lrslib-071a/0000700060175606010010000000000013742506544012636 5ustar avisなしlrslib-071a/2nash.c0000700060175606010010000000466113742506301014016 0ustar avisなし// 2nash.c v1.0a Jan 15, 2009 // Hack of nlrs.c by Conor Meagher to run lrs simultaneously on n processors for n input files // runs lrsnash 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 #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, "lrsnash %s %s > out%i", argv[1], argv[2], l); } else { int n= sprintf(buffer, "lrsnash %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("lrsnash %s %s finished first\n", argv[1], argv[2]); else { printf("lrsnash %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"); 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-071a/buffer.c0000700060175606010010000000541513742506302014253 0ustar avisなし /* 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: 50000 500 */ #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=500; void *calloc(); maxline=50000; /* 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 "lrsdriver.h" #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 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, 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-071a/cube.ext0000700060175606010010000000022513742506306014274 0ustar avisなしcube V-representation begin 8 4 rational 1 1 1 1 1 -1 1 1 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-071a/cube.ine0000700060175606010010000000017313742506306014251 0ustar avisなしcube H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 0 -1 1 0 -1 0 end lrslib-071a/ext/0000700060175606010010000000000013742506305013431 5ustar avisなしlrslib-071a/ext/metric/0000700060175606010010000000000013742506305014714 5ustar avisなしlrslib-071a/ext/metric/cp4.ext0000700060175606010010000000030513742506305016125 0ustar avisなしcp4.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-071a/ext/metric/cp5.ext0000700060175606010010000000113313742506305016126 0ustar avisなしcp5.ext V-representation *5 point cut polytope 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-071a/ext/metric/cp6.ext0000700060175606010010000000305013742506305016127 0ustar avisなしcp6.ext 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-071a/ext/metric/cp7.ext0000700060175606010010000000577613742506305016151 0ustar avisなしcp7.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-071a/ext/metric/mp5.ext0000700060175606010010000000266213742506305016150 0ustar avisなしmp5.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-071a/ext/test/0000700060175606010010000000000013742506306014411 5ustar avisなしlrslib-071a/ext/test/c30-15.ext0000700060175606010010000001117413742506305015751 0ustar avisなし*cyclic polytope n=30, d=15 V-representation begin 30 16 integer 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 1 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 1 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125 1 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016 78364164096 470184984576 1 7 49 343 2401 16807 117649 823543 5764801 40353607 282475249 1977326743 13841287201 96889010407 678223072849 4747561509943 1 8 64 512 4096 32768 262144 2097152 16777216 134217728 1073741824 8589934592 68719476736 549755813888 4398046511104 35184372088832 1 9 81 729 6561 59049 531441 4782969 43046721 387420489 3486784401 31381059609 282429536481 2541865828329 22876792454961 205891132094649 1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 100000000000 1000000000000 10000000000000 100000000000000 1000000000000000 1 11 121 1331 14641 161051 1771561 19487171 214358881 2357947691 25937424601 285311670611 3138428376721 34522712143931 379749833583241 4177248169415651 1 12 144 1728 20736 248832 2985984 35831808 429981696 5159780352 61917364224 743008370688 8916100448256 106993205379072 1283918464548864 15407021574586368 1 13 169 2197 28561 371293 4826809 62748517 815730721 10604499373 137858491849 1792160394037 23298085122481 302875106592253 3937376385699289 51185893014090757 1 14 196 2744 38416 537824 7529536 105413504 1475789056 20661046784 289254654976 4049565169664 56693912375296 793714773254144 11112006825558016 155568095557812224 1 15 225 3375 50625 759375 11390625 170859375 2562890625 38443359375 576650390625 8649755859375 129746337890625 1946195068359375 29192926025390625 437893890380859375 1 16 256 4096 65536 1048576 16777216 268435456 4294967296 68719476736 1099511627776 17592186044416 281474976710656 4503599627370496 72057594037927936 1152921504606846976 1 17 289 4913 83521 1419857 24137569 410338673 6975757441 118587876497 2015993900449 34271896307633 582622237229761 9904578032905937 168377826559400929 2862423051509815793 1 18 324 5832 104976 1889568 34012224 612220032 11019960576 198359290368 3570467226624 64268410079232 1156831381426176 20822964865671168 374813367582081024 6746640616477458432 1 19 361 6859 130321 2476099 47045881 893871739 16983563041 322687697779 6131066257801 116490258898219 2213314919066161 42052983462257059 799006685782884121 15181127029874798299 1 20 400 8000 160000 3200000 64000000 1280000000 25600000000 512000000000 10240000000000 204800000000000 4096000000000000 81920000000000000 1638400000000000000 32768000000000000000 1 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176496/184057 0 1295312/184057 0 0 0 0 1 0 0 3710000/620283 5200000/620283 0 0 0 0 0 0 1 1209010000/564094417 0 3851240000/564094417 3690360000/564094417 0 0 0 0 0 0 1 62384303750/27114776277 0 181192219375/27114776277 174854417500/27114776277 4372264375/27114776277 0 0 0 0 0 1 1396426381130000/386182442237881 723524651350000/386182442237881 1819037257580000/386182442237881 1813966897640000/386182442237881 365674941440000/386182442237881 0 0 0 0 0 1 1144638394230000/288144185543041 0 1268976764830000/288144185543041 843946135640000/288144185543041 842578440990000/288144185543041 0 0 0 723524651350000/288144185543041 0 1 0 0 87427500/14863547 93274500/14863547 0 52451500/14863547 0 0 0 0 1 0 0 29947500/4335923 15923000/4335923 0 22298500/4335923 0 0 0 0 1 279515745000/124965304289 0 963053730000/124965304289 328513805000/124965304289 0 496231465000/124965304289 0 0 0 0 1 369273935000/145215982207 0 1004570790000/145215982207 692331085000/145215982207 0 347934475000/145215982207 0 0 0 0 end volume *printcobasis 1 lrslib-071a/ext/test/vol2.ext0000600060175606010010000000053013742506305016014 0ustar avisなしvol2.ext V-representation begin 10 6 integer 1 -231 -12 -568 -351 -308 1 -91 -441 -927 -33 -330 1 -39 -924 -541 -444 -838 1 -425 -679 -140 -764 -960 1 -686 -717 -137 -721 -833 1 -920 -164 -220 -640 -262 1 -365 -685 -932 -424 -928 1 -539 -941 -513 -290 -622 1 -572 -580 -822 -964 -725 1 -19 -976 -609 -965 -158 end printcobasis volume lrslib-071a/float2rat.c0000700060175606010010000000457313742506302014704 0ustar avisなし/* * 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 #include #include "lrsdriver.h" #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) { fprintf(lrs_ofp, "%s\n", line); 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"); strcpy(Q->fname,"fourier"); /* program name */ 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-071a/games/0000700060175606010010000000000013742506301013721 5ustar avisなしlrslib-071a/games/game0000700060175606010010000000003613742506301014557 0ustar avisなし3 2 0 6 2 5 3 3 1 0 0 2 4 3 lrslib-071a/games/game10000700060175606010010000000021713742506301014641 0ustar avisなし*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 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pivots=1404509 *Player 2: vertices=14 bases=1 pivots=1851723 *Overflow checking on lrslong arithmetic *lrsnash:lrslib v.6.3 2018.5.1(128bit,lrslong.h) *445.359u 0.000s 4676Kb 2007 flts 0 swaps 0 blks-in 0 blks-out lrslib-071a/games/gamem.gmp0000700060175606010010000001254613742506301015527 0ustar avisなし*lrsnash:lrslib v.6.3 2018.5.1(64bit,lrsgmp.h) gmp v.6.1 2 1/2449 0 0 0 0 144/2449 0 0 2304/2449 2304/2449 1 0 0 144/12245 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2449 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12096/12245 2304/2449 2 1/2449 0 0 0 0 144/2449 0 0 2304/2449 2304/2449 1 0 0 144/12245 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2449 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12096/12245 2304/2449 2 0 0 0 0 0 1/17 0 0 16/17 16/17 1 0 0 1/85 0 0 0 0 0 0 0 0 0 0 0 0 0 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bases=1404287 pivots=1404509 *Player 2: vertices=14 bases=1 pivots=1851723 *lrsnash:lrslib v.6.3 2018.5.1(64bit,lrsgmp.h) *934.875u 0.015s 5032Kb 2910 flts 0 swaps 0 blks-in 0 blks-out lrslib-071a/games/gamemp0000700060175606010010000000727113742506301015124 0ustar avisなし40 16 0 -1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 2 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 2 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 2 -1 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 2 -1 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 0 0 0 0 0 2 0 -1 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 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4/7 2 1/5 0 0 0 0 0 2/5 0 0 0 2/5 0 0 0 0 0 2/5 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 1 0 5/7 0 0 0 0 0 0 0 0 0 1/7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/7 0 0 0 0 0 0 0 0 0 0 0 0 4/7 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 1 0 2/3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/3 0 0 0 0 0 0 0 0 0 0 0 0 2/3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 2 1/5 0 0 0 0 0 2/5 0 0 0 2/5 0 0 0 0 0 2/5 1 1/8 5/8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/4 0 0 0 0 0 0 0 0 1/2 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 2 1/5 0 0 0 0 0 2/5 0 0 0 2/5 0 0 0 0 0 2/5 1 0 5/7 0 0 0 0 0 1/7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/7 0 0 0 0 0 0 0 0 4/7 2 1/5 0 0 0 0 0 2/5 0 0 0 2/5 0 0 0 0 0 2/5 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 1 0 5/7 0 0 0 0 0 0 0 0 0 1/7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/7 0 0 0 0 0 0 0 0 4/7 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 1 0 2/3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/3 0 0 0 0 0 0 0 0 2/3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 2 1/5 0 0 0 0 0 2/5 0 0 0 2/5 0 0 0 0 0 2/5 1 0 2/3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/3 0 0 0 0 2/3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 2 1/5 0 0 0 0 0 2/5 0 0 0 2/5 0 0 0 0 0 2/5 1 0 2/3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/3 2/3 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 1/2 0 0 0 1/2 0 0 0 0 0 1/2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1/3 0 0 0 0 0 2/3 0 0 0 0 0 0 0 0 0 2/3 2 1/5 0 0 0 0 0 2/5 0 0 0 2/5 0 0 0 0 0 2/5 1 0 2/3 0 0 0 0 0 0 0 0 0 0 0 0 0 1/3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2/3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 *Number of equilibria found: 14952 *Player 1: vertices=8550740 bases=44081979 pivots=44082062 *Player 2: vertices=14952 bases=15975 pivots=18953496 *Overflow checking on lrslong arithmetic *lrsnash:lrslib v.6.3 2018.5.1(64bit,lrslong.h) *1619.468u 0.015s 4788Kb 1232 flts 0 swaps 0 blks-in 0 blks-out lrslib-071a/hvref.c0000700060175606010010000000632113742506306014115 0ustar avisなし#include #include #include /****************************************************************** December 30,2019 Program to make a cross reference list between H and V reps Usage (same for ext file): Add printcobasis and incidence options to cube.ine % lrs cube.ine cube.ext % xref cube.ext Edit the output file cube.ext.x so that the second line contains two integers rows maxindex where rows >= # output lines in cube.ext.x maxindex >= # input lines in cube.ine or just use 0 0 and the program will tell you which values to use % hvref cube.ext.x gives V to H and H to V cross reference tables **********************************************************************/ int main(int argc, char *argv[]) { int i=0, j=0; int first=1; int Hrep=1; int rows=0, maxindex=0; int inrows=0, outrows=0; int rowindex; char s[10000]; int x; int *nrow; int **table; FILE *lrs_ifp; if(argc > 1) { if((lrs_ifp = fopen (argv[1], "r")) == NULL) { printf ("\nBad input file name\n"); return 1; } } else lrs_ifp=stdin; x=fscanf(lrs_ifp,"%s", s); while(first && x != EOF ) { if(strcmp(s,"H-representation") == 0 || strcmp(s,"V-representation") == 0) { if(strcmp(s,"H-representation") == 0) printf("\nH-representation"); else { printf("\nV-representation"); Hrep=0; } first=0; fscanf(lrs_ifp,"%d %d",&rows,&maxindex); printf("\n%d %d",rows,maxindex); nrow=(int *)malloc((maxindex+2)*sizeof(int)); table = (int **)malloc((rows+2) * (maxindex+2) * sizeof(int)); for (i=0;i<=maxindex+1;i++) table[i] = (int*)malloc((rows+2) * sizeof(int)); for(i=0;i<=maxindex;i++) { nrow[i]=0; for(j=0;j<=rows;j++) table[i][j]=0; } } if(first) x=fscanf(lrs_ifp,"%s", s); } while(x != EOF) { first=1; x=fscanf(lrs_ifp,"%s", s); while(x != EOF && strcmp(s,"#") !=0) { i=atoi(s); if(first==1) { printf("\n%d:",i); rowindex=i; inrows++; } else { if(i>outrows) outrows=i; if(i <= maxindex && nrow[i] < rows) { nrow[i]++; table[i][ nrow[i]]=rowindex; } printf(" %d",i); } x=fscanf(lrs_ifp,"%s", s); first=0; } } if(inrows <= rows && outrows <= maxindex) { if(Hrep) printf("\n\nV-representation"); else printf("\n\nH-representation"); printf("\n%d %d",outrows,inrows); for(i=1;i<=outrows;i++) { printf("\n%d:",i); for(j=1;j<=nrow[i];j++) printf(" %d",table[i][j]); } } else printf("\n\nInput parameters too small, rerun with:"); printf("\ninput rows=%d maxindex=%d",inrows,outrows); printf("\n"); free(nrow); for (i=0;i<=maxindex+1;i++) free(table[i]); free(table); return 0; } lrslib-071a/ine/0000700060175606010010000000000013742506305013404 5ustar avisなしlrslib-071a/ine/cocoa13/0000700060175606010010000000000013742506304014633 5ustar avisなしlrslib-071a/ine/cocoa13/bv10.ine0000700060175606010010000007102213742506303016104 0ustar avisなし*ext form for perm H-representation linearity 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 begin 129 111 integer 0 10 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 4 0 0 0 0 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-12 1 4 4 3 6 -4 -12 8 -2 -4 4 12 -8 -12 4 8 4 -2 -12 8 -8 4 12 -4 12 12 12 -8 8 -4 -12 -4 8 -4 -12 6 4 -8 1 3 -4 -4 4 4 4 -12 -8 8 4 -4 -2 -2 4 -4 3 4 -4 6 4 -4 -2 1 1 -8 0 6 3 18 -6 -6 0 0 -14 -12 -12 0 2 0 2 0 2 0 0 12 12 6 -1 -6 -6 3 0 0 6 12 6 0 -6 0 0 6 6 12 6 -6 -6 -12 0 -6 0 0 0 0 0 0 -12 0 -6 0 -12 -2 -6 0 6 0 1 -3 -2 -12 6 4 4 6 0 12 6 -2 0 0 6 12 -3 -6 -12 0 -6 2 6 -1 end lrslib-071a/ine/redund/0000700060175606010010000000000013742506305014665 5ustar avisなしlrslib-071a/ine/redund/cube.ine0000700060175606010010000000020613742506305016301 0ustar avisなしcube H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 0 -1 1 0 -1 0 end redund 0 0 lrslib-071a/ine/redund/metric80_16.ine0000700060175606010010000000552413742506305017334 0ustar avisなしmetric80_16.ine H-representation *metric polytope on 6 points linearity 6 17 18 10 1 2 3 begin 80 16 integer 0 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1 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0 0 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 6 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 6 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 6 -1 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 6 -1 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 6 0 -1 -1 0 0 0 0 0 0 -1 0 0 0 0 0 6 0 -1 0 -1 0 0 0 0 0 0 -1 0 0 0 0 6 0 -1 0 0 -1 0 0 0 0 0 0 -1 0 0 0 6 0 0 -1 -1 0 0 0 0 0 0 0 0 -1 0 0 6 0 0 -1 0 -1 0 0 0 0 0 0 0 0 -1 0 6 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 -1 end redund 1 80 *noredundcheck lrslib-071a/ine/redund/mp5.ine0000700060175606010010000000207713742506305016074 0ustar avisなし*mp5.ine *metric polytope on 5 points H-representation linearity 3 1 2 3 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 redund 0 0 lrslib-071a/ine/redund/mp5a.ine0000700060175606010010000000212113742506305016223 0ustar avisなし*mp5.ine *metric polytope on 5 points *last row changed to be redundant 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 4 0 -2 -1 -1 0 0 0 -1 -1 0 end redund 1 40 lrslib-071a/ine/redund/mp5b.ine0000700060175606010010000000216313742506305016232 0ustar avisなし*mp5.ine *metric polytope on 5 points *last row is same as first H-representation begin 41 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 2 -1 -1 0 0 -1 0 0 0 0 0 end redund 1 41 *noredundcheck lrslib-071a/ine/redund/mp5c.ine0000700060175606010010000000210113742506305016223 0ustar avisなし*mp5.ine *metric polytope on 5 points H-representation linearity 3 1 2 3 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 redund 21 40 lrslib-071a/ine/redund/non_par.ine0000700060175606010010000000012313742506305017015 0ustar avisなしH-representation linearity 1 1 begin 3 3 integer 0 1 -1 0 1 0 0 0 1 end redund 2 3 lrslib-071a/ine/redund/par.ine0000700060175606010010000000033113742506305016144 0ustar avisなし*non_par with linearity given as two inequalities *either redund option deletes the given inequality *both cannot be simultaneously deleted H-representation begin 4 3 integer 0 -1 1 0 1 -1 0 1 0 0 0 1 end redund 1 4 lrslib-071a/ine/test/0000700060175606010010000000000013742506303014361 5ustar avisなしlrslib-071a/ine/test/cross4.ine0000700060175606010010000000040313742506303016273 0ustar avisなしcross4.ine H-representation begin 16 5 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 end lrslib-071a/ine/test/cube.ine0000700060175606010010000000027713742506303016005 0ustar avisなしcube *linearity 3 1 2 3 H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 0 -1 1 0 -1 0 end *extract 2 1 2 *minimize 0 1 2 3 printcobasis 1 lrslib-071a/ine/test/cyclic17_8.ine0000700060175606010010000000210013742506303016717 0ustar avisなしcylic17-8.ine begin 17 9 integer 1 -72 516 -4608 36156 -294912 2349516 -18874368 150850236 1 -63 381 -3087 20901 -151263 1049061 -7411887 51738501 1 -54 264 -1944 10956 -69984 410124 -2519424 14971836 1 -45 165 -1125 4917 -28125 130845 -703125 3370917 1 -36 84 -576 1596 -9216 27084 -147456 445116 1 -27 21 -243 21 -2187 -3219 -19683 -85659 1 -18 -24 -72 -564 -288 -9204 -1152 -142404 1 -9 -51 -9 -699 -9 -9771 -9 -144699 1 0 -60 0 -708 0 -9780 0 -144708 1 9 -51 9 -699 9 -9771 9 -144699 1 18 -24 72 -564 288 -9204 1152 -142404 1 27 21 243 21 2187 -3219 19683 -85659 1 36 84 576 1596 9216 27084 147456 445116 1 45 165 1125 4917 28125 130845 703125 3370917 1 54 264 1944 10956 69984 410124 2519424 14971836 1 63 381 3087 20901 151263 1049061 7411887 51738501 1 72 516 4608 36156 294912 2349516 18874368 150850236 end lrslib-071a/ine/test/diamond.ine0000700060175606010010000000023713742506303016476 0ustar avisなしdiamond.ine 93.7.6 Unit diamond centred at origin Last two inequalities define vertex (-1/2,0) begin 4 3 rational 1/2 -1 -1 1/2 -1 1 1/2 1 -1 1/2 1 1 end lrslib-071a/ine/test/in0.ine0000700060175606010010000000022113742506303015542 0ustar avisなしin0.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 lrslib-071a/ine/test/in1.ine0000700060175606010010000000133113742506303015546 0ustar avisなしin1.ine begin 34 5 integer 1 -299 -534 815 807 1 -887 -399 -867 -543 1 683 632 958 -181 1 -756 681 -658 470 1 -99 135 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avisなしlrslib-071a/ine/test-062/porta/bv7.ine.ieq0000700060175606010010000000236513742506305017776 0ustar avisなしDIM = 56 INEQUALITIES_SECTION -7x1-6x8-5x15-4x22-3x29-2x36-1x43+1x50==0 -7x2-6x9-5x16-4x23-3x30-2x37-1x44+1x51==0 -7x3-6x10-5x17-4x24-3x31-2x38-1x45+1x52==0 -7x4-6x11-5x18-4x25-3x32-2x39-1x46+1x53==0 -7x5-6x12-5x19-4x26-3x33-2x40-1x47+1x54==0 -7x6-6x13-5x20-4x27-3x34-2x41-1x48+1x55==0 -7x7-6x14-5x21-4x28-3x35-2x42-1x49+1x56==0 -1x1-1x2-1x3-1x4-1x5-1x6-1x7==-1 -1x8-1x9-1x10-1x11-1x12-1x13-1x14==-1 -1x15-1x16-1x17-1x18-1x19-1x20-1x21==-1 -1x22-1x23-1x24-1x25-1x26-1x27-1x28==-1 -1x29-1x30-1x31-1x32-1x33-1x34-1x35==-1 -1x36-1x37-1x38-1x39-1x40-1x41-1x42==-1 -1x43-1x44-1x45-1x46-1x47-1x48-1x49==-1 -1x1-1x8-1x15-1x22-1x29-1x36-1x43==-1 -1x2-1x9-1x16-1x23-1x30-1x37-1x44==-1 -1x3-1x10-1x17-1x24-1x31-1x38-1x45==-1 -1x4-1x11-1x18-1x25-1x32-1x39-1x46==-1 -1x5-1x12-1x19-1x26-1x33-1x40-1x47==-1 -1x6-1x13-1x20-1x27-1x34-1x41-1x48==-1 -1x1<=0 -1x2<=0 -1x3<=0 -1x4<=0 -1x5<=0 -1x6<=0 -1x7<=0 -1x8<=0 -1x9<=0 -1x10<=0 -1x11<=0 -1x12<=0 -1x13<=0 -1x14<=0 -1x15<=0 -1x16<=0 -1x17<=0 -1x18<=0 -1x19<=0 -1x20<=0 -1x21<=0 -1x22<=0 -1x23<=0 -1x24<=0 -1x25<=0 -1x26<=0 -1x27<=0 -1x28<=0 -1x29<=0 -1x30<=0 -1x31<=0 -1x32<=0 -1x33<=0 -1x34<=0 -1x35<=0 -1x36<=0 -1x37<=0 -1x38<=0 -1x39<=0 -1x40<=0 -1x41<=0 -1x42<=0 -1x43<=0 -1x44<=0 -1x45<=0 -1x46<=0 -1x47<=0 -1x48<=0 -1x49<=0 END lrslib-071a/ine/test-062/porta/c30-15.ext.poi0000700060175606010010000001100313742506305020133 0ustar avisなしDIM = 15 CONV_SECTION 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016 78364164096 470184984576 7 49 343 2401 16807 117649 823543 5764801 40353607 282475249 1977326743 13841287201 96889010407 678223072849 4747561509943 8 64 512 4096 32768 262144 2097152 16777216 134217728 1073741824 8589934592 68719476736 549755813888 4398046511104 35184372088832 9 81 729 6561 59049 531441 4782969 43046721 387420489 3486784401 31381059609 282429536481 2541865828329 22876792454961 205891132094649 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 100000000000 1000000000000 10000000000000 100000000000000 1000000000000000 11 121 1331 14641 161051 1771561 19487171 214358881 2357947691 25937424601 285311670611 3138428376721 34522712143931 379749833583241 4177248169415651 12 144 1728 20736 248832 2985984 35831808 429981696 5159780352 61917364224 743008370688 8916100448256 106993205379072 1283918464548864 15407021574586368 13 169 2197 28561 371293 4826809 62748517 815730721 10604499373 137858491849 1792160394037 23298085122481 302875106592253 3937376385699289 51185893014090757 14 196 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-1x2-1x4+1x11<=0 -1x2-1x5+1x12<=0 -1x3-1x4+1x13<=0 -1x3-1x5+1x14<=0 -1x4-1x5+1x15<=0 -2x1-2x2-2x3-2x4-2x5+1x6+1x7+1x8+1x9+1x10+1x11+1x12+1x13+1x14+1x15<=2 -1x2-1x3+1x10<=0 +1x1-1x2-1x6<=0 +2x1-2x2-2x3-2x4-2x5-1x6-1x7-1x8-1x9+1x10+1x11+1x12+1x13+1x14+1x15<=0 +2x1-1x2-1x3-1x4-1x5-2x6-2x7-2x8-2x9+1x10+1x11+1x12+1x13+1x14+1x15<=0 -1x1+1x2-2x3+1x4+1x5-1x6+2x7-1x8-1x9-2x10+1x11+1x12-2x13-2x14+1x15<=0 -1x1+1x2+1x3-2x4+1x5-1x6-1x7+2x8-1x9+1x10-2x11+1x12-2x13+1x14-2x15<=0 +2x1-1x2-1x3+1x4+1x5-2x6-2x7+2x8+2x9+1x10-1x11-1x12-1x13-1x14+1x15<=2 +1x1-2x2-1x3+1x4+1x5-2x6-1x7+1x8+1x9+2x10-2x11-2x12-1x13-1x14+1x15<=0 +2x1-1x2+1x3+1x4-1x5-2x6+2x7+2x8-2x9-1x10-1x11+1x12+1x13-1x14-1x15<=2 +1x1-2x2+1x3+1x4-1x5-2x6+1x7+1x8-1x9-2x10-2x11+2x12+1x13-1x14-1x15<=0 +1x1-2x2-1x3-1x4-1x5-2x6-1x7-1x8-1x9+2x10+2x11+2x12+1x13+1x14+1x15<=2 +2x1-1x2+1x3-1x4+1x5-2x6+2x7-2x8+2x9-1x10+1x11-1x12-1x13+1x14-1x15<=2 +1x1-2x2+1x3-1x4+1x5-2x6+1x7-1x8+1x9-2x10+2x11-2x12-1x13+1x14-1x15<=0 -1x1+1x2+1x3+1x4-2x5-1x6-1x7-1x8+2x9+1x10+1x11-2x12+1x13-2x14-2x15<=0 -1x6+1x9-1x12<=0 +1x1-1x2-1x3-1x4-1x6-1x7-1x8+1x10+1x11+1x13<=0 -1x1+2x2+1x3+1x4-1x5-2x6-1x7-1x8+1x9+2x10+2x11-2x12+1x13-1x14-1x15<=2 -2x1+1x2+1x3+1x4-1x5-2x6-2x7-2x8+2x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 -1x2-1x3-1x4+1x5+1x10+1x11-1x12+1x13-1x14-1x15<=0 +1x1-2x2-1x3-1x4+1x5-2x6-1x7-1x8+1x9+2x10+2x11-2x12+1x13-1x14-1x15<=0 -1x6-1x7-1x8+1x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 -1x1-2x2+1x3+1x4+1x5+2x6-1x7-1x8-1x9-2x10-2x11-2x12+1x13+1x14+1x15<=0 +2x1-2x2+2x3-2x4+2x5-1x6+1x7-1x8+1x9-1x10+1x11-1x12-1x13+1x14-1x15<=2 +1x1-1x2+1x3-1x4+2x5-1x6+1x7-1x8+2x9-1x10+1x11-2x12-1x13+2x14-2x15<=2 -1x2+1x5-1x12<=0 +1x1-2x2+1x3+1x4+1x5-2x6+1x7+1x8+1x9-2x10-2x11-2x12+1x13+1x14+1x15<=2 +1x1-1x2+1x3+1x4+2x5-1x6+1x7+1x8+2x9-1x10-1x11-2x12+1x13+2x14+2x15<=6 -1x2+1x3+1x4+1x5-1x10-1x11-1x12+1x13+1x14+1x15<=2 +1x1-1x2+1x3+1x5-1x6+1x7+1x9-1x10-1x12+1x14<=2 +1x1-1x2+1x4+1x5-1x6+1x8+1x9-1x11-1x12+1x15<=2 -1x6+1x7+1x8+1x9-1x10-1x11-1x12+1x13+1x14+1x15<=2 -1x1+1x2-1x3-1x4-2x5-1x6+1x7+1x8+2x9-1x10-1x11-2x12+1x13+2x14+2x15<=2 +2x1-1x2-1x3-1x4+1x5-2x6-2x7-2x8+2x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 +1x1-1x2-1x4+1x5-1x6-1x8+1x9+1x11-1x12-1x15<=0 +1x1-1x2-1x3+1x5-1x6-1x7+1x9+1x10-1x12-1x14<=0 +1x1+1x5+1x9<=2 +1x1-1x3-1x4+1x5-1x7-1x8+1x9+1x13-1x14-1x15<=0 +2x1-2x2-2x3-2x4+2x5-1x6-1x7-1x8+1x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 +2x1+2x2-2x3-2x4+2x5+1x6-1x7-1x8+1x9-1x10-1x11+1x12+1x13-1x14-1x15<=2 +1x1+1x2-1x3-1x4+2x5+1x6-1x7-1x8+2x9-1x10-1x11+2x12+1x13-2x14-2x15<=2 +1x1+1x2+1x3+1x4+2x5+1x6+1x7+1x8+2x9+1x10+1x11+2x12+1x13+2x14+2x15<=12 -1x6+1x8-1x11<=0 +1x1-1x2-1x3-1x5-1x6-1x7-1x9+1x10+1x12+1x14<=0 -1x1+2x2+1x3-1x4+1x5-2x6-1x7+1x8-1x9+2x10-2x11+2x12-1x13+1x14-1x15<=2 -2x1+1x2+1x3-1x4+1x5-2x6-2x7+2x8-2x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 -1x2-1x3+1x4-1x5+1x10-1x11+1x12-1x13+1x14-1x15<=0 +1x1-2x2-1x3+1x4-1x5-2x6-1x7+1x8-1x9+2x10-2x11+2x12-1x13+1x14-1x15<=0 -1x6-1x7+1x8-1x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 -1x6-1x7+1x10<=0 -1x1+1x2-1x4-1x5-1x6+1x8+1x9-1x11-1x12+1x15<=0 -1x1+1x2+2x3-1x4+1x5-1x6-2x7+1x8-1x9+2x10-1x11+1x12-2x13+2x14-1x15<=2 +2x1+1x2-1x3+1x4-1x5+2x6-2x7+2x8-2x9-1x10+1x11-1x12-1x13+1x14-1x15<=2 +1x1+1x2-2x3+1x4-1x5+1x6-2x7+1x8-1x9-2x10+1x11-1x12-2x13+2x14-1x15<=0 +1x1-1x2-2x3-1x4-1x5-1x6-2x7-1x8-1x9+2x10+1x11+1x12+2x13+2x14+1x15<=2 -1x1+1x2-1x3-2x4-1x5-1x6+1x7+2x8+1x9-1x10-2x11-1x12+2x13+1x14+2x15<=2 +1x10-1x11-1x13<=0 -1x1+1x2+1x3-1x4-1x6-1x7+1x8+1x10-1x11-1x13<=0 -1x7+1x8-1x13<=0 -1x1+1x3-1x4-1x5-1x7+1x8+1x9-1x13-1x14+1x15<=0 -2x1+1x2+1x3-1x4-1x5-2x6-2x7+2x8+2x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 -1x1-1x2+1x3-2x4-1x5+1x6-1x7+2x8+1x9-1x10+2x11+1x12-2x13-1x14+2x15<=2 -1x1+1x2+1x3-2x4-1x5-1x6-1x7+2x8+1x9+1x10-2x11-1x12-2x13-1x14+2x15<=0 +1x1-1x2-2x3+1x4+1x5-1x6-2x7+1x8+1x9+2x10-1x11-1x12-2x13-2x14+1x15<=0 +1x1-1x2-1x3+1x4-1x6-1x7+1x8+1x10-1x11-1x13<=0 +1x1-1x2-2x3+1x4-1x5-1x6-2x7+1x8-1x9+2x10-1x11+1x12-2x13+2x14-1x15<=0 -1x6-1x7+1x8+1x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 +2x1+1x2-1x3-1x4+1x5+2x6-2x7-2x8+2x9-1x10-1x11+1x12+1x13-1x14-1x15<=2 +1x1+1x2-2x3-1x4+1x5+1x6-2x7-1x8+1x9-2x10-1x11+1x12+2x13-2x14-1x15<=0 -1x2+1x4-1x11<=0 -1x11-1x12+1x15<=0 +2x1-1x2-1x3+1x4-1x5-2x6-2x7+2x8-2x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 +1x1-1x2+1x4-1x5-1x6+1x8-1x9-1x11+1x12-1x15<=0 +1x10-1x12-1x14<=0 -1x1+2x2+1x3-1x4-1x5-2x6-1x7+1x8+1x9+2x10-2x11-2x12-1x13-1x14+1x15<=0 -1x1+1x2+1x3-1x5-1x6-1x7+1x9+1x10-1x12-1x14<=0 +2x1-2x2+2x3+2x4-2x5-1x6+1x7+1x8-1x9-1x10-1x11+1x12+1x13-1x14-1x15<=2 +1x1-1x2+1x3+2x4-1x5-1x6+1x7+2x8-1x9-1x10-2x11+1x12+2x13-1x14-2x15<=2 -1x1+1x2+2x3+1x4-1x5-1x6-2x7-1x8+1x9+2x10+1x11-1x12+2x13-2x14-1x15<=2 +1x1-1x2+1x3+2x4+1x5-1x6+1x7+2x8+1x9-1x10-2x11-1x12+2x13+1x14+2x15<=6 +1x1-1x2+1x3+1x4-1x6+1x7+1x8-1x10-1x11+1x13<=2 -1x1+1x2+2x3-1x4-1x5-1x6-2x7+1x8+1x9+2x10-1x11-1x12-2x13-2x14+1x15<=0 +1x1-1x2-2x3-1x4+1x5-1x6-2x7-1x8+1x9+2x10+1x11-1x12+2x13-2x14-1x15<=0 +1x1+1x2-1x3+2x4+1x5+1x6-1x7+2x8+1x9-1x10+2x11+1x12-2x13-1x14+2x15<=6 +1x1+1x2-1x3+1x4+1x6-1x7+1x8-1x10+1x11-1x13<=2 +1x1+1x4+1x8<=2 +1x1-1x3+1x4-1x5-1x7+1x8-1x9-1x13+1x14-1x15<=0 +2x1-2x2-2x3+2x4-2x5-1x6-1x7+1x8-1x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 +2x1+2x2-2x3+2x4-2x5+1x6-1x7+1x8-1x9-1x10+1x11-1x12-1x13+1x14-1x15<=2 +1x1+1x2-1x3+2x4-1x5+1x6-1x7+2x8-1x9-1x10+2x11-1x12-2x13+1x14-2x15<=2 +1x1+1x2+1x3+2x4+1x5+1x6+1x7+2x8+1x9+1x10+2x11+1x12+2x13+1x14+2x15<=12 -1x1+1x2+1x3-1x4-2x5-1x6-1x7+1x8+2x9+1x10-1x11-2x12-1x13-2x14+2x15<=0 +1x8+1x9+1x15<=2 -1x7+1x9-1x14<=0 +1x1-1x3-1x7<=0 -1x3+1x5-1x14<=0 +1x1+1x2-2x3+1x4+1x5+1x6-2x7+1x8+1x9-2x10+1x11+1x12-2x13-2x14+1x15<=2 +1x1+1x2-1x3+1x4+2x5+1x6-1x7+1x8+2x9-1x10+1x11+2x12-1x13-2x14+2x15<=6 +1x2-1x3+1x4+1x5-1x10+1x11+1x12-1x13-1x14+1x15<=2 +1x1+1x2-1x3+1x5+1x6-1x7+1x9-1x10+1x12-1x14<=2 +1x1-1x3+1x4+1x5-1x7+1x8+1x9-1x13-1x14+1x15<=2 +1x6-1x7+1x8+1x9-1x10+1x11+1x12-1x13-1x14+1x15<=2 -1x1-1x2+1x3-1x4-2x5+1x6-1x7+1x8+2x9-1x10+1x11+2x12-1x13-2x14+2x15<=2 -1x3+1x4-1x13<=0 -1x13-1x14+1x15<=0 -1x1-1x3+1x7<=0 -1x6+1x7-1x10<=0 +1x1-1x2-1x4-1x5-1x6-1x8-1x9+1x11+1x12+1x15<=0 -1x1+2x2-1x3+1x4+1x5-2x6+1x7-1x8-1x9-2x10+2x11+2x12-1x13-1x14+1x15<=2 -2x1+1x2-1x3+1x4+1x5-2x6+2x7-2x8-2x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 -1x2+1x3-1x4-1x5-1x10+1x11+1x12-1x13-1x14+1x15<=0 +1x1-2x2+1x3-1x4-1x5-2x6+1x7-1x8-1x9-2x10+2x11+2x12-1x13-1x14+1x15<=0 -1x6+1x7-1x8-1x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 -1x6-1x8+1x11<=0 -1x1+1x2-1x3-1x5-1x6+1x7+1x9-1x10-1x12+1x14<=0 -1x1+1x2-1x3+2x4+1x5-1x6+1x7-2x8-1x9-1x10+2x11+1x12-2x13-1x14+2x15<=2 +2x1+1x2+1x3-1x4-1x5+2x6+2x7-2x8-2x9+1x10-1x11-1x12-1x13-1x14+1x15<=2 +1x1+1x2+1x3-2x4-1x5+1x6+1x7-2x8-1x9+1x10-2x11-1x12-2x13-1x14+2x15<=0 +2x1-2x2-2x3+2x4+2x5-1x6-1x7+1x8+1x9+1x10-1x11-1x12-1x13-1x14+1x15<=2 -1x1+1x2-2x3-1x4-1x5-1x6+2x7+1x8+1x9-2x10-1x11-1x12+2x13+2x14+1x15<=2 -1x1-2x2+1x3-1x4-1x5+2x6-1x7+1x8+1x9-2x10+2x11+2x12-1x13-1x14+1x15<=2 +1x1-1x2-1x3-2x4-1x5-1x6-1x7-2x8-1x9+1x10+2x11+1x12+2x13+1x14+2x15<=2 -2x1+2x2+2x3-2x4+2x5-1x6-1x7+1x8-1x9+1x10-1x11+1x12-1x13+1x14-1x15<=2 +1x1-1x2-1x3+1x4+2x5-1x6-1x7+1x8+2x9+1x10-1x11-2x12-1x13-2x14+2x15<=2 -1x1+1x2+1x3-1x4+2x5-1x6-1x7+1x8-2x9+1x10-1x11+2x12-1x13+2x14-2x15<=2 +1x7-1x8-1x13<=0 -1x1-1x3+1x4-1x5+1x7-1x8+1x9-1x13+1x14-1x15<=0 -2x1+1x2-1x3+1x4-1x5-2x6+2x7-2x8+2x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 -1x1-1x2-2x3+1x4-1x5+1x6+2x7-1x8+1x9+2x10-1x11+1x12-2x13+2x14-1x15<=2 -1x1+1x2-2x3+1x4-1x5-1x6+2x7-1x8+1x9-2x10+1x11-1x12-2x13+2x14-1x15<=0 +1x1-1x2+1x3-2x4+1x5-1x6+1x7-2x8+1x9-1x10+2x11-1x12-2x13+1x14-2x15<=0 +1x1-1x2+1x3-1x4-1x6+1x7-1x8-1x10+1x11-1x13<=0 +1x1-1x2+1x3-2x4-1x5-1x6+1x7-2x8-1x9-1x10+2x11+1x12-2x13-1x14+2x15<=0 -1x6+1x7-1x8+1x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 -1x10+1x11-1x13<=0 -1x1+1x2-1x3+1x4-1x6+1x7-1x8-1x10+1x11-1x13<=0 -1x6-1x9+1x12<=0 -1x1+1x2-1x3-1x4-1x6+1x7+1x8-1x10-1x11+1x13<=0 -1x1+1x2-1x6<=0 -2x1+2x2-2x3-2x4-2x5-1x6+1x7+1x8+1x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 -1x1+2x2-1x3-1x4-1x5-2x6+1x7+1x8+1x9-2x10-2x11-2x12+1x13+1x14+1x15<=0 -2x1+1x2-1x3-1x4-1x5-2x6+2x7+2x8+2x9-1x10-1x11-1x12+1x13+1x14+1x15<=2 -1x1+1x5-1x9<=0 -1x1-1x2-1x3-1x4+2x5+1x6+1x7+1x8-2x9+1x10+1x11-2x12+1x13-2x14-2x15<=0 -2x1-2x2-2x3-2x4+2x5+1x6+1x7+1x8-1x9+1x10+1x11-1x12+1x13-1x14-1x15<=0 -2x1-1x2-1x3-1x4+1x5+2x6+2x7+2x8-2x9+1x10+1x11-1x12+1x13-1x14-1x15<=2 -2x1-2x2+2x3+2x4+2x5+1x6-1x7-1x8-1x9-1x10-1x11-1x12+1x13+1x14+1x15<=2 -2x1+1x2+1x3+1x4+1x5-2x6-2x7-2x8-2x9+1x10+1x11+1x12+1x13+1x14+1x15<=2 -1x1+1x2+1x3+1x4+2x5-1x6-1x7-1x8-2x9+1x10+1x11+2x12+1x13+2x14+2x15<=6 -1x1+1x3+1x4+1x5-1x7-1x8-1x9+1x13+1x14+1x15<=2 -1x1-1x2+1x3+1x4+2x5+1x6-1x7-1x8-2x9-1x10-1x11-2x12+1x13+2x14+2x15<=2 -1x1+1x2+1x3+1x5-1x6-1x7-1x9+1x10+1x12+1x14<=2 -1x1+1x2+1x3+2x4+1x5-1x6-1x7-2x8-1x9+1x10+2x11+1x12+2x13+1x14+2x15<=6 -1x1+1x2+1x4+1x5-1x6-1x8-1x9+1x11+1x12+1x15<=2 -2x1+2x2-2x3+2x4+2x5-1x6+1x7-1x8-1x9-1x10+1x11+1x12-1x13-1x14+1x15<=2 -1x1+1x2-1x3+1x4+2x5-1x6+1x7-1x8-2x9-1x10+1x11+2x12-1x13-2x14+2x15<=2 +1x1+2x2-1x3-1x4+1x5+2x6-1x7-1x8+1x9-2x10-2x11+2x12+1x13-1x14-1x15<=2 +1x1-1x2-1x3+2x4+1x5-1x6-1x7+2x8+1x9+1x10-2x11-1x12-2x13-1x14+2x15<=2 +1x1-1x2-1x3-1x4-2x5-1x6-1x7-1x8-2x9+1x10+1x11+2x12+1x13+2x14+2x15<=2 -2x1+2x2+2x3+2x4-2x5-1x6-1x7-1x8+1x9+1x10+1x11-1x12+1x13-1x14-1x15<=2 +1x1-1x2+2x3-1x4+1x5-1x6+2x7-1x8+1x9-2x10+1x11-1x12-2x13+2x14-1x15<=2 -1x1+1x2+1x3+1x4-1x6-1x7-1x8+1x10+1x11+1x13<=2 -1x6-1x7-1x8-1x9+1x10+1x11+1x12+1x13+1x14+1x15<=2 -1x1+2x2-1x3-1x4+1x5-2x6+1x7+1x8-1x9-2x10-2x11+2x12+1x13-1x14-1x15<=0 -1x1+1x2-1x4+1x5-1x6+1x8-1x9-1x11+1x12-1x15<=0 -1x1+1x2-1x3+1x5-1x6+1x7-1x9-1x10+1x12-1x14<=0 +1x2+1x5+1x12<=2 +1x2-1x3-1x4+1x5-1x10-1x11+1x12+1x13-1x14-1x15<=0 -2x1+2x2-2x3-2x4+2x5-1x6+1x7+1x8-1x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 -1x8-1x9+1x15<=0 -1x1-1x2-1x3+1x4+1x6+1x7-1x8+1x10-1x11-1x13<=0 -1x1+1x4-1x8<=0 -2x1-1x2-1x3+1x4-1x5+2x6+2x7-2x8+2x9+1x10-1x11+1x12-1x13+1x14-1x15<=2 -2x1-2x2-2x3+2x4-2x5+1x6+1x7-1x8+1x9+1x10-1x11+1x12-1x13+1x14-1x15<=0 -1x1-1x2-1x3+2x4-1x5+1x6+1x7-2x8+1x9+1x10-2x11+1x12-2x13+1x14-2x15<=0 -1x1-1x2-1x3+2x4+1x5+1x6+1x7-2x8-1x9+1x10-2x11-1x12-2x13-1x14+2x15<=0 -1x1-1x3+1x4+1x5+1x7-1x8-1x9-1x13-1x14+1x15<=0 -1x1-1x2+1x4+1x5+1x6-1x8-1x9-1x11-1x12+1x15<=0 +1x4+1x5+1x15<=2 -1x2-1x3+1x4+1x5+1x10-1x11-1x12-1x13-1x14+1x15<=0 -2x1-2x2-2x3+2x4+2x5+1x6+1x7-1x8-1x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 -1x1-1x2+1x3+2x4+1x5+1x6-1x7-2x8-1x9-1x10-2x11-1x12+2x13+1x14+2x15<=2 +1x7-1x9-1x14<=0 -1x1-1x2-2x3-1x4+1x5+1x6+2x7+1x8-1x9+2x10+1x11-1x12+2x13-2x14-1x15<=2 -1x1-1x3-1x4+1x5+1x7+1x8-1x9+1x13-1x14-1x15<=0 -2x1+1x2-1x3-1x4+1x5-2x6+2x7+2x8-2x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 -1x1+1x2-2x3-1x4+1x5-1x6+2x7+1x8-1x9-2x10-1x11+1x12+2x13-2x14-1x15<=0 +1x1-1x2+1x3+1x4-2x5-1x6+1x7+1x8-2x9-1x10-1x11+2x12+1x13-2x14-2x15<=0 +2x1-1x2+1x3-1x4-1x5-2x6+2x7-2x8-2x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 +1x1-1x2+1x3-1x5-1x6+1x7-1x9-1x10+1x12-1x14<=0 +1x1-1x2+2x3-1x4-1x5-1x6+2x7-1x8-1x9-2x10+1x11+1x12-2x13-2x14+1x15<=0 +1x1-1x2+1x3-1x4-2x5-1x6+1x7-1x8-2x9-1x10+1x11+2x12-1x13-2x14+2x15<=0 -1x6+1x7+1x8-1x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 -1x1+2x2-1x3+1x4-1x5-2x6+1x7-1x8+1x9-2x10+2x11-2x12-1x13+1x14-1x15<=0 -1x1+1x2+1x4-1x5-1x6-1x8+1x9+1x11-1x12-1x15<=0 +1x6+1x7-1x8-1x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 -1x1-1x2-2x3+1x4+1x5+1x6+2x7-1x8-1x9+2x10-1x11-1x12-2x13-2x14+1x15<=0 +1x1+2x2-1x3+1x4-1x5+2x6-1x7+1x8-1x9-2x10+2x11-2x12-1x13+1x14-1x15<=2 +1x1+1x2+1x3-1x4-2x5+1x6+1x7-1x8-2x9+1x10-1x11-2x12-1x13-2x14+2x15<=0 -1x1+1x2+1x3+2x4-1x5-1x6-1x7-2x8+1x9+1x10+2x11-1x12+2x13-1x14-2x15<=2 +1x1-1x2+2x3+1x4-1x5-1x6+2x7+1x8-1x9-2x10-1x11+1x12+2x13-2x14-1x15<=2 +1x2+1x4+1x11<=2 +1x2-1x3+1x4-1x5-1x10+1x11-1x12-1x13+1x14-1x15<=0 -2x1+2x2-2x3+2x4-2x5-1x6+1x7-1x8+1x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 +1x11+1x12+1x15<=2 -1x10+1x12-1x14<=0 +1x2-1x3-1x10<=0 -1x1-1x2+1x6<=0 +1x6-1x7-1x10<=0 +1x1-1x3-1x4-1x5-1x7-1x8-1x9+1x13+1x14+1x15<=0 -1x1-1x2+2x3+1x4+1x5+1x6-2x7-1x8-1x9-2x10-1x11-1x12+2x13+2x14+1x15<=2 -2x1-1x2+1x3+1x4+1x5+2x6-2x7-2x8-2x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 +1x2-1x3-1x4-1x5-1x10-1x11-1x12+1x13+1x14+1x15<=0 +1x1+1x2-2x3-1x4-1x5+1x6-2x7-1x8-1x9-2x10-1x11-1x12+2x13+2x14+1x15<=0 +1x6-1x7-1x8-1x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 -1x7-1x8+1x13<=0 -1x1-1x2+1x3-1x5+1x6-1x7+1x9-1x10+1x12-1x14<=0 -1x10-1x11+1x13<=0 -1x1-1x2+1x3+1x4+1x6-1x7-1x8-1x10-1x11+1x13<=0 -1x7-1x9+1x14<=0 -1x1-1x2+1x3-1x4+1x6-1x7+1x8-1x10+1x11-1x13<=0 -1x1+1x3-1x7<=0 -2x1-1x2+1x3-1x4-1x5+2x6-2x7+2x8+2x9-1x10+1x11+1x12-1x13-1x14+1x15<=2 -2x1-2x2+2x3-2x4-2x5+1x6-1x7+1x8+1x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 -1x1-1x2+2x3-1x4-1x5+1x6-2x7+1x8+1x9-2x10+1x11+1x12-2x13-2x14+1x15<=0 -1x1-1x2+2x3-1x4+1x5+1x6-2x7+1x8-1x9-2x10+1x11-1x12-2x13+2x14-1x15<=0 -1x1+1x3-1x4+1x5-1x7+1x8-1x9-1x13+1x14-1x15<=0 -1x1-1x2+1x3+1x5+1x6-1x7-1x9-1x10-1x12+1x14<=0 +1x3+1x5+1x14<=2 -1x2+1x3-1x4+1x5-1x10+1x11-1x12-1x13+1x14-1x15<=0 -2x1-2x2+2x3-2x4+2x5+1x6-1x7+1x8-1x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 +1x13+1x14+1x15<=2 -1x2+1x3-1x10<=0 -1x10-1x12+1x14<=0 -1x1-1x2-1x3-1x4+1x6+1x7+1x8+1x10+1x11+1x13<=2 +1x7+1x8+1x13<=2 +1x8-1x9-1x15<=0 +1x1-1x5-1x9<=0 +1x4-1x5-1x15<=0 +1x1+1x2+1x3+1x4-2x5+1x6+1x7+1x8-2x9+1x10+1x11-2x12+1x13-2x14-2x15<=2 +1x1+1x2+1x3+2x4-1x5+1x6+1x7+2x8-1x9+1x10+2x11-1x12+2x13-1x14-2x15<=6 +1x2+1x3+1x4-1x5+1x10+1x11-1x12+1x13-1x14-1x15<=2 +1x1+1x2+1x4-1x5+1x6+1x8-1x9+1x11-1x12-1x15<=2 +1x1+1x3+1x4-1x5+1x7+1x8-1x9+1x13-1x14-1x15<=2 +1x6+1x7+1x8-1x9+1x10+1x11-1x12+1x13-1x14-1x15<=2 -1x1-1x2-1x3-2x4+1x5+1x6+1x7+2x8-1x9+1x10+2x11-1x12+2x13-1x14-2x15<=2 +1x13-1x14-1x15<=0 +1x3-1x5-1x14<=0 +1x10+1x11+1x13<=2 +1x11-1x12-1x15<=0 +1x2-1x5-1x12<=0 +1x6-1x9-1x12<=0 -1x1-2x2-1x3-1x4+1x5+2x6+1x7+1x8-1x9+2x10+2x11-2x12+1x13-1x14-1x15<=2 -1x1-1x2-1x4+1x5+1x6+1x8-1x9+1x11-1x12-1x15<=0 -2x1-1x2+1x3-1x4+1x5+2x6-2x7+2x8-2x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 -1x1-2x2+1x3-1x4+1x5+2x6-1x7+1x8-1x9-2x10+2x11-2x12-1x13+1x14-1x15<=0 -1x1-1x2-1x3+1x5+1x6+1x7-1x9+1x10-1x12-1x14<=0 -2x1-1x2-1x3+1x4+1x5+2x6+2x7-2x8-2x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 -1x1-1x2-1x3+1x4+2x5+1x6+1x7-1x8-2x9+1x10-1x11-2x12-1x13-2x14+2x15<=0 -1x1-2x2-1x3+1x4+1x5+2x6+1x7-1x8-1x9+2x10-2x11-2x12-1x13-1x14+1x15<=0 -1x1-1x2+1x3-1x4+2x5+1x6-1x7+1x8-2x9-1x10+1x11-2x12-1x13+2x14-2x15<=0 +2x1+1x2-1x3-1x4-1x5+2x6-2x7-2x8-2x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 +1x1+1x2-1x3-1x5+1x6-1x7-1x9-1x10-1x12+1x14<=0 +1x1+2x2-1x3-1x4-1x5+2x6-1x7-1x8-1x9-2x10-2x11-2x12+1x13+1x14+1x15<=0 +1x1+1x2-1x3-1x4-2x5+1x6-1x7-1x8-2x9-1x10-1x11-2x12+1x13+2x14+2x15<=0 +1x1+1x2-1x3+1x4-2x5+1x6-1x7+1x8-2x9-1x10+1x11-2x12-1x13+2x14-2x15<=0 -1x1-1x2+2x3+1x4-1x5+1x6-2x7-1x8+1x9-2x10-1x11+1x12+2x13-2x14-1x15<=0 -1x1+1x3+1x4-1x5-1x7-1x8+1x9+1x13-1x14-1x15<=0 +1x3+1x4+1x13<=2 -1x2+1x3+1x4-1x5-1x10-1x11+1x12+1x13-1x14-1x15<=0 -2x1-2x2+2x3+2x4-2x5+1x6-1x7-1x8+1x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 +1x6-1x7+1x8-1x9-1x10+1x11-1x12-1x13+1x14-1x15<=0 -1x1-1x2+1x3-2x4+1x5+1x6-1x7+2x8-1x9-1x10+2x11-1x12-2x13+1x14-2x15<=0 -1x1+1x2+2x3+1x4+1x5-1x6-2x7-1x8-1x9+2x10+1x11+1x12+2x13+2x14+1x15<=6 +1x6+1x8+1x11<=2 -1x1-1x2-1x3-2x4-1x5+1x6+1x7+2x8+1x9+1x10+2x11+1x12+2x13+1x14+2x15<=6 -1x1-1x2-1x3-1x5+1x6+1x7+1x9+1x10+1x12+1x14<=2 +1x7+1x9+1x14<=2 -1x8+1x9-1x15<=0 +1x1-1x4-1x8<=0 -1x4+1x5-1x15<=0 +1x1+1x2+1x3-2x4+1x5+1x6+1x7-2x8+1x9+1x10-2x11+1x12-2x13+1x14-2x15<=2 +1x1+1x2+1x3-1x4+2x5+1x6+1x7-1x8+2x9+1x10-1x11+2x12-1x13+2x14-2x15<=6 +1x2+1x3-1x4+1x5+1x10-1x11+1x12-1x13+1x14-1x15<=2 +1x1+1x2-1x4+1x5+1x6-1x8+1x9-1x11+1x12-1x15<=2 +1x1+1x3-1x4+1x5+1x7-1x8+1x9-1x13+1x14-1x15<=2 +1x6+1x7-1x8+1x9+1x10-1x11+1x12-1x13+1x14-1x15<=2 -1x1-1x2-1x3+1x4-2x5+1x6+1x7-1x8+2x9+1x10-1x11+2x12-1x13+2x14-2x15<=2 -1x13+1x14-1x15<=0 +1x3-1x4-1x13<=0 +1x10+1x12+1x14<=2 -1x11+1x12-1x15<=0 +1x2-1x4-1x11<=0 +1x6-1x8-1x11<=0 -1x1-1x2+1x4-1x5+1x6-1x8+1x9-1x11+1x12-1x15<=0 -2x1-1x2+1x3+1x4-1x5+2x6-2x7-2x8+2x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 -1x1-2x2-1x3+1x4-1x5+2x6+1x7-1x8+1x9+2x10-2x11+2x12-1x13+1x14-1x15<=2 -1x1-2x2+1x3+1x4-1x5+2x6-1x7-1x8+1x9-2x10-2x11+2x12+1x13-1x14-1x15<=0 +1x1+1x2-1x3-1x4+1x6-1x7-1x8-1x10-1x11+1x13<=0 +1x1+1x2-1x3-2x4-1x5+1x6-1x7-2x8-1x9-1x10-2x11-1x12+2x13+1x14+2x15<=0 +1x1+1x2-1x3-2x4+1x5+1x6-1x7-2x8+1x9-1x10-2x11+1x12+2x13-1x14-2x15<=0 +1x6-1x7-1x8+1x9-1x10-1x11+1x12+1x13-1x14-1x15<=0 +1x6+1x7+1x10<=2 -1x1-1x2-2x3-1x4-1x5+1x6+2x7+1x8+1x9+2x10+1x11+1x12+2x13+2x14+1x15<=6 -1x1+1x2-1x3-1x4+2x5-1x6+1x7+1x8-2x9-1x10-1x11+2x12+1x13-2x14-2x15<=0 +1x1-1x2-1x3+2x4-1x5-1x6-1x7+2x8-1x9+1x10-2x11+1x12-2x13+1x14-2x15<=0 +1x1+1x2+2x3+1x4-1x5+1x6+2x7+1x8-1x9+2x10+1x11-1x12+2x13-2x14-1x15<=6 +1x1+1x2+1x3-1x5+1x6+1x7-1x9+1x10-1x12-1x14<=2 +1x1-1x2-1x3+1x4-2x5-1x6-1x7+1x8-2x9+1x10-1x11+2x12-1x13+2x14-2x15<=0 -1x1+1x2-1x3-2x4+1x5-1x6+1x7+2x8-1x9-1x10-2x11+1x12+2x13-1x14-2x15<=0 -1x1+1x2-1x3+2x4-1x5-1x6+1x7-2x8+1x9-1x10+2x11-1x12-2x13+1x14-2x15<=0 +1x1-1x2-1x3-1x4+2x5-1x6-1x7-1x8+2x9+1x10+1x11-2x12+1x13-2x14-2x15<=0 +1x1-1x2-1x3-2x4+1x5-1x6-1x7-2x8+1x9+1x10+2x11-1x12+2x13-1x14-2x15<=0 +1x1+1x2+2x3-1x4+1x5+1x6+2x7-1x8+1x9+2x10-1x11+1x12-2x13+2x14-1x15<=6 +1x1+1x2+1x3-1x4+1x6+1x7-1x8+1x10-1x11-1x13<=2 +2x1+2x2+2x3-2x4-2x5+1x6+1x7-1x8-1x9+1x10-1x11-1x12-1x13-1x14+1x15<=2 +2x1-2x2+2x3-2x4-2x5-1x6+1x7-1x8-1x9-1x10+1x11+1x12-1x13-1x14+1x15<=0 +1x1+1x3-1x4-1x5+1x7-1x8-1x9-1x13-1x14+1x15<=0 +1x1+1x2+2x3-1x4-1x5+1x6+2x7-1x8-1x9+2x10-1x11-1x12-2x13-2x14+1x15<=2 +1x1+1x3+1x7<=2 +2x1+2x2+2x3+2x4+2x5+1x6+1x7+1x8+1x9+1x10+1x11+1x12+1x13+1x14+1x15<=12 +1x1+1x2+2x3+1x4+1x5+1x6+2x7+1x8+1x9+2x10+1x11+1x12+2x13+2x14+1x15<=12 +1x1-1x2+2x3+1x4+1x5-1x6+2x7+1x8+1x9-2x10-1x11-1x12+2x13+2x14+1x15<=6 +1x1+1x3+1x4+1x5+1x7+1x8+1x9+1x13+1x14+1x15<=6 +2x1-1x2+1x3+1x4+1x5-2x6+2x7+2x8+2x9-1x10-1x11-1x12+1x13+1x14+1x15<=6 -1x1+1x2-1x3+1x4-2x5-1x6+1x7-1x8+2x9-1x10+1x11-2x12-1x13+2x14-2x15<=0 -2x1+2x2+2x3-2x4-2x5-1x6-1x7+1x8+1x9+1x10-1x11-1x12-1x13-1x14+1x15<=0 +1x2+1x3-1x4-1x5+1x10-1x11-1x12-1x13-1x14+1x15<=0 +1x2+1x3+1x10<=2 -1x1-1x2+1x3+2x4-1x5+1x6-1x7-2x8+1x9-1x10-2x11+1x12+2x13-1x14-2x15<=0 +2x1+2x2-2x3-2x4-2x5+1x6-1x7-1x8-1x9-1x10-1x11-1x12+1x13+1x14+1x15<=0 +1x1+1x2-1x4-1x5+1x6-1x8-1x9-1x11-1x12+1x15<=0 +1x1+2x2+1x3-1x4-1x5+2x6+1x7-1x8-1x9+2x10-2x11-2x12-1x13-1x14+1x15<=2 -1x1-1x2+1x3+1x4-2x5+1x6-1x7-1x8+2x9-1x10-1x11+2x12+1x13-2x14-2x15<=0 -1x1-2x2-1x3-1x4-1x5+2x6+1x7+1x8+1x9+2x10+2x11+2x12+1x13+1x14+1x15<=6 -2x1+2x2+2x3+2x4+2x5-1x6-1x7-1x8-1x9+1x10+1x11+1x12+1x13+1x14+1x15<=6 -2x1-1x2-1x3-1x4-1x5+2x6+2x7+2x8+2x9+1x10+1x11+1x12+1x13+1x14+1x15<=6 +2x1-2x2+2x3+2x4+2x5-1x6+1x7+1x8+1x9-1x10-1x11-1x12+1x13+1x14+1x15<=6 +2x1+2x2-2x3+2x4+2x5+1x6-1x7+1x8+1x9-1x10+1x11+1x12-1x13-1x14+1x15<=6 +1x1+1x2+1x6<=2 +1x1+2x2+1x3+1x4+1x5+2x6+1x7+1x8+1x9+2x10+2x11+2x12+1x13+1x14+1x15<=12 +1x1+2x2-1x3+1x4+1x5+2x6-1x7+1x8+1x9-2x10+2x11+2x12-1x13-1x14+1x15<=6 +1x1+1x2+1x4+1x5+1x6+1x8+1x9+1x11+1x12+1x15<=6 +2x1+1x2-1x3+1x4+1x5+2x6-2x7+2x8+2x9-1x10+1x11+1x12-1x13-1x14+1x15<=6 +1x1+2x2+1x3-1x4+1x5+2x6+1x7-1x8+1x9+2x10-2x11+2x12-1x13+1x14-1x15<=6 +2x1+2x2+2x3-2x4+2x5+1x6+1x7-1x8+1x9+1x10-1x11+1x12-1x13+1x14-1x15<=6 +1x1+1x2+1x3+1x5+1x6+1x7+1x9+1x10+1x12+1x14<=6 +2x1+1x2+1x3-1x4+1x5+2x6+2x7-2x8+2x9+1x10-1x11+1x12-1x13+1x14-1x15<=6 +2x1+1x2+1x3+1x4+1x5+2x6+2x7+2x8+2x9+1x10+1x11+1x12+1x13+1x14+1x15<=12 +1x1+2x2+1x3+1x4-1x5+2x6+1x7+1x8-1x9+2x10+2x11-2x12+1x13-1x14-1x15<=6 +2x1+2x2+2x3+2x4-2x5+1x6+1x7+1x8-1x9+1x10+1x11-1x12+1x13-1x14-1x15<=6 +1x1+1x2+1x3+1x4+1x6+1x7+1x8+1x10+1x11+1x13<=6 +2x1+1x2+1x3+1x4-1x5+2x6+2x7+2x8-2x9+1x10+1x11-1x12+1x13-1x14-1x15<=6 +1x2+1x3+1x4+1x5+1x10+1x11+1x12+1x13+1x14+1x15<=6 -1x1+2x2+1x3+1x4+1x5-2x6-1x7-1x8-1x9+2x10+2x11+2x12+1x13+1x14+1x15<=6 +1x6+1x7+1x8+1x9+1x10+1x11+1x12+1x13+1x14+1x15<=6 +1x6+1x9+1x12<=2 -1x1-1x2-1x3-1x4-2x5+1x6+1x7+1x8+2x9+1x10+1x11+2x12+1x13+2x14+2x15<=6 END lrslib-071a/ine/test-062/porta/fq48-19.ine.ieq0000700060175606010010000000131213742506304020277 0ustar avisなしDIM = 18 INEQUALITIES_SECTION +1x1+1x2+1x3<=1 +1x4+1x5+1x6<=1 +1x7+1x8+1x9<=1 +1x10+1x11+1x12<=1 +1x13+1x14+1x16<=1 +1x13+1x15+1x17<=1 +1x14+1x15+1x18<=1 +1x16+1x17+1x18<=1 +1x4+1x7+1x10<=1 +1x1+1x8+1x11<=1 +1x2+1x5+1x12<=1 +1x3+1x6+1x9<=1 +1x2-1x4+1x15<=1 +1x3-1x4+1x17<=1 -1x5+1x7+1x13<=1 -1x5+1x9+1x17<=1 -1x6+1x10+1x13<=1 -1x6+1x12+1x15<=1 +1x1-1x7+1x15<=1 +1x3-1x7+1x18<=1 +1x4-1x8+1x14<=1 +1x6-1x8+1x18<=1 -1x9+1x10+1x14<=1 -1x9+1x11+1x15<=1 +1x1-1x10+1x17<=1 +1x2-1x10+1x18<=1 +1x4-1x11+1x16<=1 +1x5-1x11+1x18<=1 +1x7-1x12+1x16<=1 +1x8-1x12+1x17<=1 -1x1<=0 -1x2<=0 -1x3<=0 -1x4<=0 -1x5<=0 -1x6<=0 -1x7<=0 -1x8<=0 -1x9<=0 -1x10<=0 -1x11<=0 -1x12<=0 -1x13<=0 -1x14<=0 -1x15<=0 -1x16<=0 -1x17<=0 -1x18<=0 END lrslib-071a/ine/test-062/porta/m6.ine.ieq0000700060175606010010000000260313742506305017615 0ustar avisなしDIM = 15 INEQUALITIES_SECTION +1x1-1x2-1x6<=0 -1x1+1x2-1x6<=0 -1x1-1x2+1x6<=0 +1x1+1x2+1x6<=2 +1x1-1x3-1x7<=0 -1x1+1x3-1x7<=0 -1x1-1x3+1x7<=0 +1x1+1x3+1x7<=2 +1x1-1x4-1x8<=0 -1x1+1x4-1x8<=0 -1x1-1x4+1x8<=0 +1x1+1x4+1x8<=2 +1x1-1x5-1x9<=0 -1x1+1x5-1x9<=0 -1x1-1x5+1x9<=0 +1x1+1x5+1x9<=2 +1x2-1x3-1x10<=0 -1x2+1x3-1x10<=0 -1x2-1x3+1x10<=0 +1x2+1x3+1x10<=2 +1x2-1x4-1x11<=0 -1x2+1x4-1x11<=0 -1x2-1x4+1x11<=0 +1x2+1x4+1x11<=2 +1x2-1x5-1x12<=0 -1x2+1x5-1x12<=0 -1x2-1x5+1x12<=0 +1x2+1x5+1x12<=2 +1x3-1x4-1x13<=0 -1x3+1x4-1x13<=0 -1x3-1x4+1x13<=0 +1x3+1x4+1x13<=2 +1x3-1x5-1x14<=0 -1x3+1x5-1x14<=0 -1x3-1x5+1x14<=0 +1x3+1x5+1x14<=2 +1x4-1x5-1x15<=0 -1x4+1x5-1x15<=0 -1x4-1x5+1x15<=0 +1x4+1x5+1x15<=2 +1x6-1x7-1x10<=0 -1x6+1x7-1x10<=0 -1x6-1x7+1x10<=0 +1x6+1x7+1x10<=2 +1x6-1x8-1x11<=0 -1x6+1x8-1x11<=0 -1x6-1x8+1x11<=0 +1x6+1x8+1x11<=2 +1x6-1x9-1x12<=0 -1x6+1x9-1x12<=0 -1x6-1x9+1x12<=0 +1x6+1x9+1x12<=2 +1x7-1x8-1x13<=0 -1x7+1x8-1x13<=0 -1x7-1x8+1x13<=0 +1x7+1x8+1x13<=2 +1x7-1x9-1x14<=0 -1x7+1x9-1x14<=0 -1x7-1x9+1x14<=0 +1x7+1x9+1x14<=2 +1x8-1x9-1x15<=0 -1x8+1x9-1x15<=0 -1x8-1x9+1x15<=0 +1x8+1x9+1x15<=2 +1x10-1x11-1x13<=0 -1x10+1x11-1x13<=0 -1x10-1x11+1x13<=0 +1x10+1x11+1x13<=2 +1x10-1x12-1x14<=0 -1x10+1x12-1x14<=0 -1x10-1x12+1x14<=0 +1x10+1x12+1x14<=2 +1x11-1x12-1x15<=0 -1x11+1x12-1x15<=0 -1x11-1x12+1x15<=0 +1x11+1x12+1x15<=2 +1x13-1x14-1x15<=0 -1x13+1x14-1x15<=0 -1x13-1x14+1x15<=0 +1x13+1x14+1x15<=2 END lrslib-071a/ine/test-062/porta/mit.ine.ieq0000700060175606010010000006364413742506305020100 0ustar avisなしDIM = 8 INEQUALITIES_SECTION +4x3+4x4+2x5<=72 +2x1+2x2+10x3+12x4+6x5<=216 +4x1+2x2+8x3+8x4+8x5<=192 +12x1-6x2-8x3+16x4+8x5<=288 +4x1-2x2+4x4+4x5<=96 +5x1-1x2+4x3+6x4+6x5<=144 +8x1+2x2+10x3+12x4+12x5<=288 +4x1-2x2+4x3+2x4+4x5<=96 +7x1+1x2+10x3+8x4+10x5<=240 +8x1+2x2+12x3+8x4+12x5<=288 +8x1+2x2+8x3+16x4+8x5<=288 +4x1-2x2+8x3<=96 -6x2+8x3-4x4-8x5<=0 -4x1-6x2+8x3-8x5<=0 -2x1-2x2+4x3+2x4-2x5<=24 +24x1+6x2+40x3+16x4+32x5<=864 +2x3+2x4-2x5<=24 -4x1-10x2+16x3-24x5<=0 -1x1-1x2+4x3-12x5<=0 -6x2+16x3-8x4-40x5<=0 +4x1-2x2+16x3-16x4-32x5<=96 +8x1+2x2+16x3<=288 +4x1-2x2-8x3+8x4-8x5<=96 +8x1+2x2-8x3+24x4-24x5<=288 -2x2+8x3-8x4-24x5<=0 +1x1+1x2+4x3+8x4-8x5<=96 +12x1+6x2+16x3+40x4-16x5<=576 +4x1+2x2+16x4-16x5<=192 +8x1+6x2+24x3+32x4+16x5<=576 +12x1+6x2+20x3+32x4+16x5<=576 +16x1+10x2+40x3+56x4+16x5<=960 +7x3+7x4+6x5+1x6+1x8<=160 +4x1+4x2+21x3+21x4+18x5+1x6+3x8<=480 +4x1+4x2+12x3+4x4+8x5-4x6-2x7+4x8<=192 +16x1+8x2+28x3+28x4+24x5-4x6-2x7+4x8<=640 +8x1+6x2+28x3+28x4+24x5+4x8<=640 +8x1+8x3+8x4+8x5-4x6-2x7<=192 +12x1+4x2+16x3+16x4+16x5-4x6-2x7<=384 +20x1+12x2+42x3+42x4+36x5-4x6-2x7+6x8<=960 +9x1+1x2+11x3+9x4+10x5-3x6-2x7+1x8<=240 -2x1-2x2-4x3+4x6+2x7<=0 +22x1+4x2+24x3+28x4+24x5-8x6-4x7+4x8<=640 +60x1+20x2+76x3+84x4+72x5-20x6-10x7+12x8<=1920 +32x1+22x2+84x3+84x4+72x5-4x6-2x7+12x8<=1920 +28x1+10x2+44x3+36x4+40x5-8x6-4x7+4x8<=960 +36x1+12x2+52x3+44x4+48x5-12x6-6x7+4x8<=1152 +23x1+7x2+33x3+27x4+30x5-7x6-4x7+3x8<=720 +48x1+24x2+88x3+72x4+80x5-12x6-6x7+8x8<=1920 +96x1+40x2+160x3+128x4+144x5-28x6-14x7+16x8<=3456 +15x1+7x2+26x3+20x4+24x5-4x6-2x7+4x8<=576 +12x1+4x2+20x3+12x4+16x5-4x6-2x7<=384 +11x1+3x2+17x3+11x4+14x5-3x6-2x7+1x8<=336 +8x1+12x3+4x4+8x5-4x6-2x7<=192 +4x3-4x4-4x6-2x7<=0 -2x2+8x3-8x4-8x6-4x7+2x8<=0 +12x1-12x2+28x3-12x4+8x5-20x6-10x7+4x8<=192 +12x1-12x2+20x3-4x4+8x5-12x6-6x7+2x8<=192 +48x1+24x2+92x3+60x4+80x5-12x6-6x7+4x8<=1920 +15x1+7x2+28x3+18x4+24x5-4x6-2x7+2x8<=576 +42x1+18x2+76x3+40x4+64x5-12x6-6x7+8x8<=1536 +12x1+4x2+20x3-4x4+16x5-4x6-2x7+4x8<=384 +60x1+20x2+102x3-18x4+76x5-14x6-10x7+18x8<=1920 +60x1+20x2+102x3+46x4+76x5-14x6-10x7+2x8<=1920 +22x1+6x2+37x3+17x4+26x5-5x6-4x7+1x8<=672 +22x1+4x2+36x3+16x4+24x5-4x6-4x7<=640 +40x1+64x3+16x4+32x5-8x6-10x7<=960 +4x1-4x2+8x3-2x7<=64 -8x2+6x3-2x4-4x5+2x6-2x7<=0 -8x1-18x2+8x3-8x5+8x6-2x7<=0 -36x1-60x2+28x3+4x4-24x5+28x6-6x7+4x8<=64 -28x1-36x2+20x3+12x4-8x5+20x6-2x7+4x8<=192 -4x1-4x2+5x3+5x4+2x5+3x6+1x8<=96 -4x1-6x2+4x3+4x4+4x6<=64 +5x3+5x4+2x5+1x6+1x8<=96 +1x3+1x4<=16 +6x1+8x3-12x4+8x5+4x8<=192 +6x1+8x3+4x4+8x5<=192 +30x1+8x2+48x3+20x4+40x5-8x6-4x7+4x8<=960 +32x1+8x2+52x3+20x4+40x5-12x6-6x7+4x8<=960 +32x1+8x2+52x3-44x4+40x5-12x6-6x7+20x8<=960 +30x1+8x2+48x3-12x4+40x5-8x6-4x7+12x8<=960 +16x1+6x2+28x3+12x4+24x5-4x6-2x7+4x8<=576 +8x1+8x3+8x4+8x5-4x6-2x7+2x8<=208 +7x1-1x2+5x3+7x4+6x5-3x6-2x7+1x8<=160 +12x1-12x2+8x4+8x5-8x6-6x7<=192 +9x1-7x2+1x3+7x4+6x5-5x6-4x7+1x8<=160 +20x1+4x2+20x3+28x4+24x5-4x6-2x7+4x8<=640 +5x1-3x2+2x3+4x4+4x5-2x6-2x7<=96 +6x1+4x3+8x4+8x5<=192 +18x1+2x2+17x3+21x4+18x5-7x6-4x7+3x8<=480 +19x1+3x2+20x3+22x4+20x5-8x6-4x7+4x8<=528 +30x1+4x2+32x3+36x4+40x5-4x6-2x7+4x8<=960 +36x1+4x2+32x3+40x4+48x5-2x7+8x8<=1152 +36x1+12x2+48x3+40x4+48x5-8x6-6x7+8x8<=1152 +8x1+4x3+4x4+8x5-4x6-2x7+4x8<=192 +6x1+4x4+8x5+4x8<=192 +12x1+4x2+8x3+8x4+16x5-4x6-2x7+8x8<=384 +48x1+24x2+48x3+40x4+80x5-12x6-6x7+40x8<=1920 +16x1-2x2+20x3+12x4+16x5-4x6-4x7<=384 +24x1+32x3+16x4+24x5-8x6-6x7<=576 +17x1+1x2+23x3+13x4+18x5-5x6-4x7+1x8<=432 +28x1-12x2+36x3+12x4+24x5-12x6-10x7+4x8<=576 +52x1-36x2+92x3-12x4+40x5-52x6-26x7+12x8<=960 -4x2+14x3-10x4-4x5-6x6-6x7+2x8<=0 +72x1+32x2+120x3+104x4+112x5-16x6-10x7+8x8<=2688 -8x2+20x3-12x4-56x5+12x6-2x7+4x8<=0 +4x1-4x2+16x3-8x4-24x5+4x6-2x7<=64 +8x1+16x3-2x7<=192 -8x1-16x2+20x3+4x4-24x5+12x6-2x7+4x8<=64 -2x1-4x2+4x3-8x5+4x6<=0 +13x1-3x2+12x3+10x4+12x5-6x6-4x7+2x8<=288 +14x1-2x2+15x3+11x4+14x5-7x6-4x7+3x8<=336 -3x1-1x2+8x3+6x4-4x5+2x8<=96 -12x1+20x3+12x4-8x5-4x6-2x7+4x8<=192 -4x1-8x2+6x3-2x4-4x5+2x6-2x7+2x8<=0 +12x1-12x2+28x3-28x4+8x5-20x6-10x7+12x8<=192 +4x3-16x4-4x6-2x7+6x8<=0 +4x3-40x4-4x6-2x7+12x8<=0 +8x1+12x3-44x4+8x5-4x6-2x7+12x8<=192 -2x2-32x4+8x8<=0 +12x1-12x2+20x3-300x4+8x5-12x6-6x7+76x8<=192 +40x1+64x3-208x4+32x5-8x6-10x7+56x8<=960 +72x1+16x2+120x3-120x4+80x5-16x6-14x7+48x8<=2112 +16x1+4x2+26x3-6x4+20x5-2x6-2x7+6x8<=512 +16x1+4x2+26x3+10x4+20x5-2x6-2x7+2x8<=512 +16x1+24x3+8x4+16x5-2x7<=448 -24x1-8x2+68x3+20x4-56x5-12x6-6x7+20x8<=448 -8x1-2x2+24x3+8x4-16x5-4x6-2x7+8x8<=192 -16x1+36x3+4x4-24x5-12x6-6x7+12x8<=192 +13x1+5x2+23x3+13x4+18x5-3x6-2x7+1x8<=448 +2x1+4x3<=64 -2x1+2x2+4x3-4x4-4x6-2x7+2x8<=0 +22x3-22x4-4x5-14x6-10x7<=0 +22x3-82x4-4x5-14x6-10x7+30x8<=0 -4x2+14x3-34x4-4x5-6x6-6x7+14x8<=0 +21x1-3x2+20x3+18x4+20x5-8x6-6x7+2x8<=480 +19x1-1x2+16x3+18x4+20x5-4x6-4x7+2x8<=480 +52x1+44x3+52x4+56x5-12x6-10x7+4x8<=1344 +22x1+12x3+24x4+24x5-4x6-4x7<=576 +28x1+4x2+24x3+32x4+32x5-8x6-6x7<=768 +28x1+4x2-40x3+32x4+32x5+8x6-6x7<=768 +22x1-20x3+24x4+24x5+4x6-4x7<=576 +12x1-10x3+14x4+12x5+2x6-2x7+2x8<=320 +7x1-1x2-3x3+7x4+6x5-1x6-2x7+1x8<=160 -2x1-2x2+12x3-8x4-16x5-4x6-2x7+4x8<=0 -22x1-14x2+52x3-16x4-80x5-12x6-6x7+16x8<=0 -32x1-16x2+68x3+4x4-88x5-12x6-6x7+20x8<=192 -18x1-10x2+36x3+8x4-48x5-4x6-2x7+8x8<=128 -8x1-8x2+20x3+4x4-24x5+4x6-2x7+4x8<=64 -4x1-2x2+4x3-4x4-8x5+4x8<=0 -4x1-8x2+14x3-2x4-20x5+4x6-2x7+2x8<=0 -1x1-7x2+11x3-3x4-14x5+3x6-2x7+1x8<=0 -8x2+12x3-4x4-16x5+4x6-2x7<=0 -4x1-12x2+20x3-4x4-32x5+8x6-2x7<=0 -24x2+44x3-20x4-64x5+16x6-6x7<=0 -4x2+10x3-6x4-12x5+2x6-2x7+2x8<=0 -14x1-22x2+44x3-8x4-64x5+12x6-6x7+8x8<=0 -6x1-10x2+18x3-2x4-28x5+6x6-2x7+2x8<=0 -28x1-36x2+52x3+12x4-72x5+36x6-2x7+12x8<=192 -3x1-3x2+8x3+6x4-4x5+4x6+2x8<=96 -1x1-1x2+2x3-4x5<=0 -12x2+10x3-6x4-12x5+6x6-2x7+2x8<=0 +3x3+3x4-2x5+1x6+1x8<=48 -16x1-24x2+44x3+12x4-72x5+28x6-2x7+12x8<=192 -4x1-12x2+14x3-2x4-20x5+8x6-2x7+2x8<=0 -1x1-9x2+11x3-3x4-14x5+5x6-2x7+1x8<=0 -32x1-40x2+68x3+4x4-88x5+36x6-6x7+20x8<=192 -1x1-1x2+3x3+1x4-6x5+1x6+1x8<=16 -4x1-6x2+12x3+4x4-24x5+8x6+4x8<=64 -4x1-12x2+20x3-4x4-40x5+12x6-2x7+4x8<=0 -10x2+16x3-8x4-24x5+8x6-2x7<=0 +12x1-12x2+40x3-16x4-32x5+8x6-6x7<=192 -24x2+34x3-14x4-44x5+14x6-6x7+2x8<=0 +4x1-4x2+16x3-8x4-16x5-2x7<=64 -8x2+20x3-12x4-32x5-2x7<=0 -4x2+14x3-10x4-20x5-2x6-2x7+2x8<=0 -2x2+2x3-2x4-4x5+2x6<=0 -24x2+44x3-20x4-72x5+20x6-6x7+4x8<=0 -24x2+60x3-36x4-104x5+4x6-6x7+4x8<=0 -6x1-10x2+16x3-4x4-24x5+8x6-2x7+4x8<=0 -1x1-1x2+1x3-1x4-2x5+1x6+1x8<=0 -6x1-18x2+16x3-4x4-24x5+12x6-2x7+4x8<=0 +2x2+20x3+20x4+8x5+4x8<=384 +12x1+4x2+12x3+20x4+8x5-4x6-2x7+4x8<=384 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-4x1+6x3-2x4-4x5-2x6-2x7+2x8<=0 -4x2+6x3-2x4-4x5-2x7<=0 -4x1-2x2+12x3+12x4+4x6<=192 -8x1-8x2+16x3-24x5+4x6-2x7<=0 -20x1-4x2+28x3+4x4-24x5-4x6-6x7+4x8<=64 -20x1-4x2+24x3-24x5-4x6-6x7<=0 -8x1+8x3-8x5-4x6-2x7<=0 -5x1+1x2+6x3-2x4-4x5-4x6-2x7+2x8<=0 -24x1+28x3+4x4-24x5-12x6-6x7+4x8<=64 -46x1+10x2+42x3+6x4-36x5-18x6-14x7+6x8<=96 -18x1+6x2+14x3+2x4-12x5-10x6-6x7+2x8<=32 -112x1+40x2+84x3+12x4-72x5-76x6-38x7+12x8<=192 -6x1+2x2+4x3-4x5-4x6-2x7<=0 -16x4-2x7+8x8<=0 +12x1-12x2-4x3-28x4+8x5-4x6-6x7+20x8<=192 +40x1-38x3+42x4+36x5-2x6-10x7+6x8<=960 +40x1-8x2+20x3+36x4+40x5-4x6-10x7+4x8<=960 +8x1-2x2+8x4+8x5-2x7<=192 +18x1-6x2+4x3+16x4+16x5-4x6-6x7<=384 +8x1-8x3+8x4+8x5-2x7<=192 +20x1-20x2-10x3+14x4+12x5-14x6-10x7+2x8<=320 +8x1+6x2+20x3+36x4-24x5+4x6+12x8<=576 +1x1+1x2+4x3+6x4-4x5+2x8<=96 -16x1+8x2+20x3+12x4-8x5-12x6-6x7+4x8<=192 -12x1+20x2+60x3+52x4+8x5-20x6-10x7+12x8<=960 +12x1+8x2+26x3+26x4+20x5-4x6-2x7+4x8<=576 +48x1+24x2+68x3+100x4+40x5-12x6-6x7+20x8<=1920 +16x1+8x2+32x3+16x4+24x5-4x6-2x7<=640 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-116x1+36x2+80x3-80x5-64x6-38x7<=0 -136x1+56x2+120x3-40x4-80x5-104x6-58x7+40x8<=0 -14x1+6x2+12x3-4x4-8x5-12x6-6x7+4x8<=0 -10x1+6x2+12x3-8x4-16x5-12x6-6x7+8x8<=0 -8x1+8x2+20x3+4x4-88x5-12x6-6x7+20x8<=192 +16x2+52x3+52x4-248x5-12x6-6x7+52x8<=960 -2x2+4x3-20x4-80x5+12x6+4x8<=0 +2x1+4x3-8x4-24x5+4x6<=64 +40x1+20x2+68x3+84x4+72x5+2x6+12x8<=1920 +12x1+6x2+19x3+23x4+22x5+1x6+5x8<=576 +48x1+24x2+72x3+72x4+80x5-4x6-6x7+8x8<=1920 +4x1+4x2-4x3+4x4+8x5+4x6-2x7+4x8<=192 +68x1+12x2+60x3+84x4+72x5-20x6-14x7+12x8<=1920 -1x1-1x2+2x3-4x4-24x5+4x6+4x8<=0 -2x2+4x3-12x4-32x5+6x6+4x8<=0 +4x1-4x2+20x3-52x4-72x5+12x6-2x7+12x8<=64 +8x1+20x3-28x4-24x5+4x6-2x7+4x8<=192 +16x1+36x3-28x4-56x5+12x6-2x7+4x8<=448 +8x1+4x2+2x3+18x4-12x5-2x6-2x7+6x8<=288 +4x1+4x2-12x3+12x4-8x5+4x6-2x7+4x8<=192 +12x1-12x2-14x3+10x4+4x5-10x6-6x7+2x8<=192 +8x1-36x3+12x4-72x5-4x6-2x7+12x8<=192 +24x1+16x2+36x3+84x4-120x5+12x6-2x7+36x8<=1344 +20x1+12x2+20x3+60x4-72x5+4x6-2x7+24x8<=960 +16x1+8x2+20x3+36x4-4x6-2x7+8x8<=640 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-19x1+1x2+21x3+3x4-18x5-5x6-6x7+3x8<=48 +18x1+14x2+50x3+62x4+20x5-2x6-2x7+10x8<=1152 -2x1+2x2+2x3-2x4-4x5-2x6-2x7+2x8<=0 +4x1+2x2-4x3+12x4-40x5+4x6+8x8<=192 +4x1+2x2-4x3+12x4-24x5+4x6+6x8<=192 +3x1+1x2-2x3+8x4-16x5+2x6+4x8<=128 +4x1-4x2+20x3-20x4-40x5+4x6-2x7+4x8<=64 +12x1-12x2+52x3-36x4-104x5+20x6-6x7+4x8<=192 -6x2+12x3-20x4-40x5+8x6+4x8<=0 +12x1+4x2+24x3-32x4-64x5+8x6-2x7<=384 +6x3-18x4-4x5-2x6-2x7+6x8<=0 +8x3-20x4-8x5-4x6-2x7+6x8<=0 -8x2+24x3-40x4-208x5+32x6-2x7+16x8<=0 -8x2+24x3-40x4-144x5+24x6-2x7+16x8<=0 -8x2+24x3-40x4-112x5+16x6-2x7+16x8<=0 +8x1+20x3-60x4-152x5+20x6-2x7+4x8<=192 +4x1-4x2+20x3-84x4-264x5+36x6-2x7+12x8<=64 +16x1+12x2+26x3+42x4+36x5+6x6-2x7+6x8<=960 +20x1+12x2+34x3+42x4+36x5-2x7+6x8<=960 +20x1+16x2+18x3+42x4+36x5+2x6-6x7+6x8<=960 +8x1+8x2+20x3+36x4-88x5+4x6-2x7+20x8<=576 -132x1+60x2+84x3+12x4-72x5-76x6-58x7+12x8<=192 -20x1+12x2+20x3+12x4-8x5-12x6-10x7+4x8<=192 -3x1+3x2+6x3+6x4-2x6-2x7<=96 -16x1+16x2+48x3+48x4-8x6-10x7<=768 +1x1+1x2+6x4-20x5+4x6+4x8<=96 -3x1-5x2+10x3-8x4-72x5+14x6+8x8<=0 -4x1-12x2+32x3-24x4-176x5+32x6-2x7+16x8<=0 +12x1-12x2+60x3-60x4-152x5+28x6-6x7+4x8<=192 +12x1-12x2+76x3-76x4-184x5+28x6-10x7+12x8<=192 -48x4-2x7+16x8<=0 +12x1+8x2+12x3+36x4-24x5-2x7+12x8<=576 +4x1+4x2+4x3+12x4-8x5-4x6-2x7+4x8<=192 -12x2+32x3-32x4-96x5+16x6-2x7+8x8<=0 -24x1+8x2+24x3-8x4-16x5-16x6-10x7+8x8<=0 -52x1+28x2+64x3-40x4-80x5-48x6-30x7+40x8<=0 +12x1-12x2-20x3-156x4+8x5+28x6-6x7+60x8<=192 +12x1-12x2-20x3-380x4+8x5+28x6-6x7+116x8<=192 -2x2-4x3-40x4+4x6+12x8<=0 -6x2-8x3-24x4+8x6+10x8<=0 -8x2+36x3-28x4-152x5+20x6-6x7+4x8<=0 +2x1-2x2+12x3-8x4-32x5+4x6-2x7<=32 -2x2-4x3-4x4+4x6<=0 -6x2-8x3-8x4+8x6+2x8<=0 -6x2-1x3-5x4-2x5+5x6+1x8<=0 +16x1+12x2+48x3+48x4+32x5-4x6-2x7+8x8<=1024 +23x1+15x2+55x3+57x4+42x5-3x6-2x7+9x8<=1248 +24x1+16x2+58x3+66x4+36x5-2x6-2x7+12x8<=1344 +21x1+13x2+45x3+51x4+30x5-3x6-2x7+9x8<=1056 +20x1+12x2+40x3+48x4+24x5-4x6-2x7+8x8<=960 -8x2+24x3-24x4-112x5+20x6-2x7+8x8<=0 -4x1-12x2+32x3-24x4-144x5+24x6-2x7+16x8<=0 -8x2+24x3-24x4-80x5+12x6-2x7+8x8<=0 -8x1+8x3-24x4-80x5+8x6-2x7+24x8<=0 -6x1+2x2+4x3-16x4-48x5-4x6-2x7+16x8<=0 -14x1+10x2+20x3-16x4-48x5-20x6-10x7+16x8<=0 -20x1+12x2+32x3-24x4-80x5-16x6-14x7+24x8<=0 -14x1+2x2+20x3-8x4-16x5-12x6-6x7+8x8<=0 -12x1+4x2+16x3-8x4-16x5-8x6-6x7+8x8<=0 -2x1-4x4-8x5+4x8<=0 -4x1+4x2+12x3+4x4-88x5-4x6-2x7+20x8<=192 -1x1+3x2+4x3+6x4-36x5-2x7+6x8<=96 -4x1+12x2+4x3+12x4-72x5-12x6-10x7+12x8<=192 +4x1+4x2-22x3+10x4+4x5+6x6-2x7+2x8<=192 +28x1+16x2+54x3+62x4+44x5-2x6-2x7+10x8<=1344 +36x1+28x2+120x3+144x4+32x5+8x6-2x7+32x8<=2688 +8x1+6x2+28x3+36x4+4x6+8x8<=640 +1x1+1x2+5x3+7x4-2x5+1x6+1x8<=112 -2x1-2x2+7x3+3x4-18x5+5x6+3x8<=48 -1x1-1x2+2x3-8x5+2x6<=0 -12x1-20x2+48x3-24x4-240x5+48x6-2x7+24x8<=0 +80x1+56x2+216x3+216x4+176x5-8x6-6x7+32x8<=4864 +32x1+24x2+104x3+104x4+80x5-2x7+16x8<=2304 +24x1+14x2+44x3+60x4+24x5-4x6-2x7+12x8<=1152 +6x1+4x2+12x3+24x4-24x5+4x6+8x8<=384 +28x1+20x2+64x3+104x4-48x5+8x6-2x7+32x8<=1728 +24x1+16x2+36x3+84x4-88x5+12x6-2x7+28x8<=1344 -8x1+8x2+12x3+12x4-8x5-4x6-6x7+4x8<=192 -48x1+32x2+28x3+12x4-72x5-20x6-30x7+12x8<=192 +48x1+24x2+44x3+108x4-8x5-4x6-6x7+28x8<=1920 +20x1+12x2+20x3+60x4-40x5+4x6-2x7+16x8<=960 +28x1+16x2+28x3+84x4-40x5+4x6-2x7+20x8<=1344 +14x1+8x2+20x3+48x4-24x5+4x6+12x8<=768 +32x1+24x2+68x3+132x4-152x5+20x6-2x7+52x8<=2112 +4x1+2x2+3x3+11x4-2x5+1x6+3x8<=192 +12x1+6x2+4x3+36x4-16x5+4x6+8x8<=576 +4x1+2x2-4x3+12x4-16x5+4x6+4x8<=192 +36x1+18x2+59x3+75x4+62x5+3x6+13x8<=1728 -4x1+4x2+12x3+12x4-4x6-2x7<=192 +1x1+1x2+3x3+5x4+2x5+1x6+1x8<=96 +2x2+4x3+12x4+4x6<=192 +36x1+28x2+96x3+152x4-16x5+8x6-2x7+16x8<=2496 +12x1+12x2+36x3+60x4-8x5+4x6-2x7+4x8<=960 +18x1+26x2+76x3+120x4+4x6-6x7<=1920 +42x1+34x2+116x3+144x4+48x5-4x6-6x7+24x8<=2688 +17x1+11x2+37x3+43x4+22x5-3x6-2x7+7x8<=864 +60x1+36x2+118x3+142x4+76x5-10x6-6x7+26x8<=2880 +6x1+10x3-10x4+4x5+2x6+2x8<=192 +6x1+10x3-2x4+4x5+2x6<=192 -2x2+2x3-26x4-4x5+2x6+6x8<=0 +12x1-12x2+40x3-240x4-32x5+8x6-6x7+56x8<=192 +7x1+5x2+12x3+30x4-52x5+8x6+14x8<=480 -4x2+16x3-16x4-80x5+12x6-2x7+4x8<=0 -4x1-6x2+12x3-4x4-48x5+12x6+4x8<=0 +36x1+12x2+60x3+20x4+40x5-4x6-6x7+4x8<=1152 -2x1-8x2+16x3-12x4-56x5+12x6+4x8<=0 -10x1-16x2+32x3-12x4-120x5+28x6+12x8<=0 -9x1+1x2-16x3+6x4-36x5+20x6+6x8<=96 -1x1+1x2+6x4-4x5+4x6+2x8<=96 +10x1+6x2+12x3+24x4-16x5-4x6-2x7+8x8<=416 +4x1+4x2-6x3+10x4+4x5+2x6-2x7+2x8<=192 +4x1+4x2-8x3+12x4+2x6-2x7<=192 -4x1+2x2+3x3-1x4-2x5-3x6-2x7+1x8<=0 +12x1+12x2+44x3+52x4+16x5-4x6-2x7+8x8<=960 +8x1+8x2+28x3+28x4+16x5-4x6-2x7+4x8<=576 -3x1-5x2+9x3-1x4-10x5+1x6-2x7+1x8<=0 -3x1-7x2+9x3-1x4-10x5+3x6-2x7+1x8<=0 +16x1+24x2+88x3+88x4+48x5-8x6-6x7+16x8<=1792 +15x1+11x2+39x3+41x4+26x5-3x6-2x7+7x8<=864 +11x1+9x2+31x3+33x4+18x5-3x6-2x7+5x8<=672 +16x1+12x2+42x3+50x4+20x5-2x6-2x7+8x8<=960 +80x1+40x2+154x3+90x4+132x5-18x6-10x7+6x8<=3200 +48x1+24x2+94x3+46x4+76x5-10x6-6x7+2x8<=1920 +12x1+12x2+50x3+58x4+4x5+2x6-2x7+14x8<=1056 +12x1+12x2+44x3+52x4+8x5-4x6-2x7+12x8<=960 -6x2+20x3-20x4-56x5+8x6-2x7+6x8<=0 -8x1-8x2+24x3+8x4-16x5+8x6-2x7+8x8<=192 -3x1-1x2+2x3-4x4-8x5+2x6+4x8<=0 -11x1-1x2+2x3-20x4-40x5+6x6+20x8<=0 -18x2+3x3-13x4-10x5+13x6+3x8<=0 +6x1+4x2+16x3+20x4+8x5+2x6+4x8<=400 +64x1+40x2+144x3+176x4+96x5+8x6-2x7+32x8<=3648 +8x1+6x2+26x3+34x4+4x5+4x6+8x8<=624 +6x2+28x3+36x4+4x6-2x7<=576 +60x1+52x2+200x3+240x4+96x5+8x6-6x7+48x8<=4608 +18x1+14x2+48x3+60x4+24x5-2x7+12x8<=1152 +34x1+22x2+80x3+92x4+56x5-2x7+16x8<=1920 +36x1+22x2+74x3+82x4+52x5-8x6-4x7+14x8<=1728 +28x1+20x2+40x3+80x4-96x5-8x6-6x7+32x8<=1344 +12x1+8x2+12x3+36x4-56x5-2x7+16x8<=576 +13x1+7x2+16x3+30x4-4x5-4x6-2x7+8x8<=528 +12x1-12x2+48x3-40x4-80x5+16x6-6x7+8x8<=192 +12x1-12x2+48x3-200x4-80x5+16x6-6x7+48x8<=192 -6x2+12x3-52x4-40x5+8x6+12x8<=0 -2x2+3x3-21x4-10x5+3x6+5x8<=0 +8x1+12x3-12x4+8x5+2x6+4x8<=256 +6x1+7x3-13x4+6x5+3x6+5x8<=192 +16x1+24x3+16x5+4x6+2x8<=512 +14x1+6x2+4x3+32x4-2x6-2x7<=512 +16x1+8x2+8x3+40x4-2x6-2x7<=640 +20x1+14x2+20x3+60x4-2x6-4x7<=960 +20x1+12x2+4x3+60x4-72x5+12x6-2x7+20x8<=960 +20x1+12x2+4x3+60x4-104x5+12x6-2x7+28x8<=960 +12x1-12x2-20x3-36x4+8x5+28x6-6x7<=192 -2x2+3x3-5x4-10x5+3x6+1x8<=0 -28x1+4x2+44x3+4x4-24x5-20x6-10x7+12x8<=192 -8x1+12x3+4x4-8x5-4x6-2x7+2x8<=64 -14x1-6x2+36x3+16x4-32x5-4x6-2x7+8x8<=256 -4x1-6x2+10x3+2x4-20x5+8x6+4x8<=48 -2x1-4x2+4x3-8x5+4x6+2x8<=16 -12x1-36x2+28x3-12x4-56x5+28x6-2x7+12x8<=0 -4x1-4x2+8x3-8x5-2x7<=0 -4x1-8x2+12x3+4x4-8x5+4x6-2x7<=64 -12x1-12x2+36x3+28x4-8x5+12x6-2x7+4x8<=448 +10x1+8x2+28x3+48x4-8x5+4x6+4x8<=768 +22x1+16x2+52x3+96x4-56x5+12x6+28x8<=1536 +16x1+16x2+88x3+88x4+48x5-2x7+16x8<=1792 -6x1+10x2+20x3+24x4-4x6-6x7<=384 +12x1+28x2+104x3+144x4+8x6-6x7<=2304 +48x1+40x2+168x3+200x4+80x5+8x6-2x7+40x8<=3840 -8x2+6x3-10x4-4x5+2x6-2x7+4x8<=0 -4x1-8x2+6x3-18x4-4x5+2x6-2x7+10x8<=0 +16x1+10x2+16x3+48x4-24x5+2x6-2x7+12x8<=768 +56x1+32x2+32x3+144x4-96x5-8x6-10x7+48x8<=2304 +48x1+24x2+16x3+112x4-8x6-10x7<=1792 +56x1+32x2+32x3+144x4-8x6-10x7<=2304 +6x1+7x3-5x4+6x5+3x6+3x8<=192 +14x1+19x3-1x4+14x5+5x6+3x8<=448 +18x1+24x3-4x4+16x5+8x6+4x8<=576 +60x1+36x2+96x3+168x4+16x5-8x6-6x7+16x8<=2880 +6x1-10x3+10x4+4x5+2x6+2x8<=192 +8x1-12x3+12x4+8x5+4x6+2x8<=256 +16x1+24x4+16x5+2x6+4x8<=512 +6x1-2x3+10x4+4x5+2x8<=192 +18x1-4x3+24x4+16x5+4x6+8x8<=576 +14x1-1x3+19x4+14x5+3x6+5x8<=448 +18x1+3x3+23x4+22x5+3x6+5x8<=576 +6x1-5x3+7x4+6x5+3x6+3x8<=192 +6x1-13x3+7x4+6x5+5x6+3x8<=192 +4x1-4x2-20x3+4x4-24x5-4x6-2x7+4x8<=64 +56x1+32x2+96x3+96x4+96x5-16x6-10x7<=2304 +30x1+32x3+28x4+32x5-8x6-6x7<=768 -1x1<=0 -1x2<=0 -1x3<=0 -1x4<=0 -1x5<=0 -1x6<=0 -1x7<=0 -1x8<=0 END lrslib-071a/ine/test-062/porta/mit71-61.ine.ieq0000700060175606010010000001350113742506304020456 0ustar avisなしDIM = 60 INEQUALITIES_SECTION +384x1-192x3-768x6+512x9+768x13-768x19-192x33+384x39-64x51<=64 -2x9+6x10-6x11+2x12+2x28-6x29+6x30-2x31<=0 -2x9+2x10+2x11-2x12+2x28-2x29-2x30+2x31<=0 -2x9-2x10+2x11+2x12+2x28+2x29-2x30-2x31<=0 -2x9-6x10-6x11-2x12+2x28+6x29+6x30+2x31<=0 -4x6+8x7-4x8+8x9-16x10+8x11-4x28+8x29-4x30<=0 -4x6+4x8+8x9-8x11-4x28+4x30<=0 -4x6-8x7-4x8+8x9+16x10+8x11-4x28-8x29-4x30<=0 -8x1+8x2+24x6-24x7-24x9+24x10+8x28-8x29<=0 -8x1-8x2+24x6+24x7-24x9-24x10+8x28+8x29<=0 +64x1-96x6+64x9-16x28<=16 -1x51+6x52-12x53-3x54+12x55+8x56-3x57-12x58+6x59-1x60<=0 -1x51+4x52-4x53-1x54+1x57+4x58-4x59+1x60<=0 -1x51+2x52+1x54-4x55+1x57+2x59-1x60<=0 -1x51+2x52+4x53-3x54+4x55-8x56-3x57+4x58+2x59-1x60<=0 -1x51+4x53-1x54+1x57-4x58+1x60<=0 -1x51+3x54-3x57+1x60<=0 -1x51-2x52+4x53-3x54-4x55+8x56-3x57+4x58-2x59-1x60<=0 -1x51-2x52+1x54+4x55+1x57-2x59-1x60<=0 -1x51-4x52-4x53-1x54+1x57+4x58+4x59+1x60<=0 -1x51-6x52-12x53-3x54-12x55-8x56-3x57-12x58-6x59-1x60<=0 -2x39+8x40+2x41-8x42-4x43-8x44+4x45+8x46+8x47-8x48-2x49+2x50+2x51-10x52+16x53+4x54-12x55-8x56+2x57+8x58-2x59<=0 -2x39+4x40+2x41-4x42-4x47+4x48+2x49-2x50+2x51-6x52+4x53+4x55-2x57-4x58+2x59<=0 -2x39+8x40-2x41+8x42-4x43-8x44-4x45-8x46+8x47+8x48-2x49-2x50+2x51-6x52+4x54-4x55+8x56+2x57-8x58+2x59<=0 -2x39+4x40-2x41+4x42-4x47-4x48+2x49+2x50+2x51-2x52-4x53+4x55-2x57+4x58-2x59<=0 -2x39+2x41-4x43+8x44+4x45-8x46-2x49+2x50+2x51-2x52-8x53+4x54-4x55+8x56+2x57-2x59<=0 -2x39+2x41+4x43-4x45-2x49+2x50+2x51-2x52-4x54+4x55+2x57-2x59<=0 -2x39-2x41-4x43+8x44-4x45+8x46-2x49-2x50+2x51+2x52-8x53+4x54+4x55-8x56+2x57+2x59<=0 -2x39-2x41+4x43+4x45-2x49-2x50+2x51+2x52-4x54-4x55+2x57+2x59<=0 -2x39-4x40+2x41+4x42+4x47-4x48+2x49-2x50+2x51+2x52-4x53-4x55-2x57+4x58+2x59<=0 -2x39-4x40-2x41-4x42+4x47+4x48+2x49+2x50+2x51+6x52+4x53-4x55-2x57-4x58-2x59<=0 -2x39-8x40+2x41+8x42-4x43-8x44+4x45+8x46-8x47+8x48-2x49+2x50+2x51+6x52+4x54+4x55-8x56+2x57-8x58-2x59<=0 -2x39-8x40-2x41-8x42-4x43-8x44-4x45-8x46-8x47-8x48-2x49-2x50+2x51+10x52+16x53+4x54+12x55+8x56+2x57+8x58+2x59<=0 -4x19+8x20+8x21-4x22-16x23-4x24+8x25+8x26-4x27+8x39-24x40-8x41+24x42+8x43+16x44-8x45-16x46-8x47+8x48-4x51+16x52-20x53-4x54+8x55+8x56-4x58<=0 -4x19+8x21+4x22-4x24-8x25+4x27+8x39-16x40-8x42+8x43+16x46-8x48-4x51+8x52+4x53-4x54-8x56+4x58<=0 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-16x3-32x4-16x5+64x13+128x15+64x17-64x19-128x21-64x24-32x33-64x34-32x35+64x39+128x40+64x43-16x51-32x52-16x54<=0 -16x6+32x7-16x8+32x9-64x10+32x11+32x13-32x14-32x15+32x16-80x19+96x20+64x21-16x22-64x23-16x33+32x34-16x36+64x39-96x40-32x41+32x42+32x44-16x51+32x52-16x53<=0 -16x6+16x8+32x9-32x11+32x13-32x16-80x19+16x22+64x23-16x33+16x36+64x39-32x42-32x44-16x51+16x53<=0 -16x6-32x7-16x8+32x9+64x10+32x11+32x13+32x14+32x15+32x16-80x19-96x20-64x21-16x22-64x23-16x33-32x34-16x36+64x39+96x40+32x41+32x42+32x44-16x51-32x52-16x53<=0 -32x1+32x2+32x3-32x4+128x6-128x7-128x9+128x10-192x13+64x14+128x15+256x19-128x20-128x21+64x33-64x34-160x39+128x40+32x41+32x51-32x52<=0 -32x1-32x2+32x3+32x4+128x6+128x7-128x9-128x10-192x13-64x14-128x15+256x19+128x20+128x21+64x33+64x34-160x39-128x40-32x41+32x51+32x52<=0 -1x28+4x29-6x30+4x31-1x32<=0 -1x28+2x29-2x31+1x32<=0 -1x28+2x30-1x32<=0 -1x28-2x29+2x31+1x32<=0 -1x28-4x29-6x30-4x31-1x32<=0 END lrslib-071a/ine/test-062/porta/perm10.ine.ieq0000700060175606010010000006310313742506305020401 0ustar avisなしDIM = 10 VALID 1 2 3 4 5 6 7 8 9 10 INEQUALITIES_SECTION -1x1-1x2-1x3-1x4-1x5-1x6-1x7-1x8-1x9-1x10==-55 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x8+1x9<=54 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x8+1x10<=54 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x9+1x10<=54 +1x1+1x2+1x3+1x4+1x5+1x6+1x8+1x9+1x10<=54 +1x1+1x2+1x3+1x4+1x5+1x7+1x8+1x9+1x10<=54 +1x1+1x2+1x3+1x4+1x6+1x7+1x8+1x9+1x10<=54 +1x1+1x2+1x3+1x5+1x6+1x7+1x8+1x9+1x10<=54 +1x1+1x2+1x4+1x5+1x6+1x7+1x8+1x9+1x10<=54 +1x1+1x3+1x4+1x5+1x6+1x7+1x8+1x9+1x10<=54 +1x2+1x3+1x4+1x5+1x6+1x7+1x8+1x9+1x10<=54 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x8<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x9<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x7+1x10<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x8+1x9<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x8+1x10<=52 +1x1+1x2+1x3+1x4+1x5+1x6+1x9+1x10<=52 +1x1+1x2+1x3+1x4+1x5+1x7+1x8+1x9<=52 +1x1+1x2+1x3+1x4+1x5+1x7+1x8+1x10<=52 +1x1+1x2+1x3+1x4+1x5+1x7+1x9+1x10<=52 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0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 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 0 0 0 0 0 -1 end lrslib-071a/lpdemo.c0000700060175606010010000000606013742506302014257 0ustar avisなし/* lpdemo.c lrslib lp demo code */ /* last modified: June 20, 2001 */ /* Copyright: David Avis 2001, avis@cs.mcgill.ca */ /* Demo driver for lp code using lrs */ /* This program does lps on a set of generated cubes */ #include #include #include "lrsdriver.h" #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; strcpy(Q->fname,"lpdemo"); 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 = ", P->objnum, P->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 #include #include "lrsdriver.h" #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*lpdemo1:")) return 1; /* allocate and init structure for static problem data and read input */ Q = lrs_alloc_dat ("LRS globals"); 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 */ strcpy(Q->fname,"lpdemo1"); 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; Q->lponly=TRUE; /* we do not want all vertices generated! */ output = lrs_alloc_mp_vector (Q->n); /* Solve the LP */ if (!lrs_solve_lp(P,Q)) return 1; /* Print output */ prat ("\nObjective value = ", P->objnum, P->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 */ lrs_close ("lpdemo1:"); 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 #include #include "lrsdriver.h" #include "lrslib.h" #define LE -1L // A constraint type used here. GE and EQ are defined in lrslib.h #define ROW 0 #define COL 1 #define MAXROW 10 // maximum number of rows #define MAXCOL 10 // maximum number of columns typedef struct { long num; long den; } ratnum; // Rational number: "num/den" typedef struct { ratnum a[MAXCOL]; // Coefficients long ctype; // Constraint type (GE, LE, EQ) ratnum rhs; // 'b' } lprow; // A row in the LP problem typedef struct { // C struct to represent an LP problem long dim[2]; // Number of rows and cols lprow row[MAXROW]; // The rows } lpp; /* An LP problem: max z = (3/4)*x1 + x2 - x3 s.t. 2*x1 + (2/3)*x2 - (2/3)*x3 <= 1 x1 + 2*x2 + (1/3)*x3 <= 3/2 x1 + x2 + x3 = 1 x1 >= 0 x2 >= 0 x3 >= 0 Solution: x1 = 11/32, x2 = 9/16, x3 = 3/32, z = 93/128 */ lpp LP = // The LP problem as a C struct with coefficients as rational numbers {num,den} { {7, 3}, // Dimensions { // -------- a --------- ctype rhs // lprow contents { {{3,4}, {1,1}, {-1,1}}, GE, {0,1} }, // Objective function (goes in row 0 with constraint type GE) { {{2,1}, {2,3}, {-2,3}}, LE, {1,1} }, // Inequality constraints { {{1,1}, {2,1}, { 1,3}}, LE, {3,2} }, { {{1,1}, {1,1}, { 1,1}}, EQ, {1,1} }, // Equality constraint { {{1,1}, {0,1}, { 0,1}}, GE, {0,1} }, // Lower bounds { {{0,1}, {1,1}, { 0,1}}, GE, {0,1} }, { {{0,1}, {0,1}, { 1,1}}, GE, {0,1} } } }; //----------------------------------------------------------------------------------------// // Build an lrs representation from the C struct: // - Replace LE constraints with GE by multiplying LE rows by -1 // - Multiply the RHS column by -1 and move it in front of matrix a // - For each row, call lrs_set_row() with the associated (and possibly modified) constraint type void buildLP (lrs_dic *P, lrs_dat *Q, lpp *lp) { long num[MAXCOL]; long den[MAXCOL]; long i, j, sgn; long m = lp->dim[ROW]; long n = lp->dim[COL]; lprow *row; for (i=0; irow + i; sgn = row->ctype == LE ? -1L : 1L; // sgn = 1 for EQ too if(sgn < 0L) // ctype == LE. Multiply row by -1 and change ctype to GE row->ctype = GE; // RHS num[0] = -sgn*row->rhs.num; // Opposite sign in column 0 den[0] = row->rhs.den; // Coef. matrix for(j=0; ja[j].num; // j+1: RHS goes in column 0 den[j+1] = row->a[j].den; } // Specify constraint type and set row lrs_set_row(P,Q,i,num,den,row->ctype); /* { // Uncomment this to print the lrs input representation of the LP problem char out[40]; printf("\n"); for(j=0;jctype == GE ? "GE" : "EQ"); } // end print */ } printf("\n"); } //----------------------------------------------------------------------------------------// // This is a slightly modified version of main() in lpdemo.c int lp_solve (lpp *lp) { 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 col; /* output column index for dictionary */ // allocate and init structure for static problem data Q = lrs_alloc_dat ("LRS globals"); if (Q == NULL) return 1; strcpy(Q->fname,"lpdemo2"); Q->m = lp->dim[ROW]-1; // Rows, excluding the objective function Q->n = 1+lp->dim[COL]; // Columns, including RHS which goes in column 0 Q->lponly = TRUE; // we do not want all vertices generated! Q->maximize = TRUE; output = lrs_alloc_mp_vector (Q->n); P = lrs_alloc_dic (Q); // allocate and initialize lrs_dic if (P == NULL) return 1; // Build the LP representation in the format required by lrs buildLP(P,Q,lp); // Solve the LP if (!lrs_solve_lp(P,Q)) return 1; // Print output prat ("\nObjective value = ", P->objnum, P->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 */ return 0; } //----------------------------------------------------------------------------------------// int main(void) { lpp *lp = &LP; /* Global initialization - done once */ if ( !lrs_init ("\n*lpdemo2:")) return 1; lp_solve(lp); lrs_close ("lp:"); printf("\n"); } lrslib-071a/lrs.c0000700060175606010010000000461713742506302013605 0ustar avisなし#include #include #include #include #include #include "lrsdriver.h" int main (int argc, char *argv[]) { #ifndef MA lrs_main(argc,argv); /* legacy lrs */ return 0; #endif /* hybrid arithmetic version of lrs */ lrs_restart_dat *R; lrs_dic *P; lrs_dat *Q; char* tmp; /* when overflow occurs a new input file name is returned */ char** newargv; long overfl=0; /* =0 no overflow =1 restart overwrite =2 restart append */ long overfl2=0; /* for B128 */ long b128=0; /* =1 if _int128 available */ int lrs_stdin=0; int i; #ifdef B128 b128=1; #endif P=NULL; Q=NULL; tmp=NULL; R = lrs_alloc_restart(); if (R == NULL) exit(1); if(argc == 1) lrs_stdin=1; tmp = malloc(PATH_MAX * sizeof (char)); if ( (overfl=lrs1_main(argc,argv,&P,&Q,0,0,tmp,R)) == 0) /* set up, read input, no run */ if ( (overfl=lrs1_main(argc,argv,&P,&Q,0,1,tmp,R)) == 0) /* run reverse search */ if ( (overfl=lrs1_main(argc,argv,&P,&Q,0,2,tmp,R)) == 0) /* free memory and close */ goto byebye; if (overfl==-1) /* unrecoverable input error */ { printf("\n"); exit(1); } /* overflow condition triggered: a temporary file was created for restart */ /* create new argv for the remaining calls */ newargv = makenewargv(&argc,argv,tmp); if(b128) { fprintf(stderr,"\n*lrs:overflow possible: restarting with 128 bit arithmetic\n"); if ( (overfl2=lrs2_main(argc,newargv,&P,&Q,overfl,0,tmp,R)) == 0) if ( (overfl2=lrs2_main(argc,newargv,&P,&Q,overfl,1,tmp,R)) == 0) if ( (overfl2=lrs2_main(argc,newargv,&P,&Q,overfl,2,tmp,R)) == 0) goto done; overfl=overfl2; } /* if you change tmp file name update newargv[1] */ fprintf(stderr,"\n*lrs:overflow possible: restarting with GMP arithmetic\n"); lrsgmp_main(argc,newargv,&P,&Q,overfl,0,tmp,R); lrsgmp_main(argc,newargv,&P,&Q,overfl,1,tmp,R); lrsgmp_main(argc,newargv,&P,&Q,overfl,2,tmp,R); done: for(i = 0; i < argc; ++i) free(newargv[i]); free(newargv); byebye: free(R->redineq); free(R->facet); free(R); fprintf(stderr,"\n"); if(lrs_stdin==1) /* get rid of temporary file for stdin */ remove(tmp); free(tmp); return 0; } /* lrs.c */ lrslib-071a/lrsdriver.c0000700060175606010010000000323313742506302015012 0ustar avisなし/* This file contains functions and variables that should not be duplicated per arithmetic */ #include #include #include #include #include #include "lrsdriver.h" /* Globals; these need to be here, rather than lrsdriver.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 */ char** makenewargv(int *argc,char** argv,char *tmp) { int i; char** newargv; newargv = (char**) malloc((*argc+3) * sizeof *newargv); for(i = 0; i < *argc; ++i) { if (i != 1) { size_t length = strlen(argv[i])+1; newargv[i] = (char *) malloc(length); strncpy(newargv[i], argv[i], length); } } /* make tmp the new input file */ size_t length = strlen(tmp)+1; newargv[1] = (char *)malloc(length); strncpy(newargv[1], tmp, length); if(*argc == 1) /* input was stdin*/ *argc = 2; newargv[*argc] = NULL; return newargv; } lrs_restart_dat* lrs_alloc_restart() { int i; lrs_restart_dat *R; R = (lrs_restart_dat *) malloc (sizeof (lrs_restart_dat)); if (R == NULL) return R; R->overide=0; /* do not overide Q */ R->restart=0; /* do not do a restart */ R->facet=NULL; /* this will be allocated later when we know its size */ R->d=0; R->maxcobases=0; R->maxdepth=-1; /* will be set to MAXD in lrs*_main */ R->mindepth=0; R->maxcobases=0; for(i=0;i<10;i++) R->count[i]=0; R->depth=0; R->lrs=1; R->redund=0; R->verifyredund=0; R->redineq = NULL; return R; } lrslib-071a/lrsdriver.h0000700060175606010010000000230313742506306015020 0ustar avisなし/* This file contains functions and variables that should not be duplicated per arithmetic */ #ifndef LRS_DRIVER_H #define LRS_DRIVER_H #include #include #include #include "lrsrestart.h" struct lrs_dic_struct; typedef struct lrs_dic_struct lrs_dic; struct lrs_dat; typedef struct lrs_dat lrs_dat; long lrs_main (int argc, char *argv[]); /* legacy lrs driver, argv[1]=input file, [argc-1]=output file */ long lrs1_main(int argc, char *argv[],lrs_dic **P,lrs_dat **Q, long overf,long stage,char *tmp,lrs_restart_dat *R)/*__attribute__ ((visibility ("default") ))*/; long lrs2_main(int argc, char *argv[],lrs_dic **P,lrs_dat **Q, long overf,long stage,char *tmp,lrs_restart_dat *R)/*__attribute__ ((visibility ("default") ))*/; long lrsgmp_main(int argc, char *argv[],lrs_dic **P,lrs_dat **Q, long overf,long stage,char *tmp,lrs_restart_dat *R)/*__attribute__ ((visibility ("default") ))*/; char** makenewargv(int *argc,char** argv,char* tmp); lrs_restart_dat* lrs_alloc_restart(); extern FILE *lrs_cfp; /* output file for checkpoint information */ extern FILE *lrs_ifp; /* input file pointer */ extern FILE *lrs_ofp; /* output file pointer */ #endif lrslib-071a/lrsgmp.c0000700060175606010010000003037713742506306014317 0ustar avisなし/* lrsgmp.c library code for lrs extended precision arithmetic */ /* Version 4.1, April 3, 2001 */ /* Copyright: David Avis 2001, avis@cs.mcgill.ca */ /* Version 4.2, January 20, 2018 */ /* modified to use generic wrappers for everything in lrsgmp.c */ /* For gmp package */ /* derived from lrslong.c and lrsmp.c */ #include #include #include #include "lrsgmp.h" long lrs_digits; /* max permitted no. of digits */ long lrs_record_digits; /* this is the biggest acheived so far. */ #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 */ { lrs_mp temp1,temp2; lrs_alloc_mp(temp1); lrs_alloc_mp(temp2); copy (temp1, a); copy (temp2, b); gcd (temp1,temp2); exactdivint (a, temp1, temp2); /* temp2=a/temp1 there is no remainder */ mulint (temp2, b, a); lrs_clear_mp(temp1); lrs_clear_mp(temp2); } /* 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 */ { lrs_mp temp1; lrs_alloc_mp(temp1); copy (temp1, Na); exactdivint (temp1, Da, Na); lrs_clear_mp(temp1); } 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; lrs_mp temp1,temp2; lrs_alloc_mp(temp1); lrs_alloc_mp(temp2); mulint (Na, Nb, temp1); mulint (Nc, Nd, temp2); //i=mpz_cmp(temp1,temp2); i=mpcmp(temp1,temp2); lrs_clear_mp(temp1); lrs_clear_mp(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) */ { lrs_mp temp1; lrs_alloc_mp(temp1); 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); lrs_clear_mp(temp1); } 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); y=mptodouble (a); //(*x)=mpz_get_d (b); (*x)=mptodouble (b); (*x) = y / (*x); } /* 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 */ long plrs_readrat (lrs_mp Na, lrs_mp Da, const char* rat) { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; strcpy(in, rat); 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); } 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 input: check you have entered enough data!\n"); 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); } char *cprat (const char *name, lrs_mp Nin, lrs_mp Din) { char *num, *den, *ret; unsigned long len; lrs_mp Nt, Dt; lrs_alloc_mp (Nt); lrs_alloc_mp (Dt); copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); num = mpgetstr10(NULL, Nt); den = mpgetstr10(NULL, Dt); len = snprintf(NULL, 0, " %s %s/%s", name, num, den); ret = (char*)malloc(sizeof(char)*(len+1)); if(one(Dt)) { if (sign (Nt) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); } else { if (sign (Nt) != NEG) sprintf(ret, " %s %s/%s", name, num, den); else sprintf(ret, "%s%s/%s", name, num, den); } free(num); free(den); lrs_clear_mp(Nt); lrs_clear_mp(Dt); return ret; } char *cpmp (const char *name, lrs_mp Nin) { char *num, *ret; unsigned long len; num = mpgetstr10(NULL, Nin); len = snprintf(NULL, 0, "%s %s", name, num); ret = (char*)malloc(sizeof(char)*(len+1)); if (sign (Nin) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); free(num); return ret; } void pmp (const char *name, lrs_mp Nt) { fprintf (lrs_ofp, "%s", name); if (sign (Nt) != NEG) fprintf (lrs_ofp, " "); //mpz_out_str (lrs_ofp,10,Nt); mpoutstr (lrs_ofp,10,Nt); fprintf (lrs_ofp, " "); } void prat (const char *name, lrs_mp Nin, lrs_mp Din) /*print the long precision rational Nt/Dt */ { lrs_mp temp1, temp2; lrs_alloc_mp(temp1); lrs_alloc_mp(temp2); copy (temp1, Nin); copy (temp2, Din); reduce (temp1, temp2); fprintf (lrs_ofp, "%s", name); if (sign (temp1) != NEG) fprintf (lrs_ofp, " "); mpoutstr (lrs_ofp,10,temp1); if ( !one(temp2)) { fprintf (lrs_ofp, "/"); mpoutstr (lrs_ofp,10,temp2); } fprintf (lrs_ofp, " "); lrs_clear_mp(temp1); lrs_clear_mp(temp2); } /* 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 = (lrs_mp_vector) 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 = (lrs_mp_matrix) calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = (lrs_mp_vector) 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, const 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 */ return TRUE; } void notimpl (const 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, temp1; long i = 0L; while ((i < n) && zero (p[i])) i++; if (i == n) return; lrs_alloc_mp (divisor); lrs_alloc_mp (temp1); 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); lrs_clear_mp (temp1); } /* 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 */ { lrs_mp temp1; lrs_alloc_mp (temp1); //mpz_mul_ui (a,a,labs(ka)); mului (a,a,labs(ka)); if (ka < 0) // mpz_neg(a,a); changesign(a); mului (temp1,b,labs(kb)); if (kb < 0) // mpz_neg(temp1,temp1); changesign(temp1); //mpz_add(a,a,temp1); addint(a,temp1,a); lrs_clear_mp (temp1); } void storesign(lrs_mp a, long sa) { if ( (sa)*sign(a) < 0 ) // mpz_neg(a,a); changesign(a); } lrslib-071a/lrsgmp.h0000700060175606010010000003025513742506301014312 0ustar avisなし/* lrsgmp.h (lrs long integer arithmetic library based on gmp */ /* Copyright: David Avis 2000, avis@cs.mcgill.ca */ /* Version 4.0, April 13, 2000 */ /* Version 4.2, January 20, 2018 */ /* modified to use generic wrappers for everything in lrsgmp.c */ /* This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, 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. It is based on gmp and this file is derived from lrsmp.h and lrslong.h */ #ifdef GMP #include "gmp.h" #elif defined(FLINT) #include "fmpz.h" #include "flint.h" #endif /***********/ /* 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 /* 64 bit machines */ #define MAXD 9223372036854775807L #define BASE 1000000000L #define FORMAT "%9.9u" #define BASE_DIG 9 #define INTSIZE 16L #define BIT "64bit" #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 #ifdef MA #define suf(func) func##_gmp #else #define suf(func) func #endif #define atoaa suf(atoaa) #define atomp suf(atomp) #define comprod suf(comprod) #define divrat suf(divrat) #define lcm suf(lcm) #define linint suf(linint) #define linrat suf(linrat) #define lrs_alloc_mp_matrix suf(lrs_alloc_mp_matrix) #define lrs_alloc_mp_vector suf(lrs_alloc_mp_vector) #define lrs_clear_mp_matrix suf(lrs_clear_mp_matrix) #define lrs_clear_mp_vector suf(lrs_clear_mp_vector) #define lrs_getdigits suf(lrs_getdigits) #define lrs_mp_init suf(lrs_mp_init) #define mulrat suf(mulrat) #define myrandom suf(myrandom) #define notimpl suf(notimpl) #define pmp suf(pmp) #define prat suf(prat) #define cprat suf(cprat) #define cpmp suf(cpmp ) #define rattodouble suf(rattodouble) #define readmp suf(readmp) #define readrat suf(readrat) #define plrs_readrat suf(plrs_readrat) #define reduce suf(reduce) #define reducearray suf(reducearray) #define reduceint suf(reduceint) #define storesign suf(storesign) #define stringcpy suf(stringcpy) #define xcalloc suf(xcalloc) /**********************************/ /* MACROS */ /* dependent on mp implementation */ /**********************************/ #ifdef GMP #define addint(a, b, c) mpz_add((c),(a),(b)) #define changesign(a) mpz_neg((a),(a)) #define copy(a, b) mpz_set(a,b) #define decint(a, b) mpz_sub((a),(a),(b)) #define divint(a, b, c) mpz_tdiv_qr((c),(a),(a),(b)) #define exactdivint(a, b, c) mpz_divexact((c),(a),(b)) /*known there is no remainder */ #define getfactorial(a, b) mpz_fac_ui( (a), (b)) #define mpcmp(a,b) mpz_cmp((a),(b)) #define mp_greater(a, b) (mpz_cmp((a),(b))>0 ? 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 mpgetstr10(a,c) mpgetstr(a,10,c) #define mpgetstr(a,b,c) mpz_get_str((a),(b),(c)) #ifndef PLRS #define mpoutstr(a,b,c) mpz_out_str((a),(b),(c)) #else #define mpoutstr(a,b,c) \ {\ char *tmp = mpz_get_str(NULL,10,c);\ fprintf(lrs_ofp, "%s", tmp);\ free(tmp);\ } #endif #define mulint(a, b, c) mpz_mul((c),(a),(b)) #define mului(a, b, c) mpz_mul_ui((a),(b),(c)) #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) #elif defined(FLINT) #define addint(a, b, c) fmpz_add((c),(a),(b)) #define changesign(a) fmpz_neg((a),(a)) #define copy(a, b) fmpz_set(a,b) #define decint(a, b) fmpz_sub((a),(a),(b)) #define divint(a, b, c) fmpz_tdiv_qr((c),(a),(a),(b)) #define exactdivint(a, b, c) fmpz_divexact((c),(a),(b)) /*known there is no remainder */ #define getfactorial(a, b) fmpz_fac_ui( (a), (b)) #define mpcmp(a,b) fmpz_cmp((a),(b)) #define mp_greater(a, b) (fmpz_cmp((a),(b))>0 ? ONE : ZERO) #define gcd(a,b) fmpz_gcd((a),(a),(b)) #define itomp(in, a) fmpz_set_si( (a) , (in) ) #define mptoi(a) fmpz_get_si( (a) ) #define mptodouble(a) fmpz_get_d ( (a) ) #define mpgetstr(a,b,c) fmpz_get_str((a),(b),(c)) #define mpoutstr(a,b,c) fmpz_fprint((a),(c)) /* had a (b) */ #define mulint(a, b, c) fmpz_mul((c),(a),(b)) #define mului(a, b, c) fmpz_mul_ui((a),(b),(c)) #define one(a) (fmpz_cmp_si((a),ONE) == 0 ? ONE : ZERO) #define negative(a) (fmpz_sgn(a) < 0 ? ONE : ZERO) #define normalize(a) (void) 0 #define positive(a) (fmpz_sgn(a) > 0 ? ONE : ZERO) #define sign(a) (fmpz_sgn(a) < 0 ? NEG : POS) #define subint(a, b, c) fmpz_sub((c),(a),(b)) #define zero(a) (fmpz_sgn(a) == 0 ? ONE : ZERO) #endif /* * 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 #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*************/ /* typedefs */ /*************/ #ifdef GMP 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; #elif defined(FLINT) typedef fmpz_t lrs_mp; /* type lrs_mp holds one long integer */ typedef fmpz_t lrs_mp_t; /* for GMP same as lrs_mp for MP *lrs_mp */ typedef fmpz_t *lrs_mp_vector; typedef fmpz_t **lrs_mp_matrix; #endif /*********************/ /*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 */ #ifdef GMP #define lrs_alloc_mp(a) (mpz_init (a) ) #define lrs_clear_mp(a) (mpz_clear (a) ) #elif defined(FLINT) #define lrs_alloc_mp(a) (fmpz_init (a) ) #define lrs_clear_mp(a) (fmpz_clear (a) ) #endif 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 */ #ifdef PLRS long plrs_readrat (lrs_mp Na, lrs_mp Da, const char * rat); /* take a rational number and convert to lrs_mp */ #endif char *cprat(const char *name, lrs_mp Nt, lrs_mp Dt); /* mp rat to char */ char *cpmp(const char *name, lrs_mp Nt); /* mp int to char */ void pmp (const 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) */ 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 (const 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, const char *f); void lrs_default_digits_overflow (); void lrs_exit(int i); /* end of lrsgmp.h (vertex enumeration using lexicographic reverse search) */ lrslib-071a/lrslib.c0000700060175606010010000050762113742506306014303 0ustar avisなし/* lrslib.c library code for lrs */ /* modified by Gary Roumanis for multithread plrs compatability */ /* truncate needs mod to supress last pivot */ /* need to add a test for non-degenerate pivot step in reverse I guess */ /* Copyright: David Avis 2005,2011 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ #include #include #include #include #include "lrsrestart.h" #include "lrslib.h" static 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 size_t infileLen; /* length of cache of input file */ static char *infile = NULL; /* cache of input for restart */ static char infilename[PATH_MAX]; static char outfilename[PATH_MAX]; static char tmpfilename[PATH_MAX]; static int tmpfd; static long overflow=0; /* =0 no overflow =1 restart overwrite =2 restart append */ static long pivoting=FALSE; /* =0 no overflow =1 restart overwrite =2 restart append */ static jmp_buf buf1; static lrs_dat_p *lrs_global_list[MAX_LRS_GLOBALS + 1]; static lrs_dic *new_lrs_dic (long m, long d, long m_A); static void cache_dict (lrs_dic ** D_p, lrs_dat * global, long i, long j); static long check_cache (lrs_dic ** D_p, lrs_dat * global, long *i_p, long *j_p); static void save_basis (lrs_dic * D, lrs_dat * Q); static void lrs_dump_state (); static void pushQ (lrs_dat * global, long m, long d, long m_A); #ifndef TIMES static void ptimes (void); static double get_time(void); #endif /*******************************/ /* signals handling */ /*******************************/ #ifndef SIGNALS static void checkpoint (); static void die_gracefully (); static void setup_signals (void); static void timecheck (); #endif /*******************************/ /* functions for external use */ /*******************************/ /******************************************************************/ /* lrs_run is the main reverse search part of lrs */ /* should be called by lrsv2_main which does setup and close also */ /******************************************************************/ long lrs_run ( lrs_dic *P, lrs_dat * Q) { 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 */ /*********************************************************************************/ /* Step 1: 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 */ if(!Q->restart) for (col = startcol; col < Q->nredundcol; col++) /* print linearity space */ lrs_printoutput (Q, Lin[col]); /* Array Lin[][] holds the coeffs. */ if(Q->nredundcol > 0) lrs_clear_mp_matrix(Lin,Q->nredundcol,Q->n); /*********************************************************************************/ /* 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 { //2015.6.5 after maxcobases reached, generate subtrees that have not been enumerated //2018.1.19 fix printcobasis bug when maxcobases set //2019.5.8 new givoutput flag to avoid printing restart cobases prune=lrs_checkbound(P,Q); if (!prune && Q->giveoutput) { lrs_open_outputblock(); /* keeps output together when using mplrs */ for (col = 0; col <= P->d; col++) /* print output if any */ if (lrs_getsolution (P, Q, Q->output, col)) lrs_printoutput (Q, Q->output); lrs_close_outputblock(); } else Q->giveoutput=TRUE; /* first output supressed for restart */ /*2020.3.9 bounds on objective function check corrected */ if ((Q->maxcobases > 0) && (Q->count[2] >=Q->maxcobases)) { prune=TRUE; if( !lrs_leaf(P,Q)) /* do not return cobases of a leaf */ lrs_return_unexplored(P,Q); } save_basis(P,Q); }while (!Q->lponly && lrs_getnextbasis (&P, Q, prune)); // do ... if (Q->lponly) lrs_lpoutput(P,Q,Q->output); else lrs_printtotals (P, Q); /* print final totals, including estimates */ Q->m=P->m; lrs_free_dic(P,Q); /* note Q is not free here and can be reused */ return 0; } /*********************************************/ /* end of model test program for lrs library */ /*********************************************/ /*******************************************************/ /* redund_run is main loop for redundancy removal */ /*******************************************************/ long redund_run ( lrs_dic *P, lrs_dat * Q) { lrs_mp_matrix Ain; /* holds a copy of the input matrix to output at the end */ long ineq; /* input inequality number of current index */ long *redineq; 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 lastdv; long debug; long index; /* basic index for redundancy test */ /*********************************************************************************/ /* 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; redineq = Q->redineq; debug = Q->debug; Q->Ain = lrs_alloc_mp_matrix (m, d); /* make a copy of A matrix for output later */ Ain=Q->Ain; 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 1: 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 2: Test rows i where redineq[i]=1 for redundancy */ /*********************************************************************************/ /* 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; /* linearities are not considered for redundancy */ for (i = 0; i < nlinearity; i++) redineq[Q->linearity[i]] = 2L; if(Q->debug) fprintf (lrs_ofp, "\nredundcheck=%ld verifyredund=%ld",Q->noredundcheck, Q->verifyredund); /* Q->verifyredund always false in lrs, set by mplrs to check duplicated redundancy removal */ /* Q->noredundcheck overides this to skip verification */ if(Q->noredundcheck && Q->verifyredund) goto done; /* mplrs sets redineq[i]==-1 for guaranteed redundant inequalities */ /* these rows must be zeroed out before testing the others */ if (Q->verifyredund) /* this is never run by lrs, final step of mplrs redund */ for (index = lastdv + Q->redineq[0]; index <= m + d; index++) { ineq = Q->inequality[index - lastdv]; /* the input inequality number corr. to this index */ if( redineq[ineq]== -1 ) checkindex (P, Q, -index); /* used to zero correct row of A no LP solved */ } /* rows 0..lastdv are cost, decision variables, or linearities */ /* other rows need to be tested */ for (index = lastdv + Q->redineq[0]; index <= m + d; index++) { ineq = Q->inequality[index - lastdv]; /* the input inequality number corr. to this index */ Q->redineq[0] = ineq; /* used for restarting after arithmetic overflow */ if( redineq[ineq]==1 ) { redineq[ineq] = checkindex (P, Q, index); if (debug) fprintf (lrs_ofp, "\ncheck index=%ld, inequality=%ld, redineq=%ld", index, ineq, redineq[ineq]); if(!Q->mplrs && Q->verbose) { if( redineq[ineq]==1 ) lrs_printrow ("*re ", Q, Ain[ineq], Q->inputd); else lrs_printrow ("*nr ", Q, Ain[ineq], Q->inputd); } } } /* end for index ..... */ done: if(Q->mplrs && !Q->verifyredund) { /* return array redineq to consumer */ char *ss; int len=0; ss=(char *)malloc(20*m*sizeof(char)); for (i=1; i<=m; i++) if(redineq[i]==1) len=len+sprintf(ss+len," %ld",i); if(len>0) lrs_post_output("redund", ss); free(ss); lrs_clear_mp_matrix(Ain,P->m_A,P->d); Q->m=P->m; lrs_free_dic(P,Q); /* note Q is not free here and can be reused */ return 0; } if (Q->verbose || Q->debug) { fprintf (lrs_ofp, "\n*redineq:"); for (i = 1; i <= m; i++) fprintf (lrs_ofp, " %ld", redineq[i]); } redund_print(Ain,P,Q); lrs_clear_mp_matrix(Ain,P->m_A,P->d); Q->m=P->m; lrs_free_dic(P,Q); /* note Q is not free here and can be reused */ return 0; } /*********************************************/ void redund_print(lrs_mp_matrix Ain,lrs_dic *P,lrs_dat *Q) { long i, m; long nlinearity; /* number of linearities in input file */ long nredund; /* number of redundant rows in input file */ long *redineq=Q->redineq; m = P->m_A; /* number of rows of A matrix */ nlinearity = Q->nlinearity; /* restore as mplrs loses this */ for (i = 0; i < nlinearity; i++) redineq[Q->linearity[i]]=2; /* fprintf(lrs_ofp,"\nQ->red"); for (i = 1; i <= m; i++) fprintf(lrs_ofp," %ld",Q->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 = 0; /* 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", nlinearity+nredund, Q->n); pivoting=TRUE; /* 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); if( m==nredund) fprintf (lrs_ofp, "\n*No redundant rows found"); else { fprintf (lrs_ofp, "\n* %ld redundant row(s) found:\n", m - nredund-nlinearity); for (i=1; i<=m; i++) if(redineq[i]==1 || redineq[i]==-1) fprintf (lrs_ofp, " %ld",i); if (Q->noredundcheck) fprintf (lrs_ofp, "\n*Warning: not verified - input should be full dimensional and duplicate free"); } fprintf (lrs_ofp, "\n"); return; } /* end of redund_print */ /*******************/ /* lrs_printoutput */ /* one line only */ /*******************/ void lrs_printoutput (lrs_dat * Q, lrs_mp_vector output) { char *sss; char **ss; long i; long len=0; if (Q->countonly) return; ss = (char **)malloc((1+Q->n) * sizeof(char*)); if (Q->hull || zero (output[0])) /*non vertex */ for (i = 0; i < Q->n; i++) { ss[i]=cpmp ("", output[i]); len=len+snprintf(NULL, 0, "%s ", ss[i] ); } else for (i = 1; i < Q->n; i++) { ss[i]=cprat("", output[i], output[0]); len=len+snprintf(NULL, 0, "%s ", ss[i] ); } sss=(char*)malloc((len+5)* sizeof(char*)); len=0; if (Q->hull || zero (output[0])) /*non vertex */ for (i = 0; i < Q->n; i++) { len=len+sprintf(sss+len,"%s ",ss[i]); free(ss[i]); } else { /* vertex */ len=sprintf (sss, " 1 "); for (i = 1; i < Q->n; i++) { len=len+sprintf(sss+len, "%s ", ss[i] ); free(ss[i]); } } if(Q->mplrs) lrs_post_output("vertex",sss); else fprintf (lrs_ofp, "\n%s",sss); free(ss); free(sss); } /**************************/ /* end of lrs_printoutput */ /**************************/ /****************/ /* lrs_lpoutput */ /****************/ void lrs_lpoutput(lrs_dic * P,lrs_dat * Q, lrs_mp_vector output) { if(Q->unbounded || !Q->messages) return; lrs_mp Temp1, Temp2; long i; lrs_alloc_mp (Temp1); lrs_alloc_mp (Temp2); prat ("\n*Obj=",P->objnum, P->objden); fprintf (lrs_ofp, " pivots=%ld ",Q->count[3]); if(Q->verbose) { 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); } /***********************/ /* end of lrs_lpoutput */ /***********************/ void lrs_printrow (const 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 */ void lrs_print_header(const char *name) { if(lrs_ofp == NULL) lrs_ofp=stdout; #ifdef LRS_QUIET return; #endif fprintf (lrs_ofp,"%s", name); fprintf (lrs_ofp,TITLE); fprintf (lrs_ofp,VERSION); fprintf (lrs_ofp,"("); fprintf (lrs_ofp,BIT); fprintf (lrs_ofp,","); fprintf (lrs_ofp,ARITH); #ifdef MA fprintf (lrs_ofp,",hybrid arithmetic"); #endif #ifdef LRSLONG #ifndef SAFE fprintf (lrs_ofp,",no overflow checking"); #endif #endif fprintf (lrs_ofp,")"); if(overflow != 2) { #ifdef GMP fprintf(lrs_ofp," gmp v.%d.%d",__GNU_MP_VERSION,__GNU_MP_VERSION_MINOR); #elif defined(FLINT) fprintf(lrs_ofp," %dbit flint v.%s", FLINT_BITS, FLINT_VERSION); #endif } } long lrs_init (const char *name) /* returns TRUE if successful, else FALSE */ { #ifndef PLRS #ifndef LRS_QUIET if(overflow!=2) lrs_print_header(name); #endif #endif if (!lrs_mp_init (ZERO, stdin, stdout)) /* initialize arithmetic */ return FALSE; lrs_global_count = 0; lrs_checkpoint_seconds = 0; #ifndef SIGNALS setup_signals (); #endif return TRUE; } void lrs_close (const char *name) { #ifdef PLRS return; #endif #ifdef LRS_QUIET fprintf (lrs_ofp, "\n"); if (lrs_ofp != stdout) { fclose (lrs_ofp); lrs_ofp=NULL; } return; #endif #ifdef LRSLONG #ifdef SAFE fprintf (lrs_ofp, "\n*Overflow checking on lrslong arithmetic"); #else fprintf (lrs_ofp, "\n*Caution: no overflow checking on long integer arithemtic"); #endif #endif 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); #ifdef MA fprintf (lrs_ofp, ",hybrid arithmetic"); #endif fprintf (lrs_ofp, ")"); #ifdef MP fprintf (lrs_ofp, " max digits=%ld/%ld", DIG2DEC (lrs_record_digits), DIG2DEC (lrs_digits)); #endif #ifndef TIMES ptimes (); #endif if (lrs_ofp != stdout) { fclose (lrs_ofp); lrs_ofp=NULL; } } /***********************************/ /* allocate and initialize lrs_dat */ /***********************************/ lrs_dat * lrs_alloc_dat (const 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); return NULL; } 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->mplrs=FALSE; Q->messages=TRUE; #ifdef PLRS Q->mplrs=TRUE; #endif #ifdef LRS_QUIET Q->messages=FALSE; #endif strcpy(Q->fname,""); /* name of program, filled in later */ Q->m = 0L; Q->n = 0L; Q->inputd = 0L; Q->deepest = 0L; Q->nlinearity = 0L; Q->nredundcol = 0L; Q->runs = 0L; Q->subtreesize=MAXD; Q->seed = 1234L; Q->totalnodes = 0L; for (i = 0; i < 10; i++) { Q->count[i] = 0L; Q->cest[i] = 0.0; if(i < 5) Q->startcount[i] = 0L; } Q->count[2] = 1L; /* basis counter */ Q->startcount[2] = 0L; /* starting basis counter */ /* initialize flags */ Q->allbases = FALSE; Q->bound = FALSE; /* upper/lower bound on objective function given */ Q->countonly = FALSE; /* produce the usual output */ 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->triangulation = FALSE; Q->hull = FALSE; Q->incidence = FALSE; Q->lponly = FALSE; Q->maxdepth = MAXD; Q->mindepth = -MAXD; Q->maxoutput = 0L; Q->maxcobases = 0L; /* after maxcobases have been found unexplored subtrees reported */ Q->nash = FALSE; Q->nonnegative = FALSE; Q->printcobasis = FALSE; Q->printslack = FALSE; Q->truncate = FALSE; /* truncate tree when moving from opt vertex */ Q->extract=FALSE; 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->newstart=FALSE; Q->giveoutput=TRUE; /* set to false for first output after restart */ Q->verifyredund=FALSE; /* set to true when mplrs verifies redund output */ Q->noredundcheck=FALSE; /* set to true when mplrs skips verifying output */ Q->nextineq=15; /* start redundancy testing from this row */ Q->startcob=NULL; 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); 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[1000]; char writemode[2]="w"; /* will be set to "a" (append) for overflow or newstart */ long dec_digits = DEFAULT_DIGITS; long infilenum=0; /*input file number to open if any */ long firstline = TRUE; /*flag for picking off name at line 1 */ long i; int c; /* for fgetc */ int messages = Q->messages; /* print output for each option */ *tmpfilename='\0'; if(overflow==2) /* otherwise overwrite output */ strcpy(writemode,"a"); strcpy(outfilename, "\0"); if(argc > 1 ) { infilenum=1; if(Q->nash && argc ==2) /* legacy code to open second nash input file */ infilenum=2; if(Q->nash && argc ==4) /* legacy code for nash output file */ strcpy(outfilename,argv[3]); } if (infilenum > 0 && (lrs_ifp = fopen (argv[infilenum], "r")) == NULL) /* command line overides stdin */ { fprintf (stderr,"\n*bad input file name\n"); return (FALSE); } if (infilenum==1) { strcpy(infilename,argv[1]); if(!Q->mplrs && messages && overflow == 0 ) printf ("\n*Input taken from %s", infilename); fflush(stdout); } #ifdef LRSLONG if(infilenum==0) /* stdin gets written to a temporary file */ { strcpy(tmpfilename,"/tmp/lrs_stdinXXXXXX"); mkstemp(tmpfilename); lrs_stdin_to_file(tmpfilename); lrs_ifp=fopen (tmpfilename, "r"); strcpy(infilename,tmpfilename); } lrs_file_to_cache(lrs_ifp); #endif if(argc > 2) /* lrs has commandline arguments for newstart */ { if (!Q->nash ) { i=2; while (i < argc) /* add command line arguments here */ { if(strcmp(argv[i],"-newstart")==0) /* newstart not currently used ... */ { strcpy(writemode,"a"); Q->newstart=TRUE; } else /* command line argument overides stdout */ strcpy(outfilename,argv[i++]); } } if(strcmp(outfilename,"\0") != 0 ) { if ((lrs_ofp = fopen (outfilename, writemode)) == NULL) { fprintf (stderr,"\n*bad output file name %s\n",outfilename); return (FALSE); } else if(overflow == 0) printf ("\n*Output sent to file %s\n", outfilename); } } /*2020.5.19 new redund handling, thanks to DB */ /* symbolic link from redund to lrs needed */ /* similar links if lrs1, lrs2 or lrsgmp used */ /* any redund option in input will overide */ if(!Q->mplrs && lrs_ofp != stdout && overflow != 2 ) /* headers for the output file also */ { char *name; name=(char *) malloc(strlen(Q->fname)+5); strcpy(name,"*"); strcat(name,Q->fname); strcat(name,":"); lrs_print_header(name); free(name); } /* process input file */ if( fscanf (lrs_ifp, "%s", name) == EOF) { fprintf (stderr, "\n*no 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 (stderr, "\n*no 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 (stderr, "\nNash incompatibile with nonnegative option - skipped"); else Q->nonnegative = TRUE; } else if (firstline) { // printf("\nov=%ld mess=%ld",overflow,Q->messages); if(overflow != 2) lrs_warning(Q,"warning",name); firstline = FALSE; } if (fscanf (lrs_ifp, "%s", name) == EOF) { fprintf (stderr, "\n*no begin line\n"); return (FALSE); } } /* end of while */ if (fscanf (lrs_ifp, "%ld %ld %s", &Q->m, &Q->n, name) == EOF) { fprintf (stderr, "\n*no data in file\n"); return (FALSE); } if (strcmp (name, "integer") != 0 && strcmp (name, "rational") != 0) { fprintf (stderr,"\n*data type must be integer of rational\n"); return (FALSE); } if (Q->m == 0) { fprintf (stderr, "\n*no input given\n"); /* 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, mptwo; long i, j, m, d;; char name[100]; char mess[100]; char *ss; int c; /* fgetc actually returns an int. db */ long redundstart, redundend; long dualperturb=FALSE; /* dualperturb=TRUE: objective function perturbed */ /* assign local variables to structures */ lrs_mp_matrix A; lrs_mp_vector Gcd, Lcm; lrs_mp_vector oD=Q->output; /* Denom for obj fun, temp use of output */ long hull = Q->hull; long messages=Q->messages; lrs_alloc_mp(Temp); lrs_alloc_mp(mpone); lrs_alloc_mp(Tempn); lrs_alloc_mp(Tempd); lrs_alloc_mp(mptwo); A = P->A; m = Q->m; d = Q->inputd; Gcd = Q->Gcd; Lcm = Q->Lcm; itomp (ONE, mpone); itomp(2L,mptwo); 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 (mp_greater (Gcd[i], mpone) || mp_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 && overflow != 2) { lrs_warning(Q,"warning","*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); } #ifndef 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; if(!Q->mplrs) fprintf (lrs_ofp, "\n*%s from B#%ld to B#%ld", name, Q->strace, Q->etrace); Q->debug=TRUE; if (Q->strace <= 1) Q->debug = TRUE; } if (strcmp (name, "startingcobasis") == 0) { if(Q->nonnegative) lrs_warning(Q,"warning", "*startingcobasis incompatible with nonnegative option:skipped"); else { if(!Q->mplrs && messages && overflow != 2) fprintf (lrs_ofp, "\n*startingcobasis"); Q->givenstart = TRUE; if (!readfacets (Q, Q->inequality)) return FALSE; } } if (strcmp (name, "restart")==0 ) { if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } Q->restart = TRUE; Q->giveoutput = FALSE; /* first time only */ 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; if(!Q->mplrs && messages) 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) return(FALSE); if(!Q->mplrs && messages && overflow != 2) 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; if(!Q->mplrs && messages && overflow != 2) 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); } /* store starting counts to calculate totals of plrs/mplrs subjob */ for (i = 0; i<5; i++) Q->startcount[i] = Q->count[i]; if (!readfacets (Q, Q->facet)) return FALSE; } /* end of restart */ /* The next flags request a LP solution only */ if(Q->mplrs) { if (strncmp (name,"lponly",6)== 0) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } } else { if (strcmp (name, "lponly") == 0 || strcmp (name, "lponly_d") == 0 ) { if (Q->hull) fprintf (lrs_ofp, "\n*lponly option not valid for V-representation-skipped"); else { Q->lponly = 1; /*Dantzig's rule is default */ fprintf (lrs_ofp, "\n*Dantzig's rule"); } } if (strcmp (name, "lponly_r") == 0) { if (Q->hull) fprintf (lrs_ofp, "\n*lponly option not valid for V-representation-skipped"); else { Q->lponly = 2; /*random edge rule */ fprintf (lrs_ofp, "\n*random edge rule"); } } if (strcmp (name, "lponly_rd") == 0) { if (Q->hull) fprintf (lrs_ofp, "\n*lponly option not valid for V-representation-skipped"); else { Q->lponly = 3; /*random edge/Dantzig hybrid */ fprintf (lrs_ofp, "\n*random edge/Dantzig hybrid"); } } if (strcmp (name, "lponly_b") == 0) { if (Q->hull) fprintf (lrs_ofp, "\n*lponly option not valid for V-representation-skipped"); else { Q->lponly = 4; /*Bland' rule */ fprintf (lrs_ofp, "\n*Bland's rule"); } } } /* else !Q->mplrs */ /* The LP will be solved after initialization to get starting vertex */ if (strcmp (name, "maximize") == 0 || strcmp (name, "minimize") == 0) { if (Q->hull ) lrs_warning(Q,"warning","*minimize/maximize options not valid for V-representation-skipped"); else { if (strcmp (name, "maximize") == 0) Q->maximize = TRUE; else Q->minimize = TRUE; if(overflow != 2) lrs_warning(Q,"warning",name); if(dualperturb && overflow != 2) /* apply a perturbation to objective function */ { lrs_warning(Q,"warning","*Objective function perturbed"); copy(Temp,mptwo); } for (j = 0; j <= d; j++) { if (readrat (A[0][j], oD[j]) || dualperturb ) { if(dualperturb && j > 0 && j < d ) { linrat(A[0][j], oD[j],ONE,mpone,Temp,ONE,Tempn,Tempd); copy(A[0][j],Tempn); copy(oD[j],Tempd); mulint(mptwo,Temp,Temp); } reduce (A[0][j], oD[j]); lcm (Q->Lcm[0], oD[j]); /* update lcm of denominators */ } } for (j = 0; j <= d; j++) if (!Q->maximize) changesign (A[0][j]); storesign (Q->Lcm[0], POS); if (mp_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(messages && overflow !=2 ) lrs_printoutput(Q,A[0]); if (Q->debug) printA (P, Q); } /* else */ } /* end of LP setup */ if (strcmp (name, "volume") == 0) { if(overflow != 2) lrs_warning(Q,"warning", "*volume"); Q->getvolume = TRUE; } if (strcmp (name, "geometric") == 0) { if (hull && !Q->voronoi) lrs_warning(Q,"warning", "*geometric - option for H-representation or voronoi only, skipped"); else { lrs_warning(Q,"warning", "*geometric"); Q->geometric = TRUE; } } if (strcmp (name, "allbases") == 0) { if(overflow != 2) lrs_warning (Q,"warning", "*allbases"); Q->allbases = TRUE; } if (strcmp (name, "countonly") == 0) { if(overflow != 2) lrs_warning (Q,"warning", "*countonly"); Q->countonly = TRUE; } if (strcmp (name, "triangulation") == 0) { if (hull) { if(overflow != 2) lrs_warning (Q,"warning","*triangulation"); Q->triangulation = TRUE; Q->getvolume = TRUE; } else printf ("\n*triangulation only valid for V-representations: skipped"); } if (strcmp (name, "dualperturb") == 0) { dualperturb = TRUE; } if (strcmp (name, "incidence") == 0) { if(overflow != 2) lrs_warning (Q,"warning", "*incidence"); 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; if(overflow != 2) { if (Q->frequency > 0) sprintf(mess,"*%s %ld",name, Q->frequency); else sprintf(mess,"%s",name); lrs_warning(Q,"warning",mess); } Q->printcobasis = TRUE; } if (strcmp (name, "integervertices") == 0) /* when restarting reinitialize */ { if(fscanf (lrs_ifp, "%ld", &Q->count[4])==EOF) Q->count[4]=0; } if (strcmp (name, "printslack") == 0) { Q->printslack = TRUE; } if (strcmp (name, "cache") == 0) { if(fscanf (lrs_ifp, "%ld", &dict_limit)==EOF) dict_limit=1; if (dict_limit < 1) dict_limit = 1; if(overflow != 2) { sprintf(mess,"*%s %ld",name, dict_limit); lrs_warning(Q,"warning",mess); } } if (strcmp (name, "linearity") == 0) { if (!readlinearity (Q)) return FALSE; } if (strcmp (name, "maxdepth") == 0) { Q->maxdepth=MAXD; if(fscanf (lrs_ifp, "%lld", &Q->maxdepth)==EOF) Q->maxdepth=MAXD; if(overflow != 2) { if(Q->mplrs) /* taken from control line */ lrs_warning(Q,"warning","*maxdepth option skipped - supplied on control line in mplrs"); else fprintf (lrs_ofp, "\n*%s %lld", name, Q->maxdepth); } } if (strcmp (name, "mindepth") == 0) { Q->mindepth=0; if(fscanf (lrs_ifp, "%lld", &Q->mindepth)==EOF) Q->mindepth=0; if(overflow != 2) { if(Q->mplrs) /* taken from control line */ lrs_warning(Q,"warning","*mindepth option skipped in mplrs"); else fprintf (lrs_ofp, "\n*%s %lld", name, Q->mindepth); } } if (strcmp (name, "maxoutput") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->maxoutput)==EOF) Q->maxoutput = 100; if(overflow != 2) { if(Q->mplrs) /* taken from control line */ lrs_warning(Q,"warning","*maxoutput option skipped in mplrs"); else fprintf (lrs_ofp, "\n*%s %ld", name, Q->maxoutput); } } if (strcmp (name, "maxcobases") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->maxcobases)==EOF) Q->maxcobases = 1000; if(overflow != 2) { if(Q->mplrs) /* taken from control line */ lrs_warning(Q,"warning","*maxcobases option skipped - supplied on control line in mplrs"); else fprintf (lrs_ofp, "\n*%s %ld", name, Q->maxcobases); } } /*2019.8.24 bounds for redund */ if (strcmp (name, "redund") == 0) { strcpy(Q->fname,"redund"); for (i = 1; i <= Q->m; i++) /*reset any previous redund option except =2 values */ if (Q->redineq[i] != 2) Q->redineq[i]=0; Q->redineq[0]=1; if( fscanf (lrs_ifp, "%ld %ld", &redundstart, &redundend)==EOF) { redundstart=1; redundend=m; } if (redundstart <1 || redundstart > redundend ) redundstart=1; if (redundend < 1 || redundend > Q->m ) redundend=Q->m; for (i=redundstart;i<=redundend;i++) Q->redineq[i]=1; if(overflow != 2 ) { sprintf (mess, "%s %ld %ld", name, redundstart, redundend); lrs_warning(Q,"warning",mess); } } if (strcmp (name, "redund_list") == 0) { strcpy(Q->fname,"redund"); readredund(Q); } if (strcmp (name, "noredundcheck") == 0) { if(Q->mplrs) { if(messages && overflow != 2) lrs_warning(Q,"warning","*noredundcheck"); Q->noredundcheck = TRUE; } } if (strcmp (name, "truncate") == 0) { if (hull) { if(overflow != 2) lrs_warning(Q,"warning","*truncate - option for H-representation only, skipped"); } else { Q->truncate = TRUE; lrs_warning(Q,"warning","*truncate"); } } if (strcmp (name, "extract") == 0) { if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } Q->extract = TRUE; readremain(Q); } 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) if(overflow != 2) lrs_warning(Q,"warning","*nonnegative - option must come before begin line - skipped"); if (strcmp (name, "seed") == 0) { if(fscanf (lrs_ifp, "%ld", &Q->seed)==EOF) Q->seed = 3142; sprintf(mess,"*seed=%ld",Q->seed); if(overflow != 2) lrs_warning(Q,"warning",mess); srandom(Q->seed); } if (strcmp (name, "estimates") == 0) { if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } if(fscanf (lrs_ifp, "%ld", &Q->runs)==EOF) Q->runs=1; if(messages && overflow != 2) fprintf (lrs_ofp, "\n*%ld %s", Q->runs, name); } // 2015.2.9 Estimates will continue until estimate is less than subtree size if (strcmp (name, "subtreesize") == 0) { if(fscanf (lrs_ifp, "%lld", &Q->subtreesize)==EOF) Q->subtreesize=MAXD; if(messages && overflow != 2) fprintf (lrs_ofp, "\n*%s %lld", name, Q->subtreesize); if(Q->mplrs) { fprintf (lrs_ofp, "\n\n*** %s is an lrs option only\n", name); return(FALSE); } } if ((strcmp (name, "voronoi") == 0) || (strcmp (name, "Voronoi") == 0)) { if (!hull) { if(overflow != 2) lrs_warning(Q,"warning","*voronoi requires V-representation - option skipped"); } else { lrs_warning(Q,"warning","*voronoi"); Q->voronoi = TRUE; Q->polytope = FALSE; } } } /* end of while for reading flags */ if(Q->bound) { if(Q->maximize) ss=cprat("*Lower bound on objective function:",Q->boundn,Q->boundd); else ss=cprat("*Upper bound on objective function:",Q->boundn,Q->boundd); lrs_warning(Q,"warning",ss); free(ss); } /* Certain options are incompatible, this is fixed here */ if (Q->restart && Q->maxcobases > 0) //2015.4.3 adjust for restart Q->maxcobases = Q->maxcobases + Q->count[2]; if (Q->incidence) Q->printcobasis = TRUE; if (Q->debug) { printA (P, Q); fprintf (lrs_ofp, "\nexiting lrs_read_dic"); } fflush(lrs_ofp); fflush(stdout); /*removing tmpfiles */ fclose(lrs_ifp); lrs_ifp=NULL; if ( overflow > 0 ) /* we made a temporary file for overflow or stdin */ if(remove(infilename) != 0) lrs_warning(Q,"warning","*Could not delete temporary file"); if (*tmpfilename != '\0' ) /* we made a temporary file for stdin */ if(remove(tmpfilename) != 0) lrs_warning(Q,"warning", "*Could not delete temporary file"); *tmpfilename = '\0'; lrs_clear_mp(Temp); lrs_clear_mp(mpone); lrs_clear_mp(Tempn); lrs_clear_mp(Tempd); lrs_clear_mp(mptwo); return TRUE; } /* 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 */ /* 2017.12.22 could use no_output=2 to get early exit for criss-cross method */ { lrs_mp scale, Temp; long i, j, k; /* assign local variables to structures */ lrs_mp_matrix A; long *B, *C, *Col; long *inequality; long *linearity; long hull = Q->hull; long m, d, lastdv, nlinearity, nredundcol; 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; Col = D->Col; inequality = Q->inequality; /**2020.2.5 no linearities to remove so just select columns and quit */ if (Q->extract && Q->nlinearity == 0) return extractcols(D,Q); if(Q->verbose && overflow != 2) { 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])) { printf("\nWith voronoi option column one must be all one\n"); 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*/ } /* 2020.2.2 */ /* extract option asked to remove all linearities and output the reduced A matrix */ /* should be followed by redund to get minimum representation */ if (Q->extract) return linextractcols(D,Q); 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 (Q->count[2]==1 && (no_output==0 || Q->debug)) /* don't reprint after newstart */ { int len=0; char *header; header=(char *)malloc((100+20*Q->n)*sizeof(char)); if (Q->voronoi) len=sprintf (header, "*Voronoi Diagram: Voronoi vertices and rays are output"); else { if (hull) len=sprintf (header, "H-representation"); else len=sprintf (header, "V-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) { len=len+sprintf (header+len, "\nlinearity %ld ", nredundcol - k); /*adjust nredundcol for homog. */ for (i = 1; i <= nredundcol - k; i++) len=len+sprintf (header+len, " %ld", i); } /* end print of linearity space */ len=len+sprintf (header+len, "\nbegin"); len=len+sprintf (header+len, "\n***** %ld rational", Q->n); if(Q->mplrs) lrs_post_output("header",header); else if(Q->messages) fprintf(lrs_ofp,"\n%s",header); free(header); } /* 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) { const unsigned int Qn = Q->n; *Lin = lrs_alloc_mp_matrix (nredundcol, Qn); 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)) { lrs_clear_mp_matrix (*Lin, nredundcol, Qn); 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]); if(Q->lponly && Q->debug) printA (D, Q); } } /*2017.12.22 If you want to do criss-cross now is the time ! */ /* Do dual pivots to get primal feasibility */ if (!primalfeasible (D, Q)) { if(!Q->mplrs) fprintf (lrs_ofp, "\nend"); lrs_warning(Q,"finalwarn", "\nNo feasible solution\n"); if (Q->nash && Q->verbose ) { fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]); fprintf (lrs_ofp, " - No feasible solution"); } return FALSE; } if (Q->lponly || Q->nash ) if (Q->verbose) { fprintf (lrs_ofp, "\nNumber of pivots for feasible solution: %ld",Q->count[3]); if(Q->lponly && Q->debug) 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]); if(Q->debug) printA (D, Q); } 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 */ /* bug fix 2018.6.7 new value of d required below */ 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; long saveflag; long cob_est=0; /* estimated number of cobases in subtree from current node */ 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) { if (Q->runs > 0 && !backtrack ) /*get an estimate of remaining tree */ { //2015.2.9 do iterative estimation backtracking when estimate is small saveflag=Q->printcobasis; Q->printcobasis=FALSE; cob_est=lrs_estimate (D, Q); Q->printcobasis=saveflag; if(cob_est <= Q->subtreesize) /* stop iterative estimation */ { if(Q->verbose && cob_est > 0) /* when zero we are at a leaf */ { lrs_printcobasis(D,Q,ZERO); fprintf(lrs_ofp," cob_est= %ld *subtree",cob_est); } backtrack=TRUE; } } else // either not estimating or we are backtracking //2018.1.19 if (!backtrack && !Q->printcobasis) if (!backtrack ) if(!lrs_leaf(D,Q)) /* 2015.6.5 cobasis returned if not a leaf */ lrs_return_unexplored(D,Q); backtrack = TRUE; if (Q->maxdepth == 0 && cob_est <= Q->subtreesize) /* root estimate only */ return FALSE; /* no nextbasis */ } // if (D->depth >= Q->maxdepth) /* 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++; 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 lexflag; hull = Q->hull; lexflag = P->lexflag; if (lexflag || Q->allbases) ++(Q->count[1]); if (Q->debug) printA (P, Q); if (Q->getvolume) { linint (Q->sumdet, 1, P->det, 1); updatevolume (P, Q); } if(Q->triangulation) /* 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 */ { char *ss, *sdet, *sin_det, *sz; 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 */ long len=0; lrs_alloc_mp(Nvol); lrs_alloc_mp(Dvol); /* convert lrs_mp to char, compute length of string ss and malloc*/ sdet=cpmp(" det=", P->det); rescaledet (P, Q, Nvol, Dvol); /* scales determinant in case input rational */ sin_det=cprat("in_det=", Nvol,Dvol); sz=cprat("z=", P->objnum, P->objden); len = snprintf(NULL, 0, "%s%s%s", sdet,sin_det,sz); ss=(char*)malloc(len+(d+m)*20); /* build the printcobasis string */ len=0; if (hull) len=len+sprintf (ss+len, "F#%ld B#%ld h=%ld vertices/rays ", count[0], count[2], P->depth); else if (Q->voronoi) len=len+sprintf (ss+len, "V#%ld R#%ld B#%ld h=%ld data points ", count[1], count[0], count[2], P->depth); else len=len+sprintf (ss+len, "V#%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++) { len=len+sprintf (ss+len, " %ld", temparray[i]); if (!(col == ZERO) && (rflag == temparray[i])) /* missing cobasis element for ray */ len=len+sprintf (ss+len, "*"); } /* 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) { len=len+sprintf (ss+len," :"); firstime = FALSE; } len=len+sprintf(ss+len," %ld",inequality[B[i] - lastdv ] ); } } len=len+sprintf(ss+len," I#%ld",nincidence); sprintf (ss+len,"%s %s %s ",sdet,sin_det,sz); if(Q->mplrs) lrs_post_output("cobasis", ss); else fprintf(lrs_ofp,"\n%s",ss); free(ss); free(sdet); free(sin_det); free(sz); lrs_clear_mp(Nvol); lrs_clear_mp(Dvol); } /* end of lrs_printcobasis */ /*********************/ /* print final totals */ /*********************/ void lrs_printtotals (lrs_dic * P, lrs_dat * Q) { static int first_time=1; /* print warnings */ if(first_time) { first_time=0; if (!Q->mplrs) fprintf(lrs_ofp,"\nend"); if (Q->dualdeg) { lrs_warning(Q,"finalwarn","*Warning: Starting dictionary is dual degenerate"); lrs_warning(Q,"finalwarn","*Complete enumeration may not have been produced"); if (Q->maximize) lrs_warning(Q,"finalwarn","*Recommendation: Add dualperturb option before maximize in input file\n"); else lrs_warning(Q,"finalwarn","*Recommendation: Add dualperturb option before minimize in input file\n"); } if (Q->unbounded) { lrs_warning(Q,"finalwarn","*Warning: Starting dictionary contains rays"); lrs_warning(Q,"finalwarn","*Complete enumeration may not have been produced"); if (Q->maximize) lrs_warning(Q,"finalwarn","*Recommendation: Change or remove maximize option or add bounds\n"); else lrs_warning(Q,"finalwarn","*Recommendation: Change or remove minimize option or add bounds\n"); } if (Q->truncate) lrs_warning(Q,"finalwarn","*Tree truncated at each new vertex"); } if(!Q->hull) { if ( Q->allbases ) lrs_warning(Q,"finalwarn","*Note! Duplicate vertices/rays may be present"); else if (Q->count[0] > 1 && !Q->homogeneous) lrs_warning(Q,"finalwarn","*Note! Duplicate rays may be present"); } if(Q->mplrs) { char *vol; if (Q->hull && Q->getvolume) { rescalevolume (P, Q, Q->Nvolume, Q->Dvolume); vol=cprat("",Q->Nvolume, Q->Dvolume); lrs_post_output("volume", vol); free(vol); } return; } if(!Q->messages) return; 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 d, lastdv; d = P->d; lastdv = Q->lastdv; if(Q->hull) /* count[1] stores the number of linearities */ Q->count[1]=Q->nredundcol - Q->homogeneous; /* warnings for lrs only */ if (Q->maxdepth < MAXD) fprintf (lrs_ofp, "\n*Tree truncated at depth %lld", Q->maxdepth); if (Q->maxcobases > 0L) fprintf (lrs_ofp, "\n*maxcobases = %ld", Q->maxcobases-Q->startcount[2]); if (Q->maxoutput > 0L) fprintf (lrs_ofp, "\n*Maximum number of output lines = %ld", Q->maxoutput); /* next block with volume rescaling must come before estimates are printed */ if (Q->getvolume && Q->runs == 0) { if( Q->debug) { fprintf (lrs_ofp, "\n*Sum of det(B)="); pmp ("", Q->sumdet); } 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 (count[1] > 0 ) { fprintf (lrs_ofp, " linearities=%ld", count[1]); fprintf (lrs_ofp, " facets+linearities=%ld",count[1]+count[0]); } if(lrs_ofp != stdout) { printf ("\n*Totals: facets=%ld bases=%ld", count[0], count[2]); if (count[1] > 0) { printf (" linearities=%ld", count[1]); printf (" facets+linearities=%ld",count[1]+count[0]); } } if(Q->runs > 0) { fprintf (lrs_ofp, "\n*Estimates: facets=%.0f bases=%.0f", count[0] + cest[0], count[2] + cest[2]); if (Q->getvolume) { rescalevolume (P, Q, Q->Nvolume, Q->Dvolume); rattodouble (Q->Nvolume, Q->Dvolume, &x); for (i = 2; i < d; i++) cest[3] = cest[3] / i; /*adjust for dimension */ if(cest[3]==0) prat (" volume=", Q->Nvolume, Q->Dvolume); else fprintf (lrs_ofp, " volume=%g", cest[3] + x); } fprintf (lrs_ofp, "\n*Total number of tree nodes evaluated: %ld", Q->totalnodes); #ifndef TIMES fprintf (lrs_ofp, "\n*Estimated total running time=%.1f secs ",(count[2]+cest[2])/Q->totalnodes*get_time () ); #endif } } 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(lrs_ofp != stdout) { printf ("\n*Totals: vertices=%ld rays=%ld bases=%ld", count[1], count[0], count[2]); printf (" integer_vertices=%ld ",count[4]); if (nredundcol > 0) printf (" linearities=%ld", nredundcol); if ( count[0] + nredundcol > 0 ) { printf (" vertices+rays"); if ( nredundcol > 0 ) printf ("+linearities"); printf ("=%ld",nredundcol+count[0]+count[1]); } } /* end lrs_ofp != stdout */ if (Q->runs > 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); #ifndef TIMES fprintf (lrs_ofp, "\n*Estimated total running time=%.1f secs ",(count[2]+cest[2])/Q->totalnodes*get_time () ); #endif } } /* end of output for vertices/rays */ fprintf (lrs_ofp, "\n*Dictionary Cache: max size= %ld misses= %ld/%ld Tree Depth= %ld", dict_count, cache_misses, cache_tries, Q->deepest); if(lrs_ofp != stdout) printf ("\n*Dictionary Cache: max size= %ld misses= %ld/%ld Tree Depth= %ld", dict_count, cache_misses, cache_tries, Q->deepest); if(Q->debug) { 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]); } return; } /* end of lrs_printtotals */ /************************/ /* Estimation function */ /************************/ long lrs_estimate (lrs_dic * P, lrs_dat * Q) /*returns estimate of subtree size (no. cobases) 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); lrs_clear_mp_vector(output, Q->n); return(0L); /*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]) && (lrs_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 */ j=(long) cave[2]/Q->runs; //2015.2.9 Do not update totals if we do iterative estimating and subtree is too big if(Q->subtreesize == 0 || j <= Q->subtreesize ) 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); return(j); } /* 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 = lrs_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 = lrs_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 d, m_A; lrs_alloc_mp(Ns); lrs_alloc_mp(Nt); lrs_alloc_mp(Ars); 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]); 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); #ifdef LRSLONG unchecked_decint (Nt, Ns); /* overflow cannot happen */ #else decint (Nt, Ns); #endif 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, k=0L; long notdone=TRUE; /* assign local variables to structures */ long d = P->d; /* lponly=1 Dantzig, =2 random, =3 hybrid, =4 Bland */ if(Q->lponly <=1) /* Dantzig's rule */ while (dan_selectpivot (P, Q, &i, &j)) { pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ } if(Q->lponly ==2) /* random edge rule */ while (ran_selectpivot (P, Q, &i, &j)) { pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ } if(Q->lponly ==3) /* alternate Dantzig/randome rules */ while (notdone) { if(k % 2) /* odd for dantzig even for random */ notdone=dan_selectpivot (P, Q, &i, &j); else notdone=ran_selectpivot (P, Q, &i, &j); if(notdone) { pivot (P, Q, i, j); update (P, Q, &i, &j); /*Update B,C,i,j */ } k++; } if(Q->lponly ==4) /* Bland's rule - used for vertex enumeration */ while (selectpivot (P, Q, &i, &j)) { 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 */ { if (Q->lponly && Q->messages) fprintf (lrs_ofp, "\n*Unbounded solution"); 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 */ char mess[100]; m = P->m; d = P->d; nlinearity = Q->nlinearity; if (Q->debug) { fprintf (lrs_ofp, "\ngetabasis from inequalities given in order"); for (i = 0l; i < m; i++) fprintf (lrs_ofp, " %ld", order[i]); } for (j = 0l; j < m; j++) { i = 0l; 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); if(Q->messages) fprintf (lrs_ofp, "\nCannot find linearity in the basis"); return FALSE; } if (i <= m) { /* try to do a pivot */ k = 0l; 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])) { if(Q->messages && overflow != 2) { sprintf (mess,"*Input linearity in row %ld is redundant--converted to inequality", order[j]); lrs_warning(Q,"warning",mess); } linearity[j]=0l; Q->redineq[j]=1; /* check for redundancy if running redund */ } else { if (Q->debug) printA (P, Q); lrs_warning(Q,"warning","*No feasible solution"); return FALSE; } } } } /* 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) { lrs_warning(Q,"warning","\nError removing linearity"); return FALSE; } if (!removecobasicindex (P, Q, k)) return FALSE; d = P->d; } if (Q->debug && nlinearity > 0) printA (P, Q); /* 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 Col[k]=%ld", k, C[k],Col[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 */ /* 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 { lrs_warning(Q,"warning","\nInvalid Co-basis - does not have correct rank"); free(Cobasic); return FALSE; } } i--; } /* Suggested new code from db ends */ /* check restarting from a primal feasible dictionary */ for (i = lastdv + 1; i <= m; i++) if (negative (A[Row[i]][0])) { lrs_warning(Q,"warning","\nTrying to restart from infeasible dictionary"); free(Cobasic); return FALSE; } free(Cobasic); return TRUE; } /* end of restartpivots */ long lrs_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 */ if (Q->debug) printA(P,Q); } /* 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 *Row; lrs_mp_matrix A = P->A; long d = P->d; long m = P->m; 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 *C = P->C; long *B = P->B; 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 *Row, *Col; long d = P->d; lrs_alloc_mp(Ns); lrs_alloc_mp(Nt); 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 (mp_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); 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; long zeroonly=0; if(index < 0) /* used to zero out known redundant rows in mplrs verifyredund */ { zeroonly=1; index=-index; } 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 */ 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 (zeroonly || 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 */ /***************************************************************/ /* */ /* f 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 ) { lrs_warning(Q,"warning","\nLinearity option invalid, no indices "); return (FALSE); } if (nlinearity < 1) { lrs_warning(Q,"warning","\nLinearity option invalid, indices must be positive"); return (FALSE); } Q->linearity = (long int*) CALLOC ((nlinearity + 1), sizeof (long)); for (i = 0; i < nlinearity; i++) { if(fscanf (lrs_ifp, "%ld", &j)==EOF) { lrs_warning(Q,"warning","\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 readredund (lrs_dat * Q) /* read in and check linearity list */ { long i,j,k; char *mess; int len=0; if(fscanf (lrs_ifp, "%ld", &k)==EOF ) { lrs_warning(Q,"warning","\nredund_list option invalid: no indices "); return (FALSE); } if ( k < 0 ) { lrs_warning(Q,"warning","\nredund_list option invalid, first index must be >= 0"); return (FALSE); } for (i = 1; i <= Q->m; i++) /*reset any previous redund option except =2 values */ if (Q->redineq[i] != 2) Q->redineq[i]=0; Q->redineq[0]=1; for (i = 0; i < k; i++) { if(fscanf (lrs_ifp, "%ld", &j)==EOF) { lrs_warning(Q,"warning","\nredund_list option invalid: missing indices"); fflush(lrs_ofp); return (FALSE); } if( j< 0 || j > Q->m) { fprintf (lrs_ofp,"\nredund_list option invalid: indices not between 1 and %ld",Q->m); return (FALSE); } Q->redineq[j] = 1; } //if(!Q->mplrs && overflow != 2 ) if( overflow != 2 ) { mess=(char *)malloc(20*Q->m*sizeof(char)); len=sprintf(mess,"redund_list %ld ",k); for (i=1;i<=Q->m;i++) if(Q->redineq[i] == 1) len=len+sprintf(mess+len," %ld",i); lrs_warning(Q,"warning",mess); free(mess); } return TRUE; } /* end readredund */ 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; char str[1000000],*p,*e; /* assign local variables to structures */ long m, d; long *linearity = Q->linearity; m = Q->m; d = Q->inputd; /* modified 2018.6.7 to fix bug restarting with less than full dimension input */ /* number of restart indices is not known at this point */ j=Q->nlinearity; /* note we place these after the linearity indices */ fgets(str,1000000,lrs_ifp); /* pick up indices from the input line */ for (p = str; ; p = e) { facet[j] = strtol(p, &e, 10); if (p == e) break; if(!Q->mplrs && Q->verbose && overflow != 2) fprintf(lrs_ofp," %ld",facet[j] ); //fprintf(lrs_ofp,"\n j %ld d %ld facet %ld",j,d,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; } j++; } return TRUE; } /* end of readfacets */ long readremain (lrs_dat * Q) /* read in and check ordered list of vars for extract */ { long i, j, kk; long nremain; long k=0; long n=Q->n; long *remain; Q->remain = (long int*) CALLOC ((n + 2), sizeof (long)); remain=Q->remain; for (i=0;i n-1) { nremain = n-1; fprintf (lrs_ofp, "\n*extract: too many indices, first %ld taken",n-1); } for (i = 0; i < nremain; i++) { if(fscanf (lrs_ifp, "%ld", &j)==EOF) { fprintf (lrs_ofp, "\n*extract: missing indices"); break; } if(j>0 && j0 fill up list with remaining decision variables */ if(Q->nlinearity > 0) for (i=1;iA; Col = P->Col; Row = P->Row; remain=Q->remain; output=Q->temparray; m=P->m; n=Q->n; for(j=0;jhull) fprintf(lrs_ofp,"\nV-representation\nbegin"); else fprintf(lrs_ofp,"\nH-representation\nbegin"); fprintf(lrs_ofp,"\n%ld %ld rational",m,ncols+1); for(i=1;i<=m;i++ ) { reducearray(A[Row[i]],n); fprintf(lrs_ofp,"\n"); if(Q->hull) { for(j=0;jdebug) printA(P,Q); return 0; } /* extractcols */ long linextractcols (lrs_dic * P, lrs_dat * Q) /* 2020.2.2 */ /* extract option to output the reduced A matrix after linearities are removed */ /* should be followed by redund to get minimum representation */ { long d,i,j,k,m,n; long ii,jj; long nlinearity=Q->nlinearity; lrs_mp_matrix A; long *B, *C, *Col, *Row, *remain; A = P->A; B = P->B; C = P->C; Col = P->Col; Row = P->Row; remain=Q->remain; m=P->m; n=Q->n; d=Q->inputd; fprintf(lrs_ofp,"\n*extract col order: "); for(j=0;jhull) fprintf(lrs_ofp,"\n*columns retained:"); else fprintf(lrs_ofp,"\n*columns retained: 0"); for (j=0;jhull); if(Q->hull) fprintf(lrs_ofp,"\nV-representation\nbegin"); else fprintf(lrs_ofp,"\nH-representation\nbegin"); fprintf(lrs_ofp,"\n%ld %ld rational",m-nlinearity,1+P->d-Q->hull); for(i=nlinearity+1;i<=m;i++ ) { reducearray(A[Row[i]],n-nlinearity); fprintf(lrs_ofp,"\n"); if(!Q->hull) pmp("",A[Row[i]][0]); for(j=0;jhull) fprintf(lrs_ofp,"\n*columns retained:"); else fprintf(lrs_ofp,"\n*columns retained: 0"); for (j=0;jhull); fprintf(lrs_ofp,"\n"); if(Q->debug) printA(P,Q); return 0; } /* linextractcols */ 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; m = P->m; d = P->d; 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, const 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 */ static 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); /*2019.6.7 This ought not to happen but it does */ if( global->Qtail== *D_p) return; 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; if( dest == src) { if(global->mplrs) lrs_post_output("warning", "*copy_dict has dest=src -ignoring copy"); else fprintf(stderr,"*copy_dict has dest=src -ignoring copy"); return; } #if defined(GMP) || defined(FLINT) 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 LRSLONG 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 */ /* Looking at lrs_alloc_mp_matrix for MP and LRSLONG, A[0][0] is the * start of araw, which holds the actual values and so the memcpy below * copies the values. The pointer trees (A, A[i], A[i][j]) already point * to the appropriate places: we don't want to change the pointers, only the * values. lrs_alloc_mp_matrix is different for GMP. */ 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 #ifdef B128 memcpy (dest->A[0][0], (global->Qtail->prev)->A[0][0], (d + 1) * (lrs_digits + 1) * (m_A + 1) * sizeof (__int128)); #else memcpy (dest->A[0][0], (global->Qtail->prev)->A[0][0], (d + 1) * (lrs_digits + 1) * (m_A + 1) * sizeof (long long)); #endif #endif dest->i = src->i; dest->j = src->j; dest->m = m; dest->d = d; dest->d_orig = src->d_orig; 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 static 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; static 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 = (long int*) calloc ((m + 1), sizeof (long))); NULLRETURN (p->Row = (long int*) calloc ((m + 1), sizeof (long))); NULLRETURN (p->C = (long int*) calloc ((d + 1), sizeof (long))); NULLRETURN (p->Col = (long int*) calloc ((d + 1), sizeof (long))); #if defined(GMP) || defined(FLINT) 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; if (Q == NULL ) { if(Q->mplrs) lrs_post_output("warning","*lrs_free_dic trying to free null Q : skipped"); else fprintf(stderr,"*lrs_free_dic trying to free null Q : skipped"); return; } if (P == NULL ) { if(Q->mplrs) lrs_post_output("warning","*lrs_free_dic trying to free null P : skipped"); else fprintf(stderr,"*lrs_free_dic trying to free null P : skipped"); return; } /* 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_dic2 (lrs_dic * P, lrs_dat *Q) { /* do the same steps as for allocation, but backwards */ /* same as lrs_free_dic except no cache for P */ /* 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); free (P); } void lrs_free_dat ( lrs_dat *Q ) { if (Q == NULL) { if(Q->mplrs) lrs_post_output("warning","*lrs_free_dat trying tor free null Q : skipped"); else fprintf(stderr,"*lrs_free_dat trying tor free null Q : skipped"); return; } if(Q->extract) free(Q->remain); /* most of these items were allocated in lrs_alloc_dic */ lrs_clear_mp_vector (Q->Gcd,Q->m); lrs_clear_mp_vector (Q->Lcm,Q->m); lrs_clear_mp_vector (Q->output,Q->n); 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->facet); free (Q->redundcol); free (Q->inequality); free (Q->linearity); free (Q->redineq); free (Q->minratio); free (Q->temparray); free (Q->startcob); free (Q->name); free (Q->saved_C); lrs_global_count--; free(Q); } static 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 = 50; 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]); if (Q->nlinearity == ZERO) /* linearity may already be allocated */ Q->linearity = (long int*) CALLOC ((m + d + 1), sizeof (long)); Q->inequality = (long int*) CALLOC ((m + d + 1), sizeof (long)); Q->facet = (long int*) CALLOC ((unsigned) m + d + 1, sizeof (long)); Q->redundcol = (long int*) CALLOC ((m + d + 1), sizeof (long)); Q->minratio = (long int*) CALLOC ((m+d + 1), sizeof (long)); /* 2011.7.14 minratio[m]=0 for degen =1 for nondegen pivot*/ Q->redineq = (long int*) CALLOC ((m + d + 1), sizeof (long)); Q->temparray = (long int*) CALLOC ((unsigned) m + d + 1, sizeof (long)); Q->inequality[0] = 2L; Q->Gcd = lrs_alloc_mp_vector(m); Q->Lcm = lrs_alloc_mp_vector(m); Q->output = lrs_alloc_mp_vector(Q->n); Q->saved_C = (long int*) CALLOC (d + 1, sizeof (long)); Q->lastdv = d; /* last decision variable may be decreased */ /* if there are redundant columns */ for (i = 0; i < m+d+1; i++) { Q->redineq[i]=1; Q->inequality[i]=0; } /*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. */ static void save_basis (lrs_dic * P, lrs_dat * Q) { int i; /* assign local variables to structures */ long *C = P->C; long d; #ifndef 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 < 5; 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; #ifndef 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 (lrs_ofp, "\n\nlrs_lib: checkpointing:\n"); #ifdef MP fprintf (stderr, "lrs_lib: Current digits at %ld out of %ld\n", DIG2DEC (lrs_record_digits), DIG2DEC (lrs_digits)); #endif for (i = 0; i < lrs_global_count; i++) { print_basis (lrs_ofp, lrs_global_list[i]); } fprintf (lrs_ofp, "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) { /* legacy output which is not actually correct for V-representations as V# is not used */ /* 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"); */ if( global->hull) fprintf (fp, "\nrestart %ld %ld %ld ", global->saved_count[0], global->saved_count[2], global->saved_depth); else fprintf (fp, "\nrestart %ld %ld %ld %ld ", 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]); if(global->saved_count[4] >0) fprintf (fp, "\nintegervertices %ld", global->saved_count[4]); fprintf (fp, "\n"); } else { fprintf (fp, "lrs_lib: Computing initial basis\n"); } fflush (fp); } #ifndef SIGNALS /* If given a signal USR1 print current cobasis and continue TERM print current cobasis and terminate INT (ctrl-C) ditto HUP ditto */ static 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)); } static void timecheck () { lrs_dump_state (); errcheck ("signal", signal (SIGALRM, timecheck)); alarm (lrs_checkpoint_seconds); } static void checkpoint () { lrs_dump_state (); errcheck ("signal", signal (SIGUSR1, checkpoint)); } static void die_gracefully () { lrs_dump_state (); exit (1); } #endif #ifndef TIMES /* * Not sure about the portability of this yet, * - db */ #include #define double_time(t) ((double)(t.tv_sec)+(double)(t.tv_usec)/1000000) static 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); if(lrs_ofp != stdout) printf ("\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); } static 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 d; long j; 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 (mp_greater (Gcd[i], mpone) || mp_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; /* printf("\n*dantzig"); */ lrs_alloc_mp (coeff); *r = 0; *s = d; j = 0; k = 0; itomp(0,coeff); /*find positive cost coef */ while (k < d) { if(mp_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 = lrs_ratio (P, Q, col); if (*r != 0) { lrs_clear_mp(coeff); return (TRUE); /* pivot found */ } } lrs_clear_mp(coeff); return (FALSE); } /* end of dan_selectpivot */ long ran_selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s) /* select pivot indices using random edge rule */ /* largest coefficient with lexicographic rule to avoid cycling */ /* pivot variables are B[*r] C[*s] in locations Row[*r] Col[*s] */ { long i,j,k,col,t; /* assign local variables to structures */ lrs_mp_matrix A = P->A; long *Col = P->Col; long d = P->d; long *perm; perm = (long *) calloc ((d + 1), sizeof (long)); *r = 0; *s = d; k = 0; /* printf("\n*random edge"); */ /* generate random permutation of 0..d-1 */ for (i = 0; i < d; i++) perm[i] = i; for ( i = 0; i < d; i++) { j = random() % (d-i) + i; t = perm[j]; perm[j] = perm[i]; perm[i] = t; // Swap i and j } if(Q->debug) { printf("\n perm: "); for (i = 0; i < d; i++) printf(" %ld",perm[i]); } /*find first positive cost coef according to perm */ while (k < d && !positive(A[0][Col[perm[k]]])) k++; if ( kA; 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(mp_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 */ 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; } long lrs_leaf(lrs_dic *P, lrs_dat *Q) { /* check if current dictionary is a leaf of reverse search tree */ long col=0; long tmp=0; while (col < P->d && !reverse(P,Q,&tmp,col)) col++; if(col < P->d) return 0; /* dictionary is not a leaf */ else return 1; } /* prevent output flushes in mplrs */ void lrs_open_outputblock(void) { #ifdef PLRS open_outputblock(); #endif } /* re-enable output flushes in mplrs */ void lrs_close_outputblock(void) { #ifdef PLRS close_outputblock(); #endif } void lrs_post_output(const char *type, const char *data) { #ifdef PLRS post_output(type,data); #endif } void lrs_return_unexplored(lrs_dic *P,lrs_dat *Q) /* send cobasis data for unexplored nodes */ { #ifdef PLRS lrs_restart_dat R; int i; for (i = 0; i < P->d; i++) Q->temparray[i] = Q->inequality[P->C[i] - Q->lastdv]; R.facet=Q->temparray; R.d=P->d; R.depth=P->depth; update_R(P,Q,&R); post_R(&R); #else if(Q->verbose) { lrs_printcobasis(P,Q,ZERO); fprintf(lrs_ofp," *unexplored"); } #endif } void lrs_overflow(int parm) { lrs_dic *P; lrs_dat *Q; char *restart; char *part; int i; int try_restart=FALSE; if (lrs_global_list[0] == NULL) { #ifdef PLRS post_output("warning","*lrs_overflow has null Q "); #else fprintf(stderr,"*lrs_overflow has null Q "); #endif lrs_exit(parm); } Q = lrs_global_list[0]; /* db's cunningly hidden locations */ P = Q->Qhead; /* mplrs overflow handling */ #if defined(PLRS) && !defined(GMP) lrs_free_dic(P,Q); /* note Q is not freed here and is needed again */ overflow=1; longjmp(buf1,1); /* return to lrsv2_main */ #elif defined(GMP) || defined(FLINT) /* should not be here, but just in case ... */ printf("\n*integer overflow for gmp or flint !?"); lrs_free_all_memory (P,Q); lrs_exit(parm); #endif /* non mplrs overflow handling */ /* lrs and redund restarted at the moment */ #ifdef MA if (strcmp(Q->fname,"lrs") == 0 || strcmp(Q->fname,"redund")==0) try_restart=TRUE; #endif if(lrs_ifp != NULL) fclose(lrs_ifp); if (!try_restart ) /* hard exit */ { if (strcmp(BIT,"64bit")==0 ) { fprintf(stderr,"\n*64bit integer overflow: try running 128bit or gmp versions\n"); if (lrs_ofp != stdout) fprintf(lrs_ofp,"\n*64bit integer overflow: try running 128bit or gmp versions\n"); } else { fprintf(stderr,"\n*128bit integer overflow: try running gmp version\n"); if (lrs_ofp != stdout) fprintf(lrs_ofp,"\n*128bit integer overflow: try running gmp version\n"); } lrs_exit(parm); } /* try to restart */ if(overflow == 0) /* first overflow */ { if (*tmpfilename != '\0' ) /* we made a temporary file for stdin */ if(remove(tmpfilename) != 0) fprintf (lrs_ofp, "\nCould not delete temporary file"); strncpy(tmpfilename,"/tmp/lrs_restartXXXXXX",PATH_MAX); /* XXX in principle this file descriptor should be used instead of the name */ tmpfd = mkstemp(tmpfilename); } else strcpy(tmpfilename,infilename); if( !pivoting || strcmp(Q->fname,"redund") == 0 || Q->getvolume) /* we make restart from original input */ { overflow = 1L; lrs_cache_to_file(tmpfilename," "); } else { restart = (char *) malloc( Q->saved_d * 20+100); part = (char *) malloc( Q->saved_d * 20+100); overflow=2L; if(Q->hull) sprintf (restart," %ld %ld %ld ", Q->saved_count[2],Q->saved_count[0], Q->saved_depth); else sprintf (restart," %ld %ld %ld %ld ", Q->saved_count[1],Q->saved_count[0],Q->saved_count[2], Q->saved_depth); for (i = 0; i < Q->saved_d; i++) { sprintf (part,"%ld ", Q->inequality[Q->saved_C[i] - Q->lastdv]); strcat(restart,part); } sprintf(part,"\nintegervertices %ld",Q->saved_count[4]); strcat(restart,part); lrs_cache_to_file(tmpfilename,restart); free(restart); free(part); } Q->m=P->m; lrs_free_dic(P,Q); /* note Q is not freed here and is needed again */ if (lrs_ofp != NULL && lrs_ofp != stdout ) { fclose (lrs_ofp); lrs_ofp=NULL; } close(tmpfd); longjmp(buf1,1); /* return to lrsv2_main */ lrs_exit(parm); /* should not happen */ } void lrs_exit(int i) { fflush(stdout); exit(i); } void lrs_free_all_memory(lrs_dic * P, lrs_dat * Q) { if(Q->runs > 0) { free(Q->isave); free(Q->jsave); } if(P != NULL) /* may not have allocated P yet */ { long savem=P->m; /* need this to clear Q*/ lrs_free_dic (P,Q); /* deallocate lrs_dic */ Q->m=savem; } lrs_free_dat (Q); /* deallocate lrs_dat */ #ifdef LRSLONG free(infile); /* we cached input file for possible restart */ #endif return; } long lrs_stdin_to_file(char *filename) { FILE *fptr1, *fptr2; char c; fptr1 = stdin; fptr2 = fopen(filename, "w"); if (fptr2 == NULL) { printf("Cannot open file %s \n", filename); exit(0); } c = fgetc(fptr1); while (c != EOF) { fputc(c, fptr2); c = fgetc(fptr1); } fclose(fptr2); fptr2=NULL; return 0; } long lrs_file_to_cache(FILE *ifp) { long ret; if (ifp != NULL) if (fseek(ifp, 0L, SEEK_END) == 0) { ret = ftell(ifp); if (ret == -1) { fputs("*Error reading file", stderr); return 1; } infileLen = ret; infile = (char *) malloc(sizeof(char) * (infileLen + 1)); if (fseek(ifp, 0L, SEEK_SET) != 0) { fputs("*Error resetting input file", stderr); return 1; } infileLen = fread(infile, sizeof(char), infileLen, ifp); if ( ferror( ifp ) != 0 ) { fputs("*Error reading input file", stderr); return 1; } else infile[infileLen++] = '\0'; /* Just to be safe. */ } rewind(ifp); return 0; } long lrs_cache_to_file(char *name,const char *restart) { FILE *ofp = fopen(name, "wb"); if (ofp == NULL) { printf("*Error opening output file %s",name); return 1; } fwrite(infile, sizeof(char), infileLen, ofp); if(lrs_global_list[0]->count[2] > 1L && overflow==2) fprintf(ofp,"\nrestart %s",restart); fclose(ofp); return 0; } void lrs_setup_R(lrs_dic *P, lrs_dat *Q, lrs_restart_dat *R) { int i; R->d = P->d; /* length of R->facets */ R->m = P->m; /* number of input rows*/ Q->startcob = (long int*) CALLOC ((R->d + R->m + 1), sizeof (long)); for(i=0;id;i++) Q->startcob[i]=Q->inequality[i]; if (strcmp (Q->fname, "redund") == 0) { R->redund=1; R->lrs=0; if(R->redineq == NULL) { R->redineq = (long int*) CALLOC ((R->m + 1), sizeof (long)); for (i=0; i<= R->m; i++) R->redineq[i] = Q->redineq[i]; } } } /* lrs_setup_R */ lrs_dic *lrs_setup(int argc, char *argv[], lrs_dat **Q, lrs_restart_dat *R) /* allocate lrs_dat Q, lrs_dic P, read in the problem data and make a copy of P */ { lrs_dic *P; /* structure for holding current dictionary and indices */ lrs_ifp = stdin; lrs_ofp = stdout; if(strncmp("redund",argv[0],6)==0) { if ( !lrs_init ("\n*redund:")) return NULL; } else if ( !lrs_init ("\n*lrs:")) return NULL; *Q = lrs_alloc_dat ("LRS globals"); /* allocate and init structure for static problem data */ if (*Q == NULL) return NULL; strcpy((*Q)->fname,"lrs"); if(strncmp("redund",argv[0],6)==0) strcpy((*Q)->fname,"redund"); if((*Q)->mplrs) (*Q)->messages=R->messages; if (!lrs_read_dat (*Q, argc, argv)) /* read first part of problem data to get dimensions */ return NULL; /* and problem type: H- or V- input representation */ P = lrs_alloc_dic (*Q); /* allocate and initialize lrs_dic */ if (P == NULL ) return NULL; if (!lrs_read_dic (P, *Q)) /* read remainder of input to setup P and Q */ return NULL; return P; } /* lrs_setup */ lrs_dic *lrs_reset(lrs_dic *P_orig, lrs_dat *Q, lrs_restart_dat *R) { lrs_dic *P; long i; itomp (ZERO, Q->Nvolume); itomp (ONE, Q->Dvolume); itomp (ZERO, Q->sumdet); P=lrs_getdic (Q); Q->Qhead=P_orig; Q->Qtail=P_orig; if( P == P_orig) { if(Q->mplrs) lrs_post_output("warning", "*lrs_reset: copy_dict has dest=src -ignoring copy"); else fprintf(stderr,"*lrs_reset: copy_dict has dest=src -ignoring copy"); } copy_dict (Q,P,P_orig); /* restore original input */ Q->Qhead=P; Q->Qtail=P; /*if overiding, update Q from R */ if (R->lrs && R->overide == 1) { Q->messages=R->messages; if(R->maxdepth == -1) Q->maxdepth=MAXD; else Q->maxdepth=R->maxdepth; Q->mindepth=R->mindepth; Q->maxcobases=R->maxcobases; if (Q->maxcobases > 0) Q->maxcobases = Q->maxcobases + R->count[2]; if(R->restart==1) { Q->restart=TRUE; if(!Q->lponly) Q->giveoutput=FALSE; /* supress first output */ for(i=0;id;i++) { Q->facet[i+Q->nlinearity]=R->facet[i]; Q->inequality[i]=Q->startcob[i]; } for(i=0;i<5;i++) { Q->count[i]=R->count[i]; Q->startcount[i] = Q->count[i]; /* for mplrs subjob counts */ } } P->depth = R->depth; R->maxdepth=MAXD; } if (R->redund) { for (i=0;i<=Q->m;i++) Q->redineq[i]=R->redineq[i]; Q->verifyredund=R->verifyredund; } return P; } void update_R(lrs_dic *P, lrs_dat *Q, lrs_restart_dat *R) { int i; for (i=0;i<=4;i++) R->count[i]=Q->count[i]; R->count[5]=Q->hull; if(Q->hull) R->count[6]=Q->nredundcol-Q->homogeneous; else R->count[6]=Q->nredundcol; R->count[7]=Q->deepest; return; } #ifdef GMP /* compiled with gmp arithmetic */ long lrsgmp_main(int argc, char *argv[],lrs_dic **P_orig, lrs_dat **Q,long overf,long stage,char *tmp, lrs_restart_dat *R) { return lrsv2_main(argc,argv,P_orig,Q,overf,stage,tmp,R); } #elif defined(LRSLONG) #ifdef B128 long lrs2_main(int argc, char *argv[],lrs_dic **P_orig, lrs_dat **Q,long overf,long stage,char *tmp, lrs_restart_dat *R) { return lrsv2_main(argc,argv,P_orig,Q,overf,stage,tmp,R); } #else long lrs1_main(int argc, char *argv[],lrs_dic **P_orig, lrs_dat **Q,long overf,long stage,char *tmp, lrs_restart_dat *R) { return lrsv2_main(argc,argv,P_orig,Q,overf,stage,tmp,R); } #endif #endif long lrs_main(int argc, char *argv[]) /* legacy version, replaced by lrsv2_main but still maintained */ { lrs_dic *P; lrs_dat *Q; lrs_restart_dat *R; char* tmp; /* when overflow occurs a new input file name is returned */ long overfl=0; /* =0 no overflow =1 restart overwrite =2 restart append */ P=NULL; Q=NULL; R=NULL; tmp=NULL; R = lrs_alloc_restart(); if (R == NULL) exit(1); overfl=lrsv2_main(argc,argv,&P,&Q,0,0,tmp,R); /* set up, read input, no run */ if(overfl == -1) /* lrs_setup failed due to bad input file etc. - no cleanup*/ return 0; if(overfl == 0) lrsv2_main(argc,argv,&P,&Q,0,1,tmp,R); /* standard lrs run - argc, argv, R not used */ lrsv2_main(argc,argv,&P,&Q,0,2,tmp,R); /* free memory and close, does not access argc, argv */ free(R->facet); if (R->redund) free(R->redineq); return 0; } long lrsv2_main(int argc, char *argv[],lrs_dic **P_orig, lrs_dat **Q,long overf,long stage,char *tmp, lrs_restart_dat *R) /* compiled independently with all supported arithmetic packages */ /* should be called from one of lrsX_main where X is an arithmetic package */ { lrs_dic *P; /* structure for holding current dictionary and indices */ int i; overflow=overf; if (!setjmp(buf1)) /* normal processing - jump to end if overflow occurs */ { /* initial call: allocate lrs_dat, lrs_dic and set up the problem - no run */ if(stage==0) { *P_orig=lrs_setup(argc,argv,Q,R); if(*P_orig==NULL) { fprintf(stderr,"\n*lrs_setup failed\n"); fflush(stderr); return -1; } lrs_setup_R(*P_orig,*Q,R); return 0; } /* reverse search runs: restore P and update Q as needed from R */ if(stage==1) { P=lrs_reset(*P_orig,*Q,R); /* restore P and reset Q from R */ if(P==NULL) return -1; if(overf==2) (*Q)->giveoutput=FALSE; /* suppress first output */ if(R->redund) { redund_run(P,*Q); return 0; } lrs_run(P,*Q); /* do reverse search */ update_R(P,*Q,R); /* update counts for mplrs */ return 0; } /* final cleanup */ if(stage == 2 ) { (*Q)->Qhead=*P_orig; (*Q)->Qtail=*P_orig; lrs_free_all_memory(*P_orig,*Q); lrs_close ("lrs:"); return 0; } } /* overflow occurred */ if (R->redund ) { if(R->redineq != NULL) { overflow=2; for (i=0;i<=R->m;i++) /*i=0 contains next ineq to process */ R->redineq[i]=(*Q)->redineq[i]; } lrs_clear_mp_matrix((*Q)->Ain,(*P_orig)->m_A,(*P_orig)->d); } if (tmp != NULL) strcpy(tmp,tmpfilename); (*Q)->Qhead=*P_orig; (*Q)->Qtail=*P_orig; lrs_free_all_memory(*P_orig,*Q); fflush(lrs_ofp); return overflow; /* overflow */ } /* lrsv2_main */ void lrs_warning(lrs_dat *Q, char* type, char* ss) { if(Q->messages) { if(Q->mplrs) lrs_post_output(type,ss); else { fprintf (lrs_ofp, "\n%s",ss); if(lrs_ofp != stdout) fprintf (stderr, "\n%s",ss); } } } lrslib-071a/lrslib.h0000700060175606010010000006230013742506306014276 0ustar avisなし/* lrslib.h (vertex enumeration using lexicographic reverse search) */ #define TITLE "lrslib " #define VERSION "v.7.1 2020.10.17" #define AUTHOR "*Copyright (C) 1995,2020, 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ /*Ver 6.1 major change is new lrsnash driver and library coded by Terje Lensberg */ /*Ver 6.0 major change is mplrs wrapper for multithreading coded by Skip Jordan */ /*Ver 5.0 major change is plrs wrapper for multithreading coded by Gary Roumanis */ /*Ver 4.2* library version */ /******************************************************************************/ /* See http://cgm.cs.mcgill.ca/~avis/C/lrs.html for usage instructions */ /******************************************************************************/ #define lrs_main suf(lrs_main) #define lrsv2_main suf(lrsv2_main) #define lrs_run suf(lrs_run) #define redund_run suf(redund_run) #define redund_print suf(redund_print) #define lrs_overflow suf(lrs_overflow) #define cache_misses suf(cache_misses) #define cache_tries suf(cache_tries) #define checkcobasic suf(checkcobasic) #define checkindex suf(checkindex) #define checkpoint suf(checkpoint) #define checkredund suf(checkredund) #define copy_dict suf(copy_dict) #define dan_selectpivot suf(dan_selectpivot) #define ran_selectpivot suf(ran_selectpivot) #define dict_count suf(dict_count) #define dict_limit suf(dict_limit) #define die_gracefully suf(die_gracefully) #define digits_overflow suf(digits_overflow) #define extractcols suf(extractcols) #define getabasis suf(getabasis) #define getnextoutput suf(getnextoutput) #define infile suf(infile) #define infileLen suf(infileLen) #define infilename suf(infilename) #define ismin suf(ismin) #define lexmin suf(lexmin) #define lprat suf(lprat) #define lreadrat suf(lreadrat) #define lrs_alloc_dat suf(lrs_alloc_dat) #define lrs_alloc_dic suf(lrs_alloc_dic) #define lrs_cache_to_file suf(lrs_cache_to_file) #define lrs_cfp suf(lrs_cfp) #define lrs_checkbound suf(lrs_checkbound) #define lrs_checkpoint_seconds suf(lrs_checkpoint_seconds) #define lrs_close suf(lrs_close) #define lrs_close_outputblock suf(lrs_close_outputblock) #define lrs_degenerate suf(lrs_degenerate) #define lrs_dump_state suf(lrs_dump_state) #define lrs_estimate suf(lrs_estimate) #define lrs_exit suf(lrs_exit) #define lrs_stdin_to_file suf(lrs_stdin_to_file) #define lrs_file_to_cache suf(lrs_file_to_cache) #define lrs_free_all_memory suf(lrs_free_all_memory) #define lrs_free_dat suf(lrs_free_dat) #define lrs_free_dic suf(lrs_free_dic) #define lrs_free_dic2 suf(lrs_free_dic2) #define lrs_getdic suf(lrs_getdic) #define lrs_getfirstbasis suf(lrs_getfirstbasis) #define lrs_getinput suf(lrs_getinput) #define lrs_getnextbasis suf(lrs_getnextbasis) #define lrs_getray suf(lrs_getray) #define lrs_getsolution suf(lrs_getsolution) #define lrs_getvertex suf(lrs_getvertex) #define lrs_global_count suf(lrs_global_count) #define lrs_global_list suf(lrs_global_list) #define lrs_init suf(lrs_init) #define lrs_setup suf(lrs_setup) #define lrs_setup_R suf(lrs_setup_R) #define lrs_reset suf(lrs_reset) #define lrs_leaf suf(lrs_leaf) #define lrs_lpoutput suf(lrs_lpoutput) #define lrs_open_outputblock suf(lrs_open_outputblock) #define lrs_post_output suf(lrs_post_output) #define lrs_printcobasis suf(lrs_printcobasis) #define lrs_print_header suf(lrs_print_header) #define lrs_printoutput suf(lrs_printoutput) #define lrs_printrow suf(lrs_printrow) #define lrs_printtotals suf(lrs_printtotals) #define lrs_ratio suf(lrs_ratio) #define lrs_read_dat suf(lrs_read_dat) #define lrs_read_dic suf(lrs_read_dic) #define lrs_return_unexplored suf(lrs_return_unexplored) #define lrs_set_digits suf(lrs_set_digits) #define lrs_set_obj suf(lrs_set_obj) #define lrs_set_obj_mp suf(lrs_set_obj_mp) #define lrs_set_row suf(lrs_set_row) #define lrs_set_row_mp suf(lrs_set_row_mp) #define lrs_solvelp suf(lrs_solvelp) #define lrs_solve_lp suf(lrs_solve_lp) #define lrs_warning suf(lrs_warning) #define outfilename suf(outfilename) #define overflow suf(overflow) #define pivoting suf(pivoting) #define phaseone suf(phaseone) #define pimat suf(pimat) #define pivot suf(pivot) #define primalfeasible suf(primalfeasible) #define printA suf(printA) #define print_basis suf(print_basis) #define readfacets suf(readfacets) #define readremain suf(readremain) #define readlinearity suf(readlinearity) #define readredund suf(readredund) #define removecobasicindex suf(removecobasicindex) #define linextractcols suf(linextractcols) #define reorder suf(reorder) #define reorder1 suf(reorder1) #define rescaledet suf(rescaledet) #define rescalevolume suf(rescalevolume) #define resize suf(resize) #define restartpivots suf(restartpivots) #define reverse suf(reverse) #define save_basis suf(save_basis) #define selectpivot suf(selectpivot) #define timecheck suf(timecheck) #define tmpfilename suf(tmpfilename) #define update suf(update) #define updatevolume suf(updatevolume) #define update_R suf(update_R) #ifdef LRSLONG #define ARITH "lrslong.h" /* lrs long integer arithmetic package */ #else #if defined(GMP) || defined(FLINT) #define ARITH "lrsgmp.h" /* lrs wrapper for gmp multiple precsion arithmetic */ #else #define ARITH "lrsmp.h" /* lrs multiple precsion arithmetic */ #endif #endif #include ARITH #ifndef SIGNALS #include #include #define errcheck(s,e) if ((long)(e)==-1L){ perror(s);exit(1);} #endif #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*********************/ /*global constants */ /*********************/ #define MAX_LRS_GLOBALS 10000L /* number of allocated dictionaries */ #define MAXIMIZE 1L /* maximize the lp */ #define MINIMIZE 0L /* maximize the lp */ #define GE 1L /* constraint is >= */ #define EQ 0L /* constraint is linearity */ /*************/ /* 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 */ { long *redineq; /* holds indices of rows for redundancy check */ lrs_mp_matrix Ain; /* used only in redund to hold input matrix */ lrs_mp_vector Gcd; /* Gcd of each row of numerators */ lrs_mp_vector Lcm; /* Lcm for each row of input denominators */ lrs_mp_vector output; /* One line of output dimensioned to n */ 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[4096]; /* program name: lrs redund fourier nash */ /* initially holds order used to find starting */ /* basis, default: m,m-1,...,2,1 */ long *facet; /* cobasic indices for restart if needed */ long *redundcol; /* holds columns which are redundant */ long *inequality; /* indices of inequalities corr. to cobasic ind */ long *linearity; /* holds cobasic indices of input linearities */ long *remain; /* ordered list of vars to keep in extract */ long *startcob; /* starting cobasis if given else zeroes */ 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(facets)[1]=vertices(linearities)*/ /* [2]=cobases [3]=pivots [4]=integer vertices */ long startcount[5]; 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 */ long nextineq; /* start checking redundancy from this row:def=1*/ /**** flags ********** */ long allbases; /* TRUE if all bases should be printed */ long bound; /* TRUE if upper/lower bound on objective given */ long countonly; /* TRUE if only count totals should be output */ long debug; long dualdeg; /* TRUE if start dictionary is dual degenerate */ long etrace; /* turn off debug at basis # strace */ long extract; /* remove linearities if any and extractcols */ 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 giveoutput; /* TRUE if output should be printed,used for supressing restart first output */ long verifyredund; /* TRUE if mplrs consumer is verifying redund output */ long noredundcheck; /* TRUE if mplrs consumer skips verifying output */ 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 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 maxcobases; /* if positive, after maxcobasis unexplored subtrees reported */ long messages; /* TRUE for normal lrs output, FALSE for PLRS and LRS_QUIET */ long minimize; /* flag for LP minimization */ long long mindepth; /* do not backtrack above mindepth */ long mplrs; /* TRUE if compiled for mplrs */ 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 */ long long subtreesize; /* in estimate mode, iterates if cob_est >= subtreesize */ long triangulation; /* TRUE: the cobases printed triangulate the polytope */ long newstart; /* TRUE: lrs is restarted with new arithmetic */ /* Variables for saving/restoring cobasis, db */ long id; /* numbered sequentially */ char *name; /* passed by user */ long saved_count[5]; /* Saves Q->count[*] */ long *saved_C; lrs_mp saved_det; lrs_mp saved_sumdet; 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; /***************************/ /* mplrs hooks and hacks */ /***************************/ void lrs_open_outputblock(void); /* prevent mplrs output flushes */ void lrs_close_outputblock(void);/* re-enable mplrs output flushes */ void lrs_return_unexplored(lrs_dic *P,lrs_dat *Q); /* send cobasis data for unexplored nodes */ void lrs_post_output(const char *, const char *); /* lrs call to post_output */ #ifndef LRSLONG void lrs_overflow(int i); void lrs_exit(int i); #endif /****************/ /* PLRS */ /****************/ /* following provided by mplrs.c */ void post_output(const char *, const char *); void post_R(lrs_restart_dat *R); void open_outputblock(void); void close_outputblock(void); void mplrs_cleanstop(int checkpoint); void mplrs_emergencystop(const char *); /*******************************/ /* functions for external use */ /*******************************/ long lrsv2_main(int argc, char *argv[],lrs_dic **P,lrs_dat **Q, long overf,long stage,char *tmp,lrs_restart_dat *R); /* called from lrsX_main where X is arithmetic type */ long lrs_run ( lrs_dic *P, lrs_dat * Q); /* main reverse search function */ long redund_run ( lrs_dic *P, lrs_dat * Q); /* main redund loop */ void redund_print(lrs_mp_matrix Ain,lrs_dic *P,lrs_dat *Q); lrs_dat *lrs_alloc_dat (const char *name); /* allocate for lrs_dat structure "name" */ lrs_dic *lrs_alloc_dic (lrs_dat * Q); /* allocate for lrs_dic structure corr. to Q */ long lrs_estimate (lrs_dic * P, lrs_dat * Q); /* get estimates only and returns est number of cobases in subtree */ 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 (const char *name); /* close lrs lib program "name" */ long lrs_init (const char *name); /* initialize lrslib and arithmetic package for prog "name" */ lrs_dic *lrs_setup(int argc, char *argv[], lrs_dat **Q, lrs_restart_dat *R); /* intialize P,P_orig,Q and read data */ lrs_dic *lrs_reset(lrs_dic *P_orig, lrs_dat *Q, lrs_restart_dat *R); /* restore P form P_orig reset Q using R */ 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_print_header(const char *name); void lrs_printoutput (lrs_dat * Q, lrs_mp_vector output); /* print output array */ void lrs_printrow (const 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 */ void lrs_setup_R (lrs_dic * P, lrs_dat * Q, lrs_restart_dat * R); long lrs_solvelp (lrs_dic * P, lrs_dat * Q, long maximize);/* solve primal feas LP:TRUE bounded else FALSE */ void lrs_warning(lrs_dat *Q, char* type, char* ss); /* warnings sent to printer or mplrs */ long lrs_stdin_to_file (char *name); long lrs_file_to_cache(FILE *ifp); long lrs_cache_to_file(char *name, const char *args); /*******************************/ /* 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 lrs_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 linextractcols (lrs_dic * P, lrs_dat * Q); /* preprocess to remove input linearities */ 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 */ long ran_selectpivot (lrs_dic * P, lrs_dat * Q, long *r, long *s); /* select pivot indices using randomedge-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 */ long extractcols (lrs_dic * P, lrs_dat * Q); /* preprocess to just extract given cols */ 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, const 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 */ long readremain (lrs_dat * Q); /* read and check remain vars list for extract */ long readredund (lrs_dat * Q); /* read and check redundancy 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 */ long lrs_leaf(lrs_dic *P, lrs_dat *Q); /* true if current dictionary is leaf of reverse search tree */ void update_R(lrs_dic *P, lrs_dat *Q, lrs_restart_dat *R); /***************************************************/ /* 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_dic2 ( lrs_dic *P, lrs_dat *Q); /* same as lrs_free_dic but no cache*/ void lrs_free_dat ( lrs_dat *Q); void copy_dict (lrs_dat * global, lrs_dic * dest, lrs_dic * src); lrs_dic *alloc_memory (lrs_dat * Q); lrs_dic * lrs_getdic(lrs_dat *Q); lrs_dic *resize (lrs_dic * P, lrs_dat * Q); void lrs_free_all_memory(lrs_dic * P, lrs_dat * Q); /*******************************/ /* 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 */ lrslib-071a/lrslong.c0000700060175606010010000003360213742506306014465 0ustar avisなし/* lrslong.c library code for lrs extended precision arithmetic */ /* Version 4.0, April 13, 2000 */ /* Copyright: David Avis 1999, avis@cs.mcgill.ca */ /* Derived from prs_single.c ( rational arithmetic for lrs and prs) */ /* authored by Ambros Marzetta Revision 1.2 1998/05/27 */ #ifdef PLRS #endif #include #include #include #include "lrslong.h" long lrs_digits; /* max permitted no. of digits */ long lrs_record_digits; /* this is the biggest acheived so far. */ #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 */ { #ifndef B128 unsigned long ul, vl, r; ul = labs (*u); vl = labs (*v); #else __int128 ul, vl, r; ul = abs128 (*u); vl = abs128 (*v); #endif if (ul == 0) { *u = vl; return; } while (vl != 0) { r= ul % vl; ul = vl; vl = r; } *u = ul; } /* gcd */ 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 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 */ { lrs_mp mc, md; itomp(ZERO,mc); itomp(ZERO,md); /*just to please some compilers */ mulint (Na, Nb, mc); mulint (Nc, Nd, md); if (mp_greater(mc,md)) return (1); if (mp_greater(md,mc)) return (-1); return (0); } 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; itomp(ZERO,c); /*just to please some compilers */ 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 answer by gcd(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); } /* return char * representation of a in base 10. * use out if non-NULL, otherwise allocate and return. */ char *mpgetstr10(char *out, lrs_mp a) { char *buf=NULL; int len=0; #ifndef B128 len = snprintf(buf, 0, "%lld", *a); if (out != NULL) buf = out; else buf = (char*)malloc(sizeof(char)*(len+1)); sprintf(buf, "%lld", *a); return buf; #else /* could just allocate 41 chars or so instead of counting */ long long lower = *a % P10_INT64; long long upper = *a / P10_INT64; if (upper != 0) len=snprintf(buf, 0, "%lld", upper); else if (lower < 0) len++; /* - */ len+=snprintf(buf, 0, "%lld", abs128(lower)); if (out != NULL) buf = out; else buf = (char*)malloc(sizeof(char)*(len+1)); len = 0; if (upper != 0) len=sprintf(buf, "%lld", upper); else if (lower < 0) len+=sprintf(buf+len, "-"); /* - */ len+=sprintf(buf+len, "%lld", abs128(lower)); return buf; #endif } 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 input: check you have entered enough data!\n"); 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); } /* read a rational or integer and convert to lrs_mp with base BASE */ /* returns true if denominator is not one */ long plrs_readrat (lrs_mp Na, lrs_mp Da, const char* rat) { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; strcpy(in, rat); 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); } char *cprat (const char *name, lrs_mp Nin, lrs_mp Din) { char *num, *den, *ret; unsigned long len; lrs_mp Nt, Dt; lrs_alloc_mp (Nt); lrs_alloc_mp (Dt); copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); num = mpgetstr10(NULL, Nt); den = mpgetstr10(NULL, Dt); len = snprintf(NULL, 0, " %s %s/%s", name, num, den); ret = (char*)malloc(sizeof(char)*(len+1)); if(one(Dt)) { if (sign (Nt) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); } else { if (sign (Nt) != NEG) sprintf(ret, "%s %s/%s", name, num, den); else sprintf(ret, "%s%s/%s", name, num, den); } free(num); free(den); lrs_clear_mp(Nt); lrs_clear_mp(Dt); return ret; } char *cpmp (const char *name, lrs_mp Nin) { char *num, *ret; unsigned long len; num = mpgetstr10(NULL, Nin); len = snprintf(NULL, 0, "%s %s", name, num); ret = (char*)malloc(sizeof(char)*(len+1)); if (sign (Nin) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); free(num); return ret; } void pmp (const char *name, lrs_mp Nt) { fprintf (lrs_ofp, "%s", name); if (sign (Nt) != NEG) fprintf (lrs_ofp, " "); #ifndef B128 fprintf (lrs_ofp, "%lld", *Nt); #else { long long lower = *Nt % P10_INT64; long long upper = *Nt / P10_INT64; if (upper != 0) fprintf(lrs_ofp, "%lld", upper); else if (lower < 0) fprintf(lrs_ofp, "-"); fprintf(lrs_ofp, "%lld", abs128(lower)); } #endif 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, " "); #ifndef B128 fprintf (lrs_ofp, "%s%lld", name, *Nt); if (*Dt != 1) fprintf (lrs_ofp, "/%lld", *Dt); #else { long long lower = *Nt % P10_INT64; long long upper = *Nt / P10_INT64; fprintf(lrs_ofp, "%s", name); if (upper != 0) fprintf(lrs_ofp, "%lld", upper); else if (lower < 0) fprintf(lrs_ofp, "-"); fprintf(lrs_ofp, "%lld", abs128(lower)); if (*Dt != 1) { lower = *Dt % P10_INT64; upper = *Dt / P10_INT64; fprintf(lrs_ofp, "/"); if (upper != 0) fprintf(lrs_ofp, "%lld", upper); if (lower < 0) fprintf(lrs_ofp, "-"); fprintf(lrs_ofp, "%lld", abs128(lower)); } } #endif 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=(lrs_mp_t)calloc (1, sizeof (lrs_mp)); 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 = (lrs_mp_t *) CALLOC ((n + 1), sizeof (lrs_mp_t)); for (i = 0; i <= n; i++) p[i] = (lrs_mp_t) 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; lrs_mp_t araw; int mp_width, row_width; int i, j; mp_width = lrs_digits + 1; row_width = (n + 1) * mp_width; araw = (lrs_mp_t) calloc ((m + 1) * row_width, sizeof (lrs_mp)); a = (lrs_mp_t **) calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = (lrs_mp_t *) calloc ((n + 1), sizeof (lrs_mp_t)); 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]); /* 2015.9.9 memory leak fix */ free(p); } 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, const 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 */ { #ifndef PLRS lrs_ifp = fpin; lrs_ofp = fpout; #endif lrs_record_digits = 0; lrs_digits = 0; /* max permitted no. of digits */ return TRUE; } void notimpl (const 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-071a/lrslong.h0000700060175606010010000003333113742506306014471 0ustar avisなし/* lrslong.h (lrs long integer 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, 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. */ /* #ifdef PLRS #include using namespace std; #endif */ /***********/ /* 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 is word size */ /* MAXDm is 2^(k/2-1)-1 where k is word size */ /* MAXDa is 2^(k-2)-1 where k is 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 */ /* 64/128 bit arithmetic */ /************************************************/ #ifdef B128 /* 128 bit machines */ /* compiler does not accept big constants! */ #define MAXD 9223372036854775807L /* should be 2^127 -1 but is 2^63 - 1 */ #define MAXDm 9223372036854775807L /* 2^63 - 1 */ #define MAXDa 9223372036854775807L /* should be 2^126 -1 but is 2^63 - 1 */ /* max power of 10 fitting in signed int64 */ #define P10_INT64 1000000000000000000ULL #define BASE 1000000000L #define FORMAT "%9.9u" #define BASE_DIG 9 #define INTSIZE 16L #define BIT "128bit" #else /* 64 bit machines */ #define MAXD 9223372036854775807LL /* 2^63 - 1 */ #define MAXDm 2147483647LL /* 2^31 - 1 */ #define MAXDa 4611686018427387904LL /* 2^62 - 1 */ #define BASE 1000000000L #define FORMAT "%9.9u" #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 */ /**********************************/ #ifdef SAFE /* lazy but fast overflow checking */ #define mpsafem(a,b) *(a)>MAXDm||*(b)>MAXDm||*(a)<-MAXDm||*(b)<-MAXDm #define mpsafea(a,b) *(a)>MAXDa||*(b)>MAXDa||*(a)<-MAXDa||*(b)<-MAXDa #ifdef DEBUG #define mperrorm(a,b) fprintf(stdout," : max(|a|,|b|) > %ld\n",MAXDa);lrs_overflow(1) #define mperrora(a,b) fprintf(stdout," : max(|a|,|b|) > %ld\n",MAXDa);lrs_overflow(1) #define linint(a, ka, b, kb) if( mpsafem(a,b) ) {fprintf(stdout, "\n*linint ");mperrorm(a,b);} else *(a) = *(a) * ka + *(b) * kb #define mulint(a, b, c) if( mpsafem(a,b) ) {fprintf(stdout, "\n*mulint ");mperrorm(a,b);} else *(c) = *(a) * *(b) #define addint(a, b, c) if( mpsafea(a,b) ) {fprintf(stdout, "\n*addint ");mperrora(a,b);} else *(c) = *(a) + *(b) #define subint(a, b, c) if( mpsafea(a,b) ) {fprintf(stdout, "\n*subint ");mperrora(a,b);} else *(c) = *(a) - *(b) #define decint(a, b) if( mpsafea(a,b) ) {fprintf(stdout, "\n*decint ");mperrora(a,b);} else *(a) = *(a) - *(b) #else #define linint(a, ka, b, kb) if( mpsafem(a,b) ) lrs_overflow(1) ; else *(a) = *(a) * ka + *(b) * kb #define mulint(a, b, c) if( mpsafem(a,b) ) lrs_overflow(1) ; else *(c) = *(a) * *(b) #define addint(a, b, c) if( mpsafea(a,b) ) lrs_overflow(1) ; else *(c) = *(a) + *(b) #define subint(a, b, c) if( mpsafea(a,b) ) lrs_overflow(1) ; else *(c) = *(a) - *(b) #define decint(a, b) if( mpsafea(a,b) ) lrs_overflow(1) ; else *(a) = *(a) - *(b) #endif #else /* unprotected routines */ #define addint(a, b, c) *(c) = *(a) + *(b) #define subint(a, b, c) *(c) = *(a) - *(b) #define linint(a, ka, b, kb) *(a) = *(a) * ka + *(b) * kb #define mulint(a, b, c) *(c) = *(a) * *(b) #endif #define unchecked_decint(a, b) *(a) = *(a) - *(b) /* only safe if a,b come from mulint */ #define divint(a, b, c) *(c) = *(a) / *(b); *(a) = *(a) % *(b) #define exactdivint(a,b,c) *(c) = *(a) / *(b); #define abs128(a) (a>0? a : -1*a) #define changesign(a) (*(a) = - *(a)) #define copy(a, b) ((a)[0] = (b)[0]) #define mp_greater(a, b) (*(a) > *(b) ) #define itomp(in, a) *(a) = in #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) #ifndef B128 #define storesign(a, sa) (*(a) = labs(*(a)) * sa) #else #define storesign(a, sa) (*(a) = abs128(*(a)) * sa) #endif #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 #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) /*************/ /* typedefs */ /*************/ #ifndef B128 typedef long long lrs_mp[1]; /* type lrs_mp holds one long integer */ typedef long long *lrs_mp_t; typedef long long **lrs_mp_vector; typedef long long ***lrs_mp_matrix; #else typedef __int128 lrs_mp[1]; /* type lrs_mp holds one 128-bit integer */ typedef __int128 *lrs_mp_t; typedef __int128 **lrs_mp_vector; typedef __int128 ***lrs_mp_matrix; #endif /*********************/ /*global variables */ /*********************/ extern long lrs_digits; /* max permitted no. of digits */ extern 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 */ /*********************************************************/ /* Initialization and allocation procedures - must use! */ /******************************************************* */ //void mulint(lrs_mp a, lrs_mp b, lrs_mp c); 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); #ifndef MA #define suf(func) func #endif #ifdef MA #ifdef B128 #define suf(func) func##_2 #else #define suf(func) func##_1 #endif #endif #define atoaa suf(atoaa) #define atomp suf(atomp) #define comprod suf(comprod) #define divrat suf(divrat) #define gcd suf(gcd) #define getfactorial suf(getfactorial) #define lcm suf(lcm) #define linrat suf(linrat) #define lrs_alloc_mp_matrix suf(lrs_alloc_mp_matrix) #define lrs_alloc_mp_t suf(lrs_alloc_mp_t) #define lrs_alloc_mp_vector suf(lrs_alloc_mp_vector) #define lrs_clear_mp_matrix suf(lrs_clear_mp_matrix) #define lrs_clear_mp_vector suf(lrs_clear_mp_vector) #define lrs_digits suf(lrs_digits) #define lrs_getdigits suf(lrs_getdigits) #define lrs_overflow suf(lrs_overflow) #define lrs_mp_init suf(lrs_mp_init) #define lrs_record_digits suf(lrs_record_digits) #define mptodouble suf(mptodouble) #define mptoi suf(mptoi) #define mpgetstr10 suf(mpgetstr10) #define mulrat suf(mulrat) #define myrandom suf(myrandom) #define notimpl suf(notimpl) #define pmp suf(pmp) #define prat suf(prat) #define cprat suf(cprat) #define cpmp suf(cpmp) #define rattodouble suf(rattodouble) #define readmp suf(readmp) #define readrat suf(readrat) #define plrs_readrat suf(plrs_readrat) #define reduce suf(reduce) #define reducearray suf(reducearray) #define reduceint suf(reduceint) #define stringcpy suf(stringcpy) #define xcalloc suf(xcalloc) /*********************************************************/ /* 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 */ char *mpgetstr10(char *, lrs_mp); /* convert lrs_mp to string */ #ifdef PLRS long plrs_readrat (lrs_mp Na, lrs_mp Da, const char * rat); /* take a rational number and convert to lrs_mp */ #endif char *cprat(const char *name, lrs_mp Nt, lrs_mp Dt); /* mp rat to char */ char *cpmp(const char *name, lrs_mp Nt); /* mp int to char */ void pmp (const 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 (const 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 */ /********************************/ /* Matrix and vector allocation */ /********************************/ void lrs_clear_mp_vector (lrs_mp_vector p, long n); lrs_mp_vector lrs_alloc_mp_vector(long n); void lrs_clear_mp_vector(lrs_mp_vector p, long n); lrs_mp_matrix lrs_alloc_mp_matrix(long m, long n); void lrs_clear_mp_matrix(lrs_mp_matrix p, long m, long n); long lrs_mp_init(long dec_digits, FILE *fpin, FILE *fpout); /* how big are numbers? */ extern long lrs_digits; /* max permitted no. of digits */ extern long lrs_record_digits; /* this is the biggest achieved so far. */ /**********************************/ /* 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, const char *f); void lrs_default_digits_overflow (); void lrs_exit(int i); void lrs_overflow(int i); /* end of lrs_long.h (vertex enumeration using lexicographic reverse search) */ lrslib-071a/lrsmp.c0000700060175606010010000006025213742506305014142 0ustar avisなし/* 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA. */ #include #include #include #include "lrsmp.h" long lrs_digits=DEC2DIG(DEFAULT_DIGITS); long lrs_record_digits; /* this is the biggest acheived so far. */ /******************************************************************/ /* 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() /*********************************************************/ /* 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) { 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 long *)calloc (lrs_digits+1, sizeof (long 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 = (lrs_mp_vector) CALLOC ((n + 1), sizeof (lrs_mp *)); for (i = 0; i <= n; i++) p[i] = (long long int *)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 long *araw; int mp_width, row_width; int i, j; mp_width = lrs_digits + 1; row_width = (n + 1) * mp_width; araw = (long long int*)calloc ((m + 1) * row_width, sizeof (long long)); a = (lrs_mp_matrix) calloc ((m + 1), sizeof (lrs_mp_vector)); for (i = 0; i < m + 1; i++) { a[i] = (long long int **)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 long cy, la, lb, lc, d1, s, t, sig; long 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 (stdout, "divide error"); exit(1); } 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 long ul, vl; long i; static unsigned long 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 (mp_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 mp_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 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 length (lrs_mp a) { /* formerly a macro but conflicts with string length */ return ((a[0] > 0) ? a[0] : -a[0]); } 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 */ } /* untested */ char *mpgetstr10(char *out, lrs_mp a) { int len = 0; char *buf = NULL; int i; if (sign (a) == NEG) len++; len += snprintf(buf, 0, "%llu", a[length (a) -1]); for (i = length (a) - 2; i >= 1; i--) len +=snprintf(buf, 0, FORMAT, a[i]); if (out != NULL) buf = out; else buf = (char *)malloc(sizeof(char)*(len + 1)); len = 0; if (sign (a) == NEG) len++,sprintf(buf, "-"); len += sprintf(buf+len, "%llu", a[length (a) -1]); for (i = length (a) - 2; i >= 1; i--) len += sprintf(buf+len, FORMAT, a[i]); return buf; } char *cprat (const char *name, lrs_mp Nin, lrs_mp Din) { char *num, *den, *ret; unsigned long len; lrs_mp Nt, Dt; lrs_alloc_mp (Nt); lrs_alloc_mp (Dt); copy (Nt, Nin); copy (Dt, Din); reduce (Nt, Dt); num = mpgetstr10(NULL, Nt); den = mpgetstr10(NULL, Dt); len = snprintf(NULL, 0, " %s %s/%s", name, num, den); ret = (char*)malloc(sizeof(char)*(len+1)); if(one(Dt)) { if (sign (Nt) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); } else { if (sign (Nt) != NEG) sprintf(ret, " %s %s/%s", name, num, den); else sprintf(ret, "%s%s/%s", name, num, den); } free(num); free(den); lrs_clear_mp(Nt); lrs_clear_mp(Dt); return ret; } char *cpmp (const char *name, lrs_mp Nin) { char *num, *ret; unsigned long len; num = mpgetstr10(NULL, Nin); len = snprintf(NULL, 0, "%s %s", name, num); ret = (char*)malloc(sizeof(char)*(len+1)); if (sign (Nin) != NEG) sprintf(ret, "%s %s", name, num); else sprintf(ret, "%s%s", name, num); free(num); return ret; } /* char *cprat (const char *name, lrs_mp Nin, lrs_mp Din) { char *num, *den, *ret; unsigned long len; num = mpgetstr10(NULL, Nin); den = mpgetstr10(NULL, Din); len = snprintf(NULL, 0, "%s%s/%s", name, num, den); ret = (char*)malloc(sizeof(char)*(len+1)); sprintf(ret, "%s%s/%s", name, num, den); free(num); free(den); return ret; } */ void prat (const 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, "%llu", 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, "%llu", Dt[length (Dt) - 1]); for (i = length (Dt) - 2; i >= 1; i--) fprintf (lrs_ofp, FORMAT, Dt[i]); } fprintf (lrs_ofp, " "); } void pmp (const 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, "%llu", a[length (a) - 1]); for (i = length (a) - 2; i >= 1; i--) fprintf (lrs_ofp, FORMAT, a[i]); fprintf (lrs_ofp, " "); } 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 input: check you have entered enough data!\n"); 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 (const 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, const 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 (stdout, "\nlrsmp: overflow at digits=%ld", DIG2DEC (lrs_digits)); fprintf (stdout, "\nInitialize lrs_mp_init with n > %ldL\n", DIG2DEC (lrs_digits)); lrs_exit (1); } #ifdef PLRS /* 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 */ long plrs_readrat (lrs_mp Na, lrs_mp Da, const char* rat) { char in[MAXINPUT], num[MAXINPUT], den[MAXINPUT]; strcpy(in, rat); 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); } #endif /* end of lrsmp.c */ lrslib-071a/lrsmp.h0000700060175606010010000002342513742506301014144 0ustar avisなし/* lrsmp.h (lrs extended precision arithmetic library) */ /* Copyright: David Avis 2000, avis@cs.mcgill.ca */ /* Version 4.1, 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., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, 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 */ /***********/ #define suf(func) func /* 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 1000L /**********MACHINE DEPENDENT CONSTANTS***********/ /* MAXD is 2^(k-1)-1 where k is 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 */ /***********************************************/ /* 64 bit machines */ #define MAXD 9223372036854775807LL #define BASE 1000000000LL #define FORMAT "%9.9llu" #define BASE_DIG 9 #define INTSIZE 16L #define BIT "64bit" #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 #define CALLOC(n,s) xcalloc(n,s,__LINE__,__FILE__) extern long lrs_digits; /* max permitted no. of digits */ extern 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 */ /*************/ /* typedefs */ /*************/ typedef long long lrs_mp[MAX_DIGITS + 1]; /* type lrs_mp holds one multi-precision integer */ typedef long long *lrs_mp_t; typedef long long **lrs_mp_vector; typedef long long ***lrs_mp_matrix; /*********************************************************/ /* 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 */ long lrs_mp_init (long dec_digits, FILE * lrs_ifp, FILE * lrs_ofp); /* max number of decimal digits, fps */ 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 */ /******************************************************* */ long length (lrs_mp a); /* return length of lrs_mp integer */ 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 mp_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 */ #ifdef PLRS long plrs_readrat (lrs_mp Na, lrs_mp Da, const char * rat); /* take a rational number and convert to lrs_mp */ #endif void mptodouble (lrs_mp a, double *x); /* convert lrs_mp to double */ long mptoi (lrs_mp a); /* convert lrs_mp to long integer */ char *mpgetstr10 (char *, lrs_mp); /* convert lrs_mp to char array */ 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 (const 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 */ char *cpmp(const char *name, lrs_mp Nt); /* mp int to char */ char *cprat(const char *name, lrs_mp Nt, lrs_mp Dt); /* C version of prat */ 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 */ /* NC/DC = ka*Na/Da + kb*Nb/Db */ 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 (const 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 *xcalloc (long n, long s, long l, const char *f); void lrs_default_digits_overflow (); void digits_overflow (); void lrs_exit(int i); /* end of lrsmp.h (vertex enumeration using lexicographic reverse search) */ lrslib-071a/lrsnash.c0000700060175606010010000002212413742506306014454 0ustar avisなし/*********************************************************/ /* lrsnash is driver for computing all nash equilibria */ /* for two person games given by mxn payoff matrices A,B */ /* Usage: lrsnash [options] game [output file] */ /* */ /* game is a file containing: */ /* m n */ /* A (row by row) */ /* B (row by row) */ /* */ /* Derived from nash.c in lrslib-060 by */ /* Terje Lensberg, October 26, 2015: */ /* Simplified API via lrs_solve_nash(game *g) */ /*********************************************************/ /* Compile: gcc -O3 -o lrsnash lrsnash.c lrsnashlib.c lrslib.c lrsgmp.c -lgmp -DGMP */ char Usage[] = "usage (standard): %s [options...] \n" "usage (legacy): %s []\n" "type %s -h for more information\n\n"; char Helptext[] = "\nusage (standard): %s [options...] \n" " Input file structure: Input files to setupnash\n" " Input files can be specified separately, or by using wildcards, as in 'game*'\n" " Options:\n" " -v, --verbose Prints a trace of the solution process\n" " -d, --debug Dumps lots of information for debugging\n" " -p, --printgame Prints the payoff matrix for the game\n" " -s, --standard Promise that input files have standard structure\n" " -o, --outfile Send output to \n" " -h, --help Prints this text\n" " Short options can be grouped, as in '-ps' and '-do out.txt'\n" "usage (legacy): %s []\n" " Input file structure: Output files from setupnash\n" " Passing options with legacy input files produces an error\n" " (options must be specified in the input files)\n\n"; char LegacyMsg[] = "\nProcessing legacy input files. Alternatively, you may skip\n" "setupnash and pass its input file to this program.\n"; #include #include #include #include #include #include "lrsdriver.h" #include "lrslib.h" #include "lrsnashlib.h" //======================================================================== // Games //======================================================================== //----------------------------------------------------------------------------------------// // Reading games //----------------------------------------------------------------------------------------// char *Outfile = NULL; //----------------------------------------------------------------------------------------// int openIO(void) { if (!lrs_init("*lrsnash:")) return FALSE; fprintf(stderr, "\n"); if(Outfile != NULL) { if ((lrs_ofp = fopen(Outfile, "w")) == NULL) { fprintf(stderr, "\nBad output file name\n"); return FALSE; } } return TRUE; } void closeIO(void) { if(lrs_ofp != stdout) fprintf(stdout, "\n"); lrs_close("lrsnash:"); } #define RATWARN(name, filename) fprintf(stderr, "\nWarning: String '%s' is not a rational number in file %s.\n", name, filename); #define RECWARN(filename) fprintf(stderr, "\nWarning: Excess data in file %s.\n", filename); #define ERREXIT if(lrs_ofp != NULL) closeIO(); exit(1); #define FILEERROR(name) {fprintf(stderr, "\nError: Cannot find input file '%s'. \ Execution halted\n", name); ERREXIT} #define READERROR(name) {fprintf(stderr, "\nError: Premature end of input file '%s'. \ Execution halted\n", name); ERREXIT} #define SIZEERROR(name) {fprintf(stderr, "\nError: Number of strategies exceeds maximum (%d) in input file '%s'. \ Execution halted\n",MAXSTRAT, name); ERREXIT} //----------------------------------------------------------------------------------------// // Simple function to convert string to (num, den) int tl_readrat(long *num, long *den, char *str) { char *div = strchr(str, '/'); if(div == NULL) { *num = atol(str); *den = 1; } else if(div == str || *(div+1) == 0) { // str = '/x' or str = 'x/' return FALSE; } else { *div = 0; // Note: 'str' is modified here *num = atol(str); *den = atol(div+1); } return TRUE; } //----------------------------------------------------------------------------------------// int readGame(game * g, const char *filename) { FILE *IN; long pos, s, t, nr, nc; char in[MAXINPUT]; strcpy(((gInfo *)g->aux)->name, filename); if ((IN = fopen(filename, "r")) == NULL) FILEERROR(filename); if (fscanf(IN, "%ld %ld", &nr, &nc) < 2) READERROR(filename); if (nr > MAXSTRAT || nc > MAXSTRAT) SIZEERROR(filename); g->nstrats[ROW] = nr; g->nstrats[COL] = nc; initFwidth(g); // Read payoffs for (pos = 0; pos < 2; pos++) { for (s = 0; s < nr; s++) { for (t = 0; t < nc; t++) { if (fscanf(IN, "%s", in) < 1) READERROR(filename); updateFwidth(g, t, pos, in); if (!tl_readrat (&g->payoff[s][t][pos].num, &g->payoff[s][t][pos].den, in)) RATWARN(in, filename); } } } if (fscanf(IN, "%s", in) == 1) // Too many payoff entries RECWARN(filename); fclose(IN); return TRUE; } //----------------------------------------------------------------------------------------// //======================================================================== // Command line processing //======================================================================== // Flags to be set from command line options static long Print_game_flag; static long Standard_input_flag; void printUsage(const char *progname) { fprintf(stderr, Usage, progname, progname, progname); } void printInfo(const char *progname) { fprintf(stderr, Helptext, progname, progname); } //----------------------------------------------------------------------------------------// // Collects flags and reads list of games int getArgs(int argc, char **argv) { int c, error = FALSE; const char shortOptions[] = ":vdpsho:"; if (argc < 2) { printUsage(argv[0]); return FALSE; } while (1) { static struct option long_options[] = { {"verbose", no_argument, 0, 'v'}, {"debug", no_argument, 0, 'd'}, {"printgame", no_argument, 0, 'p'}, {"standard", no_argument, 0, 's'}, {"outfile", required_argument, 0, 'o'}, {"help", no_argument, 0, 'h'} // {0, 0, 0, 0} }; /* getopt_long stores the option index here. */ int option_index = 0; c = getopt_long(argc, argv, shortOptions, long_options, &option_index); /* Detect the end of the options. */ if (c == -1) break; switch (c) { case '?': fprintf(stderr, "\nError: Unknown option '-%c'.\n", optopt); error = TRUE; break; case ':': fprintf(stderr, "\nError: Missing argument to option '-%c'.\n", optopt); error = TRUE; break; case 'v': Verbose_flag = TRUE; break; case 'd': Debug_flag = TRUE; break; case 'p': Print_game_flag = TRUE; break; case 's': Standard_input_flag = TRUE; break; case 'h': printInfo(argv[0]); return FALSE; break; case 'o': Outfile = optarg; break; default: abort(); } } if(error) { fprintf(stderr, "Execution halted\n"); return FALSE; } return TRUE; } //----------------------------------------------------------------------------------------// // Checks if an input file is legacy (contains letters) int isLegacy(const char *filename) { FILE *fp; int i, n, foundLetter = FALSE; char buf[100]; if((fp = fopen(filename, "r")) == NULL) FILEERROR(filename); n = fread(buf, sizeof(char), 100, fp); for(i=0;iaux = &GI; if(!getArgs(argc, argv)) // Read options and input file names. When we get here: return 1; // optind is a global integer supplied by getopt, and // argv[optind] is the first non-option argument in argv if(Standard_input_flag // Assume standard input files if user set the flag, || optind == argc - 1 // or if only one input file, || !isLegacy(argv[optind])) // or if the first input file is not legacy { if(!openIO()) return 1; while (optind < argc) { // Handle standard input file[s] if(readGame(g, argv[optind++])) { if(Print_game_flag) printGame(g); lrs_solve_nash(g); } } closeIO(); } else { // Handle legacy input files fprintf (stderr, "%s", LegacyMsg); // Print a message to user lrs_solve_nash_legacy(argc, argv); } return 0; } lrslib-071a/lrsnashlib.c0000700060175606010010000011775113742506302015152 0ustar avisなし/*******************************************************/ /* lrsnashlib is a library of routines for computing */ /* computing all nash equilibria for two person games */ /* given by mxn payoff matrices A,B */ /* */ /* */ /* Main user callable function is */ /* lrs_solve_nash(game *g) */ /* */ /* Requires lrsnashlib.h lrslib.h lrslib.c */ /* */ /* Sample driver: lrsnash.c */ /* Derived from nash.c in lrslib-060 */ /* by Terje Lensberg, October 26, 2015: */ /*******************************************************/ #include #include #include "lrsdriver.h" #include "lrslib.h" #include "lrsnashlib.h" static long FirstTime; /* set this to true for every new game to be solved */ long Debug_flag; long Verbose_flag; //======================================================================== // Standard solver. Modified version of main() from lrsNash //======================================================================== int lrs_solve_nash(game * g) { lrs_dic *P1; /* 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_mp_matrix A2orig; lrs_dic *P2orig; /* we will save player 2's dictionary in getabasis */ long *linindex; /* for faster restart of player 2 */ 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. */ /*********************************************************************************/ /* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */ /*********************************************************************************/ FirstTime=TRUE; /* This is done for each new game */ Q1 = lrs_alloc_dat("LRS globals"); /* allocate and init structure for static problem data */ if (Q1 == NULL) { return 0; } Q1->nash = TRUE; Q1->n = g->nstrats[ROW] + 2; Q1->m = g->nstrats[ROW] + g->nstrats[COL] + 1; Q1->debug = Debug_flag; Q1->verbose = Verbose_flag; P1 = lrs_alloc_dic(Q1); /* allocate and initialize lrs_dic */ if (P1 == NULL) { return 0; } BuildRep(P1, Q1, g, 1, 0); output1 = lrs_alloc_mp_vector(Q1->n + Q1->m); /* output holds one line of output from dictionary */ /* allocate and init structure for player 2's problem data */ Q2 = lrs_alloc_dat("LRS globals"); if (Q2 == NULL) { return 0; } Q2->debug = Debug_flag; Q2->verbose = Verbose_flag; Q2->nash = TRUE; Q2->n = g->nstrats[COL] + 2; Q2->m = g->nstrats[ROW] + g->nstrats[COL] + 1; P2orig = lrs_alloc_dic(Q2); /* allocate and initialize lrs_dic */ if (P2orig == NULL) { return 0; } BuildRep(P2orig, Q2, g, 0, 1); A2orig = P2orig->A; output2 = lrs_alloc_mp_vector(Q1->n + Q1->m); /* output holds one line of output from dictionary */ linindex = calloc((P2orig->m + P2orig->d + 2), sizeof(long)); /* for next time */ fprintf(lrs_ofp, "\n"); // fprintf (lrs_ofp, "***** %ld %ld rational\n", 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(P1, Q1, P2orig, Q2, &numequilib, output2, linindex); 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, "*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 */ /* 2015.10.10 new code to clear P2orig */ Q2->Qhead = P2orig; /* reset this or you crash free_dic */ P2orig->A = A2orig; /* reset this or you crash free_dic */ lrs_free_dic(P2orig, Q2); /* deallocate lrs_dic */ lrs_free_dat(Q2); /* deallocate lrs_dat */ free(linindex); // lrs_close("nash:"); fprintf(lrs_ofp, "\n"); 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(lrs_dic * P1, lrs_dat * Q1, lrs_dic * P2orig, lrs_dat * Q2, long *numequilib, lrs_mp_vector output, long linindex[]) { 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, linindex)) 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, long linindex[]) /* 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, *Col; long *inequality; long *linearity; long hull = Q->hull; long m, d, lastdv, nlinearity, nredundcol; 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; 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, linindex)) { 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) { const unsigned int Qn = Q->n; *Lin = lrs_alloc_mp_matrix(nredundcol, Qn); 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)) { lrs_clear_mp_matrix(*Lin, nredundcol, Qn); return FALSE; } } } /* end if nredundcol > 0 */ if (Q->verbose) { fprintf(lrs_ofp, "\nNumber of pivots for starting dictionary: %ld", 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"); } return FALSE; } if (Q->verbose) { fprintf(lrs_ofp, "\nNumber of pivots for feasible solution: %ld", 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[], long linindex[]) /* 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. */ { /* 2015.10.10 linindex now preallocated and received as parameter so we can free it */ // static long firsttime = TRUE; /* stays true until first valid dictionary built */ 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; //2015.9.15 /* after first time we update the change in linearities from the last time, saving many pivots */ if (!FirstTime) { for (i = 1; i <= m + d; i++) linindex[i] = FALSE; if (Q->debug) fprintf(lrs_ofp, "\nlindex ="); for (i = 0; i < nlinearity; i++) { linindex[d + linearity[i]] = TRUE; if (Q->debug) 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 < d && (linindex[C[k]] || zero(A[Row[i]][Col[k]]))) k++; if (k < d) { j = i; /* note this index changes in update, cannot use i!) */ if (C[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 .. */ } else { /* we have not had a successful dictionary built from the given linearities */ /* 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, "*Input linearity in row %ld is redundant--skipped\n", order[j]); #endif linearity[j] = 0; } else { if (Q->debug) printA(P, Q); if (Q->debug || 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; /* lrs bug fix, 2009.6.27, nash 2015.9.16 */ 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; /* 2015.9.15 bug fix : we needed first *successful* time */ FirstTime = FALSE; } /* else firsttime ... we have built a dictionary from the given linearities */ /* we continue from here after loading dictionary */ 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, "%ld ", player); for (i = 1; i < Q->n; i++) prat("", output[i], output[0]); fprintf(lrs_ofp, "\n"); fflush(lrs_ofp); return TRUE; } /* end lrs_nashoutput */ //======================================================================== // Old style solver. Included for backward compatibility //======================================================================== int lrs_solve_nash_legacy (int argc, char *argv[]) // Handles legacy input files { lrs_dic *P1; /* 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_mp_matrix A2orig; lrs_dic *P2orig; /* we will save player 2's dictionary in getabasis */ long *linindex; /* for faster restart of player 2 */ 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: %s input1 input2 [outputfile] \n", argv[0]); 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; /*********************************************************************************/ /* 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 */ strcpy(Q1->fname,"nash"); /* program name */ 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; strcpy(Q2->fname,"nash"); /* program name */ 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)); P2orig = lrs_alloc_dic (Q2); /* allocate and initialize lrs_dic */ if (P2orig == NULL) return 1; if (!lrs_read_dic (P2orig, Q2)) /* read remainder of input to setup P2 and Q2 */ return 1; A2orig = P2orig->A; output2 = lrs_alloc_mp_vector (Q1->n + Q1->m); /* output holds one line of output from dictionary */ linindex = calloc ((P2orig->m + P2orig->d + 2), sizeof (long)); /* for next time*/ fprintf (lrs_ofp, "\n***** %ld %ld rational\n", 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(P1,Q1,P2orig,Q2,&numequilib,output2,linindex); 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 */ /* 2015.10.10 new code to clear P2orig */ Q2->Qhead = P2orig; /* reset this or you crash free_dic */ P2orig->A=A2orig; /* reset this or you crash free_dic */ lrs_free_dic (P2orig,Q2); /* deallocate lrs_dic */ lrs_free_dat (Q2); /* deallocate lrs_dat */ free (linindex); lrs_close ("nash:"); return 0; } /*********************************************/ /* end of nash driver */ /*********************************************/ //========================================================================== // Building the problem representations (adapted from Gambit-enummixed) //========================================================================== // // These two functions are based upon the program setupnash.c from the // lrslib distribution, and the user's guide documentation. // There are two separate functions, one for each player's problem. // According to the user's guide, the ordering of the constraint rows // is significant, and differs between the players; for player 1's problem // the nonnegativity constraints come first, whereas for player 2's problem // they appear later. Experiments suggest this is in fact true, and // reversing them breaks something. // //----------------------------------------------------------------------------------------// void FillNonnegativityRows(lrs_dic * P, lrs_dat * Q, int firstRow, int lastRow, int n) { const int MAXCOL = 1000; /* maximum number of columns */ long num[MAXCOL], den[MAXCOL]; long row, col; for (row = firstRow; row <= lastRow; row++) { num[0] = 0; den[0] = 1; for (col = 1; col < n; col++) { num[col] = (row - firstRow + 1 == col) ? 1 : 0; den[col] = 1; } lrs_set_row(P, Q, row, num, den, GE); } } //----------------------------------------------------------------------------------------// void FillConstraintRows(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2, int firstRow) { const int MAXCOL = 1000; /* maximum number of columns */ long num[MAXCOL], den[MAXCOL]; ratnum x; int row, s, t; for (row = firstRow; row < firstRow + g->nstrats[p1]; row++) { num[0] = 0; den[0] = 1; s = row - firstRow; for (t = 0; t < g->nstrats[p2]; t++) { x = p1 == ROW ? g->payoff[s][t][p1] : g->payoff[t][s][p1]; num[t + 1] = -x.num; den[t + 1] = x.den; } num[g->nstrats[p2] + 1] = 1; den[g->nstrats[p2] + 1] = 1; lrs_set_row(P, Q, row, num, den, GE); } } //----------------------------------------------------------------------------------------// void FillLinearityRow(lrs_dic * P, lrs_dat * Q, int m, int n) { const int MAXCOL = 1000; /* maximum number of columns */ long num[MAXCOL], den[MAXCOL]; int i; num[0] = -1; den[0] = 1; for (i = 1; i < n - 1; i++) { num[i] = 1; den[i] = 1; } num[n - 1] = 0; den[n - 1] = 1; lrs_set_row(P, Q, m, num, den, EQ); } // // TL added this to get first row of ones. Don't know if it's needed //----------------------------------------------------------------------------------------// void FillFirstRow(lrs_dic * P, lrs_dat * Q, int n) { const int MAXCOL = 1000; /* maximum number of columns */ long num[MAXCOL], den[MAXCOL]; int i; for (i = 0; i < n; i++) { num[i] = 1; den[i] = 1; } lrs_set_row(P, Q, 0, num, den, GE); } // // Build the H-representation for player p1 //----------------------------------------------------------------------------------------// void BuildRep(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2) { long m = Q->m; /* number of inequalities */ long n = Q->n; if (p1 == 0) { FillConstraintRows(P, Q, g, p1, p2, 1); FillNonnegativityRows(P, Q, g->nstrats[p1] + 1, g->nstrats[ROW] + g->nstrats[COL], n); } else { FillNonnegativityRows(P, Q, 1, g->nstrats[p2], n); FillConstraintRows(P, Q, g, p1, p2, g->nstrats[p2] + 1); // 1 here } FillLinearityRow(P, Q, m, n); // TL added this to get first row of ones. (Is this necessary?) FillFirstRow(P, Q, n); } //----------------------------------------------------------------------------------------// void printGame(game * g) { int s, t; char out[2][MAXINPUT]; fprintf(lrs_ofp, "\n--------------------------------------------------------------------------------\n"); fprintf(lrs_ofp, "%s payoff matrix:\n", ((gInfo *)g->aux)->name); for (s = 0; s < g->nstrats[ROW]; s++) { for (t = 0; t < g->nstrats[COL]; t++) { if(g->payoff[s][t][ROW].den == 1) sprintf(out[ROW], "%ld,", g->payoff[s][t][ROW].num); else sprintf(out[ROW], "%ld/%ld,", g->payoff[s][t][ROW].num, g->payoff[s][t][ROW].den); if(g->payoff[s][t][COL].den == 1) sprintf(out[COL], "%ld", g->payoff[s][t][COL].num); else sprintf(out[COL], "%ld/%ld", g->payoff[s][t][COL].num, g->payoff[s][t][COL].den); fprintf(lrs_ofp, "%*s%-*s ", ((gInfo *)g->aux)->fwidth[t][ROW]+1, out[ROW], ((gInfo *)g->aux)->fwidth[t][COL], out[COL]); } fprintf(lrs_ofp, "\n"); } fprintf(lrs_ofp, "\nNash equilibria:\n"); fflush(lrs_ofp); } // Functions to set field widths for pretty printing of payoff matrices void setFwidth(game *g, int len) { int pos, t; for (t = 0; t < g->nstrats[COL]; t++) for (pos = 0; pos < 2; pos++) ((gInfo *)g->aux)->fwidth[t][pos] = len; } void initFwidth(game *g) { int pos, t; for (t = 0; t < g->nstrats[COL]; t++) for (pos = 0; pos < 2; pos++) ((gInfo *)g->aux)->fwidth[t][pos] = 0; } void updateFwidth(game *g, int col, int pos, char *str) { int len = strlen(str); if(len > ((gInfo *)g->aux)->fwidth[col][pos]) ((gInfo *)g->aux)->fwidth[col][pos] = len; } /******************** end of lrsnashlib.c ***************************/ lrslib-071a/lrsnashlib.h0000700060175606010010000000467613742506301015157 0ustar avisなし/*******************************************************/ /* lrsnashlib is a library of routines for computing */ /* computing all nash equilibria for two person games */ /* given by mxn payoff matrices A,B */ /* */ /* */ /* Main user callable function is */ /* lrs_solve_nash(game *g) */ /* */ /* Sample driver: lrsnash.c */ /* Derived from nash.c in lrslib-060 */ /* by Terje Lensberg, October 26, 2015: */ /*******************************************************/ /* minor mod 2018.2.12 to set Q->fname="nash" */ /*************/ /* Games */ /*************/ #define MAXSTRAT 200 #define ROW 0 #define COL 1 typedef struct { long num; long den; } ratnum; typedef struct { long nstrats[2]; ratnum payoff[MAXSTRAT][MAXSTRAT][2]; // For auxiliary information void *aux; } game; typedef struct { char name[100]; int fwidth[MAXSTRAT][2]; // Column field widths (for output) } gInfo; int lrs_solve_nash(game * g); long nash2_main(lrs_dic * P1, lrs_dat * Q1, lrs_dic * P2orig, lrs_dat * Q2, long *numequilib, lrs_mp_vector output, long linindex[]); /* 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 linindex[]); long getabasis2(lrs_dic * P, lrs_dat * Q, lrs_dic * P2orig, long order[], long linindex[]); long lrs_nashoutput(lrs_dat * Q, lrs_mp_vector output, long player); /* returns TRUE and prints output if not the origin */ int lrs_solve_nash_legacy (int argc, char *argv[]); void BuildRep(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2); void FillFirstRow(lrs_dic * P, lrs_dat * Q, int n); void FillLinearityRow(lrs_dic * P, lrs_dat * Q, int m, int n); void FillConstraintRows(lrs_dic * P, lrs_dat * Q, const game * g, int p1, int p2, int firstRow); void FillNonnegativityRows(lrs_dic * P, lrs_dat * Q, int firstRow, int lastRow, int n); void printGame(game * g); void setFwidth(game *g, int len); void initFwidth(game *g); void updateFwidth(game *g, int col, int pos, char *str); extern long Debug_flag; extern long Verbose_flag; lrslib-071a/lrsrestart.h0000700060175606010010000000305413742506301015210 0ustar avisなしtypedef struct lrs_restart_dat /* for restarting from a given cobasis */ { long *facet; /* cobasic indices for restart */ long overide; /* TRUE if Q parameters should be updated */ long restart; /* TRUE if we supply restart cobasis */ long lrs; /* TRUE if we are doing a lrs run */ long m; /* number of input rows */ long d; /* number of cobasic indices */ long count[10]; /* count[0]=rays(facets) [1]=verts. [2]=base [3]=pivots */ /* count[4]=integer vertices [5]=1 for hull */ /* [6]=nlinearities [7]=deepest */ long depth; /* depth of restart node */ long maxcobases; /* if positive, after maxcobasis unexplored subtrees reported */ long long maxdepth; /* max depth to search to in treee */ long long mindepth; /* do not backtrack above mindepth */ long redund; /* TRUE if we are doing a redund run */ long verifyredund; /* a worker checks redundancy and gives output */ long messages; /* TRUE if lrs should post_output messages */ long *redineq; /* a list of row numbers to check redundancy */ } lrs_restart_dat; lrs_restart_dat* lrs_alloc_restart(); lrslib-071a/makefile0000700060175606010010000002661213742506302014340 0ustar avisなし#makefile for lrslib-071 2020.5.23 # C compiler requires __int128 support for 128bit arithmetic (eg. gcc v. 4.6.0 or later for 128bit integer support) # otherwise use %make lrs64 to compile # add -DTIMES if your compiler does *not* support ptimes() and get_time() # add -DSIGNALS if your compiler does *not* support #try uncommenting next line if cc is the default C compiler #CC = gcc default: lrs #choose line below instead if __int128 not supported #default: lrs64 lrsgmp #make lrs lrs,lrsgmp hybrid and gmp versions #make lrs64 lrs,lrsgmp compilers without 128 bit support #make mplrs mplrs,mplrsgmp hybrid and gmp versions, make sure mpicc and an MPI library is installed #make mplrs64 mplrs,mplrsgmp for compilers without 128 bit support #make flint lrs and mplrs with FLINT arithmetic #make single makes lrs with various arithmetic packages (depending on compiler),lrsnash #make singlemplrs makes mplrs with various arithmetic packages (depending on compiler) #make allmp uses native mp and long arithmetic #make demo various demo programs for lrslib #make lrsnash Nash equilibria for 2-person games: lrsnash (gmp), lrsnash1 (64bit), lrsnash2 (128bit) #make fourier Fourier elimination (buggy, needs fixing) #make clean removes binaries #INCLUDEDIR = /usr/include #LIBDIR = /usr/lib #Kyoto machines usage INCLUDEDIR = /usr/local/include LIBDIR = /usr/local/lib CFLAGS = -O3 -Wall #CFLAGS = -g -Wall #use this if you want only output file contain data between begin/end lines #CFLAGS = -O3 -Wall -DLRS_QUIET SHLIB_CFLAGS = -fPIC mpicxx=mpicc LRSOBJ=lrs.o lrslong1.o lrslong2.o lrslib1.o lrslib2.o lrslibgmp.o lrsgmp.o lrsdriver.o MPLRSOBJ=lrslong1-mplrs.o lrslong2-mplrs.o lrslib1-mplrs.o lrslib2-mplrs.o lrslibgmp-mplrs.o lrsgmp-mplrs.o lrsdriver-mplrs.o mplrs.o LRSOBJ64=lrs64.o lrslong1.o lrslib1.o lrslibgmp.o lrsgmp.o lrsdriver.o MPLRSOBJ64=lrslong1-mplrs.o lrslib1-mplrs.o lrslibgmp-mplrs.o lrsgmp-mplrs.o lrsdriver-mplrs.o mplrs64.o lrs: ${LRSOBJ} $(CC) ${CFLAGS} -DMA -DB128 -L${LIBDIR} -o lrs ${LRSOBJ} -lgmp $(CC) -O3 -DGMP -I${INCLUDEDIR} -o lrsgmp lrs.c lrslib.c lrsgmp.c lrsdriver.c -L${LIBDIR} -lgmp $(CC) -O3 hvref.c -o hvref ln -s -f lrs redund ln -s -f lrsgmp redundgmp lrs64: ${LRSOBJ64} $(CC) ${CFLAGS} -DMA -L${LIBDIR} -o lrs ${LRSOBJ64} -lgmp lrs.o: lrs.c $(CC) ${CFLAGS} -DMA -DB128 -c -o lrs.o lrs.c lrs64.o: lrs.c $(CC) ${CFLAGS} -DMA -c -o lrs64.o lrs.c lrslong1.o: lrslong.c lrslong.h $(CC) ${CFLAGS} -DMA -DSAFE -DLRSLONG -c -o lrslong1.o lrslong.c lrslong2.o: lrslong.c lrslong.h $(CC) ${CFLAGS} -DMA -DSAFE -DB128 -DLRSLONG -c -o lrslong2.o lrslong.c lrslib1.o: lrslib.c lrslib.h $(CC) ${CFLAGS} -DMA -DSAFE -DLRSLONG -c -o lrslib1.o lrslib.c lrslib2.o: lrslib.c lrslib.h $(CC) ${CFLAGS} -DMA -DSAFE -DB128 -DLRSLONG -c -o lrslib2.o lrslib.c lrslibgmp.o: lrslib.c lrslib.h $(CC) ${CFLAGS} -DMA -DGMP -I${INCLUDEDIR} -c -o lrslibgmp.o lrslib.c lrsgmp.o: lrsgmp.c lrsgmp.h $(CC) ${CFLAGS} -DMA -DGMP -I${INCLUDEDIR} -c -o lrsgmp.o lrsgmp.c lrslong1-mplrs.o: lrslong.c lrslong.h $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -DMA -DSAFE -DLRSLONG -DPLRS -c -o lrslong1-mplrs.o lrslong.c lrslong2-mplrs.o: lrslong.c lrslong.h $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -DMA -DSAFE -DB128 -DLRSLONG -DPLRS -c -o lrslong2-mplrs.o lrslong.c lrslib1-mplrs.o: lrslib.c lrslib.h $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -DMA -DSAFE -DLRSLONG -DPLRS -c -o lrslib1-mplrs.o lrslib.c lrslib2-mplrs.o: lrslib.c lrslib.h $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -DMA -DSAFE -DB128 -DLRSLONG -DPLRS -c -o lrslib2-mplrs.o lrslib.c lrslibgmp-mplrs.o: lrslib.c lrslib.h $(mpicxx) ${CFLAGS} -DMA -DTIMES -DSIGNALS -DGMP -DPLRS -I${INCLUDEDIR} -c -o lrslibgmp-mplrs.o lrslib.c lrsgmp-mplrs.o: lrsgmp.c lrsgmp.h $(mpicxx) ${CFLAGS} -DMA -DTIMES -DSIGNALS -DGMP -DPLRS -I${INCLUDEDIR} -c -o lrsgmp-mplrs.o lrsgmp.c lrsdriver-mplrs.o: lrsdriver.c lrsdriver.h lrslib.h $(mpicxx) $(CFLAGS) -c -o lrsdriver-mplrs.o lrsdriver.c mplrs.o: mplrs.c mplrs.h lrslib.h lrsgmp.h $(mpicxx) ${CFLAGS} -I${INCLUDEDIR} -DMA -DPLRS -DTIMES -DB128 -DSIGNALS -D_WITH_GETLINE -c -o mplrs.o mplrs.c mplrs64.o: mplrs.c mplrs.h lrslib.h lrsgmp.h $(mpicxx) ${CFLAGS} -I${INCLUDEDIR} -DMA -DPLRS -DTIMES -DSIGNALS -D_WITH_GETLINE -c -o mplrs64.o mplrs.c mplrs: ${MPLRSOBJ} mplrsgmp $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DPLRS -DMA -DB128 -L${LIBDIR} -o mplrs ${MPLRSOBJ} -lgmp mplrs64: ${MPLRSOBJ64} mplrsgmp $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DPLRS -DMA -L${LIBDIR} -o mplrs ${MPLRSOBJ64} -lgmp mplrsgmp: mplrs.c mplrs.h lrslib.c lrslib.h lrsgmp.c lrsgmp.h lrsdriver.h lrsdriver.c $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DPLRS -DGMP -I${INCLUDEDIR} mplrs.c lrslib.c lrsgmp.c lrsdriver.c -L${LIBDIR} -o mplrsgmp -lgmp mplrs1: mplrs.c mplrs.h lrslib.c lrslib.h lrslong.c lrslong.h lrsdriver.h lrsdriver.c $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DPLRS -DSAFE -DLRSLONG mplrs.c lrslib.c lrslong.c lrsdriver.c -o mplrs1 mplrs2: mplrs.c mplrs.h lrslib.c lrslib.h lrslong.c lrslong.h lrsdriver.h lrsdriver.c $(mpicxx) ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DPLRS -DSAFE -DLRSLONG -DB128 mplrs.c lrslib.c lrslong.c lrsdriver.c -o mplrs2 mplrsmp: mplrs.c mplrs.h lrslib.c lrslib.h lrsmp.c lrsmp.h lrsdriver.h lrsdriver.c $(mpicxx) ${CFLAGS} -DMP -DTIMES -DSIGNALS -D_WITH_GETLINE -DPLRS mplrs.c lrslib.c lrsmp.c lrsdriver.c -o mplrsmp singlemplrs: mplrsgmp mplrs1 mplrs2 flint: lrs.c lrslib.c lrslib.h lrsgmp.c lrsgmp.h @test -d ${INCLUDEDIR}/flint || { echo ${INCLUDEDIR}/flint not found; exit 1; } $(CC) -O3 -DFLINT -I${INCLUDEDIR} -I${INCLUDEDIR}/flint lrs.c lrsdriver.c lrslib.c lrsgmp.c -L${LIBDIR} -lflint -o lrsflint -lgmp mplrsflint: mplrs.c mplrs.h lrslib.c lrslib.h lrsgmp.c lrsgmp.h lrsdriver.c lrsdriver.h ${mpicxx} ${CFLAGS} -DTIMES -DSIGNALS -D_WITH_GETLINE -DFLINT -I${INCLUDEDIR}/flint -DPLRS -o mplrsflint mplrs.c lrsdriver.c lrslib.c lrsgmp.c -L${LIBDIR} -lflint -lgmp #comment out lines with -DB128 if __int128 not supported by your C compiler lrsgmp: lrs.c lrslib.c lrslib.h lrsgmp.c lrsgmp.h lrsdriver.h lrsdriver.c $(CC) -O3 -DGMP -I${INCLUDEDIR} -o lrsgmp lrs.c lrslib.c lrsgmp.c lrsdriver.c -L${LIBDIR} -lgmp single: lrs.c lrslong.c lrslong.h lrslib.c lrslib.h lrsgmp.c lrsgmp.h lrsdriver.h lrsdriver.c $(CC) -O3 -DSAFE -DLRSLONG -o lrs1 lrs.c lrslib.c lrslong.c lrsdriver.c $(CC) -O3 -DB128 -DSAFE -DLRSLONG -o lrs2 lrs.c lrslib.c lrslong.c lrsdriver.c ln -s -f lrs1 redund1 ln -s -f lrs2 redund2 allmp: lrs.c lrslib.c lrslib.h lrsmp.c lrsmp.h lrsdriver.h lrsdriver.c $(CC) -Wall -O3 -o lrs lrs.c lrslib.c lrsdriver.c lrsmp.c $(CC) -Wall -O3 -DSAFE -DLRSLONG -o lrs1 lrs.c lrslib.c lrsdriver.c lrslong.c $(CC) -Wall -O3 -DSAFE -DLRSLONG -DB128 -o lrs2 lrs.c lrslib.c lrsdriver.c lrslong.c $(CC) -O3 -DLRS_QUIET -o lrsnash lrsnash.c lrsnashlib.c lrslib.c lrsdriver.c lrsmp.c $(CC) -O3 -o setnash setupnash.c lrslib.c lrsdriver.c lrsmp.c $(CC) -O3 -o setnash2 setupnash2.c lrslib.c lrsdriver.c lrsmp.c $(CC) -O3 -o 2nash 2nash.c demo: lpdemo1.c lrslib.c lrsdriver.c lrslib.h lrsgmp.c lrsgmp.h $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o lpdemo1 lpdemo1.c lrslib.c lrsdriver.c lrsgmp.c -lgmp -DGMP $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o lpdemo lpdemo.c lrslib.c lrsdriver.c lrsgmp.c -lgmp -DGMP $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o lpdemo2 lpdemo2.c lrslib.c lrsdriver.c lrsgmp.c -lgmp -DGMP $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o vedemo vedemo.c lrslib.c lrsdriver.c lrsgmp.c -lgmp -DGMP $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o chdemo chdemo.c lrslib.c lrsdriver.c lrsgmp.c -lgmp -DGMP lrsnash: lrsnash.c nashdemo.c lrsnashlib.c lrslib.c lrsnashlib.h lrslib.h lrsgmp.c lrsgmp.h lrslong.h lrsdriver.h lrsdriver.c $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o lrsnashgmp lrsnash.c lrsnashlib.c lrslib.c lrsgmp.c lrsdriver.c -lgmp -DGMP $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o lrsnash1 lrsnash.c lrsnashlib.c lrslib.c lrslong.c lrsdriver.c -DLRSLONG -DSAFE $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o lrsnash2 lrsnash.c lrsnashlib.c lrslib.c lrslong.c lrsdriver.c -DLRSLONG -DSAFE -DB128 $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o nashdemo nashdemo.c lrsnashlib.c lrslib.c lrsgmp.c lrsdriver.c -lgmp -DGMP $(CC) -O3 -I${INCLUDEDIR} -L${LIBDIR} -o 2nash 2nash.c cp lrsnashgmp lrsnash fourier: fourier.c lrslib.h lrslib.c lrsgmp.h lrsgmp.c $(CC) -O3 -DGMP -I${INCLUDEDIR} fourier.c lrslib.c lrsdriver.c lrsgmp.c -L${LIBDIR} -lgmp -o fourier ###################################################################### # From here on the author is David Bremner to whom you should turn for help # # Shared library variables SONAME ?=liblrs.so.1 SOMINOR ?=.0.0 SHLIB ?=$(SONAME)$(SOMINOR) SHLINK ?=liblrs.so SHLIBOBJ=lrslong1-shr.o lrslong2-shr.o lrslib1-shr.o lrslib2-shr.o \ lrslibgmp-shr.o lrsgmp-shr.o lrsdriver-shr.o SHLIBBIN=lrs-shared lrsnash-shared # Building (linking) the shared library, and relevant symlinks. ${SHLIB}: ${SHLIBOBJ} $(CC) -shared -Wl,-soname=$(SONAME) $(SHLIBFLAGS) -o $@ ${SHLIBOBJ} -lgmp ${SONAME}: ${SHLIB} ln -sf ${SHLIB} ${SONAME} ${SHLINK}: ${SONAME} ln -sf $< $@ # binaries linked against the shared library all-shared: ${SHLIBBIN} lrs-shared: ${SHLINK} lrs.o $(CC) lrs.o -o $@ -L . -llrs lrsnash-shared: ${SHLINK} lrsnash.c $(CC) -DGMP -DMA lrsnash.c lrsnashlib.c -I${INCLUDEDIR} -o $@ -L . -llrs -lgmp # build object files for the shared library lrslib1-shr.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DSAFE -DLRSLONG -c -o $@ lrslib.c lrsdriver-shr.o: lrsdriver.c $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -c -o $@ $< lrslong1-shr.o: lrslong.c lrslong.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DSAFE -DLRSLONG -c -o $@ lrslong.c lrslong2-shr.o: lrslong.c lrslong.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DSAFE -DB128 -DLRSLONG -c -o $@ lrslong.c lrslibgmp-shr.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DGMP -I${INCLUDEDIR} -c -o $@ lrslib.c lrsgmp-shr.o: lrsgmp.c lrsgmp.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DGMP -I${INCLUDEDIR} -c -o $@ lrsgmp.c lrslib2-shr.o: lrslib.c lrslib.h $(CC) ${CFLAGS} ${SHLIB_CFLAGS} -DMA -DSAFE -DB128 -DLRSLONG -c -o $@ lrslib.c ###################################################################### # install targets # where to install binaries, libraries, include files prefix ?= /usr/local INSTALL_INCLUDES=lrslib.h lrsdriver.h lrsgmp.h lrslong.h lrsmp.h install: all-shared install-common mkdir -p $(DESTDIR)${prefix}/bin for file in ${SHLIBBIN}; do cp $${file} $(DESTDIR)${prefix}/bin/$$(basename $$file -shared); done mkdir -p $(DESTDIR)${prefix}/lib install -t $(DESTDIR)${prefix}/lib $(SHLIB) cd $(DESTDIR)${prefix}/lib && ln -sf $(SHLIB) $(SHLINK) cd $(DESTDIR)${prefix}/lib && ln -sf $(SHLIB) $(SONAME) install-common: mkdir -p $(DESTDIR)${prefix}/include/lrslib install -t $(DESTDIR)${prefix}/include/lrslib ${INSTALL_INCLUDES} ###################################################################### clean: rm -f lrs lrs1 lrsgmp lrs1n lpdemo lpdemo1 lpdemo2 mplrs1 mplrs mplrsmp mplrsgmp lrs2 mplrs2 lrsflint mplrsflint *.o *.exe *.so rm -f hvref setnash setnash2 fourier lrsnashgmp lrsnash lrsnash1 lrsnash2 nashdemo 2nash vedemo rm -f ${LRSOBJ} ${LRSOBJ64} ${SHLIBOBJ} ${SHLIB} ${SONAME} ${SHLINK} rm -f ${SHLIBBIN} lrslib-071a/man/0000700060175606010010000000000013742506306013405 5ustar avisなしlrslib-071a/man/lrs.10000700060175606010010000004765213742506306014310 0ustar avisなし.TH "LRS" "1" "2020.7.28" "July 2020" "lrs 7\&.2" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SH "NAME" lrs - Convert between representations of convex polyhedra, remove redundant inequalities, convex hull computation, volume, triangulation, solution to linear programs in exact precision. .SH "SYNOPSIS" .HP \w'\fBlrs\fR\ [input-file] [output-file]\ 'u \fBlrs\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBredund\fR\ [input-file] [output-file]\ 'u \fBredund\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBfel\fR\ [input-file] [output-file]\ 'u \fBfel\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBhvref/xref\fR\ [input-file] \ 'u \fBhvref/xvref\fR\ \fI[input-file]\fR .SH "DESCRIPTION" .PP These programs are part of and must be compiled with \fIlrslib\fR which is a C library. All computations are done in exact arithmetic. .PP A polyhedron can be described by a list of inequalities (\fIH\-representation)\fR or as by a list of its vertices and extreme rays (\fIV\-representation)\fR\&. .PP \fIlrs\fR converts an H\-representation of a polyhedron to its V\-representation and vice versa, known respectively as the \fIvertex enumeration\fR and \fIfacet enumeration\fR problems\& (see Example (1) below). For V-representations the volume can be computed and a triangulation produced. lrs can also be used to solve a linear program, remove linearities from a system, and extract a subset of columns. .PP \fIredund\fR removes redundant inequalities in an input H-representation and outputs the remaining inequalities\&. For a V-representation it outputs all extreme points and extreme rays, often called the \fIconvex hull\fR problem. Both outputs can be piped directly into \fIlrs\fR. \fIredund\fR is a link to \fIlrs\fR which performs these functions via the \fBredund\fR and \fBredund_list\fR options. See Example (2) below. .PP \fIfel\fR projects an input H-representation onto a given set of variables using Fourier-Motzkin elimination. For a V-representation it extracts the specified columns. The output is non-redundant and can be can be piped directly into \fIlrs\fR. \fIfel\fR is a link to \fIlrs\fR which performs these functions via the \fBeliminate\fR and \fBproject\fR options. .PP \fIhvref/xvref\fR\ produce a cross reference list between H- and V-representations. See \fBUTILITIES\fR. .PP \fImplrs\fR is Skip Jordan's parallel wrapper based on MPI for \fIlrs/redund\fR using the same input and output formats. See: \m[blue]\fBman mplrs \fR \m[] .PP Fukuda\*(Aqs \m[blue]\fBFAQ page\fR\m[]\&\s-2\u[1] contains a more detailed introduction to the problem, along with many useful tips for the new user\&. User's guide for \m[blue]\fBlsrslib\fR\m[]\u[8] .SH "FILE FORMATS" .PP File formats were developed jointly with Komei Fukuda and are compatible with \m[blue]\fBcdd/cddlib\fR\m[]\&\s-2\u[2]\d\s+2\&. .br The input for \fIlrs/redund\fR is an H\- or V\-representation of a polyhedron\&. name H-representation [\fIor\fR V-representation] {options} {linearities} begin m n rational [\fIor\fR integer] {input matrix} end {options} \fIname\fR is a user supplied name for the polyhedron\&.\ \& Comments may appear before the begin or after the end and should begin with a special character such as "*"\&. .PP If the representation is not specified H\-representation is assumed. The input coefficients are read in free format, and are not checked for type\&. Coefficients are separated by white space\&. m is the number of rows and n the number of columns of the input matrix\&. .SS "H\-representation" .PP m is the number of input rows, each being an inequality or equation. .br n is the number of input columns and d=n-1 is the dimension of the input. .br An inequality or equation of the form: .PP b + a_1 x_1 + \&.\&.\&. + a_d x_d >=\ \& 0\& .PP b + a_1 x_1 + \&.\&.\&. + a_d x_d =\ \& 0\& .PP is input as the line: .PP b \ a_1 \&.\&.\&. a_d .PP The coefficients can be entered as integers or rationals in the format x/y\&. To distinguish an equation a \fBlinearity\fR option must be supplied before the \fBbegin\fR line (see below). .SS "V\-representation" .PP m is the number of input rows, each being a vertex, ray or line. .br n is the number of input columns and d=n-1 is dimension of the input. .br Each vertex is given in the form: .PP 1 \ v_1 \ \ v_1 \&.\&.\&.\ v_d .PP Each ray is given in the form: .PP 0\ \&\ \& r_1 \&\ \& r_2\&.\&.\&.\ \&\ \& r_d .PP where r_1 \ \&.\&.\&.\ \&\ \& r_d is a point on the ray\&. .PP There must be at least one vertex in each file\&. For bounded polyhedra there will be no rays entered\&. The coefficients can be entered as integers or rationals in the format x/y\&. An input line can be specified as a ray and then included in the \fBlinearity\fR option (see below). .PP \fBNote for cdd users\fR: Note the input files for \fIlrs\fR are read in free format. \fIlrs\fR will look for exactly m*n rationals or integers separated by white space (blank, carriage return, tab etc\&.). \fIlrs\fR will not "drop" extra columns of input if n is less than the number of columns supplied\&. .SH "OPTIONS" .PP Almost all options are placed \fBafter\fR the end statement, maintaining compatibility with \fIcdd\fR\&. Where this is not the case, it will be mentioned explicitly\&. .PP \fBallbases\fR This option instructs \fIlrs\fR to list each vertex (or facet) for each of its bases\&. This option is often combined with printcobasis\&. .PP \fBbound\ \& x \fR (H\-representation only). Either the maximize or minimize option should be selected\&. x is an integer or rational\&. For maximization (resp\&. minimization) the reverse search tree is truncated\ \& whenever the current objective value is less (resp\&. more) than x\&. .PP \fBcache n\fR \ \ \ \ (default n=50) .br \fIlrs\fR stores the latest\ \& n dictionaries in the reverse search tree\&. This speeds up the backtracking step, but requires more memory\&. .PP \fBdebug\ \& startingcobasis endingcobasis\fR .br Print out cryptic but detailed trace, dictionaries etc\&. starting at #B=startingcobasis and ending at #B=endingcobasis\&. \fBdebug 0 0\fR gives a complete trace\&. .PP \fBdigits n\fR (lrsmp arithmetic only - placed before the begin statement) .br n is the maximum number of decimal digits to be used\&. If this is exceeded the program terminates with a message and can usually be restarted with the \fbrestart\fR option. The default is set to 100 digits\&. At the end of a run a message is given informing the user of the maximum integer size encountered\&. .PP \fBdualperturb\fR If lrs is executed with the \fBmaximize\fR or \fBminimize\fR option, the reverse search tree is rooted at an optimum vertex for this function\&. If there are multiple optimum vertices, the output will often not be complete\&. This option gives a small perturbation to the objective to avoid this\&. A warning message is given if the starting dictionary is dual degenerate\&. .PP \fBestimates k\fR .br Estimate the output size\&. Used in conjunction with \fBmaxdepth\fR. See: \m[blue]\fBEstimation\fR\m[]\&\s-2\u[3]\d\s+2 .PP \fBeliminate k i_1 i_2 ... i_k \fR (new in v7.2) .br \fI(H-representation)\fR Eliminates k variables in an H-representation corresponding to cols i_1 .. i_k by projection onto the remaining variables using the Fourier-Motzkin method. Variables are eliminated in the order given and redundancy is removed after each iteration. .br \fI(V-representation)\fR Delete the k given columns from the input matrix and remove redundancies (cf. \fBextract\fR where redundancies are not removed). .br Column indices are between 1 and n-1 and column zero cannot be eliminated. The output as a valid lrs input file. See also \fBproject\fR and \fBextract\fR .PP \fBextract [ k i_1 i_2 ... i_k ] \fR (new in v7.1) .br \fI(H-representation)\fR A preprocessing step to remove linearities (if any) in an H-representation and resize the A matrix. The output as a valid lrs input file. The resulting file will not contain any equations but may not be full dimensional as there may be additional linearities in the remaining inequalities. Options in the input file are stripped. The user can specify the k columns i_1 i_2 ... i_k to retain otherwise if k=0 the columns are considered in the order 1,2,..n-1. Linear dependent columns are skipped and additional indices are taken from 1,2,...,n-1 as necessary. If there are no linearities in the input file the given columns are retained and the other ones are deleted. .br \fI(V-representation)\fR Extract the given columns from the input file outputing a valid lrs input file. Options are stripped. .PP \fBgeometric\ \&\ \&\fR (H\-representation\ \& or voronoi option only) Each ray is printed together with the vertex with which it is incident\&. .PP \fBincidence\fR This option automatically switches on \fBprintcobasis\fR. For input H\-representation, indices of all input inequalities that contain the vertex/ray that is about to be output\&. For input V\-representation, indices of all input vertices/rays that lie on the facet that is about to be output\&. A starred index indicates that this vertex\ \& is also in the cobasis, but is not contained in the facet\&. It arises due to the lifting operation used with input V\-representations\&. .PP \fBlinearity\ \& k\ \& i_1 \ i_2 \ \&... \ i_k \fR .br (H-representation) The k rows i_1 \ i_2 \ \&... \ i_k \fR \ of the input file represent equations\&. (V-representation) The k rows, which should have a zero in column 1, represent lines in space (rather than rays). .PP \fBlponly\fR Solve the LP given by the input H-representation with objective function specified by the \fBmaximize\fR or \fBminimize\fR options and terminate. Use with \fBverbose\fR option to get dual variables. See: \m[blue]\fBLinear Programming\fR\m[]\&\s-2\u[4]\d\s+2 .PP \fBmaxdepth k\fR .br The search will be truncated at depth k\&. All bases with depth less than or equal to k will be computed\&.\ \& k is\ \& a non\-negative integer, and this option is used for estimates \- see \m[blue]\fBEstimation\fR\m[]\&\s-2\u[3]\d\s+2 \fBNote\fR: For H\-representations, rays at depth k will not be reported\&. For V\-representations, facets at depth k will not be reported\&. .PP \fBmaximize\ \& b \ a_1 \&.\&.\&. a_{n-1} \fR\ \& (H\-representation\ \& only) .br \fBminimize\ \& b \ a_1 \&.\&.\&. a_{n-1} \fR\ \& (H\-representation\ \& only) .br The starting vertex maximizes (or minimizes) the function \ b + a_1 x_1+ \&.\&.\&. + a_{n-1} x_{n-1}. .br The \fBdualperturb\fR option may be needed to avoid dual degeneracy\&. .PP \fBmaxoutput n\fR .br Limits number of output lines produced (either vertices+rays or facets) to n .PP \fBmindepth k\fR .br Backtracking will be terminated at depth k. .PP \fBnonnegative\fR (This option must come before the begin statement - H\-representation only) \ \& Bug: Can only be used if the origin is a vertex of the polyhedron\ \& For problems where the input is an H\-representation of the form b+Ax>=0, x>=0 (ie\&. all variables non\-negative, all constraints inequalities) it is not necessary to give the non\-negative constraints explicitly if the nonnegative option is used\&. This option cannot be used for V\-representations, or with the linearity option (in which case the linearities will be treated as inequalities)\&. This option may be used with redund , but the implied nonnegativity constraints are not tested themselves for redundancy\&. .PP \fBproject k i_1 i_2 ... i_k \fR (new in v7.2) .br \fI(H-representation)\fR Project the polyhedron onto the k variables corresponding to cols i_1 .. i_k using the Fourier-Motzkin method. Column indices are between 1 and n-1 and column zero is automatically retained. Variables not contained in the list are eliminated in increasing order and redundancy is removed after each iteration. .br \fI(V-representation)\fR Extract the k given columns from the input matrix and remove redundancies. Column indices are between 1 and n-1 and column zero is automatically extracted (cf. \fBextract\fR where redundancies are not removed). .br The output as a valid lrs input file. See also \fBeliminate\fR and \fBextract\fR .PP \fBprintcobasis\ k\fR .br Every k-th cobasis is printed. If k is omitted, the cobasis is printed for each vertex/ray/facet that is output\&. For a long run it is useful to print the cobasis occasionally so that the program can be restarted if necessary\&. \fIH\-representation\fR: the cobasis is a list the indices of the inequalities from the input file that define the current vertex or ray\&. For rays the cobasis is the cobasis of the vertex from which the ray emanates\&. One of the indices is starred, this indicates the inequality to be dropped from the cobasis to define the ray\&. If the \fBallbases\fR option is used, all cobases will be printed\&. \fIV\-representation\fR: the cobasis is a list of the input vertices/rays that define the current facet\&. See option \fBincidence\fR for more information\&. .PP \fBprintslack\fR (H\-representation only) A list of the indices of the input inequalities that are satisfied strictly for the current vertex, ie\&. corresponding slack variable is positive\&. If nonnegative is set, the list will also include indices n+i for each decision variable x_i which is positive\&. .PP \fBredund start end \fR (new in v7.1) .br Check input lines with line numbers from start to end and remove any redundant lines. .br \fBredund 0 0\fR will check all input lines. See \m[blue]\fBredund\fR\m[]\&\s-2\u[7]\d\s+2 .PP \fBredund_list k i_1 i_2 ... i_k\fR (new in v7.1) .br Check the k input line numbers with indices i_1 i_2 ... i_k and remove any redundant lines. See \m[blue]\fBredund\fR\m[]\&\s-2\u[7]\d\s+2 .PP \fBrestart\ \& V# R# B# depth {facet #s or vertex/ray #s\fR} .br \fIlrs\fR can be restarted from any known cobasis\&. The calculation will proceed to normal termination\&. All of the information is contained in the output from a \fBprintcobasis\fR option\&.\ \& The \fBorder of the indices is very important,\fR enter them exactly as they appear in the output from the previously terminated run\&. .PP Note that if some cobasic index is followed by a "*",\ \& then the index only, without the "*", is included in the restart line\&. \fBCaution:\fR When restarting, output from the restart dictionary may be duplicated, and the final totals of number of vertices/rays/facets may reflect this\&. .PP \fBstartingcobasis i_1 \ i_2 \ ... \ i_{n-1}\fR .br lrs will start from the given cobasis which which is a list of the inequalities (for H\-representation) or vertices/rays (for V\-representation) that define it. If it is invalid, or this option is not specified, \fIlrs\fR will find its own starting cobasis\&. .PP \fBtruncate\fR \ The reverse search tree is truncated(pruned)\ \& whenever a new vertex is encountered\&. Note: This does note necessarily produce the set of all vertices adjacent to the optimum vertex in the polyhedron, but just a subset of them\&. .PP \fBverbose\fR Print slightly more detailed information about the run\&. .PP \fBvolume\fR (V\-representation only) Compute the volume and, if the \fBverbose\fR option is also included, output a \fBtriangulation\fR. See \m[blue]\fBVolume Computation\fR\m[]\&\s-2\u[5]\d\s+2 .PP \fBvoronoi\fR (V\-representation\ \& only \- place immediately after end statement) .br Compute Voronoi diagram \- see \m[blue]\fBVoronoi Diagrams\fR\m[]\&\s-2\u[6]\d\s+2 .SH "ARITHMETIC" From version 7.1 \fIlrs/redund/mplrs\fR use hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP. .PP Various arithmetic versions are available and can be built from the makefile: .PP \fBlrs1\fR Fixed length 64 bit integer arithmetic, terminates on overflow. .PP \fBlrs2\fR Fixed length 128 bit integer arithmetic, terminates on overflow. .PP \fBlrsmp\fR Built in extended precision integer arithmetic, uses \fBdigits\fR option above. .PP \fBlrsgmp\fR GNU MP which must be installed first from https://gmplib.org/. .PP \fBlrsflint\fR FLINT hybrid arithmetic which must be installed first from http://www.flintlib.org/ .SH "EXAMPLES" .PP (1) Convert the H-representation of a cube given cube by 6 the six inequalities .br -1 <= x_i <= 1 , i=1,2,3 into its V-representation consisting of 8 vertices. .PP % cat cube.ine cube.ine H-representation begin 6 4 rational 1 1 0 0 1 0 1 0 1 0 0 1 1 -1 0 0 1 0 0 -1 1 0 -1 0 end % lrs cube.ine *lrs:lrslib v.6.3 2018.4.11(64bit,lrslong.h,overflow checking) *Input taken from file cube.ine cube.ine V-representation begin ***** 4 rational 1 1 1 1 1 -1 1 1 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 *Totals: vertices=8 rays=0 bases=8 integer_vertices=8 .PP (2) Compute the extreme points of a set of 10 points in R^3 .PP % cat c.ext V-representation begin 10 4 rational 1 1 1 1 1 0 1 1 1 1/2 0 1/3 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1/3 1/4 1 1 0 1 1 0 0 1 end % redund c.ext *redund:lrslib v.7.2 2020.6.8(64bit,lrslong.h,hybrid arithmetic) *Input taken from c.ext V-representation begin 8 4 rational 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 end *Input had 10 rows and 4 columns * 2 redundant row(s) found: 3 8 .SH "UTILITIES" .PP \fBhvref/xref\fR Cross reference listing between V- and H-representations (new in v7.1) In the example below we start from an H-representation of cube.ine but the same steps apply to the V-representation cube.ext. It is recommended to first remove any redundancies from the input file using redund. 1. Add \fBprintcobasis\fR and \fBincidence\fR options to cube.ine % lrs cube.ine cube.ext .br % xref cube.ext 2. Edit the output file cube.ext.x to insert a second line that contains two integers rows maxindex where rows >= # output lines in cube.ext.x maxindex >= # input lines in cube.ine or just use 0 0 and run hvref, the output will tell you which values to use. % hvref cube.ext.x .SH "NOTES" .IP " 1." 4 FAQ page .RS 4 \%https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html .RE .IP " 2." 4 cdd .RS 4 \%https://inf.ethz.ch/personal/fukudak/cdd_home/ .RE .IP " 3." 4 Estimation. .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Estimation .RE .IP " 4." 4 Linear Programming .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Linear%20Programming .RE .IP " 5." 4 Volume Computation. .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Volume%20Computation .RE .IP "6." 4 Voronoi Diagrams. .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#Voronoi%20Diagrams .RE .IP "7." 4 redund: extreme point enumeration and eliminating redundant inequalities .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund .RE .IP "8." 4 User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html .RE .SH AUTHOR David Avis .SH "SEE ALSO" .BR mplrs (1), .BR lrslib (1), .BR lrsnash (1) lrslib-071a/man/lrslib.10000700060175606010010000001023213742506306014757 0ustar avisなし'\" t .\" Title: LRSLIB .\" Author: [FIXME: author] [see http://www.docbook.org/tdg5/en/html/author] .\" Generator: DocBook XSL Stylesheets vsnapshot .\" Date: 06/10/2020 .\" Manual: lrslib 0.42b .\" Source: July 2009(rev. June 2020) .\" Language: English .\" .TH "LRSLIB" "1" "2020.06.10" "July 2009" "lrslib 7\&.1" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SH "NAME" lrslib: Convert between representations of convex polyhedra, remove redundant inequalities, convex hull computation, solve linear programs in exact precision, compute Nash-equibria in 2-person games\&. .SH "SYNOPSIS" .HP \w'\fBlrs\fR\ [input-file] [output-file]\ 'u \fBlrs\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBredund\fR\ [input-file] [output-file]\ 'u \fBredund\fR\ \fI[input-file] [output-file]\fR .HP \w'\fBmpirun\fR -np \fInum_proc\fR \fBmplrs\fR\ \fIinput-file [output-file] [options...]\fR\ 'u \fBmpirun\fR -np \fInum-proc\fR \fBmplrs\fR\ \fIinput-file [output-file] [options]\fR .HP \w'\fBlrsnash\fR\ [input-file] \ 'u \fBlrsnash\fR\ \fI[options] [input-file] \fR .HP \w'\fBhvref/xref\fR\ [input-file] \ 'u \fBhvref/xvref\fR\ \fI[input-file]\fR .SH "DESCRIPTION" .PP A polyhedron can be described by a list of inequalities (\fIH\-representation)\fR or as by a list of its vertices and extreme rays (\fIV\-representation)\fR\&. \fIlrslib\fR is a C library containing programs to manipulate these representations. All computations are done in exact arithmetic. .PP \fIlrs\fR converts an H\-representation of a polyhedron to its V\-representation and vice versa, known respectively as the \fIvertex enumeration\fR and \fIfacet enumeration\fR problems\& (see Example (1) below). lrs can also be used to solve a linear program, remove linearities from a system, and extract a subset of columns. .PP \fIredund\fR removes redundant inequalities in an input H-representation and outputs the remaining inequalities\&. For a V-representation input it outputs all extreme points and extreme rays. Both outputs can be piped directly into \fIlrs\fR. \fIredund\fR is a link to \fIlrs\fR which performs these functions via the \fBredund\fR and \fBredund_list\fR options. .PP \fImplrs\fR is Skip Jordan's parallel wrapper for \fIlrs/redund\fR. .PP \fIlrsnash\fR is Terje Lensberg's application of \fIlrs\fR for finding Nash-equilibria in 2-person games\&. .PP \fIhvref/xvref\fR\ produce a cross reference list between H- and V-representations. .SH "ARITHMETIC" From version 7.1 \fIlrs/redund/mplrs\fR use hybrid arithmetic with overflow checking, starting in 64bit integers, moving to 128bit (if available) and then GMP. Overflow checking is conservative to improve performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b triggers an overflow if either a or b is at least 2^62. Typically problems that can be solved in 64bits run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP. .PP Various arithmetic versions are available and can be built from the makefile: .SH "NOTES" .PP User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html .RE .SH AUTHOR David Avis .SH "SEE ALSO" .BR lrs (1), .BR mplrs (1), .BR lrsnash (1), lrslib-071a/man/lrsnash.10000700060175606010010000001075013742506306015147 0ustar avisなし.TH "LRSNASH" "1" "2020.7.28" "July 2020" "lrslib 7\&.2" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie (.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SH "NAME" lrsnash: \ Compute Nash-equibria in 2-person games\&. .SH "SYNOPSIS" .HP \w'\fBlrsnash\fR \ [options...] [input-file] \ 'u \fBlrsnash\fR \ [options...] [input-file] .HP \w'\fBlrsnash1\fR\ [options...] [input-file] \ 'u \fBlrsnash1\fR\ [options...] [input-file] .HP \w'\fBlrsnash2\fR\ [options...] [input-file] \ 'u \fBlrsnash2\fR\ [options...] [input-file] .HP \w'\fBnashdemo\fR\ \ 'u \fBnashdemo\fR\ .PP options: -v, --verbose Prints a trace of the solution process -d, --debug Dumps lots of information for debugging -p, --printgame Prints the payoff matrix for the game -s, --standard Promise that input files have standard structure -o, --outfile Send output to -h, --help Prints this text Short options can be grouped, as in '-ps' and '-do out.txt' .SH DESCRIPTION .PP These C programs are distributed as part of the \m[blue]\fBlsrslib\fR\m[]\u[2] package and must be compiled with it. Alice has a payoff matrix A and Bob has a playoff matrix B, both of dimension m by n. Alice assigns probabilities x to the rows and Bob y to the columns. Alice receives payoff x^T A y and Bob receives x^T B y. A Nash equilibriam occurs for pairs x,y for which neither player can improve their expected payoff by unilateraly changing strategies. .PP \fIlrsnash\fR is an application of \fIlrs\fR for finding Nash-equilibria in 2-person matrix games using a method described in \u[1]. It uses GMP exact extended precision arithmetic. \fIlrsnash1\fR is the same as \fIlrsnash\fR except that it uses 64 bit exact arithmetic and terminates if overflow is detected. It is about 3-4 times faster. \fIlrsnash2\fR is the same as \fIlrsnash\fR except that it uses 128 bit exact arithmetic and terminates if overflow is detected. It is about twice as fast. It requires a C compiler with __int128 support (eg. gcc v. 4.6.0 or later). \fInashdemo\fR is a simple template for \fIlrsnash\fR. It builds two 3x4 matrices A and B and computes their equilibria. The running time may be significantly different depending on the order of the two matrices in the input. For large problems it may be advantageous to run \fIlrsnash\fR twice in parallel with the matrices in different orders. There is also a more complex legacy input format recognized by \fIlrsnash\fR that is described in \u[1]. .SH FILE FORMATS .PP The input file consists of two integers m and n on line 1 followed by two mxn payoff matrices A and B: m n A (row by row) B (row by row) .SH EXAMPLE The input file game has two 3x2 payoff matrices: %cat game 3 2 0 6 2 5 3 3 1 0 0 2 4 3 % lrsnash game 2 1/3 2/3 4 1 2/3 1/3 0 2/3 2 2/3 1/3 3 1 0 1/3 2/3 8/3 2 1 0 3 1 0 0 1 4 *Number of equilibria found: 3 *Player 1: vertices=5 bases=5 pivots=8 *Player 2: vertices=3 bases=1 pivots=8 \fBInterpretation\fR There are 3 Nash equilibria. For the first one: 2 1/3 2/3 4 .br Bob(player 2) plays column 1 and 2 with probablilities y=(1/3, 2/3) and the payoff to Alice(player 1) is 4. 1 2/3 1/3 0 2/3 .br Alice plays rows 1,2,3 with probabilities x=(2/3, 1/3, 0) and the payoff to Bob is 2/3. .SH NOTES .IP 1. 4 D. Avis, G. Rosenberg, R. Savani, B. von Stengel, \fIEnumeration of Nash Equilibria for Two-Player Games\fR, Economic Theory 42(2009) 9-37 .IP 2. 4 User's guide for lrslib .RS 4 \%http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html .RE .SH AUTHORS David Avis and Terje Lensberg .SH "SEE ALSO" .BR lrslib (1) lrslib-071a/man/mplrs.10000700060175606010010000001145513742506306014635 0ustar avisなし.TH "MPLRS" "1" "2020.7.28" "July 2020" "mplrs 7\&.2" .\" ----------------------------------------------------------------- .\" * Define some portability stuff .\" ----------------------------------------------------------------- .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .\" http://bugs.debian.org/507673 .\" http://lists.gnu.org/archive/html/groff/2009-02/msg00013.html .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" ----------------------------------------------------------------- .\" * set default formatting .\" ----------------------------------------------------------------- .\" disable hyphenation .nh .\" disable justification (adjust text to left margin only) .ad l .\" ----------------------------------------------------------------- .\" * MAIN CONTENT STARTS HERE * .\" ----------------------------------------------------------------- .SH "NAME" mplrs \- Convert between representations of convex polyhedra (parallel version)\&. .SH "SYNOPSIS" .HP \w'\fB\ mpirun\ \fR\fBmplrs\fR\ 'u \fB mpirun \fR \-np \fInum_proc\ \fR\fBmplrs\fR \fIinfile\fR [\fIoutfile\fR] [\fIoption\fR...] .br .SH "DESCRIPTION" .PP A polyhedron can be described by a list of inequalities (\fIH\-representation)\fR or as by a list of its vertices and extreme rays (\fIV\-representation)\fR\&. \fIlrs\fR is a C program that converts a H\-representation of a polyhedron to its V\-representation, and vice versa\&.\ \& These problems are known respectively at the \fIvertex enumeration\fR and \fIconvex hull problems\fR\&. .PP .SH "USAGE" .PP The number of processors \fInum_proc\fR specified to \fBmpirun\fR should be 4 or higher Unlike lrs (1), \fBmplrs\fR does not support options after the end statement of the input file\&. .SS "OPTIONS" .PP \fBmplrs\fR supports the following options\&. .RS 4 \fB\-id \fR [2] the depth of the original tree search to populate the job queue L .RE .RS 4 \fB\-maxc \fR[50 (*scale)] a producer stops and returns all subtrees that are not leaves to L after generating\ \& maxc nodes\ \&\ \&\ \& .RE .RS 4 \fB\-maxd \fR[0] a producer returns all subtrees that are not leaves at depth maxd\&. Zero if not used .RE .RS 4 \fB\-lmin \fR[3] if job queue |L|\fR[lmin] if job queue |L|>np*lmax then then maxc is replaced by maxc*scale .RE .RS 4 \fB\-scale \fR[100]used by lmax .RE .RS 4 \fB\-hist \fRstore parallelization data in for use by gnuplot, see below .RE .RS 4 \fB\-temp \fR[/tmp/] store a temporary file for each process\&. Should be specified if /tmp not writeable\&. Using " \-temp\ \& \&./ " will write temporary files to the current directory .RE .RS 4 \fB\-freq \fR store frequency data in for use by gnuplot, see below .RE .RS 4 \fB\-stop \fR terminate mplrs if a file with name is created in the current directory .RE .RS 4 \fB\-checkp \fR if mplrs is terminated by \-stop or \-time then it can be restarted using this and \-restart .RE .RS 4 \fB\-restart \fR restart mplrs using previously created \&. If used with \-checkp file names should be different! .RE .RS 4 \fB\-time \fR terminate mplrs after of elapsed time .RE .RS 4 \fB\-countonly\fR don\*(Aqt output vertices/rays/facets, just count them .RE .RS 4 \fB\-maxbuf \fR[500] controls maximum size of worker output buffers .RE .RS 4 \fB\-stopafter \fR exit after approximately cobases have been computed (no guarantee about how many vertices/rays/facets computed) .RE .RS 4 \fB\-redund\fR perform redundancy check of input file (also see redund ) .RE The parameters \fB\-hist\fR and \fB\-freq\fR give interesting information about the degree of parallelization\&. .SH "EXAMPLE" .PP Input file mp5\&.ine is run with 8 processors\&. The output file mp5\&.mplrs is in the distribution\&. This produced 378 subtrees that were enumerated in parallel using 6 producer cores,\ \& 1 core controlling the run and 1 core collecting the output\&. .sp .if n \{\ .RS 4 .\} .nf mai20% mpirun \-np 8 mplrs mp5\&.ine mp5\&.mplrs *mplrs:lrslib v\&.6\&.0 2015\&.7\&.13(lrsgmp\&.h)8 processes *Copyright (C) 1995,2015, David Avis\ \&\ \& avis@cs\&.mcgill\&.ca *Input taken from mp5\&.ine *Output written to: mp5\&.mplrs *Starting depth of 2 maxcobases=50 maxdepth=0 lmin=3 lmax=3 scale=100 *Phase 1 time: 0 seconds\&. *Total number of jobs: 378, L became empty 4 times *Totals: vertices=32 rays=0 bases=9041 integer\-vertices=16 *Elapsed time: 1 seconds\&. 2\&.285u 0\&.137s 0:01\&.86 129\&.5%\ \&\ \&\ \& 0+0k 0+9976io 36pf+0w .fi .if n \{\ .RE .\} .SH "SEE ALSO" .BR lrs (1), .BR lrslib (1) lrslib-071a/mit.ine0000700060175606010010000005040513742506302014123 0ustar avisなしmit.ine begin 729 9 integer 72 0 0 -4 -4 -2 0 0 0 216 -2 -2 -10 -12 -6 0 0 0 192 -4 -2 -8 -8 -8 0 0 0 288 -12 6 8 -16 -8 0 0 0 96 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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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. Author: Charles Jordan skip@ist.hokudai.ac.jp Based on plrs.cpp by Gary Roumanis Initial lrs Author: David Avis avis@cs.mcgill.ca */ /* #include "lrslib.h" */ /* included in mplrs.h */ #include "mplrs.h" #include #include #include #include #include #include /* global variables */ mplrsv mplrs; /* state of this process */ masterv master; /* state of the master */ consumerv consumer; /* state of the consumer */ char argv0[] = "mplrs-internal"; /* warning removal for C++ */ /****************** * initialization * ******************/ int main(int argc, char **argv) { mplrs_init(argc, argv); mprintf2(("%d: initialized on %s\n",mplrs.rank,mplrs.host)); if (mplrs.size<3) return mplrs_fallback(); if (mplrs.rank == MASTER) return mplrs_master(); else if (mplrs.rank == CONSUMER) return mplrs_consumer(); else return mplrs_worker(); } void mplrs_init(int argc, char **argv) { int i,j,count; int header[4]; char c; time_t curt = time(NULL); char *tim, *tim1; char *offs, *tmp; long *wred = NULL; /* redineq for redund */ /* make timestamp for filenames */ tim = ctime(&curt); tim1 = tim+4; tim1[3] = tim1[6] = '_'; tim1[15]='\0'; /* start MPI */ MPI_Init(&argc, &argv); MPI_Comm_rank(MPI_COMM_WORLD, &mplrs.rank); MPI_Comm_size(MPI_COMM_WORLD, &mplrs.size); MPI_Get_processor_name(mplrs.host, &count); /* allocate mp for volume calculation, from plrs */ lrs_alloc_mp(mplrs.tN); lrs_alloc_mp(mplrs.tD); lrs_alloc_mp(mplrs.Vnum); lrs_alloc_mp(mplrs.Vden); lrs_alloc_mp(mplrs.Tnum); lrs_alloc_mp(mplrs.Tden); itomp(ZERO, mplrs.Vnum); itomp(ONE, mplrs.Vden); gettimeofday(&mplrs.start, NULL); mplrs_initstrucs(); /* initialize default values of globals */ /* process commandline arguments, set input and output files */ mplrs_commandline(argc, argv); if (mplrs.rank == MASTER) { /* open input file for reading on master, histogram * file for writing on master, if used. */ mplrs_initfiles(); master_sendfile(); /* may have produced warnings from stage 0 lrs, flush them. */ if (mplrs.output_list == NULL) /* need to prod consumer */ post_output("warning"," "); /* see waiting_initial */ process_output(); /* before starting a flush */ clean_outgoing_buffers(); } else { /* open output file for writing on consumer, open histogram file * for writing on consumer, if used. */ if (mplrs.rank == CONSUMER) mplrs_initfiles(); /* receive input file from master */ MPI_Recv(header, 4, MPI_INT, 0, 20, MPI_COMM_WORLD, MPI_STATUS_IGNORE); count = header[0]; mplrs.abortinit = header[3]; mplrs.input = malloc(sizeof(char)*(count+1)); if (!mplrs.abortinit) /* don't need if aborting, may be big */ MPI_Recv(mplrs.input, header[0], MPI_CHAR, 0, 20, MPI_COMM_WORLD, MPI_STATUS_IGNORE); mplrs.input[count] = '\0'; if (header[1]>0 && mplrs.rank == CONSUMER) /* sigh ... */ { consumer.redineq = calloc((header[2]+1), sizeof(long)); mplrs.redund = 1; } else if (header[1]>0) /* handle redund split */ { wred = malloc(header[1]*sizeof(long)); MPI_Recv(wred, header[1], MPI_LONG, 0, 20, MPI_COMM_WORLD, MPI_STATUS_IGNORE); count+=snprintf(NULL, 0, "\nredund_list %d", header[1]); for (i=0; i9; i++) j = j/10; i += 6+strlen(tim1); /* mplrs_TIMESTAMP */ i += strlen(mplrs.tfn_prefix) + strlen(mplrs.input_filename) + i + 6; /* _%d.ine\0 */ mplrs.tfn = malloc(sizeof(char) * i); sprintf(mplrs.tfn, "%smplrs_%s%s_%d.ine", mplrs.tfn_prefix, tim1, mplrs.input_filename, mplrs.rank); /* flatten directory structure in mplrs.input_filename * for mplrs.tfn, to prevent writing to non-existent * subdirectories in e.g. /tmp */ i = strlen(mplrs.tfn_prefix) + 6 + strlen(tim1); j = strlen(mplrs.tfn); for (; im_A; else /* overflow in mplrs_worker_init and non-hybrid, can't start run */ m = 0; header[2] = m; if (mplrs.overflow!=3 && mplrs.R->redund && mplrs.abortinit == 0) { master.redund = 1; for (i=1; i<=m; i++) if (mplrs.R->redineq[i] == 1) rcount++; } /* check free TODO*/ if (mplrs.overflow != 3 && !mplrs.abortinit) { mplrs.lrs_main(0,NULL,&mplrs.P,&mplrs.Q,0,2,NULL,mplrs.R); } c = fgetc(master.input); while (c!=EOF) { count++; c = fgetc(master.input); } if (mplrs.countonly) extra = 10; /* \ncountonly */ buf = malloc(sizeof(char)*(count+extra)); fseek(master.input, 0, SEEK_SET); for (i=0; i0) { header[1]++; rem--; } for (j=0; jredineq[rstart] == 1 ) { wred[j] = rstart++; break; } } } else if (master.redund) /* this worker gets no jobs */ header[1] = header[2] = 0; /* not actually needed */ mprintf2(("M: Sending input file to %d\n", i)); MPI_Send(header, 4, MPI_INT, i, 20, MPI_COMM_WORLD); if (!mplrs.abortinit) /* don't need if aborting, may be big */ MPI_Send(buf, count+extra, MPI_CHAR, i, 20, MPI_COMM_WORLD); if (header[1]>0 && i!=CONSUMER) /* send redund portion */ MPI_Send(wred, header[1], MPI_LONG,i,20,MPI_COMM_WORLD); } /* fseek(master.input, 0, SEEK_SET); */ fclose(master.input); free(mplrs.R->redineq); free(mplrs.R->facet); free(mplrs.R); free(wred); free(buf); } /* initialize default values of global structures, before commandline */ void mplrs_initstrucs(void) { mplrs.cobasis_list = NULL; mplrs.lrs_main = mplrs_init_lrs_main; mplrs.P = NULL; mplrs.Q = NULL; mplrs.R = NULL; mplrs.caughtsig = 0; mplrs.abortinit = 0; mplrs.overflow = 0; mplrs.rays = 0; mplrs.vertices = 0; mplrs.bases = 0; mplrs.facets = 0; mplrs.linearities = 0; mplrs.intvertices = 0; mplrs.deepest = 0; mplrs.my_tag = 100; mplrs.tfn_prefix = DEF_TEMP; mplrs.tfn = NULL; mplrs.tfile = NULL; mplrs.input_filename = DEF_INPUT; mplrs.input = NULL; mplrs.output_list = NULL; mplrs.ol_tail = NULL; mplrs.outnum = 0; mplrs.finalwarn = malloc(sizeof(char)*32); mplrs.finalwarn_len = 32; mplrs.curwarn = malloc(sizeof(char)*32); mplrs.curwarn_len = 32; mplrs.finalwarn[0] = '\0'; mplrs.curwarn[0] = '\0'; mplrs.maxbuf = DEF_MAXBUF; /* maximum # lines to buffer */ mplrs.outputblock = 0; /* don't block initial output */ mplrs.redund = 0; mplrs.countonly = 0; master.cobasis_list = NULL; master.size_L = 0; master.tot_L = 0; master.num_empty = 0; master.num_producers = 0; master.checkpointing = 0; master.cleanstop = 0; master.messages = 1; master.lmin = DEF_LMIN; master.lmax = DEF_LMAX; master.orig_lmax = 1; master.scalec = DEF_SCALEC; master.initdepth = DEF_ID; master.maxdepth = DEF_MAXD; master.maxcobases = DEF_MAXC; master.maxncob = DEF_MAXNCOB; master.lponly = 0; master.redund = 0; master.time_limit = 0; master.hist_filename = DEF_HIST; master.hist = NULL; master.doing_histogram = 0; master.freq_filename = DEF_FREQ; master.freq = NULL; master.restart_filename = DEF_RESTART; master.restart = NULL; master.checkp_filename = DEF_CHECKP; master.checkp = NULL; master.stop_filename = DEF_STOP; master.stop = NULL; master.input = NULL; consumer.prodreq = NULL; consumer.prodibf = NULL; consumer.incoming = NULL; consumer.output_filename = DEF_OUTPUT; consumer.output = stdout; consumer.oflow_flag = 0; consumer.num_producers = 0; consumer.waiting_initial = 2; /* 2: waiting initial and master warnings */ consumer.final_print = 1; consumer.final_redundcheck = 0; } /* process commandline arguments */ void mplrs_commandline(int argc, char **argv) { int i, arg, firstfile=1; for (i=1; i master.lmax) master.lmax = arg; continue; } else if (!strcmp(argv[i], "-lmax")) { arg = atoi(argv[i+1]); i++; if (arg<1 ) bad_args(); master.lmax = arg; master.orig_lmax = 0; if (master.lmin > master.lmax) master.lmin = arg; continue; } else if (!strcmp(argv[i], "-scale")) { arg = atoi(argv[i+1]); i++; if (arg<1) bad_args(); master.scalec = arg; continue; } else if (!strcmp(argv[i], "-hist")) { master.hist_filename = argv[i+1]; i++; continue; } else if (!strcmp(argv[i], "-freq")) { master.freq_filename = argv[i+1]; i++; continue; } else if (!strcmp(argv[i], "-stopafter")) { arg = atoi(argv[i+1]); i++; if (arg<1) bad_args(); master.maxncob = arg; continue; } else if (!strcmp(argv[i], "-countonly")) { mplrs.countonly = 1; continue; } else if (!strcmp(argv[i], "-maxbuf")) { arg = atoi(argv[i+1]); i++; if (arg<1) bad_args(); mplrs.maxbuf = arg; continue; } else if (!strcmp(argv[i], "-id")) { arg = atoi(argv[i+1]); i++; if (arg<0) bad_args(); master.initdepth = arg; continue; } else if (!strcmp(argv[i], "-maxd")) { arg = atoi(argv[i+1]); i++; if (arg<1) bad_args(); master.maxdepth = arg; continue; } else if (!strcmp(argv[i], "-maxc")) { arg = atoi(argv[i+1]); i++; if (arg<0) bad_args(); master.maxcobases = arg; continue; } else if (!strcmp(argv[i], "-checkp")) { master.checkp_filename = argv[i+1]; i++; continue; } else if (!strcmp(argv[i], "-lponly")) { master.lponly = 1; continue; } else if (!strcmp(argv[i], "-redund")) { master.redund = 1; continue; } else if (!strcmp(argv[i], "-stop")) { master.stop_filename = argv[i+1]; i++; continue; } else if (!strcmp(argv[i], "-time")) { arg = atoi(argv[i+1]); i++; if (arg<1) bad_args(); master.time_limit = arg; continue; } else if (!strcmp(argv[i], "-restart")) { master.restart_filename = argv[i+1]; i++; continue; } else if (!strcmp(argv[i], "-temp")) { mplrs.tfn_prefix = argv[i+1]; i++; continue; } else if (firstfile == 1) { mplrs.input_filename = argv[i]; firstfile = 2; } else if (firstfile == 2) { consumer.output_filename = argv[i]; firstfile = 3; } else bad_args(); } if (master.orig_lmax) /* default lmax behavior is lmax=lmin */ master.lmax = (master.lmin>0? master.lmin: 0); if (mplrs.input_filename==NULL) /* need an input file */ bad_args(); if ((master.stop_filename!=NULL || master.time_limit!=0) && master.checkp_filename==NULL) bad_args(); /* need checkpoint file if stop condition given */ } /* open input file on master, histogram (if exists) on master, * output (if exists) on consumer */ void mplrs_initfiles(void) { if (mplrs.rank == MASTER) { master.input = fopen(mplrs.input_filename, "r"); if (master.input == NULL) { printf("Unable to open %s for reading [%s].\n", mplrs.input_filename, mplrs.host); /* MPI_Finalize(); */ exit(0); } if (master.hist_filename != NULL) { master.hist = fopen(master.hist_filename, "w"); if (master.hist == NULL) { printf("Unable to open %s for writing [%s].\n", master.hist_filename, mplrs.host); /* MPI_Finalize(); */ exit(0); } master.doing_histogram = 1; mprintf2(("M: Prepared histogram (%s)\n", master.hist_filename)); } if (master.freq_filename != NULL) { master.freq = fopen(master.freq_filename, "w"); if (master.freq == NULL) { printf("Unable to open %s for writing [%s].\n", master.freq_filename, mplrs.host); exit(0); } mprintf2(("M: Prepared frequency file (%s)\n", master.freq_filename)); } if (master.checkp_filename !=NULL) { master.checkp = fopen(master.checkp_filename, "w"); if (master.checkp == NULL) { printf("Unable to open %s for writing [%s].\n", master.checkp_filename, mplrs.host); /* MPI_Finalize(); */ exit(0); } mprintf2(("M: Prepared checkpoint file (%s)\n", master.checkp_filename)); } if (master.restart_filename != NULL) { master.restart = fopen(master.restart_filename, "r"); if (master.restart == NULL) { printf("Unable to open %s for reading [%s].\n", master.restart_filename, mplrs.host); /* MPI_Finalize(); */ exit(0); } mprintf2(("M: Opened restart file (%s)\n", master.restart_filename)); } } if (mplrs.rank == CONSUMER) { if (consumer.output_filename == NULL) return; consumer.output = fopen(consumer.output_filename, "w"); if (consumer.output == NULL) { printf("Unable to open %s for writing [%s].\n", consumer.output_filename, mplrs.host); /* MPI_Finalize(); */ exit(0); } } } /* free the lrs_mp allocated in mplrs_init */ void mplrs_freemps(void) { lrs_clear_mp(mplrs.tN); lrs_clear_mp(mplrs.tD); lrs_clear_mp(mplrs.Vnum); lrs_clear_mp(mplrs.Vden); lrs_clear_mp(mplrs.Tnum); lrs_clear_mp(mplrs.Tden); } /* Bad commandline arguments. Complain and die. */ void bad_args(void) { if (mplrs.rank == CONSUMER) printf("Invalid arguments.\n%s\n", USAGE); mplrs_freemps(); MPI_Finalize(); exit(0); } /* fallback -- meaningless if <3 processes * better would be to fallback to normal lrs if <4 processes */ int mplrs_fallback(void) { if (mplrs.rank==0) printf("mplrs requires at least 3 processes.\n"); mplrs_freemps(); MPI_Finalize(); exit(0); return 0; /* unreachable */ } /********** * master * **********/ int mplrs_master(void) { int i; int loopiter = 0; /* do some things only sometimes */ MPI_Request ign = MPI_REQUEST_NULL; /* a request we'll ignore */ struct timeval cur, last; /* for histograms */ int flag = 0;; int phase = 1; /* In phase1? */ int done = -1; /* need a negative int to send to finished workers */ int ncob=0; /* for printing sizes of sub-problems and for -stopafter*/ unsigned long tot_ncob = 0; int want_stop = 0; int check = 0; /* inform consumer whether checkpointing */ gettimeofday(&last, NULL); master.num_producers = 0; /* nobody working right now */ master.act_producers = malloc(sizeof(unsigned int)*mplrs.size); master.live_workers = mplrs.size - 2; master.workin = malloc(sizeof(int)*mplrs.size); master.mworkers = malloc(sizeof(MPI_Request)*mplrs.size); master.incoming = NULL; master.sigbuf = malloc(sizeof(float)*mplrs.size); master.sigcheck = malloc(sizeof(MPI_Request)*mplrs.size); if (master.restart!=NULL) { master_restart(); phase = 0; } for (i=0; i0 || master.live_workers>0) { loopiter++; /* sometimes check if we should update histogram etc */ if (!(loopiter&0x1ff)) { if (master.maxncob>0 && master.maxncob<=tot_ncob) want_stop = 1; if (master.doing_histogram) print_histogram(&cur, &last); } /* sometimes check if we should checkpoint */ /* don't check in phase 1 to ensure the consumer sees a 'begin' and exits */ if (!(loopiter&0x7ff) && phase!=1) // && !master.checkpointing && !master.cleanstop) { if (master.stop_filename!=NULL || master.time_limit!=0) check_stop(); master_checksigs(); if (master.cleanstop) want_stop = 1; } recv_producer_lists(); if (master.redund && phase==1) /* send out redund jobs */ { for (i=0; i<=master.max_redundworker; i++) { if (i==CONSUMER || i==MASTER) continue; MPI_Wait(master.mworkers+i, MPI_STATUS_IGNORE); send_work(i,phase); MPI_Irecv(master.workin+i, 1, MPI_UNSIGNED,i, 6, MPI_COMM_WORLD, master.mworkers+i); } phase = 0; master.tot_L = master.max_redundworker - 1; } /* check if anyone wants work */ for (i=0; i0 && master.cobasis_list==NULL) { break; /* no work to give now, but some may * appear later */ } if (phase==1 && i!=INITIAL && master.cleanstop==0) continue; /* INITIAL gets the first bit */ /* need cleanstop condition for * overflows in mplrs_worker_init() */ MPI_Test(master.mworkers+i, &flag, MPI_STATUS_IGNORE); if (!flag) continue; /* i is not ready for more work */ ncob = master.workin[i]; tot_ncob+=ncob; mprintf2(("M: %d looking for work\n", i)); if ((master.cobasis_list!=NULL || phase==1) && !master.checkpointing && !want_stop) { /* and not checkpointing! */ send_work(i,phase); MPI_Irecv(master.workin+i, 1, MPI_UNSIGNED,i, 6, MPI_COMM_WORLD, master.mworkers+i); phase=0; if (master.freq!=NULL && ncob>0) fprintf(master.freq, "%d\n", ncob); continue; } /* else tell worker we've finished */ mprintf(("M: Saying goodbye to %d, %d left\n", i, master.live_workers-1)); MPI_Isend(&done, 1, MPI_INT, i, 8, MPI_COMM_WORLD,&ign); MPI_Request_free(&ign); master.live_workers--; if (master.freq!=NULL && ncob>0) fprintf(master.freq, "%d\n", ncob); } clean_outgoing_buffers(); } /* don't checkpoint if we actually finished the run */ if (master.checkpointing && master.cobasis_list==NULL) master.checkpointing = 0; if (master.checkpointing) /* checkpointing */ check = CHECKFLAG; /* inform consumer if checkpointing or not */ mprintf2(("M: Telling consumer whether or not checkpointing (%d)\n", check)); MPI_Send(&check, 1, MPI_INT, CONSUMER, 1, MPI_COMM_WORLD); if (master.checkpointing) master_checkpoint(); send_master_stats(); mplrs_freemps(); if (master.freq != NULL) fclose(master.freq); if (master.hist != NULL) fclose(master.hist); if (master.checkp != NULL) fclose(master.checkp); free(mplrs.finalwarn); free(mplrs.curwarn); MPI_Finalize(); free(master.workin); free(master.mworkers); free(master.act_producers); free(master.sigbuf); free(master.sigcheck); return 0; } /* prepare to receive remaining cobases from target. * Since we don't yet know the size of buffers needed, we * only Irecv the header and will Irecv the actual cobases later */ void master_add_incoming(int target) { msgbuf *msg = malloc(sizeof(msgbuf)); msg->req = malloc(sizeof(MPI_Request)*3); msg->buf = malloc(sizeof(void *)*3); msg->buf[0] = malloc(sizeof(int) * 3); /* (strlen,lengths,tag) */ msg->buf[1] = NULL; /* sizes not known yet */ msg->buf[2] = NULL; msg->count = 3; msg->target = target; msg->queue = 1; msg->tags = NULL; msg->sizes = NULL; msg->types = NULL; msg->next = master.incoming; master.incoming = msg; MPI_Irecv(msg->buf[0], 3, MPI_INT, target, 10, MPI_COMM_WORLD,msg->req); return; } /* check our list of incoming messages from producers about cobases * to add to L. Add any from messages that have completed. * If the header has completed (msg->queue==1 and header completed), * add the remaining MPI_Irecv's. * Update num_producers to keep track of how many messages the master * is owed (workers are not allowed to exit until num_producers==0 and * L is empty). * Also update size_L */ void recv_producer_lists(void) { msgbuf *msg, *prev=NULL, *next; int *header; int flag; for (msg = master.incoming; msg; msg=next) { next = msg->next; MPI_Test(msg->req, &flag, MPI_STATUS_IGNORE); if (!flag) /* header has not completed yet */ { prev = msg; continue; } header = (int *)msg->buf[0]; if (msg->queue) /* header completed, and need to Irecv now */ { if (header[0]==-1) /* producer returns NOTHING */ { master.num_producers--; master.act_producers[msg->target]--; free_msgbuf(msg); if (prev) prev->next = next; else master.incoming = next; continue; } msg->buf[1]= malloc(sizeof(char)*header[1]); msg->buf[2]= malloc(sizeof(int)*header[0]); MPI_Irecv(msg->buf[1], header[1], MPI_CHAR, msg->target, header[2], MPI_COMM_WORLD, msg->req+1); MPI_Irecv(msg->buf[2], header[0], MPI_INT, msg->target, header[2], MPI_COMM_WORLD, msg->req+2); msg->queue=0; prev = msg; continue; } /* header completed, did the rest? */ MPI_Testall(2, msg->req+1, &flag, MPI_STATUSES_IGNORE); if (!flag) /* not yet */ { prev = msg; continue; } mprintf2(("M: %d returned non-empty producer list (%d, %d)\n", msg->target, header[0], header[1])); process_returned_cobases(msg); mprintf2(("M: Now have size_L=%lu\n",master.size_L)); if (prev) prev->next = next; else master.incoming = next; master.num_producers--; master.act_producers[msg->target]--; free_msgbuf(msg); } return; } /* msg is a completed, non-empty buffer containing cobases to add to * L. Process it, add them to L, and update size_L * Basically the inverse of return_unfinished_cobases() */ void process_returned_cobases(msgbuf *msg) { int *header = (int *)msg->buf[0]; char *str = (char *)msg->buf[1]; int *lengths = (int *)msg->buf[2]; int i; char *cob; for (i=0; ireq = malloc(sizeof(MPI_Request)*2); msg->buf = malloc(sizeof(void *)*2); /*{length of work string, int maxdepth, int maxcobases, bool lponly, bool messages, 3x future use} */ msg->buf[0] = malloc(sizeof(int) * 8); header = (int *)msg->buf[0]; header[4] = master.messages; master.messages = 0; if (phase==0) /* normal */ { cob = master.cobasis_list; master.cobasis_list = cob->next; header[0] = strlen((char *)cob->data); msg->buf[1] = cob->data; setparams(header); /* scale if needed */ master.size_L--; if (master.size_L == 0) master.num_empty++; mprintf(("M: Sending work to %d (%d,%d,%d) %s\n", target, header[0], header[1], header[2], (char*)msg->buf[1])); msg->count = 2; free(cob); } else /* phase 1 */ { header[0] = 0; /* header[0]==0 means initial phase 1 */ header[1] = master.initdepth; header[2] = master.maxcobases; if (master.redund) /* redund turns off budget */ header[1] = header[2] = 0; mprintf(("M: Sending phase 1 to %d (%d,%d)\n", target, header[1], header[2])); msg->buf[1] = NULL; msg->count = 1; } msg->target = target; msg->queue = 0; msg->tags = NULL; msg->sizes = NULL; msg->types = NULL; /* ready to send */ MPI_Isend(header, 8, MPI_INT, target, 1, MPI_COMM_WORLD, msg->req); if (phase==0) MPI_Isend(msg->buf[1], header[0], MPI_CHAR, target, 1, MPI_COMM_WORLD, msg->req+1); master_add_incoming(target); /* prepare to receive remaining cobases */ msg->next = mplrs.outgoing; mplrs.outgoing = msg; master.act_producers[target]++; master.num_producers++; return; } /* header is a work header (length, maxd, maxc) not yet set. * Set the parameters (maxd, maxc) as desired. */ void setparams(int *header) { /* if L is too small, use maxdepth */ if (master.lmin>0 && (master.size_L < mplrs.size*master.lmin)) header[1] = master.maxdepth; else /* don't have too small L, so no maxdepth */ header[1] = 0; header[2] = master.maxcobases; if (master.lmax>0 && (master.size_L > mplrs.size * master.lmax)) header[2] = header[2] * master.scalec; header[3] = master.lponly; } /* check if we want to stop now. * if master.stop_filename exists or time limit exceeded, * set master.checkpointing = 1. * this is not an immediate stop -- we wait for current workers to * complete the tasks they've been assigned, stopping after that. */ void check_stop(void) { struct timeval cur; int flag = 0; if (master.checkpointing || master.cleanstop) return; /* already stopping */ if (master.stop_filename) { mprintf2(("M: checking stop file %s\n", master.stop_filename)); master.stop = fopen(master.stop_filename, "r"); if (master.stop!=NULL) { flag=1; fclose(master.stop); } } if (master.time_limit!=0) { mprintf2(("M: checking if time exceeded\n")); gettimeofday(&cur, NULL); if (cur.tv_sec - mplrs.start.tv_sec > master.time_limit) flag=1; } if (flag!=0) { mprintf(("M: Stop condition detected, checkpointing!\n")); master.checkpointing = 1; } } void master_stop_consumer(int already_stopping) { MPI_Request ign; int check[3] = {STOPFLAG,0,0}; mprintf2(("M: telling consumer to stop, already_stopping:%d checkpointing:%d\n", already_stopping, master.checkpointing)); if (!already_stopping) MPI_Isend(check, 3, MPI_INT, CONSUMER, 7, MPI_COMM_WORLD, &ign); master.cleanstop = 1; } /* check if we've caught a signal, or we've received a message from someone * that has. If so, we want to checkpoint like above * The similar mplrs_cleanstop also uses this... */ void master_checksigs(void) { int i, flag, size=mplrs.size; float junk=0; MPI_Request ign; int already_stopping = master.checkpointing || master.cleanstop; if (mplrs.caughtsig == 1 && !already_stopping) { mprintf(("M: I caught signal, checkpointing!\n")); /* this master.checkpointing must be inside a !already_stopping * condition, see comment below */ master.checkpointing = 1; already_stopping = 1; } for (i=1; inext; str = (char*)list->data; len = strlen(str)+1; /* include \0 */ MPI_Send(&len, 1, MPI_INT, CONSUMER, 1, MPI_COMM_WORLD); MPI_Send(str, len, MPI_CHAR, CONSUMER, 1, MPI_COMM_WORLD); free(str); free(list); } len = -1; MPI_Send(&len, 1, MPI_INT, CONSUMER, 1, MPI_COMM_WORLD); } void master_checkpointfile(void) { slist *list, *next; char *vol = cprat("", mplrs.Vnum, mplrs.Vden); fprintf(master.checkp, "mplrs4\n%llu %llu %llu %llu %llu\n%s\n%llu\n", mplrs.rays, mplrs.vertices, mplrs.bases, mplrs.facets, mplrs.intvertices,vol,mplrs.deepest); free(vol); for (list=master.cobasis_list; list; list=next) { next = list->next; fprintf(master.checkp, "%s\n", (char *)list->data); free(list->data); free(list); master.size_L--; } /* fclose(master.checkp); */ /* not here */ return; } /* we want to restart. load L and counting stats from restart file, * send counting stats to consumer (after notifying consumer of restart) */ void master_restart(void) { char *line=NULL; char *vol=NULL; size_t size=0, vsize=0; ssize_t len=0; int restart[3] = {RESTARTFLAG,0,0}; int ver; /* check 'mplrs1' header */ len = getline(&line, &size, master.restart); if (len!=7 || (strcmp("mplrs1\n",line) && strcmp("mplrs2\n",line) && strcmp("mplrs3\n",line) && strcmp("mplrs4\n",line))) { printf("Unknown checkpoint format\n"); /* MPI_Finalize(); */ exit(0); } mprintf2(("M: found checkpoint header\n")); sscanf(line,"mplrs%d\n",&ver); /* get counting stats */ fscanf(master.restart, "%llu %llu %llu %llu %llu\n", &mplrs.rays, &mplrs.vertices, &mplrs.bases, &mplrs.facets, &mplrs.intvertices); if (ver<3) /* volume added in mplrs3 */ printf("*Old checkpoint file, volume may be incorrect\n"); else /* get volume */ { len = getline(&vol, &vsize, master.restart); if (len<=1) { printf("Broken checkpoint file\n"); exit(0); } vol[len-1] = '\0'; /* remove '\n' */ #if defined(MA) || defined(GMP) || defined(FLINT) plrs_readrat(mplrs.Tnum, mplrs.Tden, vol); copy(mplrs.tN, mplrs.Vnum); copy(mplrs.tD, mplrs.Vden); linrat(mplrs.tN, mplrs.tD, 1L, mplrs.Tnum, mplrs.Tden, 1L, mplrs.Vnum, mplrs.Vden); #else if (strcmp(vol,"0")) printf("*Checkpoint volume ignored, use gmp or hybrid mplrs\n"); #endif free(vol); } if (ver<4) /* tree depth added in mplrs4 */ printf("*Old checkpoint file, tree depth may be incorrect\n"); else fscanf(master.restart, "%llu\n", &mplrs.deepest); /* get L */ while((len = getline(&line, &size, master.restart))!= -1) { if (line[0]=='\n') /* ignore blank lines */ { free(line); line = NULL; size=0; continue; } line[strlen(line)-1]='\0'; /* replace \n by \0 */ master.cobasis_list = addlist(master.cobasis_list, line); master.size_L++; line = NULL; size = 0; } master.tot_L = master.size_L; /* maybe should save and retrieve */ mprintf(("M: Restarted with |L|=%lu\n",master.size_L)); fclose(master.restart); MPI_Send(restart, 3, MPI_INT, CONSUMER, 7, MPI_COMM_WORLD); send_counting_stats(CONSUMER); mplrs.rays = 0; mplrs.vertices = 0; mplrs.bases = 0; mplrs.facets = 0; mplrs.intvertices = 0; return; } /* check if we should update the histogram and then do it */ void print_histogram(struct timeval *cur, struct timeval *last) { float sec; int i; int act; gettimeofday(cur,NULL); if (cur->tv_sec > last->tv_sec) { sec = (float)(cur->tv_sec - mplrs.start.tv_sec) + ((float)(cur->tv_usec - mplrs.start.tv_usec))/1000000; act=0; for (i=0; itv_sec = cur->tv_sec; last->tv_usec = cur->tv_usec; } } /********** * worker * **********/ int mplrs_worker(void) { char *starting_cobasis; /* header for incoming work: * {length of work string, int maxdepth, int maxcobases, 5xfuture use} */ int header[8]={0,0,0,0,0,0,0,0}; MPI_Request req = MPI_REQUEST_NULL; unsigned int ncob=0; /* used for # cobases in prev. job */ unsigned int tot_ncob=0; int len; int flag; if (!mplrs.abortinit) /* didn't receive file if parsing failed */ mplrs_worker_init(); while (1) { ncob = mplrs.bases - tot_ncob; /* #cobases in last job */ tot_ncob = mplrs.bases; /* #cobases done so far */ /* check signals */ mplrs_handlesigs(); /* ask for work */ mprintf2(("%d: Asking master for work\n",mplrs.rank)); MPI_Isend(&ncob, 1, MPI_UNSIGNED, MASTER, 6, MPI_COMM_WORLD, &req); flag = 0; while (1) /* was MPI_Wait(&req, MPI_STATUS_IGNORE); */ { MPI_Test(&req, &flag, MPI_STATUS_IGNORE); if (flag) break; clean_outgoing_buffers(); } starting_cobasis = NULL; /* get response */ MPI_Recv(header, 8, MPI_INT, MASTER, MPI_ANY_TAG, MPI_COMM_WORLD, MPI_STATUS_IGNORE); mprintf2(("%d: Message received from master\n",mplrs.rank)); len = header[0]; if (len==-1) /* no more work to do */ return mplrs_worker_finished(); if (len>0) { starting_cobasis = malloc(sizeof(char)*(len+1)); MPI_Recv(starting_cobasis, len, MPI_CHAR, MASTER, MPI_ANY_TAG, MPI_COMM_WORLD, MPI_STATUS_IGNORE); starting_cobasis[len] = '\0'; } mplrs.outputblock = 0; /* enable maxbuf-based flushing */ /* do work */ do_work(header, starting_cobasis); free(starting_cobasis); /* send output and unfinished cobases */ mplrs.outputblock = 0; /* enable maxbuf-based flushing */ process_output(); process_curwarn(); return_unfinished_cobases(); clean_outgoing_buffers(); /* check buffered sends, * free if finished */ } return 0; /* unreachable */ } /* run lrs_main. * easy in the non-hybrid case. in the hybrid case, runs the appropriate one, * cleaning up and proceeding to the next arithmetic package as needed until * finishing the run. * for now only use with stage != 0, TODO: handle init run too * header, starting_cobasis only used if header non-NULL */ void run_lrs(int argc, char **argv, long o, long stage, const int *header, char *starting_cobasis) { long ret = 1; #ifndef MA if (mplrs.overflow != 3) ret = mplrs.lrs_main(argc, argv, &mplrs.P, &mplrs.Q, o, stage, NULL, mplrs.R); if (ret == 1 || (ret==2 && mplrs.redund)) { mplrs.overflow = 3; worker_report_overflow(); } return; #else /* hybrid */ while ((ret == 1) || (ret==2 && mplrs.redund)) /* overflow */ { ret = mplrs.lrs_main(argc, argv, &mplrs.P, &mplrs.Q, o, stage, NULL, mplrs.R); mprintf3(("%d: lrs_main returned %ld (overflow status %d)\n", mplrs.rank, ret, mplrs.overflow)); if (ret == 0) /* done */ break; if (stage!=0) overflow_cleanup(); mprintf2(("%d: overflow in run_lrs, trying next\n", mplrs.rank)); #ifdef B128 if (mplrs.lrs_main == lrs1_main) { mplrs.overflow = 1; mplrs.lrs_main = lrs2_main; mplrs_worker_init(); /* re-init */ if (header!=NULL) set_restart(header, starting_cobasis); if (consumer.final_redundcheck) consumer_setredineq(); continue; } #endif mplrs.overflow = 2; mplrs.lrs_main = lrsgmp_main; mplrs_worker_init(); /* re-init */ if (header != NULL) set_restart(header, starting_cobasis); if (consumer.final_redundcheck) consumer_setredineq(); continue; } mprintf2(("%d: lrs_main finished, package status %d\n", mplrs.rank, mplrs.overflow)); return; #endif } void mplrs_worker_init(void) { char *argv[] = {argv0, mplrs.tfn}; long o = 1; if ((mplrs.rank == MASTER && master.redund) || (mplrs.rank == CONSUMER && mplrs.redund)) argv[0] = "redund"; /* hack for -redund */ if (mplrs.R != NULL) { /* overflow happened, free and re-init */ free(mplrs.R->redineq); free(mplrs.R->facet); free(mplrs.R); } mplrs.R = lrs_alloc_restart(); mprintf2(("%d: calling lrs_main to setup P & Q\n", mplrs.rank)); /* temp hack to test message requests */ /* initialization done on the master to get the full redund line. * stage=1 done on INITIAL because the master never does stage=1 */ /* note we must be careful about returns below in order to fix this * up on MASTER and INITIAL */ if(mplrs.rank == MASTER) mplrs.R->messages=1; else mplrs.R->messages=0; if (mplrs.rank != MASTER) { mplrs.tfile = fopen(mplrs.tfn, "w"); fprintf(mplrs.tfile, "%s", mplrs.input); fclose(mplrs.tfile); } while (o != 0) { o = mplrs.lrs_main(2,argv,&mplrs.P,&mplrs.Q,0,0,NULL,mplrs.R); if (o == -1) { mprintf(("%d: failed lrs setup, want to exit\n", mplrs.rank)); mplrs.abortinit = 1; break; } if (o == 1) { #ifdef MA mprintf2(("%d: overflow in init, trying next arithmetic\n", mplrs.rank)); overflow_cleanup(); /* 2020.6.1 : avoid multiple warnings etc when master overflows in setup */ #ifdef B128 /* hybrid with B128 */ if (mplrs.lrs_main == lrs1_main) { mplrs.lrs_main = lrs2_main; mplrs.overflow = 1; } else { mplrs.lrs_main = lrsgmp_main; mplrs.overflow = 2; } #else /* hybrid but no B128 */ mplrs.lrs_main = lrsgmp_main; mplrs.overflow = 2; #endif #else /* not hybrid, stop on overflow */ mprintf(("%d: overflow in init, fatal\n", mplrs.rank)); worker_report_overflow(); mplrs.overflow = 3; /* fatal overflow */ break; #endif } } mprintf3(("%d: lrs_main setup finished (%ld)\n", mplrs.rank, o)); mplrs.R->facet = calloc(mplrs.R->d+1, sizeof(long)); if (mplrs.rank != MASTER) remove(mplrs.tfn); mplrs.R->overide = 1; process_curwarn(); } /* This worker has finished. Tell the consumer, send counting stats * and exit. */ int mplrs_worker_finished(void) { int done[3] = {-1,-1,-1}; mprintf((" %d: All finished! Informing consumer.\n",mplrs.rank)); while (mplrs.outgoing) /* needed? negligible in any case */ { clean_outgoing_buffers(); } MPI_Send(&done, 3, MPI_INT, CONSUMER, 7, MPI_COMM_WORLD); send_counting_stats(CONSUMER); /* free P & Q */ /* overflows free themselves in lrslib? abortinit didn't allocate */ if (mplrs.overflow != 3 && !mplrs.abortinit) { mplrs.lrs_main(0,NULL,&mplrs.P,&mplrs.Q,0,2,NULL,mplrs.R); } if (mplrs.R != NULL) { free(mplrs.R->redineq); free(mplrs.R->facet); free(mplrs.R); } free(mplrs.tfn); free(mplrs.input); mplrs_freemps(); free(mplrs.finalwarn); free(mplrs.curwarn); MPI_Finalize(); return 0; } /* Go through our outgoing MPI_Isends, free anything that has completed. * Also, if any of these are queued and the header has completed, then * send the remaining data. * Don't use with incoming buffers. */ void clean_outgoing_buffers(void) { msgbuf *msg, *next, *prev=NULL; for (msg = mplrs.outgoing; msg; msg=next) { next = msg->next; if (!outgoing_msgbuf_completed(msg)) { prev = msg; continue; } if (prev) prev->next = next; else mplrs.outgoing = next; free_msgbuf(msg); } } /* had an overflow; discard any buffered output and * unfinished cobases. some output may have already been * sent (due to -maxbuf) so duplication still possible. * also resets mplrs.outputblock = 0 */ void overflow_cleanup(void) { outlist *out = mplrs.output_list, *next; slist *list, *lnext; mplrs.outputblock = 0; /* discard output */ mplrs.outnum = 0; /* clearing buffer */ mplrs.output_list = NULL; mplrs.ol_tail = NULL; for (; out; out=next) { next = out->next; free(out->type); free(out->data); free(out); } /* discard cobases */ for (list=mplrs.cobasis_list; list; list=lnext) { lnext = list->next; free(list->data); free(list); } mplrs.cobasis_list = NULL; /* discard curwarn */ mplrs.curwarn[0] = '\0'; } /* set up restart parameters in mplrs.R */ /* header[1] gives maxdepth, header[2] gives maxcobases, * if header[0] > 0, * starting_cobasis gives the starting cobasis. * if header[0] == 0, starting at initial input (phase 1) * header[4] gives desired bool for R->messages */ void set_restart(const int *header, char *starting_cobasis) { lrs_restart_dat *R = mplrs.R; int i, j, len; long depth = 0; /* if restarting from earlier checkpoint, * then we want to fall back to old depth-0 * behavior */ /* prepare input file */ mplrs.initializing = 0; /* reset counts */ for (i=0; i<10; i++) R->count[i] = 0; R->messages = header[4]; if (header[0]>0) { /* ugly: recover depth after '!' marker */ len = strlen(starting_cobasis); for (i=0; idepth = depth; R->mindepth = depth; R->restart = 1; if (id; j++) { if (ifacet[j] = atol(starting_cobasis+i); else R->facet[j] = 0; mprintf3(("%ld ", R->facet[j])); for (; icount[2] = 1; /* why? to get begin line... */ R->depth = 0; R->restart = 0; } if (header[1]>0) R->maxdepth = header[1] + depth; if (header[2]>0) R->maxcobases = header[2]; #if 0 /* 2018.4.28 TODO lponly ? countonly now set on master */ if (mplrs.initializing != 1 && header[3]==1) /* lponly option, only in*/ fprintf(mplrs.tfile, "lponly\n"); /* non-initial jobs */ #endif return; } /* update counts in mplrs.rays, etc via mplrs.R */ /* see lrsrestart.h */ void update_counts(void) { lrs_restart_dat *R = mplrs.R; int hull = R->count[5]; long deepest = mplrs.deepest; /* silly, avoid sign comparison warning */ long linearities = mplrs.linearities; /* silly, avoid warning */ if (!hull) mplrs.rays += R->count[0]; else mplrs.facets += R->count[0]; if (!hull) mplrs.vertices += R->count[1]; mplrs.bases += R->count[2]; mplrs.intvertices += R->count[4]; if (linearities < R->count[6]) mplrs.linearities = R->count[6]; if (deepest < R->count[7]) mplrs.deepest = R->count[7]; } /* header[1] gives maxdepth, header[2] gives maxcobases, * if header[0] > 0, * starting_cobasis gives the starting cobasis. * if header[0] == 0, starting at initial input (phase 1) * header[4] gives desired bool for R->messages */ void do_work(const int *header, char *starting_cobasis) { char *argv[] = {argv0, mplrs.tfn}; mprintf3(("%d: Received work (%d,%d,%d)\n",mplrs.rank,header[0], header[1],header[2])); set_restart(header, starting_cobasis); mprintf2(("%d: Calling run_lrs\n",mplrs.rank)); run_lrs(2, argv, 0, 1, header, starting_cobasis); mprintf2(("%d: run_lrs returned, updating counts\n",mplrs.rank)); update_counts(); } /* lrs reported overflow; tell the master and prepare to finish */ void worker_report_overflow(void) { float junk = -1; mprintf(("%d: reporting overflow\n", mplrs.rank)); if (mplrs.rank == MASTER) { /* possible now since master does worker_init to get m and redund options */ mplrs.overflow = 3; return; } send_output(2, dupstr("*possible overflow: try using gmp or hybrid mplrs\n")); /* inform master, wait for reply */ MPI_Send(&junk, 1, MPI_FLOAT, MASTER, 9, MPI_COMM_WORLD); MPI_Recv(&junk, 1, MPI_FLOAT,MASTER,9,MPI_COMM_WORLD,MPI_STATUS_IGNORE); } /* The worker has finished its work. Process the output, preparing * and sending the output to the consumer, and preparing the unfinished * cobases for return_unfinished_cobases(). */ void process_output(void) { outlist *out = mplrs.output_list, *next; char *out_string=NULL; /* for output file if exists */ char *serr_string=NULL; /* for stdout */ char *redund_string=NULL; /* for redund */ const char *type; const char *data; int len = 1024; int len2 = 256; int len3 = 256; mplrs.outnum = 0; /* clearing buffer */ mplrs.output_list = NULL; mplrs.ol_tail = NULL; out_string = malloc(sizeof(char)*len); out_string[0]='\0'; serr_string = malloc(sizeof(char)*len2); serr_string[0]='\0'; redund_string = malloc(sizeof(char)*len3); redund_string[0]='\0'; /* reverse when initializing to get correct order */ #if 0 /* TODO fixme */ if (mplrs.initializing) out = reverse_list(out); #endif while (out) { type = out->type; data = out->data; if (!strcmp(type, "vertex")) out_string = append_out(out_string, &len, data); else if (!strcmp(type, "ray")) out_string = append_out(out_string, &len, data); else if (!strcmp(type, "unexp")) /* no longer used */ process_cobasis(data); else if (!strcmp(type, "cobasis")) out_string = append_out(out_string, &len, data); else if (!strcmp(type, "V cobasis")) out_string = append_out(out_string, &len, data); else if (!strcmp(type, "facet count")) /* no longer used */ mplrs.facets += atoi(data); else if (!strcmp(type, "ray count")) /* no longer used */ mplrs.rays += atoi(data); else if (!strcmp(type, "basis count")) /* no longer used */ mplrs.bases += atoi(data); else if (!strcmp(type, "vertex count")) /* no longer used */ mplrs.vertices += atoi(data); else if (!strcmp(type, "integer vertex count")) /* no longer used */ mplrs.intvertices += atoi(data); else if (!strcmp(type, "tree depth")) /* no longer used */ { if (mplrs.deepest < strtoul(data,NULL,10)) mplrs.deepest = strtoul(data,NULL,10); } else if (!strcmp(type, "linearities")) /* no longer used */ { if (mplrs.linearities < strtoul(data,NULL,10)) mplrs.linearities = strtoul(data,NULL,10); } else if (!strcmp(type, "volume")) /* still used */ { #if defined(MA) || defined(GMP) || defined(FLINT) plrs_readrat(mplrs.Tnum, mplrs.Tden, data); copy(mplrs.tN, mplrs.Vnum); copy(mplrs.tD, mplrs.Vden); linrat(mplrs.tN, mplrs.tD, 1L, mplrs.Tnum, mplrs.Tden, 1L, mplrs.Vnum, mplrs.Vden); #endif } else if (!strcmp(type, "options warning")) { /* only do warnings once, otherwise repeated */ if (mplrs.initializing) out_string = append_out(out_string, &len, data); } else if (!strcmp(type, "header")) { /*only do header if initializing, otherwise repeated*/ if (mplrs.initializing) out_string = append_out(out_string, &len, data); } else if(!strcmp(type, "redund")) { /* handle redund inequalities: TODO better */ redund_string = append_out(redund_string, &len3, data); } else if (!strcmp(type, "debug")) { out_string = append_out(out_string, &len, data); } else if (!strcmp(type, "warning")) { /* warnings always go to output file and stderr if output is not stdout */ out_string = append_out(out_string, &len, data); if(consumer.output != stdout) serr_string = append_out(serr_string, &len2, data); } else if (!strcmp(type, "finalwarn")) { /* these are printed at end of run */ mplrs.curwarn = append_out(mplrs.curwarn, &mplrs.curwarn_len, data); /* but also to stderr now */ serr_string = append_out(serr_string, &len2, data); } next = out->next; free(out->type); free(out->data); free(out); out = next; } if (strlen(out_string)>0 && strcmp(out_string, "\n")) send_output(1, out_string); else free(out_string); if (strlen(serr_string)>0 && strcmp(serr_string, "\n")) send_output(0, serr_string); else free(serr_string); if (strlen(redund_string)>0 && strcmp(redund_string, "\n")) send_output(3, redund_string); else free(redund_string); } /* if we've produced anything for finalwarn, add it to finalwarn now. * buffered in curwarn to clear on overflow, avoiding multiple copies */ void process_curwarn(void) { if (strlen(mplrs.curwarn)>0) { mplrs.finalwarn = append_out(mplrs.finalwarn, &mplrs.finalwarn_len,mplrs.curwarn); mplrs.curwarn[0] = '\0'; } } /* send this string to the consumer to output. * If dest==1, then it goes to the output file (stdout if no output file). * If dest==0, then it goes to stderr. * If dest==2, it's an overflow message: only the first one printed (stderr) * If dest==3, it's a redund output: consumer handles specially * * The pointer str is surrendered to send_output and should not be changed * It will be freed once the send is complete. */ /* str should not be NULL */ void send_output(int dest, char *str) { msgbuf *msg = malloc(sizeof(msgbuf)); int *header = malloc(sizeof(int)*3); header[0] = dest; header[1] = strlen(str); header[2] = mplrs.my_tag; /* to ensure the dest/str pair * remains intact even if another * send happens in between */ msg->req = malloc(sizeof(MPI_Request)*2); msg->buf = malloc(sizeof(void *)*2); msg->buf[0] = header; msg->buf[1] = str; msg->count = 2; msg->target = CONSUMER; msg->queue = 1; msg->tags = malloc(sizeof(int)*2); msg->sizes = malloc(sizeof(int)*2); msg->types = malloc(sizeof(MPI_Datatype)*2); msg->types[1] = MPI_CHAR; msg->sizes[1] = header[1]+1; msg->tags[1] = mplrs.my_tag; mplrs.my_tag++; msg->next = mplrs.outgoing; mplrs.outgoing = msg; MPI_Isend(header, 3, MPI_INT, CONSUMER, 7, MPI_COMM_WORLD, msg->req); } /* lrs returned this unexplored cobasis - send it along. * For now converts to a string and re-uses the old code, * but avoids horrible process_cobasis(). TODO: send along as * longs instead. */ void post_R(lrs_restart_dat *cob) { int i=0, offs=0; int arg = 0; int hull = cob->count[5]; char *newcob = NULL; while (arg == 0) { arg = offs; if (hull == 0) offs = snprintf(newcob,arg," %ld %ld %ld!%ld ", cob->count[1],cob->count[0], cob->count[2],cob->depth); else offs = snprintf(newcob,arg," %ld %ld!%ld ", cob->count[1],cob->count[2], cob->depth); for (i=0; id; i++) offs += snprintf(newcob+offs,arg,"%ld ", cob->facet[i]); if (newcob == NULL) newcob = malloc(sizeof(char)*(offs+1)); } mplrs.cobasis_list = addlist(mplrs.cobasis_list, newcob); } /* process_cobasis is no longer used */ /* called from process_output to handle a 'cobasis', * add to queue to return to master */ /* awful string-hacking, basically copied from plrs processCobasis() */ /* First, if first characters are 'F#', it's a hull. otherwise it's not. * Then, remove ignore_chars. * Then, remove everything starting from the first 'I' * Then, copy everything verbatim, except: * if it's a hull, replace everything between second and third spaces * by '0' * if it's not a hull, replace everything between third and fourth * spaces by '0' * (this is resetting the depth to be 0 for a restart) */ void process_cobasis(const char *newcob) { int nlen = strlen(newcob); char *buf = malloc(sizeof(char) * (nlen+1)); int i,j,k; int num_spaces=0; /* we count the number of spaces */ char ignore_chars[] = "#VRBh=facetsFvertices/rays"; char c; int num_ignore = strlen(ignore_chars); int hull = 0; /*int replace = 0;*/ /* no longer hacking depth to 0 */ mprintf3(("%d: process_cobasis( %s )", mplrs.rank, newcob)); if (nlen>1 && newcob[0]=='F' && newcob[1]=='#') hull = 1; for (i=0,j=0; i<=nlen; i++) { c = newcob[i]; /* ignore ignore_chars */ for (k=0; k<=num_ignore; k++) if (c == ignore_chars[k]) break; if (k<=num_ignore) continue; if (c=='I') break; if (c==' ') /* count spaces to set depth to 0 for restart */ { num_spaces++; if ( (num_spaces==2 && hull==1) || (num_spaces==3 && hull==0) ) { /*replace = 1;*/ buf[j++]='!'; /* mark depth ... */ continue; } #if 0 else if ( (num_spaces==3 && hull==1) || (num_spaces==4 && hull==0) ) replace = 0; #endif buf[j++] = c; /* copy other spaces */ continue; } #if 0 if (replace == 1) /* remove three lines here */ buf[j++]='0';/* to play with mindepth */ else /* leaving only the next line */ #endif buf[j++]=c; } buf[j]='\0'; mprintf3((" produced %s\n",buf)); mplrs.cobasis_list = addlist(mplrs.cobasis_list, buf); } slist *addlist(slist *list, void *buf) { slist *n = malloc(sizeof(struct slist)); n->data = buf; n->next = list; return n; } /* mplrs.cobasis_list may have things to send to the master. * Send the header, and then the cobases to add to L. */ void return_unfinished_cobases(void) { int listsize; slist *list, *next; int *lengths=NULL; char *cobases=NULL; int size = 0; int i; int start; /* header is (strlen(cobases), length of lengths, mplrs.my_tag) */ int *header = malloc(sizeof(int)*3); msgbuf *msg = malloc(sizeof(msgbuf)); msg->target = MASTER; for (listsize=0, list=mplrs.cobasis_list; list; list=list->next) { listsize++; size += strlen((char *)list->data); } if (listsize == 0) { header[0] = -1; header[1] = -1; header[2] = -1; msg->buf = malloc(sizeof(void *)); msg->buf[0] = header; msg->count = 1; msg->req = malloc(sizeof(MPI_Request)); msg->queue = 0; msg->tags = NULL; msg->sizes = NULL; msg->types = NULL; MPI_Isend(header, 3, MPI_INT, MASTER, 10, MPI_COMM_WORLD, msg->req); msg->next = mplrs.outgoing; mplrs.outgoing = msg; return; } lengths = malloc(sizeof(int)*listsize); /*allows unconcatenate*/ cobases = malloc(sizeof(char)*(size+1));/*concatenated + 1 \0*/ for (start=0, i=0, list=mplrs.cobasis_list; list; list=next, i++) { next = list->next; strcpy(cobases+start, (char *)list->data); lengths[i] = strlen((char *)list->data); start+=lengths[i]; free(list->data); free(list); } /* final \0 is there */ header[0] = listsize; header[1] = size+1; header[2] = mplrs.my_tag; msg->req = malloc(sizeof(MPI_Request) * 3); msg->buf = malloc(sizeof(void *) * 3); msg->buf[0] = header; msg->buf[1] = cobases; msg->buf[2] = lengths; msg->count = 3; msg->queue = 0; msg->tags = NULL; msg->sizes = NULL; msg->types = NULL; mprintf2(("%d: Queued send of %d cobases for L\n",mplrs.rank,listsize)); MPI_Isend(header, 3, MPI_INT, MASTER, 10, MPI_COMM_WORLD, msg->req); MPI_Isend(cobases, header[1], MPI_CHAR, MASTER, mplrs.my_tag, MPI_COMM_WORLD, msg->req+1); MPI_Isend(lengths, listsize, MPI_INT, MASTER, mplrs.my_tag, MPI_COMM_WORLD, msg->req+2); mplrs.my_tag++; msg->next = mplrs.outgoing; mplrs.outgoing = msg; mplrs.cobasis_list = NULL; } /* dest is a string in a buffer with size *size. * Append src and a newline to the string, realloc()ing as necessary, * returning the new pointer and updating size. */ char *append_out(char *dest, int *size, const char *src) { int len1 = strlen(dest); int len2 = strlen(src); int newsize = *size; char *newp = dest; if (src[len2-1]=='\n') /* remove trailing \n, added below */ len2--; if (len1 + len2 + 2 > *size) { newsize = newsize<<1; while ((newsize < len1+len2+2) && newsize) newsize = newsize<<1; if (!newsize) newsize = len1+len2+2; newp = realloc(dest, sizeof(char) * newsize); if (!newp) { newsize = len1+len2+2; newp = realloc(dest, sizeof(char) * newsize); if (!newp) { printf("%d: Error no memory (%d)\n",mplrs.rank, newsize); /* MPI_Finalize(); */ exit(2); } } *size = newsize; } strncat(newp, src, len2); newp[len1+len2]='\n'; newp[len1+len2+1]='\0'; return newp; } /************ * consumer * ************/ int mplrs_consumer(void) { int i; int check = 0; initial_print(); /* print version and other information */ /* initialize MPI_Requests and 3*int buffers for incoming messages */ consumer.prodreq = malloc(sizeof(MPI_Request)*mplrs.size); consumer.prodibf = malloc(sizeof(int)*3*mplrs.size); consumer.num_producers = mplrs.size - 2; consumer.overflow = malloc(sizeof(int)*mplrs.size); if (mplrs.redund) /* don't wait for a begin when doing redund */ consumer.waiting_initial = 0; for (i=0; i0 || consumer.incoming || (consumer.waiting_initial && consumer.final_print)) { /*printf("%d %d %d %d\n", consumer.num_producers, consumer.incoming, consumer.waiting_initial, consumer.final_print); */ /* check if someone is trying to send us output */ /* if so, queue any incoming messages */ consumer_start_incoming(); /* check for completed message to process */ consumer_proc_messages(); /* check signals */ mplrs_handlesigs(); } mprintf2(("C: getting stats and exiting\n")); for (i=0; iredineq); free(mplrs.R->facet); free(mplrs.R); } free(consumer.redineq); mplrs_freemps(); free(mplrs.finalwarn); free(mplrs.curwarn); MPI_Finalize(); return 0; } /* check if anyone is trying to send us their output */ /* if master is trying, probably means we're going to checkpoint */ /* in any case, queue any incoming messages */ void consumer_start_incoming(void) { int i; int flag; for (i=0; ireq = malloc(sizeof(MPI_Request)*2); newmsg->buf = malloc(sizeof(void *)); newmsg->buf[0] = malloc(sizeof(char)*(header[1]+1)); newmsg->count = 1; newmsg->target = target; newmsg->next = curhead; newmsg->queue = 0; newmsg->tags = NULL; newmsg->sizes = NULL; newmsg->types = NULL; newmsg->data = header[0]; /* bound for stdout or output file */ /* get my_tag from producer via header[2] to uniquely identify msg */ MPI_Irecv(newmsg->buf[0], header[1]+1, MPI_CHAR, target, header[2], MPI_COMM_WORLD, newmsg->req); mprintf3(("C: Receiving from %d (%d,%d,%d)",target,header[0],header[1], header[2])); return newmsg; } /* update consumer.redineq with the redundant inequalities in rstring */ /* these came from process from (used for an optimization) */ void consumer_process_redund(const char *rstring, int from) { const char *start=rstring; char *endptr=NULL; long index; int i=0; mprintf2(("C: processing redund_string %s\n", rstring)); do { index = strtol(start, &endptr, 10); if (index!=0) { mprintf3(("C: got redundant inequality %ld\n",index)); i++; consumer.redineq[index] = from; start = endptr; } } while (index!=0); mprintf2(("C: got %d redundant inequalities\n", i)); } /* check our incoming messages, process and remove anything that * has completed */ void consumer_proc_messages(void) { msgbuf *msg, *prev=NULL, *next; int i,len,omit; for (msg=consumer.incoming; msg; msg=next) { omit = 0; next=msg->next; if (outgoing_msgbuf_completed(msg)) { if (consumer.waiting_initial && consumer.final_print && msg->target != INITIAL && msg->target != MASTER) { prev = msg; /* 2020.5.29 need to update prev * so we don't lose this msg */ continue; } /* final_print condition is false when overflow * has occurred. No longer important to print all * output, but need to print or discard it in case * overflow prevents us from seeing "begin" */ /* we wait on all other output until we've printed * the initial output containing ...begin\n * to ensure pretty output, if this is the begin, * flip the flag. */ if (consumer.waiting_initial == 1 && msg->target == INITIAL) { len=strlen((char *)msg->buf[0])-5; for (i=0; ibuf[0]+i,6)) { mprintf3(("C: found begin\n")); phase1_print(); consumer.waiting_initial = 0; break; } if (consumer.waiting_initial) /* no begin here*/ { /* can happen in 7.1 */ prev=msg; /* wait for a begin line */ continue; } } else if (consumer.waiting_initial == 2 && msg->target == INITIAL) { /* could combine with other condition above */ /* maybe easier to read if separate */ prev = msg; /* 2020.5.29 same here*/ continue; /* wait for master to report warnings */ } else if (consumer.waiting_initial == 2 && msg->target == MASTER) { consumer.waiting_initial = 1; /* if no master warning messages produced, * master sends a space to prod us along. * don't print that space. */ if (!strcmp(msg->buf[0], " \n")) omit = 1; } /* print the 'begin' only after phase1_print */ if (msg->data == 1 && !omit) { fprintf(consumer.output, "%s", (char*)msg->buf[0]); /* flush to get more streaminess to output * file and not break inside a line, as * requested */ fflush(consumer.output); } else if (msg->data == 2 && !omit) { if (!consumer.oflow_flag) { consumer.oflow_flag = 1; fprintf(stderr,"%s",(char*)msg->buf[0]); } } else if (msg->data == 3 && !omit) /* redund string */ consumer_process_redund((char*)msg->buf[0], msg->target); else if (!omit) /* headed to stderr */ fprintf(stderr, "%s", (char*)msg->buf[0]); free_msgbuf(msg); if (prev) prev->next = next; else consumer.incoming = next; continue; } prev=msg; } } /* We are checkpointing instead of a normal exit. * Send counting stats to master, then exit quietly */ int consumer_checkpoint(void) { int len; char *str; char *vol = cprat("", mplrs.Vnum, mplrs.Vden); send_counting_stats(MASTER); mprintf(("C: in consumer_checkpoint\n")); MPI_Recv(&len, 1, MPI_INT, MASTER, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE); if (len == -1) /* master produces checkpoint file */ { mplrs_freemps(); MPI_Finalize(); return 0; } fprintf(consumer.output, "*Checkpoint file follows this line\n"); fprintf(consumer.output, "mplrs4\n%llu %llu %llu %llu %llu\n%s\n%llu\n", mplrs.rays, mplrs.vertices, mplrs.bases, mplrs.facets, mplrs.intvertices,vol,mplrs.deepest); free(vol); while (1) { MPI_Recv(&len, 1, MPI_INT, MASTER, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE); if (len<0) break; str = malloc(sizeof(char)*len); MPI_Recv(str, len, MPI_CHAR, MASTER, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE); fprintf(consumer.output,"%s\n",str); free(str); } fprintf(consumer.output,"*Checkpoint finished above this line\n"); mplrs_freemps(); MPI_Finalize(); return 0; } /* check whether this outgoing msgbuf has completed. * If the msg is queued (msg->queue == 1), * then if the first part has completed, send the remaining parts * Don't use with *queued* incoming msgbuf. */ int outgoing_msgbuf_completed(msgbuf *msg) { int flag; int count = msg->count; int i; if (msg->queue != 1) { MPI_Testall(count, msg->req, &flag, MPI_STATUSES_IGNORE); return flag; } MPI_Test(msg->req, &flag, MPI_STATUS_IGNORE); if (!flag) return flag; /* first completed, send the rest of the queued send */ mprintf3(("%d: Sending second part of queued send to %d\n", mplrs.rank, msg->target)); for (i=1; ibuf[i]) MPI_Isend(msg->buf[i], msg->sizes[i], msg->types[i], msg->target, msg->tags[i], MPI_COMM_WORLD, msg->req+i); } msg->queue = 0; return 0; } void free_msgbuf(msgbuf *msg) { int i; for (i=0; icount; i++) free(msg->buf[i]); free(msg->buf); free(msg->req); free(msg->tags); free(msg->sizes); free(msg->types); free(msg); return; } outlist *reverse_list(outlist* head) { outlist * last = head, * new_head = NULL; while(last) { outlist * tmp = last; last = last->next; tmp->next = new_head; new_head = tmp; } return new_head; } /* send stats on size of L, etc */ void send_master_stats(void) { unsigned long stats[4] = {master.tot_L, master.num_empty, 0, 0}; mprintf3(("M: Sending master_stats to consumer\n")); MPI_Send(stats, 4, MPI_UNSIGNED_LONG, CONSUMER, 1, MPI_COMM_WORLD); return; } /* get master stats on size of L, etc */ void recv_master_stats(void) { unsigned long stats[4] = {0,0,0,0}; MPI_Recv(stats, 4, MPI_UNSIGNED_LONG, MASTER, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE); master.tot_L = stats[0]; master.num_empty = stats[1]; return; } /* send stats to target for final print */ void send_counting_stats(int target) { char *vol = cprat("", mplrs.Vnum, mplrs.Vden); unsigned long long stats[10] = {mplrs.rays, mplrs.vertices, mplrs.bases, mplrs.facets, mplrs.intvertices, strlen(vol)+1, mplrs.deepest, mplrs.overflow, mplrs.linearities, strlen(mplrs.finalwarn)+1}; mprintf3(("%d: sending counting stats to %d\n", mplrs.rank, target)); MPI_Send(stats, 10, MPI_UNSIGNED_LONG_LONG, target, 1, MPI_COMM_WORLD); MPI_Send(vol, stats[5], MPI_CHAR, target, 1, MPI_COMM_WORLD); MPI_Send(mplrs.finalwarn, stats[9], MPI_CHAR, target, 1, MPI_COMM_WORLD); free(vol); return; } /* gets counting stats from target */ void recv_counting_stats(int target) { char *vol, *finalwarn; unsigned long long stats[10]; MPI_Recv(stats, 10, MPI_UNSIGNED_LONG_LONG, target, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE); mprintf3(("%d: got counting stats from %d\n", mplrs.rank, target)); mplrs.rays+=stats[0]; mplrs.vertices+=stats[1]; mplrs.bases+=stats[2]; mplrs.facets+=stats[3]; mplrs.intvertices+=stats[4]; if (stats[6] > mplrs.deepest) mplrs.deepest = stats[6]; if (mplrs.rank == CONSUMER) consumer.overflow[target] = stats[7]; if (stats[8] > mplrs.linearities) mplrs.linearities = stats[8]; vol = malloc(sizeof(char)*stats[5]); MPI_Recv(vol, stats[5], MPI_CHAR, target, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE); /* following safe even #ifdef LRSLONG, volume always 0/1 */ plrs_readrat(mplrs.Tnum, mplrs.Tden, vol); copy(mplrs.tN, mplrs.Vnum); copy(mplrs.tD, mplrs.Vden); linrat(mplrs.tN, mplrs.tD, 1L, mplrs.Tnum, mplrs.Tden, 1L, mplrs.Vnum, mplrs.Vden); free(vol); finalwarn = malloc(sizeof(char)*stats[9]); MPI_Recv(finalwarn, stats[9], MPI_CHAR, target, 1, MPI_COMM_WORLD, MPI_STATUS_IGNORE); if (stats[9]>2) mplrs.finalwarn = append_out(mplrs.finalwarn, &mplrs.finalwarn_len, finalwarn); free(finalwarn); return; } /* do the initial print */ void initial_print(void) { #ifdef MA fprintf(consumer.output, "*mplrs:%s%s(hybrid arithmetic)%d processes\n", TITLE, VERSION, mplrs.size); #elif defined(GMP) fprintf(consumer.output, "*mplrs:%s%s(%s gmp v.%d.%d)%d processes\n", TITLE,VERSION,ARITH,__GNU_MP_VERSION, __GNU_MP_VERSION_MINOR,mplrs.size); #elif defined(FLINT) fprintf(consumer.output, "*mplrs:%s%s(%s, %dbit flint v.%s)%d processes\n", TITLE,VERSION,ARITH,FLINT_BITS,FLINT_VERSION, mplrs.size); #elif defined(SAFE) fprintf(consumer.output, "*mplrs:%s%s(%s,%s,overflow checking)%d processes\n", TITLE,VERSION,BIT,ARITH,mplrs.size); #else fprintf(consumer.output, "*mplrs:%s%s(%s,%s,no overflow checking)%d processes\n", TITLE,VERSION,BIT,ARITH,mplrs.size); #endif fprintf(consumer.output, "*Input taken from %s\n", mplrs.input_filename); if (mplrs.redund == 0) { fprintf(consumer.output, "*Starting depth of %d maxcobases=%d ", master.initdepth, master.maxcobases); fprintf(consumer.output, "maxdepth=%d lmin=%d lmax=%d scale=%d\n", master.maxdepth, master.lmin, master.lmax, master.scalec); if (mplrs.countonly) fprintf(consumer.output, "*countonly\n"); } else fprintf(consumer.output, "*redund\n"); if (consumer.output==stdout) return; #ifdef MA printf("*mplrs:%s%s(hybrid arithmetic)%d processes\n", TITLE, VERSION, mplrs.size); #elif defined(GMP) printf("*mplrs:%s%s(%s gmp v.%d.%d)%d processes\n", TITLE,VERSION,ARITH,__GNU_MP_VERSION, __GNU_MP_VERSION_MINOR,mplrs.size); #elif defined(FLINT) printf("*mplrs:%s%s(%s, %dbit flint v.%s)%d processes\n", TITLE,VERSION,ARITH,FLINT_BITS,FLINT_VERSION, mplrs.size); #elif defined(SAFE) printf("*mplrs:%s%s(%s,%s,overflow checking)%d processes\n", TITLE,VERSION,BIT,ARITH,mplrs.size); #else printf("*mplrs:%s%s(%s,%s,no overflow checking)%d processes\n", TITLE,VERSION,BIT,ARITH,mplrs.size); #endif printf("*Input taken from %s\n",mplrs.input_filename); printf("*Output written to: %s\n",consumer.output_filename); if (mplrs.redund == 0) { printf("*Starting depth of %d maxcobases=%d ", master.initdepth, master.maxcobases); printf("maxdepth=%d lmin=%d lmax=%d scale=%d\n", master.maxdepth, master.lmin, master.lmax, master.scalec); if (mplrs.countonly) printf("*countonly\n"); } else printf("*redund\n"); } /* do the "*Phase 1 time: " print */ void phase1_print(void) { struct timeval cur; gettimeofday(&cur, NULL); fprintf(consumer.output, "*Phase 1 time: %ld seconds.\n", cur.tv_sec-mplrs.start.tv_sec); if (consumer.output_filename == NULL) return; printf("*Phase 1 time: %ld seconds.\n",cur.tv_sec-mplrs.start.tv_sec); return; } /* sigh... when doing redund, we re-run a final redund check of all * detected redundant lines, in order to avoid removing e.g. all * identical copies of a fixed line (when each on a different worker). * this is done on the consumer. but then lrslib does post_output, which * normally can't be done on the consumer. so here we intercept the data * produced by this final redund run, and update consumer.redineq ... */ void consumer_finalredund_handler(const char *data) { int i, m = mplrs.P->m_A; for (i=0; i<=m; i++) consumer.redineq[i] = 0; consumer_process_redund(data, CONSUMER); } /* set R->redineq using consumer.redineq, for final check */ void consumer_setredineq(void) { int i, m, max, maxi; int *counts = calloc(mplrs.size, sizeof(int)); m = mplrs.P->m_A; /* hack output to file (if using file). * done here in case of re-init on overflow (eg redund on mit.ine) */ lrs_ofp = consumer.output; /* optimization per DA, with current way of splitting redund * we can choose the worker (maxi) that produced the most redundant * inequalities and not recheck those at the end */ for (i=1; i<=m; i++) if (consumer.redineq[i]!=0) counts[consumer.redineq[i]]++; max = -1; maxi = -1; /* not needed, for warning removal only */ for (i=0; imax) { max=counts[i]; maxi = i; } free(counts); mprintf(("C: resetting redineq for final check (maxi:%d,max:%d) on:", maxi,max)); for (i=1; i<=m; i++) { if (consumer.redineq[i] == maxi && max>0) /* DA: max=0 means no redundancies found*/ mplrs.R->redineq[i] = -1; else if (consumer.redineq[i] > 0) { mplrs.R->redineq[i] = 1; mprintf((" %d", i)); } else if (mplrs.R->redineq[i] != 2) mplrs.R->redineq[i] = 0; } mprintf(("\n")); mplrs.R->verifyredund = 1; } /* do the final print */ void final_print(void) { char *argv[] = {argv0}; struct timeval end; char *vol=NULL; #ifdef MA int i, num64=0, num128=0, numgmp=0; #endif if (mplrs.redund) { mplrs_worker_init(); consumer_setredineq(); mprintf(("C: calling lrs_main for final redund check\n")); lrs_ofp = consumer.output; /* HACK to get redund output in * output file ... */ consumer.final_redundcheck = 1; run_lrs(1, argv, 0, 1, NULL, NULL); mprintf(("C: lrs_main returned from final redund check\n")); if (mplrs.overflow != 3) mplrs.lrs_main(0,NULL,&mplrs.P,&mplrs.Q,0,2,NULL,mplrs.R); } else fprintf(consumer.output, "end\n"); if (strlen(mplrs.finalwarn)>1) /*avoid spurious newline from append_out*/ fprintf(consumer.output, "%s", mplrs.finalwarn); /* after the (expensive) final redund check */ gettimeofday(&end, NULL); fprintf(consumer.output, "*Total number of jobs: %lu, L became empty %lu times, tree depth %llu\n", master.tot_L, master.num_empty,mplrs.deepest); if (consumer.output_filename != NULL) printf("*Total number of jobs: %lu, L became empty %lu times, tree depth %llu\n", master.tot_L, master.num_empty,mplrs.deepest); #ifdef MA for (i=0; i0) { if(!zero(mplrs.Vnum)) { vol = cprat("*Volume=",mplrs.Vnum,mplrs.Vden); fprintf(consumer.output,"%s\n",vol); free(vol); } fprintf(consumer.output,"*Totals: facets=%llu bases=%llu", mplrs.facets, mplrs.bases); if (mplrs.linearities > 0) fprintf(consumer.output, " linearities=%llu facets+linearities=%llu", mplrs.linearities,mplrs.linearities+mplrs.facets); fputc('\n', consumer.output); } else if (mplrs.redund == 0 && (mplrs.rays+mplrs.vertices>0)) /*DA: seems like V-rep output not redund!?*/ { /* yes, H-rep output is above, V-rep here, * just 'else' would also get redund runs */ fprintf(consumer.output, "*Totals: vertices=%llu rays=%llu bases=%llu integer-vertices=%llu", mplrs.vertices,mplrs.rays,mplrs.bases,mplrs.intvertices); if (mplrs.linearities > 0) fprintf(consumer.output, " linearities=%llu", mplrs.linearities); if (mplrs.rays+mplrs.linearities>0) { fprintf(consumer.output," vertices+rays"); if (mplrs.linearities>0) fprintf(consumer.output, "+linearities"); fprintf(consumer.output, "=%llu", mplrs.vertices+mplrs.rays+mplrs.linearities); } fputc('\n', consumer.output); } fprintf(consumer.output, "*Elapsed time: %ld seconds.\n", end.tv_sec - mplrs.start.tv_sec); if (consumer.output_filename == NULL) return; if (mplrs.facets>0) { if (!zero(mplrs.Vnum)) { vol = cprat("*Volume=",mplrs.Vnum,mplrs.Vden); printf("%s\n", vol); free(vol); } printf("*Totals: facets=%llu bases=%llu", mplrs.facets, mplrs.bases); if (mplrs.linearities > 0) printf(" linearities=%llu facets+linearities=%llu", mplrs.linearities,mplrs.linearities+mplrs.facets); putchar('\n'); } else if (mplrs.redund == 0 && (mplrs.rays+mplrs.vertices>0)) { printf("*Totals: vertices=%llu rays=%llu bases=%llu integer-vertices=%llu", mplrs.vertices,mplrs.rays,mplrs.bases,mplrs.intvertices); if (mplrs.linearities > 0) printf(" linearities=%llu", mplrs.linearities); if (mplrs.rays+mplrs.linearities>0) { printf(" vertices+rays"); if (mplrs.linearities>0) printf("+linearities"); printf("=%llu", mplrs.vertices+mplrs.rays+mplrs.linearities); } putchar('\n'); } printf("*Elapsed time: %ld seconds.\n", end.tv_sec - mplrs.start.tv_sec); } void open_outputblock(void) { mplrs.outputblock++; } void close_outputblock(void) { mplrs.outputblock--; if (okay_to_flush()) { process_output(); /* before starting a flush */ clean_outgoing_buffers(); } } /* the condition on whether we should do a maxbuf-based * flush of the output. Bit complicated and used twice * so broken out here. */ int okay_to_flush(void) { return (mplrs.outnum++ > mplrs.maxbuf && /* buffer type = dupstr(type); out->data = dupstr(data); out->next = NULL; if (mplrs.output_list == NULL) mplrs.output_list = out; else mplrs.ol_tail->next = out; mplrs.ol_tail = out; if (okay_to_flush() && data[strlen(data)-1]=='\n') { process_output(); /* before starting a flush */ clean_outgoing_buffers(); } } /* strdup */ char *dupstr(const char *str) { char *buf = malloc(sizeof(char)*(strlen(str)+1)); strcpy(buf,str); return buf; } lrslib-071a/mplrs.h0000700060175606010010000002643413742506301014147 0ustar avisなし/* mplrs.h: header for mplrs.c This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. Author: Charles Jordan skip@ist.hokudai.ac.jp Based on plrs by Gary Roumanis Initial lrs Author: David Avis avis@cs.mcgill.ca */ #ifndef MPLRSH #define MPLRSH 1 #ifdef MA #define GMP #endif #include "lrsdriver.h" #include "lrslib.h" #include #include #include #include #include #include extern FILE *lrs_ofp; /* hack to get redund final print in output file */ #define USAGE "Usage is: \n mpirun -np mplrs \n or \n mpirun -np mplrs -id -maxc -maxd -lmin -lmax -scale -maxbuf -countonly -hist -temp -freq -stop -checkp -restart -time -stopafter -redund" /* Default values for options. */ #define DEF_LMIN 3 /* default -lmin */ #define DEF_LMAX 0 /* default -lmax. but note orig_lmax behavior! */ #define DEF_ID 2 /* default -id */ #define DEF_MAXD 0 /* default -maxd */ #define DEF_MAXC 50 /* default -maxc */ #define DEF_MAXNCOB 0 /* default -stopafter (disabled) */ #define DEF_MAXBUF 500 /* default -maxbuf */ #define DEF_TEMP "/tmp/" /* default prefix for temporary files * use /a/b to get files /a/bfilename, * use /a/b/ to get files /a/b/filename */ #define DEF_INPUT NULL /* default input filename (or NULL) */ #define DEF_OUTPUT NULL /* default output filename (or NULL) */ #define DEF_HIST NULL /* default histogram filename (or NULL) */ #define DEF_RESTART NULL/* default restart filename (or NULL) */ #define DEF_FREQ NULL /* default sub-problem size filename (NULL) */ #define DEF_CHECKP NULL /* default checkpoint filename (or NULL) */ #define DEF_STOP NULL /* default stop-signal filename (or NULL) */ #define DEF_SCALEC 100 /* default multiplicative scaling factor for maxc, * used when L is too large (controlled by lmax) */ #if defined(MA) || (defined(LRSLONG) && !defined(B128)) #define mplrs_init_lrs_main lrs1_main #elif defined(LRSLONG) /* B128 */ #define mplrs_init_lrs_main lrs2_main #elif defined(GMP) #define mplrs_init_lrs_main lrsgmp_main #elif defined(FLINT) #define mplrs_init_lrs_main lrsv2_main #elif defined(MP) #define mplrs_init_lrs_main lrsv2_main #endif /* singly linked list */ typedef struct slist { void *data; struct slist *next; } slist; typedef struct outlist { char *type; char *data; struct outlist *next; } outlist; /* A linked-list of buffers for MPI communications. * req[0...count-1] correspond to buf[0...count-1] * * When req[i] completes, should free buf[i]. * When all reqs complete, should free buf, req, tags,sizes,types. */ typedef struct msgbuf { MPI_Request *req; void **buf; int count; int target; int data; /* optional, use yourself if needed for something */ int queue; /* if 1, send items 1...count after 0 has completed */ /* queue pointers must be NULL or something free()able */ int *tags; /* tags to use on items 1...count if queued */ int *sizes; /* sizes of sends if queued */ MPI_Datatype *types; /* types of sends if queued */ struct msgbuf *next; } msgbuf; /* A structure containing the state of this process. * Each process has one. */ typedef struct mplrsv { /* MPI communication buffers */ msgbuf *outgoing; slist *cobasis_list; long (*lrs_main)(int, char **, lrs_dic **, lrs_dat **, long, long, char *, lrs_restart_dat *); lrs_dic *P; lrs_dat *Q; lrs_restart_dat *R; int caughtsig; /* flag for catching a signal */ unsigned int abortinit; /* lrs_main stage 0 (setup) failed? */ unsigned int overflow; /* 0: lrslong 1:lrslong2 2:lrsgmp */ /* counts */ unsigned long long rays; unsigned long long vertices; unsigned long long bases; unsigned long long facets; unsigned long long linearities; unsigned long long intvertices; unsigned long long deepest; unsigned long long nredundcol; lrs_mp Tnum, Tden, tN, tD, Vnum, Vden; struct timeval start, end; /* MPI info */ int rank; /* my rank */ int size; /* number of MPI processes */ int my_tag; /* to distinguish MPI sends */ char host[MPI_MAX_PROCESSOR_NAME]; /* name of this host */ /* output_list */ outlist *output_list; outlist *ol_tail; char *finalwarn; /* for process_output "finalwarn" */ int finalwarn_len; /* length allocated for finalwarn */ char *curwarn; /* to discard "finalwarn" messages on */ int curwarn_len; /* overflow, preventing duplicates */ /* for convenience */ const char *tfn_prefix; char *tfn; FILE *tfile; int initializing; /* in phase 1? */ int countonly; /* countonly */ int outnum; /* number of output lines buffered */ int maxbuf; /* maximum number of output lines to buffer before flush */ int outputblock; /* temporarily prevent a maxbuf-based output flush */ int redund; /* bool: is this a redund run? */ char *input_filename; /* input filename */ char *input; /* buffer for contents of input file */ } mplrsv; /* A structure for variables only the master needs */ typedef struct masterv { slist *cobasis_list; /* list of work to do (L) */ unsigned long tot_L; /* total size of L (total # jobs) */ unsigned long size_L; /* current size of L (for histograms * and scaling) */ unsigned long num_empty; /* number of times L became empty */ unsigned int num_producers; /* number of producers running */ unsigned int *act_producers; /* whether each producer owes us * remaining bases message. * Needed only for histograms. */ unsigned int live_workers; /* number that haven't exited */ /* MPI communication buffers */ int *workin; /* incoming messages from producers desiring work */ MPI_Request *mworkers; /* MPI_Requests for these messages */ msgbuf *incoming; /* incoming cobases from producers */ float *sigbuf; /*incoming signal/termination requests*/ MPI_Request *sigcheck; /* MPI_Requests for reporting these*/ int checkpointing; /* are we checkpointing now? */ int cleanstop; /* was a cleanstop requested? */ int messages; /* do we want to set R->messages? */ /* user options */ unsigned int lmin; /* option -lmin */ unsigned int lmax; /* option -lmax */ int orig_lmax; /*user changed lmax? if not,lmax=lmin*/ unsigned int scalec; /* option -scale*/ unsigned int initdepth; /* option -id */ unsigned int maxdepth; /* option -maxd */ unsigned int maxcobases; /* option -maxc */ unsigned int time_limit; /* option -time */ unsigned long maxncob; /* option -stopafter */ int lponly; /* bool for -lponly option */ int redund; /* bool for -redund option */ int max_redundworker; /* max id for a worker * used if m>np-2 */ /* files */ char *hist_filename; /*histogram filename (or NULL)*/ FILE *hist; int doing_histogram; /* are we doing a histogram? */ char *freq_filename; /*are we outputting sub-problem sizes?*/ FILE *freq; char *restart_filename; /* restart from a checkpoint */ FILE *restart; char *checkp_filename; /* filename to save checkpoint*/ FILE *checkp; char *stop_filename; /* option -stop */ FILE *stop; FILE *input; } masterv; /* A structure for variables only the consumer needs */ typedef struct consumerv { /* MPI communication buffers */ /* for headers */ MPI_Request *prodreq; /* consumer keeps an open request * for each producer and master */ int *prodibf; /* and two ints as a receive buffer */ /* for content */ msgbuf *incoming; /* incoming MPI communication buffers */ /* output */ char *output_filename; /* output filename (or NULL) */ FILE *output; /* output file (NULL for stdout) */ /* status */ unsigned int num_producers; /* number of producers still going */ /* other */ unsigned int oflow_flag; /* 0: no overflow message yet */ int *overflow; /* number of overflowed workers*/ int waiting_initial; /* waiting for initial producer, * hold output until after 'begin' */ int final_print; /* do the final print? (bool) */ long *redineq; /* bool vector for redund, which rows redundant */ int final_redundcheck; /* are we in the final redund check? */ } consumerv; /* MASTER and CONSUMER and INITIAL must be different */ #define MASTER 0 /* the MPI process that becomes master */ #define CONSUMER 1 /* the MPI process that becomes consumer */ #define INITIAL 2 #define CHECKFLAG -3 /* must be distinct negative values */ #define RESTARTFLAG -4 #define STOPFLAG -5 /* define MDEBUG to get many mplrs debug messages */ #ifdef MDEBUG #define mprintf(a) printf a #else #define mprintf(a) #endif /* define MDEBUG2 to get even more */ #ifdef MDEBUG2 #define mprintf2(a) printf a #else #define mprintf2(a) #endif /* define MDEBUG3 to get lots */ #ifdef MDEBUG3 #define mprintf3(a) printf a #else #define mprintf3(a) #endif /* function prototypes */ void mplrs_init(int, char **); void mplrs_caughtsig(int); void master_sendfile(void); void mplrs_initstrucs(); void mplrs_commandline(int, char **); void mplrs_initfiles(void); void bad_args(void); int mplrs_fallback(void); int mplrs_master(void); void send_work(int, int); void recv_producer_lists(void); void process_returned_cobases(msgbuf *); void setparams(int *); void check_stop(void); void master_stop_consumer(int); void master_checksigs(void); void master_restart(void); void master_checkpoint(void); void master_checkpointfile(void); void master_checkpointconsumer(void); void print_histogram(struct timeval *, struct timeval *); int mplrs_worker(void); void mplrs_worker_init(void); void clean_outgoing_buffers(void); /* shared with master */ void do_work(const int *, char *); void worker_report_overflow(void); void process_output(void); void process_curwarn(void); void send_output(int, char *); void process_cobasis(const char *); slist *addlist(slist *, void *); void return_unfinished_cobases(void); char *append_out(char *, int *, const char *); int mplrs_worker_finished(void); int mplrs_consumer(void); void consumer_start_incoming(void); msgbuf *consumer_queue_incoming(int *, int); void consumer_proc_messages(void); int consumer_checkpoint(void); int outgoing_msgbuf_completed(msgbuf *); void free_msgbuf(msgbuf *); outlist *reverse_list(outlist*); void send_master_stats(void); void recv_master_stats(void); void send_counting_stats(int); void recv_counting_stats(int); void initial_print(void); void phase1_print(void); void consumer_setredineq(void); void final_print(void); char *dupstr(const char *str); int okay_to_flush(void); void post_output(const char *, const char *); void open_outputblock(void); void close_outputblock(void); void mplrs_cleanstop(int); void mplrs_emergencystop(const char *); void overflow_cleanup(void); void set_restart(const int *, char *); #endif /* MPLRSH */ lrslib-071a/nashdemo.c0000700060175606010010000000330213742506301014570 0ustar avisなし/*********************************************************/ /* nashdemo is a simple template for lrsnashlib.c */ /* */ /* It builds two 3x4 matrices A B and computes */ /* their equilibria */ /*********************************************************/ /* Compile: gcc -O3 -o nashdemo nashdemo.c lrsnashlib.c lrslib.c lrsgmp.c -lgmp -DGMP Usage: nashdemo */ #include #include #include #include "lrsdriver.h" #include "lrslib.h" #include "lrsnashlib.h" int main() { long s,t; game Game; // Storage for one game game *g = &Game; gInfo GI= {.name="Game"}; // Input file name could go here if there is one g->aux = &GI; if ( !lrs_init ("\n*nashdemo:")) // Done once but essential for lrslib usage ! return 1; g->nstrats[ROW]=3; // row player g->nstrats[COL]=4; // col player setFwidth(g,4); // field length for printing games for(s=0;s<3;s++) // Game 1: load payoff matrices with some integers for(t=0;t<4;t++) { g->payoff[s][t][ROW].num=s+t; g->payoff[s][t][COL].num=s*t; g->payoff[s][t][ROW].den=1; g->payoff[s][t][COL].den=1; } printGame(g); lrs_solve_nash(g); for(s=0;s<3;s++) // Game 2: load payoff matrices with some rationals for(t=0;t<4;t++) { g->payoff[s][t][ROW].num=s+t; g->payoff[s][t][COL].num=1; g->payoff[s][t][ROW].den=2; g->payoff[s][t][COL].den=3; } printGame(g); lrs_solve_nash(g); return 0; } lrslib-071a/plotD.gp0000700060175606010010000000105513742506306014250 0ustar avisなしset terminal postscript landscape enhanced color set output 'plotD.ps' set yzeroaxis set boxwidth 50 set title "Frequency distribution of subtree sizes" set xlabel "Size of subtree" set ylabel "Frequency" set style fill solid 1.0 noborder bin_width = 1; bin_number(x) = floor(x/bin_width) rounded(x) = bin_width * ( bin_number(x) ) plot [0:*] 'freq' using (rounded($1)):(1) smooth frequency with boxes set title "Frequency distribution of subtree sizes up to 100 nodes" set boxwidth 1 plot [0:100] 'freq' using (rounded($1)):(1) smooth frequency with boxes lrslib-071a/plotL.gp0000700060175606010010000000051613742506302014255 0ustar avisなしset terminal postscript landscape enhanced color set output 'plotL.ps' set autoscale set title "Number of cores vs time" set xlabel "time (secs)" set ylabel "cores" plot 'hist' using 1:2 set title "Size of job list L vs time" set ylabel "L" plot 'hist' using 1:3 set title "Requests vs time" set ylabel "cores" plot 'hist' using 1:4 lrslib-071a/rat2float.c0000700060175606010010000000741113742506306014702 0ustar avisなし/* * Reads a polyhedron file on stdin , with rationals and outputs * an approximation in decimal floating point * * David Bremner. bremner@cs.mcgill.ca * */ /* Hacked by DA, April 20 2006 * * first argument overides stdin * if column 0=0 then first non zero column scaled to +/-1 (otherwise big ugly integers come out) */ static char rcsid[]="$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 mplrs -redund filename 2020.4.27 Changes in mplrs relative to 7.0: 1. All C++ code removed or rewritten in C; C++ compiler no longer required. 2. mplrs uses the new lrslib API (2019.11.8) instead of temporary files for parallel jobs. 3. Support for parallel redund runs using the redund option in input files. 4. Compiler warnings removed. 5. Additional warning and informational messages printed when relevant. 6. New option -redund, for redund runs without adding option to file. 7. Avoid duplicate output lines that were possible on an overflow in hybrid mode. 8. Fix a rare bug that could omit output lines at the start of a run. 2020.2.5 The extract option is a preprocessing step to remove linearities (if any) and resize the A matrix using standard lrs processing, which is output as a valid lrs input file. The resulting file will not contain any equations but may not be full dimensional. Options in the input file are stripped. User can specify the cols to retain (where this possible by linear independence). If there are no linearities in the input file the columns in the option are retained and the other ones are deleted. This is useful for projecting a V-representation. extract 0 retains columns in order 1,2,...,n extract k i1 .. ik retains columns in order i1,...,ik then the missing 1..n as necessary Column 0 is always retained. Use redund to remove redundancies from the output as necessary. A full lrs run is not performed, however output can be piped: % lrs file | redund | lrs 2019.12.30 hvref makes a cross reference list between H and V reps Usage (same for ext file): Add printcobasis and incidence options to cube.ine % lrs cube.ine cube.ext % xref cube.ext Edit the output file cube.ext.x so that the second line contains two integers rows maxindex where rows >= # output lines in cube.ext.x maxindex >= # input lines in cube.ine or just use 0 0 and the program will tell you which values to use % hvref cube.ext.x 2019.11.8 New redund option causes lrs to perform redund function: redund start end limits redundancy checking to input rows numbered start,...,end. Defaults start=1 and end=m is legacy redund and can be obtained by redund 0 0 lrs_main has been rewritten as lrsv2_main to avoid temporary files in mplrs. It now passes pointers to P and Q back to mplrs and is called 3 times according to the stage flag. stage=0 performs problem setup and reads the input file stage=1 performs reverse search or redund function stage=2 performs clean up and closes files 2019.6.13 If lrs is compiled with -DLRS_QUIET lrs produces an ouput file with only the data between the begin and end lines, ie. a matrix of the V or H representation. The only exception is if the input is a V-rep and output has linearities in which case line one has the linearity information -------------------------------------------------------------------------------------- 2019.1.5 Various pivot rules are implemented for solving LPs using variations of the lponly option. To get pivot counts correct it is best to use lrsgmp at least for now lponly default, currently Dantzig's rule lponly_b Bland's rule, which is used for vertex enumeration lponly_d Dantzig's rule, the only rule used up to Version 7.1 lponly_r random edge rule lponly_rd alernates random edege and Dantzig ----------------------------------------------------------------------------- 2018.7.1 Version 7.0 (lrslib-070) User's guide: http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE70.html Recommended makes: %make # lrs,redund(hybrid arithmetic), lrsgmp, redundgmp %make mplrs # mplrs(hybrid arithmetic), mplrsgmp 1. hybrid (64bit/128bit/GMP) arithmetic implemented: speedups of roughly 3-5 times (64bit) and 2 times(128bit) over GMP for problems using small integers. 2. overflow checking for 64/128 bit arithmetic 3. __int128 (gcc v.4.6.0 or later) and FLINT arithmetic now supported 4. lrsgmp, mplrsgmp uses only GMP arithmetic, same as lrslib-062 5. lrs/redund/mplrs start in 64 bit moving to 128 bit and then to gmp arithmetic as necessary 6. single arithmetic versions of lrs/mplrs available for comparison purposes 7. single arithmetic versions of lrsnash are available with overflow checking 8. plrs is no longer supported 9. removing the -DSAFE option disables overflow checking in 64/128 bit mode and results are unpredicable if overflow occurs 10. mplrs now prints maximum tree depth at end and supports printcobasis option in input files Shared library: To make just the shared library, and appropriate symlinks, % make liblrs.o This is a *multiarithmatic* library that contains the lrslib API suffixed with _1, _2, and _gmp. To use as a replacement for the old liblrsgmp.so, use CFLAGS+= "-DGMP -DMA" The -DMA is new, and enables rewriting of your existing function call lrs_foo(...) to lrs_foo_gmp(...). This is C preprocessor macros, and is optional, you can also call the _1, _2, and _gmp versions directly. ----------------------------------------------------------------------------- 2016.5.27 Several changes to mplrs: 1. New command-line options -countonly, -stopafter , -maxbuf . 2. Volume output. 3. Counting statistics on number of jobs, size of L, number of times empty changed to longs. 4. Performance improvements for problems with large outputs. ----------------------------------------------------------------------------- 2016.3.28 Changed default to 64-bit arithmetic when using lrslong and lrsmp arithmetic. For 32bit machines a -DB32 compile flag is now required for make allmp and for compiles of lrs1/mplrs1/plrs1. ----------------------------------------------------------------------------- 2016.1.18 countonly option follows the end line and suppresses output of vertices/rays/facets 2015.11.20 Current version is lrslib-061 Version 6.1 1. Contains lrsnash.c and lrsnashlib.c replacing nash.c with a library version and simpler interface that does not require setupnash. Big thanks to Terje Lensberg for this. nashdemo.c is a very basic template for setting up games and calling the library function lrs_solve_nash(game *g). To compile: % make lrsnash you get binaries lrsnash and nashdemo. % nashdemo just runs the demo, no parameters % lrsnash game finds the equlibrium for game, which is in setupnash format (recommended!) % lrsnash game1 game2 finds the equilibrium for the same game in legacy nash format The usersguide will be updated in due course 2. mplrs, plrs, lrs had some memory leaks and a few other issues that are fixed in this release (hopefully and thankfully) -------------------------------------------------------------------------------- 2015.10.10 memory leak in nash fixed 2015.10.3 OpenMPI has memory leaks in version 1.8.6. We tested mplrs with version 1.10.0 and found no leaks. 2015.9.16 Bug in nash caused by duplicated rows and columns fixed 2015.9.14 Fixed some lrs memory leaks caused by nonnegative and linearity output 2015.7.13 This a major revision of lrslib which contains mplrs.c, the MPI parallel version of lrs written by Skip Jordan and derived from plrs which was written by Gary Roumanis. Tests of mplrs on Tsubame2 with up to 1200 cores by Kazuki Yoshizoe show near linear speedups. lrs has some new options which are primarily for use by mplrs. To install mplrs see: http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html#mplrs You will need an MPI library and mpic++ installed. If you feel lucky try: % make mplrs Defalut usage: % mpirun -np p mplrs [ ] where p>3 is the number of core to be used. If you use openmpi the hosts available and slots on each host may be in /usr/local/etc/openmpi-default-hostfile Other options available are described in http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html#mplrs In particular plots can be made during the mplrs run of the job queue length, number of processors active etc. The makefile was modified by David Bremner. Please direct any complaints to bremner@unb.ca New option: maxcobases n After maxbases have been generated the cobases of the unexplored subtrees are reported. Each of these can be restarted as a separate lrs run with suitable mindepth option set ------------------------------------------------------------------------------ Older versions 2014.12.4 With gcc 4.8 plrs does not compile. Changed memory ordering (plrs.cpp line 168) from plrs_output* consume_list = output_list.exchange(0,boost::memory_order_consume); to plrs_output* consume_list = output_list.exchange(0,boost::memory_order_acquire); For more details see here: https://bitsharestalk.org/index.php?topic=15.msg14109#msg14109 To get plrsmp to compile I converted the length macro to a function call (conflict with str1.length in lrslib.c line 2792) 2014.12.2 From version 1.56.0 the boost library contains the Atomic library, so boost_atomic is no longer included in the lrs distribution. The instructions below for installing plrs are now simpler. ----------------------------------------------------------------------------- 2014.9.27 lrslib-050 released lrslib-050 contains a multi-thread version of lrs called plrs. The input/output files for plrs are the same as for lrs, however plrs is intended just for vertex or facet enumeration, and other functionality of lrs is not available. Usage is % plrs [ ] [ -mt ] [ -id ] -mt specifies the number parallel threads calling lrs (default 12) -id specifies the initial depth of the RS tree to generate before parallelization (default 5) Setup instructions for plrs. Use version 1.57.0 or later of the boost libary 1. Install boost library from http://www.boost.org/ into prefix/boost157 If you have root permission, prefix=/usr/include (or just do not specify it) However you can install boost locally wherever you like. Instructions for installing the library are located here http://www.boost.org/doc/libs/1_57_0/more/getting_started/unix-variants.html. Look at section 5 for an easy install. ***Important: make a note of the path given at the end of the install process **** 2. Update the makefile to include the paths you recorded in step 1. "make plrs" will make plrs with the gmp library (assuming the gmp library is already installed on that machine). "make plrsmp" will make plrs with the standard lrsmp arithmetic library and plrs1 with the long integer library. ------------------------------------------------------------------------------- 2013.5.22 modification to printcobasis so that the objective value is printed ------------------------------------------------------------------------------ 2012.9.27 initial release of multithread version of lrs called plrs that uses a wrapper written by Gary Roumanis. It needs the Boost libraries at http://www.boost.org plrs setup instructions are in the file readme_plrs I regret that I cannot give any additional support for the correct installation of boost libraries. Note: makefile has now changed so that make all gives gmp arithmetic library make allmp uses native mp arithmetic if gmp not available ----------------------------------------------------------------------------- 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-071a/redund0000777060175606010010000000000013742506302014564 2lrsustar avisなしlrslib-071a/redundgmp0000777060175606010010000000000013742506301015773 2lrsgmpustar avisなしlrslib-071a/setupnash.c0000700060175606010010000000666313742506306015026 0ustar avisなし#include #include #include "lrsdriver.h" #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 "lrsdriver.h" #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 "lrsdriver.h" #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;j! $1.x perl -nle 'print $1 if /s (.+?)I/' $1 |sed 's/ ://'|sed 's/[^ ]*\* //' | sed 's/$/ #/'| nl >> $1.x