void lpx_check_int(LPX *lp, LPXKKT *kkt)
{ /* check integer feasibility conditions */
int ae_ind, re_ind;
double ae_max, re_max;
glp_check_kkt(lp, GLP_MIP, GLP_KKT_PE, &ae_max, &ae_ind, &re_max,
&re_ind);
kkt->pe_ae_max = ae_max;
kkt->pe_ae_row = ae_ind;
kkt->pe_re_max = re_max;
kkt->pe_re_row = re_ind;
if (re_max <= 1e-9)
kkt->pe_quality = 'H';
else if (re_max <= 1e-6)
kkt->pe_quality = 'M';
else if (re_max <= 1e-3)
kkt->pe_quality = 'L';
else
kkt->pe_quality = '?';
glp_check_kkt(lp, GLP_MIP, GLP_KKT_PB, &ae_max, &ae_ind, &re_max,
&re_ind);
kkt->pb_ae_max = ae_max;
kkt->pb_ae_ind = ae_ind;
kkt->pb_re_max = re_max;
kkt->pb_re_ind = re_ind;
if (re_max <= 1e-9)
kkt->pb_quality = 'H';
else if (re_max <= 1e-6)
kkt->pb_quality = 'M';
else if (re_max <= 1e-3)
kkt->pb_quality = 'L';
else
kkt->pb_quality = '?';
return;
}
void pyglpk_kkt_check(glp_prob *lp, int scaling, pyglpk_kkt_t *kkt)
{
#if GLPK_VERSION(4, 49)
int m = glp_get_num_rows(lp);
/* check primal equality constraints */
glp_check_kkt(lp, GLP_SOL, GLP_KKT_PE,
&(kkt->pe_ae_max), &(kkt->pe_ae_row),
&(kkt->pe_re_max), &(kkt->pe_re_row));
kkt->pe_quality = quality(kkt->pe_re_max);
/* check primal bound constraints */
glp_check_kkt(lp, GLP_SOL, GLP_KKT_PB,
&(kkt->pb_ae_max), &(kkt->pb_ae_ind),
&(kkt->pb_re_max), &(kkt->pb_re_ind));
kkt->pb_quality = quality(kkt->pb_re_max);
/* check dual equality constraints */
glp_check_kkt(lp, GLP_SOL, GLP_KKT_DE,
&(kkt->de_ae_max), &(kkt->de_ae_col),
&(kkt->de_re_max), &(kkt->de_re_col));
kkt->de_ae_col = kkt->de_ae_col == 0 ? 0 : kkt->de_ae_col - m;
kkt->de_re_col = kkt->de_re_col == 0 ? 0 : kkt->de_re_col - m;
kkt->de_quality = quality(kkt->de_re_max);
/* check dual bound constraints */
glp_check_kkt(lp, GLP_SOL, GLP_KKT_DB,
&(kkt->db_ae_max), &(kkt->db_ae_ind),
&(kkt->db_re_max), &(kkt->db_re_ind));
kkt->db_quality = quality(kkt->db_re_max);
#else
lpx_check_kkt(lp, scaling, kkt);
#endif
}
bool glpk_wrapper::check_unsat_error_kkt(double precision) {
double ae_max_1; // largest absolute error
int ae_ind_1; // number of row the largest absolute error
double re_max_1; // largest relative error
int re_ind_1; // number of row with the largest relative error
double ae_max_2; // largest absolute error
int ae_ind_2; // variable with the largest absolute error
double re_max_2; // largest relative error
int re_ind_2; // variable with the largest relative error
int sol;
if (solver_type == SIMPLEX || solver_type == EXACT) {
sol = GLP_SOL;
} else {
sol = GLP_IPT;
}
// check primal equality constraints
glp_check_kkt(lp, sol, GLP_KKT_PE, &ae_max_1, &ae_ind_1, &re_max_1, &re_ind_1);
// check primal bound constraints
glp_check_kkt(lp, sol, GLP_KKT_PB, &ae_max_2, &ae_ind_2, &re_max_2, &re_ind_2);
return ae_max_1 < precision && ae_max_1 < ae_max_2;
}
void glpk_wrapper::get_error_bounds(double * errors) {
int n = domain.size();
int * nbr_non_zero = new int[n];
for (int i = 0; i < n; i++) {
errors[i] = INFINITY;
nbr_non_zero[i] = 0;
}
// get the error on the KKT condition
int sol;
if (solver_type == SIMPLEX || solver_type == EXACT) {
sol = GLP_SOL;
} else {
sol = GLP_IPT;
}
double ae_max; // largest absolute error
int ae_ind; // number of row (PE), column (DE), or variable (PB, DB) with the largest absolute error
double re_max; // largest relative error
int re_ind; // number of row (PE), column (DE), or variable (PB, DB) with the largest relative error
// GLP_KKT_PE — check primal equality constraints
glp_check_kkt(lp, sol, GLP_KKT_PE, &ae_max, &ae_ind, &re_max, &re_ind);
// a sparse vector for the coeffs in the row
int row_size = 1;
int * row_idx = new int[n + 1];
double * row_coeff = new double[n + 1];
// PE
// gives the distance between the auxiliary var and A * strucutral variable
int m = glp_get_num_rows(lp);
for (int i = 1; i <= m ; ++i) {
// get the coeffs for that constraint
row_size = glp_get_mat_row(lp, i, row_idx, row_coeff);
for (int j = 1; j <= row_size; j++) {
int v = row_idx[j] - 1; // GLPK indexing
nbr_non_zero[v] += 1;
int c = row_coeff[j];
// relative error
errors[v] = std::min(errors[v], get_row_value(i) * re_max / c);
// absolute error
errors[v] = std::min(errors[v], ae_max / c);
}
}
// variables that don't matter
for (int i = 0; i < n; i++) {
if (nbr_non_zero[i] == 0) {
errors[i] = 0;
}
DREAL_LOG_INFO << "glpk_wrapper::get_error_bounds: error for " << domain.get_name(i) << " is " << errors[i];
}
delete[] nbr_non_zero;
delete[] row_idx;
delete[] row_coeff;
}
void pyglpk_int_check(glp_prob *lp, pyglpk_kkt_t *kkt)
{
#if GLPK_VERSION(4, 49)
/* check primal equality constraints */
glp_check_kkt(lp, GLP_MIP, GLP_KKT_PE,
&(kkt->pe_ae_max), &(kkt->pe_ae_row),
&(kkt->pe_re_max), &(kkt->pe_re_row));
kkt->pe_quality = quality(kkt->pe_re_max);
/* check primal bound constraints */
glp_check_kkt(lp, GLP_MIP, GLP_KKT_PB,
&(kkt->pb_ae_max), &(kkt->pb_ae_ind),
&(kkt->pb_re_max), &(kkt->pb_re_ind));
kkt->pb_quality = quality(kkt->pb_re_max);
#else
lpx_check_int(lp, kkt);
#endif
}
int glp_print_mip(glp_prob *P, const char *fname)
{ /* write MIP solution in printable format */
glp_file *fp;
GLPROW *row;
GLPCOL *col;
int i, j, t, ae_ind, re_ind, ret;
double ae_max, re_max;
xprintf("Writing MIP solution to '%s'...\n", fname);
fp = glp_open(fname, "w");
if (fp == NULL)
{ xprintf("Unable to create '%s' - %s\n", fname, get_err_msg());
ret = 1;
goto done;
}
xfprintf(fp, "%-12s%s\n", "Problem:",
P->name == NULL ? "" : P->name);
xfprintf(fp, "%-12s%d\n", "Rows:", P->m);
xfprintf(fp, "%-12s%d (%d integer, %d binary)\n", "Columns:",
P->n, glp_get_num_int(P), glp_get_num_bin(P));
xfprintf(fp, "%-12s%d\n", "Non-zeros:", P->nnz);
t = glp_mip_status(P);
xfprintf(fp, "%-12s%s\n", "Status:",
t == GLP_OPT ? "INTEGER OPTIMAL" :
t == GLP_FEAS ? "INTEGER NON-OPTIMAL" :
t == GLP_NOFEAS ? "INTEGER EMPTY" :
t == GLP_UNDEF ? "INTEGER UNDEFINED" : "???");
xfprintf(fp, "%-12s%s%s%.10g (%s)\n", "Objective:",
P->obj == NULL ? "" : P->obj,
P->obj == NULL ? "" : " = ", P->mip_obj,
P->dir == GLP_MIN ? "MINimum" :
P->dir == GLP_MAX ? "MAXimum" : "???");
xfprintf(fp, "\n");
xfprintf(fp, " No. Row name Activity Lower bound "
" Upper bound\n");
xfprintf(fp, "------ ------------ ------------- ------------- "
"-------------\n");
for (i = 1; i <= P->m; i++)
{ row = P->row[i];
xfprintf(fp, "%6d ", i);
if (row->name == NULL || strlen(row->name) <= 12)
xfprintf(fp, "%-12s ", row->name == NULL ? "" : row->name);
else
xfprintf(fp, "%s\n%20s", row->name, "");
xfprintf(fp, "%3s", "");
xfprintf(fp, "%13.6g ",
fabs(row->mipx) <= 1e-9 ? 0.0 : row->mipx);
if (row->type == GLP_LO || row->type == GLP_DB ||
row->type == GLP_FX)
xfprintf(fp, "%13.6g ", row->lb);
else
xfprintf(fp, "%13s ", "");
if (row->type == GLP_UP || row->type == GLP_DB)
xfprintf(fp, "%13.6g ", row->ub);
else
xfprintf(fp, "%13s ", row->type == GLP_FX ? "=" : "");
xfprintf(fp, "\n");
}
xfprintf(fp, "\n");
xfprintf(fp, " No. Column name Activity Lower bound "
" Upper bound\n");
xfprintf(fp, "------ ------------ ------------- ------------- "
"-------------\n");
for (j = 1; j <= P->n; j++)
{ col = P->col[j];
xfprintf(fp, "%6d ", j);
if (col->name == NULL || strlen(col->name) <= 12)
xfprintf(fp, "%-12s ", col->name == NULL ? "" : col->name);
else
xfprintf(fp, "%s\n%20s", col->name, "");
xfprintf(fp, "%s ",
col->kind == GLP_CV ? " " :
col->kind == GLP_IV ? "*" : "?");
xfprintf(fp, "%13.6g ",
fabs(col->mipx) <= 1e-9 ? 0.0 : col->mipx);
if (col->type == GLP_LO || col->type == GLP_DB ||
col->type == GLP_FX)
xfprintf(fp, "%13.6g ", col->lb);
else
xfprintf(fp, "%13s ", "");
if (col->type == GLP_UP || col->type == GLP_DB)
xfprintf(fp, "%13.6g ", col->ub);
else
xfprintf(fp, "%13s ", col->type == GLP_FX ? "=" : "");
xfprintf(fp, "\n");
}
xfprintf(fp, "\n");
xfprintf(fp, "Integer feasibility conditions:\n");
xfprintf(fp, "\n");
glp_check_kkt(P, GLP_MIP, GLP_KKT_PE, &ae_max, &ae_ind, &re_max,
&re_ind);
xfprintf(fp, "KKT.PE: max.abs.err = %.2e on row %d\n",
ae_max, ae_ind);
xfprintf(fp, " max.rel.err = %.2e on row %d\n",
re_max, re_ind);
xfprintf(fp, "%8s%s\n", "",
re_max <= 1e-9 ? "High quality" :
re_max <= 1e-6 ? "Medium quality" :
re_max <= 1e-3 ? "Low quality" : "SOLUTION IS WRONG");
xfprintf(fp, "\n");
glp_check_kkt(P, GLP_MIP, GLP_KKT_PB, &ae_max, &ae_ind, &re_max,
&re_ind);
xfprintf(fp, "KKT.PB: max.abs.err = %.2e on %s %d\n",
ae_max, ae_ind <= P->m ? "row" : "column",
ae_ind <= P->m ? ae_ind : ae_ind - P->m);
xfprintf(fp, " max.rel.err = %.2e on %s %d\n",
re_max, re_ind <= P->m ? "row" : "column",
re_ind <= P->m ? re_ind : re_ind - P->m);
xfprintf(fp, "%8s%s\n", "",
re_max <= 1e-9 ? "High quality" :
re_max <= 1e-6 ? "Medium quality" :
re_max <= 1e-3 ? "Low quality" : "SOLUTION IS INFEASIBLE");
xfprintf(fp, "\n");
xfprintf(fp, "End of output\n");
#if 0 /* FIXME */
xfflush(fp);
#endif
if (glp_ioerr(fp))
{ xprintf("Write error on '%s' - %s\n", fname, get_err_msg());
ret = 1;
goto done;
}
ret = 0;
done:
if (fp != NULL) glp_close(fp);
return ret;
}
int glp_print_ipt(glp_prob *P, const char *fname)
{ /* write interior-point solution in printable format */
glp_file *fp;
GLPROW *row;
GLPCOL *col;
int i, j, t, ae_ind, re_ind, ret;
double ae_max, re_max;
xprintf("Writing interior-point solution to '%s'...\n", fname);
fp = glp_open(fname, "w");
if (fp == NULL)
{ xprintf("Unable to create '%s' - %s\n", fname, get_err_msg());
ret = 1;
goto done;
}
xfprintf(fp, "%-12s%s\n", "Problem:",
P->name == NULL ? "" : P->name);
xfprintf(fp, "%-12s%d\n", "Rows:", P->m);
xfprintf(fp, "%-12s%d\n", "Columns:", P->n);
xfprintf(fp, "%-12s%d\n", "Non-zeros:", P->nnz);
t = glp_ipt_status(P);
xfprintf(fp, "%-12s%s\n", "Status:",
t == GLP_OPT ? "OPTIMAL" :
t == GLP_UNDEF ? "UNDEFINED" :
t == GLP_INFEAS ? "INFEASIBLE (INTERMEDIATE)" :
t == GLP_NOFEAS ? "INFEASIBLE (FINAL)" : "???");
xfprintf(fp, "%-12s%s%s%.10g (%s)\n", "Objective:",
P->obj == NULL ? "" : P->obj,
P->obj == NULL ? "" : " = ", P->ipt_obj,
P->dir == GLP_MIN ? "MINimum" :
P->dir == GLP_MAX ? "MAXimum" : "???");
xfprintf(fp, "\n");
xfprintf(fp, " No. Row name Activity Lower bound "
" Upper bound Marginal\n");
xfprintf(fp, "------ ------------ ------------- ------------- "
"------------- -------------\n");
for (i = 1; i <= P->m; i++)
{ row = P->row[i];
xfprintf(fp, "%6d ", i);
if (row->name == NULL || strlen(row->name) <= 12)
xfprintf(fp, "%-12s ", row->name == NULL ? "" : row->name);
else
xfprintf(fp, "%s\n%20s", row->name, "");
xfprintf(fp, "%3s", "");
xfprintf(fp, "%13.6g ",
fabs(row->pval) <= 1e-9 ? 0.0 : row->pval);
if (row->type == GLP_LO || row->type == GLP_DB ||
row->type == GLP_FX)
xfprintf(fp, "%13.6g ", row->lb);
else
xfprintf(fp, "%13s ", "");
if (row->type == GLP_UP || row->type == GLP_DB)
xfprintf(fp, "%13.6g ", row->ub);
else
xfprintf(fp, "%13s ", row->type == GLP_FX ? "=" : "");
if (fabs(row->dval) <= 1e-9)
xfprintf(fp, "%13s", "< eps");
else
xfprintf(fp, "%13.6g ", row->dval);
xfprintf(fp, "\n");
}
xfprintf(fp, "\n");
xfprintf(fp, " No. Column name Activity Lower bound "
" Upper bound Marginal\n");
xfprintf(fp, "------ ------------ ------------- ------------- "
"------------- -------------\n");
for (j = 1; j <= P->n; j++)
{ col = P->col[j];
xfprintf(fp, "%6d ", j);
if (col->name == NULL || strlen(col->name) <= 12)
xfprintf(fp, "%-12s ", col->name == NULL ? "" : col->name);
else
xfprintf(fp, "%s\n%20s", col->name, "");
xfprintf(fp, "%3s", "");
xfprintf(fp, "%13.6g ",
fabs(col->pval) <= 1e-9 ? 0.0 : col->pval);
if (col->type == GLP_LO || col->type == GLP_DB ||
col->type == GLP_FX)
xfprintf(fp, "%13.6g ", col->lb);
else
xfprintf(fp, "%13s ", "");
if (col->type == GLP_UP || col->type == GLP_DB)
xfprintf(fp, "%13.6g ", col->ub);
else
xfprintf(fp, "%13s ", col->type == GLP_FX ? "=" : "");
if (fabs(col->dval) <= 1e-9)
xfprintf(fp, "%13s", "< eps");
else
xfprintf(fp, "%13.6g ", col->dval);
xfprintf(fp, "\n");
}
xfprintf(fp, "\n");
xfprintf(fp, "Karush-Kuhn-Tucker optimality conditions:\n");
xfprintf(fp, "\n");
glp_check_kkt(P, GLP_IPT, GLP_KKT_PE, &ae_max, &ae_ind, &re_max,
&re_ind);
xfprintf(fp, "KKT.PE: max.abs.err = %.2e on row %d\n",
ae_max, ae_ind);
xfprintf(fp, " max.rel.err = %.2e on row %d\n",
re_max, re_ind);
xfprintf(fp, "%8s%s\n", "",
re_max <= 1e-9 ? "High quality" :
re_max <= 1e-6 ? "Medium quality" :
re_max <= 1e-3 ? "Low quality" : "PRIMAL SOLUTION IS WRONG");
xfprintf(fp, "\n");
glp_check_kkt(P, GLP_IPT, GLP_KKT_PB, &ae_max, &ae_ind, &re_max,
&re_ind);
xfprintf(fp, "KKT.PB: max.abs.err = %.2e on %s %d\n",
ae_max, ae_ind <= P->m ? "row" : "column",
ae_ind <= P->m ? ae_ind : ae_ind - P->m);
xfprintf(fp, " max.rel.err = %.2e on %s %d\n",
re_max, re_ind <= P->m ? "row" : "column",
re_ind <= P->m ? re_ind : re_ind - P->m);
xfprintf(fp, "%8s%s\n", "",
re_max <= 1e-9 ? "High quality" :
re_max <= 1e-6 ? "Medium quality" :
re_max <= 1e-3 ? "Low quality" : "PRIMAL SOLUTION IS INFEASIBL"
"E");
xfprintf(fp, "\n");
glp_check_kkt(P, GLP_IPT, GLP_KKT_DE, &ae_max, &ae_ind, &re_max,
&re_ind);
xfprintf(fp, "KKT.DE: max.abs.err = %.2e on column %d\n",
ae_max, ae_ind == 0 ? 0 : ae_ind - P->m);
xfprintf(fp, " max.rel.err = %.2e on column %d\n",
re_max, re_ind == 0 ? 0 : re_ind - P->m);
xfprintf(fp, "%8s%s\n", "",
re_max <= 1e-9 ? "High quality" :
re_max <= 1e-6 ? "Medium quality" :
re_max <= 1e-3 ? "Low quality" : "DUAL SOLUTION IS WRONG");
xfprintf(fp, "\n");
glp_check_kkt(P, GLP_IPT, GLP_KKT_DB, &ae_max, &ae_ind, &re_max,
&re_ind);
xfprintf(fp, "KKT.DB: max.abs.err = %.2e on %s %d\n",
ae_max, ae_ind <= P->m ? "row" : "column",
ae_ind <= P->m ? ae_ind : ae_ind - P->m);
xfprintf(fp, " max.rel.err = %.2e on %s %d\n",
re_max, re_ind <= P->m ? "row" : "column",
re_ind <= P->m ? re_ind : re_ind - P->m);
xfprintf(fp, "%8s%s\n", "",
re_max <= 1e-9 ? "High quality" :
re_max <= 1e-6 ? "Medium quality" :
re_max <= 1e-3 ? "Low quality" : "DUAL SOLUTION IS INFEASIBLE")
;
xfprintf(fp, "\n");
xfprintf(fp, "End of output\n");
#if 0 /* FIXME */
xfflush(fp);
#endif
if (glp_ioerr(fp))
{ xprintf("Write error on '%s' - %s\n", fname, get_err_msg());
ret = 1;
goto done;
}
ret = 0;
done:
if (fp != NULL) glp_close(fp);
return ret;
}
void lpx_check_kkt(LPX *lp, int scaled, LPXKKT *kkt)
{ /* check Karush-Kuhn-Tucker conditions */
int ae_ind, re_ind;
double ae_max, re_max;
xassert(scaled == scaled);
glp_check_kkt(lp, GLP_SOL, GLP_KKT_PE, &ae_max, &ae_ind, &re_max,
&re_ind);
kkt->pe_ae_max = ae_max;
kkt->pe_ae_row = ae_ind;
kkt->pe_re_max = re_max;
kkt->pe_re_row = re_ind;
if (re_max <= 1e-9)
kkt->pe_quality = 'H';
else if (re_max <= 1e-6)
kkt->pe_quality = 'M';
else if (re_max <= 1e-3)
kkt->pe_quality = 'L';
else
kkt->pe_quality = '?';
glp_check_kkt(lp, GLP_SOL, GLP_KKT_PB, &ae_max, &ae_ind, &re_max,
&re_ind);
kkt->pb_ae_max = ae_max;
kkt->pb_ae_ind = ae_ind;
kkt->pb_re_max = re_max;
kkt->pb_re_ind = re_ind;
if (re_max <= 1e-9)
kkt->pb_quality = 'H';
else if (re_max <= 1e-6)
kkt->pb_quality = 'M';
else if (re_max <= 1e-3)
kkt->pb_quality = 'L';
else
kkt->pb_quality = '?';
glp_check_kkt(lp, GLP_SOL, GLP_KKT_DE, &ae_max, &ae_ind, &re_max,
&re_ind);
kkt->de_ae_max = ae_max;
if (ae_ind == 0)
kkt->de_ae_col = 0;
else
kkt->de_ae_col = ae_ind - lp->m;
kkt->de_re_max = re_max;
if (re_ind == 0)
kkt->de_re_col = 0;
else
kkt->de_re_col = ae_ind - lp->m;
if (re_max <= 1e-9)
kkt->de_quality = 'H';
else if (re_max <= 1e-6)
kkt->de_quality = 'M';
else if (re_max <= 1e-3)
kkt->de_quality = 'L';
else
kkt->de_quality = '?';
glp_check_kkt(lp, GLP_SOL, GLP_KKT_DB, &ae_max, &ae_ind, &re_max,
&re_ind);
kkt->db_ae_max = ae_max;
kkt->db_ae_ind = ae_ind;
kkt->db_re_max = re_max;
kkt->db_re_ind = re_ind;
if (re_max <= 1e-9)
kkt->db_quality = 'H';
else if (re_max <= 1e-6)
kkt->db_quality = 'M';
else if (re_max <= 1e-3)
kkt->db_quality = 'L';
else
kkt->db_quality = '?';
kkt->cs_ae_max = 0.0, kkt->cs_ae_ind = 0;
kkt->cs_re_max = 0.0, kkt->cs_re_ind = 0;
kkt->cs_quality = 'H';
return;
}