void
find_interior_DS(int nlhs, mxArray * plhs[], int nrhs, const mxArray * prhs[])
{
/* uses Dual Simplex method */
/* We would like to find an iterior point
for a polyhedron in H representation
A x <= b.
*/
dd_ErrorType error=dd_NoError;
dd_LPSolverType solver=dd_DualSimplex;
dd_LPPtr lp, lp1; /* pointer to LP data structure that is not visible by user. */
dd_MatrixPtr A;
int j;
dd_set_global_constants(); /* First, this must be called once to use cddlib. */
/* Input an LP using the cdd library */
/* lp = MB_get_LP_MatrixPtr(prhs[0]); */
if (A=FT_get_H_MatrixPtr(prhs[0])) {
/* set objective */
A->objective = dd_LPmin;
for (j = 0; j < A->colsize; j++)
dd_set_d(A->rowvec[j],0.0);
lp=dd_Matrix2LP(A, &error);
dd_FreeMatrix(A);
}else{
mexErrMsgTxt("Error in the setting of LP matrix.");
}
lp1=dd_MakeLPforInteriorFinding(lp);
dd_LPSolve(lp1,solver,&error);
if (error!=dd_NoError) dd_WriteErrorMessages(stdout, error);
/* Take the solution. */
plhs[0] = MB_set_LPsol_MatrixPtr(lp1);
/* Free allocated spaces. */
dd_FreeLPData(lp);
dd_FreeLPData(lp1);
}
int main(int argc, char *argv[])
{
/* The original LP data m x n matrix
= | b -A |
| c0 c^T |,
where the LP to be solved is to
maximize c^T x + c0
subj. to
A x <= b.
*/
dd_ErrorType err=dd_NoError;
dd_LPSolverType solver=dd_DualSimplex;
/* either DualSimplex or CrissCross */
dd_LPPtr lp,lp1;
/* pointer to LP data structure that is not visible by user. */
dd_LPSolutionPtr lps,lps1;
/* pointer to LP solution data that is visible by user. */
dd_MatrixPtr M;
dd_colrange j;
dd_DataFileType inputfile;
dd_set_global_constants();
printf("\n--- Solving an LP with dd_LPSolve, and Finding an Interior Point ---\n");
/* Input an LP using the cdd library */
dd_SetInputFile(&reading,inputfile,&err);
if (err!=dd_NoError) goto _L99;
M=dd_PolyFile2Matrix(reading, &err);
if (err!=dd_NoError) goto _L99;
/* dd_WriteMatrix(stdout, M); */
lp=dd_Matrix2LP(M, &err);
if (err!=dd_NoError) goto _L99;
/* Solve the LP by cdd LP solver. */
printf("\n--- Running dd_LPSolve ---\n");
solver=dd_DualSimplex;
dd_LPSolve(lp, solver, &err); /* Solve the LP */
if (err!=dd_NoError) goto _L99;
/* Write the LP solutions by cdd LP reporter. */
/* dd_WriteLPResult(stdout, lp, err); */
/* dd_WriteLPResult(writing, lp, err); */
/* One can access the solutions by loading them. See dd_WriteLPResult
for outputing the results correctly. */
lps=dd_CopyLPSolution(lp);
if (lps->LPS==dd_Optimal){
printf("Optimal solution found:\n");
printf(" primal_solution\n");
for (j=1; j<lps->d; j++) {
printf(" %3ld : ",j);
dd_WriteNumber(stdout,lps->sol[j]);
printf("\n");
}
printf(" dual_solution\n");
for (j=1; j<lps->d; j++){
if (lps->nbindex[j+1]>0) {
printf(" %3ld : ",lps->nbindex[j+1]);
dd_WriteNumber(stdout,lps->dsol[j]); printf("\n");
}
}
printf(" optimal_value : "); dd_WriteNumber(stdout,lps->optvalue);
printf("\n");
}
/* Find an interior point with cdd LP library. */
printf("\n--- Running dd_FindInteriorPoint ---\n");
lp1=dd_MakeLPforInteriorFinding(lp);
printf("The LP to be solved for finding an interior point:\n");
dd_WriteLP(stdout,lp1);
dd_LPSolve(lp1,solver,&err);
if (err!=dd_NoError) goto _L99;
/* Write an interior point. */
lps1=dd_CopyLPSolution(lp1);
if (dd_Positive(lps1->optvalue)){
printf("\nAn interior point found: (");
for (j=1; j <(lps1->d)-1; j++) {
dd_WriteNumber(stdout,lps1->sol[j]);
}
printf(")\n");
}
if (dd_Negative(lps1->optvalue))
printf("\nThe feasible region is empty.\n");
if (dd_EqualToZero(lps1->optvalue))
printf("\nThe feasible region is nonempty but has no interior point.\n");
/* Free allocated spaces. */
dd_FreeLPSolution(lps);
dd_FreeLPData(lp);
dd_FreeLPSolution(lps1);
dd_FreeLPData(lp1);
dd_FreeMatrix(M);
_L99:;
if (err!=dd_NoError) dd_WriteErrorMessages(stdout, err);
dd_free_global_constants(); /* At the end, this should be called. */
return 0;
}
