//----------------------------------------------------------------------------------------//
// 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;
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 iteratereversesearch(lrs_dic *P, lrs_dat *Q, lrs_mp_vector output, long* startingcobasis, long** bases)
{
printf("\nRunning reverse search with the starting cobasis: ");
int i;
for (i=0; i<P->d; i++) {
printf("%ld ", startingcobasis[i]);
}
Q->printcobasis = TRUE;
Q->givenstart = TRUE;
readfacets (Q, Q->inequality);
long prune = FALSE;
long col;
int basesindex = 0;
int maxnbases = 0;
do
{
prune=lrs_checkbound(P,Q);
if (!prune)
{
long temp[P->d];
for (col = 0; col <= P->d; col++)
{
lrs_getsolution_helper(P, Q, output, col, temp);
if (lrs_getsolution (P, Q, output, col))
{
lrs_printoutput (Q, output);
}
}
for (i=0; i<P->d; i++) {
bases[basesindex][i] = temp[i];
}
}
basesindex++;
maxnbases++;
}
while (!Q->lponly && lrs_getnextbasis (&P, Q, prune));
return maxnbases;
}
int
main (int argc, char *argv[])
{
lrs_dic *P1,*P2; /* structure for holding current dictionary and indices */
lrs_dat *Q1,*Q2; /* structure for holding static problem data */
lrs_mp_vector output1; /* holds one line of output; ray,vertex,facet,linearity */
lrs_mp_vector output2; /* holds one line of output; ray,vertex,facet,linearity */
lrs_mp_matrix Lin; /* holds input linearities if any are found */
lrs_dic *P2orig; /* we will save player 2's dictionary in getabasis */
long col; /* output column index for dictionary */
long startcol = 0;
long prune = FALSE; /* if TRUE, getnextbasis will prune tree and backtrack */
long numequilib=0; /* number of nash equilibria found */
long oldnum=0;
/* global variables lrs_ifp and lrs_ofp are file pointers for input and output */
/* they default to stdin and stdout, but may be overidden by command line parms. */
if(argc <= 2 )
{ printf("Usage: nash input1 input2 [outputfile] \n");
return 1;
}
/***************************************************
Step 0:
Do some global initialization that should only be done once,
no matter how many lrs_dat records are allocated. db
***************************************************/
if ( !lrs_init ("\n*nash:"))
return 1;
printf(AUTHOR);
/*********************************************************************************/
/* Step 1: Allocate lrs_dat, lrs_dic and set up the problem */
/*********************************************************************************/
Q1 = lrs_alloc_dat ("LRS globals"); /* allocate and init structure for static problem data */
if (Q1 == NULL)
return 1;
Q1->nash=TRUE;
if (!lrs_read_dat (Q1, argc, argv)) /* read first part of problem data to get dimensions */
return 1; /* and problem type: H- or V- input representation */
P1 = lrs_alloc_dic (Q1); /* allocate and initialize lrs_dic */
if (P1 == NULL)
return 1;
if (!lrs_read_dic (P1, Q1)) /* read remainder of input to setup P1 and Q1 */
return 1;
output1 = lrs_alloc_mp_vector (Q1->n + Q1->m); /* output holds one line of output from dictionary */
fclose(lrs_ifp);
/* allocate and init structure for player 2's problem data */
printf ("\n*Second input taken from file %s\n", argv[2]);
Q2 = lrs_alloc_dat ("LRS globals");
if (Q2 == NULL)
return 1;
Q2->nash=TRUE;
if (!lrs_read_dat (Q2, 2, argv)) /* read first part of problem data to get dimensions */
return 1; /* and problem type: H- or V- input representation */
if (Q2->nlinearity > 0)
free(Q2->linearity); /* we will start again */
Q2->linearity = CALLOC ((Q2->m + 2), sizeof (long));
P2 = lrs_alloc_dic (Q2); /* allocate and initialize lrs_dic */
if (P2 == NULL)
return 1;
if (!lrs_read_dic (P2, Q2)) /* read remainder of input to setup P2 and Q2 */
return 1;
output2 = lrs_alloc_mp_vector (Q1->n + Q1->m); /* output holds one line of output from dictionary */
P2orig = lrs_getdic(Q2); /* allocate and initialize lrs_dic */
if (P2orig == NULL)
return 1;
copy_dict(Q2,P2orig,P2);
fprintf (lrs_ofp, "\n***** %ld %ld rational", Q1->n, Q2->n);
/*********************************************************************************/
/* Step 2: Find a starting cobasis from default of specified order */
/* P1 is created to hold active dictionary data and may be cached */
/* Lin is created if necessary to hold linearity space */
/* Print linearity space if any, and retrieve output from first dict. */
/*********************************************************************************/
if (!lrs_getfirstbasis (&P1, Q1, &Lin, TRUE))
return 1;
if (Q1->dualdeg)
{
printf("\n*Warning! Dual degenerate, ouput may be incomplete");
printf("\n*Recommendation: Add dualperturb option before maximize in first input file\n");
}
if (Q1->unbounded)
{
printf("\n*Warning! Unbounded starting dictionary for p1, output may be incomplete");
printf("\n*Recommendation: Change/remove maximize option, or include bounds \n");
}
/* Pivot to a starting dictionary */
/* There may have been column redundancy */
/* If so the linearity space is obtained and redundant */
/* columns are removed. User can access linearity space */
/* from lrs_mp_matrix Lin dimensions nredundcol x d+1 */
if (Q1->homogeneous && Q1->hull)
startcol++; /* col zero not treated as redundant */
for (col = startcol; col < Q1->nredundcol; col++) /* print linearity space */
lrs_printoutput (Q1, Lin[col]); /* Array Lin[][] holds the coeffs. */
/*********************************************************************************/
/* Step 3: Terminate if lponly option set, otherwise initiate a reverse */
/* search from the starting dictionary. Get output for each new dict. */
/*********************************************************************************/
/* We initiate reverse search from this dictionary */
/* getting new dictionaries until the search is complete */
/* User can access each output line from output which is */
/* vertex/ray/facet from the lrs_mp_vector output */
/* prune is TRUE if tree should be pruned at current node */
do
{
prune=lrs_checkbound(P1,Q1);
if (!prune && lrs_getsolution (P1, Q1, output1, col))
{
oldnum=numequilib;
nash2_main(argc,argv,P1,Q1,P2orig,Q2,&numequilib,output2);
if (numequilib > oldnum || Q1->verbose)
{
if(Q1->verbose)
prat(" \np2's obj value: ",P1->objnum,P1->objden);
lrs_nashoutput (Q1, output1, 1L);
fprintf (lrs_ofp, "\n");
}
}
}
while (lrs_getnextbasis (&P1, Q1, prune));
fprintf(lrs_ofp,"\n*Number of equilibria found: %ld",numequilib);
fprintf (lrs_ofp,"\n*Player 1: vertices=%ld bases=%ld pivots=%ld", Q1->count[1], Q1->count[2],Q1->count[3]);
fprintf (lrs_ofp,"\n*Player 2: vertices=%ld bases=%ld pivots=%ld", Q2->count[1], Q2->count[2],Q2->count[3]);
lrs_clear_mp_vector(output1, Q1->m + Q1->n);
lrs_clear_mp_vector(output2, Q1->m + Q1->n);
lrs_free_dic (P1,Q1); /* deallocate lrs_dic */
lrs_free_dat (Q1); /* deallocate lrs_dat */
/* 2006.10.10 not sure what is going on with three lines below - sometimes crashes */
/* Q2->Qhead = P2; */ /* reset this or you crash free_dic */
/* lrs_free_dic (P2,Q2); */ /* deallocate lrs_dic */
/* lrs_free_dat (Q2); */ /* deallocate lrs_dat */
lrs_close ("nash:");
return 0;
}
struct GMPmat *V2H(struct GMPmat *inp) /* This function is untested */
{
lrs_dic *P;
lrs_dat *Q;
lrs_mp_vector output;
lrs_mp_matrix Lin;
long i;
long col;
assert( my_lrs_init () == 0 );
Q = lrs_alloc_dat ("LRS globals");
assert ( Q != NULL );
Q->m = GMPmat_Rows(inp);
Q->n = GMPmat_Cols(inp);
Q->hull = TRUE;
Q->polytope = TRUE;
output = lrs_alloc_mp_vector (Q->n);
lrs_mp_vector num, den;
num = lrs_alloc_mp_vector(GMPmat_Cols(inp));
den = lrs_alloc_mp_vector(GMPmat_Cols(inp));
P = lrs_alloc_dic (Q);
assert ( P != NULL );
struct GMPmat *retMat;
retMat = GMPmat_create(0, GMPmat_Cols(inp), 1);
mpq_t *curRow;
curRow = calloc(GMPmat_Cols(inp), sizeof(mpq_t));
assert( curRow != NULL );
mpq_row_init(curRow, GMPmat_Cols(inp));
for (i = 1; i <= GMPmat_Rows(inp); ++i)
{
GMPmat_getRow(num, den, inp, i-1);
lrs_set_row_mp(P ,Q ,i ,num ,den , GE);
}
assert ( lrs_getfirstbasis (&P, Q, &Lin, TRUE) );
for (col = 0L; col < Q->nredundcol; col++)
lrs_printoutput (Q, Lin[col]);
do
{
for (col = 0; col <= P->d; col++)
if (lrs_getsolution (P, Q, output, col)){
mpz_to_mpq(curRow, output, GMPmat_Cols(retMat));
retMat = GMPmat_appendRow(retMat, curRow);
GMPmal_everyNrows(retMat, pN, "inequalities");
}
}
while (lrs_getnextbasis (&P, Q, FALSE));
mpq_row_clean( curRow, GMPmat_Cols(retMat) );
lrs_clear_mp_vector ( output, Q->n);
lrs_clear_mp_vector ( num, Q->n);
lrs_clear_mp_vector ( den, Q->n);
lrs_free_dic ( P , Q);
lrs_free_dat ( Q );
GMPmat_destroy(inp);
return retMat;
}
struct GMPmat *H2V(struct GMPmat *inp)
{
lrs_dic *Pv, *Ph; /* structure for holding current dictionary and indices */
lrs_dat *Qv, *Qh; /* 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 */
size_t i, j, cols, rows;
long col; /* output column index for dictionary */
/* Global initialization - done once */
assert( my_lrs_init () == 0 );
Qv = lrs_alloc_dat ("LRS globals");
assert( Qv!= NULL );
Qv->m = GMPmat_Rows(inp);
Qv->n = GMPmat_Cols(inp);
output = lrs_alloc_mp_vector (Qv->n);
lrs_mp_vector num, den;
num = lrs_alloc_mp_vector(GMPmat_Cols(inp));
den = lrs_alloc_mp_vector(GMPmat_Cols(inp));
Pv = lrs_alloc_dic (Qv); /* allocate and initialize lrs_dic */
assert( Pv != NULL );
struct GMPmat *Helper;
Helper = GMPmat_create(0, GMPmat_Cols(inp), 1);
mpq_t *curRow;
curRow = calloc(GMPmat_Cols(inp), sizeof(mpq_t));
assert( curRow != NULL );
mpq_row_init(curRow, GMPmat_Cols(inp));
for (i = 1; i <= GMPmat_Rows(inp); ++i)
{
GMPmat_getRow(num, den, inp, i-1);
lrs_set_row_mp(Pv,Qv,i,num,den,GE);
}
assert( lrs_getfirstbasis (&Pv, Qv, &Lin, TRUE) );
for (col = 0L; col < Qv->nredundcol; col++) /* print linearity space */
lrs_printoutput (Qv, Lin[col]);
do
{
for (col = 0L; col <= Pv->d; col++)
if (lrs_getsolution (Pv, Qv, output, col)) {
mpz_to_mpq(curRow, output, GMPmat_Cols(Helper));
Helper = GMPmat_appendRow(Helper, curRow);
GMPmal_everyNrows(Helper, pN, "vertices/rays");
}
}
while (lrs_getnextbasis (&Pv, Qv, FALSE));
mpq_row_clean(curRow, GMPmat_Cols(Helper));
lrs_clear_mp_vector (output, Qv->n);
lrs_clear_mp_vector (num, Qv->n);
lrs_clear_mp_vector (den, Qv->n);
lrs_free_dic (Pv,Qv); /* deallocate lrs_dic */
lrs_free_dat (Qv); /* deallocate lrs_dat */
// lrs_close ("lrsTrial:");
GMPmat_destroy(inp);
return Helper;
}
struct GMPmat *projection(struct GMPmat *inp, int d)
{
lrs_dic *Pv, *Ph; /* structure for holding current dictionary and indices */
lrs_dat *Qv, *Qh; /* 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 */
size_t i, j, cols, rows;
long col; /* output column index for dictionary */
/* Global initialization - done once */
assert( my_lrs_init () == 0 );
Qv = lrs_alloc_dat ("LRS globals");
assert( Qv!= NULL );
Qv->m = GMPmat_Rows(inp);
Qv->n = GMPmat_Cols(inp);
output = lrs_alloc_mp_vector (Qv->n);
lrs_mp_vector num, den;
num = lrs_alloc_mp_vector(GMPmat_Cols(inp));
den = lrs_alloc_mp_vector(GMPmat_Cols(inp));
Pv = lrs_alloc_dic (Qv); /* allocate and initialize lrs_dic */
assert( Pv != NULL );
struct GMPmat *Helper;
Helper = GMPmat_create(0, GMPmat_Cols(inp), 1);
mpq_t *curRow;
curRow = calloc(GMPmat_Cols(inp), sizeof(mpq_t));
assert( curRow != NULL );
mpq_row_init(curRow, GMPmat_Cols(inp));
for (i = 1; i <= GMPmat_Rows(inp); ++i)
{
GMPmat_getRow(num, den, inp, i-1);
lrs_set_row_mp(Pv,Qv,i,num,den,GE);
}
assert( lrs_getfirstbasis (&Pv, Qv, &Lin, TRUE) );
for (col = 0L; col < Qv->nredundcol; col++) /* print linearity space */
lrs_printoutput (Qv, Lin[col]);
do
{
for (col = 0L; col <= Pv->d; col++)
if (lrs_getsolution (Pv, Qv, output, col)) {
mpz_to_mpq(curRow, output, GMPmat_Cols(Helper));
Helper = GMPmat_appendRow(Helper, curRow);
GMPmal_everyNrows(Helper, pN, "vertices/rays");
}
}
while (lrs_getnextbasis (&Pv, Qv, FALSE));
mpq_row_clean(curRow, GMPmat_Cols(Helper));
lrs_clear_mp_vector (output, Qv->n);
lrs_clear_mp_vector (num, Qv->n);
lrs_clear_mp_vector (den, Qv->n);
lrs_free_dic (Pv,Qv); /* deallocate lrs_dic */
lrs_free_dat (Qv); /* deallocate lrs_dat */
Helper = reducevertices(Helper);
Qh = lrs_alloc_dat ("LRS globals");
assert( Qh != NULL );
Qh->m = GMPmat_Rows(Helper);
Qh->n = GMPmat_Cols(Helper) - d;
Qh->hull = TRUE; /* convex hull problem: facet enumeration */
Qh->polytope = TRUE; /* input is a polytope */
output = lrs_alloc_mp_vector (Qh->n);
num = lrs_alloc_mp_vector (Qh->n);
den = lrs_alloc_mp_vector (Qh->n);
Ph = lrs_alloc_dic (Qh);
assert( Ph != NULL );
struct GMPmat *retVal;
retVal = GMPmat_create(0, Qh->n, 0);
rows = GMPmat_Rows (Helper);
cols = GMPmat_Cols (retVal);
curRow = calloc(cols, sizeof(mpq_t));
assert( curRow != NULL );
mpq_row_init(curRow, cols);
mpq_t curVal;
mpq_init(curVal);
for (i = 0; i < rows; ++i)
{
for (j = 0; j < cols; ++j)
{
GMPmat_getValue (curVal, Helper, i, j);
mpz_set (num[j], mpq_numref(curVal));
mpz_set (den[j], mpq_denref(curVal));
}
lrs_set_row_mp (Ph, Qh, i+1 ,num, den, GE);
}
mpq_clear(curVal);
assert( lrs_getfirstbasis (&Ph, Qh, &Lin, TRUE) );
for (col = 0L; col < Qh->nredundcol; col++) /* print linearity space */
lrs_printoutput (Qh, Lin[col]);
do
{
for (col = 0L; col <= Ph->d; col++)
if (lrs_getsolution (Ph, Qh, output, col)){
mpz_to_mpq(curRow, output, GMPmat_Cols(retVal));
retVal = GMPmat_appendRow(retVal, curRow);
GMPmal_everyNrows(retVal, pN, "inequalities");
}
}
while (lrs_getnextbasis (&Ph, Qh, FALSE));
GMPmat_destroy(Helper);
mpq_row_clean(curRow, GMPmat_Cols(retVal));
lrs_clear_mp_vector (output, Qh->n);
lrs_clear_mp_vector (num, Qh->n);
lrs_clear_mp_vector (den, Qh->n);
lrs_free_dic (Ph,Qh);
lrs_free_dat (Qh);
// lrs_close ("lrsTrial:");
printf ("\n");
GMPmat_destroy(inp);
return retVal;
}
