lrslib-043/0000755001553201777760000000000011762051230012114 5ustar avisnogrouplrslib-043/makefile0000755001553201777760000001210111607605134013620 0ustar avisnogroup# Makefile for lrslib including lrs and redund # 2008.1.15 # # choose one of the first 4 and gmp if applicable - see README # # make all normal version for 32bit machines with timing/signals handling # make all64 for machines with 64bit integers, eg. DEC Alpha # make ansi ansi standard version for 32bit machines without signals handling # make nosigs ansi standard version for 32bit machines without timing/signals handling # make demo compile the demo programs (vanilla machine) # make gmp uses gmp arithmetic, set paths for include files *first* # make clean to clean all executables #Select one of the following INCLUDE,LIB paths only needed for gmp version #linux at mcgill with gmp version 3 INCLUDEDIR = /usr/local/include LIBDIR = /usr/local/lib #linux at mcgill with gmp version 2 #INCLUDEDIR = /labs/cgm/gmp2/include #LIBDIR = /labs/cgm/gmp2/lib all: lrs.c lrslib.c lrslib.h lrsmp.c lrsmp.h lrslong.c lrslong.h redund.c buffer.c nash.c 2nash.c gcc -O3 -DTIMES -DSIGNALS -o lrs lrs.c lrslib.c lrsmp.c gcc -O3 -DTIMES -DSIGNALS -o redund redund.c lrslib.c lrsmp.c gcc -O3 -DTIMES -DSIGNALS -DLONG -o lrs1 lrs.c lrslib.c lrslong.c gcc -O3 -DTIMES -DSIGNALS -DLONG -o redund1 redund.c lrslib.c lrslong.c gcc -O3 -DLRS_QUIET -DTIMES -DSIGNALS -o nash nash.c lrslib.c lrsmp.c gcc -O3 -o setupnash setupnash.c lrslib.c lrsmp.c gcc -O3 -o setupnash2 setupnash2.c lrslib.c lrsmp.c gcc -Wall -O3 -o fourier fourier.c lrslib.c lrsmp.c gcc -O3 -o buffer buffer.c gcc -O3 -o 2nash 2nash.c gmp: fourier.c 2gnash.c lrs.c redund.c lrslib.h lrslib.c lrsgmp.h lrsgmp.c nash.c gcc -O3 -static -DTIMES -DSIGNALS -DGMP -I${INCLUDEDIR} lrs.c lrslib.c lrsgmp.c -L${LIBDIR} -lgmp -o glrs gcc -O3 -static -DTIMES -DSIGNALS -DGMP -I${INCLUDEDIR} redund.c lrslib.c lrsgmp.c -L${LIBDIR} -lgmp -o gredund gcc -O3 -static -DLRS_QUIET -DTIMES -DSIGNALS -DGMP -I${INCLUDEDIR} nash.c lrslib.c lrsgmp.c -L${LIBDIR} -lgmp -o gnash gcc -O3 -static -DTIMES -DSIGNALS -DGMP -I${INCLUDEDIR} fourier.c lrslib.c lrsgmp.c -L${LIBDIR} -lgmp -o gfourier gcc -O3 -o buffer buffer.c gcc -O3 -o 2gnash 2gnash.c gcc -O3 -static -DTIMES -DSIGNALS -DGMP -I${INCLUDEDIR} fourier.c lrslib.c lrsgmp.c -L${LIBDIR} -lgmp -o gfourier gnash: lrslib.h lrslib.c lrsgmp.h lrsgmp.c nash.c 2gnash.c gcc -O3 -static -DLRS_QUIET -DTIMES -DSIGNALS -DGMP -I${INCLUDEDIR} nash.c lrslib.c lrsgmp.c -L${LIBDIR} -lgmp -o gnash gcc -O3 -o 2gnash 2gnash.c all64: lrs.c lrslib.c lrslib.h lrsmp.c lrsmp.h lrslong.c lrslong.h redund.c buffer.c gcc -DTIMES -DSIGNALS -DB64 -O3 -o lrs lrs.c lrslib.c lrsmp.c gcc -DTIMES -DSIGNALS -DB64 -O3 -o redund redund.c lrslib.c lrsmp.c gcc -DTIMES -DSIGNALS -DLONG -DB64 -O3 -o lrs1 lrs.c lrslib.c lrslong.c gcc -DTIMES -DSIGNALS -DLONG -DB64 -O3 -o redund1 redund.c lrslib.c lrslong.c gcc -O3 -o buffer buffer.c ansi: lrs.c lrslib.c lrslib.h lrsmp.c lrsmp.h lrslong.c lrslong.h redund.c buffer.c nash.c gcc -ansi -DTIMES -O3 -o lrs lrs.c lrslib.c lrsmp.c gcc -ansi -DTIMES -O3 -o redund redund.c lrslib.c lrsmp.c gcc -ansi -DTIMES -DLONG -O3 -o lrs1 lrs.c lrslib.c lrslong.c gcc -ansi -DTIMES -DLONG -O3 -o redund1 redund.c lrslib.c lrslong.c gcc -O3 -o buffer buffer.c gcc -Wall -ansi -O3 -o nash nash.c lrslib.c lrsmp.c nosigs: lrs.c lrslib.c lrslib.h lrsmp.c lrsmp.h lrslong.c lrslong.h redund.c buffer.c gcc -ansi -O3 -o lrs lrs.c lrslib.c lrsmp.c gcc -ansi -O3 -o redund redund.c lrslib.c lrsmp.c gcc -ansi -O3 -DLONG -o lrs1 lrs.c lrslib.c lrslong.c gcc -ansi -O3 -DLONG -o redund1 redund.c lrslib.c lrslong.c gcc -ansi -O3 -o buffer buffer.c lrs: lrs.c lrslib.c lrslong.c lrsmp.c gcc -Wall -ansi -O3 -o lrs lrs.c lrslib.c lrsmp.c redund: redund.c lrslib.c lrslong.c lrsmp.c gcc -Wall -ansi -O3 -o redund redund.c lrslib.c lrsmp.c nash: setupnash2.c setupnash.c nash.c lrslib.c lrsmp.c 2nash.c gcc -Wall -DTIMES -ansi -O3 -o nash nash.c lrslib.c lrsmp.c gcc -Wall -o setupnash setupnash.c lrslib.c lrsmp.c gcc -Wall -o setupnash2 setupnash2.c lrslib.c lrsmp.c gcc -O3 -o 2nash 2nash.c fourier: fourier.c lrslib.c lrslong.c lrsmp.c gcc -Wall -O3 -o fourier fourier.c lrslib.c lrsmp.c gcc -O3 -static -DTIMES -DSIGNALS -DGMP -I${INCLUDEDIR} fourier.c lrslib.c lrsgmp.c -L${LIBDIR} -lgmp -o gfourier demo: lpdemo.c chdemo.c vedemo.c lrslib.c lrslong.c lrsmp.c gcc -Wall -ansi -O3 -o lpdemo lpdemo.c lrslib.c lrsmp.c gcc -Wall -ansi -O3 -o vedemo vedemo.c lrslib.c lrsmp.c gcc -Wall -ansi -O3 -o chdemo chdemo.c lrslib.c lrsmp.c float: float2rat.c rat2float.c lrsmp.c gcc -DLRSMP -Wall -ansi -o float2rat float2rat.c lrsmp.c gcc -DLRSMP -Wall -ansi -o rat2float rat2float.c lrsmp.c clean: rm -rf lrs lrs1 redund redund1 buffer glrs gredund rm -rf foo gfoo rm -rf lpdemo vedemo chdemo rm -rf fourier gfourier rm -rf nash gnash setupnash setupnash2 foo: foo.c lrslib.h lrslib.c lrsmp.h lrsmp.c gcc -O3 -static -DTIMES -DSIGNALS foo.c lrslib.c lrsmp.c -L${LIBDIR} -o foo gfoo: foo.c lrslib.h lrslib.c lrsgmp.h lrsgmp.c gcc -O3 -static -DTIMES -DSIGNALS -DGMP -I${INCLUDEDIR} foo.c lrslib.c lrsgmp.c -L${LIBDIR} -lgmp -o gfoo lrslib-043/cube.ine0000755001553201777760000000020311607605134013533 0ustar avisnogroupcube *cube of side 2 centred at origin H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 -1 0 1 0 0 -1 end lrslib-043/lrslib.c0000755001553201777760000035621111762050461013567 0ustar avisnogroup/* lrslib.c library code for lrs */ /* last modified: 2012.6.1 */ /* truncate needs mod to supress last pivot */ /* need to add a test for non-degenerate pivot step in reverse I guess */ /* Copyright: David Avis 2003,2011 avis@cs.mcgill.ca */ /* 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 2 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, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */ #include #include #include "lrslib.h" /* Globals; these need to be here, rather than lrslib.h, so they are not multiply defined. */ FILE *lrs_cfp; /* output file for checkpoint information */ FILE *lrs_ifp; /* input file pointer */ FILE *lrs_ofp; /* output file pointer */ unsigned long dict_count, dict_limit, cache_tries, cache_misses; /* Variables and functions global to this file only */ static long lrs_checkpoint_seconds = 0; static long lrs_global_count = 0; /* Track how many lrs_dat records are allocated */ static lrs_dat_p *lrs_global_list[MAX_LRS_GLOBALS + 1]; static void lrs_dump_state (); /*******************************/ /* functions for external use */ /*******************************/ /*******************************************************/ /* lrs_main is driver for lrs.c does H/V enumeration */ /* showing function calls intended for public use */ /*******************************************************/ long lrs_main (int argc, char *argv[]) { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_vector output; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ long col; /* output column index for dictionary */ long startcol = 0; long prune = FALSE; /* if TRUE, getnextbasis will prune tree and backtrack */ /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ /* they default to stdin and stdout, but may be overidden by command line parms. */ /*************************************************** Step 0: Do some global initialization that should only be done once, no matter how many lrs_dat records are allocated. db ***************************************************/ if ( !lrs_init ("\n*lrs:")) return 1; printf(AUTHOR); /*********************************************************************************/ /* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */ /*********************************************************************************/ Q = lrs_alloc_dat ("LRS globals"); /* allocate and init structure for static problem data */ if (Q == NULL) return 1; if (!lrs_read_dat (Q, argc, argv)) /* read first part of problem data to get dimensions */ return 1; /* and problem type: H- or V- input representation */ P = lrs_alloc_dic (Q); /* allocate and initialize lrs_dic */ if (P == NULL) return 1; if (!lrs_read_dic (P, Q)) /* read remainder of input to setup P and Q */ return 1; output = lrs_alloc_mp_vector (Q->n); /* output holds one line of output from dictionary */ /*********************************************************************************/ /* Step 2: Find a starting cobasis from default of specified order */ /* P is created to hold active dictionary data and may be cached */ /* Lin is created if necessary to hold linearity space */ /* Print linearity space if any, and retrieve output from first dict. */ /*********************************************************************************/ if (!lrs_getfirstbasis (&P, Q, &Lin, FALSE)) return 1; /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ if (Q->homogeneous && Q->hull) startcol++; /* col zero not treated as redundant */ for (col = startcol; col < Q->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q, Lin[col]); /* Array Lin[][] holds the coeffs. */ /*********************************************************************************/ /* Step 3: Terminate if lponly option set, otherwise initiate a reverse */ /* search from the starting dictionary. Get output for each new dict. */ /*********************************************************************************/ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ /* prune is TRUE if tree should be pruned at current node */ do { prune=lrs_checkbound(P,Q); if (!prune) for (col = 0; col <= P->d; col++) if (lrs_getsolution (P, Q, output, col)) lrs_printoutput (Q, output); } while (!Q->lponly && lrs_getnextbasis (&P, Q, prune)); if (Q->lponly) lrs_lpoutput(P,Q,output); else lrs_printtotals (P, Q); /* print final totals, including estimates */ lrs_clear_mp_vector(output, Q->n); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ lrs_close ("lrs:"); return 0; } /*********************************************/ /* end of model test program for lrs library */ /*********************************************/ /*******************************************************/ /* redund_main is driver for redund.c, removes all */ /* redundant rows from an H or V-representation */ /* showing function calls intended for public use */ /*******************************************************/ long redund_main (int argc, char *argv[]) { lrs_mp_matrix Ain; /* holds a copy of the input matrix to output at the end */ long *redineq; /* redineq[i]=0 if ineq i non-red,1 if red,2 linearity */ long ineq; /* input inequality number of current index */ lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ long i, j, d, m; long nlinearity; /* number of linearities in input file */ long nredund; /* number of redundant rows in input file */ long lastdv; long debug; long index; /* basic index for redundancy test */ /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ /* they default to stdin and stdout, but may be overidden by command line parms. */ /* Lin is global 2-d array for linearity space if it is found (redund columns) */ lrs_ifp = stdin; lrs_ofp = stdout; /*************************************************** Step 0: Do some global initialization that should only be done once, no matter how many lrs_dat records are allocated. db ***************************************************/ if ( !lrs_init ("\n*redund:")) return 1; printf (AUTHOR); /*********************************************************************************/ /* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */ /*********************************************************************************/ Q = lrs_alloc_dat ("LRS globals"); /* allocate and init structure for static problem data */ if (Q == NULL) return 1; if (!lrs_read_dat (Q, argc, argv)) /* read first part of problem data to get dimensions */ return 1; /* and problem type: H- or V- input representation */ P = lrs_alloc_dic (Q); /* allocate and initialize lrs_dic */ if (P == NULL) return 1; if (!lrs_read_dic (P, Q)) /* read remainder of input to setup P and Q */ return 1; /* if non-negative flag is set, non-negative constraints are not input */ /* explicitly, and are not checked for redundancy */ m = P->m_A; /* number of rows of A matrix */ d = P->d; debug = Q->debug; redineq = calloc ((m + 1), sizeof (long)); Ain = lrs_alloc_mp_matrix (m, d); /* make a copy of A matrix for output later */ for (i = 1; i <= m; i++) { for (j = 0; j <= d; j++) copy (Ain[i][j], P->A[i][j]); if (debug) lrs_printrow ("*", Q, Ain[i], d); } /*********************************************************************************/ /* Step 2: Find a starting cobasis from default of specified order */ /* Lin is created if necessary to hold linearity space */ /*********************************************************************************/ if (!lrs_getfirstbasis (&P, Q, &Lin, TRUE)) return 1; /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ /*********************************************************************************/ /* Step 3: Test each row of the dictionary to see if it is redundant */ /*********************************************************************************/ /* note some of these may have been changed in getting initial dictionary */ m = P->m_A; d = P->d; nlinearity = Q->nlinearity; lastdv = Q->lastdv; if (debug) fprintf (lrs_ofp, "\ncheckindex m=%ld, n=%ld, nlinearity=%ld lastdv=%ld", m,d,nlinearity,lastdv); /* linearities are not considered for redundancy */ for (i = 0; i < nlinearity; i++) redineq[Q->linearity[i]] = 2L; /* rows 0..lastdv are cost, decision variables, or linearities */ /* other rows need to be tested */ for (index = lastdv + 1; index <= m + d; index++) { ineq = Q->inequality[index - lastdv]; /* the input inequality number corr. to this index */ redineq[ineq] = checkindex (P, Q, index); if (debug) fprintf (lrs_ofp, "\ncheck index=%ld, inequality=%ld, redineq=%ld", index, ineq, redineq[ineq]); if (redineq[ineq] == ONE) { fprintf (lrs_ofp, "\n*row %ld was redundant and removed", ineq); fflush (lrs_ofp); } } /* end for index ..... */ if (debug) { fprintf (lrs_ofp, "\n*redineq:"); for (i = 1; i <= m; i++) fprintf (lrs_ofp, " %ld", redineq[i]); } if (!Q->hull) fprintf (lrs_ofp, "\nH-representation"); else fprintf (lrs_ofp, "\nV-representation"); /* linearities will be printed first in output */ if (nlinearity > 0) { fprintf (lrs_ofp, "\nlinearity %ld", nlinearity); for (i = 1; i <= nlinearity; i++) fprintf (lrs_ofp, " %ld", i); } nredund = nlinearity; /* count number of non-redundant inequalities */ for (i = 1; i <= m; i++) if (redineq[i] == 0) nredund++; fprintf (lrs_ofp, "\nbegin"); fprintf (lrs_ofp, "\n%ld %ld rational", nredund, Q->n); /* print the linearities first */ for (i = 0; i < nlinearity; i++) lrs_printrow ("", Q, Ain[Q->linearity[i]], Q->inputd); for (i = 1; i <= m; i++) if (redineq[i] == 0) lrs_printrow ("", Q, Ain[i], Q->inputd); fprintf (lrs_ofp, "\nend"); fprintf (lrs_ofp, "\n*Input had %ld rows and %ld columns", m, Q->n); fprintf (lrs_ofp, ": %ld row(s) redundant", m - nredund); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ lrs_close ("redund:"); return 0; } /*********************************************/ /* end of redund.c */ /*********************************************/ /*******************/ /* lrs_printoutput */ /*******************/ void lrs_printoutput (lrs_dat * Q, lrs_mp_vector output) { long i; fprintf (lrs_ofp, "\n"); if (Q->hull || zero (output[0])) /*non vertex */ { for (i = 0; i < Q->n; i++) pmp ("", output[i]); } else { /* vertex */ fprintf (lrs_ofp, " 1 "); for (i = 1; i < Q->n; i++) prat ("", output[i], output[0]); } fflush(lrs_ofp); } /**************************/ /* end of lrs_printoutput */ /**************************/ /****************/ /* lrs_lpoutput */ /****************/ void lrs_lpoutput(lrs_dic * P,lrs_dat * Q, lrs_mp_vector output) { #ifndef LRS_QUIET lrs_mp Temp1, Temp2; long i; lrs_alloc_mp (Temp1); lrs_alloc_mp (Temp2); fprintf (lrs_ofp, "\n*LP solution only requested"); prat ("\n\n*Objective function has value ", P->objnum, P->objden); fprintf (lrs_ofp, "\n\n*Primal: "); for (i = 1; i < Q->n; i++) { fprintf(lrs_ofp,"x_%ld=",i); prat ("", output[i], output[0]); } if(Q->nlinearity > 0) fprintf (lrs_ofp, "\n\n*Linearities in input file - partial dual solution only"); fprintf (lrs_ofp, "\n\n*Dual: "); for (i = 0; i < P->d; i++) { fprintf(lrs_ofp,"y_%ld=",Q->inequality[P->C[i]-Q->lastdv]); changesign(P->A[0][P->Col[i]]); mulint(Q->Lcm[P->Col[i]],P->A[0][P->Col[i]],Temp1); mulint(Q->Gcd[P->Col[i]],P->det,Temp2); prat("",Temp1,Temp2); changesign(P->A[0][P->Col[i]]); } fprintf (lrs_ofp, "\n"); lrs_clear_mp (Temp1); lrs_clear_mp (Temp2); #endif } /***********************/ /* end of lrs_lpoutput */ /***********************/ void lrs_printrow (char name[], lrs_dat * Q, lrs_mp_vector output, long rowd) /* print a row of A matrix in output in "original" form */ /* rowd+1 is the dimension of output vector */ /* if input is H-rep. output[0] contains the RHS */ /* if input is V-rep. vertices are scaled by 1/output[1] */ { long i; fprintf (lrs_ofp, "\n%s", name); if (!Q->hull) /* input was inequalities, print directly */ { for (i = 0; i <= rowd; i++) pmp ("", output[i]); return; } /* input was vertex/ray */ if (zero (output[1])) /*non-vertex */ { for (i = 1; i <= rowd; i++) pmp ("", output[i]); } else { /* vertex */ fprintf (lrs_ofp, " 1 "); for (i = 2; i <= rowd; i++) prat ("", output[i], output[1]); } return; } /* end of lrs_printrow */ long lrs_getsolution (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output, long col) /* check if column indexed by col in this dictionary */ /* contains output */ /* col=0 for vertex 1....d for ray/facet */ { long j; /* cobasic index */ lrs_mp_matrix A = P->A; long *Row = P->Row; if (col == ZERO) /* check for lexmin vertex */ return lrs_getvertex (P, Q, output); /* check for rays: negative in row 0 , positive if lponly */ if (Q->lponly) { if (!positive (A[0][col])) return FALSE; } else if (!negative (A[0][col])) return FALSE; /* and non-negative for all basic non decision variables */ j = Q->lastdv + 1; while (j <= P->m && !negative (A[Row[j]][col])) j++; if (j <= P->m) return FALSE; if (Q->geometric || Q->allbases || lexmin (P, Q, col) || Q->lponly) return lrs_getray (P, Q, col, Q->n, output); return FALSE; /* no more output in this dictionary */ } /* end of lrs_getsolution */ long lrs_init (char *name) /* returns TRUE if successful, else FALSE */ { printf ("%s", name); printf (TITLE); printf (VERSION); printf ("("); printf (BIT); printf (","); printf (ARITH); if (!lrs_mp_init (ZERO, stdin, stdout)) /* initialize arithmetic */ return FALSE; printf (")"); lrs_global_count = 0; lrs_checkpoint_seconds = 0; #ifdef SIGNALS setup_signals (); #endif return TRUE; } void lrs_close (char *name) { fprintf (lrs_ofp, "\n*%s", name); fprintf (lrs_ofp, TITLE); fprintf (lrs_ofp, VERSION); fprintf (lrs_ofp, "("); fprintf (lrs_ofp, BIT); fprintf (lrs_ofp, ","); fprintf (lrs_ofp, ARITH); fprintf (lrs_ofp, ")"); #ifdef MP fprintf (lrs_ofp, " max digits=%ld/%ld", DIG2DEC (lrs_record_digits), DIG2DEC (lrs_digits)); #endif #ifdef TIMES ptimes (); #endif fprintf (lrs_ofp, "\n"); fclose (lrs_ifp); if (lrs_ofp != stdout) fclose (lrs_ofp); } /***********************************/ /* allocate and initialize lrs_dat */ /***********************************/ lrs_dat * lrs_alloc_dat (char *name) { lrs_dat *Q; long i; if (lrs_global_count >= MAX_LRS_GLOBALS) { fprintf (stderr, "Fatal: Attempt to allocate more than %ld global data blocks\n", MAX_LRS_GLOBALS); exit (1); } Q = (lrs_dat *) malloc (sizeof (lrs_dat)); if (Q == NULL) return Q; /* failure to allocate */ lrs_global_list[lrs_global_count] = Q; Q->id = lrs_global_count; lrs_global_count++; Q->name=(char *) CALLOC ((unsigned) strlen(name)+1, sizeof (char)); strcpy(Q->name,name); /* initialize variables */ Q->m = 0L; Q->n = 0L; Q->inputd = 0L; Q->deepest = 0L; Q->nlinearity = 0L; Q->nredundcol = 0L; Q->runs = 0L; Q->seed = 1234L; Q->totalnodes = 0L; for (i = 0; i < 10; i++) { Q->count[i] = 0L; Q->cest[i] = 0.0; } Q->count[2] = 1L; /* basis counter */ /* initialize flags */ Q->allbases = FALSE; Q->bound = FALSE; /* upper/lower bound on objective function given */ Q->debug = FALSE; Q->frequency = 0L; Q->dualdeg = FALSE; /* TRUE if dual degenerate starting dictionary */ Q->geometric = FALSE; Q->getvolume = FALSE; Q->homogeneous = TRUE; Q->polytope = FALSE; Q->hull = FALSE; Q->incidence = FALSE; Q->lponly = FALSE; Q->maxdepth = MAXD; Q->mindepth = -MAXD; Q->maxoutput = 0L; Q->nash = FALSE; Q->nonnegative = FALSE; Q->printcobasis = FALSE; Q->printslack = FALSE; Q->truncate = FALSE; /* truncate tree when moving from opt vertex */ Q->verbose=FALSE; Q->voronoi = FALSE; Q->maximize = FALSE; /*flag for LP maximization */ Q->minimize = FALSE; /*flag for LP minimization */ Q->restart = FALSE; /* TRUE if restarting from some cobasis */ Q->givenstart = FALSE; /* TRUE if a starting cobasis is given */ Q->strace = -1L; /* turn on debug at basis # strace */ Q->etrace = -1L; /* turn off debug at basis # etrace */ Q->saved_flag = 0; /* no cobasis saved initially, db */ lrs_alloc_mp (Q->Nvolume); lrs_alloc_mp (Q->Dvolume); lrs_alloc_mp (Q->sumdet); lrs_alloc_mp (Q->saved_det); lrs_alloc_mp (Q->boundn); lrs_alloc_mp (Q->boundd); itomp (ZERO, Q->Nvolume); itomp (ONE, Q->Dvolume); itomp (ZERO, Q->sumdet); /* 2012.6.1 */ Q->unbounded = FALSE; return Q; } /* end of allocate and initialize lrs_dat */ /*******************************/ /* lrs_read_dat */ /*******************************/ long lrs_read_dat (lrs_dat * Q, int argc, char *argv[]) { char name[100]; long dec_digits = 0; long infile=0; /*input file number to open if any */ long firstline = TRUE; /*flag for picking off name at line 1 */ int c; /* for fgetc */ if(argc > 1 ) infile=1; if(Q->nash && argc == 2) /* open second nash input file */ infile=2; if (infile > 0) /* command line argument overides stdin */ { if ((lrs_ifp = fopen (argv[infile], "r")) == NULL) { printf ("\nBad input file name\n"); return (FALSE); } else { if (infile==1) printf ("\n*Input taken from file %s", argv[infile]); } } /* command line argument overides stdout */ if ((!Q->nash && argc == 3) || (Q->nash && argc == 4)) { if ((lrs_ofp = fopen (argv[argc-1], "w")) == NULL) { printf ("\nBad output file name\n"); return (FALSE); } else printf ("\n*Output sent to file %s\n", argv[argc-1]); } /* process input file */ if( fscanf (lrs_ifp, "%s", name) == EOF) { fprintf (lrs_ofp, "\nNo begin line"); return (FALSE); } while (strcmp (name, "begin") != 0) /*skip until "begin" found processing options */ { if (strncmp (name, "*", 1) == 0) /* skip any line beginning with * */ { c = name[0]; while (c != EOF && c != '\n') c = fgetc (lrs_ifp); } else if (strcmp (name, "H-representation") == 0) Q->hull = FALSE; else if ((strcmp (name, "hull") == 0) || (strcmp (name, "V-representation") == 0)) { Q->hull = TRUE; Q->polytope = TRUE; /* will be updated as input read */ } else if (strcmp (name, "digits") == 0) { if (fscanf (lrs_ifp, "%ld", &dec_digits) == EOF) { fprintf (lrs_ofp, "\nNo begin line"); return (FALSE); } if (!lrs_set_digits(dec_digits)) return (FALSE); } else if (strcmp (name, "linearity") == 0) { if (!readlinearity (Q)) return FALSE; } else if (strcmp (name, "nonnegative") == 0) { if(Q->nash) fprintf (lrs_ofp, "\nNash incompatibile with nonnegative option - skipped"); else Q->nonnegative = TRUE; } else if (firstline) { stringcpy (Q->fname, name); fprintf (lrs_ofp, "\n%s", Q->fname); firstline = FALSE; } if (fscanf (lrs_ifp, "%s", name) == EOF) { fprintf (lrs_ofp, "\nNo begin line"); return (FALSE); } } /* end of while */ if (fscanf (lrs_ifp, "%ld %ld %s", &Q->m, &Q->n, name) == EOF) { fprintf (lrs_ofp, "\nNo data in file"); return (FALSE); } if (strcmp (name, "integer") != 0 && strcmp (name, "rational") != 0) { fprintf (lrs_ofp, "\nData type must be integer of rational"); return (FALSE); } if (Q->m == 0) { fprintf (lrs_ofp, "\nNo input given"); /* program dies ungracefully */ return (FALSE); } /* inputd may be reduced in preprocessing of linearities and redund cols */ return TRUE; } /* end of lrs_read_dat */ /****************************/ /* set up lrs_dic structure */ /****************************/ long lrs_read_dic (lrs_dic * P, lrs_dat * Q) /* read constraint matrix and set up problem and dictionary */ { lrs_mp Temp,Tempn,Tempd, mpone, mpten; lrs_mp_vector oD; /* Denom for objective function */ long i, j; char name[100]; int c; /* fgetc actually returns an int. db */ /* assign local variables to structures */ lrs_mp_matrix A; lrs_mp_vector Gcd, Lcm; long hull = Q->hull; long m, d; long dualperturb=FALSE; /* dualperturb=TRUE: objective function perturbed */ lrs_alloc_mp(Temp); lrs_alloc_mp(mpone); lrs_alloc_mp(Tempn); lrs_alloc_mp(Tempd); lrs_alloc_mp(mpten); A = P->A; m = Q->m; d = Q->inputd; Gcd = Q->Gcd; Lcm = Q->Lcm; oD = lrs_alloc_mp_vector (d); itomp (ONE, mpone); itomp (ONE, A[0][0]); itomp (ONE, Lcm[0]); itomp (ONE, Gcd[0]); for (i = 1; i <= m; i++) /* read in input matrix row by row */ { itomp (ONE, Lcm[i]); /* Lcm of denominators */ itomp (ZERO, Gcd[i]); /* Gcd of numerators */ for (j = hull; j <= d; j++) /* hull data copied to cols 1..d */ { if (readrat (A[i][j], A[0][j])) lcm (Lcm[i], A[0][j]); /* update lcm of denominators */ copy (Temp, A[i][j]); gcd (Gcd[i], Temp); /* update gcd of numerators */ } if (hull) { itomp (ZERO, A[i][0]); /*for hull, we have to append an extra column of zeroes */ if (!one (A[i][1]) || !one (A[0][1])) /* all rows must have a one in column one */ Q->polytope = FALSE; } if (!zero (A[i][hull])) /* for H-rep, are zero in column 0 */ Q->homogeneous = FALSE; /* for V-rep, all zero in column 1 */ storesign (Gcd[i], POS); storesign (Lcm[i], POS); if (greater (Gcd[i], mpone) || greater (Lcm[i], mpone)) for (j = 0; j <= d; j++) { exactdivint (A[i][j], Gcd[i], Temp); /*reduce numerators by Gcd */ mulint (Lcm[i], Temp, Temp); /*remove denominators */ exactdivint (Temp, A[0][j], A[i][j]); /*reduce by former denominator */ } } /* end of for i= */ /* 2010.4.26 patch */ if(Q->nonnegative) /* set up Gcd and Lcm for nonexistent nongative inequalities */ for (i=m+1;i<=m+d;i++) { itomp (ONE, Lcm[i]); itomp (ONE, Gcd[i]); } if (Q->homogeneous && Q->verbose) { fprintf (lrs_ofp, "\n*Input is homogeneous, column 1 not treated as redundant"); } /* read in flags */ while (fscanf (lrs_ifp, "%s", name) != EOF) { if (strncmp (name, "*", 1) == 0) /* skip any line beginning with * */ { c = name[0]; while (c != EOF && c != '\n') c = fgetc (lrs_ifp); } if (strcmp (name, "checkpoint") == 0) { long seconds; if(fscanf (lrs_ifp, "%ld", &seconds) == EOF) { fprintf (lrs_ofp, "\nInvalid checkpoint option"); return (FALSE); } #ifdef SIGNALS if (seconds > 0) { lrs_checkpoint_seconds = seconds; errcheck ("signal", signal (SIGALRM, timecheck)); alarm (lrs_checkpoint_seconds); } #endif } if (strcmp (name, "debug") == 0) { Q->etrace =0; if(fscanf (lrs_ifp, "%ld %ld", &Q->strace, &Q->etrace)==EOF) Q->strace =0; fprintf (lrs_ofp, "\n*%s from B#%ld to B#%ld", name, Q->strace, Q->etrace); Q->verbose=TRUE; if (Q->strace <= 1) Q->debug = TRUE; } if (strcmp (name, "startingcobasis") == 0) { if(Q->nonnegative) fprintf (lrs_ofp, "\n*startingcobasis incompatible with nonnegative option:skipped"); else { fprintf (lrs_ofp, "\n*startingcobasis"); Q->givenstart = TRUE; if (!readfacets (Q, Q->inequality)) return FALSE; } } if (strcmp (name, "restart") == 0) { Q->restart = TRUE; if(Q->voronoi) { if(fscanf (lrs_ifp, "%ld %ld %ld %ld", &Q->count[1], &Q->count[0], &Q->count[2], &P->depth)==EOF) return FALSE; fprintf (lrs_ofp, "\n*%s V#%ld R#%ld B#%ld h=%ld data points", name, Q->count[1], Q->count[0], Q->count[2], P->depth); } else if(hull) { if( fscanf (lrs_ifp, "%ld %ld %ld", &Q->count[0], &Q->count[2], &P->depth)==EOF) fprintf (lrs_ofp, "\n*%s F#%ld B#%ld h=%ld vertices/rays", name, Q->count[0], Q->count[2], P->depth); } else { if(fscanf (lrs_ifp, "%ld %ld %ld %ld", &Q->count[1], &Q->count[0], &Q->count[2], &P->depth)==EOF) return FALSE; fprintf (lrs_ofp, "\n*%s V#%ld R#%ld B#%ld h=%ld facets", name, Q->count[1], Q->count[0], Q->count[2], P->depth); } if (!readfacets (Q, Q->facet)) return FALSE; } /* end of restart */ /* The next flag request a LP solution only */ if (strcmp (name, "lponly") == 0) { if (Q->hull) fprintf (lrs_ofp, "\n*lponly option not valid for V-representation-skipped"); else Q->lponly = TRUE; } /* The LP will be solved after initialization to get starting vertex */ /* Used also with lponly flag */ if (strcmp (name, "maximize") == 0 || strcmp (name, "minimize") == 0) { if (Q->hull) fprintf (lrs_ofp, "\n*%s option not valid for V-representation-skipped", name); else { { if (strcmp (name, "maximize") == 0) Q->maximize = TRUE; else Q->minimize = TRUE; } fprintf (lrs_ofp,"\n*%s", name); if(dualperturb) /* apply a perturbation to objective function */ { fprintf (lrs_ofp, " - Objective function perturbed"); itomp(10L,mpten); copy(Temp,mpten); for (j = 0; j <= 10; j++) mulint(mpten,Temp,Temp); } fprintf (lrs_ofp, ": "); for (j = 0; j <= d; j++) { if (readrat (A[0][j], oD[j]) || dualperturb ) { if(dualperturb && j > 0 && j < d ) { if (Q->maximize) linrat(A[0][j], oD[j],ONE,mpone,Temp,ONE,Tempn,Tempd); else linrat(A[0][j], oD[j],ONE,mpone,Temp,-1L,Tempn,Tempd); copy(A[0][j],Tempn); copy(oD[j],Tempd); mulint(mpten,Temp,Temp); } reduce (A[0][j], oD[j]); lcm (Q->Lcm[0], oD[j]); /* update lcm of denominators */ } prat ("", A[0][j], oD[j]); if (!Q->maximize) changesign (A[0][j]); } storesign (Q->Lcm[0], POS); if (greater (Q->Lcm[0], mpone)) for (j = 0; j <= d; j++) { mulint (Q->Lcm[0], A[0][j], A[0][j]); /*remove denominators */ copy (Temp, A[0][j]); exactdivint (Temp, oD[j], A[0][j]); } if (Q->debug) printA (P, Q); } } /* end of LP setup */ if (strcmp (name, "volume") == 0) { fprintf (lrs_ofp, "\n*%s", name); Q->getvolume = TRUE; } if (strcmp (name, "geometric") == 0) { fprintf (lrs_ofp, "\n*%s", name); if (hull & !Q->voronoi) fprintf (lrs_ofp, " - option for H-representation or voronoi only, skipped"); else Q->geometric = TRUE; } if (strcmp (name, "allbases") == 0) { fprintf (lrs_ofp, "\n*%s", name); Q->allbases = TRUE; } if (strcmp (name, "dualperturb") == 0) { dualperturb = TRUE; } if (strcmp (name, "incidence") == 0) { fprintf (lrs_ofp, "\n*%s", name); Q->incidence = TRUE; } if (strcmp (name, "#incidence") == 0) /* number of incident inequalities only */ { Q->printcobasis = TRUE; } if (strcmp (name, "printcobasis") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->frequency)==EOF) /*2010.7.7 set default to zero = print only when outputting vertex/ray/facet */ Q->frequency=0; fprintf (lrs_ofp, "\n*%s", name); if (Q->frequency > 0) fprintf(lrs_ofp," %ld", Q->frequency); Q->printcobasis = TRUE; } if (strcmp (name, "printslack") == 0) { Q->printslack = TRUE; } if (strcmp (name, "cache") == 0) { if(fscanf (lrs_ifp, "%ld", &dict_limit)==EOF) dict_limit=1; fprintf (lrs_ofp, "\n*cache %ld", dict_limit); if (dict_limit < 1) dict_limit = 1; } if (strcmp (name, "linearity") == 0) { if (!readlinearity (Q)) return FALSE; } if (strcmp (name, "maxdepth") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->maxdepth)==EOF) Q->maxdepth=1; fprintf (lrs_ofp, "\n*%s %ld", name, Q->maxdepth); } if (strcmp (name, "maxoutput") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->maxoutput)==EOF) Q->maxoutput = 100; fprintf (lrs_ofp, "\n*%s %ld", name, Q->maxoutput); } if (strcmp (name, "mindepth") == 0) { if( fscanf (lrs_ifp, "%ld", &Q->mindepth)==EOF) Q->mindepth = 0; fprintf (lrs_ofp, "\n*%s %ld", name, Q->mindepth); } if (strcmp (name, "truncate") == 0) { fprintf (lrs_ofp, "\n*%s", name); if (!hull) Q->truncate = TRUE; else fprintf (lrs_ofp, " - option for H-representation only, skipped"); } if (strcmp (name, "verbose") == 0) Q->verbose = TRUE; if (strcmp (name, "bound") == 0) { readrat(Q->boundn,Q->boundd); Q->bound = TRUE; } if (strcmp (name, "nonnegative") == 0) { fprintf (lrs_ofp, "\n*%s", name); fprintf (lrs_ofp, " - option must come before begin line - skipped"); } if (strcmp (name, "seed") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->seed)==EOF) Q->seed = 3142; fprintf (lrs_ofp, "\n*seed= %ld ", Q->seed); } if (strcmp (name, "estimates") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->runs)==EOF) Q->runs=1; fprintf (lrs_ofp, "\n*%ld %s", Q->runs, name); } if ((strcmp (name, "voronoi") == 0) || (strcmp (name, "Voronoi") == 0)) { if (!hull) fprintf (lrs_ofp, "\n*voronoi requires V-representation - option skipped"); else { Q->voronoi = TRUE; Q->polytope = FALSE; } } } /* end of while for reading flags */ if (Q->polytope) Q->getvolume = TRUE; /* might as well get volume, it doesn't cost much */ if (Q->bound && Q->maximize) prat("\n*Lower bound on objective function:",Q->boundn,Q->boundd); if (Q->bound && Q->minimize) prat("\n*Upper bound on objective function:",Q->boundn,Q->boundd); /* Certain options are incompatible, this is fixed here */ if (Q->restart) Q->getvolume = FALSE; /* otherwise incorrect volume reported */ if (Q->incidence) { Q->printcobasis = TRUE; /* 2010.5.7 No need to reset this, as it may have been set by printcobasis */ /* Q->frequency = ZERO; */ } if (Q->debug) { printA (P, Q); fprintf (lrs_ofp, "\nexiting lrs_read_dic"); } lrs_clear_mp(Temp); lrs_clear_mp(mpone); lrs_clear_mp(Tempn); lrs_clear_mp(Tempd); lrs_clear_mp(mpten); lrs_clear_mp_vector (oD,d); return TRUE; } /********* end of lrs_read_dic ***************/ /* In lrs_getfirstbasis and lrs_getnextbasis we use D instead of P */ /* since the dictionary P may change, ie. &P in calling routine */ #define D (*D_p) long lrs_getfirstbasis (lrs_dic ** D_p, lrs_dat * Q, lrs_mp_matrix * Lin, long no_output) /* gets first basis, FALSE if none */ /* P may get changed if lin. space Lin found */ /* no_output is TRUE supresses output headers */ { lrs_mp scale, Temp; long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A; long *B, *C, *Row, *Col; long *inequality; long *linearity; long hull = Q->hull; long m, d, lastdv, nlinearity, nredundcol; static long ocount=0; lrs_alloc_mp(Temp); lrs_alloc_mp(scale); if (Q->lponly) no_output = TRUE; m = D->m; d = D->d; lastdv = Q->lastdv; nredundcol = 0L; /* will be set after getabasis */ nlinearity = Q->nlinearity; /* may be reset if new linearity read or in getabasis*/ linearity = Q->linearity; A = D->A; B = D->B; C = D->C; Row = D->Row; Col = D->Col; inequality = Q->inequality; if (Q->nlinearity > 0 && Q->nonnegative) { fprintf (lrs_ofp, "\n*linearity and nonnegative options incompatible"); fprintf (lrs_ofp, " - all linearities are skipped"); fprintf (lrs_ofp, "\n*add nonnegative constraints explicitly and "); fprintf (lrs_ofp, " remove nonnegative option"); } if (Q->nlinearity && Q->voronoi) fprintf (lrs_ofp, "\n*linearity and Voronoi options set - results unpredictable"); if (Q->lponly && !Q->maximize && !Q->minimize) fprintf (lrs_ofp, "\n*LP has no objective function given - assuming all zero"); if (Q->runs > 0) /* arrays for estimator */ { Q->isave = (long *) CALLOC ((unsigned) (m * d), sizeof (long)); Q->jsave = (long *) CALLOC ((unsigned) (m * d), sizeof (long)); } /* default is to look for starting cobasis using linearies first, then */ /* filling in from last rows of input as necessary */ /* linearity array is assumed sorted here */ /* note if restart/given start inequality indices already in place */ /* from nlinearity..d-1 */ for (i = 0; i < nlinearity; i++) /* put linearities first in the order */ inequality[i] = linearity[i]; k = 0; /* index for linearity array */ if (Q->givenstart) k = d; else k = nlinearity; for (i = m; i >= 1; i--) { j = 0; while (j < k && inequality[j] != i) j++; /* see if i is in inequality */ if (j == k) inequality[k++] = i; } if (Q->debug) { fprintf (lrs_ofp, "\n*Starting cobasis uses input row order"); for (i = 0; i < m; i++) fprintf (lrs_ofp, " %ld", inequality[i]); } /* for voronoi convert to h-description using the transform */ /* a_0 .. a_d-1 -> (a_0^2 + ... a_d-1 ^2)-2a_0x_0-...-2a_d-1x_d-1 + x_d >= 0 */ /* note constant term is stored in column d, and column d-1 is all ones */ /* the other coefficients are multiplied by -2 and shifted one to the right */ if (Q->debug) printA (D, Q); if (Q->voronoi) { Q->hull = FALSE; hull = FALSE; for (i = 1; i <= m; i++) { if (zero (A[i][1])) { fprintf (lrs_ofp, "\nWith voronoi option column one must be all one"); return (FALSE); } copy (scale, A[i][1]); /*adjust for scaling to integers of rationals */ itomp (ZERO, A[i][0]); for (j = 2; j <= d; j++) /* transform each input row */ { copy (Temp, A[i][j]); mulint (A[i][j], Temp, Temp); linint (A[i][0], ONE, Temp, ONE); linint (A[i][j - 1], ZERO, A[i][j], -TWO); mulint (scale, A[i][j - 1], A[i][j - 1]); } /* end of for (j=1;..) */ copy (A[i][d], scale); mulint (scale, A[i][d], A[i][d]); } /* end of for (i=1;..) */ if (Q->debug) printA (D, Q); } /* end of if(voronoi) */ if (!Q->maximize && !Q->minimize) for (j = 0; j <= d; j++) itomp (ZERO, A[0][j]); /* Now we pivot to standard form, and then find a primal feasible basis */ /* Note these steps MUST be done, even if restarting, in order to get */ /* the same index/inequality correspondance we had for the original prob. */ /* The inequality array is used to give the insertion order */ /* and is defaulted to the last d rows when givenstart=FALSE */ if(Q->nonnegative) { /* no need for initial pivots here, labelling already done */ Q->lastdv = d; Q->nredundcol = 0; } else { if (!getabasis (D, Q, inequality)) return FALSE; /* bug fix 2009.12.2 */ nlinearity=Q->nlinearity; /*may have been reset if some lins are redundant*/ } if(Q->debug) { fprintf(lrs_ofp,"\nafter getabasis"); printA(D, Q); } nredundcol = Q->nredundcol; lastdv = Q->lastdv; d = D->d; /********************************************************************/ /* now we start printing the output file unless no output requested */ /********************************************************************/ if (!no_output || Q->debug) { if (Q->voronoi) fprintf (lrs_ofp, "\n*Voronoi Diagram: Voronoi vertices and rays are output"); if (hull) fprintf (lrs_ofp, "\nH-representation"); else fprintf (lrs_ofp, "\nV-representation"); /* Print linearity space */ /* Don't print linearity if first column zero in hull computation */ if (hull && Q->homogeneous) k = 1; /* 0 normally, 1 for homogeneous case */ else k = 0; if (nredundcol > k) { fprintf (lrs_ofp, "\nlinearity %ld ", nredundcol - k); /*adjust nredundcol for homog. */ for (i = 1; i <= nredundcol - k; i++) fprintf (lrs_ofp, " %ld", i); } /* end print of linearity space */ fprintf (lrs_ofp, "\nbegin"); fprintf (lrs_ofp, "\n***** %ld rational", Q->n); } /* end of if !no_output ....... */ /* Reset up the inequality array to remember which index is which input inequality */ /* inequality[B[i]-lastdv] is row number of the inequality with index B[i] */ /* inequality[C[i]-lastdv] is row number of the inequality with index C[i] */ for (i = 1; i <= m; i++) inequality[i] = i; if (nlinearity > 0) /* some cobasic indices will be removed */ { for (i = 0; i < nlinearity; i++) /* remove input linearity indices */ inequality[linearity[i]] = 0; k = 1; /* counter for linearities */ for (i = 1; i <= m - nlinearity; i++) { while (k <= m && inequality[k] == 0) k++; /* skip zeroes in corr. to linearity */ inequality[i] = inequality[k++]; } } /* end if linearity */ if (Q->debug) { fprintf (lrs_ofp, "\ninequality array initialization:"); for (i = 1; i <= m - nlinearity; i++) fprintf (lrs_ofp, " %ld", inequality[i]); } if (nredundcol > 0) { *Lin = lrs_alloc_mp_matrix (nredundcol, Q->n); for (i = 0; i < nredundcol; i++) { if (!(Q->homogeneous && Q->hull && i == 0)) /* skip redund col 1 for homog. hull */ { lrs_getray (D, Q, Col[0], D->C[0] + i - hull, (*Lin)[i]); /* adjust index for deletions */ } if (!removecobasicindex (D, Q, 0L)) return FALSE; } } /* end if nredundcol > 0 */ if (Q->lponly || Q->nash ) if (Q->verbose) { fprintf (lrs_ofp, "\nNumber of pivots for starting dictionary: %ld",Q->count[3]); ocount=Q->count[3]; if(Q->lponly) printA (D, Q); } /* Do dual pivots to get primal feasibility */ if (!primalfeasible (D, Q)) { #ifndef LRS_QUIET fprintf (lrs_ofp, "\nNo feasible solution"); #endif if (Q->nash && Q->verbose ) { fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]); fprintf (lrs_ofp, " - No feasible solution"); ocount=Q->count[3]; } return FALSE; } if (Q->lponly || Q->nash ) if (Q->verbose) { fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]); ocount=Q->count[3]; if(Q->lponly) printA (D, Q); } /* Now solve LP if objective function was given */ if (Q->maximize || Q->minimize) { Q->unbounded = !lrs_solvelp (D, Q, Q->maximize); if (Q->lponly) { if (Q->verbose) { fprintf (lrs_ofp, "\nNumber of pivots for optimum solution: %ld",Q->count[3]); printA (D, Q); ocount=Q->count[3]; } lrs_clear_mp(Temp); lrs_clear_mp(scale); return TRUE; } else /* check to see if objective is dual degenerate */ { j = 1; while (j <= d && !zero (A[0][j])) j++; if (j <= d) Q->dualdeg = TRUE; } } else /* re-initialize cost row to -det */ { for (j = 1; j <= d; j++) { copy (A[0][j], D->det); storesign (A[0][j], NEG); } itomp (ZERO, A[0][0]); /* zero optimum objective value */ } /* reindex basis to 0..m if necessary */ /* we use the fact that cobases are sorted by index value */ if (Q->debug) printA (D, Q); while (C[0] <= m) { i = C[0]; j = inequality[B[i] - lastdv]; inequality[B[i] - lastdv] = inequality[C[0] - lastdv]; inequality[C[0] - lastdv] = j; C[0] = B[i]; B[i] = i; reorder1 (C, Col, ZERO, d); } if (Q->debug) { fprintf (lrs_ofp, "\n*Inequality numbers for indices %ld .. %ld : ", lastdv + 1, m + d); for (i = 1; i <= m - nlinearity; i++) fprintf (lrs_ofp, " %ld ", inequality[i]); printA (D, Q); } if (Q->restart) { if (Q->debug) fprintf (lrs_ofp, "\nPivoting to restart co-basis"); if (!restartpivots (D, Q)) return FALSE; D->lexflag = lexmin (D, Q, ZERO); /* see if lexmin basis */ if (Q->debug) printA (D, Q); } /* Check to see if necessary to resize */ if (Q->inputd > D->d) *D_p = resize (D, Q); lrs_clear_mp(Temp); lrs_clear_mp(scale); return TRUE; } /********* end of lrs_getfirstbasis ***************/ /*****************************************/ /* getnextbasis in reverse search order */ /*****************************************/ long lrs_getnextbasis (lrs_dic ** D_p, lrs_dat * Q, long backtrack) /* gets next reverse search tree basis, FALSE if none */ /* switches to estimator if maxdepth set */ /* backtrack TRUE means backtrack from here */ { /* assign local variables to structures */ long i = 0L, j = 0L; long m = D->m; long d = D->d; if (backtrack && D->depth == 0) return FALSE; /* cannot backtrack from root */ if (Q->maxoutput > 0 && Q->count[0]+Q->count[1]-Q->hull >= Q->maxoutput) return FALSE; /* output limit reached */ while ((j < d) || (D->B[m] != m)) /*main while loop for getnextbasis */ { if (D->depth >= Q->maxdepth) { backtrack = TRUE; if (Q->runs > 0) /*get an estimate of remaining tree */ lrs_estimate (D, Q); if (Q->maxdepth == 0) /* estimate only */ return FALSE; /* no nextbasis */ } /* if ( Q->truncate && negative(D->A[0][0]))*/ /* truncate when moving from opt. vertex */ /* backtrack = TRUE; 2011.7.14 */ if (backtrack) /* go back to prev. dictionary, restore i,j */ { backtrack = FALSE; if (check_cache (D_p, Q, &i, &j)) { if (Q->debug) fprintf (lrs_ofp, "\n Cached Dict. restored to depth %ld\n", D->depth); } else { D->depth--; selectpivot (D, Q, &i, &j); pivot (D, Q, i, j); update (D, Q, &i, &j); /*Update B,C,i,j */ } if (Q->debug) { fprintf (lrs_ofp, "\n Backtrack Pivot: indices i=%ld j=%ld depth=%ld", i, j, D->depth); printA (D, Q); }; j++; /* go to next column */ } /* end of if backtrack */ if (D->depth < Q->mindepth) break; /* try to go down tree */ /* 2011.7.14 patch */ while ((j < d) && (!reverse (D, Q, &i, j) || (Q->truncate && Q->minratio[D->m]==1))) j++; if (j == d ) backtrack = TRUE; else /*reverse pivot found */ { cache_dict (D_p, Q, i, j); /* Note that the next two lines must come _after_ the call to cache_dict */ D->depth++; if (D->depth > Q->deepest) Q->deepest++; pivot (D, Q, i, j); update (D, Q, &i, &j); /*Update B,C,i,j */ D->lexflag = lexmin (D, Q, ZERO); /* see if lexmin basis */ Q->count[2]++; Q->totalnodes++; save_basis (*D_p, Q); if (Q->strace == Q->count[2]) Q->debug = TRUE; if (Q->etrace == Q->count[2]) Q->debug = FALSE; return TRUE; /*return new dictionary */ } } /* end of main while loop for getnextbasis */ return FALSE; /* done, no more bases */ } /*end of lrs_getnextbasis */ /*************************************/ /* print out one line of output file */ /*************************************/ long lrs_getvertex (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output) /*Print out current vertex if it is lexmin and return it in output */ /* return FALSE if no output generated */ { lrs_mp_matrix A = P->A; long i; long ind; /* output index */ long ired; /* counts number of redundant columns */ /* assign local variables to structures */ long *redundcol = Q->redundcol; long *count = Q->count; long *B = P->B; long *Row = P->Row; long lastdv = Q->lastdv; long hull; long m, d; long lexflag; hull = Q->hull; m = P->m; d = P->d; lexflag = P->lexflag; if (lexflag || Q->allbases) ++(Q->count[1]); if (Q->debug) printA (P, Q); linint (Q->sumdet, 1, P->det, 1); if (Q->getvolume) { updatevolume (P, Q); if(Q->verbose) /* this will print out a triangulation */ lrs_printcobasis(P,Q,ZERO); } /*print cobasis if printcobasis=TRUE and count[2] a multiple of frequency */ /* or for lexmin basis, except origin for hull computation - ugly! */ if (Q->printcobasis) if ((lexflag && !hull) || ((Q->frequency > 0) && (count[2] == (count[2] / Q->frequency) * Q->frequency))) lrs_printcobasis (P, Q, ZERO); if (hull) return FALSE; /* skip printing the origin */ if (!lexflag && !Q->allbases && !Q->lponly) /* not lexmin, and not printing forced */ return FALSE; /* copy column 0 to output */ i = 1; ired = 0; copy (output[0], P->det); for (ind = 1; ind < Q->n; ind++) /* extract solution */ if ((ired < Q->nredundcol) && (redundcol[ired] == ind)) /* column was deleted as redundant */ { itomp (ZERO, output[ind]); ired++; } else /* column not deleted as redundant */ { getnextoutput (P, Q, i, ZERO, output[ind]); i++; } reducearray (output, Q->n); if (lexflag && one(output[0])) ++Q->count[4]; /* integer vertex */ /* uncomment to print nonzero basic variables printf("\n nonzero basis: vars"); for(i=1;i<=lastdv; i++) { if ( !zero(A[Row[i]][0]) ) printf(" %ld ",B[i]); } */ /* printslack inequality indices */ if (Q->printslack) { fprintf(lrs_ofp,"\nslack ineq:"); for(i=lastdv+1;i<=P->m; i++) { if (!zero(A[Row[i]][0])) fprintf(lrs_ofp," %ld ", Q->inequality[B[i]-lastdv]); } } return TRUE; } /* end of lrs_getvertex */ long lrs_getray (lrs_dic * P, lrs_dat * Q, long col, long redcol, lrs_mp_vector output) /*Print out solution in col and return it in output */ /*redcol =n for ray/facet 0..n-1 for linearity column */ /*hull=1 implies facets will be recovered */ /* return FALSE if no output generated in column col */ { long i; long ind; /* output index */ long ired; /* counts number of redundant columns */ /* assign local variables to structures */ long *redundcol = Q->redundcol; long *count = Q->count; long hull = Q->hull; long n = Q->n; long *B = P->B; long *Row = P->Row; long lastdv = Q->lastdv; if (Q->debug) { printA (P, Q); for (i = 0; i < Q->nredundcol; i++) fprintf (lrs_ofp, " %ld", redundcol[i]); fflush(lrs_ofp); } if (redcol == n) { ++count[0]; if (Q->printcobasis) lrs_printcobasis (P, Q, col); } i = 1; ired = 0; for (ind = 0; ind < n; ind++) /* print solution */ { if (ind == 0 && !hull) /* must have a ray, set first column to zero */ itomp (ZERO, output[0]); else if ((ired < Q->nredundcol) && (redundcol[ired] == ind)) /* column was deleted as redundant */ { if (redcol == ind) /* true for linearity on this cobasic index */ /* we print reduced determinant instead of zero */ copy (output[ind], P->det); else itomp (ZERO, output[ind]); ired++; } else /* column not deleted as redundant */ { getnextoutput (P, Q, i, col, output[ind]); i++; } } reducearray (output, n); /* printslack for rays: 2006.10.10 */ /* printslack inequality indices */ if (Q->printslack) { fprintf(lrs_ofp,"\nslack ineq:"); for(i=lastdv+1;i<=P->m; i++) { if (!zero(P->A[Row[i]][col])) fprintf(lrs_ofp," %ld ", Q->inequality[B[i]-lastdv]); } } return TRUE; } /* end of lrs_getray */ void getnextoutput (lrs_dic * P, lrs_dat * Q, long i, long col, lrs_mp out) /* get A[B[i][col] and copy to out */ { long row; long m = P->m; long d = P->d; long lastdv = Q->lastdv; lrs_mp_matrix A = P->A; long *B = P->B; long *Row = P->Row; long j; if (i == d && Q->voronoi) return; /* skip last column if voronoi set */ row = Row[i]; if (Q->nonnegative) /* if m+i basic get correct value from dictionary */ /* the slack for the inequality m-d+i contains decision */ /* variable x_i. We first see if this is in the basis */ /* otherwise the value of x_i is zero, except for a ray */ /* when it is one (det/det) for the actual column it is in */ { for (j = lastdv+ 1; j <= m; j++) { if ( Q->inequality[B[j]-lastdv] == m-d+i ) { copy (out, A[Row[j]][col]); return; } } /* did not find inequality m-d+i in basis */ if ( i == col ) copy(out,P->det); else itomp(ZERO,out); } else copy (out, A[row][col]); } /* end of getnextoutput */ void lrs_printcobasis (lrs_dic * P, lrs_dat * Q, long col) /* col is output column being printed */ { long i; long rflag; /* used to find inequality number for ray column */ /* assign local variables to structures */ lrs_mp_matrix A = P->A; lrs_mp Nvol, Dvol; /* hold rescaled det of current basis */ long *B = P->B; long *C = P->C; long *Col = P->Col; long *Row = P->Row; long *inequality = Q->inequality; long *temparray = Q->temparray; long *count = Q->count; long hull = Q->hull; long d = P->d; long lastdv = Q->lastdv; long m=P->m; long firstime=TRUE; long nincidence; /* count number of tight inequalities */ lrs_alloc_mp(Nvol); lrs_alloc_mp(Dvol); if (hull) fprintf (lrs_ofp, "\nF#%ld B#%ld h=%ld vertices/rays ", count[0], count[2], P->depth); else if (Q->voronoi) fprintf (lrs_ofp, "\nV#%ld R#%ld B#%ld h=%ld data points ", count[1], count[0], count[2], P->depth); else fprintf (lrs_ofp, "\nV#%ld R#%ld B#%ld h=%ld facets ", count[1], count[0], count[2], P->depth); rflag = (-1); for (i = 0; i < d; i++) { temparray[i] = inequality[C[i] - lastdv]; if (Col[i] == col) rflag = temparray[i]; /* look for ray index */ } for (i = 0; i < d; i++) reorder (temparray, d); for (i = 0; i < d; i++) { fprintf (lrs_ofp, " %ld", temparray[i]); if (!(col == ZERO) && (rflag == temparray[i])) /* missing cobasis element for ray */ fprintf (lrs_ofp, "*"); } /* get and print incidence information */ if ( col == 0 ) nincidence = d; else nincidence = d-1; for(i=lastdv+1;i<=m;i++) if ( zero (A[Row[i]][0] )) if( ( col == ZERO ) || zero (A[Row[i]] [col]) ) { nincidence++; if( Q->incidence ) { if (firstime) { fprintf (lrs_ofp," :"); firstime = FALSE; } fprintf(lrs_ofp," %ld",inequality[B[i] - lastdv ] ); } } fprintf(lrs_ofp," I#%ld",nincidence); pmp (" det=", P->det); fflush (lrs_ofp); rescaledet (P, Q, Nvol, Dvol); /* scales determinant in case input rational */ prat(" in_det=",Nvol,Dvol); lrs_clear_mp(Nvol); lrs_clear_mp(Dvol); } /* end of lrs_printcobasis */ /*********************/ /* print final totals */ /*********************/ void lrs_printtotals (lrs_dic * P, lrs_dat * Q) { long i; double x; /* local assignments */ double *cest = Q->cest; long *count = Q->count; long *inequality = Q->inequality; long *linearity = Q->linearity; long *temparray = Q->temparray; long *C = P->C; long hull = Q->hull; long homogeneous = Q->homogeneous; long nlinearity = Q->nlinearity; long nredundcol = Q->nredundcol; long m, d, lastdv; m = P->m; d = P->d; lastdv = Q->lastdv; fprintf (lrs_ofp, "\nend"); if (Q->dualdeg) { fprintf (lrs_ofp, "\n*Warning: Starting dictionary is dual degenerate"); fprintf (lrs_ofp, "\n*Complete enumeration may not have been produced"); if (Q->maximize) fprintf(lrs_ofp,"\n*Recommendation: Add dualperturb option before maximize in input file\n"); else fprintf(lrs_ofp,"\n*Recommendation: Add dualperturb option before minimize in input file\n"); } if (Q->unbounded) { fprintf (lrs_ofp, "\n*Warning: Starting dictionary contains rays"); fprintf (lrs_ofp, "\n*Complete enumeration may not have been produced"); if (Q->maximize) fprintf(lrs_ofp,"\n*Recommendation: Change or remove maximize option or add bounds\n"); else fprintf(lrs_ofp,"\n*Recommendation: Change or remove minimize option or add bounds\n"); } if (Q->truncate) fprintf(lrs_ofp,"\n*Tree truncated at each new vertex"); if (Q->maxdepth < MAXD) fprintf (lrs_ofp, "\n*Tree truncated at depth %ld", Q->maxdepth); if (Q->maxoutput > 0L) fprintf (lrs_ofp, "\n*Maximum number of output lines = %ld", Q->maxoutput); #ifdef LONG fprintf (lrs_ofp, "\n*Caution: no overflow checking with long integer arithemtic"); #else if( Q->verbose) { fprintf (lrs_ofp, "\n*Sum of det(B)="); pmp ("", Q->sumdet); } #endif /* next block with volume rescaling must come before estimates are printed */ if (Q->getvolume) { rescalevolume (P, Q, Q->Nvolume, Q->Dvolume); if (Q->polytope) prat ("\n*Volume=", Q->Nvolume, Q->Dvolume); else prat ("\n*Pseudovolume=", Q->Nvolume, Q->Dvolume); } if (hull) /* output things that are specific to hull computation */ { fprintf (lrs_ofp, "\n*Totals: facets=%ld bases=%ld", count[0], count[2]); if (nredundcol > homogeneous) /* don't count column 1 as redundant if homogeneous */ { fprintf (lrs_ofp, " linearities=%ld", nredundcol - homogeneous); fprintf (lrs_ofp, " facets+linearities=%ld",nredundcol-homogeneous+count[0]); } if ((cest[2] > 0) || (cest[0] > 0)) { fprintf (lrs_ofp, "\n*Estimates: facets=%.0f bases=%.0f", count[0] + cest[0], count[2] + cest[2]); if (Q->getvolume) { rattodouble (Q->Nvolume, Q->Dvolume, &x); for (i = 2; i < d; i++) cest[3] = cest[3] / i; /*adjust for dimension */ fprintf (lrs_ofp, " volume=%g", cest[3] + x); } fprintf (lrs_ofp, "\n*Total number of tree nodes evaluated: %ld", Q->totalnodes); #ifdef TIMES fprintf (lrs_ofp, "\n*Estimated total running time=%.1f secs ",(count[2]+cest[2])/Q->totalnodes*get_time () ); #endif } /* Should not happen since we homogenize */ /* if ( Q-> restart || Q->allbases || (count[0] > 1 && !Q->homogeneous && !Q->polytope)) fprintf (lrs_ofp, "\n*Note! Duplicate facets may be present"); */ } else /* output things specific to vertex/ray computation */ { fprintf (lrs_ofp, "\n*Totals: vertices=%ld rays=%ld bases=%ld", count[1], count[0], count[2]); fprintf (lrs_ofp, " integer_vertices=%ld ",count[4]); if (nredundcol > 0) fprintf (lrs_ofp, " linearities=%ld", nredundcol); if ( count[0] + nredundcol > 0 ) { fprintf (lrs_ofp, " vertices+rays"); if ( nredundcol > 0 ) fprintf (lrs_ofp, "+linearities"); fprintf (lrs_ofp, "=%ld",nredundcol+count[0]+count[1]); } if ((cest[2] > 0) || (cest[0] > 0)) { fprintf (lrs_ofp, "\n*Estimates: vertices=%.0f rays=%.0f", count[1]+cest[1], count[0]+cest[0]); fprintf (lrs_ofp, " bases=%.0f integer_vertices=%.0f ",count[2]+cest[2], count[4]+cest[4]); if (Q->getvolume) { rattodouble (Q->Nvolume, Q->Dvolume, &x); for (i = 2; i <= d-homogeneous; i++) cest[3] = cest[3] / i; /*adjust for dimension */ fprintf (lrs_ofp, " pseudovolume=%g", cest[3] + x); } fprintf (lrs_ofp, "\n*Total number of tree nodes evaluated: %ld", Q->totalnodes); #ifdef TIMES fprintf (lrs_ofp, "\n*Estimated total running time=%.1f secs ",(count[2]+cest[2])/Q->totalnodes*get_time () ); #endif } if (Q->restart || Q->allbases) /* print warning */ fprintf (lrs_ofp, "\n*Note! Duplicate vertices/rays may be present"); else if ( (count[0] > 1 && !Q->homogeneous)) fprintf (lrs_ofp, "\n*Note! Duplicate rays may be present"); } /* end of output for vertices/rays */ if(!Q->verbose) return; fprintf (lrs_ofp, "\n*Input size m=%ld rows n=%ld columns", P->m, Q->n); if (hull) fprintf (lrs_ofp, " working dimension=%ld", d - 1 + homogeneous); else fprintf (lrs_ofp, " working dimension=%ld", d); fprintf (lrs_ofp, "\n*Starting cobasis defined by input rows"); for (i = 0; i < nlinearity; i++) temparray[i] = linearity[i]; for (i = nlinearity; i < lastdv; i++) temparray[i] = inequality[C[i - nlinearity] - lastdv]; for (i = 0; i < lastdv; i++) reorder (temparray, lastdv); for (i = 0; i < lastdv; i++) fprintf (lrs_ofp, " %ld", temparray[i]); fprintf (lrs_ofp, "\n*Dictionary Cache: max size= %ld misses= %ld/%ld Tree Depth= %ld", dict_count, cache_misses, cache_tries, Q->deepest); } /* end of lrs_printtotals */ /************************/ /* Estimation function */ /************************/ void lrs_estimate (lrs_dic * P, lrs_dat * Q) /*get estimate of tree size from current node */ /*current node is not counted. */ /*cest[0]rays [1]vertices [2]bases [3]volume */ /* [4] integer vertices */ { lrs_mp_vector output; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp Nvol, Dvol; /* hold volume of current basis */ long estdepth = 0; /* depth of basis/vertex in subtree for estimate */ long i = 0, j = 0, k, nchild, runcount, col; double prod = 0.0; double cave[] = {0.0, 0.0, 0.0, 0.0, 0.0}; double nvertices, nbases, nrays, nvol, nivertices; long rays = 0; double newvol = 0.0; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *isave = Q->isave; long *jsave = Q->jsave; double *cest = Q->cest; long d = P->d; lrs_alloc_mp(Nvol); lrs_alloc_mp(Dvol); /* Main Loop of Estimator */ output = lrs_alloc_mp_vector (Q->n); /* output holds one line of output from dictionary */ for (runcount = 1; runcount <= Q->runs; runcount++) { /* runcount counts number of random probes */ j = 0; nchild = 1; prod = 1; nvertices = 0.0; nbases = 0.0; nrays = 0.0; nvol = 0.0; nivertices =0.0; while (nchild != 0) /* while not finished yet */ { nchild = 0; while (j < d) { if (reverse (P, Q, &i, j)) { isave[nchild] = i; jsave[nchild] = j; nchild++; } j++; } if (estdepth == 0 && nchild == 0) { cest[0] = cest[0] + rays; /* may be some rays here */ lrs_clear_mp(Nvol); lrs_clear_mp(Dvol); return; /*subtree is a leaf */ } prod = prod * nchild; nbases = nbases + prod; if (Q->debug) { fprintf (lrs_ofp, " degree= %ld ", nchild); fprintf (lrs_ofp, "\nPossible reverse pivots: i,j="); for (k = 0; k < nchild; k++) fprintf (lrs_ofp, "%ld,%ld ", isave[k], jsave[k]); } if (nchild > 0) /*reverse pivot found choose random child */ { k = myrandom (Q->seed, nchild); Q->seed = myrandom (Q->seed, 977L); i = isave[k]; j = jsave[k]; if (Q->debug) fprintf (lrs_ofp, " selected pivot k=%ld seed=%ld ", k, Q->seed); estdepth++; Q->totalnodes++; /* calculate total number of nodes evaluated */ pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ if (lexmin (P, Q, ZERO)) /* see if lexmin basis for vertex */ { nvertices = nvertices + prod; /* integer vertex estimate */ if( lrs_getvertex(P,Q,output)) { --Q->count[1]; if (one(output[0] )) { --Q->count[4]; nivertices = nivertices + prod; } } } rays = 0; for (col = 1; col <= d; col++) if (negative (A[0][col]) && (ratio (P, Q, col) == 0) && lexmin (P, Q, col)) rays++; nrays = nrays + prod * rays; /* update ray info */ if (Q->getvolume) { rescaledet (P, Q, Nvol, Dvol); /* scales determinant in case input rational */ rattodouble (Nvol, Dvol, &newvol); nvol = nvol + newvol * prod; /* adjusts volume for degree */ } j = 0; } } cave[0] = cave[0] + nrays; cave[1] = cave[1] + nvertices; cave[2] = cave[2] + nbases; cave[3] = cave[3] + nvol; cave[4] = cave[4] + nivertices; /* backtrack to root and do it again */ while (estdepth > 0) { estdepth = estdepth - 1; selectpivot (P, Q, &i, &j); pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ /*fprintf(lrs_ofp,"\n0 +++"); */ if (Q->debug) { fprintf (lrs_ofp, "\n Backtrack Pivot: indices i,j %ld %ld ", i, j); printA (P, Q); } j++; } } /* end of for loop on runcount */ for (i = 0; i < 5; i++) cest[i] = cave[i] / Q->runs + cest[i]; lrs_clear_mp(Nvol); lrs_clear_mp(Dvol); lrs_clear_mp_vector(output, Q->n); } /* end of lrs_estimate */ /*********************************/ /* Internal functions */ /*********************************/ /* Basic Dictionary functions */ /******************************* */ long reverse (lrs_dic * P, lrs_dat * Q, long *r, long s) /* find reverse indices */ /* TRUE if B[*r] C[s] is a reverse lexicographic pivot */ { long i, j, enter, row, col; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long d = P->d; enter = C[s]; col = Col[s]; if (Q->debug) { fprintf (lrs_ofp, "\n+reverse: col index %ld C %ld Col %ld ", s, enter, col); fflush (lrs_ofp); } if (!negative (A[0][col])) { if (Q->debug) fprintf (lrs_ofp, " Pos/Zero Cost Coeff"); Q->minratio[P->m]=0; /* 2011.7.14 */ return (FALSE); } *r = ratio (P, Q, col); if (*r == 0) /* we have a ray */ { if (Q->debug) fprintf (lrs_ofp, " Pivot col non-negative: ray found"); Q->minratio[P->m]=0; /* 2011.7.14 */ return (FALSE); } row = Row[*r]; /* check cost row after "pivot" for smaller leaving index */ /* ie. j s.t. A[0][j]*A[row][col] < A[0][col]*A[row][j] */ /* note both A[row][col] and A[0][col] are negative */ for (i = 0; i < d && C[i] < B[*r]; i++) if (i != s) { j = Col[i]; if (positive (A[0][j]) || negative (A[row][j])) /*or else sign test fails trivially */ if ((!negative (A[0][j]) && !positive (A[row][j])) || comprod (A[0][j], A[row][col], A[0][col], A[row][j]) == -1) { /*+ve cost found */ if (Q->debug) { fprintf (lrs_ofp, "\nPositive cost found: index %ld C %ld Col %ld", i, C[i], j); fflush(lrs_ofp); } Q->minratio[P->m]=0; /* 2011.7.14 */ return (FALSE); } } if (Q->debug) { fprintf (lrs_ofp, "\n+end of reverse : indices r %ld s %ld \n", *r, s); fflush (stdout); } return (TRUE); } /* end of reverse */ long selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s) /* select pivot indices using lexicographic rule */ /* returns TRUE if pivot found else FALSE */ /* pivot variables are B[*r] C[*s] in locations Row[*r] Col[*s] */ { long j, col; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Col = P->Col; long d = P->d; *r = 0; *s = d; j = 0; /*find positive cost coef */ while ((j < d) && (!positive (A[0][Col[j]]))) j++; if (j < d) /* pivot column found! */ { *s = j; col = Col[j]; /*find min index ratio */ *r = ratio (P, Q, col); if (*r != 0) return (TRUE); /* unbounded */ } return (FALSE); } /* end of selectpivot */ /******************************************************* */ void pivot (lrs_dic * P, lrs_dat * Q, long bas, long cob) /* Qpivot routine for array A */ /* indices bas, cob are for Basis B and CoBasis C */ /* corresponding to row Row[bas] and column */ /* Col[cob] respectively */ { long r, s; long i, j; lrs_mp Ns, Nt, Ars; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long m, d, m_A; lrs_alloc_mp(Ns); lrs_alloc_mp(Nt); lrs_alloc_mp(Ars); m = P->m; d = P->d; m_A = P->m_A; Q->count[3]++; /* count the pivot */ r = Row[bas]; s = Col[cob]; /* Ars=A[r][s] */ if (Q->debug) { fprintf (lrs_ofp, "\n pivot B[%ld]=%ld C[%ld]=%ld ", bas, B[bas], cob, C[cob]); printA(P,Q); fflush (stdout); } copy (Ars, A[r][s]); storesign (P->det, sign (Ars)); /*adjust determinant to new sign */ for (i = 0; i <= m_A; i++) if (i != r) for (j = 0; j <= d; j++) if (j != s) { /* A[i][j]=(A[i][j]*Ars-A[i][s]*A[r][j])/P->det; */ mulint (A[i][j], Ars, Nt); mulint (A[i][s], A[r][j], Ns); decint (Nt, Ns); exactdivint (Nt, P->det, A[i][j]); } /* end if j .... */ if (sign (Ars) == POS) { for (j = 0; j <= d; j++) /* no need to change sign if Ars neg */ /* A[r][j]=-A[r][j]; */ if (!zero (A[r][j])) changesign (A[r][j]); } /* watch out for above "if" when removing this "}" ! */ else for (i = 0; i <= m_A; i++) if (!zero (A[i][s])) changesign (A[i][s]); /* A[r][s]=P->det; */ copy (A[r][s], P->det); /* restore old determinant */ copy (P->det, Ars); storesign (P->det, POS); /* always keep positive determinant */ if (Q->debug) { fprintf (lrs_ofp, " depth=%ld ", P->depth); pmp ("det=", P->det); fflush(stdout); } /* set the new rescaled objective function value */ mulint (P->det, Q->Lcm[0], P->objden); mulint (Q->Gcd[0], A[0][0], P->objnum); if (!Q->maximize) changesign (P->objnum); if (zero (P->objnum)) storesign (P->objnum, POS); else reduce (P->objnum,P->objden); lrs_clear_mp(Ns); lrs_clear_mp(Nt); lrs_clear_mp(Ars); } /* end of pivot */ long primalfeasible (lrs_dic * P, lrs_dat * Q) /* Do dual pivots to get primal feasibility */ /* Note that cost row is all zero, so no ratio test needed for Dual Bland's rule */ { long primalinfeasible = TRUE; long i, j; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Row = P->Row; long *Col = P->Col; long m, d, lastdv; m = P->m; d = P->d; lastdv = Q->lastdv; /*temporary: try to get new start after linearity */ while (primalinfeasible) { i=lastdv+1; while (i <= m && !negative (A[Row[i]][0]) ) i++; if (i <= m ) { j = 0; /*find a positive entry for in row */ while (j < d && !positive (A[Row[i]][Col[j]])) j++; if (j >= d) return (FALSE); /* no positive entry */ pivot (P, Q, i, j); update (P, Q, &i, &j); } else primalinfeasible = FALSE; } /* end of while primalinfeasibile */ return (TRUE); } /* end of primalfeasible */ long lrs_solvelp (lrs_dic * P, lrs_dat * Q, long maximize) /* Solve primal feasible lp by Dantzig`s rule and lexicographic ratio test */ /* return TRUE if bounded, FALSE if unbounded */ { long i, j; /* assign local variables to structures */ long d = P->d; while (dan_selectpivot (P, Q, &i, &j)) { Q->count[3]++; pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ } if (Q->debug) printA (P, Q); if (j < d && i == 0) /* selectpivot gives information on unbounded solution */ { #ifndef LRS_QUIET if (Q->lponly) fprintf (lrs_ofp, "\n*Unbounded solution"); #endif return FALSE; } return TRUE; } /* end of lrs_solvelp */ long getabasis (lrs_dic * P, lrs_dat * Q, long order[]) /* Pivot Ax<=b to standard form */ /*Try to find a starting basis by pivoting in the variables x[1]..x[d] */ /*If there are any input linearities, these appear first in order[] */ /* Steps: (a) Try to pivot out basic variables using order */ /* Stop if some linearity cannot be made to leave basis */ /* (b) Permanently remove the cobasic indices of linearities */ /* (c) If some decision variable cobasic, it is a linearity, */ /* and will be removed. */ { long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long *linearity = Q->linearity; long *redundcol = Q->redundcol; long m, d, nlinearity; long nredundcol = 0L; /* will be calculated here */ m = P->m; d = P->d; nlinearity = Q->nlinearity; if (Q->debug) { fprintf (lrs_ofp, "\ngetabasis from inequalities given in order"); for (i = 0; i < m; i++) fprintf (lrs_ofp, " %ld", order[i]); } for (j = 0; j < m; j++) { i = 0; while (i <= m && B[i] != d + order[j]) i++; /* find leaving basis index i */ if (j < nlinearity && i > m) /* cannot pivot linearity to cobasis */ { if (Q->debug) printA (P, Q); #ifndef LRS_QUIET fprintf (lrs_ofp, "\nCannot find linearity in the basis"); #endif return FALSE; } if (i <= m) { /* try to do a pivot */ k = 0; while (C[k] <= d && zero (A[Row[i]][Col[k]])) k++; if (C[k] <= d) { pivot (P, Q, i, k); update (P, Q, &i, &k); } else if (j < nlinearity) { /* cannot pivot linearity to cobasis */ if (zero (A[Row[i]][0])) { #ifndef LRS_QUIET fprintf (lrs_ofp, "\n*Input linearity in row %ld is redundant--converted to inequality", order[j]); #endif linearity[j]=0; } else { if (Q->debug) printA (P, Q); #ifndef LRS_QUIET fprintf (lrs_ofp, "\n*Input linearity in row %ld is inconsistent with earlier linearities", order[j]); fprintf (lrs_ofp, "\n*No feasible solution"); #endif return FALSE; } } /* end if j < nlinearity */ } /* end of if i <= m .... */ } /* end of for */ /* update linearity array to get rid of redundancies */ i = 0; k = 0; /* counters for linearities */ while (k < nlinearity) { while (k < nlinearity && linearity[k] == 0) k++; if (k < nlinearity) linearity[i++] = linearity[k++]; } nlinearity = i; /* bug fix, 2009.6.27 */ Q->nlinearity = i; /* column dependencies now can be recorded */ /* redundcol contains input column number 0..n-1 where redundancy is */ k = 0; while (k < d && C[k] <= d) { if (C[k] <= d) /* decision variable still in cobasis */ redundcol[nredundcol++] = C[k] - Q->hull; /* adjust for hull indices */ k++; } /* now we know how many decision variables remain in problem */ Q->nredundcol = nredundcol; Q->lastdv = d - nredundcol; if (Q->debug) { fprintf (lrs_ofp, "\nend of first phase of getabasis: "); fprintf (lrs_ofp, "lastdv=%ld nredundcol=%ld", Q->lastdv, Q->nredundcol); fprintf (lrs_ofp, "\nredundant cobases:"); for (i = 0; i < nredundcol; i++) fprintf (lrs_ofp, " %ld", redundcol[i]); printA (P, Q); } /* Remove linearities from cobasis for rest of computation */ /* This is done in order so indexing is not screwed up */ for (i = 0; i < nlinearity; i++) { /* find cobasic index */ k = 0; while (k < d && C[k] != linearity[i] + d) k++; if (k >= d) { fprintf (lrs_ofp, "\nError removing linearity"); return FALSE; } if (!removecobasicindex (P, Q, k)) return FALSE; d = P->d; } if (Q->debug && nlinearity > 0) printA (P, Q); /* set index value for first slack variable */ /* Check feasability */ if (Q->givenstart) { i = Q->lastdv + 1; while (i <= m && !negative (A[Row[i]][0])) i++; if (i <= m) fprintf (lrs_ofp, "\n*Infeasible startingcobasis - will be modified"); } return TRUE; } /* end of getabasis */ long removecobasicindex (lrs_dic * P, lrs_dat * Q, long k) /* remove the variable C[k] from the problem */ /* used after detecting column dependency */ { long i, j, cindex, deloc; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Col = P->Col; long m, d; m = P->m; d = P->d; if (Q->debug) fprintf (lrs_ofp, "\nremoving cobasic index k=%ld C[k]=%ld", k, C[k]); cindex = C[k]; /* cobasic index to remove */ deloc = Col[k]; /* matrix column location to remove */ for (i = 1; i <= m; i++) /* reduce basic indices by 1 after index */ if (B[i] > cindex) B[i]--; for (j = k; j < d; j++) /* move down other cobasic variables */ { C[j] = C[j + 1] - 1; /* cobasic index reduced by 1 */ Col[j] = Col[j + 1]; } if (deloc != d) { /* copy col d to deloc */ for (i = 0; i <= m; i++) copy (A[i][deloc], A[i][d]); /* reassign location for moved column */ j = 0; while (Col[j] != d) j++; Col[j] = deloc; } P->d--; if (Q->debug) printA (P, Q); return TRUE; } /* end of removecobasicindex */ lrs_dic * resize (lrs_dic * P, lrs_dat * Q) /* resize the dictionary after some columns are deleted, ie. inputd>d */ /* a new lrs_dic record is created with reduced size, and items copied over */ { lrs_dic *P1; /* to hold new dictionary in case of resizing */ long i, j; long m, d, m_A; m = P->m; d = P->d; m_A = P->m_A; /* get new dictionary record */ P1 = new_lrs_dic (m, d, m_A); /* copy data from P to P1 */ P1->i = P->i; P1->j = P->j; P1->depth = P->depth; P1->m = P->m; P1->d = P1->d_orig = d; P1->lexflag = P->lexflag; P1->m_A = P->m_A; copy (P1->det, P->det); copy (P1->objnum, P->objnum); copy (P1->objden, P->objden); for (i = 0; i <= m; i++) { P1->B[i] = P->B[i]; P1->Row[i] = P->Row[i]; } for (i = 0; i <= m_A; i++) { for (j = 0; j <= d; j++) copy (P1->A[i][j], P->A[i][j]); } for (j = 0; j <= d; j++) { P1->Col[j] = P->Col[j]; P1->C[j] = P->C[j]; } if (Q->debug) { fprintf (lrs_ofp, "\nDictionary resized from d=%ld to d=%ld", Q->inputd, P->d); printA (P1, Q); } lrs_free_dic (P,Q); /* Reassign cache pointers */ Q->Qhead = P1; Q->Qtail = P1; P1->next = P1; P1->prev = P1; return P1; } /********* resize ***************/ long restartpivots (lrs_dic * P, lrs_dat * Q) /* facet contains a list of the inequalities in the cobasis for the restart */ /* inequality contains the relabelled inequalities after initialization */ { long i, j, k; long *Cobasic; /* when restarting, Cobasic[j]=1 if j is in cobasis */ /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long *inequality = Q->inequality; long *facet = Q->facet; long nlinearity = Q->nlinearity; long m, d, lastdv; m = P->m; d = P->d; lastdv = Q->lastdv; Cobasic = (long *) CALLOC ((unsigned) m + d + 2, sizeof (long)); if (Q->debug) fprintf(lrs_ofp,"\nCobasic flags in restartpivots"); /* set Cobasic flags */ for (i = 0; i < m + d + 1; i++) Cobasic[i] = 0; for (i = 0; i < d; i++) /* find index corresponding to facet[i] */ { j = 1; while (facet[i + nlinearity] != inequality[j]) j++; Cobasic[j + lastdv] = 1; if (Q->debug) fprintf(lrs_ofp," %ld %ld;",facet[i+nlinearity],j+lastdv); } /* Note that the order of doing the pivots is important, as */ /* the B and C vectors are reordered after each pivot */ /* code below replaced 2006.10.30 */ /* for (i = m; i >= d + 1; i--) if (Cobasic[B[i]]) { k = d - 1; while ((k >= 0) && (zero (A[Row[i]][Col[k]]) || Cobasic[C[k]])) k--; if (k >= 0) { pivot (P, Q, i, k); update (P, Q, &i, &k); } else { fprintf (lrs_ofp, "\nInvalid Co-basis - does not have correct rank"); free(Cobasic); return FALSE; } } */ /*end of code that was replaced */ /* Suggested new code from db starts */ i=m; while (i>d){ while(Cobasic[B[i]]){ k = d - 1; while ((k >= 0) && (zero (A[Row[i]][Col[k]]) || Cobasic[C[k]])){ k--; } if (k >= 0) { /*db asks: should i really be modified here? (see old code) */ /*da replies: modifying i only makes is larger, and so */ /*the second while loop will put it back where it was */ /*faster (and safer) as done below */ long ii=i; pivot (P, Q, ii, k); update (P, Q, &ii, &k); } else { fprintf (lrs_ofp, "\nInvalid Co-basis - does not have correct rank"); free(Cobasic); return FALSE; } } i--; } /* Suggested new code from db ends */ if (lexmin (P, Q, ZERO)) --Q->count[1]; /* decrement vertex count if lexmin */ /* check restarting from a primal feasible dictionary */ for (i = lastdv + 1; i <= m; i++) if (negative (A[Row[i]][0])) { fprintf (lrs_ofp, "\nTrying to restart from infeasible dictionary"); free(Cobasic); return FALSE; } free(Cobasic); return TRUE; } /* end of restartpivots */ long ratio (lrs_dic * P, lrs_dat * Q, long col) /*find lex min. ratio */ /* find min index ratio -aig/ais, ais<0 */ /* if multiple, checks successive basis columns */ /* recoded Dec 1997 */ { long i, j, comp, ratiocol, basicindex, start, nstart, cindex, bindex; long firstime; /*For ratio test, true on first pass,else false */ lrs_mp Nmin, Dmin; long degencount, ndegencount; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *Row = P->Row; long *Col = P->Col; long *minratio = Q->minratio; long m, d, lastdv; m = P->m; d = P->d; lastdv = Q->lastdv; nstart=0; ndegencount=0; degencount = 0; minratio[P->m]=1; /*2011.7.14 non-degenerate pivot flag */ for (j = lastdv + 1; j <= m; j++) { /* search rows with negative coefficient in dictionary */ /* minratio contains indices of min ratio cols */ if (negative (A[Row[j]][col])) { minratio[degencount++] = j; if(zero (A[Row[j]][0])) minratio[P->m]=0; /*2011.7.14 degenerate pivot flag */ } } /* end of for loop */ if (Q->debug) { fprintf (lrs_ofp, " Min ratios: "); for (i = 0; i < degencount; i++) fprintf (lrs_ofp, " %ld ", B[minratio[i]]); } if (degencount == 0) return (degencount); /* non-negative pivot column */ lrs_alloc_mp(Nmin); lrs_alloc_mp(Dmin); ratiocol = 0; /* column being checked, initially rhs */ start = 0; /* starting location in minratio array */ bindex = d + 1; /* index of next basic variable to consider */ cindex = 0; /* index of next cobasic variable to consider */ basicindex = d; /* index of basis inverse for current ratio test, except d=rhs test */ while (degencount > 1) /*keep going until unique min ratio found */ { if (B[bindex] == basicindex) /* identity col in basis inverse */ { if (minratio[start] == bindex) /* remove this index, all others stay */ { start++; degencount--; } bindex++; } else /* perform ratio test on rhs or column of basis inverse */ { firstime = TRUE; /*get next ratio column and increment cindex */ if (basicindex != d) ratiocol = Col[cindex++]; for (j = start; j < start + degencount; j++) { i = Row[minratio[j]]; /* i is the row location of the next basic variable */ comp = 1; /* 1: lhs>rhs; 0:lhs=rhs; -1: lhsdebug) { fprintf (lrs_ofp, " ratiocol=%ld degencount=%ld ", ratiocol, degencount); fprintf (lrs_ofp, " Min ratios: "); for (i = start; i < start + degencount; i++) fprintf (lrs_ofp, " %ld ", B[minratio[i]]); } } /*end of while loop */ lrs_clear_mp(Nmin); lrs_clear_mp(Dmin); return (minratio[start]); } /* end of ratio */ long lexmin (lrs_dic * P, lrs_dat * Q, long col) /*test if basis is lex-min for vertex or ray, if so TRUE */ /* FALSE if a_r,g=0, a_rs !=0, r > s */ { /*do lexmin test for vertex if col=0, otherwise for ray */ long r, s, i, j; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long m = P->m; long d = P->d; for (i = Q->lastdv + 1; i <= m; i++) { r = Row[i]; if (zero (A[r][col])) /* necessary for lexmin to fail */ for (j = 0; j < d; j++) { s = Col[j]; if (B[i] > C[j]) /* possible pivot to reduce basis */ { if (zero (A[r][0])) /* no need for ratio test, any pivot feasible */ { if (!zero (A[r][s])) return (FALSE); } else if (negative (A[r][s]) && ismin (P, Q, r, s)) { return (FALSE); } } /* end of if B[i] ... */ } } if ((col != ZERO) && Q->debug) { fprintf (lrs_ofp, "\n lexmin ray in col=%ld ", col); printA (P, Q); } return (TRUE); } /* end of lexmin */ long ismin (lrs_dic * P, lrs_dat * Q, long r, long s) /*test if A[r][s] is a min ratio for col s */ { long i; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long m_A = P->m_A; for (i = 1; i <= m_A; i++) if ((i != r) && negative (A[i][s]) && comprod (A[i][0], A[r][s], A[i][s], A[r][0])) { return (FALSE); } return (TRUE); } void update (lrs_dic * P, lrs_dat * Q, long *i, long *j) /*update the B,C arrays after a pivot */ /* involving B[bas] and C[cob] */ { long leave, enter; /* assign local variables to structures */ long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long m = P->m; long d = P->d; leave = B[*i]; enter = C[*j]; B[*i] = enter; reorder1 (B, Row, *i, m + 1); C[*j] = leave; reorder1 (C, Col, *j, d); /* restore i and j to new positions in basis */ for (*i = 1; B[*i] != enter; (*i)++); /*Find basis index */ for (*j = 0; C[*j] != leave; (*j)++); /*Find co-basis index */ } /* end of update */ long lrs_degenerate (lrs_dic * P, lrs_dat * Q) /* TRUE if the current dictionary is primal degenerate */ /* not thoroughly tested 2000/02/15 */ { long i; long *B, *Row; lrs_mp_matrix A = P->A; long d = P->d; long m = P->m; B = P->B; Row = P->Row; for (i = d + 1; i <= m; i++) if (zero (A[Row[i]][0])) return TRUE; return FALSE; } /*********************************************************/ /* Miscellaneous */ /******************************************************* */ void reorder (long a[], long range) /*reorder array in increasing order with one misplaced element */ { long i, temp; for (i = 0; i < range - 1; i++) if (a[i] > a[i + 1]) { temp = a[i]; a[i] = a[i + 1]; a[i + 1] = temp; } for (i = range - 2; i >= 0; i--) if (a[i] > a[i + 1]) { temp = a[i]; a[i] = a[i + 1]; a[i + 1] = temp; } } /* end of reorder */ void reorder1 (long a[], long b[], long newone, long range) /*reorder array a in increasing order with one misplaced element at index newone */ /*elements of array b are updated to stay aligned with a */ { long temp; while (newone > 0 && a[newone] < a[newone - 1]) { temp = a[newone]; a[newone] = a[newone - 1]; a[newone - 1] = temp; temp = b[newone]; b[newone] = b[newone - 1]; b[--newone] = temp; } while (newone < range - 1 && a[newone] > a[newone + 1]) { temp = a[newone]; a[newone] = a[newone + 1]; a[newone + 1] = temp; temp = b[newone]; b[newone] = b[newone + 1]; b[++newone] = temp; } } /* end of reorder1 */ void rescaledet (lrs_dic * P, lrs_dat * Q, lrs_mp Vnum, lrs_mp Vden) /* rescale determinant to get its volume */ /* Vnum/Vden is volume of current basis */ { lrs_mp gcdprod; /* to hold scale factors */ long i; /* assign local variables to structures */ long *B = P->B; long *C = P->C; long m, d, lastdv; lrs_alloc_mp(gcdprod); m = P->m; d = P->d; lastdv = Q->lastdv; itomp (ONE, gcdprod); itomp (ONE, Vden); for (i = 0; i < d; i++) if (B[i] <= m) { mulint (Q->Gcd[Q->inequality[C[i] - lastdv]], gcdprod, gcdprod); mulint (Q->Lcm[Q->inequality[C[i] - lastdv]], Vden, Vden); } mulint (P->det, gcdprod, Vnum); reduce (Vnum, Vden); lrs_clear_mp(gcdprod); } /* end rescaledet */ void rescalevolume (lrs_dic * P, lrs_dat * Q, lrs_mp Vnum, lrs_mp Vden) /* adjust volume for dimension */ { lrs_mp temp, dfactorial; /* assign local variables to structures */ long lastdv = Q->lastdv; lrs_alloc_mp(temp); lrs_alloc_mp(dfactorial); /*reduce Vnum by d factorial */ getfactorial (dfactorial, lastdv); mulint (dfactorial, Vden, Vden); if (Q->hull && !Q->homogeneous) { /* For hull option multiply by d to correct for lifting */ itomp (lastdv, temp); mulint (temp, Vnum, Vnum); } reduce (Vnum, Vden); lrs_clear_mp(temp); lrs_clear_mp(dfactorial); } void updatevolume (lrs_dic * P, lrs_dat * Q) /* rescale determinant and update the volume */ { lrs_mp tN, tD, Vnum, Vden; lrs_alloc_mp(tN); lrs_alloc_mp(tD); lrs_alloc_mp(Vnum); lrs_alloc_mp(Vden); rescaledet (P, Q, Vnum, Vden); copy (tN, Q->Nvolume); copy (tD, Q->Dvolume); linrat (tN, tD, ONE, Vnum, Vden, ONE, Q->Nvolume, Q->Dvolume); if (Q->debug) { prat ("\n*Volume=", Q->Nvolume, Q->Dvolume); pmp (" Vnum=", Vnum); pmp (" Vden=", Vden); } lrs_clear_mp(tN); lrs_clear_mp(tD); lrs_clear_mp(Vnum); lrs_clear_mp(Vden); } /* end of updatevolume */ /***************************************************/ /* Routines for redundancy checking */ /***************************************************/ long checkredund (lrs_dic * P, lrs_dat * Q) /* Solve primal feasible lp by least subscript and lex min basis method */ /* to check redundancy of a row in objective function */ /* returns TRUE if redundant, else FALSE */ { lrs_mp Ns, Nt; long i, j; long r, s; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B, *C, *Row, *Col; long d = P->d; lrs_alloc_mp(Ns); lrs_alloc_mp(Nt); B = P->B; C = P->C; Row = P->Row; Col = P->Col; while (selectpivot (P, Q, &i, &j)) { Q->count[2]++; /* sign of new value of A[0][0] */ /* is A[0][s]*A[r][0]-A[0][0]*A[r][s] */ r = Row[i]; s = Col[j]; mulint (A[0][s], A[r][0], Ns); mulint (A[0][0], A[r][s], Nt); if (greater (Ns, Nt)) { lrs_clear_mp(Ns); lrs_clear_mp(Nt); return FALSE; /* non-redundant */ } pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ } lrs_clear_mp(Ns); lrs_clear_mp(Nt); return !(j < d && i == 0); /* unbounded is also non-redundant */ } /* end of checkredund */ long checkcobasic (lrs_dic * P, lrs_dat * Q, long index) /* TRUE if index is cobasic and nonredundant */ /* FALSE if basic, or degen. cobasic, where it will get pivoted out */ { /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B, *C, *Row, *Col; long d = P->d; long m = P->m; long debug = Q->debug; long i = 0; long j = 0; long s; B = P->B; C = P->C; Row = P->Row; Col = P->Col; while ((j < d) && C[j] != index) j++; if (j == d) return FALSE; /* not cobasic index */ /* index is cobasic */ if (debug) fprintf (lrs_ofp, "\nindex=%ld cobasic", index); /* not debugged for new LOC s=LOC[index]; */ s = Col[j]; i = Q->lastdv + 1; while ((i <= m) && (zero (A[Row[i]][s]) || !zero (A[Row[i]][0]))) i++; if (i > m) { if (debug) fprintf (lrs_ofp, " is non-redundant"); return TRUE; } if (debug) fprintf (lrs_ofp, " is degenerate B[i]=%ld", B[i]); pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ return FALSE; /*index is no longer cobasic */ } /* end of checkcobasic */ long checkindex (lrs_dic * P, lrs_dat * Q, long index) /* 0 if index is non-redundant inequality */ /* 1 if index is redundant inequality */ /* 2 if index is input linearity */ /*NOTE: row is returned all zero if redundant!! */ { long i, j; lrs_mp_matrix A = P->A; long *Row = P->Row; long *B = P->B; long d = P->d; long m = P->m; if (Q->debug) printA (P, Q); /* each slack index must be checked for redundancy */ /* if in cobasis, it is pivoted out if degenerate */ /* else it is non-redundant */ if (checkcobasic (P, Q, index)) return ZERO; /* index is basic */ /* not debugged for new LOC i=LOC[index]; */ j = 1; while ((j <= m) && (B[j] != index)) j++; i = Row[j]; /* copy row i to cost row, and set it to zero */ for (j = 0; j <= d; j++) { copy (A[0][j], A[i][j]); changesign (A[0][j]); itomp (ZERO, A[i][j]); } if (checkredund (P, Q)) return ONE; /* non-redundant, copy back and change sign */ for (j = 0; j <= d; j++) { copy (A[i][j], A[0][j]); changesign (A[i][j]); } return ZERO; } /* end of checkindex */ /***************************************************************/ /* */ /* Package of I/O routines */ /* */ /***************************************************************/ void lprat (const char *name, long Nt, long Dt) /*print the long precision rational Nt/Dt without reducing */ { if ( Nt > 0 ) fprintf (lrs_ofp, " "); fprintf (lrs_ofp, "%s%ld", name, Nt); if (Dt != 1) fprintf (lrs_ofp, "/%ld", Dt); fprintf (lrs_ofp, " "); } /* lprat */ long lreadrat (long *Num, long *Den) /* read a rational string and convert to long */ /* returns true if denominator is not one */ { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; if(fscanf (lrs_ifp, "%s", in) == EOF) return(FALSE); atoaa (in, num, den); /*convert rational to num/dem strings */ *Num = atol (num); if (den[0] == '\0') { *Den = 1L; return (FALSE); } *Den = atol (den); return (TRUE); } void lrs_getinput(lrs_dic *P,lrs_dat *Q,long *num,long *den, long m, long d) /* code for reading data matrix in lrs/cdd format */ { long j,row; printf("\nEnter each row: b_i a_ij j=1..%ld",d); for (row=1;row<=m;row++) { printf("\nEnter row %ld: ",row ); for(j=0;j<=d;j++) { lreadrat(&num[j],&den[j]); lprat(" ",num[j],den[j]); } lrs_set_row(P,Q,row,num,den,GE); } printf("\nEnter objective row c_j j=1..%ld: ",d); num[0]=0; den[0]=1; for(j=1;j<=d;j++) { lreadrat(&num[j],&den[j]); lprat(" ",num[j],den[j]); } lrs_set_obj(P,Q,num,den,MAXIMIZE); } long readlinearity (lrs_dat * Q) /* read in and check linearity list */ { long i, j; long nlinearity; if(fscanf (lrs_ifp, "%ld", &nlinearity)==EOF ) { fprintf (lrs_ofp, "\nLinearity option invalid, no indices "); return (FALSE); } if (nlinearity < 1) { fprintf (lrs_ofp, "\nLinearity option invalid, indices must be positive"); return (FALSE); } Q->linearity = CALLOC ((nlinearity + 1), sizeof (long)); for (i = 0; i < nlinearity; i++) { if(fscanf (lrs_ifp, "%ld", &j)==EOF) { fprintf (lrs_ofp, "\nLinearity option invalid, missing indices"); return (FALSE); } Q->linearity[i] = j; } for (i = 1; i < nlinearity; i++) /*sort in order */ reorder (Q->linearity, nlinearity); Q->nlinearity = nlinearity; Q->polytope = FALSE; return TRUE; } /* end readlinearity */ long readfacets (lrs_dat * Q, long facet[]) /* read and check facet list for obvious errors during start/restart */ /* this must be done after linearity option is processed!! */ { long i, j; /* assign local variables to structures */ long m, d; long *linearity = Q->linearity; m = Q->m; d = Q->inputd; for (j = Q->nlinearity; j < d; j++) /* note we place these after the linearity indices */ { if(fscanf (lrs_ifp, "%ld", &facet[j])==EOF) { fprintf (lrs_ofp, "\nrestart: facet list missing indices"); return (FALSE); } fprintf (lrs_ofp, " %ld", facet[j]); /* 2010.4.26 nonnegative option needs larger range of indices */ if(Q->nonnegative) if (facet[j] < 1 || facet[j] > m+d) { fprintf (lrs_ofp, "\n Start/Restart cobasic indices must be in range 1 .. %ld ", m+d); return FALSE; } if(!Q->nonnegative) if (facet[j] < 1 || facet[j] > m) { fprintf (lrs_ofp, "\n Start/Restart cobasic indices must be in range 1 .. %ld ", m); return FALSE; } for (i = 0; i < Q->nlinearity; i++) if (linearity[i] == facet[j]) { fprintf (lrs_ofp, "\n Start/Restart cobasic indices should not include linearities"); return FALSE; } /* bug fix 2011.8.1 reported by Steven Wu*/ for (i = Q->nlinearity; i < j; i++) /* end bug fix 2011.8.1 */ if (facet[i] == facet[j]) { fprintf (lrs_ofp, "\n Start/Restart cobasic indices must be distinct"); return FALSE; } } return TRUE; } /* end of readfacets */ void printA (lrs_dic * P, lrs_dat * Q) /* print the integer m by n array A with B,C,Row,Col vectors */ { long i, j; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long m, d, lastdv; m = P->m; d = P->d; lastdv = Q->lastdv; fprintf (lrs_ofp, "\n Basis "); for (i = 0; i <= m; i++) fprintf (lrs_ofp, "%ld ", B[i]); fprintf (lrs_ofp, " Row "); for (i = 0; i <= m; i++) fprintf (lrs_ofp, "%ld ", Row[i]); fprintf (lrs_ofp, "\n Co-Basis "); for (i = 0; i <= d; i++) fprintf (lrs_ofp, "%ld ", C[i]); fprintf (lrs_ofp, " Column "); for (i = 0; i <= d; i++) fprintf (lrs_ofp, "%ld ", Col[i]); pmp (" det=", P->det); fprintf (lrs_ofp, "\n"); i=0; while ( i<= m ) { for (j = 0; j <= d; j++) pimat (P, i, j, A[Row[i]][Col[j]], "A"); fprintf (lrs_ofp, "\n"); if (i==0 && Q->nonnegative) /* skip basic rows - don't exist! */ i=d; i++; fflush (stdout); } fflush (stdout); } void pimat (lrs_dic * P, long r, long s, lrs_mp Nt, char name[]) /*print the long precision integer in row r col s of matrix A */ { long *B = P->B; long *C = P->C; if (s == 0) fprintf (lrs_ofp, "%s[%ld][%ld]=", name, B[r], C[s]); else fprintf (lrs_ofp, "[%ld]=", C[s]); pmp ("", Nt); } /***************************************************************/ /* */ /* Routines for caching, allocating etc. */ /* */ /***************************************************************/ /* From here mostly Bremner's handiwork */ void cache_dict (lrs_dic ** D_p, lrs_dat * global, long i, long j) { if (dict_limit > 1) { /* save row, column indicies */ (*D_p)->i = i; (*D_p)->j = j; /* Make a new, blank spot at the end of the queue to copy into */ pushQ (global, (*D_p)->m, (*D_p)->d, (*D_p)->m_A); copy_dict (global, global->Qtail, *D_p); /* Copy current dictionary */ } *D_p = global->Qtail; } void copy_dict (lrs_dat * global, lrs_dic * dest, lrs_dic * src) { long m = src->m; long m_A = src->m_A; /* number of rows in A */ long d = src->d; long r,s; #ifdef GMP for ( r=0;r<=m_A;r++) for( s=0;s<=d;s++) copy(dest->A[r][s],src->A[r][s]); #else /* fast copy for MP and LONG arithmetic */ /* Note that the "A" pointer trees need not be copied, since they always point to the same places within the corresponding space */ /* I wish I understood the above remark. For the time being, do it the easy way for Nash */ if(global->nash) { for ( r=0;r<=m_A;r++) for( s=0;s<=d;s++) copy(dest->A[r][s],src->A[r][s]); } else memcpy (dest->A[0][0], (global->Qtail->prev)->A[0][0], (d + 1) * (lrs_digits + 1) * (m_A + 1) * sizeof (long)); #endif dest->i = src->i; dest->j = src->j; dest->m = m; dest->d = d; dest->m_A = src->m_A; dest->depth = src->depth; dest->lexflag = src->lexflag; copy (dest->det, src->det); copy (dest->objnum, src->objnum); copy (dest->objden, src->objden); if (global->debug) fprintf (lrs_ofp, "\nSaving dict at depth %ld\n", src->depth); memcpy (dest->B, src->B, (m + 1) * sizeof (long)); memcpy (dest->C, src->C, (d + 1) * sizeof (long)); memcpy (dest->Row, src->Row, (m + 1) * sizeof (long)); memcpy (dest->Col, src->Col, (d + 1) * sizeof (long)); } /* * pushQ(lrs_dat *globals,m,d): * this routine ensures that Qtail points to a record that * may be copied into. * * It may create a new record, or it may just move the head pointer * forward so that know that the old record has been overwritten. */ #if 0 #define TRACE(s) fprintf(stderr,"\n%s %p %p\n",s,global->Qhead,global->Qtail); #else #define TRACE(s) #endif void pushQ (lrs_dat * global, long m, long d ,long m_A) { if ((global->Qtail->next) == global->Qhead) { /* the Queue is full */ if (dict_count < dict_limit) { /* but we are allowed to create more */ lrs_dic *p; p = new_lrs_dic (m, d, m_A); if (p) { /* we successfully created another record */ p->next = global->Qtail->next; (global->Qtail->next)->prev = p; (global->Qtail->next) = p; p->prev = global->Qtail; dict_count++; global->Qtail = p; TRACE ("Added new record to Q"); } else { /* virtual memory exhausted. bummer */ global->Qhead = global->Qhead->next; global->Qtail = global->Qtail->next; TRACE ("VM exhausted"); } } else { /* * user defined limit reached. start overwriting the * beginning of Q */ global->Qhead = global->Qhead->next; global->Qtail = global->Qtail->next; TRACE ("User limit"); } } else { global->Qtail = global->Qtail->next; TRACE ("Reusing"); } } lrs_dic * lrs_getdic(lrs_dat *Q) /* create another dictionary for Q without copying any values */ /* derived from lrs_alloc_dic, used by nash.c */ { lrs_dic *p; long m; m = Q->m; /* nonnegative flag set means that problem is d rows "bigger" */ /* since nonnegative constraints are not kept explicitly */ if(Q->nonnegative) m = m+Q->inputd; p = new_lrs_dic (m, Q->inputd, Q->m); if (!p) return NULL; p->next = p; p->prev = p; Q->Qhead = p; Q->Qtail = p; return p; } #define NULLRETURN(e) if (!(e)) return NULL; lrs_dic * new_lrs_dic (long m, long d, long m_A) { lrs_dic *p; NULLRETURN (p = (lrs_dic *) malloc (sizeof (lrs_dic))); NULLRETURN (p->B = calloc ((m + 1), sizeof (long))); NULLRETURN (p->Row = calloc ((m + 1), sizeof (long))); NULLRETURN (p->C = calloc ((d + 1), sizeof (long))); NULLRETURN (p->Col = calloc ((d + 1), sizeof (long))); #ifdef GMP lrs_alloc_mp(p->det); lrs_alloc_mp(p->objnum); lrs_alloc_mp(p->objden); #endif p->d_orig=d; p->A=lrs_alloc_mp_matrix(m_A,d); return p; } void lrs_free_dic (lrs_dic * P, lrs_dat *Q) { /* do the same steps as for allocation, but backwards */ /* gmp variables cannot be cleared using free: use lrs_clear_mp* */ lrs_dic *P1; /* repeat until cache is empty */ do { /* I moved these here because I'm not certain the cached dictionaries need to be the same size. Well, it doesn't cost anything to be safe. db */ long d = P->d_orig; long m_A = P->m_A; lrs_clear_mp_matrix (P->A,m_A,d); /* "it is a ghastly error to free something not assigned my malloc" KR167 */ /* so don't try: free (P->det); */ lrs_clear_mp (P->det); lrs_clear_mp (P->objnum); lrs_clear_mp (P->objden); free (P->Row); free (P->Col); free (P->C); free (P->B); /* go to next record in cache if any */ P1 =P->next; free (P); P=P1; } while (Q->Qhead != P ); } void lrs_free_dat ( lrs_dat *Q ) { long m=Q->m; /* most of these items were allocated in lrs_alloc_dic */ lrs_clear_mp_vector (Q->Gcd,m); lrs_clear_mp_vector (Q->Lcm,m); lrs_clear_mp (Q->sumdet); lrs_clear_mp (Q->Nvolume); lrs_clear_mp (Q->Dvolume); lrs_clear_mp (Q->saved_det); lrs_clear_mp (Q->boundd); lrs_clear_mp (Q->boundn); free (Q->inequality); free (Q->facet); free (Q->redundcol); free (Q->linearity); free (Q->minratio); free (Q->temparray); free (Q->name); free (Q->saved_C); lrs_global_count--; free(Q); } long check_cache (lrs_dic ** D_p, lrs_dat * global, long *i_p, long *j_p) { /* assign local variables to structures */ cache_tries++; if (global->Qtail == global->Qhead) { TRACE ("cache miss"); /* Q has only one element */ cache_misses++; return 0; } else { global->Qtail = global->Qtail->prev; *D_p = global->Qtail; *i_p = global->Qtail->i; *j_p = global->Qtail->j; TRACE ("restoring dict"); return 1; } } lrs_dic * lrs_alloc_dic (lrs_dat * Q) /* allocate and initialize lrs_dic */ { lrs_dic *p; long i, j; long m, d, m_A; if (Q->hull) /* d=col dimension of A */ Q->inputd = Q->n; /* extra column for hull */ else Q->inputd = Q->n - 1; m = Q->m; d = Q->inputd; m_A = m; /* number of rows in A */ /* nonnegative flag set means that problem is d rows "bigger" */ /* since nonnegative constraints are not kept explicitly */ if(Q->nonnegative) m = m+d; p = new_lrs_dic (m, d, m_A); if (!p) return NULL; p->next = p; p->prev = p; Q->Qhead = p; Q->Qtail = p; dict_count = 1; dict_limit = 10; cache_tries = 0; cache_misses = 0; /* Initializations */ p->d = p->d_orig = d; p->m = m; p->m_A = m_A; p->depth = 0L; p->lexflag = TRUE; itomp (ONE, p->det); itomp (ZERO, p->objnum); itomp (ONE, p->objden); /*m+d+1 is the number of variables, labelled 0,1,2,...,m+d */ /* initialize array to zero */ for (i = 0; i <= m_A; i++) for (j = 0; j <= d; j++) itomp (ZERO, p->A[i][j]); Q->inequality = CALLOC ((m + 1), sizeof (long)); if (Q->nlinearity == ZERO) /* linearity may already be allocated */ Q->linearity = CALLOC ((m + 1), sizeof (long)); Q->facet = (long *) CALLOC ((unsigned) d + 1, sizeof (long)); Q->redundcol = CALLOC ((d + 1), sizeof (long)); Q->minratio = CALLOC ((m + 1), sizeof (long)); /* 2011.7.14 minratio[m]=0 for degen =1 for nondegen pivot*/ Q->temparray = CALLOC ((unsigned) d + 1, sizeof (long)); Q->inequality[0] = 2L; Q->Gcd = lrs_alloc_mp_vector(m); Q->Lcm = lrs_alloc_mp_vector(m); Q->saved_C = CALLOC (d + 1, sizeof (long)); Q->lastdv = d; /* last decision variable may be decreased */ /* if there are redundant columns */ /*initialize basis and co-basis indices, and row col locations */ /*if nonnegative, we label differently to avoid initial pivots */ /* set basic indices and rows */ if(Q->nonnegative) for (i = 0; i <= m; i++) { p->B[i] = i; if (i <= d ) p->Row[i]=0; /* no row for decision variables */ else p->Row[i]=i-d; } else for (i = 0; i <= m; i++) { if (i == 0 ) p->B[0]=0; else p->B[i] = d + i; p->Row[i] = i; } for (j = 0; j < d; j++) { if(Q->nonnegative) p->C[j] = m+j+1; else p->C[j] = j + 1; p->Col[j] = j + 1; } p->C[d] = m + d + 1; p->Col[d] = 0; return p; } /* end of lrs_alloc_dic */ /* this routine makes a copy of the information needed to restart, so that we can guarantee that if a signal is received, we can guarantee that nobody is messing with it. This as opposed to adding all kinds of critical regions in the main line code. It is also used to make sure that in case of overflow, we have a valid cobasis to restart from. */ void save_basis (lrs_dic * P, lrs_dat * Q) { int i; /* assign local variables to structures */ long *C = P->C; long d; #ifdef SIGNALS sigset_t oset, blockset; sigemptyset (&blockset); sigaddset (&blockset, SIGTERM); sigaddset (&blockset, SIGHUP); sigaddset (&blockset, SIGUSR1); errcheck ("sigprocmask", sigprocmask (SIG_BLOCK, &blockset, &oset)); #endif d = P->d; Q->saved_flag = 1; for (i = 0; i < 3; i++) Q->saved_count[i] = Q->count[i]; for (i = 0; i < d + 1; i++) Q->saved_C[i] = C[i]; copy (Q->saved_det, P->det); Q->saved_d = P->d; Q->saved_depth = P->depth; #ifdef SIGNALS errcheck ("sigprocmask", sigprocmask (SIG_SETMASK, &oset, 0)); #endif } /* digits overflow is a call from lrs_mp package */ void digits_overflow () { fprintf (lrs_ofp, "\nOverflow at digits=%ld", DIG2DEC (lrs_digits)); fprintf (lrs_ofp, "\nRerun with option: digits n, where n > %ld\n", DIG2DEC (lrs_digits)); lrs_dump_state (); notimpl(""); } static void lrs_dump_state () { long i; fprintf (stderr, "\n\nlrs_lib: checkpointing:\n"); fprintf (stderr, "lrs_lib: Current digits at %ld out of %ld\n", DIG2DEC (lrs_record_digits), DIG2DEC (lrs_digits)); for (i = 0; i < lrs_global_count; i++) { print_basis (stderr, lrs_global_list[i]); } fprintf (stderr, "lrs_lib: checkpoint finished\n"); } /* print out the saved copy of the basis */ void print_basis (FILE * fp, lrs_dat * global) { int i; /* assign local variables to structures */ fprintf (fp, "lrs_lib: State #%ld: (%s)\t", global->id, global->name); if (global->saved_flag) { fprintf (fp, "V#%ld R#%ld B#%ld h=%ld facets ", global->saved_count[1], global->saved_count[0], global->saved_count[2], global->saved_depth); for (i = 0; i < global->saved_d; i++) fprintf (fp, "%ld ", global->inequality[global->saved_C[i] - global->lastdv]); pmp (" det=", global->saved_det); fprintf (fp, "\n"); } else { fprintf (fp, "lrs_lib: Computing initial basis\n"); } fflush (fp); } #ifdef SIGNALS /* If given a signal USR1 print current cobasis and continue TERM print current cobasis and terminate INT (ctrl-C) ditto HUP ditto */ void setup_signals () { errcheck ("signal", signal (SIGTERM, die_gracefully)); errcheck ("signal", signal (SIGALRM, timecheck)); errcheck ("signal", signal (SIGHUP, die_gracefully)); errcheck ("signal", signal (SIGINT, die_gracefully)); errcheck ("signal", signal (SIGUSR1, checkpoint)); } void timecheck () { lrs_dump_state (); errcheck ("signal", signal (SIGALRM, timecheck)); alarm (lrs_checkpoint_seconds); } void checkpoint () { lrs_dump_state (); errcheck ("signal", signal (SIGUSR1, checkpoint)); } void die_gracefully () { lrs_dump_state (); exit (1); } #endif #ifdef TIMES /* * Not sure about the portability of this yet, * - db */ #include #define double_time(t) ((double)(t.tv_sec)+(double)(t.tv_usec)/1000000) void ptimes () { struct rusage rusage; getrusage (RUSAGE_SELF, &rusage); fprintf (lrs_ofp, "\n*%0.3fu %0.3fs %ldKb %ld flts %ld swaps %ld blks-in %ld blks-out \n", double_time (rusage.ru_utime), double_time (rusage.ru_stime), rusage.ru_maxrss, rusage.ru_majflt, rusage.ru_nswap, rusage.ru_inblock, rusage.ru_oublock); } double get_time() { struct rusage rusage; getrusage (RUSAGE_SELF, &rusage); return ( double_time (rusage.ru_utime)); } #endif /* Routines based on lp_solve */ void lrs_set_row(lrs_dic *P, lrs_dat *Q, long row, long num[], long den[], long ineq) /* convert to lrs_mp then call lrs_set_row */ { lrs_mp_vector Num, Den; long m,d; long j; m = P->m; d = P->d; Num=lrs_alloc_mp_vector(d+1); Den=lrs_alloc_mp_vector(d+1); for (j=0;j<=d;j++) { itomp(num[j],Num[j]); itomp(den[j],Den[j]); } lrs_set_row_mp(P,Q,row,Num,Den,ineq); lrs_clear_mp_vector(Num,d+1); lrs_clear_mp_vector(Den,d+1); } void lrs_set_row_mp(lrs_dic *P, lrs_dat *Q, long row, lrs_mp_vector num, lrs_mp_vector den, long ineq) /* set row of dictionary using num and den arrays for rational input */ /* ineq = 1 (GE) - ordinary row */ /* = 0 (EQ) - linearity */ { lrs_mp Temp, mpone; lrs_mp_vector oD; /* denominator for row */ long i, j; /* assign local variables to structures */ lrs_mp_matrix A; lrs_mp_vector Gcd, Lcm; long hull; long m, d; lrs_alloc_mp(Temp); lrs_alloc_mp(mpone); hull = Q->hull; A = P->A; m = P->m; d = P->d; Gcd = Q->Gcd; Lcm = Q->Lcm; oD = lrs_alloc_mp_vector (d); itomp (ONE, mpone); itomp (ONE, oD[0]); i=row; itomp (ONE, Lcm[i]); /* Lcm of denominators */ itomp (ZERO, Gcd[i]); /* Gcd of numerators */ for (j = hull; j <= d; j++) /* hull data copied to cols 1..d */ { copy( A[i][j],num[j-hull]); copy(oD[j],den[j-hull]); if (!one(oD[j])) lcm (Lcm[i], oD[j]); /* update lcm of denominators */ copy (Temp, A[i][j]); gcd (Gcd[i], Temp); /* update gcd of numerators */ } if (hull) { itomp (ZERO, A[i][0]); /*for hull, we have to append an extra column of zeroes */ if (!one (A[i][1]) || !one (oD[1])) /* all rows must have a one in column one */ Q->polytope = FALSE; } if (!zero (A[i][hull])) /* for H-rep, are zero in column 0 */ Q->homogeneous = FALSE; /* for V-rep, all zero in column 1 */ storesign (Gcd[i], POS); storesign (Lcm[i], POS); if (greater (Gcd[i], mpone) || greater (Lcm[i], mpone)) for (j = 0; j <= d; j++) { exactdivint (A[i][j], Gcd[i], Temp); /*reduce numerators by Gcd */ mulint (Lcm[i], Temp, Temp); /*remove denominators */ exactdivint (Temp, oD[j], A[i][j]); /*reduce by former denominator */ } if ( ineq == EQ ) /* input is linearity */ { Q->linearity[Q->nlinearity]=row; Q->nlinearity++; } /* 2010.4.26 Set Gcd and Lcm for the non-existant rows when nonnegative set */ if(Q->nonnegative && row==m) for(j=1;j<=d;j++) { itomp (ONE, Lcm[m+j]); itomp (ONE, Gcd[m+j]); } lrs_clear_mp_vector (oD,d); lrs_clear_mp(Temp); lrs_clear_mp(mpone); } /* end of lrs_set_row_mp */ void lrs_set_obj(lrs_dic *P, lrs_dat *Q, long num[], long den[], long max) { long i; if (max == MAXIMIZE) Q->maximize=TRUE; else { Q->minimize=TRUE; for(i=0;i<=P->d;i++) num[i]=-num[i]; } lrs_set_row(P,Q,0L,num,den,GE); } void lrs_set_obj_mp(lrs_dic *P, lrs_dat *Q, lrs_mp_vector num, lrs_mp_vector den, long max) { long i; if (max == MAXIMIZE) Q->maximize=TRUE; else { Q->minimize=TRUE; for(i=0;i<=P->d;i++) changesign(num[i]); } lrs_set_row_mp(P,Q,0L,num,den,GE); } long lrs_solve_lp(lrs_dic *P, lrs_dat *Q) /* user callable function to solve lp only */ { lrs_mp_matrix Lin; /* holds input linearities if any are found */ long col; Q->lponly = TRUE; if (!lrs_getfirstbasis (&P, Q, &Lin, FALSE)) return FALSE; /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ for (col = 0; col < Q->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q, Lin[col]); /* Array Lin[][] holds the coeffs. */ return TRUE; } /* end of lrs_solve_lp */ long dan_selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s) /* select pivot indices using dantzig simplex method */ /* largest coefficient with lexicographic rule to avoid cycling */ /* Bohdan Kaluzny's handiwork */ /* returns TRUE if pivot found else FALSE */ /* pivot variables are B[*r] C[*s] in locations Row[*r] Col[*s] */ { long j,k,col; lrs_mp coeff; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Col = P->Col; long d = P->d; lrs_alloc_mp (coeff); *r = 0; *s = d; j = 0; k = 0; itomp(0,coeff); /*find positive cost coef */ while (k < d) { if(greater(A[0][Col[k]],coeff)) { j = k; copy(coeff,A[0][Col[j]]); } k++; } if (positive(coeff)) /* pivot column found! */ { *s = j; col = Col[j]; /*find min index ratio */ *r = ratio (P, Q, col); if (*r != 0) { lrs_clear_mp(coeff); return (TRUE); /* unbounded */ } } lrs_clear_mp(coeff); return (FALSE); } /* end of dan_selectpivot */ long phaseone (lrs_dic * P, lrs_dat * Q) /* Do a dual pivot to get primal feasibility (pivot in X_0)*/ /* Bohdan Kaluzny's handiwork */ { long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Row = P->Row; long *Col = P->Col; long m, d; lrs_mp b_vector; lrs_alloc_mp (b_vector); m = P->m; d = P->d; i = 0; k = d+1; itomp(0,b_vector); fprintf (lrs_ofp, "\nLP: Phase One: Dual pivot on artificial variable"); /*find most negative b vector */ while (k <= m) { if(greater(b_vector,A[Row[k]][0])) { i = k; copy(b_vector,A[Row[i]][0]); } k++; } if (negative(b_vector)) /* pivot row found! */ { j = 0; /*find a positive entry for in row */ while (j < d && !positive (A[Row[i]][Col[j]])) j++; if (j >= d) { lrs_clear_mp (b_vector); return (FALSE); /* no positive entry */ } pivot (P, Q, i, j); update (P, Q, &i, &j); } lrs_clear_mp (b_vector); return (TRUE); } long lrs_set_digits(long dec_digits) { /* convert user specified decimal digits to mp digits */ fprintf (lrs_ofp, "\n*digits %ld", dec_digits); if (dec_digits > 0) lrs_digits = DEC2DIG (dec_digits); if (lrs_digits > MAX_DIGITS) { fprintf (lrs_ofp, "\nDigits must be at most %ld\nChange MAX_DIGITS and recompile", DIG2DEC (MAX_DIGITS)); fflush(stdout); return (FALSE); } return (TRUE); } long lrs_checkbound(lrs_dic *P, lrs_dat *Q) { /* check bound on objective and return TRUE if exceeded */ if(!Q->bound) return FALSE; if( Q->maximize && comprod(Q->boundn,P->objden,P->objnum,Q->boundd) == 1 ) { if(Q->verbose) { prat(" \nObj value: ",P->objnum,P->objden); fprintf(lrs_ofp," Pruning "); } return TRUE; } if( Q->minimize && comprod(Q->boundn,P->objden,P->objnum,Q->boundd) == -1 ) { if(Q->verbose) { prat(" \nObj value: ",P->objnum,P->objden); fprintf(lrs_ofp," Pruning "); } return TRUE; } return FALSE; } lrslib-043/redtest.ine0000755001553201777760000000027611607605134014301 0ustar avisnogroupcube *cube of side 2 centred at origin linearity 4 1 2 5 6 H-representation begin 9 4 rational 1 1 0 0 -1 -1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 -1 0 0 1 0 -1 0 1 0 0 -1 end printcobasis lrslib-043/lrslib.h0000755001553201777760000004541611762050120013566 0ustar avisnogroup/* lrslib.h (vertex enumeration using lexicographic reverse search) */ #define TITLE "lrslib " #define VERSION "v.4.3 2012.6.1" #define AUTHOR "\n*Copyright (C) 1995,2011, David Avis avis@cs.mcgill.ca " /* 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 2 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, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */ /*Ver 4.2* library version */ /******************************************************************************/ /* See http://cgm.cs.mcgill.ca/~avis/C/lrs.html for usage instructions */ /******************************************************************************/ /* Selection of arithmetic package */ /*************************************/ #ifdef LONG #define ARITH "lrslong.h" /* lrs long integer arithmetic package */ #else #ifdef GMP #define ARITH "lrsgmp.h" /* lrs wrapper for gmp multiple precsion arithmetic */ #else #define ARITH "lrsmp.h" /* lrs multiple precsion arithmetic */ #define MP #endif #endif #include ARITH #ifdef SIGNALS #include #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #ifdef TIMES void ptimes (); double get_time(); #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /* make this include file includable in a C++ file Note that lrsgmp.h should not be inside an extern "C" {} block */ #ifdef __cplusplus extern "C" { #endif /*************/ /* typedefs */ /*************/ /******************************************************************************/ /* Indexing after initialization */ /* Basis Cobasis */ /* --------------------------------------- ----------------------------- */ /* | i |0|1| .... |lastdv|lastdv+1|...|m| | j | 0 | 1 | ... |d-1| d | */ /* |-----|+|+|++++++|++++++|--------|---|-| |----|---|---|-----|---|+++++| */ /* |B[i] |0|1| .... |lastdv|lastdv+1|...|m| |C[j]|m+1|m+2| ... |m+d|m+d+1| */ /* -----|+|+|++++++|++++++|????????|???|?| ----|???|???|-----|???|+++++| */ /* */ /* Row[i] is row location for B[i] Col[j] is column location for C[j] */ /* ----------------------------- ----------------------------- */ /* | i |0|1| ..........|m-1|m| | j | 0 | 1 | ... |d-1| d | */ /* |-------|+|-|-----------|---|-| |------|---|---|--- |---|++++| */ /* |Row[i] |0|1|...........|m-1|m| |Col[j]| 1 | 2 | ... | d | 0 | */ /* --------|+|*|***********|***|*| ------|***|***|*****|***|++++| */ /* */ /* + = remains invariant * = indices may be permuted ? = swapped by pivot */ /* */ /* m = number of input rows n= number of input columns */ /* input dimension inputd = n-1 (H-rep) or n (V-rep) */ /* lastdv = inputd-nredundcol (each redundant column removes a dec. var) */ /* working dimension d=lastdv-nlinearity (an input linearity removes a slack) */ /* obj function in row 0, index 0=B[0] col 0 has index m+d+1=C[d] */ /* H-rep: b-vector in col 0, A matrix in columns 1..n-1 */ /* V-rep: col 0 all zero, b-vector in col 1, A matrix in columns 1..n */ /******************************************************************************/ typedef struct lrs_dic_struct /* dynamic dictionary data */ { lrs_mp_matrix A; long m; /* A has m+1 rows, row 0 is cost row */ long m_A; /* =m or m-d if nonnegative flag set */ long d; /* A has d+1 columns, col 0 is b-vector */ long d_orig; /* value of d as A was allocated (E.G.) */ long lexflag; /* true if lexmin basis for this vertex */ long depth; /* depth of basis/vertex in reverse search tree */ long i, j; /* last pivot row and column pivot indices */ lrs_mp det; /* current determinant of basis */ lrs_mp objnum; /* objective numerator value */ lrs_mp objden; /* objective denominator value */ long *B, *Row; /* basis, row location indices */ long *C, *Col; /* cobasis, column location indices */ struct lrs_dic_struct *prev, *next; } lrs_dic; typedef struct lrs_dat /* global problem data */ { lrs_mp_vector Gcd; /* Gcd of each row of numerators */ lrs_mp_vector Lcm; /* Lcm for each row of input denominators */ lrs_mp sumdet; /* sum of determinants */ lrs_mp Nvolume; /* volume numerator */ lrs_mp Dvolume; /* volume denominator */ lrs_mp boundn; /* objective bound numerator */ lrs_mp boundd; /* objective bound denominator */ long unbounded; /* lp unbounded */ char fname[100]; /* input file name from line 1 of input */ long *inequality; /* indices of inequalities corr. to cobasic ind */ /* initially holds order used to find starting */ /* basis, default: m,m-1,...,2,1 */ long *facet; /* cobasic indices for restart in needed */ long *redundcol; /* holds columns which are redundant */ long *linearity; /* holds cobasic indices of input linearities */ long *minratio; /* used for lexicographic ratio test */ long *temparray; /* for sorting indices, dimensioned to d */ long *isave, *jsave; /* arrays for estimator, malloc'ed at start */ long inputd; /* input dimension: n-1 for H-rep, n for V-rep */ long m; /* number of rows in input file */ long n; /* number of columns in input file */ long lastdv; /* index of last dec. variable after preproc */ /* given by inputd-nredundcol */ long count[10]; /* count[0]=rays [1]=verts. [2]=base [3]=pivots */ /* count[4]=integer vertices */ long deepest; /* max depth ever reached in search */ long nredundcol; /* number of redundant columns */ long nlinearity; /* number of input linearities */ long totalnodes; /* count total number of tree nodes evaluated */ long runs; /* probes for estimate function */ long seed; /* seed for random number generator */ double cest[10]; /* ests: 0=rays,1=vert,2=bases,3=vol,4=int vert */ /**** flags ********** */ long allbases; /* TRUE if all bases should be printed */ long bound; /* TRUE if upper/lower bound on objective given */ long debug; long dualdeg; /* TRUE if start dictionary is dual degenerate */ long etrace; /* turn off debug at basis # strace */ long frequency; /* frequency to print cobasis indices */ long geometric; /* TRUE if incident vertex prints after each ray */ long getvolume; /* do volume calculation */ long givenstart; /* TRUE if a starting cobasis is given */ long homogeneous; /* TRUE if all entries in column one are zero */ long hull; /* do convex hull computation if TRUE */ long incidence; /* print all tight inequalities (vertices/rays) */ long lponly; /* true if only lp solution wanted */ long maxdepth; /* max depth to search to in treee */ long maximize; /* flag for LP maximization */ long maxoutput; /* if positive, maximum number of output lines */ long minimize; /* flag for LP minimization */ long mindepth; /* do not backtrack above mindepth */ long nash; /* TRUE for computing nash equilibria */ long nonnegative; /* TRUE if last d constraints are nonnegativity */ long polytope; /* TRUE for facet computation of a polytope */ long printcobasis; /* TRUE if all cobasis should be printed */ long printslack; /* TRUE if indices of slack inequal. printed */ long truncate; /* TRUE: truncate tree when moving from opt vert*/ long verbose; /* FALSE for minimalist output */ long restart; /* TRUE if restarting from some cobasis */ long strace; /* turn on debug at basis # strace */ long voronoi; /* compute voronoi vertices by transformation */ /* Variables for saving/restoring cobasis, db */ long id; /* numbered sequentially */ char *name; /* passed by user */ long saved_count[3]; /* How often to print out current cobasis */ long *saved_C; lrs_mp saved_det; long saved_depth; long saved_d; long saved_flag; /* There is something in the saved cobasis */ /* Variables for cacheing dictionaries, db */ lrs_dic *Qhead, *Qtail; } lrs_dat, lrs_dat_p; /*********************/ /*global variables */ /*********************/ #define MAX_LRS_GLOBALS 100L #define MAXIMIZE 1L /* maximize the lp */ #define MINIMIZE 0L /* maximize the lp */ #define GE 1L /* constraint is >= */ #define EQ 0L /* constraint is linearity */ extern FILE *lrs_cfp; /* output file for checkpoint information */ extern unsigned long dict_count, dict_limit, cache_tries, cache_misses; extern lrs_dic *PBnew; /* we will save Bob's dictionary in getabasis */ /*******************************/ /* functions for external use */ /*******************************/ long lrs_main (int argc, char *argv[]); /* lrs driver, argv[1]=input file, [argc-1]=output file */ long redund_main (int argc, char *argv[]); /* redund driver, argv[1]=input file, [2]=output file */ lrs_dat *lrs_alloc_dat (char *name); /* allocate for lrs_dat structure "name" */ lrs_dic *lrs_alloc_dic (lrs_dat * Q); /* allocate for lrs_dic structure corr. to Q */ void lrs_estimate (lrs_dic * P, lrs_dat * Q); /* get estimates only */ long lrs_read_dat (lrs_dat * Q, int argc, char *argv[]); /* read header and set up lrs_dat */ long lrs_read_dic (lrs_dic * P, lrs_dat * Q); /* read input and set up problem and lrs_dic */ long lrs_checkbound (lrs_dic *P, lrs_dat * Q); /* TRUE if current objective value exceeds specified bound */ long lrs_getfirstbasis (lrs_dic ** P_p, lrs_dat * Q, lrs_mp_matrix * Lin,long no_output); /* gets first basis, FALSE if none,P may get changed if lin. space Lin found */ /* no_output is TRUE supresses output headers */ /* P may get changed if lin. space Lin found */ void lrs_getinput(lrs_dic *P,lrs_dat *Q,long *num,long *den, long m, long d); /* reads input matrix b A in lrs/cdd format */ long lrs_getnextbasis (lrs_dic ** dict_p, lrs_dat * Q, long prune); /* gets next lrs tree basis, FALSE if none */ /* backtrack if prune is TRUE */ long lrs_getsolution (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output, long col); long lrs_getray (lrs_dic * P, lrs_dat * Q, long col, long comment, lrs_mp_vector output); long lrs_getvertex (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output); void lrs_close (char *name); /* close lrs lib program "name" */ long lrs_init (char *name); /* initialize lrslib and arithmetic package for prog "name" */ void lrs_lpoutput(lrs_dic * P,lrs_dat * Q, lrs_mp_vector output); /* print LP primal and dual solutions */ void lrs_printcobasis (lrs_dic * P, lrs_dat * Q, long col); /* print cobasis for column col(verted or ray) */ void lrs_printoutput (lrs_dat * Q, lrs_mp_vector output); /* print output array */ void lrs_printrow (char name[], lrs_dat * Q, lrs_mp_vector output, long rowd); /*print row of A matrix in output[0..rowd] */ void lrs_printsol (lrs_dic * P, lrs_dat * Q, long col, long comment); /* print out solution from col, comment= */ /* 0=normal,-1=geometric ray,1..inputd=linearity */ void lrs_printtotals (lrs_dic * P, lrs_dat * Q); /* print final totals for lrs */ long lrs_set_digits (long dec_digits ); /* set lrsmp digits to equiv. of decimal dec_digits */ long lrs_solvelp (lrs_dic * P, lrs_dat * Q, long maximize); /* solve primal feas LP:TRUE bounded else FALSE */ /*******************************/ /* functions for internal use */ /*******************************/ /* basic dictionary functions */ /*******************************/ long getabasis (lrs_dic * P, lrs_dat * Q, long order[]); /* Try to find a starting basis */ void getnextoutput (lrs_dic * P, lrs_dat * Q, long i, long col, lrs_mp out); /* get A[B[i][col] and copy to out */ long ismin (lrs_dic * P, lrs_dat * Q, long r, long s); /* test if A[r][s] is a min ratio for col s */ long lexmin (lrs_dic * P, lrs_dat * Q, long col); /* test A to see if current basis is lexmin */ void pivot (lrs_dic * P, lrs_dat * Q, long bas, long cob); /* Qpivot routine for array A */ long primalfeasible (lrs_dic * P, lrs_dat * Q); /* Do dual pivots to get primal feasibility */ long ratio (lrs_dic * P, lrs_dat * Q, long col); /* find lex min. ratio */ long removecobasicindex (lrs_dic * P, lrs_dat * Q, long k); /* remove C[k] from problem */ long restartpivots (lrs_dic * P, lrs_dat * Q); /* restart problem from given cobasis */ long reverse (lrs_dic * P, lrs_dat * Q, long *r, long s); /* TRUE if B[*r] C[s] is a reverse lex-pos pivot */ long selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s); /* select pivot indices using lexicographic rule */ long dan_selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s); /* select pivot indices using dantzig-lex rule */ void update (lrs_dic * P, lrs_dat * Q, long *i, long *j); /* update the B,C, LOC arrays after a pivot */ void updatevolume (lrs_dic * P, lrs_dat * Q); /* rescale determinant and update the volume */ /*******************************/ /* other functions using P,Q */ /*******************************/ long lrs_degenerate (lrs_dic * P, lrs_dat * Q); /* TRUE if the dictionary is primal degenerate */ void print_basis (FILE * fp, lrs_dat * Q); void printA (lrs_dic * P, lrs_dat * Q); /* raw print of dictionary, bases for debugging */ void pimat (lrs_dic * P, long r, long s, lrs_mp Nt, char name[]); /* print the row r col s of A */ long readfacets (lrs_dat * Q, long facet[]); /* read and check facet list */ long readlinearity (lrs_dat * Q); /* read and check linearity list */ void rescaledet (lrs_dic * P, lrs_dat * Q, lrs_mp Vnum, lrs_mp Vden); /* rescale determinant to get its volume */ void rescalevolume (lrs_dic * P, lrs_dat * Q, lrs_mp Vnum, lrs_mp Vden); /* adjust volume for dimension */ /***************************************************/ /* Routines for redundancy checking */ /***************************************************/ long checkredund (lrs_dic * P, lrs_dat * Q); /* solve primal lp to check redund of obj fun. */ /* returns TRUE if redundant, else FALSE */ long checkcobasic (lrs_dic * P, lrs_dat * Q, long index); /* TRUE if index is cobasic and nondegenerate */ /* FALSE if basic, or degen. cobasic, where it will get pivoted out */ long checkindex (lrs_dic * P, lrs_dat * Q, long index); /* index=0 non-red.,1 red., 2 input linearity */ /* NOTE: row is returned all zero if redundant!! */ /***************************************************/ /* Routines for caching and restoring dictionaries */ /***************************************************/ void lrs_free_dic ( lrs_dic *P, lrs_dat *Q); void lrs_free_dat ( lrs_dat *Q); void cache_dict (lrs_dic ** D_p, lrs_dat * global, long i, long j); long check_cache (lrs_dic ** D_p, lrs_dat * global, long *i_p, long *j_p); void copy_dict (lrs_dat * global, lrs_dic * dest, lrs_dic * src); void pushQ (lrs_dat * global, long m, long d, long m_A); void save_basis (lrs_dic * D, lrs_dat * Q); lrs_dic *alloc_memory (lrs_dat * Q); lrs_dic * lrs_getdic(lrs_dat *Q); lrs_dic *new_lrs_dic (long m, long d, long m_A); lrs_dic *resize (lrs_dic * P, lrs_dat * Q); /*******************************/ /* signals handling */ /*******************************/ void checkpoint (); void die_gracefully (); void setup_signals (); void timecheck (); /*******************************/ /* utilities */ /*******************************/ void lprat (const char *name, long Num, long Den); /* Print Num/Den without reducing */ long lreadrat (long *Num, long *Den); /* read a rational string and convert to long integers */ void reorder (long a[], long range); /* reorder array in increasing order with one misplaced element */ void reorder1 (long a[], long b[], long newone, long range); /* reorder array a in increasing order with misplaced element newone */ /* elements of b go along for the ride */ /***************************/ /* lp_solve like functions */ /***************************/ long lrs_solve_lp(lrs_dic *P, lrs_dat *Q); /* solve lp only for given dictionary */ void lrs_set_row(lrs_dic *P, lrs_dat *Q, long row, long num[], long den[], long ineq); /* load row i of dictionary from num[]/den[] ineq=GE */ void lrs_set_row_mp(lrs_dic *P, lrs_dat *Q, long row, lrs_mp_vector num, lrs_mp_vector den, long ineq); /* same as lrs_set_row except num/den is lrs_mp type */ void lrs_set_obj(lrs_dic *P, lrs_dat *Q, long num[], long den[], long max); /* set up objective function with coeffs num[]/den[] max=MAXIMIZE or MINIMIZE */ void lrs_set_obj_mp(lrs_dic *P, lrs_dat *Q, lrs_mp_vector num, lrs_mp_vector den, long max); /* same as lrs_set_obj but num/den has lrs_mp type */ /* end of lrslib.h (vertex enumeration using lexicographic reverse search) */ #ifdef __cplusplus } #endif lrslib-043/vedemo.c0000755001553201777760000000721311607605134013553 0ustar avisnogroup/* vedemo.c lrslib vertex enumeration demo */ /* last modified: May 29, 2001 */ /* Copyright: David Avis 2001, avis@cs.mcgill.ca */ /* Demo driver for ve code using lrs */ /* This program computes vertices of generated cubes */ /* given by H-representation */ #include #include #include "lrslib.h" #define MAXCOL 1000 /* maximum number of colums */ void makecube (lrs_dic *P, lrs_dat *Q); int main (int argc, char *argv[]) { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_vector output; /* one line of output:ray,vertex,facet,linearity */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ long i; long col; /* output column index for dictionary */ /* Global initialization - done once */ if ( !lrs_init ("\n*vedemo:")) return 1; /* compute the vertices of a set of hypercubes given by */ /* their H-representations. */ for(i=1;i<=3;i++) { /* allocate and init structure for static problem data */ Q = lrs_alloc_dat ("LRS globals"); if (Q == NULL) return 1; /* now flags in lrs_dat can be set */ Q->n=i+2; /* number of input columns (dimension + 1 ) */ Q->m=2*i+2; /* number of input rows = number of inequalities */ output = lrs_alloc_mp_vector (Q->n); P = lrs_alloc_dic (Q); /* allocate and initialize lrs_dic */ if (P == NULL) return 1; /* Build polyhedron: constraints and objective */ makecube(P,Q); /* code from here is borrowed from lrs_main */ /* Pivot to a starting dictionary */ if (!lrs_getfirstbasis (&P, Q, &Lin, FALSE)) return 1; /* There may have been column redundancy */ /* (although not for this example of hypercubes) */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ for (col = 0L; col < Q->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q, Lin[col]); /* Array Lin[][] holds the coeffs. */ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* a vertex/ray/facet from the lrs_mp_vector output */ do { for (col = 0; col <= P->d; col++) if (lrs_getsolution (P, Q, output, col)) lrs_printoutput (Q, output); } while (lrs_getnextbasis (&P, Q, FALSE)); lrs_printtotals (P, Q); /* print final totals */ /* free space : do not change order of next 3 lines! */ lrs_clear_mp_vector (output, Q->n); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ } /* end of loop for i= ... */ lrs_close ("vedemo:"); printf("\n"); return 0; } /* end of main */ void makecube (lrs_dic *P, lrs_dat *Q) /* generate H-representation of a unit hypercube */ { long num[MAXCOL]; long den[MAXCOL]; long row, j; long m=Q->m; /* number of inequalities */ long n=Q->n; /* hypercube has dimension n-1 */ for (row=1;row<=m;row++) { for(j=0;j0 ? ONE : ZERO) #define gcd(a,b) mpz_gcd((a),(a),(b)) #define itomp(in, a) mpz_set_si( (a) , (in) ) #define mptoi(a) mpz_get_si( (a) ) #define mptodouble(a) mpz_get_d ( (a) ) #define mulint(a, b, c) mpz_mul((c),(a),(b)) #define one(a) (mpz_cmp_si((a),ONE) == 0 ? ONE : ZERO) #define negative(a) (mpz_sgn(a) < 0 ? ONE : ZERO) #define normalize(a) (void) 0 #define positive(a) (mpz_sgn(a) > 0 ? ONE : ZERO) #define sign(a) (mpz_sgn(a) < 0 ? NEG : POS) #define subint(a, b, c) mpz_sub((c),(a),(b)) #define zero(a) (mpz_sgn(a) == 0 ? ONE : ZERO) /* * convert between decimal and machine (longword digits). Notice lovely * implementation of ceiling function :-) */ #define DEC2DIG(d) ( (d) % BASE_DIG ? (d)/BASE_DIG+1 : (d)/BASE_DIG) #define DIG2DEC(d) ((d)*BASE_DIG) #ifndef OMIT_SIGNALS #include #include /* labs */ #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #ifndef OMIT_TIMES void ptimes (); #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*************/ /* typedefs */ /*************/ typedef mpz_t lrs_mp; /* type lrs_mp holds one long integer */ typedef mpz_t lrs_mp_t; /* for GMP same as lrs_mp for MP *lrs_mp */ typedef mpz_t *lrs_mp_vector; typedef mpz_t **lrs_mp_matrix; /*********************/ /*global variables */ /*********************/ extern long lrs_digits; /* max permitted no. of digits */ extern long lrs_record_digits; /* this is the biggest acheived so far. */ #include extern FILE *lrs_ifp; /* input file pointer */ extern FILE *lrs_ofp; /* output file pointer */ /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ long lrs_mp_init (long dec_digits, FILE * lrs_ifp, FILE * lrs_ofp); /* max number of decimal digits, fps */ void lrs_mp_close (); #define lrs_alloc_mp(a) (mpz_init (a) ) #define lrs_clear_mp(a) (mpz_clear (a) ) lrs_mp_vector lrs_alloc_mp_vector (long n); /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n); /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp */ void lrs_clear_mp_vector (lrs_mp_vector p, long n); /* clear lrs_mp_vector for n+1 lrs_mp numbers */ void lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n); /* clear m by n lrs_mp_matrix */ /*********************************************************/ /* Core library functions - depend on mp implementation */ /******************************************************* */ void atomp (const char s[], lrs_mp a); /* convert string to lrs_mp integer */ long compare (lrs_mp a, lrs_mp b); /* a ? b and returns -1,0,1 for <,=,> */ void linint (lrs_mp a, long ka, lrs_mp b, long kb); /* compute a*ka+b*kb --> a */ void pmp (char name[], lrs_mp a); /* print the long precision integer a */ void prat (char name[], lrs_mp Nt, lrs_mp Dt); /* reduce and print Nt/Dt */ void readmp (lrs_mp a); /* read an integer and convert to lrs_mp */ long readrat (lrs_mp Na, lrs_mp Da); /* read a rational or int and convert to lrs_mp */ void reduce (lrs_mp Na, lrs_mp Da); /* reduces Na Da by gcd(Na,Da) */ void storesign(lrs_mp Na, long sa); /* change sign of Na to sa=POS/NEG */ /*********************************************************/ /* Standard arithmetic & misc. functions */ /* should be independent of mp implementation */ /******************************************************* */ void atoaa (const char in[], char num[], char den[]); /* convert rational string in to num/den strings */ long atos (char s[]); /* convert s to integer */ long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd); /* +1 if Na*Nb > Nc*Nd,-1 if Na*Nb > Nc*Nd else 0 */ void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */ void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc); void lcm (lrs_mp a, lrs_mp b); /* a = least common multiple of a, b; b is saved */ void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */ long myrandom (long num, long nrange); /* return a random number in range 0..nrange-1 */ void notimpl (char s[]); /* bail out - help! */ void rattodouble (lrs_mp a, lrs_mp b, double *x); /* convert lrs_mp rational to double */ void reduceint (lrs_mp Na, lrs_mp Da); /* divide Na by Da and return it */ void reducearray (lrs_mp_vector p, long n); /* find gcd of p[0]..p[n-1] and divide through by */ void scalerat (lrs_mp Na, lrs_mp Da, long ka); /* scales rational by ka */ /**********************************/ /* Miscellaneous functions */ /******************************** */ void lrs_getdigits (long *a, long *b); /* send digit information to user */ void stringcpy (char *s, char *t); /* copy t to s pointer version */ #ifndef __STDC__ void *calloc (); void *malloc (); #endif void *xcalloc (long n, long s, long l, char *f); void lrs_default_digits_overflow (); /* end of lrs_mp.h (vertex enumeration using lexicographic reverse search) */ lrslib-043/lp.ine0000755001553201777760000000026511607605134013240 0ustar avisnogroupcube *cube of side 2 centred at origin H-representation begin 6 4 rational 2/4 -2/4 4/10 -6/12 1 0 -1 0 1 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 1 end maximize 0 1 1 1 lponly debug *verbose lrslib-043/ext/0000755001553201777760000000000011607605134012722 5ustar avisnogrouplrslib-043/ext/test/0000755001553201777760000000000011607605134013701 5ustar avisnogrouplrslib-043/ext/test/tsp5.ext0000755001553201777760000000071311607605134015322 0ustar avisnogrouptsp5.ext V-representation begin 12 11 rational 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 end lrslib-043/ext/test/cut32_16.ext0000755001553201777760000000343511607605134015701 0ustar avisnogroupcut32_16.ext digits 50 V-representation *6 point cut polytope begin 32 16 integer 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 1 1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 1 1 1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 1 1 1 1 -1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 1 1 1 -1 1 1 1 1 1 1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 -1 1 1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 1 1 -1 1 1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 1 1 1 -1 -1 -1 1 1 1 1 -1 1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 1 -1 1 1 1 -1 1 1 -1 1 -1 -1 1 1 1 -1 -1 1 1 1 1 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 1 1 1 1 1 -1 1 -1 -1 1 -1 1 1 -1 1 1 -1 1 1 1 1 1 -1 -1 -1 -1 1 1 -1 1 1 1 1 -1 1 -1 -1 -1 1 1 -1 -1 1 1 -1 1 1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 1 1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 1 1 -1 -1 1 1 1 -1 1 -1 -1 1 1 -1 -1 1 1 1 -1 -1 1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 1 1 -1 1 1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 1 1 -1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 -1 end lrslib-043/ext/test/cyclic25_13.ext0000755001553201777760000000612011607605134016345 0ustar avisnogroupcyclic25_13.ine H-representation digits 300 begin 25 13 integer 1 -156 1690 -22464 265018 -3234816 38683450 -465813504 5585476858 -67077144576 804783054010 -9659108818944 115904429355898 1 -143 1391 -17303 185783 -2093663 22895951 -253333223 2782380263 -30653319983 337043838911 -3709051717943 40794692425943 1 -130 1118 -13000 125450 -1300000 12865658 -130000000 1295714810 -13000000000 129857319098 -1300000000000 12995123528570 1 -117 871 -9477 80743 -767637 6774391 -62178597 555322183 -5036466357 45185516311 -407953774917 3666707502823 1 -104 650 -6656 48698 -425984 3273530 -27262976 213818618 -1744830464 13815962810 -111669149696 888476726138 1 -91 455 -4459 26663 -218491 1395095 -10706059 70657223 -524596891 3529497335 -25705247659 175060262183 1 -78 286 -2808 12298 -101088 472186 -3639168 17549818 -131010048 643379386 -4716361728 23421698938 1 -65 143 -1625 3575 -40625 68783 -1015625 792935 -25390625 -15727777 -634765625 -1702643305 1 -52 26 -832 -1222 -13312 -81094 -212992 -3433222 -3407872 -129049414 -54525952 -4658367622 1 -39 -65 -351 -3497 -3159 -124865 -28431 -4199897 -255879 -141913265 -2302911 -4869562697 1 -26 -130 -104 -4342 -416 -133510 -1664 -4281862 -6656 -142667590 -26624 -4876418182 1 -13 -169 -13 -4537 -13 -134329 -13 -4285177 -13 -142680889 -13 -4876471417 1 0 -182 0 -4550 0 -134342 0 -4285190 0 -142680902 0 -4876471430 1 13 -169 13 -4537 13 -134329 13 -4285177 13 -142680889 13 -4876471417 1 26 -130 104 -4342 416 -133510 1664 -4281862 6656 -142667590 26624 -4876418182 1 39 -65 351 -3497 3159 -124865 28431 -4199897 255879 -141913265 2302911 -4869562697 1 52 26 832 -1222 13312 -81094 212992 -3433222 3407872 -129049414 54525952 -4658367622 1 65 143 1625 3575 40625 68783 1015625 792935 25390625 -15727777 634765625 -1702643305 1 78 286 2808 12298 101088 472186 3639168 17549818 131010048 643379386 4716361728 23421698938 1 91 455 4459 26663 218491 1395095 10706059 70657223 524596891 3529497335 25705247659 175060262183 1 104 650 6656 48698 425984 3273530 27262976 213818618 1744830464 13815962810 111669149696 888476726138 1 117 871 9477 80743 767637 6774391 62178597 555322183 5036466357 45185516311 407953774917 3666707502823 1 130 1118 13000 125450 1300000 12865658 130000000 1295714810 13000000000 129857319098 1300000000000 12995123528570 1 143 1391 17303 185783 2093663 22895951 253333223 2782380263 30653319983 337043838911 3709051717943 40794692425943 1 156 1690 22464 265018 3234816 38683450 465813504 5585476858 67077144576 804783054010 9659108818944 115904429355898 end lrslib-043/ext/test/cut16_11.ext0000755001553201777760000000101411607605134015665 0ustar avisnogroupcut16_11.ext V-representation *5 point cut polytope begin 16 11 integer 1 1 1 -1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 1 -1 -1 -1 1 1 -1 1 1 1 -1 -1 1 1 -1 1 1 1 -1 1 -1 1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 1 1 1 -1 -1 1 1 -1 1 1 1 1 -1 1 -1 1 -1 1 1 -1 1 1 -1 1 1 -1 1 1 -1 1 1 -1 -1 1 1 1 1 -1 -1 1 1 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 1 1 -1 1 end lrslib-043/ext/metric/0000755001553201777760000000000011607605134014205 5ustar avisnogrouplrslib-043/ext/metric/cp7.ext0000755001553201777760000000577611607605134015442 0ustar avisnogroupcp7.ext *Complete Cut Polytope on 7 vertices *The number of facets is 116,764. V-representation begin 64 22 integer 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 end lrslib-043/ext/metric/mp5.ext0000755001553201777760000000266211607605134015441 0ustar avisnogroupmp5.ext V-representation begin 32 11 rational 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 2/3 2/3 1/3 1/3 2/3 1/3 1/3 1/3 1/3 2/3 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1/3 2/3 2/3 2/3 1/3 1/3 1/3 2/3 2/3 2/3 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1/3 1/3 2/3 2/3 2/3 1/3 1/3 1/3 1/3 2/3 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 2/3 1/3 2/3 2/3 1/3 2/3 2/3 1/3 1/3 2/3 1 1/3 2/3 1/3 1/3 1/3 2/3 2/3 1/3 1/3 2/3 1 2/3 1/3 1/3 1/3 1/3 1/3 1/3 2/3 2/3 2/3 1 0 0 1 0 0 1 0 1 0 1 1 2/3 2/3 2/3 1/3 2/3 2/3 1/3 2/3 1/3 1/3 1 1 0 1 0 1 0 1 1 0 1 1 2/3 1/3 1/3 2/3 1/3 1/3 2/3 2/3 1/3 1/3 1 1/3 1/3 1/3 2/3 2/3 2/3 1/3 2/3 1/3 1/3 1 1/3 1/3 1/3 1/3 2/3 2/3 2/3 2/3 2/3 2/3 1 0 1 0 0 1 0 0 1 1 0 1 2/3 1/3 2/3 1/3 1/3 2/3 1/3 1/3 2/3 1/3 1 1/3 2/3 1/3 2/3 1/3 2/3 1/3 1/3 2/3 1/3 1 1/3 1/3 2/3 1/3 2/3 1/3 2/3 1/3 2/3 1/3 1 1 1 0 0 0 1 1 1 1 0 1 1/3 2/3 2/3 1/3 1/3 1/3 2/3 2/3 1/3 1/3 1 1 0 0 0 1 1 1 0 0 0 1 2/3 2/3 1/3 2/3 2/3 1/3 2/3 1/3 2/3 1/3 1 0 0 0 0 0 0 0 0 0 0 end lrslib-043/ext/metric/cp5.ext0000755001553201777760000000114511607605134015422 0ustar avisnogroupcp5.ext V-representation *5 point cut polytope digits 40 begin 16 11 integer 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 end lrslib-043/ext/metric/cp6.ext0000755001553201777760000000306211607605134015423 0ustar avisnogroupcp6.ext digits 50 V-representation *6 point cut cone begin 32 16 integer 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 end lrslib-043/ext/metric/cp4.ext0000755001553201777760000000030511607605134015416 0ustar avisnogroupcp4.ext V-representation begin 8 7 integer 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 end startingcobasis 2 3 4 5 6 7 8 lrslib-043/rat2float.c0000755001553201777760000000741111607605134014172 0ustar avisnogroup/* * Reads a polyhedron file on stdin , with rationals and outputs * an approximation in decimal floating point * * David Bremner. bremner@cs.mcgill.ca * */ /* Hacked by DA, April 20 2006 * * first argument overides stdin * if column 0=0 then first non zero column scaled to +/-1 (otherwise big ugly integers come out) */ static char rcsid[]="$Id: rat2float.c,v 1.2 2006/04/04 12:33:38 bremner Exp $"; #include #include #include #include FILE *lrs_ifp; /* input file pointer */ #define DOCSTRING "\n\ $Id: rat2float.ds,v 1.3 2006/04/04 12:34:35 bremner Exp $ \n\ \n\ float takes a polytope file with rational or integer coefficents, \n\ and outputs an approximately equivelent one with floating point \n\ coefficents.\n\ \n\ WARNING: Assumes that numerator and denominator will fit in long integer,\n\ unless compiled with multiprecision support.\n\ \n\ \n\ \n\ " int usage(){ fprintf(stderr,"\n%s\n",rcsid);fprintf(stderr,DOCSTRING); exit(1); } #define CHECK_HELP if (argc > 1 && argv[1][0]=='-' && argv[1][1]=='h') usage(); #ifdef LRSMP #include "lrsmp.h" #endif #ifndef LRSMP typedef long integer_t; #define zero(n) (n==0) #define one(n) (n==1) #define pmp(s,n) printf("%s %d ",s,n) #define readrat(n,d) my_readrat(&n,&d); void my_readrat(long *num_p, long * denom_p) { char buf[BUFSIZ]; char *p; fscanf(lrs_ifp,"%s",buf); if (p=index(buf,'/')){ *p=0; *denom_p=atol(&p[1]); } else { *denom_p=1; } *num_p=atol(buf); } void rattodouble(integer_t num, integer_t denom, double *out_p){ *out_p=(double)num/(double)denom; } #else typedef lrs_mp integer_t; #define MP_DIGITS 1000L #endif int main(argc,argv) int argc; char **argv; { long int n; int j; integer_t num,denom,sdenom; double out; int scale; /* if column 0 is zero, scale column 1 to 1 */ char format[BUFSIZ]; char buf[BUFSIZ]; char inputm[BUFSIZ]; CHECK_HELP; if(argc > 1 ) /* command line argument overides stdin */ { if ((lrs_ifp = fopen (argv[1], "r")) == NULL) { printf ("\nBad input file name\n"); return(1); } } else lrs_ifp=stdin; #ifdef LRSMP lrs_mp_init (MP_DIGITS,lrs_ifp,stdout); #endif sprintf(format,"%%.%dlf ",DBL_DIG); while ( fgets(buf,BUFSIZ,lrs_ifp) !=NULL ) { fputs(buf,stdout); if (strncmp(buf,"begin",5)==0) break; } /* in lrs output m is undefined */ if (fscanf(lrs_ifp,"%s %ld %s",inputm,&n,buf)==EOF){ fprintf(stderr,"No begin line"); exit(1); } printf("%s %ld real\n",inputm,n); /* for (i=0;i #include #include "lrslong.h" long digits; long record_digits; #define MAXINPUT 1000 /*max length of any input rational */ void gcd (lrs_mp u, lrs_mp v) /* Returns u=gcd(u,v) using classic Euclid's algorithm. v is destroyed. Knuth, II, p.320 */ { unsigned long ul, vl, r; ul = labs (*u); vl = labs (*v); if (ul == 0) { *u = vl; return; } while (vl != 0) { r = ul % vl; ul = vl; vl = r; } *u = ul; } /* gcd */ void lcm (a, b) /* a = least common multiple of a, b; b is preserved */ lrs_mp a, b; { lrs_mp u, v; copy (u, a); copy (v, b); gcd (u, v); exactdivint (a, u, v); /* v=a/u a contains remainder = 0 */ mulint (v, b, a); } /* end of lcm */ /***************************************************************/ /* */ /* Package of routines for rational arithmetic */ /* (Built on top of package for multiprecision arithmetic */ /* */ /***************************************************************/ void reduce (lrs_mp Na, lrs_mp Da) /* reduces Na/Da by gcd(Na,Da) */ { lrs_mp Nb, Db, Nc, Dc; copy (Nb, Na); copy (Db, Da); storesign (Nb, POS); storesign (Db, POS); copy (Nc, Na); copy (Dc, Da); gcd (Nb, Db); /* Nb is the gcd(Na,Da) */ exactdivint (Nc, Nb, Na); exactdivint (Dc, Nb, Da); } void reduceint (lrs_mp Na, lrs_mp Da) /* divide Na by Da and return */ { lrs_mp Temp; copy (Temp, Na); exactdivint (Temp, Da, Na); } long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd) /* +1 if Na*Nb > Nc*Nd */ /* -1 if Na*Nb < Nc*Nd */ /* 0 if Na*Nb = Nc*Nd */ { long mc; mc = *Na * *Nb - *Nc * *Nd; if (mc > 0) return 1; if (mc < 0) return -1; return 0; } void linrat (Na, Da, ka, Nb, Db, kb, Nc, Dc) /* computes Nc/Dc = ka*Na/Da +kb* Nb/Db and reduces answer by gcd(Nc,Dc) */ lrs_mp Na, Da, Nb, Db, Nc, Dc; long ka, kb; { lrs_mp c; mulint (Na, Db, Nc); mulint (Da, Nb, c); linint (Nc, ka, c, kb); /* Nc = (ka*Na*Db)+(kb*Da*Nb) */ mulint (Da, Db, Dc); /* Dc = Da*Db */ reduce (Nc, Dc); } void divrat (Na, Da, Nb, Db, Nc, Dc) /* computes Nc/Dc = (Na/Da) / ( Nb/Db ) and reduces answer by gcd(Nc,Dc) */ lrs_mp Na, Da, Nb, Db, Nc, Dc; { mulint (Na, Db, Nc); mulint (Da, Nb, Dc); reduce (Nc, Dc); } void mulrat (Na, Da, Nb, Db, Nc, Dc) /* computes Nc/Dc = Na/Da * Nb/Db and reduces answer by gcd(Nc,Dc) */ lrs_mp Na, Da, Nb, Db, Nc, Dc; { mulint (Na, Nb, Nc); mulint (Da, Db, Dc); reduce (Nc, Dc); } /***************************************************************/ /* */ /* Conversion and I/O functions */ /* */ /***************************************************************/ void atomp (const char *s, lrs_mp a) /*convert string to lrs_mp integer */ /* based on atoi KR p.58 */ { long diff, ten, i, sig; lrs_mp mpone; itomp (ONE, mpone); ten = 10L; for (i = 0; s[i] == ' ' || s[i] == '\n' || s[i] == '\t'; i++); /*skip white space */ sig = POS; if (s[i] == '+' || s[i] == '-') /* sign */ sig = (s[i++] == '+') ? POS : NEG; itomp (0L, a); while (s[i] >= '0' && s[i] <= '9') { diff = s[i] - '0'; linint (a, ten, mpone, diff); i++; } storesign (a, sig); if (s[i]) { fprintf (stderr, "\nIllegal character in number: '%s'\n", s + i); exit (1); } } /* end of atomp */ void atoaa (const char *in, char *num, char *den) /* convert rational string in to num/den strings */ { long i, j; for (i = 0; in[i] != '\0' && in[i] != '/'; i++) num[i] = in[i]; num[i] = '\0'; den[0] = '\0'; if (in[i] == '/') { for (j = 0; in[j + i + 1] != '\0'; j++) den[j] = in[i + j + 1]; den[j] = '\0'; } } /* end of atoaa */ void mptodouble (lrs_mp a, double *x) /* convert lrs_mp to double */ { (*x) = (*a); } long mptoi (lrs_mp a) /* convert lrs_mp to long */ { return (*a); } void rattodouble (lrs_mp a, lrs_mp b, double *x) /* convert lrs_mp rati onal to double */ { double y; mptodouble (a, &y); mptodouble (b, x); *x = y / (*x); } long readrat (lrs_mp Na, lrs_mp Da) /* read a rational or integer and convert to lrs_mp */ /* returns true if denominator is not one */ { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; if(fscanf (lrs_ifp, "%s", in)==EOF) { fprintf (lrs_ofp, "\nInvalid rational input"); exit(1); } if(!strcmp(in,"end")) /*premature end of input file */ { return (999L); } atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } void readmp (lrs_mp a) /* read an integer and convert to lrs_mp */ { long in; if(fscanf (lrs_ifp, "%ld", &in)==EOF) { fprintf (lrs_ofp, "\nInvalid integer input"); exit(1); } itomp (in, a); } void pmp (char name[], lrs_mp Nt) { fprintf (lrs_ofp, "%s", name); if (sign (Nt) != NEG) fprintf (lrs_ofp, " "); fprintf (lrs_ofp, "%ld", *Nt); fprintf (lrs_ofp, " "); } void prat (const char *name, lrs_mp Nin, lrs_mp Din) /*print the long precision rational Nt/Dt */ { lrs_mp Nt, Dt; copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); if (sign (Nt) != NEG) fprintf (lrs_ofp, " "); fprintf (lrs_ofp, "%s%ld", name, *Nt); if (*Dt != 1) fprintf (lrs_ofp, "/%ld", *Dt); fprintf (lrs_ofp, " "); } /* prat */ /***************************************************************/ /* */ /* Memory allocation functions */ /* */ /***************************************************************/ lrs_mp_t lrs_alloc_mp_t () /* dynamic allocation of lrs_mp number */ { lrs_mp_t p; p=(long *)calloc (1, sizeof (long)); return p; } lrs_mp_vector lrs_alloc_mp_vector (long n) /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ { lrs_mp_vector p; long i; p = CALLOC ((n + 1), sizeof (lrs_mp *)); for (i = 0; i <= n; i++) p[i] = CALLOC (1, sizeof (lrs_mp)); return p; } void lrs_clear_mp_vector (lrs_mp_vector p, long n) /* free space allocated to p */ { long i; for (i = 0; i <= n; i++) free (p[i]); free (p); } lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n) /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp numbers */ { lrs_mp_matrix a; long *araw; int mp_width, row_width; int i, j; mp_width = lrs_digits + 1; row_width = (n + 1) * mp_width; araw = calloc ((m + 1) * row_width, sizeof (long)); a = calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = calloc ((n + 1), sizeof (lrs_mp *)); for (j = 0; j < n + 1; j++) a[i][j] = (araw + i * row_width + j * mp_width); } return a; } void lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n) /* free space allocated to lrs_mp_matrix p */ { long i; /* p[0][0] is araw, the actual matrix storage address */ free(p[0][0]); for (i = 0; i < m + 1; i++) free (p[i]); } void lrs_getdigits (long *a, long *b) { /* send digit information to user */ *a = DIG2DEC (ZERO); *b = DIG2DEC (ZERO); return; } void * xcalloc (long n, long s, long l, char *f) { void *tmp; tmp = calloc (n, s); if (tmp == 0) { char buf[200]; sprintf (buf, "\n\nFatal error on line %ld of %s", l, f); perror (buf); exit (1); } return tmp; } long lrs_mp_init (long dec_digits, FILE * fpin, FILE * fpout) /* max number of decimal digits for the computation */ /* long int version */ { lrs_ifp = fpin; lrs_ofp = fpout; lrs_record_digits = 0; lrs_digits = 0; /* max permitted no. of digits */ return TRUE; } void notimpl (char s[]) { fflush (stdout); fprintf (stderr, "\nAbnormal Termination %s\n", s); exit (1); } /***************************************************************/ /* */ /* Misc. functions */ /* */ /***************************************************************/ void reducearray (lrs_mp_vector p, long n) /* find largest gcd of p[0]..p[n-1] and divide through */ { lrs_mp divisor; lrs_mp Temp; long i = 0L; while ((i < n) && zero (p[i])) i++; if (i == n) return; copy (divisor, p[i]); storesign (divisor, POS); i++; while (i < n) { if (!zero (p[i])) { copy (Temp, p[i]); storesign (Temp, POS); gcd (divisor, Temp); } i++; } /* reduce by divisor */ for (i = 0; i < n; i++) if (!zero (p[i])) reduceint (p[i], divisor); } /* end of reducearray */ long myrandom (long num, long nrange) /* return a random number in range 0..nrange-1 */ { long i; i = (num * 401 + 673) % nrange; return (i); } void getfactorial (lrs_mp factorial, long k) /* compute k factorial in lrs_mp */ { lrs_mp temp; long i; itomp (ONE, factorial); for (i = 2; i <= k; i++) { itomp (i, temp); mulint (temp, factorial, factorial); } } /* end of getfactorial */ void stringcpy (char *s, char *t) /*copy t to s pointer version */ { while (((*s++) = (*t++)) != '\0'); } lrslib-043/readme0000755001553201777760000001722011607605134013307 0ustar avisnogroupREADME file for lrslib : reverse search vertex enumeration program/CH package ----------------------------------------------------------------------------- Documentation is currently being maintained at the URL: http://cgm.cs.mcgill.ca/~avis/lrs.html ----------------------------------------------------------------------------- 2010.5.7 incidence no longer resets printcobasis frequency to zero. If the printcobasis n option is used, the frequency will be n. Otherwise the default n=0 is used, and cobasis is printed only for lexmin bases. ----------------------------------------------------------------------------- 2010.4.26 bug when incidence and nonnegative options used together reported by Jochen Koenemannkfix was fixed. Bug in fourier reported by Laszlo David for input which is not full dimensional. I am temporarily removing fourier from distribution. ----------------------------------------------------------------------------- 2009.12.2 bug fix for redund caused problems in nash, reported by James Heather. Hopefully this new version solves both issues. ----------------------------------------------------------------------------- 2009.9.10 bug in redund reported by Alden Walker, when linearities are redundant, has been fixed. It is now under test, so please report any bugs! this bug also can cause printcobasis option to be incorrect for lrs under this condition. Problems still seem to arise in fourier from time to time, so please report any anomalities. ----------------------------------------------------------------------------- 2009.2.5 bug in fourier when using linearity option pointed out by Conor Meagher. Option disabled. 2nash driver uses two processors to run nash with input files in both orders. terminates when first process terminates. Thanks again to Conor for this. ----------------------------------------------------------------------------- 2007.6.6 printcobasis output line modified to give also in_det det= the determinant of the current basis, which is always integer. in_det= the determinant of the input rows corresponding to the current basis. lrs rescales input rows if they are rational or have a common divisor, so in these cases det and in_det are different. For V-representation, the volume will be the sum of the in_det of each basis, divided by the dimension (n-1)! ------------------------------------------------------------------- 2006.10.31 Modified code for restartpivots, to allow DB to do something. Estimator now provides estimate of running time=time*bases/tree nodes Triangulation printed if getvolume and verbose options used ----------------------------------------------------------------------------- 2006.10.11 Bug fix for nash, and inclusion of polytope version ----------------------------------------------------------------------------- available by using setupnash2 ----------------------------------------------------------------------------- 2006.3.1 incidence option now can be used compatibly with printcobasis n ----------------------------------------------------------------------------- 2006.2.14 Version 4.2b Bug fixed related to memory allocation for linearity reported by David Haws. If you use the linearity option, you should upgrade to this version. In the case of inconsistent linearities, the first inconsistent linearity is now reported before termination. ---------------------------------------------------------------------------- 2005.11.20 Version 4.2a Bug fixed relating to miscaled lp dual variables output when lponly set maxoutput n Option limits output lines to n: either rays+vertices, or facets ---------------------------------------------------------------------------- 2005.6.1 Version 4.2 with two new drivers: nash.c which computes all Nash equilibria of a two person non-cooperative game, and uses setupnash.c to create the input files. fourier.c which does Fourier elimination on an H-representation to project it to a lower dimensional space. Contributed by Tallman Nkgau. Other changes: lrs with the lponly option now provides dual variables for the optimum solution. Bug fix to mpdouble (reported by several users.) _____________________________________________________________________________ 2004.9.23 Version 4.2 updated with a patch from Bremner that has something to do with C++. 2003.10.24 Version 4.2 which appears here is a prerelease version, is not fully tested, and will be modified frequently. However you are more than welcome to try it - please report any bugs! Merci beaucoup. 2002.10.28 lrslib v.4.2 minor modifications to v.4.1 This is a pre-release for test purposes. Please report bugs! Nonnegative option was fixed to allow input where origin is not necessarily a vertex. A memory leak was fixed. A quiet mode is added - compile with LRS_QUIET set. ------------------------------------------------------------------------------ 2001.6.20 lrslib v.4.1 lpsolve like procedures to build input data added. Demo programs are: vedemo.c vertex enumeration chdemo.c facet enumeration lpdemo.c linear programs They can be build using: make demo Proper garbage collection implemented to clean up after each problem has been solved. See http://cgm.cs.mcgill.ca/~avis/C/lrslib/lrslib.html for documentation. ------------------------------------------------------------------------------- 2000.6.14 Various binaries are available in the directory binaries. Currently available: binaries/debian Debian Linux binaries/sun Sun Ultra Sparc binaries/win98 Windows 95/98 ------------------------------------------------------------------------------ 2000.6.14 lrslib v.4.0 which supercedes all previous versions of the programs lrs and redund. New Features: ------------ 1. Library version allows customization of the search function, access to the output as it is produced, and access to lrs from other programs. 2. Problems need no longer be in full dimension. This allows the input of equations, partial enumeration on facets, ridges etc. 3. Choice of arithmetic packages. Currently available are: lrsmp Extended precision arithmetic used in previous releases lrslong Fixed length long integer arithmetic. No overflow checking but 5-10 times faster. lrsgmp Requires preinstallation of GNU GMP package, available at http://www.swox.com/gmp/ The standard "make all" gives lrs/redund with lrsmp, and lrs1/redund1 with lrslong. 4. redund was completely rewritten and is faster than before. The previous version did not remove redundancy in the starting basis and should be discarded. Installation: ------------ 1. From website go to "Download" and retrieve the file lrslib-040.tar.gz 2. Unpack with: % gunzip lrslib-040.tar.gz % tar xvf lrslib-040.tar 3. Go to the new directory % cd lrslib-040 4. make binaries by typing % make all (most 32 bit unix machines) or % make all64 (64 bit integer machines such as DEC Alpha) If the make fails, it is usually due to timing and/or interrupt handling routines. In this case try: % make nosigs 5. If successful you should get binaries: lrs redund lrs1 redund1 6. Test the program lrs by typing: lrs cube.ine and you should get output resembling the file cube.ext 7. You will find additional test files in the directories: ine and ext 8. For GNU gmp library, edit the makefile to set the INCLUDE and LIB paths for the location of the gmp libarary, and type: %make gmp You should get binaries glrs and gredund lrslib-043/2nash.exe0000755001553201777760000006301511607605134013650 0ustar avisnogroupMZÿÿ¸@€º´ Í!¸LÍ!This program cannot be run in DOS mode. $PEL ^44L.^à 80@À£—€ `D.textˆ`P`.datad0@`À/4@@0À.bss8P€@À.idataD`@0À/14 p"@B/296€$B/45(&B/57| *B/71)°,BU‰åƒìƒäð¡P@…ÀtÌÙ}þ·Eþf%Àðf‰Eþ·Eþf ?f‰EþÙmþÇ$0@è³ÉÃU‰åƒìÇ$@0@较ì…ÀtgÇD$O0@‰$诃ì…ÀtPÇD$P@Ç$@@ÿС\2@…Àt3Ç$e0@èzƒì…Àt3ÇD$r0@‰$èkƒì…ÀtÇ$\2@ÿÐÉá0@…Àt¸ë¥t&¡0@…ÀuÛÉÃt&U‰åƒìÇ$@0@èƒì…Àt'ÇD$†0@‰$èƒì…ÀtÇ$@@ÿÐÉÃt&¡0@…ÀuçÉÃL$ƒäðÿqüU‰åì(‰]ô‹‰Mð‰uø‰}ü‹yèǃàðèHt$#Cýƒæðƒø‡&訃øÿ‰„§…À„÷èƒøÿ‰Ff„Œ…À„œEì‰$臃û‰…ìþÿÿ„H;„òÇD$ÇD$1@òþÿÿ‰$èZ‰$èZ‹…ìþÿÿ;F…Ý‹G‰D$‹GÇ$Ó0@‰D$è9Ç$(1@èU‹G‰D$‹GÇ$ð0@‰D$èÇD$ÇD$1@‰$èë‰$èëÇ$w1@èçèò‹@‰$èßÇD$ Ç$èÛÇ$è×Ç$ 0@èÓ‹Mð1À‹]ô‹uø‹}ü‰ì]aüËG‰D$‹GÇ$Ó0@‰D$è|‹G‰D$‹GÇ$ð0@‰D$èbÇD$ÇD$1@éÕþÿÿt&;…ï‹Gòþÿÿ‰D$‹GÇ$Ó0@‰D$è ‹G Ç$R1@‰D$è ‹G ÇD$ÇD$c1@‰$‰D$ èÞ‰$èÞ‹…ìþÿÿ;Fue‹G‰D$‹GÇ$Ó0@‰D$èÁÇ$(1@èÝ‹G Ç$R1@‰D$袋G ÇD$ÇD$c1@‰$‰D$ ès‰$èséƒþÿÿÇD$ÇD$1@‰$èN‰$èNé^þÿÿòþÿÿÇD$ÇD$1@‰$è#‰$è#é@ÿÿÿÇ$»0@èòÇ$è.ÇD$‹G‰D$ ‹Gòþÿÿ‰D$ÇD$À0@‰$èÒ‰$èÒÇ$è®ÇD$‹G‰D$ ‹Gë¾ÿ%\a@ÿ%`a@QL$=réƒ -=wë)Áƒ ‰à‰Ì‹‹@PÃU‰åƒì‹EÇD$‰$臃ìÿô`@ÿ%ð`@ÿ% a@ÿ%4a@ÿ%ø`@ÿ%Ta@ÿ%Da@ÿ%La@ÿ%8a@ÿ%a@ÿ%ì`@ÿ%(a@ÿ%a@ÿ%‹…\ýÿÿƒì‰D$‹…TýÿÿÇD$‰\$ ‰<$‰D$èƒìéÛþÿÿ‰t$Ç$è«ÇD$€‰ÆE ‰D$ ‹E‰D$…pÿÿÿ‰…Týÿÿ‰$臅öÆEXýÿÿ‰…\ýÿÿ„+ÿÿÿ]ð‰\$ ÇD$ÇD$ÇD$.2@Ç$ÿÿÿÿ范ì‰4$èA‰\$ ‰t$ÇD$Ç$ÿÿÿÿ‰D$èaƒì‰\$ ÇD$ÇD$ÇD$”1@Ç$ÿÿÿÿè6‹…Xýÿÿƒì‰D$‹…Týÿÿ‰\$ ÇD$Ç$ÿÿÿÿ‰D$èƒì‰4$è4éÇýÿÿ´&U‰åƒìH…ɉ]ô‰Ë‰uø‰Æ‰}ü‰UÐu ‹]ô‹uø‹}ü‰ì]ÃEÔÇD$‰D$‰4$èºƒì …À„£‹Eèƒø@toƒøtj‹Eà}ð‰|$ ÇD$@‰D$‹EÔ‰$艋EЃì‰\$‰D$‰4$è3‹Eèƒø@t…ƒøt€‹Eð‰|$ ‰D$‹Eà‰D$‹EÔ‰$èIƒìé[ÿÿÿ‹EЉ\$‰4$‰D$èí‹Eèƒø@„;ÿÿÿƒø}ðu³é.ÿÿÿ‰t$ÇD$Ç$œ1@èlûÿÿ¶¿U‰åƒì(¡`2@‰]ô‰uø‰}ü…Àt ‹]ô‹uø‹}ü‰ì]ú@@ê@@ƒúÇ`2@~Ùƒú ¸@@~'‹=@@…ÿ…‰‹5@@…öu‹@@…Ûu¸ @@‹…Éuj‹P…Òuc‹Pƒú…*X û@@s„‹s¶S†@‰Eà‹ƒú¸@‹ˆ@tiƒú „ȃú„—ÇEð‰T$Ç$2@è€úÿÿ=@@‰Ãƒ+ÿÿÿuì‹S¹‚@‹’@ƒÃ‰Uì‰òèÝýÿÿû@@rÕéøþÿÿ·†@f…Àyu ÿÿ)øȉEð‹Eà¹Uðè¨ýÿÿƒÃ û@@‚=ÿÿÿé¼þÿÿt&‹U඄Ày@ ÿÿÿ)øȉEð‹Eà¹UðèjýÿÿëÀ‹Eà)ùUð‰Mð¹èQýÿÿë§)øȉEðëŽ)øȉEðëÉT$Ç$Ð1@èùÿÿU‰å]ÃU‰å]ÃU‰å]ÃU‰å]Ãÿ%,a@ÿ%$a@ÿ%@a@ÿ%a@U‰åSƒì‹]ÇD$xP@‹E ‰$èóôÿÿ‰]‹]üÇE xP@ƒìÉéUÿ% a@U¸‰å] ÿ%a@ÿ%Pa@ÿ%Ha@ÿ%a@ÿ%0a@ÿ%a@ÿ%la@ÿ%pa@ÿ%ta@ÿ%ha@ÿ%€a@ÿ%|a@ÿ%xa@U‰å]éçîÿÿ´&U‰å]éwïÿÿÿÿÿÿP!@ÿÿÿÿ`!@¨@ @cyggcc_s-1.dll__register_frame_infocyggcj-9.dll_Jv_RegisterClasses__deregister_frame_infoUsage: 2nash A B [outfile]forknash %s %s > out%inash %s %s finished first output file: out /bin/mv -f out%i out/bin/rm -f out%iplayer numbers will be reversed in outputoutput file: %s /bin/mv -f out%i %sthe other process will be : VirtualQuery failed for %d bytes at address %p Unknown pseudo relocation protocol version %d. 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0ustar avisnogroup/*******************************************************/ /* nash is driver for computing all nash equilibria */ /* for two person games given by payoff matrices A,B */ /* Usage: nash game1 game2 [gameout] */ /* (use setupnash.c to create game1 game2 from A,B */ /* Options available to limit the search based on */ /* objective function value (see USERGUIDE.html */ /* June 1, 2005 */ /*******************************************************/ #include #include #include "lrslib.h" long nash2_main (int argc, char *argv[], lrs_dic *P1, lrs_dat *Q1, lrs_dic *P2orig, lrs_dat *Q2, long *numequilib, lrs_mp_vector output); /* lrs driver, argv[2]= 2nd input file for nash equilibria */ long lrs_getfirstbasis2 (lrs_dic ** D_p, lrs_dat * Q, lrs_dic *P2orig, lrs_mp_matrix * Lin, long no_output); long getabasis2 (lrs_dic * P, lrs_dat * Q, lrs_dic * P2orig, long order[]); long lrs_nashoutput (lrs_dat * Q, lrs_mp_vector output, long player); /* returns TRUE and prints output if not the origin */ int main (int argc, char *argv[]) { lrs_dic *P1,*P2; /* structure for holding current dictionary and indices */ lrs_dat *Q1,*Q2; /* structure for holding static problem data */ lrs_mp_vector output1; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp_vector output2; /* holds one line of output; ray,vertex,facet,linearity */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ lrs_dic *P2orig; /* we will save player 2's dictionary in getabasis */ long col; /* output column index for dictionary */ long startcol = 0; long prune = FALSE; /* if TRUE, getnextbasis will prune tree and backtrack */ long numequilib=0; /* number of nash equilibria found */ long oldnum=0; /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ /* they default to stdin and stdout, but may be overidden by command line parms. */ if(argc <= 2 ) { printf("Usage: nash input1 input2 [outputfile] \n"); return 1; } /*************************************************** Step 0: Do some global initialization that should only be done once, no matter how many lrs_dat records are allocated. db ***************************************************/ if ( !lrs_init ("\n*nash:")) return 1; printf(AUTHOR); /*********************************************************************************/ /* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */ /*********************************************************************************/ Q1 = lrs_alloc_dat ("LRS globals"); /* allocate and init structure for static problem data */ if (Q1 == NULL) return 1; Q1->nash=TRUE; if (!lrs_read_dat (Q1, argc, argv)) /* read first part of problem data to get dimensions */ return 1; /* and problem type: H- or V- input representation */ P1 = lrs_alloc_dic (Q1); /* allocate and initialize lrs_dic */ if (P1 == NULL) return 1; if (!lrs_read_dic (P1, Q1)) /* read remainder of input to setup P1 and Q1 */ return 1; output1 = lrs_alloc_mp_vector (Q1->n + Q1->m); /* output holds one line of output from dictionary */ fclose(lrs_ifp); /* allocate and init structure for player 2's problem data */ printf ("\n*Second input taken from file %s\n", argv[2]); Q2 = lrs_alloc_dat ("LRS globals"); if (Q2 == NULL) return 1; Q2->nash=TRUE; if (!lrs_read_dat (Q2, 2, argv)) /* read first part of problem data to get dimensions */ return 1; /* and problem type: H- or V- input representation */ if (Q2->nlinearity > 0) free(Q2->linearity); /* we will start again */ Q2->linearity = CALLOC ((Q2->m + 2), sizeof (long)); P2 = lrs_alloc_dic (Q2); /* allocate and initialize lrs_dic */ if (P2 == NULL) return 1; if (!lrs_read_dic (P2, Q2)) /* read remainder of input to setup P2 and Q2 */ return 1; output2 = lrs_alloc_mp_vector (Q1->n + Q1->m); /* output holds one line of output from dictionary */ P2orig = lrs_getdic(Q2); /* allocate and initialize lrs_dic */ if (P2orig == NULL) return 1; copy_dict(Q2,P2orig,P2); fprintf (lrs_ofp, "\n***** %ld %ld rational", Q1->n, Q2->n); /*********************************************************************************/ /* Step 2: Find a starting cobasis from default of specified order */ /* P1 is created to hold active dictionary data and may be cached */ /* Lin is created if necessary to hold linearity space */ /* Print linearity space if any, and retrieve output from first dict. */ /*********************************************************************************/ if (!lrs_getfirstbasis (&P1, Q1, &Lin, TRUE)) return 1; if (Q1->dualdeg) { printf("\n*Warning! Dual degenerate, ouput may be incomplete"); printf("\n*Recommendation: Add dualperturb option before maximize in first input file\n"); } if (Q1->unbounded) { printf("\n*Warning! Unbounded starting dictionary for p1, output may be incomplete"); printf("\n*Recommendation: Change/remove maximize option, or include bounds \n"); } /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ if (Q1->homogeneous && Q1->hull) startcol++; /* col zero not treated as redundant */ for (col = startcol; col < Q1->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q1, Lin[col]); /* Array Lin[][] holds the coeffs. */ /*********************************************************************************/ /* Step 3: Terminate if lponly option set, otherwise initiate a reverse */ /* search from the starting dictionary. Get output for each new dict. */ /*********************************************************************************/ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ /* prune is TRUE if tree should be pruned at current node */ do { prune=lrs_checkbound(P1,Q1); if (!prune && lrs_getsolution (P1, Q1, output1, col)) { oldnum=numequilib; nash2_main(argc,argv,P1,Q1,P2orig,Q2,&numequilib,output2); if (numequilib > oldnum || Q1->verbose) { if(Q1->verbose) prat(" \np2's obj value: ",P1->objnum,P1->objden); lrs_nashoutput (Q1, output1, 1L); fprintf (lrs_ofp, "\n"); } } } while (lrs_getnextbasis (&P1, Q1, prune)); fprintf(lrs_ofp,"\n*Number of equilibria found: %ld",numequilib); fprintf (lrs_ofp,"\n*Player 1: vertices=%ld bases=%ld pivots=%ld", Q1->count[1], Q1->count[2],Q1->count[3]); fprintf (lrs_ofp,"\n*Player 2: vertices=%ld bases=%ld pivots=%ld", Q2->count[1], Q2->count[2],Q2->count[3]); lrs_clear_mp_vector(output1, Q1->m + Q1->n); lrs_clear_mp_vector(output2, Q1->m + Q1->n); lrs_free_dic (P1,Q1); /* deallocate lrs_dic */ lrs_free_dat (Q1); /* deallocate lrs_dat */ /* 2006.10.10 not sure what is going on with three lines below - sometimes crashes */ /* Q2->Qhead = P2; */ /* reset this or you crash free_dic */ /* lrs_free_dic (P2,Q2); */ /* deallocate lrs_dic */ /* lrs_free_dat (Q2); */ /* deallocate lrs_dat */ lrs_close ("nash:"); return 0; } /*********************************************/ /* end of nash driver */ /*********************************************/ /**********************************************************/ /* nash2_main is a second driver used in computing nash */ /* equilibria on a second polytope interleaved with first */ /**********************************************************/ long nash2_main (int argc, char *argv[], lrs_dic *P1, lrs_dat *Q1, lrs_dic *P2orig, lrs_dat *Q2, long *numequilib, lrs_mp_vector output) { lrs_dic *P2; /* This can get resized, cached etc. Loaded from P2orig */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ long col; /* output column index for dictionary */ long startcol = 0; long prune = FALSE; /* if TRUE, getnextbasis will prune tree and backtrack */ long nlinearity; long *linearity; static long firstwarning=TRUE; /* FALSE if dual deg warning for Q2 already given */ static long firstunbounded=TRUE; /* FALSE if dual deg warning for Q2 already given */ long i,j; /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ /* they default to stdin and stdout, but may be overidden by command line parms. */ /*********************************************************************************/ /* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */ /*********************************************************************************/ P2=lrs_getdic(Q2); copy_dict(Q2,P2,P2orig); /* Here we take the linearities generated by the current vertex of player 1*/ /* and append them to the linearity in player 2's input matrix */ /* next is the key magic linking player 1 and 2 */ /* be careful if you mess with this! */ linearity=Q2->linearity; nlinearity=0; for(i=Q1->lastdv+1;i <= P1->m; i++) { if (!zero(P1->A[P1->Row[i]][0])) { j = Q1->inequality[P1->B[i]-Q1->lastdv]; if (Q1->nlinearity ==0 || j < Q1->linearity[0]) linearity[nlinearity++]= j; } } /* add back in the linearity for probs summing to one */ if (Q1->nlinearity > 0) linearity[nlinearity++]= Q1->linearity[0]; /*sort linearities */ for (i = 1; i < nlinearity; i++) reorder (linearity, nlinearity); if(Q2->verbose) { fprintf(lrs_ofp,"\np2: linearities %ld",nlinearity); for (i=0;i < nlinearity; i++) fprintf(lrs_ofp," %ld",linearity[i]); } Q2->nlinearity = nlinearity; Q2->polytope = FALSE; /*********************************************************************************/ /* Step 2: Find a starting cobasis from default of specified order */ /* P2 is created to hold active dictionary data and may be cached */ /* Lin is created if necessary to hold linearity space */ /* Print linearity space if any, and retrieve output from first dict. */ /*********************************************************************************/ if (!lrs_getfirstbasis2 (&P2, Q2, P2orig, &Lin, TRUE)) goto sayonara; if (firstwarning && Q2->dualdeg) { firstwarning=FALSE; printf("\n*Warning! Dual degenerate, ouput may be incomplete"); printf("\n*Recommendation: Add dualperturb option before maximize in second input file\n"); } if (firstunbounded && Q2->unbounded) { firstunbounded=FALSE; printf("\n*Warning! Unbounded starting dictionary for p2, output may be incomplete"); printf("\n*Recommendation: Change/remove maximize option, or include bounds \n"); } /* Pivot to a starting dictionary */ /* There may have been column redundancy */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ if (Q2->homogeneous && Q2->hull) startcol++; /* col zero not treated as redundant */ /* for (col = startcol; col < Q2->nredundcol; col++)*/ /* print linearity space */ /*lrs_printoutput (Q2, Lin[col]);*/ /* Array Lin[][] holds the coeffs. */ /*********************************************************************************/ /* Step 3: Terminate if lponly option set, otherwise initiate a reverse */ /* search from the starting dictionary. Get output for each new dict. */ /*********************************************************************************/ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ /* prune is TRUE if tree should be pruned at current node */ do { prune=lrs_checkbound(P2,Q2); col=0; if (!prune && lrs_getsolution (P2, Q2, output, col)) { if (Q2->verbose) prat(" \np1's obj value: ",P2->objnum,P2->objden); if (lrs_nashoutput (Q2, output, 2L)) (*numequilib)++; } } while (lrs_getnextbasis (&P2, Q2, prune)); sayonara: lrs_free_dic(P2,Q2); return 0; } /*********************************************/ /* end of nash2_main */ /*********************************************/ /* In lrs_getfirstbasis and lrs_getnextbasis we use D instead of P */ /* since the dictionary P may change, ie. &P in calling routine */ #define D (*D_p) long lrs_getfirstbasis2 (lrs_dic ** D_p, lrs_dat * Q, lrs_dic * P2orig, lrs_mp_matrix * Lin, long no_output) /* gets first basis, FALSE if none */ /* P may get changed if lin. space Lin found */ /* no_output is TRUE supresses output headers */ { long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A; long *B, *C, *Row, *Col; long *inequality; long *linearity; long hull = Q->hull; long m, d, lastdv, nlinearity, nredundcol; static long ocount=0; m = D->m; d = D->d; lastdv = Q->lastdv; nredundcol = 0L; /* will be set after getabasis */ nlinearity = Q->nlinearity; /* may be reset if new linearity read */ linearity = Q->linearity; A = D->A; B = D->B; C = D->C; Row = D->Row; Col = D->Col; inequality = Q->inequality; /* default is to look for starting cobasis using linearies first, then */ /* filling in from last rows of input as necessary */ /* linearity array is assumed sorted here */ /* note if restart/given start inequality indices already in place */ /* from nlinearity..d-1 */ for (i = 0; i < nlinearity; i++) /* put linearities first in the order */ inequality[i] = linearity[i]; k = 0; /* index for linearity array */ if (Q->givenstart) k = d; else k = nlinearity; for (i = m; i >= 1; i--) { j = 0; while (j < k && inequality[j] != i) j++; /* see if i is in inequality */ if (j == k) inequality[k++] = i; } if (Q->debug) { fprintf (lrs_ofp, "\n*Starting cobasis uses input row order"); for (i = 0; i < m; i++) fprintf (lrs_ofp, " %ld", inequality[i]); } if (!Q->maximize && !Q->minimize) for (j = 0; j <= d; j++) itomp (ZERO, A[0][j]); /* Now we pivot to standard form, and then find a primal feasible basis */ /* Note these steps MUST be done, even if restarting, in order to get */ /* the same index/inequality correspondance we had for the original prob. */ /* The inequality array is used to give the insertion order */ /* and is defaulted to the last d rows when givenstart=FALSE */ if (!getabasis2 (D, Q,P2orig, inequality)) return FALSE; if(Q->debug) { fprintf(lrs_ofp,"\nafter getabasis2"); printA(D, Q); } nredundcol = Q->nredundcol; lastdv = Q->lastdv; d = D->d; /********************************************************************/ /* now we start printing the output file unless no output requested */ /********************************************************************/ if (!no_output || Q->debug) { fprintf (lrs_ofp, "\nV-representation"); /* Print linearity space */ /* Don't print linearity if first column zero in hull computation */ k = 0; if (nredundcol > k) { fprintf (lrs_ofp, "\nlinearity %ld ", nredundcol - k); /*adjust nredundcol for homog. */ for (i = 1; i <= nredundcol - k; i++) fprintf (lrs_ofp, " %ld", i); } /* end print of linearity space */ fprintf (lrs_ofp, "\nbegin"); fprintf (lrs_ofp, "\n***** %ld rational", Q->n); } /* end of if !no_output ....... */ /* Reset up the inequality array to remember which index is which input inequality */ /* inequality[B[i]-lastdv] is row number of the inequality with index B[i] */ /* inequality[C[i]-lastdv] is row number of the inequality with index C[i] */ for (i = 1; i <= m; i++) inequality[i] = i; if (nlinearity > 0) /* some cobasic indices will be removed */ { for (i = 0; i < nlinearity; i++) /* remove input linearity indices */ inequality[linearity[i]] = 0; k = 1; /* counter for linearities */ for (i = 1; i <= m - nlinearity; i++) { while (k <= m && inequality[k] == 0) k++; /* skip zeroes in corr. to linearity */ inequality[i] = inequality[k++]; } } /* end if linearity */ if (Q->debug) { fprintf (lrs_ofp, "\ninequality array initialization:"); for (i = 1; i <= m - nlinearity; i++) fprintf (lrs_ofp, " %ld", inequality[i]); } if (nredundcol > 0) { *Lin = lrs_alloc_mp_matrix (nredundcol, Q->n); for (i = 0; i < nredundcol; i++) { if (!(Q->homogeneous && Q->hull && i == 0)) /* skip redund col 1 for homog. hull */ { lrs_getray (D, Q, Col[0], D->C[0] + i - hull, (*Lin)[i]); /* adjust index for deletions */ } if (!removecobasicindex (D, Q, 0L)) return FALSE; } } /* end if nredundcol > 0 */ if (Q->verbose) { fprintf (lrs_ofp, "\nNumber of pivots for starting dictionary: %ld",Q->count[3]); ocount=Q->count[3]; } /* Do dual pivots to get primal feasibility */ if (!primalfeasible (D, Q)) { if ( Q->verbose ) { fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]); fprintf (lrs_ofp, " - No feasible solution"); ocount=Q->count[3]; } return FALSE; } if (Q->verbose) { fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]); ocount=Q->count[3]; } /* Now solve LP if objective function was given */ if (Q->maximize || Q->minimize) { Q->unbounded = !lrs_solvelp (D, Q, Q->maximize); /* check to see if objective is dual degenerate */ j = 1; while (j <= d && !zero (A[0][j])) j++; if (j <= d) Q->dualdeg = TRUE; } else /* re-initialize cost row to -det */ { for (j = 1; j <= d; j++) { copy (A[0][j], D->det); storesign (A[0][j], NEG); } itomp (ZERO, A[0][0]); /* zero optimum objective value */ } /* reindex basis to 0..m if necessary */ /* we use the fact that cobases are sorted by index value */ if (Q->debug) printA (D, Q); while (C[0] <= m) { i = C[0]; j = inequality[B[i] - lastdv]; inequality[B[i] - lastdv] = inequality[C[0] - lastdv]; inequality[C[0] - lastdv] = j; C[0] = B[i]; B[i] = i; reorder1 (C, Col, ZERO, d); } if (Q->debug) { fprintf (lrs_ofp, "\n*Inequality numbers for indices %ld .. %ld : ", lastdv + 1, m + d); for (i = 1; i <= m - nlinearity; i++) fprintf (lrs_ofp, " %ld ", inequality[i]); printA (D, Q); } if (Q->restart) { if (Q->debug) fprintf (lrs_ofp, "\nPivoting to restart co-basis"); if (!restartpivots (D, Q)) return FALSE; D->lexflag = lexmin (D, Q, ZERO); /* see if lexmin basis */ if (Q->debug) printA (D, Q); } /* Check to see if necessary to resize */ if (Q->inputd > D->d) *D_p = resize (D, Q); return TRUE; } /********* end of lrs_getfirstbasis ***************/ long getabasis2 (lrs_dic * P, lrs_dat * Q, lrs_dic * P2orig, long order[]) /* Pivot Ax<=b to standard form */ /*Try to find a starting basis by pivoting in the variables x[1]..x[d] */ /*If there are any input linearities, these appear first in order[] */ /* Steps: (a) Try to pivot out basic variables using order */ /* Stop if some linearity cannot be made to leave basis */ /* (b) Permanently remove the cobasic indices of linearities */ /* (c) If some decision variable cobasic, it is a linearity, */ /* and will be removed. */ { long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *B = P->B; long *C = P->C; long *Row = P->Row; long *Col = P->Col; long *linearity = Q->linearity; long *redundcol = Q->redundcol; long m, d, nlinearity; long nredundcol = 0L; /* will be calculated here */ static long firsttime=TRUE; static long *linindex; m = P->m; d = P->d; nlinearity = Q->nlinearity; if(firsttime) { firsttime = FALSE; linindex = calloc ((m + d + 2), sizeof (long)); } else /* after first time we update the change in linearities from the last time, saving many pivots */ { for(i=1;i<=m+d;i++) linindex[i]=FALSE; if(Q->debug) fprintf(lrs_ofp,"\nlindex ="); for(i=0;idebug) fprintf(lrs_ofp," %ld",d+linearity[i]); } for(i=1;i<=m;i++) { if(linindex[B[i]]) /* pivot out unwanted linearities */ { k=0; while(k B[j]) /* decrease i or we may skip a linearity */ i--; pivot (P, Q, j, k); update (P, Q, &j, &k); } else { /* this is not necessarily an error, eg. two identical rows/cols in payoff matrix */ if(! zero(A[Row[i]][0])) /* error condition */ { if(Q->debug || Q->verbose) { fprintf(lrs_ofp,"\n*Infeasible linearity i=%ld B[i]=%ld",i,B[i]); if (Q->debug) printA(P,Q); } return(FALSE); } if(Q->debug || Q->verbose) { fprintf(lrs_ofp,"\n*Couldn't remove linearity i=%ld B[i]=%ld",i,B[i]); } } } /* if linindex */ } /* for i ..*/ goto hotstart; } /* standard lrs processing is done on only the first call to getabasis2 */ if (Q->debug) { fprintf (lrs_ofp, "\ngetabasis from inequalities given in order"); for (i = 0; i < m; i++) fprintf (lrs_ofp, " %ld", order[i]); } for (j = 0; j < m; j++) { i = 0; while (i <= m && B[i] != d + order[j]) i++; /* find leaving basis index i */ if (j < nlinearity && i > m) /* cannot pivot linearity to cobasis */ { if (Q->debug) printA (P, Q); #ifndef LRS_QUIET fprintf (lrs_ofp, "\nCannot find linearity in the basis"); #endif return FALSE; } if (i <= m) { /* try to do a pivot */ k = 0; while (C[k] <= d && zero (A[Row[i]][Col[k]])) k++; if (C[k] <= d) { pivot (P, Q, i, k); update (P, Q, &i, &k); } else if (j < nlinearity) { /* cannot pivot linearity to cobasis */ if (zero (A[Row[i]][0])) { #ifndef LRS_QUIET fprintf (lrs_ofp, "\n*Input linearity in row %ld is redundant--skipped", order[j]); #endif linearity[j] = 0; } else { if (Q->debug) printA (P, Q); if (Q->verbose) fprintf (lrs_ofp, "\nInconsistent linearities"); return FALSE; } } /* end if j < nlinearity */ } /* end of if i <= m .... */ } /* end of for */ /* update linearity array to get rid of redundancies */ i = 0; k = 0; /* counters for linearities */ while (k < nlinearity) { while (k < nlinearity && linearity[k] == 0) k++; if (k < nlinearity) linearity[i++] = linearity[k++]; } nlinearity = i; /* column dependencies now can be recorded */ /* redundcol contains input column number 0..n-1 where redundancy is */ k = 0; while (k < d && C[k] <= d) { if (C[k] <= d) /* decision variable still in cobasis */ redundcol[nredundcol++] = C[k] - Q->hull; /* adjust for hull indices */ k++; } /* now we know how many decision variables remain in problem */ Q->nredundcol = nredundcol; Q->lastdv = d - nredundcol; /* if not first time we continue from here after loading dictionary */ hotstart: if (Q->debug) { fprintf (lrs_ofp, "\nend of first phase of getabasis2: "); fprintf (lrs_ofp, "lastdv=%ld nredundcol=%ld", Q->lastdv, Q->nredundcol); fprintf (lrs_ofp, "\nredundant cobases:"); for (i = 0; i < nredundcol; i++) fprintf (lrs_ofp, " %ld", redundcol[i]); printA (P, Q); } /* here we save dictionary for use next time, *before* we resize */ copy_dict(Q,P2orig,P); /* Remove linearities from cobasis for rest of computation */ /* This is done in order so indexing is not screwed up */ for (i = 0; i < nlinearity; i++) { /* find cobasic index */ k = 0; while (k < d && C[k] != linearity[i] + d) k++; if (k >= d) { if(Q->debug || Q->verbose) { fprintf (lrs_ofp, "\nCould not remove cobasic index"); } /* not neccesarily an error as eg., could be repeated row/col in payoff */ } else { removecobasicindex (P, Q, k); d = P->d; } } if (Q->debug && nlinearity > 0) printA (P, Q); /* set index value for first slack variable */ /* Check feasability */ if (Q->givenstart) { i = Q->lastdv + 1; while (i <= m && !negative (A[Row[i]][0])) i++; if (i <= m) fprintf (lrs_ofp, "\n*Infeasible startingcobasis - will be modified"); } return TRUE; } /* end of getabasis2 */ long lrs_nashoutput (lrs_dat * Q, lrs_mp_vector output, long player) { long i; long origin=TRUE; /* do not print the origin for either player */ for (i = 1; i < Q->n; i++) if(!zero(output[i])) origin=FALSE; if (origin) return FALSE; fprintf (lrs_ofp, "\n%ld ",player); for (i = 1; i < Q->n; i++) prat ("", output[i], output[0]); fflush(lrs_ofp); return TRUE; } /* end lrs_nashoutput */ lrslib-043/game0000755001553201777760000000003611607605134012760 0ustar avisnogroup3 2 0 6 2 5 3 3 1 0 0 2 4 3 lrslib-043/2gnash.c0000755001553201777760000000500211607605134013450 0ustar avisnogroup// 2gnash.c v1.0 Jan 15, 2009 // Hack of nlrs.c by Conor Meagher to run lrs simultaneously on n processors for n input files // runs gnash on input files A B in both orders simultaneously, terminating when first proc finishes // output goes in third argument if any, else in file: out #include #include #include #include int main(int argc, char *argv[]) { pid_t cpid[argc - 1], w; char buffer [250]; int status,l,j; if (argc < 3 || argc > 4) { printf("Usage: 2gnash A B [outfile]\n"); return(0); } for(l = 1; l < 3; l++) { cpid[l -1] = fork(); if (cpid[l -1] == -1) { perror("fork"); exit(EXIT_FAILURE); } if(cpid[l-1] == 0) { //forked threads // n= sprintf(buffer, "lrs %s > out%i", argv[l], l); if(l==1) { int n= sprintf(buffer, "gnash %s %s > out%i", argv[1], argv[2], l); } else { int n= sprintf(buffer, "gnash %s %s > out%i", argv[2], argv[1], l); } int i=system(buffer); _exit(0); } } // main thread w = wait(&status); for(j = 1; j < 3; j++) { if(w == cpid[j-1]) { // this child finished first if(j==1) printf("gnash %s %s finished first\n", argv[1], argv[2]); else { printf("gnash %s %s finished first\n", argv[2], argv[1]); printf("player numbers will be reversed in output\n"); } if(argc == 4) { printf("output file: %s\n", argv[3]); int n = sprintf(buffer, "/bin/mv -f out%i %s", j, argv[3]); } else { printf("output file: out\n", argv[2], argv[1]); int n = sprintf(buffer, "/bin/mv -f out%i out", j); } int i = system(buffer); } else { // printf("terminating lrs of file %s\n", argv[j]); int n = sprintf(buffer, "/bin/rm -f out%i", j); int i = system(buffer); } } printf("the other process will be "); /*...will be killed */ fflush(stdout); kill(0,9); exit(EXIT_SUCCESS); } lrslib-043/chdemo.c0000755001553201777760000000736611607605134013544 0ustar avisnogroup/* chdemo.c lrslib vertex enumeration demo */ /* last modified: May 29, 2001 */ /* Copyright: David Avis 2001, avis@cs.mcgill.ca */ /* Demo driver for convex hull computation using lrs */ /* This program computes facets of cyclic polytopes */ #include #include #include "lrslib.h" #define MAXCOL 1000 /* maximum number of colums */ void makecyclic (lrs_dic *P, lrs_dat *Q); int main (int argc, char *argv[]) { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_vector output; /* one line of output:ray,vertex,facet,linearity */ lrs_mp_matrix Lin; /* holds input linearities if any are found */ long i; long col; /* output column index for dictionary */ /* Global initialization - done once */ if ( !lrs_init ("\n*chdemo:")) return 1; /* compute the convex hull of a set of cyclic polytopes */ /* given by V-representations, dimension 2,...,7 */ for(i=1;i<=6;i++) { /* allocate and init structure for static problem data */ Q = lrs_alloc_dat ("LRS globals"); if (Q == NULL) return 1; /* now flags in lrs_dat can be set */ Q->m=i+3; /* number of input rows = number of vertices */ Q->n=i+2; /* number of input columns (dimension + 1 ) */ Q->hull = TRUE; /* convex hull problem: facet enumeration */ Q->polytope= TRUE; /* input is a polytope */ Q->getvolume= TRUE; /* compute the volume */ output = lrs_alloc_mp_vector (Q->n); P = lrs_alloc_dic (Q); /* allocate and initialize lrs_dic */ if (P == NULL) return 1; /* Build polyhedron: constraints and objective */ printf("\n\n*cyclic polytope: %ld vertices in R^%ld",Q->m,Q->n-1); makecyclic(P,Q); /* code from here is borrowed from lrs_main */ /* Pivot to a starting dictionary */ if (!lrs_getfirstbasis (&P, Q, &Lin, FALSE)) return 1; /* There may have been column redundancy */ /* (although not for this example of cyclic polytopes) */ /* If so the linearity space is obtained and redundant */ /* columns are removed. User can access linearity space */ /* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */ for (col = 0L; col < Q->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q, Lin[col]); /* Array Lin[][] holds the coeffs. */ /* We initiate reverse search from this dictionary */ /* getting new dictionaries until the search is complete */ /* User can access each output line from output which is */ /* vertex/ray/facet from the lrs_mp_vector output */ do { for (col = 0; col <= P->d; col++) if (lrs_getsolution (P, Q, output, col)) lrs_printoutput (Q, output); } while (lrs_getnextbasis (&P, Q, FALSE)); lrs_printtotals (P, Q); /* print final totals */ /* free space : do not change order of next 3 lines! */ lrs_clear_mp_vector (output, Q->n); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ } /* end of loop for i=3 ... */ lrs_close ("chdemo:"); printf("\n"); return 0; } /* end of main */ void makecyclic (lrs_dic *P, lrs_dat *Q) /* generate vertices of a cyclic polytope */ /* (t, t^2, ..., t^n-1 ), t=1..m */ { long num[MAXCOL]; long den[MAXCOL]; long row, j, t; long m=Q->m; long n=Q->n; for (row=1;row<=m;row++) { t=1; for(j=0;j #include #include "lrslib.h" #define MAXLINE 1000 /* Usage: setupnash2 game game1.ine game2.ine */ /* Reads input file game containing */ /* m n */ /* A matrix (m by n rationals ) */ /* B matrix (m by n rationals ) */ /* Outputs: two files game1.ine game2.ine */ /* that are used by nash */ /* This program builds polytope form: */ /* Bx<=1, x>=0; Ay <=1, y>=0 */ /* MATRICES SHOULD HAVE POSITIVE ENTRIES */ int main (int argc, char *argv[]) { long m,n,i,j; long Anum[100][100], Bnum[100][100]; long Aden[100][100], Bden[100][100]; if ( argc < 3 ) { printf ("\nUsage: setupnash2 infile outfile1 outfile2\n"); return(FALSE); } if ((lrs_ifp = fopen (argv[1], "r")) == NULL) { printf ("\nBad input file name\n"); return (FALSE); } else printf ("\n*Input taken from file %s", argv[1]); if(fscanf(lrs_ifp,"%ld %ld",&m,&n)==EOF) { printf("\nInvalid m,n"); return(FALSE); } if( m > 1000 || n > 1000) { printf ("\nm=%ld n=%ld",m,n); printf ("\nBoth m and n must be at most 1000\n"); return(FALSE); } /* process input file */ /* read A matrix */ for (i=0;i #include #include "lrslib.h" #define MAXCOL 1000 /* maximum number of variables. */ /**************************************************************************/ void fel_abort(char str[]) { printf("%s\n", str ); exit(1); } /*************************************************************************/ /*******************************************************************/ /* Function to read all lines above the "matrix" in the input file.*/ /* Adapted from Prof. Avis' function in lrslib.c. */ /*******************************************************************/ long readHfile(lrs_dat *Q) { char line[100]; char ch; long firstline = TRUE; if(fscanf(lrs_ifp, "%s", line)==EOF) exit(1); while (strcmp(line, "begin") != 0) { if (strncmp(line, "*", 1) == 0) { ch = line[0]; while ((ch != EOF) && (ch != '\n')) ch = fgetc(lrs_ifp); } else if (strcmp(line, "H-representation") == 0) { Q->hull = FALSE; } else if (strcmp(line, "linearity")==0) { /* disabled 2009.2.5 due to bug in linearity handling */ /* if (!readlinearity(Q)) */ fprintf(lrs_ofp, "\nfourier does not handle linearity option:\n replace each linearity by two inequalities\n"); return (FALSE); } else if (firstline) { stringcpy(Q->fname, line); fprintf(lrs_ofp, "%s\n", Q->fname); firstline = FALSE; } if (fscanf(lrs_ifp, "%s", line) == EOF) { fprintf(lrs_ofp, "No begin line\n"); return (FALSE); } } /* end of while */ if (fscanf(lrs_ifp, "%ld %ld %s", &Q->m, &Q->n, line) == EOF) { fprintf(lrs_ofp, "No data in file\n"); return (FALSE); } if (!((strcmp(line, "rational") == 0) || (strcmp(line, "integer") == 0))) { fprintf(lrs_ofp, "Data type must be rational\n"); return (FALSE); } if (Q->m == 0) { fprintf(lrs_ofp, "No input given\n"); return (FALSE); } return (TRUE); } /***************************************************************/ /* Function to read in the dictionary from input file. */ /***************************************************************/ long readHmat(lrs_dic *P, lrs_dat *Q, long *project) { char line[100]; char ch; long p, i; if (!lrs_read_dic(P, Q)) { fprintf(lrs_ofp, "Data matrix not properly formatted\n"); return (FALSE); } /* "lrs_read_dic" doesn't handle option "project", so improvise */ if (fseek(lrs_ifp, 0L, 0) <= 0) /* rewind file. */ { while (fscanf(lrs_ifp, "%s", line) != EOF) { if (strncmp(line, "*", 1) == 0) { ch = line[0]; while ((ch != EOF) && (ch != '\n')) ch = fgetc(lrs_ifp); } if (strcmp(line, "project") == 0) { if(fscanf(lrs_ifp, "%ld", &p)==EOF) { fprintf(lrs_ofp, "No variables to project.\n"); return (FALSE); } project[0] = p; if (p <= 0) { fprintf(lrs_ofp, "No variables to project.\n"); return (FALSE); } for(i=1; i<=project[0]; i++) { if (fscanf(lrs_ifp, "%ld", &p) == EOF) { fprintf(lrs_ofp, "Missing variables in 'project' line.\n"); return (FALSE); } project[i] = p; } } } } else { fprintf(lrs_ofp, "Can't process input file\n"); return (FALSE); } return (TRUE); } /*******************************************************************************/ void linear_dep(lrs_dic *P, lrs_dat *Q, long *Dep) { long d; long nlinearity; lrs_mp_matrix A; long i, j, k, row, col,m; d = P->d; nlinearity = Q->nlinearity; A = lrs_alloc_mp_matrix(nlinearity+1, d+2); for(i=0;iA[i][j]); itomp(ZERO, A[i][d+1]); } for(col=1;col<=d;col++) { row = -1; for(i=1;i<=nlinearity;i++) if ((zero(A[i][d+1]))&& !zero(A[i][col])) { row = i; break; } if (row > 0) for(k=1;k<=nlinearity;k++) { if ((zero(A[k][d+1]))&&(!zero(A[k][col])) && (k!=row)) { printf("row=%ld k = %ld\n", row, k); if (sign(A[k][col])*sign(A[row][col]) < 0) { copy(A[0][0], A[k][col]); copy(A[0][1], A[row][col]); storesign(A[0][0], POS); storesign(A[0][1], POS); for(i=0;i<=d;i++) { mulint(A[0][0], A[row][i], A[0][2]); mulint(A[0][1], A[k][i], A[0][3]); addint(A[0][2], A[0][3], A[k][i]); } } else { copy(A[0][0], A[k][col]); copy(A[0][1], A[row][col]); storesign(A[0][0], NEG); storesign(A[0][1], POS); for(i=0;i<=d;i++) { mulint(A[0][0], A[row][i], A[0][2]); mulint(A[0][1], A[k][i], A[0][3]); addint(A[0][2], A[0][3], A[k][i]); } } itomp(ONE, A[row][d+1]); for(i=1;i<=nlinearity; i++) { for(m=0;m<=d;m++) pmp("", A[i][m]); fprintf(lrs_ofp, "\n"); } fprintf(lrs_ofp, "\n"); } } } for(row=1,i=0;row<=nlinearity;row++) { for(k=0,i=0;k<=d;k++) if(zero(A[row][k])) i++; if (i==d+1) Dep[row] =1; } } /********************************************************************************/ /* groups[i] = +1 if A[i][col] > 0, groups[i] = -1 if A[i][col] < 0, */ /* groups[i] = 0 if A[i][col] = 0, groups[m+1] = # of rows with <0 entry */ /* in column 'col', and groups[m+2] = # of rows with > 0 entry in column 'col' */ /********************************************************************************/ void lrs_compute_groups(lrs_dat *Q, lrs_dic *P, long col, long *groups) { long i, row; long m; m = Q->m; for(i=0;i<= m+2; i++) { groups[i] = 0; } for(row = 1; row <= Q->m; row++) { if (sign(P->A[row][col]) < 0) { groups[row] = -1; groups[m+1]++; } else if (zero(P->A[row][col])) { groups[0]++; } else { groups[row] = 1; groups[m+2]++; } } } /*******************************************************************/ /* Function to copy matrix A from dictionary P to dictionary P1. */ /* The column (variable) with index 'skip' is left out. */ /* Set skip to '-1' if no column is to be left out. */ /* Adapted from Prof. Avis' function in lrslib.c. */ /*******************************************************************/ void copydicA(lrs_dic *P1, lrs_dic *P, long skip_row, long skip_col) { long i, j; long d, m_A; d = P->d; /* dimension of space of variables */ m_A = P->m_A; if (skip_col > 0) { if (skip_row > 0) { for (i = 1; i < skip_row; i++) { for(j = 0; j < skip_col; j++) copy (P1->A[i][j], P->A[i][j]); for(j = skip_col+1; j <= d; j++) copy (P1->A[i][j-1], P->A[i][j]); } for (i = skip_row+1; i <= m_A; i++) { for(j = 0; j < skip_col; j++) copy (P1->A[i-1][j], P->A[i][j]); for(j = skip_col+1; j <= d; j++) copy (P1->A[i-1][j-1], P->A[i][j]); } } else { for (i = 1; i <= m_A; i++) { for(j = 0; j < skip_col; j++) copy (P1->A[i-1][j], P->A[i][j]); for(j = skip_col+1; j <= d; j++) copy (P1->A[i-1][j-1], P->A[i][j]); } } } else { if (skip_row > 0) { for (i = 1; i < skip_row; i++) for(j = 0; j <= d; j++) copy (P1->A[i][j], P->A[i][j]); for (i = skip_row+1; i <= m_A; i++) for(j = 0; j <= d; j++) copy (P1->A[i-1][j], P->A[i][j]); } else { for (i = 1; i <= m_A; i++) for(j = 0; j <= d; j++) copy (P1->A[i][j], P->A[i][j]); } } } /***************************************************************/ /* copy linearity from iQ to Q */ /***************************************************************/ void copy_linearity(lrs_dat *Q, lrs_dat *iQ) { long nlinearity; long i; nlinearity = iQ->nlinearity; if (nlinearity > 0) { Q->linearity = CALLOC ((nlinearity +1), sizeof (long)); for(i=0; i < nlinearity; i++) Q->linearity[i] = iQ->linearity[i]; Q->nlinearity = nlinearity; Q->polytope = FALSE; } } /***************************************************************/ void put_linearities_first(lrs_dat *Q, lrs_dic *P) { long nlinearity; long i, row; lrs_mp Temp; lrs_alloc_mp(Temp); nlinearity = Q->nlinearity; for(row=1; row <= nlinearity; row++) { if (Q->linearity[row-1] != row) { for(i=0;i<=P->d; i++) { copy(Temp, P->A[row][i]); copy(P->A[row][i], P->A[Q->linearity[row-1]][i]); copy(P->A[Q->linearity[row-1]][i], Temp); } copy(Temp, Q->Gcd[row]); copy(Q->Gcd[row], Q->Gcd[Q->linearity[row-1]]); copy(Q->Gcd[Q->linearity[row-1]], Temp); copy(Temp, Q->Lcm[row]); copy(Q->Lcm[row], Q->Lcm[Q->linearity[row-1]]); copy(Q->Lcm[Q->linearity[row-1]], Temp); Q->linearity[row-1] = row; } } lrs_clear_mp(Temp); } /***************************************************************/ /* Function to compute redundancies. redineq[i] = 1 if row i */ /* is redundant. Adapted from Prof. Avis' function in lrslib.c.*/ /***************************************************************/ long compute_redundancy(long *redineq, lrs_dic *P, lrs_dat *Q) { long ineq; long d, m; long nlinearity; long lastdv, index; lrs_mp_matrix Lin; m = P->m_A; d = P->d; if (!lrs_getfirstbasis(&P, Q, &Lin, TRUE)) { return (FALSE); } m = P->m_A; d = P->d; nlinearity = Q->nlinearity; lastdv = Q->lastdv; for(index = lastdv +1;index <= m+d; index++) { ineq = Q->inequality[index-lastdv]; redineq[ineq] = checkindex(P, Q, index); } return (TRUE); } /******************************************************************/ /* Function to project original space to space of variables */ /* contained in the array 'variables'. */ /******************************************************************/ void lrs_project_var(lrs_dic **iP, lrs_dat **iQ, long *variables, long stat) { lrs_dic *P1, *P2, *tP2, *P; lrs_dat *Q1, *Q2, *tQ2, *Q; long *redineq, *tgroups; long i, j, k, l, m, n, red, col, row; long empty_set; long *var_remove; /* variables to be removed */ long count; /* could do with less of these monsters */ lrs_mp Temp, Temp1, Lcm, div1, div2, Temp2, Temp3, Temp4, Temp5; lrs_alloc_mp(Temp); lrs_alloc_mp(Temp1);lrs_alloc_mp(Temp2); lrs_alloc_mp(Temp3); lrs_alloc_mp(Temp4);lrs_alloc_mp(Temp5); lrs_alloc_mp(Lcm); lrs_alloc_mp(div1);lrs_alloc_mp(div2); if (stat) { fprintf(lrs_ofp, "*Number of\t Number after\t Number of\n"); fprintf(lrs_ofp, "*Inequalties\t Removing Var.\t Redundancies\n"); fprintf(lrs_ofp, "*============================================\n"); } /* create a copy of iP, iQ */ if( (Q = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q->m = (*iQ)->m; Q->n = (*iQ)->n; n = (*iQ)->n; if (( P = lrs_alloc_dic(Q)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(P, (*iP),-1, -1); var_remove = CALLOC ((n + 2), sizeof (long)); if (var_remove == NULL) fel_abort("ERROR>Can't allocate memory."); var_remove[0]=0; for(l=1; l<=n-1; l++) { var_remove[0]++; var_remove[l] = l; } for(l=1;l<=variables[0];l++) { var_remove[variables[l]] = 0; var_remove[0]--; } for (i = 1; i <= n-1; i++) /* main loop */ { count = 0; if (var_remove[i]) { if (stat) fprintf(lrs_ofp, "*%11ld ", Q->m); /* create a copy of P, Q */ if( (Q1 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q1->m = Q->m; Q1->n = Q->n; if (( P1 = lrs_alloc_dic(Q1)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(P1, P, -1, -1); col = var_remove[i]; /* column to be removed */ for(l=i+1;l<=n-1;l++) /* fix variables for second round */ { if ((var_remove[l]) && (var_remove[l] > col)) var_remove[l]--; } tgroups = CALLOC ((Q1->m+4), sizeof (long)); if (tgroups == NULL) fel_abort("ERROR>Can't allocate memory."); /* compute groupings tgroups[0] = # of rows with '0' in column 'col' */ lrs_compute_groups(Q1, P1, col, tgroups); /* check for overflow */ if (tgroups[Q1->m +1] > 0) if (tgroups[Q1->m + 2] > (MAXD/tgroups[Q1->m +1])) { fel_abort("ERROR>Overflow...too many rows produced."); } /* create P2, Q2 */ if( (Q2 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); empty_set = (!tgroups[Q1->m +1] && tgroups[Q1->m +2]) || (tgroups[Q1->m +1] && !tgroups[Q1->m +2]) || (!(tgroups[Q1->m +1] + tgroups[Q1->m +2])); if (empty_set) /* one of the sets is empty, just remove the variable */ { Q2->m = Q1->m; Q2->n = (Q1->n) - 1; if (( P2 = lrs_alloc_dic(Q2)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(P2, P1,-1, col); if (stat) fprintf(lrs_ofp, "%13ld", Q2->m); } else { Q2->m = (tgroups[Q1->m + 1]*tgroups[Q1->m +2]) + tgroups[0]; Q2->n = (Q1->n)-1; if (stat) fprintf(lrs_ofp, "%13ld ", Q2->m); if (( P2 = lrs_alloc_dic(Q2)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); row = 1; for(j = 1; j <= Q1->m; j++) { if (tgroups[j] < 0) for(k=1; k <= Q1->m; k++) { if (tgroups[k] > 0) { copy(div1, P1->A[j][col]); copy(div2, P1->A[k][col]); storesign(div1, POS); copy(Lcm, div1); lcm(Lcm, div2); copy(Temp, Lcm); copy(Temp1, div1); divint(Temp, Temp1, Temp2); copy(Temp, Lcm); copy(Temp1, div2); divint(Temp, Temp1, Temp3); for(l=0;l< col; l++) { copy(Temp, P1->A[j][l]); copy(Temp1, P1->A[k][l]); mulint(Temp,Temp2 ,Temp4); mulint(Temp1,Temp3,Temp5); addint(Temp4, Temp5, P2->A[row][l]); } for(l=col+1;ln; l++) { copy(Temp, P1->A[j][l]); copy(Temp1, P1->A[k][l]); mulint(Temp,Temp2 ,Temp4); mulint(Temp1,Temp3,Temp5); addint(Temp4, Temp5, P2->A[row][l-1]); } reducearray(P2->A[row], Q2->n); row++; } /* end if (tgroups[k]) */ } /* end for k */ } /* end for j*/ for(j=1;j<=Q1->m;j++) { if (tgroups[j]==0) /* just copy row, coefficient was '0' */ { for(l=0;lA[row][l], P1->A[j][l]); for(l=col+1;ln;l++) copy(P2->A[row][l-1], P1->A[j][l]); reducearray(P2->A[row], Q2->n); row++; } } } /* end else */ /* create temp P2, Q2 */ lrs_free_dic(P1, Q1); lrs_free_dat(Q1); for(row=1;row<=Q2->m;row++) { l = 0; for(j=1;jn; j++) if (zero(P2->A[row][j])) l++; if (l==Q2->n -1 ) { count++; } } if( (tQ2 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); tQ2->m = Q2->m; tQ2->n = Q2->n; if (( tP2 = lrs_alloc_dic(tQ2)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(tP2, P2, -1, -1); /* find redundacies */ m = tQ2->m; redineq = CALLOC ((m+1), sizeof (long)); if (redineq == NULL) fel_abort("ERROR>Can't allocate memory."); if (!compute_redundancy(redineq, tP2, tQ2)) fel_abort("ERROR>Can't pivot in redundancy LP"); red = 0; for(row=1;row<=Q2->m; row++) if (redineq[row] == 1L) { red++; } if (stat) fprintf(lrs_ofp, "%12ld%8ld\n", red, count); /* make new P, Q */ lrs_free_dic(P , Q ); lrs_free_dat(Q ); if( (Q = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q->m = Q2->m - red; Q->n = Q2->n; if (( P = lrs_alloc_dic(Q)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); /* copy to P (from P2) nonredundant rows */ k = 0; for(row=1;row<=Q2->m; row++) if (redineq[row] != 1L) { k++; for(l=0;l<=(Q2->n)-1;l++) copy(P->A[k][l], P2->A[row][l]); } free(redineq); free(tgroups); lrs_free_dic(tP2, tQ2); lrs_free_dat(tQ2); lrs_free_dic(P2, Q2); lrs_free_dat(Q2); } /* end if (var_remove[i]) */ }/* end "for i " */ *iP = P; *iQ = Q; lrs_clear_mp(Temp); lrs_clear_mp(Temp1);lrs_clear_mp(Temp2); lrs_clear_mp(Temp3); lrs_clear_mp(Temp4);lrs_clear_mp(Temp5); lrs_clear_mp(Lcm); lrs_clear_mp(div1);lrs_clear_mp(div2); } /*********************************************************************/ void full_fel(lrs_dic *iP, lrs_dat *iQ, long *variables) { lrs_dic *P1, *P2, *P; lrs_dat *Q1, *Q2, *Q; long *proj, *redineq; /* for variables to project to */ long i, j, k, l, m, n, lindep, col, row, red; long *var_remove; /* variables to be removed */ long *Dep; /*Dep[0] not used, Dep[i] = 1 if eqn lin. dep., else 0 */ long nlinearity; long eqn; long last=0; /* =1 if equation used to remove var. =2 if FME used */ /* could do with less of these monsters */ lrs_mp Temp, Temp1, div1; /* create a copy of iP, iQ */ if( (Q = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q->m = iQ->m; Q->n = iQ->n; copy_linearity(Q, iQ); n = iQ->n; if (( P = lrs_alloc_dic(Q)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(P, iP,-1, -1); var_remove = CALLOC ((n + 2), sizeof (long)); if (var_remove == NULL) fel_abort("ERROR>Can't allocate memory."); var_remove[0]=0; for(l=1; l<=n-1; l++) { var_remove[0]++; var_remove[l] = l; } for(l=1;l<=variables[0];l++) { var_remove[variables[l]] = 0; var_remove[0]--; } nlinearity = iQ->nlinearity; for (i = 1; i <= n-1; i++) /* main loop */ { if (var_remove[i]) { /* create a copy of P, Q */ if( (Q1 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q1->m = Q->m; Q1->n = Q->n; copy_linearity(Q1, Q); if (( P1 = lrs_alloc_dic(Q1)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(P1, P,-1, -1); col = var_remove[i]; /* column to be removed */ for(l=i+1;l<=n-1;l++) /* fix variables for second round */ { if ((var_remove[l]) && (var_remove[l] > col)) var_remove[l]--; } for(l=1, eqn=-1; l <= nlinearity; l++) if (!zero(P1->A[l][col])) { eqn = l; /* use this linearity row to eliminate col */ break; } if (eqn > 0) { last = 1; for(l=eqn-1;llinearity[l] = Q1->linearity[l+1] -1; } nlinearity--; Q1->nlinearity = nlinearity; for(j=0;j<=P1->d;j++) { if ((j!=col) && !zero(P1->A[eqn][j])) changesign(P1->A[eqn][j]); } copy(div1, P1->A[eqn][col]); for(k=1;k<=P1->m;k++) { if (k!=eqn) { for(j=0;j<=P1->d;j++) { if (j!=col) { if (zero(P1->A[k][col])) break; mulint(P1->A[k][col], P1->A[eqn][j], Temp); mulint(P1->A[k][j], div1, Temp1); addint(Temp, Temp1, P1->A[k][j]); if (negative(div1)) { if (!zero(P1->A[k][j])) { changesign(P1->A[k][j]); } } } } itomp(0L, P1->A[k][col]); reducearray(P1->A[k], Q1->n); } } /* make new P, Q */ lrs_free_dic(P , Q ); lrs_free_dat(Q ); if( (Q = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q->m = Q1->m -1; Q->n = Q1->n -1; copy_linearity(Q, Q1); if (( P = lrs_alloc_dic(Q)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); copydicA(P, P1, eqn, col); lrs_free_dic(P1 , Q1 ); lrs_free_dat(Q1 ); } else { last = 2; if( (Q2 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q2->m = Q1->m - Q1->nlinearity; Q2->n = Q1->n; if (( P2 = lrs_alloc_dic(Q2)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); /* copy inequalities */ for(row=Q1->nlinearity+1;row<=Q1->m; row++) { for(l=0;l<=(Q1->n)-1;l++) copy(P2->A[row-Q1->nlinearity][l], P1->A[row][l]); } proj = CALLOC ((Q1->n +2), sizeof (long)); for(l=1;ln;l++) proj[l-1] = l; proj[0] = Q1->n-2; lrs_project_var(&P2, &Q2, proj, FALSE); /* make new P, Q */ lrs_free_dic(P , Q ); lrs_free_dat(Q ); if( (Q = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q->m = Q1->nlinearity + P2->m_A;; Q->n = Q1->n - 1; copy_linearity(Q, Q1); if (( P = lrs_alloc_dic(Q)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); for(row=1;row<=Q1->nlinearity; row++) { for(l=0;lA[row][l], P1->A[row][l]); for(l=col+1;l<=(Q->n)-1;l++) copy(P->A[row][l-1], P1->A[row][l]); } for(row=1;row<=P2->m_A; row++) { for(l=0;l<=(Q->n)-1;l++) copy(P->A[row][l], P2->A[row][l]); } lrs_free_dic(P1 , Q1 ); lrs_free_dat(Q1 ); lrs_free_dic(P2 , Q2 ); lrs_free_dat(Q2 ); } } } /* remove linearly dependent linearities */ Dep = CALLOC ((Q->nlinearity+2), sizeof (long)); linear_dep(P, Q, Dep); for(l=1, lindep=0; l <= Q->nlinearity; l++) if (Dep[l]) lindep++; /*if (last==1) perform one last redundancy checking */ if( (Q1 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q1->m = Q->m - Q->nlinearity; Q1->n = Q->n; if (( P1 = lrs_alloc_dic(Q1)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); for(row=Q->nlinearity+1;row<=Q->m; row++) { for(l=0;l<=(Q->n)-1;l++) copy(P1->A[row-Q->nlinearity][l], P->A[row][l]); } m = Q1->m; redineq = CALLOC ((m+1), sizeof (long)); if (redineq == NULL) fel_abort("ERROR>Can't allocate memory."); if (!compute_redundancy(redineq, P1, Q1)) fel_abort("ERROR>Can't pivot in redundancy LP"); for(row=1,red=0;row<=m; row++) if (redineq[row] == 1L) { red++; } lrs_free_dic(P1 , Q1 ); lrs_free_dat(Q1 ); /* assemble final result */ if( (Q2 = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); Q2->m = (m-red) + (Q->nlinearity - lindep); Q2->n = Q->n; Q2->nlinearity = 0L; if (( P2 = lrs_alloc_dic(Q2)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); for(l=1, row=1;l<=Q->nlinearity;l++) if (!Dep[l]) { for(i=0;i<=Q->n-1;i++) copy(P2->A[row][i], P->A[l][i]); row++; } for(l=Q->nlinearity+1;l<=Q->m;l++) if (redineq[l-Q->nlinearity]!=1L) { for(i=0;i<=Q->n-1;i++) copy(P2->A[row][i], P->A[l][i]); row++; } Q2->nlinearity = Q->nlinearity - lindep; for(l=1;l<=Q2->nlinearity;l++) Q2->linearity[l-1] = l; lrs_free_dic(P , Q ); lrs_free_dat(Q ); fprintf(lrs_ofp, "H-representation\n"); if (Q2->nlinearity > 0) { fprintf(lrs_ofp, "linearity %ld", Q2->nlinearity); for(row=0; rownlinearity;row++) fprintf(lrs_ofp, " %ld", Q2->linearity[row]); fprintf(lrs_ofp, "\n"); } fprintf(lrs_ofp, "begin\n"); fprintf(lrs_ofp, "%ld %ld %s", Q2->m, Q2->n, "rational"); for(row=1;row<=Q2->m; row++) lrs_printrow("", Q2, P2->A[row], Q2->inputd); fprintf(lrs_ofp, "\nend\n"); } /***************************************************************/ int main(int argc, char *argv[]) { lrs_dic *P; /* holds dictionary */ lrs_dat *Q; /* holds information about dictionary */ FILE *infile, *outfile; long *proj; /* try opening files */ if (argc < 2) fel_abort(USAGE); if ((infile = fopen(argv[1], "r")) == NULL) fel_abort("ERROR>Can't open input file"); if (argc == 2) outfile = stdout; else if ((outfile = fopen(argv[2], "a")) == NULL) fel_abort("ERROR>Can't open output file"); /* initialize lrs */ if (!lrs_init("Fourier Elimination\n")) fel_abort("ERROR>Can't initialize lrs"); /* set lrs global file pointers */ lrs_ifp = infile; lrs_ofp = outfile; /* allocate space for problem */ if( (Q = lrs_alloc_dat("LRS GLOBALS")) == NULL) fel_abort("ERROR>Can't allocate memory for structures"); if (!readHfile(Q)) /* get info about data from input file */ { fprintf(stderr, "Can't read input file\n"); exit(1); } if (( P = lrs_alloc_dic(Q)) == NULL) fel_abort("ERROR>Can't allocate dictionary space"); proj = CALLOC ((MAXCOL), sizeof (long)); /* variables to project to are stored here */ if (!readHmat(P, Q, proj)) /* read in the matrix/dictionary */ { fprintf(stderr, "Can't read input file\n"); exit(1); } /* lrs_project_var(P, Q, proj, TRUE); compute projection, TRUE means print statistics */ /* clean up */ put_linearities_first(Q, P); full_fel(P, Q, proj); /* fprintf(lrs_ofp, "H-representation\n"); if (Q->nlinearity > 0) { fprintf(lrs_ofp, "linearity %ld", Q->nlinearity); for(row=0; rownlinearity;row++) fprintf(lrs_ofp, " %ld", Q->linearity[row]); fprintf(lrs_ofp, "\n"); } fprintf(lrs_ofp, "begin\n"); fprintf(lrs_ofp, "%ld %ld %s", Q->m, Q->n, "rational"); for(row=1;row<=Q->m; row++) lrs_printrow("", Q, P->A[row], Q->inputd); fprintf(lrs_ofp, "\nend\n"); */ lrs_free_dic(P, Q); lrs_free_dat(Q); lrs_close("Fourier Elimination\n"); printf("\n"); return(0); } lrslib-043/2nash.c0000755001553201777760000000466411607605134013316 0ustar avisnogroup// 2nash.c v1.0 Jan 15, 2009 // Hack of nlrs.c by Conor Meagher to run lrs simultaneously on n processors for n input files // runs nash on input files A B in both orders simultaneously, terminating when first proc finishes // output goes in third argument if any, else in file: out #include #include #include #include int main(int argc, char *argv[]) { pid_t cpid[argc - 1], w; char buffer [250]; int status,l,j; if (argc < 3 || argc > 4) { printf("Usage: 2nash A B [outfile]\n"); return(0); } for(l = 1; l < 3; l++) { cpid[l -1] = fork(); if (cpid[l -1] == -1) { perror("fork"); exit(EXIT_FAILURE); } if(cpid[l-1] == 0) { //forked threads // n= sprintf(buffer, "lrs %s > out%i", argv[l], l); if(l==1) { int n= sprintf(buffer, "nash %s %s > out%i", argv[1], argv[2], l); } else { int n= sprintf(buffer, "nash %s %s > out%i", argv[2], argv[1], l); } int i=system(buffer); _exit(0); } } // main thread w = wait(&status); for(j = 1; j < 3; j++) { if(w == cpid[j-1]) { // this child finished first if(j==1) printf("nash %s %s finished first\n", argv[1], argv[2]); else { printf("nash %s %s finished first\n", argv[2], argv[1]); printf("player numbers will be reversed in output\n"); } if(argc == 4) { printf("output file: %s\n", argv[3]); int n = sprintf(buffer, "/bin/mv -f out%i %s", j, argv[3]); } else { printf("output file: out\n", argv[2], argv[1]); int n = sprintf(buffer, "/bin/mv -f out%i out", j); } int i = system(buffer); } else { int n = sprintf(buffer, "/bin/rm -f out%i", j); int i = system(buffer); } } printf("the other process will be "); /*...will be killed */ fflush(stdout); kill(0,9); exit(EXIT_SUCCESS); } lrslib-043/lrsgmp.c0000755001553201777760000002421611607605134013602 0ustar avisnogroup/* lrsgmp.c library code for lrs extended precision arithmetic */ /* Version 4.1, April 3, 2001 */ /* Copyright: David Avis 2001, avis@cs.mcgill.ca */ /* For gmp package */ /* derived from lrslong.c and lrsmp.c */ #include #include #include "lrsgmp.h" long lrs_digits; /* max permitted no. of digits */ long lrs_record_digits; /* this is the biggest acheived so far. */ extern FILE *lrs_ifp; /* input file pointer */ extern FILE *lrs_ofp; /* output file pointer */ long digits; long record_digits; /* these are allocated once and used as temporary storage where needed */ lrs_mp temp1,temp2,temp3; #define MAXINPUT 1000 /*max length of any input rational */ void lcm (lrs_mp a, lrs_mp b) /* a = least common multiple of a, b; b is preserved */ { copy (temp1, a); copy (temp2, b); gcd (temp1,temp2); exactdivint (a, temp1, temp2); /* temp2=a/temp1 there is no remainder */ mulint (temp2, b, a); } /* end of lcm */ /***************************************************************/ /* */ /* Package of routines for rational arithmetic */ /* (Built on top of package for multiprecision arithmetic */ /* */ /***************************************************************/ void reduce (lrs_mp Na, lrs_mp Da) /* reduces Na/Da by gcd(Na,Da) */ { lrs_mp Nb, Db, Nc, Dc; lrs_alloc_mp(Nb); lrs_alloc_mp(Db); lrs_alloc_mp(Nc); lrs_alloc_mp(Dc); copy (Nb, Na); copy (Db, Da); storesign (Nb, POS); storesign (Db, POS); copy (Nc, Na); copy (Dc, Da); gcd (Nb, Db); /* Nb is the gcd(Na,Da) */ exactdivint (Nc, Nb, Na); exactdivint (Dc, Nb, Da); lrs_clear_mp(Nb); lrs_clear_mp(Db); lrs_clear_mp(Nc); lrs_clear_mp(Dc); } void reduceint (lrs_mp Na, lrs_mp Da) /* divide Na by Da and return */ { copy (temp1, Na); exactdivint (temp1, Da, Na); } long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd) /* +1 if Na*Nb > Nc*Nd */ /* -1 if Na*Nb < Nc*Nd */ /* 0 if Na*Nb = Nc*Nd */ { long i; mulint (Na, Nb, temp1); mulint (Nc, Nd, temp2); i=mpz_cmp(temp1,temp2); if (i > 0) return (ONE); else if (i < 0) return (-ONE); else return (ZERO); } void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = ka*Na/Da +kb* Nb/Db and reduces answer by gcd(Nc,Dc) */ { mulint (Na, Db, Nc); mulint (Da, Nb, temp1); linint (Nc, ka, temp1, kb); /* Nc = (ka*Na*Db)+(kb*Da*Nb) */ mulint (Da, Db, Dc); /* Dc = Da*Db */ reduce (Nc, Dc); } void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */ { mulint (Na, Db, Nc); mulint (Da, Nb, Dc); reduce (Nc, Dc); } void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */ { mulint (Na, Nb, Nc); mulint (Da, Db, Dc); reduce (Nc, Dc); } /***************************************************************/ /* */ /* Conversion and I/O functions */ /* */ /***************************************************************/ void atomp (const char *s, lrs_mp a) /*convert string to lrs_mp integer */ /* based on atoi KR p.58 */ { long diff, ten, i, sig; lrs_mp mpone; lrs_alloc_mp (mpone); itomp (ONE, mpone); ten = 10L; for (i = 0; s[i] == ' ' || s[i] == '\n' || s[i] == '\t'; i++); /*skip white space */ sig = POS; if (s[i] == '+' || s[i] == '-') /* sign */ sig = (s[i++] == '+') ? POS : NEG; itomp (0L, a); while (s[i] >= '0' && s[i] <= '9') { diff = s[i] - '0'; linint (a, ten, mpone, diff); i++; } storesign (a, sig); if (s[i]) { fprintf (stderr, "\nIllegal character in number: '%s'\n", s + i); exit (1); } lrs_clear_mp (mpone); } /* end of atomp */ void atoaa (const char *in, char *num, char *den) /* convert rational string in to num/den strings */ { long i, j; for (i = 0; in[i] != '\0' && in[i] != '/'; i++) num[i] = in[i]; num[i] = '\0'; den[0] = '\0'; if (in[i] == '/') { for (j = 0; in[j + i + 1] != '\0'; j++) den[j] = in[i + j + 1]; den[j] = '\0'; } } /* end of atoaa */ void rattodouble (lrs_mp a, lrs_mp b, double *x) /* convert lrs_mp rati onal to double */ { double y; y=mpz_get_d (a); (*x)=mpz_get_d (b); (*x) = y / (*x); } long readrat (lrs_mp Na, lrs_mp Da) /* read a rational or integer and convert to lrs_mp */ /* returns true if denominator is not one */ { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; if(fscanf (lrs_ifp, "%s", in)==EOF) { fprintf (lrs_ofp, "\nInvalid rational input"); exit(1); } if(!strcmp(in,"end")) /*premature end of input file */ { return (999L); } atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } void pmp (char *name, lrs_mp Nt) { fprintf (lrs_ofp, "%s", name); if (sign (Nt) != NEG) fprintf (lrs_ofp, " "); mpz_out_str (lrs_ofp,10,Nt); fprintf (lrs_ofp, " "); } void prat (char *name, lrs_mp Nin, lrs_mp Din) /*print the long precision rational Nt/Dt */ { copy (temp1, Nin); copy (temp2, Din); reduce (temp1, temp2); fprintf (lrs_ofp, "%s", name); if (sign (temp1) != NEG) fprintf (lrs_ofp, " "); mpz_out_str (lrs_ofp,10,temp1); if ( !one(temp2)) { fprintf (lrs_ofp, "/"); mpz_out_str (lrs_ofp,10,temp2); } fprintf (lrs_ofp, " "); } /* prat */ void readmp (lrs_mp a) /* read an integer and convert to lrs_mp */ { long in; if(fscanf (lrs_ifp, "%ld", &in)==EOF) { fprintf (lrs_ofp, "\nInvalid integer input"); exit(1); } itomp (in, a); } /***************************************************************/ /* */ /* Memory allocation functions */ /* */ /***************************************************************/ lrs_mp_vector lrs_alloc_mp_vector (long n) /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ { lrs_mp_vector p; long i; p = CALLOC ((n + 1), sizeof (lrs_mp )); for (i = 0; i <= n; i++) lrs_alloc_mp(p[i]); return p; } void lrs_clear_mp_vector (lrs_mp_vector p, long n) /* free space allocated to p */ { long i; for (i=0; i<=n; i++) lrs_clear_mp (p[i] ); free (p); } lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n) /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp numbers */ { lrs_mp_matrix a; int i, j; a = calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = calloc ((n + 1), sizeof (lrs_mp )); for (j = 0; j < n + 1; j++) lrs_alloc_mp (a[i][j]); } return a; } void lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n) /* free space allocated to p */ { long i,j; for (i = 0; i < m + 1; i++) { for (j = 0; j < n + 1; j++) lrs_clear_mp (p[i][j]); free (p[i]); } free (p); } void lrs_getdigits (long *a, long *b) { /* send digit information to user */ *a = ZERO; *b = ZERO; return; } void * xcalloc (long n, long s, long l, char *f) { void *tmp; tmp = calloc (n, s); if (tmp == 0) { char buf[200]; sprintf (buf, "\n\nFatal error on line %ld of %s", l, f); perror (buf); exit (1); } return tmp; } long lrs_mp_init (long dec_digits, FILE * fpin, FILE * fpout) /* max number of decimal digits for the computation */ /* long int version */ { lrs_ifp = fpin; lrs_ofp = fpout; lrs_record_digits = 0; /* not used for gmp arithmetic */ lrs_digits = 0; /* not used for gmp arithmetic */ lrs_alloc_mp(temp1); lrs_alloc_mp(temp2); lrs_alloc_mp(temp3); #ifndef LRS_QUIET printf(" gmp v.%d.%d",__GNU_MP_VERSION,__GNU_MP_VERSION_MINOR); #endif return TRUE; } void lrs_mp_close() { lrs_clear_mp(temp1); lrs_clear_mp(temp2); lrs_clear_mp(temp3); } void notimpl (char s[]) { fflush (stdout); fprintf (stderr, "\nAbnormal Termination %s\n", s); exit (1); } /***************************************************************/ /* */ /* Misc. functions */ /* */ /***************************************************************/ /* find largest gcd of p[0]..p[n-1] and divide through */ void reducearray (lrs_mp_vector p, long n) { lrs_mp divisor; long i = 0L; while ((i < n) && zero (p[i])) i++; if (i == n) return; lrs_alloc_mp (divisor); copy (divisor, p[i]); storesign (divisor, POS); i++; while (i < n) { if (!zero (p[i])) { copy (temp1, p[i]); storesign (temp1, POS); gcd (divisor, temp1); } i++; } for (i = 0; i < n; i++) if (!zero (p[i])) reduceint (p[i], divisor); lrs_clear_mp (divisor); } /* end of reducearray */ long myrandom (long num, long nrange) /* return a random number in range 0..nrange-1 */ { long i; i = (num * 401 + 673) % nrange; return (i); } void stringcpy (char *s, char *t) /*copy t to s pointer version */ { while (((*s++) = (*t++)) != '\0'); } void linint(lrs_mp a, long ka, lrs_mp b, long kb) /* a=a*ka+b*kb, b unchanged */ { mpz_mul_ui (a,a,labs(ka)); if (ka < 0) mpz_neg(a,a); mpz_mul_ui (temp1,b,labs(kb)); if (kb < 0) mpz_neg(temp1,temp1); mpz_add(a,a,temp1); } void storesign(lrs_mp a, long sa) { if ( (sa)*sign(a) < 0 ) mpz_neg(a,a); } lrslib-043/lrs.c0000755001553201777760000000022611607605134013071 0ustar avisnogroup#include #include #include "lrslib.h" int main (int argc, char *argv[]) { lrs_main(argc,argv); printf("\n"); return 0; } lrslib-043/lrsmp.h0000755001553201777760000002306611607605134013442 0ustar avisnogroup/* lrsmp.h (lrs extended precision arithmetic library) */ /* Copyright: David Avis 2000, avis@cs.mcgill.ca */ /* Version 4.0, February 17, 2000 */ /* 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 2 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, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */ /******************************************************************************/ /* See http://cgm.cs.mcgill.ca/~avis/C/lrs.html for lrs usage instructions */ /******************************************************************************/ /* This package contains the extended precision routines used by lrs and some other miscellaneous routines. The maximum precision depends on the parameter MAX_DIGITS defined below, with usual default of 255L. This gives a maximum of 1020 decimal digits on 32 bit machines. The procedure lrs_mp_init(dec_digits) may set a smaller number of dec_digits, and this is useful if arrays or matrices will be used. */ /***********/ /* defines */ /***********/ /* this is number of longwords. Increasing this won't cost you that much since only variables other than the A matrix are allocated this size. Changing affects running time in small but not very predictable ways. */ #define MAX_DIGITS 255L /* this is in decimal digits, you pay in memory if you increase this, unless you override by a line with digits n before the begin line of your file. */ #define DEFAULT_DIGITS 100L /**********MACHINE DEPENDENT CONSTANTS***********/ /* MAXD is 2^(k-1)-1 where k=16,32,64 word size */ /* MAXD must be at least 2*BASE^2 */ /* If BASE is 10^k, use "%k.ku" for FORMAT */ /* INTSIZE is number of bytes for integer */ /* 32/64 bit machines */ /***********************************************/ #ifndef B64 /*32 bit machines */ #define FORMAT "%4.4lu" #define MAXD 2147483647L #define BASE 10000L #define BASE_DIG 4 #define INTSIZE 8L #define BIT "32bit" #else /* 64 bit machines */ #define MAXD 9223372036854775807L #define BASE 1000000000L #define FORMAT "%9.9lu" #define BASE_DIG 9 #define INTSIZE 16L #define BIT "64bit" #endif #define MAXINPUT 1000 /*max length of any input rational */ #define POS 1L #define NEG -1L #ifndef TRUE #define TRUE 1L #endif #ifndef FALSE #define FALSE 0L #endif #define ONE 1L #define TWO 2L #define ZERO 0L /**********************************/ /* MACROS */ /* dependent on mp implementation */ /**********************************/ #define exactdivint(a,b,c) divint((a),(b),(c)) /*should use special code here */ #define positive(a) (((a)[0] < 2 || ((a)[0]==2 && (a)[1]==0))?FALSE:TRUE) #define negative(a) (((a)[0] > -2 || ((a)[0]==-2 && (a)[1]==0))?FALSE:TRUE) #define zero(a) ((((a)[0]==2 || (a)[0]==-2) && (a)[1]==0)?TRUE:FALSE) #define one(a) (((a)[0]==2 && (a)[1]==1)?TRUE:FALSE) #define length(a) (((a)[0] > 0) ? (a)[0] : -(a)[0]) #define sign(a) (((a)[0] < 0) ? NEG : POS) #define storesign(a,sa) a[0]=((a)[0] > 0) ? (sa)*((a)[0]) : -(sa)*((a)[0]) #define changesign(a) a[0]= -(a)[0] #define storelength(a,la) a[0]=((a)[0] > 0) ? (la) : -(la) /* * convert between decimal and machine (longword digits). Notice lovely * implementation of ceiling function :-) */ #define DEC2DIG(d) ( (d) % BASE_DIG ? (d)/BASE_DIG+1 : (d)/BASE_DIG) #define DIG2DEC(d) ((d)*BASE_DIG) #include #ifdef SIGNALS #include #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #ifdef TIMES void ptimes (); #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*************/ /* typedefs */ /*************/ typedef long lrs_mp[MAX_DIGITS + 1]; /* type lrs_mp holds one multi-precision integer */ typedef long *lrs_mp_t; typedef long **lrs_mp_vector; typedef long ***lrs_mp_matrix; /*********************/ /*global variables */ /*********************/ long lrs_digits; /* max permitted no. of digits */ long lrs_record_digits; /* this is the biggest acheived so far. */ FILE *lrs_ifp; /* input file pointer */ FILE *lrs_ofp; /* output file pointer */ /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ /* next two functions are not used by lrsmp, but are for lrsgmp compatability */ #define lrs_alloc_mp(a) #define lrs_clear_mp(a) lrs_mp_t lrs_alloc_mp_t(); /* dynamic allocation of lrs_mp */ lrs_mp_vector lrs_alloc_mp_vector (long n); /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n); /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp */ void lrs_clear_mp_vector (lrs_mp_vector a, long n); void lrs_clear_mp_matrix (lrs_mp_matrix a, long m, long n); long lrs_mp_init (long dec_digits, FILE * lrs_ifp, FILE * lrs_ofp); /* max number of decimal digits, fps */ /*********************************************************/ /* Core library functions - depend on mp implementation */ /******************************************************* */ void atomp (char s[], lrs_mp a); /* convert string to lrs_mp integer */ long compare (lrs_mp a, lrs_mp b); /* a ? b and returns -1,0,1 for <,=,> */ void copy (lrs_mp a, lrs_mp b); /* assigns a=b */ void divint (lrs_mp a, lrs_mp b, lrs_mp c); /* c=a/b, a contains remainder on return */ void gcd (lrs_mp u, lrs_mp v); /* returns u=gcd(u,v) destroying v */ long greater (lrs_mp a, lrs_mp b); /* tests if a > b and returns (TRUE=POS) */ void itomp (long in, lrs_mp a); /* convert integer i to lrs_mp */ void linint (lrs_mp a, long ka, lrs_mp b, long kb); /* compute a*ka+b*kb --> a */ void mptodouble (lrs_mp a, double *x); /* convert lrs_mp to double */ long mptoi (lrs_mp a); /* convert lrs_mp to long integer */ void mulint (lrs_mp a, lrs_mp b, lrs_mp c); /* multiply two integers a*b --> c */ void normalize (lrs_mp a); /* normalize lrs_mp after computation */ void pmp (char name[], lrs_mp a); /* print the long precision integer a */ void prat (char name[], lrs_mp Nt, lrs_mp Dt); /* reduce and print Nt/Dt */ void readmp (lrs_mp a); /* read an integer and convert to lrs_mp */ long readrat (lrs_mp Na, lrs_mp Da); /* read a rational or int and convert to lrs_mp */ void reduce (lrs_mp Na, lrs_mp Da); /* reduces Na Da by gcd(Na,Da) */ /*********************************************************/ /* Standard arithmetic & misc. functions */ /* should be independent of mp implementation */ /******************************************************* */ void atoaa (char in[], char num[], char den[]); /* convert rational string in to num/den strings */ void addint (lrs_mp a, lrs_mp b, lrs_mp c); /* compute c=a+b */ long atos (char s[]); /* convert s to integer */ long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd); /* +1 if Na*Nb > Nc*Nd,-1 if Na*Nb > Nc*Nd else 0 */ void decint (lrs_mp a, lrs_mp b); /* compute a=a-b */ void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */ void getfactorial (lrs_mp factorial, long k); /* compute k factorial in lrs_mp */ void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc); void lcm (lrs_mp a, lrs_mp b); /* a = least common multiple of a, b; b is saved */ void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */ long myrandom (long num, long nrange); /* return a random number in range 0..nrange-1 */ void notimpl (char s[]); /* bail out - help! */ void rattodouble (lrs_mp a, lrs_mp b, double *x); /* convert lrs_mp rational to double */ void reduceint (lrs_mp Na, lrs_mp Da); /* divide Na by Da and return it */ void reducearray (lrs_mp_vector p, long n); /* find gcd of p[0]..p[n-1] and divide through by */ void scalerat (lrs_mp Na, lrs_mp Da, long ka); /* scales rational by ka */ void subint (lrs_mp a, lrs_mp b, lrs_mp c); /* compute c=a-b */ /**********************************/ /* Miscellaneous functions */ /******************************** */ void free (void *); void lrs_getdigits (long *a, long *b); /* send digit information to user */ void stringcpy (char *s, char *t); /* copy t to s pointer version */ void *calloc (); void *malloc (); void *xcalloc (long n, long s, long l, char *f); void lrs_default_digits_overflow (); void digits_overflow (); /* end of lrsmp.h (vertex enumeration using lexicographic reverse search) */ lrslib-043/float2rat.c0000755001553201777760000000457311607605134014200 0ustar avisnogroup/* * Reads a polyhedron file on stdin with rationals and outputs * an approximation in decimal floating point * * David Bremner. bremner@cs.mcgill.ca * */ /* Hacked by DA, April 20 2006 * * first argument overides stdin * if column 0=0 then column 1 scaled to 1 (otherwise big ugly integers come out) * since lrs does not define m (# of output lines) this is skipped * lines are converted until "end" is read */ static char rcsid[]="$Id: float2rat.c,v 1.1.1.1 2006/04/03 20:42:10 bremner Exp $"; #include #include #include #include FILE *lrs_ifp; /* input file pointer */ #define DOCSTRING "\n\ $Id: float2rat.ds,v 1.2 2006/04/03 21:15:39 bremner Exp $\n\ \n\ Converts floating point coefficent $f$ to rational by the \n\ simple expedient of outputing 10^k*f/10^k for appropriate \n\ $k$. Does no reduction of numbers. In particular this may cause overflow in \n\ old versions of lrs input (and I'm not about cdd).\n\ " int usage(){ fprintf(stderr,"\n%s\n",rcsid);fprintf(stderr,DOCSTRING); exit(1); } #define CHECK_HELP if (argc > 1 && argv[1][0]=='-' && argv[1][1]=='h') usage(); int main(argc,argv) int argc; char **argv; { long int m,n; int i,j; long atol(); char buf[BUFSIZ]; CHECK_HELP; if(argc > 1 ) /* command line argument overides stdin */ { if ((lrs_ifp = fopen (argv[1], "r")) == NULL) { printf ("\nBad input file name\n"); return(1); } } else lrs_ifp=stdin; while ( fgets(buf,BUFSIZ,lrs_ifp) !=NULL ) { fputs(buf,stdout); if (strncmp(buf,"begin",5)==0) break; } if (fscanf(lrs_ifp,"%ld %ld %s",&m,&n,buf)==EOF){ fprintf(stderr,"No begin line"); exit(1); } printf("%ld %ld rational\n",m,n); for (i=0;i User's Guide for lrs

     lrslib programmer's guide      Version 4.1

 June 20, 2001                                       Copyright(C) 2001                lrs home page
  David Avis          avis@cs.mcgill.ca       http://cgm.cs.mcgill.ca/~avis
 
  • Introduction
  • Installation
  • Demos
  • User's Manual
  • Acknowledgements and References

    • Introduction

    lrslib consists of the following main components

    Libraries:

        lrslib:  A callable library of functions implementing lrs and redund
        lrsmp: An extended precision arithmetic package for lrslib
        lrslong: A fixed precision integer package for lrslib
        lrsgmp: An interface for lrslib to the GNU MP arithmetic package.

    Main Drivers:
        lrs.c:                Transform H-representation to V-representation or vice versa
        redund.c        Remove redundancies from H or V-representation

    Demo drivers:
        vedemo.c        Generate vertices of a set of hypercubes
        chdemo.c        Generate facets from a set of generated cyclic polytopes
        lpdemo.c          Solve a series of lp problems on generated cubes

    Utilities:
        buffer.c           Remove duplicates output (parallel geometric rays in unbounded non-pointed polyhedra)

    The demo drivers use an "lp-solve" like procedures to construct the input matrix (and objective function if needed). These programs should be easily modifiable to solve similar problems for other polyhedra. Normally all that is necessary is for the user to modify the procedure used to generate the polyhedron: makecube in the case of vedemo and makecyclic in the case of chdemo.

    For the moment, the only documentation I can offer for the main drivers and library procedures are the comments in the individual programs. Consult the User's manual for usage instructions.

    These programs can be distributed freely under the GNU GENERAL PUBLIC LICENSE. Please read the file COPYING carefully before using.  Please inform the author of any interesting applications for which lrs was helpful.

    Installation

    From lrs home page,  click on  "Download" and retrieve the file lrslib-041.tar.gz
        Unpack with:
           % gunzip lrslib-041.tar.gz
           % tar xvf lrslib-041.tar

        Go to the new directory
        % cd lrslib-041
     

    Installation with built in arithmetic libraries.

         make binaries by typing
           % make all               (most 32 bit unix machines)
        or
          % make all64              (64 bit integer machines such as DEC Alpha)
        or
          % make nosigs        ( 32 bit machines without signals/timing routines)

        Test the program by typing:        lrs  cube.ine
                                                                          redund cubetop.ine

    Install demos.

          %make demo

         Test the programs by typing:   vedemo, chdemo, lpdemo or lpdemo1

    Installation with GNU MP library

    To use the GNU MP library, it is necessary to first install it and record its location. The
    default makefile assumes: /usr/local/include and /usr/local/lib for headers and binaries
    respectively. Edit the gmp: section of "makefile" appropriately.

        make binaries by typing
          % make gmp

        Test the programs by typing:    glrs cube.ine
                                                                        gredund cube.ine

    Demos

    Demo drivers that are designed for user modification are included with this release:

    vedemo.c           vertex enumeration
    chdemo.c           facet enumeration
    lpdemo.c            linear programming

    Main components of all demos

    The main components of each demo are similar, and concern problem set up, memory allocation and memory cleanup:

     long  lrs_init (char *name);     /* initialize lrslib and arithmetic package for prog "name" */

     
    This procedure is called once at the beginning of the driver, and does basic setup functions. "name" will be output with some information about version numer or lrslib and which arithmetic package is used. FALSE is returned in case of failure.


    lrs_dat  *lrs_alloc_dat (char *name);    /* allocate for lrs_dat structure "name"       */
     

    This procedure produces a structure of type lrs_dat (usually saved in variable Q) which has basically static information about the problem. This includes a large number of flags and a few arrays for indices. All flags are set at default values (see lrslib.h) but can be overridden after the function has been called. A NULL pointer is returned in case of failure. It is called once for each problem to be solved.


    lrs_dic  *lrs_alloc_dic (lrs_dat * Q);   /* allocate for lrs_dic structure corr. to Q   */
     

    This procedure produces a structure of type lrs_dic (usually saved in variable P) which has basically dynamic  information about the problem. This includes mainly the dictionary matrix, basic and cobasic indices and their row and column locations. For vertex or facet enumeration additional  lrs_dic structures are created automatically and cached, to speed up backtracking. A NULL pointer is returned in case of failure.


    void lrs_free_dic ( lrs_dic *P, lrs_dat *Q);

    Free the space allocated for lrs_dic structures. This includes all cached structures. This procedure must be called before lrs_free_dat. It should be called before starting a new problem.


    void lrs_free_dat ( lrs_dat *Q);

    Free the space allocated for lrs_dat structure. It should be called before starting a new problem.
    void lrs_close (char *name);    /* close lrs lib program "name"                 */
    Final clean up. This is called once at the end of the run.
    Building the data matrix

    For an H-representation, the data for the problem b+Ax >= 0 is entered row by row. This is illustrated in program makecube(lrs_dic P, lrs_dat Q) (in vedemo.c).The procedure for entering a row of data is:

    void lrs_set_row(lrs_dic *P, lrs_dat *Q, long row, long num[], long den[], long ineq);
     

    Here row is the row number of the current row in the matrix, a long integer from 1 to Q->m. The long arrays num[] and den[] contain the numerator and denominator coeficients, and have length Q->n.  The long integer ineq is replaced by either GE  (TRUE) or EQ (FALSE) to represent an inequality or equation respectively.
    A V-representation is built in a similar way, as illustrated in makecyclic(lrs_dic P, lrs_dat Q)  (in chdemo.c). This also makes use of lrs_set_row. For a vertex, num[0]=1L, and for an extreme ray or linearity num[0]=0L. (In both cases den[0]=1L). ineq is TRUE for a vertex or extreme ray, and FALSE for a linearity.

    If an objective function is required (eg., linear programming) it can be set up using:

    void lrs_set_obj(lrs_dic *P, lrs_dat *Q, long num[], long den[], long max);

    The long arrays num, den hold the objective function coeficients. num[0] is a constant term. The long integer max has values MAXIMIZE(TRUE) or MINIMIZE(FALSE).
    There are two additional procedures that perform the same functions, but where the coefficients are given in lrs_mp format:

    void lrs_set_row_mp(lrs_dic *P, lrs_dat *Q, long row, lrs_mp_vector num, lrs_mp_vector den, long ineq);

    void lrs_set_obj_mp(lrs_dic *P, lrs_dat *Q, lrs_mp_vector num, lrs_mp_vector den, long max);


    Reverse search: vedemo and chdemo

    After constructing the input data, reverse search is used to generate all vertices/rays(vedemo) or facets(chdemo). Unless the tree search will be customized in some way, there is no need to change this part of the demo programs. To
    begin a starting basis is found using:

    long lrs_getfirstbasis (lrs_dic ** P,  lrs_dat * Q, lrs_mp_matrix * Lin, long no_output);

    If there are redundant columns in the input data, a linearity space is computed and stored in matrix Lin. The procedure returns
    long lrs_getnextbasis (lrs_dic **P, lrs_dat * Q, long prune);
    This procedure returns FALSE when there are no more bases to find. The variable prune can be set to TRUE to cause the reverse search to prune the tree at the current vertex, ie. to backtrack rather than going deeper in the tree.
    Output extraction

    A dictionary potentially represents one vertex and several extreme rays (vertex enumeration) or several facets (facet enumeration). Due to degeneracy, the same vertex/ray/facet may be generated several times. The procedure

    long lrs_getsolution (lrs_dic * P, lrs_dat * Q, lrs_mp_vector output, long col);

    checks each column col of the dictionary to see if it contains some output, and if so returns TRUE with output[] containing the respective integer coefficients. To avoid duplication, only the lexicographically minimum representation of a given output is extracted by lrs_getsolution. The output coefficients need to be divided by P->det to get the correct rational output. This is done by the  procedure

    void lrs_printoutput (lrs_dat * Q, lrs_mp_vector output);

    Linear Programming

    The program lpdemo.c solves a set of linear programs on hypercubes, using makecube to construct the constraint matrices. Once the dictionary has been generated, a single call to

    long lrs_solvelp (lrs_dic * P, lrs_dat * Q, long maximize);

    solves the linear program.

    Acknowledgements and References

    I would like to thank many people for helping with this implementation project. Komei Fukuda encouraged me from the start, collaborated in designing the file formats, and provided many suggestions for improving the code. David Bremner implemented memory allocation, caching and signals. Jerry Quinn coded the integer divide routine. Bug reports were provided by many users, for which I thank them. In particular Gerardo Garbulsky's extensive use of earlier versions suggested many refinements, Ambros Marzetta demonstrated the importance of caching and Andreas Enge helped debug the volume computation. Oleg Pikhurko convinced me of the need for the lp-solve like procedures described in the Demos section.

    D. Avis,  "lrs: A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm," In: Polytopes - Combinatorics and Computation, G. Kalai & G. Ziegler eds., Birkhauser-Verlag, DMV Seminar Band 29, pp. 177-198 (2000).
    http://cgm.cs.mcgill.ca/~avis/doc/avis/Av98a.ps

    D. Avis, "Computational Experience with the Reverse Search Vertex Enumeration Algorithm," Optimization Methods and Software,  Vol. 10, pp.107-124 (1998)
    http://cgm.cs.mcgill.ca/~avis/doc/avis/Av98b.ps

    D. Avis, D. Bremner, and R. Seidel, "How Good are Convex Hull Algorithms?," Computational Geometry: Theory and Applications, Vol 7,pp.265-301(1997). http://cgm.cs.mcgill.ca/~avis/doc/avis/ABS96a.ps

    D. Avis and L. Devroye, "Estimating the Number of Vertices of a Polyhedron," pp. 179-190 in Snapshots of Computational and Discrete Geometry, ed. D. Avis and P. Bose, School of Computer Science, McGill University (1994). http://cgm.cs.mcgill.ca/~avis/doc/avis/AD94a.ps

    D. Avis and K. Fukuda, "A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra," Discrete and Computational Geometry, Vol. 8, pp. 295-313 (1992).  http://cgm.cs.mcgill.ca/~avis/doc/avis/AF92b.ps

    D. Bremner, K. Fukuda and A. Marzetta, Primal-Dual Methods for Vertex and Facet Enumeration, 13th ACM
    Symposium on Computational Geometry SCG 1997, 49-56. lrslib-043/COPYING0000755001553201777760000004307611607605134013172 0ustar avisnogroup GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. 675 Mass Ave, Cambridge, MA 02139, USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too. 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If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), 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 distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program. If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances. It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice. This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License. 8. If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License. 9. The Free Software Foundation may publish revised and/or new versions of the 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 a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation. 10. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally. NO WARRANTY 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, 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. 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE 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. END OF TERMS AND CONDITIONS Appendix: 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 convey 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) 19yy 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 2 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, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. Also add information on how to contact you by electronic and paper mail. If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) 19yy name of author Gnomovision 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, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This 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 Library General Public License instead of this License. lrslib-043/mp5.ine0000755001553201777760000000207111607605134013323 0ustar avisnogroupmp5.ine *metric polytope on 5 points H-representation begin 40 11 integer 2 -1 -1 0 0 -1 0 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 -1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 -1 0 0 0 0 0 -1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 0 -1 1 0 0 0 0 1 0 0 0 0 1 -1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 1 0 -1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 0 1 -1 0 0 0 0 0 1 0 0 0 -1 1 0 0 0 0 0 1 2 0 0 0 0 -1 -1 0 -1 0 0 0 0 0 0 0 1 1 0 -1 0 0 0 0 0 0 0 -1 1 0 1 0 0 0 0 0 0 0 1 -1 0 1 0 0 2 0 0 0 0 -1 0 -1 0 -1 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 0 -1 0 1 0 1 0 0 0 0 0 0 1 0 -1 0 1 0 2 0 0 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 -1 1 0 0 1 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 0 1 1 0 0 -1 2 0 0 0 0 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 1 1 -1 0 -1 1 0 0 1 0 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 2 -1 0 -1 0 0 -1 0 0 0 0 0 1 0 -1 0 0 1 0 0 0 0 2 -1 0 0 -1 0 0 -1 0 0 0 0 1 0 0 -1 0 0 1 0 0 0 2 0 -1 -1 0 0 0 0 -1 0 0 2 0 -1 0 -1 0 0 0 0 -1 0 2 0 0 -1 -1 0 0 0 0 0 -1 end printcobasis incidence lrslib-043/ine/0000755001553201777760000000000011607605134012675 5ustar avisnogrouplrslib-043/ine/cyc.ine0000755001553201777760000000020211607605134014145 0ustar avisnogroupV-representation *cyclic polytope: 5 vertices in R^3 begin 5 4 integer 1 1 1 1 1 2 4 8 1 3 9 27 1 4 16 64 1 5 25 125 end *debug lrslib-043/ine/cube.ine0000755001553201777760000000022211607605134014307 0ustar avisnogroupcube *cube of side 2 centred at origin H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 -1 0 1 0 0 -1 end printcobasis 1 lrslib-043/ine/cubetop.ine0000755001553201777760000000025111607605134015034 0ustar avisnogroupcube *top facet of cube *nonnegative linearity 1 3 H-representation begin 6 4 integer 1 -1 0 0 1 0 -1 0 1 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 1 end lrslib-043/ine/cube2.ine0000755001553201777760000000022211607605134014371 0ustar avisnogroupcube *cube of side 2 centred at origin H-representation begin 6 4 rational 2 2 0 0 3 0 3 0 1 0 0 1 1 -1 0 0 1 0 -1 0 1 0 0 -1 end printcobasis 1 lrslib-043/ine/test/0000755001553201777760000000000011607605134013654 5ustar avisnogrouplrslib-043/ine/test/in4.ine0000755001553201777760000000042411607605134015046 0ustar avisnogroupin4.ine begin 12 8 integer 10 -8 -1 -2 -3 -3 -2 -2 10 8 -2 -2 0 0 2 0 10 -11 3 -2 -1 -1 -1 -3 5 23 -4 -2 -3 0 0 1 27 5 -4 -1 3 9 11 -12 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 end nonnegative lrslib-043/ine/test/tsp5.ine0000755001553201777760000000163411607605134015253 0ustar avisnogrouptsp5.ine H-representation linearity 5 1 2 3 4 5 begin 25 11 rational -2 1 1 1 1 0 0 0 0 0 0 -2 1 0 0 0 1 1 1 0 0 0 -3 1 1 1 0 1 1 0 1 0 0 1 -1 0 -1 0 0 -1 0 0 1 0 1 -1 -1 0 0 -1 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 -1 -1 0 0 -1 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 2 -1 0 0 0 -1 -1 0 0 0 0 -1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 1 1 1 0 0 0 0 0 0 0 -2 1 1 1 0 1 1 0 0 0 0 2 -1 -1 -1 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 2 -1 0 -1 0 0 -1 0 0 0 0 3 -1 -1 -1 0 -1 -1 0 0 0 0 -1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 1 1 0 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 end lrslib-043/ine/test/in7.ine0000755001553201777760000000150611607605134015053 0ustar avisnogroupin7.ine begin 20 11 integer 10000 -915 -828 -303 -632 -786 -231 -12 -568 -351 -308 10000 -930 -217 -480 -704 -700 -91 -441 -927 -33 -330 10000 -765 -616 -962 -274 -276 -39 -924 -541 -444 -838 10000 -747 -470 -506 -329 -481 -425 -679 -140 -764 -960 10000 -243 -664 -760 -333 -456 -686 -717 -137 -721 -833 10000 -682 -107 -380 -720 -382 -920 -164 -220 -640 -262 10000 -145 -942 -873 -570 -973 -365 -685 -932 -424 -928 10000 -183 -612 -402 -869 -681 -539 -941 -513 -290 -622 10000 -669 -694 -353 -941 -209 -572 -580 -822 -964 -725 10000 -188 -646 -87 -552 -330 -19 -976 -609 -965 -158 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 end nonnegative lrslib-043/ine/test/trunc10.ine0000755001553201777760000000601711607605134015654 0ustar avisnogrouptrunc10.ine * delta= 1/10 eps0=1/20 scut=1/40 pcut=1/40 * begin 112 11 integer 3 5 -5 -5 -5 -5 -5 -5 -5 -5 20 3 -5 -5 -5 -5 -5 -5 -5 -5 -5 20 3 0 10 0 0 0 0 0 0 0 20 3 0 20 0 0 0 0 0 0 0 10 3 5 20 -5 -5 -5 -5 -5 -5 -5 -5 3 -5 20 -5 -5 -5 -5 -5 -5 -5 -5 3 0 20 10 0 0 0 0 0 0 0 3 0 20 0 10 0 0 0 0 0 0 3 0 20 0 0 10 0 0 0 0 0 3 0 20 0 0 0 10 0 0 0 0 3 0 20 0 0 0 0 10 0 0 0 3 0 20 0 0 0 0 0 10 0 0 3 0 20 0 0 0 0 0 0 10 0 3 0 0 10 0 0 0 0 0 0 20 3 0 0 20 0 0 0 0 0 0 10 3 5 -5 20 -5 -5 -5 -5 -5 -5 -5 3 -5 -5 20 -5 -5 -5 -5 -5 -5 -5 3 0 10 20 0 0 0 0 0 0 0 3 0 0 20 10 0 0 0 0 0 0 3 0 0 20 0 10 0 0 0 0 0 3 0 0 20 0 0 10 0 0 0 0 3 0 0 20 0 0 0 10 0 0 0 3 0 0 20 0 0 0 0 10 0 0 3 0 0 20 0 0 0 0 0 10 0 3 0 0 0 10 0 0 0 0 0 20 3 0 0 0 20 0 0 0 0 0 10 3 5 -5 -5 20 -5 -5 -5 -5 -5 -5 3 -5 -5 -5 20 -5 -5 -5 -5 -5 -5 3 0 10 0 20 0 0 0 0 0 0 3 0 0 10 20 0 0 0 0 0 0 3 0 0 0 20 10 0 0 0 0 0 3 0 0 0 20 0 10 0 0 0 0 3 0 0 0 20 0 0 10 0 0 0 3 0 0 0 20 0 0 0 10 0 0 3 0 0 0 20 0 0 0 0 10 0 3 0 0 0 0 10 0 0 0 0 20 3 0 0 0 0 20 0 0 0 0 10 3 5 -5 -5 -5 20 -5 -5 -5 -5 -5 3 -5 -5 -5 -5 20 -5 -5 -5 -5 -5 3 0 10 0 0 20 0 0 0 0 0 3 0 0 10 0 20 0 0 0 0 0 3 0 0 0 10 20 0 0 0 0 0 3 0 0 0 0 20 10 0 0 0 0 3 0 0 0 0 20 0 10 0 0 0 3 0 0 0 0 20 0 0 10 0 0 3 0 0 0 0 20 0 0 0 10 0 3 0 0 0 0 0 10 0 0 0 20 3 0 0 0 0 0 20 0 0 0 10 3 5 -5 -5 -5 -5 20 -5 -5 -5 -5 3 -5 -5 -5 -5 -5 20 -5 -5 -5 -5 3 0 10 0 0 0 20 0 0 0 0 3 0 0 10 0 0 20 0 0 0 0 3 0 0 0 10 0 20 0 0 0 0 3 0 0 0 0 10 20 0 0 0 0 3 0 0 0 0 0 20 10 0 0 0 3 0 0 0 0 0 20 0 10 0 0 3 0 0 0 0 0 20 0 0 10 0 3 0 0 0 0 0 0 10 0 0 20 3 0 0 0 0 0 0 20 0 0 10 3 5 -5 -5 -5 -5 -5 20 -5 -5 -5 3 -5 -5 -5 -5 -5 -5 20 -5 -5 -5 3 0 10 0 0 0 0 20 0 0 0 3 0 0 10 0 0 0 20 0 0 0 3 0 0 0 10 0 0 20 0 0 0 3 0 0 0 0 10 0 20 0 0 0 3 0 0 0 0 0 10 20 0 0 0 3 0 0 0 0 0 0 20 10 0 0 3 0 0 0 0 0 0 20 0 10 0 3 0 0 0 0 0 0 0 10 0 20 3 0 0 0 0 0 0 0 20 0 10 3 5 -5 -5 -5 -5 -5 -5 20 -5 -5 3 -5 -5 -5 -5 -5 -5 -5 20 -5 -5 3 0 10 0 0 0 0 0 20 0 0 3 0 0 10 0 0 0 0 20 0 0 3 0 0 0 10 0 0 0 20 0 0 3 0 0 0 0 10 0 0 20 0 0 3 0 0 0 0 0 10 0 20 0 0 3 0 0 0 0 0 0 10 20 0 0 3 0 0 0 0 0 0 0 20 10 0 3 0 0 0 0 0 0 0 0 10 20 3 0 0 0 0 0 0 0 0 20 10 3 5 -5 -5 -5 -5 -5 -5 -5 20 -5 3 -5 -5 -5 -5 -5 -5 -5 -5 20 -5 3 0 10 0 0 0 0 0 0 20 0 3 0 0 10 0 0 0 0 0 20 0 3 0 0 0 10 0 0 0 0 20 0 3 0 0 0 0 10 0 0 0 20 0 3 0 0 0 0 0 10 0 0 20 0 3 0 0 0 0 0 0 10 0 20 0 3 0 0 0 0 0 0 0 10 20 0 1 10 -10 -10 -10 -10 -10 -10 -10 -10 -10 1 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 39 40 0 0 0 0 0 0 0 0 0 39 -40 0 0 0 0 0 0 0 0 0 1 0 8 0 0 0 0 0 0 0 0 1 0 0 8 0 0 0 0 0 0 0 1 0 0 0 8 0 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 1 0 0 0 0 0 8 0 0 0 0 1 0 0 0 0 0 0 8 0 0 0 1 0 0 0 0 0 0 0 8 0 0 1 0 0 0 0 0 0 0 0 8 0 1 0 0 0 0 0 0 0 0 0 8 7 0 -8 0 0 0 0 0 0 0 0 7 0 0 -8 0 0 0 0 0 0 0 7 0 0 0 -8 0 0 0 0 0 0 7 0 0 0 0 -8 0 0 0 0 0 7 0 0 0 0 0 -8 0 0 0 0 7 0 0 0 0 0 0 -8 0 0 0 7 0 0 0 0 0 0 0 -8 0 0 7 0 0 0 0 0 0 0 0 -8 0 7 0 0 0 0 0 0 0 0 0 -8 end printcobasis startingcobasis 82 83 84 85 86 87 88 89 90 112 lrslib-043/ine/test/in0.ine0000755001553201777760000000023411607605134015041 0ustar avisnogroupin0.ine begin 8 6 integer 9 -2 -3 -3 -2 -2 9 -2 0 0 2 0 9 -2 -1 -1 -1 -3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 end nonegative lrslib-043/ine/test/kkd38_6.ine0000755001553201777760000000453711607605134015536 0ustar avisnogroupkkd38_6.ine digits 120 begin 38 7 integer 2919394390774395218459334 -4379091595292464054287507 -36492430237104184038520181 -253987324572060483286422939 -1691789494531258045567157717 -11149182918946980113429731347 -73511950112254277868261780941 7 -21 -133 -777 -4669 -29001 -184813 7 -14 -112 -728 -4564 -28784 -184372 7 -7 -77 -595 -4109 -27307 -179717 7 0 -28 -336 -2884 -21840 -156148 7 7 35 91 -301 -7133 -75445 7 14 112 728 4396 25424 141772 7 21 203 1617 12131 88641 638723 7 28 308 2800 23996 200368 1650188 7 35 427 4319 41251 384335 3535267 7 42 560 6216 65324 670992 6815180 7 49 707 8533 97811 1098349 12216107 7 56 868 11312 140476 1712816 20717068 7 63 1043 14595 195251 2570043 33602843 7 70 1232 18424 264236 3735760 52521932 7 77 1435 22841 349699 5286617 79549555 7 84 1652 27888 454076 7311024 117255692 7 91 1883 33607 579971 9909991 168778163 7 98 2128 40040 730156 13197968 237900748 7 105 2387 47229 907571 17303685 329136347 7 112 2660 55216 1115324 22370992 447815180 7 119 2947 64043 1356691 28559699 600178027 7 126 3248 73752 1635116 36046416 793474508 7 133 3563 84385 1954211 45025393 1036066403 7 140 3892 95984 2317756 55709360 1337536012 7 147 4235 108591 2729699 68330367 1708799555 7 154 4592 122248 3194156 83140624 2162225612 7 161 4963 136997 3715411 100413341 2711758603 7 168 5348 152880 4297916 120443568 3373047308 7 175 5747 169939 4946291 143549035 4163578427 7 182 6160 188216 5665324 170070992 5102815180 7 189 6587 207753 6459971 200375049 6212340947 7 196 7028 228592 7335356 234852016 7516007948 7 203 7483 250775 8296771 273918743 9040090963 7 210 7952 274344 9349676 318018960 10813446092 7 217 8435 299341 10499699 367624117 12867674555 7 224 8932 325808 11752636 423234224 15237291532 -2919394390774395218459333 4379091595292464054287507 36492430237104184038520181 253987324572060483286422939 1691789494531258045567157717 11149182918946980113429731347 73511950112254277868261780941 end lrslib-043/ine/test/kq20_11a.ine0000755001553201777760000000153311607605134015575 0ustar avisnogroupkq20_11.ine H-representation nonnegative begin 10 11 integer 10000 -915 -828 -303 -632 -786 -231 -12 -568 -351 -308 10000 -930 -217 -480 -704 -700 -91 -441 -927 -33 -330 10000 -765 -616 -962 -274 -276 -39 -924 -541 -444 -838 10000 -747 -470 -506 -329 -481 -425 -679 -140 -764 -960 10000 -243 -664 -760 -333 -456 -686 -717 -137 -721 -833 10000 -682 -107 -380 -720 -382 -920 -164 -220 -640 -262 10000 -145 -942 -873 -570 -973 -365 -685 -932 -424 -928 10000 -183 -612 -402 -869 -681 -539 -941 -513 -290 -622 10000 -669 -694 -353 -941 -209 -572 -580 -822 -964 -725 10000 -188 -646 -87 -552 -330 -19 -976 -609 -965 -158 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 end lrslib-043/ine/test/metric40_11.ine0000755001553201777760000000205211607605134016303 0ustar avisnogroupmetric40-11.ine *metric polytope on 5 points H-representation begin 40 11 integer 0 0 0 1 1 0 0 0 0 0 -1 0 0 1 0 1 0 0 0 0 -1 0 0 0 1 1 0 0 0 0 -1 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 1 0 1 0 0 -1 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 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12 -48 24 -48 48 16 -24 48 -48 -24 -48 48 -24 -48 48 48 48 48 -48 48 48 48 48 24 -24 24 24 12 12 -24 12 24 -24 48 48 24 12 -24 4 -24 4 -12 -48 -24 12 -24 -24 -24 -48 -12 -48 12 -48 48 24 -48 -48 -24 48 -48 -24 -48 -24 -48 -48 -24 6 -24 -24 24 24 24 24 12 -24 -24 24 12 48 -12 48 -48 6 -24 48 -24 -24 3 48 -24 48 -48 -12 24 -48 -48 -12 48 3 -24 48 48 24 -8 24 -24 -24 48 -8 -48 6 24 24 24 24 12 -48 24 12 -24 48 48 6 -8 -48 12 -48 -24 24 -8 -12 6 24 -24 -24 -24 24 6 24 -12 12 1 -12 1 end lrslib-043/ine/mit/mit31-20.ine0000755001553201777760000000266111607605134015347 0ustar avisnogroupmit31-20.ine begin 31 20 integer 1 -6 12 3 0 0 0 -12 -8 0 0 12 3 0 0 0 -6 0 1 0 1 2 -1 2 -2 0 -4 4 -4 -2 0 2 0 1 -2 2 0 0 0 1 1 0 -3 0 0 2 0 0 -2 0 4 0 0 -1 0 -2 0 2 0 -1 1 0 1 -2 -2 0 0 0 0 2 0 2 0 1 -2 0 0 0 0 -1 1 0 -3 2 -2 0 0 0 0 2 0 -2 0 1 2 0 0 0 0 -1 1 -2 -1 0 0 2 0 0 2 0 0 0 0 -1 0 0 0 -2 0 1 1 -2 -5 2 2 -4 4 4 0 2 -8 2 0 1 2 2 0 -4 0 1 1 -2 3 -2 -2 0 4 4 -4 -2 0 -2 0 1 2 -2 0 0 0 1 1 -2 -1 2 -2 0 4 -4 4 -2 0 2 0 1 -2 -2 0 0 0 1 1 -4 1 2 2 -4 0 0 4 -2 0 -2 0 1 -2 0 0 4 0 -1 1 -4 5 0 0 2 0 0 -2 0 -4 0 0 -1 0 2 0 2 0 -1 1 -6 11 2 2 -4 -4 -4 -8 2 8 2 0 1 2 -2 0 -4 0 1 1 6 12 3 0 0 0 12 8 0 0 12 3 0 0 0 6 0 1 0 1 4 4 1 0 0 0 0 0 0 0 -4 -1 0 0 0 -4 0 -1 0 1 2 0 -1 0 0 0 -4 0 0 0 0 -1 0 0 0 2 0 1 0 1 2 -4 3 0 0 0 4 -8 0 0 -4 3 0 0 0 2 0 1 0 1 0 -4 1 0 0 0 0 0 0 0 4 -1 0 0 0 0 0 -1 0 1 0 0 -3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 -1 0 1 -2 -4 3 0 0 0 -4 8 0 0 -4 3 0 0 0 -2 0 1 0 1 -2 0 -1 0 0 0 4 0 0 0 0 -1 0 0 0 -2 0 1 0 1 -4 4 1 0 0 0 0 0 0 0 -4 -1 0 0 0 4 0 -1 0 1 6 11 2 2 4 4 4 8 2 8 2 0 1 2 2 0 4 0 1 1 4 5 0 0 -2 0 0 2 0 -4 0 0 -1 0 -2 0 -2 0 -1 1 4 1 2 2 4 0 0 -4 -2 0 -2 0 1 -2 0 0 -4 0 -1 1 2 3 -2 -2 0 -4 -4 4 -2 0 -2 0 1 2 2 0 0 0 1 1 2 -1 0 0 -2 0 0 -2 0 0 0 0 -1 0 0 0 2 0 1 1 2 -1 -2 2 0 4 -4 -4 2 0 -2 0 1 -2 2 0 0 0 1 1 2 -5 2 2 4 -4 -4 0 2 -8 2 0 1 2 -2 0 4 0 1 1 0 -3 -2 2 0 0 0 0 -2 0 2 0 1 2 0 0 0 0 -1 1 0 -3 0 0 -2 0 0 2 0 4 0 0 -1 0 2 0 -2 0 -1 1 -2 -1 -2 2 0 -4 4 4 2 0 -2 0 1 -2 -2 0 0 0 1 end lrslib-043/ine/truss2.ine0000755001553201777760000000363711607605134014650 0ustar avisnogrouptruss *example H-representation begin 12 7 rational 0 -1107121100 -7094932300 -509288900 1581271400 -2991877000 121979199 0 -1107129000 7032470300 34962123 1920391300 -2980227600 193723910 0 1475107100 151545650 -3894269700 384905410 5325424500 -2983380400 0 990727340 29341662 -1558120400 283839350 961245970 4544466400 0 -1839194200 389088800 -7787625500 -3393884800 -3104674100 -993856820 0 990727340 29341662 -1558120400 283839350 961245970 4544466400 0 105491630 -60552183 -2291864200 6864742100 1279634800 -3346341200 0 -1223784100 35749168 -1440369600 930993540 -3004955300 -25679281 0 -935892200 -129544890 1528908700 2954193399 -2958306400 427239050 0 29586836 -16982840 -642790400 1925328000 358894280 -938535540 0 0 0 0 0 0 0 0 990727340 29341662 -1558120400 283839350 961245970 4544466400 end lrslib-043/lrsmp.c0000755001553201777760000005300711607605134013433 0ustar avisnogroup/* lrsmp.c library code for lrs extended precision arithmetic */ /* Version 4.0c, August 26, 2009 */ /* minor change to check result of fscanf */ /* Copyright: David Avis 1999, avis@cs.mcgill.ca */ /* 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 2 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, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */ /******************************************************************/ /* digit overflow is caught by digits_overflow at the end of this */ /* file, make sure it is either user supplied or uncomment */ /* the define below */ /******************************************************************/ #define digits_overflow() lrs_default_digits_overflow() #include #include #include "lrsmp.h" /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ long lrs_mp_init (long dec_digits, FILE * fpin, FILE * fpout) /* max number of decimal digits for the computation */ { /* global variables lrs_ifp and lrs_ofp are file pointers for input and output */ lrs_ifp = fpin; lrs_ofp = fpout; lrs_record_digits = 0; if (dec_digits <= 0) dec_digits = DEFAULT_DIGITS; lrs_digits = DEC2DIG (dec_digits); /* max permitted no. of digits */ if (lrs_digits > MAX_DIGITS) { fprintf (lrs_ofp, "\nDigits must be at most %ld\nChange MAX_DIGITS and recompile\n", DIG2DEC (MAX_DIGITS)); lrs_digits = MAX_DIGITS; return FALSE; } return TRUE; } lrs_mp_t lrs_alloc_mp_t () /* dynamic allocation of lrs_mp number */ { lrs_mp_t p; p=(long *)calloc (lrs_digits+1, sizeof (long)); return p; } lrs_mp_vector lrs_alloc_mp_vector (long n) /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ { lrs_mp_vector p; long i; p = CALLOC ((n + 1), sizeof (lrs_mp *)); for (i = 0; i <= n; i++) p[i] = CALLOC (1, sizeof (lrs_mp)); return p; } void lrs_clear_mp_vector (lrs_mp_vector p, long n) /* free space allocated to p */ { long i; for (i=0; i<=n; i++) free (p[i] ); free (p); } lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n) /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp numbers */ { lrs_mp_matrix a; long *araw; int mp_width, row_width; int i, j; mp_width = lrs_digits + 1; row_width = (n + 1) * mp_width; araw = calloc ((m + 1) * row_width, sizeof (long)); a = calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = calloc ((n + 1), sizeof (lrs_mp *)); for (j = 0; j < n + 1; j++) a[i][j] = (araw + i * row_width + j * mp_width); } return a; } void lrs_clear_mp_matrix (lrs_mp_matrix p, long m, long n) /* free space allocated to lrs_mp_matrix p */ { long i; /* p[0][0] is araw, the actual matrix storage address */ free(p[0][0]); for (i = 0; i < m + 1; i++) free (p[i]); free(p); } /*********************************************************/ /* Core library functions - depend on mp implementation */ /******************************************************* */ void copy (lrs_mp a, lrs_mp b) /* assigns a=b */ { long i; for (i = 0; i <= length (b); i++) a[i] = b[i]; } /********************************************************/ /* Divide two multiple precision integers (c=a/b). */ /* a is destroyed and contains the remainder on return. */ /* From Knuth Vol.2 SemiNumerical Algorithms */ /* coded by J. Quinn */ /********************************************************/ void divint (lrs_mp a, lrs_mp b, lrs_mp c) /* c=a/b, a contains remainder on return */ { long cy, la, lb, lc, d1, s, t, sig; long i, j, qh; /* figure out and save sign, do everything with positive numbers */ sig = sign (a) * sign (b); la = length (a); lb = length (b); lc = la - lb + 2; if (la < lb) { storelength (c, TWO); storesign (c, POS); c[1] = 0; normalize (c); return; } for (i = 1; i < lc; i++) c[i] = 0; storelength (c, lc); storesign (c, (sign (a) == sign (b)) ? POS : NEG); /******************************/ /* division by a single word: */ /* do it directly */ /******************************/ if (lb == 2) { cy = 0; t = b[1]; for (i = la - 1; i > 0; i--) { cy = cy * BASE + a[i]; a[i] = 0; cy -= (c[i] = cy / t) * t; } a[1] = cy; storesign (a, (cy == 0) ? POS : sign (a)); storelength (a, TWO); /* set sign of c to sig (**mod**) */ storesign (c, sig); normalize (c); return; } else { /* mp's are actually DIGITS+1 in length, so if length of a or b = */ /* DIGITS, there will still be room after normalization. */ /****************************************************/ /* Step D1 - normalize numbers so b > floor(BASE/2) */ d1 = BASE / (b[lb - 1] + 1); if (d1 > 1) { cy = 0; for (i = 1; i < la; i++) { cy = (a[i] = a[i] * d1 + cy) / BASE; a[i] %= BASE; } a[i] = cy; cy = 0; for (i = 1; i < lb; i++) { cy = (b[i] = b[i] * d1 + cy) / BASE; b[i] %= BASE; } b[i] = cy; } else { a[la] = 0; /* if la or lb = DIGITS this won't work */ b[lb] = 0; } /*********************************************/ /* Steps D2 & D7 - start and end of the loop */ for (j = 0; j <= la - lb; j++) { /*************************************/ /* Step D3 - determine trial divisor */ if (a[la - j] == b[lb - 1]) qh = BASE - 1; else { s = (a[la - j] * BASE + a[la - j - 1]); qh = s / b[lb - 1]; while (qh * b[lb - 2] > (s - qh * b[lb - 1]) * BASE + a[la - j - 2]) qh--; } /*******************************************************/ /* Step D4 - divide through using qh as quotient digit */ cy = 0; for (i = 1; i <= lb; i++) { s = qh * b[i] + cy; a[la - j - lb + i] -= s % BASE; cy = s / BASE; if (a[la - j - lb + i] < 0) { a[la - j - lb + i] += BASE; cy++; } } /*****************************************************/ /* Step D6 - adjust previous step if qh is 1 too big */ if (cy) { qh--; cy = 0; for (i = 1; i <= lb; i++) /* add a back in */ { a[la - j - lb + i] += b[i] + cy; cy = a[la - j - lb + i] / BASE; a[la - j - lb + i] %= BASE; } } /***********************************************************************/ /* Step D5 - write final value of qh. Saves calculating array indices */ /* to do it here instead of before D6 */ c[la - lb - j + 1] = qh; } /**********************************************************************/ /* Step D8 - unnormalize a and b to get correct remainder and divisor */ for (i = lc; c[i - 1] == 0 && i > 2; i--); /* strip excess 0's from quotient */ storelength (c, i); if (i == 2 && c[1] == 0) storesign (c, POS); cy = 0; for (i = lb - 1; i >= 1; i--) { cy = (a[i] += cy * BASE) % d1; a[i] /= d1; } for (i = la; a[i - 1] == 0 && i > 2; i--); /* strip excess 0's from quotient */ storelength (a, i); if (i == 2 && a[1] == 0) storesign (a, POS); if (cy) fprintf (lrs_ofp, "divide error"); for (i = lb - 1; i >= 1; i--) { cy = (b[i] += cy * BASE) % d1; b[i] /= d1; } } } /* end of divint */ void gcd (lrs_mp u, lrs_mp v) /*returns u=gcd(u,v) destroying v */ /*Euclid's algorithm. Knuth, II, p.320 modified to avoid copies r=u,u=v,v=r Switches to single precision when possible for greater speed */ { lrs_mp r; unsigned long ul, vl; long i; static unsigned long maxspval = MAXD; /* Max value for the last digit to guarantee */ /* fitting into a single long integer. */ static long maxsplen; /* Maximum digits for a number that will fit */ /* into a single long integer. */ static long firstime = TRUE; if (firstime) /* initialize constants */ { for (maxsplen = 2; maxspval >= BASE; maxsplen++) maxspval /= BASE; firstime = FALSE; } if (greater (v, u)) goto bigv; bigu: if (zero (v)) return; if ((i = length (u)) < maxsplen || (i == maxsplen && u[maxsplen - 1] < maxspval)) goto quickfinish; divint (u, v, r); normalize (u); bigv: if (zero (u)) { copy (u, v); return; } if ((i = length (v)) < maxsplen || (i == maxsplen && v[maxsplen - 1] < maxspval)) goto quickfinish; divint (v, u, r); normalize (v); goto bigu; /* Base 10000 only at the moment */ /* when u and v are small enough, transfer to single precision integers */ /* and finish with euclid's algorithm, then transfer back to lrs_mp */ quickfinish: ul = vl = 0; for (i = length (u) - 1; i > 0; i--) ul = BASE * ul + u[i]; for (i = length (v) - 1; i > 0; i--) vl = BASE * vl + v[i]; if (ul > vl) goto qv; qu: if (!vl) { for (i = 1; ul; i++) { u[i] = ul % BASE; ul = ul / BASE; } storelength (u, i); return; } ul %= vl; qv: if (!ul) { for (i = 1; vl; i++) { u[i] = vl % BASE; vl = vl / BASE; } storelength (u, i); return; } vl %= ul; goto qu; } long compare (lrs_mp a, lrs_mp b) /* a ? b and returns -1,0,1 for <,=,> */ { long i; if (a[0] > b[0]) return 1L; if (a[0] < b[0]) return -1L; for (i = length (a) - 1; i >= 1; i--) { if (a[i] < b[i]) { if (sign (a) == POS) return -1L; else return 1L; } if (a[i] > b[i]) { if (sign (a) == NEG) return -1L; else return 1L; } } return 0L; } long greater (lrs_mp a, lrs_mp b) /* tests if a > b and returns (TRUE=POS) */ { long i; if (a[0] > b[0]) return (TRUE); if (a[0] < b[0]) return (FALSE); for (i = length (a) - 1; i >= 1; i--) { if (a[i] < b[i]) { if (sign (a) == POS) return (0); else return (1); } if (a[i] > b[i]) { if (sign (a) == NEG) return (0); else return (1); } } return (0); } void itomp (long in, lrs_mp a) /* convert integer i to multiple precision with base BASE */ { long i; a[0] = 2; /* initialize to zero */ for (i = 1; i < lrs_digits; i++) a[i] = 0; if (in < 0) { storesign (a, NEG); in = in * (-1); } i = 0; while (in != 0) { i++; a[i] = in - BASE * (in / BASE); in = in / BASE; storelength (a, i + 1); } } /* end of itomp */ void linint (lrs_mp a, long ka, lrs_mp b, long kb) /*compute a*ka+b*kb --> a */ /***Handbook of Algorithms and Data Structures P.239 ***/ { long i, la, lb; la = length (a); lb = length (b); for (i = 1; i < la; i++) a[i] *= ka; if (sign (a) != sign (b)) kb = (-kb); if (lb > la) { storelength (a, lb); for (i = la; i < lb; i++) a[i] = 0; } for (i = 1; i < lb; i++) a[i] += kb * b[i]; normalize (a); } /***end of linint***/ void mptodouble (lrs_mp a, double *x) /* convert lrs_mp to double */ { long i, la; double y = 1.0; (*x) = 0; la = length (a); for (i = 1; i < la; i++) { (*x) = (*x) + y * a[i]; y = y * BASE; } if (negative (a)) (*x)= -(*x); } void mulint (lrs_mp a, lrs_mp b, lrs_mp c) /* multiply two integers a*b --> c */ /***Handbook of Algorithms and Data Structures, p239 ***/ { long nlength, i, j, la, lb; /*** b and c may coincide ***/ la = length (a); lb = length (b); nlength = la + lb - 2; if (nlength > lrs_digits) digits_overflow (); for (i = 0; i < la - 2; i++) c[lb + i] = 0; for (i = lb - 1; i > 0; i--) { for (j = 2; j < la; j++) if ((c[i + j - 1] += b[i] * a[j]) > MAXD - (BASE - 1) * (BASE - 1) - MAXD / BASE) { c[i + j - 1] -= (MAXD / BASE) * BASE; c[i + j] += MAXD / BASE; } c[i] = b[i] * a[1]; } storelength (c, nlength); storesign (c, sign (a) == sign (b) ? POS : NEG); normalize (c); } /***end of mulint ***/ void normalize (lrs_mp a) { long cy, i, la; la = length (a); start: cy = 0; for (i = 1; i < la; i++) { cy = (a[i] += cy) / BASE; a[i] -= cy * BASE; if (a[i] < 0) { a[i] += BASE; cy--; } } while (cy > 0) { a[i++] = cy % BASE; cy /= BASE; } if (cy < 0) { a[la - 1] += cy * BASE; for (i = 1; i < la; i++) a[i] = (-a[i]); storesign (a, sign (a) == POS ? NEG : POS); goto start; } while (a[i - 1] == 0 && i > 2) i--; if (i > lrs_record_digits) { if ((lrs_record_digits = i) > lrs_digits) digits_overflow (); }; storelength (a, i); if (i == 2 && a[1] == 0) storesign (a, POS); } /* end of normalize */ long mptoi (lrs_mp a) /* convert lrs_mp to long integer */ { long len = length (a); if (len == 2) return sign (a) * a[1]; if (len == 3) return sign (a) * (a[1] + BASE * a[2]); notimpl ("mp to large for conversion to long"); return 0; /* never executed */ } void pmp (char name[], lrs_mp a) /*print the long precision integer a */ { long i; fprintf (lrs_ofp, "%s", name); if (sign (a) == NEG) fprintf (lrs_ofp, "-"); else fprintf (lrs_ofp, " "); fprintf (lrs_ofp, "%lu", a[length (a) - 1]); for (i = length (a) - 2; i >= 1; i--) fprintf (lrs_ofp, FORMAT, a[i]); fprintf (lrs_ofp, " "); } void prat (char name[], lrs_mp Nin, lrs_mp Din) /*reduce and print Nin/Din */ { lrs_mp Nt, Dt; long i; fprintf (lrs_ofp, "%s", name); /* reduce fraction */ copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); /* print out */ if (sign (Nin) * sign (Din) == NEG) fprintf (lrs_ofp, "-"); else fprintf (lrs_ofp, " "); fprintf (lrs_ofp, "%lu", Nt[length (Nt) - 1]); for (i = length (Nt) - 2; i >= 1; i--) fprintf (lrs_ofp, FORMAT, Nt[i]); if (!(Dt[0] == 2 && Dt[1] == 1)) /* rational */ { fprintf (lrs_ofp, "/"); fprintf (lrs_ofp, "%lu", Dt[length (Dt) - 1]); for (i = length (Dt) - 2; i >= 1; i--) fprintf (lrs_ofp, FORMAT, Dt[i]); } fprintf (lrs_ofp, " "); } void readmp (lrs_mp a) /* read an integer and convert to lrs_mp with base BASE */ { char in[MAXINPUT]; if(fscanf (lrs_ifp, "%s", in)==EOF) { fprintf (lrs_ofp, "\nInvalid integer input"); exit(1); } atomp (in, a); } long readrat (lrs_mp Na, lrs_mp Da) /* read a rational or integer and convert to lrs_mp with base BASE */ /* returns true if denominator is not one */ /* returns 999 if premature end of file */ { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; if(fscanf (lrs_ifp, "%s", in)==EOF) { fprintf (lrs_ofp, "\nInvalid rational input"); exit(1); } if(!strcmp(in,"end")) /*premature end of input file */ { return (999L); } atoaa (in, num, den); /*convert rational to num/dem strings */ atomp (num, Na); if (den[0] == '\0') { itomp (1L, Da); return (FALSE); } atomp (den, Da); return (TRUE); } void addint (lrs_mp a, lrs_mp b, lrs_mp c) /* compute c=a+b */ { copy (c, a); linint (c, 1, b, 1); } void atomp (char s[], lrs_mp a) /*convert string to lrs_mp integer */ { lrs_mp mpone; long diff, ten, i, sig; itomp (1L, mpone); ten = 10L; for (i = 0; s[i] == ' ' || s[i] == '\n' || s[i] == '\t'; i++); /*skip white space */ sig = POS; if (s[i] == '+' || s[i] == '-') /* sign */ sig = (s[i++] == '+') ? POS : NEG; itomp (0L, a); while (s[i] >= '0' && s[i] <= '9') { diff = s[i] - '0'; linint (a, ten, mpone, diff); i++; } storesign (a, sig); if (s[i]) { fprintf (stderr, "\nIllegal character in number: '%s'\n", s + i); exit (1); } } /* end of atomp */ void subint (lrs_mp a, lrs_mp b, lrs_mp c) /* compute c=a-b */ { copy (c, a); linint (a, 1, b, -1); } void decint (lrs_mp a, lrs_mp b) /* compute a=a-b */ { linint (a, 1, b, -1); } long myrandom (long num, long nrange) /* return a random number in range 0..nrange-1 */ { long i; i = (num * 401 + 673) % nrange; return (i); } long atos (char s[]) /* convert s to integer */ { long i, j; j = 0; for (i = 0; s[i] >= '0' && s[i] <= '9'; ++i) j = 10 * j + s[i] - '0'; return (j); } void stringcpy (char *s, char *t) /*copy t to s pointer version */ { while (((*s++) = (*t++)) != '\0'); } void rattodouble (lrs_mp a, lrs_mp b, double *x) /* convert lrs_mp rational to double */ { double y; mptodouble (a, &y); mptodouble (b, x); *x = y / (*x); } void atoaa (char in[], char num[], char den[]) /* convert rational string in to num/den strings */ { long i, j; for (i = 0; in[i] != '\0' && in[i] != '/'; i++) num[i] = in[i]; num[i] = '\0'; den[0] = '\0'; if (in[i] == '/') { for (j = 0; in[j + i + 1] != '\0'; j++) den[j] = in[i + j + 1]; den[j] = '\0'; } } /* end of atoaa */ void lcm (lrs_mp a, lrs_mp b) /* a = least common multiple of a, b; b is preserved */ { lrs_mp u, v; copy (u, a); copy (v, b); gcd (u, v); exactdivint (a, u, v); /* v=a/u no remainder*/ mulint (v, b, a); } /* end of lcm */ void reducearray (lrs_mp_vector p, long n) /* find largest gcd of p[0]..p[n-1] and divide through */ { lrs_mp divisor; lrs_mp Temp; long i = 0L; while ((i < n) && zero (p[i])) i++; if (i == n) return; copy (divisor, p[i]); storesign (divisor, POS); i++; while (i < n) { if (!zero (p[i])) { copy (Temp, p[i]); storesign (Temp, POS); gcd (divisor, Temp); } i++; } /* reduce by divisor */ for (i = 0; i < n; i++) if (!zero (p[i])) reduceint (p[i], divisor); } /* end of reducearray */ void reduceint (lrs_mp Na, lrs_mp Da) /* divide Na by Da and return */ { lrs_mp Temp; copy (Temp, Na); exactdivint (Temp, Da, Na); } void reduce (lrs_mp Na, lrs_mp Da) /* reduces Na Da by gcd(Na,Da) */ { lrs_mp Nb, Db, Nc, Dc; copy (Nb, Na); copy (Db, Da); storesign (Nb, POS); storesign (Db, POS); copy (Nc, Na); copy (Dc, Da); gcd (Nb, Db); /* Nb is the gcd(Na,Da) */ exactdivint (Nc, Nb, Na); exactdivint (Dc, Nb, Da); } long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd) /* +1 if Na*Nb > Nc*Nd */ /* -1 if Na*Nb < Nc*Nd */ /* 0 if Na*Nb = Nc*Nd */ { lrs_mp mc, md; mulint (Na, Nb, mc); mulint (Nc, Nd, md); linint (mc, ONE, md, -ONE); if (positive (mc)) return (1); if (negative (mc)) return (-1); return (0); } void notimpl (char s[]) { fflush (stdout); fprintf (stderr, "\nAbnormal Termination %s\n", s); exit (1); } void getfactorial (lrs_mp factorial, long k) /* compute k factorial in lrs_mp */ { lrs_mp temp; long i; itomp (ONE, factorial); for (i = 2; i <= k; i++) { itomp (i, temp); mulint (temp, factorial, factorial); } } /* end of getfactorial */ /***************************************************************/ /* Package of routines for rational arithmetic */ /***************************************************************/ void scalerat (lrs_mp Na, lrs_mp Da, long ka) /* scales rational by ka */ { lrs_mp Nt; copy (Nt, Na); itomp (ZERO, Na); linint (Na, ZERO, Nt, ka); reduce (Na, Da); } void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = ka*Na/Da +kb* Nb/Db and reduces answer by gcd(Nc,Dc) */ { lrs_mp c; mulint (Na, Db, Nc); mulint (Da, Nb, c); linint (Nc, ka, c, kb); /* Nc = (ka*Na*Db)+(kb*Da*Nb) */ mulint (Da, Db, Dc); /* Dc = Da*Db */ reduce (Nc, Dc); } void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = (Na/Da) / ( Nb/Db ) and reduces answer by gcd(Nc,Dc) */ { mulint (Na, Db, Nc); mulint (Da, Nb, Dc); reduce (Nc, Dc); } void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc) /* computes Nc/Dc = Na/Da * Nb/Db and reduces by gcd(Nc,Dc) */ { mulint (Na, Nb, Nc); mulint (Da, Db, Dc); reduce (Nc, Dc); } /* End package of routines for rational arithmetic */ /***************************************************************/ /* */ /* End of package for multiple precision arithmetic */ /* */ /***************************************************************/ void * xcalloc (long n, long s, long l, char *f) { void *tmp; tmp = calloc (n, s); if (tmp == 0) { char buf[200]; sprintf (buf, "\n\nFatal error on line %ld of %s", l, f); perror (buf); exit (1); } return tmp; } void lrs_getdigits (long *a, long *b) { /* send digit information to user */ *a = DIG2DEC (lrs_digits); *b = DIG2DEC (lrs_record_digits); return; } void lrs_default_digits_overflow () { fprintf (lrs_ofp, "\nOverflow at digits=%ld", DIG2DEC (lrs_digits)); fprintf (lrs_ofp, "\nInitialize lrs_mp_init with n > %ldL\n", DIG2DEC (lrs_digits)); exit (1); } /* end of lrsmp.c */ lrslib-043/game20000755001553201777760000000020511607605134013040 0ustar avisnogroup*game: player 2 H-representation linearity 1 6 begin 6 4 rational 0 0 -6 1 0 -2 -5 1 0 -3 -3 1 0 1 0 0 0 0 1 0 -1 1 1 0 end lrslib-043/game10000755001553201777760000000021711607605134013042 0ustar avisnogroup*game: player 1 H-representation linearity 1 6 begin 6 5 rational 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 -1 0 -4 1 0 0 -2 -3 1 -1 1 1 1 0 end lrslib-043/redund.c0000755001553201777760000000023011607605134013545 0ustar avisnogroup#include #include #include "lrslib.h" int main (int argc, char *argv[]) { redund_main(argc,argv); printf("\n"); return 0; } lrslib-043/buffer.c0000755001553201777760000000541111607605134013543 0ustar avisnogroup /* buffer.c Reads standard input and builds a circular buffer of maxbuffer lines */ /* input line should have max length maxline and is printed only if it is not in the buffer */ /* calling arguments: maxline maxbuffer */ /* defaults: 5000 50 */ #include #include #include #define MAXBUFFER 5000 /*max number of lines in buffer */ char *line; int maxline; int Getline(void); void notimpl(char s[]); int main(int argc, char *argv[]) { extern int maxline; extern char *line; int i; int bufsize; int next; int count, counton; char *c; char *buffer [MAXBUFFER]; int maxbuffer=50; void *calloc(); maxline=5000; /* allocate space for buffer */ if (argc >= 2 ) maxline=atoi(argv[1])+2; /* allow for \n and \0 */ if (maxline <= 2 ) notimpl("line length must be greater than zero"); if (argc >= 3 ) maxbuffer=atoi(argv[2]); if (maxbuffer <= 0 ) notimpl("buffer length must be greater than zero"); for(i=0;i 0 ) { i=0; if(strncmp(line,"end",3)==0) counton=0; while ( i <= bufsize && (strcmp(line,buffer[i])) != 0 ) i++; if ( i > bufsize ) /* write out line and put in buffer */ { next++; if ( next > maxbuffer-1 ) next=0; if ( bufsize < maxbuffer-1 ) bufsize++; c=strcpy(buffer[next],line); printf("%s",line); if(counton)count++; } if(strncmp(line,"begin",5)==0) counton=1; } printf("\n*Number of output lines between begin/end = %d",count); if(count > maxbuffer ) printf("\n*Buffer size of %d lines exceeded-some duplicates may remain",maxbuffer); else printf("\n*All duplicates removed"); printf("\n"); return 0; } /* getline from KR P.32 */ int Getline(void) { int c,i; extern int maxline; extern char *line; for (i=0;i #include #include "lrslib.h" #define MAXLINE 1000 /* Usage: setupnash game game1.ine game2.ine */ /* Reads input file game containing */ /* m n */ /* A matrix (m by n rationals ) */ /* B matrix (m by n rationals ) */ /* Outputs: two files game1.ine game2.ine */ /* that are used by nash */ int main (int argc, char *argv[]) { long m,n,i,j; long Anum[100][100], Bnum[100][100]; long Aden[100][100], Bden[100][100]; if ( argc < 3 ) { printf ("\nUsage: setupnash infile outfile1 outfile2\n"); return(FALSE); } if ((lrs_ifp = fopen (argv[1], "r")) == NULL) { printf ("\nBad input file name\n"); return (FALSE); } else printf ("\n*Input taken from file %s", argv[1]); if(fscanf(lrs_ifp,"%ld %ld",&m,&n)==EOF) { printf("\nInvalid m,n"); return(FALSE); } if( m > 1000 || n > 1000) { printf ("\nm=%ld n=%ld",m,n); printf ("\nBoth m and n must at most 1000\n"); return(FALSE); } /* process input file */ /* read A matrix */ for (i=0;i #include #include "lrslib.h" #define MAXCOL 1000 /* maximum number of colums */ long num[MAXCOL]; long den[MAXCOL]; void makecube (lrs_dic *P, lrs_dat *Q); int main (int argc, char *argv[]) { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_dat *Q; /* structure for holding static problem data */ lrs_mp_vector output; /* one line of output:ray,vertex,facet,linearity */ long i; long m; /* number of constraints in the problem */ long n; /* number of variables in the problem + 1 */ long col; /* output column index for dictionary */ /* Global initialization - done once */ if ( !lrs_init ("\n*lpdemo:")) return 1; /* generate cubes with dimension d */ for(i=1;i<=2;i++) { n=10; m=18; /* number of rows for cube dimension d */ /* allocate and init structure for static problem data */ Q = lrs_alloc_dat ("LRS globals"); if (Q == NULL) return 1; Q->m=m; Q->n=n; Q->lponly=TRUE; /* we do not want all vertices generated! */ output = lrs_alloc_mp_vector (Q->n); P = lrs_alloc_dic (Q); /* allocate and initialize lrs_dic */ if (P == NULL) return 1; /* Build polyhedron: constraints and objective */ makecube(P,Q); /* Solve the LP */ if (!lrs_solve_lp(P,Q)) return 1; /* Print output */ prat ("\nObjective value = ", Q->objnum, Q->objden); for (col = 0; col < Q->n; col++) if (lrs_getsolution (P, Q, output, col)) lrs_printoutput (Q, output); /* free space : do not change order of next lines! */ lrs_clear_mp_vector (output, Q->n); lrs_free_dic (P,Q); /* deallocate lrs_dic */ lrs_free_dat (Q); /* deallocate lrs_dat */ } /* end of loop for i=1 ... */ lrs_close ("lpdemo:"); printf("\n"); return 0; } /* end of main */ /* code to generate unit cube and objective function */ void makecube (lrs_dic *P, lrs_dat *Q) /* generate H-representation of a unit hypercube */ /* with dimension n-1 */ { long num[MAXCOL]; long den[MAXCOL]; long row, j; long m=Q->m; long n=Q->n; for (row=1;row<=m;row++) { /* set up a cube */ for(j=0;j *(b) ) #define itomp(in, a) *(a) = in #define linint(a, ka, b, kb) *(a) = *(a) * ka + *(b) * kb #define mulint(a, b, c) *(c) = *(a) * *(b) #define one(a) (*(a) == 1) #define negative(a) (*(a) < 0) #define normalize(a) (void) 0 #define positive(a) (*(a) > 0) #define sign(a) (*(a) < 0 ? NEG : POS) #define storesign(a, sa) (*(a) = labs(*(a)) * sa) #define subint(a, b, c) *(c) = *(a) - *(b) #define zero(a) (*(a) == 0) /* * convert between decimal and machine (longword digits). Notice lovely * implementation of ceiling function :-) */ #define DEC2DIG(d) ( (d) % BASE_DIG ? (d)/BASE_DIG+1 : (d)/BASE_DIG) #define DIG2DEC(d) ((d)*BASE_DIG) #ifndef OMIT_SIGNALS #include #include /* labs */ #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #ifndef OMIT_TIMES void ptimes (); #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*************/ /* typedefs */ /*************/ typedef long lrs_mp[1]; /* type lrs_mp holds one long integer */ typedef long *lrs_mp_t; typedef long **lrs_mp_vector; typedef long ***lrs_mp_matrix; /*********************/ /*global variables */ /*********************/ long lrs_digits; /* max permitted no. of digits */ long lrs_record_digits; /* this is the biggest acheived so far. */ FILE *lrs_ifp; /* input file pointer */ FILE *lrs_ofp; /* output file pointer */ /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ long lrs_mp_init (long dec_digits, FILE * lrs_ifp, FILE * lrs_ofp); /* max number of decimal digits, fps */ #define lrs_alloc_mp(a) #define lrs_clear_mp(a) lrs_mp_t lrs_alloc_mp_t(); /* dynamic allocation of lrs_mp */ lrs_mp_vector lrs_alloc_mp_vector (long n); /* allocate lrs_mp_vector for n+1 lrs_mp numbers */ lrs_mp_matrix lrs_alloc_mp_matrix (long m, long n); /* allocate lrs_mp_matrix for m+1 x n+1 lrs_mp */ void lrs_clear_mp_vector (lrs_mp_vector a, long n); void lrs_clear_mp_matrix (lrs_mp_matrix a, long m, long n); /*********************************************************/ /* Core library functions - depend on mp implementation */ /******************************************************* */ void atomp (const char s[], lrs_mp a); /* convert string to lrs_mp integer */ long compare (lrs_mp a, lrs_mp b); /* a ? b and returns -1,0,1 for <,=,> */ void gcd (lrs_mp u, lrs_mp v); /* returns u=gcd(u,v) destroying v */ void mptodouble (lrs_mp a, double *x); /* convert lrs_mp to double */ long mptoi (lrs_mp a); /* convert lrs_mp to long integer */ void pmp (char name[], lrs_mp a); /* print the long precision integer a */ void prat (const char name[], lrs_mp Nt, lrs_mp Dt); /* reduce and print Nt/Dt */ void readmp (lrs_mp a); /* read an integer and convert to lrs_mp */ long readrat (lrs_mp Na, lrs_mp Da); /* read a rational or int and convert to lrs_mp */ void reduce (lrs_mp Na, lrs_mp Da); /* reduces Na Da by gcd(Na,Da) */ /*********************************************************/ /* Standard arithmetic & misc. functions */ /* should be independent of mp implementation */ /******************************************************* */ void atoaa (const char in[], char num[], char den[]); /* convert rational string in to num/den strings */ long atos (char s[]); /* convert s to integer */ long comprod (lrs_mp Na, lrs_mp Nb, lrs_mp Nc, lrs_mp Nd); /* +1 if Na*Nb > Nc*Nd,-1 if Na*Nb > Nc*Nd else 0 */ void divrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc = (Na/Da) /( Nb/Db ) and reduce */ void getfactorial (lrs_mp factorial, long k); /* compute k factorial in lrs_mp */ void linrat (lrs_mp Na, lrs_mp Da, long ka, lrs_mp Nb, lrs_mp Db, long kb, lrs_mp Nc, lrs_mp Dc); void lcm (lrs_mp a, lrs_mp b); /* a = least common multiple of a, b; b is saved */ void mulrat (lrs_mp Na, lrs_mp Da, lrs_mp Nb, lrs_mp Db, lrs_mp Nc, lrs_mp Dc); /* computes Nc/Dc=(Na/Da)*(Nb/Db) and reduce */ long myrandom (long num, long nrange); /* return a random number in range 0..nrange-1 */ void notimpl (char s[]); /* bail out - help! */ void rattodouble (lrs_mp a, lrs_mp b, double *x); /* convert lrs_mp rational to double */ void reduceint (lrs_mp Na, lrs_mp Da); /* divide Na by Da and return it */ void reducearray (lrs_mp_vector p, long n); /* find gcd of p[0]..p[n-1] and divide through by */ void scalerat (lrs_mp Na, lrs_mp Da, long ka); /* scales rational by ka */ /**********************************/ /* Miscellaneous functions */ /******************************** */ void lrs_getdigits (long *a, long *b); /* send digit information to user */ void stringcpy (char *s, char *t); /* copy t to s pointer version */ void *calloc (); void *malloc (); void *xcalloc (long n, long s, long l, char *f); void lrs_default_digits_overflow (); /* end of lrs_mp.h (vertex enumeration using lexicographic reverse search) */