angles in degrees (bc,ac,ab) : 90.00000000 90.00000000 90.00000000 ! number of conventional unit cells : 1 1 1 ! reduction to primitive cell : T ! Wyckoff positions : ! species : 1, Mg ! 0.000000000 0.000000000 0.000000000 ! 0.5084600000 0.7774200000 0.2500000000 ! species : 2, Si ! 0.7353000000E-01 0.5940300000 0.2500000000 ! species : 3, O ! 0.7340800000 0.5915500000 0.2500000000 ! 0.2216000000 0.4470400000 0.2500000000 ! 0.2225300000 0.6631600000 0.4669700000 avec 8.980000000 0.000000000 0.000000000 0.000000000 0.000000000 11.29680000 0.000000000 19.26010000 0.000000000 atoms 3 : nspecies 'Mg.in' : spfname 8 : natoms; atposl, bfcmt below 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.50000000 0.00000000 0.00000000 0.00000000 0.00000000 0.50000000 0.00000000 0.50000000 0.00000000 0.00000000 0.00000000 0.50000000 0.50000000 0.50000000 0.00000000 0.00000000 0.00000000 0.50846000 0.25000000 0.77742000 0.00000000 0.00000000 0.00000000 0.49154000 0.75000000 0.22258000 0.00000000 0.00000000 0.00000000 0.00846000 0.75000000 0.72258000 0.00000000 0.00000000 0.00000000 0.99154000 0.25000000 0.27742000 0.00000000 0.00000000 0.00000000 'Si.in' : spfname 4 : natoms; atposl, bfcmt below 0.07353000 0.25000000 0.59403000 0.00000000 0.00000000 0.00000000 0.92647000 0.75000000 0.40597000 0.00000000 0.00000000 0.00000000 0.57353000 0.75000000 0.90597000 0.00000000 0.00000000 0.00000000 0.42647000 0.25000000 0.09403000 0.00000000 0.00000000 0.00000000 'O.in' : spfname 16 : natoms; atposl, bfcmt below 0.73408000 0.25000000 0.59155000 0.00000000 0.00000000 0.00000000 0.26592000 0.75000000 0.40845000 0.00000000 0.00000000 0.00000000 0.23408000 0.75000000 0.90845000 0.00000000 0.00000000 0.00000000 0.76592000 0.25000000 0.09155000 0.00000000 0.00000000 0.00000000 0.22160000 0.25000000 0.44704000 0.00000000 0.00000000 0.00000000 0.77840000 0.75000000 0.55296000 0.00000000 0.00000000 0.00000000 0.72160000 0.75000000 0.05296000 0.00000000 0.00000000 0.00000000 0.27840000 0.25000000 0.94704000 0.00000000 0.00000000 0.00000000 0.22253000 0.46697000 0.66316000 0.00000000 0.00000000 0.00000000 0.77747000 0.53303000 0.33684000 0.00000000 0.00000000 0.00000000 0.77747000 0.96697000 0.33684000 0.00000000 0.00000000 0.00000000 0.22253000 0.03303000 0.66316000 0.00000000 0.00000000 0.00000000 0.72253000 0.53303000 0.83684000 0.00000000 0.00000000 0.00000000 0.27747000 0.46697000 0.16316000 0.00000000 0.00000000 0.00000000 0.27747000 0.03303000 0.16316000 0.00000000 0.00000000 0.00000000 0.72253000 0.96697000 0.83684000 0.00000000 0.00000000 0.00000000 elk-7.2.42/examples/Mossbauer/Mg2SiO4/PaxHeaders.21776/spacegroup.in0000644000000000000000000000013214061636520021531 xustar0030 mtime=1623670096.152101344 30 atime=1623670096.152101344 30 ctime=1623670096.152101344 elk-7.2.42/examples/Mossbauer/Mg2SiO4/spacegroup.in0000644002504400250440000000113314061636520023564 0ustar00dewhurstdewhurst00000000000000 'Pbnm' : hrmg 8.9800 19.2601 11.2968 : a, b, c 90.0 90.0 90.0 : bc, ac, ab 1 1 1 : ncell .true. : primcell 3 : nspecies 'Mg' : spsymb, spfname 2 : nwpos 0.00000 0.00000 0.00000 : wpos 0.50846 0.77742 0.25000 'Si' 1 0.07353 0.59403 0.25000 'O' 3 0.73408 0.59155 0.25000 0.22160 0.44704 0.25000 0.22253 0.66316 0.46697 elk-7.2.42/examples/Mossbauer/PaxHeaders.21776/Co-hcp0000644000000000000000000000013214061636520016741 xustar0030 mtime=1623670096.154101342 30 atime=1623670096.153101343 30 ctime=1623670096.154101342 elk-7.2.42/examples/Mossbauer/Co-hcp/0000755002504400250440000000000014061636520021053 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Mossbauer/Co-hcp/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020121 xustar0030 mtime=1623670096.155101341 30 atime=1623670096.155101341 30 ctime=1623670096.155101341 elk-7.2.42/examples/Mossbauer/Co-hcp/elk.in0000644002504400250440000000406214061636520022160 0ustar00dewhurstdewhurst00000000000000 ! Calculating the Mossbauer effect hyperfine parameters for hcp Co, namely the ! contact charge density, the contact magnetic hyperfine field and the electric ! field gradient (EFG). ! The hyperfine magnetic field is difficult to calculate accurately. This is ! mainly because most of the contact magnetisation arises from the polarised ! core s states. One therefore has to switch on core polarisation with ! 'spincore=.true.', but in addition any semi-core s states should also be moved ! to the core and thus treated with the full Dirac equation. Also note that the ! field is quite sensitive to the number of empty states and k-points. ! Also note that the hyperfine field also depends strongly on the choice of ! functional with GGA functions usually yielding larger values. Try running the ! calculation again with PBE (xctype=20). ! Experimentally the hyperfine field is 21.9 Tesla [J. Phys. Soc. Jpn. 33, 1591 ! (1972)]. tasks 0 110 : isomer shift and hyperfine field 115 : electric field gradient ! enable calculation of the dipole magnetic field tbdip .true. ! enable calculation of the current density (i.e. orbital) contribution to the ! dipole field tjr .true. ! enable spin-orbit coupling spinorb .true. ! switch on core polarisation for hyperfine field spincore .true. ! lmaxi should be at least 2 for the EFG calculation lmaxi 2 ! external field for breaking spin symmetry bfieldc 0.0 0.0 0.001 ! very large number of empty states required for hyperfine field nempty 80 ! conduction local-orbitals required lorbcnd .true. ! large number of k-points required ngridk 14 14 10 avec 2.368866000 4.102996268 0.000000000 4.737732000 0.000000000 0.000000000 0.000000000 0.000000000 7.690240000 sppath '../../../species/' atoms 1 : nspecies 'Co.in' : spfname 2 : natoms; atposl, bfcmt below 0.66666667 0.66666667 0.75000000 0.33333333 0.33333333 0.25000000 elk-7.2.42/examples/Mossbauer/PaxHeaders.21776/Fe0000644000000000000000000000013114061636520016161 xustar0030 mtime=1623670096.159101337 29 atime=1623670096.15610134 30 ctime=1623670096.159101337 elk-7.2.42/examples/Mossbauer/Fe/0000755002504400250440000000000014061636520020274 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Mossbauer/Fe/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017342 xustar0030 mtime=1623670096.158101338 30 atime=1623670096.157101339 30 ctime=1623670096.158101338 elk-7.2.42/examples/Mossbauer/Fe/elk.in0000644002504400250440000000425214061636520021402 0ustar00dewhurstdewhurst00000000000000 ! Calculating the Mossbauer effect hyperfine parameters for bcc Fe, namely the ! contact charge density, the contact magnetic hyperfine field and the electric ! field gradient (EFG). In this case the EFG is zero because of symmetry. ! The hyperfine magnetic field is difficult to calculate accurately. This is ! partly due to the neglect of the orbital and dipolar contributions, but mainly ! because most of the contact magnetisation arises from the polarised core s ! states. One therefore has to switch on core polarisation with ! 'spincore=.true.', but in addition any semi-core s states should also be moved ! to the core and thus treated with the full Dirac equation. Consequently, this ! example requires a special species file (Fe.in), in which the 3s states are in ! the core. Note that the field is quite sensitive to the number of empty states ! and k-points. ! Also note that the hyperfine field also depends strongly on the choice of ! functional with GGA functions usually yielding larger values. Try running the ! calculation again with PBE (xctype=20). ! Experimentally the hyperfine field is 33.9 Tesla [J. Phys. Soc. Jpn. 33, 159 ! (1972)]. A complete derivation of the formulae can be found in Phys. Rev. B ! 53, 3271 (1987). tasks 0 110 : isomer shift and hyperfine field 115 : electric field gradient ! enable calculation of the dipole field tbdip .true. ! enable calculation of the current density (i.e. orbital) contribution to the ! dipole field tjr .true. ! enable spin-orbit coupling spinorb .true. ! switch on core polarisation for hyperfine field spincore .true. ! lmaxi should be at least 2 for the EFG calculation lmaxi 2 ! external field for breaking spin symmetry bfieldc 0.0 0.0 0.001 ! very large number of empty states required for hyperfine field nempty 80 ! enable conduction local-orbitals lorbcnd .true. ! large number of k-points required ngridk 14 14 14 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 2.708 atoms 1 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/examples/Mossbauer/Fe/PaxHeaders.21776/Fe.in0000644000000000000000000000013214061636520017121 xustar0030 mtime=1623670096.159101337 30 atime=1623670096.159101337 30 ctime=1623670096.159101337 elk-7.2.42/examples/Mossbauer/Fe/Fe.in0000644002504400250440000000311414061636520021155 0ustar00dewhurstdewhurst00000000000000 'Fe' : spsymb 'iron' : spname -26.0000 : spzn 101799.2074 : spmass 0.392232E-06 2.0000 34.5962 500 : sprmin, rmt, sprmax, nrmt 10 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 4.00000 F 3 2 3 2.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.1817 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2816 0 T elk-7.2.42/examples/Mossbauer/PaxHeaders.21776/Co-fcc0000644000000000000000000000013214061636520016722 xustar0030 mtime=1623670096.161101335 30 atime=1623670096.160101336 30 ctime=1623670096.161101335 elk-7.2.42/examples/Mossbauer/Co-fcc/0000755002504400250440000000000014061636520021034 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Mossbauer/Co-fcc/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020102 xustar0030 mtime=1623670096.161101335 30 atime=1623670096.161101335 30 ctime=1623670096.161101335 elk-7.2.42/examples/Mossbauer/Co-fcc/elk.in0000644002504400250440000000400514061636520022136 0ustar00dewhurstdewhurst00000000000000 ! Calculating the Mossbauer effect hyperfine parameters for fcc Co, namely the ! contact charge density, the contact magnetic hyperfine field and the electric ! field gradient (EFG). ! The hyperfine magnetic field is difficult to calculate accurately. This is ! mainly because most of the contact magnetisation arises from the polarised ! core s states. One therefore has to switch on core polarisation with ! 'spincore=.true.', but in addition any semi-core s states should also be moved ! to the core and thus treated with the full Dirac equation. Also note that the ! field is quite sensitive to the number of empty states and k-points. ! Also note that the hyperfine field also depends strongly on the choice of ! functional, with GGA usually yielding larger values. Try running the ! calculation again with PBE (xctype=20). This may be the better choice of ! functional for Mossbauer related quantities because of the large density ! gradients near the nucleus. tasks 0 110 : isomer shift and hyperfine field 115 : electric field gradient ! uncomment the following lines to enable GGA (PBE) !xctype ! 20 ! !msmooth ! 4 ! enable calculation of the dipole magnetic field tbdip .true. ! enable calculation of the current density (i.e. orbital) contribution to the ! dipole field tjr .true. ! enable spin-orbit coupling spinorb .true. ! switch on core polarisation for hyperfine field spincore .true. ! lmaxi should be at least 2 for the EFG calculation lmaxi 2 ! external field for breaking spin symmetry bfieldc 0.0 0.0 0.001 ! very large number of empty states required for hyperfine field nempty 80 ! conduction local-orbitals required lorbcnd .true. ! large number of k-points required ngridk 14 14 14 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.3448 sppath '../../../species/' atoms 1 : nspecies 'Co.in' : spfname 1 : natoms; atposl, bfcmt below 0.0 0.0 0.0 elk-7.2.42/examples/Mossbauer/PaxHeaders.21776/NiF20000644000000000000000000000013214061636520016366 xustar0030 mtime=1623670096.165101332 30 atime=1623670096.163101333 30 ctime=1623670096.165101332 elk-7.2.42/examples/Mossbauer/NiF2/0000755002504400250440000000000014061636520020500 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Mossbauer/NiF2/PaxHeaders.21776/MOSSBAUER.OUT0000644000000000000000000000013214061636520020374 xustar0030 mtime=1623670096.164101333 30 atime=1623670096.164101333 30 ctime=1623670096.164101333 elk-7.2.42/examples/Mossbauer/NiF2/MOSSBAUER.OUT0000644002504400250440000001013714061636520022433 0ustar00dewhurstdewhurst00000000000000 Species : 1 (Ni), atom : 1 approximate nuclear radius : 0.7325707712E-04 number of mesh points to nuclear radius : 170 density at nuclear center : 27065.61626 density at nuclear surface : 19469.68536 average contact charge density : 21799.30518 contact magnetic moment (mu_B) : 0.3556682277 -0.3250408784E-02 -0.5961585217E-04 contact field : 0.7942691198E-04 -0.7258729125E-06 -0.1331325846E-07 tesla : 18.66943519 -0.1706177033 -0.3129304790E-02 spin and orbital dipole field : -0.6038677809E-05 0.1166101164E-05 0.6342070908E-08 tesla : -1.419401827 0.2740941271 0.1490714908E-02 Species : 1 (Ni), atom : 2 approximate nuclear radius : 0.7325707712E-04 number of mesh points to nuclear radius : 170 density at nuclear center : 27065.62041 density at nuclear surface : 19469.68809 average contact charge density : 21799.30825 contact magnetic moment (mu_B) : 0.3560239771 -0.3179352632E-02 0.3878445782E-04 contact field : 0.7950635701E-04 -0.7100048359E-06 0.8661245165E-08 tesla : 18.68810889 -0.1668878840 0.2035840892E-02 spin and orbital dipole field : -0.6143126486E-05 -0.5623083484E-06 -0.2821446664E-06 tesla : -1.443952673 -0.1321715651 -0.6631859950E-01 Species : 2 (F), atom : 1 approximate nuclear radius : 0.5278478738E-04 number of mesh points to nuclear radius : 89 density at nuclear center : 469.6748179 density at nuclear surface : 458.0181065 average contact charge density : 518.3705591 contact magnetic moment (mu_B) : -0.2076757064 0.1757535181E-02 -0.5037678888E-04 contact field : -0.4637760353E-04 0.3924882270E-06 -0.1125001466E-07 tesla : -10.90113718 0.9225504727E-01 -0.2644335709E-02 spin and orbital dipole field : -0.3840346331E-04 -0.1592687822E-04 -0.2577673716E-07 tesla : -9.026801516 -3.743640704 -0.6058867353E-02 Species : 2 (F), atom : 2 approximate nuclear radius : 0.5278478738E-04 number of mesh points to nuclear radius : 89 density at nuclear center : 469.6746466 density at nuclear surface : 458.0179388 average contact charge density : 518.3703693 contact magnetic moment (mu_B) : -0.2078531243 0.1740868591E-02 -0.1670018648E-04 contact field : -0.4641722404E-04 0.3887662872E-06 -0.3729442605E-08 tesla : -10.91045005 0.9138019878E-01 -0.8766120359E-03 spin and orbital dipole field : -0.3847659363E-04 0.1653003236E-04 -0.5230842188E-08 tesla : -9.043990926 3.885413145 -0.1229518646E-02 Species : 2 (F), atom : 3 approximate nuclear radius : 0.5278478738E-04 number of mesh points to nuclear radius : 89 density at nuclear center : 469.6748179 density at nuclear surface : 458.0181065 average contact charge density : 518.3705591 contact magnetic moment (mu_B) : -0.2076757064 0.1757535181E-02 -0.5037678888E-04 contact field : -0.4637760353E-04 0.3924882270E-06 -0.1125001466E-07 tesla : -10.90113718 0.9225504727E-01 -0.2644335709E-02 spin and orbital dipole field : -0.3840346331E-04 -0.1592687822E-04 -0.2577673716E-07 tesla : -9.026801516 -3.743640704 -0.6058867353E-02 Species : 2 (F), atom : 4 approximate nuclear radius : 0.5278478738E-04 number of mesh points to nuclear radius : 89 density at nuclear center : 469.6746466 density at nuclear surface : 458.0179388 average contact charge density : 518.3703693 contact magnetic moment (mu_B) : -0.2078531243 0.1740868591E-02 -0.1670018648E-04 contact field : -0.4641722404E-04 0.3887662872E-06 -0.3729442605E-08 tesla : -10.91045005 0.9138019878E-01 -0.8766120359E-03 spin and orbital dipole field : -0.3847659363E-04 0.1653003236E-04 -0.5230842188E-08 tesla : -9.043990926 3.885413145 -0.1229518646E-02 Note that the contact term is implicitly included in the spin dipole field but may not match exactly with the directly calculated value. elk-7.2.42/examples/Mossbauer/NiF2/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017546 xustar0030 mtime=1623670096.166101331 30 atime=1623670096.165101332 30 ctime=1623670096.166101331 elk-7.2.42/examples/Mossbauer/NiF2/elk.in0000644002504400250440000000403114061636520021601 0ustar00dewhurstdewhurst00000000000000 ! Calculating the zero field resonance frequencies for NiF2. ! The ground state is antiferromagnetic with moments in the a-b plane. ! Nonetheless, the experimentally measured hyperfine field originates from ! domain walls, as explained in R. G. Shulman, Journal of Applied Physics 32, ! S126 (1961). ! The zero field estimate are ~0.7 T and ~1.3 T in good agreement with the ! results provided by this example. ! Example by Pietro Bonfa. tasks 0 ! ground-state calculation 110 ! determine the magnetic hyperfine field lmaxi 2 rgkmax 5.5 gmaxvr 16.0 ! enable calculation of the dipole field tbdip .true. ! enable calculation of the current density (i.e. orbital) contribution to the ! dipole field tjr .true. ! enable spin-orbit coupling spinorb .true. ! switch on core polarisation for hyperfine field spincore .true. sppath '../../../species/' ! external field for breaking spin symmetry bfieldc 0.01 0.0 0.0 reducebf 0.75 ! very large number of empty states required for hyperfine field nempty 40 ! enable conduction local-orbitals lorbcnd .true. ! large number of k-points required ngridk 6 6 6 avec 1.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0000000000 0.0000000000 0.6619957537 scale 8.9006099310 atoms 2 : nspecies 'Ni.in' : spfname 2 0.000000000000000 0.000000000000000 0.000000000000000 0.00100000 0.00100000 0.00000000 0.500000000000000 0.500000000000000 0.500000000000000 -0.00100000 -0.00100000 0.00000000 'F.in' : spfname 4 0.303300000000000 0.303300000000000 0.000000000000000 0.00000000 0.00000000 0.00000000 0.196700000000000 0.803300000000000 0.500000000000000 0.00000000 0.00000000 0.00000000 0.696700000000000 0.696700000000000 0.000000000000000 0.00000000 0.00000000 0.00000000 0.803300000000000 0.196700000000000 0.500000000000000 0.00000000 0.00000000 0.00000000 elk-7.2.42/examples/PaxHeaders.21776/TDDFT-optics0000644000000000000000000000013214061636520016034 xustar0030 mtime=1623670096.196101303 30 atime=1623670096.166101331 30 ctime=1623670096.196101303 elk-7.2.42/examples/TDDFT-optics/0000755002504400250440000000000014061636520020146 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/Ar-bootstrap-single0000644000000000000000000000013214061636520021670 xustar0030 mtime=1623670096.170101327 30 atime=1623670096.168101329 30 ctime=1623670096.170101327 elk-7.2.42/examples/TDDFT-optics/Ar-bootstrap-single/0000755002504400250440000000000014061636520024002 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/Ar-bootstrap-single/PaxHeaders.21776/Ar_expt_eV.dat0000644000000000000000000000013214061636520024473 xustar0030 mtime=1623670096.169101328 30 atime=1623670096.169101328 30 ctime=1623670096.169101328 elk-7.2.42/examples/TDDFT-optics/Ar-bootstrap-single/Ar_expt_eV.dat0000644002504400250440000000645114061636520026536 0ustar00dewhurstdewhurst00000000000000#Phys. Rev. B 76 161103(R) (2007) 11.6284 0.0621413 11.6956 0.198027 11.7548 0.412014 11.7982 0.723684 11.8416 1.05486 11.885 1.48357 11.9165 1.81486 11.9283 2.10733 11.9401 2.32178 11.9559 2.49718 11.9637 2.88722 11.9754 3.23821 11.9793 3.62829 11.9831 4.01837 11.9832 3.82331 11.9869 4.54499 11.9944 6.22242 11.9945 6.02736 11.9946 5.63724 11.9981 7.39274 11.9982 7.00262 11.9982 6.80756 11.9983 6.6125 12.0017 8.56305 12.0017 8.36799 12.0018 8.17293 12.0019 7.97788 12.002 7.58776 12.0053 9.92843 12.0054 9.53831 12.0054 9.34325 12.0055 9.14819 12.0056 8.75807 12.009 10.7086 12.0091 10.5136 12.0092 10.1234 12.0128 11.5864 12.0129 10.9036 12.0166 11.9764 12.0167 11.7814 12.0205 12.3665 12.0243 12.9516 12.0243 12.7566 12.0244 12.5615 12.0281 13.3417 12.0282 13.1467 12.032 13.7318 12.0357 14.473 12.0358 14.1219 12.0359 13.9268 12.0438 13.7902 12.0479 13.4001 12.0479 13.205 12.0519 13.0099 12.052 12.8148 12.0522 11.9956 12.056 12.4247 12.0643 11.0592 12.0683 10.669 12.0684 10.474 12.0685 10.0839 12.0725 9.88876 12.0726 9.49864 12.0726 9.30358 12.0767 9.10849 12.0769 8.23072 12.085 7.56744 12.089 7.17729 12.0891 6.98223 12.0931 6.59207 12.0932 6.39701 12.0972 6.00685 12.1054 5.10951 12.1094 4.91441 12.1134 4.52425 12.1174 4.32915 12.1255 3.7439 12.1295 3.5488 12.1335 3.3537 12.1375 3.15861 12.1415 2.96351 12.1495 2.49529 12.157 4.17272 12.1571 3.97766 12.1608 4.95292 12.1608 4.75786 12.1609 4.5628 12.1645 5.73312 12.1645 5.53806 12.1646 5.343 12.1647 5.14794 12.1682 6.51331 12.1683 6.31825 12.1684 5.92814 12.1719 7.48857 12.172 7.29351 12.1721 6.90339 12.1721 6.70833 12.1757 8.26877 12.1758 7.87865 12.1758 7.68359 12.1794 9.04897 12.1795 8.85391 12.1796 8.46379 12.1831 9.98521 12.1833 9.43904 12.1868 11.2726 12.1869 10.8239 12.1945 11.7796 12.1946 11.5846 12.1984 12.1697 12.2022 12.5598 12.2023 12.3647 12.2059 13.4375 12.2141 12.6767 12.2181 12.2866 12.2182 12.0915 12.2222 11.7013 12.2264 10.7455 12.2345 10.2578 12.2385 10.0627 12.2425 9.67254 12.2427 8.83378 12.2466 9.22386 12.2546 8.77515 12.2547 8.44355 12.2587 8.24845 12.2628 7.8583 12.2628 7.66324 12.2668 7.46814 12.2708 7.27304 12.2709 7.07798 12.2749 6.88288 12.275 6.43425 12.283 6.1806 12.287 5.9855 12.291 5.59534 12.2911 5.40028 12.2951 5.20518 12.2952 4.67853 12.3191 3.85905 12.339 3.44923 12.3588 3.29299 12.4103 2.98039 12.4262 2.74617 12.45 2.23878 12.4699 1.90699 12.4937 1.51664 12.5214 1.22378 12.5373 0.892029 12.5611 0.755256 12.573 0.540576 12.6007 0.403764 12.6402 0.286344 12.6679 0.149532 12.7035 0.0711618 12.7668 0.0510392 12.8142 0.1286 12.8497 0.245289 12.8932 0.322888 12.9248 0.400603 12.9722 0.49767 13.0078 0.575347 13.0591 0.594352 13.1145 0.593812 13.1896 0.59308 13.2409 0.63159 13.2805 0.611699 13.32 0.708843 13.3634 0.805948 13.4148 0.961494 13.4582 1.07811 13.4819 1.35096 13.4976 1.76043 13.5093 2.03339 13.5211 2.4234 13.5289 2.6769 13.5685 2.44244 13.5884 2.14966 13.6043 1.72037 13.6281 1.2325 13.6598 0.998116 13.6796 0.744347 13.7034 0.705104 13.7231 0.997499 13.7507 1.25081 13.7664 1.42621 13.802 1.26981 13.8219 1.03555 13.8298 0.859917 13.8575 0.742612 13.901 0.878729 13.9128 1.07367 13.9325 1.21002 13.9523 1.09279 13.976 0.917009 14.0077 0.858183 14.0393 0.994416 14.0748 1.07209 14.0867 1.11099 14.1183 1.11068 14.1459 1.16893 14.1776 1.1101 14.1973 1.0709 14.2487 1.0704 14.3199 1.14773 14.3673 1.10825 14.4345 1.1076 14.474 1.10721 elk-7.2.42/examples/TDDFT-optics/Ar-bootstrap-single/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023050 xustar0030 mtime=1623670096.171101326 30 atime=1623670096.170101327 30 ctime=1623670096.171101326 elk-7.2.42/examples/TDDFT-optics/Ar-bootstrap-single/elk.in0000644002504400250440000000143114061636520025104 0ustar00dewhurstdewhurst00000000000000 ! This example produces the dielectric function of solid argon using a single ! iteration of the bootstrap kernel [Phys. Rev. Lett. 107, 186401]. This ! approximation works particularly well for calculating excitonic binding ! energies. ! A file with experimental data in units of eV is included in this directory. tasks 0 120 320 scissor 0.22 swidth 0.005 ! bootstrap kernal with single iteration fxctype 211 gmaxrf 0.0 wplot 6000 100 2 0.0 1.0 nempty 10 avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 10.030 sppath '../../../species/' atoms 1 : nspecies 'Ar.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 ngridk 8 8 8 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/LiF-bootstrap-single0000644000000000000000000000013214061636520022000 xustar0030 mtime=1623670096.172101325 30 atime=1623670096.171101326 30 ctime=1623670096.172101325 elk-7.2.42/examples/TDDFT-optics/LiF-bootstrap-single/0000755002504400250440000000000014061636520024112 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/LiF-bootstrap-single/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023160 xustar0030 mtime=1623670096.173101324 30 atime=1623670096.173101324 30 ctime=1623670096.173101324 elk-7.2.42/examples/TDDFT-optics/LiF-bootstrap-single/elk.in0000644002504400250440000000121614061636520025215 0ustar00dewhurstdewhurst00000000000000 ! Optical response of LiF with the single iteration bootstrap kernel. tasks 0 120 320 ! single iteration bootstrap fxctype 211 scissor 0.1916 swidth 0.008 ! LFE are included gmaxrpa 2.0 lradstp 2 nempty 10 wplot 8000 100 0 0.0 1.0 avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 ngridk 8 8 8 vkloff 0.625 0.5 0.25 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/Ni-MOKE0000644000000000000000000000013214061636520017133 xustar0030 mtime=1623670096.175101322 30 atime=1623670096.174101323 30 ctime=1623670096.175101322 elk-7.2.42/examples/TDDFT-optics/Ni-MOKE/0000755002504400250440000000000014061636520021245 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/Ni-MOKE/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020313 xustar0030 mtime=1623670096.176101321 30 atime=1623670096.176101321 30 ctime=1623670096.176101321 elk-7.2.42/examples/TDDFT-optics/Ni-MOKE/elk.in0000644002504400250440000000121314061636520022345 0ustar00dewhurstdewhurst00000000000000 ! Magneto-optical Kerr effect for ferromagnetic nickel. For good accuracy of the ! Kerr rotation a k-point grid of 20x20x20 is required. tasks 0 120 122 ! the relaxation time is taken to be 1/swidth swidth 0.01 spinpol .true. ! spin-orbit coupling is required for MOKE spinorb .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 10 10 10 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/Ge0000644000000000000000000000013014061636520016365 xustar0029 mtime=1623670096.17710132 30 atime=1623670096.176101321 29 ctime=1623670096.17710132 elk-7.2.42/examples/TDDFT-optics/Ge/0000755002504400250440000000000014061636520020501 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/Ge/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520017553 xustar0029 mtime=1623670096.17810132 29 atime=1623670096.17810132 29 ctime=1623670096.17810132 elk-7.2.42/examples/TDDFT-optics/Ge/elk.in0000644002504400250440000000141114061636520021601 0ustar00dewhurstdewhurst00000000000000 ! High quality density of states, band structure and linear optical tensor of ! germanium with spin-orbit coupling (Andrew Chizmeshya) tasks 0 10 20 120 121 spinorb .true. xctype 3 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 5.3451 nempty 20 wplot 1000 150 0 -0.5 2.0 lmaxapw 10 lmaxo 8 gmaxvr 12.0 sppath '../../../species/' atoms 1 : nspecies 'Ge.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 10 10 10 vkloff 0.25 0.25 0.75 plot1d 3 200 : nvp1d, npp1d 0.5 0.0 1.0 : vlvp1d 0.0 0.0 1.0 0.5 0.5 1.0 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/LiF-bootstrap0000644000000000000000000000013214061636520020521 xustar0030 mtime=1623670096.180101318 30 atime=1623670096.179101319 30 ctime=1623670096.180101318 elk-7.2.42/examples/TDDFT-optics/LiF-bootstrap/0000755002504400250440000000000014061636520022633 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/LiF-bootstrap/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021701 xustar0030 mtime=1623670096.180101318 30 atime=1623670096.180101318 30 ctime=1623670096.180101318 elk-7.2.42/examples/TDDFT-optics/LiF-bootstrap/elk.in0000644002504400250440000000251714061636520023743 0ustar00dewhurstdewhurst00000000000000 ! Time-dependent density functional theory (TDDFT) optical spectrum of lithium ! fluoride. This material has a prominent excitonic peak, which is absent in the ! usual RPA dielectric function. The 'bootstrap' TDDFT kernel is used, see: ! arXiv:1107.0199v1 [cond-mat.mtrl-sci] ! The scissor shift is taken to be the difference between the experimental gap, ! 14.2 eV [Phys. Rev. B 13, 5530 (1976)], and the LDA gap, 8.97 eV. tasks 0 ! ground-state calculation 120 ! compute momentum matrix elements 121 ! compute RPA dielectric function with no local field contributions 320 ! compute TDDFT dielectric function with local field contributions ! scissor shift scissor 0.192 xctype 3 ! bootstrap kernel fxctype 210 ! smearing width swidth 0.01 ! G-vector cut-off of exchange-correlation kernel and response function gmaxrf 0.0 nempty 8 lradstp 2 wplot 800 100 0 : nwplot, ngrkf, nswplot 0.0 1.5 : wplot avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 ngridk 8 8 8 vkloff 0.25 0.5 0.625 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/TiO20000644000000000000000000000013214061636520016611 xustar0030 mtime=1623670096.182101316 30 atime=1623670096.181101317 30 ctime=1623670096.182101316 elk-7.2.42/examples/TDDFT-optics/TiO2/0000755002504400250440000000000014061636520020723 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/TiO2/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017771 xustar0030 mtime=1623670096.183101315 30 atime=1623670096.182101316 30 ctime=1623670096.183101315 elk-7.2.42/examples/TDDFT-optics/TiO2/elk.in0000644002504400250440000000127314061636520022031 0ustar00dewhurstdewhurst00000000000000 ! Linear optical spectrum of titanium dioxide. The inverse lifetime is ! determined by swidth. Note that many more k-points are required for good ! convergence of the optical spectrum. tasks 0 120 121 swidth 0.005 ! use Broyden mixing for fast convergence mixtype 3 avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.6441 scale 8.6806 sppath '../../../species/' atoms 2 : nspecies 'Ti.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.5 0.5 0.5 'O.in' 4 0.3048 0.3048 0.0 0.6952 0.6952 0.0 0.1952 0.8048 0.5 0.8048 0.1952 0.5 ngridk 4 4 4 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/LiF-LRC0000644000000000000000000000013214061636520017124 xustar0030 mtime=1623670096.185101313 30 atime=1623670096.184101314 30 ctime=1623670096.185101313 elk-7.2.42/examples/TDDFT-optics/LiF-LRC/0000755002504400250440000000000014061636520021236 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/LiF-LRC/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020304 xustar0030 mtime=1623670096.186101312 30 atime=1623670096.185101313 30 ctime=1623670096.186101312 elk-7.2.42/examples/TDDFT-optics/LiF-LRC/elk.in0000644002504400250440000000242714061636520022346 0ustar00dewhurstdewhurst00000000000000 ! Time-dependent density functional theory (TDDFT) optical spectrum of lithium ! fluoride. This material has a prominent excitonic peak, which is absent in the ! usual RPA dielectric function. The TDDFT kernel fxc is described in ! Phys. Rev. B 69, p155112 (2004) as the 'long-range contribution' and requires ! a material-dependent parameter alpha. tasks 0 ! ground-state calculation 120 ! compute momentum matrix elements 121 ! compute RPA dielectric function with no local field contributions 320 ! compute TDDFT dielectric function with local field contributions ! long-range contribution kernel fxctype 200 ! parameter alpha for long-range contribution kernel fxclrc 5.5 ! G-vector cut-off of exchange-correlation kernel and response function gmaxrf 1.0 swidth 0.01 nempty 8 lradstp 2 wplot 800 100 0 : nwplot, ngrkf, nswplot 0.0 1.5 : wplot avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 ngridk 4 4 4 vkloff 0.25 0.5 0.625 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/LiF0000644000000000000000000000013214061636520016506 xustar0030 mtime=1623670096.187101311 30 atime=1623670096.186101312 30 ctime=1623670096.187101311 elk-7.2.42/examples/TDDFT-optics/LiF/0000755002504400250440000000000014061636520020620 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/LiF/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520017672 xustar0029 mtime=1623670096.18810131 29 atime=1623670096.18810131 29 ctime=1623670096.18810131 elk-7.2.42/examples/TDDFT-optics/LiF/elk.in0000644002504400250440000000112214061636520021717 0ustar00dewhurstdewhurst00000000000000 ! Linear optical spectrum of lithium fluoride. tasks 0 120 121 ! the inverse lifetime is determined by swidth swidth 0.01 nempty 10 lradstp 2 wplot 400 100 0 : nwplot, ngrkf, nswplot 0.0 1.5 : wplot avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 ngridk 10 10 10 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/diamond-ALDA0000644000000000000000000000013214061636520020146 xustar0030 mtime=1623670096.190101308 30 atime=1623670096.189101309 30 ctime=1623670096.190101308 elk-7.2.42/examples/TDDFT-optics/diamond-ALDA/0000755002504400250440000000000014061636520022260 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/diamond-ALDA/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021326 xustar0030 mtime=1623670096.190101308 30 atime=1623670096.190101308 30 ctime=1623670096.190101308 elk-7.2.42/examples/TDDFT-optics/diamond-ALDA/elk.in0000644002504400250440000000117414061636520023366 0ustar00dewhurstdewhurst00000000000000 ! Dielectric function of diamond calculated at finite q-vector using ALDA. tasks 0 120 320 ! q-vector in lattice coordinates vecql 0.5 0.5 0.5 xctype 3 fxctype 3 ! G-vector cut-off for the RPA and ALDA response function gmaxrf 3.0 nempty 10 swidth 0.01 wplot 500 100 1 0.0 1.5 avec 3.3637 3.3637 0.0 3.3637 0.0 3.3637 0.0 3.3637 3.3637 sppath '../../../species/' atoms 1 : nspecies 'C.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 8 8 8 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/Al0000644000000000000000000000013214061636520016370 xustar0030 mtime=1623670096.192101307 30 atime=1623670096.191101308 30 ctime=1623670096.192101307 elk-7.2.42/examples/TDDFT-optics/Al/0000755002504400250440000000000014061636520020502 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/Al/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017550 xustar0030 mtime=1623670096.193101306 30 atime=1623670096.192101307 30 ctime=1623670096.193101306 elk-7.2.42/examples/TDDFT-optics/Al/elk.in0000644002504400250440000000130414061636520021603 0ustar00dewhurstdewhurst00000000000000 ! Linear optical response of aluminium including intra-band contributions. ! The plasma frequency is also determined and written to PLASMA.OUT. tasks 0 120 121 ! include intra-band excitations intraband .true. swidth 0.01 ! dense k-point set required ngridk 24 24 24 ! larger number of empty states required nempty 8 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 ! lattice constant at room temperature scale 3.8267 ! this is the relative path to the species files sppath '../../../species/' atoms 1 : nspecies 'Al.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/LiF-RBO0000644000000000000000000000013214061636520017126 xustar0030 mtime=1623670096.195101304 30 atime=1623670096.194101305 30 ctime=1623670096.195101304 elk-7.2.42/examples/TDDFT-optics/LiF-RBO/0000755002504400250440000000000014061636520021240 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/LiF-RBO/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020306 xustar0030 mtime=1623670096.196101303 30 atime=1623670096.195101304 30 ctime=1623670096.196101303 elk-7.2.42/examples/TDDFT-optics/LiF-RBO/elk.in0000644002504400250440000000201214061636520022336 0ustar00dewhurstdewhurst00000000000000 ! Example for the revised bootstrap kernel (RBO) of S. Rigamonti, et al., ! Phys. Rev. Lett. 114, 146402. tasks 0 ! ground-state calculation 120 ! compute momentum matrix elements 121 ! compute RPA dielectric function with no local field contributions 320 ! compute TDDFT dielectric function with local field contributions ! scissor shift scissor 0.192 xctype 3 ! RBO kernel fxctype 212 ! smearing width swidth 0.01 ! G-vector cut-off of exchange-correlation kernel and response function gmaxrf 0.0 nempty 8 lradstp 2 wplot 800 100 0 : nwplot, ngrkf, nswplot 0.0 1.5 : wplot avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 ngridk 8 8 8 vkloff 0.25 0.5 0.625 elk-7.2.42/examples/TDDFT-optics/PaxHeaders.21776/Ne-RBO0000644000000000000000000000012614061636520017021 xustar0028 mtime=1623670096.1991013 30 atime=1623670096.196101303 28 ctime=1623670096.1991013 elk-7.2.42/examples/TDDFT-optics/Ne-RBO/0000755002504400250440000000000014061636520021130 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-optics/Ne-RBO/PaxHeaders.21776/Ne_expt_eV.dat0000644000000000000000000000013214061636520021621 xustar0030 mtime=1623670096.198101301 30 atime=1623670096.198101301 30 ctime=1623670096.198101301 elk-7.2.42/examples/TDDFT-optics/Ne-RBO/Ne_expt_eV.dat0000644002504400250440000000153414061636520023661 0ustar00dewhurstdewhurst00000000000000#Phys. Rev. B 72 035127 (2005) 16.7861 0.308771 16.8999 0.402363 17.0137 0.464459 17.0863 0.621367 17.1279 0.747024 17.1799 0.904096 17.2318 1.04542 17.2631 1.2184 17.3047 1.3913 17.3154 1.56445 17.3366 1.87924 17.3369 2.05247 17.3478 2.41458 17.3587 2.72946 17.3694 2.9341 17.3697 3.09158 17.3806 3.4222 17.3809 3.59543 17.3812 3.7844 17.3815 3.95763 17.3924 4.2725 17.3927 4.46147 17.3929 4.60321 17.4036 4.80785 17.4039 4.96532 17.4042 5.1543 17.4045 5.32752 17.4158 5.86287 17.478 5.98836 17.4877 5.62608 17.5179 5.12191 17.5279 4.9486 17.5482 4.74371 17.5787 4.46001 17.5884 4.08198 17.597 3.07404 17.6059 2.22358 17.6154 1.75106 17.6653 0.679801 17.7264 0.159635 17.7882 0.0489118 18.0156 0.0628692 18.2223 0.0612415 18.4704 0.0750361 18.7909 0.104009 19.1424 0.164233 19.2354 0.163501 19.4628 0.16171 19.5662 0.176644 19.804 0.206268 20.1245 0.282484 elk-7.2.42/examples/TDDFT-optics/Ne-RBO/PaxHeaders.21776/elk.in0000644000000000000000000000012414061636520020177 xustar0028 mtime=1623670096.1991013 28 atime=1623670096.1991013 28 ctime=1623670096.1991013 elk-7.2.42/examples/TDDFT-optics/Ne-RBO/elk.in0000644002504400250440000000120314061636520022227 0ustar00dewhurstdewhurst00000000000000 ! Example for the revised bootstrap kernel (RBO) of S. Rigamonti, et al., ! Phys. Rev. Lett. 114, 146402. tasks 0 120 320 scissor 0.360 lradstp 2 ! local field effects (LFE) not included gmaxrpa 0.0 swidth 0.005 ! RBO kernel fxctype 212 wplot 5000 100 1 0.0 1.1 nempty 20 avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 8.440 sppath '../../../species/' atoms 1 : nspecies 'Ne.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 ngridk 10 10 10 vkloff 0.625 0.5 0.25 elk-7.2.42/examples/PaxHeaders.21776/fractional-species0000644000000000000000000000013214061636520017443 xustar0030 mtime=1623670096.201101298 30 atime=1623670096.200101299 30 ctime=1623670096.201101298 elk-7.2.42/examples/fractional-species/0000755002504400250440000000000014061636520021555 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/fractional-species/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020623 xustar0030 mtime=1623670096.202101297 30 atime=1623670096.202101297 30 ctime=1623670096.202101297 elk-7.2.42/examples/fractional-species/elk.in0000644002504400250440000000154114061636520022661 0ustar00dewhurstdewhurst00000000000000 ! In this example the code generates a fractional atomic species file called ! 'A.in' which is then used in a ground-state calculation to find the moment. ! This allows for easy use of the virtual crystal approximation (VCA). tasks 0 ! generate a fractional atomic species charge -26.2 and write to the file 'A.in' fspecies -26.2 'A' spinpol .true. ! small magnetic field in the z-direction bfieldc 0.0 0.0 0.01 ! fairly large number of empty states required for magnetic cases nempty 8 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 2.708 ! Now use the file 'A.in' in the atoms block atoms 1 : nspecies 'A.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/PaxHeaders.21776/magnetism0000644000000000000000000000013214061636520015654 xustar0030 mtime=1623670096.233101268 30 atime=1623670096.203101296 30 ctime=1623670096.233101268 elk-7.2.42/examples/magnetism/0000755002504400250440000000000014061636520017766 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/PaxHeaders.21776/Fe-FSM-MT-AFM0000644000000000000000000000013214061636520017550 xustar0030 mtime=1623670096.205101295 30 atime=1623670096.204101295 30 ctime=1623670096.205101295 elk-7.2.42/examples/magnetism/Fe-FSM-MT-AFM/0000755002504400250440000000000014061636520021662 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Fe-FSM-MT-AFM/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020730 xustar0030 mtime=1623670096.206101294 30 atime=1623670096.206101294 30 ctime=1623670096.206101294 elk-7.2.42/examples/magnetism/Fe-FSM-MT-AFM/elk.in0000644002504400250440000000213414061636520022765 0ustar00dewhurstdewhurst00000000000000 ! Antiferromagnetic bcc iron example with fixed spin moment in muffin-tin. ! Rememeber to put a small magnetic fields on atoms with same symmetry as ! fixed moment. This in order to correctly symmetrize the magnetization. ! Run by Fredrik Bultmark, Francesco Cricchio, Lars Nordstrom. tasks 0 ! antiferromagnetic local fixed spin moment calculation fsmtype 2 mommtfix 1 1 0.0 0.0 1.0 : is, ia, mommtfix 1 2 0.0 0.0 -1.0 : is, ia, mommtfix ! FSM step length: reduce to improve convergence taufsm 0.01 lmaxapw 10 ! fairly large number of empty states required for magnetic cases nempty 8 avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 scale 6.6 sppath '../../../species/' ! note small magnetic fields on atoms with same symmetry as fixed moment atoms 1 : nspecies 'Fe.in' : spfname 2 : natoms 0.0 0.0 0.0 0.0 0.0 0.001 : atposl, bfcmt 0.5 0.5 0.5 0.0 0.0 -0.001 ! this k-point set is too small for calculation of accurate moments ngridk 4 4 4 elk-7.2.42/examples/magnetism/PaxHeaders.21776/Fe-spiral0000644000000000000000000000013214061636520017476 xustar0030 mtime=1623670096.208101292 30 atime=1623670096.207101293 30 ctime=1623670096.208101292 elk-7.2.42/examples/magnetism/Fe-spiral/0000755002504400250440000000000014061636520021610 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Fe-spiral/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020656 xustar0030 mtime=1623670096.208101292 30 atime=1623670096.208101292 30 ctime=1623670096.208101292 elk-7.2.42/examples/magnetism/Fe-spiral/elk.in0000644002504400250440000000135214061636520022714 0ustar00dewhurstdewhurst00000000000000 ! Spin-spiral state for Gamma-Fe. Care should be taken to ensure that the ! calculation is fully converged. tasks 0 spinsprl .true. ! spin-spiral q-vector in lattice coordinates vqlss 0.1 0.1 0.0 ! fairly large large cut-off required rgkmax 8.5 gmaxvr 14.0 nempty 8 ! spiral magnetic field along q with perpendicular component only bfieldc 0.05 0.0 0.0 ! tight convergence required epspot 1.e-7 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.375 sppath '../../../species/' atoms 1 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 elk-7.2.42/examples/magnetism/PaxHeaders.21776/Cr-mono0000644000000000000000000000013214061636520017166 xustar0030 mtime=1623670096.213101287 30 atime=1623670096.209101291 30 ctime=1623670096.213101287 elk-7.2.42/examples/magnetism/Cr-mono/0000755002504400250440000000000014061636520021300 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Cr-mono/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020346 xustar0030 mtime=1623670096.211101289 30 atime=1623670096.211101289 30 ctime=1623670096.211101289 elk-7.2.42/examples/magnetism/Cr-mono/elk.in0000644002504400250440000000236314061636520022407 0ustar00dewhurstdewhurst00000000000000 ! Unsupported monolayer of Cr with the symmetry and lattice constant of a ! monolayer on the Ag(111) surface (see Phys. Rev. B 69, 24415 (2004)), which ! exhibits a non-collinear Neel state. Small magnetic fields 120 degrees apart ! are applied to each of the three atoms. ! Try plotting the 2D magnetisation density in OpenDX (version 4.3.2) using the ! files provided. tasks 0 72 spinpol .true. ! note that the number of empty states should be large because non-collinear ! effects are obtained in the second-variational step nempty 8 avec 1.5 0.86602540378 0.0 1.5 -0.86602540378 0.0 0.0 0.0 1.0 scale1 5.50836 : 7.79/sqrt(2) scale2 5.50836 scale3 7.0 sppath '../../../species/' ! note that the magnetic fields are in Cartesian coordinates atoms 1 : nspecies 'Cr.in' : spfname 3 : natoms 0.0 0.0 0.0 0.0 0.1 0.0 : atposl, bfcmt 0.333333333333 0.333333333333 0.0 -0.086602540378 -0.05 0.0 0.666666666667 0.666666666667 0.0 0.086602540378 -0.05 0.0 ngridk 2 2 1 vkloff 0.5 0.5 0.0 plot2d 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0 200 200 elk-7.2.42/examples/magnetism/Cr-mono/PaxHeaders.21776/mag2d.general0000644000000000000000000000013214061636520021574 xustar0030 mtime=1623670096.212101288 30 atime=1623670096.212101288 30 ctime=1623670096.212101288 elk-7.2.42/examples/magnetism/Cr-mono/mag2d.general0000644002504400250440000000027314061636520023633 0ustar00dewhurstdewhurst00000000000000file = MAG2D.OUT grid = 200 x 200 format = ascii interleaving = field majority = column header = lines 1 field = locations, field0 structure = 2-vector, 3-vector type = float, float end elk-7.2.42/examples/magnetism/Cr-mono/PaxHeaders.21776/mag2d.net0000644000000000000000000000013214061636520020745 xustar0030 mtime=1623670096.214101286 30 atime=1623670096.213101287 30 ctime=1623670096.214101286 elk-7.2.42/examples/magnetism/Cr-mono/mag2d.net0000644002504400250440000002211314061636520023001 0ustar00dewhurstdewhurst00000000000000// // time: Sat Jun 16 15:49:00 2007 // // version: 3.2.0 (format), 4.4.0 (DX) // // // MODULE main // workspace: width = 565, height = 623 // layout: snap = 0, width = 50, height = 50, align = NN // macro main( ) -> ( ) { // // node Import[1]: x = 47, y = 39, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "mag2d.general" // main_Import_1_out_1 = Import( main_Import_1_in_1, main_Import_1_in_2, main_Import_1_in_3, main_Import_1_in_4, main_Import_1_in_5, main_Import_1_in_6 ) [instance: 1, cache: 1]; // // node Sample[1]: x = 216, y = 66, inputs = 2, label = Sample // input[2]: defaulting = 0, visible = 1, type = 1, value = 2000 // main_Sample_1_out_1 = Sample( main_Import_1_out_1, main_Sample_1_in_2 ) [instance: 1, cache: 1]; // // node Compute[1]: x = 84, y = 147, inputs = 3, label = Compute // input[1]: defaulting = 0, visible = 0, type = 32, value = "$0/mag($0)" // expression: value = a/mag(a) // name[2]: value = a // name[3]: value = b // main_Compute_1_out_1 = Compute( main_Compute_1_in_1, main_Sample_1_out_1, main_Compute_1_in_3 ) [instance: 1, cache: 1]; // // node AutoGlyph[1]: x = 44, y = 254, inputs = 7, label = AutoGlyph // input[2]: defaulting = 0, visible = 1, type = 32, value = "rocket2D" // input[3]: defaulting = 0, visible = 1, type = 5, value = 7.0 // input[4]: defaulting = 0, visible = 1, type = 5, value = 0.25 // input[5]: defaulting = 0, visible = 1, type = 5, value = 0.05 // main_AutoGlyph_1_out_1 = AutoGlyph( main_Compute_1_out_1, main_AutoGlyph_1_in_2, main_AutoGlyph_1_in_3, main_AutoGlyph_1_in_4, main_AutoGlyph_1_in_5, main_AutoGlyph_1_in_6, main_AutoGlyph_1_in_7 ) [instance: 1, cache: 1]; // // node Color[1]: x = 108, y = 341, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "black" // main_Color_1_out_1 = Color( main_AutoGlyph_1_out_1, main_Color_1_in_2, main_Color_1_in_3, main_Color_1_in_4, main_Color_1_in_5 ) [instance: 1, cache: 1]; // // node Compute[2]: x = 348, y = 66, inputs = 3, label = Compute // input[1]: defaulting = 0, visible = 0, type = 32, value = "mag($0)" // expression: value = mag(a) // name[2]: value = a // name[3]: value = b // main_Compute_2_out_1 = Compute( main_Compute_2_in_1, main_Import_1_out_1, main_Compute_2_in_3 ) [instance: 2, cache: 1]; // // node RubberSheet[1]: x = 467, y = 146, inputs = 4, label = RubberSheet // main_RubberSheet_1_out_1 = RubberSheet( main_Compute_2_out_1, main_RubberSheet_1_in_2, main_RubberSheet_1_in_3, main_RubberSheet_1_in_4 ) [instance: 1, cache: 1]; // // node Translate[1]: x = 283, y = 189, inputs = 2, label = Translate // input[2]: defaulting = 0, visible = 1, type = 8, value = [0 0 -3] // main_Translate_1_out_1 = Translate( main_RubberSheet_1_out_1, main_Translate_1_in_2 ) [instance: 1, cache: 1]; // // node Colormap[2]: x = 479, y = 260, inputs = 19, label = Colormap // input[1]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 0.66315789] [0.60691824 0.0] } // input[2]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[3]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[4]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[5]: defaulting = 0, visible = 0, type = 32, value = "Colormap_2" // input[7]: defaulting = 1, visible = 0, type = 5, value = 9.2432623e-05 // input[8]: defaulting = 1, visible = 0, type = 5, value = 0.9849546 // input[9]: defaulting = 1, visible = 0, type = 1, value = 20 // input[12]: defaulting = 0, visible = 0, type = 16777221, value = { 9.2432623e-05 0.9849546 } // input[17]: defaulting = 0, visible = 0, type = 5, value = 9.2432623e-05 // input[18]: defaulting = 0, visible = 0, type = 5, value = 0.9849546 // window: position = (0.2998,0.0000), size = 0.6348x0.5859 // main_Colormap_2_out_1[cache: 2], main_Colormap_2_out_2[cache: 2] = Colormap( main_Colormap_2_in_1, main_Colormap_2_in_2, main_Colormap_2_in_3, main_Colormap_2_in_4, main_Colormap_2_in_5, main_Translate_1_out_1, main_Colormap_2_in_7, main_Colormap_2_in_8, main_Colormap_2_in_9, main_Colormap_2_in_10, main_Colormap_2_in_11, main_Colormap_2_in_12, main_Colormap_2_in_13, main_Colormap_2_in_14, main_Colormap_2_in_15, main_Colormap_2_in_16, main_Colormap_2_in_17, main_Colormap_2_in_18, main_Colormap_2_in_19 ) [instance: 2, cache: 1]; // // node Color[3]: x = 339, y = 334, inputs = 5, label = Color // main_Color_3_out_1 = Color( main_Translate_1_out_1, main_Colormap_2_out_1, main_Color_3_in_3, main_Color_3_in_4, main_Color_3_in_5 ) [instance: 3, cache: 1]; // // node Collect[1]: x = 214, y = 419, inputs = 2, label = Collect // main_Collect_1_out_1 = Collect( main_Color_1_out_1, main_Color_3_out_1 ) [instance: 1, cache: 1]; // // node AutoCamera[1]: x = 363, y = 493, inputs = 9, label = AutoCamera // input[3]: defaulting = 0, visible = 0, type = 5, value = 15.0 // input[4]: defaulting = 0, visible = 0, type = 1, value = 800 // input[5]: defaulting = 0, visible = 0, type = 5, value = 0.6 // input[7]: defaulting = 0, visible = 0, type = 3, value = 0 // input[8]: defaulting = 1, visible = 0, type = 5, value = 20.0 // input[9]: defaulting = 0, visible = 0, type = 32, value = "white" // main_AutoCamera_1_out_1 = AutoCamera( main_Collect_1_out_1, main_AutoCamera_1_in_2, main_AutoCamera_1_in_3, main_AutoCamera_1_in_4, main_AutoCamera_1_in_5, main_AutoCamera_1_in_6, main_AutoCamera_1_in_7, main_AutoCamera_1_in_8, main_AutoCamera_1_in_9 ) [instance: 1, cache: 1]; // // node Render[1]: x = 252, y = 561, inputs = 3, label = Render // main_Render_1_out_1 = Render( main_Collect_1_out_1, main_AutoCamera_1_out_1, main_Render_1_in_3 ) [instance: 1, cache: 1]; // // node Display[2]: x = 139, y = 557, inputs = 8, label = Display // depth: value = 24 // window: position = (0.0869,0.1107), size = 0.7949x0.6797 // main_Display_2_out_1[cache: 2] = Display( main_Render_1_out_1, main_Display_2_in_2, main_Display_2_in_3, main_Display_2_in_4, main_Display_2_in_5, main_Display_2_in_6, main_Display_2_in_7, main_Display_2_in_8 ) [instance: 2, cache: 1]; // network: end of macro body } main_Import_1_in_1 = "mag2d.general"; main_Import_1_in_2 = NULL; main_Import_1_in_3 = NULL; main_Import_1_in_4 = NULL; main_Import_1_in_5 = NULL; main_Import_1_in_6 = NULL; main_Import_1_out_1 = NULL; main_Sample_1_in_2 = 2000; main_Sample_1_out_1 = NULL; main_Compute_1_in_1 = "$0/mag($0)"; main_Compute_1_in_3 = NULL; main_Compute_1_out_1 = NULL; main_AutoGlyph_1_in_2 = "rocket2D"; main_AutoGlyph_1_in_3 = 7.0; main_AutoGlyph_1_in_4 = 0.25; main_AutoGlyph_1_in_5 = 0.05; main_AutoGlyph_1_in_6 = NULL; main_AutoGlyph_1_in_7 = NULL; main_AutoGlyph_1_out_1 = NULL; main_Color_1_in_2 = "black"; main_Color_1_in_3 = NULL; main_Color_1_in_4 = NULL; main_Color_1_in_5 = NULL; main_Color_1_out_1 = NULL; main_Compute_2_in_1 = "mag($0)"; main_Compute_2_in_3 = NULL; main_Compute_2_out_1 = NULL; main_RubberSheet_1_in_2 = NULL; main_RubberSheet_1_in_3 = NULL; main_RubberSheet_1_in_4 = NULL; main_RubberSheet_1_out_1 = NULL; main_Translate_1_in_2 = [0 0 -3]; main_Translate_1_out_1 = NULL; main_Colormap_2_in_1 = { [0.0 0.66315789] [0.60691824 0.0] }; main_Colormap_2_in_2 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_2_in_3 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_2_in_4 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_2_in_5 = "Colormap_2"; main_Colormap_2_in_7 = NULL; main_Colormap_2_in_8 = NULL; main_Colormap_2_in_9 = NULL; main_Colormap_2_in_10 = NULL; main_Colormap_2_in_11 = NULL; main_Colormap_2_in_12 = { 9.2432623e-05 0.9849546 }; main_Colormap_2_in_13 = NULL; main_Colormap_2_in_14 = NULL; main_Colormap_2_in_15 = NULL; main_Colormap_2_in_16 = NULL; main_Colormap_2_in_17 = 9.2432623e-05; main_Colormap_2_in_18 = 0.9849546; main_Colormap_2_in_19 = NULL; main_Colormap_2_out_1 = NULL; main_Color_3_in_3 = NULL; main_Color_3_in_4 = NULL; main_Color_3_in_5 = NULL; main_Color_3_out_1 = NULL; main_Collect_1_out_1 = NULL; main_AutoCamera_1_in_2 = NULL; main_AutoCamera_1_in_3 = 15.0; main_AutoCamera_1_in_4 = 800; main_AutoCamera_1_in_5 = 0.6; main_AutoCamera_1_in_6 = NULL; main_AutoCamera_1_in_7 = 0; main_AutoCamera_1_in_8 = NULL; main_AutoCamera_1_in_9 = "white"; main_AutoCamera_1_out_1 = NULL; main_Render_1_in_3 = NULL; main_Render_1_out_1 = NULL; main_Display_2_in_2 = NULL; main_Display_2_in_3 = "X24,,"; main_Display_2_in_4 = NULL; main_Display_2_in_5 = NULL; main_Display_2_in_6 = NULL; main_Display_2_in_7 = NULL; main_Display_2_in_8 = NULL; Executive("product version 4 4 0"); $sync main(); elk-7.2.42/examples/magnetism/PaxHeaders.21776/Fe-FSM-MT-FM0000644000000000000000000000013214061636520017447 xustar0030 mtime=1623670096.216101284 30 atime=1623670096.215101285 30 ctime=1623670096.216101284 elk-7.2.42/examples/magnetism/Fe-FSM-MT-FM/0000755002504400250440000000000014061636520021561 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Fe-FSM-MT-FM/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020627 xustar0030 mtime=1623670096.216101284 30 atime=1623670096.216101284 30 ctime=1623670096.216101284 elk-7.2.42/examples/magnetism/Fe-FSM-MT-FM/elk.in0000644002504400250440000000135214061636520022665 0ustar00dewhurstdewhurst00000000000000 ! Ferromagnetic bcc iron example with fixed spin moment in muffin-tin. ! Run by Fredrik Bultmark, Francesco Cricchio, Lars Nordstrom. tasks 0 ! ferromagnetic local fixed spin moment calculation fsmtype 2 mommtfix 1 1 0.0 0.0 1.0 : ia, is, mommtfix ! FSM step length: reduce to improve convergence taufsm 0.01 lmaxapw 10 ! fairly large number of empty states required for magnetic cases nempty 8 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 2.708 atoms 1 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt sppath '../../../species/' ngridk 6 6 6 elk-7.2.42/examples/magnetism/PaxHeaders.21776/Fe0000644000000000000000000000013214061636520016206 xustar0030 mtime=1623670096.219101281 30 atime=1623670096.218101283 30 ctime=1623670096.219101281 elk-7.2.42/examples/magnetism/Fe/0000755002504400250440000000000014061636520020320 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Fe/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017366 xustar0030 mtime=1623670096.219101281 30 atime=1623670096.219101281 30 ctime=1623670096.219101281 elk-7.2.42/examples/magnetism/Fe/elk.in0000644002504400250440000000126614061636520021430 0ustar00dewhurstdewhurst00000000000000 ! Ferromagnetic bcc iron example. Note the small global magnetic field, which ! is needed to break spin symmetry. Check the total moment of the cell in the ! file INFO.OUT. tasks 0 spinpol .true. ! small magnetic field in the z-direction bfieldc 0.0 0.0 0.01 ! fairly large number of empty states required for magnetic cases nempty 8 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 2.708 sppath '../../../species/' atoms 1 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/magnetism/PaxHeaders.21776/Eu0000644000000000000000000000013014061636520016223 xustar0029 mtime=1623670096.22110128 30 atime=1623670096.220101281 29 ctime=1623670096.22110128 elk-7.2.42/examples/magnetism/Eu/0000755002504400250440000000000014061636520020337 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Eu/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520017411 xustar0029 mtime=1623670096.22110128 29 atime=1623670096.22110128 29 ctime=1623670096.22110128 elk-7.2.42/examples/magnetism/Eu/elk.in0000644002504400250440000000101614061636520021440 0ustar00dewhurstdewhurst00000000000000 ! Ferromagnetic bcc Eu example (thanks to Sandro Massidda for fixing a problem ! with the Eu.in species file). tasks 0 10 spinpol .true. spinorb .true. bfieldc 0.0 0.0 0.01 nempty 8 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 4.30385 sppath '../../../species/' atoms 1 : nspecies 'Eu.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 8 8 8 elk-7.2.42/examples/magnetism/PaxHeaders.21776/Fe-FSM0000644000000000000000000000013214061636520016631 xustar0030 mtime=1623670096.224101277 30 atime=1623670096.223101278 30 ctime=1623670096.224101277 elk-7.2.42/examples/magnetism/Fe-FSM/0000755002504400250440000000000014061636520020743 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Fe-FSM/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020011 xustar0030 mtime=1623670096.224101277 30 atime=1623670096.224101277 30 ctime=1623670096.224101277 elk-7.2.42/examples/magnetism/Fe-FSM/elk.in0000644002504400250440000000141614061636520022050 0ustar00dewhurstdewhurst00000000000000 ! Ferromagnetic bcc iron fixed spin moment example. tasks 0 ! small mixing parameter required beta0 0.05 ! FSM step length: reduce to improve convergence taufsm 0.01 spinpol .true. ! total fixed spin moment required fsmtype 1 ! fixed spin moment vector momfix 0.0 0.0 1.0 ! small magnetic field in the z-direction bfieldc 0.0 0.0 0.01 ! fairly large number of empty states required for magnetic cases nempty 8 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 2.708 sppath '../../../species/' atoms 1 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/magnetism/PaxHeaders.21776/FeCo-MAE0000644000000000000000000000013214061636520017070 xustar0030 mtime=1623670096.226101275 30 atime=1623670096.225101276 30 ctime=1623670096.226101275 elk-7.2.42/examples/magnetism/FeCo-MAE/0000755002504400250440000000000014061636520021202 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/FeCo-MAE/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020250 xustar0030 mtime=1623670096.226101275 30 atime=1623670096.226101275 30 ctime=1623670096.226101275 elk-7.2.42/examples/magnetism/FeCo-MAE/elk.in0000644002504400250440000000261014061636520022304 0ustar00dewhurstdewhurst00000000000000 ! Determination of the magnetic anisotropy energy (MAE) for Fe_(1-x)Co_x where ! x = 1/2 and the unit cell is tetragonal of L1_0 type. ! The MAE is determined from a set of fixed spin moment direction calculations ! performed automatically with task = 28. The number of direction points used is ! given by the parameter 'npmae'. The estimation becomes more accurate as the ! number of points increases, but the calculation takes longer. The MAE is also ! strongly dependent on the number of k-points, the number used in this example ! is insufficient for a reliable result. ! Example updated by James Glasbrenner and others. tasks 28 ! high angular momentum cut-off needed for accurate densities and potentials lmaxapw 14 lmaxo 14 ! number of magnetisation direction points; the estimate of the MAE improves ! with the number of points; in this case, the Cartesian x, y and z directions ! are used npmae 3 ! very tight convergence required epspot 1.e-8 epsengy 1.e-6 rgkmax 8.0 ngridk 4 4 4 swidth 0.01 mixtype 3 ! artificial strained lattice avec 0.5 0.5 0.0 0.0 1.0 0.0 0.0 0.0 1.0 scale1 6.8 scale2 6.8 scale3 7.0 sppath '../../../species/' atoms 2 : nspecies 'Fe.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'Co.in' 1 0.0 0.5 0.5 elk-7.2.42/examples/magnetism/PaxHeaders.21776/Fe-AFM0000644000000000000000000000013214061636520016607 xustar0030 mtime=1623670096.229101272 30 atime=1623670096.228101273 30 ctime=1623670096.229101272 elk-7.2.42/examples/magnetism/Fe-AFM/0000755002504400250440000000000014061636520020721 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Fe-AFM/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017767 xustar0030 mtime=1623670096.229101272 30 atime=1623670096.229101272 30 ctime=1623670096.229101272 elk-7.2.42/examples/magnetism/Fe-AFM/elk.in0000644002504400250440000000116614061636520022030 0ustar00dewhurstdewhurst00000000000000 ! Antiferromagnetic fcc iron example tasks 0 spinpol .true. ! fairly large number of empty states required for magnetic cases nempty 8 avec 0.5 0.5 0.0 0.5 -0.5 0.0 0.0 0.0 1.0 scale 6.82 sppath '../../../species/' ! note the magnetic fields on each atom atoms 1 : nspecies 'Fe.in' : spfname 2 : natoms 0.0 0.0 0.0 0.0 0.0 0.1 : atposl, bfcmt 0.5 0.5 0.5 0.0 0.0 -0.1 ! this k-point set is too small for calculation of accurate moments ngridk 2 2 2 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/magnetism/PaxHeaders.21776/Fe-spiral-supercell0000644000000000000000000000013014061636520021470 xustar0029 mtime=1623670096.23110127 30 atime=1623670096.230101271 29 ctime=1623670096.23110127 elk-7.2.42/examples/magnetism/Fe-spiral-supercell/0000755002504400250440000000000014061636520023604 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Fe-spiral-supercell/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520022656 xustar0029 mtime=1623670096.23110127 29 atime=1623670096.23110127 29 ctime=1623670096.23110127 elk-7.2.42/examples/magnetism/Fe-spiral-supercell/elk.in0000644002504400250440000000210014061636520024700 0ustar00dewhurstdewhurst00000000000000 ! Spin-spiral state for Gamma-Fe calculated supercells instead of the spiral ! Bloch state anzatz. This is required for functionals which do not preserve ! the anzatz self-consistently. ! The code runs in the same way as the phonon supercell calculations. The ! supercells are generated automatically from the q-points given by ngridq. Like ! phonons, several instances of the code can be started in the same directory, ! allowing for parallel generation of the q-dependent ground-states. ! Note that automatic k-point generation is always enabled for this task. tasks 350 ! q-point set on which the spiral ground-states are to be computed ngridq 2 2 2 highq .true. avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.375 sppath '../../../species/' atoms 1 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 -0.01 0.0 0.0 : atposl, bfcmt ! define a fixed spin direction in the muffin-tin fsmtype -2 mommtfix 1 1 1.0 0.0 0.0 elk-7.2.42/examples/magnetism/PaxHeaders.21776/Ni0000644000000000000000000000013214061636520016222 xustar0030 mtime=1623670096.234101268 30 atime=1623670096.233101268 30 ctime=1623670096.234101268 elk-7.2.42/examples/magnetism/Ni/0000755002504400250440000000000014061636520020334 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/magnetism/Ni/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017402 xustar0030 mtime=1623670096.234101268 30 atime=1623670096.234101268 30 ctime=1623670096.234101268 elk-7.2.42/examples/magnetism/Ni/elk.in0000644002504400250440000000120114061636520021431 0ustar00dewhurstdewhurst00000000000000 ! Ferromagnetic nickel example. A small global magnetic field is required to ! break spin symmetry. Check the total spin moment of the cell in the file ! INFO.OUT. Note that large k-point grids are required for obtaining accurate ! moments. tasks 0 spinpol .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/PaxHeaders.21776/non-linear-optics0000644000000000000000000000013214061636520017231 xustar0030 mtime=1623670096.237101265 30 atime=1623670096.235101267 30 ctime=1623670096.237101265 elk-7.2.42/examples/non-linear-optics/0000755002504400250440000000000014061636520021343 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/non-linear-optics/PaxHeaders.21776/GaAs0000644000000000000000000000013214061636520020044 xustar0030 mtime=1623670096.238101264 30 atime=1623670096.237101265 30 ctime=1623670096.238101264 elk-7.2.42/examples/non-linear-optics/GaAs/0000755002504400250440000000000014061636520022156 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/non-linear-optics/GaAs/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021224 xustar0030 mtime=1623670096.238101264 30 atime=1623670096.238101264 30 ctime=1623670096.238101264 elk-7.2.42/examples/non-linear-optics/GaAs/elk.in0000644002504400250440000000161314061636520023262 0ustar00dewhurstdewhurst00000000000000 ! Susceptibility for non-linear optical second-harmonic generation in GaAs. The ! inverse lifetime is determined by swidth. Note that many k-points and empty ! states are required for good convergence. Various contributions to the ! susceptibility are also written to file. ! For details, see Physica Scripta T109, 128 (2004). tasks 0 120 125 nempty 15 scissor 0.031 swidth 0.008 ! components of the optical tensor optcomp 1 2 3 wplot 400 100 0 : nwplot, ngrkf, nswplot 0.0 0.3 : wplot mixtype 3 avec 5.3435 5.3435 0.0000 5.3435 0.0000 5.3435 0.0000 5.3435 5.3435 sppath '../../../species/' atoms 2 : nspecies 'Ga.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'As.in' 1 0.25 0.25 0.25 ngridk 12 12 12 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/PaxHeaders.21776/tensor-moments0000644000000000000000000000013014061636520016660 xustar0029 mtime=1623670096.24210126 30 atime=1623670096.239101263 29 ctime=1623670096.24210126 elk-7.2.42/examples/tensor-moments/0000755002504400250440000000000014061636520020774 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/tensor-moments/PaxHeaders.21776/NiO-LDA+U-FLL0000644000000000000000000000013214061636520020560 xustar0030 mtime=1623670096.241101261 30 atime=1623670096.240101262 30 ctime=1623670096.241101261 elk-7.2.42/examples/tensor-moments/NiO-LDA+U-FLL/0000755002504400250440000000000014061636520022672 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/tensor-moments/NiO-LDA+U-FLL/PaxHeaders.21776/elk.in0000644000000000000000000000013014061636520021736 xustar0029 mtime=1623670096.24210126 30 atime=1623670096.241101261 29 ctime=1623670096.24210126 elk-7.2.42/examples/tensor-moments/NiO-LDA+U-FLL/elk.in0000644002504400250440000000275614061636520024007 0ustar00dewhurstdewhurst00000000000000 ! NiO in AFMII structure with LDA+U and fully-localised-limit (FLL) double ! counting (dftu=1). Values of Slater parameters for Ni are taken from ! literature. Calculate the tensor moment decomposition of the density ! matrix and of the Hartree-Fock LDA+U energy in TMDFTU.OUT with task=400 ! (see PRB 80, 035121 (2009)). ! Observe the large 011 (spin-polarization), 404 (high multipole of charge) and ! the almost degenerate 413, 414, 415 (high multipoles of magnetization) ! contributions to the exchange energy. ! Compare the case with and without spin-orbit coupling (spinorb). ! Example by Francesco Cricchio. tasks 0 400 ! DFT+U block ! here FLL double counting is used (dftu=1) with Slater parameters as specified dft+u 1 2 : dftu, inpdftu 1 2 0.29399 0.30078 0.18799 : is, l, f0, f2, f4 spinpol .true. scale 7.893389 avec 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 atoms 2 : nspecies 'Ni.in' : spfname 2 : natoms; atpos, bfcmt below 0.0 0.0 0.0 0.0 0.0 -0.01 0.5 0.5 0.5 0.0 0.0 0.01 'O.in' : spfname 2 : natoms; atpos, bfcmt below 0.25 0.25 0.25 0.0 0.0 0.0 0.75 0.75 0.75 0.0 0.0 0.0 ! fairly high number of empty states nempty 8 sppath '../../../species/' ! this grid is too small for accurate magnetic moment ngridk 4 4 4 elk-7.2.42/examples/tensor-moments/PaxHeaders.21776/US-LDA+SOC+U0000644000000000000000000000013114061636520020426 xustar0030 mtime=1623670096.243101259 29 atime=1623670096.24210126 30 ctime=1623670096.243101259 elk-7.2.42/examples/tensor-moments/US-LDA+SOC+U/0000755002504400250440000000000014061636520022541 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/tensor-moments/US-LDA+SOC+U/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021607 xustar0030 mtime=1623670096.244101258 30 atime=1623670096.244101258 30 ctime=1623670096.244101258 elk-7.2.42/examples/tensor-moments/US-LDA+SOC+U/elk.in0000644002504400250440000000413714061636520023651 0ustar00dewhurstdewhurst00000000000000 ! US in FM structure with magnetic moment along easy-axis [111] with LDA+SOC+U ! and automatic interpolation double counting (dftu=3). Values of Slater ! parameters for Uranium are calculated through a Yukawa potential with ! screening length automatically determined such that U=1.0 eV (0.036749 Ha). ! In this way there is only one free parameter to be chosen. ! Check the tensor moment decomposition of the density matrix and of the ! Hartree-Fock DFT+U energy (and its convergence) in TMDFTU.OUT (see PRB 80, ! 035121 (2009)). Observe the large 011 (spin-polarization), 110 (SOC-like term) ! and 615 (large multipole of magnetization density) contributions to the ! exchange-energy. ! Example by Francesco Cricchio. tasks 0 ! DFT+U block ! here interpolation double-counting is used (dftu=3) ! inpdftu=5 corresponds to determine the Yukawa screening length that produces ! U=1 eV (0.036749 Ha) through a secant algorithm dft+u 3 5 : dftu,inpdftu 1 3 0.0367493060 : is, l, U fixed ! the tensor moments are calculated and written to file at every iteration tmwrite .true. spinpol .true. spinorb .true. scale 10.36175041 ! fcc lattice vectors avec 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 atoms 2 : nspecies 'U.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 'S.in' : spfname 1 : natoms 0.5 0.5 0.5 0.0 0.0 0.0 : atposl, bfcmt ! small global magnetic field along easy-axis [111] bfieldc -0.01 -0.01 -0.01 ! this rgkmax is too small for an accurate calculation ! rgkmax for actinides must usually be increased around 9.0-9.5 rgkmax 8.0 ! convergence of magnetic moment with number of empty states ! must be checked nempty 8 sppath '../../../species/' ! low convergence parameters for testing epspot 1.d-4 epsengy 1.d-2 ! larger betamax might help convergence betamax 1.0 beta0 0.05 ! this grid is too small for accurate magnetic moment ngridk 4 4 4 elk-7.2.42/examples/PaxHeaders.21776/DFT+U0000644000000000000000000000013214061636520014505 xustar0030 mtime=1623670096.261101242 30 atime=1623670096.245101257 30 ctime=1623670096.261101242 elk-7.2.42/examples/DFT+U/0000755002504400250440000000000014061636520016617 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/DFT+U/PaxHeaders.21776/FeAl-LDA+U-INT0000644000000000000000000000013214061636520016542 xustar0030 mtime=1623670096.247101256 30 atime=1623670096.246101256 30 ctime=1623670096.247101256 elk-7.2.42/examples/DFT+U/FeAl-LDA+U-INT/0000755002504400250440000000000014061636520020654 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/DFT+U/FeAl-LDA+U-INT/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017722 xustar0030 mtime=1623670096.248101255 30 atime=1623670096.248101255 30 ctime=1623670096.248101255 elk-7.2.42/examples/DFT+U/FeAl-LDA+U-INT/elk.in0000644002504400250440000000240714061636520021762 0ustar00dewhurstdewhurst00000000000000 ! FeAl in CsCl (B2) structure using LDA+U and interpolation between AMF and ! FLL double counting (dftu=3). Compare the total DOS and partial DOS with the ! one calculated with bare LDA. Note the opening of a gap and the increased ! localization of Fe d-electrons. Note the interpolation factor in file ! ALPHADU.OUT about 0.1, this value is a sign of a weakly correlated compound ! (see PRB 67, 153106 (2003)). ! Example created by Fredrik Bultmark, Francesco Cricchio and Lars Nordstrom. tasks 0 10 ! DFT+U block ! here an interpolation between AMF and FLL double counting is used (dftu=3) ! inpdftu=1 corresponds to provide U and J as input dft+u 3 1 : dftu,inpdftu 1 2 0.183 0.034911967 : is, l, U, J spinpol .true. ! small field along z to break symmetry bfieldc 0.0 0.0 -0.01 scale 5.496 avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 atoms 2 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 'Al.in' 1 0.5 0.5 0.5 0.0 0.0 0.0 : atposl, bfcmt sppath '../../../species/' ! fair number of empty states nempty 8 ! fair number of k-points ngridk 8 8 8 elk-7.2.42/examples/DFT+U/PaxHeaders.21776/NiO-LDA+U-optimized0000644000000000000000000000013214061636520017772 xustar0030 mtime=1623670096.250101253 30 atime=1623670096.249101254 30 ctime=1623670096.250101253 elk-7.2.42/examples/DFT+U/NiO-LDA+U-optimized/0000755002504400250440000000000014061636520022104 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/DFT+U/NiO-LDA+U-optimized/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021152 xustar0030 mtime=1623670096.251101252 30 atime=1623670096.250101253 30 ctime=1623670096.251101252 elk-7.2.42/examples/DFT+U/NiO-LDA+U-optimized/elk.in0000644002504400250440000000356514061636520023220 0ustar00dewhurstdewhurst00000000000000 ! Optimized LDA+U calculation for NiO AFMII with only one free parameter. ! The double counting is automatically chosen by doing an interpolation ! between FLL and AMF (dftu=3). The Slater parameters are determined through ! a Yukawa potential. Hence there is only one free parameter, the potential ! screening length lambda (see PRB 80, 035121 (2009)). Here lambda=1.5 ! provides realistic values of Slater parameters which are printed in FDU.OUT. ! Try to plot the magnetic moment as function of lambda. ! Analyze total and partial DOS (t2g and eg states) and compare with bare LDA. ! Look at the file ALPHADU.OUT where the interpolation factor is printed out. ! (see PRB 67, 153106 (2003)). Such a factor is about 0.5 for NiO. ! Compare the value of the interpolation factor with the example Fe-LDA+U-INT ! (weakly correlated system). ! Example by Francesco Cricchio. tasks 0 10 ! DFT+U block ! here an interpolation between AMF and FLL double counting is used (dftu=3) ! inpdftu=4 corresponds to calculate the Slater parameters through a Yukawa ! potential with screening length lambda, which constitutes the only free ! parameter in the calculation dft+u 3 4 : dftu, inpdftu 1 2 1.5 : is, l, lambda spinpol .true. scale 7.893389 avec 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 atoms 2 : nspecies 'Ni.in' : spfname 2 : natoms; atpos, bfcmt below 0.0 0.0 0.0 0.0 0.0 -0.01 0.5 0.5 0.5 0.0 0.0 0.01 'O.in' : spfname 2 : natoms; atpos, bfcmt below 0.25 0.25 0.25 0.0 0.0 0.0 0.75 0.75 0.75 0.0 0.0 0.0 ! fairly high number of empty states nempty 8 sppath '../../../species/' ! this grid is too small for accurate magnetic moment ngridk 4 4 4 elk-7.2.42/examples/DFT+U/PaxHeaders.21776/FeAl-LDA0000644000000000000000000000013214061636520015712 xustar0030 mtime=1623670096.252101251 30 atime=1623670096.251101252 30 ctime=1623670096.252101251 elk-7.2.42/examples/DFT+U/FeAl-LDA/0000755002504400250440000000000014061636520020024 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/DFT+U/FeAl-LDA/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520017076 xustar0029 mtime=1623670096.25310125 29 atime=1623670096.25310125 29 ctime=1623670096.25310125 elk-7.2.42/examples/DFT+U/FeAl-LDA/elk.in0000644002504400250440000000124514061636520021131 0ustar00dewhurstdewhurst00000000000000 ! FeAl in CsCl (B2) structure using LDA. Compare with LDA+U case. ! Example Created by Fredrik Bultmark, Francesco Cricchio and Lars Nordstrom. tasks 0 10 spinpol .true. ! small field along z to break symmetry bfieldc 0.0 0.0 -0.01 scale 5.496 avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 atoms 2 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 'Al.in' 1 0.5 0.5 0.5 0.0 0.0 0.0 : atposl, bfcmt sppath '../../../species/' ! fair number of empty states nempty 8 ngridk 8 8 8 elk-7.2.42/examples/DFT+U/PaxHeaders.21776/NiO-LDA0000644000000000000000000000013114061636520015567 xustar0030 mtime=1623670096.254101249 29 atime=1623670096.25310125 30 ctime=1623670096.254101249 elk-7.2.42/examples/DFT+U/NiO-LDA/0000755002504400250440000000000014061636520017702 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/DFT+U/NiO-LDA/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016750 xustar0030 mtime=1623670096.255101248 30 atime=1623670096.255101248 30 ctime=1623670096.255101248 elk-7.2.42/examples/DFT+U/NiO-LDA/elk.in0000644002504400250440000000147314061636520021012 0ustar00dewhurstdewhurst00000000000000 ! NiO in AFMII structure with LDA for comparison with LDA+U case. ! Example by Fredrik Bultmark, Francesco Cricchio and Lars Nordstrom. tasks 0 10 spinpol .true. scale 7.893389 avec 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 atoms 2 : nspecies 'Ni.in' : spfname 2 : natoms; atpos, bfcmt below 0.0 0.0 0.0 0.0 0.0 -0.01 0.5 0.5 0.5 0.0 0.0 0.01 'O.in' : spfname 2 : natoms; atpos, bfcmt below 0.25 0.25 0.25 0.0 0.0 0.0 0.75 0.75 0.75 0.0 0.0 0.0 ! fairly high number of empty states nempty 8 sppath '../../../species/' ! this grid is too small for accurate magnetic moment ngridk 4 4 4 elk-7.2.42/examples/DFT+U/PaxHeaders.21776/NiO-LDA+U-FLL-Ykwa0000644000000000000000000000013214061636520017314 xustar0030 mtime=1623670096.257101246 30 atime=1623670096.256101247 30 ctime=1623670096.257101246 elk-7.2.42/examples/DFT+U/NiO-LDA+U-FLL-Ykwa/0000755002504400250440000000000014061636520021426 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/DFT+U/NiO-LDA+U-FLL-Ykwa/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020474 xustar0030 mtime=1623670096.257101246 30 atime=1623670096.257101246 30 ctime=1623670096.257101246 elk-7.2.42/examples/DFT+U/NiO-LDA+U-FLL-Ykwa/elk.in0000644002504400250440000000337214061636520022536 0ustar00dewhurstdewhurst00000000000000 ! NiO in AFMII structure with LDA+U and fully-localised-limit (FLL) double ! counting (dftu=1). With inpdftu=4 the values of Slater parameters are ! conveniently calculated through a screened Yukawa potential with screening ! length lambda provided as input (see PRB 80, 035121 (2009)). Here lambda=1.5 ! gives realistic values of Slater integrals which are printed in FDU.OUT. ! Try to plot the magnetic moments of Ni as function of lambda. ! If inpdftu=5 the code will automatically determine the screening length ! corresponding to the fixed value of U (udufix) provided as input. ! Example by Francesco Cricchio. tasks 0 ! DFT+U block ! here FLL double counting is used (dftu=1) ! inpdftu=4 corresponds to calculate the Slater parameters self-consistently ! through a Yukawa potential with screening length lambda dft+u 1 4 : dftu, inpdftu 1 2 1.5 : is, l, lambda ! alternatively try inpdftu=5; this will determine the screening length ! corresponding to U=0.29399 Ha (8 eV) through a secant algorithm !dft+u ! 1 5 : dftu, inpdftu ! 1 2 0.29399 : is, l, U fixed spinpol .true. scale 7.893389 avec 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 atoms 2 : nspecies 'Ni.in' : spfname 2 : natoms; atpos, bfcmt below 0.0 0.0 0.0 0.0 0.0 -0.01 0.5 0.5 0.5 0.0 0.0 0.01 'O.in' : spfname 2 : natoms; atpos, bfcmt below 0.25 0.25 0.25 0.0 0.0 0.0 0.75 0.75 0.75 0.0 0.0 0.0 sppath '../../../species/' ! fairly high number of empty states nempty 8 ! this grid is too small for accurate magnetic moment ngridk 4 4 4 elk-7.2.42/examples/DFT+U/PaxHeaders.21776/FeAl-LDA+U-AMF0000644000000000000000000000013214061636520016513 xustar0030 mtime=1623670096.259101244 30 atime=1623670096.258101245 30 ctime=1623670096.259101244 elk-7.2.42/examples/DFT+U/FeAl-LDA+U-AMF/0000755002504400250440000000000014061636520020625 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/DFT+U/FeAl-LDA+U-AMF/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017673 xustar0030 mtime=1623670096.260101244 30 atime=1623670096.260101244 30 ctime=1623670096.260101244 elk-7.2.42/examples/DFT+U/FeAl-LDA+U-AMF/elk.in0000644002504400250440000000251014061636520021726 0ustar00dewhurstdewhurst00000000000000 ! FeAl in CsCl (B2) structure using LDA+U and "around mean field" (AMF) double ! counting (dftu=2). Compare the total DOS and partial DOS with the one calculated ! with bare LDA. Note the opening of a gap and the increased localization of Fe ! d-electrons. Note the non-magnetic solution for U about 0.1837 Ha (5 eV) ! (the exact value of U depends on the muffin-tin (MT) radius used since DFT+U ! is applied only inside mt spheres). Try to plot the magnetic moment as ! function of U for different MT radius. Example created by Fredrik Bultmark, ! Francesco Cricchio and Lars Nordstrom. tasks 0 10 ! DFT+U block ! here AMF double counting is used (dftu=2) ! inpdftu=1 corresponds to provide U and J as input dft+u 2 1 : dftu, inpdftu 1 2 0.183 0.034911967 : is, l, U, J spinpol .true. ! small field along z to break symmetry bfieldc 0.0 0.0 -0.01 scale 5.496 avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 atoms 2 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 'Al.in' 1 0.5 0.5 0.5 0.0 0.0 0.0 : atposl, bfcmt sppath '../../../species/' ! fair number of empty states nempty 8 ! fair number of k-points ngridk 8 8 8 elk-7.2.42/examples/DFT+U/PaxHeaders.21776/NiO-LDA+U-FLL0000644000000000000000000000013214061636520016403 xustar0030 mtime=1623670096.262101242 30 atime=1623670096.261101242 30 ctime=1623670096.262101242 elk-7.2.42/examples/DFT+U/NiO-LDA+U-FLL/0000755002504400250440000000000014061636520020515 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/DFT+U/NiO-LDA+U-FLL/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017563 xustar0030 mtime=1623670096.262101242 30 atime=1623670096.262101242 30 ctime=1623670096.262101242 elk-7.2.42/examples/DFT+U/NiO-LDA+U-FLL/elk.in0000644002504400250440000000304414061636520021621 0ustar00dewhurstdewhurst00000000000000 ! NiO in AFMII structure with LDA+U and fully-localised-limit (FLL) double ! counting (dftu=1). Values of Slater parameters for Ni are taken from ! literature. ! Analyze total and partial DOS (t2g and eg states) and compare with bare LDA. ! Notice the increasing of the gap (~4eV) and of magnetic moment to ~1.69 u_b. ! The increasing of magnetic moment is typical of FLL double counting. ! Example by Francesco Cricchio. tasks 0 10 ! DFT+U block ! here FLL double counting is used (dftu=1) ! inpdftu=1 corresponds to provide U and J in Hartree as input ! inpdftu=2 or 3 corresponds to, respectively, Slater or Racah parameters ! inpdftu=4 or 5 corresponds to calculating the Slater parameters through a ! Yukawa potential (see example NiO-LDA+U-FLL-Ykwa and PRB 80, 035121 (2009)) dft+u 1 2 : dftu,inpdftu 1 2 0.29399 0.30078 0.18799 : is, l, f0, f2, f4 spinpol .true. scale 7.893389 avec 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 atoms 2 : nspecies 'Ni.in' : spfname 2 : natoms; atpos, bfcmt below 0.0 0.0 0.0 0.0 0.0 -0.01 0.5 0.5 0.5 0.0 0.0 0.01 'O.in' : spfname 2 : natoms; atpos, bfcmt below 0.25 0.25 0.25 0.0 0.0 0.0 0.75 0.75 0.75 0.0 0.0 0.0 ! fairly high number of empty states nempty 8 sppath '../../../species/' ! this grid is too small for accurate magnetic moment ngridk 4 4 4 elk-7.2.42/examples/PaxHeaders.21776/Fermi-surface0000644000000000000000000000013114061636520016357 xustar0030 mtime=1623670096.280101225 29 atime=1623670096.26410124 30 ctime=1623670096.280101225 elk-7.2.42/examples/Fermi-surface/0000755002504400250440000000000014061636520020472 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Fermi-surface/PaxHeaders.21776/Ni0000644000000000000000000000013214061636520016726 xustar0030 mtime=1623670096.271101233 30 atime=1623670096.265101239 30 ctime=1623670096.271101233 elk-7.2.42/examples/Fermi-surface/Ni/0000755002504400250440000000000014061636520021040 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Fermi-surface/Ni/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020106 xustar0030 mtime=1623670096.266101238 30 atime=1623670096.266101238 30 ctime=1623670096.266101238 elk-7.2.42/examples/Fermi-surface/Ni/elk.in0000644002504400250440000000142714061636520022147 0ustar00dewhurstdewhurst00000000000000 ! Ferromagnetic nickel Fermi surface. Note that the spin-up and -down surfaces ! are separated into the files FERMISURF_UP.OUT and FERMISURF_DN.OUT. ! Use OpenDX with the files in this directory to produce the 3D plot. tasks 0 100 ! define box corners and grid size for 3D plot, first point is the origin plot3d 0.0 0.0 0.0 : vclp3d 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 40 40 40 : np3d spinpol .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 8 8 8 elk-7.2.42/examples/Fermi-surface/Ni/PaxHeaders.21776/fermi.net0000644000000000000000000000013214061636520020615 xustar0030 mtime=1623670096.268101236 30 atime=1623670096.267101237 30 ctime=1623670096.268101236 elk-7.2.42/examples/Fermi-surface/Ni/fermi.net0000644002504400250440000003707514061636520022666 0ustar00dewhurstdewhurst00000000000000// // time: Thu Nov 6 12:08:29 2008 // // version: 3.2.0 (format), 4.4.0 (DX) // // // MODULE main // workspace: width = 372, height = 548 // layout: snap = 0, width = 50, height = 50, align = NN // macro main( ) -> ( ) { // // node Import[1]: x = 147, y = 71, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "fermi_up.general" // main_Import_1_out_1 = Import( main_Import_1_in_1, main_Import_1_in_2, main_Import_1_in_3, main_Import_1_in_4, main_Import_1_in_5, main_Import_1_in_6 ) [instance: 1, cache: 1]; // // node Isosurface[1]: x = 146, y = 196, inputs = 6, label = Isosurface // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.0 // main_Isosurface_1_out_1 = Isosurface( main_Import_1_out_1, main_Isosurface_1_in_2, main_Isosurface_1_in_3, main_Isosurface_1_in_4, main_Isosurface_1_in_5, main_Isosurface_1_in_6 ) [instance: 1, cache: 1]; // // node Color[1]: x = 154, y = 315, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "green" // main_Color_1_out_1 = Color( main_Isosurface_1_out_1, main_Color_1_in_2, main_Color_1_in_3, main_Color_1_in_4, main_Color_1_in_5 ) [instance: 1, cache: 1]; // // node Import[2]: x = 291, y = 73, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "fermi_dn.general" // main_Import_2_out_1 = Import( main_Import_2_in_1, main_Import_2_in_2, main_Import_2_in_3, main_Import_2_in_4, main_Import_2_in_5, main_Import_2_in_6 ) [instance: 2, cache: 1]; // // node Isosurface[2]: x = 290, y = 194, inputs = 6, label = Isosurface // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.0 // main_Isosurface_2_out_1 = Isosurface( main_Import_2_out_1, main_Isosurface_2_in_2, main_Isosurface_2_in_3, main_Isosurface_2_in_4, main_Isosurface_2_in_5, main_Isosurface_2_in_6 ) [instance: 2, cache: 1]; // // node Color[2]: x = 300, y = 313, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "yellow" // main_Color_2_out_1 = Color( main_Isosurface_2_out_1, main_Color_2_in_2, main_Color_2_in_3, main_Color_2_in_4, main_Color_2_in_5 ) [instance: 2, cache: 1]; // // node Collect[1]: x = 231, y = 399, inputs = 2, label = Collect // main_Collect_1_out_1 = Collect( main_Color_1_out_1, main_Color_2_out_1 ) [instance: 1, cache: 1]; // // node Image[2]: x = 283, y = 486, inputs = 49, label = Image // input[1]: defaulting = 0, visible = 0, type = 32, value = "Image_2" // input[4]: defaulting = 0, visible = 0, type = 1, value = 1 // input[5]: defaulting = 0, visible = 0, type = 8, value = [0.459851 0.459851 0.459851] // input[6]: defaulting = 0, visible = 0, type = 8, value = [5.36756 3.53923 7.97489] // input[7]: defaulting = 0, visible = 0, type = 5, value = 5.08525 // input[8]: defaulting = 0, visible = 0, type = 1, value = 640 // input[9]: defaulting = 0, visible = 0, type = 5, value = 0.75 // input[10]: defaulting = 0, visible = 0, type = 8, value = [-0.0834371 0.940039 -0.330704] // input[11]: defaulting = 1, visible = 0, type = 5, value = 30.0002 // input[12]: defaulting = 0, visible = 0, type = 1, value = 0 // input[14]: defaulting = 0, visible = 0, type = 1, value = 1 // input[15]: defaulting = 1, visible = 0, type = 32, value = "none" // input[16]: defaulting = 1, visible = 0, type = 32, value = "none" // input[17]: defaulting = 1, visible = 0, type = 1, value = 1 // input[18]: defaulting = 1, visible = 0, type = 1, value = 1 // input[19]: defaulting = 0, visible = 0, type = 1, value = 0 // input[29]: defaulting = 1, visible = 0, type = 3, value = 0 // input[41]: defaulting = 0, visible = 0, type = 32, value = "none" // depth: value = 24 // window: position = (0.0104,0.0600), size = 0.4542x0.5800, screen = 0 // internal caching: 1 // main_Image_2_out_1, main_Image_2_out_2, main_Image_2_out_3 = Image( main_Image_2_in_1, main_Collect_1_out_1, main_Image_2_in_3, main_Image_2_in_4, main_Image_2_in_5, main_Image_2_in_6, main_Image_2_in_7, main_Image_2_in_8, main_Image_2_in_9, main_Image_2_in_10, main_Image_2_in_11, main_Image_2_in_12, main_Image_2_in_13, main_Image_2_in_14, main_Image_2_in_15, main_Image_2_in_16, main_Image_2_in_17, main_Image_2_in_18, main_Image_2_in_19, main_Image_2_in_20, main_Image_2_in_21, main_Image_2_in_22, main_Image_2_in_23, main_Image_2_in_24, main_Image_2_in_25, main_Image_2_in_26, main_Image_2_in_27, main_Image_2_in_28, main_Image_2_in_29, main_Image_2_in_30, main_Image_2_in_31, main_Image_2_in_32, main_Image_2_in_33, main_Image_2_in_34, main_Image_2_in_35, main_Image_2_in_36, main_Image_2_in_37, main_Image_2_in_38, main_Image_2_in_39, main_Image_2_in_40, main_Image_2_in_41, main_Image_2_in_42, main_Image_2_in_43, main_Image_2_in_44, main_Image_2_in_45, main_Image_2_in_46, main_Image_2_in_47, main_Image_2_in_48, main_Image_2_in_49 ) [instance: 2, cache: 1]; // network: end of macro body CacheScene(main_Image_2_in_1, main_Image_2_out_1, main_Image_2_out_2); } main_Import_1_in_1 = "fermi_up.general"; main_Import_1_in_2 = NULL; main_Import_1_in_3 = NULL; main_Import_1_in_4 = NULL; main_Import_1_in_5 = NULL; main_Import_1_in_6 = NULL; main_Import_1_out_1 = NULL; main_Isosurface_1_in_2 = 0.0; main_Isosurface_1_in_3 = NULL; main_Isosurface_1_in_4 = NULL; main_Isosurface_1_in_5 = NULL; main_Isosurface_1_in_6 = NULL; main_Isosurface_1_out_1 = NULL; main_Color_1_in_2 = "green"; main_Color_1_in_3 = NULL; main_Color_1_in_4 = NULL; main_Color_1_in_5 = NULL; main_Color_1_out_1 = NULL; main_Import_2_in_1 = "fermi_dn.general"; main_Import_2_in_2 = NULL; main_Import_2_in_3 = NULL; main_Import_2_in_4 = NULL; main_Import_2_in_5 = NULL; main_Import_2_in_6 = NULL; main_Import_2_out_1 = NULL; main_Isosurface_2_in_2 = 0.0; main_Isosurface_2_in_3 = NULL; main_Isosurface_2_in_4 = NULL; main_Isosurface_2_in_5 = NULL; main_Isosurface_2_in_6 = NULL; main_Isosurface_2_out_1 = NULL; main_Color_2_in_2 = "yellow"; main_Color_2_in_3 = NULL; main_Color_2_in_4 = NULL; main_Color_2_in_5 = NULL; main_Color_2_out_1 = NULL; main_Collect_1_out_1 = NULL; macro Image( id, object, where, useVector, to, from, width, resolution, aspect, up, viewAngle, perspective, options, buttonState = 1, buttonUpApprox = "none", buttonDownApprox = "none", buttonUpDensity = 1, buttonDownDensity = 1, renderMode = 0, defaultCamera, reset, backgroundColor, throttle, RECenable = 0, RECfile, RECformat, RECresolution, RECaspect, AAenable = 0, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, interactionMode, title, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels, webOptions) -> ( object, camera, where) { ImageMessage( id, backgroundColor, throttle, RECenable, RECfile, RECformat, RECresolution, RECaspect, AAenable, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels, interactionMode, title, renderMode, buttonUpApprox, buttonDownApprox, buttonUpDensity, buttonDownDensity) [instance: 1, cache: 1]; autoCamera = AutoCamera( object, "front", object, resolution, aspect, [0,1,0], perspective, viewAngle, backgroundColor) [instance: 1, cache: 1]; realCamera = Camera( to, from, width, resolution, aspect, up, perspective, viewAngle, backgroundColor) [instance: 1, cache: 1]; coloredDefaultCamera = UpdateCamera(defaultCamera, background=backgroundColor) [instance: 1, cache: 1]; nullDefaultCamera = Inquire(defaultCamera, "is null + 1") [instance: 1, cache: 1]; resetCamera = Switch( nullDefaultCamera, coloredDefaultCamera, autoCamera) [instance: 1, cache: 1]; resetNull = Inquire( reset, "is null + 1") [instance: 2, cache: 1]; reset = Switch( resetNull, reset, 0) [instance: 2, cache: 1]; whichCamera = Compute( "($0 != 0 || $1 == 0) ? 1 : 2", reset, useVector) [instance: 1, cache: 1]; camera = Switch( whichCamera, resetCamera, realCamera) [instance: 3, cache: 1]; AAobject = AutoAxes( object, camera, AAlabels, AAticks, AAcorners, AAframe, AAadjust, AAcursor, AAgrid, AAcolors, AAannotation, AAlabelscale, AAfont, AAxTickLocs, AAyTickLocs, AAzTickLocs, AAxTickLabels, AAyTickLabels, AAzTickLabels) [instance: 1, cache: 1]; switchAAenable = Compute("$0+1", AAenable) [instance: 2, cache: 1]; object = Switch( switchAAenable, object, AAobject) [instance:4, cache: 1]; SWapproximation_options = Switch( buttonState, buttonUpApprox, buttonDownApprox) [instance: 5, cache: 1]; SWdensity_options = Switch( buttonState, buttonUpDensity, buttonDownDensity) [instance: 6, cache: 1]; HWapproximation_options = Format( "%s,%s", buttonDownApprox, buttonUpApprox) [instance: 1, cache: 1]; HWdensity_options = Format( "%d,%d", buttonDownDensity, buttonUpDensity) [instance: 2, cache: 1]; switchRenderMode = Compute( "$0+1", renderMode) [instance: 3, cache: 1]; approximation_options = Switch( switchRenderMode, SWapproximation_options, HWapproximation_options) [instance: 7, cache: 1]; density_options = Switch( switchRenderMode, SWdensity_options, HWdensity_options) [instance: 8, cache: 1]; renderModeString = Switch( switchRenderMode, "software", "hardware")[instance: 9, cache: 1]; object_tag = Inquire( object, "object tag")[instance: 3, cache: 1]; annoted_object = Options( object, "send boxes", 0, "cache", 1, "object tag", object_tag, "ddcamera", whichCamera, "rendering approximation", approximation_options, "render every", density_options, "button state", buttonState, "rendering mode", renderModeString) [instance: 1, cache: 1]; RECresNull = Inquire( RECresolution, "is null + 1") [instance: 4, cache: 1]; ImageResolution = Inquire( camera, "camera resolution") [instance: 5, cache: 1]; RECresolution = Switch( RECresNull, RECresolution, ImageResolution) [instance: 10, cache: 1]; RECaspectNull = Inquire( RECaspect, "is null + 1") [instance: 6, cache: 1]; ImageAspect = Inquire( camera, "camera aspect") [instance: 7, cache: 1]; RECaspect = Switch( RECaspectNull, RECaspect, ImageAspect) [instance: 11, cache: 1]; switchRECenable = Compute( "$0 == 0 ? 1 : (($2 == $3) && ($4 == $5)) ? ($1 == 1 ? 2 : 3) : 4", RECenable, switchRenderMode, RECresolution, ImageResolution, RECaspect, ImageAspect) [instance: 4, cache: 1]; NoRECobject, RECNoRerenderObject, RECNoRerHW, RECRerenderObject = Route(switchRECenable, annoted_object); Display( NoRECobject, camera, where, throttle) [instance: 1, cache: 1]; image = Render( RECNoRerenderObject, camera) [instance: 1, cache: 1]; Display( image, NULL, where, throttle) [instance: 2, cache: 1]; WriteImage( image, RECfile, RECformat) [instance: 1, cache: 1]; rec_where = Display( RECNoRerHW, camera, where, throttle) [instance: 1, cache: 0]; rec_image = ReadImageWindow( rec_where) [instance: 1, cache: 1]; WriteImage( rec_image, RECfile, RECformat) [instance: 1, cache: 1]; RECupdateCamera = UpdateCamera( camera, resolution=RECresolution, aspect=RECaspect) [instance: 2, cache: 1]; Display( RECRerenderObject, camera, where, throttle) [instance: 1, cache: 1]; RECRerenderObject = ScaleScreen( RECRerenderObject, NULL, RECresolution, camera) [instance: 1, cache: 1]; image = Render( RECRerenderObject, RECupdateCamera) [instance: 2, cache: 1]; WriteImage( image, RECfile, RECformat) [instance: 2, cache: 1]; } main_Image_2_in_1 = "Image_2"; main_Image_2_in_3 = "X24,,"; main_Image_2_in_4 = 1; main_Image_2_in_5 = [0.459851 0.459851 0.459851]; main_Image_2_in_6 = [5.36756 3.53923 7.97489]; main_Image_2_in_7 = 5.08525; main_Image_2_in_8 = 640; main_Image_2_in_9 = 0.75; main_Image_2_in_10 = [-0.0834371 0.940039 -0.330704]; main_Image_2_in_11 = NULL; main_Image_2_in_12 = 0; main_Image_2_in_13 = NULL; main_Image_2_in_14 = 1; main_Image_2_in_15 = NULL; main_Image_2_in_16 = NULL; main_Image_2_in_17 = NULL; main_Image_2_in_18 = NULL; main_Image_2_in_19 = 0; main_Image_2_in_20 = NULL; main_Image_2_in_21 = NULL; main_Image_2_in_22 = NULL; main_Image_2_in_23 = NULL; main_Image_2_in_25 = NULL; main_Image_2_in_26 = NULL; main_Image_2_in_27 = NULL; main_Image_2_in_28 = NULL; main_Image_2_in_29 = NULL; main_Image_2_in_30 = NULL; main_Image_2_in_31 = NULL; main_Image_2_in_32 = NULL; main_Image_2_in_33 = NULL; main_Image_2_in_34 = NULL; main_Image_2_in_35 = NULL; main_Image_2_in_36 = NULL; main_Image_2_in_37 = NULL; main_Image_2_in_38 = NULL; main_Image_2_in_39 = NULL; main_Image_2_in_40 = NULL; main_Image_2_in_41 = "none"; main_Image_2_in_42 = NULL; main_Image_2_in_43 = NULL; main_Image_2_in_44 = NULL; main_Image_2_in_45 = NULL; main_Image_2_in_46 = NULL; main_Image_2_in_47 = NULL; main_Image_2_in_48 = NULL; main_Image_2_in_49 = NULL; Executive("product version 4 4 0"); $sync main(); elk-7.2.42/examples/Fermi-surface/Ni/PaxHeaders.21776/fermi_dn.general0000644000000000000000000000013214061636520022125 xustar0030 mtime=1623670096.270101234 30 atime=1623670096.269101235 30 ctime=1623670096.270101234 elk-7.2.42/examples/Fermi-surface/Ni/fermi_dn.general0000644002504400250440000000030514061636520024160 0ustar00dewhurstdewhurst00000000000000file = ./FERMISURF_DN.OUT grid = 40 x 40 x 40 format = ascii interleaving = field majority = column header = lines 1 field = locations, field0 structure = 3-vector, scalar type = float, float end elk-7.2.42/examples/Fermi-surface/Ni/PaxHeaders.21776/fermi_up.general0000644000000000000000000000013214061636520022150 xustar0030 mtime=1623670096.271101233 30 atime=1623670096.271101233 30 ctime=1623670096.271101233 elk-7.2.42/examples/Fermi-surface/Ni/fermi_up.general0000644002504400250440000000030514061636520024203 0ustar00dewhurstdewhurst00000000000000file = ./FERMISURF_UP.OUT grid = 40 x 40 x 40 format = ascii interleaving = field majority = column header = lines 1 field = locations, field0 structure = 3-vector, scalar type = float, float end elk-7.2.42/examples/Fermi-surface/PaxHeaders.21776/Al0000644000000000000000000000013214061636520016714 xustar0030 mtime=1623670096.276101229 30 atime=1623670096.272101232 30 ctime=1623670096.276101229 elk-7.2.42/examples/Fermi-surface/Al/0000755002504400250440000000000014061636520021026 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Fermi-surface/Al/PaxHeaders.21776/elk.in0000644000000000000000000000013014061636520020072 xustar0029 mtime=1623670096.27410123 30 atime=1623670096.273101231 29 ctime=1623670096.27410123 elk-7.2.42/examples/Fermi-surface/Al/elk.in0000644002504400250440000000062014061636520022127 0ustar00dewhurstdewhurst00000000000000 ! Fermi surface plot of aluminium. tasks 0 100 ! define box corners and grid size for 3D plot, first point is the origin plot3d 0.0 0.0 0.0 : vclp3d 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 40 40 40 : np3d avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.8267 sppath '../../../species/' atoms 1 'Al.in' 1 0.0 0.0 0.0 ngridk 6 6 6 elk-7.2.42/examples/Fermi-surface/Al/PaxHeaders.21776/fermi.general0000644000000000000000000000013214061636520021432 xustar0030 mtime=1623670096.275101229 30 atime=1623670096.275101229 30 ctime=1623670096.275101229 elk-7.2.42/examples/Fermi-surface/Al/fermi.general0000644002504400250440000000030214061636520023462 0ustar00dewhurstdewhurst00000000000000file = ./FERMISURF.OUT grid = 40 x 40 x 40 format = ascii interleaving = field majority = column header = lines 1 field = locations, field0 structure = 3-vector, scalar type = float, float end elk-7.2.42/examples/Fermi-surface/Al/PaxHeaders.21776/fermi.net0000644000000000000000000000013214061636520020603 xustar0030 mtime=1623670096.277101228 30 atime=1623670096.276101229 30 ctime=1623670096.277101228 elk-7.2.42/examples/Fermi-surface/Al/fermi.net0000644002504400250440000002203614061636520022643 0ustar00dewhurstdewhurst00000000000000// // time: Fri Jul 15 15:49:55 2011 // // version: 3.2.0 (format), 4.4.4 (DX) // // // MODULE main // workspace: width = 620, height = 667 // layout: snap = 0, width = 50, height = 50, align = NN // macro main( ) -> ( ) { // // node Camera[1]: x = 404, y = 490, inputs = 9, label = Camera // input[2]: defaulting = 0, visible = 1, type = 8, value = [1 1 1] // input[3]: defaulting = 0, visible = 1, type = 5, value = 6.0 // input[4]: defaulting = 0, visible = 1, type = 1, value = 800 // input[5]: defaulting = 0, visible = 1, type = 5, value = 0.65 // input[9]: defaulting = 0, visible = 1, type = 32, value = "white" // main_Camera_1_out_1 = Camera( main_Camera_1_in_1, main_Camera_1_in_2, main_Camera_1_in_3, main_Camera_1_in_4, main_Camera_1_in_5, main_Camera_1_in_6, main_Camera_1_in_7, main_Camera_1_in_8, main_Camera_1_in_9 ) [instance: 1, cache: 1]; // // node Caption[1]: x = 46, y = 444, inputs = 9, label = Caption // input[1]: defaulting = 0, visible = 1, type = 32, value = "Aluminium Fermi surface" // input[6]: defaulting = 0, visible = 0, type = 1, value = 25 // main_Caption_1_out_1 = Caption( main_Caption_1_in_1, main_Caption_1_in_2, main_Caption_1_in_3, main_Caption_1_in_4, main_Caption_1_in_5, main_Caption_1_in_6, main_Caption_1_in_7, main_Caption_1_in_8, main_Caption_1_in_9 ) [instance: 1, cache: 1]; // // node Color[6]: x = 141, y = 504, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "black" // main_Color_6_out_1 = Color( main_Caption_1_out_1, main_Color_6_in_2, main_Color_6_in_3, main_Color_6_in_4, main_Color_6_in_5 ) [instance: 6, cache: 1]; // // node Import[1]: x = 258, y = 10, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "fermi.general" // main_Import_1_out_1 = Import( main_Import_1_in_1, main_Import_1_in_2, main_Import_1_in_3, main_Import_1_in_4, main_Import_1_in_5, main_Import_1_in_6 ) [instance: 1, cache: 1]; // // node Isosurface[3]: x = 57, y = 106, inputs = 6, label = Isosurface // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.0 // main_Isosurface_3_out_1 = Isosurface( main_Import_1_out_1, main_Isosurface_3_in_2, main_Isosurface_3_in_3, main_Isosurface_3_in_4, main_Isosurface_3_in_5, main_Isosurface_3_in_6 ) [instance: 3, cache: 1]; // // node Color[3]: x = 171, y = 194, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "yellow" // input[4]: defaulting = 0, visible = 0, type = 32, value = "front colors" // main_Color_3_out_1 = Color( main_Isosurface_3_out_1, main_Color_3_in_2, main_Color_3_in_3, main_Color_3_in_4, main_Color_3_in_5 ) [instance: 3, cache: 1]; // // node Color[4]: x = 50, y = 286, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "blue" // input[4]: defaulting = 0, visible = 0, type = 32, value = "back colors" // main_Color_4_out_1 = Color( main_Color_3_out_1, main_Color_4_in_2, main_Color_4_in_3, main_Color_4_in_4, main_Color_4_in_5 ) [instance: 4, cache: 1]; // // node Translate[2]: x = 166, y = 364, inputs = 2, label = Translate // input[2]: defaulting = 0, visible = 1, type = 8, value = [0 1.2 2.0] // main_Translate_2_out_1 = Translate( main_Color_4_out_1, main_Translate_2_in_2 ) [instance: 2, cache: 1]; // // node Refine[2]: x = 473, y = 83, inputs = 2, label = Refine // input[2]: defaulting = 0, visible = 1, type = 1, value = 1 // main_Refine_2_out_1 = Refine( main_Import_1_out_1, main_Refine_2_in_2 ) [instance: 2, cache: 1]; // // node MapToPlane[1]: x = 317, y = 129, inputs = 3, label = MapToPlane // input[2]: defaulting = 1, visible = 1, type = 8, value = [1,1,1] // input[3]: defaulting = 0, visible = 1, type = 8, value = [1,1,1] // main_MapToPlane_1_out_1 = MapToPlane( main_Refine_2_out_1, main_MapToPlane_1_in_2, main_MapToPlane_1_in_3 ) [instance: 1, cache: 1]; // // node Isosurface[2]: x = 508, y = 170, inputs = 6, label = Isosurface // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.0 // input[3]: defaulting = 1, visible = 1, type = 1, value = 10 // main_Isosurface_2_out_1 = Isosurface( main_MapToPlane_1_out_1, main_Isosurface_2_in_2, main_Isosurface_2_in_3, main_Isosurface_2_in_4, main_Isosurface_2_in_5, main_Isosurface_2_in_6 ) [instance: 2, cache: 1]; // // node Color[5]: x = 324, y = 241, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "black" // main_Color_5_out_1 = Color( main_Isosurface_2_out_1, main_Color_5_in_2, main_Color_5_in_3, main_Color_5_in_4, main_Color_5_in_5 ) [instance: 5, cache: 1]; // // node Ribbon[1]: x = 500, y = 264, inputs = 2, label = Ribbon // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.01 // main_Ribbon_1_out_1 = Ribbon( main_Color_5_out_1, main_Ribbon_1_in_2 ) [instance: 1, cache: 1]; // // node Shade[1]: x = 492, y = 358, inputs = 8, label = Shade // input[2]: defaulting = 0, visible = 1, type = 3, value = 0 // main_Shade_1_out_1 = Shade( main_Ribbon_1_out_1, main_Shade_1_in_2, main_Shade_1_in_3, main_Shade_1_in_4, main_Shade_1_in_5, main_Shade_1_in_6, main_Shade_1_in_7, main_Shade_1_in_8 ) [instance: 1, cache: 1]; // // node Translate[1]: x = 360, y = 360, inputs = 2, label = Translate // input[2]: defaulting = 0, visible = 1, type = 8, value = [2.0 1.2 0] // main_Translate_1_out_1 = Translate( main_Shade_1_out_1, main_Translate_1_in_2 ) [instance: 1, cache: 1]; // // node Collect[1]: x = 265, y = 458, inputs = 3, label = Collect // main_Collect_1_out_1 = Collect( main_Color_6_out_1, main_Translate_2_out_1, main_Translate_1_out_1 ) [instance: 1, cache: 1]; // // node Display[3]: x = 287, y = 605, inputs = 8, label = Display // depth: value = 24 // main_Display_3_out_1[cache: 2] = Display( main_Collect_1_out_1, main_Camera_1_out_1, main_Display_3_in_3, main_Display_3_in_4, main_Display_3_in_5, main_Display_3_in_6, main_Display_3_in_7, main_Display_3_in_8 ) [instance: 3, cache: 1]; // network: end of macro body } main_Camera_1_in_1 = NULL; main_Camera_1_in_2 = [1 1 1]; main_Camera_1_in_3 = 6.0; main_Camera_1_in_4 = 800; main_Camera_1_in_5 = 0.65; main_Camera_1_in_6 = NULL; main_Camera_1_in_7 = NULL; main_Camera_1_in_8 = NULL; main_Camera_1_in_9 = "white"; main_Camera_1_out_1 = NULL; main_Caption_1_in_1 = "Aluminium Fermi surface"; main_Caption_1_in_2 = NULL; main_Caption_1_in_3 = NULL; main_Caption_1_in_4 = NULL; main_Caption_1_in_5 = NULL; main_Caption_1_in_6 = 25; main_Caption_1_in_7 = NULL; main_Caption_1_in_8 = NULL; main_Caption_1_in_9 = NULL; main_Caption_1_out_1 = NULL; main_Color_6_in_2 = "black"; main_Color_6_in_3 = NULL; main_Color_6_in_4 = NULL; main_Color_6_in_5 = NULL; main_Color_6_out_1 = NULL; main_Import_1_in_1 = "fermi.general"; main_Import_1_in_2 = NULL; main_Import_1_in_3 = NULL; main_Import_1_in_4 = NULL; main_Import_1_in_5 = NULL; main_Import_1_in_6 = NULL; main_Import_1_out_1 = NULL; main_Isosurface_3_in_2 = 0.0; main_Isosurface_3_in_3 = NULL; main_Isosurface_3_in_4 = NULL; main_Isosurface_3_in_5 = NULL; main_Isosurface_3_in_6 = NULL; main_Isosurface_3_out_1 = NULL; main_Color_3_in_2 = "yellow"; main_Color_3_in_3 = NULL; main_Color_3_in_4 = "front colors"; main_Color_3_in_5 = NULL; main_Color_3_out_1 = NULL; main_Color_4_in_2 = "blue"; main_Color_4_in_3 = NULL; main_Color_4_in_4 = "back colors"; main_Color_4_in_5 = NULL; main_Color_4_out_1 = NULL; main_Translate_2_in_2 = [0 1.2 2.0]; main_Translate_2_out_1 = NULL; main_Refine_2_in_2 = 1; main_Refine_2_out_1 = NULL; main_MapToPlane_1_in_2 = NULL; main_MapToPlane_1_in_3 = [1,1,1]; main_MapToPlane_1_out_1 = NULL; main_Isosurface_2_in_2 = 0.0; main_Isosurface_2_in_3 = NULL; main_Isosurface_2_in_4 = NULL; main_Isosurface_2_in_5 = NULL; main_Isosurface_2_in_6 = NULL; main_Isosurface_2_out_1 = NULL; main_Color_5_in_2 = "black"; main_Color_5_in_3 = NULL; main_Color_5_in_4 = NULL; main_Color_5_in_5 = NULL; main_Color_5_out_1 = NULL; main_Ribbon_1_in_2 = 0.01; main_Ribbon_1_out_1 = NULL; main_Shade_1_in_2 = 0; main_Shade_1_in_3 = NULL; main_Shade_1_in_4 = NULL; main_Shade_1_in_5 = NULL; main_Shade_1_in_6 = NULL; main_Shade_1_in_7 = NULL; main_Shade_1_in_8 = NULL; main_Shade_1_out_1 = NULL; main_Translate_1_in_2 = [2.0 1.2 0]; main_Translate_1_out_1 = NULL; main_Collect_1_out_1 = NULL; main_Display_3_in_3 = "X24,,"; main_Display_3_in_4 = NULL; main_Display_3_in_5 = NULL; main_Display_3_in_6 = NULL; main_Display_3_in_7 = NULL; main_Display_3_in_8 = NULL; Executive("product version 4 4 4"); $sync main(); elk-7.2.42/examples/Fermi-surface/PaxHeaders.21776/Fe0000644000000000000000000000013214061636520016712 xustar0030 mtime=1623670096.278101227 30 atime=1623670096.277101228 30 ctime=1623670096.278101227 elk-7.2.42/examples/Fermi-surface/Fe/0000755002504400250440000000000014061636520021024 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Fermi-surface/Fe/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020072 xustar0030 mtime=1623670096.279101226 30 atime=1623670096.279101226 30 ctime=1623670096.279101226 elk-7.2.42/examples/Fermi-surface/Fe/elk.in0000644002504400250440000000146114061636520022131 0ustar00dewhurstdewhurst00000000000000 ! Fermi surface of ferromagnetic bcc iron. Use XCrysDen for visualisation. ! Run code and then use ! xcrysden --bxsf FERMISURF(_UP/_DN).bxsf ! to display the spin up and down Fermi surfaces. tasks 0 102 : this generates the XCrysDen Fermi Surface .bxsf file ! 3D Fermi surface box defined in terms of reciprocal lattice vectors plot3d 0.0 0.0 0.0 : origin (first corner) 1.0 0.0 0.0 : second corner, etc. 0.0 1.0 0.0 0.0 0.0 1.0 12 12 12 : number of points in each direction spinpol .true. bfieldc 0.0 0.0 0.01 ! fairly large number of empty states required for magnetic cases nempty 8 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 2.708 sppath '../../../species/' atoms 1 'Fe.in' 1 0.0 0.0 0.0 ngridk 4 4 4 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/Fermi-surface/PaxHeaders.21776/MgB20000644000000000000000000000013214061636520017107 xustar0030 mtime=1623670096.284101221 30 atime=1623670096.280101225 30 ctime=1623670096.284101221 elk-7.2.42/examples/Fermi-surface/MgB2/0000755002504400250440000000000014061636520021221 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Fermi-surface/MgB2/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020267 xustar0030 mtime=1623670096.281101224 30 atime=1623670096.281101224 30 ctime=1623670096.281101224 elk-7.2.42/examples/Fermi-surface/MgB2/elk.in0000644002504400250440000000144414061636520022327 0ustar00dewhurstdewhurst00000000000000 ! Fermi surface of MgB2 plotted with OpenDX. In this example, the surfaces from ! different bands are separated in the 3D plot. tasks 0 101 ngridk 6 6 4 ! plot a 2x2x2 reciprocal space cell plot3d 0.0 0.0 0.0 2.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 2.0 24 24 16 avec 5.8316944 0.0 0.0 -2.9158472 5.050395498 0.0 0.0 0.0 6.65939438 sppath '../../../species/' atoms 2 : nspecies 'Mg.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'B.in' : spfname 2 : natoms; atposl below 0.3333333333 0.6666666667 0.5 0.6666666667 0.3333333333 0.5 elk-7.2.42/examples/Fermi-surface/MgB2/PaxHeaders.21776/fermi.general0000644000000000000000000000013214061636520021625 xustar0030 mtime=1623670096.283101222 30 atime=1623670096.282101223 30 ctime=1623670096.283101222 elk-7.2.42/examples/Fermi-surface/MgB2/fermi.general0000644002504400250440000000035614061636520023666 0ustar00dewhurstdewhurst00000000000000file = FERMISURF.OUT grid = 24 x 24 x 16 format = ascii interleaving = field majority = column header = lines 1 field = locations, field0, field1, field2 structure = 3-vector, scalar, scalar, scalar type = float, float, float, float end elk-7.2.42/examples/Fermi-surface/MgB2/PaxHeaders.21776/fermi.net0000644000000000000000000000013214061636520020776 xustar0030 mtime=1623670096.284101221 30 atime=1623670096.284101221 30 ctime=1623670096.284101221 elk-7.2.42/examples/Fermi-surface/MgB2/fermi.net0000644002504400250440000001624214061636520023040 0ustar00dewhurstdewhurst00000000000000// // time: Mon Sep 3 18:12:53 2012 // // version: 3.2.0 (format), 4.4.4 (DX) // // // MODULE main // workspace: width = 527, height = 582 // layout: snap = 0, width = 50, height = 50, align = NN // macro main( ) -> ( ) { // // node Import[1]: x = 151, y = 24, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "fermi.general" // main_Import_1_out_1 = Import( main_Import_1_in_1, main_Import_1_in_2, main_Import_1_in_3, main_Import_1_in_4, main_Import_1_in_5, main_Import_1_in_6 ) [instance: 1, cache: 1]; // // node Select[1]: x = 240, y = 119, inputs = 3, label = Select // input[2]: defaulting = 0, visible = 1, type = 1, value = 0 // main_Select_1_out_1 = Select( main_Import_1_out_1, main_Select_1_in_2, main_Select_1_in_3 ) [instance: 1, cache: 1]; // // node Isosurface[1]: x = 182, y = 209, inputs = 6, label = Isosurface // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.0 // main_Isosurface_1_out_1 = Isosurface( main_Select_1_out_1, main_Isosurface_1_in_2, main_Isosurface_1_in_3, main_Isosurface_1_in_4, main_Isosurface_1_in_5, main_Isosurface_1_in_6 ) [instance: 1, cache: 1]; // // node Color[1]: x = 199, y = 297, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "red" // main_Color_1_out_1 = Color( main_Isosurface_1_out_1, main_Color_1_in_2, main_Color_1_in_3, main_Color_1_in_4, main_Color_1_in_5 ) [instance: 1, cache: 1]; // // node Select[2]: x = 319, y = 120, inputs = 3, label = Select // input[2]: defaulting = 0, visible = 1, type = 1, value = 1 // main_Select_2_out_1 = Select( main_Import_1_out_1, main_Select_2_in_2, main_Select_2_in_3 ) [instance: 2, cache: 1]; // // node Isosurface[2]: x = 310, y = 211, inputs = 6, label = Isosurface // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.0 // main_Isosurface_2_out_1 = Isosurface( main_Select_2_out_1, main_Isosurface_2_in_2, main_Isosurface_2_in_3, main_Isosurface_2_in_4, main_Isosurface_2_in_5, main_Isosurface_2_in_6 ) [instance: 2, cache: 1]; // // node Color[2]: x = 316, y = 299, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "yellow" // main_Color_2_out_1 = Color( main_Isosurface_2_out_1, main_Color_2_in_2, main_Color_2_in_3, main_Color_2_in_4, main_Color_2_in_5 ) [instance: 2, cache: 1]; // // node Select[3]: x = 409, y = 122, inputs = 3, label = Select // input[2]: defaulting = 0, visible = 1, type = 1, value = 2 // main_Select_3_out_1 = Select( main_Import_1_out_1, main_Select_3_in_2, main_Select_3_in_3 ) [instance: 3, cache: 1]; // // node Isosurface[3]: x = 449, y = 213, inputs = 6, label = Isosurface // input[2]: defaulting = 0, visible = 1, type = 5, value = 0.0 // main_Isosurface_3_out_1 = Isosurface( main_Select_3_out_1, main_Isosurface_3_in_2, main_Isosurface_3_in_3, main_Isosurface_3_in_4, main_Isosurface_3_in_5, main_Isosurface_3_in_6 ) [instance: 3, cache: 1]; // // node Color[3]: x = 444, y = 300, inputs = 5, label = Color // input[2]: defaulting = 0, visible = 1, type = 32, value = "green" // main_Color_3_out_1 = Color( main_Isosurface_3_out_1, main_Color_3_in_2, main_Color_3_in_3, main_Color_3_in_4, main_Color_3_in_5 ) [instance: 3, cache: 1]; // // node Collect[1]: x = 299, y = 392, inputs = 3, label = Collect // main_Collect_1_out_1 = Collect( main_Color_1_out_1, main_Color_2_out_1, main_Color_3_out_1 ) [instance: 1, cache: 1]; // // node AutoCamera[2]: x = 422, y = 412, inputs = 9, label = AutoCamera // input[2]: defaulting = 0, visible = 1, type = 8, value = [1.0 -0.25 0.5] // input[3]: defaulting = 0, visible = 0, type = 5, value = 4.0 // input[4]: defaulting = 0, visible = 0, type = 1, value = 800 // input[6]: defaulting = 0, visible = 0, type = 8, value = [0 0 1] // main_AutoCamera_2_out_1 = AutoCamera( main_Collect_1_out_1, main_AutoCamera_2_in_2, main_AutoCamera_2_in_3, main_AutoCamera_2_in_4, main_AutoCamera_2_in_5, main_AutoCamera_2_in_6, main_AutoCamera_2_in_7, main_AutoCamera_2_in_8, main_AutoCamera_2_in_9 ) [instance: 2, cache: 1]; // // node Render[1]: x = 255, y = 507, inputs = 3, label = Render // main_Render_1_out_1 = Render( main_Collect_1_out_1, main_AutoCamera_2_out_1, main_Render_1_in_3 ) [instance: 1, cache: 1]; // // node Display[1]: x = 451, y = 520, inputs = 8, label = Display // depth: value = 24 // window: position = (0.0089,0.0231), size = 0.4240x0.5944, screen = 0 // main_Display_1_out_1[cache: 2] = Display( main_Render_1_out_1, main_Display_1_in_2, main_Display_1_in_3, main_Display_1_in_4, main_Display_1_in_5, main_Display_1_in_6, main_Display_1_in_7, main_Display_1_in_8 ) [instance: 1, cache: 1]; // network: end of macro body } main_Import_1_in_1 = "fermi.general"; main_Import_1_in_2 = NULL; main_Import_1_in_3 = NULL; main_Import_1_in_4 = NULL; main_Import_1_in_5 = NULL; main_Import_1_in_6 = NULL; main_Import_1_out_1 = NULL; main_Select_1_in_2 = 0; main_Select_1_in_3 = NULL; main_Select_1_out_1 = NULL; main_Isosurface_1_in_2 = 0.0; main_Isosurface_1_in_3 = NULL; main_Isosurface_1_in_4 = NULL; main_Isosurface_1_in_5 = NULL; main_Isosurface_1_in_6 = NULL; main_Isosurface_1_out_1 = NULL; main_Color_1_in_2 = "red"; main_Color_1_in_3 = NULL; main_Color_1_in_4 = NULL; main_Color_1_in_5 = NULL; main_Color_1_out_1 = NULL; main_Select_2_in_2 = 1; main_Select_2_in_3 = NULL; main_Select_2_out_1 = NULL; main_Isosurface_2_in_2 = 0.0; main_Isosurface_2_in_3 = NULL; main_Isosurface_2_in_4 = NULL; main_Isosurface_2_in_5 = NULL; main_Isosurface_2_in_6 = NULL; main_Isosurface_2_out_1 = NULL; main_Color_2_in_2 = "yellow"; main_Color_2_in_3 = NULL; main_Color_2_in_4 = NULL; main_Color_2_in_5 = NULL; main_Color_2_out_1 = NULL; main_Select_3_in_2 = 2; main_Select_3_in_3 = NULL; main_Select_3_out_1 = NULL; main_Isosurface_3_in_2 = 0.0; main_Isosurface_3_in_3 = NULL; main_Isosurface_3_in_4 = NULL; main_Isosurface_3_in_5 = NULL; main_Isosurface_3_in_6 = NULL; main_Isosurface_3_out_1 = NULL; main_Color_3_in_2 = "green"; main_Color_3_in_3 = NULL; main_Color_3_in_4 = NULL; main_Color_3_in_5 = NULL; main_Color_3_out_1 = NULL; main_Collect_1_out_1 = NULL; main_AutoCamera_2_in_2 = [1.0 -0.25 0.5]; main_AutoCamera_2_in_3 = 4.0; main_AutoCamera_2_in_4 = 800; main_AutoCamera_2_in_5 = NULL; main_AutoCamera_2_in_6 = [0 0 1]; main_AutoCamera_2_in_7 = NULL; main_AutoCamera_2_in_8 = NULL; main_AutoCamera_2_in_9 = NULL; main_AutoCamera_2_out_1 = NULL; main_Render_1_in_3 = NULL; main_Render_1_out_1 = NULL; main_Display_1_in_2 = NULL; main_Display_1_in_3 = "X24,,"; main_Display_1_in_4 = NULL; main_Display_1_in_5 = NULL; main_Display_1_in_6 = NULL; main_Display_1_in_7 = NULL; main_Display_1_in_8 = NULL; Executive("product version 4 4 4"); $sync main(); elk-7.2.42/examples/PaxHeaders.21776/OEP0000644000000000000000000000013114061636520014312 xustar0030 mtime=1623670096.288101217 29 atime=1623670096.28510122 30 ctime=1623670096.288101217 elk-7.2.42/examples/OEP/0000755002504400250440000000000014061636520016425 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/OEP/PaxHeaders.21776/HEG0000644000000000000000000000013214061636520014716 xustar0030 mtime=1623670096.287101218 30 atime=1623670096.286101219 30 ctime=1623670096.287101218 elk-7.2.42/examples/OEP/HEG/0000755002504400250440000000000014061636520017030 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/OEP/HEG/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016076 xustar0030 mtime=1623670096.288101217 30 atime=1623670096.287101218 30 ctime=1623670096.288101217 elk-7.2.42/examples/OEP/HEG/elk.in0000644002504400250440000000070214061636520020132 0ustar00dewhurstdewhurst00000000000000 ! Optimised effetive potential (OEP) ground state of the homogenous electron ! gas. The Wigner radius (r_s) is written to INFO.OUT. Note that the exchange ! energy is only computed during the last iteration. tasks 0 xctype -1 chgexs 10.0 ! use the unit cell of aluminium avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.75 ! note that low density gases require denser k-point grids! ngridk 2 2 2 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/OEP/PaxHeaders.21776/Si0000644000000000000000000000013214061636520014666 xustar0030 mtime=1623670096.289101217 30 atime=1623670096.288101217 30 ctime=1623670096.289101217 elk-7.2.42/examples/OEP/Si/0000755002504400250440000000000014061636520017000 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/OEP/Si/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016046 xustar0030 mtime=1623670096.290101216 30 atime=1623670096.290101216 30 ctime=1623670096.290101216 elk-7.2.42/examples/OEP/Si/elk.in0000644002504400250440000000217014061636520020103 0ustar00dewhurstdewhurst00000000000000 ! Optimised effective potential calculation of silicon. An iterative proceedure ! is used to find the optimised potential [Phys. Rev. Lett. 98, 196405 (2007)]. ! Note that the exact exchange energy is calculated only during the last ! self-consistent loop, which is the reason why the final total energy is ! different from those calculated in previous loops. tasks 0 20 ! exact exchange only (no correlation) xctype -1 ! large number of OEP iterations to converge the gap maxitoep 300 ! large number of empty states required nempty 15 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 4 4 4 ! These are the vertices to be joined for the band structure plot plot1d 7 200 : nvp1d, npp1d 0.0 0.0 1.0 : vlvp1d 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 elk-7.2.42/examples/PaxHeaders.21776/TDDFT-time-evolution0000644000000000000000000000013214061636520017513 xustar0030 mtime=1623670096.300101206 30 atime=1623670096.291101215 30 ctime=1623670096.300101206 elk-7.2.42/examples/TDDFT-time-evolution/0000755002504400250440000000000014061636520021625 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-time-evolution/PaxHeaders.21776/Si-ramp0000644000000000000000000000013014061636520021021 xustar0029 mtime=1623670096.29610121 30 atime=1623670096.292101214 29 ctime=1623670096.29610121 elk-7.2.42/examples/TDDFT-time-evolution/Si-ramp/0000755002504400250440000000000014061636520023135 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-time-evolution/Si-ramp/PaxHeaders.21776/CURRENT_TD.OUT0000644000000000000000000000013214061636520023202 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-0.9984099758E-01 -0.2758447829E-04 -0.1624846949E-04 509.0000000 -0.1001148404 -0.2559798823E-04 -0.1975428543E-04 509.5000000 -0.1003878164 -0.2616663453E-04 -0.2432949727E-04 510.0000000 -0.1006613872 -0.3373675427E-04 -0.2412244469E-04 510.5000000 -0.1009364738 -0.4203770581E-04 -0.1726293576E-04 511.0000000 -0.1012116071 -0.4423018270E-04 -0.8171082722E-05 elk-7.2.42/examples/TDDFT-time-evolution/Si-ramp/PaxHeaders.21776/elk.in0000644000000000000000000000013114061636520022202 xustar0030 mtime=1623670096.297101209 29 atime=1623670096.29610121 30 ctime=1623670096.297101209 elk-7.2.42/examples/TDDFT-time-evolution/Si-ramp/elk.in0000644002504400250440000000174714061636520024251 0ustar00dewhurstdewhurst00000000000000 ! Silicon exposed to an intense, linearly increasing electric field. See the ! manual for details on the 'ramp' vector potential. This is a computationally ! expensive example that is best run with MPI on a cluster. tasks 0 450 460 ! no shifting of the atomic positions for the ground-state run tshift .false. xctype 20 highq .true. nxoapwlo 1 mixtype 3 nempty 20.0 autokpt .false. tstime 500 dtimes 0.5 ! vector potential ramp parameters ! 1 - 3 : polarisation vector (including amplitude) ! 4 : start time of ramp ! 5 : linear coefficient ! 6 : quadratic coefficient ramp 1 1.0 0.0 0.0 0.0 0.0 0.0025 ngridk 12 12 12 vkloff 0.25 0.5 0.625 avec 5.13 5.13 0.0 5.13 0.0 5.13 0.0 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 elk-7.2.42/examples/TDDFT-time-evolution/PaxHeaders.21776/FeCo-Ehrenfest0000644000000000000000000000013214061636520022250 xustar0030 mtime=1623670096.299101207 30 atime=1623670096.298101208 30 ctime=1623670096.299101207 elk-7.2.42/examples/TDDFT-time-evolution/FeCo-Ehrenfest/0000755002504400250440000000000014061636520024362 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-time-evolution/FeCo-Ehrenfest/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023430 xustar0030 mtime=1623670096.299101207 30 atime=1623670096.299101207 30 ctime=1623670096.299101207 elk-7.2.42/examples/TDDFT-time-evolution/FeCo-Ehrenfest/elk.in0000644002504400250440000000365514061636520025476 0ustar00dewhurstdewhurst00000000000000 ! TDDFT time evolution of FeCo with Ehrenfest nuclear dynamics. This is a ! two-step process: first the forces under the influence of a laser pulse are ! calculated. In the second step, the same calculation is repeated but this time ! the forces are used to find the motion of the nuclei. The back-reaction of ! this nuclear motion is applied to the electronic system. ! This approach is valid only for small amplitude nuclear motion. tasks 0 ! ground-state run 450 ! generate the laser pulse A-field 460 ! time evolution with laser pulse and forces calculated 462 ! same time evolution with Ehrenfest dynamics using the previous forces ! calculate forces at each time step tforce .true. ! total simulation time tstime 400.0 ! Simulation time step, ideally about 1 attosecond. It is critically important ! to make sure that the time evolution is stable, particularly for magnetism ! which can diverge even in the absence of a laser field. Any simulation should ! be run first with a laser field of amplitude zero to make sure that all ! observables remain constant over the total simulation time. Reducing the time ! step can improve stability. dtimes 0.4 ! laser pulse parameters ! 1 - 3 : polarisation vector (including amplitude) ! 4 : frequency ! 5 : phase in degrees ! 6 : chirp rate ! 7 : peak time ! 8 : full-width at half-maximum pulse 1 : number of laser pulses 0.0 0.0 150.0 0.03 0.0 0.0 240.0 120.0 nxoapwlo 1 tshift .false. spinorb .true. bfieldc 0.0 0.0 0.001 nempty 20 ngridk 4 4 4 ! artificial strained lattice avec 0.5 0.5 0.0 0.0 1.0 0.0 0.0 0.0 1.0 scale1 6.8 scale2 6.8 scale3 7.0 sppath '../../../species/' atoms 2 : nspecies 'Fe.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'Co.in' 1 0.0 0.5 0.5 elk-7.2.42/examples/TDDFT-time-evolution/PaxHeaders.21776/Ni-laser-pulse0000644000000000000000000000013214061636520022313 xustar0030 mtime=1623670096.301101205 30 atime=1623670096.300101206 30 ctime=1623670096.301101205 elk-7.2.42/examples/TDDFT-time-evolution/Ni-laser-pulse/0000755002504400250440000000000014061636520024425 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/TDDFT-time-evolution/Ni-laser-pulse/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023473 xustar0030 mtime=1623670096.301101205 30 atime=1623670096.301101205 30 ctime=1623670096.301101205 elk-7.2.42/examples/TDDFT-time-evolution/Ni-laser-pulse/elk.in0000644002504400250440000000476114061636520025540 0ustar00dewhurstdewhurst00000000000000 ! Simulation of an intense ultra-short laser pulse acting on fcc nickel. ! The laser pulse is represented by a time-dependent vector potential which is ! constructed from an arbitrary superposition of planes waves each multiplied ! with a Gaussian envelope function. ! The time-dependent vector potential and laser pulse parameters are written to ! AFIELDT.OUT and TD_INFO.OUT, respectively. The power density of the laser ! pulse is written to AFPDT.OUT. Time units are atomic, one of which is equal to ! 24.18884328 attoseconds. ! The total macroscopic current is written to the file JTOT_TD.OUT and may be ! directly plotted. The total moment magnitude as a function of time is stored ! in the file MOMENTM_TD.OUT. Observe that the moment declines considerably ! after the laser pulse has stopped. ! This example is insufficiently converged for a production run, and all ! observables should be carefully checked for convergence with respect to the ! usual parameters. tasks 0 450 460 ! no shifting of the atomic positions for the ground-state run tshift .false. ! tight ground-state convergence epspot 1.e-7 lradstp 5 rgkmax 8.0 ngridk 8 8 8 ! automatic conversion of species to LAPW + linearised l.o. instead of APW+l.o. nxoapwlo 1 ! large number of empty states required nempty 16 ! total simulation time tstime 500.0 ! Simulation time step, ideally about 1 attosecond. It is critically important ! to make sure that the time evolution is stable, particularly for magnetism ! which can diverge even in the absence of a laser field. Any simulation should ! be run first with a laser field of amplitude zero to make sure that all ! observables remain constant over the total simulation time. Reducing the time ! step can improve stability. dtimes 0.1 ! laser pulse parameters ! 1 - 3 : polarisation vector (including amplitude) ! 4 : frequency ! 5 : phase in degrees ! 6 : chirp rate ! 7 : peak time ! 8 : full-width at half-maximum pulse 1 : number of laser pulses 0.0 0.0 250.0 0.03 0.0 0.0 240.0 120.0 ! plot the 2D magnetisation every ntswrite time steps tdmag2d .true. ntswrite 100 spinpol .true. spinorb .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/examples/PaxHeaders.21776/hybrids0000644000000000000000000000012614061636520015337 xustar0028 mtime=1623670096.3071012 30 atime=1623670096.303101204 28 ctime=1623670096.3071012 elk-7.2.42/examples/hybrids/0000755002504400250440000000000014061636520017446 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/hybrids/PaxHeaders.21776/Si-libxc0000644000000000000000000000013214061636520017006 xustar0030 mtime=1623670096.305101202 30 atime=1623670096.304101203 30 ctime=1623670096.305101202 elk-7.2.42/examples/hybrids/Si-libxc/0000755002504400250440000000000014061636520021120 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/hybrids/Si-libxc/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020166 xustar0030 mtime=1623670096.305101202 30 atime=1623670096.305101202 30 ctime=1623670096.305101202 elk-7.2.42/examples/hybrids/Si-libxc/elk.in0000644002504400250440000000112714061636520022224 0ustar00dewhurstdewhurst00000000000000 ! Hybrid functional example using libxc. Note that the DFT step should be run ! separately with task=0. Then the hybrid step should be run with task=5. ! Example by Tyrel McQueen. tasks 0 ! first run task=0 with PBE... xctype 100 101 130 !...then uncomment the following and run with task=5 for hybrid GGA ! (note that only the correlation functional is set) !xctype ! 100 0 406 lmaxo 6 gmaxvr 10.0 ngridk 2 2 2 nempty 8 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 'Si.in' 2 0.00 0.00 0.00 0.25 0.25 0.25 elk-7.2.42/examples/hybrids/PaxHeaders.21776/Si0000644000000000000000000000013014061636520015705 xustar0030 mtime=1623670096.308101199 28 atime=1623670096.3071012 30 ctime=1623670096.308101199 elk-7.2.42/examples/hybrids/Si/0000755002504400250440000000000014061636520020021 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/hybrids/Si/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017067 xustar0030 mtime=1623670096.308101199 30 atime=1623670096.308101199 30 ctime=1623670096.308101199 elk-7.2.42/examples/hybrids/Si/elk.in0000644002504400250440000000057414061636520021132 0ustar00dewhurstdewhurst00000000000000 ! Hybrid functional using the native PBE functional. ! Example by Tyrel McQueen. tasks 0 5 xctype 20 hybrid .true. ! hybrid mixing parameter hybmix 0.25 lmaxo 6 gmaxvr 10.0 ngridk 2 2 2 nempty 10 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 'Si.in' 2 0.00 0.00 0.00 0.25 0.25 0.25 elk-7.2.42/examples/PaxHeaders.21776/meta-GGA0000644000000000000000000000013214061636520015212 xustar0030 mtime=1623670096.313101194 30 atime=1623670096.309101198 30 ctime=1623670096.313101194 elk-7.2.42/examples/meta-GGA/0000755002504400250440000000000014061636520017324 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/meta-GGA/PaxHeaders.21776/GaAs-SCAN0000644000000000000000000000013214061636520016547 xustar0030 mtime=1623670096.312101195 30 atime=1623670096.310101197 30 ctime=1623670096.312101195 elk-7.2.42/examples/meta-GGA/GaAs-SCAN/0000755002504400250440000000000014061636520020661 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/meta-GGA/GaAs-SCAN/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017727 xustar0030 mtime=1623670096.312101195 30 atime=1623670096.312101195 30 ctime=1623670096.312101195 elk-7.2.42/examples/meta-GGA/GaAs-SCAN/elk.in0000644002504400250440000000212214061636520021761 0ustar00dewhurstdewhurst00000000000000 ! Variational meta-GGA example using the strongly constrained and appropriately ! normed (SCAN) functional of J. Sun, A. Ruzsinszky and J. P. Perdew, ! Phys. Rev. Lett. 115, 036402 (2015). ! ! Unfortunately, the original functional is numerically unstable when used with ! Elk. Instead we use the numerically stable 'regularised' version of SCAN ! developed by A. P. Bartók and J. R. Yates, J. Chem. Phys. 150, 161101 (2019). ! ! This example requires the Libxc functional library. tasks 0 20 highq .true. ! set additional options required for meta-GGA metagga .true. ! regularised SCAN xctype 100 493 494 ngridk 4 4 4 plot1d 7 200 0.0 0.0 1.0 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 avec 5.3435 5.3435 0.0000 5.3435 0.0000 5.3435 0.0000 5.3435 5.3435 sppath '../../../species/' atoms 2 : nspecies 'Ga.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'As.in' 1 0.25 0.25 0.25 elk-7.2.42/examples/meta-GGA/PaxHeaders.21776/Si-Tran-Blaha0000644000000000000000000000013214061636520017474 xustar0030 mtime=1623670096.314101193 30 atime=1623670096.313101194 30 ctime=1623670096.314101193 elk-7.2.42/examples/meta-GGA/Si-Tran-Blaha/0000755002504400250440000000000014061636520021606 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/meta-GGA/Si-Tran-Blaha/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020654 xustar0030 mtime=1623670096.315101192 30 atime=1623670096.314101193 30 ctime=1623670096.315101192 elk-7.2.42/examples/meta-GGA/Si-Tran-Blaha/elk.in0000644002504400250440000000225314061636520022713 0ustar00dewhurstdewhurst00000000000000 ! Band structure of silicon using meta-GGA. Note that the libxc library has to ! be linked into the code. See the manual for instructions on how to do this. ! LAPW appears to be required to obtain accurate kinetic energy densities. ! Compare the meta-GGA and LDA band structures and band gaps. tasks 0 20 ! use the Tran-Blaha meta-GGA functional for exchange and LDA for correlation ! [Phys. Rev. Lett. 102, 226401 (2009)] xctype 100 208 12 ! double the number of points in the muffin-tin nrmtscf 2 ! use LAPW nxoapwlo 1 ! smooth the gradients to ensure convergence msmooth 2 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 14 14 14 ! These are the vertices to be joined for the band structure plot plot1d 7 200 : nvp1d, npp1d 0.0 0.0 1.0 : vlvp1d 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 elk-7.2.42/examples/PaxHeaders.21776/phonons-superconductivity0000644000000000000000000000013214061636520021155 xustar0030 mtime=1623670096.390101123 30 atime=1623670096.316101192 30 ctime=1623670096.390101123 elk-7.2.42/examples/phonons-superconductivity/0000755002504400250440000000000014061636520023267 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/phonons-superconductivity/PaxHeaders.21776/GaAs-DFPT0000644000000000000000000000013114061636520022522 xustar0030 mtime=1623670096.321101187 29 atime=1623670096.31710119 30 ctime=1623670096.321101187 elk-7.2.42/examples/phonons-superconductivity/GaAs-DFPT/0000755002504400250440000000000014061636520024635 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/phonons-superconductivity/GaAs-DFPT/PaxHeaders.21776/PHDISP.OUT0000644000000000000000000000012714061636520024164 xustar0029 mtime=1623670096.31810119 29 atime=1623670096.31810119 29 ctime=1623670096.31810119 elk-7.2.42/examples/phonons-superconductivity/GaAs-DFPT/PHDISP.OUT0000644002504400250440000012662414061636520026230 0ustar00dewhurstdewhurst00000000000000 0.000000000 0.1536768326E-10 0.1588994284E-01 0.1350455454E-04 0.3177988568E-01 0.2703428035E-04 0.4766982851E-01 0.4061314416E-04 0.6355977135E-01 0.5426273974E-04 0.7944971419E-01 0.6800118985E-04 0.9533965703E-01 0.8184215000E-04 0.1112295999 0.9579394125E-04 0.1271195427 0.1098588339E-03 0.1430094855 0.1240324987E-03 0.1588994284 0.1383036361E-03 0.1747893712 0.1526537889E-03 0.1906793141 0.1670573397E-03 0.2065692569 0.1814816874E-03 0.2224591997 0.1958875971E-03 0.2383491426 0.2102297134E-03 0.2542390854 0.2244572224E-03 0.2701290283 0.2385146522E-03 0.2860189711 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0.1163404660E-02 3.131998853 0.1163860803E-02 3.147396179 0.1164013240E-02 elk-7.2.42/examples/phonons-superconductivity/GaAs-DFPT/PaxHeaders.21776/PHDLINES.OUT0000644000000000000000000000013214061636520024377 xustar0030 mtime=1623670096.320101188 30 atime=1623670096.320101188 30 ctime=1623670096.320101188 elk-7.2.42/examples/phonons-superconductivity/GaAs-DFPT/PHDLINES.OUT0000644002504400250440000000106014061636520026431 0ustar00dewhurstdewhurst00000000000000 0.000000000 -0.9116315967E-03 0.000000000 0.1823263193E-02 0.5879278850 -0.9116315967E-03 0.5879278850 0.1823263193E-02 1.419383474 -0.9116315967E-03 1.419383474 0.1823263193E-02 1.928543958 -0.9116315967E-03 1.928543958 0.1823263193E-02 2.437704442 -0.9116315967E-03 2.437704442 0.1823263193E-02 2.731668384 -0.9116315967E-03 2.731668384 0.1823263193E-02 3.147396179 -0.9116315967E-03 3.147396179 0.1823263193E-02 elk-7.2.42/examples/phonons-superconductivity/GaAs-DFPT/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023703 xustar0030 mtime=1623670096.322101186 30 atime=1623670096.322101186 30 ctime=1623670096.322101186 elk-7.2.42/examples/phonons-superconductivity/GaAs-DFPT/elk.in0000644002504400250440000000177614061636520025753 0ustar00dewhurstdewhurst00000000000000 ! Phonon dispersion of GaAs calculated with density functional perturbation ! theory (DFPT). Note the large number of radial mesh points required for ! convergence. This is because the gradients calculated in the muffin-tin ! have to be particularly accurate. ! Also note that the LO-TO splitting is not included in the dispersion. tasks 0 : ground state calculation 205 : phonon calculation with DFPT 220 : phonon dispersion plot ! scale up the number of radial mesh points nrmtscf 6.0 ngridq 2 2 2 ngridk 4 4 4 plot1d 7 200 0.0 0.0 1.0 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 avec 5.3435 5.3435 0.0000 5.3435 0.0000 5.3435 0.0000 5.3435 5.3435 sppath '../../../species/' atoms 2 : nspecies 'Ga.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'As.in' 1 0.25 0.25 0.25 elk-7.2.42/examples/phonons-superconductivity/PaxHeaders.21776/Nb-DFPT0000644000000000000000000000013214061636520022247 xustar0030 mtime=1623670096.338101171 30 atime=1623670096.323101185 30 ctime=1623670096.338101171 elk-7.2.42/examples/phonons-superconductivity/Nb-DFPT/0000755002504400250440000000000014061636520024361 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72.92485177 0.2356776139E-12 2.145206374 74.87579337 0.1759225704E-12 2.145365976 76.82673498 0.1309578187E-12 2.145513623 78.77767658 0.9724010491E-13 2.145650478 80.72861819 0.7204139109E-13 2.145183350 elk-7.2.42/examples/phonons-superconductivity/Nb-DFPT/PaxHeaders.21776/MCMILLAN.OUT0000644000000000000000000000012714061636520024115 xustar0029 mtime=1623670096.32810118 29 atime=1623670096.32810118 29 ctime=1623670096.32810118 elk-7.2.42/examples/phonons-superconductivity/Nb-DFPT/MCMILLAN.OUT0000644002504400250440000000053214061636520026146 0ustar00dewhurstdewhurst00000000000000 Electron-phonon coupling constant, lambda : 1.150620532 Logarithmic average frequency : 0.7088838913E-03 RMS average frequency : 0.7567470325E-03 Coulomb pseudopotential, mu* : 0.1500000000 McMillan-Allen-Dynes superconducting critical temperature [Eq. 34, Phys. 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elk-7.2.42/examples/phonons-superconductivity/Nb-DFPT/PaxHeaders.21776/PHLWLINES.OUT0000644000000000000000000000013214061636520024262 xustar0030 mtime=1623670096.337101172 30 atime=1623670096.337101172 30 ctime=1623670096.337101172 elk-7.2.42/examples/phonons-superconductivity/Nb-DFPT/PHLWLINES.OUT0000644002504400250440000000132014061636520026313 0ustar00dewhurstdewhurst00000000000000 0.000000000 -0.2106191682E-04 0.000000000 0.4212383364E-04 0.8859326103 -0.2106191682E-04 0.8859326103 0.4212383364E-04 1.771865221 -0.2106191682E-04 1.771865221 0.4212383364E-04 2.794852083 -0.2106191682E-04 2.794852083 0.4212383364E-04 3.518213030 -0.2106191682E-04 3.518213030 0.4212383364E-04 4.029706461 -0.2106191682E-04 4.029706461 0.4212383364E-04 4.541199892 -0.2106191682E-04 4.541199892 0.4212383364E-04 5.264560839 -0.2106191682E-04 5.264560839 0.4212383364E-04 6.517458752 -0.2106191682E-04 6.517458752 0.4212383364E-04 elk-7.2.42/examples/phonons-superconductivity/Nb-DFPT/PaxHeaders.21776/elk.in0000644000000000000000000000013014061636520023425 xustar0029 mtime=1623670096.33910117 30 atime=1623670096.338101171 29 ctime=1623670096.33910117 elk-7.2.42/examples/phonons-superconductivity/Nb-DFPT/elk.in0000644002504400250440000000357014061636520025471 0ustar00dewhurstdewhurst00000000000000 ! This example generates a good quality phonon dispersion for bcc niobium using ! density functional perturbation theory (DFPT). The superconducting critical ! temperature is also computed using McMillan's formula and by solving the ! Eliashberg equations. ! The phonon dispersion and vertex location lines are included with this ! example in the files PHDISP.OUT and PHDLINES.OUT, respectively. tasks 0 : generate the ground-state 205 : generate the dynamical matrices with DFPT ! number of phonon q-points ngridq 4 4 4 ! add extra local-orbitals for accurate electron-phonon coupling nxlo 1 ! larger cut-off required rgkmax 8.0 ngridk 8 8 8 ! larger smearing width required for stable phonon dispersion swidth 0.005 stype 1 ! increase the number of muffin-tin points (for accurate gradients) nrmtscf 2.0 ! after all the dynamical matrix DYN---.OUT files have been calculated then ! uncomment the following lines and run again ! large k-point required for accurate electron-phonon coupling !ngridk ! 24 24 24 !tasks ! 1 : ground state with larger k-point set ! 210 : phonon DOS ! 220 : plot the phonon dispersion ! 240 : electron-phonon matrix elements ! 245 : phonon line-widths ! 250 : Eliashberg function, alpha^2F ! 260 : solving the Eliashberg equations ! number of temperature steps for Eliashberg calculation ntemp 40 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 ! use LDA equilibrium lattice constant scale 3.071 sppath '../../../species/' atoms 1 : nspecies 'Nb.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 plot1d 9 400 0.5 0.5 0.5 0.25 0.25 0.25 0.0 0.0 0.0 -0.5 0.5 0.5 -0.5 0.5 0.0 -0.75 0.25 0.25 -0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.5 0.0 elk-7.2.42/examples/phonons-superconductivity/PaxHeaders.21776/Si-DFPT0000644000000000000000000000013114061636520022262 xustar0030 mtime=1623670096.340101169 29 atime=1623670096.33910117 30 ctime=1623670096.340101169 elk-7.2.42/examples/phonons-superconductivity/Si-DFPT/0000755002504400250440000000000014061636520024375 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/phonons-superconductivity/Si-DFPT/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023443 xustar0030 mtime=1623670096.341101168 30 atime=1623670096.341101168 30 ctime=1623670096.341101168 elk-7.2.42/examples/phonons-superconductivity/Si-DFPT/elk.in0000644002504400250440000000245714061636520025510 0ustar00dewhurstdewhurst00000000000000 ! Phonon dispersion of silicon. ! You can submit the same job (with task=205) on as many machines as you like, ! but they must be be able to see the same directory. Each machine with compute ! a row of a particular dynamical matrix. When run with task=220, the code ! assembles all the pieces to construct the dynamical matrices throughout the ! Brillouin zone. ! The final output (PHDISP.OUT and PHDLINES.OUT) is included with this example. tasks 0 205 220 ! scale the number of radial mesh points in the muffin-tins; this is so that ! gradients are accurately calculated nrmtscf 4 ! limit the maximum number of self-consistent loops maxscl 30 ! phonon q-point grid ngridq 4 4 4 ! k-point grid should be commensurate with the q-point grid ngridk 4 4 4 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ! These are the vertices to be joined for the phonon dispersion plot plot1d 7 200 : nvp1d, npp1d 1.0 0.0 0.0 0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 elk-7.2.42/examples/phonons-superconductivity/PaxHeaders.21776/Al-DFPT0000644000000000000000000000013214061636520022244 xustar0030 mtime=1623670096.356101154 30 atime=1623670096.341101168 30 ctime=1623670096.356101154 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/0000755002504400250440000000000014061636520024356 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/PaxHeaders.21776/ALPHA2F.OUT0000644000000000000000000000013214061636520023727 xustar0030 mtime=1623670096.343101166 30 atime=1623670096.343101166 30 ctime=1623670096.343101166 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/ALPHA2F.OUT0000644002504400250440000004410414061636520025767 0ustar00dewhurstdewhurst00000000000000 -0.1808426262E-03 0.1486312544E-03 -0.1768640889E-03 0.2753909944E-03 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ctime=1623670096.346101164 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/MCMILLAN.OUT0000644002504400250440000000053214061636520026143 0ustar00dewhurstdewhurst00000000000000 Electron-phonon coupling constant, lambda : 0.4237123761 Logarithmic average frequency : 0.1068940640E-02 RMS average frequency : 0.1161090651E-02 Coulomb pseudopotential, mu* : 0.1500000000 McMillan-Allen-Dynes superconducting critical temperature [Eq. 34, Phys. 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B 12, 905 (1975)] (kelvin) : 0.5132416494 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/PaxHeaders.21776/PHDISP.OUT0000644000000000000000000000013214061636520023701 xustar0030 mtime=1623670096.348101162 30 atime=1623670096.348101162 30 ctime=1623670096.348101162 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/PHDISP.OUT0000644002504400250440000005331214061636520025742 0ustar00dewhurstdewhurst00000000000000 0.000000000 -0.3420208952E-10 0.1367793241E-01 0.1395975825E-04 0.2735586482E-01 0.2811116802E-04 0.4103379724E-01 0.4263638565E-04 0.5471172965E-01 0.5769959260E-04 0.6838966206E-01 0.7344031904E-04 0.8206759447E-01 0.8996898946E-04 0.9574552688E-01 0.1073647223E-03 0.1094234593 0.1256751165E-03 0.1231013917 0.1449175914E-03 0.1367793241 0.1650818093E-03 0.1504572565 0.1861327570E-03 0.1641351889 0.2080141521E-03 0.1778131214 0.2306519397E-03 0.1914910538 0.2539577266E-03 0.2051689862 0.2778320642E-03 0.2188469186 0.3021675364E-03 0.2325248510 0.3268516307E-03 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0.6848711426E-05 2.573278970 0.6751169228E-05 2.586912398 0.6643865132E-05 2.600545825 0.6530956421E-05 2.614179253 0.6416391268E-05 2.627812680 0.6303838836E-05 2.641446107 0.6196636344E-05 2.655079535 0.6097752075E-05 2.668712962 0.6009762480E-05 2.682346390 0.5934840880E-05 2.695979817 0.5874754882E-05 2.709613245 0.5830869496E-05 2.723246672 0.5804153083E-05 2.736880099 0.5795183581E-05 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/PaxHeaders.21776/PHLWLINES.OUT0000644000000000000000000000013214061636520024257 xustar0030 mtime=1623670096.355101155 30 atime=1623670096.355101155 30 ctime=1623670096.355101155 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/PHLWLINES.OUT0000644002504400250440000000050014061636520026307 0ustar00dewhurstdewhurst00000000000000 0.000000000 -0.7273581532E-05 0.000000000 0.1454716306E-04 0.8343538771 -0.7273581532E-05 0.8343538771 0.1454716306E-04 2.014308446 -0.7273581532E-05 2.014308446 0.1454716306E-04 2.736880099 -0.7273581532E-05 2.736880099 0.1454716306E-04 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023424 xustar0030 mtime=1623670096.356101154 30 atime=1623670096.356101154 30 ctime=1623670096.356101154 elk-7.2.42/examples/phonons-superconductivity/Al-DFPT/elk.in0000644002504400250440000000346414061636520025470 0ustar00dewhurstdewhurst00000000000000 ! Phonon spectrum and solving the Eliashberg equations to find the temperature- ! dependent superconducting gap. This uses density functional perturbation ! theory (DFPT) to calculate the phonon modes. ! You can submit the same phonon job (task=205) on as many machines as you like, ! but they must be be able to see the same directory. Each machine will compute ! a row of a particular dynamical matrix. The code assembles all the pieces to ! construct the dynamical and electron-phonon coupling matrices throughout the ! Brillouin zone. ! Example by Antonio Sanna. tasks 0 205 ! phonon q-point grid ngridq 4 4 4 ! add extra local-orbitals for accurate electron-phonon coupling nxlo 1 ngridk 8 8 8 ! larger smearing width required for stable phonon dispersion swidth 0.005 stype 1 ! increase the number of muffin-tin points (for accurate gradients) nrmtscf 1.5 ! uncomment the following lines for electron-phonon and Eliashberg calculations !ngridk ! 28 28 28 !tasks ! 1 : ground-state run ! 210 : phonon DOS ! 220 : phonon dispersion ! 240 : electron-phonon matrix elements ! 245 : phonon line-widths ! 250 : Eliashberg function, alpha^2F ! 260 : solving the Eliashberg equations ! number of temperature steps for Eliashberg calculation ntemp 80 ! use Broyden mixing mixtype 3 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 ! we use the LDA equilibrium lattice constant scale 3.7653 sppath '../../../species/' atoms 1 : nspecies 'Al.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 plot1d 4 200 : nvp1d, npp1d 0.0 0.0 0.0 : vlvp1d 0.5 0.5 0.0 1.0 0.0 0.0 0.5 0.0 0.0 elk-7.2.42/examples/phonons-superconductivity/PaxHeaders.21776/Nb-supercell0000644000000000000000000000013214061636520023510 xustar0030 mtime=1623670096.358101152 30 atime=1623670096.357101153 30 ctime=1623670096.358101152 elk-7.2.42/examples/phonons-superconductivity/Nb-supercell/0000755002504400250440000000000014061636520025622 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/phonons-superconductivity/Nb-supercell/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520024670 xustar0030 mtime=1623670096.359101152 30 atime=1623670096.358101152 30 ctime=1623670096.359101152 elk-7.2.42/examples/phonons-superconductivity/Nb-supercell/elk.in0000644002504400250440000000700514061636520026727 0ustar00dewhurstdewhurst00000000000000 ! Example of how to determine the electron-phonon coupling parameters and ! superconducting transition temperature T_c. ! Note that these calculations are very time-consuming and require many ! computers sharing a common directory to run efficiently. It is also important ! to make sure the results are converged with respect to the various input ! parameters and err on the side of caution. Electron-phonon coupling is still ! an experimental feature at this stage. ! Follow the steps below for niobium on a 4x4x4 q-point grid. This is a time- ! consuming example, so the main results are included in this directory. avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 ! LDA equilibrium lattice parameter scale 3.071 sppath '../../../species/' atoms 1 : nspecies 'Nb.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 ! use efficient Broyden mixing mixtype 3 ! larger smearing width required swidth 0.005 stype 1 !--------------------------------------------------------------------------! ! Step 1: Compute the dynamical matrices and potential derivatives ! !--------------------------------------------------------------------------! ! This step should be run on as many computers as possible which share the same ! directory on a networked file system - just keep submitting jobs to the queue ! from the same directory. As usual, each job can be individually parallel ! using OpenMP. ! The code works by determining which DYN_Qqqqq_qqqq_qqqq_Sss_Aaa_Pp.OUT files ! need to be calculated. These files contain a single row of a dynamical matrix. ! If a calculation fails to complete, just delete that particular DYN file and ! re-run the code. All the DYN files must be calculated before proceeding to the ! next step. tasks 200 ! the q-point grid ngridq 4 4 4 ! add extra local-orbitals for accurate electron-phonon coupling nxlo 1 ! larger cut-off required rgkmax 8.0 ! this is an important parameter which fixes the k-point density irrespective ! of the size of the phonon supercell radkpt 40.0 !-----------------------------------------------------------------------! ! Step 2: Phonon dispersion curves and electron-phonon coupling ! !-----------------------------------------------------------------------! ! This should be run on one computer. You can plot the dispersion curves in the ! file PHDISP.OUT along with lines corresponding to high symmetry points stored ! in PHDLINES.OUT. The phonon linewidths along the same directions are in the ! file PHLWIDTH.OUT (PHLWLINES.OUT). The electron-phonon coupling parameter, ! lambda, and the estimated T_c is stored in MCMILLAN.OUT. You can also plot the ! Eliashberg function in ALPHA2F.OUT. Compare with the results of Bauer et al. ! in PRB 57, 11276 (1998). ! Uncomment the tasks below and run. !tasks ! 0 ! ground-state run ! 220 ! plot the phonon dispersion ! 240 ! generate the q-dependent phonon linewidths and coupling constants ! 245 ! plot the phonon linewidths ! 250 ! Eliashberg function, coupling constant, and superconducting T_c ! fine k-point grid required for accurate electron-phonon coupling; it should ! also be commensurate with the q-point grid ngridk 32 32 32 ! vertex location lines for the dispersion curves and phonon linewidths plot1d 9 400 0.5 0.5 0.5 0.25 0.25 0.25 0.0 0.0 0.0 -0.5 0.5 0.5 -0.5 0.5 0.0 -0.75 0.25 0.25 -0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.5 0.0 elk-7.2.42/examples/phonons-superconductivity/PaxHeaders.21776/Al-supercell0000644000000000000000000000013014061636520023503 xustar0029 mtime=1623670096.36110115 30 atime=1623670096.360101151 29 ctime=1623670096.36110115 elk-7.2.42/examples/phonons-superconductivity/Al-supercell/0000755002504400250440000000000014061636520025617 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/phonons-superconductivity/Al-supercell/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520024665 xustar0030 mtime=1623670096.362101149 30 atime=1623670096.362101149 30 ctime=1623670096.362101149 elk-7.2.42/examples/phonons-superconductivity/Al-supercell/elk.in0000644002504400250440000000354714061636520026733 0ustar00dewhurstdewhurst00000000000000 ! Phonon spectrum and solving the Eliashberg equations to find the temperature- ! dependent superconducting gap. This example uses finite displacements and a ! supercell to determine the phonon modes. ! You can submit the same phonon job (task=200) on as many machines as you like, ! but they must be be able to see the same directory. Each machine will compute ! a row of a particular dynamical matrix. The code assembles all the pieces to ! construct the dynamical and electron-phonon coupling matrices throughout the ! Brillouin zone. ! Example by Antonio Sanna. tasks 200 ! phonon q-point grid ngridq 4 4 4 ! add extra local-orbitals for accurate electron-phonon coupling nxlo 1 swidth 0.005 stype 1 ! uncomment the following lines for electron-phonon and Eliashberg calculations !tasks ! 0 : ground-state run ! 210 : phonon DOS ! 220 : phonon dispersion ! 240 : electron-phonon matrix elements ! 245 : phonon line-widths ! 250 : Eliashberg function, alpha^2F ! 260 : solving the Eliashberg equations ! number of temperature steps for Eliashberg calculation ntemp 80 ! k-point grid density is determined by the radius radkpt ! (only used for the phonon calculation) radkpt 40.0 ! fine k-point mesh required for the electron-phonon coupling (must be ! commensurate with q-point mesh) ngridk 24 24 24 ! use Broyden mixing mixtype 3 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 ! we use the LDA equilibrium lattice constant scale 3.7653 sppath '../../../species/' atoms 1 : nspecies 'Al.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 plot1d 4 200 : nvp1d, npp1d 0.0 0.0 0.0 : vlvp1d 0.5 0.5 0.0 1.0 0.0 0.0 0.5 0.0 0.0 elk-7.2.42/examples/phonons-superconductivity/PaxHeaders.21776/Ni-supercell0000644000000000000000000000013214061636520023517 xustar0030 mtime=1623670096.367101144 30 atime=1623670096.363101148 30 ctime=1623670096.367101144 elk-7.2.42/examples/phonons-superconductivity/Ni-supercell/0000755002504400250440000000000014061636520025631 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/phonons-superconductivity/Ni-supercell/PaxHeaders.21776/PHDISP.OUT0000644000000000000000000000013214061636520025154 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elk-7.2.42/examples/phonons-superconductivity/Ni-supercell/PaxHeaders.21776/PHDLINES.OUT0000644000000000000000000000013214061636520025373 xustar0030 mtime=1623670096.366101145 30 atime=1623670096.366101145 30 ctime=1623670096.366101145 elk-7.2.42/examples/phonons-superconductivity/Ni-supercell/PHDLINES.OUT0000644002504400250440000000062014061636520027426 0ustar00dewhurstdewhurst00000000000000 0.000000000 -0.9092470720E-03 0.000000000 0.1818494042E-02 0.9434212173 -0.9092470720E-03 0.9434212173 0.1818494042E-02 1.886842435 -0.9092470720E-03 1.886842435 0.1818494042E-02 3.221041515 -0.9092470720E-03 3.221041515 0.1818494042E-02 4.038068256 -0.9092470720E-03 4.038068256 0.1818494042E-02 elk-7.2.42/examples/phonons-superconductivity/Ni-supercell/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520024677 xustar0030 mtime=1623670096.368101143 30 atime=1623670096.368101143 30 ctime=1623670096.368101143 elk-7.2.42/examples/phonons-superconductivity/Ni-supercell/elk.in0000644002504400250440000000202014061636520026726 0ustar00dewhurstdewhurst00000000000000 ! Ferromagnetic nickel phonon example. Note that 'task=200' can be run on as ! many computers as you like, but within the same network file system (NFS) ! directory. Once all the DYN_Qqqqq_qqqq_qqqq_Sss_Aaa_Pp.OUT files are ! generated, run 'task=220' to generate the phonon dispersion and compare to ! arXiv:cond-mat/0609352v1. A previously calculated dispersion has been included ! in this directory. tasks 200 rgkmax 8.2 lmaxapw 8 beta0 0.01 ! this variable determines the density of k-points for the phonon calculation radkpt 50.0 ngridq 4 4 4 epspot 5.e-7 nempty 8 spinpol .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt plot1d 5 400 0.0 0.0 0.0 0.5 0.5 0.0 0.5 0.0 -0.5 0.0 0.0 0.0 0.5 0.0 0.0 elk-7.2.42/examples/phonons-superconductivity/PaxHeaders.21776/MgB2-DFPT0000644000000000000000000000013214061636520022437 xustar0030 mtime=1623670096.388101125 30 atime=1623670096.369101142 30 ctime=1623670096.388101125 elk-7.2.42/examples/phonons-superconductivity/MgB2-DFPT/0000755002504400250440000000000014061636520024551 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0.000000000 0.3777154501E-02 0.000000000 0.3785670324E-02 0.000000000 0.3794186147E-02 0.000000000 0.3802701970E-02 0.000000000 0.3811217793E-02 0.000000000 0.3819733616E-02 0.000000000 0.3828249439E-02 0.000000000 0.3836765262E-02 0.000000000 0.3845281084E-02 0.000000000 0.3853796907E-02 0.000000000 0.3862312730E-02 0.000000000 elk-7.2.42/examples/phonons-superconductivity/MgB2-DFPT/PaxHeaders.21776/MCMILLAN.OUT0000644000000000000000000000012714061636520024305 xustar0029 mtime=1623670096.37210114 29 atime=1623670096.37210114 29 ctime=1623670096.37210114 elk-7.2.42/examples/phonons-superconductivity/MgB2-DFPT/MCMILLAN.OUT0000644002504400250440000000052614061636520026341 0ustar00dewhurstdewhurst00000000000000 Electron-phonon coupling constant, λ : 0.7517516009 Logarithmic average frequency : 0.2228044595E-02 RMS average frequency : 0.2443047380E-02 Coulomb pseudopotential, μ* : 0.1500000000 McMillan-Allen-Dynes superconducting critical temperature [Eq. 34, Phys. Rev. B 12, 905 (1975)] (kelvin) : 19.67328712 elk-7.2.42/examples/phonons-superconductivity/MgB2-DFPT/PaxHeaders.21776/PHDISP.OUT0000644000000000000000000000013214061636520024074 xustar0030 mtime=1623670096.377101135 30 atime=1623670096.373101139 30 ctime=1623670096.377101135 elk-7.2.42/examples/phonons-superconductivity/MgB2-DFPT/PHDISP.OUT0000644002504400250440000121233214061636520026135 0ustar00dewhurstdewhurst00000000000000 0.000000000 -0.1061101723E-09 0.2347351854E-02 0.2982571869E-05 0.4694703708E-02 0.5978634816E-05 0.7042055561E-02 0.9001551456E-05 0.9389407415E-02 0.1206443158E-04 0.1173675927E-01 0.1518001570E-04 0.1408411112E-01 0.1836056976E-04 0.1643146298E-01 0.2161779360E-04 0.1877881483E-01 0.2496274484E-04 0.2112616668E-01 0.2840577914E-04 0.2347351854E-01 0.3195650673E-04 0.2582087039E-01 0.3562376471E-04 0.2816822225E-01 0.3941560370E-04 0.3051557410E-01 0.4333928745E-04 0.3286292595E-01 0.4740130332E-04 0.3521027781E-01 0.5160738186E-04 0.3755762966E-01 0.5596252345E-04 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xustar0030 mtime=1623670096.387101126 30 atime=1623670096.387101126 30 ctime=1623670096.387101126 elk-7.2.42/examples/phonons-superconductivity/MgB2-DFPT/PHLWLINES.OUT0000644002504400250440000000057414061636520026515 0ustar00dewhurstdewhurst00000000000000 0.000000000 -0.6444628166E-03 0.000000000 0.1288925633E-02 0.6220482413 -0.6444628166E-03 0.6220482413 0.1288925633E-02 1.093801350 -0.6444628166E-03 1.093801350 0.1288925633E-02 1.874502964 -0.6444628166E-03 1.874502964 0.1288925633E-02 2.346256073 -0.6444628166E-03 2.346256073 0.1288925633E-02 elk-7.2.42/examples/phonons-superconductivity/MgB2-DFPT/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023617 xustar0030 mtime=1623670096.389101124 30 atime=1623670096.389101124 30 ctime=1623670096.389101124 elk-7.2.42/examples/phonons-superconductivity/MgB2-DFPT/elk.in0000644002504400250440000000304014061636520025651 0ustar00dewhurstdewhurst00000000000000 ! This example generates a phonon dispersion for the superconductor MgB2 using ! density functional perturbation theory (DFPT). The superconducting critical ! temperature is also computed using McMillan's formula and by solving the ! Eliashberg equations. tasks 0 : ground state run 205 : compute the dynamical matrices ! number of phonon q-points ngridq 4 4 4 ! the k-point grid has to be commensurate with the q-point grid ngridk 8 8 8 ! larger smearing width required for stable phonon dispersion swidth 0.005 stype 1 ! increase the number of muffin-tin points (for accurate gradients) nrmtscf 2 ! after all the dynamical matrix DYN---.OUT files have been calculated then ! uncomment the following lines and run again !ngridk ! 24 24 24 !tasks ! 1 : ground state with larger k-point set ! 210 : phonon DOS ! 220 : plot the phonon dispersion ! 240 : electron-phonon matrix elements ! 245 : phonon line-widths ! 250 : Eliashberg function, alpha^2F plot1d 5 1000 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.5 avec 5.83170 0.000000000 0.0000 -2.91585 5.050400347 0.0000 0.00000 0.000000000 6.6594 sppath '../../../species/' atoms 2 : nspecies 'Mg.in' : spfname 1 : natoms; atposl below 0.00000000 0.00000000 0.00000000 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0.3579879699E-03 0.000000000 0.3587968992E-03 0.000000000 0.3596058284E-03 0.000000000 0.3604147577E-03 0.000000000 0.3612236870E-03 0.000000000 0.3620326162E-03 0.000000000 0.3628415455E-03 0.000000000 0.3636504748E-03 0.000000000 0.3644594040E-03 0.000000000 0.3652683333E-03 0.000000000 0.3660772626E-03 0.000000000 0.3668861918E-03 0.000000000 elk-7.2.42/examples/phonons-superconductivity/Pb-DFPT/PaxHeaders.21776/MCMILLAN.OUT0000644000000000000000000000012714061636520024117 xustar0029 mtime=1623670096.39310112 29 atime=1623670096.39310112 29 ctime=1623670096.39310112 elk-7.2.42/examples/phonons-superconductivity/Pb-DFPT/MCMILLAN.OUT0000644002504400250440000000053214061636520026150 0ustar00dewhurstdewhurst00000000000000 Electron-phonon coupling constant, lambda : 1.300391767 Logarithmic average frequency : 0.1973053899E-03 RMS average frequency : 0.2216534818E-03 Coulomb pseudopotential, mu* : 0.1500000000 McMillan-Allen-Dynes superconducting critical temperature [Eq. 34, Phys. Rev. B 12, 905 (1975)] (kelvin) : 5.458024982 elk-7.2.42/examples/phonons-superconductivity/Pb-DFPT/PaxHeaders.21776/PHDISP.OUT0000644000000000000000000000013214061636520023706 xustar0030 mtime=1623670096.395101118 30 atime=1623670096.394101119 30 ctime=1623670096.395101118 elk-7.2.42/examples/phonons-superconductivity/Pb-DFPT/PHDISP.OUT0000644002504400250440000005331214061636520025747 0ustar00dewhurstdewhurst00000000000000 0.000000000 0.4369966343E-10 0.1815415904E-01 0.1235050197E-04 0.3630831809E-01 0.2452237058E-04 0.5446247713E-01 0.3634506762E-04 0.7261663618E-01 0.4766399921E-04 0.9077079522E-01 0.5834786129E-04 0.1089249543 0.6829519893E-04 0.1270791133 0.7743985703E-04 0.1452332724 0.8575494396E-04 0.1633874314 0.9325486435E-04 0.1815415904 0.9999491923E-04 0.1996957495 0.1060679597E-03 0.2178499085 0.1115976761E-03 0.2360040676 0.1167283845E-03 0.2541582266 0.1216116868E-03 0.2723123857 0.1263911062E-03 0.2904665447 0.1311865587E-03 0.3086207037 0.1360810123E-03 0.3267748628 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0.5247272973E-06 0.9457229453 0.5039732049E-06 0.9639908826 0.4802718441E-06 0.9822588200 0.4766169574E-06 1.000526757 0.5065564807E-06 1.018794695 0.5375564138E-06 1.037062632 0.5718033898E-06 1.055330570 0.6106559975E-06 1.073598507 0.6538361053E-06 1.091866444 0.6990001045E-06 1.110134382 0.7418432493E-06 1.128402319 0.7768364671E-06 1.146670256 0.7985205436E-06 1.164938194 0.8030201304E-06 1.183206131 0.7892487674E-06 1.201474069 0.7593210322E-06 1.219742006 0.7179935776E-06 1.238009943 0.6713655992E-06 1.256277881 0.6253458849E-06 1.274545818 0.5843937778E-06 1.292813755 0.5508099053E-06 1.311081693 0.5245753231E-06 1.329349630 0.5035921850E-06 1.347617568 0.4842053389E-06 1.365885505 0.4619763698E-06 1.384153442 0.4326954929E-06 1.402421380 0.3934997563E-06 1.420689317 0.3438022988E-06 1.438957254 0.2856770052E-06 1.457225192 0.2234780153E-06 1.475493129 0.1627611427E-06 1.493761067 0.1088623384E-06 1.512029004 0.6561971002E-07 1.530296941 0.3463897826E-07 1.548564879 0.1526079753E-07 1.566832816 0.5126519426E-08 1.585100753 0.1074924417E-08 1.603368691 0.7787725621E-10 1.621636628 0.5290416243E-12 1.639815148 0.6522583335E-10 1.657993667 0.8935857227E-09 1.676172187 0.4289662910E-08 1.694350707 0.1294480580E-07 1.712529226 0.3001080994E-07 1.730707746 0.5858816636E-07 1.748886266 0.1012005956E-06 1.767064785 0.1593288612E-06 1.785243305 0.2330685469E-06 1.803421824 0.3209593167E-06 1.821600344 0.4200096692E-06 1.839778864 0.5259147140E-06 1.857957383 0.6334388010E-06 1.876135903 0.7369134939E-06 1.894314422 0.8307872913E-06 1.912492942 0.9101584541E-06 1.930671462 0.9712267579E-06 1.948849981 0.1011613028E-05 1.967028501 0.1030514805E-05 1.985207021 0.1028689414E-05 2.003385540 0.1008278685E-05 2.021564060 0.9725092402E-06 2.039742579 0.9253159754E-06 2.057921099 0.8709423764E-06 2.076099619 0.8135691100E-06 2.094278138 0.7570127379E-06 2.112456658 0.7045212418E-06 2.130635178 0.6586750351E-06 2.148813697 0.6213842627E-06 2.166992217 0.5939583686E-06 2.185170736 0.5772144346E-06 2.203349256 0.5715880252E-06 2.221527776 0.5700686257E-06 2.239706295 0.5656657315E-06 2.257884815 0.5588344154E-06 2.276063335 0.5502989175E-06 2.294241854 0.5410077067E-06 2.312420374 0.5320822337E-06 2.330598893 0.5247687209E-06 2.348777413 0.5204022703E-06 2.366955933 0.5203912784E-06 2.385134452 0.5262280593E-06 2.403312972 0.5395292106E-06 2.421491492 0.5621070387E-06 2.439670011 0.5960710364E-06 2.457848531 0.6439540473E-06 2.476027050 0.7088462326E-06 2.494205570 0.7944929300E-06 2.512384090 0.9052658700E-06 2.530562609 0.1045874423E-05 2.548741129 0.1220715417E-05 2.566919649 0.1432925238E-05 2.585098168 0.1683401129E-05 2.603276688 0.1970089313E-05 2.621455207 0.2287670477E-05 2.639633727 0.2627611773E-05 2.657812247 0.2978517500E-05 2.675990766 0.3326736623E-05 2.694169286 0.3657196726E-05 2.712347805 0.3954417260E-05 2.730526325 0.4203627303E-05 2.748704845 0.4391890268E-05 2.766883364 0.4509127679E-05 2.785061884 0.4548938379E-05 2.802738302 0.4477792022E-05 2.820414720 0.4272005885E-05 2.838091138 0.3953165560E-05 2.855767556 0.3553005403E-05 2.873443974 0.3108121168E-05 2.891120392 0.2654391319E-05 2.908796810 0.2222280582E-05 2.926473228 0.1833851822E-05 2.944149646 0.1501785929E-05 2.961826064 0.1230179116E-05 2.979502482 0.1016510934E-05 2.997178900 0.8540431890E-06 3.014855318 0.7340164692E-06 3.032531736 0.6472740214E-06 3.050208154 0.5852401154E-06 3.067884572 0.5404005782E-06 3.085560990 0.5065173666E-06 3.103237408 0.4787635053E-06 3.120913826 0.4538486565E-06 3.138505173 0.4555160690E-06 3.156096520 0.4603639162E-06 3.173687868 0.4679691788E-06 3.191279215 0.4777368804E-06 3.208870562 0.4890051874E-06 3.226461909 0.5011250282E-06 3.244053256 0.5135068877E-06 3.261644603 0.5256428403E-06 3.279235950 0.5371143052E-06 3.296827297 0.5475928236E-06 3.314418644 0.5568376104E-06 3.332009992 0.5646913647E-06 3.349601339 0.5710747351E-06 3.367192686 0.5759794649E-06 3.384784033 0.5794602198E-06 3.402375380 0.5816252119E-06 3.419966727 0.5826258688E-06 3.437558074 0.5826458977E-06 3.455149421 0.5818901534E-06 3.472740768 0.5805737235E-06 3.490332115 0.5789116099E-06 3.507923463 0.5771093161E-06 3.525514810 0.5753545674E-06 3.543106157 0.5738103016E-06 3.560697504 0.5726089918E-06 3.578288851 0.5718482999E-06 3.595880198 0.5715880252E-06 elk-7.2.42/examples/phonons-superconductivity/Pb-DFPT/PaxHeaders.21776/PHLWLINES.OUT0000644000000000000000000000013214061636520024264 xustar0030 mtime=1623670096.402101112 30 atime=1623670096.402101112 30 ctime=1623670096.402101112 elk-7.2.42/examples/phonons-superconductivity/Pb-DFPT/PHLWLINES.OUT0000644002504400250440000000106014061636520026316 0ustar00dewhurstdewhurst00000000000000 0.000000000 -0.3411702858E-05 0.000000000 0.6823407304E-05 0.6717038846 -0.3411702858E-05 0.6717038846 0.6823407304E-05 1.621636628 -0.3411702858E-05 1.621636628 0.6823407304E-05 2.203349256 -0.3411702858E-05 2.203349256 0.6823407304E-05 2.785061884 -0.3411702858E-05 2.785061884 0.6823407304E-05 3.120913826 -0.3411702858E-05 3.120913826 0.6823407304E-05 3.595880198 -0.3411702858E-05 3.595880198 0.6823407304E-05 elk-7.2.42/examples/phonons-superconductivity/Pb-DFPT/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023431 xustar0030 mtime=1623670096.403101111 30 atime=1623670096.403101111 30 ctime=1623670096.403101111 elk-7.2.42/examples/phonons-superconductivity/Pb-DFPT/elk.in0000644002504400250440000000232114061636520025464 0ustar00dewhurstdewhurst00000000000000 ! Calculation of electron-phonon coupling and superconductivity in lead using ! density functional perturbation theory (DFPT). tasks 0 : ground-state run 205 : dynamical matrices and density derivatives with DFPT ngridq 4 4 4 ! large number of muffin-tin points required for accurate derivatives nrmtscf 3 ! large cut-off required for lead rgkmax 8.0 ! add extra local-orbitals for accurate electron-phonon coupling nxlo 2 ngridk 12 12 12 ! larger smearing width required for stable phonon dispersion swidth 0.005 stype 1 ! Uncomment the following lines and run to determine the electron-phonon ! coupling and superconducting T_c. !ngridk ! 24 24 24 !tasks ! 1 ! 210 ! 220 ! 240 ! 245 ! 250 avec 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 scale 9.3541 sppath '../../../species/' atoms 1 : nspecies 'Pb.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 plot1d 7 200 : nvp1d, npp1d 0.0 0.0 1.0 : vlvp1d 0.5 0.5 1.0 0.0 0.0 0.0 0.5 0.0 0.0 0.5 0.5 0.0 0.5 0.25 -0.25 0.5 0.0 0.0 elk-7.2.42/examples/PaxHeaders.21776/ultra-long-range0000644000000000000000000000013214061636520017046 xustar0030 mtime=1623670096.406101108 30 atime=1623670096.405101109 30 ctime=1623670096.406101108 elk-7.2.42/examples/ultra-long-range/0000755002504400250440000000000014061636520021160 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ultra-long-range/PaxHeaders.21776/Cr-SDW0000644000000000000000000000013214061636520020045 xustar0030 mtime=1623670096.407101107 30 atime=1623670096.406101108 30 ctime=1623670096.407101107 elk-7.2.42/examples/ultra-long-range/Cr-SDW/0000755002504400250440000000000014061636520022157 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/ultra-long-range/Cr-SDW/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021225 xustar0030 mtime=1623670096.407101107 30 atime=1623670096.407101107 30 ctime=1623670096.407101107 elk-7.2.42/examples/ultra-long-range/Cr-SDW/elk.in0000644002504400250440000000347314061636520023271 0ustar00dewhurstdewhurst00000000000000 ! Ultracell simulation of the spin density wave in bcc Cr. ! See: T. Muller, S. Sharma, E. K. U. Gross, and J. K. Dewhurst, ! Phys. Rev. Lett. 125, 256402 (2020) or arXiv:2008.12573 ! First run a ground state calculation with a single unit cell while keeping ! the moments in each muffin-tin fixed to zero. tasks 0 ngridk 6 6 6 mixtype 1 beta0 0.01 ! Now uncomment the following lines and run the ultracell calculation. !tasks ! 700 ! ultracell ground-state calculation ! 771 ! 1D magnetisation density plot ! !beta0 ! 0.001 ! very small mixing parameter required for ultra long-range calculations ! !ngridk ! 1 6 6 ! reduce k-points to prevent kappa-point overlap maxthd1 -4 nxlo 1 lorbcnd .true. nempty 10 tplotq0 .false. plot1d 2 10000 0.0 0.0 0.0 21.0 0.0 0.0 taufsm 0.001 ! start with a random magnetic field in the ultracell rndbfcu 1.0 ! reduce the magnetic field at each step reducebf 0.85 ! Fix the moment in each muffin-tin to zero. This is done for both the unit cell ! and the Q=0 term of the ultracell. fsmtype 2 mommtfix 1 1 0.0 0.0 0.0 1 2 0.0 0.0 0.0 maxscl 2000 epspot 1.e-8 ! switch on spin-orbit coupling spinorb .true. ! keep the magnetisation collinear along the z-axis cmagz .true. avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 scale 5.4897 ! ultracell lattice parameters avecu 21.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 scaleu 5.4897 ! ultracell Q-point grid (see article for description). ngridq 21 1 1 sppath '../../../species/' ! single antiferromagnetic unit cell atoms 1 : nspecies 'Cr.in' : spfname 2 : natoms 0.0 0.0 0.0 0.0 0.0 0.01 : atposl, bfcmt 0.5 0.5 0.5 0.0 0.0 -0.01 elk-7.2.42/examples/PaxHeaders.21776/Wannier900000644000000000000000000000013214061636520015444 xustar0030 mtime=1623670096.412101102 30 atime=1623670096.408101106 30 ctime=1623670096.412101102 elk-7.2.42/examples/Wannier90/0000755002504400250440000000000014061636520017556 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Wannier90/PaxHeaders.21776/Ge0000644000000000000000000000013214061636520015777 xustar0030 mtime=1623670096.410101104 30 atime=1623670096.409101105 30 ctime=1623670096.410101104 elk-7.2.42/examples/Wannier90/Ge/0000755002504400250440000000000014061636520020111 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Wannier90/Ge/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017157 xustar0030 mtime=1623670096.411101103 30 atime=1623670096.411101103 30 ctime=1623670096.411101103 elk-7.2.42/examples/Wannier90/Ge/elk.in0000644002504400250440000000203414061636520021213 0ustar00dewhurstdewhurst00000000000000 ! Interpolation of the Ge band structure using Wannier90. tasks 0 20 550 highq .true. ngridk 4 4 4 plot1d 6 200 : nvp1d, npp1d 0.25 0.75 0.5 : vlvp1d 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.5 0.25 0.75 0.5 0.375 0.75 0.375 ! bands to be used for the Wannier functions idxw90 1-25 ! extra lines to be included in the .win file xlwin bands_plot = true kpath = true kpath_task = bands kpath_num_points = 500 begin kpoint_path W 0.25 0.75 0.5 L 0.5 0.5 0.5 L 0.5 0.5 0.5 G 0.0 0.0 0.0 G 0.0 0.0 0.0 X 0.0 0.5 0.5 X 0.0 0.5 0.5 W 0.25 0.75 0.5 W 0.25 0.75 0.5 K 0.375 0.75 0.375 end kpoint_path avec 5.3460 5.3460 0.0000 5.3460 0.0000 5.3460 0.0000 5.3460 5.3460 sppath '../../../species/' atoms 1 : nspecies 'Ge.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 elk-7.2.42/examples/Wannier90/PaxHeaders.21776/Si-Hartree-Fock0000644000000000000000000000013214061636520020267 xustar0030 mtime=1623670096.413101101 30 atime=1623670096.412101102 30 ctime=1623670096.413101101 elk-7.2.42/examples/Wannier90/Si-Hartree-Fock/0000755002504400250440000000000014061636520022401 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Wannier90/Si-Hartree-Fock/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021447 xustar0030 mtime=1623670096.414101101 30 atime=1623670096.414101101 30 ctime=1623670096.414101101 elk-7.2.42/examples/Wannier90/Si-Hartree-Fock/elk.in0000644002504400250440000000230414061636520023503 0ustar00dewhurstdewhurst00000000000000 ! Interpolation of the Si Hartree-Fock band structure using Wannier90. tasks 0 : LDA ground state 20 : LDA band structure 5 : Hartree-Fock calculation 550 : Wannier90 interpolated band structure ! large number of empty states nempty 10 ngridk 4 4 4 plot1d 6 200 : nvp1d, npp1d 0.25 0.75 0.5 : vlvp1d 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.5 0.25 0.75 0.5 0.375 0.75 0.375 ! bands to be used for the Wannier functions idxw90 1-16 ! extra lines to be included in the .win file xlwin bands_plot = true kpath = true kpath_task = bands kpath_num_points = 500 begin kpoint_path W 0.25 0.75 0.5 L 0.5 0.5 0.5 L 0.5 0.5 0.5 G 0.0 0.0 0.0 G 0.0 0.0 0.0 X 0.0 0.5 0.5 X 0.0 0.5 0.5 W 0.25 0.75 0.5 W 0.25 0.75 0.5 K 0.375 0.75 0.375 end kpoint_path avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 elk-7.2.42/examples/PaxHeaders.21776/Born-effective-charge0000644000000000000000000000013014061636520017753 xustar0030 mtime=1623670096.416101099 28 atime=1623670096.4151011 30 ctime=1623670096.416101099 elk-7.2.42/examples/Born-effective-charge/0000755002504400250440000000000014061636520022067 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Born-effective-charge/PaxHeaders.21776/GaAs0000644000000000000000000000013214061636520020570 xustar0030 mtime=1623670096.417101098 30 atime=1623670096.416101099 30 ctime=1623670096.417101098 elk-7.2.42/examples/Born-effective-charge/GaAs/0000755002504400250440000000000014061636520022702 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Born-effective-charge/GaAs/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021750 xustar0030 mtime=1623670096.417101098 30 atime=1623670096.417101098 30 ctime=1623670096.417101098 elk-7.2.42/examples/Born-effective-charge/GaAs/elk.in0000644002504400250440000000110714061636520024004 0ustar00dewhurstdewhurst00000000000000 ! Calculation of the Born effective charges for GaAs using the method of ! R. D. King-Smith and David Vanderbilt, Phys. Rev. B 47, 1651(R) (1993). tasks 208 deltaph 0.01 ngridk 4 4 4 ! number of k-point subdivisions for the phase sum along k‖ nkspolar 8 avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 10.6826 sppath '../../../species/' atoms 2 : nspecies 'Ga.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'As.in' 1 0.25 0.25 0.25 elk-7.2.42/examples/PaxHeaders.21776/Delta-value0000644000000000000000000000013214061636520016033 xustar0030 mtime=1623670096.422101093 30 atime=1623670096.418101097 30 ctime=1623670096.422101093 elk-7.2.42/examples/Delta-value/0000755002504400250440000000000014061636520020145 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Delta-value/PaxHeaders.21776/H0000644000000000000000000000013214061636520016222 xustar0030 mtime=1623670096.421101094 30 atime=1623670096.420101095 30 ctime=1623670096.421101094 elk-7.2.42/examples/Delta-value/H/0000755002504400250440000000000014061636520020334 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Delta-value/H/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017402 xustar0030 mtime=1623670096.421101094 30 atime=1623670096.421101094 30 ctime=1623670096.421101094 elk-7.2.42/examples/Delta-value/H/elk.in0000644002504400250440000000130314061636520021434 0ustar00dewhurstdewhurst00000000000000 ! Dense metallic hydrogen is surprisingly difficult for LAPW codes because the ! muffin-tin radii are so small. This requires that the cut-off rgkmax is also ! small to keep the matrix sizes reasonable. tasks 0 mixtype 3 xctype 20 rgkmax 5.0 autolinengy .true. gmaxvr 24.0 nxlo 3 lorbcnd .true. rmtdelta 0.0 avec 7.57324755 0.00000000 0.00000000 -3.78662378 6.55862477 0.00000000 0.00000000 0.00000000 9.45443212 sppath '../../../species/' atoms 1 'H.in' 4 0.3333333333 0.6666666667 0.17498 0.6666666667 0.3333333333 0.82502 0.6666666667 0.3333333333 0.67498 0.3333333333 0.6666666667 0.32502 ngridk 10 10 8 elk-7.2.42/examples/Delta-value/PaxHeaders.21776/Os0000644000000000000000000000013214061636520016414 xustar0030 mtime=1623670096.423101092 30 atime=1623670096.422101093 30 ctime=1623670096.423101092 elk-7.2.42/examples/Delta-value/Os/0000755002504400250440000000000014061636520020526 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/Delta-value/Os/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017574 xustar0030 mtime=1623670096.424101091 30 atime=1623670096.424101091 30 ctime=1623670096.424101091 elk-7.2.42/examples/Delta-value/Os/elk.in0000644002504400250440000000227214061636520021634 0ustar00dewhurstdewhurst00000000000000 ! Input file for a very well convered hcp osmium calculation. This is the result ! of very careful comparisons with Wien2k to determine the true GGA equilibrium ! volume and bulk modulus. With thanks to Maric Dulak. ! See: https://sourceforge.net/p/elk/discussion/897820/thread/aecdbcf1/#cb4d ! This is also part of the effort to systematically compare solid state codes, ! basis sets and potentials and encapsulate the results in a single number, the ! Delta-value. See https://molmod.ugent.be/deltacodesdft . tasks 0 mixtype 3 xctype 20 ! set very high quality options vhighq .true. ! parameters from Delta-value dataset avec 5.21365989 0.0 0.0 2.60682995 4.51516191 0.0 0.0 0.0 8.23342334 atoms 1 'Os.in' 2 0.0 0.0 0.0 0.33333333333333 0.33333333333333 0.5 ecvcut -3.5 species 76 'Os' 'osmium' 190.23 2.4 22 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 2 6 0 1 2 elk-7.2.42/examples/PaxHeaders.21776/GW0000644000000000000000000000013114061636520014204 xustar0030 mtime=1623670096.463101055 29 atime=1623670096.42510109 30 ctime=1623670096.463101055 elk-7.2.42/examples/GW/0000755002504400250440000000000014061636520016317 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/GW/PaxHeaders.21776/Si-GW-band-structure0000644000000000000000000000013214061636520020033 xustar0030 mtime=1623670096.438101078 30 atime=1623670096.426101089 30 ctime=1623670096.438101078 elk-7.2.42/examples/GW/Si-GW-band-structure/0000755002504400250440000000000014061636520022145 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/GW/Si-GW-band-structure/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520021213 xustar0030 mtime=1623670096.427101089 30 atime=1623670096.427101089 30 ctime=1623670096.427101089 elk-7.2.42/examples/GW/Si-GW-band-structure/elk.in0000644002504400250440000000205614061636520023253 0ustar00dewhurstdewhurst00000000000000 ! GW spectral function band structure of silicon. ! This is an extremely expensive calculation and requires about 3 days on 200 CPU cores. tasks 0 20 620 ! type of analytic continuation used for the self-energy actype 10 ! use LAPW nxoapwlo 1 ! 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// // node RubberSheet[1]: x = 276, y = 45, inputs = 4, label = RubberSheet // main_RubberSheet_1_out_1 = RubberSheet( main_Import_1_out_1, main_RubberSheet_1_in_2, main_RubberSheet_1_in_3, main_RubberSheet_1_in_4 ) [instance: 1, cache: 1]; // // node Colormap[1]: x = 387, y = 153, inputs = 19, label = Colormap // input[1]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 0.35833333] [0.056847545 0.16666667] } // input[2]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[3]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 0.0] [0.037634409 1.0] } // input[4]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[5]: defaulting = 0, visible = 0, type = 32, value = "Colormap_1" // input[7]: defaulting = 1, visible = 0, type = 5, value = 0.094054289 // input[8]: defaulting = 1, visible = 0, type = 5, value = 6684.0454 // input[9]: defaulting = 1, visible = 0, type = 1, value = 20 // input[12]: defaulting = 0, visible = 0, type = 16777221, value = { 0.094054289 6684.0454 } // input[17]: defaulting = 0, visible = 0, type = 5, value = 0.094054289 // input[18]: defaulting = 0, visible = 0, type = 5, value = 6684.0454 // window: position = (0.0200,0.0744), size = 0.9706x0.5844 // main_Colormap_1_out_1[cache: 2], main_Colormap_1_out_2[cache: 2] = Colormap( main_Colormap_1_in_1, main_Colormap_1_in_2, main_Colormap_1_in_3, main_Colormap_1_in_4, main_Colormap_1_in_5, main_RubberSheet_1_out_1, main_Colormap_1_in_7, main_Colormap_1_in_8, main_Colormap_1_in_9, main_Colormap_1_in_10, main_Colormap_1_in_11, main_Colormap_1_in_12, main_Colormap_1_in_13, main_Colormap_1_in_14, main_Colormap_1_in_15, main_Colormap_1_in_16, main_Colormap_1_in_17, main_Colormap_1_in_18, main_Colormap_1_in_19 ) [instance: 1, cache: 1]; // // node Color[3]: x = 142, y = 190, inputs = 5, label = Color // main_Color_3_out_1 = Color( main_RubberSheet_1_out_1, main_Colormap_1_out_1, main_Color_3_in_3, main_Color_3_in_4, main_Color_3_in_5 ) [instance: 3, cache: 1]; // // node Shade[1]: x = 320, y = 256, inputs = 8, label = Shade // input[2]: defaulting = 0, visible = 1, type = 3, value = 0 // main_Shade_1_out_1 = Shade( main_Color_3_out_1, main_Shade_1_in_2, main_Shade_1_in_3, main_Shade_1_in_4, main_Shade_1_in_5, main_Shade_1_in_6, main_Shade_1_in_7, main_Shade_1_in_8 ) [instance: 1, cache: 1]; // // node AutoCamera[1]: x = 440, y = 352, inputs = 9, label = AutoCamera // input[3]: defaulting = 0, visible = 0, type = 5, value = 3.35 // input[4]: defaulting = 0, visible = 0, type = 1, value = 2048 // input[5]: defaulting = 0, visible = 0, type = 5, value = 1.07 // main_AutoCamera_1_out_1 = AutoCamera( main_Shade_1_out_1, main_AutoCamera_1_in_2, main_AutoCamera_1_in_3, main_AutoCamera_1_in_4, main_AutoCamera_1_in_5, main_AutoCamera_1_in_6, main_AutoCamera_1_in_7, main_AutoCamera_1_in_8, main_AutoCamera_1_in_9 ) [instance: 1, cache: 1]; // // node Render[1]: x = 251, y = 352, inputs = 3, label = Render // main_Render_1_out_1 = Render( main_Shade_1_out_1, main_AutoCamera_1_out_1, main_Render_1_in_3 ) [instance: 1, cache: 1]; // // node Display[1]: x = 204, y = 461, inputs = 8, label = Display // depth: value = 24 // window: position = (0.5225,-0.8433), size = 1.2888x2.4800 // main_Display_1_out_1[cache: 2] = Display( main_Render_1_out_1, main_Display_1_in_2, main_Display_1_in_3, main_Display_1_in_4, main_Display_1_in_5, main_Display_1_in_6, main_Display_1_in_7, main_Display_1_in_8 ) [instance: 1, cache: 1]; // // node WriteImage[1]: x = 431, y = 514, inputs = 4, label = WriteImage // input[3]: defaulting = 0, visible = 1, type = 32, value = "tiff" // WriteImage( main_Render_1_out_1, main_WriteImage_1_in_2, main_WriteImage_1_in_3, main_WriteImage_1_in_4 ) [instance: 1, cache: 1]; // network: end of macro body } main_Import_1_in_1 = "plot2d.general"; main_Import_1_in_2 = NULL; main_Import_1_in_3 = NULL; main_Import_1_in_4 = NULL; main_Import_1_in_5 = NULL; main_Import_1_in_6 = NULL; main_Import_1_out_1 = NULL; main_RubberSheet_1_in_2 = NULL; main_RubberSheet_1_in_3 = NULL; main_RubberSheet_1_in_4 = NULL; main_RubberSheet_1_out_1 = NULL; main_Colormap_1_in_1 = { [0.0 0.35833333] [0.056847545 0.16666667] }; main_Colormap_1_in_2 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_1_in_3 = { [0.0 0.0] [0.037634409 1.0] }; main_Colormap_1_in_4 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_1_in_5 = "Colormap_1"; main_Colormap_1_in_7 = NULL; main_Colormap_1_in_8 = NULL; main_Colormap_1_in_9 = NULL; main_Colormap_1_in_10 = NULL; main_Colormap_1_in_11 = NULL; main_Colormap_1_in_12 = { 0.094054289 6684.0454 }; main_Colormap_1_in_13 = NULL; main_Colormap_1_in_14 = NULL; main_Colormap_1_in_15 = NULL; main_Colormap_1_in_16 = NULL; main_Colormap_1_in_17 = 0.094054289; main_Colormap_1_in_18 = 6684.0454; main_Colormap_1_in_19 = NULL; main_Colormap_1_out_1 = NULL; main_Color_3_in_3 = NULL; main_Color_3_in_4 = NULL; main_Color_3_in_5 = NULL; main_Color_3_out_1 = NULL; main_Shade_1_in_2 = 0; main_Shade_1_in_3 = NULL; main_Shade_1_in_4 = NULL; main_Shade_1_in_5 = NULL; main_Shade_1_in_6 = NULL; main_Shade_1_in_7 = NULL; main_Shade_1_in_8 = NULL; main_Shade_1_out_1 = NULL; main_AutoCamera_1_in_2 = NULL; main_AutoCamera_1_in_3 = 3.35; main_AutoCamera_1_in_4 = 2048; main_AutoCamera_1_in_5 = 1.07; main_AutoCamera_1_in_6 = NULL; main_AutoCamera_1_in_7 = NULL; main_AutoCamera_1_in_8 = NULL; main_AutoCamera_1_in_9 = NULL; main_AutoCamera_1_out_1 = NULL; main_Render_1_in_3 = NULL; main_Render_1_out_1 = NULL; main_Display_1_in_2 = NULL; main_Display_1_in_3 = "X24,,"; main_Display_1_in_4 = NULL; main_Display_1_in_5 = NULL; main_Display_1_in_6 = NULL; main_Display_1_in_7 = NULL; main_Display_1_in_8 = NULL; main_WriteImage_1_in_2 = NULL; main_WriteImage_1_in_3 = "tiff"; main_WriteImage_1_in_4 = NULL; Executive("product version 4 4 4"); $sync main(); elk-7.2.42/examples/GW/PaxHeaders.21776/sc-rho-GW0000644000000000000000000000013214061636520015713 xustar0030 mtime=1623670096.441101075 30 atime=1623670096.440101076 30 ctime=1623670096.441101075 elk-7.2.42/examples/GW/sc-rho-GW/0000755002504400250440000000000014061636520020025 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/GW/sc-rho-GW/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017073 xustar0030 mtime=1623670096.441101075 30 atime=1623670096.441101075 30 ctime=1623670096.441101075 elk-7.2.42/examples/GW/sc-rho-GW/elk.in0000644002504400250440000000171114061636520021130 0ustar00dewhurstdewhurst00000000000000 ! Self-consistent density GW example. First the density is calculated from the ! GW Green's function, then the Kohn-Sham equations are inverted to find a new ! exchange-correlation potential and Kohn-Sham orbitals. This processes is ! repeated until self-consistency is reached. tasks 0 630 ! take the screened interaction W to be diagonal twdiag .true. ! Matsubara frequency cut-off wmaxgw 30.0 ! response function G-vector cut-off gmaxrf 2.0 ! temperature of many-body system (determines Matsubara frequency spacing) tempk 1500.0 ! use LAPW nxoapwlo 1 ! adaptive linear mixing mixtype 1 ! large number of empty states required nempty 20 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 2 2 2 elk-7.2.42/examples/GW/PaxHeaders.21776/Cu0000644000000000000000000000013214061636520014554 xustar0030 mtime=1623670096.445101072 30 atime=1623670096.442101074 30 ctime=1623670096.445101072 elk-7.2.42/examples/GW/Cu/0000755002504400250440000000000014061636520016666 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/GW/Cu/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015734 xustar0030 mtime=1623670096.444101073 30 atime=1623670096.443101074 30 ctime=1623670096.444101073 elk-7.2.42/examples/GW/Cu/elk.in0000644002504400250440000000152214061636520017771 0ustar00dewhurstdewhurst00000000000000 ! GW approximation applied to copper. Note that this calculation uses more ! k-points than q-points. tasks 0 600 610 ! switch on spin-coupling spinorb .true. ! temperature of the electronic system (determines Matsubara frequency spacing) tempk 1500.0 nempty 8 ! Matsubara frequency cut-off wmaxgw 6.0 ! 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GW spectral function of silicon. tasks 0 600 610 ! use LAPW nxoapwlo 1 ! add conduction local-orbitals lorbcnd .true. ! 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Hartree-Fock ground state of the homogenous electron gas. The Wigner radius ! (r_s) is written to INFO.OUT. Note that the exact exchange energy is only ! computed during the last iteration. tasks 0 20 620 actype 10 plot1d 2 50 : nvp1d, npp1d 0.0 0.0 1.0 : vlvp1d 0.5 0.5 1.0 ! 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elk-7.2.42/examples/GW/HEG/plot2d.net0000644002504400250440000001457214061636520020647 0ustar00dewhurstdewhurst00000000000000// // time: Fri Apr 27 18:31:27 2018 // // version: 3.2.0 (format), 4.4.4 (DX) // // // MODULE main // workspace: width = 462, height = 562 // layout: snap = 0, width = 50, height = 50, align = NN // macro main( ) -> ( ) { // // node Import[1]: x = 56, y = 47, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "plot2d.general" // main_Import_1_out_1 = Import( main_Import_1_in_1, main_Import_1_in_2, main_Import_1_in_3, main_Import_1_in_4, main_Import_1_in_5, main_Import_1_in_6 ) [instance: 1, cache: 1]; // // node RubberSheet[1]: x = 276, y = 45, inputs = 4, label = RubberSheet // main_RubberSheet_1_out_1 = RubberSheet( main_Import_1_out_1, main_RubberSheet_1_in_2, main_RubberSheet_1_in_3, main_RubberSheet_1_in_4 ) [instance: 1, cache: 1]; // // node Colormap[1]: x = 388, y = 153, inputs = 19, label = Colormap // input[1]: defaulting = 0, visible = 0, type = 16777224, value = { [0.091397849 0.0] [0.18010753 0.16589862] } // input[2]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[3]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 0.0] [0.077956989 1.0] } // input[4]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[5]: defaulting = 0, visible = 0, type = 32, value = "Colormap_1" // input[7]: defaulting = 1, visible = 0, type = 5, value = 0.037809622 // input[8]: defaulting = 1, visible = 0, type = 5, value = 1896.2094 // input[9]: defaulting = 1, visible = 0, type = 1, value = 20 // input[12]: defaulting = 0, visible = 0, type = 16777221, value = { 0.037809622 1896.2094 } // input[17]: defaulting = 0, visible = 0, type = 5, value = 0.037809622 // input[18]: defaulting = 0, visible = 0, type = 5, value = 1896.2094 // window: position = (0.1088,0.0511), size = 0.8838x0.5656 // main_Colormap_1_out_1[cache: 2], main_Colormap_1_out_2[cache: 2] = Colormap( main_Colormap_1_in_1, main_Colormap_1_in_2, main_Colormap_1_in_3, main_Colormap_1_in_4, main_Colormap_1_in_5, main_RubberSheet_1_out_1, main_Colormap_1_in_7, main_Colormap_1_in_8, main_Colormap_1_in_9, main_Colormap_1_in_10, main_Colormap_1_in_11, main_Colormap_1_in_12, main_Colormap_1_in_13, main_Colormap_1_in_14, main_Colormap_1_in_15, main_Colormap_1_in_16, main_Colormap_1_in_17, main_Colormap_1_in_18, main_Colormap_1_in_19 ) [instance: 1, cache: 1]; // // node Color[3]: x = 142, y = 190, inputs = 5, label = Color // main_Color_3_out_1 = Color( main_RubberSheet_1_out_1, main_Colormap_1_out_1, main_Color_3_in_3, main_Color_3_in_4, main_Color_3_in_5 ) [instance: 3, cache: 1]; // // node Shade[1]: x = 320, y = 256, inputs = 8, label = Shade // input[2]: defaulting = 0, visible = 1, type = 3, value = 0 // main_Shade_1_out_1 = Shade( main_Color_3_out_1, main_Shade_1_in_2, main_Shade_1_in_3, main_Shade_1_in_4, main_Shade_1_in_5, main_Shade_1_in_6, main_Shade_1_in_7, main_Shade_1_in_8 ) [instance: 1, cache: 1]; // // node AutoCamera[1]: x = 356, y = 371, inputs = 9, label = AutoCamera // input[3]: defaulting = 0, visible = 0, type = 5, value = 1.0 // input[4]: defaulting = 0, visible = 0, type = 1, value = 200 // input[5]: defaulting = 0, visible = 0, type = 5, value = 3.8 // main_AutoCamera_1_out_1 = AutoCamera( main_Shade_1_out_1, main_AutoCamera_1_in_2, main_AutoCamera_1_in_3, main_AutoCamera_1_in_4, main_AutoCamera_1_in_5, main_AutoCamera_1_in_6, main_AutoCamera_1_in_7, main_AutoCamera_1_in_8, main_AutoCamera_1_in_9 ) [instance: 1, cache: 1]; // // node Render[1]: x = 217, y = 445, inputs = 3, label = Render // main_Render_1_out_1 = Render( main_Shade_1_out_1, main_AutoCamera_1_out_1, main_Render_1_in_3 ) [instance: 1, cache: 1]; // // node Display[1]: x = 373, y = 500, inputs = 8, label = Display // depth: value = 24 // window: position = (0.0063,0.0000), size = 0.1338x0.9156 // main_Display_1_out_1[cache: 2] = Display( main_Render_1_out_1, main_Display_1_in_2, main_Display_1_in_3, main_Display_1_in_4, main_Display_1_in_5, main_Display_1_in_6, main_Display_1_in_7, main_Display_1_in_8 ) [instance: 1, cache: 1]; // network: end of macro body } main_Import_1_in_1 = "plot2d.general"; main_Import_1_in_2 = NULL; main_Import_1_in_3 = NULL; main_Import_1_in_4 = NULL; main_Import_1_in_5 = NULL; main_Import_1_in_6 = NULL; main_Import_1_out_1 = NULL; main_RubberSheet_1_in_2 = NULL; main_RubberSheet_1_in_3 = NULL; main_RubberSheet_1_in_4 = NULL; main_RubberSheet_1_out_1 = NULL; main_Colormap_1_in_1 = { [0.091397849 0.0] [0.18010753 0.16589862] }; main_Colormap_1_in_2 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_1_in_3 = { [0.0 0.0] [0.077956989 1.0] }; main_Colormap_1_in_4 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_1_in_5 = "Colormap_1"; main_Colormap_1_in_7 = NULL; main_Colormap_1_in_8 = NULL; main_Colormap_1_in_9 = NULL; main_Colormap_1_in_10 = NULL; main_Colormap_1_in_11 = NULL; main_Colormap_1_in_12 = { 0.037809622 1896.2094 }; main_Colormap_1_in_13 = NULL; main_Colormap_1_in_14 = NULL; main_Colormap_1_in_15 = NULL; main_Colormap_1_in_16 = NULL; main_Colormap_1_in_17 = 0.037809622; main_Colormap_1_in_18 = 1896.2094; main_Colormap_1_in_19 = NULL; main_Colormap_1_out_1 = NULL; main_Color_3_in_3 = NULL; main_Color_3_in_4 = NULL; main_Color_3_in_5 = NULL; main_Color_3_out_1 = NULL; main_Shade_1_in_2 = 0; main_Shade_1_in_3 = NULL; main_Shade_1_in_4 = NULL; main_Shade_1_in_5 = NULL; main_Shade_1_in_6 = NULL; main_Shade_1_in_7 = NULL; main_Shade_1_in_8 = NULL; main_Shade_1_out_1 = NULL; main_AutoCamera_1_in_2 = NULL; main_AutoCamera_1_in_3 = 1.0; main_AutoCamera_1_in_4 = 200; main_AutoCamera_1_in_5 = 3.8; main_AutoCamera_1_in_6 = NULL; main_AutoCamera_1_in_7 = NULL; main_AutoCamera_1_in_8 = NULL; main_AutoCamera_1_in_9 = NULL; main_AutoCamera_1_out_1 = NULL; main_Render_1_in_3 = NULL; main_Render_1_out_1 = NULL; main_Display_1_in_2 = NULL; main_Display_1_in_3 = "X24,,"; main_Display_1_in_4 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GW band gap calculation of LiF. Plot the total spectral function TSFGW.OUT to ! find the indirect gap. tasks 0 600 610 ! G-vector cut-off of local contribution to RPA gmaxrf 3.0 ! temperature of system (determines the Matsubara frequency spacing) tempk 1500.0 nempty 8 wplot 800 100 0 : nwplot, ngrkf, nswplot -1.5 1.5 : wplot avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 ngridk 4 4 4 elk-7.2.42/examples/PaxHeaders.21776/RDMFT0000644000000000000000000000013214061636520014544 xustar0030 mtime=1623670096.469101049 30 atime=1623670096.467101051 30 ctime=1623670096.469101049 elk-7.2.42/examples/RDMFT/0000755002504400250440000000000014061636520016656 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/RDMFT/PaxHeaders.21776/NiO0000644000000000000000000000013214061636520015231 xustar0030 mtime=1623670096.472101047 30 atime=1623670096.469101049 30 ctime=1623670096.472101047 elk-7.2.42/examples/RDMFT/NiO/0000755002504400250440000000000014061636520017343 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0.5424000000 23.15583333 0.5448000000 23.98750000 0.5472000000 22.43500000 0.5496000000 18.89666667 0.5520000000 16.63333333 0.5544000000 15.11333333 0.5568000000 13.59583333 0.5592000000 12.42333333 0.5616000000 11.14750000 0.5640000000 10.05500000 0.5664000000 8.917500000 0.5688000000 7.934166667 0.5712000000 6.838333333 0.5736000000 5.934166667 0.5760000000 5.045000000 0.5784000000 4.368333333 0.5808000000 3.731666667 0.5832000000 3.260833333 0.5856000000 2.792500000 0.5880000000 2.370000000 0.5904000000 1.945833333 0.5928000000 1.700000000 0.5952000000 1.330833333 0.5976000000 1.141666667 elk-7.2.42/examples/RDMFT/NiO/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016411 xustar0030 mtime=1623670096.472101047 30 atime=1623670096.472101047 30 ctime=1623670096.472101047 elk-7.2.42/examples/RDMFT/NiO/elk.in0000644002504400250440000000150314061636520020445 0ustar00dewhurstdewhurst00000000000000 ! Reduced density matrix functional theory (RDMFT) example for NiO. tasks 0 300 10 swidth 0.001 dosocc .false. dos 500 100 0 -0.6 0.6 ! maximum number of RDMFT self-consistent loops rdmmaxscl 2 ! maximum number of iterations per self-consistent loop for determining the ! natural orbitals via steepest-descent maxitc 10 ! maximum number of iterations per self-consistent loop for determining the ! occupation numbers via steepest-descent maxitn 100 ! RDMFT exchange-correlation functional, in this case the 'power functional' rdmxctype 2 ! coefficient of the power functional rdmalpha 0.65 nempty 10 ngridk 4 4 4 vkloff 0.25 0.5 0.625 avec 1.00 1.00 0.00 1.00 0.00 1.00 0.00 1.00 1.00 scale 3.9468 sppath '../../../species/' atoms 2 'Ni.in' 1 0.0 0.0 0.0 'O.in' 1 0.5 0.5 0.5 elk-7.2.42/examples/PaxHeaders.21776/XMCD0000644000000000000000000000013214061636520014423 xustar0030 mtime=1623670096.474101045 30 atime=1623670096.473101046 30 ctime=1623670096.474101045 elk-7.2.42/examples/XMCD/0000755002504400250440000000000014061636520016535 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/XMCD/PaxHeaders.21776/Fe0000644000000000000000000000013214061636520014755 xustar0030 mtime=1623670096.477101042 30 atime=1623670096.474101045 30 ctime=1623670096.477101042 elk-7.2.42/examples/XMCD/Fe/0000755002504400250440000000000014061636520017067 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/XMCD/Fe/PaxHeaders.21776/Fe_lo.in0000644000000000000000000000013214061636520016406 xustar0030 mtime=1623670096.476101043 30 atime=1623670096.476101043 30 ctime=1623670096.476101043 elk-7.2.42/examples/XMCD/Fe/Fe_lo.in0000644002504400250440000000366014061636520020450 0ustar00dewhurstdewhurst00000000000000 'Fe_lo' : spsymb 'iron' : spname -26.0000 : spzn 101799.2074 : spmass 0.392232E-06 2.0000 35.6837 500 : sprmin, rmt, sprmax, nrmt 10 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 T 2 1 1 2.00000 F 2 1 2 4.00000 F 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 4.00000 F 3 2 3 2.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -26.0000 0 T 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -3.6844 0 T 1 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -2.4317 0 T 2 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -0.5316 0 T elk-7.2.42/examples/XMCD/Fe/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016135 xustar0030 mtime=1623670096.477101042 30 atime=1623670096.477101042 30 ctime=1623670096.477101042 elk-7.2.42/examples/XMCD/Fe/elk.in0000644002504400250440000000252014061636520020171 0ustar00dewhurstdewhurst00000000000000 ! Soft x-ray absorption spectroscopy example for bcc Fe, including XAS, XMCD, ! and XMLD. Species file Fe_lo.in has an additional local orbital at the 2p ! energy. Spin-orbit coupling has to be included for 2p 1/2 - 2p 3/2 splitting. ! XAS, XMCD, and XMLD are computed via first order optical response. Fe is ! cubic, hence the following relations hold for B || z: ! ! XAS = 1/3 * Im[ 2*eps_xx + eps_zz ] = 1/3 * Tr(Im[eps]) ! XMCD = Im[ sigma_xy ] = -2*Re[ eps_xy ] ! XMLD = Im[ eps_xx - eps_zz ] ! ! Similarly, the real parts of the epsilon and sigma tensor are related to the ! Faraday effect. A much larger number of k-points is necessary for a well ! converged spectrum. ! Example by Markus Meinert. tasks 0 120 121 wplot 400 200 0 25.0 26.5 ! compute the xx, xy, and zz components optcomp 1 1 1 2 3 3 spinpol .true. spinorb .true. ! use GGA xctype 20 ngridk 8 8 8 bfieldc 0.0 0.0 0.01 ! large number of empty states necessary for "continuum" absorption nempty 20 ! a Lorentzian broadening is applied to the spectrum swidth 0.01 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 2.708 atoms 1 : nspecies 'Fe_lo.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/examples/PaxHeaders.21776/libxc0000644000000000000000000000013014061636520014767 xustar0029 mtime=1623670096.47910104 30 atime=1623670096.478101041 29 ctime=1623670096.47910104 elk-7.2.42/examples/libxc/0000755002504400250440000000000014061636520017103 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/libxc/PaxHeaders.21776/Al0000644000000000000000000000013114061636520015324 xustar0030 mtime=1623670096.480101039 29 atime=1623670096.47910104 30 ctime=1623670096.480101039 elk-7.2.42/examples/libxc/Al/0000755002504400250440000000000014061636520017437 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/libxc/Al/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520016505 xustar0030 mtime=1623670096.481101038 30 atime=1623670096.480101039 30 ctime=1623670096.481101038 elk-7.2.42/examples/libxc/Al/elk.in0000644002504400250440000000161614061636520020546 0ustar00dewhurstdewhurst00000000000000 ! Test of libxc (http://www.tddft.org/programs/octopus/wiki/index.php/Libxc). ! The library must be downloaded and compiled separately. Follow the ! instructions in the Elk manual for installation of libxc. tasks 0 ! libxc is selected with xctype(1)=100. The remaining two numbers are the ! exchange and correlation functionals, respectively - in this case Slater ! exchange and Perdew-Wang correlation. Refer to the file ! 'elk/src/libxc_funcs.f90' for the complete list of functionals and ! associated numbers. xctype 100 1 13 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.8267 ! this is the relative path to the species files sppath '../../../species/' atoms 1 : nspecies 'Al.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 ngridk 4 4 4 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/PaxHeaders.21776/miscellaneous0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.491101029 30 atime=1623670096.481101038 30 ctime=1623670096.491101029 elk-7.2.42/examples/miscellaneous/0000755002504400250440000000000014061636520020645 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/miscellaneous/PaxHeaders.21776/GaAs-effective-mass0000644000000000000000000000013214061636520022245 xustar0030 mtime=1623670096.484101035 30 atime=1623670096.483101037 30 ctime=1623670096.484101035 elk-7.2.42/examples/miscellaneous/GaAs-effective-mass/0000755002504400250440000000000014061636520024357 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/miscellaneous/GaAs-effective-mass/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520023425 xustar0030 mtime=1623670096.484101035 30 atime=1623670096.484101035 30 ctime=1623670096.484101035 elk-7.2.42/examples/miscellaneous/GaAs-effective-mass/elk.in0000644002504400250440000000120514061636520025460 0ustar00dewhurstdewhurst00000000000000 ! Effective mass tensors of GaAs using the Perdew-Burke-Ernzerhof GGA functional. ! Try recalculating the tensors with spin-orbit coupling switched on. tasks 0 25 ! k-point at which the effective mass is to be calculated for all states vklem 0.5 0.0 0.0 xctype 20 avec 5.3435 5.3435 0.0000 5.3435 0.0000 5.3435 0.0000 5.3435 5.3435 sppath '../../../species/' atoms 2 : nspecies 'Ga.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'As.in' 1 0.25 0.25 0.25 ngridk 4 4 4 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/miscellaneous/PaxHeaders.21776/Al-STM0000644000000000000000000000013214061636520017530 xustar0030 mtime=1623670096.489101031 30 atime=1623670096.485101035 30 ctime=1623670096.489101031 elk-7.2.42/examples/miscellaneous/Al-STM/0000755002504400250440000000000014061636520021642 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/miscellaneous/Al-STM/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520020710 xustar0030 mtime=1623670096.487101033 30 atime=1623670096.487101033 30 ctime=1623670096.487101033 elk-7.2.42/examples/miscellaneous/Al-STM/elk.in0000644002504400250440000000142014061636520022742 0ustar00dewhurstdewhurst00000000000000 ! STM image of the surface of aluminium with an embedded oygen atom. Try using ! OpenDX to plot the image. tasks 0 162 ! the z-coordinate of the plotting plane is the 'height' of the STM tip plot2d 0.0 0.0 0.25 2.0 0.0 0.25 0.0 2.0 0.25 200 200 ! use small cut-off just for testing rgkmax 6.0 avec 15.0 0.0 0.0 0.0 15.0 0.0 0.0 0.0 7.5 sppath '../../../species/' atoms 2 : nspecies 'Al.in' : spfname 7 : natoms; atposl below 0.0 0.0 0.0 0.0 0.5 0.0 0.50 0.0 0.0 0.25 0.25 0.0 0.25 0.75 0.0 0.75 0.25 0.0 0.75 0.75 0.0 'O.in' 1 0.5 0.5 0.0 ngridk 1 1 1 vkloff 0.25 0.625 0.0 elk-7.2.42/examples/miscellaneous/Al-STM/PaxHeaders.21776/stm2d.general0000644000000000000000000000013214061636520022175 xustar0030 mtime=1623670096.488101032 30 atime=1623670096.488101032 30 ctime=1623670096.488101032 elk-7.2.42/examples/miscellaneous/Al-STM/stm2d.general0000644002504400250440000000027314061636520024234 0ustar00dewhurstdewhurst00000000000000file = ./STM2D.OUT grid = 200 x 200 format = ascii interleaving = field majority = column header = lines 1 field = locations, field0 structure = 2-vector, scalar type = float, float end elk-7.2.42/examples/miscellaneous/Al-STM/PaxHeaders.21776/stm2d.net0000644000000000000000000000013014061636520021344 xustar0029 mtime=1623670096.49010103 30 atime=1623670096.489101031 29 ctime=1623670096.49010103 elk-7.2.42/examples/miscellaneous/Al-STM/stm2d.net0000644002504400250440000001263514061636520023412 0ustar00dewhurstdewhurst00000000000000// // time: Sun Oct 15 18:48:57 2006 // // version: 3.2.0 (format), 4.3.2 (DX) // // // MODULE main // workspace: width = 392, height = 525 // layout: snap = 0, width = 50, height = 50, align = NN // macro main( ) -> ( ) { // // node Import[1]: x = 40, y = 40, inputs = 6, label = Import // input[1]: defaulting = 0, visible = 1, type = 32, value = "stm2d.general" // main_Import_1_out_1 = Import( main_Import_1_in_1, main_Import_1_in_2, main_Import_1_in_3, main_Import_1_in_4, main_Import_1_in_5, main_Import_1_in_6 ) [instance: 1, cache: 1]; // // node Colormap[1]: x = 245, y = 132, inputs = 19, label = Colormap // input[1]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 0.0] [1.0 0.0] } // input[2]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 0.0] [1.0 0.0] } // input[3]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 0.0] [1.0 1.0] } // input[4]: defaulting = 0, visible = 0, type = 16777224, value = { [0.0 1.0] [1.0 1.0] } // input[5]: defaulting = 0, visible = 0, type = 32, value = "Colormap_1" // input[7]: defaulting = 1, visible = 0, type = 5, value = 0.0043241107 // input[8]: defaulting = 1, visible = 0, type = 5, value = 0.045520809 // input[9]: defaulting = 1, visible = 0, type = 1, value = 20 // input[12]: defaulting = 0, visible = 0, type = 16777221, value = { 0.0043241107 0.045520809 } // input[17]: defaulting = 0, visible = 0, type = 5, value = 0.0043241107 // input[18]: defaulting = 0, visible = 0, type = 5, value = 0.045520809 // window: position = (0.0000,0.0000), size = 0.6348x0.5859 // main_Colormap_1_out_1[cache: 2], main_Colormap_1_out_2[cache: 2] = Colormap( main_Colormap_1_in_1, main_Colormap_1_in_2, main_Colormap_1_in_3, main_Colormap_1_in_4, main_Colormap_1_in_5, main_Import_1_out_1, main_Colormap_1_in_7, main_Colormap_1_in_8, main_Colormap_1_in_9, main_Colormap_1_in_10, main_Colormap_1_in_11, main_Colormap_1_in_12, main_Colormap_1_in_13, main_Colormap_1_in_14, main_Colormap_1_in_15, main_Colormap_1_in_16, main_Colormap_1_in_17, main_Colormap_1_in_18, main_Colormap_1_in_19 ) [instance: 1, cache: 1]; // // node Color[1]: x = 81, y = 206, inputs = 5, label = Color // main_Color_1_out_1 = Color( main_Import_1_out_1, main_Colormap_1_out_1, main_Color_1_in_3, main_Color_1_in_4, main_Color_1_in_5 ) [instance: 1, cache: 1]; // // node AutoCamera[1]: x = 300, y = 292, inputs = 9, label = AutoCamera // input[3]: defaulting = 0, visible = 0, type = 5, value = 35.0 // input[4]: defaulting = 0, visible = 0, type = 1, value = 512 // input[5]: defaulting = 0, visible = 0, type = 5, value = 1.0 // input[9]: defaulting = 0, visible = 0, type = 32, value = "white" // main_AutoCamera_1_out_1 = AutoCamera( main_Color_1_out_1, main_AutoCamera_1_in_2, main_AutoCamera_1_in_3, main_AutoCamera_1_in_4, main_AutoCamera_1_in_5, main_AutoCamera_1_in_6, main_AutoCamera_1_in_7, main_AutoCamera_1_in_8, main_AutoCamera_1_in_9 ) [instance: 1, cache: 1]; // // node Render[1]: x = 174, y = 347, inputs = 3, label = Render // main_Render_1_out_1 = Render( main_Color_1_out_1, main_AutoCamera_1_out_1, main_Render_1_in_3 ) [instance: 1, cache: 1]; // // node Display[1]: x = 142, y = 463, inputs = 8, label = Display // depth: value = 24 // window: position = (0.0000,0.0000), size = 0.5137x0.7214 // main_Display_1_out_1[cache: 2] = Display( main_Render_1_out_1, main_Display_1_in_2, main_Display_1_in_3, main_Display_1_in_4, main_Display_1_in_5, main_Display_1_in_6, main_Display_1_in_7, main_Display_1_in_8 ) [instance: 1, cache: 1]; // network: end of macro body } main_Import_1_in_1 = "stm2d.general"; main_Import_1_in_2 = NULL; main_Import_1_in_3 = NULL; main_Import_1_in_4 = NULL; main_Import_1_in_5 = NULL; main_Import_1_in_6 = NULL; main_Import_1_out_1 = NULL; main_Colormap_1_in_1 = { [0.0 0.0] [1.0 0.0] }; main_Colormap_1_in_2 = { [0.0 0.0] [1.0 0.0] }; main_Colormap_1_in_3 = { [0.0 0.0] [1.0 1.0] }; main_Colormap_1_in_4 = { [0.0 1.0] [1.0 1.0] }; main_Colormap_1_in_5 = "Colormap_1"; main_Colormap_1_in_7 = NULL; main_Colormap_1_in_8 = NULL; main_Colormap_1_in_9 = NULL; main_Colormap_1_in_10 = NULL; main_Colormap_1_in_11 = NULL; main_Colormap_1_in_12 = { 0.0043241107 0.045520809 }; main_Colormap_1_in_13 = NULL; main_Colormap_1_in_14 = NULL; main_Colormap_1_in_15 = NULL; main_Colormap_1_in_16 = NULL; main_Colormap_1_in_17 = 0.0043241107; main_Colormap_1_in_18 = 0.045520809; main_Colormap_1_in_19 = NULL; main_Colormap_1_out_1 = NULL; main_Color_1_in_3 = NULL; main_Color_1_in_4 = NULL; main_Color_1_in_5 = NULL; main_Color_1_out_1 = NULL; main_AutoCamera_1_in_2 = NULL; main_AutoCamera_1_in_3 = 35.0; main_AutoCamera_1_in_4 = 512; main_AutoCamera_1_in_5 = 1.0; main_AutoCamera_1_in_6 = NULL; main_AutoCamera_1_in_7 = NULL; main_AutoCamera_1_in_8 = NULL; main_AutoCamera_1_in_9 = "white"; main_AutoCamera_1_out_1 = NULL; main_Render_1_in_3 = NULL; main_Render_1_out_1 = NULL; main_Display_1_in_2 = NULL; main_Display_1_in_3 = "X24,,"; main_Display_1_in_4 = NULL; main_Display_1_in_5 = NULL; main_Display_1_in_6 = NULL; main_Display_1_in_7 = NULL; main_Display_1_in_8 = NULL; Executive("product version 4 3 2"); $sync main(); elk-7.2.42/examples/miscellaneous/PaxHeaders.21776/Al-exp[iq.r]0000644000000000000000000000013214061636520020743 xustar0030 mtime=1623670096.495101025 30 atime=1623670096.491101029 30 ctime=1623670096.495101025 elk-7.2.42/examples/miscellaneous/Al-exp[iq.r]/0000755002504400250440000000000014061636520023055 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/miscellaneous/Al-exp[iq.r]/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520022123 xustar0030 mtime=1623670096.495101025 30 atime=1623670096.495101025 30 ctime=1623670096.495101025 elk-7.2.42/examples/miscellaneous/Al-exp[iq.r]/elk.in0000644002504400250440000000114714061636520024163 0ustar00dewhurstdewhurst00000000000000 ! Computes < i,k+q | exp(iq.r) | j,k > matrix elements. The q-vector is ! stored in vecql and the outputted k-points are selected with kstlist. ! Note that q should be chosen commensurate with the k-point grid. tasks 0 130 vecql 0.0 0.0 0.125 kstlist 1 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.8267 ! this is the relative path to the species files sppath '../../../species/' atoms 1 : nspecies 'Al.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 ngridk 8 8 8 elk-7.2.42/examples/PaxHeaders.21776/structural-optimisation0000644000000000000000000000013214061636520020615 xustar0030 mtime=1623670096.505101016 30 atime=1623670096.496101024 30 ctime=1623670096.505101016 elk-7.2.42/examples/structural-optimisation/0000755002504400250440000000000014061636520022727 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/structural-optimisation/PaxHeaders.21776/Si-atom-opt0000644000000000000000000000013214061636520022726 xustar0030 mtime=1623670096.498101023 30 atime=1623670096.497101023 30 ctime=1623670096.498101023 elk-7.2.42/examples/structural-optimisation/Si-atom-opt/0000755002504400250440000000000014061636520025040 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/structural-optimisation/Si-atom-opt/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520024106 xustar0030 mtime=1623670096.499101022 30 atime=1623670096.499101022 30 ctime=1623670096.499101022 elk-7.2.42/examples/structural-optimisation/Si-atom-opt/elk.in0000644002504400250440000000107714061636520026150 0ustar00dewhurstdewhurst00000000000000 ! Silicon geometry optimisation example. The equilibrium atomic positions are ! found using tasks=2. Updated positions are written to GEOMETRY_OPT.OUT for ! each optimisation step. tasks 2 ! use Broyden mixing of the potential mixtype 3 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.27 0.27 0.27 ngridk 2 2 2 vkloff 0.5 0.5 0.5 elk-7.2.42/examples/structural-optimisation/PaxHeaders.21776/BaTiO3-lattice-opt0000644000000000000000000000013014061636520024057 xustar0029 mtime=1623670096.50110102 30 atime=1623670096.500101021 29 ctime=1623670096.50110102 elk-7.2.42/examples/structural-optimisation/BaTiO3-lattice-opt/0000755002504400250440000000000014061636520026173 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/structural-optimisation/BaTiO3-lattice-opt/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520025245 xustar0029 mtime=1623670096.50110102 29 atime=1623670096.50110102 29 ctime=1623670096.50110102 elk-7.2.42/examples/structural-optimisation/BaTiO3-lattice-opt/elk.in0000644002504400250440000000135114061636520027276 0ustar00dewhurstdewhurst00000000000000 ! Example taken from the Elk forum demonstrating the lattice optimisation of ! BaTiO3 using the PBEsol functional. With thanks to David Tompsett. ! See: http://sourceforge.net/p/elk/discussion/897820/thread/db2127bd/#24b6 tasks 2 latvopt 1 epspot 1.e-7 epsstress 1.e-3 mixtype 3 xctype 22 lmaxapw 8 rgkmax 8.0 gmaxvr 18.0 ngridk 10 10 10 avec 7.576 0.0 0.0 0.0 7.576 0.0 0.0 0.0 7.576 sppath '../../../species/' atoms 3 : nspecies 'Ba.in' : spfname 1 : natoms; atpos below 0.0 0.0 0.0 'Ti.in' 1 0.5 0.5 0.5 'O.in' 3 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 elk-7.2.42/examples/structural-optimisation/PaxHeaders.21776/Ge-lattice-opt0000644000000000000000000000013214061636520023373 xustar0030 mtime=1623670096.503101018 30 atime=1623670096.502101019 30 ctime=1623670096.503101018 elk-7.2.42/examples/structural-optimisation/Ge-lattice-opt/0000755002504400250440000000000014061636520025505 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/structural-optimisation/Ge-lattice-opt/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520024553 xustar0030 mtime=1623670096.504101017 30 atime=1623670096.504101017 30 ctime=1623670096.504101017 elk-7.2.42/examples/structural-optimisation/Ge-lattice-opt/elk.in0000644002504400250440000000265414061636520026617 0ustar00dewhurstdewhurst00000000000000 ! Unit cell optimisation for Ge with the PBE functional. This is performed with ! geometric optimisation in which the lattice vectors are changed. ! Setting 'latvopt' to 1 performs full unconstrained optimisation of the lattice ! vectors. Setting it to 2 results in an iso-volumetric optimisation. In both ! cases, the atomic positions are also optimised. To constrain the atomic ! positions, set the nuclear mass to be a negative number in the species file. ! As the calculation progresses, you can plot the files TOTENERGY_OPT.OUT and ! STRESSMAX.OUT to see the change in the total energy and stress tensor. The ! modulus of the maximum force on the atoms is written to FORCEMAX.OUT. ! The updated unit cell geometry is written to GEOMETRY_OPT.OUT. The last entry ! in this file contains the final lattice parameters and atomic positions. tasks 2 ! unconstrained optimisation of the lattice vectors latvopt 1 mixtype 3 ! switch on high-quality parameters for accurate stress tensors highq .true. ! switch off automatic determination of the k-point grid autokpt .false. ngridk 4 4 4 ! PBE exchange-correlation functional xctype 20 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 5.3451 sppath '../../../species/' atoms 1 : nspecies 'Ge.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 elk-7.2.42/examples/structural-optimisation/PaxHeaders.21776/MgB2-lattice-opt0000644000000000000000000000013214061636520023567 xustar0030 mtime=1623670096.506101015 30 atime=1623670096.505101016 30 ctime=1623670096.506101015 elk-7.2.42/examples/structural-optimisation/MgB2-lattice-opt/0000755002504400250440000000000014061636520025701 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/examples/structural-optimisation/MgB2-lattice-opt/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520024747 xustar0030 mtime=1623670096.506101015 30 atime=1623670096.506101015 30 ctime=1623670096.506101015 elk-7.2.42/examples/structural-optimisation/MgB2-lattice-opt/elk.in0000644002504400250440000000330414061636520027004 0ustar00dewhurstdewhurst00000000000000 ! Automatic determination of the c/a ratio of MgB2. This is performed with ! geometric optimisation which involves changing of the lattice vectors whilst ! maintaining the unit cell volume. ! Setting 'latvopt' to 1 performs full unconstrained optimisation of the lattice ! vectors. Setting it to 2 results in an optimisation over all strain tensors ! except isotropic scaling. In both cases, the atomic positions are also ! optimised. To constrain the atomic positions, set 'atpopt' to 0 or change the ! nuclear mass to be a negative number in a particular species file. In the case ! of MgB2, the atomic positions remain fixed because of symmetry. ! As the calculation progresses, you can plot the files TOTENERGY_OPT.OUT and ! STRESSMAX.OUT to see the change in the total energy and stress tensor. The ! modulus of the maximum force on the atoms is written to FORCEMAX.OUT. ! The updated unit cell geometry is written to GEOMETRY_OPT.OUT. The last entry ! in this file contains the final lattice parameters and atomic positions. tasks 2 ! lattice vector optimisation while maintaining the unit cell volume latvopt 2 ! high-quality calculation for precise total energies highq .true. ! speed the calculation up with Broyden mixing mixtype 3 avec 5.8316944 0.0 0.0 -2.9158472 5.050395498 0.0 0.0 0.0 6.659394380 ! decrease the unit cell volume to increase the pressure scale 0.9 sppath '../../../species/' atoms 2 : nspecies 'Mg.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'B.in' 2 0.33333333 0.66666667 0.5 0.66666667 0.33333333 0.5 elk-7.2.42/PaxHeaders.21776/tests0000644000000000000000000000013214061636520013214 xustar0030 mtime=1623670096.955100598 30 atime=1623670096.513101009 30 ctime=1623670096.955100598 elk-7.2.42/tests/0000755002504400250440000000000014061636520015326 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/PaxHeaders.21776/test.sh0000644000000000000000000000013214061636520014604 xustar0030 mtime=1623670096.515101007 30 atime=1623670096.515101007 30 ctime=1623670096.515101007 elk-7.2.42/tests/test.sh0000755002504400250440000000064414061636520016650 0ustar00dewhurstdewhurst00000000000000#! /bin/sh # Test suite script for the Elk Code for i in test_* do cd $i echo echo "Running test in directory $i..." \rm -f *.OUT gmon.out fort.* OMP_NUM_THREADS=8 OMP_STACKSIZE=20M ../../src/elk > test.log NERROR=`grep -c Error test.log` if test $NERROR -gt 0 then echo " Failed! See test.log and output files" else echo " Passed" \rm -f *.OUT test.log fort.* gmon.out fi cd .. done elk-7.2.42/tests/PaxHeaders.21776/test-mpi.sh0000644000000000000000000000013214061636520015367 xustar0030 mtime=1623670096.516101006 30 atime=1623670096.516101006 30 ctime=1623670096.516101006 elk-7.2.42/tests/test-mpi.sh0000755002504400250440000000072414061636520017432 0ustar00dewhurstdewhurst00000000000000#! /bin/sh # Test suite script for the Elk Code for i in test_* do cd $i echo echo "Running test in directory $i..." \rm -f *.OUT gmon.out fort.* OMP_NUM_THREADS=2 OMP_STACKSIZE=20M OMP_PROC_BIND=true OMP_PLACES=cores mpirun -n 4 ../../src/elk > test.log NERROR=`grep -c Error test.log` if test $NERROR -gt 0 then echo " Failed! See test.log and output files" else echo " Passed" \rm -f *.OUT test.log fort.* gmon.out fi cd .. done elk-7.2.42/tests/PaxHeaders.21776/test_0040000644000000000000000000000013214061636520014556 xustar0030 mtime=1623670096.535100988 30 atime=1623670096.517101005 30 ctime=1623670096.535100988 elk-7.2.42/tests/test_004/0000755002504400250440000000000014061636520016670 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_004/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.519101003 30 atime=1623670096.519101003 30 ctime=1623670096.519101003 elk-7.2.42/tests/test_004/TEST_400.OUT_0000644002504400250440000000014114061636520020556 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 12.0280730058 elk-7.2.42/tests/test_004/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016521 xustar0030 mtime=1623670096.520101002 30 atime=1623670096.520101002 30 ctime=1623670096.520101002 elk-7.2.42/tests/test_004/TEST_000.OUT_0000644002504400250440000000012614061636520020555 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -106.907708836 elk-7.2.42/tests/test_004/PaxHeaders.21776/TEST_121.OUT_0000644000000000000000000000012114061636520016523 xustar0027 mtime=1623670096.522101 27 atime=1623670096.522101 27 ctime=1623670096.522101 elk-7.2.42/tests/test_004/TEST_121.OUT_0000644002504400250440000012273714061636520020576 0ustar00dewhurstdewhurst00000000000000'optical conductivity' 3 800 0.100000000000E-01 1 0.324757249585E-03 0.00000000000 2 0.324762751516E-03 -0.121774874327E-03 3 0.324779258109E-03 -0.243553873785E-03 4 0.324806771757E-03 -0.365341124101E-03 5 0.324845296452E-03 -0.487140752198E-03 6 0.324894837782E-03 -0.608956886796E-03 7 0.324955402936E-03 -0.730793659007E-03 8 0.325027000708E-03 -0.852655202937E-03 9 0.325109641493E-03 -0.974545656287E-03 10 0.325203337300E-03 -0.109646916096E-02 11 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-0.228406191644E-05 0.488474830356E-04 787 -0.313291955896E-05 0.734300302556E-04 788 0.382240514031E-03 -0.104059203328E-01 789 -0.136203181813E-05 0.235781451428E-04 790 -0.228719861890E-05 0.488472417007E-04 791 -0.136615441143E-05 0.235778094197E-04 792 0.383565082203E-03 -0.104441118583E-01 793 0.384628480782E-03 -0.105435987857E-01 794 -0.317622847522E-05 0.746117152297E-04 795 -0.231797585005E-05 0.497101962395E-04 796 -0.317046864448E-05 0.746121595385E-04 797 0.384785233458E-03 -0.105496898471E-01 798 -0.139008901786E-05 0.240942944327E-04 799 -0.232120396184E-05 0.497099494728E-04 800 -0.139433889621E-05 0.240939502523E-04 elk-7.2.42/tests/test_004/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.528100995 30 atime=1623670096.528100995 30 ctime=1623670096.528100995 elk-7.2.42/tests/test_004/TEST_500.OUT_0000644002504400250440000000013514061636520020562 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.507612944006E-12 elk-7.2.42/tests/test_004/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.529100994 30 atime=1623670096.529100994 30 ctime=1623670096.529100994 elk-7.2.42/tests/test_004/TEST_510.OUT_0000644002504400250440000000014514061636520020564 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.324637504049 elk-7.2.42/tests/test_004/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.531100992 30 atime=1623670096.530100993 30 ctime=1623670096.531100992 elk-7.2.42/tests/test_004/TEST_705.OUT_0000644002504400250440000000010114061636520020562 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_004/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.532100991 30 atime=1623670096.532100991 30 ctime=1623670096.532100991 elk-7.2.42/tests/test_004/TEST_900.OUT_0000644002504400250440000000007014061636520020564 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 749 elk-7.2.42/tests/test_004/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.534100989 30 atime=1623670096.534100989 30 ctime=1623670096.534100989 elk-7.2.42/tests/test_004/TEST_910.OUT_0000644002504400250440000000144714061636520020576 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 24 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.206465308646 5 0.206465308646 6 -0.206465308646 7 0.412930617293 8 0.412930617293 9 -0.412930617293 10 0.412930617293 11 0.00000000000 12 0.00000000000 13 0.619395925939 14 0.206465308646 15 -0.206465308646 16 0.825861234586 17 0.412930617293 18 -0.412930617293 19 0.825861234586 20 0.00000000000 21 0.00000000000 22 0.825861234586 23 0.412930617293 24 0.00000000000 elk-7.2.42/tests/test_004/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015736 xustar0030 mtime=1623670096.536100987 30 atime=1623670096.535100988 30 ctime=1623670096.536100987 elk-7.2.42/tests/test_004/elk.in0000644002504400250440000000136014061636520017773 0ustar00dewhurstdewhurst00000000000000 tasks 0 120 121 180 185 186 187 500 test .true. mixtype 3 nxoapwlo 1 scissor 0.21 lmaxo 5 gmaxvr 0.0 nvbse 3 ncbse 3 gmaxrf 2.0 swidth 0.005 nempty 8 wplot 800 100 0 0.0 1.5 avec 3.80402 3.80402 0.00000 3.80402 0.00000 3.80402 0.00000 3.80402 3.80402 sppath '../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms 0.0000 0.0000 0.0000 0.0 0.0 0.0 : atposl, bfcmt 'F.in' : spfname 1 : natoms 0.5000 0.5000 0.5000 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 elk-7.2.42/tests/PaxHeaders.21776/test_0080000644000000000000000000000013214061636520014562 xustar0030 mtime=1623670096.549100975 30 atime=1623670096.537100986 30 ctime=1623670096.549100975 elk-7.2.42/tests/test_008/0000755002504400250440000000000014061636520016674 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_008/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.538100985 30 atime=1623670096.538100985 30 ctime=1623670096.538100985 elk-7.2.42/tests/test_008/TEST_500.OUT_0000644002504400250440000000013514061636520020566 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 238.639941981 elk-7.2.42/tests/test_008/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.540100984 30 atime=1623670096.540100984 30 ctime=1623670096.540100984 elk-7.2.42/tests/test_008/TEST_510.OUT_0000644002504400250440000000014514061636520020570 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.141876418301E-02 elk-7.2.42/tests/test_008/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.541100983 30 atime=1623670096.541100983 30 ctime=1623670096.541100983 elk-7.2.42/tests/test_008/TEST_400.OUT_0000644002504400250440000000014114061636520020562 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 51.9943489727 elk-7.2.42/tests/test_008/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.543100981 30 atime=1623670096.542100982 30 ctime=1623670096.543100981 elk-7.2.42/tests/test_008/TEST_450.OUT_0000644002504400250440000000014014061636520020566 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.179711098243E-17 elk-7.2.42/tests/test_008/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000012714061636520016531 xustar0029 mtime=1623670096.54410098 29 atime=1623670096.54410098 29 ctime=1623670096.54410098 elk-7.2.42/tests/test_008/TEST_000.OUT_0000644002504400250440000000012614061636520020561 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -2540.92553041 elk-7.2.42/tests/test_008/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016541 xustar0030 mtime=1623670096.546100978 30 atime=1623670096.545100979 30 ctime=1623670096.546100978 elk-7.2.42/tests/test_008/TEST_705.OUT_0000644002504400250440000000010114061636520020566 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 96 elk-7.2.42/tests/test_008/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.547100977 30 atime=1623670096.547100977 30 ctime=1623670096.547100977 elk-7.2.42/tests/test_008/TEST_900.OUT_0000644002504400250440000000007014061636520020570 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 8385 elk-7.2.42/tests/test_008/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.548100976 30 atime=1623670096.548100976 30 ctime=1623670096.548100976 elk-7.2.42/tests/test_008/TEST_910.OUT_0000644002504400250440000000174114061636520020577 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 30 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.237999443454 5 0.00000000000 6 0.00000000000 7 0.475998886908 8 0.00000000000 9 0.00000000000 10 0.237999443454 11 0.237999443454 12 0.00000000000 13 0.475998886908 14 0.237999443454 15 0.00000000000 16 0.475998886908 17 0.475998886908 18 0.00000000000 19 0.237999443454 20 0.237999443454 21 0.237999443454 22 0.475998886908 23 0.237999443454 24 0.237999443454 25 0.475998886908 26 0.475998886908 27 0.237999443454 28 0.475998886908 29 0.475998886908 30 0.475998886908 elk-7.2.42/tests/test_008/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015742 xustar0030 mtime=1623670096.550100974 30 atime=1623670096.550100974 30 ctime=1623670096.550100974 elk-7.2.42/tests/test_008/elk.in0000644002504400250440000000114314061636520017776 0ustar00dewhurstdewhurst00000000000000 ! Antiferromagnetic bcc iron example with fixed spin moment in muffin-tin. tasks 0 500 test .true. mixtype 1 fsmtype 2 mommtfix 1 1 0.0 0.0 1.0 : is, ia, mommtfix 1 2 0.0 0.0 -1.0 : is, ia, mommtfix swidth 0.01 rgkmax 6.0 avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 scale 6.6 sppath '../../species/' atoms 1 : nspecies 'Fe.in' : spfname 2 : natoms 0.0 0.0 0.0 0.0 0.0 0.001 : atposl, bfcmt 0.5 0.5 0.5 0.0 0.0 -0.001 ngridk 4 4 4 elk-7.2.42/tests/PaxHeaders.21776/test_0120000644000000000000000000000013014061636520014553 xustar0029 mtime=1623670096.56510096 30 atime=1623670096.551100973 29 ctime=1623670096.56510096 elk-7.2.42/tests/test_012/0000755002504400250440000000000014061636520016667 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.552100973 30 atime=1623670096.552100973 30 ctime=1623670096.552100973 elk-7.2.42/tests/test_012/TEST_400.OUT_0000644002504400250440000000014114061636520020555 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 25.9808139618 elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016520 xustar0030 mtime=1623670096.554100971 30 atime=1623670096.554100971 30 ctime=1623670096.554100971 elk-7.2.42/tests/test_012/TEST_000.OUT_0000644002504400250440000000012614061636520020554 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -483.830347581 elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000012714061636520016531 xustar0029 mtime=1623670096.55510097 29 atime=1623670096.55510097 29 ctime=1623670096.55510097 elk-7.2.42/tests/test_012/TEST_500.OUT_0000644002504400250440000000013514061636520020561 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 126.871484710 elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.557100968 30 atime=1623670096.556100969 30 ctime=1623670096.557100968 elk-7.2.42/tests/test_012/TEST_510.OUT_0000644002504400250440000000014514061636520020563 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.361958276467E-01 elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.558100967 30 atime=1623670096.558100967 30 ctime=1623670096.558100967 elk-7.2.42/tests/test_012/TEST_910.OUT_0000644002504400250440000000144714061636520020575 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 24 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.205241634672 5 0.205241634672 6 -0.205241634672 7 0.410483269343 8 0.410483269343 9 -0.410483269343 10 0.410483269343 11 0.00000000000 12 0.00000000000 13 0.615724904015 14 0.205241634672 15 -0.205241634672 16 0.820966538686 17 0.410483269343 18 -0.410483269343 19 0.820966538686 20 0.00000000000 21 0.00000000000 22 0.820966538686 23 0.410483269343 24 0.00000000000 elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.560100965 30 atime=1623670096.559100966 30 ctime=1623670096.560100965 elk-7.2.42/tests/test_012/TEST_705.OUT_0000644002504400250440000000010114061636520020561 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.561100964 30 atime=1623670096.561100964 30 ctime=1623670096.561100964 elk-7.2.42/tests/test_012/TEST_900.OUT_0000644002504400250440000000007014061636520020563 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 3287 elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_750.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.563100962 30 atime=1623670096.562100963 30 ctime=1623670096.563100962 elk-7.2.42/tests/test_012/TEST_750.OUT_0000644002504400250440000000036114061636520020571 0ustar00dewhurstdewhurst00000000000000'total forces' 2 6 0.100000000000E-02 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.00000000000 5 0.00000000000 6 0.00000000000 elk-7.2.42/tests/test_012/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015735 xustar0030 mtime=1623670096.564100961 30 atime=1623670096.564100961 30 ctime=1623670096.564100961 elk-7.2.42/tests/test_012/elk.in0000644002504400250440000000126014061636520017771 0ustar00dewhurstdewhurst00000000000000 ! Phonon and electron-phonon coupling test for Nb. tasks 0 200 220 240 245 250 500 test .true. mixtype 3 wplot 50 100 2 0.0 1.0 ngridq 2 2 2 radkpt 20.0 ngridk 4 4 4 rgkmax 6.0 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.8267 sppath '../../species/' atoms 1 : nspecies 'Al.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt plot1d 9 400 0.5 0.5 0.5 0.25 0.25 0.25 0.0 0.0 0.0 -0.5 0.5 0.5 -0.5 0.5 0.0 -0.75 0.25 0.25 -0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.5 0.0 elk-7.2.42/tests/test_012/PaxHeaders.21776/TEST_251.OUT_0000644000000000000000000000012714061636520016534 xustar0029 mtime=1623670096.56510096 29 atime=1623670096.56510096 29 ctime=1623670096.56510096 elk-7.2.42/tests/test_012/TEST_251.OUT_0000644002504400250440000000016314061636520020565 0ustar00dewhurstdewhurst00000000000000'electron-phonon coupling constant, lambda' 2 1 0.500000000000E-01 1 11.8169157388 elk-7.2.42/tests/PaxHeaders.21776/test_0160000644000000000000000000000013214061636520014561 xustar0030 mtime=1623670096.585100942 30 atime=1623670096.566100959 30 ctime=1623670096.585100942 elk-7.2.42/tests/test_016/0000755002504400250440000000000014061636520016673 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.567100958 30 atime=1623670096.567100958 30 ctime=1623670096.567100958 elk-7.2.42/tests/test_016/TEST_500.OUT_0000644002504400250440000000013514061636520020565 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 52.4280948128 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.569100957 30 atime=1623670096.569100957 30 ctime=1623670096.569100957 elk-7.2.42/tests/test_016/TEST_510.OUT_0000644002504400250440000000014514061636520020567 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.212820897505E-01 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.570100956 30 atime=1623670096.570100956 30 ctime=1623670096.570100956 elk-7.2.42/tests/test_016/TEST_000.OUT_0000644002504400250440000000012614061636520020560 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -28450.0801749 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_820.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.572100954 30 atime=1623670096.572100954 30 ctime=1623670096.572100954 elk-7.2.42/tests/test_016/TEST_820.OUT_0000644002504400250440000000014014061636520020566 0ustar00dewhurstdewhurst00000000000000'Norm of tensor moments' 2 1 0.100000000000E-03 1 10.4191777592 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_830.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.573100953 30 atime=1623670096.573100953 30 ctime=1623670096.573100953 elk-7.2.42/tests/test_016/TEST_830.OUT_0000644002504400250440000000016614061636520020577 0ustar00dewhurstdewhurst00000000000000'Norm of DFT+U Hartree-Fock exchange energies' 2 1 0.100000000000E-03 1 0.673450120995E-01 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.575100951 30 atime=1623670096.574100952 30 ctime=1623670096.575100951 elk-7.2.42/tests/test_016/TEST_705.OUT_0000644002504400250440000000010114061636520020565 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 6 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000012714061636520016541 xustar0029 mtime=1623670096.57610095 29 atime=1623670096.57610095 29 ctime=1623670096.57610095 elk-7.2.42/tests/test_016/TEST_900.OUT_0000644002504400250440000000007014061636520020567 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 7991 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.578100948 30 atime=1623670096.577100949 30 ctime=1623670096.578100948 elk-7.2.42/tests/test_016/TEST_910.OUT_0000644002504400250440000000023414061636520020572 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 3 0.100000000000E-07 1 0.530584787921 2 0.227393480538 3 0.757978268459E-01 elk-7.2.42/tests/test_016/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015741 xustar0030 mtime=1623670096.579100947 30 atime=1623670096.579100947 30 ctime=1623670096.579100947 elk-7.2.42/tests/test_016/elk.in0000644002504400250440000000132214061636520017774 0ustar00dewhurstdewhurst00000000000000 ! DFT+U test tasks 0 400 500 maxscl 2 test .true. swidth 0.05 dft+u 3 5 : dftu,inpdftu 1 3 0.1469972 : is, l, U fixed spinpol .true. spinorb .true. scale 10.36175041 avec 0.0 0.5 0.5 0.5 0.0 0.5 0.5 0.5 0.0 atoms 2 : nspecies 'U.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 'S.in' : spfname 1 : natoms 0.5 0.5 0.5 0.0 0.0 0.0 : atposl, bfcmt bfieldc -2.0 -2.0 -2.0 reducebf 0.5 sppath '../../species/' ngridk 1 1 1 vkloff 0.25 0.5 0.625 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.581100946 30 atime=1623670096.580100946 30 ctime=1623670096.581100946 elk-7.2.42/tests/test_016/TEST_400.OUT_0000644002504400250440000000014114061636520020561 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 107.995994386 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.582100945 30 atime=1623670096.582100945 30 ctime=1623670096.582100945 elk-7.2.42/tests/test_016/TEST_450.OUT_0000644002504400250440000000014014061636520020565 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 2.25873743538 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.583100944 30 atime=1623670096.583100944 30 ctime=1623670096.583100944 elk-7.2.42/tests/test_016/TEST_800.OUT_0000644002504400250440000000014414061636520020570 0ustar00dewhurstdewhurst00000000000000'DFT+U energy for each atom' 2 1 0.100000000000E-03 1 0.284223549814E-02 elk-7.2.42/tests/test_016/PaxHeaders.21776/TEST_810.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.585100942 30 atime=1623670096.585100942 30 ctime=1623670096.585100942 elk-7.2.42/tests/test_016/TEST_810.OUT_0000644002504400250440000000475514061636520020605 0ustar00dewhurstdewhurst00000000000000'U and J parameters' 2 80 0.100000000000E-03 1 0.146997241390 2 0.221042638132E-01 3 0.00000000000 4 0.00000000000 5 0.00000000000 6 0.00000000000 7 0.00000000000 8 0.00000000000 9 0.00000000000 10 0.00000000000 11 0.00000000000 12 0.00000000000 13 0.00000000000 14 0.00000000000 15 0.00000000000 16 0.00000000000 17 0.00000000000 18 0.00000000000 19 0.00000000000 20 0.00000000000 21 0.00000000000 22 0.00000000000 23 0.00000000000 24 0.00000000000 25 0.00000000000 26 0.00000000000 27 0.00000000000 28 0.00000000000 29 0.00000000000 30 0.00000000000 31 0.00000000000 32 0.00000000000 33 0.00000000000 34 0.00000000000 35 0.00000000000 36 0.00000000000 37 0.00000000000 38 0.00000000000 39 0.00000000000 40 0.00000000000 41 0.00000000000 42 0.00000000000 43 0.00000000000 44 0.00000000000 45 0.00000000000 46 0.00000000000 47 0.00000000000 48 0.00000000000 49 0.00000000000 50 0.00000000000 51 0.00000000000 52 0.00000000000 53 0.00000000000 54 0.00000000000 55 0.00000000000 56 0.00000000000 57 0.00000000000 58 0.00000000000 59 0.00000000000 60 0.00000000000 61 0.00000000000 62 0.00000000000 63 0.00000000000 64 0.00000000000 65 0.00000000000 66 0.00000000000 67 0.00000000000 68 0.00000000000 69 0.00000000000 70 0.00000000000 71 0.00000000000 72 0.00000000000 73 0.00000000000 74 0.00000000000 75 0.00000000000 76 0.00000000000 77 0.00000000000 78 0.00000000000 79 0.00000000000 80 0.00000000000 elk-7.2.42/tests/PaxHeaders.21776/test_0200000644000000000000000000000013214061636520014554 xustar0030 mtime=1623670096.599100929 30 atime=1623670096.586100941 30 ctime=1623670096.599100929 elk-7.2.42/tests/test_020/0000755002504400250440000000000014061636520016666 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_610.OUT_0000644000000000000000000000012714061636520016532 xustar0029 mtime=1623670096.58710094 29 atime=1623670096.58710094 29 ctime=1623670096.58710094 elk-7.2.42/tests/test_020/TEST_610.OUT_0000644002504400250440000001417514061636520020573 0ustar00dewhurstdewhurst00000000000000'total GW spectral function' 2 200 0.500000000000E-01 1 0.643445764404 2 0.634496885783 3 0.625844894078 4 0.617478292124 5 0.609386173229 6 0.601558185456 7 0.593984498437 8 0.586655772542 9 0.579563130200 10 0.572698129338 11 0.566052738533 12 0.559619313171 13 0.553390574491 14 0.547359589344 15 0.541519751114 16 0.535864762130 17 0.530388617195 18 0.525085588112 19 0.519950209198 20 0.514977263757 21 0.510161771386 22 0.505498975985 23 0.500984334727 24 0.496613507400 25 0.492382346704 26 0.488286888659 27 0.484323344320 28 0.480488091242 29 0.476777665882 30 0.473188756412 31 0.469718195628 32 0.466362954834 33 0.463120138199 34 0.459986975100 35 0.456960817219 36 0.454039131611 37 0.451219498385 38 0.448499601881 39 0.445877230901 40 0.443350272199 41 0.440916707392 42 0.438574609208 43 0.436322138340 44 0.434157540376 45 0.432079142451 46 0.430085350649 47 0.428174647667 48 0.426345589667 49 0.424596804436 50 0.422926988905 51 0.421334909020 52 0.419819393644 53 0.418379336592 54 0.417013693832 55 0.415721481460 56 0.414501774911 57 0.413353707223 58 0.412276467951 59 0.411269302094 60 0.410331509252 61 0.409462442896 62 0.408661508682 63 0.407928164638 64 0.407261920316 65 0.406662336275 66 0.406129023493 67 0.405661643186 68 0.405259906610 69 0.404923575312 70 0.404652458870 71 0.404446419354 72 0.404305367124 73 0.404229263161 74 0.404218118908 75 0.404271997129 76 0.404391011639 77 0.404575329019 78 0.404825168763 79 0.405140804166 80 0.405522563332 81 0.405970830530 82 0.406486047549 83 0.407068714463 84 0.407719392132 85 0.408438703201 86 0.409227334426 87 0.410086038562 88 0.411015636872 89 0.412017021259 90 0.413091155422 91 0.414239080322 92 0.415461923226 93 0.416760881145 94 0.418137246583 95 0.419592401941 96 0.421127821930 97 0.422745085946 98 0.424445877347 99 0.426231984306 100 0.428105315366 101 0.430067903637 102 0.432121908808 103 0.434269633664 104 0.436513525216 105 0.438856189158 106 0.441300432830 107 0.443849088202 108 0.446505397880 109 0.449272650059 110 0.452154354578 111 0.455154202022 112 0.458276278637 113 0.461525075550 114 0.464905102620 115 0.468420372617 116 0.472077037859 117 0.475880834279 118 0.479837182810 119 0.483954943405 120 0.488242530740 121 0.492697460272 122 0.497335827852 123 0.502164365068 124 0.507193380801 125 0.512434249440 126 0.517894057464 127 0.523586662469 128 0.529524787199 129 0.535722821461 130 0.542195551085 131 0.548959876014 132 0.556034996329 133 0.563440036360 134 0.571196888751 135 0.579332183120 136 0.587871919564 137 0.596847414301 138 0.606293244795 139 0.616248062611 140 0.626757523145 141 0.637831129327 142 0.649560890412 143 0.661907885803 144 0.675213479387 145 0.689381706714 146 0.704498980954 147 0.720694662239 148 0.738110401756 149 0.756890768551 150 0.777236323055 151 0.799364197706 152 0.823546731428 153 0.850105787007 154 0.879435667844 155 0.911991216059 156 0.948341465883 157 0.989205491527 158 1.03540574342 159 1.08780136039 160 1.14739475786 161 1.21502400700 162 1.29122928021 163 1.37555416652 164 1.46589875314 165 1.55774848665 166 1.64377989402 167 1.71534408660 168 1.76547581361 169 1.79272368186 170 1.80210537580 171 1.80276454326 172 1.80426881857 173 1.81409053279 174 1.83697250673 175 1.87564074712 176 1.93197121320 177 2.00717094975 178 2.10297527018 179 2.22132711926 180 2.36506154232 181 2.53789076771 182 2.74456723882 183 2.99097553037 184 3.28408438872 185 3.63162535830 186 4.04113989031 187 4.51795689945 188 5.06143439827 189 5.65910047148 190 6.27974167180 191 6.86971619164 192 7.35985356461 193 7.68910642343 194 7.83322929379 195 7.81664509741 196 7.69482426520 197 7.52031167146 198 7.31931797684 199 7.09121022351 200 6.82610762462 elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016523 xustar0030 mtime=1623670096.589100938 30 atime=1623670096.589100938 30 ctime=1623670096.589100938 elk-7.2.42/tests/test_020/TEST_400.OUT_0000644002504400250440000000014114061636520020554 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 12.0281676211 elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016517 xustar0030 mtime=1623670096.590100937 30 atime=1623670096.590100937 30 ctime=1623670096.590100937 elk-7.2.42/tests/test_020/TEST_000.OUT_0000644002504400250440000000012614061636520020553 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -106.905850836 elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.592100935 30 atime=1623670096.592100935 30 ctime=1623670096.592100935 elk-7.2.42/tests/test_020/TEST_800.OUT_0000644002504400250440000000026414061636520020566 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 3 0.100000000000E-07 1 216.963990922 2 28.1249542511 3 19.7640709318 elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.593100934 30 atime=1623670096.593100934 30 ctime=1623670096.593100934 elk-7.2.42/tests/test_020/TEST_500.OUT_0000644002504400250440000000013514061636520020560 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.115177788557E-02 elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.594100934 30 atime=1623670096.594100934 30 ctime=1623670096.594100934 elk-7.2.42/tests/test_020/TEST_510.OUT_0000644002504400250440000000014514061636520020562 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.323820711187 elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.596100932 30 atime=1623670096.595100932 30 ctime=1623670096.596100932 elk-7.2.42/tests/test_020/TEST_705.OUT_0000644002504400250440000000010114061636520020560 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.597100931 30 atime=1623670096.597100931 30 ctime=1623670096.597100931 elk-7.2.42/tests/test_020/TEST_900.OUT_0000644002504400250440000000007014061636520020562 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 3215 elk-7.2.42/tests/test_020/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000012714061636520016535 xustar0029 mtime=1623670096.59810093 29 atime=1623670096.59810093 29 ctime=1623670096.59810093 elk-7.2.42/tests/test_020/TEST_910.OUT_0000644002504400250440000000144714061636520020574 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 24 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.206465308646 5 0.206465308646 6 -0.206465308646 7 0.412930617293 8 0.412930617293 9 -0.412930617293 10 0.412930617293 11 0.00000000000 12 0.00000000000 13 0.619395925939 14 0.206465308646 15 -0.206465308646 16 0.825861234586 17 0.412930617293 18 -0.412930617293 19 0.825861234586 20 0.00000000000 21 0.00000000000 22 0.825861234586 23 0.412930617293 24 0.00000000000 elk-7.2.42/tests/test_020/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015734 xustar0030 mtime=1623670096.599100929 30 atime=1623670096.599100929 30 ctime=1623670096.599100929 elk-7.2.42/tests/test_020/elk.in0000644002504400250440000000052714061636520017775 0ustar00dewhurstdewhurst00000000000000 tasks 0 600 610 500 test .true. gmaxrf 3.0 tempk 5000.0 nempty 6 wplot 200 100 0 -0.1 0.3 avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../species/' atoms 2 'Li.in' 1 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 ngridk 4 4 4 ngridq 2 2 2 elk-7.2.42/tests/PaxHeaders.21776/test_0240000644000000000000000000000013214061636520014560 xustar0030 mtime=1623670096.610100919 30 atime=1623670096.601100927 30 ctime=1623670096.610100919 elk-7.2.42/tests/test_024/0000755002504400250440000000000014061636520016672 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_024/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.602100926 30 atime=1623670096.602100926 30 ctime=1623670096.602100926 elk-7.2.42/tests/test_024/TEST_705.OUT_0000644002504400250440000000010114061636520020564 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 2 elk-7.2.42/tests/test_024/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.603100925 30 atime=1623670096.603100925 30 ctime=1623670096.603100925 elk-7.2.42/tests/test_024/TEST_900.OUT_0000644002504400250440000000007014061636520020566 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 22257 elk-7.2.42/tests/test_024/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.605100923 30 atime=1623670096.604100924 30 ctime=1623670096.605100923 elk-7.2.42/tests/test_024/TEST_910.OUT_0000644002504400250440000000052614061636520020575 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 9 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.338173181022 5 -0.195244417682 6 0.00000000000 7 0.676346362044 8 0.00000000000 9 0.00000000000 elk-7.2.42/tests/test_024/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015740 xustar0030 mtime=1623670096.606100922 30 atime=1623670096.606100922 30 ctime=1623670096.606100922 elk-7.2.42/tests/test_024/elk.in0000644002504400250440000000100514061636520017771 0ustar00dewhurstdewhurst00000000000000 tasks 0 500 test .true. rgkmax 6.0 lmaxi 3 maxscl 2 ngridk 2 2 1 avec 4.644946479927 -8.045281629256 0.0 4.644946479927 8.045281629256 0.0 0.0 0.0 10.21472485866 sppath '../../species/' atoms 2 'Si.in' 3 0.4650 0.0000 0.0000 0.0000 0.4650 0.666666667 0.5350 0.5350 0.333333333 'O.in' 6 0.415 0.272 0.1200 0.728 0.143 0.786666667 0.857 0.585 0.453333333 0.272 0.415 0.546666667 0.143 0.728 0.8800 0.585 0.857 0.213333333 elk-7.2.42/tests/test_024/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.607100921 30 atime=1623670096.607100921 30 ctime=1623670096.607100921 elk-7.2.42/tests/test_024/TEST_500.OUT_0000644002504400250440000000013514061636520020564 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.551428634218E-11 elk-7.2.42/tests/test_024/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000012714061636520016535 xustar0029 mtime=1623670096.60810092 29 atime=1623670096.60810092 29 ctime=1623670096.60810092 elk-7.2.42/tests/test_024/TEST_510.OUT_0000644002504400250440000000014514061636520020566 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.287035111991 elk-7.2.42/tests/test_024/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.610100919 30 atime=1623670096.609100919 30 ctime=1623670096.610100919 elk-7.2.42/tests/test_024/TEST_400.OUT_0000644002504400250440000000014114061636520020560 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 89.9132303250 elk-7.2.42/tests/test_024/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016523 xustar0030 mtime=1623670096.611100918 30 atime=1623670096.611100918 30 ctime=1623670096.611100918 elk-7.2.42/tests/test_024/TEST_000.OUT_0000644002504400250440000000012614061636520020557 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1334.10496730 elk-7.2.42/tests/PaxHeaders.21776/test_0260000644000000000000000000000013214061636520014562 xustar0030 mtime=1623670096.625100905 30 atime=1623670096.612100917 30 ctime=1623670096.625100905 elk-7.2.42/tests/test_026/0000755002504400250440000000000014061636520016674 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_026/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015742 xustar0030 mtime=1623670096.613100916 30 atime=1623670096.613100916 30 ctime=1623670096.613100916 elk-7.2.42/tests/test_026/elk.in0000644002504400250440000000104414061636520017776 0ustar00dewhurstdewhurst00000000000000 ! Twice-integrated electron momentum density (EMD) plot for ferromagnetic Ni. tasks 0 170 171 500 test .true. plot1d 2 10 0.0 0.0 0.0 1.0 1.0 0.0 hkmax 4.d0 ngridk 8 8 8 spinpol .true. bfieldc 0.0 0.0 -0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.322 sppath '../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016541 xustar0030 mtime=1623670096.614100915 30 atime=1623670096.614100915 30 ctime=1623670096.614100915 elk-7.2.42/tests/test_026/TEST_705.OUT_0000644002504400250440000000010114061636520020566 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.616100913 30 atime=1623670096.615100914 30 ctime=1623670096.616100913 elk-7.2.42/tests/test_026/TEST_900.OUT_0000644002504400250440000000007014061636520020570 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 2109 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.617100912 30 atime=1623670096.617100912 30 ctime=1623670096.617100912 elk-7.2.42/tests/test_026/TEST_910.OUT_0000644002504400250440000000531014061636520020573 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 87 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.118211644100 5 0.118211644100 6 -0.118211644100 7 0.236423288199 8 0.236423288199 9 -0.236423288199 10 0.354634932299 11 0.354634932299 12 -0.354634932299 13 0.472846576398 14 0.472846576398 15 -0.472846576398 16 0.236423288199 17 0.00000000000 18 0.00000000000 19 0.354634932299 20 0.118211644100 21 -0.118211644100 22 0.472846576398 23 0.236423288199 24 -0.236423288199 25 0.591058220498 26 0.354634932299 27 -0.354634932299 28 0.709269864597 29 0.472846576398 30 -0.472846576398 31 0.827481508697 32 0.591058220498 33 -0.591058220498 34 0.945693152796 35 0.709269864597 36 -0.709269864597 37 0.472846576398 38 0.00000000000 39 0.00000000000 40 0.591058220498 41 0.118211644100 42 -0.118211644100 43 0.709269864597 44 0.236423288199 45 -0.236423288199 46 0.827481508697 47 0.354634932299 48 -0.354634932299 49 0.945693152796 50 0.472846576398 51 -0.472846576398 52 0.709269864597 53 0.138777878078E-16 54 -0.138777878078E-16 55 0.827481508697 56 0.118211644100 57 -0.118211644100 58 0.945693152796 59 0.236423288199 60 -0.236423288199 61 0.945693152796 62 0.00000000000 63 0.00000000000 64 0.472846576398 65 0.236423288199 66 0.00000000000 67 0.591058220498 68 0.354634932299 69 -0.118211644100 70 0.709269864597 71 0.472846576398 72 -0.236423288199 73 0.709269864597 74 0.236423288199 75 -0.138777878078E-16 76 0.827481508697 77 0.354634932299 78 -0.118211644100 79 0.945693152796 80 0.472846576398 81 -0.236423288199 82 0.945693152796 83 0.236423288199 84 0.00000000000 85 0.945693152796 86 0.472846576398 87 0.00000000000 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.618100911 30 atime=1623670096.618100911 30 ctime=1623670096.618100911 elk-7.2.42/tests/test_026/TEST_500.OUT_0000644002504400250440000000013514061636520020566 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 50.8063077715 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000012714061636520016537 xustar0029 mtime=1623670096.61910091 29 atime=1623670096.61910091 29 ctime=1623670096.61910091 elk-7.2.42/tests/test_026/TEST_510.OUT_0000644002504400250440000000014514061636520020570 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.137832582520E-02 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.621100908 30 atime=1623670096.620100909 30 ctime=1623670096.621100908 elk-7.2.42/tests/test_026/TEST_400.OUT_0000644002504400250440000000014114061636520020562 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9938369951 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.622100907 30 atime=1623670096.622100907 30 ctime=1623670096.622100907 elk-7.2.42/tests/test_026/TEST_450.OUT_0000644002504400250440000000014014061636520020566 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.698965619447 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.623100907 30 atime=1623670096.623100907 30 ctime=1623670096.623100907 elk-7.2.42/tests/test_026/TEST_000.OUT_0000644002504400250440000000012614061636520020561 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1518.39244469 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_170.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.625100905 30 atime=1623670096.624100906 30 ctime=1623670096.625100905 elk-7.2.42/tests/test_026/TEST_170.OUT_0000644002504400250440000000516014061636520020574 0ustar00dewhurstdewhurst00000000000000'electron momentum density' 2 84 0.100000000000E-03 1 0.628149607360 2 0.152157226560 3 0.628149456924 4 0.398371096365 5 0.152154705657 6 0.398371108518 7 0.228537399096 8 0.628149389482 9 0.228536520868 10 0.228538735058 11 0.113953490963 12 0.228535382092 13 0.628149401274 14 0.398371109990 15 0.182034761119 16 0.597158412286E-01 17 0.182034752787 18 0.426972176817E-01 19 0.228535146045 20 0.946585628685E-01 21 0.228538670065 22 0.597162166796E-01 23 0.956076445109E-01 24 0.152156459300 25 0.398371103635 26 0.946600965435E-01 27 0.152155287565 28 0.597166546672E-01 29 0.152154761714 30 0.392637652514E-01 31 0.496020913148E-01 32 0.113953493262 33 0.781273825605E-01 34 0.946582967607E-01 35 0.496018566021E-01 36 0.388402390487E-01 37 0.388410374161E-01 38 0.113953501407 39 0.228537422826 40 0.152157034479 41 0.956076447696E-01 42 0.956076429119E-01 43 0.182034754031 44 0.392636888277E-01 45 0.182034769335 46 0.946602768470E-01 47 0.228536583927 48 0.597153645518E-01 49 0.781273839199E-01 50 0.152155386528 51 0.496021401143E-01 52 0.496017243591E-01 53 0.152156621576 54 0.946585311740E-01 55 0.946600155805E-01 56 0.392640744618E-01 57 0.781273808103E-01 58 0.113953501913 59 0.392633923090E-01 60 0.946582989504E-01 61 0.426972274934E-01 62 0.388410151816E-01 63 0.496017645439E-01 64 0.496020699752E-01 65 0.426972232466E-01 66 0.388402434729E-01 67 0.597153706563E-01 68 0.946603162069E-01 69 0.597166809046E-01 70 0.392640654979E-01 71 0.388410064623E-01 72 0.426972250276E-01 73 0.388402485692E-01 74 0.392633754605E-01 75 0.781273811226E-01 76 0.597157668532E-01 77 0.597162453737E-01 78 0.956076358982E-01 79 0.388402572691E-01 80 0.496021741329E-01 81 0.496017418498E-01 82 0.388410291113E-01 83 0.392637581665E-01 84 0.392636960683E-01 elk-7.2.42/tests/test_026/PaxHeaders.21776/TEST_171.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.626100904 30 atime=1623670096.626100904 30 ctime=1623670096.626100904 elk-7.2.42/tests/test_026/TEST_171.OUT_0000644002504400250440000000573114061636520020601 0ustar00dewhurstdewhurst00000000000000'integrated EMD' 2 96 0.100000000000E-03 1 0.220450032485E-01 2 0.632822354453E-01 3 0.101418039214 4 0.134024557527 5 0.165793304400 6 0.196798698041 7 0.228647435925 8 0.259312754536 9 0.286260464430 10 0.310402889286 11 0.336895815110 12 0.366555755147 13 0.399441185409 14 0.433418304813 15 0.470219243082 16 0.516557258816 17 0.571068068629 18 0.631662762747 19 0.698730640881 20 0.775594219122 21 0.859949239200 22 0.946929986052 23 1.03539972735 24 1.11971410289 25 1.20492281464 26 1.29394564860 27 1.38908218050 28 1.48576071568 29 1.57748567452 30 1.64725200873 31 1.71427032148 32 1.78646088630 33 1.87576194119 34 1.97763085545 35 2.07409183623 36 2.16698982012 37 2.28048907716 38 2.47843202938 39 2.74658825881 40 3.05483199931 41 3.32855995228 42 3.58950175720 43 3.82723837461 44 3.97779352745 45 4.09758173742 46 4.18994665308 47 4.27139912642 48 4.35521803568 49 4.35521803506 50 4.27139904625 51 4.18994602850 52 4.09758032984 53 3.97779215830 54 3.82723803830 55 3.58950182080 56 3.32856011301 57 3.05483234047 58 2.74658840598 59 2.47843210999 60 2.28048907468 61 2.16698986180 62 2.07409179712 63 1.97763089886 64 1.87576204429 65 1.78646096752 66 1.71426997903 67 1.64725181411 68 1.57748564079 69 1.48576126172 70 1.38908497718 71 1.29395112449 72 1.20492560743 73 1.11971494413 74 1.03540027236 75 0.946930841764 76 0.859949848546 77 0.775594207932 78 0.698730566092 79 0.631662650831 80 0.571068001014 81 0.516557222047 82 0.470219243810 83 0.433418312590 84 0.399441195618 85 0.366555774841 86 0.336895834576 87 0.310402919399 88 0.286260365464 89 0.259312441568 90 0.228647124709 91 0.196798561853 92 0.165793157238 93 0.134024235729 94 0.101417719776 95 0.632820944802E-01 96 0.220449756519E-01 elk-7.2.42/tests/PaxHeaders.21776/test_0220000644000000000000000000000013214061636520014556 xustar0030 mtime=1623670096.640100891 30 atime=1623670096.626100904 30 ctime=1623670096.640100891 elk-7.2.42/tests/test_022/0000755002504400250440000000000014061636520016670 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.628100902 30 atime=1623670096.628100902 30 ctime=1623670096.628100902 elk-7.2.42/tests/test_022/TEST_900.OUT_0000644002504400250440000000007014061636520020564 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 2109 elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.629100901 30 atime=1623670096.629100901 30 ctime=1623670096.629100901 elk-7.2.42/tests/test_022/TEST_910.OUT_0000644002504400250440000001052214061636520020570 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 141 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.943421217294E-01 5 0.943421217294E-01 6 -0.943421217294E-01 7 0.188684243459 8 0.188684243459 9 -0.188684243459 10 0.283026365188 11 0.283026365188 12 -0.283026365188 13 0.377368486918 14 0.377368486918 15 -0.377368486918 16 0.471710608647 17 0.471710608647 18 -0.471710608647 19 0.188684243459 20 -0.308963289789E-17 21 0.308963289789E-17 22 0.283026365188 23 0.943421217294E-01 24 -0.943421217294E-01 25 0.377368486918 26 0.188684243459 27 -0.188684243459 28 0.471710608647 29 0.283026365188 30 -0.283026365188 31 0.566052730377 32 0.377368486918 33 -0.377368486918 34 0.660394852106 35 0.471710608647 36 -0.471710608647 37 0.754736973835 38 0.566052730377 39 -0.566052730377 40 0.849079095565 41 0.660394852106 42 -0.660394852106 43 0.943421217294 44 0.754736973835 45 -0.754736973835 46 0.377368486918 47 -0.617926579578E-17 48 0.617926579578E-17 49 0.471710608647 50 0.943421217294E-01 51 -0.943421217294E-01 52 0.566052730377 53 0.188684243459 54 -0.188684243459 55 0.660394852106 56 0.283026365188 57 -0.283026365188 58 0.754736973835 59 0.377368486918 60 -0.377368486918 61 0.849079095565 62 0.471710608647 63 -0.471710608647 64 0.943421217294 65 0.566052730377 66 -0.566052730377 67 0.566052730377 68 -0.247170631831E-16 69 0.247170631831E-16 70 0.660394852106 71 0.943421217294E-01 72 -0.943421217294E-01 73 0.754736973835 74 0.188684243459 75 -0.188684243459 76 0.849079095565 77 0.283026365188 78 -0.283026365188 79 0.943421217294 80 0.377368486918 81 -0.377368486918 82 0.754736973835 83 -0.123585315916E-16 84 0.123585315916E-16 85 0.849079095565 86 0.943421217294E-01 87 -0.943421217294E-01 88 0.943421217294 89 0.188684243459 90 -0.188684243459 91 0.943421217294 92 0.00000000000 93 0.00000000000 94 0.377368486918 95 0.188684243459 96 -0.169674207057E-16 97 0.471710608647 98 0.283026365188 99 -0.943421217294E-01 100 0.566052730377 101 0.377368486918 102 -0.188684243459 103 0.660394852106 104 0.471710608647 105 -0.283026365188 106 0.566052730377 107 0.188684243459 108 0.524215183334E-16 109 0.660394852106 110 0.283026365188 111 -0.943421217294E-01 112 0.754736973835 113 0.377368486918 114 -0.188684243459 115 0.849079095565 116 0.471710608647 117 -0.283026365188 118 0.943421217294 119 0.566052730377 120 -0.377368486918 121 0.754736973835 122 0.188684243459 123 0.385437305256E-16 124 0.849079095565 125 0.283026365188 126 -0.943421217294E-01 127 0.943421217294 128 0.377368486918 129 -0.188684243459 130 0.943421217294 131 0.188684243459 132 -0.724785719370E-16 133 0.754736973835 134 0.377368486918 135 -0.339348414114E-16 136 0.849079095565 137 0.471710608647 138 -0.943421217294E-01 139 0.943421217294 140 0.377368486918 141 -0.616904170270E-16 elk-7.2.42/tests/test_022/PaxHeaders.21776/elk.in0000644000000000000000000000012414061636520015737 xustar0028 mtime=1623670096.6301009 28 atime=1623670096.6301009 28 ctime=1623670096.6301009 elk-7.2.42/tests/test_022/elk.in0000644002504400250440000000110514061636520017770 0ustar00dewhurstdewhurst00000000000000 ! Magnetic response of fcc nickel. tasks 0 330 500 test .true. nempty 10 lorbcnd .true. emaxrf 1.5 gmaxrf 2.0 wplot 60 100 1 0 0.020 ! q-vector of response function vecql 0.1 0.3 0.0 ngridk 10 10 10 spinpol .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.632100898 30 atime=1623670096.631100899 30 ctime=1623670096.632100898 elk-7.2.42/tests/test_022/TEST_705.OUT_0000644002504400250440000000010114061636520020562 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.633100897 30 atime=1623670096.633100897 30 ctime=1623670096.633100897 elk-7.2.42/tests/test_022/TEST_500.OUT_0000644002504400250440000000013514061636520020562 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 52.6888436363 elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.634100896 30 atime=1623670096.634100896 30 ctime=1623670096.634100896 elk-7.2.42/tests/test_022/TEST_510.OUT_0000644002504400250440000000014514061636520020564 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.728636163930E-03 elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.635100895 30 atime=1623670096.635100895 30 ctime=1623670096.635100895 elk-7.2.42/tests/test_022/TEST_400.OUT_0000644002504400250440000000014114061636520020556 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9937748749 elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.637100894 30 atime=1623670096.636100894 30 ctime=1623670096.637100894 elk-7.2.42/tests/test_022/TEST_450.OUT_0000644002504400250440000000014014061636520020562 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.721275606048 elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016521 xustar0030 mtime=1623670096.638100893 30 atime=1623670096.638100893 30 ctime=1623670096.638100893 elk-7.2.42/tests/test_022/TEST_000.OUT_0000644002504400250440000000012614061636520020555 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1518.39249410 elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.639100892 30 atime=1623670096.639100892 30 ctime=1623670096.639100892 elk-7.2.42/tests/test_022/TEST_800.OUT_0000644002504400250440000000301014061636520020560 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 47 0.100000000000E-07 1 4156.52649632 2 538.808845910 3 122.281077681 4 53.2067305730 5 29.7036699563 6 18.9436528129 7 378.633726982 8 131.915119909 9 59.6996144004 10 33.1294509551 11 20.8866383293 12 24.1480573225 13 39.8247961001 14 76.6221168207 15 191.109192697 16 89.6935829837 17 52.8305196423 18 32.3142045935 19 21.1792161666 20 18.7172333061 21 28.0029635091 22 44.9516730037 23 39.4977235641 24 27.8283415094 25 19.6878350783 26 14.3061427077 27 19.7706217330 28 22.1479831303 29 17.0639418646 30 13.1063464662 31 14.1544228910 32 70.5026233452 33 40.4627055245 34 25.3002738051 35 17.0626173734 36 35.3392864088 37 23.9798340158 38 16.8448151671 39 18.9724996792 40 27.4485942715 41 20.7913378523 42 15.5388968693 43 14.2001311974 44 13.5917268552 45 17.6443345168 46 13.2018441244 47 12.1733944017 elk-7.2.42/tests/test_022/PaxHeaders.21776/TEST_330.OUT_0000644000000000000000000000013014061636520016525 xustar0029 mtime=1623670096.64110089 30 atime=1623670096.640100891 29 ctime=1623670096.64110089 elk-7.2.42/tests/test_022/TEST_330.OUT_0000644002504400250440000000626314061636520020573 0ustar00dewhurstdewhurst00000000000000'transverse response function' 3 60 0.100000000000E-01 1 0.996580799549 -0.469470374673E-01 2 0.983398747574 -0.497274490118E-01 3 0.971183956003 -0.523112457605E-01 4 0.959252122957 -0.539683222028E-01 5 0.946487985673 -0.552442217555E-01 6 0.932977266238 -0.573283942629E-01 7 0.919449734708 -0.606922297579E-01 8 0.906431283593 -0.656085002218E-01 9 0.895178052194 -0.725410490133E-01 10 0.888011680377 -0.802252137379E-01 11 0.884949173316 -0.846981404739E-01 12 0.881878640102 -0.844224145068E-01 13 0.877039006894 -0.819860762917E-01 14 0.871237290892 -0.776552577550E-01 15 0.862748410451 -0.711093863680E-01 16 0.850452869081 -0.647486470722E-01 17 0.835644044392 -0.604043086196E-01 18 0.819682864128 -0.583083772304E-01 19 0.803230959579 -0.582732409781E-01 20 0.786607923215 -0.602815639016E-01 21 0.770171949218 -0.645893257962E-01 22 0.754704792583 -0.716226022974E-01 23 0.741849120316 -0.814449484888E-01 24 0.733792549822 -0.922844533600E-01 25 0.730256008584 -0.100093401180 26 0.727238579735 -0.103113100251 27 0.721992235264 -0.103024948415 28 0.712954915302 -0.101695163779 29 0.699582166262 -0.102616724366 30 0.684475485802 -0.108821744228 31 0.671108166646 -0.120835069477 32 0.662684322465 -0.137972758987 33 0.662772696344 -0.157744883705 34 0.673416965683 -0.175232971037 35 0.694507224793 -0.183265601867 36 0.717552961539 -0.172905113722 37 0.727000848966 -0.148448929496 38 0.720087249826 -0.124403690959 39 0.703956844667 -0.108133842271 40 0.684817351869 -0.100260042518 41 0.666470243681 -0.995746097357E-01 42 0.651889981076 -0.104213425621 43 0.643030017901 -0.110610507784 44 0.638473005568 -0.114564577382 45 0.634298062024 -0.115229076840 46 0.629017434047 -0.114935723930 47 0.623547319249 -0.114401203707 48 0.617574348230 -0.113391701917 49 0.611231322523 -0.112813849415 50 0.605602956702 -0.111891849415 51 0.599053794056 -0.109456515589 52 0.590217531941 -0.107557973475 53 0.580682001615 -0.107794265799 54 0.571970722622 -0.109503689755 55 0.563937349298 -0.111751567967 56 0.556455560394 -0.115163895837 57 0.551440728289 -0.119367484064 58 0.548610792085 -0.121132672939 59 0.544143338774 -0.120216658684 60 0.537105509434 -0.120068280973 elk-7.2.42/tests/PaxHeaders.21776/test_0010000644000000000000000000000013114061636520014552 xustar0030 mtime=1623670096.654100878 29 atime=1623670096.64110089 30 ctime=1623670096.654100878 elk-7.2.42/tests/test_001/0000755002504400250440000000000014061636520016665 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_001/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015733 xustar0030 mtime=1623670096.643100888 30 atime=1623670096.643100888 30 ctime=1623670096.643100888 elk-7.2.42/tests/test_001/elk.in0000644002504400250440000000222314061636520017767 0ustar00dewhurstdewhurst00000000000000 tasks 0 1 115 500 test .true. lmaxi 2 stype 1 swidth 0.01 mixtype 3 ! small cut-off for testing purposes rgkmax 6.0 maxscl 4 avec 7.2246 0.0 0.0 0.0 7.3442 0.0 0.0 0.0 22.0733 sppath '../../species/' atoms 4 : nspecies 'Y.in' : spfname 1 : natoms 0.5 0.5 0.5 0.0 0.0 0.0 : atposl, bfcmt 'Ba.in' 2 : natoms 0.5 0.5 0.1843 0.0 0.0 0.0 : atposl, bfcmt 0.5 0.5 0.8157 0.0 0.0 0.0 'Cu.in' 3 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 0.0 0.0 0.3556 0.0 0.0 0.0 0.0 0.0 0.6444 0.0 0.0 0.0 'O.in' 7 : natoms 0.0 0.5 0.0 0.0 0.0 0.0 : atposl, bfcmt 0.5 0.0 0.3773 0.0 0.0 0.0 0.5 0.0 0.6227 0.0 0.0 0.0 0.0 0.5 0.3789 0.0 0.0 0.0 0.0 0.5 0.6211 0.0 0.0 0.0 0.0 0.0 0.1584 0.0 0.0 0.0 0.0 0.0 0.8416 0.0 0.0 0.0 ngridk 2 2 1 vkloff 0.25 0.5 0.5 elk-7.2.42/tests/test_001/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016523 xustar0030 mtime=1623670096.644100887 30 atime=1623670096.644100887 30 ctime=1623670096.644100887 elk-7.2.42/tests/test_001/TEST_500.OUT_0000644002504400250440000000013514061636520020557 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 30.3494495419 elk-7.2.42/tests/test_001/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.646100885 30 atime=1623670096.646100885 30 ctime=1623670096.646100885 elk-7.2.42/tests/test_001/TEST_510.OUT_0000644002504400250440000000014514061636520020561 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.215059763688E-01 elk-7.2.42/tests/test_001/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016522 xustar0030 mtime=1623670096.647100884 30 atime=1623670096.647100884 30 ctime=1623670096.647100884 elk-7.2.42/tests/test_001/TEST_400.OUT_0000644002504400250440000000014114061636520020553 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 294.004413959 elk-7.2.42/tests/test_001/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016516 xustar0030 mtime=1623670096.649100882 30 atime=1623670096.648100883 30 ctime=1623670096.649100882 elk-7.2.42/tests/test_001/TEST_000.OUT_0000644002504400250440000000012614061636520020552 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -25088.8810469 elk-7.2.42/tests/test_001/PaxHeaders.21776/TEST_115.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.650100882 30 atime=1623670096.650100882 30 ctime=1623670096.650100882 elk-7.2.42/tests/test_001/TEST_115.OUT_0000644002504400250440000000053114061636520020561 0ustar00dewhurstdewhurst00000000000000'electric field gradient' 2 9 0.100000000000E-02 1 0.366071812579 2 0.664624598943E-16 3 0.182271996545E-15 4 0.664624598943E-16 5 0.481042848245 6 0.204196962395E-16 7 0.182271996545E-15 8 0.204196962395E-16 9 -0.847114660824 elk-7.2.42/tests/test_001/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000012714061636520016534 xustar0029 mtime=1623670096.65210088 29 atime=1623670096.65210088 29 ctime=1623670096.65210088 elk-7.2.42/tests/test_001/TEST_910.OUT_0000644002504400250440000000037114061636520020566 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 6 0.100000000000E-07 1 0.108711646790 2 0.213882564036 3 0.142325463505 4 0.543558233949 5 0.213882564036 6 0.142325463505 elk-7.2.42/tests/test_001/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.653100879 30 atime=1623670096.653100879 30 ctime=1623670096.653100879 elk-7.2.42/tests/test_001/TEST_705.OUT_0000644002504400250440000000010114061636520020557 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 8 elk-7.2.42/tests/test_001/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.655100877 30 atime=1623670096.655100877 30 ctime=1623670096.655100877 elk-7.2.42/tests/test_001/TEST_900.OUT_0000644002504400250440000000007014061636520020561 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 34171 elk-7.2.42/tests/PaxHeaders.21776/test_0050000644000000000000000000000013214061636520014557 xustar0030 mtime=1623670096.668100865 30 atime=1623670096.656100876 30 ctime=1623670096.668100865 elk-7.2.42/tests/test_005/0000755002504400250440000000000014061636520016671 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_005/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.658100874 30 atime=1623670096.657100875 30 ctime=1623670096.658100874 elk-7.2.42/tests/test_005/TEST_705.OUT_0000644002504400250440000000010114061636520020563 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 8 elk-7.2.42/tests/test_005/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.659100873 30 atime=1623670096.659100873 30 ctime=1623670096.659100873 elk-7.2.42/tests/test_005/TEST_910.OUT_0000644002504400250440000000144714061636520020577 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 24 0.100000000000E-07 1 0.581776417331E-01 2 0.174532925199 3 0.407243492132 4 0.523598775598 5 0.639954059065 6 -0.581776417331E-01 7 0.523598775598 8 -0.290888208666 9 0.872664625997 10 0.989019909463 11 0.174532925199 12 0.407243492132 13 -0.407243492132 14 0.639954059065 15 0.872664625997 16 0.581776417331E-01 17 1.10537519293 18 0.407243492132 19 0.581776417331E-01 20 0.174532925199 21 1.33808575986 22 0.523598775598 23 0.639954059065 24 0.872664625997 elk-7.2.42/tests/test_005/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.661100871 30 atime=1623670096.660100872 30 ctime=1623670096.661100871 elk-7.2.42/tests/test_005/TEST_500.OUT_0000644002504400250440000000013514061636520020563 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 33.9674460614 elk-7.2.42/tests/test_005/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000012714061636520016534 xustar0029 mtime=1623670096.66210087 29 atime=1623670096.66210087 29 ctime=1623670096.66210087 elk-7.2.42/tests/test_005/TEST_510.OUT_0000644002504400250440000000014514061636520020565 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.373130903843E-02 elk-7.2.42/tests/test_005/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.663100869 30 atime=1623670096.663100869 30 ctime=1623670096.663100869 elk-7.2.42/tests/test_005/TEST_400.OUT_0000644002504400250440000000014114061636520020557 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 25.9973369269 elk-7.2.42/tests/test_005/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.665100868 30 atime=1623670096.664100868 30 ctime=1623670096.665100868 elk-7.2.42/tests/test_005/TEST_450.OUT_0000644002504400250440000000014014061636520020563 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 2.46663876336 elk-7.2.42/tests/test_005/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016522 xustar0030 mtime=1623670096.666100867 30 atime=1623670096.666100867 30 ctime=1623670096.666100867 elk-7.2.42/tests/test_005/TEST_000.OUT_0000644002504400250440000000012614061636520020556 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1270.46826012 elk-7.2.42/tests/test_005/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015737 xustar0030 mtime=1623670096.667100866 30 atime=1623670096.667100866 30 ctime=1623670096.667100866 elk-7.2.42/tests/test_005/elk.in0000644002504400250440000000076514061636520020004 0ustar00dewhurstdewhurst00000000000000 ! Spin-spiral state for Gamma-Fe. tasks 0 500 test .true. maxscl 5 spinsprl .true. vqlss 0.1 0.1 0.0 rgkmax 6.5 bfieldc 0.05 0.0 0.0 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.375 sppath '../../species/' atoms 1 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 2 2 2 vkloff 0.25 0.5 0.625 elk-7.2.42/tests/test_005/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.669100864 30 atime=1623670096.669100864 30 ctime=1623670096.669100864 elk-7.2.42/tests/test_005/TEST_900.OUT_0000644002504400250440000000007014061636520020565 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 2229 elk-7.2.42/tests/PaxHeaders.21776/test_0090000644000000000000000000000013214061636520014563 xustar0030 mtime=1623670096.687100847 30 atime=1623670096.670100863 30 ctime=1623670096.687100847 elk-7.2.42/tests/test_009/0000755002504400250440000000000014061636520016675 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016542 xustar0030 mtime=1623670096.671100862 30 atime=1623670096.671100862 30 ctime=1623670096.671100862 elk-7.2.42/tests/test_009/TEST_705.OUT_0000644002504400250440000000010114061636520020567 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 24 elk-7.2.42/tests/test_009/PaxHeaders.21776/elk.in0000644000000000000000000000013014061636520015741 xustar0029 mtime=1623670096.67310086 30 atime=1623670096.672100861 29 ctime=1623670096.67310086 elk-7.2.42/tests/test_009/elk.in0000644002504400250440000000064614061636520020006 0ustar00dewhurstdewhurst00000000000000 ! Electron loss near-edge spectroscopy (ELNES) for boron nitride. tasks 0 140 500 test .true. xctype 5 maxscl 6 rgkmax 6.0 lradstp 2 spinorb .true. vecql 0.0 0.0 0.5 wplot 50 100 3 18.5 19.0 emaxelnes -10.0 ngridk 2 2 2 avec 3.4204 3.4204 0.0000 3.4204 0.0000 3.4204 0.0000 3.4204 3.4204 atoms 2 'B.in' 1 0.00 0.00 0.00 0.0 0.0 0.0 'N+.in' 1 0.25 0.25 0.25 0.0 0.0 0.0 elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.674100859 30 atime=1623670096.674100859 30 ctime=1623670096.674100859 elk-7.2.42/tests/test_009/TEST_900.OUT_0000644002504400250440000000007014061636520020571 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 2277 elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.675100858 30 atime=1623670096.675100858 30 ctime=1623670096.675100858 elk-7.2.42/tests/test_009/TEST_910.OUT_0000644002504400250440000000052614061636520020600 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 9 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.459243458892 5 0.459243458892 6 -0.459243458892 7 0.918486917784 8 0.00000000000 9 0.00000000000 elk-7.2.42/tests/test_009/PaxHeaders.21776/B.in0000644000000000000000000000013214061636520015351 xustar0030 mtime=1623670096.677100856 30 atime=1623670096.677100856 30 ctime=1623670096.677100856 elk-7.2.42/tests/test_009/B.in0000644002504400250440000000172214061636520017410 0ustar00dewhurstdewhurst00000000000000 'B' : spsymb 'boron' : spname -5.00000 : spzn 19707.24740 : spmass 0.894427E-06 1.8000 43.3288 300 : sprmin, rmt, sprmax, nrmt 3 : spnst 1 0 1 2.00000 T : spn, spl, spk, spocc, spcore 2 0 1 2.00000 F 2 1 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 2 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F elk-7.2.42/tests/test_009/PaxHeaders.21776/N+.in0000644000000000000000000000013214061636520015440 xustar0030 mtime=1623670096.679100855 30 atime=1623670096.678100855 30 ctime=1623670096.679100855 elk-7.2.42/tests/test_009/N+.in0000644002504400250440000000253414061636520017501 0ustar00dewhurstdewhurst00000000000000 'N+' : spsymb 'nitrogen with pseudo core-hole' : spname -8.00000 : spzn 25532.72506 : spmass 0.755929E-06 1.4500 26.9237 300 : sprmin, rmt, sprmax, nrmt 4 : spnst 1 0 1 2.00000 F : spn, spl, spk, spocc, spcore 2 0 1 2.00000 F 2 1 1 1.00000 F 2 1 2 2.50000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 3 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F -0.6020 0 T 0 3 0.1500 0 F 0.1500 1 F -20.0000 0 T elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.680100854 30 atime=1623670096.680100854 30 ctime=1623670096.680100854 elk-7.2.42/tests/test_009/TEST_500.OUT_0000644002504400250440000000013514061636520020567 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 166.666666638 elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.681100853 30 atime=1623670096.681100853 30 ctime=1623670096.681100853 elk-7.2.42/tests/test_009/TEST_510.OUT_0000644002504400250440000000014514061636520020571 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.484273556000E-01 elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.683100851 30 atime=1623670096.683100851 30 ctime=1623670096.683100851 elk-7.2.42/tests/test_009/TEST_450.OUT_0000644002504400250440000000014014061636520020567 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.322632677020E-25 elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013114061636520016531 xustar0030 mtime=1623670096.685100849 29 atime=1623670096.68410085 30 ctime=1623670096.685100849 elk-7.2.42/tests/test_009/TEST_400.OUT_0000644002504400250440000000014114061636520020563 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 12.5000313987 elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.686100848 30 atime=1623670096.686100848 30 ctime=1623670096.686100848 elk-7.2.42/tests/test_009/TEST_000.OUT_0000644002504400250440000000012614061636520020562 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -99.9816651181 elk-7.2.42/tests/test_009/PaxHeaders.21776/TEST_140.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.688100846 30 atime=1623670096.687100847 30 ctime=1623670096.688100846 elk-7.2.42/tests/test_009/TEST_140.OUT_0000644002504400250440000000311414061636520020567 0ustar00dewhurstdewhurst00000000000000'ELNES cross-section' 2 50 0.100000000000E-01 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.00000000000 5 0.00000000000 6 0.00000000000 7 0.00000000000 8 0.00000000000 9 0.00000000000 10 0.00000000000 11 0.119956766630E-10 12 0.296036648951E-09 13 0.314275301088E-08 14 0.160129784706E-07 15 0.589467143256E-07 16 0.176258730598E-06 17 0.478702639757E-06 18 0.139481395327E-05 19 0.377535835793E-05 20 0.789416311994E-05 21 0.125236403833E-04 22 0.148952428844E-04 23 0.134761292590E-04 24 0.918086150243E-05 25 0.473361283208E-05 26 0.187024320394E-05 27 0.621177592065E-06 28 0.204698275476E-06 29 0.536833357911E-07 30 0.183398328605E-07 31 0.276734646540E-06 32 0.220396694200E-05 33 0.134038727493E-04 34 0.855803563238E-04 35 0.221355713979E-03 36 0.402739577356E-03 37 0.480354723714E-03 38 0.448110161005E-03 39 0.327831911948E-03 40 0.273027789621E-03 41 0.295981699785E-03 42 0.394257867871E-03 43 0.528593328604E-03 44 0.699537511425E-03 45 0.891627313153E-03 46 0.106298959676E-02 47 0.118815490967E-02 48 0.128677078155E-02 49 0.140575607217E-02 50 0.155981254512E-02 elk-7.2.42/tests/PaxHeaders.21776/test_0130000644000000000000000000000013214061636520014556 xustar0030 mtime=1623670096.702100833 30 atime=1623670096.688100846 30 ctime=1623670096.702100833 elk-7.2.42/tests/test_013/0000755002504400250440000000000014061636520016670 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_013/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015736 xustar0030 mtime=1623670096.690100844 30 atime=1623670096.689100845 30 ctime=1623670096.690100844 elk-7.2.42/tests/test_013/elk.in0000644002504400250440000000125014061636520017771 0ustar00dewhurstdewhurst00000000000000 ! Force test with spin-orbit coupling, removal of the source term from B_xc and ! application of a constanst A-field tasks 0 500 test .true. spinorb .true. nosource .true. tforce .true. bfieldc 0.0 0.0 0.1 afieldc 0.0 0.5 0.0 rgkmax 6.0 maxscl 4 scale 5.496 avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 atoms 2 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.1 0.2 0.3 : atposl, bfcmt 'Al.in' 1 0.51 0.52 0.485 0.4 0.4 -0.4 : atposl, bfcmt sppath '../../species/' ngridk 4 4 4 vkloff 0.25 0.5 0.625 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.691100843 30 atime=1623670096.691100843 30 ctime=1623670096.691100843 elk-7.2.42/tests/test_013/TEST_705.OUT_0000644002504400250440000000010114061636520020562 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 1 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.693100841 30 atime=1623670096.692100843 30 ctime=1623670096.693100841 elk-7.2.42/tests/test_013/TEST_900.OUT_0000644002504400250440000000007014061636520020564 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 4945 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.694100841 30 atime=1623670096.694100841 30 ctime=1623670096.694100841 elk-7.2.42/tests/test_013/TEST_910.OUT_0000644002504400250440000001357714061636520020605 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 192 0.100000000000E-07 1 0.714517979801E-01 2 0.142903595960 3 0.178629494950 4 0.357258989901 5 0.142903595960 6 0.178629494950 7 0.643066181821 8 0.142903595960 9 0.178629494950 10 0.928873373742 11 0.142903595960 12 0.178629494950 13 0.714517979801E-01 14 0.428710787881 15 0.178629494950 16 0.357258989901 17 0.428710787881 18 0.178629494950 19 0.643066181821 20 0.428710787881 21 0.178629494950 22 0.928873373742 23 0.428710787881 24 0.178629494950 25 0.714517979801E-01 26 0.714517979801 27 0.178629494950 28 0.357258989901 29 0.714517979801 30 0.178629494950 31 0.643066181821 32 0.714517979801 33 0.178629494950 34 0.928873373742 35 0.714517979801 36 0.178629494950 37 0.714517979801E-01 38 1.00032517172 39 0.178629494950 40 0.357258989901 41 1.00032517172 42 0.178629494950 43 0.643066181821 44 1.00032517172 45 0.178629494950 46 0.928873373742 47 1.00032517172 48 0.178629494950 49 0.714517979801E-01 50 0.142903595960 51 0.464436686871 52 0.357258989901 53 0.142903595960 54 0.464436686871 55 0.643066181821 56 0.142903595960 57 0.464436686871 58 0.928873373742 59 0.142903595960 60 0.464436686871 61 0.714517979801E-01 62 0.428710787881 63 0.464436686871 64 0.357258989901 65 0.428710787881 66 0.464436686871 67 0.643066181821 68 0.428710787881 69 0.464436686871 70 0.928873373742 71 0.428710787881 72 0.464436686871 73 0.714517979801E-01 74 0.714517979801 75 0.464436686871 76 0.357258989901 77 0.714517979801 78 0.464436686871 79 0.643066181821 80 0.714517979801 81 0.464436686871 82 0.928873373742 83 0.714517979801 84 0.464436686871 85 0.714517979801E-01 86 1.00032517172 87 0.464436686871 88 0.357258989901 89 1.00032517172 90 0.464436686871 91 0.643066181821 92 1.00032517172 93 0.464436686871 94 0.928873373742 95 1.00032517172 96 0.464436686871 97 0.714517979801E-01 98 0.142903595960 99 0.750243878791 100 0.357258989901 101 0.142903595960 102 0.750243878791 103 0.643066181821 104 0.142903595960 105 0.750243878791 106 0.928873373742 107 0.142903595960 108 0.750243878791 109 0.714517979801E-01 110 0.428710787881 111 0.750243878791 112 0.357258989901 113 0.428710787881 114 0.750243878791 115 0.643066181821 116 0.428710787881 117 0.750243878791 118 0.928873373742 119 0.428710787881 120 0.750243878791 121 0.714517979801E-01 122 0.714517979801 123 0.750243878791 124 0.357258989901 125 0.714517979801 126 0.750243878791 127 0.643066181821 128 0.714517979801 129 0.750243878791 130 0.928873373742 131 0.714517979801 132 0.750243878791 133 0.714517979801E-01 134 1.00032517172 135 0.750243878791 136 0.357258989901 137 1.00032517172 138 0.750243878791 139 0.643066181821 140 1.00032517172 141 0.750243878791 142 0.928873373742 143 1.00032517172 144 0.750243878791 145 0.714517979801E-01 146 0.142903595960 147 1.03605107071 148 0.357258989901 149 0.142903595960 150 1.03605107071 151 0.643066181821 152 0.142903595960 153 1.03605107071 154 0.928873373742 155 0.142903595960 156 1.03605107071 157 0.714517979801E-01 158 0.428710787881 159 1.03605107071 160 0.357258989901 161 0.428710787881 162 1.03605107071 163 0.643066181821 164 0.428710787881 165 1.03605107071 166 0.928873373742 167 0.428710787881 168 1.03605107071 169 0.714517979801E-01 170 0.714517979801 171 1.03605107071 172 0.357258989901 173 0.714517979801 174 1.03605107071 175 0.643066181821 176 0.714517979801 177 1.03605107071 178 0.928873373742 179 0.714517979801 180 1.03605107071 181 0.714517979801E-01 182 1.00032517172 183 1.03605107071 184 0.357258989901 185 1.00032517172 186 1.03605107071 187 0.643066181821 188 1.00032517172 189 1.03605107071 190 0.928873373742 191 1.00032517172 192 1.03605107071 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000012714061636520016532 xustar0029 mtime=1623670096.69510084 29 atime=1623670096.69510084 29 ctime=1623670096.69510084 elk-7.2.42/tests/test_013/TEST_500.OUT_0000644002504400250440000000013514061636520020562 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 117.676510445 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.697100838 30 atime=1623670096.697100838 30 ctime=1623670096.697100838 elk-7.2.42/tests/test_013/TEST_510.OUT_0000644002504400250440000000014514061636520020564 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.100334394303E-03 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.698100837 30 atime=1623670096.698100837 30 ctime=1623670096.698100837 elk-7.2.42/tests/test_013/TEST_400.OUT_0000644002504400250440000000014114061636520020556 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 38.9880840437 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.700100835 30 atime=1623670096.700100835 30 ctime=1623670096.700100835 elk-7.2.42/tests/test_013/TEST_450.OUT_0000644002504400250440000000014014061636520020562 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 1.36964954732 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016521 xustar0030 mtime=1623670096.701100834 30 atime=1623670096.701100834 30 ctime=1623670096.701100834 elk-7.2.42/tests/test_013/TEST_000.OUT_0000644002504400250440000000012614061636520020555 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1515.93184246 elk-7.2.42/tests/test_013/PaxHeaders.21776/TEST_750.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.703100832 30 atime=1623670096.703100832 30 ctime=1623670096.703100832 elk-7.2.42/tests/test_013/TEST_750.OUT_0000644002504400250440000000036114061636520020572 0ustar00dewhurstdewhurst00000000000000'total forces' 2 6 0.100000000000E-02 1 -0.159456002110E-01 2 -0.363728131894E-01 3 0.280818063166E-01 4 0.159456002110E-01 5 0.363728131894E-01 6 -0.280818063166E-01 elk-7.2.42/tests/PaxHeaders.21776/test_0170000644000000000000000000000013214061636520014562 xustar0030 mtime=1623670096.718100818 30 atime=1623670096.704100831 30 ctime=1623670096.718100818 elk-7.2.42/tests/test_017/0000755002504400250440000000000014061636520016674 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000012714061636520016545 xustar0029 mtime=1623670096.70510083 29 atime=1623670096.70510083 29 ctime=1623670096.70510083 elk-7.2.42/tests/test_017/TEST_705.OUT_0000644002504400250440000000010114061636520020566 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 24 elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.707100829 30 atime=1623670096.707100829 30 ctime=1623670096.707100829 elk-7.2.42/tests/test_017/TEST_900.OUT_0000644002504400250440000000007014061636520020570 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 725 elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.708100828 30 atime=1623670096.708100828 30 ctime=1623670096.708100828 elk-7.2.42/tests/test_017/TEST_910.OUT_0000644002504400250440000000037114061636520020575 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 6 0.100000000000E-07 1 -0.138777878078E-16 2 0.146981971254 3 0.587927885017 4 0.293963942509 5 0.440945913763 6 0.293963942509 elk-7.2.42/tests/test_017/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015742 xustar0030 mtime=1623670096.710100826 30 atime=1623670096.710100826 30 ctime=1623670096.710100826 elk-7.2.42/tests/test_017/elk.in0000644002504400250440000000120314061636520017773 0ustar00dewhurstdewhurst00000000000000 ! RDMFT test tasks 0 300 500 test .true. rdmmaxscl 1 maxitn 2 maxitc 2 mixtype 3 rgkmax 6.0 lmaxo 5 gmaxvr 0.0 avec 5.3435 5.3435 0.0000 5.3435 0.0000 5.3435 0.0000 5.3435 5.3435 sppath '../../species/' atoms 2 : nspecies 'Ga.in' : spfname 1 : natoms 0.00 0.00 0.00 0.0 0.0 0.0 : atposl, bfcmt 'As.in' : spfname 1 : natoms 0.25 0.25 0.25 0.0 0.0 0.0 : atposl, bfcmt ngridk 2 1 1 vkloff 0.25 0.5 0.625 elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.711100825 30 atime=1623670096.711100825 30 ctime=1623670096.711100825 elk-7.2.42/tests/test_017/TEST_500.OUT_0000644002504400250440000000013514061636520020566 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.188737914285E-11 elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.713100823 30 atime=1623670096.713100823 30 ctime=1623670096.713100823 elk-7.2.42/tests/test_017/TEST_510.OUT_0000644002504400250440000000014514061636520020570 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.117176067378 elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.714100822 30 atime=1623670096.714100822 30 ctime=1623670096.714100822 elk-7.2.42/tests/test_017/TEST_400.OUT_0000644002504400250440000000014114061636520020562 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 63.9848926557 elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013014061636520016523 xustar0029 mtime=1623670096.71610082 30 atime=1623670096.715100821 29 ctime=1623670096.71610082 elk-7.2.42/tests/test_017/TEST_000.OUT_0000644002504400250440000000012614061636520020561 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -4199.45151923 elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.717100819 30 atime=1623670096.717100819 30 ctime=1623670096.717100819 elk-7.2.42/tests/test_017/TEST_800.OUT_0000644002504400250440000000022514061636520020571 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 2 0.100000000000E-07 1 159.645293857 2 40.1466806379 elk-7.2.42/tests/test_017/PaxHeaders.21776/TEST_300.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.718100818 30 atime=1623670096.718100818 30 ctime=1623670096.718100818 elk-7.2.42/tests/test_017/TEST_300.OUT_0000644002504400250440000000013414061636520020563 0ustar00dewhurstdewhurst00000000000000'RDMFT total energy' 2 1 0.100000000000E-05 1 -4061.15741384 elk-7.2.42/tests/PaxHeaders.21776/test_0210000644000000000000000000000013214061636520014555 xustar0030 mtime=1623670096.736100802 30 atime=1623670096.720100816 30 ctime=1623670096.736100802 elk-7.2.42/tests/test_021/0000755002504400250440000000000014061636520016667 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.721100816 30 atime=1623670096.721100816 30 ctime=1623670096.721100816 elk-7.2.42/tests/test_021/TEST_705.OUT_0000644002504400250440000000010114061636520020561 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 24 elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.723100814 30 atime=1623670096.722100815 30 ctime=1623670096.723100814 elk-7.2.42/tests/test_021/TEST_910.OUT_0000644002504400250440000000237014061636520020571 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 39 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.280567949614 5 -0.935226498715E-01 6 -0.935226498715E-01 7 0.561135899229 8 -0.187045299743 9 -0.187045299743 10 0.187045299743 11 0.187045299743 12 -0.187045299743 13 0.467613249357 14 0.935226498715E-01 15 -0.280567949614 16 0.748181198972 17 0.416333634234E-16 18 -0.374090599486 19 0.374090599486 20 0.374090599486 21 -0.374090599486 22 0.935226498715E-01 23 0.935226498715E-01 24 0.935226498715E-01 25 0.374090599486 26 0.416333634234E-16 27 0.555111512313E-16 28 0.654658549100 29 -0.935226498715E-01 30 -0.935226498715E-01 31 0.280567949614 32 0.280567949614 33 -0.935226498715E-01 34 0.561135899229 35 0.187045299743 36 -0.187045299743 37 0.187045299743 38 0.187045299743 39 0.187045299743 elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016520 xustar0030 mtime=1623670096.724100813 30 atime=1623670096.724100813 30 ctime=1623670096.724100813 elk-7.2.42/tests/test_021/TEST_000.OUT_0000644002504400250440000000012614061636520020554 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -2462.70040632 elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_196.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.726100811 30 atime=1623670096.725100812 30 ctime=1623670096.726100811 elk-7.2.42/tests/test_021/TEST_196.OUT_0000644002504400250440000000500014061636520020570 0ustar00dewhurstdewhurst00000000000000'magnetic structure factors' 3 47 0.100000000000E-03 1 0.360662979879E-17 -0.752316384526E-35 2 0.268160030473E-01 0.174442587749E-16 3 0.204349623262E-01 -0.295425916892E-17 4 0.343103864039E-17 -0.177199292566E-17 5 0.333946734739E-19 0.271186068393E-16 6 0.349610699680E-17 -0.258819387363E-16 7 0.158945129930E-01 -0.231730982241E-16 8 0.125662877341E-01 -0.156431079097E-16 9 0.123650629359E-01 -0.171396955003E-16 10 0.257242305141E-17 -0.392495769369E-17 11 0.670856983231E-18 -0.137693675906E-16 12 0.101549635630E-01 0.715857005925E-17 13 0.837998994307E-02 -0.635982518000E-17 14 0.852459608710E-18 -0.999668284350E-17 15 0.108994038147E-17 0.239134341669E-16 16 0.922176900710E-18 0.111876111673E-16 17 0.134567099513E-17 0.470780912084E-17 18 -0.270631223350E-18 -0.208912206111E-16 19 0.692621737160E-02 0.327002192070E-16 20 0.648561881437E-02 0.953973857581E-17 21 0.542643158559E-02 -0.168150300082E-16 22 0.583535548224E-02 0.179188008853E-16 23 0.253218498953E-18 0.151313965698E-16 24 0.450096174614E-02 -0.415696294621E-17 25 0.391282776716E-02 0.325613624054E-17 26 0.406516639407E-02 0.304333917599E-17 27 0.404079555187E-18 0.130443073877E-17 28 0.116687286570E-17 0.103134731658E-16 29 0.660426314751E-18 -0.110656384229E-16 30 0.488600272079E-19 -0.220567379465E-17 31 0.692903488748E-18 0.222735783810E-16 32 0.328095477303E-02 0.312554349175E-17 33 0.329522832899E-02 -0.786002681333E-17 34 0.277977148342E-02 -0.844518491276E-17 35 0.329296975286E-18 0.753859323056E-17 36 -0.411438249030E-18 -0.128918414572E-17 37 0.322693493950E-18 0.590890184005E-17 38 0.234877914992E-02 -0.582236069366E-17 39 0.239281686733E-02 0.166768160478E-17 40 0.221389769953E-02 -0.102493080121E-16 41 0.198785905308E-02 -0.143550144392E-17 42 0.179402522246E-02 -0.831982685290E-17 43 0.253519148070E-18 -0.212435863171E-17 44 0.184169513299E-18 0.479081834967E-17 45 0.418451462994E-18 0.483825219472E-17 46 0.753528807804E-18 0.580725788638E-17 47 0.288999343574E-19 0.599699326656E-18 elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000012714061636520016535 xustar0029 mtime=1623670096.72710081 29 atime=1623670096.72710081 29 ctime=1623670096.72710081 elk-7.2.42/tests/test_021/TEST_900.OUT_0000644002504400250440000000007014061636520020563 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 8623 elk-7.2.42/tests/test_021/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015735 xustar0030 mtime=1623670096.729100808 30 atime=1623670096.728100809 30 ctime=1623670096.729100808 elk-7.2.42/tests/test_021/elk.in0000644002504400250440000000060314061636520017771 0ustar00dewhurstdewhurst00000000000000 tasks 0 195 196 500 test .true. spinpol .true. scale 8.397946 avec 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 atoms 2 'Mn.in' 2 0.0 0.0 0.0 0.0 0.0 -0.01 0.5 0.5 0.5 0.0 0.0 0.01 'O.in' 2 0.25 0.25 0.25 0.0 0.0 0.0 0.75 0.75 0.75 0.0 0.0 0.0 sppath '../../species/' ngridk 4 4 4 hmaxvr 4.0 reduceh .true. elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.730100807 30 atime=1623670096.730100807 30 ctime=1623670096.730100807 elk-7.2.42/tests/test_021/TEST_500.OUT_0000644002504400250440000000013514061636520020561 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.364462465345E-04 elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.732100805 30 atime=1623670096.731100806 30 ctime=1623670096.732100805 elk-7.2.42/tests/test_021/TEST_510.OUT_0000644002504400250440000000014514061636520020563 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.297252590802E-01 elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.733100804 30 atime=1623670096.733100804 30 ctime=1623670096.733100804 elk-7.2.42/tests/test_021/TEST_400.OUT_0000644002504400250440000000014114061636520020555 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 66.0189750624 elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.735100803 30 atime=1623670096.734100803 30 ctime=1623670096.735100803 elk-7.2.42/tests/test_021/TEST_450.OUT_0000644002504400250440000000014014061636520020561 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.190358142232E-16 elk-7.2.42/tests/test_021/PaxHeaders.21776/TEST_195.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.736100802 30 atime=1623670096.736100802 30 ctime=1623670096.736100802 elk-7.2.42/tests/test_021/TEST_195.OUT_0000644002504400250440000000477714061636520020613 0ustar00dewhurstdewhurst00000000000000'density structure factors' 3 47 0.100000000000E-04 1 0.222781435049 -0.422188091550E-20 2 0.279227815598E-16 -0.100613961607E-15 3 -0.499672690647E-17 0.208166817117E-16 4 0.897007263975E-01 0.135152018688E-16 5 0.897768785632E-01 -0.180311484630E-15 6 0.159095660612 0.186495395185E-15 7 -0.454329203628E-16 0.175207071074E-15 8 -0.383059051417E-16 0.131838984174E-15 9 0.386910154599E-16 0.147451495458E-15 10 0.128978032193 0.351884567384E-16 11 0.129015063858 0.131678818255E-15 12 0.176367710446E-16 -0.711236625150E-16 13 0.142193705461E-16 0.676542155631E-16 14 0.709436814581E-01 0.112758925900E-15 15 0.709341248128E-01 -0.272338629723E-15 16 0.709477925096E-01 -0.130872505244E-15 17 0.110367577233 -0.585743802893E-16 18 0.110427114574 0.251856285785E-15 19 0.942729468141E-16 -0.409394740331E-15 20 -0.317247762292E-16 -0.130104260698E-15 21 -0.569907707573E-16 0.249800180541E-15 22 0.589359969812E-16 -0.260208521397E-15 23 0.980833639283E-01 -0.246063963717E-15 24 -0.188196496129E-16 0.763278329430E-16 25 0.116252787585E-16 -0.555111512313E-16 26 0.149561685161E-16 -0.624500451352E-16 27 0.583608605111E-01 -0.239360482710E-16 28 0.582951480310E-01 -0.200844158044E-15 29 0.583174080396E-01 0.219343636467E-15 30 0.886603807723E-01 0.468098844888E-16 31 0.886390603924E-01 -0.465159784733E-15 32 0.171031763893E-16 -0.780625564190E-16 33 -0.367501630734E-16 0.170002900646E-15 34 0.464200545546E-16 0.215105711021E-15 35 0.816397356155E-01 -0.205649513993E-15 36 0.816031991382E-01 0.362014962831E-16 37 0.816175977784E-01 -0.172322801706E-15 38 0.357218849923E-16 0.164798730218E-15 39 0.100857532958E-16 -0.468375338514E-16 40 -0.642570321362E-16 0.300974523082E-15 41 0.103723934382E-16 0.546437894933E-16 42 -0.581154871633E-16 0.274953670942E-15 43 0.505039365445E-01 0.738723790411E-16 44 0.502376906810E-01 -0.156536268617E-15 45 0.504649595069E-01 -0.172111463728E-15 46 0.505015282088E-01 -0.203490800318E-15 47 0.502809158028E-01 -0.235818252568E-16 elk-7.2.42/tests/PaxHeaders.21776/test_0230000644000000000000000000000013214061636520014557 xustar0030 mtime=1623670096.756100783 30 atime=1623670096.737100801 30 ctime=1623670096.756100783 elk-7.2.42/tests/test_023/0000755002504400250440000000000014061636520016671 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_023/PaxHeaders.21776/elk.in0000644000000000000000000000012414061636520015740 xustar0028 mtime=1623670096.7381008 28 atime=1623670096.7381008 28 ctime=1623670096.7381008 elk-7.2.42/tests/test_023/elk.in0000644002504400250440000000123714061636520017777 0ustar00dewhurstdewhurst00000000000000 ! Time-dependent density functional theory (TDDFT) optical spectrum of lithium ! fluoride. tasks 0 120 121 125 320 500 test .true. spinorb .true. scissor 0.192 xctype 3 ! bootstrap kernel fxctype 210 lmaxi 2 swidth 0.01 gmaxrf 1.5 nempty 10 ngridk 8 8 8 wplot 50 100 0 0.0 1.5 avec 3.80402 3.80402 0.0 3.80402 0.0 3.80402 0.0 3.80402 3.80402 sppath '../../species/' atoms 2 : nspecies 'Li.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'F.in' 1 0.5 0.5 0.5 elk-7.2.42/tests/test_023/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.740100798 30 atime=1623670096.740100798 30 ctime=1623670096.740100798 elk-7.2.42/tests/test_023/TEST_705.OUT_0000644002504400250440000000010114061636520020563 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_023/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.741100797 30 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30 ctime=1623670096.765100775 elk-7.2.42/tests/test_025/TEST_705.OUT_0000644002504400250440000000010114061636520020565 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 8 elk-7.2.42/tests/test_025/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.767100773 30 atime=1623670096.766100774 30 ctime=1623670096.767100773 elk-7.2.42/tests/test_025/TEST_500.OUT_0000644002504400250440000000013514061636520020565 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 54.5616810221 elk-7.2.42/tests/test_025/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.768100772 30 atime=1623670096.768100772 30 ctime=1623670096.768100772 elk-7.2.42/tests/test_025/TEST_510.OUT_0000644002504400250440000000014514061636520020567 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.763751005576E-03 elk-7.2.42/tests/test_025/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.769100771 30 atime=1623670096.769100771 30 ctime=1623670096.769100771 elk-7.2.42/tests/test_025/TEST_400.OUT_0000644002504400250440000000014114061636520020561 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 26.9957255510 elk-7.2.42/tests/test_025/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.771100769 30 atime=1623670096.771100769 30 ctime=1623670096.771100769 elk-7.2.42/tests/test_025/TEST_450.OUT_0000644002504400250440000000014014061636520020565 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 1.69601931816 elk-7.2.42/tests/test_025/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.772100768 30 atime=1623670096.772100768 30 ctime=1623670096.772100768 elk-7.2.42/tests/test_025/TEST_000.OUT_0000644002504400250440000000012614061636520020560 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1391.14531330 elk-7.2.42/tests/test_025/PaxHeaders.21776/TEST_110.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.774100766 30 atime=1623670096.774100766 30 ctime=1623670096.774100766 elk-7.2.42/tests/test_025/TEST_110.OUT_0000644002504400250440000000022714061636520020564 0ustar00dewhurstdewhurst00000000000000'hyperfine field' 2 3 0.100000000000E-03 1 -0.340090424683E-20 2 0.396169903440E-20 3 0.115535438996E-03 elk-7.2.42/tests/test_025/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015741 xustar0030 mtime=1623670096.775100765 30 atime=1623670096.775100765 30 ctime=1623670096.775100765 elk-7.2.42/tests/test_025/elk.in0000644002504400250440000000111014061636520017767 0ustar00dewhurstdewhurst00000000000000 ! Mossbauer hyperfine field for fcc Co including spin and orbital dipole terms. tasks 0 110 500 test .true. tbdip .true. tjr .true. spinorb .true. spincore .true. lorbcnd .true. bfieldc 0.0 0.0 0.01 nempty 10 ! large number of k-points required ngridk 8 8 8 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.3448 sppath '../../species/' atoms 1 : nspecies 'Co.in' : spfname 1 : natoms; atposl, bfcmt below 0.0 0.0 0.0 elk-7.2.42/tests/PaxHeaders.21776/test_0020000644000000000000000000000013214061636520014554 xustar0030 mtime=1623670096.789100752 30 atime=1623670096.776100764 30 ctime=1623670096.789100752 elk-7.2.42/tests/test_002/0000755002504400250440000000000014061636520016666 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_002/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.778100763 30 atime=1623670096.777100764 30 ctime=1623670096.778100763 elk-7.2.42/tests/test_002/TEST_705.OUT_0000644002504400250440000000010114061636520020560 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_002/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015734 xustar0030 mtime=1623670096.779100762 30 atime=1623670096.779100762 30 ctime=1623670096.779100762 elk-7.2.42/tests/test_002/elk.in0000644002504400250440000000064214061636520017773 0ustar00dewhurstdewhurst00000000000000 tasks 0 500 test .true. maxscl 5 rgkmax 6.5 spinpol .true. bfieldc 0.0 0.0 0.5 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 2.708 sppath '../../species/' atoms 1 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 elk-7.2.42/tests/test_002/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.780100761 30 atime=1623670096.780100761 30 ctime=1623670096.780100761 elk-7.2.42/tests/test_002/TEST_900.OUT_0000644002504400250440000000007014061636520020562 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 2315 elk-7.2.42/tests/test_002/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.782100759 30 atime=1623670096.782100759 30 ctime=1623670096.782100759 elk-7.2.42/tests/test_002/TEST_910.OUT_0000644002504400250440000000144714061636520020574 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 24 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.290028863884 5 0.290028863884 6 -0.652074116947E-17 7 0.580057727768 8 0.580057727768 9 -0.130414823389E-16 10 0.580057727768 11 0.290028863884 12 0.290028863884 13 0.580057727768 14 0.580057727768 15 0.580057727768 16 1.16011545554 17 1.16011545554 18 0.580057727768 19 1.16011545554 20 0.870086591652 21 0.870086591652 22 1.16011545554 23 1.16011545554 24 1.16011545554 elk-7.2.42/tests/test_002/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.783100758 30 atime=1623670096.783100758 30 ctime=1623670096.783100758 elk-7.2.42/tests/test_002/TEST_500.OUT_0000644002504400250440000000013514061636520020560 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 27.0587039573 elk-7.2.42/tests/test_002/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.785100756 30 atime=1623670096.785100756 30 ctime=1623670096.785100756 elk-7.2.42/tests/test_002/TEST_510.OUT_0000644002504400250440000000014514061636520020562 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.433821754615E-02 elk-7.2.42/tests/test_002/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016523 xustar0030 mtime=1623670096.786100755 30 atime=1623670096.786100755 30 ctime=1623670096.786100755 elk-7.2.42/tests/test_002/TEST_400.OUT_0000644002504400250440000000014114061636520020554 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 25.9972158035 elk-7.2.42/tests/test_002/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.788100753 30 atime=1623670096.788100753 30 ctime=1623670096.788100753 elk-7.2.42/tests/test_002/TEST_450.OUT_0000644002504400250440000000014014061636520020560 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 2.73278028082 elk-7.2.42/tests/test_002/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016517 xustar0030 mtime=1623670096.789100752 30 atime=1623670096.789100752 30 ctime=1623670096.789100752 elk-7.2.42/tests/test_002/TEST_000.OUT_0000644002504400250440000000012614061636520020553 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1270.55032831 elk-7.2.42/tests/PaxHeaders.21776/test_0060000644000000000000000000000013214061636520014560 xustar0030 mtime=1623670096.812100731 30 atime=1623670096.790100752 30 ctime=1623670096.812100731 elk-7.2.42/tests/test_006/0000755002504400250440000000000014061636520016672 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000012714061636520016543 xustar0029 mtime=1623670096.79210075 29 atime=1623670096.79210075 29 ctime=1623670096.79210075 elk-7.2.42/tests/test_006/TEST_705.OUT_0000644002504400250440000000010114061636520020564 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 24 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.793100749 30 atime=1623670096.793100749 30 ctime=1623670096.793100749 elk-7.2.42/tests/test_006/TEST_900.OUT_0000644002504400250440000000007014061636520020566 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 8873 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.795100747 30 atime=1623670096.794100748 30 ctime=1623670096.795100747 elk-7.2.42/tests/test_006/TEST_910.OUT_0000644002504400250440000001357714061636520020607 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 192 0.100000000000E-07 1 0.183727464068E-01 2 0.551182392204E-01 3 0.128609224848 4 0.165354717661 5 0.202100210475 6 -0.183727464068E-01 7 0.312336688915 8 0.349082181729 9 -0.165354717661 10 0.459318660170 11 0.496064152983 12 -0.312336688915 13 0.165354717661 14 -0.918637320339E-01 15 0.275591196102 16 0.312336688915 17 0.551182392204E-01 18 0.128609224848 19 0.459318660170 20 0.202100210475 21 -0.183727464068E-01 22 0.606300631424 23 0.349082181729 24 -0.165354717661 25 0.312336688915 26 -0.238845703288 27 0.422573167356 28 0.459318660170 29 -0.918637320339E-01 30 0.275591196102 31 0.606300631424 32 0.551182392204E-01 33 0.128609224848 34 0.753282602678 35 0.202100210475 36 -0.183727464068E-01 37 0.459318660170 38 -0.385827674543 39 0.569555138610 40 0.606300631424 41 -0.238845703288 42 0.422573167356 43 0.753282602678 44 -0.918637320339E-01 45 0.275591196102 46 0.900264573933 47 0.551182392204E-01 48 0.128609224848 49 -0.128609224848 50 0.202100210475 51 0.275591196102 52 0.183727464068E-01 53 0.349082181729 54 0.128609224848 55 0.165354717661 56 0.496064152983 57 -0.183727464068E-01 58 0.312336688915 59 0.643046124238 60 -0.165354717661 61 0.183727464068E-01 62 0.551182392204E-01 63 0.422573167356 64 0.165354717661 65 0.202100210475 66 0.275591196102 67 0.312336688915 68 0.349082181729 69 0.128609224848 70 0.459318660170 71 0.496064152983 72 -0.183727464068E-01 73 0.165354717661 74 -0.918637320339E-01 75 0.569555138610 76 0.312336688915 77 0.551182392204E-01 78 0.422573167356 79 0.459318660170 80 0.202100210475 81 0.275591196102 82 0.606300631424 83 0.349082181729 84 0.128609224848 85 0.312336688915 86 -0.238845703288 87 0.716537109865 88 0.459318660170 89 -0.918637320339E-01 90 0.569555138610 91 0.606300631424 92 0.551182392204E-01 93 0.422573167356 94 0.753282602678 95 0.202100210475 96 0.275591196102 97 -0.275591196102 98 0.349082181729 99 0.422573167356 100 -0.128609224848 101 0.496064152983 102 0.275591196102 103 0.183727464068E-01 104 0.643046124238 105 0.128609224848 106 0.165354717661 107 0.790028095492 108 -0.183727464068E-01 109 -0.128609224848 110 0.202100210475 111 0.569555138610 112 0.183727464068E-01 113 0.349082181729 114 0.422573167356 115 0.165354717661 116 0.496064152983 117 0.275591196102 118 0.312336688915 119 0.643046124238 120 0.128609224848 121 0.183727464068E-01 122 0.551182392204E-01 123 0.716537109865 124 0.165354717661 125 0.202100210475 126 0.569555138610 127 0.312336688915 128 0.349082181729 129 0.422573167356 130 0.459318660170 131 0.496064152983 132 0.275591196102 133 0.165354717661 134 -0.918637320339E-01 135 0.863519081119 136 0.312336688915 137 0.551182392204E-01 138 0.716537109865 139 0.459318660170 140 0.202100210475 141 0.569555138610 142 0.606300631424 143 0.349082181729 144 0.422573167356 145 -0.422573167356 146 0.496064152983 147 0.569555138610 148 -0.275591196102 149 0.643046124238 150 0.422573167356 151 -0.128609224848 152 0.790028095492 153 0.275591196102 154 0.183727464068E-01 155 0.937010066746 156 0.128609224848 157 -0.275591196102 158 0.349082181729 159 0.716537109865 160 -0.128609224848 161 0.496064152983 162 0.569555138610 163 0.183727464068E-01 164 0.643046124238 165 0.422573167356 166 0.165354717661 167 0.790028095492 168 0.275591196102 169 -0.128609224848 170 0.202100210475 171 0.863519081119 172 0.183727464068E-01 173 0.349082181729 174 0.716537109865 175 0.165354717661 176 0.496064152983 177 0.569555138610 178 0.312336688915 179 0.643046124238 180 0.422573167356 181 0.183727464068E-01 182 0.551182392204E-01 183 1.01050105237 184 0.165354717661 185 0.202100210475 186 0.863519081119 187 0.312336688915 188 0.349082181729 189 0.716537109865 190 0.459318660170 191 0.496064152983 192 0.569555138610 elk-7.2.42/tests/test_006/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015740 xustar0030 mtime=1623670096.796100746 30 atime=1623670096.796100746 30 ctime=1623670096.796100746 elk-7.2.42/tests/test_006/elk.in0000644002504400250440000000135714061636520020003 0ustar00dewhurstdewhurst00000000000000 ! GaAs using the Perdew-Burke-Ernzerhof GGA functional and spin-orbit coupling. tasks 0 10 25 120 121 125 180 185 186 187 500 test .true. bsefull .true. swidth 0.01 wplot 50 100 4 0.0 0.5 rgkmax 6.0 xctype 20 spinorb .true. avec 5.3435 5.3435 0.0000 5.3435 0.0000 5.3435 0.0000 5.3435 5.3435 sppath '../../species/' atoms 2 : nspecies 'Ga.in' : spfname 1 : natoms 0.00 0.00 0.00 0.0 0.0 0.0 : atposl, bfcmt 'As.in' : spfname 1 : natoms 0.25 0.25 0.25 0.0 0.0 0.0 : atposl, bfcmt ngridk 4 4 4 vkloff 0.25 0.5 0.625 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.798100744 30 atime=1623670096.797100745 30 ctime=1623670096.798100744 elk-7.2.42/tests/test_006/TEST_500.OUT_0000644002504400250440000000013514061636520020564 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 1.09584638942 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.799100743 30 atime=1623670096.799100743 30 ctime=1623670096.799100743 elk-7.2.42/tests/test_006/TEST_510.OUT_0000644002504400250440000000014514061636520020566 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.687664057384E-01 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.801100741 30 atime=1623670096.800100742 30 ctime=1623670096.801100741 elk-7.2.42/tests/test_006/TEST_400.OUT_0000644002504400250440000000014114061636520020560 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 63.9851369261 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000012714061636520016540 xustar0029 mtime=1623670096.80210074 29 atime=1623670096.80210074 29 ctime=1623670096.80210074 elk-7.2.42/tests/test_006/TEST_450.OUT_0000644002504400250440000000014014061636520020564 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.731763086095E-20 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016523 xustar0030 mtime=1623670096.803100739 30 atime=1623670096.803100739 30 ctime=1623670096.803100739 elk-7.2.42/tests/test_006/TEST_000.OUT_0000644002504400250440000000012614061636520020557 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -4205.21476167 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_010.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.805100738 30 atime=1623670096.805100738 30 ctime=1623670096.805100738 elk-7.2.42/tests/test_006/TEST_010.OUT_0000644002504400250440000000612014061636520020560 0ustar00dewhurstdewhurst00000000000000'total DOS' 2 100 0.200000000000E-01 1 0.00000000000 2 0.295787200865E-01 3 0.226752015598 4 0.966612414599 5 2.67934514281 6 5.38397608013 7 8.20656819373 8 9.91960888238 9 9.98048822365 10 9.26998514973 11 9.10010586418 12 9.88034275399 13 10.6185512018 14 10.2355044269 15 8.73434857970 16 7.27767199193 17 6.88877746403 18 7.60004179141 19 8.59714817968 20 9.10135871450 21 8.94671458326 22 8.42909309822 23 7.95480696909 24 7.71187649695 25 7.69107454735 26 7.71586658842 27 7.67288347948 28 7.65987632122 29 8.05167524719 30 9.09340940949 31 10.5250992930 32 11.5274368422 33 11.4392888689 34 10.4094443104 35 9.39737400669 36 9.31257883264 37 10.2486975110 38 11.5010066540 39 12.2479622531 40 12.1690464990 41 11.5047253671 42 10.7312934134 43 10.2621190672 44 10.3018964800 45 10.8495426950 46 11.6670562126 47 12.4180929053 48 12.8223762347 49 12.8338406129 50 12.5976573510 51 0.00000000000 52 0.296358158220E-01 53 0.228198059822 54 0.972396906816 55 2.69064950420 56 5.39661191527 57 8.20973276225 58 9.90824409624 59 9.95891645042 60 9.25306274798 61 9.09489141365 62 9.88567912191 63 10.6251558057 64 10.2386469899 65 8.73319339109 66 7.27563622464 67 6.89061890592 68 7.61076711861 69 8.61767370721 70 9.12587556451 71 8.96439839904 72 8.42930072703 73 7.93424101286 74 7.67457387970 75 7.65272776268 76 7.68962459242 77 7.66759361156 78 7.66783394901 79 8.06611983237 80 9.10878277071 81 10.5423311049 82 11.5433181967 83 11.4498309110 84 10.4143177626 85 9.40050402205 86 9.31742026025 87 10.2537831608 88 11.5027422748 89 12.2446374935 90 12.1617139511 91 11.4968231384 92 10.7253063691 93 10.2595885879 94 10.3017247045 95 10.8506239242 96 11.6689852834 97 12.4219925943 98 12.8287861611 99 12.8418393368 100 12.6058483182 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_025.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.806100737 30 atime=1623670096.806100737 30 ctime=1623670096.806100737 elk-7.2.42/tests/test_006/TEST_025.OUT_0000644002504400250440000000022614061636520020567 0ustar00dewhurstdewhurst00000000000000'effective mass' 2 3 0.100000000000E-05 1 0.709875051567 2 0.709877207332 3 0.709877988628 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_121.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.808100735 30 atime=1623670096.808100735 30 ctime=1623670096.808100735 elk-7.2.42/tests/test_006/TEST_121.OUT_0000644002504400250440000000523114061636520020565 0ustar00dewhurstdewhurst00000000000000'optical conductivity' 3 50 0.100000000000E-01 1 0.784830441454E-02 0.00000000000 2 0.805613916128E-02 -0.763462377010E-02 3 0.859460172249E-02 -0.153617048741E-01 4 0.938720780578E-02 -0.233686047080E-01 5 0.103955486738E-01 -0.322935327582E-01 6 0.122845721435E-01 -0.425186167438E-01 7 0.153770586144E-01 -0.546157746712E-01 8 0.217832861694E-01 -0.697008010780E-01 9 0.362976447188E-01 -0.842350519252E-01 10 0.489177838428E-01 -0.945490242888E-01 11 0.749999461934E-01 -0.109971730363 12 0.106312908731 -0.108853635181 13 0.126481595513 -0.970370634605E-01 14 0.157772240006 -0.995467936799E-01 15 0.194647495903 -0.622961076822E-01 16 0.201036131942 -0.156841804533E-01 17 0.180559939433 0.127098189213E-01 18 0.164296375219 0.178839736076E-01 19 0.164189238460 0.157397036950E-01 20 0.172660779809 0.307688083937E-01 21 0.184879176828 0.409154194455E-01 22 0.182934072125 0.904129011234E-01 23 0.147746350877 0.110473349499 24 0.115279145093 0.108624226030 25 0.107547705246 0.961859971439E-01 26 0.102838967581 0.101944039011 27 0.938979897713E-01 0.102537885341 28 0.794894062477E-01 0.105742904462 29 0.714130908987E-01 0.998698905249E-01 30 0.636354953480E-01 0.985504279889E-01 31 0.563779426202E-01 0.937454507965E-01 32 0.541406671479E-01 0.857560841387E-01 33 0.574703520359E-01 0.906323807642E-01 34 0.451005547915E-01 0.938595055443E-01 35 0.357133042580E-01 0.869844242685E-01 36 0.331322474929E-01 0.798935916884E-01 37 0.318716580343E-01 0.743166383871E-01 38 0.329530401827E-01 0.709134888898E-01 39 0.327933920041E-01 0.696854257516E-01 40 0.328924762058E-01 0.670144081803E-01 41 0.347867061053E-01 0.683336921036E-01 42 0.308457529624E-01 0.719471455730E-01 43 0.257576898143E-01 0.689543915700E-01 44 0.244775653831E-01 0.665975832766E-01 45 0.232924150756E-01 0.641737064763E-01 46 0.222575826298E-01 0.640817666500E-01 47 0.194563452125E-01 0.619407742099E-01 48 0.190816542076E-01 0.591626413806E-01 49 0.192069511441E-01 0.585967622732E-01 50 0.175794179589E-01 0.580335567132E-01 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_125.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.810100733 30 atime=1623670096.809100734 30 ctime=1623670096.810100733 elk-7.2.42/tests/test_006/TEST_125.OUT_0000644002504400250440000001237014061636520020573 0ustar00dewhurstdewhurst00000000000000'non-linear susceptibility' 3 100 0.100000000000E-01 1 -0.275459574106 -0.599868366272E-01 2 -0.316948646955 -0.615137209350E-01 3 -0.364873399301 -0.616255543498E-01 4 -0.390865811732 -0.677651941849E-01 5 -0.237142739629 -0.527313741831 6 -2.30048890680 0.201702935482 7 -1.07224299779 1.07047253535 8 0.990548737749 1.00597896882 9 -1.18431759697 2.00973193079 10 -0.190574337797 2.13841868683 11 0.354761508294 3.49406681273 12 7.41378461059 4.00720718606 13 4.22456478762 -4.70869685246 14 -1.72584793859 -2.73487636458 15 -0.769392196007E-01 -1.18867240013 16 -0.610068133144 -0.178881424933 17 -0.549897120398E-01 -1.04645197566 18 0.439734940495 -0.226053989747 19 -1.19792429766 -1.06030329218 20 -0.343954634226 -0.404153262717 21 -1.56145710547 0.996587054877 22 0.576791108724 1.06054851505 23 0.913169977464E-01 0.129126084876 24 0.488192380954 0.330933644328 25 0.636079601012E-01 -0.499276264406 26 0.343899534851 0.187155676608 27 -0.307768225594 -0.327343600174 28 0.325345292292E-01 0.736100259513 29 0.103945304342 -0.519787323244 30 -0.142621633132 -0.137204863681 31 -0.265560623935 0.181681465197 32 0.146537112055 0.109675580372 33 -0.360521783284E-01 0.443267902216E-01 34 0.488186895492E-01 0.101103198228 35 0.112059342158 0.815530346337E-01 36 0.857698424570E-01 0.128997098565E-01 37 0.768510071576E-01 0.667712023244E-01 38 0.116261209133 -0.986516651858E-01 39 -0.200617309150E-01 -0.277010634711E-01 40 -0.129187702547E-02 0.903012475030E-02 41 0.182907127565E-01 0.306250636173E-01 42 0.396600595173E-01 0.276471747986E-02 43 0.101382422576E-01 0.574515117498E-02 44 -0.893090155994E-02 -0.160580603939E-02 45 -0.706315020728E-02 0.541174017852E-01 46 0.355922199873E-01 0.255906846798E-01 47 0.238665573333E-01 0.587689905330E-02 48 0.473237861419E-02 0.144737785374E-01 49 -0.761903955418E-02 0.279329894069E-01 50 0.187841382796E-01 0.352470397174E-01 51 -1.42978641689 -16.3379529649 52 -2.59187354419 -20.8861383453 53 -5.55661480363 -28.9080712521 54 -16.9738899422 -45.8797914750 55 -94.5929471681 -45.3493018084 56 -57.5576375974 33.8352633377 57 -22.4364419727 39.8232130429 58 2.63090509234 20.8467224116 59 -9.62556772813 10.7169942163 60 -19.1598258627 -0.996370312697 61 -12.0608194351 32.9606630879 62 7.45614745455 13.4305498642 63 0.259736517621 8.52315055013 64 -2.46896205652 7.59927835749 65 -1.06247224791 8.85214585622 66 -1.55642189848 7.21203316904 67 -0.332153381076 7.66294049921 68 -0.473925484713 5.84757163710 69 -0.242429215510 5.72968096039 70 -0.479243683882 4.86688570533 71 -0.804904588301 4.76714737942 72 -0.742474672487 4.77604532364 73 -0.582174766729 4.60488521760 74 -0.458368368377 4.45408874237 75 -0.143306290569 4.12091696071 76 -0.141333845436 3.79556531966 77 -0.178598280337 3.48765398890 78 -0.245507177465 3.30635829921 79 -0.279178115468 3.25295378005 80 -0.285061523153 3.16368576130 81 -0.238309211501 3.01817539645 82 -0.243357123161 2.93251174340 83 -0.188639654780 2.81421785768 84 -0.182753028459 2.72801378401 85 -0.157360870996 2.61435071712 86 -0.159719557827 2.52131849386 87 -0.143707363681 2.42308082851 88 -0.147192525501 2.34605960220 89 -0.157717060997 2.27639449828 90 -0.152522491022 2.21756784655 91 -0.153410956967 2.15156423636 92 -0.157596533920 2.10838410039 93 -0.136143661199 2.06280130163 94 -0.120872958646 2.00409472101 95 -0.118508145517 1.94784193349 96 -0.109269126953 1.90082648288 97 -0.104787117802 1.84858330134 98 -0.102114796002 1.80244513776 99 -0.101021062699 1.76015893319 100 -0.996356097973E-01 1.71420592418 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.811100732 30 atime=1623670096.811100732 30 ctime=1623670096.811100732 elk-7.2.42/tests/test_006/TEST_800.OUT_0000644002504400250440000000061514061636520020572 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 10 0.100000000000E-07 1 1712.43342568 2 221.982051261 3 50.3781715177 4 221.982051260 5 155.992040644 6 54.3472682978 7 78.7344360286 8 36.9525587541 9 54.3472682979 10 29.0461395875 elk-7.2.42/tests/test_006/PaxHeaders.21776/TEST_187.OUT_0000644000000000000000000000013014061636520016541 xustar0029 mtime=1623670096.81310073 30 atime=1623670096.812100731 29 ctime=1623670096.81310073 elk-7.2.42/tests/test_006/TEST_187.OUT_0000644002504400250440000000523514061636520020605 0ustar00dewhurstdewhurst00000000000000'BSE optical conductivity' 3 50 0.100000000000E-02 1 0.603986088645E-02 0.00000000000 2 -0.260725754765E-02 0.00000000000 3 -0.432881388566E-02 0.00000000000 4 -0.537571762167E-03 0.00000000000 5 0.816060294839E-02 0.00000000000 6 -0.232968075166E-02 0.00000000000 7 0.396818125296E-02 0.00000000000 8 0.236662364126E-03 0.00000000000 9 0.400490632243E-02 0.00000000000 10 0.619908658089E-02 -0.598274457890E-02 11 -0.269120937763E-02 0.152836274121E-02 12 -0.439386413917E-02 0.437013931681E-04 13 -0.605253449778E-03 0.156022019660E-02 14 0.841358512472E-02 -0.806901766737E-02 15 -0.237825863649E-02 0.101587686670E-02 16 0.403051230831E-02 0.316214061238E-03 17 0.204464811682E-03 0.104766413248E-02 18 0.407743326488E-02 -0.397944392763E-02 19 0.671348237456E-02 -0.122692116435E-01 20 -0.296891170907E-02 0.319845417482E-02 21 -0.459737867144E-02 0.682725300744E-04 22 -0.834351786110E-03 0.326014694006E-02 23 0.923851623237E-02 -0.166171805345E-01 24 -0.253535851855E-02 0.210916884348E-02 25 0.422760198331E-02 0.657841091464E-03 26 0.960265352416E-04 0.216997857736E-02 27 0.430668604818E-02 -0.809945540894E-02 28 0.771588627113E-02 -0.192256730468E-01 29 -0.353809153806E-02 0.519568360070E-02 30 -0.496643475427E-02 0.435278791448E-04 31 -0.132413726345E-02 0.527873270397E-02 32 0.108773171558E-01 -0.262342516189E-01 33 -0.284255018261E-02 0.337914137671E-02 34 0.459415678106E-02 0.105920527538E-02 35 -0.132658138865E-03 0.345846194750E-02 36 0.473310691347E-02 -0.125214955486E-01 37 0.953323410496E-02 -0.273701567936E-01 38 -0.466046525159E-02 0.781689850873E-02 39 -0.555213837075E-02 -0.935964665303E-04 40 -0.234259239939E-02 0.789011719161E-02 41 0.139399784721E-01 -0.377813030121E-01 42 -0.340460660975E-02 0.498235417582E-02 43 0.520666147439E-02 0.158151234930E-02 44 -0.594152077116E-03 0.504339139857E-02 45 0.544799788062E-02 -0.174563267919E-01 46 0.130222144788E-01 -0.375069970474E-01 47 -0.710640577573E-02 0.115761242284E-01 48 -0.642773991659E-02 -0.499286887140E-03 49 -0.467588213668E-02 0.115247469622E-01 50 0.200735910543E-01 -0.526338761968E-01 elk-7.2.42/tests/PaxHeaders.21776/test_0100000644000000000000000000000012714061636520014557 xustar0029 mtime=1623670096.82410072 29 atime=1623670096.81310073 29 ctime=1623670096.82410072 elk-7.2.42/tests/test_010/0000755002504400250440000000000014061636520016665 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_010/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016522 xustar0030 mtime=1623670096.815100728 30 atime=1623670096.815100728 30 ctime=1623670096.815100728 elk-7.2.42/tests/test_010/TEST_400.OUT_0000644002504400250440000000014114061636520020553 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 9.99660565444 elk-7.2.42/tests/test_010/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016516 xustar0030 mtime=1623670096.816100727 30 atime=1623670096.816100727 30 ctime=1623670096.816100727 elk-7.2.42/tests/test_010/TEST_000.OUT_0000644002504400250440000000012614061636520020552 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -79.0782174520 elk-7.2.42/tests/test_010/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016523 xustar0030 mtime=1623670096.818100725 30 atime=1623670096.818100725 30 ctime=1623670096.818100725 elk-7.2.42/tests/test_010/TEST_500.OUT_0000644002504400250440000000013514061636520020557 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.666133814564E-12 elk-7.2.42/tests/test_010/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.819100725 30 atime=1623670096.819100725 30 ctime=1623670096.819100725 elk-7.2.42/tests/test_010/TEST_510.OUT_0000644002504400250440000000014514061636520020561 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.184259173457 elk-7.2.42/tests/test_010/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.821100723 30 atime=1623670096.820100724 30 ctime=1623670096.821100723 elk-7.2.42/tests/test_010/TEST_705.OUT_0000644002504400250440000000010114061636520020557 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 2 elk-7.2.42/tests/test_010/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.822100722 30 atime=1623670096.822100722 30 ctime=1623670096.822100722 elk-7.2.42/tests/test_010/TEST_900.OUT_0000644002504400250440000000007014061636520020561 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 9771 elk-7.2.42/tests/test_010/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015733 xustar0030 mtime=1623670096.823100721 30 atime=1623670096.823100721 30 ctime=1623670096.823100721 elk-7.2.42/tests/test_010/elk.in0000644002504400250440000000103614061636520017770 0ustar00dewhurstdewhurst00000000000000 ! Water molecule in a box. tasks 0 500 test .true. xctype 2 tefvit .true. maxscl 2 molecule .true. avec 5.0 0.0 0.0 0.0 5.0 0.0 0.0 0.0 5.0 rgkmax 7.0 gmaxvr 14.0 sppath '../../species/' atoms 2 : nspecies 'O.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atpos, bfcmt 'H.in' 2 1.811 0.0 0.0 0.0 0.0 0.0 -0.451907959 1.753710409 0.0 0.0 0.0 0.0 elk-7.2.42/tests/test_010/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.825100719 30 atime=1623670096.825100719 30 ctime=1623670096.825100719 elk-7.2.42/tests/test_010/TEST_910.OUT_0000644002504400250440000000023414061636520020564 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 3 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 elk-7.2.42/tests/PaxHeaders.21776/test_0140000644000000000000000000000013214061636520014557 xustar0030 mtime=1623670096.838100707 30 atime=1623670096.825100719 30 ctime=1623670096.838100707 elk-7.2.42/tests/test_014/0000755002504400250440000000000014061636520016671 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_014/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.827100717 30 atime=1623670096.827100717 30 ctime=1623670096.827100717 elk-7.2.42/tests/test_014/TEST_800.OUT_0000644002504400250440000000026414061636520020571 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 3 0.100000000000E-07 1 394.581580334 2 51.1494504119 3 35.9439292598 elk-7.2.42/tests/test_014/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.829100715 30 atime=1623670096.828100716 30 ctime=1623670096.829100715 elk-7.2.42/tests/test_014/TEST_910.OUT_0000644002504400250440000000144714061636520020577 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 24 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.153099057192 5 0.153099057192 6 -0.153099057192 7 0.306198114385 8 0.306198114385 9 -0.306198114385 10 0.306198114385 11 0.00000000000 12 0.00000000000 13 0.459297171577 14 0.153099057192 15 -0.153099057192 16 0.612396228770 17 0.306198114385 18 -0.306198114385 19 0.612396228770 20 0.00000000000 21 0.00000000000 22 0.612396228770 23 0.306198114385 24 0.00000000000 elk-7.2.42/tests/test_014/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.830100714 30 atime=1623670096.830100714 30 ctime=1623670096.830100714 elk-7.2.42/tests/test_014/TEST_705.OUT_0000644002504400250440000000010114061636520020563 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_014/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.832100713 30 atime=1623670096.831100713 30 ctime=1623670096.832100713 elk-7.2.42/tests/test_014/TEST_900.OUT_0000644002504400250440000000007014061636520020565 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 7799 elk-7.2.42/tests/test_014/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015737 xustar0030 mtime=1623670096.833100712 30 atime=1623670096.833100712 30 ctime=1623670096.833100712 elk-7.2.42/tests/test_014/elk.in0000644002504400250440000000071414061636520017776 0ustar00dewhurstdewhurst00000000000000 ! Optimised effective potential (OEP) test tasks 0 500 test .true. xctype -1 maxscl 4 maxitoep 100 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 0.25 0.25 0.25 0.0 0.0 0.0 ngridk 4 4 4 ngridq 2 2 2 elk-7.2.42/tests/test_014/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.834100711 30 atime=1623670096.834100711 30 ctime=1623670096.834100711 elk-7.2.42/tests/test_014/TEST_500.OUT_0000644002504400250440000000013514061636520020563 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 76.3337188320 elk-7.2.42/tests/test_014/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.836100709 30 atime=1623670096.836100709 30 ctime=1623670096.836100709 elk-7.2.42/tests/test_014/TEST_510.OUT_0000644002504400250440000000014514061636520020565 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.101834193353E-01 elk-7.2.42/tests/test_014/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.837100708 30 atime=1623670096.837100708 30 ctime=1623670096.837100708 elk-7.2.42/tests/test_014/TEST_400.OUT_0000644002504400250440000000014114061636520020557 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9784638947 elk-7.2.42/tests/test_014/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016522 xustar0030 mtime=1623670096.839100706 30 atime=1623670096.839100706 30 ctime=1623670096.839100706 elk-7.2.42/tests/test_014/TEST_000.OUT_0000644002504400250440000000012614061636520020556 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -530.380772300 elk-7.2.42/tests/PaxHeaders.21776/test_0180000644000000000000000000000013214061636520014563 xustar0030 mtime=1623670096.854100692 30 atime=1623670096.840100705 30 ctime=1623670096.854100692 elk-7.2.42/tests/test_018/0000755002504400250440000000000014061636520016675 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016542 xustar0030 mtime=1623670096.841100704 30 atime=1623670096.841100704 30 ctime=1623670096.841100704 elk-7.2.42/tests/test_018/TEST_705.OUT_0000644002504400250440000000010114061636520020567 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.842100703 30 atime=1623670096.842100703 30 ctime=1623670096.842100703 elk-7.2.42/tests/test_018/TEST_900.OUT_0000644002504400250440000000007014061636520020571 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 3511 elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.844100701 30 atime=1623670096.844100701 30 ctime=1623670096.844100701 elk-7.2.42/tests/test_018/TEST_910.OUT_0000644002504400250440000000144714061636520020603 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 24 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.251891649582 5 0.251891649582 6 0.384969705319E-17 7 0.503783299164 8 0.503783299164 9 0.769939410638E-17 10 0.503783299164 11 0.251891649582 12 0.251891649582 13 0.503783299164 14 0.503783299164 15 0.503783299164 16 1.00756659833 17 1.00756659833 18 0.503783299164 19 1.00756659833 20 0.755674948747 21 0.755674948747 22 1.00756659833 23 1.00756659833 24 1.00756659833 elk-7.2.42/tests/test_018/PaxHeaders.21776/elk.in0000644000000000000000000000012414061636520015744 xustar0028 mtime=1623670096.8451007 28 atime=1623670096.8451007 28 ctime=1623670096.8451007 elk-7.2.42/tests/test_018/elk.in0000644002504400250440000000066314061636520020005 0ustar00dewhurstdewhurst00000000000000 tasks 0 205 210 500 test .true. wplot 200 100 10 0.0 1.0 swidth 0.01 rgkmax 6.5 ngridq 2 2 2 ngridk 4 4 4 avec 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 scale 3.118 sppath '../../species/' atoms 1 : nspecies 'Nb.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.847100699 30 atime=1623670096.847100699 30 ctime=1623670096.847100699 elk-7.2.42/tests/test_018/TEST_500.OUT_0000644002504400250440000000013514061636520020567 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 25.5286833860 elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.848100698 30 atime=1623670096.848100698 30 ctime=1623670096.848100698 elk-7.2.42/tests/test_018/TEST_510.OUT_0000644002504400250440000000014514061636520020571 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.157007976838E-01 elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.850100696 30 atime=1623670096.850100696 30 ctime=1623670096.850100696 elk-7.2.42/tests/test_018/TEST_400.OUT_0000644002504400250440000000014114061636520020563 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 41.0025904631 elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.851100695 30 atime=1623670096.851100695 30 ctime=1623670096.851100695 elk-7.2.42/tests/test_018/TEST_000.OUT_0000644002504400250440000000012614061636520020562 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -3816.44181165 elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.853100693 30 atime=1623670096.852100694 30 ctime=1623670096.853100693 elk-7.2.42/tests/test_018/TEST_800.OUT_0000644002504400250440000000026414061636520020575 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 3 0.100000000000E-07 1 231.402239370 2 29.8969231706 3 12.8329633332 elk-7.2.42/tests/test_018/PaxHeaders.21776/TEST_210.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.854100692 30 atime=1623670096.854100692 30 ctime=1623670096.854100692 elk-7.2.42/tests/test_018/TEST_210.OUT_0000644002504400250440000001415514061636520020574 0ustar00dewhurstdewhurst00000000000000'phonon DOS' 2 200 0.100000000000E-01 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.00000000000 5 0.00000000000 6 0.00000000000 7 0.00000000000 8 0.00000000000 9 0.753171514035E-05 10 0.753171514035E-04 11 0.444371193281E-03 12 0.188292878509E-02 13 0.634923586331E-02 14 0.179857357552E-01 15 0.447383879337E-01 16 0.101115786331 17 0.213210302765 18 0.425265742541 19 0.804590533298 20 1.43784961058 21 2.41589554356 22 3.81160018679 23 5.66621474410 24 7.99404194252 25 10.8030327627 26 14.1096992348 27 17.9355770429 28 22.2880472679 29 27.1533871248 30 32.5137313854 31 38.3826496896 32 44.8231046656 33 51.9339325004 34 59.8026918933 35 68.4605239757 36 77.8580307387 37 87.8836524174 38 98.4086971060 39 109.342121432 40 120.666803296 41 132.449082045 42 144.827270095 43 157.977890767 44 172.068047711 45 187.192811259 46 203.345342612 47 220.431656009 48 238.341236081 49 257.006940101 50 276.435516483 51 296.687680895 52 317.851795418 53 340.008861138 54 363.205303548 55 387.430337231 56 412.635407731 57 438.802700030 58 466.038642284 59 494.617629940 60 524.920084909 61 557.272170624 62 591.782911173 63 628.292543814 64 666.489632128 65 706.124755834 66 747.193687130 67 789.968983723 68 834.890136257 69 882.388119512 70 932.781891584 71 986.298839972 72 1043.20388523 73 1103.91147755 74 1168.98978944 75 1239.06876853 76 1314.79362674 77 1396.96024040 78 1486.81450583 79 1586.35662564 80 1698.39888201 81 1826.15224094 82 1972.15949480 83 2136.68561436 84 2316.17406851 85 2502.82694115 86 2686.12329490 87 2856.01058972 88 3006.28476106 89 3136.33611657 90 3250.43727774 91 3355.26597871 92 3457.27232006 93 3561.19674824 94 3670.03863323 95 3785.93221708 96 3911.12831268 97 4048.45207140 98 4200.75586924 99 4369.03859743 100 4549.33738881 101 4729.50835192 102 4888.15849345 103 4998.05669647 104 5034.40597890 105 4984.92657211 106 4856.35441533 107 4673.07609753 108 4468.13466397 109 4271.51047331 110 4101.84933581 111 3964.94411450 112 3857.80688259 113 3774.49108988 114 3710.19762790 115 3662.49251746 116 3630.52940466 117 3613.82663130 118 3611.57587363 119 3622.60810402 120 3645.73076073 121 3680.21050074 122 3726.30669121 123 3785.73773815 124 3861.89454023 125 3959.75600299 126 4085.55549944 127 4245.99322326 128 4446.25136103 129 4686.27638233 130 4956.31704084 131 5234.71736589 132 5491.09922887 133 5695.22297173 134 5827.52079434 135 5885.34531389 136 5881.16328638 137 5834.03960677 138 5759.56869126 139 5663.89173720 140 5544.24513484 141 5394.81199248 142 5213.78042296 143 5007.63352584 144 4790.37335708 145 4578.72722334 146 4386.23657102 147 4219.60510610 148 4078.49698188 149 3958.07100517 150 3852.13504919 151 3755.53249503 152 3665.16684372 153 3580.06086023 154 3500.78798425 155 3428.77285225 156 3365.73223083 157 3313.62217670 158 3274.99799997 159 3253.51791995 160 3254.03812045 161 3282.10247104 162 3342.87585540 163 3440.00226796 164 3574.85794388 165 3746.59843730 166 3952.89562477 167 4190.58336908 168 4454.76040659 169 4735.11380078 170 5010.23595686 171 5243.68138730 172 5387.24813951 173 5393.94632475 174 5236.49943999 175 4920.97283065 176 4486.31926211 177 3988.68695774 178 3479.55569264 179 2989.91684776 180 2527.99440831 181 2088.69794410 182 1667.09598430 183 1267.62355930 184 905.036976104 185 598.105610293 186 360.729161815 187 195.667753213 188 93.9230184564 189 39.1335867948 190 13.8039015578 191 3.97840257144 192 0.886015905680 193 0.137378484160 194 0.114933973042E-01 195 0.00000000000 196 0.00000000000 197 0.00000000000 198 0.00000000000 199 0.00000000000 200 0.00000000000 elk-7.2.42/tests/PaxHeaders.21776/test_0280000644000000000000000000000013214061636520014564 xustar0030 mtime=1623670096.870100677 30 atime=1623670096.855100691 30 ctime=1623670096.870100677 elk-7.2.42/tests/test_028/0000755002504400250440000000000014061636520016676 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.857100689 30 atime=1623670096.857100689 30 ctime=1623670096.857100689 elk-7.2.42/tests/test_028/TEST_400.OUT_0000644002504400250440000000014114061636520020564 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 155.990251759 elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_750.OUT_0000644000000000000000000000013214061636520016543 xustar0030 mtime=1623670096.858100688 30 atime=1623670096.858100688 30 ctime=1623670096.858100688 elk-7.2.42/tests/test_028/TEST_750.OUT_0000644002504400250440000000051614061636520020602 0ustar00dewhurstdewhurst00000000000000'total forces' 2 9 0.100000000000E-02 1 0.380571577963E-02 2 0.229146648016E-19 3 0.00000000000 4 -0.190285788982E-02 5 0.329584653315E-02 6 -0.765295801317E-41 7 -0.190285788982E-02 8 -0.329584653315E-02 9 0.765295801317E-41 elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_440.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.860100686 30 atime=1623670096.859100688 30 ctime=1623670096.860100686 elk-7.2.42/tests/test_028/TEST_440.OUT_0000644002504400250440000000020114061636520020565 0ustar00dewhurstdewhurst00000000000000'Stress tensor components' 2 2 0.100000000000E-01 1 0.217000917473E-01 2 0.539785760338E-02 elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.861100686 30 atime=1623670096.861100686 30 ctime=1623670096.861100686 elk-7.2.42/tests/test_028/TEST_510.OUT_0000644002504400250440000000014514061636520020572 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.215371690688E-01 elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.863100684 30 atime=1623670096.862100685 30 ctime=1623670096.863100684 elk-7.2.42/tests/test_028/TEST_500.OUT_0000644002504400250440000000013514061636520020570 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 26.5934368192 elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016541 xustar0030 mtime=1623670096.864100683 30 atime=1623670096.864100683 30 ctime=1623670096.864100683 elk-7.2.42/tests/test_028/TEST_910.OUT_0000644002504400250440000000301714061636520020577 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 48 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.184209741270 5 -0.106353544083 6 0.00000000000 7 0.368419482539 8 -0.212707088167 9 0.00000000000 10 0.368419482539 11 0.00000000000 12 0.00000000000 13 0.921048706349 14 -0.106353544083 15 0.00000000000 16 0.00000000000 17 0.00000000000 18 0.139678490521 19 0.184209741270 20 -0.106353544083 21 0.139678490521 22 0.368419482539 23 -0.212707088167 24 0.139678490521 25 0.552629223809 26 -0.319060632250 27 0.139678490521 28 0.368419482539 29 0.00000000000 30 0.139678490521 31 0.921048706349 32 -0.106353544083 33 0.139678490521 34 0.00000000000 35 0.00000000000 36 0.279356981042 37 0.184209741270 38 -0.106353544083 39 0.279356981042 40 0.368419482539 41 -0.212707088167 42 0.279356981042 43 0.368419482539 44 0.00000000000 45 0.279356981042 46 0.921048706349 47 -0.106353544083 48 0.279356981042 elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.866100681 30 atime=1623670096.865100682 30 ctime=1623670096.866100681 elk-7.2.42/tests/test_028/TEST_900.OUT_0000644002504400250440000000007014061636520020572 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 20599 elk-7.2.42/tests/test_028/PaxHeaders.21776/elk.in0000644000000000000000000000012714061636520015750 xustar0029 mtime=1623670096.86710068 29 atime=1623670096.86710068 29 ctime=1623670096.86710068 elk-7.2.42/tests/test_028/elk.in0000644002504400250440000000122414061636520020000 0ustar00dewhurstdewhurst00000000000000 ! Stress tensor of hexagonal tellurium. tasks 0 440 500 test .true. tforce .true. epsengy 1.e-6 msmooth 4 ptnucl .false. maxlatvstp 1 lorbcnd .true. autolinengy .true. ngridk 4 4 4 swidth 0.01 avec 4.2636082 -7.3847860 0.0000000 4.2636082 7.3847860 0.0000000 0.0000000 0.0000000 11.2457997 sppath '../../species/' atoms 1 : nspecies 'Te.in' : spfname 3 : natoms; atposl below -0.268334780 -0.268334780 0.000000000 0.268334780 0.000000000 0.333333333 0.000000000 0.268334780 0.666666666 elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016543 xustar0030 mtime=1623670096.869100678 30 atime=1623670096.868100679 30 ctime=1623670096.869100678 elk-7.2.42/tests/test_028/TEST_705.OUT_0000644002504400250440000000010114061636520020570 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 6 elk-7.2.42/tests/test_028/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.870100677 30 atime=1623670096.870100677 30 ctime=1623670096.870100677 elk-7.2.42/tests/test_028/TEST_000.OUT_0000644002504400250440000000012614061636520020563 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -20455.5724274 elk-7.2.42/tests/PaxHeaders.21776/test_0270000644000000000000000000000013214061636520014563 xustar0030 mtime=1623670096.882100666 30 atime=1623670096.871100676 30 ctime=1623670096.882100666 elk-7.2.42/tests/test_027/0000755002504400250440000000000014061636520016675 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_027/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016542 xustar0030 mtime=1623670096.872100675 30 atime=1623670096.872100675 30 ctime=1623670096.872100675 elk-7.2.42/tests/test_027/TEST_705.OUT_0000644002504400250440000000010114061636520020567 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 4 elk-7.2.42/tests/test_027/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.873100674 30 atime=1623670096.873100674 30 ctime=1623670096.873100674 elk-7.2.42/tests/test_027/TEST_900.OUT_0000644002504400250440000000007014061636520020571 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 8873 elk-7.2.42/tests/test_027/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.875100673 30 atime=1623670096.874100674 30 ctime=1623670096.875100673 elk-7.2.42/tests/test_027/TEST_910.OUT_0000644002504400250440000001052214061636520020575 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 141 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.294085021773 5 0.294085021773 6 -0.294085021773 7 0.588170043546 8 0.00000000000 9 0.00000000000 10 -0.367606277216E-01 11 0.367606277216E-01 12 0.367606277216E-01 13 0.257324394051 14 0.330845649494 15 -0.257324394051 16 0.551409415824 17 0.367606277216E-01 18 0.367606277216E-01 19 -0.735212554432E-01 20 0.735212554432E-01 21 0.735212554432E-01 22 0.220563766330 23 0.367606277216 24 -0.220563766330 25 0.514648788102 26 0.735212554432E-01 27 0.735212554432E-01 28 -0.110281883165 29 0.110281883165 30 0.110281883165 31 0.183803138608 32 0.404366904938 33 -0.183803138608 34 0.477888160381 35 0.110281883165 36 0.110281883165 37 -0.147042510886 38 0.147042510886 39 0.147042510886 40 0.147042510886 41 0.441127532659 42 -0.147042510886 43 0.441127532659 44 0.147042510886 45 0.147042510886 46 -0.183803138608 47 0.183803138608 48 0.183803138608 49 0.110281883165 50 0.477888160381 51 -0.110281883165 52 0.404366904938 53 0.183803138608 54 0.183803138608 55 -0.220563766330 56 0.220563766330 57 0.220563766330 58 0.735212554432E-01 59 0.514648788102 60 -0.735212554432E-01 61 0.367606277216 62 0.220563766330 63 0.220563766330 64 -0.257324394051 65 0.257324394051 66 0.257324394051 67 0.367606277216E-01 68 0.551409415824 69 -0.367606277216E-01 70 0.330845649494 71 0.257324394051 72 0.257324394051 73 -0.294085021773 74 0.294085021773 75 0.294085021773 76 0.00000000000 77 0.588170043546 78 0.00000000000 79 -0.330845649494 80 0.330845649494 81 0.330845649494 82 -0.367606277216E-01 83 0.624930671267 84 0.367606277216E-01 85 0.257324394051 86 0.330845649494 87 0.330845649494 88 -0.367606277216 89 0.367606277216 90 0.367606277216 91 -0.735212554432E-01 92 0.661691298989 93 0.735212554432E-01 94 0.220563766330 95 0.367606277216 96 0.367606277216 97 -0.404366904938 98 0.404366904938 99 0.404366904938 100 -0.110281883165 101 0.698451926710 102 0.110281883165 103 0.183803138608 104 0.404366904938 105 0.404366904938 106 -0.441127532659 107 0.441127532659 108 0.441127532659 109 -0.147042510886 110 0.735212554432 111 0.147042510886 112 0.147042510886 113 0.441127532659 114 0.441127532659 115 -0.477888160381 116 0.477888160381 117 0.477888160381 118 -0.183803138608 119 0.771973182154 120 0.183803138608 121 0.110281883165 122 0.477888160381 123 0.477888160381 124 -0.514648788102 125 0.514648788102 126 0.514648788102 127 -0.220563766330 128 0.808733809875 129 0.220563766330 130 0.735212554432E-01 131 0.514648788102 132 0.514648788102 133 -0.551409415824 134 0.551409415824 135 0.551409415824 136 -0.257324394051 137 0.845494437597 138 0.257324394051 139 0.367606277216E-01 140 0.551409415824 141 0.551409415824 elk-7.2.42/tests/test_027/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015743 xustar0030 mtime=1623670096.876100672 30 atime=1623670096.876100672 30 ctime=1623670096.876100672 elk-7.2.42/tests/test_027/elk.in0000644002504400250440000000046714061636520020007 0ustar00dewhurstdewhurst00000000000000 ! Calculation of the Born effective charges for GaAs. tasks 208 500 test .true. deltaph 0.01 ngridk 2 2 2 nkspolar 8 avec 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 scale 10.6826 sppath '../../species/' atoms 2 'Ga.in' 1 0.0 0.0 0.0 'As.in' 1 0.25 0.25 0.25 elk-7.2.42/tests/test_027/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.877100671 30 atime=1623670096.877100671 30 ctime=1623670096.877100671 elk-7.2.42/tests/test_027/TEST_500.OUT_0000644002504400250440000000013514061636520020567 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 5.40374552954 elk-7.2.42/tests/test_027/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000012714061636520016540 xustar0029 mtime=1623670096.87810067 29 atime=1623670096.87810067 29 ctime=1623670096.87810067 elk-7.2.42/tests/test_027/TEST_510.OUT_0000644002504400250440000000014514061636520020571 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.560022467131E-02 elk-7.2.42/tests/test_027/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.880100668 30 atime=1623670096.879100669 30 ctime=1623670096.880100668 elk-7.2.42/tests/test_027/TEST_400.OUT_0000644002504400250440000000014114061636520020563 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 63.9851353992 elk-7.2.42/tests/test_027/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.881100667 30 atime=1623670096.881100667 30 ctime=1623670096.881100667 elk-7.2.42/tests/test_027/TEST_000.OUT_0000644002504400250440000000012614061636520020562 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -4198.64842022 elk-7.2.42/tests/test_027/PaxHeaders.21776/TEST_208.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.882100666 30 atime=1623670096.882100666 30 ctime=1623670096.882100666 elk-7.2.42/tests/test_027/TEST_208.OUT_0000644002504400250440000000023514061636520020575 0ustar00dewhurstdewhurst00000000000000'Born effective charge' 2 3 0.100000000000E-02 1 -2.19737642162 2 -0.418107058480E-03 3 -0.934399804095E-03 elk-7.2.42/tests/PaxHeaders.21776/test_0030000644000000000000000000000013214061636520014555 xustar0030 mtime=1623670096.895100654 30 atime=1623670096.883100665 30 ctime=1623670096.895100654 elk-7.2.42/tests/test_003/0000755002504400250440000000000014061636520016667 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_003/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015735 xustar0030 mtime=1623670096.884100664 30 atime=1623670096.884100664 30 ctime=1623670096.884100664 elk-7.2.42/tests/test_003/elk.in0000644002504400250440000000067314061636520020000 0ustar00dewhurstdewhurst00000000000000 tasks 0 500 test .true. xctype 21 maxscl 10 tforce .true. mixtype 3 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 0.27 0.27 0.27 0.0 0.0 0.0 ngridk 2 2 2 vkloff 0.5 0.5 0.5 elk-7.2.42/tests/test_003/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.886100662 30 atime=1623670096.886100662 30 ctime=1623670096.886100662 elk-7.2.42/tests/test_003/TEST_705.OUT_0000644002504400250440000000010114061636520020561 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 12 elk-7.2.42/tests/test_003/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.887100661 30 atime=1623670096.887100661 30 ctime=1623670096.887100661 elk-7.2.42/tests/test_003/TEST_900.OUT_0000644002504400250440000000007014061636520020563 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 7799 elk-7.2.42/tests/test_003/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013014061636520016530 xustar0029 mtime=1623670096.88910066 30 atime=1623670096.888100661 29 ctime=1623670096.88910066 elk-7.2.42/tests/test_003/TEST_910.OUT_0000644002504400250440000000037114061636520020570 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 6 0.100000000000E-07 1 0.153099057192 2 0.153099057192 3 0.153099057192 4 0.459297171577 5 0.459297171577 6 -0.153099057192 elk-7.2.42/tests/test_003/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.890100659 30 atime=1623670096.890100659 30 ctime=1623670096.890100659 elk-7.2.42/tests/test_003/TEST_500.OUT_0000644002504400250440000000013514061636520020561 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.555111986930E-12 elk-7.2.42/tests/test_003/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016526 xustar0030 mtime=1623670096.892100657 30 atime=1623670096.891100658 30 ctime=1623670096.892100657 elk-7.2.42/tests/test_003/TEST_510.OUT_0000644002504400250440000000014514061636520020563 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.846319056770E-01 elk-7.2.42/tests/test_003/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.893100656 30 atime=1623670096.893100656 30 ctime=1623670096.893100656 elk-7.2.42/tests/test_003/TEST_400.OUT_0000644002504400250440000000014114061636520020555 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9921531661 elk-7.2.42/tests/test_003/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016520 xustar0030 mtime=1623670096.894100655 30 atime=1623670096.894100655 30 ctime=1623670096.894100655 elk-7.2.42/tests/test_003/TEST_000.OUT_0000644002504400250440000000012614061636520020554 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -580.223475221 elk-7.2.42/tests/test_003/PaxHeaders.21776/TEST_750.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.896100653 30 atime=1623670096.896100653 30 ctime=1623670096.896100653 elk-7.2.42/tests/test_003/TEST_750.OUT_0000644002504400250440000000036114061636520020571 0ustar00dewhurstdewhurst00000000000000'total forces' 2 6 0.100000000000E-02 1 0.177938835190E-01 2 0.177938835190E-01 3 0.177938835190E-01 4 -0.177938835190E-01 5 -0.177938835190E-01 6 -0.177938835190E-01 elk-7.2.42/tests/PaxHeaders.21776/test_0070000644000000000000000000000013214061636520014561 xustar0030 mtime=1623670096.919100632 30 atime=1623670096.897100652 30 ctime=1623670096.919100632 elk-7.2.42/tests/test_007/0000755002504400250440000000000014061636520016673 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013014061636520016533 xustar0029 mtime=1623670096.89910065 30 atime=1623670096.898100651 29 ctime=1623670096.89910065 elk-7.2.42/tests/test_007/TEST_900.OUT_0000644002504400250440000000007014061636520020567 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 2801 elk-7.2.42/tests/test_007/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015741 xustar0030 mtime=1623670096.900100649 30 atime=1623670096.900100649 30 ctime=1623670096.900100649 elk-7.2.42/tests/test_007/elk.in0000644002504400250440000000136614061636520020004 0ustar00dewhurstdewhurst00000000000000 ! FeAl in CsCl (B2) structure using GGA+U and interpolation between AMF and ! FLL double counting. tasks 0 15 16 500 test .true. kstlist 4 8 mixtype 1 msmooth 4 wplot 50 100 2 0.0 0.25 gmaxvr 10.0 xctype 20 dft+u 3 1 : dftu, inpdftu 1 2 0.183 0.034911967 : is, l, U, J spinpol .true. bfieldc 0.0 0.0 -0.01 scale 5.496 avec 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0 atoms 2 : nspecies 'Fe.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 'Al.in' 1 0.5 0.5 0.5 0.0 0.0 0.0 : atposl, bfcmt sppath '../../species/' ngridk 4 4 4 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.902100648 30 atime=1623670096.902100648 30 ctime=1623670096.902100648 elk-7.2.42/tests/test_007/TEST_705.OUT_0000644002504400250440000000010114061636520020565 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016536 xustar0030 mtime=1623670096.904100646 30 atime=1623670096.904100646 30 ctime=1623670096.904100646 elk-7.2.42/tests/test_007/TEST_910.OUT_0000644002504400250440000000174114061636520020576 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 30 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.285807191920 5 0.00000000000 6 0.00000000000 7 0.571614383841 8 0.00000000000 9 0.00000000000 10 0.285807191920 11 0.285807191920 12 0.00000000000 13 0.571614383841 14 0.285807191920 15 0.00000000000 16 0.571614383841 17 0.571614383841 18 0.00000000000 19 0.285807191920 20 0.285807191920 21 0.285807191920 22 0.571614383841 23 0.285807191920 24 0.285807191920 25 0.571614383841 26 0.571614383841 27 0.285807191920 28 0.571614383841 29 0.571614383841 30 0.571614383841 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.906100644 30 atime=1623670096.906100644 30 ctime=1623670096.906100644 elk-7.2.42/tests/test_007/TEST_500.OUT_0000644002504400250440000000013514061636520020565 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 85.1145929024 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.908100642 30 atime=1623670096.907100643 30 ctime=1623670096.908100642 elk-7.2.42/tests/test_007/TEST_510.OUT_0000644002504400250440000000014514061636520020567 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.110435201142E-02 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.909100641 30 atime=1623670096.909100641 30 ctime=1623670096.909100641 elk-7.2.42/tests/test_007/TEST_400.OUT_0000644002504400250440000000014114061636520020561 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 38.9880138586 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.911100639 30 atime=1623670096.911100639 30 ctime=1623670096.911100639 elk-7.2.42/tests/test_007/TEST_450.OUT_0000644002504400250440000000014014061636520020565 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.531032238472 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.913100637 30 atime=1623670096.913100637 30 ctime=1623670096.913100637 elk-7.2.42/tests/test_007/TEST_800.OUT_0000644002504400250440000000014414061636520020570 0ustar00dewhurstdewhurst00000000000000'DFT+U energy for each atom' 2 1 0.100000000000E-03 1 0.122669742967E-01 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_810.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.915100636 30 atime=1623670096.914100636 30 ctime=1623670096.915100636 elk-7.2.42/tests/test_007/TEST_810.OUT_0000644002504400250440000000475514061636520020605 0ustar00dewhurstdewhurst00000000000000'U and J parameters' 2 80 0.100000000000E-03 1 0.183000000000 2 0.349119670000E-01 3 0.00000000000 4 0.00000000000 5 0.00000000000 6 0.00000000000 7 0.00000000000 8 0.00000000000 9 0.00000000000 10 0.00000000000 11 0.00000000000 12 0.00000000000 13 0.00000000000 14 0.00000000000 15 0.00000000000 16 0.00000000000 17 0.00000000000 18 0.00000000000 19 0.00000000000 20 0.00000000000 21 0.00000000000 22 0.00000000000 23 0.00000000000 24 0.00000000000 25 0.00000000000 26 0.00000000000 27 0.00000000000 28 0.00000000000 29 0.00000000000 30 0.00000000000 31 0.00000000000 32 0.00000000000 33 0.00000000000 34 0.00000000000 35 0.00000000000 36 0.00000000000 37 0.00000000000 38 0.00000000000 39 0.00000000000 40 0.00000000000 41 0.00000000000 42 0.00000000000 43 0.00000000000 44 0.00000000000 45 0.00000000000 46 0.00000000000 47 0.00000000000 48 0.00000000000 49 0.00000000000 50 0.00000000000 51 0.00000000000 52 0.00000000000 53 0.00000000000 54 0.00000000000 55 0.00000000000 56 0.00000000000 57 0.00000000000 58 0.00000000000 59 0.00000000000 60 0.00000000000 61 0.00000000000 62 0.00000000000 63 0.00000000000 64 0.00000000000 65 0.00000000000 66 0.00000000000 67 0.00000000000 68 0.00000000000 69 0.00000000000 70 0.00000000000 71 0.00000000000 72 0.00000000000 73 0.00000000000 74 0.00000000000 75 0.00000000000 76 0.00000000000 77 0.00000000000 78 0.00000000000 79 0.00000000000 80 0.00000000000 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.916100634 30 atime=1623670096.916100634 30 ctime=1623670096.916100634 elk-7.2.42/tests/test_007/TEST_000.OUT_0000644002504400250440000000012614061636520020560 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1515.73951144 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_015.OUT_0000644000000000000000000000013214061636520016532 xustar0030 mtime=1623670096.918100633 30 atime=1623670096.918100633 30 ctime=1623670096.918100633 elk-7.2.42/tests/test_007/TEST_015.OUT_0000644002504400250440000000040614061636520020567 0ustar00dewhurstdewhurst00000000000000'total muffin-tin angular momentum' 2 6 0.100000000000E-02 1 0.377657086577E-17 2 -0.919065354963E-18 3 0.259466620087 4 0.483583453545E-18 5 0.334120609772E-17 6 -0.554513869150E-02 elk-7.2.42/tests/test_007/PaxHeaders.21776/TEST_016.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.920100631 30 atime=1623670096.920100631 30 ctime=1623670096.920100631 elk-7.2.42/tests/test_007/TEST_016.OUT_0000644002504400250440000000041614061636520020571 0ustar00dewhurstdewhurst00000000000000'muffin-tin angular momentum for one state' 2 6 0.100000000000E-02 1 0.104883896277E-06 2 0.332930327660E-06 3 0.132660349122 4 -0.936830057932E-06 5 0.916928052435E-06 6 0.156280379029 elk-7.2.42/tests/PaxHeaders.21776/test_0110000644000000000000000000000013114061636520014553 xustar0030 mtime=1623670096.935100617 29 atime=1623670096.92110063 30 ctime=1623670096.935100617 elk-7.2.42/tests/test_011/0000755002504400250440000000000014061636520016666 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_011/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016530 xustar0030 mtime=1623670096.923100628 30 atime=1623670096.922100629 30 ctime=1623670096.923100628 elk-7.2.42/tests/test_011/TEST_900.OUT_0000644002504400250440000000007014061636520020562 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 7799 elk-7.2.42/tests/test_011/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.924100627 30 atime=1623670096.924100627 30 ctime=1623670096.924100627 elk-7.2.42/tests/test_011/TEST_705.OUT_0000644002504400250440000000010114061636520020560 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests/test_011/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.926100625 30 atime=1623670096.925100626 30 ctime=1623670096.926100625 elk-7.2.42/tests/test_011/TEST_910.OUT_0000644002504400250440000000037114061636520020567 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 6 0.100000000000E-07 1 0.153099057192 2 0.153099057192 3 0.153099057192 4 0.459297171577 5 0.459297171577 6 -0.153099057192 elk-7.2.42/tests/test_011/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015734 xustar0030 mtime=1623670096.927100624 30 atime=1623670096.927100624 30 ctime=1623670096.927100624 elk-7.2.42/tests/test_011/elk.in0000644002504400250440000000066714061636520020002 0ustar00dewhurstdewhurst00000000000000 ! Hartree-Fock calculation of silicon. tasks 0 5 500 test .true. maxscl 2 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt 0.25 0.25 0.25 0.0 0.0 0.0 ngridk 2 2 2 vkloff 0.5 0.5 0.5 elk-7.2.42/tests/test_011/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016524 xustar0030 mtime=1623670096.929100622 30 atime=1623670096.929100622 30 ctime=1623670096.929100622 elk-7.2.42/tests/test_011/TEST_500.OUT_0000644002504400250440000000013514061636520020560 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.695818068940E-12 elk-7.2.42/tests/test_011/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016525 xustar0030 mtime=1623670096.931100621 30 atime=1623670096.931100621 30 ctime=1623670096.931100621 elk-7.2.42/tests/test_011/TEST_510.OUT_0000644002504400250440000000014514061636520020562 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.348480655365 elk-7.2.42/tests/test_011/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013114061636520016522 xustar0030 mtime=1623670096.933100619 29 atime=1623670096.93210062 30 ctime=1623670096.933100619 elk-7.2.42/tests/test_011/TEST_400.OUT_0000644002504400250440000000014114061636520020554 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9921684681 elk-7.2.42/tests/test_011/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016517 xustar0030 mtime=1623670096.934100618 30 atime=1623670096.934100618 30 ctime=1623670096.934100618 elk-7.2.42/tests/test_011/TEST_000.OUT_0000644002504400250440000000012614061636520020553 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -579.532441954 elk-7.2.42/tests/test_011/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.935100617 30 atime=1623670096.935100617 30 ctime=1623670096.935100617 elk-7.2.42/tests/test_011/TEST_800.OUT_0000644002504400250440000000026414061636520020566 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 3 0.100000000000E-07 1 394.581580334 2 51.1494504119 3 35.9439292598 elk-7.2.42/tests/PaxHeaders.21776/test_0150000644000000000000000000000013214061636520014560 xustar0030 mtime=1623670096.954100599 30 atime=1623670096.936100616 30 ctime=1623670096.954100599 elk-7.2.42/tests/test_015/0000755002504400250440000000000014061636520016672 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016537 xustar0030 mtime=1623670096.938100614 30 atime=1623670096.937100615 30 ctime=1623670096.938100614 elk-7.2.42/tests/test_015/TEST_705.OUT_0000644002504400250440000000010114061636520020564 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 24 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.939100613 30 atime=1623670096.939100613 30 ctime=1623670096.939100613 elk-7.2.42/tests/test_015/TEST_900.OUT_0000644002504400250440000000007014061636520020566 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 7247 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.940100612 30 atime=1623670096.940100612 30 ctime=1623670096.940100612 elk-7.2.42/tests/test_015/TEST_910.OUT_0000644002504400250440000000066314061636520020577 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 12 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.597004528775 5 -0.199001509592 6 -0.199001509592 7 0.398003019183 8 0.398003019183 9 -0.398003019183 10 0.199001509592 11 0.199001509592 12 0.199001509592 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000012714061636520016534 xustar0029 mtime=1623670096.94210061 29 atime=1623670096.94210061 29 ctime=1623670096.94210061 elk-7.2.42/tests/test_015/TEST_500.OUT_0000644002504400250440000000013514061636520020564 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 49.6073399761 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016531 xustar0030 mtime=1623670096.943100609 30 atime=1623670096.943100609 30 ctime=1623670096.943100609 elk-7.2.42/tests/test_015/TEST_510.OUT_0000644002504400250440000000014514061636520020566 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.614743356983E-01 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.945100608 30 atime=1623670096.945100608 30 ctime=1623670096.945100608 elk-7.2.42/tests/test_015/TEST_400.OUT_0000644002504400250440000000014114061636520020560 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 72.0070954290 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.946100607 30 atime=1623670096.946100607 30 ctime=1623670096.946100607 elk-7.2.42/tests/test_015/TEST_450.OUT_0000644002504400250440000000014014061636520020564 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.376223233397E-16 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520016533 xustar0030 mtime=1623670096.948100605 30 atime=1623670096.947100606 30 ctime=1623670096.948100605 elk-7.2.42/tests/test_015/TEST_800.OUT_0000644002504400250440000000020314061636520020563 0ustar00dewhurstdewhurst00000000000000'DFT+U energy for each atom' 2 2 0.100000000000E-03 1 0.836291508083 2 0.836291508083 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_810.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.949100604 30 atime=1623670096.949100604 30 ctime=1623670096.949100604 elk-7.2.42/tests/test_015/TEST_810.OUT_0000644002504400250440000000475514061636520020604 0ustar00dewhurstdewhurst00000000000000'U and J parameters' 2 80 0.100000000000E-03 1 0.293989988143 2 0.460208922680E-01 3 0.00000000000 4 0.00000000000 5 0.00000000000 6 0.00000000000 7 0.00000000000 8 0.00000000000 9 0.00000000000 10 0.00000000000 11 0.00000000000 12 0.00000000000 13 0.00000000000 14 0.00000000000 15 0.00000000000 16 0.00000000000 17 0.00000000000 18 0.00000000000 19 0.00000000000 20 0.00000000000 21 0.00000000000 22 0.00000000000 23 0.00000000000 24 0.00000000000 25 0.00000000000 26 0.00000000000 27 0.00000000000 28 0.00000000000 29 0.00000000000 30 0.00000000000 31 0.00000000000 32 0.00000000000 33 0.00000000000 34 0.00000000000 35 0.00000000000 36 0.00000000000 37 0.00000000000 38 0.00000000000 39 0.00000000000 40 0.00000000000 41 0.00000000000 42 0.00000000000 43 0.00000000000 44 0.00000000000 45 0.00000000000 46 0.00000000000 47 0.00000000000 48 0.00000000000 49 0.00000000000 50 0.00000000000 51 0.00000000000 52 0.00000000000 53 0.00000000000 54 0.00000000000 55 0.00000000000 56 0.00000000000 57 0.00000000000 58 0.00000000000 59 0.00000000000 60 0.00000000000 61 0.00000000000 62 0.00000000000 63 0.00000000000 64 0.00000000000 65 0.00000000000 66 0.00000000000 67 0.00000000000 68 0.00000000000 69 0.00000000000 70 0.00000000000 71 0.00000000000 72 0.00000000000 73 0.00000000000 74 0.00000000000 75 0.00000000000 76 0.00000000000 77 0.00000000000 78 0.00000000000 79 0.00000000000 80 0.00000000000 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016523 xustar0030 mtime=1623670096.951100602 30 atime=1623670096.950100603 30 ctime=1623670096.951100602 elk-7.2.42/tests/test_015/TEST_000.OUT_0000644002504400250440000000012614061636520020557 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -3197.50498280 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_820.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.952100601 30 atime=1623670096.952100601 30 ctime=1623670096.952100601 elk-7.2.42/tests/test_015/TEST_820.OUT_0000644002504400250440000000014014061636520020565 0ustar00dewhurstdewhurst00000000000000'Norm of tensor moments' 2 1 0.100000000000E-03 1 91.2305548010 elk-7.2.42/tests/test_015/PaxHeaders.21776/TEST_830.OUT_0000644000000000000000000000012414061636520016537 xustar0028 mtime=1623670096.9531006 28 atime=1623670096.9531006 28 ctime=1623670096.9531006 elk-7.2.42/tests/test_015/TEST_830.OUT_0000644002504400250440000000016614061636520020576 0ustar00dewhurstdewhurst00000000000000'Norm of DFT+U Hartree-Fock exchange energies' 2 1 0.100000000000E-03 1 2.16721144871 elk-7.2.42/tests/test_015/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015740 xustar0030 mtime=1623670096.955100598 30 atime=1623670096.955100598 30 ctime=1623670096.955100598 elk-7.2.42/tests/test_015/elk.in0000644002504400250440000000132214061636520017773 0ustar00dewhurstdewhurst00000000000000 ! DFT+U test tasks 0 400 500 maxscl 3 test .true. dft+u 1 5 : dftu, inpdftu 1 2 0.29399 : is, l, U fixed swidth 0.05 spinpol .true. scale 7.893389 avec 1.0 0.5 0.5 0.5 1.0 0.5 0.5 0.5 1.0 atoms 2 : nspecies 'Ni.in' : spfname 2 : natoms; atpos, bfcmt below 0.0 0.0 0.0 0.0 0.0 -2.0 0.5 0.5 0.5 0.0 0.0 2.0 'O.in' : spfname 2 : natoms; atpos, bfcmt below 0.25 0.25 0.25 0.0 0.0 0.0 0.75 0.75 0.75 0.0 0.0 0.0 reducebf 0.5 sppath '../../species/' ngridk 2 2 2 elk-7.2.42/tests/PaxHeaders.21776/test_0190000644000000000000000000000013214061636520014564 xustar0030 mtime=1623670096.968100586 30 atime=1623670096.955100598 30 ctime=1623670096.968100586 elk-7.2.42/tests/test_019/0000755002504400250440000000000014061636520016676 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests/test_019/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520015744 xustar0030 mtime=1623670096.957100597 30 atime=1623670096.957100597 30 ctime=1623670096.957100597 elk-7.2.42/tests/test_019/elk.in0000644002504400250440000000071714061636520020006 0ustar00dewhurstdewhurst00000000000000 ! TDDFT time evolution test tasks 0 450 460 500 test .true. ramdisk .true. tshift .false. lradstp 5 rgkmax 6.0 ngridk 4 4 4 nempty 6 tstime 50.0 dtimes 1.0 pulse 1 0.0 0.0 250.0 0.03 0.0 0.0 30.0 10.0 ntswrite 0 spinpol .true. spinorb .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../species/' atoms 1 'Ni.in' 1 0.0 0.0 0.0 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520016543 xustar0030 mtime=1623670096.958100595 30 atime=1623670096.958100595 30 ctime=1623670096.958100595 elk-7.2.42/tests/test_019/TEST_705.OUT_0000644002504400250440000000010114061636520020570 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 4 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.959100595 30 atime=1623670096.959100595 30 ctime=1623670096.959100595 elk-7.2.42/tests/test_019/TEST_900.OUT_0000644002504400250440000000007014061636520020572 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 2109 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520016541 xustar0030 mtime=1623670096.961100593 30 atime=1623670096.960100594 30 ctime=1623670096.961100593 elk-7.2.42/tests/test_019/TEST_910.OUT_0000644002504400250440000000360314061636520020600 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 60 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.235855304324 5 0.235855304324 6 -0.235855304324 7 0.471710608647 8 0.471710608647 9 -0.471710608647 10 0.707565912971 11 0.707565912971 12 -0.707565912971 13 0.471710608647 14 0.00000000000 15 0.00000000000 16 0.707565912971 17 0.235855304324 18 -0.235855304324 19 0.943421217294 20 0.471710608647 21 -0.471710608647 22 0.707565912971 23 -0.235855304324 24 0.235855304324 25 0.943421217294 26 0.00000000000 27 0.00000000000 28 1.17927652162 29 0.235855304324 30 -0.235855304324 31 0.943421217294 32 -0.471710608647 33 0.471710608647 34 1.17927652162 35 -0.235855304324 36 0.235855304324 37 0.00000000000 38 0.00000000000 39 0.471710608647 40 0.471710608647 41 0.471710608647 42 0.00000000000 43 0.707565912971 44 0.707565912971 45 -0.235855304324 46 0.943421217294 47 0.471710608647 48 0.00000000000 49 0.943421217294 50 0.00000000000 51 0.471710608647 52 0.00000000000 53 0.00000000000 54 0.943421217294 55 0.707565912971 56 0.707565912971 57 0.235855304324 58 0.00000000000 59 0.00000000000 60 1.41513182594 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520016534 xustar0030 mtime=1623670096.962100592 30 atime=1623670096.962100592 30 ctime=1623670096.962100592 elk-7.2.42/tests/test_019/TEST_500.OUT_0000644002504400250440000000013514061636520020570 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 70.1899859819 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636520016535 xustar0030 mtime=1623670096.963100591 30 atime=1623670096.963100591 30 ctime=1623670096.963100591 elk-7.2.42/tests/test_019/TEST_510.OUT_0000644002504400250440000000014514061636520020572 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.182636792935E-02 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000012714061636520016537 xustar0029 mtime=1623670096.96410059 29 atime=1623670096.96410059 29 ctime=1623670096.96410059 elk-7.2.42/tests/test_019/TEST_400.OUT_0000644002504400250440000000014114061636520020564 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9993302808 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636520016540 xustar0030 mtime=1623670096.966100588 30 atime=1623670096.966100588 30 ctime=1623670096.966100588 elk-7.2.42/tests/test_019/TEST_450.OUT_0000644002504400250440000000014014061636520020570 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.591058878524 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520016527 xustar0030 mtime=1623670096.967100587 30 atime=1623670096.967100587 30 ctime=1623670096.967100587 elk-7.2.42/tests/test_019/TEST_000.OUT_0000644002504400250440000000012614061636520020563 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1518.38040797 elk-7.2.42/tests/test_019/PaxHeaders.21776/TEST_460.OUT_0000644000000000000000000000013214061636520016541 xustar0030 mtime=1623670096.968100586 30 atime=1623670096.968100586 30 ctime=1623670096.968100586 elk-7.2.42/tests/test_019/TEST_460.OUT_0000644002504400250440000000024714061636520020601 0ustar00dewhurstdewhurst00000000000000'total current of last time step' 2 3 0.100000000000E-03 1 0.00000000000 2 0.173472347598E-17 3 0.108735818842 elk-7.2.42/PaxHeaders.21776/tests-libxc0000644000000000000000000000013114061636521014313 xustar0030 mtime=1623670097.052100508 29 atime=1623670096.97510058 30 ctime=1623670097.052100508 elk-7.2.42/tests-libxc/0000755002504400250440000000000014061636521016426 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests-libxc/PaxHeaders.21776/test_0060000644000000000000000000000013214061636520015657 xustar0030 mtime=1623670096.989100567 30 atime=1623670096.976100579 30 ctime=1623670096.989100567 elk-7.2.42/tests-libxc/test_006/0000755002504400250440000000000014061636520017771 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520017633 xustar0030 mtime=1623670096.978100577 30 atime=1623670096.978100577 30 ctime=1623670096.978100577 elk-7.2.42/tests-libxc/test_006/TEST_900.OUT_0000644002504400250440000000007014061636520021665 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 7799 elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017037 xustar0030 mtime=1623670096.979100576 30 atime=1623670096.979100576 30 ctime=1623670096.979100576 elk-7.2.42/tests-libxc/test_006/elk.in0000644002504400250440000000043314061636520021074 0ustar00dewhurstdewhurst00000000000000 ! Hybrid functional test. tasks 0 5 500 test .true. xctype 100 0 406 ngridk 6 6 6 ngridq 3 3 3 nempty 8 avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../species/' atoms 1 'Si.in' 2 0.00 0.00 0.00 0.25 0.25 0.25 elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520017634 xustar0030 mtime=1623670096.981100574 30 atime=1623670096.981100574 30 ctime=1623670096.981100574 elk-7.2.42/tests-libxc/test_006/TEST_910.OUT_0000644002504400250440000000301714061636520021672 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 48 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.102066038128 5 0.102066038128 6 -0.102066038128 7 0.204132076257 8 0.204132076257 9 -0.204132076257 10 0.306198114385 11 0.306198114385 12 -0.306198114385 13 0.204132076257 14 0.358605526043E-17 15 -0.358605526043E-17 16 0.306198114385 17 0.102066038128 18 -0.102066038128 19 0.408264152513 20 0.204132076257 21 -0.204132076257 22 0.510330190642 23 0.306198114385 24 -0.306198114385 25 0.612396228770 26 0.408264152513 27 -0.408264152513 28 0.408264152513 29 0.717211052085E-17 30 -0.717211052085E-17 31 0.510330190642 32 0.102066038128 33 -0.102066038128 34 0.612396228770 35 0.204132076257 36 -0.204132076257 37 0.612396228770 38 0.00000000000 39 0.00000000000 40 0.408264152513 41 0.204132076257 42 -0.241695203552E-16 43 0.510330190642 44 0.306198114385 45 -0.102066038128 46 0.612396228770 47 0.204132076257 48 0.174638430682E-16 elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520017636 xustar0030 mtime=1623670096.982100573 30 atime=1623670096.982100573 30 ctime=1623670096.982100573 elk-7.2.42/tests-libxc/test_006/TEST_705.OUT_0000644002504400250440000000010114061636520021663 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520017627 xustar0030 mtime=1623670096.984100571 30 atime=1623670096.984100571 30 ctime=1623670096.984100571 elk-7.2.42/tests-libxc/test_006/TEST_500.OUT_0000644002504400250440000000013514061636520021663 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.390500825608E-11 elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000012714061636520017634 xustar0029 mtime=1623670096.98510057 29 atime=1623670096.98510057 29 ctime=1623670096.98510057 elk-7.2.42/tests-libxc/test_006/TEST_510.OUT_0000644002504400250440000000014514061636520021665 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.827208033236E-01 elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636520017626 xustar0030 mtime=1623670096.987100569 30 atime=1623670096.987100569 30 ctime=1623670096.987100569 elk-7.2.42/tests-libxc/test_006/TEST_400.OUT_0000644002504400250440000000014114061636520021657 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9912511507 elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636520017622 xustar0030 mtime=1623670096.988100568 30 atime=1623670096.988100568 30 ctime=1623670096.988100568 elk-7.2.42/tests-libxc/test_006/TEST_000.OUT_0000644002504400250440000000012614061636520021656 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -580.163931813 elk-7.2.42/tests-libxc/test_006/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636520017632 xustar0030 mtime=1623670096.990100566 30 atime=1623670096.990100566 30 ctime=1623670096.990100566 elk-7.2.42/tests-libxc/test_006/TEST_800.OUT_0000644002504400250440000000032314061636520021665 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 4 0.100000000000E-07 1 887.808555744 2 115.086263427 3 80.8738408354 4 40.8197509399 elk-7.2.42/tests-libxc/PaxHeaders.21776/test_0040000644000000000000000000000013214061636521015656 xustar0030 mtime=1623670097.004100553 30 atime=1623670096.991100565 30 ctime=1623670097.004100553 elk-7.2.42/tests-libxc/test_004/0000755002504400250440000000000014061636521017770 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636520017634 xustar0030 mtime=1623670096.992100564 30 atime=1623670096.992100564 30 ctime=1623670096.992100564 elk-7.2.42/tests-libxc/test_004/TEST_705.OUT_0000644002504400250440000000010114061636520021661 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636520017631 xustar0030 mtime=1623670096.994100562 30 atime=1623670096.994100562 30 ctime=1623670096.994100562 elk-7.2.42/tests-libxc/test_004/TEST_900.OUT_0000644002504400250440000000007014061636520021663 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 7799 elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636520017632 xustar0030 mtime=1623670096.995100561 30 atime=1623670096.995100561 30 ctime=1623670096.995100561 elk-7.2.42/tests-libxc/test_004/TEST_910.OUT_0000644002504400250440000000531014061636520021666 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 87 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.765495285962E-01 5 0.765495285962E-01 6 -0.765495285962E-01 7 0.153099057192 8 0.153099057192 9 -0.153099057192 10 0.229648585789 11 0.229648585789 12 -0.229648585789 13 0.306198114385 14 0.306198114385 15 -0.306198114385 16 0.153099057192 17 0.00000000000 18 0.00000000000 19 0.229648585789 20 0.765495285962E-01 21 -0.765495285962E-01 22 0.306198114385 23 0.153099057192 24 -0.153099057192 25 0.382747642981 26 0.229648585789 27 -0.229648585789 28 0.459297171577 29 0.306198114385 30 -0.306198114385 31 0.535846700174 32 0.382747642981 33 -0.382747642981 34 0.612396228770 35 0.459297171577 36 -0.459297171577 37 0.306198114385 38 0.00000000000 39 0.00000000000 40 0.382747642981 41 0.765495285962E-01 42 -0.765495285962E-01 43 0.459297171577 44 0.153099057192 45 -0.153099057192 46 0.535846700174 47 0.229648585789 48 -0.229648585789 49 0.612396228770 50 0.306198114385 51 -0.306198114385 52 0.459297171577 53 0.138777878078E-16 54 -0.138777878078E-16 55 0.535846700174 56 0.765495285962E-01 57 -0.765495285962E-01 58 0.612396228770 59 0.153099057192 60 -0.153099057192 61 0.612396228770 62 0.00000000000 63 0.00000000000 64 0.306198114385 65 0.153099057192 66 0.00000000000 67 0.382747642981 68 0.229648585789 69 -0.765495285962E-01 70 0.459297171577 71 0.306198114385 72 -0.153099057192 73 0.459297171577 74 0.153099057192 75 -0.138777878078E-16 76 0.535846700174 77 0.229648585789 78 -0.765495285962E-01 79 0.612396228770 80 0.306198114385 81 -0.153099057192 82 0.612396228770 83 0.153099057192 84 0.00000000000 85 0.612396228770 86 0.306198114385 87 0.00000000000 elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636520017035 xustar0030 mtime=1623670096.997100559 30 atime=1623670096.997100559 30 ctime=1623670096.997100559 elk-7.2.42/tests-libxc/test_004/elk.in0000644002504400250440000000072414061636520021075 0ustar00dewhurstdewhurst00000000000000 ! Tran-Blaha meta-GGA functional test. tasks 0 120 121 500 test .true. xctype 100 208 12 nrmtscf 2 nxoapwlo 1 msmooth 2 ptnucl .false. avec 5.13 5.13 0.00 5.13 0.00 5.13 0.00 5.13 5.13 sppath '../../species/' atoms 1 : nspecies 'Si.in' : spfname 2 : natoms; atposl below 0.0 0.0 0.0 0.25 0.25 0.25 ngridk 8 8 8 elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636520017625 xustar0030 mtime=1623670096.998100558 30 atime=1623670096.998100558 30 ctime=1623670096.998100558 elk-7.2.42/tests-libxc/test_004/TEST_500.OUT_0000644002504400250440000000013514061636520021661 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.339003194219E-08 elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636521017627 xustar0030 mtime=1623670097.000100557 30 atime=1623670097.000100557 30 ctime=1623670097.000100557 elk-7.2.42/tests-libxc/test_004/TEST_510.OUT_0000644002504400250440000000014514061636521021664 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.460326559149E-01 elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636521017625 xustar0030 mtime=1623670097.001100556 30 atime=1623670097.001100556 30 ctime=1623670097.001100556 elk-7.2.42/tests-libxc/test_004/TEST_400.OUT_0000644002504400250440000000014114061636521021656 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9973348103 elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636521017621 xustar0030 mtime=1623670097.003100554 30 atime=1623670097.003100554 30 ctime=1623670097.003100554 elk-7.2.42/tests-libxc/test_004/TEST_000.OUT_0000644002504400250440000000012614061636521021655 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -538.189221047 elk-7.2.42/tests-libxc/test_004/PaxHeaders.21776/TEST_121.OUT_0000644000000000000000000000013214061636521017625 xustar0030 mtime=1623670097.005100552 30 atime=1623670097.004100553 30 ctime=1623670097.005100552 elk-7.2.42/tests-libxc/test_004/TEST_121.OUT_0000644002504400250440000006370314061636521021673 0ustar00dewhurstdewhurst00000000000000'optical conductivity' 3 500 0.100000000000E-01 1 0.790149431269E-03 0.00000000000 2 0.790245256092E-03 -0.790117479646E-03 3 0.790532820425E-03 -0.158042657900E-02 4 0.791012393981E-03 -0.237111909737E-02 5 0.791684426925E-03 -0.316238719368E-02 6 0.792549550851E-03 -0.395442356725E-02 7 0.793608580154E-03 -0.474742163975E-02 8 0.794862513792E-03 -0.554157573870E-02 9 0.796312537464E-03 -0.633708128295E-02 10 0.797960026203E-03 -0.713413497056E-02 11 0.799806547391E-03 -0.793293496945E-02 12 0.801853864216E-03 -0.873368111128E-02 13 0.804103939583E-03 -0.953657508903E-02 14 0.806558940488E-03 -0.103418206587E-01 15 0.809221242885E-03 -0.111496238457E-01 16 0.812093437057E-03 -0.119601931561E-01 17 0.815178333512E-03 -0.127737397939E-01 18 0.818478969444E-03 -0.135904778840E-01 19 0.821998615764E-03 -0.144106247025E-01 20 0.825740784753E-03 -0.152344009136E-01 21 0.829709238357E-03 -0.160620308150E-01 22 0.833907997164E-03 -0.168937425921E-01 23 0.838341350105E-03 -0.177297685803E-01 24 0.843013864925E-03 -0.185703455394E-01 25 0.847930399469E-03 -0.194157149367E-01 26 0.853096113833E-03 -0.202661232434E-01 27 0.858516483450E-03 -0.211218222427E-01 28 0.864197313156E-03 -0.219830693520E-01 29 0.870144752330E-03 -0.228501279591E-01 30 0.876365311154E-03 -0.237232677747E-01 31 0.882865878104E-03 -0.246027652012E-01 32 0.889653738749E-03 -0.254889037200E-01 33 0.896736595951E-03 -0.263819742978E-01 34 0.904122591599E-03 -0.272822758144E-01 35 0.911820329966E-03 -0.281901155126E-01 36 0.919838902849E-03 -0.291058094723E-01 37 0.928187916617E-03 -0.300296831109E-01 38 0.936877521333E-03 -0.309620717113E-01 39 0.945918442128E-03 -0.319033209806E-01 40 0.955322013010E-03 -0.328537876405E-01 41 0.965100213334E-03 -0.338138400540E-01 42 0.975265707150E-03 -0.347838588886E-01 43 0.985831885708E-03 -0.357642378209E-01 44 0.996812913382E-03 -0.367553842855E-01 45 0.100822377736E-02 -0.377577202715E-01 46 0.102008034141E-02 -0.387716831697E-01 47 0.103239940420E-02 -0.397977266772E-01 48 0.104519876243E-02 -0.408363217611E-01 49 0.105849727951E-02 -0.418879576890E-01 50 0.107231496009E-02 -0.429531431298E-01 51 0.108667303117E-02 -0.440324073334E-01 52 0.110159403047E-02 -0.451263013931E-01 53 0.111710190273E-02 -0.462353996020E-01 54 0.113322210490E-02 -0.473603009078E-01 55 0.114998172102E-02 -0.485016304790E-01 56 0.116740958807E-02 -0.496600413895E-01 57 0.118553643380E-02 -0.508362164354E-01 58 0.120439502807E-02 -0.520308700956E-01 59 0.122402034906E-02 -0.532447506503E-01 60 0.124444976639E-02 -0.544786424736E-01 61 0.126572324283E-02 -0.557333685172E-01 62 0.128788355717E-02 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0.720124989027E-01 467 0.150495002792E-01 0.806270348387E-01 468 0.105184545053E-01 0.761833576801E-01 469 0.114372700666E-01 0.747955284690E-01 470 0.840604026332E-02 0.761862282039E-01 471 0.527007186791E-02 0.727046784413E-01 472 0.479837219581E-02 0.686438419783E-01 473 0.625646969224E-02 0.647482734822E-01 474 0.100390299340E-01 0.618607118288E-01 475 0.152117900539E-01 0.650942886586E-01 476 0.128517781177E-01 0.659307105867E-01 477 0.164844916763E-01 0.670176984105E-01 478 0.128391734630E-01 0.712929596134E-01 479 0.100733784191E-01 0.679308434411E-01 480 0.131548433267E-01 0.670230062489E-01 481 0.128955142061E-01 0.707377726632E-01 482 0.813668624571E-02 0.710772367215E-01 483 0.577186089331E-02 0.674996494384E-01 484 0.701193471588E-02 0.638354885545E-01 485 0.101068807566E-01 0.647308225107E-01 486 0.801615720438E-02 0.660407575052E-01 487 0.619432812545E-02 0.642311361935E-01 488 0.650124300323E-02 0.613993679243E-01 489 0.829317354830E-02 0.598503362123E-01 490 0.101028223347E-01 0.594395675132E-01 491 0.126787857773E-01 0.624056904019E-01 492 0.819432552296E-02 0.639479962746E-01 493 0.596750837315E-02 0.611175750571E-01 494 0.577504085205E-02 0.577803389124E-01 495 0.736400472417E-02 0.546910008369E-01 496 0.117150037072E-01 0.523586024978E-01 497 0.134951319715E-01 0.570622420490E-01 498 0.111107103726E-01 0.547916705768E-01 499 0.140617918133E-01 0.521297521032E-01 500 0.168586596006E-01 0.521439581133E-01 elk-7.2.42/tests-libxc/PaxHeaders.21776/test.sh0000644000000000000000000000013214061636521015704 xustar0030 mtime=1623670097.006100551 30 atime=1623670097.006100551 30 ctime=1623670097.006100551 elk-7.2.42/tests-libxc/test.sh0000755002504400250440000000064414061636521017750 0ustar00dewhurstdewhurst00000000000000#! /bin/sh # Test suite script for the Elk Code for i in test_* do cd $i echo echo "Running test in directory $i..." \rm -f *.OUT gmon.out fort.* OMP_NUM_THREADS=8 OMP_STACKSIZE=20M ../../src/elk > test.log NERROR=`grep -c Error test.log` if test $NERROR -gt 0 then echo " Failed! See test.log and output files" else echo " Passed" \rm -f *.OUT test.log fort.* gmon.out fi cd .. done elk-7.2.42/tests-libxc/PaxHeaders.21776/test_0010000644000000000000000000000013214061636521015653 xustar0030 mtime=1623670097.019100539 30 atime=1623670097.008100549 30 ctime=1623670097.019100539 elk-7.2.42/tests-libxc/test_001/0000755002504400250440000000000014061636521017765 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests-libxc/test_001/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636521017627 xustar0030 mtime=1623670097.009100548 30 atime=1623670097.009100548 30 ctime=1623670097.009100548 elk-7.2.42/tests-libxc/test_001/TEST_900.OUT_0000644002504400250440000000007014061636521021661 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 8873 elk-7.2.42/tests-libxc/test_001/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636521017632 xustar0030 mtime=1623670097.011100546 30 atime=1623670097.011100546 30 ctime=1623670097.011100546 elk-7.2.42/tests-libxc/test_001/TEST_705.OUT_0000644002504400250440000000010114061636521021657 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 24 elk-7.2.42/tests-libxc/test_001/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636521017630 xustar0030 mtime=1623670097.012100545 30 atime=1623670097.012100545 30 ctime=1623670097.012100545 elk-7.2.42/tests-libxc/test_001/TEST_910.OUT_0000644002504400250440000000174114061636521021670 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 30 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.146981971254 5 0.146981971254 6 -0.146981971254 7 0.293963942509 8 0.293963942509 9 -0.293963942509 10 0.440945913763 11 0.440945913763 12 -0.440945913763 13 0.293963942509 14 0.00000000000 15 0.00000000000 16 0.440945913763 17 0.146981971254 18 -0.146981971254 19 0.587927885017 20 0.293963942509 21 -0.293963942509 22 0.587927885017 23 0.00000000000 24 0.00000000000 25 0.734909856272 26 0.146981971254 27 -0.146981971254 28 0.587927885017 29 0.293963942509 30 0.00000000000 elk-7.2.42/tests-libxc/test_001/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636521017033 xustar0030 mtime=1623670097.014100544 30 atime=1623670097.014100544 30 ctime=1623670097.014100544 elk-7.2.42/tests-libxc/test_001/elk.in0000644002504400250440000000074614061636521021077 0ustar00dewhurstdewhurst00000000000000 tasks 0 500 test .true. maxscl 2 ! set additional options required for meta-GGA metagga .true. ! regularised SCAN xctype 100 493 494 ngridk 4 4 4 avec 5.3435 5.3435 0.0000 5.3435 0.0000 5.3435 0.0000 5.3435 5.3435 sppath '../../species/' atoms 2 : nspecies 'Ga.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'As.in' 1 0.25 0.25 0.25 elk-7.2.42/tests-libxc/test_001/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636521017623 xustar0030 mtime=1623670097.015100543 30 atime=1623670097.015100543 30 ctime=1623670097.015100543 elk-7.2.42/tests-libxc/test_001/TEST_500.OUT_0000644002504400250440000000013514061636521021657 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 0.445518870377E-03 elk-7.2.42/tests-libxc/test_001/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636521017624 xustar0030 mtime=1623670097.017100541 30 atime=1623670097.016100542 30 ctime=1623670097.017100541 elk-7.2.42/tests-libxc/test_001/TEST_510.OUT_0000644002504400250440000000014514061636521021661 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.247937820660E-01 elk-7.2.42/tests-libxc/test_001/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000012714061636521017626 xustar0029 mtime=1623670097.01810054 29 atime=1623670097.01810054 29 ctime=1623670097.01810054 elk-7.2.42/tests-libxc/test_001/TEST_400.OUT_0000644002504400250440000000014114061636521021653 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 63.9987772467 elk-7.2.42/tests-libxc/test_001/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636521017616 xustar0030 mtime=1623670097.019100539 30 atime=1623670097.019100539 30 ctime=1623670097.019100539 elk-7.2.42/tests-libxc/test_001/TEST_000.OUT_0000644002504400250440000000012614061636521021652 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -4219.25406464 elk-7.2.42/tests-libxc/PaxHeaders.21776/test_0020000644000000000000000000000013214061636521015654 xustar0030 mtime=1623670097.036100523 30 atime=1623670097.020100538 30 ctime=1623670097.036100523 elk-7.2.42/tests-libxc/test_002/0000755002504400250440000000000014061636521017766 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_800.OUT_0000644000000000000000000000013214061636521017627 xustar0030 mtime=1623670097.022100536 30 atime=1623670097.021100537 30 ctime=1623670097.022100536 elk-7.2.42/tests-libxc/test_002/TEST_800.OUT_0000644002504400250440000000301014061636521021656 0ustar00dewhurstdewhurst00000000000000'regularised Coulomb Green''s function (gclq)' 2 47 0.100000000000E-07 1 4156.52649632 2 538.808845910 3 122.281077681 4 53.2067305730 5 29.7036699563 6 18.9436528129 7 378.633726982 8 131.915119909 9 59.6996144004 10 33.1294509551 11 20.8866383293 12 24.1480573225 13 39.8247961001 14 76.6221168207 15 191.109192697 16 89.6935829837 17 52.8305196423 18 32.3142045935 19 21.1792161666 20 18.7172333061 21 28.0029635091 22 44.9516730037 23 39.4977235641 24 27.8283415094 25 19.6878350783 26 14.3061427077 27 19.7706217330 28 22.1479831303 29 17.0639418646 30 13.1063464662 31 14.1544228910 32 70.5026233452 33 40.4627055245 34 25.3002738051 35 17.0626173734 36 35.3392864088 37 23.9798340158 38 16.8448151671 39 18.9724996792 40 27.4485942715 41 20.7913378523 42 15.5388968693 43 14.2001311974 44 13.5917268552 45 17.6443345168 46 13.2018441244 47 12.1733944017 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636521017633 xustar0030 mtime=1623670097.023100535 30 atime=1623670097.023100535 30 ctime=1623670097.023100535 elk-7.2.42/tests-libxc/test_002/TEST_705.OUT_0000644002504400250440000000010114061636521021660 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 48 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636521017630 xustar0030 mtime=1623670097.024100534 30 atime=1623670097.024100534 30 ctime=1623670097.024100534 elk-7.2.42/tests-libxc/test_002/TEST_900.OUT_0000644002504400250440000000007014061636521021662 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 2109 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636521017631 xustar0030 mtime=1623670097.026100533 30 atime=1623670097.026100533 30 ctime=1623670097.026100533 elk-7.2.42/tests-libxc/test_002/TEST_910.OUT_0000644002504400250440000001052214061636521021666 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 141 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.943421217294E-01 5 0.943421217294E-01 6 -0.943421217294E-01 7 0.188684243459 8 0.188684243459 9 -0.188684243459 10 0.283026365188 11 0.283026365188 12 -0.283026365188 13 0.377368486918 14 0.377368486918 15 -0.377368486918 16 0.471710608647 17 0.471710608647 18 -0.471710608647 19 0.188684243459 20 -0.308963289789E-17 21 0.308963289789E-17 22 0.283026365188 23 0.943421217294E-01 24 -0.943421217294E-01 25 0.377368486918 26 0.188684243459 27 -0.188684243459 28 0.471710608647 29 0.283026365188 30 -0.283026365188 31 0.566052730377 32 0.377368486918 33 -0.377368486918 34 0.660394852106 35 0.471710608647 36 -0.471710608647 37 0.754736973835 38 0.566052730377 39 -0.566052730377 40 0.849079095565 41 0.660394852106 42 -0.660394852106 43 0.943421217294 44 0.754736973835 45 -0.754736973835 46 0.377368486918 47 -0.617926579578E-17 48 0.617926579578E-17 49 0.471710608647 50 0.943421217294E-01 51 -0.943421217294E-01 52 0.566052730377 53 0.188684243459 54 -0.188684243459 55 0.660394852106 56 0.283026365188 57 -0.283026365188 58 0.754736973835 59 0.377368486918 60 -0.377368486918 61 0.849079095565 62 0.471710608647 63 -0.471710608647 64 0.943421217294 65 0.566052730377 66 -0.566052730377 67 0.566052730377 68 -0.247170631831E-16 69 0.247170631831E-16 70 0.660394852106 71 0.943421217294E-01 72 -0.943421217294E-01 73 0.754736973835 74 0.188684243459 75 -0.188684243459 76 0.849079095565 77 0.283026365188 78 -0.283026365188 79 0.943421217294 80 0.377368486918 81 -0.377368486918 82 0.754736973835 83 -0.123585315916E-16 84 0.123585315916E-16 85 0.849079095565 86 0.943421217294E-01 87 -0.943421217294E-01 88 0.943421217294 89 0.188684243459 90 -0.188684243459 91 0.943421217294 92 0.00000000000 93 0.00000000000 94 0.377368486918 95 0.188684243459 96 -0.169674207057E-16 97 0.471710608647 98 0.283026365188 99 -0.943421217294E-01 100 0.566052730377 101 0.377368486918 102 -0.188684243459 103 0.660394852106 104 0.471710608647 105 -0.283026365188 106 0.566052730377 107 0.188684243459 108 0.524215183334E-16 109 0.660394852106 110 0.283026365188 111 -0.943421217294E-01 112 0.754736973835 113 0.377368486918 114 -0.188684243459 115 0.849079095565 116 0.471710608647 117 -0.283026365188 118 0.943421217294 119 0.566052730377 120 -0.377368486918 121 0.754736973835 122 0.188684243459 123 0.385437305256E-16 124 0.849079095565 125 0.283026365188 126 -0.943421217294E-01 127 0.943421217294 128 0.377368486918 129 -0.188684243459 130 0.943421217294 131 0.188684243459 132 -0.724785719370E-16 133 0.754736973835 134 0.377368486918 135 -0.339348414114E-16 136 0.849079095565 137 0.471710608647 138 -0.943421217294E-01 139 0.943421217294 140 0.377368486918 141 -0.616904170270E-16 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636521017034 xustar0030 mtime=1623670097.027100531 30 atime=1623670097.027100531 30 ctime=1623670097.027100531 elk-7.2.42/tests-libxc/test_002/elk.in0000644002504400250440000000116414061636521021073 0ustar00dewhurstdewhurst00000000000000 ! Magnetic response of fcc nickel. tasks 0 330 500 test .true. xctype 100 532 12 fxctype 100 532 12 nempty 10 lorbcnd .true. emaxrf 1.5 gmaxrf 2.0 wplot 60 100 1 0 0.020 ! q-vector of response function vecql 0.1 0.3 0.0 ngridk 10 10 10 spinpol .true. bfieldc 0.0 0.0 0.01 avec 1.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 1.0 scale 3.33 sppath '../../species/' atoms 1 : nspecies 'Ni.in' : spfname 1 : natoms 0.0 0.0 0.0 0.0 0.0 0.0 : atposl, bfcmt elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000012714061636521017630 xustar0029 mtime=1623670097.02910053 29 atime=1623670097.02910053 29 ctime=1623670097.02910053 elk-7.2.42/tests-libxc/test_002/TEST_500.OUT_0000644002504400250440000000013514061636521021660 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 53.6728337563 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636521017625 xustar0030 mtime=1623670097.030100529 30 atime=1623670097.030100529 30 ctime=1623670097.030100529 elk-7.2.42/tests-libxc/test_002/TEST_510.OUT_0000644002504400250440000000014514061636521021662 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.735401857616E-03 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636521017630 xustar0030 mtime=1623670097.032100527 30 atime=1623670097.032100527 30 ctime=1623670097.032100527 elk-7.2.42/tests-libxc/test_002/TEST_450.OUT_0000644002504400250440000000014014061636521021660 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 0.717102384687 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636521017623 xustar0030 mtime=1623670097.033100526 30 atime=1623670097.033100526 30 ctime=1623670097.033100526 elk-7.2.42/tests-libxc/test_002/TEST_400.OUT_0000644002504400250440000000014114061636521021654 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 27.9937806752 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636521017617 xustar0030 mtime=1623670097.035100524 30 atime=1623670097.034100525 30 ctime=1623670097.035100524 elk-7.2.42/tests-libxc/test_002/TEST_000.OUT_0000644002504400250440000000012614061636521021653 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -1517.12685504 elk-7.2.42/tests-libxc/test_002/PaxHeaders.21776/TEST_330.OUT_0000644000000000000000000000013214061636521017625 xustar0030 mtime=1623670097.036100523 30 atime=1623670097.036100523 30 ctime=1623670097.036100523 elk-7.2.42/tests-libxc/test_002/TEST_330.OUT_0000644002504400250440000000626314061636521021671 0ustar00dewhurstdewhurst00000000000000'transverse response function' 3 60 0.100000000000E-01 1 0.998468668586 -0.467042890415E-01 2 0.985261897011 -0.486037651406E-01 3 0.971912618420 -0.502850618013E-01 4 0.958102726051 -0.523419580670E-01 5 0.944201496382 -0.553721113013E-01 6 0.930730655250 -0.595414706669E-01 7 0.918178380178 -0.651052973886E-01 8 0.907978191269 -0.721874971119E-01 9 0.901924830318 -0.787094245618E-01 10 0.898436562487 -0.811604223683E-01 11 0.893750043204 -0.799875584366E-01 12 0.887748559229 -0.773913675379E-01 13 0.880643306880 -0.727474346220E-01 14 0.870467155338 -0.666074773645E-01 15 0.857042817548 -0.613756123922E-01 16 0.841788288865 -0.581728302883E-01 17 0.825728652153 -0.569616659916E-01 18 0.809289037295 -0.575833393136E-01 19 0.792690161340 -0.601180927884E-01 20 0.776278554441 -0.649169212772E-01 21 0.760900713235 -0.724766080842E-01 22 0.748340402278 -0.828295377633E-01 23 0.740839130170 -0.939616741375E-01 24 0.737794813543 -0.101658324942 25 0.735046563823 -0.104464986103 26 0.729983666129 -0.104025373616 27 0.720762340665 -0.102280282986 28 0.706964788296 -0.103126391868 29 0.691551386960 -0.109652621861 30 0.678341355731 -0.122250189178 31 0.670857091368 -0.139712982417 32 0.672277203998 -0.158543200705 33 0.682832721950 -0.173740736331 34 0.701713784809 -0.180551212822 35 0.722946901617 -0.171215506618 36 0.732249764812 -0.147995055563 37 0.725700355344 -0.124372409799 38 0.709773720630 -0.108053070388 39 0.690580085935 -0.999636062228E-01 40 0.671903572962 -0.990759417282E-01 41 0.656763378276 -0.103775743359 42 0.647494382827 -0.110679163245 43 0.643061965617 -0.115162947191 44 0.639165540102 -0.115912291152 45 0.633904554118 -0.115573028877 46 0.628496215701 -0.115082639294 47 0.622590002816 -0.113851263362 48 0.615839321359 -0.113042749875 49 0.609730146172 -0.112524673186 50 0.603380797421 -0.110643704804 51 0.594934596123 -0.108752585498 52 0.585483703316 -0.108835474560 53 0.576807157190 -0.110508422966 54 0.568867822837 -0.112611250499 55 0.561208336924 -0.115783159187 56 0.555842511749 -0.120171785482 57 0.553206834004 -0.122399134785 58 0.549315484639 -0.121392290026 59 0.542453345564 -0.120700834983 60 0.534983151095 -0.122666669642 elk-7.2.42/tests-libxc/PaxHeaders.21776/test_0030000644000000000000000000000013214061636521015655 xustar0030 mtime=1623670097.051100509 30 atime=1623670097.037100522 30 ctime=1623670097.051100509 elk-7.2.42/tests-libxc/test_003/0000755002504400250440000000000014061636521017767 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013014061636521017632 xustar0029 mtime=1623670097.03910052 30 atime=1623670097.038100521 29 ctime=1623670097.03910052 elk-7.2.42/tests-libxc/test_003/TEST_705.OUT_0000644002504400250440000000010114061636521021661 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 1 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636521017035 xustar0030 mtime=1623670097.040100519 30 atime=1623670097.040100519 30 ctime=1623670097.040100519 elk-7.2.42/tests-libxc/test_003/elk.in0000644002504400250440000000111314061636521021066 0ustar00dewhurstdewhurst00000000000000 ! Test of Libxc GGA, spin-polarised and with forces. tasks 0 500 test .true. xctype 100 101 130 tforce .true. ngridk 4 4 4 autoswidth .true. autolinengy .true. msmooth 4 spinorb .true. cmagz .true. bfieldc 0.0 0.0 0.1 avec 0.5 0.5 0.0 0.0 1.0 0.0 0.0 0.0 1.0 scale1 6.8 scale2 6.8 scale3 7.0 sppath '../../species/' atoms 2 : nspecies 'Fe.in' : spfname 1 : natoms; atposl below 0.0 0.0 0.0 'Co.in' 1 0.1 0.51 0.48 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636521017631 xustar0030 mtime=1623670097.042100518 30 atime=1623670097.041100519 30 ctime=1623670097.042100518 elk-7.2.42/tests-libxc/test_003/TEST_900.OUT_0000644002504400250440000000007014061636521021663 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 4735 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636521017632 xustar0030 mtime=1623670097.043100517 30 atime=1623670097.043100517 30 ctime=1623670097.043100517 elk-7.2.42/tests-libxc/test_003/TEST_910.OUT_0000644002504400250440000001357714061636521021704 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 192 0.100000000000E-07 1 0.00000000000 2 0.00000000000 3 0.00000000000 4 0.461998919646 5 0.00000000000 6 0.00000000000 7 0.923997839291 8 0.00000000000 9 0.00000000000 10 1.38599675894 11 0.00000000000 12 0.00000000000 13 -0.230999459823 14 0.230999459823 15 0.00000000000 16 0.230999459823 17 0.230999459823 18 0.00000000000 19 0.692998379468 20 0.230999459823 21 0.00000000000 22 1.15499729911 23 0.230999459823 24 0.00000000000 25 -0.461998919646 26 0.461998919646 27 0.00000000000 28 0.00000000000 29 0.461998919646 30 0.00000000000 31 0.461998919646 32 0.461998919646 33 0.00000000000 34 0.923997839291 35 0.461998919646 36 0.00000000000 37 -0.692998379468 38 0.692998379468 39 0.00000000000 40 -0.230999459823 41 0.692998379468 42 0.00000000000 43 0.230999459823 44 0.692998379468 45 0.00000000000 46 0.692998379468 47 0.692998379468 48 0.00000000000 49 0.00000000000 50 0.00000000000 51 0.224399475256 52 0.461998919646 53 0.00000000000 54 0.224399475256 55 0.923997839291 56 0.00000000000 57 0.224399475256 58 1.38599675894 59 0.00000000000 60 0.224399475256 61 -0.230999459823 62 0.230999459823 63 0.224399475256 64 0.230999459823 65 0.230999459823 66 0.224399475256 67 0.692998379468 68 0.230999459823 69 0.224399475256 70 1.15499729911 71 0.230999459823 72 0.224399475256 73 -0.461998919646 74 0.461998919646 75 0.224399475256 76 0.00000000000 77 0.461998919646 78 0.224399475256 79 0.461998919646 80 0.461998919646 81 0.224399475256 82 0.923997839291 83 0.461998919646 84 0.224399475256 85 -0.692998379468 86 0.692998379468 87 0.224399475256 88 -0.230999459823 89 0.692998379468 90 0.224399475256 91 0.230999459823 92 0.692998379468 93 0.224399475256 94 0.692998379468 95 0.692998379468 96 0.224399475256 97 0.00000000000 98 0.00000000000 99 0.448798950513 100 0.461998919646 101 0.00000000000 102 0.448798950513 103 0.923997839291 104 0.00000000000 105 0.448798950513 106 1.38599675894 107 0.00000000000 108 0.448798950513 109 -0.230999459823 110 0.230999459823 111 0.448798950513 112 0.230999459823 113 0.230999459823 114 0.448798950513 115 0.692998379468 116 0.230999459823 117 0.448798950513 118 1.15499729911 119 0.230999459823 120 0.448798950513 121 -0.461998919646 122 0.461998919646 123 0.448798950513 124 0.00000000000 125 0.461998919646 126 0.448798950513 127 0.461998919646 128 0.461998919646 129 0.448798950513 130 0.923997839291 131 0.461998919646 132 0.448798950513 133 -0.692998379468 134 0.692998379468 135 0.448798950513 136 -0.230999459823 137 0.692998379468 138 0.448798950513 139 0.230999459823 140 0.692998379468 141 0.448798950513 142 0.692998379468 143 0.692998379468 144 0.448798950513 145 0.00000000000 146 0.00000000000 147 0.673198425769 148 0.461998919646 149 0.00000000000 150 0.673198425769 151 0.923997839291 152 0.00000000000 153 0.673198425769 154 1.38599675894 155 0.00000000000 156 0.673198425769 157 -0.230999459823 158 0.230999459823 159 0.673198425769 160 0.230999459823 161 0.230999459823 162 0.673198425769 163 0.692998379468 164 0.230999459823 165 0.673198425769 166 1.15499729911 167 0.230999459823 168 0.673198425769 169 -0.461998919646 170 0.461998919646 171 0.673198425769 172 0.00000000000 173 0.461998919646 174 0.673198425769 175 0.461998919646 176 0.461998919646 177 0.673198425769 178 0.923997839291 179 0.461998919646 180 0.673198425769 181 -0.692998379468 182 0.692998379468 183 0.673198425769 184 -0.230999459823 185 0.692998379468 186 0.673198425769 187 0.230999459823 188 0.692998379468 189 0.673198425769 190 0.692998379468 191 0.692998379468 192 0.673198425769 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636521017625 xustar0030 mtime=1623670097.045100515 30 atime=1623670097.044100516 30 ctime=1623670097.045100515 elk-7.2.42/tests-libxc/test_003/TEST_500.OUT_0000644002504400250440000000013514061636521021661 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 94.4986855083 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000013214061636521017626 xustar0030 mtime=1623670097.046100514 30 atime=1623670097.046100514 30 ctime=1623670097.046100514 elk-7.2.42/tests-libxc/test_003/TEST_510.OUT_0000644002504400250440000000014514061636521021663 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.416630653768E-03 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636521017624 xustar0030 mtime=1623670097.047100513 30 atime=1623670097.047100513 30 ctime=1623670097.047100513 elk-7.2.42/tests-libxc/test_003/TEST_400.OUT_0000644002504400250440000000014114061636521021655 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 52.9968822942 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_450.OUT_0000644000000000000000000000013214061636521017631 xustar0030 mtime=1623670097.049100511 30 atime=1623670097.049100511 30 ctime=1623670097.049100511 elk-7.2.42/tests-libxc/test_003/TEST_450.OUT_0000644002504400250440000000014014061636521021661 0ustar00dewhurstdewhurst00000000000000'total moment magnitude' 2 1 0.100000000000E-02 1 2.57197608251 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000012714061636521017624 xustar0029 mtime=1623670097.05010051 29 atime=1623670097.05010051 29 ctime=1623670097.05010051 elk-7.2.42/tests-libxc/test_003/TEST_000.OUT_0000644002504400250440000000012614061636521021654 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -2666.40054816 elk-7.2.42/tests-libxc/test_003/PaxHeaders.21776/TEST_750.OUT_0000644000000000000000000000013214061636521017634 xustar0030 mtime=1623670097.052100508 30 atime=1623670097.052100508 30 ctime=1623670097.052100508 elk-7.2.42/tests-libxc/test_003/TEST_750.OUT_0000644002504400250440000000036114061636521021671 0ustar00dewhurstdewhurst00000000000000'total forces' 2 6 0.100000000000E-02 1 0.107027513496E-01 2 0.129273071582E-01 3 -0.108836085491E-01 4 -0.107027513496E-01 5 -0.129273071582E-01 6 0.108836085491E-01 elk-7.2.42/tests-libxc/PaxHeaders.21776/test_0050000644000000000000000000000013214061636521015657 xustar0030 mtime=1623670097.065100496 30 atime=1623670097.052100508 30 ctime=1623670097.065100496 elk-7.2.42/tests-libxc/test_005/0000755002504400250440000000000014061636521017771 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/TEST_705.OUT_0000644000000000000000000000013214061636521017636 xustar0030 mtime=1623670097.054100506 30 atime=1623670097.054100506 30 ctime=1623670097.054100506 elk-7.2.42/tests-libxc/test_005/TEST_705.OUT_0000644002504400250440000000010114061636521021663 0ustar00dewhurstdewhurst00000000000000'number of crystal symmetries' 1 1 1 8 elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/TEST_900.OUT_0000644000000000000000000000013214061636521017633 xustar0030 mtime=1623670097.055100506 30 atime=1623670097.055100506 30 ctime=1623670097.055100506 elk-7.2.42/tests-libxc/test_005/TEST_900.OUT_0000644002504400250440000000007014061636521021665 0ustar00dewhurstdewhurst00000000000000'number of G-vectors' 1 1 1 34171 elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636521017037 xustar0030 mtime=1623670097.057100504 30 atime=1623670097.057100504 30 ctime=1623670097.057100504 elk-7.2.42/tests-libxc/test_005/elk.in0000644002504400250440000000154014061636521021074 0ustar00dewhurstdewhurst00000000000000 ! Test of the finite temperature exchange-correlation functional KSDT. ! See Karasiev, et al., Phys. Rev. Lett. 112, 076403 (2014) tasks 0 500 test .true. xctype 100 259 0 ! temperature in Kelvin tempk 500.0 rgkmax 6.0 maxscl 10 tforce .true. avec 7.2246 0.0 0.0 0.0 7.3442 0.0 0.0 0.0 22.0733 sppath '../../species/' atoms 4 : nspecies 'Y.in' : spfname 1 : natoms; atposl below 0.5 0.5 0.5 'Ba.in' 2 0.5 0.5 0.1843 0.5 0.5 0.8157 'Cu.in' 3 0.0 0.0 0.0 0.0 0.0 0.3556 0.0 0.0 0.6444 'O.in' 7 0.0 0.5 0.0 0.5 0.0 0.3773 0.5 0.0 0.6227 0.0 0.5 0.3789 0.0 0.5 0.6211 0.0 0.0 0.1584 0.0 0.0 0.8416 ngridk 2 2 1 vkloff 0.25 0.5 0.5 elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/TEST_910.OUT_0000644000000000000000000000013214061636521017634 xustar0030 mtime=1623670097.058100503 30 atime=1623670097.058100503 30 ctime=1623670097.058100503 elk-7.2.42/tests-libxc/test_005/TEST_910.OUT_0000644002504400250440000000037114061636521021672 0ustar00dewhurstdewhurst00000000000000'k-points (Cartesian)' 2 6 0.100000000000E-07 1 0.108711646790 2 0.213882564036 3 0.142325463505 4 0.543558233949 5 0.213882564036 6 0.142325463505 elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/TEST_500.OUT_0000644000000000000000000000013214061636521017627 xustar0030 mtime=1623670097.060100501 30 atime=1623670097.059100502 30 ctime=1623670097.060100501 elk-7.2.42/tests-libxc/test_005/TEST_500.OUT_0000644002504400250440000000013514061636521021663 0ustar00dewhurstdewhurst00000000000000'DOS at Fermi energy' 2 1 0.500000000000E-02 1 4.11694522056 elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/TEST_510.OUT_0000644000000000000000000000012414061636521017631 xustar0028 mtime=1623670097.0611005 28 atime=1623670097.0611005 28 ctime=1623670097.0611005 elk-7.2.42/tests-libxc/test_005/TEST_510.OUT_0000644002504400250440000000014514061636521021665 0ustar00dewhurstdewhurst00000000000000'estimated indirect band gap' 2 1 0.200000000000E-01 1 0.188330161805E-01 elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/TEST_400.OUT_0000644000000000000000000000013214061636521017626 xustar0030 mtime=1623670097.063100498 30 atime=1623670097.062100499 30 ctime=1623670097.063100498 elk-7.2.42/tests-libxc/test_005/TEST_400.OUT_0000644002504400250440000000014114061636521021657 0ustar00dewhurstdewhurst00000000000000'calculated total charge' 2 1 0.100000000000E-05 1 294.001986280 elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/TEST_000.OUT_0000644000000000000000000000013214061636521017622 xustar0030 mtime=1623670097.064100497 30 atime=1623670097.064100497 30 ctime=1623670097.064100497 elk-7.2.42/tests-libxc/test_005/TEST_000.OUT_0000644002504400250440000000012614061636521021656 0ustar00dewhurstdewhurst00000000000000'total energy' 2 1 0.100000000000E-03 1 -25129.0485518 elk-7.2.42/tests-libxc/test_005/PaxHeaders.21776/TEST_750.OUT_0000644000000000000000000000013214061636521017636 xustar0030 mtime=1623670097.065100496 30 atime=1623670097.065100496 30 ctime=1623670097.065100496 elk-7.2.42/tests-libxc/test_005/TEST_750.OUT_0000644002504400250440000000236014061636521021674 0ustar00dewhurstdewhurst00000000000000'total forces' 2 39 0.100000000000E-02 1 0.00000000000 2 -0.657911313253E-50 3 0.133440267383E-18 4 0.00000000000 5 -0.657911313253E-50 6 0.325493704577E-01 7 0.00000000000 8 -0.657911313253E-50 9 -0.325493704577E-01 10 0.00000000000 11 -0.657911313253E-50 12 0.133440267383E-18 13 0.00000000000 14 -0.657911313253E-50 15 0.127709979611E-01 16 0.00000000000 17 -0.657911313253E-50 18 -0.127709979611E-01 19 0.00000000000 20 -0.657911313253E-50 21 0.133440267383E-18 22 0.00000000000 23 -0.657911313253E-50 24 -0.332225990492E-02 25 0.00000000000 26 -0.657911313253E-50 27 0.332225990492E-02 28 0.00000000000 29 0.789493575904E-49 30 0.730387536037E-02 31 0.00000000000 32 -0.657911313253E-50 33 -0.730387536037E-02 34 0.00000000000 35 -0.657911313253E-50 36 0.645753500535E-02 37 0.00000000000 38 -0.657911313253E-50 39 -0.645753500535E-02 elk-7.2.42/PaxHeaders.21776/species0000644000000000000000000000013114061636521013505 xustar0030 mtime=1623670097.271100305 29 atime=1623670097.07210049 30 ctime=1623670097.271100305 elk-7.2.42/species/0000755002504400250440000000000014061636521015620 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/species/PaxHeaders.21776/Ac.in0000644000000000000000000000013214061636521014436 xustar0030 mtime=1623670097.079100483 30 atime=1623670097.079100483 30 ctime=1623670097.079100483 elk-7.2.42/species/Ac.in0000644002504400250440000000425214061636521016476 0ustar00dewhurstdewhurst00000000000000 'Ac' : spsymb 'actinium' : spname -89.0000 : spzn 413795.6860 : spmass 0.212000E-06 3.0000 58.5155 800 : rminsp, rmt, rmaxsp, nrmt 26 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 6 2 2 1.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.8323 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.4862 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6749 0 T elk-7.2.42/species/PaxHeaders.21776/Ag.in0000644000000000000000000000013214061636521014442 xustar0030 mtime=1623670097.081100481 30 atime=1623670097.081100481 30 ctime=1623670097.081100481 elk-7.2.42/species/Ag.in0000644002504400250440000000356614061636521016511 0ustar00dewhurstdewhurst00000000000000 'Ag' : spsymb 'silver' : spname -47.0000 : spzn 196631.6997 : spmass 0.291730E-06 2.6000 49.0510 600 : rminsp, rmt, rmaxsp, nrmt 15 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.4920 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0961 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2735 0 T elk-7.2.42/species/PaxHeaders.21776/Al.in0000644000000000000000000000013214061636521014447 xustar0030 mtime=1623670097.083100479 30 atime=1623670097.083100479 30 ctime=1623670097.083100479 elk-7.2.42/species/Al.in0000644002504400250440000000227614061636521016513 0ustar00dewhurstdewhurst00000000000000 'Al' : spsymb 'aluminium' : spname -13.0000 : spzn 49184.33492 : spmass 0.554700E-06 2.2000 57.4918 400 : rminsp, rmt, rmaxsp, nrmt 6 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 F 2 1 2 4.00000 F 3 0 1 2.00000 F 3 1 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.5562 0 T elk-7.2.42/species/PaxHeaders.21776/Am.in0000644000000000000000000000013214061636521014450 xustar0030 mtime=1623670097.085100478 30 atime=1623670097.085100478 30 ctime=1623670097.085100478 elk-7.2.42/species/Am.in0000644002504400250440000000453214061636521016511 0ustar00dewhurstdewhurst00000000000000 'Am' : spsymb 'americium' : spname -95.0000 : spzn 442961.9018 : spmass 0.205196E-06 3.0000 51.9446 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 3.00000 F 5 3 4 4.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.0774 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8674 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7549 0 T elk-7.2.42/species/PaxHeaders.21776/Ar.in0000644000000000000000000000013214061636521014455 xustar0030 mtime=1623670097.087100476 30 atime=1623670097.086100477 30 ctime=1623670097.087100476 elk-7.2.42/species/Ar.in0000644002504400250440000000233214061636521016512 0ustar00dewhurstdewhurst00000000000000 'Ar' : spsymb 'argon' : spname -18.0000 : spzn 72820.74919 : spmass 0.471405E-06 2.0000 28.6848 400 : rminsp, rmt, rmaxsp, nrmt 7 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8916 0 T elk-7.2.42/species/PaxHeaders.21776/As.in0000644000000000000000000000013214061636521014456 xustar0030 mtime=1623670097.089100474 30 atime=1623670097.088100475 30 ctime=1623670097.089100474 elk-7.2.42/species/As.in0000644002504400250440000000321614061636521016515 0ustar00dewhurstdewhurst00000000000000 'As' : spsymb 'arsenic' : spname -33.0000 : spzn 136573.7219 : spmass 0.348155E-06 2.4000 42.0399 500 : rminsp, rmt, rmaxsp, nrmt 12 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 2.00000 F 4 1 1 1.00000 F 4 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.4917 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5401 0 T elk-7.2.42/species/PaxHeaders.21776/At.in0000644000000000000000000000013214061636521014457 xustar0030 mtime=1623670097.090100473 30 atime=1623670097.090100473 30 ctime=1623670097.090100473 elk-7.2.42/species/At.in0000644002504400250440000000373614061636521016525 0ustar00dewhurstdewhurst00000000000000 'At' : spsymb 'astatine' : spname -85.0000 : spzn 382806.5818 : spmass 0.216930E-06 2.8000 39.4078 700 : rminsp, rmt, rmaxsp, nrmt 24 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 3.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.3831 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7106 0 T elk-7.2.42/species/PaxHeaders.21776/Au.in0000644000000000000000000000013214061636521014460 xustar0030 mtime=1623670097.092100471 30 atime=1623670097.092100471 30 ctime=1623670097.092100471 elk-7.2.42/species/Au.in0000644002504400250440000000431614061636521016521 0ustar00dewhurstdewhurst00000000000000 'Au' : spsymb 'gold' : spname -79.0000 : spzn 359048.0559 : spmass 0.225018E-06 2.8000 39.2245 700 : rminsp, rmt, rmaxsp, nrmt 22 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 T 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.9275 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0422 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2406 0 T elk-7.2.42/species/PaxHeaders.21776/Ba.in0000644000000000000000000000013214061636521014435 xustar0030 mtime=1623670097.094100469 30 atime=1623670097.094100469 30 ctime=1623670097.094100469 elk-7.2.42/species/Ba.in0000644002504400250440000000371214061636521016475 0ustar00dewhurstdewhurst00000000000000 'Ba' : spsymb 'barium' : spname -56.0000 : spzn 250331.8069 : spmass 0.267261E-06 2.8000 55.5566 700 : rminsp, rmt, rmaxsp, nrmt 18 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.2515 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.2408 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6670 0 T elk-7.2.42/species/PaxHeaders.21776/Be.in0000644000000000000000000000013214061636521014441 xustar0030 mtime=1623670097.096100467 30 atime=1623670097.096100467 30 ctime=1623670097.096100467 elk-7.2.42/species/Be.in0000644002504400250440000000167214061636521016504 0ustar00dewhurstdewhurst00000000000000 'Be' : spsymb 'beryllium' : spname -4.00000 : spzn 16428.20279 : spmass 0.100000E-05 1.8000 44.5601 300 : rminsp, rmt, rmaxsp, nrmt 2 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 2 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F elk-7.2.42/species/PaxHeaders.21776/Bi.in0000644000000000000000000000013214061636521014445 xustar0030 mtime=1623670097.098100466 30 atime=1623670097.097100467 30 ctime=1623670097.098100466 elk-7.2.42/species/Bi.in0000644002504400250440000000373614061636521016513 0ustar00dewhurstdewhurst00000000000000 'Bi' : spsymb 'bismuth' : spname -83.0000 : spzn 380947.9282 : spmass 0.219529E-06 2.8000 45.2810 700 : rminsp, rmt, rmaxsp, nrmt 24 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 1.00000 F 6 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9498 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5393 0 T elk-7.2.42/species/PaxHeaders.21776/B.in0000644000000000000000000000013214061636521014274 xustar0030 mtime=1623670097.099100465 30 atime=1623670097.099100465 30 ctime=1623670097.099100465 elk-7.2.42/species/B.in0000644002504400250440000000172614061636521016337 0ustar00dewhurstdewhurst00000000000000 'B' : spsymb 'boron' : spname -5.00000 : spzn 19707.24741 : spmass 0.894427E-06 1.8000 50.1216 300 : rminsp, rmt, rmaxsp, nrmt 3 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 2 1 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 2 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F elk-7.2.42/species/PaxHeaders.21776/Bk.in0000644000000000000000000000013214061636521014447 xustar0030 mtime=1623670097.101100463 30 atime=1623670097.101100463 30 ctime=1623670097.101100463 elk-7.2.42/species/Bk.in0000644002504400250440000000453214061636521016510 0ustar00dewhurstdewhurst00000000000000 'Bk' : spsymb 'berkelium' : spname -97.0000 : spzn 450253.4557 : spmass 0.203069E-06 3.0000 52.0199 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 5.00000 F 5 3 4 4.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1057 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.9965 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7758 0 T elk-7.2.42/species/PaxHeaders.21776/Br.in0000644000000000000000000000013214061636521014456 xustar0030 mtime=1623670097.103100461 30 atime=1623670097.103100461 30 ctime=1623670097.103100461 elk-7.2.42/species/Br.in0000644002504400250440000000321614061636521016515 0ustar00dewhurstdewhurst00000000000000 'Br' : spsymb 'bromine' : spname -35.0000 : spzn 145656.0815 : spmass 0.338062E-06 2.4000 34.9262 500 : rminsp, rmt, rmaxsp, nrmt 12 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 3.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.4430 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7453 0 T elk-7.2.42/species/PaxHeaders.21776/Ca.in0000644000000000000000000000013214061636521014436 xustar0030 mtime=1623670097.105100459 30 atime=1623670097.105100459 30 ctime=1623670097.105100459 elk-7.2.42/species/Ca.in0000644002504400250440000000261214061636521016474 0ustar00dewhurstdewhurst00000000000000 'Ca' : spsymb 'calcium' : spname -20.0000 : spzn 73057.72469 : spmass 0.447214E-06 2.4000 50.3684 500 : rminsp, rmt, rmaxsp, nrmt 8 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.7208 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.0235 0 T elk-7.2.42/species/PaxHeaders.21776/Cd.in0000644000000000000000000000013214061636521014441 xustar0030 mtime=1623670097.107100457 30 atime=1623670097.107100457 30 ctime=1623670097.107100457 elk-7.2.42/species/Cd.in0000644002504400250440000000334214061636521016500 0ustar00dewhurstdewhurst00000000000000 'Cd' : spsymb 'cadmium' : spname -48.0000 : spzn 204912.7175 : spmass 0.288675E-06 2.6000 41.8471 600 : rminsp, rmt, rmaxsp, nrmt 15 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.3934 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.4270 0 T elk-7.2.42/species/PaxHeaders.21776/Ce.in0000644000000000000000000000013214061636521014442 xustar0030 mtime=1623670097.109100455 30 atime=1623670097.108100456 30 ctime=1623670097.109100455 elk-7.2.42/species/Ce.in0000644002504400250440000000374614061636521016511 0ustar00dewhurstdewhurst00000000000000 'Ce' : spsymb 'cerium' : spname -58.0000 : spzn 255415.8429 : spmass 0.262613E-06 2.8000 75.2635 700 : rminsp, rmt, rmaxsp, nrmt 19 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 2.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.3797 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7361 0 T elk-7.2.42/species/PaxHeaders.21776/Cf.in0000644000000000000000000000013214061636521014443 xustar0030 mtime=1623670097.110100454 30 atime=1623670097.110100454 30 ctime=1623670097.110100454 elk-7.2.42/species/Cf.in0000644002504400250440000000453214061636521016504 0ustar00dewhurstdewhurst00000000000000 'Cf' : spsymb 'californium' : spname -98.0000 : spzn 457545.0097 : spmass 0.202031E-06 3.0000 52.0569 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 6.00000 F 5 3 4 4.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1183 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0620 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7850 0 T elk-7.2.42/species/PaxHeaders.21776/C.in0000644000000000000000000000013214061636521014275 xustar0030 mtime=1623670097.112100453 30 atime=1623670097.112100453 30 ctime=1623670097.112100453 elk-7.2.42/species/C.in0000644002504400250440000000220614061636521016332 0ustar00dewhurstdewhurst00000000000000 'C' : spsymb 'carbon' : spname -6.00000 : spzn 21894.16672 : spmass 0.816497E-06 1.8000 39.9481 300 : rminsp, rmt, rmaxsp, nrmt 4 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 2 1 1 1.00000 F 2 1 2 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5012 0 T elk-7.2.42/species/PaxHeaders.21776/Cl.in0000644000000000000000000000013214061636521014451 xustar0030 mtime=1623670097.114100451 30 atime=1623670097.114100451 30 ctime=1623670097.114100451 elk-7.2.42/species/Cl.in0000644002504400250440000000233214061636521016506 0ustar00dewhurstdewhurst00000000000000 'Cl' : spsymb 'chlorine' : spname -17.0000 : spzn 64626.86545 : spmass 0.485071E-06 2.2000 33.0920 400 : rminsp, rmt, rmaxsp, nrmt 7 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 3.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7601 0 T elk-7.2.42/species/PaxHeaders.21776/Cm.in0000644000000000000000000000013214061636521014452 xustar0030 mtime=1623670097.116100449 30 atime=1623670097.116100449 30 ctime=1623670097.116100449 elk-7.2.42/species/Cm.in0000644002504400250440000000456614061636521016522 0ustar00dewhurstdewhurst00000000000000 'Cm' : spsymb 'curium' : spname -96.0000 : spzn 450253.4557 : spmass 0.204124E-06 3.0000 55.3054 800 : rminsp, rmt, rmaxsp, nrmt 28 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 3.00000 F 5 3 4 4.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 6 2 2 1.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2184 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0481 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8489 0 T elk-7.2.42/species/PaxHeaders.21776/Co.in0000644000000000000000000000013214061636521014454 xustar0030 mtime=1623670097.118100447 30 atime=1623670097.117100448 30 ctime=1623670097.118100447 elk-7.2.42/species/Co.in0000644002504400250440000000312614061636521016513 0ustar00dewhurstdewhurst00000000000000 'Co' : spsymb 'cobalt' : spname -27.0000 : spzn 107428.6517 : spmass 0.384900E-06 2.4000 40.1486 500 : rminsp, rmt, rmaxsp, nrmt 10 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 4.00000 F 3 2 3 3.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.3834 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.3072 0 T elk-7.2.42/species/PaxHeaders.21776/Cr.in0000644000000000000000000000013214061636521014457 xustar0030 mtime=1623670097.120100445 30 atime=1623670097.119100446 30 ctime=1623670097.120100445 elk-7.2.42/species/Cr.in0000644002504400250440000000335214061636521016517 0ustar00dewhurstdewhurst00000000000000 'Cr' : spsymb 'chromium' : spname -24.0000 : spzn 94783.09194 : spmass 0.408248E-06 2.4000 51.1100 500 : rminsp, rmt, rmaxsp, nrmt 10 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 3.00000 F 3 2 3 2.00000 F 4 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.7020 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.6530 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1134 0 T elk-7.2.42/species/PaxHeaders.21776/Cs.in0000644000000000000000000000013214061636521014460 xustar0030 mtime=1623670097.121100444 30 atime=1623670097.121100444 30 ctime=1623670097.121100444 elk-7.2.42/species/Cs.in0000644002504400250440000000371214061636521016520 0ustar00dewhurstdewhurst00000000000000 'Cs' : spsymb 'caesium' : spname -55.0000 : spzn 242271.8144 : spmass 0.269680E-06 2.8000 68.3104 700 : rminsp, rmt, rmaxsp, nrmt 18 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.6912 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9872 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.4810 0 T elk-7.2.42/species/PaxHeaders.21776/Cu.in0000644000000000000000000000013214061636521014462 xustar0030 mtime=1623670097.123100442 30 atime=1623670097.123100442 30 ctime=1623670097.123100442 elk-7.2.42/species/Cu.in0000644002504400250440000000312614061636521016521 0ustar00dewhurstdewhurst00000000000000 'Cu' : spsymb 'copper' : spname -29.0000 : spzn 115837.2717 : spmass 0.371391E-06 2.4000 42.9740 500 : rminsp, rmt, rmaxsp, nrmt 10 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.6152 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1918 0 T elk-7.2.42/species/PaxHeaders.21776/Dy.in0000644000000000000000000000012714061636521014473 xustar0029 mtime=1623670097.12510044 29 atime=1623670097.12510044 29 ctime=1623670097.12510044 elk-7.2.42/species/Dy.in0000644002504400250440000000422614061636521016530 0ustar00dewhurstdewhurst00000000000000 'Dy' : spsymb 'dysprosium' : spname -66.0000 : spzn 296219.3788 : spmass 0.246183E-06 2.8000 48.9249 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 4.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1037 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.7987 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8849 0 T elk-7.2.42/species/PaxHeaders.21776/elk.in0000644000000000000000000000013214061636521014666 xustar0030 mtime=1623670097.127100439 30 atime=1623670097.127100439 30 ctime=1623670097.127100439 elk-7.2.42/species/elk.in0000644002504400250440000006662314061636521016740 0ustar00dewhurstdewhurst00000000000000 ! This is a special input file for Elk which generates the default species ! files. No task is required: the code generates the file as soon as it ! encounters a 'species' block. Note the masses are the 'standard atomic weight' ! and are in relative atomic mass units (i.e. multiples of 1/12 times the mass ! of carbon-12); taken from J. S. Coursey, D. J. Schwab, and R. A. Dragoset ! (2005), Atomic Weights and Isotopic Compositions (version 2.4.1). species 1 : atomic number 'H' 'hydrogen' : symbol, name 1.00794 : standard atomic weight (units of 1/12 carbon-12) 1.4 : muffin-tin radius 1 : number of occupied states 1 0 1 1 : n, l, k, occupancy for each state species 2 'He' 'helium' 4.002602 1.4 1 1 0 1 2 species 3 'Li' 'lithium' 6.941 1.8 2 1 0 1 2 2 0 1 1 species 4 'Be' 'beryllium' 9.012182 1.8 2 1 0 1 2 2 0 1 2 species 5 'B' 'boron' 10.811 1.8 3 1 0 1 2 2 0 1 2 2 1 1 1 species 6 'C' 'carbon' 12.0107 1.8 4 1 0 1 2 2 0 1 2 2 1 1 1 2 1 2 1 species 7 'N' 'nitrogen' 14.0067 1.8 4 1 0 1 2 2 0 1 2 2 1 1 1 2 1 2 2 species 8 'O' 'oxygen' 15.9994 1.8 4 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 2 species 9 'F' 'fluorine' 18.9984032 2.0 4 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 3 species 10 'Ne' 'neon' 20.1797 1.6 4 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 species 11 'Na' 'sodium' 22.989770 2.2 5 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 1 species 12 'Mg' 'magnesium' 24.3050 2.2 5 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 species 13 'Al' 'aluminium' 26.981538 2.2 6 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 1 species 14 'Si' 'silicon' 28.0855 2.2 7 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 1 3 1 2 1 species 15 'P' 'phosphorus' 30.973761 2.2 7 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 1 3 1 2 2 species 16 'S' 'sulphur' 32.065 2.2 7 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 2 species 17 'Cl' 'chlorine' 35.453 2.2 7 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 3 species 18 'Ar' 'argon' 39.948 2.0 7 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 species 19 'K' 'potassium' 39.0983 2.4 8 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 4 0 1 1 species 20 'Ca' 'calcium' 40.078 2.4 8 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 4 0 1 2 species 21 'Sc' 'scandium' 44.955910 2.4 9 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 1 4 0 1 2 species 22 'Ti' 'titanium' 47.867 2.4 9 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 2 4 0 1 2 species 23 'V' 'vanadium' 50.9415 2.4 9 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 3 4 0 1 2 species 24 'Cr' 'chromium' 51.9961 2.4 10 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 3 3 2 3 2 4 0 1 1 species 25 'Mn' 'manganese' 54.938049 2.4 10 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 3 3 2 3 2 4 0 1 2 species 26 'Fe' 'iron' 55.845 2.4 10 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 2 4 0 1 2 species 27 'Co' 'cobalt' 58.933200 2.4 10 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 3 4 0 1 2 species 28 'Ni' 'nickel' 58.6934 2.4 10 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 4 4 0 1 2 species 29 'Cu' 'copper' 63.546 2.4 10 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 1 species 30 'Zn' 'zinc' 65.409 2.4 10 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 species 31 'Ga' 'gallium' 69.723 2.4 11 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 1 species 32 'Ge' 'germanium' 72.64 2.4 12 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 1 4 1 2 1 species 33 'As' 'arsenic' 74.92160 2.4 12 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 1 4 1 2 2 species 34 'Se' 'selenium' 78.96 2.4 12 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 2 species 35 'Br' 'bromine' 79.904 2.4 12 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 3 species 36 'Kr' 'krypton' 83.798 2.2 12 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 species 37 'Rb' 'rubidium' 85.4678 2.6 13 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 5 0 1 1 species 38 'Sr' 'strontium' 87.62 2.6 13 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 5 0 1 2 species 39 'Y' 'yttrium' 88.90585 2.6 14 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 1 5 0 1 2 species 40 'Zr' 'zirconium' 91.224 2.6 14 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 2 5 0 1 2 species 41 'Nb' 'niobium' 92.90638 2.6 15 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 3 4 2 3 1 5 0 1 1 species 42 'Mo' 'molybdenum' 95.94 2.6 15 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 3 4 2 3 2 5 0 1 1 species 43 'Tc' 'technetium' 98.0 2.6 15 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 2 5 0 1 1 species 44 'Ru' 'ruthenium' 101.07 2.6 15 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 3 5 0 1 1 species 45 'Rh' 'rhodium' 102.90550 2.6 15 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 4 5 0 1 1 species 46 'Pd' 'palladium' 106.42 2.6 14 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 species 47 'Ag' 'silver' 107.8682 2.6 15 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 1 species 48 'Cd' 'cadmium' 112.411 2.6 15 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 species 49 'In' 'indium' 114.818 2.6 16 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 1 species 50 'Sn' 'tin' 118.710 2.6 17 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 1 5 1 2 1 species 51 'Sb' 'antimony' 121.760 2.6 17 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 1 5 1 2 2 species 52 'Te' 'tellurium' 127.60 2.6 17 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 2 5 1 2 2 species 53 'I' 'iodine' 126.90447 2.6 17 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 2 5 1 2 3 species 54 'Xe' 'xenon' 131.293 2.4 17 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 2 5 1 2 4 species 55 'Cs' 'caesium' 132.90545 2.8 18 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 1 species 56 'Ba' 'barium' 137.327 2.8 18 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 57 'La' 'lanthanum' 138.9055 2.8 19 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 1 6 0 1 2 species 58 'Ce' 'cerium' 140.116 2.8 19 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 2 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 59 'Pr' 'praseodymium' 140.90765 2.8 19 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 3 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 60 'Nd' 'neodymium' 144.24 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 3 4 3 4 1 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 61 'Pm' 'promethium' 145.0 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 3 4 3 4 2 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 62 'Sm' 'samarium' 150.36 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 3 4 3 4 3 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 63 'Eu' 'europium' 151.964 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 3 4 3 4 4 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 64 'Gd' 'gadolinium' 157.25 2.8 21 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 3 4 3 4 4 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 1 6 0 1 2 species 65 'Tb' 'terbium' 158.92534 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 5 4 3 4 4 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 66 'Dy' 'dysprosium' 162.500 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 4 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 67 'Ho' 'holmium' 164.93032 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 5 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 68 'Er' 'erbium' 167.259 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 6 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 69 'Tm' 'thulium' 168.93421 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 7 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 70 'Yb' 'ytterbium' 173.04 2.8 20 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 6 0 1 2 species 71 'Lu' 'lutetium' 174.967 2.8 21 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 1 6 0 1 2 species 72 'Hf' 'hafnium' 178.49 2.8 21 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 2 6 0 1 2 species 73 'Ta' 'tantalum' 180.9479 2.8 21 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 3 6 0 1 2 species 74 'W' 'tungsten' 183.84 2.8 22 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 3 5 2 3 1 6 0 1 2 species 75 'Re' 'rhenium' 186.207 2.8 22 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 3 5 2 3 2 6 0 1 2 species 76 'Os' 'osmium' 190.23 2.8 22 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 2 6 0 1 2 species 77 'Ir' 'iridium' 192.217 2.8 22 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 3 6 0 1 2 species 78 'Pt' 'platinum' 195.078 2.8 22 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 5 6 0 1 1 species 79 'Au' 'gold' 196.96655 2.8 22 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 1 species 80 'Hg' 'mercury' 200.59 2.8 22 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 species 81 'Tl' 'thallium' 204.3833 2.8 23 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 1 species 82 'Pb' 'lead' 207.2 2.8 24 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 1 6 1 2 1 species 83 'Bi' 'bismuth' 208.98038 2.8 24 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 1 6 1 2 2 species 84 'Po' 'polonium' 209.0 2.8 24 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 2 6 1 2 2 species 85 'At' 'astatine' 210.0 2.8 24 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 2 6 1 2 3 species 86 'Rn' 'radon' 222.0 2.6 24 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 2 6 1 2 4 species 87 'Fr' 'francium' 223.0 3.0 25 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 1 species 88 'Ra' 'radium' 226.0 3.0 25 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 89 'Ac' 'actinium' 227.0 3.0 26 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 2 6 1 2 4 6 2 2 1 7 0 1 2 species 90 'Th' 'thorium' 232.0381 3.0 26 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 6 0 1 2 6 1 1 2 6 1 2 4 6 2 2 2 7 0 1 2 species 91 'Pa' 'protactinium' 231.03588 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 2 6 0 1 2 6 1 1 2 6 1 2 4 6 2 2 1 7 0 1 2 species 92 'U' 'uranium' 238.02891 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 3 6 0 1 2 6 1 1 2 6 1 2 4 6 2 2 1 7 0 1 2 species 93 'Np' 'neptunium' 237.0 3.0 28 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 3 5 3 4 1 6 0 1 2 6 1 1 2 6 1 2 4 6 2 2 1 7 0 1 2 species 94 'Pu' 'plutonium' 244.0 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 3 5 3 4 3 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 95 'Am' 'americium' 243.0 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 3 5 3 4 4 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 96 'Cm' 'curium' 247.0 3.0 28 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 3 5 3 4 4 6 0 1 2 6 1 1 2 6 1 2 4 6 2 2 1 7 0 1 2 species 97 'Bk' 'berkelium' 247.0 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 5 5 3 4 4 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 98 'Cf' 'californium' 251.0 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 6 5 3 4 4 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 99 'Es' 'einsteinium' 252.0 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 6 5 3 4 5 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 100 'Fm' 'fermium' 257.0 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 6 5 3 4 6 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 101 'Md' 'mendelevium' 258.0 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 6 5 3 4 7 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 102 'No' 'nobelium' 259.0 3.0 27 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 6 5 3 4 8 6 0 1 2 6 1 1 2 6 1 2 4 7 0 1 2 species 103 'Lr' 'lawrencium' 262.0 3.0 28 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 6 5 3 4 8 6 0 1 2 6 1 1 2 6 1 2 4 6 2 2 1 7 0 1 2 species 104 'Rf' 'rutherfordium' 261.0 3.0 28 1 0 1 2 2 0 1 2 2 1 1 2 2 1 2 4 3 0 1 2 3 1 1 2 3 1 2 4 3 2 2 4 3 2 3 6 4 0 1 2 4 1 1 2 4 1 2 4 4 2 2 4 4 2 3 6 4 3 3 6 4 3 4 8 5 0 1 2 5 1 1 2 5 1 2 4 5 2 2 4 5 2 3 6 5 3 3 6 5 3 4 8 6 0 1 2 6 1 1 2 6 1 2 4 6 2 2 2 7 0 1 2 elk-7.2.42/species/PaxHeaders.21776/Er.in0000644000000000000000000000013214061636521014461 xustar0030 mtime=1623670097.129100437 30 atime=1623670097.129100437 30 ctime=1623670097.129100437 elk-7.2.42/species/Er.in0000644002504400250440000000422614061636521016522 0ustar00dewhurstdewhurst00000000000000 'Er' : spsymb 'erbium' : spname -68.0000 : spzn 304894.5051 : spmass 0.242536E-06 2.8000 49.0284 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 6.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1037 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.9077 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9177 0 T elk-7.2.42/species/PaxHeaders.21776/Es.in0000644000000000000000000000013214061636521014462 xustar0030 mtime=1623670097.131100435 30 atime=1623670097.131100435 30 ctime=1623670097.131100435 elk-7.2.42/species/Es.in0000644002504400250440000000453214061636521016523 0ustar00dewhurstdewhurst00000000000000 'Es' : spsymb 'einsteinium' : spname -99.0000 : spzn 459367.8982 : spmass 0.201008E-06 3.0000 51.0277 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 6.00000 F 5 3 4 5.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1339 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.1315 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7952 0 T elk-7.2.42/species/PaxHeaders.21776/Eu.in0000644000000000000000000000013214061636521014464 xustar0030 mtime=1623670097.133100433 30 atime=1623670097.133100433 30 ctime=1623670097.133100433 elk-7.2.42/species/Eu.in0000644002504400250440000000422614061636521016525 0ustar00dewhurstdewhurst00000000000000 'Eu' : spsymb 'europium' : spname -63.0000 : spzn 277013.4257 : spmass 0.251976E-06 2.8000 52.2803 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 3.00000 F 4 3 4 4.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.0972 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.6436 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8355 0 T elk-7.2.42/species/PaxHeaders.21776/Fe.in0000644000000000000000000000013214061636521014445 xustar0030 mtime=1623670097.135100431 30 atime=1623670097.134100432 30 ctime=1623670097.135100431 elk-7.2.42/species/Fe.in0000644002504400250440000000335214061636521016505 0ustar00dewhurstdewhurst00000000000000 'Fe' : spsymb 'iron' : spname -26.0000 : spzn 101799.2074 : spmass 0.392232E-06 2.4000 42.6274 500 : rminsp, rmt, rmaxsp, nrmt 10 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 4.00000 F 3 2 3 2.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.4344 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.1817 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2816 0 T elk-7.2.42/species/PaxHeaders.21776/F.in0000644000000000000000000000012714061636521014304 xustar0029 mtime=1623670097.13610043 29 atime=1623670097.13610043 29 ctime=1623670097.13610043 elk-7.2.42/species/F.in0000644002504400250440000000243214061636521016336 0ustar00dewhurstdewhurst00000000000000 'F' : spsymb 'fluorine' : spname -9.00000 : spzn 34631.97042 : spmass 0.666667E-06 2.0000 27.0542 300 : rminsp, rmt, rmaxsp, nrmt 4 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 2 1 1 2.00000 F 2 1 2 3.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.0894 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.4142 0 T elk-7.2.42/species/PaxHeaders.21776/Fm.in0000644000000000000000000000013214061636521014455 xustar0030 mtime=1623670097.138100428 30 atime=1623670097.138100428 30 ctime=1623670097.138100428 elk-7.2.42/species/Fm.in0000644002504400250440000000453214061636521016516 0ustar00dewhurstdewhurst00000000000000 'Fm' : spsymb 'fermium' : spname -100.000 : spzn 468482.3406 : spmass 0.200000E-06 3.0000 55.4667 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 6.00000 F 5 3 4 6.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1486 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.2021 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8046 0 T elk-7.2.42/species/PaxHeaders.21776/Fr.in0000644000000000000000000000013214061636521014462 xustar0030 mtime=1623670097.140100427 30 atime=1623670097.140100427 30 ctime=1623670097.140100427 elk-7.2.42/species/Fr.in0000644002504400250440000000421614061636521016522 0ustar00dewhurstdewhurst00000000000000 'Fr' : spsymb 'francium' : spname -87.0000 : spzn 406504.1321 : spmass 0.214423E-06 3.0000 70.3136 800 : rminsp, rmt, rmaxsp, nrmt 25 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0328 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.0471 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.4089 0 T elk-7.2.42/species/PaxHeaders.21776/Ga.in0000644000000000000000000000013214061636521014442 xustar0030 mtime=1623670097.142100425 30 atime=1623670097.142100425 30 ctime=1623670097.142100425 elk-7.2.42/species/Ga.in0000644002504400250440000000273614061636521016507 0ustar00dewhurstdewhurst00000000000000 'Ga' : spsymb 'gallium' : spname -31.0000 : spzn 127097.2538 : spmass 0.359211E-06 2.4000 55.5610 500 : rminsp, rmt, rmaxsp, nrmt 11 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 2.00000 F 4 1 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7036 0 T elk-7.2.42/species/PaxHeaders.21776/Gd.in0000644000000000000000000000013214061636521014445 xustar0030 mtime=1623670097.144100423 30 atime=1623670097.143100424 30 ctime=1623670097.144100423 elk-7.2.42/species/Gd.in0000644002504400250440000000426214061636521016506 0ustar00dewhurstdewhurst00000000000000 'Gd' : spsymb 'gadolinium' : spname -64.0000 : spzn 286649.2142 : spmass 0.250000E-06 2.8000 51.1390 700 : rminsp, rmt, rmaxsp, nrmt 21 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 3.00000 F 4 3 4 4.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 1.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.3108 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8262 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9546 0 T elk-7.2.42/species/PaxHeaders.21776/Ge.in0000644000000000000000000000013214061636521014446 xustar0030 mtime=1623670097.146100421 30 atime=1623670097.145100422 30 ctime=1623670097.146100421 elk-7.2.42/species/Ge.in0000644002504400250440000000321614061636521016505 0ustar00dewhurstdewhurst00000000000000 'Ge' : spsymb 'germanium' : spname -32.0000 : spzn 132414.6195 : spmass 0.353553E-06 2.4000 46.1060 500 : rminsp, rmt, rmaxsp, nrmt 12 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 2.00000 F 4 1 1 1.00000 F 4 1 2 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.0759 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.4380 0 T elk-7.2.42/species/PaxHeaders.21776/He.in0000644000000000000000000000012714061636521014453 xustar0029 mtime=1623670097.14710042 29 atime=1623670097.14710042 29 ctime=1623670097.14710042 elk-7.2.42/species/He.in0000644002504400250440000000206214061636521016504 0ustar00dewhurstdewhurst00000000000000 'He' : spsymb 'helium' : spname -2.00000 : spzn 7296.297095 : spmass 0.141421E-05 1.4000 24.1776 200 : rminsp, rmt, rmaxsp, nrmt 1 : nstsp 1 0 1 2.00000 F : nsp, lsp, ksp, occsp, spcore 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5703 0 T elk-7.2.42/species/PaxHeaders.21776/Hf.in0000644000000000000000000000013214061636521014450 xustar0030 mtime=1623670097.149100418 30 atime=1623670097.149100418 30 ctime=1623670097.149100418 elk-7.2.42/species/Hf.in0000644002504400250440000000426214061636521016511 0ustar00dewhurstdewhurst00000000000000 'Hf' : spsymb 'hafnium' : spname -72.0000 : spzn 325367.3656 : spmass 0.235702E-06 2.8000 49.2272 700 : rminsp, rmt, rmaxsp, nrmt 21 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 2.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5852 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.4529 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.2221 0 T elk-7.2.42/species/PaxHeaders.21776/Hg.in0000644000000000000000000000013214061636521014451 xustar0030 mtime=1623670097.151100416 30 atime=1623670097.151100416 30 ctime=1623670097.151100416 elk-7.2.42/species/Hg.in0000644002504400250440000000364614061636521016517 0ustar00dewhurstdewhurst00000000000000 'Hg' : spsymb 'mercury' : spname -80.0000 : spzn 365653.2012 : spmass 0.223607E-06 2.8000 37.4626 700 : rminsp, rmt, rmaxsp, nrmt 22 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.2710 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.3442 0 T elk-7.2.42/species/PaxHeaders.21776/H.in0000644000000000000000000000013214061636521014302 xustar0030 mtime=1623670097.153100415 30 atime=1623670097.153100415 30 ctime=1623670097.153100415 elk-7.2.42/species/H.in0000644002504400250440000000163614061636521016345 0ustar00dewhurstdewhurst00000000000000 'H' : spsymb 'hydrogen' : spname -1.00000 : spzn 1837.362219 : spmass 0.200000E-05 1.4000 36.6488 200 : rminsp, rmt, rmaxsp, nrmt 1 : nstsp 1 0 1 1.00000 F : nsp, lsp, ksp, occsp, spcore 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 2 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F elk-7.2.42/species/PaxHeaders.21776/Ho.in0000644000000000000000000000013214061636521014461 xustar0030 mtime=1623670097.155100413 30 atime=1623670097.154100414 30 ctime=1623670097.155100413 elk-7.2.42/species/Ho.in0000644002504400250440000000422614061636521016522 0ustar00dewhurstdewhurst00000000000000 'Ho' : spsymb 'holmium' : spname -67.0000 : spzn 300649.5811 : spmass 0.244339E-06 2.8000 51.3086 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 5.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1044 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8527 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9014 0 T elk-7.2.42/species/PaxHeaders.21776/I.in0000644000000000000000000000013214061636521014303 xustar0030 mtime=1623670097.157100411 30 atime=1623670097.156100412 30 ctime=1623670097.157100411 elk-7.2.42/species/I.in0000644002504400250440000000343214061636521016342 0ustar00dewhurstdewhurst00000000000000 'I' : spsymb 'iodine' : spname -53.0000 : spzn 231332.6970 : spmass 0.274721E-06 2.6000 41.0205 600 : rminsp, rmt, rmaxsp, nrmt 17 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 3.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8184 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6456 0 T elk-7.2.42/species/PaxHeaders.21776/In.in0000644000000000000000000000012714061636521014465 xustar0029 mtime=1623670097.15810041 29 atime=1623670097.15810041 29 ctime=1623670097.15810041 elk-7.2.42/species/In.in0000644002504400250440000000337614061636521016527 0ustar00dewhurstdewhurst00000000000000 'In' : spsymb 'indium' : spname -49.0000 : spzn 209300.4100 : spmass 0.285714E-06 2.6000 56.2447 600 : rminsp, rmt, rmaxsp, nrmt 16 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 5 1 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.7840 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6687 0 T elk-7.2.42/species/PaxHeaders.21776/Ir.in0000644000000000000000000000013214061636521014465 xustar0030 mtime=1623670097.160100408 30 atime=1623670097.160100408 30 ctime=1623670097.160100408 elk-7.2.42/species/Ir.in0000644002504400250440000000431614061636521016526 0ustar00dewhurstdewhurst00000000000000 'Ir' : spsymb 'iridium' : spname -77.0000 : spzn 350390.1559 : spmass 0.227921E-06 2.8000 41.0330 700 : rminsp, rmt, rmaxsp, nrmt 22 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 T 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 4.00000 F 5 2 3 3.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.2294 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8716 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2478 0 T elk-7.2.42/species/PaxHeaders.21776/K.in0000644000000000000000000000013214061636521014305 xustar0030 mtime=1623670097.162100406 30 atime=1623670097.162100406 30 ctime=1623670097.162100406 elk-7.2.42/species/K.in0000644002504400250440000000261214061636521016343 0ustar00dewhurstdewhurst00000000000000 'K' : spsymb 'potassium' : spname -19.0000 : spzn 71271.84084 : spmass 0.458831E-06 2.4000 62.3191 500 : rminsp, rmt, rmaxsp, nrmt 8 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 4 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.2928 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6889 0 T elk-7.2.42/species/PaxHeaders.21776/Kr.in0000644000000000000000000000013214061636521014467 xustar0030 mtime=1623670097.164100404 30 atime=1623670097.164100404 30 ctime=1623670097.164100404 elk-7.2.42/species/Kr.in0000644002504400250440000000321614061636521016526 0ustar00dewhurstdewhurst00000000000000 'Kr' : spsymb 'krypton' : spname -36.0000 : spzn 152754.4092 : spmass 0.333333E-06 2.2000 31.7038 500 : rminsp, rmt, rmaxsp, nrmt 12 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.9818 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8532 0 T elk-7.2.42/species/PaxHeaders.21776/La.in0000644000000000000000000000013214061636521014447 xustar0030 mtime=1623670097.166100403 30 atime=1623670097.165100403 30 ctime=1623670097.166100403 elk-7.2.42/species/La.in0000644002504400250440000000352214061636521016506 0ustar00dewhurstdewhurst00000000000000 'La' : spsymb 'lanthanum' : spname -57.0000 : spzn 253209.2364 : spmass 0.264906E-06 2.8000 50.7129 700 : rminsp, rmt, rmaxsp, nrmt 19 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 1.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.4321 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7953 0 T elk-7.2.42/species/PaxHeaders.21776/Li.in0000644000000000000000000000013214061636521014457 xustar0030 mtime=1623670097.168100401 30 atime=1623670097.167100402 30 ctime=1623670097.168100401 elk-7.2.42/species/Li.in0000644002504400250440000000211614061636521016514 0ustar00dewhurstdewhurst00000000000000 'Li' : spsymb 'lithium' : spname -3.00000 : spzn 12652.66897 : spmass 0.115470E-05 1.8000 57.7730 300 : rminsp, rmt, rmaxsp, nrmt 2 : nstsp 1 0 1 2.00000 F : nsp, lsp, ksp, occsp, spcore 2 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8784 0 T elk-7.2.42/species/PaxHeaders.21776/Lr.in0000644000000000000000000000012414061636521014471 xustar0028 mtime=1623670097.1691004 28 atime=1623670097.1691004 28 ctime=1623670097.1691004 elk-7.2.42/species/Lr.in0000644002504400250440000000456614061636521016540 0ustar00dewhurstdewhurst00000000000000 'Lr' : spsymb 'lawrencium' : spname -103.000 : spzn 477596.7830 : spmass 0.197066E-06 3.0000 68.3662 800 : rminsp, rmt, rmaxsp, nrmt 28 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 6.00000 F 5 3 4 8.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 6 2 2 1.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.3668 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.5853 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9447 0 T elk-7.2.42/species/PaxHeaders.21776/Lu.in0000644000000000000000000000013214061636521014473 xustar0030 mtime=1623670097.171100398 30 atime=1623670097.171100398 30 ctime=1623670097.171100398 elk-7.2.42/species/Lu.in0000644002504400250440000000426214061636521016534 0ustar00dewhurstdewhurst00000000000000 'Lu' : spsymb 'lutetium' : spname -71.0000 : spzn 318945.3295 : spmass 0.237356E-06 2.8000 60.6496 700 : rminsp, rmt, rmaxsp, nrmt 21 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 1.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.3291 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.2383 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.0908 0 T elk-7.2.42/species/PaxHeaders.21776/Md.in0000644000000000000000000000013214061636521014453 xustar0030 mtime=1623670097.173100396 30 atime=1623670097.173100396 30 ctime=1623670097.173100396 elk-7.2.42/species/Md.in0000644002504400250440000000453214061636521016514 0ustar00dewhurstdewhurst00000000000000 'Md' : spsymb 'mendelevium' : spname -101.000 : spzn 470305.2291 : spmass 0.199007E-06 3.0000 49.0271 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 6.00000 F 5 3 4 7.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1623 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.2742 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8134 0 T elk-7.2.42/species/PaxHeaders.21776/Mg.in0000644000000000000000000000013214061636521014456 xustar0030 mtime=1623670097.175100394 30 atime=1623670097.175100394 30 ctime=1623670097.175100394 elk-7.2.42/species/Mg.in0000644002504400250440000000246614061636521016523 0ustar00dewhurstdewhurst00000000000000 'Mg' : spsymb 'magnesium' : spname -12.0000 : spzn 44305.30462 : spmass 0.577350E-06 2.2000 45.4518 400 : rminsp, rmt, rmaxsp, nrmt 5 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 2 1 1 2.00000 F 2 1 2 4.00000 F 3 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.9139 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.7134 0 T elk-7.2.42/species/PaxHeaders.21776/Mn.in0000644000000000000000000000013214061636521014465 xustar0030 mtime=1623670097.177100392 30 atime=1623670097.177100392 30 ctime=1623670097.177100392 elk-7.2.42/species/Mn.in0000644002504400250440000000335214061636521016525 0ustar00dewhurstdewhurst00000000000000 'Mn' : spsymb 'manganese' : spname -25.0000 : spzn 100145.9369 : spmass 0.400000E-06 2.4000 41.1948 500 : rminsp, rmt, rmaxsp, nrmt 10 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 3.00000 F 3 2 3 2.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.1372 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.9857 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2553 0 T elk-7.2.42/species/PaxHeaders.21776/Mo.in0000644000000000000000000000013014061636521014464 xustar0029 mtime=1623670097.17910039 30 atime=1623670097.178100391 29 ctime=1623670097.17910039 elk-7.2.42/species/Mo.in0000644002504400250440000000356614061636521016535 0ustar00dewhurstdewhurst00000000000000 'Mo' : spsymb 'molybdenum' : spname -42.0000 : spzn 174887.9212 : spmass 0.308607E-06 2.6000 48.6428 600 : rminsp, rmt, rmaxsp, nrmt 15 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 3.00000 F 4 2 3 2.00000 F 5 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.3643 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.3863 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1404 0 T elk-7.2.42/species/PaxHeaders.21776/Na.in0000644000000000000000000000013114061636521014450 xustar0030 mtime=1623670097.181100389 29 atime=1623670097.18010039 30 ctime=1623670097.181100389 elk-7.2.42/species/Na.in0000644002504400250440000000246614061636521016516 0ustar00dewhurstdewhurst00000000000000 'Na' : spsymb 'sodium' : spname -11.0000 : spzn 41907.78700 : spmass 0.603023E-06 2.2000 56.6436 400 : rminsp, rmt, rmaxsp, nrmt 5 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 2 1 1 2.00000 F 2 1 2 4.00000 F 3 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0701 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.0570 0 T elk-7.2.42/species/PaxHeaders.21776/Nb.in0000644000000000000000000000013214061636521014452 xustar0030 mtime=1623670097.182100388 30 atime=1623670097.182100388 30 ctime=1623670097.182100388 elk-7.2.42/species/Nb.in0000644002504400250440000000356614061636521016521 0ustar00dewhurstdewhurst00000000000000 'Nb' : spsymb 'niobium' : spname -41.0000 : spzn 169357.9703 : spmass 0.312348E-06 2.6000 49.8649 600 : rminsp, rmt, rmaxsp, nrmt 15 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 3.00000 F 4 2 3 1.00000 F 5 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.1446 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.2440 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1141 0 T elk-7.2.42/species/PaxHeaders.21776/Nd.in0000644000000000000000000000013214061636521014454 xustar0030 mtime=1623670097.184100386 30 atime=1623670097.184100386 30 ctime=1623670097.184100386 elk-7.2.42/species/Nd.in0000644002504400250440000000422614061636521016515 0ustar00dewhurstdewhurst00000000000000 'Nd' : spsymb 'neodymium' : spname -60.0000 : spzn 262933.4350 : spmass 0.258199E-06 2.8000 57.1546 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 3.00000 F 4 3 4 1.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.0620 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.4878 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7795 0 T elk-7.2.42/species/PaxHeaders.21776/Ne.in0000644000000000000000000000013214061636521014455 xustar0030 mtime=1623670097.186100384 30 atime=1623670097.186100384 30 ctime=1623670097.186100384 elk-7.2.42/species/Ne.in0000644002504400250440000000243214061636521016513 0ustar00dewhurstdewhurst00000000000000 'Ne' : spsymb 'neon' : spname -10.0000 : spzn 36785.34276 : spmass 0.632456E-06 1.6000 24.5143 300 : rminsp, rmt, rmaxsp, nrmt 4 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 2 1 1 2.00000 F 2 1 2 4.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.3272 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.4961 0 T elk-7.2.42/species/PaxHeaders.21776/Ni.in0000644000000000000000000000013214061636521014461 xustar0030 mtime=1623670097.188100382 30 atime=1623670097.188100382 30 ctime=1623670097.188100382 elk-7.2.42/species/Ni.in0000644002504400250440000000312614061636521016520 0ustar00dewhurstdewhurst00000000000000 'Ni' : spsymb 'nickel' : spname -28.0000 : spzn 106991.5230 : spmass 0.377964E-06 2.4000 42.8623 500 : rminsp, rmt, rmaxsp, nrmt 10 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 4.00000 F 3 2 3 4.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.5905 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.3317 0 T elk-7.2.42/species/PaxHeaders.21776/N.in0000644000000000000000000000012714061636521014314 xustar0029 mtime=1623670097.19010038 29 atime=1623670097.19010038 29 ctime=1623670097.19010038 elk-7.2.42/species/N.in0000644002504400250440000000220614061636521016345 0ustar00dewhurstdewhurst00000000000000 'N' : spsymb 'nitrogen' : spname -7.00000 : spzn 25532.65214 : spmass 0.755929E-06 1.8000 34.9411 300 : rminsp, rmt, rmaxsp, nrmt 4 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 2 1 1 1.00000 F 2 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6770 0 T elk-7.2.42/species/PaxHeaders.21776/No.in0000644000000000000000000000013214061636521014467 xustar0030 mtime=1623670097.192100378 30 atime=1623670097.191100379 30 ctime=1623670097.192100378 elk-7.2.42/species/No.in0000644002504400250440000000453214061636521016530 0ustar00dewhurstdewhurst00000000000000 'No' : spsymb 'nobelium' : spname -102.000 : spzn 472128.1176 : spmass 0.198030E-06 3.0000 49.0598 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 6.00000 F 5 3 4 8.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1751 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.3481 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8216 0 T elk-7.2.42/species/PaxHeaders.21776/Np.in0000644000000000000000000000013214061636521014470 xustar0030 mtime=1623670097.193100378 30 atime=1623670097.193100378 30 ctime=1623670097.193100378 elk-7.2.42/species/Np.in0000644002504400250440000000456614061636521016540 0ustar00dewhurstdewhurst00000000000000 'Np' : spsymb 'neptunium' : spname -93.0000 : spzn 432024.5709 : spmass 0.207390E-06 3.0000 54.0533 800 : rminsp, rmt, rmaxsp, nrmt 28 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 3.00000 F 5 3 4 1.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 6 2 2 1.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1316 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8240 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7920 0 T elk-7.2.42/species/PaxHeaders.21776/O.in0000644000000000000000000000013214061636521014311 xustar0030 mtime=1623670097.195100376 30 atime=1623670097.195100376 30 ctime=1623670097.195100376 elk-7.2.42/species/O.in0000644002504400250440000000220614061636521016346 0ustar00dewhurstdewhurst00000000000000 'O' : spsymb 'oxygen' : spname -8.00000 : spzn 29165.12202 : spmass 0.707107E-06 1.8000 30.4661 300 : rminsp, rmt, rmaxsp, nrmt 4 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 F 2 1 1 2.00000 F 2 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8728 0 T elk-7.2.42/species/PaxHeaders.21776/Os.in0000644000000000000000000000013214061636521014474 xustar0030 mtime=1623670097.197100374 30 atime=1623670097.197100374 30 ctime=1623670097.197100374 elk-7.2.42/species/Os.in0000644002504400250440000000454214061636521016536 0ustar00dewhurstdewhurst00000000000000 'Os' : spsymb 'osmium' : spname -76.0000 : spzn 346768.0765 : spmass 0.229416E-06 2.8000 47.1620 700 : rminsp, rmt, rmaxsp, nrmt 22 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 4.00000 F 5 2 3 2.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 8 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8559 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.3540 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.7397 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2159 0 T elk-7.2.42/species/PaxHeaders.21776/Pa.in0000644000000000000000000000013214061636521014453 xustar0030 mtime=1623670097.199100372 30 atime=1623670097.199100372 30 ctime=1623670097.199100372 elk-7.2.42/species/Pa.in0000644002504400250440000000430614061636521016513 0ustar00dewhurstdewhurst00000000000000 'Pa' : spsymb 'protactinium' : spname -91.0000 : spzn 421152.6452 : spmass 0.209657E-06 3.0000 62.3511 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 2.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 6 2 2 1.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.6682 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7444 0 T elk-7.2.42/species/PaxHeaders.21776/Pb.in0000644000000000000000000000012714061636521014460 xustar0029 mtime=1623670097.20110037 29 atime=1623670097.20110037 29 ctime=1623670097.20110037 elk-7.2.42/species/Pb.in0000644002504400250440000000373614061636521016522 0ustar00dewhurstdewhurst00000000000000 'Pb' : spsymb 'lead' : spname -82.0000 : spzn 377702.4940 : spmass 0.220863E-06 2.8000 53.2955 700 : rminsp, rmt, rmaxsp, nrmt 24 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 1.00000 F 6 1 2 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7322 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.4439 0 T elk-7.2.42/species/PaxHeaders.21776/Pd.in0000644000000000000000000000013214061636521014456 xustar0030 mtime=1623670097.203100368 30 atime=1623670097.203100368 30 ctime=1623670097.203100368 elk-7.2.42/species/Pd.in0000644002504400250440000000353214061636521016516 0ustar00dewhurstdewhurst00000000000000 'Pd' : spsymb 'palladium' : spname -46.0000 : spzn 193991.7925 : spmass 0.294884E-06 2.6000 41.5324 500 : rminsp, rmt, rmaxsp, nrmt 14 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 6.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.1380 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8352 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1522 0 T elk-7.2.42/species/PaxHeaders.21776/P.in0000644000000000000000000000013214061636521014312 xustar0030 mtime=1623670097.205100366 30 atime=1623670097.204100367 30 ctime=1623670097.205100366 elk-7.2.42/species/P.in0000644002504400250440000000233214061636521016347 0ustar00dewhurstdewhurst00000000000000 'P' : spsymb 'phosphorus' : spname -15.0000 : spzn 56461.71226 : spmass 0.516398E-06 2.2000 39.7177 400 : rminsp, rmt, rmaxsp, nrmt 7 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 1.00000 F 3 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5151 0 T elk-7.2.42/species/PaxHeaders.21776/Pm.in0000644000000000000000000000013214061636521014467 xustar0030 mtime=1623670097.207100364 30 atime=1623670097.206100365 30 ctime=1623670097.207100364 elk-7.2.42/species/Pm.in0000644002504400250440000000422614061636521016530 0ustar00dewhurstdewhurst00000000000000 'Pm' : spsymb 'promethium' : spname -61.0000 : spzn 264318.8303 : spmass 0.256074E-06 2.8000 52.1574 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 3.00000 F 4 3 4 2.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.0768 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.5401 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7991 0 T elk-7.2.42/species/PaxHeaders.21776/Po.in0000644000000000000000000000013214061636521014471 xustar0030 mtime=1623670097.208100364 30 atime=1623670097.208100364 30 ctime=1623670097.208100364 elk-7.2.42/species/Po.in0000644002504400250440000000373614061636521016537 0ustar00dewhurstdewhurst00000000000000 'Po' : spsymb 'polonium' : spname -84.0000 : spzn 380983.6933 : spmass 0.218218E-06 2.8000 43.2445 700 : rminsp, rmt, rmaxsp, nrmt 24 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.1481 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6144 0 T elk-7.2.42/species/PaxHeaders.21776/Pr.in0000644000000000000000000000013214061636521014474 xustar0030 mtime=1623670097.210100362 30 atime=1623670097.210100362 30 ctime=1623670097.210100362 elk-7.2.42/species/Pr.in0000644002504400250440000000374614061636521016543 0ustar00dewhurstdewhurst00000000000000 'Pr' : spsymb 'praseodymium' : spname -59.0000 : spzn 256858.9326 : spmass 0.260378E-06 2.8000 55.7748 700 : rminsp, rmt, rmaxsp, nrmt 19 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 3.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.4342 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7585 0 T elk-7.2.42/species/PaxHeaders.21776/Pt.in0000644000000000000000000000012714061636521014502 xustar0029 mtime=1623670097.21210036 29 atime=1623670097.21210036 29 ctime=1623670097.21210036 elk-7.2.42/species/Pt.in0000644002504400250440000000431614061636521016537 0ustar00dewhurstdewhurst00000000000000 'Pt' : spsymb 'platinum' : spname -78.0000 : spzn 355605.4398 : spmass 0.226455E-06 2.8000 40.1191 700 : rminsp, rmt, rmaxsp, nrmt 22 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 T 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 4.00000 F 5 2 3 5.00000 F 6 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.5235 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.9151 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2143 0 T elk-7.2.42/species/PaxHeaders.21776/Pu.in0000644000000000000000000000013214061636521014477 xustar0030 mtime=1623670097.214100358 30 atime=1623670097.214100358 30 ctime=1623670097.214100358 elk-7.2.42/species/Pu.in0000644002504400250440000000453214061636521016540 0ustar00dewhurstdewhurst00000000000000 'Pu' : spsymb 'plutonium' : spname -94.0000 : spzn 444784.7903 : spmass 0.206284E-06 3.0000 57.5498 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 3.00000 F 5 3 4 3.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.0579 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.7999 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7412 0 T elk-7.2.42/species/PaxHeaders.21776/Ra.in0000644000000000000000000000013214061636521014455 xustar0030 mtime=1623670097.216100356 30 atime=1623670097.215100357 30 ctime=1623670097.216100356 elk-7.2.42/species/Ra.in0000644002504400250440000000421614061636521016515 0ustar00dewhurstdewhurst00000000000000 'Ra' : spsymb 'radium' : spname -88.0000 : spzn 411972.7976 : spmass 0.213201E-06 3.0000 54.9631 800 : rminsp, rmt, rmaxsp, nrmt 25 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.4469 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.2846 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5588 0 T elk-7.2.42/species/PaxHeaders.21776/Rb.in0000644000000000000000000000013214061636521014456 xustar0030 mtime=1623670097.218100354 30 atime=1623670097.217100355 30 ctime=1623670097.218100354 elk-7.2.42/species/Rb.in0000644002504400250440000000302614061636521016514 0ustar00dewhurstdewhurst00000000000000 'Rb' : spsymb 'rubidium' : spname -37.0000 : spzn 155798.2684 : spmass 0.328798E-06 2.6000 62.8187 600 : rminsp, rmt, rmaxsp, nrmt 13 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 5 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.1744 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5784 0 T elk-7.2.42/species/PaxHeaders.21776/Re.in0000644000000000000000000000013214061636521014461 xustar0030 mtime=1623670097.220100352 30 atime=1623670097.220100352 30 ctime=1623670097.220100352 elk-7.2.42/species/Re.in0000644002504400250440000000454214061636521016523 0ustar00dewhurstdewhurst00000000000000 'Re' : spsymb 'rhenium' : spname -75.0000 : spzn 339434.5961 : spmass 0.230940E-06 2.8000 40.0180 700 : rminsp, rmt, rmaxsp, nrmt 22 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 3.00000 F 5 2 3 2.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 8 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.5110 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.1270 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.6149 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1881 0 T elk-7.2.42/species/PaxHeaders.21776/Rf.in0000644000000000000000000000013214061636521014462 xustar0030 mtime=1623670097.222100351 30 atime=1623670097.222100351 30 ctime=1623670097.222100351 elk-7.2.42/species/Rf.in0000644002504400250440000000456614061636521016532 0ustar00dewhurstdewhurst00000000000000 'Rf' : spsymb 'rutherfordium' : spname -104.000 : spzn 475773.8945 : spmass 0.196116E-06 3.0000 53.3658 800 : rminsp, rmt, rmaxsp, nrmt 28 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 6.00000 F 5 3 4 8.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 6 2 2 2.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5604 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.8179 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.0541 0 T elk-7.2.42/species/PaxHeaders.21776/Rh.in0000644000000000000000000000013214061636521014464 xustar0030 mtime=1623670097.224100349 30 atime=1623670097.224100349 30 ctime=1623670097.224100349 elk-7.2.42/species/Rh.in0000644002504400250440000000356614061636521016533 0ustar00dewhurstdewhurst00000000000000 'Rh' : spsymb 'rhodium' : spname -45.0000 : spzn 187585.2510 : spmass 0.298142E-06 2.6000 45.1320 600 : rminsp, rmt, rmaxsp, nrmt 15 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 4.00000 F 5 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.0301 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.8089 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.2190 0 T elk-7.2.42/species/PaxHeaders.21776/Rn.in0000644000000000000000000000013214061636521014472 xustar0030 mtime=1623670097.226100347 30 atime=1623670097.226100347 30 ctime=1623670097.226100347 elk-7.2.42/species/Rn.in0000644002504400250440000000373614061636521016540 0ustar00dewhurstdewhurst00000000000000 'Rn' : spsymb 'radon' : spname -86.0000 : spzn 404681.2436 : spmass 0.215666E-06 2.6000 38.0087 700 : rminsp, rmt, rmaxsp, nrmt 24 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.6273 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8085 0 T elk-7.2.42/species/PaxHeaders.21776/Ru.in0000644000000000000000000000013214061636521014501 xustar0030 mtime=1623670097.228100345 30 atime=1623670097.227100346 30 ctime=1623670097.228100345 elk-7.2.42/species/Ru.in0000644002504400250440000000356614061636521016550 0ustar00dewhurstdewhurst00000000000000 'Ru' : spsymb 'ruthenium' : spname -44.0000 : spzn 184239.3392 : spmass 0.301511E-06 2.6000 48.8112 600 : rminsp, rmt, rmaxsp, nrmt 15 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 3.00000 F 5 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.8048 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.6670 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1922 0 T elk-7.2.42/species/PaxHeaders.21776/Sb.in0000644000000000000000000000013214061636521014457 xustar0030 mtime=1623670097.229100344 30 atime=1623670097.229100344 30 ctime=1623670097.229100344 elk-7.2.42/species/Sb.in0000644002504400250440000000343214061636521016516 0ustar00dewhurstdewhurst00000000000000 'Sb' : spsymb 'antimony' : spname -51.0000 : spzn 221954.9019 : spmass 0.280056E-06 2.6000 44.3358 600 : rminsp, rmt, rmaxsp, nrmt 17 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 5 1 1 1.00000 F 5 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.2137 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.4804 0 T elk-7.2.42/species/PaxHeaders.21776/Sc.in0000644000000000000000000000013214061636521014460 xustar0030 mtime=1623670097.231100342 30 atime=1623670097.231100342 30 ctime=1623670097.231100342 elk-7.2.42/species/Sc.in0000644002504400250440000000307214061636521016517 0ustar00dewhurstdewhurst00000000000000 'Sc' : spsymb 'scandium' : spname -21.0000 : spzn 81949.61066 : spmass 0.436436E-06 2.4000 55.5111 500 : rminsp, rmt, rmaxsp, nrmt 9 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 1.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0100 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.2267 0 T elk-7.2.42/species/PaxHeaders.21776/Se.in0000644000000000000000000000012714061636521014466 xustar0029 mtime=1623670097.23310034 29 atime=1623670097.23310034 29 ctime=1623670097.23310034 elk-7.2.42/species/Se.in0000644002504400250440000000321614061636521016521 0ustar00dewhurstdewhurst00000000000000 'Se' : spsymb 'selenium' : spname -34.0000 : spzn 143935.2748 : spmass 0.342997E-06 2.4000 38.3229 500 : rminsp, rmt, rmaxsp, nrmt 12 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.9444 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6402 0 T elk-7.2.42/species/PaxHeaders.21776/Si.in0000644000000000000000000000013214061636521014466 xustar0030 mtime=1623670097.235100339 30 atime=1623670097.235100339 30 ctime=1623670097.235100339 elk-7.2.42/species/Si.in0000644002504400250440000000210614061636521016522 0ustar00dewhurstdewhurst00000000000000 'Si' : spsymb 'silicon' : spname -14.0000 : spzn 51196.73454 : spmass 0.534522E-06 2.2000 47.8169 400 : rminsp, rmt, rmaxsp, nrmt 7 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 1.00000 F 3 1 2 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 2 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F elk-7.2.42/species/PaxHeaders.21776/S.in0000644000000000000000000000013214061636521014315 xustar0030 mtime=1623670097.237100337 30 atime=1623670097.237100337 30 ctime=1623670097.237100337 elk-7.2.42/species/S.in0000644002504400250440000000233214061636521016352 0ustar00dewhurstdewhurst00000000000000 'S' : spsymb 'sulphur' : spname -16.0000 : spzn 58450.91926 : spmass 0.500000E-06 2.2000 36.9680 400 : rminsp, rmt, rmaxsp, nrmt 7 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 3 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.6346 0 T elk-7.2.42/species/PaxHeaders.21776/Sm.in0000644000000000000000000000013214061636521014472 xustar0030 mtime=1623670097.239100335 30 atime=1623670097.238100336 30 ctime=1623670097.239100335 elk-7.2.42/species/Sm.in0000644002504400250440000000422614061636521016533 0ustar00dewhurstdewhurst00000000000000 'Sm' : spsymb 'samarium' : spname -62.0000 : spzn 274089.5126 : spmass 0.254000E-06 2.8000 52.2193 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 3.00000 F 4 3 4 3.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.0883 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.5919 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8177 0 T elk-7.2.42/species/PaxHeaders.21776/Sn.in0000644000000000000000000000013214061636521014473 xustar0030 mtime=1623670097.240100334 30 atime=1623670097.240100334 30 ctime=1623670097.240100334 elk-7.2.42/species/Sn.in0000644002504400250440000000343214061636521016532 0ustar00dewhurstdewhurst00000000000000 'Sn' : spsymb 'tin' : spname -50.0000 : spzn 216395.0920 : spmass 0.282843E-06 2.6000 49.2770 600 : rminsp, rmt, rmaxsp, nrmt 17 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 5 1 1 1.00000 F 5 1 2 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.1993 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9327 0 T elk-7.2.42/species/PaxHeaders.21776/Sr.in0000644000000000000000000000013214061636521014477 xustar0030 mtime=1623670097.242100332 30 atime=1623670097.242100332 30 ctime=1623670097.242100332 elk-7.2.42/species/Sr.in0000644002504400250440000000302614061636521016535 0ustar00dewhurstdewhurst00000000000000 'Sr' : spsymb 'strontium' : spname -38.0000 : spzn 159721.4890 : spmass 0.324443E-06 2.6000 52.2837 600 : rminsp, rmt, rmaxsp, nrmt 13 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 5 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 4 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.5031 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8259 0 T elk-7.2.42/species/PaxHeaders.21776/Ta.in0000644000000000000000000000012714061636521014463 xustar0029 mtime=1623670097.24410033 29 atime=1623670097.24410033 29 ctime=1623670097.24410033 elk-7.2.42/species/Ta.in0000644002504400250440000000426214061636521016520 0ustar00dewhurstdewhurst00000000000000 'Ta' : spsymb 'tantalum' : spname -73.0000 : spzn 329847.8433 : spmass 0.234082E-06 2.8000 43.8533 700 : rminsp, rmt, rmaxsp, nrmt 21 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 3.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8655 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.6690 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.3498 0 T elk-7.2.42/species/PaxHeaders.21776/Tb.in0000644000000000000000000000013214061636521014460 xustar0030 mtime=1623670097.246100328 30 atime=1623670097.246100328 30 ctime=1623670097.246100328 elk-7.2.42/species/Tb.in0000644002504400250440000000422614061636521016521 0ustar00dewhurstdewhurst00000000000000 'Tb' : spsymb 'terbium' : spname -65.0000 : spzn 289703.1722 : spmass 0.248069E-06 2.8000 52.3997 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 5.00000 F 4 3 4 4.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1036 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.7464 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.8687 0 T elk-7.2.42/species/PaxHeaders.21776/Tc.in0000644000000000000000000000013214061636521014461 xustar0030 mtime=1623670097.248100326 30 atime=1623670097.248100326 30 ctime=1623670097.248100326 elk-7.2.42/species/Tc.in0000644002504400250440000000356614061636521016530 0ustar00dewhurstdewhurst00000000000000 'Tc' : spsymb 'technetium' : spname -43.0000 : spzn 178643.0715 : spmass 0.304997E-06 2.6000 48.7280 600 : rminsp, rmt, rmaxsp, nrmt 15 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 4.00000 F 4 2 3 2.00000 F 5 0 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.5825 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.5257 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1656 0 T elk-7.2.42/species/PaxHeaders.21776/Te.in0000644000000000000000000000013214061636521014463 xustar0030 mtime=1623670097.250100324 30 atime=1623670097.249100325 30 ctime=1623670097.250100324 elk-7.2.42/species/Te.in0000644002504400250440000000343214061636521016522 0ustar00dewhurstdewhurst00000000000000 'Te' : spsymb 'tellurium' : spname -52.0000 : spzn 232600.5707 : spmass 0.277350E-06 2.6000 40.9670 600 : rminsp, rmt, rmaxsp, nrmt 17 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.5022 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5594 0 T elk-7.2.42/species/PaxHeaders.21776/Th.in0000644000000000000000000000013214061636521014466 xustar0030 mtime=1623670097.251100324 30 atime=1623670097.251100324 30 ctime=1623670097.251100324 elk-7.2.42/species/Th.in0000644002504400250440000000425214061636521016526 0ustar00dewhurstdewhurst00000000000000 'Th' : spsymb 'thorium' : spname -90.0000 : spzn 422979.5805 : spmass 0.210819E-06 3.0000 51.7499 800 : rminsp, rmt, rmaxsp, nrmt 26 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 6 2 2 2.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.2122 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.6772 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7795 0 T elk-7.2.42/species/PaxHeaders.21776/Ti.in0000644000000000000000000000013214061636521014467 xustar0030 mtime=1623670097.253100322 30 atime=1623670097.253100322 30 ctime=1623670097.253100322 elk-7.2.42/species/Ti.in0000644002504400250440000000307214061636521016526 0ustar00dewhurstdewhurst00000000000000 'Ti' : spsymb 'titanium' : spname -22.0000 : spzn 87256.20310 : spmass 0.426401E-06 2.4000 46.2267 500 : rminsp, rmt, rmaxsp, nrmt 9 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 2.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.2872 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.4164 0 T elk-7.2.42/species/PaxHeaders.21776/Tl.in0000644000000000000000000000012714061636521014476 xustar0029 mtime=1623670097.25510032 29 atime=1623670097.25510032 29 ctime=1623670097.25510032 elk-7.2.42/species/Tl.in0000644002504400250440000000370214061636521016531 0ustar00dewhurstdewhurst00000000000000 'Tl' : spsymb 'thallium' : spname -81.0000 : spzn 372567.9640 : spmass 0.222222E-06 2.8000 57.1183 700 : rminsp, rmt, rmaxsp, nrmt 23 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 4.00000 F 5 2 3 6.00000 F 6 0 1 2.00000 F 6 1 1 1.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.5798 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.5217 0 T elk-7.2.42/species/PaxHeaders.21776/Tm.in0000644000000000000000000000013214061636521014473 xustar0030 mtime=1623670097.257100318 30 atime=1623670097.256100319 30 ctime=1623670097.257100318 elk-7.2.42/species/Tm.in0000644002504400250440000000422614061636521016534 0ustar00dewhurstdewhurst00000000000000 'Tm' : spsymb 'thulium' : spname -69.0000 : spzn 307948.2261 : spmass 0.240772E-06 2.8000 53.8678 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 7.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1016 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.9638 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9340 0 T elk-7.2.42/species/PaxHeaders.21776/U.in0000644000000000000000000000013214061636521014317 xustar0030 mtime=1623670097.259100316 30 atime=1623670097.258100317 30 ctime=1623670097.259100316 elk-7.2.42/species/U.in0000644002504400250440000000430614061636521016357 0ustar00dewhurstdewhurst00000000000000 'U' : spsymb 'uranium' : spname -92.0000 : spzn 433900.1591 : spmass 0.208514E-06 3.0000 56.2869 800 : rminsp, rmt, rmaxsp, nrmt 27 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 T 4 3 4 8.00000 T 5 0 1 2.00000 T 5 1 1 2.00000 T 5 1 2 4.00000 T 5 2 2 4.00000 T 5 2 3 6.00000 T 5 3 3 3.00000 F 6 0 1 2.00000 F 6 1 1 2.00000 F 6 1 2 4.00000 F 6 2 2 1.00000 F 7 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 6 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.7461 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7688 0 T elk-7.2.42/species/PaxHeaders.21776/V.in0000644000000000000000000000013214061636521014320 xustar0030 mtime=1623670097.260100315 30 atime=1623670097.260100315 30 ctime=1623670097.260100315 elk-7.2.42/species/V.in0000644002504400250440000000307214061636521016357 0ustar00dewhurstdewhurst00000000000000 'V' : spsymb 'vanadium' : spname -23.0000 : spzn 92860.67375 : spmass 0.417029E-06 2.4000 46.3855 500 : rminsp, rmt, rmaxsp, nrmt 9 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 F 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 3.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.5646 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.6038 0 T elk-7.2.42/species/PaxHeaders.21776/W.in0000644000000000000000000000013214061636521014321 xustar0030 mtime=1623670097.262100313 30 atime=1623670097.262100313 30 ctime=1623670097.262100313 elk-7.2.42/species/W.in0000644002504400250440000000454214061636521016363 0ustar00dewhurstdewhurst00000000000000 'W' : spsymb 'tungsten' : spname -74.0000 : spzn 335119.8190 : spmass 0.232495E-06 2.8000 47.0748 700 : rminsp, rmt, rmaxsp, nrmt 22 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 5 2 2 3.00000 F 5 2 3 1.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 8 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.1774 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.8962 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.4828 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.1560 0 T elk-7.2.42/species/PaxHeaders.21776/Xe.in0000644000000000000000000000013214061636521014467 xustar0030 mtime=1623670097.264100312 30 atime=1623670097.264100312 30 ctime=1623670097.264100312 elk-7.2.42/species/Xe.in0000644002504400250440000000343214061636521016526 0ustar00dewhurstdewhurst00000000000000 'Xe' : spsymb 'xenon' : spname -54.0000 : spzn 239332.4978 : spmass 0.272166E-06 2.4000 34.6139 600 : rminsp, rmt, rmaxsp, nrmt 17 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 F 4 2 3 6.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.1523 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.7334 0 T elk-7.2.42/species/PaxHeaders.21776/Yb.in0000644000000000000000000000012714061636521014471 xustar0029 mtime=1623670097.26610031 29 atime=1623670097.26610031 29 ctime=1623670097.26610031 elk-7.2.42/species/Yb.in0000644002504400250440000000422614061636521016526 0ustar00dewhurstdewhurst00000000000000 'Yb' : spsymb 'ytterbium' : spname -70.0000 : spzn 315432.6234 : spmass 0.239046E-06 2.8000 49.1291 700 : rminsp, rmt, rmaxsp, nrmt 20 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 T 4 1 1 2.00000 T 4 1 2 4.00000 T 4 2 2 4.00000 T 4 2 3 6.00000 T 4 3 3 6.00000 F 4 3 4 8.00000 F 5 0 1 2.00000 F 5 1 1 2.00000 F 5 1 2 4.00000 F 6 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 7 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 3 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.0982 0 T 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0212 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.9503 0 T elk-7.2.42/species/PaxHeaders.21776/Y.in0000644000000000000000000000013214061636521014323 xustar0030 mtime=1623670097.268100308 30 atime=1623670097.267100309 30 ctime=1623670097.268100308 elk-7.2.42/species/Y.in0000644002504400250440000000330614061636521016362 0ustar00dewhurstdewhurst00000000000000 'Y' : spsymb 'yttrium' : spname -39.0000 : spzn 162065.4502 : spmass 0.320256E-06 2.6000 53.7982 600 : rminsp, rmt, rmaxsp, nrmt 14 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 1.00000 F 5 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.7619 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.0082 0 T elk-7.2.42/species/PaxHeaders.21776/Zn.in0000644000000000000000000000013214061636521014502 xustar0030 mtime=1623670097.269100307 30 atime=1623670097.269100307 30 ctime=1623670097.269100307 elk-7.2.42/species/Zn.in0000644002504400250440000000312614061636521016541 0ustar00dewhurstdewhurst00000000000000 'Zn' : spsymb 'zinc' : spname -30.0000 : spzn 119233.3129 : spmass 0.365148E-06 2.4000 39.2020 500 : rminsp, rmt, rmaxsp, nrmt 10 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 F 3 1 2 4.00000 F 3 2 2 4.00000 F 3 2 3 6.00000 F 4 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -3.0221 0 T 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -0.3778 0 T elk-7.2.42/species/PaxHeaders.21776/Zr.in0000644000000000000000000000013214061636521014506 xustar0030 mtime=1623670097.271100305 30 atime=1623670097.271100305 30 ctime=1623670097.271100305 elk-7.2.42/species/Zr.in0000644002504400250440000000330614061636521016545 0ustar00dewhurstdewhurst00000000000000 'Zr' : spsymb 'zirconium' : spname -40.0000 : spzn 166291.1791 : spmass 0.316228E-06 2.6000 48.4669 600 : rminsp, rmt, rmaxsp, nrmt 14 : nstsp 1 0 1 2.00000 T : nsp, lsp, ksp, occsp, spcore 2 0 1 2.00000 T 2 1 1 2.00000 T 2 1 2 4.00000 T 3 0 1 2.00000 T 3 1 1 2.00000 T 3 1 2 4.00000 T 3 2 2 4.00000 T 3 2 3 6.00000 T 4 0 1 2.00000 F 4 1 1 2.00000 F 4 1 2 4.00000 F 4 2 2 2.00000 F 5 0 1 2.00000 F 1 : apword 0.1500 0 F : apwe0, apwdm, apwve 0 : nlx 5 : nlorb 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 2 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve 0.1500 1 F 0 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -2.0002 0 T 1 2 : lorbl, lorbord 0.1500 0 F : lorbe0, lorbdm, lorbve -1.1708 0 T elk-7.2.42/PaxHeaders.21776/utilities0000644000000000000000000000013214061636521014066 xustar0030 mtime=1623670097.289100288 30 atime=1623670097.277100299 30 ctime=1623670097.289100288 elk-7.2.42/utilities/0000755002504400250440000000000014061636521016200 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/utilities/PaxHeaders.21776/elk-bands0000644000000000000000000000013214061636521015726 xustar0030 mtime=1623670097.280100297 30 atime=1623670097.279100298 30 ctime=1623670097.280100297 elk-7.2.42/utilities/elk-bands/0000755002504400250440000000000014061636521020040 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/utilities/elk-bands/PaxHeaders.21776/elk-bands0000644000000000000000000000013214061636521017566 xustar0030 mtime=1623670097.281100296 30 atime=1623670097.280100297 30 ctime=1623670097.281100296 elk-7.2.42/utilities/elk-bands/elk-bands0000755002504400250440000001572614061636521021641 0ustar00dewhurstdewhurst00000000000000#!/bin/bash # # Copyright (C) 2010 M. G. Blaber # This file is distributed under the terms of the GNU General Public License. # See the file COPYING for license details. # # http://elk.sourceforge.net/ # # Marty's plotting program for elk band structures. # Changelog: # v0.2 - Fixed a bug regarding white space noticed by Kay Dewhurst # # Description: # -Plots the bands from elk, including labels that you have specified in your # elk.in file (see below for details) # -Notes on the necessary files and programs and Usage are given below. # -I recommend adding this script to your "path", a guide is given in the # Installation Notes below. # # A sample plot1d block is given below: # ------------- # plot1d # 3 100 : nvp1d, npp1d # 0.0 0.0 1.0 !G : vlvp1d # 0.5 0.5 1.0 !X # 0.0 0.0 0.0 !G # -------------- # #Some user defineable plot parameters (You may always change the parameters of #individual plots by editing elk-bands.gps) plot_width="15 cm" #For publication, change to 8.5 cm plot_height="10 cm" #For publication, change to 6 - 10 cm plot_font="Times, 18" #For publication, change to 12 border_linewidth="2" band_linewidth="1" #This number is scaled by border_linewidth internally by gnuplot # # # REQUIRED FILES: # elk.in BAND.OUT BANDLINES.OUT # # REQUIRED PROGRAMS: # awk gnuplot # # USAGE: # elk-bands # OR (energies in eV) # elk-bands [min_energy] [max_energy] # eg: elk-bands -5 10 # # INSTALLATION NOTES: # HOW TO ADD elk-bands TO YOUR PATH # -Make a new directory in your home folder named bin: # mkdir /home/username/bin # -Add this new directory to your path by editing your bashrc file, # /home/username/.bashrc # and add the following line: # export PATH=$PATH:/home/username/bin # To update the path variable for the terminal you are currently in, type: # source ~/.bashrc # ########### me="elk-bands" version="0.2" input_file=elk.in band_file=BAND.OUT bandlines_file=BANDLINES.OUT #Output: gps_file=$me.gps eps_file=$me.eps echo "- Welcome to $me version $version" echo "- Use ~ in front of any character in the labels list to make that letter greek!" echo "---------------------------------------------" ######### # Check Dependencies # Error Message dependencies_usage="ERROR - Programs required by $me not found. $me requires the following programs: - awk - gnuplot Your local package manager should have them, alternatively you can grab them from: http://www.gnu.org/software/gawk/ http://www.gnuplot.info/ " # awk check check=$(which awk 2>&1) if [ ! $? -eq 0 ]; then echo "Ahhhhhhhhhhhhhh - No awk found" echo "$dependencies_usage" exit 1 fi # gnuplot check check=$(which gnuplot 2>&1) if [ ! $? -eq 0 ]; then echo "Ahhhhhhhhhhhhhh - No gnuplot found" echo "$dependencies_usage" exit 1 fi echo "- Found awk and gnuplot" ######### # Check for input files # Error message inputfiles_usage="ERROR - Some file required by $me not found. $me requires the following files: $input_file $band_file $bandlines_file" # Check for f in $input_file $band_file $bandlines_file; do if [ ! -f $f ]; then echo "Ooops, can't find $f" echo "$inputfiles_usage" exit 1 fi done echo "- Found $input_file $band_file $bandlines_file" ######### # Check Parameters # Error message usage="Welcome to $me $version Usage (energies in eV): $me [min energy] [max energy] eg: elk-bands -5.5 10.0 " # Check if [ $1 ]; then if [ $2 ]; then min_energy=$1 max_energy=$2 else echo "ERROR - Please provide both energies" exit 1 fi else #no parameters provided min_energy="-15" max_energy="15" fi ######### # Get the labels and check them # Error for when someone forgets the labels in elk.in label_usage="ERROR - Labels not found. All tildes ~ convert the following letter to a greek symbol. $me requires the plot1d block in $input_file to look like: ------------------------ plot1d 7 400 : nvp1d, npp1d 0.0 0.0 1.0 ~G : vlvp1d 0.5 0.5 1.0 X 0.0 0.0 0.0 ~G 0.5 0.0 0.0 L 0.5 0.5 0.0 Merry Christmas 0.5 0.25 -0.25 W 0.5 0.0 0.0 L ------------------------- ERROR - Labels not defined correctly - scroll back up to see what went wrong " # Read the labels from elk.in and put them in a file label_names.tmp cat $input_file | awk '{ if($1=="plot1d"){go=1} if(go==2){number_of_labels=$1} if(go>number_of_labels+2){go=0} if(go>2){ for (i = 4; i <= NF; i++){printf("%s ", $i)} printf("\n") } if(go>0){go=go+1} }' | sed 's/://g' | sed 's/vlvp1d//g' | sed 's/ / /g' > label_names.tmp #Check the labels. no_label_line=$(cat label_names.tmp | awk '{if($1==""){print NR; exit}}') if [ $no_label_line ]; then echo "ERROR - No label found on line $((no_label_line+2)) of plot1d block" echo "$label_usage" exit 1 fi # Get the positions of the labels from bandlines file cat $bandlines_file | awk 'BEGIN{last=-1}{ if($1!=""){ if($1!=last){last=$1;print $1} } }' > label_positions.tmp # Match up the labels with their positions and remove the exclamation marks if they exist paste label_positions.tmp label_names.tmp | sed 's/!//' > labels.tmp rm label_names.tmp label_positions.tmp #this thing joins all the labels together into a format gnuplot can understand. labels=$(cat labels.tmp | awk '{ for (i = 2; i <= NF; i++){if (i==2){label=$i}else{label=label " " $i}} printf("%s%s%s %f, ",q,label,q,$1) label="" }' q=\" ) #Replace all instances of capital G with the gamma symbol labels=$(echo $labels | sed 's/~\(.\)/\{\/Symbol \1\}/g' ) if [[ $labels == *"{/Symbol }"* ]] then echo "WARNING -> There is a space after a \"~\" in the labels block... get rid of it."; fi echo "- Found labels" ######### # Write elk-bands.gps, the file which gnuplot uses. #this is a neat trick to spew out a file without having to use quotes. the end of the file is labeled _EOF cat > bands.tmp << _EOF set terminal postscript enhanced eps colour lw $border_linewidth dashlength 2 font "$plot_font" size $plot_width, $plot_height set style data lines set output "$eps_file" set ylabel "Energy (eV)" set grid noytics xtics #this puts vertical lines on the band structure according to xtics below set xtics( $labels ) set mytics 5 #minor y tics, the number of little tics in between labeled tics. unset key #change this to "set key top left" or something if you want the key in the plot #if you use "set key" then the title "Bands" will appear in the key plot [:][$min_energy:$max_energy] \ "BAND.OUT" using 1:((\$2)*27.21138386) title "Bands" lw $band_linewidth lt 1 lc rgb "black",\ 0.0 lt -1 notitle _EOF #this thing just removes the final comma from the end of the "set xtics ( )" line. cat bands.tmp | sed 's/, )/)/' > $gps_file rm bands.tmp rm labels.tmp echo "- Plotting file written to $gps_file" gnuplot $gps_file if [ ! $? -eq 0 ]; then echo "Unfortunately, some sort of unforseen error has occurred, try posting a message on the forum at http://sourceforge.net/projects/elk/forums/ " else echo "- Band plot is ready in $eps_file" fi echo "" exit 0 elk-7.2.42/utilities/PaxHeaders.21776/elk-optics0000644000000000000000000000013214061636521016140 xustar0030 mtime=1623670097.282100295 30 atime=1623670097.281100296 30 ctime=1623670097.282100295 elk-7.2.42/utilities/elk-optics/0000755002504400250440000000000014061636521020252 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/utilities/elk-optics/PaxHeaders.21776/elk-optics.py0000644000000000000000000000013214061636521020641 xustar0030 mtime=1623670097.283100294 30 atime=1623670097.283100294 30 ctime=1623670097.283100294 elk-7.2.42/utilities/elk-optics/elk-optics.py0000644002504400250440000000726514061636521022710 0ustar00dewhurstdewhurst00000000000000#!/usr/bin/python # # Copyright (C) 2015 by Markus Meinert # This file is distributed under the terms of the GNU General Public License. # See the file COPYING for license details. # # http://elk.sourceforge.net/ # # elk-optics.py v1.0 # # This script comes with no warranty. Check the results # carefully for production use. # # Description: # Reads all EPSILON_ii.OUT files in the present directory # and computes optical quantities. Diagonal components only. # # Input: EPSILON_ii.OUT # # Output: energy (eV), Re(eps), Im(eps), # refractive index Re(n), Im(n), # normal incidence reflectivity R, # absorption coefficient alpha (m^-1), # EELS -1/Im(eps) # # Output is written to optics_ii.out # import sys, os, math, cmath # check which files of type EPSILON_ii.OUT exist and # return a list of present components def get_components(): possible = ['11', '22', '33'] present = [] for p in possible: testfilename = 'EPSILON_%s.OUT' % p if os.path.isfile(testfilename): present.append(p) return present # read the EPSILON_ii.OUT file # return lists of energies and complex eps def read_epsilon(filename): handle = open(filename, 'r') content = handle.readlines() handle.close() data = [[],[]] for line in content: l = line.split() if l == []: continue data[0].append(float(l[0])) data[1].append(float(l[1])) # energies are read from first column of the first data block # real part of epsilon is read from the second column of the first data block (first half of the data) # imaginary part of epsilon is read from the second column of the second data block (second half of the data) datalength = int( len( data[0] ) / 2.) energies = data[0][0:datalength] eps_cplx = [complex(a,b) for a,b in zip(data[1][0:datalength], data[1][datalength:])] return energies, eps_cplx # compute optical properties from energies and complex epsilon def write_optical_properties(energies, eps_cplx, component): # complex refractive index N and extinction coefficient kappa # complex refractive index: N = n_r + ik N = [cmath.sqrt(x1) for x1 in eps_cplx] k = [cmath.sqrt(x1).imag for x1 in eps_cplx] # normal incidence reflectivity from complex refractive index R = [abs((1.-x1)/(1.+x1))**2 for x1 in N] # absorption coefficient in SI units from extinction coefficient and energy Ha_to_J = 27.21138602 * 1.6021766208E-19 hbar = 6.626070040E-34 / (2 * math.pi) c = 2.99792458E8 Ha_to_omegaSI = Ha_to_J / hbar alpha = [2 * (x1 * Ha_to_omegaSI) / c * x2 for x1, x2 in zip(energies, k)] # format data and write to file optics_ii.out data = zip(energies, eps_cplx, N, R, alpha) output = '%14s %14s %14s %14s %14s %14s %14s %14s\n' % ('# energy (eV)', 'Re(eps)', 'Im(eps)', 'Re(n)', 'Im(n)', 'R', 'alpha (m^-1)', 'EELS') for line in data: output += '%14.6e %14.6e %14.6e %14.6e %14.6e %14.6e %14.6e %14.6e\n' % (line[0]*27.21138602, line[1].real, line[1].imag, line[2].real, line[2].imag, line[3], line[4], -(1/line[1]).imag) outfilename = 'optics_%s.out' % component outfile = open(outfilename, 'w') outfile.write(output) outfile.close() # main loop over diagonal components of the epsilon tensor print('===================') print('| elk-optics v1.0 |') print('===================') print print('Looking for EPSILON_ii.OUT files...') components = get_components() if components == []: sys.exit('No EPSILON_ii.OUT files found. Exit.\n') else: print('Files found:') for c in components: print(' EPSILON_%s.OUT') % c print for c in components: filename = 'EPSILON_%s.OUT' % c print('Working on %s ...') % filename energies, eps_cplx = read_epsilon(filename) write_optical_properties(energies, eps_cplx, c) print('Optical properties written to optics_%s.out') % c print elk-7.2.42/utilities/PaxHeaders.21776/wien2k-elk0000644000000000000000000000013214061636521016036 xustar0030 mtime=1623670097.286100291 30 atime=1623670097.284100293 30 ctime=1623670097.286100291 elk-7.2.42/utilities/wien2k-elk/0000755002504400250440000000000014061636521020150 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/utilities/wien2k-elk/PaxHeaders.21776/se.pl0000644000000000000000000000013214061636521017057 xustar0030 mtime=1623670097.286100291 30 atime=1623670097.286100291 30 ctime=1623670097.286100291 elk-7.2.42/utilities/wien2k-elk/se.pl0000755002504400250440000000221614061636521021120 0ustar00dewhurstdewhurst00000000000000#!/usr/bin/perl if (@ARGV<1) { print "Script for conversion Wien2K struct files to spacegroup.in files used in exciting/elk\n"; print "The only argument is the name of the struct file, spacegroup.in is written to standard output\n"; print "Use at your own risk. \n Jerzy Goraus 2009\n"; exit; }; open(STR,$ARGV[0]) or die "can't open ",$ARGV[0]," file\n "; @STRUCT=; ($TMP,$GROUP)=split(/\_/,$STRUCT[1]); ($GROUP,$TMP)=split(/\n/,$GROUP); ($GROUP,$TMP)=split(/\ /,$GROUP); ($TMP,$LA,$LB,$LC,$AA,$AB,$AG)=split(/\s+/,$STRUCT[3]); $ATCNT=0; print " '",$GROUP,"\'\n ",$LA," ",$LB," ",$LC,"\n ",$AA," ",$AB," ",$AG,"\n 1 1 1\n .false.\n "; foreach (@STRUCT) { $BUF=$_; if (/ATOM/) { ($TMP,$X,$Y,$Z)=split(/=/,$BUF); ($X,$TMP)=split(/\ /,$X); ($Y,$TMP)=split(/\ /,$Y); $ATCNT+=1; # print "\n",$X, " ", $Y," ", $Z; $RESULT = sprintf(" %lf %lf %lf\n", $X,$Y,$Z); }; if (/NPT/) { $ATL=substr($_,0,2); $_=$ATL; s/\s//g; $ATL=$_; # print $ATL; $TAB{$ATL}=$TAB{$ATL}.$RESULT; $TABN{$ATL}+=1; }; }; $NUM=keys(TAB); print " ",$NUM ,"\n"; foreach (keys(TAB)) { print " '",$_,"' '",$_,".in'\n"; print " ",$TABN{$_},"\n"; print $TAB{$_}; } elk-7.2.42/utilities/PaxHeaders.21776/blocks2columns0000644000000000000000000000013114061636521017025 xustar0030 mtime=1623670097.288100289 29 atime=1623670097.28710029 30 ctime=1623670097.288100289 elk-7.2.42/utilities/blocks2columns/0000755002504400250440000000000014061636521021140 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/utilities/blocks2columns/PaxHeaders.21776/blocks2columns.py0000644000000000000000000000013214061636521022415 xustar0030 mtime=1623670097.288100289 30 atime=1623670097.288100289 30 ctime=1623670097.288100289 elk-7.2.42/utilities/blocks2columns/blocks2columns.py0000644002504400250440000000400714061636521024453 0ustar00dewhurstdewhurst00000000000000#!/usr/bin/python # elk blocks to columns by Markus Meinert # update January 2015, fixed a bug related to blank lines # Usage: blocks2columns.py PDOS_S01_A0001.OUT # blocks2columns.py TDOS.OUT # blocks2columns.py BAND.OUT import sys, os print("\n =========================\n | elk blocks to columns |\n =========================\n") # Read the file. filename = sys.argv[1] f = open(filename, 'r') data = f.readlines() f.close() # Analyze the file. # Number of lines. nlines = len(data) print(" Number of lines: %i " % nlines) # Count blank lines to determine number of datasets. ndatasets = 0 for line in data: if line.split() == []: ndatasets += 1 # If last line is not blank, add one to ndatasets and nlines. if data[-1].split() != []: ndatasets += 1 nlines += 1 print(" Number of datasets: %i " % ndatasets) # Number of lines per block is: nlinesperblock = (nlines - ndatasets)/ndatasets print(" Number of lines per block: %i " % nlinesperblock) # Collect the datasets into a list of lists with a double-loop over datasets and lines. datasets = [] for i in range(0,ndatasets): currentset = [] for j in range(i*nlinesperblock + i, (i*nlinesperblock + i) + nlinesperblock): currentset.append(data[j].split()) # Split each line by empty spaces. datasets.append(currentset) output = "" # Generate a head line output += "#%21s" % "x-axis" for i in range(1,ndatasets+1): blockname = "block_%i" % i output += "%22s" % blockname output += "\n" # Merge the datasets line-wise. for i in range(0,nlinesperblock): # x-axis as first column, read from first block line = '%22.13e' % (float(datasets[0][i][0])) # Append the block values as columns. for j in range(0, ndatasets): line += '%22.13e' % (float(datasets[j][i][1])) line += "\n" output += line filename = filename + ".columns" if os.path.exists(filename): print("\n Output file %s exists. Exit.\n" % filename) else: f = open(filename, 'w') f.write(output) f.close() print("\n Output filename: %s\n Done.\n" % filename) elk-7.2.42/utilities/PaxHeaders.21776/xps0000644000000000000000000000013214061636521014700 xustar0030 mtime=1623670097.294100284 30 atime=1623670097.289100288 30 ctime=1623670097.294100284 elk-7.2.42/utilities/xps/0000755002504400250440000000000014061636521017012 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/utilities/xps/PaxHeaders.21776/CROSEC0000644000000000000000000000013214061636521015656 xustar0030 mtime=1623670097.291100287 30 atime=1623670097.291100287 30 ctime=1623670097.291100287 elk-7.2.42/utilities/xps/CROSEC0000644002504400250440000000307614061636521017721 0ustar00dewhurstdewhurst00000000000000Crossection data for elements, E=1486eV ATOM=Xx 1.00E-0, 1.00E-0, 1.00E-0, 1.0 ATOM=Es 0.00E-0, 0.00E-0, 0.00E-0, 0.0 ATOM=Ag 0.29E-3, 0.77E-3, 0.21E-1, 0.0 ATOM=Al 0.78E-3, 0.59E-4, 0.53E-4, 0.0 ATOM=Bi 0.13E-2, 0.13E-2, 0.72E-3, 0.3632 ATOM=Ti 0.50E-3, 0.74E-3, 0.17E-3, 0.0 ATOM=V 0.51E-3, 0.74E-3, 0.42E-3, 0.0 ATOM=Cr 0.18E-3, 0.74E-3, 0.88E-3, 0.0 ATOM=Mn 0.58E-3, 0.74E-3, 0.14E-2, 0.0 ATOM=Fe 0.70E-3, 0.74E-3, 0.22E-2, 0.0 ATOM=Co 0.71E-3, 0.74E-3, 0.37E-2, 0.0 ATOM=Ni 0.83E-3, 0.74E-3, 0.59E-2, 0.0 ATOM=Cu 0.27E-3, 0.74E-3, 0.12E-1, 0.0 ATOM=La 0.29E-3, 0.21E-3, 0.76E-3, 0.22E-2 ATOM=Ce 0.31E-3, 0.21E-3, 0.94E-3, 0.22E-2 ATOM=Gd 0.43E-3, 0.21E-3, 0.94E-3, 0.21E-1 ATOM=Tb 0.36E-3, 0.21E-3, 0.94E-3, 0.29E-1 ATOM=Dy 0.31E-3, 0.21E-3, 0.94E-3, 0.37E-1 ATOM=Ho 0.27E-3, 0.21E-3, 0.94E-3, 0.46E-1 ATOM=Ge 0.15E-2, 0.75E-3, 0.19E-1, 0.0 ATOM=Ga 0.12E-2, 0.74E-3, 0.45E-3, 0.0 ATOM=In 0.10E-2, 0.77E-3, 0.94E-3, 0.0 ATOM=Pb 0.11E-2, 0.61E-3, 0.72E-3, 0.3330 ATOM=Pd 0.29E-3, 0.77E-3, 0.16E-1, 0.0 ATOM=Sb 0.14E-2, 0.16E-2, 0.76E-3, 0.0 ATOM=Si 0.10E-2, 0.17E-3, 0.53E-4, 0.0 ATOM=Sn 0.12E-2, 0.77E-3, 0.76E-3, 0.0 ATOM=Y 0.48E-3, 0.77E-3, 0.45E-3, 0.0 ATOM=Bi 0.13E-2, 0.14E-2, 0.43E-1, 0.3632 ATOM=Rh 0.23E-3, 0.77e-3, 0.12e-1, 0 ATOM=Ir 0.58e-3, 0.21e-3, 0.16e-1, 0 ATOM=Eu 0.35e-3, 0.11e-1, 0.94e-3, 0.17e-1 elk-7.2.42/utilities/xps/PaxHeaders.21776/conv.c0000644000000000000000000000013214061636521016066 xustar0030 mtime=1623670097.293100285 30 atime=1623670097.293100285 30 ctime=1623670097.293100285 elk-7.2.42/utilities/xps/conv.c0000644002504400250440000000335714061636521020133 0ustar00dewhurstdewhurst00000000000000#include #include #include #include #include #define N 100000 // Convolution with Lorentz and Fermi function, // compile with: gcc conv.c -oconv -lm // modify the N above if needed. // Use at your own risk. // Jerzy Goraus (2003) typedef struct { double x,y; } pT; pT p1[N],p2[N]; double a_lor,Ef; int cmp1(pT *t1, pT *t2) { double t=t1->x-t2->x; return (int)(2*t/fabs(t)); } inline double lor(double x) { return (1/(1+x*x*a_lor)); } inline double fermi(double x) { return 1/(1+exp((x-Ef)/0.02569)); } main (int argc, char **argv) { int m=4,i1; double *tabl=malloc(1600); FILE *f; double dE=0.4,Ef=0,DE=0.2; char *buffer=malloc(256); if (!((argc==2)||(argc==4))) { printf("\nconv: convolution with Lorentz and Fermi function\n\ conv [{ FWHM Ef }]\nfilename is xy ascii data file,\ FWHM - Full Width at Half Maximum default : 0.4eV \n \ Ef - Fermi Energy default : 0 eV n\n");exit(0); } if (argc==4) { sscanf(argv[2],"%lf",&dE); sscanf(argv[3],"%lf",&Ef); if (dE>20) {printf("%i value too high\n",m);exit(1);} }; a_lor=4/(dE*dE); srand (time (NULL)); double y,sum; int i=0,k,n1=0,n2=0; f = fopen (argv[1], "r"); if (f==NULL) { printf("can't open for reading %s\n",argv[1]); exit(1);} while (!feof(f)) { fgets(buffer,255,f); sscanf(buffer,"%lf %lf",&(p1[n1].x),&(p1[n1].y)); n1++; assert(n1; close(STR); $atcnt=0; print "\nElements : "; for ($i=0; $i<$#str; $i++) { $_=$str[$i]; if (/atoms\n/) { $i++; $_=$str[$i]; s/\s//g; ($ATCNT,$TMP)=split(/:/); } if (/spinpol/) { $i++; $_=$str[$i]; if (/true/) { $SPOL=1;} } if (/in\'/) { ($ELNAME,$TMP)=split(/\./); $_=$ELNAME; s/\'//; $ELNAME=$_; #print "\n",$ELNAME; $_=$str[$i+1]; s/\s//g; ($MULT,$TMP)=split(/:/); push @atoms, $ELNAME; print $ELNAME," (",$MULT,") "; $mtab{$ELNAME}=$MULT; $idxtab{$ELNAME}=$atidx; $atidx++; #print "|",$MULT,"|"; } } if ($SPOL ) { print "\nMagnetic case\n"; } else { print "\nNon-magnetic case\n";} #print $ATCNT; open(CRS,"./CROSEC") or die "Can't open CROSEC"; # Here enter the position of CROSEC print "\nRead CROSEC"; @crs=; close(CRS); foreach ($i=1 ; $i<@crs; $i++) { $_=$crs[$i]; if (/ATOM=/) { $A=substr($_,5); $A=~s/\s//g; } else { $CR{$A}=$_; } } print "\n"; $NDOS=0; foreach (@atoms) { $ELNAME=$_; for ($i=1; $i<=$mtab{$_}; $i++) { $fname=sprintf("PDOS_S%02d_A%04d.OUT", $idxtab{$_}, $i); print "\nRead : ",$fname ; open(pdos, $fname) or die "Can't open $fname\n"; @pdos=; close(pdos); if ($NDOS==0) { foreach (@pdos) { if (/\d/) {$NDOS++}; } $NDOS/=32; $NDOS++; #- init to 0 for ($j=0; $j<$NDOS-1; $j++) { $atw_su[$j]=0; $atw_pu[$j]=0; $atw_du[$j]=0; $atw_fu[$j]=0; $atw_sd[$j]=0; $atw_pd[$j]=0; $atw_dd[$j]=0; $atw_fd[$j]=0; $att_su[$j]=0; $att_pu[$j]=0; $att_du[$j]=0; $att_fu[$j]=0; $att_sd[$j]=0; $att_pd[$j]=0; $att_dd[$j]=0; $att_fd[$j]=0; $attc_su[$j]=0; $attc_pu[$j]=0; $attc_du[$j]=0; $attc_fu[$j]=0; $attc_sd[$j]=0; $attc_pd[$j]=0; $attc_dd[$j]=0; $attc_fd[$j]=0; } } $atfout=sprintf("_%s_%04d.dat",$ELNAME,$i); open(atpart, ">".$atfout) or die "Can't open output file $atfout\n"; if ($SPOL ) { print atpart "# spin up - s,p,d,f and spin down s,p,d,f\n"; } else { print atpart "# s, p, d, f\n";} for ($q=0; $q<$#pdos; $q++) { ($TMP,$pdosx[$q],$pdosy[$q])=split(/\s+/,$pdos[$q]); $pdosx[$q]*=$FACTOR; $pdosy[$q]/=$FACTOR; } for ($j=0; $j<$NDOS-1; $j++) { $at_su[$j]=$pdosy[$j]; if ($SPOL ) {$at_sd[$j]=$pdosy[$j+16*$NDOS];} $at_pu[$j]=0; $at_pd[$j]=0; $at_du[$j]=0; $at_dd[$j]=0; $at_fu[$j]=0; $at_fd[$j]=0; for ($q=1; $q<4; $q++) { $at_pu[$j]+=$pdosy[$j+$q*$NDOS]; if ($SPOL ) {$at_pd[$j]+=$pdosy[$j+16*$NDOS+$q*$NDOS];} } for ($q=4; $q<9; $q++) { $at_du[$j]+=$pdosy[$j+$q*$NDOS]; if ($SPOL ) {$at_dd[$j]+=$pdosy[$j+16*$NDOS+$q*$NDOS];} } for ($q=9; $q<16; $q++) { $at_fu[$j]+=$pdosy[$j+$q*$NDOS]; if ($SPOL ) {$at_fd[$j]+=$pdosy[$j+16*$NDOS+$q*$NDOS];} } print atpart $pdosx[$j], " ",$at_su[$j]," ",$at_pu[$j]," ",$at_du[$j]," ",$at_fu[$j]; if ($SPOL ) { print atpart " ",$at_sd[$j]," ",$at_pd[$j]," ",$at_dd[$j]," ",$at_fd[$j],"\n";} else {print atpart "\n";} $atw_su[$j]+=$at_su[$j]; $atw_pu[$j]+=$at_pu[$j]; $atw_du[$j]+=$at_du[$j]; $atw_fu[$j]+=$at_fu[$j]; $atw_sd[$j]+=$at_sd[$j]; $atw_pd[$j]+=$at_pd[$j]; $atw_dd[$j]+=$at_dd[$j]; $atw_fd[$j]+=$at_fd[$j]; } close atpart; print "\nWritten ",$atfout; #-- $gatfout=sprintf("_g_%s_%04d",$ELNAME,$i); open(GNU,">".$gatfout.".gnu") or die "can't open $gatfout\n"; print GNU $TERM,"\n",$OPT,"\n"; print GNU "set output \"$gatfout.$SUF\"\n"; print GNU "set xlabel \"Eb [eV]\"\n"; print GNU "set ylabel \"DOS [st/eV f.u.]\"\n"; print GNU "set title \"$ELNAME - $i\"\n"; print GNU "plot \"$atfout\" using 1:2 smooth uniq t 's' "; printf GNU ", \"$atfout\" using 1:3 smooth uniq t \'p\' "; printf GNU ", \"$atfout\" using 1:4 smooth uniq t \'d\' "; printf GNU ", \"$atfout\" using 1:5 smooth uniq t \'f\' "; if ($SPOL ) { print GNU ", \"$atfout\" using 1:6 smooth uniq t \'s\' "; print GNU ", \"$atfout\" using 1:7 smooth uniq t \'p\' "; print GNU ", \"$atfout\" using 1:8 smooth uniq t \'d\' "; print GNU ", \"$atfout\" using 1:9 smooth uniq t \'f\' "; } close(GNU); print "\nWritten ",$gatfout,".gnu"; #-- } $atwfout=sprintf("_%s.dat",$ELNAME); #at - atomic DOS, atw - given specie dos, att - total dos , attc - total dos with crossection open(atwpart, ">".$atwfout) or die "Can't open output file $atwfout \n"; if ($SPOL ) { print atwpart "# spin up - s,p,d,f and spin down s,p,d,f\n"; } else { print atwpart "# s, p, d, f\n";} if ($CR{$ELNAME} ne "") { ($Ks,$Kp,$Kd,$Kf)=split(/\,/,$CR{$ELNAME}); } else {$Ks=$Kp=$Kd=$Kf=0; print "\n----------------- No $ELNAME in CROSEC, Using 0 as crossection\n";}; for ($j=0; $j<$NDOS-1; $j++) { $att_su[$j]+=$atw_su[$j]; $att_pu[$j]+=$atw_pu[$j]; $att_du[$j]+=$atw_du[$j]; $att_fu[$j]+=$atw_fu[$j]; $att_sd[$j]+=$atw_sd[$j]; $att_pd[$j]+=$atw_pd[$j]; $att_dd[$j]+=$atw_dd[$j]; $att_fd[$j]+=$atw_fd[$j]; $attc_su[$j]+=$atw_su[$j]*$Ks; $attc_pu[$j]+=$atw_pu[$j]*$Kp; $attc_du[$j]+=$atw_du[$j]*$Kd; $attc_fu[$j]+=$atw_fu[$j]*$Kf; $attc_sd[$j]+=$atw_sd[$j]*$Ks; $attc_pd[$j]+=$atw_pd[$j]*$Kp; $attc_dd[$j]+=$atw_dd[$j]*$Kd; $attc_fd[$j]+=$atw_fd[$j]*$Kf; print atwpart $pdosx[$j], " ",$atw_su[$j]," ",$atw_pu[$j]," ",$atw_du[$j]," ",$atw_fu[$j]; if ($SPOL ) { print atwpart " ",$atw_sd[$j]," ",$atw_pd[$j]," ",$atw_dd[$j]," ",$atw_fd[$j],"\n";} else {print atwpart "\n";} } close atwpart; #- $gatwfout=sprintf("_g_%s",$ELNAME); open(GNU,">".$gatwfout.".gnu") or die "can't open $gatwfout\n"; print GNU $TERM,"\n",$OPT,"\n"; print GNU "set output \"$gatwfout.$SUF\"\n"; print GNU "set xlabel \"Eb [eV]\"\n"; print GNU "set ylabel \"DOS [st/eV f.u.]\"\n"; print GNU "set title \"$ELNAME \"\n"; print GNU "plot \"$atwfout\" using 1:2 smooth uniq t 's' "; printf GNU ", \"$atwfout\" using 1:3 smooth uniq t \'p\' "; printf GNU ", \"$atwfout\" using 1:4 smooth uniq t \'d\' "; printf GNU ", \"$atwfout\" using 1:5 smooth uniq t \'f\' "; if ($SPOL ) { print GNU ", \"$atwfout\" using 1:6 smooth uniq t \'s\' "; print GNU ", \"$atwfout\" using 1:7 smooth uniq t \'p\' "; print GNU ", \"$atwfout\" using 1:8 smooth uniq t \'d\' "; print GNU ", \"$atwfout\" using 1:9 smooth uniq t \'f\' "; } close(GNU); print "\nWritten ",$gatwfout,".gnu"; #- print "\nWritten ",$atwfout; for ($j=0; $j<$NDOS-1; $j++) { $atw_su[$j]=0; $atw_pu[$j]=0; $atw_du[$j]=0; $atw_fu[$j]=0; $atw_sd[$j]=0; $atw_pd[$j]=0; $atw_dd[$j]=0; $atw_fd[$j]=0; } } open(att, ">_TDOS.dat") or die "Can't open output file TDOS.dat \n"; open(attc, ">_cTDOS.dat") or die "Can't open output file cTDOS.dat \n"; for ($j=0; $j<$NDOS-1; $j++) { $u=$att_su[$j]+$att_pu[$j]+$att_du[$j]+$att_fu[$j]; $d=$att_sd[$j]+$att_pd[$j]+$att_dd[$j]+$att_fd[$j]; $uc=$attc_su[$j]+$attc_pu[$j]+$attc_du[$j]+$attc_fu[$j]; $dc=$attc_sd[$j]+$attc_pd[$j]+$attc_dd[$j]+$attc_fd[$j]; if ($SPOL ) { print att $pdosx[$j], " ",$u-$d," ",$u," ",$d,"\n"; print attc $pdosx[$j], " ",$uc-$dc," ",$uc," ",$dc,"\n"; } else { print att $pdosx[$j], " ",$u,"\n"; print attc $pdosx[$j], " ",$u,"\n"; } } close att; print "\nWritten _TDOS.dat"; close attc; print "\nWritten _cTDOS.dat"; print "\n"; elk-7.2.42/PaxHeaders.21776/COPYING0000644000000000000000000000013214061636521013163 xustar0030 mtime=1623670097.303100275 30 atime=1623670097.302100276 30 ctime=1623670097.303100275 elk-7.2.42/COPYING0000644002504400250440000012356414061636521015233 0ustar00dewhurstdewhurst00000000000000 GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. 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The Corresponding Source for a work in source code form is that same work. 2. Basic Permissions. All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited permission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. 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If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own removal in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. 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All other non-permissive additional terms are considered "further restrictions" within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way. 8. 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Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, you do not qualify to receive new licenses for the same material under section 10. 9. Acceptance Not Required for Having Copies. You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so. 10. Automatic Licensing of Downstream Recipients. Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An "entity transaction" is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party's predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it. 11. Patents. A "contributor" is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor's "contributor version". A contributor's "essential patent claims" are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, "control" includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contributor's essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a "patent license" is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To "grant" such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. "Knowingly relying" means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient's use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is "discriminatory" if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law. 12. No Surrender of Others' Freedom. If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program. 13. Use with the GNU Affero General Public License. Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such. 14. Revised Versions of this License. The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License "or any later version" applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version. 15. Disclaimer of Warranty. THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 16. Limitation of Liability. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. 17. Interpretation of Sections 15 and 16. If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS How to Apply These Terms to Your New Programs If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. Copyright (C) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: Copyright (C) This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see . The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . -------------------------------------------------------------------------------- GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. This version of the GNU Lesser General Public License incorporates the terms and conditions of version 3 of the GNU General Public License, supplemented by the additional permissions listed below. 0. Additional Definitions. As used herein, "this License" refers to version 3 of the GNU Lesser General Public License, and the "GNU GPL" refers to version 3 of the GNU General Public License. "The Library" refers to a covered work governed by this License, other than an Application or a Combined Work as defined below. An "Application" is any work that makes use of an interface provided by the Library, but which is not otherwise based on the Library. Defining a subclass of a class defined by the Library is deemed a mode of using an interface provided by the Library. A "Combined Work" is a work produced by combining or linking an Application with the Library. The particular version of the Library with which the Combined Work was made is also called the "Linked Version". The "Minimal Corresponding Source" for a Combined Work means the Corresponding Source for the Combined Work, excluding any source code for portions of the Combined Work that, considered in isolation, are based on the Application, and not on the Linked Version. The "Corresponding Application Code" for a Combined Work means the object code and/or source code for the Application, including any data and utility programs needed for reproducing the Combined Work from the Application, but excluding the System Libraries of the Combined Work. 1. Exception to Section 3 of the GNU GPL. You may convey a covered work under sections 3 and 4 of this License without being bound by section 3 of the GNU GPL. 2. Conveying Modified Versions. If you modify a copy of the Library, and, in your modifications, a facility refers to a function or data to be supplied by an Application that uses the facility (other than as an argument passed when the facility is invoked), then you may convey a copy of the modified version: a) under this License, provided that you make a good faith effort to ensure that, in the event an Application does not supply the function or data, the facility still operates, and performs whatever part of its purpose remains meaningful, or b) under the GNU GPL, with none of the additional permissions of this License applicable to that copy. 3. Object Code Incorporating Material from Library Header Files. The object code form of an Application may incorporate material from a header file that is part of the Library. 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Each version is given a distinguishing version number. If the Library as you received it specifies that a certain numbered version of the GNU Lesser General Public License "or any later version" applies to it, you have the option of following the terms and conditions either of that published version or of any later version published by the Free Software Foundation. If the Library as you received it does not specify a version number of the GNU Lesser General Public License, you may choose any version of the GNU Lesser General Public License ever published by the Free Software Foundation. If the Library as you received it specifies that a proxy can decide whether future versions of the GNU Lesser General Public License shall apply, that proxy's public statement of acceptance of any version is permanent authorization for you to choose that version for the Library. elk-7.2.42/PaxHeaders.21776/README0000644000000000000000000000013214061636521013010 xustar0030 mtime=1623670097.310100269 30 atime=1623670097.310100269 30 ctime=1623670097.310100269 elk-7.2.42/README0000644002504400250440000000377014061636521015054 0ustar00dewhurstdewhurst00000000000000 +------------------------------+ | The Elk FP-LAPW Code | +------------------------------+ This code is distributed under the terms of the GNU General Public License. See the file COPYING for license details. Elk is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. Elk is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with Elk. If not, see http://www.gnu.org/licenses/. Elk can be compiled by first running "./setup" in this directory followed by "make all". This will compile the main code as well as several auxiliary programs. For optimal performance we strongly recommend that you tune the Fortran compiler options in the file "make.inc" and use machine-optimised BLAS/LAPACK libraries. Setting the OpenMP and MPI options of your compiler will enable Elk to run in parallel mode on multiprocessor systems and clusters. A test suite is available: entering "make test" will check the output of your executable against a standard set. This may take some time to complete. Auxiliary programs include "spacegroup" for producing crystal geometries from spacegroup data, and "eos" for fitting equations of state to energy-volume data. Elk is updated regularly with new features and bug fixes. Features not listed as "experimental" may be used for production but, as with any code, please check the consistency of your results carefully. -------------------------------------------------------------------------------- J. K. Dewhurst, S. Sharma L. Nordstrom, F. Cricchio, O. Granas E. K. U. Gross elk-7.2.42/PaxHeaders.21776/release_notes.txt0000644000000000000000000000013014061636521015517 xustar0029 mtime=1623670097.31910026 30 atime=1623670097.317100262 29 ctime=1623670097.31910026 elk-7.2.42/release_notes.txt0000644002504400250440000013310114061636521017555 0ustar00dewhurstdewhurst00000000000000elk-7.2.42 -added new RAM disk feature which allows Elk to store direct-access files in memory and can dramatically speed up calculations; enable this by setting 'ramdisk' to .true. in elk.in -many optimisations throughout the code -fixed an issue with the scissors operator in optical response code (task=320, 330, 331) for materials which are nearly metallic; thanks to Peter Elliott for pointing this out -further improved the electron-phonon mean-field code -added variables 'scalex', 'scaley' and 'scalez' to the input file; these allow scaling of the unit cell in the Cartesian directions elk-7.1.14 -optimised the second-variational procedure by changing the muffin-tin dot products to single-precision arithmetic; this speeds up this step by at least a factor of two for large systems without losing overall precision or stability -removed 'mixpack', 'phmixpack' and 'mixpacku' routines; Kohn-Sham potentials and fields are now stored in a single array accessed by pointer arrays; this removes the need for packing before and unpacking after mixing -increased speed of direct access reads by removing unnecessary 'close' statements -added an example for the ultra long-range method; see the input file in elk/examples/ultra-long-range/Cr-SDW/ -changed the Wannier90 .win file to improve the wannierisation convergence rate -fixed several bugs in the electron-phonon mean-field method -updated BLAS and LAPACK to version 3.9.0 -minor improvements and bug fixes elk-7.0.12 -Chung-Yu Wang added electron-phonon mean-field theory; this is a new method and still highly experimental -Alyn James wrote an interface for Elk to the DMFT code TRIQS; this interface is maintained in a separate branch of the Elk code: https://github.com/AlynJ/Elk_interface-TRIQS -fixed serious problem with DFT+U for dftu=3 (interpolation of FLL and AFM); this bug was introduced some time ago; we recommend that you check any previous calculations which use dftu=3 -lots of optimisations throughout the code -further improved Ehrenfest dynamics -added the calculation of Born effective charges using Ehrenfest dynamics (task=478); this is intended as a test for the method; Born effective charges are more accurately calculated with the King-Smith and Vanderbilt method (task=208) -Pietro Bonfa found and fixed several problems with the calculation of Mössbauer hyperfine fields -PB also added a new Mössbauer example: antiferromagnetic NiF2; see the examples/Mossbauer/NiF2 directory -Ronald Cohen fixed a bug in iso-volumetric lattice optimisation -RC also discovered a problem with the Wu-Cohen '06 GGA functional which has now been fixed -RC also suggested an efficiency improvement to the non-linear optics code -added tests for non-linear optics -Antonio Sanna helped fix a bug with TD forces -Karel Carva discovered that lmaxo should be at least 7 for phonopy calculations -change the default ntswrite from 10 to 500 time steps in order to reduce I/O -confirmed compatibility with Libxc version 5.1.0 -Further improved the ultra long-range code; the method has now been published: T. Müller, S. Sharma, E. K. U. Gross, and J. K. Dewhurst, Phys. Rev. Lett. 125, 256402 (2020). elk-6.8.4 -Born effective charges using the method of R. D. King-Smith and David Vanderbilt, Phys. Rev. B 47, 1651(R) (1993) are now available; see the directory elk/examples/Born-effective-charge -added Ehrenfest dynamics to the code; see the directory elk/examples/TDDFT-time-evolution/FeCo-Ehrenfest (highly experimental) -upgraded code to be compatible with Libxc version 5; note changes to the make.inc file -the Libxc SCAN functional no longer works with Elk, the regularised version of A. P. Bartók and J. R. Yates, J. Chem. Phys. 150, 161101 (2019) works and should be used instead; see the meta-GGA examples -Aldo Romero and his group interfaced PyProcar to Elk and confirmed that it worked with non-collinear magnetism; PyProcar is a robust, open-source Python library used for pre- and post-processing of the electronic structure data from DFT calculations -implemented a great many optimisations throughout the entire code; more aggressive use of the stack instead of the heap, this may require the user to increase the stack space -added the incomplete basis set (IBS) correction to forces from time-dependent vector potential, A(t) -fixed bug related to lattice optimisation with non-symmorphic symmetries thanks to Andrew Shyichuk and Jack Whaley-Baldwin -added several new tests, including one for the stress tensor -updated physical constants to CODATA 2018 -fixed wavefunction and STM plotting thanks to Andrew Shyichuk -fixed bug in GW band structure code thanks to Antik Sihi -fixed problem with fixed tensor moment calculations -fixed problem in TDDFT real-time restart thanks to Peter Elliott -Peter Elliott and JKD also added Maxwell's equations for the macroscopic induced vector potential -updated and improved the ultra long-range code -forces are now written during a TDDFT run every 'ntsforce' time steps -matrix sizes larger than those addressable with four byte integers can now be used with BSE and MPI -Hartree-Fock information is now written to HF_INFO.OUT rather than INFO.OUT -parallelised the Brillouin zone integration (brzint) which considerably speeds up DOS calculations -modified how the potential of the optimised effective potential (OEP) iteration scheme is initialised -removed obsolete command from ProTex Perl script -added tests for Libxc and MPI; run 'make test-libxc' and 'make test-MPI' respectively, or 'make test-all' to test everything -fixed problem with hybrid functionals introduced a few versions back; also added a test for hybrids elk-6.3.2 -very large speedup of the first-variational Hamiltonian and overlap matrix setup; this is particularly apparent for large systems -made all of the numerical radial integrals much more efficient by storing the spline integration weights; this speeds up most of the code -switched radial integral infinitesimal from 1/3 d(r^3) to r^2dr; this improves numerical accuracy and returns to the convention of version 5.2.14 -added full (l,m) and spin characters for plotting the band structure with so-called 'fat bands'; these are performed with new tasks 22 and 23; thanks to Jagdish Kumar for the suggestion -Jagdish Kumar also fixed a problem with the phonon thermodynamic quantities which had an unnecessary prefactor of the number of atoms; see here -fixed a problem with occurs with constant electric fields (when efieldc is made finite) and crystals with non-symmorphic symmetries -Michael Fechner improved the fixed spin moment code by removing the requirement that unspecified muffin-tin fixed moments are checked for symmetry compliance -added 1D plotting of the magnetisation density, exchange-correlation magnetic field, electric field and m(r) x B_xc(r) with tasks 71, 81, 141 and 151, respectively -added density, potential and magnetisation plotting for ultra long-range calculations with tasks 731, 732, 733, 741, 742, 743, 771, 772 and 773 -constant electric fields can now be included in ultra long-range calculations; this can be done by setting the vector efielduc -an arbitrary external Coulomb potential can now be read in for use in the ultra long-range calculations; set trdvclr=.true. and the potential is read from the file VCLR.OUT elk-6.2.8 -Wannier90 interface added thanks to Arsenii Gerasimov, Yaroslav Kvashnin and Lars Nordström; and based on the original work of Duc Le and Jon Lafuente Bartolomé -the Wannier90 interface can be used to produce Hartree-Fock band structures (see example) and also works with non-collinear spin-polarised calculations -ultra long-range (ULR) calculations now available thanks to Tristan Müller (experimental) -self-consistent density GW calculations now available thanks to Arkardy Davydov and others; this is a new method still undergoing testing and is thus experimental -GW density matrix can now be written to file with task=640; the natural orbitals and occupation numbers are written to EVECSV.OUT and OCCSV.OUT, respectively -classical spin and orbital dipole magnetic fields can now be calculated and added to the Kohn-Sham field (set tbdip=.true. and tcden=.true.) -extensive optimisations throughout the code: every task should be noticeably faster -improved OpenMP parallelism -improved accuracy of the Mössbauer hyperfine field calculations -added spin and orbital dipole terms to the hyperfine field -updated constants and conversion factors to CODATA 2018 -added Andrew Shyichuk's improved check for requirement of the Tran-Blaha constant -variational meta-GGA functionals (like SCAN) now work with forces -added Roger Mason's fix to make FFTW thread-safe -René Wirnata has created the Elk Optics Analyzer that helps to visualize and post-process optics output data -regenerated species files with lower order local-orbitals -improved k-point convergence of the electron-phonon coupling constant for calculation of superconducting properties -upgraded to LAPACK 3.8.0 -changed default 'radkpt' from 30 to 40 -many minor improvements and bug fixes elk-5.2.14 -Youzhao Lan found a bug which prevented potential-only meta-GGA functionals (like Tran-Blaha) from being used; this has now been fixed -fixed meta-GGA atomic forces; thanks to Michael Porer for pointing out the problem -Eike Schwier discovered a conflicting MPI variable name and also reported that the code crashes when generating species files; both problems are now fixed -linear-response TDDFT off-diagonal components for q=0 now available (experimental) elk-5.2.10 -GW code is much improved and also faster; the Pade analytic continuation of the self-energy is more stable and reliable -OpenMP parallelism greatly improved; nesting is now permanently switched on and the number of threads is controlled by Elk itself; this should improve scaling on hundreds of CPU cores; please report any problems you have with parallelism on the forum -GW spectral function band-structures are now possible; this feature is still experimental -Yaroslav Kvashnin and Lars Nordström found and fixed a bug in the fixed spin moment direction code -fully variational meta-GGA (in the generalised Kohn-Sham sense) is now running in conjunction with Libxc (experimental) -variational meta-GGA works only with collinear magnetism; let us know if you have an idea on how to extend it to the non-collinear case -Elk now interfaces to Libxc version 4 -- please update your library from version 2 -gauge invariant current density plots in 2D and 3D now available (tasks 372 and 373) -the entire code is much faster, particularly advanced methods like Hartree-Fock, RDMFT, BSE and GW; this is in part due to a 'coarse' Fourier grid for the wavefunctions -the lmaxi has been changed from 3 to 1 and several optimisations based on this have been hard-coded into Elk -Broyden mixing (mixtype=3) is now the default; magnetic calculations will now converge using a small bfieldc or bfcmt thanks to an improved magnetisation initialisation scheme -real-time TDDFT calculations no longer require 'nosym=.true.' but rather 'tshift=.false.' and are much faster as a consequence -2D and 3D current density plotting now available with tasks 272 and 273, respectively -task 480 generates a linear-response dielectric function calculation from a time-evolution run -lots of optimisations everywhere in the code, including additional OpenMP directives -lots of minor improvements and bug fixes -cleaned up and improved examples -several direct access files are not closed after reading which speeds up file I/O; please report any problems with this on the forum elk-4.3.6 -GW approximation now available thanks to Arkadiy Davydov; this is a finite temperature Matsubara implementation; currently it only calculates the k-point resolved spectral function on the real axis; see the 'examples/GW' directory (experimental) -the GW approximation works with spin-orbit coupling and non-collinear magnetism; it can also be run after the optimized effective potential (OEP) method -significant optimisations for Hartree-Fock, OEP, RDMFT and BSE -fixed an minor bug in BSE -greatly improved the stability of lattice optimisation; also reduced the variable 'deltast' to 0.001 -improved the convergence of the electron-phonon coupling parameter with respect to k-points; thanks to Xianxin Wu for the careful testing -removed the variable 'epseph' which determined the sampling window for electron-phonon coupling -added new automatic test for TDDFT time-evolution -upgraded to LAPACK 3.7.0 -Elk now uses the LAPACK routine zheevd for diagonalisation which is faster than zheev -changed the variable 'rstsf' to 'ssxc' -the smearing width 'swidth' can now be set with temperature in kelvin using the variable 'tempk' elk-4.0.15 -changed muffin-tin functions to a 'packed' convention; this improves the memory efficiency and speed for the whole code; completely backward and forward compatible -Michael Fechner found a serious bug in DFT+U which has now been fixed; may affect systems with atoms to which DFT+U is applied and which have symmetric equivalents; MF added to list of contributors -fixed a problem with the laser pulse power density plot (AFPDT.OUT) thanks to Peter Elliot and Tristan Mueller -added the ability to randomize the orbitals at the start of a time-evolution run; use the variable 'rndevt0' to set the random amplitude -improved the accuracy of the Hellmann-Feynman force on the atoms; this also improves the supercell phonon calculations -added the reduced Stoner theory (RST) modification to the exchange-correlation functionals, see: L. Ortenzi, I. I. Mazin, P. Blaha, and L. Boeri, Phys. Rev. B 86, 064437 (2012); use the parameter `rstsf´ to adjust the spin scaling -removed the Pulay mixer (mixtype=2) as it was consistently inferior to Broyden -changed the variables 'lmaxinr' and 'lmaxvr' to 'lmaxi' and 'lmaxo', respectively; the old variables still work in elk.in elk-3.3.15 -lots of optimisations of both speed and memory; many tasks should be noticeably faster -added new 'robust adaptive mixer' (mixtype=4) which should be able to converge almost anything; there are no mixing parameters for this mixer; useful for materials searches when you have to be guaranteed convergence; slower to converge than the default mixing and Broyden mixing -added missing term to DFPT phonons corresponding to the first-order change in occupancies and the Fermi energy for q=0; the phonon dispersion for MgB2 is now in excellent agreement with experiment and previous calculations -the electron-phonon coupling code was greatly improved; produces very good coupling constants for Al, Nb, Pb and MgB2; all of which are in the 'examples/phonons-superconductivity' directory -new variable 'epseph' controls the Fermi surface sampling of the electron-phonon coupling matrix elements -Markus Meinert created a script for calculating optical constants from the diagonal components of the dielectric tensor; it calculates the complex refractive index, reflectivity, absorption coefficient and EELS spectrum; available in the utilities directory -real-time TDDFT now outputs a time-dependent DOS and effective temperature at each time step -setting 'uhighq=.true.' results in an ultra-high-quality calculation; when you absolutely have to have the best elk-3.1.12 -Important: fixed an inaccuracy in the scalar relativistic part of the code which has existed for around 12 years; this may slightly affect calculations of heavy elements; special thanks to Stefaan Cottenier, José A. Flores Livas and Marcin Dulak for the extensive calculations -real-time evolution now works with DFT+U (experimental) -added 'ramp' vector potential to time evolution code; this can simulate constant and constantly increasing electric fields; see manual for details; see the example Si-ramp -lots of optimisations everywhere: code should be noticeably faster -José made some changes to the 'highq' and 'vhighq' options -fixed bug with non-collinear optimised effective potential (OEP) -new task (150) writes out the Kohn-Sham-Dirac eigenvalues of the atomic species -SS added two new f_xc kernels: single iteration bootstrap (fxctype=211) and revised bootstrap (RBO) (fxctype=212), see S. Rigamonti, et al., Phys. Rev. Lett. 114, 146402; added two examples: Ne-RBO and LiF-RBO -improved the accuracy of the magnetic anisotropy energy (MAE) calculation by rotating the spherical coverings of the spherical harmonic transform; thanks to James Glasbrenner for testing -David Ernsting found and fixed a bug in the Compton interpolation routine -improved the stability of structural optimisation -removed the smoothing option from the exchange-correlation magnetic field source projection routine -the number of first-variational states for magnetic systems was twice as large as it needed to be: now fixed -improved the vim syntax highlighting generator; run 'make vim' again -organised the examples into categories -minor bug fixes and improvements -note for developers: changed some of the variable names related to atomic species (purely cosmetic) elk-3.0.18 -fixed electron-phonon coupling again; thanks to Karel Carva and Elie Moujaes for the careful testing and discussion -DFPT phonons now work with MPI -SS added the 'single-iteration bootstrap kernel' for linear optics calculations; this is selected with fxctype=211; see the example 'Ar-bootstrap-single' -SS fixed a problem with RDMFT which had appeared in recent versions -SS made minor changes to the non-linear optics code -Important: fixed problem with the option 'cmagz' for forcing spin-orbit calculations to be collinear; this may affect MAE calculations; thanks to Martin Gmitra for finding this and the careful testing -Important: fixed a problem with the magnetisation directions selected for MAE calculations -reworked the 'ncgga' option for non-collinear GGA calculations; should be much more reliable now -several important optimisations; the Hamiltonian matrix setup and density symmetrisation are now faster -magnetic anisotropy energy (MAE) calculation now outputs the direction vectors; thanks to Galya Madzharova and Yu-ichiro Matsushita for the suggestion -added option 'vhighq' for very high quality calculations;see example 'Os-Delta' -'highq' and 'vhighq' options now write out the parameters which are changed -increased default 'lmaxmat' from 6 to 7 -added new option 'nxlo'; this adds extra local-orbitals to the species in order to make the APW functions smoother; this can make calculations, particularly of excited state properties, more accurate -syntax highlighting now available for the vim editor; just run 'make vim' and highlighting will be enabled elk-3.0.4 -real-time propagation for solids now available thanks to the considerable efforts of Kevin Krieger over the past three years; see the example 'Ni-laser-pulse'; this feature is highly experimental -1D, 2D and 3D integrated electron momentum density (EMD) plots now available thanks to David Ernsting and Stephen Dugdale; these plots can be compared directly to Compton scattering profiles; see the examples 'Li-Compton' and 'Ni-Compton'; still experimental -electron-phonon coupling has now been fixed and is also available for linear-response phonons -large number of optimizations made throughout code -code is more memory efficient in many areas -Arkardy Davydov found a bug in OpenMP nested parallelism for BSE which has now been fixed -fixed bug in magnetic anisotropy energy (MAE) calculation found by José A. Flores Livas -added option for automatically converting species from APW+l.o. to LAPW; see option 'nxapwlo' in manual -greatly improved unit cell optimisation algorithm; now should be very stable; see example 'Ge-lattice-opt' -Markus Meinert updated his 'blocks2columns.py' python code which should now work correctly with EPSILON_xx.OUT files -modified the 'highq' defaults thanks to testest performed by Don Hamann described here -full charge and spin response function can be written to file using task=331 -supercell phonons calculation now work with MPI -removed use of OpenMP ATOMIC directive because of bug in ifort version 11 elk-2.3.22 -Lars Nordström, Francesco Cricchio and JKD added fixed tensor moment (FTM) calculations (experimental) -LN made changes to the mixer routine which makes restarts smoother -the Hamiltonian is now made real for systems with inversion symmetry; this was removed in the previous release because of a bug; the FV step is now up to four times faster -fixed problem with symmetry breaking of tetragonal systems during lattice optimisation pointed out by various users -further improved and stabilised lattice optimisation -fixed a long-standing bug related to electron-phonon coupling pointed out by Matthieu Verstraete and Ryotaro Arita -fixed a problem with electron-phonon coupling introduced in a previous version, discovered by user 'wuhuagumu' and Heung-Sik Kim -TDDFT reponse code for both charge and magnetism has been made faster and more memory efficient -creating a STOP file in the running directory now cleanly stops a structural optimisation run; as requested by James Mudd -problem with nested OpenMP has now been fixed -more OpenMP parallel loops have been added -extended the use of BLAS throughout the code -fixed bug which affected the running of task=120 -removed the 'frozencr' option for the moment because the core energy was incorrectly calculated; this will be restored in a later release -various optimisations and minor bug fixes elk-2.3.16 -DFT+U now works with multiple entries per atom; every mention of LDA+U has now changed to DFT+U to reflect the generality of the method, and to give it an air of respectibility; for example, the block 'lda+u' is now 'dft+u'; old input files will still work fine -greatly improved the magnetic anisotropy energy (MAE) calculations, thanks to suggestions by various users; the crystal is now rotated instead of the magnetisation direction -fractional atomic species can now be generated on the fly using the 'fspecies' block; see the example 'fractional-species'; note that the atomic mass is only an estimate in these species files; this is useful for the virtual crystal approximation (VCA) -spin-orbit coupling can now be used with strictly collinear calculations by using 'cmagz=.true.'; this will speed up the calculation considerably; use only when the system is genuinely collinear -unstable non-collinear GGA calculations can now be stabilised by setting 'ncgga=.true.' -improved the speed and stability of the lattice vector optimisation; thanks to forum discussions regarding BaTiO3 -added the lattice optimisation of BaTiO3 to the examples directory; thanks to David Tompsett -geometry optimisation should now work fine with MPI -added highly converged osmium example 'Os-convergence' thanks to a lengthy discussion on the forum started by Marcin Dulak; also increased the value of 'lmaxmat' for the 'highq' option thanks to Marcin's careful testing -Important: greatly improved the code setup and compilation thanks to suggestions by Marcin Dulak; all compiler options are now in the file 'elk/make.inc'; the Makefile in 'elk/src' no longer requires modification -new variable 'rotavec' available in elk.in; this is a rotation specified in axis-angle convention which allows the rotation of the crystal axes -thanks go to Rich Martin and collaborator Wen for useful testing and suggestions -improved the DFPT phonon calculations and added the example 'Nb-phonon-DFPT' -decreased the chance of accidentally triggering the convergence indicator in the self-consistent loop thanks to a suggestion from Markus Meinert -fixed problem with the routine 'nonlinopt', pointed out by user Sabrina and Koichi Kitahara -improved the OpenMP efficiency in parts by using '$OMP ATOMIC' instead of '$OMP CRITICAL' -changed the names of various internal subroutines; for example 'seceqnfv' is now 'eveqnfv' -thanks go to Igor Mazin, Konrad Bussmann and James Glasbrenner for some very useful improvments -fixed problem with species generation and MPI pointed out by Marcin Dulak -fixed problem with use of Fortran 'APPEND' flag thanks to user Alaska -updated the fundamental constants and conversion factors to CODATA 2008 recommended values -Important: updated code for compatibility with Libxc version 2.2.0; see the manual and note the change in compilation instructions -fixed problem with the routine 'energyfdu' which affected DFT+U calculations with 'inpdftu=4' (input of Yukawa screening length) -Important: temporarily switched of the conversion of the Hamiltonian to a real symmetric problem because of possible bug; the only effect of this is that the code is slower for systems with inversion symmetry; this will be fixed in the next release -minor bug fixes and optimisations elk-2.2.10 -fixed problem reported by Sonu Sharma and Michael Fechner with calculation of expectation values L, S and J -slightly improved the magnetic anisotropy energy (MAE) calculation -added new variable 'socscf' which scales the spin-orbit interaction term in the Hamiltonian; this allows calculation by interpolation of the MAE for cases where the MAE is small -added new variables to VARIABLES.OUT elk-2.2.9 -fixed problem with fixed spin moment (FSM) calculations pointed out by Jagdish Kumar -added new output file VARIABLES.OUT; this is for developers wanting to interface their codes to Elk; it contains most of the useful variables required for reading the Elk binary files; if you would like a variable added then just send me a mail; enabled when 'wrtvars' is set to .true. -minor cosmetic changes elk-2.2.8 -Important: fixed serious bug discovered by Jan Balluff and Markus Meinert which produced erroneous magnetic moments with GGA; this only affects version 2.2.5; sorry about that -even more substantial speed-ups for most parts of the code -fixed MPI problem with the magnetic anisotropy energy (MAE) routine reported by Konrad Bussmann and José A. Flores-Livas -minor bug fixes and improvements elk-2.2.5 -dramatic speed-up for most parts of the code thanks to some (fairly obvious) optimisations -greatly improved lattice vector optimisation -automatic determination of the magnetic anisotropy energy (MAE) with 'task=28' (experimental); see the example 'FeCo-MAE' -the variable 'nempty' is now a real number; see manual entry -magnitude of total magnetisation vector written to MOMENTM.OUT -improved the species files -made the linearisation energy search more reliable -reduced the annoying 'linearisation energy not found' warning elk-2.2.1 -added full structural optimisation; setting 'latvopt=1' performs unconstrained optimisation of the lattice vectors; 'latvopt=2' performs iso-volumetric optimisation; see the example 'MgB2-lattice-opt' -minor bug fixes and optimisations -all tests should now report 'Passed' elk-2.1.25 -fixed several problems with the previous (beta) release; thanks to Markus Meinert for the exhaustive checking -magnetic hyperfine fields are now correctly calculated thanks to MM -added missing items to the manual -added the example 'Si-phonon-DFPT' -thanks to Kari Ruotsalainen, Aleksay Golovchan and Vladimir Nazarov for pointing out bugs in 2.1.22 - now fixed -added estimation of direct gap to INFO.OUT; thanks to user Sean for the idea -this is the version that will be used for the Elk Turorial -see you in Lausanne! elk-2.1.22 (beta) -Important: this is a beta version and should not be used for production work; a production release will be made in a few weeks -Important: this version is not backwards compatible; calculations will have to be converged from scratch -density functional perturbation theory (DFPT) phonons now available; only for spin-unpolarised calculations at the moment; spin-polarisation will be added for the next release; use with task=205; still experimental and generates incorrect results for certain symmetries - we're still working on this; see the example 'Al-phonon-DFPT' -full frequency-dependent magnetic response function now available; works with non-collinear magnetism, etc.; use task=330; see example 'Ni-magnetic-response' -iterative diagonalisation greatly improved; now uses the method of P. Blaha, et al., J. Comp. Phys. 229, p453 (2010) -upgraded code to handle libxc version 2 -hybrid functionals should now work with libxc (experimental) -upgraded LAPACK to version 3.4.2 -block name dos changed to wplot; changed variable 'nwdos' to 'nwplot' -variable 'gmaxrpa' changed to 'gmaxrf'; this is the response function G-vector cut-off -BSE and TDDFT now faster, more accurate and memory efficient; thanks to M. Meinert for discussions -task 188 changed to 320 -reintroduced the variables 'lmaxinr' and 'fracinr'; this improves stability -lots of optimisations -added more MPI parallelism -various minor bug fixes -conduction state local-orbitals can now be switched on; use 'lorbcnd=.true.'; this can improve both ground-state and response function calculations; this is switched on automatically when 'highq=.true.' -most species files have been changed; mostly larger muffin-tin radii -Important: Markus Meinert suggested a change to 'nempty'; this variable now represents the number of states per atom and spin; this scales automatically as the number of atoms is increased -default 'nempty' is now 4 -M. Meinert changed the default Broyden parameters after extensive testing -LN fixed bug in XCrysDen Fermi surface plotting -LN also reduced the number of states which contribution to the Fermi surface plot to the minimum -supercell phonon calculations can now be restarted with 'task=202' -Frank Wagner discovered a bug which affects certain types of symmetries in rare instances; this has now been fixed -Important: default smearing function is now Fermi-Dirac (stype=3) -entropy contribution now added to the total energy -default smearing width reduced to 0.001 Ha, corresponding to room temperature -M. Meinert added a blocks-to-columns script; this is in the 'utilities' directory -Oscar Grånäs added to list of main authors elk-1.4.22 -Important:fixed bug in BSE calculations owing to incorrect rotation of dielectric function matrix elements; thanks to Arkardy Davydov for pointing this out -BSE is now three separate tasks: 185 writes the BSE Hamiltonian to file, 186 diagonalises the Hamiltonian and 187 produces the BSE dielectric function; thanks to Markus Meinert for suggesting this -adiabatic local density approximation (ALDA) for linear-response TDDFT now available; see example 'diamond-TDDFT-ALDA' -added Markus' suggestion that the Tran-Blaha constant can now be read in with the variable 'c_tb09' -added new variable 'highq'; set this to .true. and the most important parameters are set for a high-quality, well-converged calculation; see the settings in the file 'readinput.f90'; thanks to Igor Mazin for all the testing -removed the variables 'lmaxinr' and 'fracinr' as they were unnecessary -simplified TDDFT routines -Important: the variable 'radkpt' has been redefined and should be made larger by 2π ; (sorry about this, the original scale for this variable was correct!) -fixed problem with MPI that caused some LDA+U runs to crash; thanks to Alaska Subedi for pointing this out -added documentation -several minor bug fixes and optimisations elk-1.4.18 -Important:fixed severe bug affecting spin-unpolarised native GGA functionals, thanks to Jiji Pulikkotil for pointing out a problem with Mg3Sb2 which led to its discovery; this now makes structural optimisation truly variational for PBE -Important:fixed severe bug affecting spin-polarised 'libxc' GGA functionals -thanks to Miguel Marques and Silvana Botti for the week-long collaboration at Université Lyon where, amongst other things, we rewrote the meta-GGA interface to 'libxc' -thanks to Markus Meinert for careful testing of meta-GGA with various systems -MM also added questions and answers to the FAQ -meta-GGA now works for collinear magnetism only: it is inconsistent with non-collinearity -Henning Glawe pointed out a bug affecting the generation of the k-point set when 'autokpt=.true.' -Important: the variable 'radkpt' has been redefined and should be made smaller by a factor of 2π -SS fixed a bug in the plotting of spin-polarised Fermi surfaces -electron momentum density now available with 'task=170'; thanks to S. Dugdale and D. Ernsting for discussions -lattice vectors, atomic positions and muffin-tin magnetic fields can now be randomised by setting the random amplitudes 'rndavec', 'rndatposc' and 'rndbfcmt' to positive values; this is useful for checking stability of a calculation -the k-points corresponding to the indirect band-gap are now reported to 'INFO.OUT' -lots of optimisations and simplifications elk-1.4.5 -potential-only meta-GGA now available in conjunction with Libxc as an experimental feature; see the example 'Si-meta-GGA'; thanks to Miguel Marques for discussions -finite q-vector linear response TDDFT now available thanks to SS -Important: variable 'autormt' has been removed and automatic scaling of the muffin-tin radii is now always on; a new simpler algorithm for computing the radii was implemented; non-overlapping muffin-tins will not be rescaled; calculations may need to be reconverged -changed parameter for estimation of the nuclear radius from Z to A; thanks to Giorgio Concas for pointing this out -Kohn-Sham band gap written to 'GAP.OUT' after each iteration -3D nesting function plot now available; use 'task=105' -fixed problem with a constant in the BSE exchange term -fixed problem of TDDFT freezing with MPI -lots of optimisations and simplifications elk-1.3.31 -fixed problem with OpenMP 'reduction' clause in calculation of dielectric function -no other changes elk-1.3.30 -removed factor of 2 from the BSE exchange term, this has little effect on spectra in the optical range; spotted by Markus Meinert after careful investigation of core-state BSE spectra -M. Meinert also improved the 'CaO-BSE-core' and 'Fe-XMCD' examples -fixed problem with symmetry discovered by Alexey Baranov -calculation of the partial DOS is now parallel, thanks to suggestions from Anton Filanovich -various optimisations; including some ideas from Anton Kozhevnikov -iterative diagonalisation is now much faster -improved the adaptive mixing scheme -improved the initial stability of the self-consistent loop, thanks to discussions with Lars Nordstrom Notes for developers -inverse indices from 'idxis', 'idxia', 'idxil' and 'idxim' for species, atoms and angular momenta are now available, thanks to A. Kozhevnikov -the arguments to hmlaa, hmlalo, hmllolo, olpaa, olpalo, olplolo have changed elk-1.3.22 -fixed a problem which occurs with version 10 of the Intel compiler -simplified the 'setup' script and added OpenMP compiler options by default -no other changes elk-1.3.20 -added directionality to the TDDFT code; thanks also to Vladimir Nazarov for discussions -a pre-print is now available for the new TDDFT 'bootstrap' kernel: arXiv:1107.0199v1 [cond-mat.mtrl-sci] -added the scissor correction to the RPA inverse dielectric function in EPSINV_RPA.OUT -fixed a problem with running geometry optimisation with MPI; thanks to Arkady Davydov and Antonio Sanna for discussions -geometry optmimisation has changed: now the geometry, interatomic distances, final total energies and forces are stored for each optimisation step in GEOMETRY_OPT.OUT, IADIST_OPT.OUT, TOTENERGY_OPT.OUT and FORCES_OPT.OUT -removed geometry optmisation from the ground-state calculation and put it in a separate subroutine -reduced pseudocharge density constant (lnpsd) because the spherical bessel function order could be too large; may change total energies slightly -q-points and weights written to QPOINTS.OUT -minor changes and optimisations elk-1.3.15 -fixed serious bug introduced in the last version affecting some tasks (for example DOS plots) for crystals with non-symorphic symmetries; thanks to Vladimir Nazarov and Daniel Rohr for pointing this out -VM also fixed the graphene example, in which the atomic coordinates were (embarrassingly) incorrect; also included a high-precision DOS plot to demonstrate the Dirac-like band structure -SS, JKD, Antonio Sanna and Hardy Gross added a new TDDFT functional, called the 'bootstrap' kernel, which produces remarkably good linear optical response functions (article currently in preparation); see the example 'LiF-TDDFT' -Antonio Sanna added the Eliashberg equations for finding the superconducting gap as a function of temperature; see the example 'Al-Eliashberg' -improved the electron-phonon coupling calculation (task=240); this is faster, more accurate and now works for spin-spirals; now also parallelised with MPI -removed packed matrix format everwhere in the code, along with the variable 'tpmat'; the first-variational matrices are now stored in upper triangular format; this takes more memory, but is faster -Anton Kozhevnikov fixed a small problem with calculating the nuclear-nuclear energy -various optimisations, simplifications and minor bug fixes -this version of the code with be used in the CECAM Tutorial Notes for developers -the order of indeices for the q- and w-dependent inverse dielectric function, epsinv, have changed from (w,G,G') to (G,G',w) elk-1.3.2 -linear response time-dependent density functional theory (TDDFT) now available for calculating the q->0 dielectric response; see the example 'LiF-TDDFT' (experimental) -fixed a problem with the BSE calculation which made the response function too large -added the possibility of using arbitrary states in the BSE kernel thanks to discussions with Markus Meinert; this enables the calulation of core state BSE spectra; see the example 'CaO-BSE-core' (experimental) -MM also added an X-ray magnetic circular dichroism (XMCD) example: 'Fe-XMCD' -BSE calculations are now faster, thanks to discussions with MM -Alexey Baranov made several changes to the structure factor code, including adding an energy window, 'wsfac', for the calculations; see the example 'MnO-str-factors' -Tyrel McQueen suggested a way to speed up the Hartree-Fock calculation; this has been implemented and also considerably speeds up OEP and RDMFT -TMcQ also made some ongoing changes to the hybrid functional code -made the radial Dirac and Schrodinger integrators yet more stable; thanks to AB and Frank Wagner for discussions -fixed a problem with the ordinary RPA dielectric function; only affects calculations which have a scissor shift which made epsilon slightly too small -real symmetric diagonalisation now used for the first-variational eigenvalue problem for crystals with inversion symmetry; this can speed up the calculation by a factor of three; this is thanks to discussions with Lars Nordstrom; Important: the atomic basis may be shifted to a different position and old output files may need to be reconverged -fixed a stability problem which occurs when using GGA functionals by removing G-vector truncation of the effective potential introduced in version 1.0.16; thanks to Greg Walker for discovering this -LDA+U calculations are now faster thanks to fast evaluation of the atomic density matrix -Broyden mixing scheme now available: this seems to be both fast and stable (use 'mixtype=3') -removed Anderson mixing -improved starting guess for the density in ground-state calculations -upgraded to LAPACK 3.3.1 -various optimisations and simplifications Notes for developers -the arrays haa, halo, hlolo, oalo, ololo are now smaller and the indexing has been rearranged elk-1.2.20 -the Bethe-Salpeter equation (BSE) for linear optics now works beyond the Tamm-Dankoff approximation -RPA and BSE calculations now use full wavefunctions instead of plane waves -removed the Coulomb regulator from the calculation of RPA dielectric function, instead used the analytic results for the head and the wings of the matrix (thanks to Vladimir Nazarov for discussions) -improved the stability of radial Dirac and Schrodinger integrators (thanks to Alexei Baranov, Frank Wagner and Ondrej Certik for discussions) -added more block descriptions to the manual (thanks to various people for pointing out omissions) -various optimisations elk-1.2.15 -SS and JKD added the Bethe-Salpeter equation (BSE) for linear optics calculations. This feature works with LDA+U, magnetism and spin-orbit coupling. It is also parallelised with MPI and can be run across a cluster. See the 'LiF-BSE' and 'Si-BSE' examples. Currently an experimental feature -Alexey Baranov added density and magnetic structure factors: see the 'MnO-str-factors' example -AB also fixed a problem with output of the spacegroup code -full frequency and G vector dependent RPA inverse dielectric function now available with 'task=180'. Works with metals, insulators, magnetism and SOC, and can be calculated for arbitrary complex frequencies. Also parallelised with OpenMP and MPI. Thanks to Anton Kozhevnikov for discussions -added lots more MPI parallelism and made the code more MPI-friendly -many optimisations across the whole code -Simone Chiesa, Anton Kozhevnikov and Adolfo Eguiluz found a problem in the plotting of the partial DOS which has now been fixed -the first-variational eigenvalue matrices can now be stored and diagonalised in non-packed storage mode: use 'tpmat=.false.'. This can speed up calculations at the expense of memory -Tyrel McQueen found a bug in the 'findprim' routine, now fixed -TMcQ also suggested a change to how the code connects the points of the 'plot1d' vertices -Martin Stankovski suggested that 'ecvcut' be made into an input variable, allowing the core-valence cut-off to be adjusted -added the phonon calculation of Ni to the examples -Jerzy Goraus contributed a script for calculating VB-XPS spectra from PDOS* files; and also one for converting the Wien2K struct file to spacegroup.in -modified some species files thanks to tests done by J. Goraus -Henning Glawe suggested including the version number in the release directory -upgraded to LAPACK 3.3.0 -made tolerance for finding the linearisation energies (epsband) much smaller: this improves the overall stability of the self-consistent loop Notes for developers -arguments to 'genppts' have changed; also the non-reduced k-points are now stored in the remaining part of the reduced k-point arrays elk-1.1.4 -message passing interface (MPI) parallel runs now available; scalable to hundreds of cores across a cluster; can also be used as hybrid OpenMP+MPI parallelism for maximum efficiency; with thanks to Bhagawan Sahu for help with testing; see manual for compilation and running instructions -S. Sharma added susceptibility tensor for non-linear optical second-harmonic generation (SHG); see example 'GaAs-NLO' for details -added spin-orbit correction to momentum matrix elements; affects linear and non-linear optics -optical calculations now work in combination with spin-spirals -updated interface to version 1.0 of the ETSF exchange-correlation library, libxc; thanks to M. Marques and T. McQueen for assistance -fixed bug spotted by T. McQueen involving using multiple tasks in conjunction with 'primcell=.true.' -A. Kozhevnikov fixed bug in 'xc_pwca.f90' -A. Kozhevnikov also fixed serious bug in 'getevecfv.f90' -F. Cricchio changed the order of lattice vector angles in 'spacegroup' utility to 'bc, ac, ab' which corresponds to the convention alpha, beta, gamma -removed scissor correction from eigenvalue solver; now it is used, as before, only in optics calculations -T. McQueen suggested an improvement to the routine which generates the path in reciprocal space for bandstructure plots, 'connect.f90', which has been implemented -fixed problem with XCrysDen Fermi surface plots, spotted by FC -various optimisations and simplifications Notes for developers -arguments to 'zpotcoul' have changed in anticipation of linear-response phonons; should now be called in conjunction with 'genzvclmt' elk-1.0.17 -fixed problem with Fermi surface generation introduced in the last version -E. K. U. Gross added to list of main developers -no other changes elk-1.0.16 -fixed problem in linear optics calculations for metals - thanks to Antonio Sanna, Fabio Bernardini and Sandro Massida for pointing this out -FC and LN added option for automatic determination of APW linearisation energies (use 'autolinengy=.true.') -Marty Blaber made a script which allows for semi-automatic labeling of the vertex locations with gnuplot (found in the 'elk/utilities' directory) -FC and LN fixed problem with some compilers when writing FERMISURF.OUT -FC and LN fixed problem with writing XCrysDen Fermi surface plots -Anton Kozhevnikov found and fixed a problem with the generation of the irreducible representation file 'ELMIREP.OUT' -Torbjörn Björkman added a new routine which automatically determines the smearing width from the k-point density. See 'autoswidth' in the manual and the example 'Nb-autoswidth' for details -added a constant electric field E in the form of a saw-tooth potential: set the vector 'efieldc' (experimental) -added a constant vector potential A to the Hamiltonian to generate constant currents: set the variable 'afieldc' (experimental) -FC and LN fixed problem with a spin-polarised GGA routine -FC and LN pointed out that the energy term associated with the excess charge compensating background should be zero. This term has now been removed -code now more memory efficient thanks to smarter array allocation -the variable 'rgkmax' can now be made arbitrarily large without risk of instability -removed variable 'cfdamp' -Anton Kozhevnikov pointed out that the radial functions were being redundantly calculated for equivalent atoms -- now fixed -Anton Filanovich added several questions to the FAQ -scissors correction (given by the variable 'scissor') now applied consistently immediately after the generation of the eigenvalues -FC and LN removed the spherical harmonic transform matrices with rank lmmaxapw -added dielectric function calculation for arbitrary q-vector, see 'LiF-Yambo' example (experimental) -by setting 'gmaxvr=0', the G-vector cut-off for the potential and density is automatically determined from 'gmaxvr=2*gkmax+epslat' -various bug fixes, simplifications and optimisations elk-7.2.42/PaxHeaders.21776/Makefile0000644000000000000000000000013214061636521013570 xustar0030 mtime=1623670097.326100254 30 atime=1623670097.325100255 30 ctime=1623670097.326100254 elk-7.2.42/Makefile0000644002504400250440000000066714061636521015636 0ustar00dewhurstdewhurst00000000000000 MAKE = make include make.inc all: cd src; $(MAKE) all cd src/eos; $(MAKE) cd src/spacegroup; $(MAKE) clean: cd src; $(MAKE) cleanall cd src/eos; $(MAKE) clean cd src/spacegroup; $(MAKE) clean rm -f *.o *.mod *~ fort.* ifc* *.gcno *.exe test: cd tests; ./test.sh test-libxc: cd tests-libxc; ./test.sh test-mpi: cd tests; ./test-mpi.sh test-all: $(MAKE) test $(MAKE) test-libxc $(MAKE) test-mpi vim: cd src; ./vimelk elk-7.2.42/PaxHeaders.21776/setup0000644000000000000000000000013214061636521013213 xustar0030 mtime=1623670097.332100248 30 atime=1623670097.332100248 30 ctime=1623670097.332100248 elk-7.2.42/setup0000755002504400250440000000630314061636521015255 0ustar00dewhurstdewhurst00000000000000#! /bin/sh # Setup script for the Elk Code # generic values MAKE="make" F90="f90" F90_OPTS="-O3" F77=$F90 F77_OPTS=$F90_OPTS AR="ar" LIB_SYS="" LIB_LPK="lapack.a blas.a" LIB_FFT="fftlib.a" SRC_OMP="" # get system type from user GETSYS () { clear echo "Choose compiler:" echo echo " 1. Intel Fortran (ifort) with OpenMP" echo " 2. GNU Fortran (gfortran) with OpenMP" echo " 3. Portland Group Fortran (pgf90) with OpenMP" echo " 4. G95 (g95)" echo " 5. NAG Fortran (nagfor)" echo " 6. IBM Fortran (xlf90_r) with OpenMP" echo echo " 20. Intel Fortran profiling (debug only)" echo " 21. GNU Fortran code check (debug only)" echo " 22. G95 code check (debug only)" echo echo " o. Other x. Exit" echo read SYS if [ "$SYS" = x ] ; then exit 0 elif [ "$SYS" = o ] ; then echo "Enter Fortran 90 compiler command:" read F90 echo "Enter Fortran 90 compiler options:" read F90_OPTS echo "Enter Fortran 77 compiler command:" read F77 echo "Enter Fortran 77 compiler options:" read F77_OPTS elif [ "$SYS" = 1 ] ; then F90="ifort" F90_OPTS="-O3 -ip -unroll -no-prec-div -qopenmp" F77=$F90 F77_OPTS="$F90_OPTS -assume protect_parens" elif [ "$SYS" = 2 ] ; then F90="gfortran" F90_OPTS="-O3 -ffast-math -funroll-loops -fopenmp" F77=$F90 F77_OPTS=$F90_OPTS elif [ "$SYS" = 3 ] ; then F90="pgf90" F90_OPTS="-O3 -mp -lpthread" F77=$F90 F77_OPTS=$F90_OPTS elif [ "$SYS" = 4 ] ; then F90="g95" F90_OPTS="-O3 -fno-second-underscore" F77=$F90 F77_OPTS=$F90_OPTS SRC_OMP="omp_stub.f90" elif [ "$SYS" = 5 ] ; then F90="nagfor" F90_OPTS="-O4 −openmp -kind=byte -dusty -dcfuns" F77=$F90 F77_OPTS=$F90_OPTS elif [ "$SYS" = 6 ] ; then F90="xlf90_r" F90_OPTS="-O3 -qsmp=omp" F77=$F90 F77_OPTS=$F90_OPTS elif [ "$SYS" = 20 ] ; then F90="ifort" F90_OPTS="-O3 -ip -unroll -no-prec-div -g -p" F77=$F90 F77_OPTS="$F90_OPTS -assume protect_parens" SRC_OMP="omp_stub.f90" elif [ "$SYS" = 21 ] ; then F90="gfortran" F90_OPTS="-O3 -fcheck=all -finit-real=snan -Wextra -Wall" F77=$F90 F77_OPTS=$F90_OPTS SRC_OMP="omp_stub.f90" elif [ "$SYS" = 22 ] ; then F90="g95" F90_OPTS="-O3 -Wall -std=f95 -pedantic -fbounds-check -fno-second-underscore -ftrace=full" F77=$F90 F77_OPTS="-O3 -fno-second-underscore" SRC_OMP="omp_stub.f90" else GETSYS fi } GETSYS # produce the make.inc file echo > make.inc echo "MAKE = $MAKE" >> make.inc echo "F90 = $F90" >> make.inc echo "F90_OPTS = $F90_OPTS" >> make.inc echo "F77 = $F77" >> make.inc echo "F77_OPTS = $F77_OPTS" >> make.inc echo "AR = $AR" >> make.inc echo "LIB_SYS = $LIB_SYS" >> make.inc echo "# LAPACK and BLAS libraries" >> make.inc echo "LIB_LPK = $LIB_LPK" >> make.inc echo "LIB_FFT = $LIB_FFT" >> make.inc echo "SRC_OMP = $SRC_OMP" >> make.inc cat make.def >> make.inc echo echo "You can now edit the compiler options in 'make.inc' to use optimised" echo "BLAS/LAPACK/FFT libraries, MPI parallelisation and Libxc." echo "See the Elk manual for details." echo echo "Then run 'make' to compile the code." echo echo echo "To enable syntax highlighting in vim run 'make vim'" echo elk-7.2.42/PaxHeaders.21776/make.def0000644000000000000000000000013214061636521013525 xustar0030 mtime=1623670097.340100241 30 atime=1623670097.339100242 30 ctime=1623670097.340100241 elk-7.2.42/make.def0000644002504400250440000000532414061636521015566 0ustar00dewhurstdewhurst00000000000000 #------------------------------------------------------------------------------- SRC_MPI = mpi_stub.f90 # To enable MPI parallelism the MPI version of the Fortran compiler must be # used. This is usually mpif90 or mpiifort. Uncomment the following lines and # run 'make clean' followed by 'make'. #F90 = mpif90 #F77 = mpif90 #SRC_MPI = #------------------------------------------------------------------------------- #------------------------------------------------------------------------------- SRC_MKL = mkl_stub.f90 # To enable MKL parallelism, link with the MKL library then uncomment the # following line and run 'make clean' followed by 'make'. #SRC_MKL = #------------------------------------------------------------------------------- #------------------------------------------------------------------------------- SRC_OBLAS = oblas_stub.f90 # To enable OpenBLAS parallelism, link with the OpenBLAS library then uncomment # the following line and run 'make clean' followed by 'make'. #SRC_OBLAS = #------------------------------------------------------------------------------- #------------------------------------------------------------------------------- SRC_BLIS = blis_stub.f90 # To enable BLIS parallelism, link with the BLIS library then uncomment the # following line and run 'make clean' followed by 'make'. #SRC_BLIS = #------------------------------------------------------------------------------- #------------------------------------------------------------------------------- SRC_libxc = libxcifc_stub.f90 # To enable Libxc first download and compile version 5.x of the library. Next # copy the files libxcf90.a and libxc.a to the elk/src directory. Then uncomment # the following lines and run 'make clean' followed by 'make'. #LIB_libxc = libxcf90.a libxc.a #SRC_libxc = libxcf90.f90 libxcifc.f90 #------------------------------------------------------------------------------- #------------------------------------------------------------------------------- SRC_FFT = zfftifc.f90 # To use a different FFT library, copy the relevant library or include files to # the elk/src directory (eg. mkl_dfti.f90), uncomment the appropriate lines # below and run 'make clean' followed by 'make'. #SRC_FFT = zfftifc_fftw.f90 #LIB_FFT = libfftw3.a #SRC_FFT = mkl_dfti.f90 zfftifc_mkl.f90 #------------------------------------------------------------------------------- #------------------------------------------------------------------------------- SRC_W90S = w90_stub.f90 # To enable the Wannier90 library copy libwannier.a to the elk/src directory. # Then uncomment the following lines and run 'make clean' followed by 'make'. #SRC_W90S = #LIB_W90 = libwannier.a #------------------------------------------------------------------------------- elk-7.2.42/PaxHeaders.21776/docs0000644000000000000000000000013214061636525013007 xustar0030 mtime=1623670101.146096708 30 atime=1623670101.126096727 30 ctime=1623670101.146096708 elk-7.2.42/docs/0000755002504400250440000000000014061636525015121 5ustar00dewhurstdewhurst00000000000000elk-7.2.42/docs/PaxHeaders.21776/Brillouin_zones.pdf0000644000000000000000000000013214061636525016734 xustar0030 mtime=1623670101.130096723 30 atime=1623670101.128096725 30 ctime=1623670101.130096723 elk-7.2.42/docs/Brillouin_zones.pdf0000644002504400250440000057763414061636525021017 0ustar00dewhurstdewhurst00000000000000%PDF-1.4 % 6 0 obj << /Length 71 /Filter /FlateDecode >> stream x3T0BC]=seUeɁTA3000#5Vp Ct;N? ! endstream endobj 5 0 obj << /Type /Page /Contents 6 0 R /Resources 4 0 R /MediaBox [0 0 507.249 517.809] /Parent 7 0 R >> endobj 3 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (/var/tmp/10089666731916source1.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 8 0 R /BBox [0 0 507.25 517.81] /Resources << /XObject << /Im1 9 0 R >>/ProcSet [ /PDF /ImageB ] >> /Filter /FlateDecode /Length 10 0 R >> stream H*25032U0BSCs= C039K3P%+ n endstream endobj 8 0 obj << /ModDate (D:20020211151125+01'00') /CreationDate (D:20020211150909+01'00') /Creator (Acrobat 5.0 Image Conversion Plug-in for Windows) /Producer (Acrobat 5.0 Image Conversion Plug-in for Windows) >> endobj 9 0 obj << /Type /XObject /Subtype /Image /Name /Im1 /Width 4228 /Height 4316 /BitsPerComponent 1 /Decode [ 1 0] /Filter /CCITTFaxDecode /DecodeParms << /K -1 /Columns 4228 /Rows 4316 /BlackIs1 true >> /ColorSpace /DeviceGray /Length 11 0 R >> stream XR0G}5K4W QL/.܂D,D$l*r@醐A~UKE}uv8LÄת^t}._5UOIn1. nuW]m`UGi{9'/W7tȩ30q;_ v=K8  m.K]WUKaWnx_TگWL]uvPXwLX.-k__]|OzW_"ݏ__*o^u {]f+_$m F#o-.4Gk0 | f1030odcYt\\>YF̎ ܁ɅVgUF"xlyϺ,H.n4N}>Y荣/0hZ 1B!@] Ͱ`h!@h#:1-YUy0@#6DGoB\Dvn#E0R8˲>^0 kraC <J xLsR)D ._? xX(s. @9-CQovD  A{{ M>0oIo >aIl> ;ۆ{}&z]*}'}xo`ag&mJx7j0?6WHpaA0Pn"}&M tA 0m0 >aa0} q}& `aA0MȭuH7úL1 >PML60aanao ; ke~ݜL aoޓoxk <0L>z7°eoOOA-29xH0ܮx!iNqC.&@U p/ 6lS28dc$'3 sHd'J\h6 Ze~"8-ِ0F٘-Ve٠00#p[r8|#| 2a&G[#n6 ]F# `G/ i""""pH}40"1`*B:L6{)|a RR P'H2!ܛAd2aW;q6Zt Xn8I QY P6h<&@R6TidptHc9: Ae7Zh:HK2id6aLNn !&$PVd<A(m' aaI#"I[tm+ .A;t,7Ki6ү-KIwKl4 {ẮJ۠m' ?$zN Imt+ tItu^ MRvVj$[I#'[i8nǴ7Iv ҭvVVÄa^J:++l0{I+kᇯ _e47A%!ޫtn I,67IxinÄN7ivk/na]^aM۠maU^Wm-AvJ}aKt%m/mҭ7Ivݺ[`ä vo /m[ ქT-,EZV/ X0*tI0wIml ^T짥väuTvD A$إtL$t$-I]-[ +/IۥMl:J tl%aXt7I+Kn Km+oJW :UiXnv,: ?Eb .Hʵl=fFnM <7 ]\7I0t[aa!n]VpKp\47Iw m%Kۥ::]Km^/l anpKzl%]U:I턖ݺIz 0V/zuKl% : -pV{iv%[h.wnWIv[aJҬ7Iv}aKtOa]i;aImiTaҧm/aZm+^-W Tqmp;i{MnI6l:^^ޒ m ^퇪iS-I0taUN/m!]vA*K :^M~XnA;i6aKh-I}+ ={i;m`[i6tÄm"%}oKڧl:UN^鴷 :I4Im\m-OU; V ۥVn/a[Am%m't0MKlKm[xnl8*V!!-t@>ᇥr{a+ alF :Ka|7+8]I&P[eTKa[l?t7ZmtoJW- xa[KzI6 A^?VKm/ixn]T%i n i]m~]/taa >ix[vհa!i8n]¶NAX`VNWt* l?Kh-m' >a&tm+ Mv^a%l%íw[mm/a_ mҼ7I-mޗx7Zav^tmI0[i]%XaK:[꽄m/ Kp އKmUmiv޽0m tm+p%7I-֜7m/amvݾ/ a[a+xNh mqt鰗am;l$Wl$t]֛Kw_}' ]Z[~ V^AWj 5nv[zIV]Ynm ;V I]Jޗ碌l%~^4h&mK&SJ^I~[Wl%WKUn}wJ_l%umt~m~/ISޒi}w[kin}aԉ&^h*_uKմ}}ui'wU^5@˙ϯoTB)0,&@ڂr zT9r(h&ީb""Mx'S *.JJ#\ӯ, (OwDG !w,L).f uQ,He[!,ڲxjCf%`x6Ckw2:H6#mŔkO]nfG[d !YdEz# u) oe@d ܎ckWLlG* ":WzR<a%\\[Eu0<3Kx߬RQ"-OT $zR#y )No\ȐB8 ᰸rzFF3x4MuHʨQ#u{{jxfB"=]Sato[_mv%ˁE?28$uZZ=.G~+B$9&a7O[W}l Rumu{s#\OWݿ@ˁGCM_iޢ@9F; T@jAFJfiOzDn$[_7R~@nV"Q {6k#DKTo]'K-_6>ti7Jմi'O M+Ioi7M' 'VrRoI=:[n Sk}P!;ImuIIMoo! mo:t[z7\7NڒMK{VtVuK|+nҭ"Nm-, aS}л m$]:oA}%A}o[zMXNB?>m>:Z _k{adj:XL! 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Iu\3%L| o v/HrWg,3O+t#Pā,YHHnuۇM\V%.L@]b 2_ "q9aq(Px;{:h@|΂!ϠjnenPٮ_~|hH5=Y1(}9ȡ J+8IfO/gL\ڎg3ƌeh/ӆU׍`{y5ݡruᦇ>\ #0jp{MpmHTphiYuS^ҙlDj0Q@[QUyU%`-Ѣmjs ];^e 3goW)ԦRv:=u iYY45,m CouVJoRGrkbS U*k'R"wQyXO̜1@uX@ҭV5Je~UGR/zQ@U(I3wdEW8w$t?I{=U-huӼ?| 8ꛣː\i endstream endobj 2376 0 obj << /Length 2853 /Filter /FlateDecode >> stream xks6T in/νތJ6mIN-"(H'7X]{Ѝ e^X$ ) i'ώ޽K2z>rPXbaQȈhL"_Uif%1pXO' ᚇ]zӣskD* |£dHh /C:y7Xw_e 1cs`Pu/4y/Ug~Vq2_UM")a׭4DK2^iiHEC;Y%YQߦ,/sז!s6~h`LݰSiY6(J_$6redtjjΧUIC1/fi6E2$0M{ `jIӹ6)\zeNr;QkelZ46[Lgirk)i0[*a(fmP;~r߂½*^L?L2$iw#Ny\NEqiTm|䃺/|qH#ixU\ C tN0(O`U^@{I0eo4Fc~SER.Ddl=췯{cG,Is~Ve pw'oN޼>/!KEXa$5 }Km%!@j1PQ[% #-U#%]"< ׿DhXCӑVHahd;y&Yt;j W#}9]TD?]NuQrSh,!`@\pIZ*u CvgNb+uTuiemR\VJ:Q Ao)J%o̶6ض`d@(;0Vʟ$E}_2~ 9<`I)(`HF]I*3X@[C=[3bucP/UmcI~T7SU-'N=m6 $Vfn`uEywӊC(:ܝ>-Z@DݘxMըs8|3nu[CWis^u!jVA~bM_%4ywL/ҚN^/~JMB/nUvZhj9걟J:MbyX-B 9P1NᢞFpU%W>`N! m˾PKf>iHf^UL>ExO`8.4+S5jx-?.IU|bO_ j-l6;E |Yg|+4⼖is=WiUj/ֳ*Ҥ_T,Ѕ{P5b`:rXL}jXY14*ɱ /3cGqQa6SCݸ?ln C=S C[ig午W5ͬ1041-?%5&alW`w)ZWCjw(N5i4't p('4Za=ogR*d5'W} نGZ5a콧gXk؀"g%k<[]Ѿ캱PN*T؁k MKIy.֑dsQ2DH9 Yxp"{wޜkr֞|--8YΌTU;@ ̬d; r#)@U9G[q+'9FgC#Npw2#t6,3+";Fuh򍃖]=r:sOv ?]*1ȵg&=0~ZaAj$*~?㎄~|MPV95 h;Μꔻ+ɀgXPcj钾+JM6ZC@:ekM.mvFoK^CCB߆]ԙy+7`*xwK*v>WPs)sv?فL 1nau/ #f:6tM'(W`dhH+'mo Pʞ\[zK~M$/阒?@o]SPπT| 9B R_us}ޱIJ~<@ww桰 t0LLywӓ7uٛw~^7#El~ U1`{~ (CH$[6~p=ד1' w|YKCkŞ endstream endobj 2381 0 obj << /Length 779 /Filter /FlateDecode >> stream xIO@s%<F@TTCH0ިc c H=TQ[S~ {rD#%QZ!-$&C?}A8pC,)sGaL:Qr,eƷq% "ɨId4꺞$ĺU< 8P2<݇l& Kԃ?w5w\^k(+ my}UuPJV'w;FOVczI\)Y1q֤p,Ή7ڇnQ0U]tVYq^هYYd./r$ye>uT4S|9E:rWi]5We|o4ʢ/wh|^;5Lʗv[7㣮un/$SښNUz8Nuc6FY+{`m jʜ2NdL}VkNAZc#Vm|L5k-.޶Va (þۅ7uc%eIAq°}59`L9_xރ>[.0BrF72 針Xj0)Bs~Iòc*C1h9}¨%&۳6yk_C|:j0U&BIݥ3ؾr;ےV='-$RgnVY*f߆m>&[%h`+>[! ߊص`rF&k%A￿u endstream endobj 2385 0 obj << /Length 983 /Filter /FlateDecode >> stream xVs6~_Gg8iٸ3=`&}WH&kgzq$oWo(z;AD( 2(&xL}0$~zW#"Jq(CI$'XSB-}a2a=&Sk%ɪ].'dV2ϣ4K+!sjF%8$!Ur`qx #;ֵk0+7E`$rRHeQW NQSv8x`c<|6}7zkh*ӍQSxkZWƓytu?``Ki]O!rfENm_E?4T勞68JMhPOqIq~#s$}&?lk[4(LMYCۓyzlV9DM7uqmg!OډWwI hA-,Ī>+,BIk<(+u)+vP͊5]Mb*wܚAO4!ƞskj f%;t}n: v*AE$SxT39WBLp$~:}~"hPE5V981Cއ3-{j)P`TgzMޖn-{(FՏK^UĆP Aj **#iVZyUEck0e.mSbp|g ߊ˴7U1xDѮ훎r(Q-JIQS-G] `H~uS1'FYy.(JS 'pC#.h*<1J[E'3wƛ:.ªRntFYC%h҅f >h'ߣN endstream endobj 2389 0 obj << /Length 1302 /Filter /FlateDecode >> stream xW[s6~੃[` iM6v5J_#1xqɴ3Otst@F3\y`7B# (0812A׸x]O,d 1uf:5>3 6B6s¦>2wSljc:I4z9R\e.l6.?iS/2.ԡ` vB/4l4w47=25waO#VիuoE2l17g GBǝGZ0cI)7DM"D7$*^j*;:0{g$tb@f=f%!0J,X7 6$\Hڈ! 95pNrZ1G̵:A!j5DO}H6zT2BҺ${jDmnb'Dg[VL;h )(=6t@1N4asE>ba!4sԞoDMXy'f3 }qoJ#O c5x0rPy*>¢Kd^[LHܢyƚV\㢴Ȏ$ٮԤiVZGpsqe~)W_~[[őy3 CiL)!H3 ̑|K=?Llm}kz(RSK`bX( 2r%S/F.~mQ i{*Ġ - <`h)ghqSsY уd[hUN$9U4TKYJZճӘW"qX(U@\xEuaC!˪uGi{߉8J2$U9u3ܙZ?v8њe U@x$=u^> stream xWS6_᏾+zZv~R)!љLq]݁iH;Nh[[yW+= T:^$2WoۣHbű$1+vZP:-Nޞ}Zyq6? #~i'ifo#V2O,iLuVVx'3̪+Se% KW=5~},,1k?)sk ÅL%cw\W, sۦ+:Z5qz~m^ävӒAUyʩ!|dHT'JꦷNu)ЅiWI+̲?,[~^ XDr9R'f{!@pyv_TqvM6@p 1h/QLd[Er[MG$FnEq 439闓{m΀@?WiucKST:#Ut~EJr#ƦXW'yt3W>Kσ[2[upRbT{>Qo 砖ͽ;0yXA;Q :5 Y辂̿ˋ+Wuuj8Km^`L1;tqt~<$¯z7MwYWx c6t''>Ϳ_rwME(O0h0ȐAzm1gl-DJqGo= *\FSb٘mPD-sz ƔnjdL['hkN~%έC>[lFqQ#>zѶ5´f|ELz=n#O1!#•w0&$r4,#g8l7h?>l7}NN./^,`?ivAM8#_f:p3J(v /Yٚ+S?>!rA|zYZGߑ#)Pc1AfRɝ#O]#nAtӪXCd[Ϟm >&驍!~$pi̗Δ޸mpOӼ[f>G8Y*uUs1 y0΁䱟F 5Άq9E؀<, a/Bۭi茪'u|G`}fz##~%0mWs vº ^IjM@v4m| Iơ 05, s!D5㘕KsZv Op6)t~|0Fd%Roy2pV"1g^\V-|2U$t /'E%!Y\8:nܡe394j;1dZ7B$Ի1,\\za@aXiX-Sq2KܝVI@tȥqNH}`@ZIFbxYUX endstream endobj 2397 0 obj << /Length 1317 /Filter /FlateDecode >> stream xڭXR8}W1يBښ8|2 ۲$d) $Gݧ-q) ?"~;s/LeOgK8ę- &iD$O/ N~aNyn@6s/V<B!Os| }䓑K̽LrU\Ce-<_Yr 6b"ĭ'"Q$f6lx6|r8 Sq)0U,kYSZUR"7ӦOIxNl]xNy9ϣ8vҫ w#ݟ}GD&[:X#B" OeH:A.LVb.nIQAjXteѥiG-ZQfW"&]`% .9\6aua X81Zu6Q)$PdFl" JJPJR.ZT"+E-ejXLD*;]οu$Uׄ)YEbțR|%?SsG?aN&=6,яZ>TYb˾|l`xKe3DNjײτeg=+|Cw>¡ϣ,F1f*c|h0ޅF&2f0փlѠ3enY5Y*@Zke]=fMU|:G9k".p@ 1@790~tƂ]϶ JT X (@<0)þXALjANƑ;B=<ʄI?}WֶUoC4R"JHwqޔ [j{z gK~fDr#2ǖJaeHOGZc?n b3=dQT- =ctvtEV´PsZo~1L?/[̀4iRh%TГ}WmԫĞ_ynO)F ZPZf-ٳe bqbm ZDYO176eU&(TEߨPVBE!uUҵ~6tv{ ;KTo+-Xcﴝ 461䵋<a @ endstream endobj 2401 0 obj << /Length 1254 /Filter /FlateDecode >> stream xWsFУ"NONqRN,#AItgǺ~bPc aIF3$7ƧBbߌMzgW5(ubw]#ddf|1C't-R7\Ũɧe7OJN^_?l.3 R dP$(6^o&ѕ1r#rp].> ƎOTeRp~ 9UtYe_/9kPd}@x0~3UʋY-(s|/F&,bOn'0oȼм]1ۍ]h9}"pEB/ةOLZz_ipeBa_e $UH=OŌv_2_ZYT:m4"QHOnG=^ UvW2%$ܾePk;/d(\?i) [#G7DBw??HXzۑ9gDp^%le^8GK֍ 愅bc|%  D_5Qnx̅13ƽOG!mö NݱL9=!?ʼn~Bp҄f5Wt?lkr딏3Q{p5mbccDɴWxs.ԑŠZ:7VU@u"S ǝGZ8X\&7ٳN0 <~k>CN6$^m)9R {uNF=T]K2'>aUi:NԆ!ЁpoV)ۃT+(6'fԮȅ9MF  i endstream endobj 2406 0 obj << /Length 989 /Filter /FlateDecode >> stream xV[sF~W4{J~s Nq93$`$I,AIʴðZ-|)|ߢPaITP $&5->ZW"Jq(%C)'XR4Fp=Jt\:y:s=H2ȖHx]Or '!a~n %8$!5> 8Re>o݀;7. N(}V$VL!%[K9ϖe:cpdzE{A}^ѧAw㈤U^(I6NqzSt"-Uʹ߼BszH[dqZڗI%vfru,6ΫPR*sɖ,yDdX7s,v Q,yMXklQNJ̫]~7A{zV RL0 +QLUjƹ\<5w( {M|Fi~ˤ- k pmDľi*τ41[Z B (þ αFJjI ru^WfWLow!ańKB@$KMC{( zzjz2̓aUnڢk4(i}BΡ0js- MLhp̅"eEas~@oH<  ?ύfd̗`M]C,ApQFe=<2L 0\F=]/lrXqu?ȫEz2`6.uPiӆs"-601ѱR38T8UJPR> stream xVn8}WlK޲uRXtc)XrK[!eזo]"E33(J-?i5De*6vqv% [b)X34'X(FI%Q,]]inזޮTvo:e{uooKXY!]cbm=,mfshs8 ڴAsޜa/o 37oD YqgHFQbXFsks8\]1R\;]FwJk )9fBWB.)B%xgeX PK:wC]I0UH[ VR EҟLJ1)#Ė$)'l;z7(CA\!6%uX)y$d1V"+(DS;[z83ؘpy(:lj#K>|V r~5|N΁Bf[ 4LlBO,ӱUJoӆK(DU`xhLfE>"y>GSʊOy+|ЊiZ=V٫\ v“1-84\ Nt$e/ f-AY ɔdr5.'L:tf ]C%\ nA2m8xS cNtpDt^m 3`uu3LKٸqJ}i& q9cE!:} M.кyѻxׁ+]|L/I6N`@30Kԝby@(_q__HAKӢ'X Y{=v6>ٱb8;1טpckO1LOZiuB)Ȱw~\eMʶ/Z8ŠMr0"q֤a>'Z[(LP endstream endobj 2414 0 obj << /Length 1599 /Filter /FlateDecode >> stream xYmo6_!, 1W췮MtX_bo"Ɏ[R$9KHڮ(Z;wzgϜGhJ: Gy? ٩HcM܁_a$`,t>N//߾y>8{씈>v&T"UuV r 3*Z5uEߘNK[;]lpeCàPH%Cڪ#ɨ3i&f&MGOkД6h?M4ka kApd/Gcoò9kxwJ@ %t {R# =/ pEw@(`C_.aIe*:GjihVHч a ¿D|LGmW !pbigC7!||-a1h4MŃ!A!3 Bu8l N=*g4]Ad9$xPăj ́Bdvũ@_K~'OW>x9B>Q$(J1& H7FZgx&Har V\` wʏu;-lbLw:z[TuW"!\i}Ts_a/[(r<'-JxnCJrDE' ;^Qf$a+> stream xYn6}߯hy#mAFtQ"q{Fjiim/#q833IbPɁOK֐rPJ(e8PѠSd>suw7j01P#-JnHpS%$aRIoEHL.Dq4.`dg2"< g<;i!?a B 3bŷH%̴h-U}'lzIG5U7*MȋB|Qq˘))ȎPR3+ ۘwL4JׄT#q hʜZ-d zLw-$`(Cns#ẅVbIn~Ox 0 H 0RU 0"ϑݍ < ӌHA&8,pVt `/̚%DgĨ ̰8B0G @A=3y`U, Yrr-&#{2.©+zT\\lo2Ԑzp˗7o~u\6*^\߆4r $҃x0/y~=}p^ݏvW*ݷ_?/?͏pQ8d`J #F>4#vHk< @Id<is]S&hijh a&IӤ4i>1rid4Djx6 nʇpS\ 7>QCBz&2YQnx'ơY7ڑ|OۋǼcXW@0wR$e;B,mIyps9c܍^Foh psGin8:1ˉCbÝp/1"40/-s,5dM۫O\̠ m=YLrL'bɫ1ξXv=P^i&jQhB&]w5iO9C9bHuոRli5uB,%p鋎˙8p!v{ N0gilcպ'XcS"W%,ia|pS' 7Xɻt<@ endstream endobj 2419 0 obj << /Length 814 /Filter /FlateDecode >> stream xn@y%Ξs&IJUU A vjwlCKؙg~N&<#1aPPŌ5JEV4"cr`qԑpNR@11@`TaP8"מ-AyI -?< ]j0t8k\027 Y+_:#2*\1 Jea)$t]tcԁqY[:r;1ƳG3YD 0< i"{{ ;iw;v2E :g/i\LcD۴3tތmҜȏkV\QKPZ,Ӹҥv//to+2l_<ƭe|䮟ܛqxh"ʬ4qysC+JH pY.oBLU"Cv޵vU4墼7k;he8M yAxv՗$(]$h6sU6O7]v5+tZj=Ȓ0GBB@-,ɀiՠk0]yO01#0,(Y %)Jf5qU;@OI0O( ϧdqӏ׫OëSp$/'හm8`qu-,˸u?(5mdVܦ꡹6GI 0;vr%PvfOókx5R O`*TIJk| endstream endobj 2423 0 obj << /Length 1455 /Filter /FlateDecode >> stream xڽXmo6_!,_df*JNK04]XYJ[?~GR%GNlGԤt|xXs{g“H`JaBkf}aֻﯓޛ N,B'&3KRK2,g["PaψLFChDJX:]>V/[1ϵiѥfF kƀMEÐn:QɚJIȤoȦ_D??g9Hb ;ӗMG:(%.b2 y B7-#{DRd(3K.&>uѩޭ $H@"N.K< *J N}Rx0s5j@ՈLYovnZ|Ƈfq*y/`GJ/>|4@Rg7g{.rdCJ O UNpe&q 33Q0,zm<M:B2+^fQ<'yj-%g`#f ճ WQL*%>̢0idAyTB T޵K[O ɷA*`!ق\s»LU!Bv"=U`7jZV}+пiQ\&灰LjM j)j>?J(/Ճ'm'Ln}ɾ6VʷթY6A%pjd* hQ %Вd %-f 9|ƊY\ 1?  yo08K'Ҧ#(ɋYGI+io45:O mۘblsIӽOŝcMZ ߚg#J^MHxPrW×B _V1:<3 E6#`)eg]/vX"0g X?yc_c]b 9RJcdoYbnڧҾyhW?sz2YPDY;#%<_D+#u'v%yI+MDͿGK? 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[[1 ~4Rƥ4*QR,}-x*%ӖZT2kPV0_N> stream xW]oF}Wі`2LXJ Vvr$d8@q!MTE={9;ĹN`*@2p$s_rΝ!;'!H A 0$  J7 w{_q#R/eW,FLIg[.0p:ާ6l D Zb* 0DM@a"v}[ H 1$¢Et0" `"&i@_e E+5dz+O2wQƗb40% ~-Vejo7*];q^Ksxq9 ,;Άu\D>VΠs{iTejuR>مdBG: ;hw6t_l?D}-tq_uцg @SYD?{ Ǫz2fi8IQpЪUǕe2jL=܍X.YFebyzFzf'sdÛٟoRjI-8852P!3l8{7enj($u ݴX Tcz|a:1_T洯rReU*:UqVm\kGcBt5߹kct>憹ye3|fj>BoQ-ud}f!-.R4hۭa0{ufuSUwg ԫw67CMOb>pQ%rni$Jj'F6IN Dme|_leeC 8 C^W2Nu ;W:fzY7]ȣռQw5I~>; >jQmD@: Gu'vT7P6ڽ(~ӰNvB9 6g:~E֨9̍M/"s #_[ 1 endstream endobj 2755 0 obj << /Length 1495 /Filter /FlateDecode >> stream xڵXS8_O7L,7AK׹i{7$&i]I&1(jڧv0g/ܡ#HFP?|Ry{@:/Gu%13:!wBAC=;|7:x7O2r/{a ޜNgOW.W@zt<ɥ;mΊ̒j,U^G*i+,``<&:YR 2bjd9V~hKmZ4u#O?Oǃ3sCpudžu7G|{I9~WHĢۊ&$sṴ+pwyA'fqQ-jY(\v2R)2r+myܲ_B-zp`&ڢtưq,I#I9X!))' <- KW\qFF#$_IYVE:[qR0j,Vjqe6a'Yʋwf"d?m+CxnJ3t{yULE9GلX͸+y, QzPӢ2ty1,1JYeyP%jt Ԋ58lQcN<.{) >8|9`:2LRr}˃3u rPSy3䃤lcU'j^4%|3pqq$p0CE @rjWizutoͧIė~Wh[ΐ0x}f9Q*̤,^u^qXP3U|[]h w2xZ̃^͔7Iv]),epb-[./)BMYHU@o>תr]K稥=鲦(߆__rV#2C"˱)Uq7I\_wnw3mmO٬ x]DuWoQ~8⦎nA7`-xxt3@m̩\U;oy#bEUE~67W]ʢ\ݣs6kB^n)oȐ~tCQhbtyaeZ_@['.b5kM&=n_b&aCMl;&8v׺pXg"f~iZ;}D},_vyS}nV'UMA֘m%>/W+8&uT1 i e{m[:1-Qdx2! endstream endobj 2760 0 obj << /Length 1374 /Filter /FlateDecode >> stream xڽWrH}WUb!>Z^Ye|Qʅ1EyFI6`b%t'LI>`q>\i8#$^Ds8Mtv/$S[IUAY77f|x(Us}U r}CNW}=xnprԍf%C7l0}aaZՋ,tSk|4.OgpvW*)~*\u7#\)pEEۣIEڂ w1pa2J;֝t,ȣ^7 My&q?Ueb/7j=P`xMW&&0WǣCh&#F{ ݽLyUc$&T?m:fCRΓm碙~ 5 uT=qQ$>%P ZG7fU*1VQ~ӥaUR^zIױyJ[=+BE{}ډ˰~֋vZY_OGWx '`L=Mk~bو>C[?;<[si͟q/z{;0yu:țl+/c4x4zHս{ƺ_*UQUayR !Nr Z)ԑ‡plm7WMfgh֚yRtZ^ H%a[ )75h@&[%)M*0[OvԪ> stream xYMo7W8Ù! 9An4AA*H }CǁZKVvۋv1͒+B lP(0QŸD TSBF9蕭 %M)Q@Q,: qtTщ|vHbv$yhUeG@5ajrl#cBѻhC Tx@5oƔEtc* Q+P x'V-CS R!DG,a [H1BØAĚ1iH:Ż+nWtwU߳gO݄7a}zn|_;4c5>|}}|Mi~8INEh*-{ &z޴-_ >σx&x{78e0sp3\ VW:AlACvcΈ{Z؛j~<%^pfｆoZ]0-7 V:/pO1i"4aϼdzޥS`g[ӡV[yLߎU\_8|>n+J٠R62i"WAʦ1IGELH ֵze="i;#ω"ȳuc>ߘã*bL={e5Ff.O5˿Wcp7%{6ieiuдo;}vȬNEr(7j)=#3"n*ȸM{oLY0ɝxH4}fkul;{[6P e3{fDu7'yJO{l]a[Eh_4 DɊ8-3<V> stream xڽWms8ίG3Xo %mr$z3ms"xV 84LZ=i~?Xq,|a.G|*5>w00bb9t}`X y̳Èql}C)^'feHʍIV. 78z!d_c| wc憽2MA2L)ǔ5 LRYVfx1/ڈ6(dIPy)2 Wh_g7C}L?_޼3Bp'QpPE>']PfiXt, pb]Qrх3:!dQaVWRfSi;%$X>:ߖE8N[JY$ھD8iuLeT5CP"XV:a[/ۨ (x-KY[ 9v}㗪5 |Sj hV7vSaGfԑ%jzHs)­C*ڮ,@HrAeFW]qt63pqJtvR]UC' W f?6t!bo=j2Uu>WCXsZ!(qJ 8(2$4Y3m€?q`u? (_4ߗI*d¸19")OCpZv^݌ˮs5=u Ԕf, $:c/rYO{2ְZ*RTg;7uH>a a? ymԣo Xgc~B4S}h#c 1˾cYUE&`vHЮ0'4=oC[ :AP8BwG#4Q!4Q!4%Q1OYDk&5@ԺRFk_E9m(G'Y+zk,kra <=oF+l@UGE jľ,C4,kJd6O0&Y^(/ 27[> stream xYms6_FI^ 0~HcunڹsCKT)ɱD*^&H.v¿','uB5QTIk3 4~;HOf7(4[$p&qGޟ]~?c,sgۤaӼ:7,KGZ%P`Jg?d3$Hb^*L6vnre_&Ҩn\on\grӍ4cw`@FINs&nD0Nݾw##7#nҷ;:>3E4N9mvmۖ5XDu.S MUe3aFAO?^}y?`ieO#7Wo~ͧ D6ԷPRNzW]֭>uSۍ[z /my@ 'v^|Y6skmlyJo0)3/z6eO)J]Z\dC*b$[h)Zu}Q/"x Y9/!Ȕ&9-k m;eT43ZGiA~MFx.%&â _1d0 ;ד@N$ бr w~>^_HvoEySڅ‡.?\׮{ 4;@Vy8r"/SHa==> @),/y*z 2^Ux/?0ӓ|q+}_;ani^W!P-vecbi 'ib n>J6,o*p"*A}U{Uᵨ {tC]bQA;L*+wi1tؼ+OY/m[VM]ΟZ* !@|:\jX&\\!b$<:_ؔ~;+ R< :ޞe4>4LjrYgPg0@t<)3p5>,;0QKuźh0*qL%ÉQ{\[*"TCYh聨/RYx*Di^.#@#"ܙWUGEԑ=|s=4tӾy/26(!%>˰` \UP_ڊ XaK,UÏ @0.#f7ZNr ~vl#,ݘF7(4KE0 Sưe/4o!!.iƶbE1sEgyt݌w >&tqXi.p ӵ:,J2;K])꟢֓4ui YF3v1=2bIylįq8b1!mlS}; :֩ ^ୂ/B5 %򖇄]S&/!v2h9ܜ?wsǚ0GnɹoEi"9 ቗" n:'$cN  endstream endobj 2773 0 obj << /Length 1734 /Filter /FlateDecode >> stream xY[s8~0o]-;Hdo0wh5љ@MF&#51[`Hdw<<  ExUE Ie01-r5.2́=e'eotwzf-mСѓ#xBoRNOc*lp"8?Ϝ$rB oҾ|H⬖h0$=̝=`WfUbeay'F) z4?i FW]ĮNqYNc|_d]^̒"ębIKcZe&_bў]DDDX+K~"_Qa9KK1 a#E3iޡ8^aqffВڐ6_+MXe:_%g=GJuES2Ekx<E3*<#Iʇ tMQE 9!& gJM 9ۯq>~:O &]fBcESKIE IpNYmȾBZʨJ\pH]Z"A@jomD}(2f[|"BGk"8> Jþ$*hK_ y[}]Hk*#M +F?bvBtnG?Fw`dMVf8emz` A#)`HE&U1hE£\ެ&$?Yv7 DCL\O+R۩9Zy9"-+k=IIxhQoJ? 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