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+/* glpapi10.c (solution checking routines) */
+
+/***********************************************************************
+* This code is part of GLPK (GNU Linear Programming Kit).
+*
+* Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
+* 2009, 2010, 2011, 2013 Andrew Makhorin, Department for Applied
+* Informatics, Moscow Aviation Institute, Moscow, Russia. All rights
+* reserved. E-mail: <mao@gnu.org>.
+*
+* GLPK 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 3 of the License, or
+* (at your option) any later version.
+*
+* GLPK 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 GLPK. If not, see <http://www.gnu.org/licenses/>.
+***********************************************************************/
+
+#include "env.h"
+#include "prob.h"
+
+void glp_check_kkt(glp_prob *P, int sol, int cond, double *_ae_max,
+ int *_ae_ind, double *_re_max, int *_re_ind)
+{ /* check feasibility and optimality conditions */
+ int m = P->m;
+ int n = P->n;
+ GLPROW *row;
+ GLPCOL *col;
+ GLPAIJ *aij;
+ int i, j, ae_ind, re_ind;
+ double e, sp, sn, t, ae_max, re_max;
+ if (!(sol == GLP_SOL || sol == GLP_IPT || sol == GLP_MIP))
+ xerror("glp_check_kkt: sol = %d; invalid solution indicator\n",
+ sol);
+ if (!(cond == GLP_KKT_PE || cond == GLP_KKT_PB ||
+ cond == GLP_KKT_DE || cond == GLP_KKT_DB ||
+ cond == GLP_KKT_CS))
+ xerror("glp_check_kkt: cond = %d; invalid condition indicator "
+ "\n", cond);
+ ae_max = re_max = 0.0;
+ ae_ind = re_ind = 0;
+ if (cond == GLP_KKT_PE)
+ { /* xR - A * xS = 0 */
+ for (i = 1; i <= m; i++)
+ { row = P->row[i];
+ sp = sn = 0.0;
+ /* t := xR[i] */
+ if (sol == GLP_SOL)
+ t = row->prim;
+ else if (sol == GLP_IPT)
+ t = row->pval;
+ else if (sol == GLP_MIP)
+ t = row->mipx;
+ else
+ xassert(sol != sol);
+ if (t >= 0.0) sp += t; else sn -= t;
+ for (aij = row->ptr; aij != NULL; aij = aij->r_next)
+ { col = aij->col;
+ /* t := - a[i,j] * xS[j] */
+ if (sol == GLP_SOL)
+ t = - aij->val * col->prim;
+ else if (sol == GLP_IPT)
+ t = - aij->val * col->pval;
+ else if (sol == GLP_MIP)
+ t = - aij->val * col->mipx;
+ else
+ xassert(sol != sol);
+ if (t >= 0.0) sp += t; else sn -= t;
+ }
+ /* absolute error */
+ e = fabs(sp - sn);
+ if (ae_max < e)
+ ae_max = e, ae_ind = i;
+ /* relative error */
+ e /= (1.0 + sp + sn);
+ if (re_max < e)
+ re_max = e, re_ind = i;
+ }
+ }
+ else if (cond == GLP_KKT_PB)
+ { /* lR <= xR <= uR */
+ for (i = 1; i <= m; i++)
+ { row = P->row[i];
+ /* t := xR[i] */
+ if (sol == GLP_SOL)
+ t = row->prim;
+ else if (sol == GLP_IPT)
+ t = row->pval;
+ else if (sol == GLP_MIP)
+ t = row->mipx;
+ else
+ xassert(sol != sol);
+ /* check lower bound */
+ if (row->type == GLP_LO || row->type == GLP_DB ||
+ row->type == GLP_FX)
+ { if (t < row->lb)
+ { /* absolute error */
+ e = row->lb - t;
+ if (ae_max < e)
+ ae_max = e, ae_ind = i;
+ /* relative error */
+ e /= (1.0 + fabs(row->lb));
+ if (re_max < e)
+ re_max = e, re_ind = i;
+ }
+ }
+ /* check upper bound */
+ if (row->type == GLP_UP || row->type == GLP_DB ||
+ row->type == GLP_FX)
+ { if (t > row->ub)
+ { /* absolute error */
+ e = t - row->ub;
+ if (ae_max < e)
+ ae_max = e, ae_ind = i;
+ /* relative error */
+ e /= (1.0 + fabs(row->ub));
+ if (re_max < e)
+ re_max = e, re_ind = i;
+ }
+ }
+ }
+ /* lS <= xS <= uS */
+ for (j = 1; j <= n; j++)
+ { col = P->col[j];
+ /* t := xS[j] */
+ if (sol == GLP_SOL)
+ t = col->prim;
+ else if (sol == GLP_IPT)
+ t = col->pval;
+ else if (sol == GLP_MIP)
+ t = col->mipx;
+ else
+ xassert(sol != sol);
+ /* check lower bound */
+ if (col->type == GLP_LO || col->type == GLP_DB ||
+ col->type == GLP_FX)
+ { if (t < col->lb)
+ { /* absolute error */
+ e = col->lb - t;
+ if (ae_max < e)
+ ae_max = e, ae_ind = m+j;
+ /* relative error */
+ e /= (1.0 + fabs(col->lb));
+ if (re_max < e)
+ re_max = e, re_ind = m+j;
+ }
+ }
+ /* check upper bound */
+ if (col->type == GLP_UP || col->type == GLP_DB ||
+ col->type == GLP_FX)
+ { if (t > col->ub)
+ { /* absolute error */
+ e = t - col->ub;
+ if (ae_max < e)
+ ae_max = e, ae_ind = m+j;
+ /* relative error */
+ e /= (1.0 + fabs(col->ub));
+ if (re_max < e)
+ re_max = e, re_ind = m+j;
+ }
+ }
+ }
+ }
+ else if (cond == GLP_KKT_DE)
+ { /* A' * (lambdaR - cR) + (lambdaS - cS) = 0 */
+ for (j = 1; j <= n; j++)
+ { col = P->col[j];
+ sp = sn = 0.0;
+ /* t := lambdaS[j] - cS[j] */
+ if (sol == GLP_SOL)
+ t = col->dual - col->coef;
+ else if (sol == GLP_IPT)
+ t = col->dval - col->coef;
+ else
+ xassert(sol != sol);
+ if (t >= 0.0) sp += t; else sn -= t;
+ for (aij = col->ptr; aij != NULL; aij = aij->c_next)
+ { row = aij->row;
+ /* t := a[i,j] * (lambdaR[i] - cR[i]) */
+ if (sol == GLP_SOL)
+ t = aij->val * row->dual;
+ else if (sol == GLP_IPT)
+ t = aij->val * row->dval;
+ else
+ xassert(sol != sol);
+ if (t >= 0.0) sp += t; else sn -= t;
+ }
+ /* absolute error */
+ e = fabs(sp - sn);
+ if (ae_max < e)
+ ae_max = e, ae_ind = m+j;
+ /* relative error */
+ e /= (1.0 + sp + sn);
+ if (re_max < e)
+ re_max = e, re_ind = m+j;
+ }
+ }
+ else if (cond == GLP_KKT_DB)
+ { /* check lambdaR */
+ for (i = 1; i <= m; i++)
+ { row = P->row[i];
+ /* t := lambdaR[i] */
+ if (sol == GLP_SOL)
+ t = row->dual;
+ else if (sol == GLP_IPT)
+ t = row->dval;
+ else
+ xassert(sol != sol);
+ /* correct sign */
+ if (P->dir == GLP_MIN)
+ t = + t;
+ else if (P->dir == GLP_MAX)
+ t = - t;
+ else
+ xassert(P != P);
+ /* check for positivity */
+#if 1 /* 08/III-2013 */
+ /* the former check was correct */
+ /* the bug reported by David Price is related to violation
+ of complementarity slackness, not to this condition */
+ if (row->type == GLP_FR || row->type == GLP_LO)
+#else
+ if (row->stat == GLP_NF || row->stat == GLP_NL)
+#endif
+ { if (t < 0.0)
+ { e = - t;
+ if (ae_max < e)
+ ae_max = re_max = e, ae_ind = re_ind = i;
+ }
+ }
+ /* check for negativity */
+#if 1 /* 08/III-2013 */
+ /* see comment above */
+ if (row->type == GLP_FR || row->type == GLP_UP)
+#else
+ if (row->stat == GLP_NF || row->stat == GLP_NU)
+#endif
+ { if (t > 0.0)
+ { e = + t;
+ if (ae_max < e)
+ ae_max = re_max = e, ae_ind = re_ind = i;
+ }
+ }
+ }
+ /* check lambdaS */
+ for (j = 1; j <= n; j++)
+ { col = P->col[j];
+ /* t := lambdaS[j] */
+ if (sol == GLP_SOL)
+ t = col->dual;
+ else if (sol == GLP_IPT)
+ t = col->dval;
+ else
+ xassert(sol != sol);
+ /* correct sign */
+ if (P->dir == GLP_MIN)
+ t = + t;
+ else if (P->dir == GLP_MAX)
+ t = - t;
+ else
+ xassert(P != P);
+ /* check for positivity */
+#if 1 /* 08/III-2013 */
+ /* see comment above */
+ if (col->type == GLP_FR || col->type == GLP_LO)
+#else
+ if (col->stat == GLP_NF || col->stat == GLP_NL)
+#endif
+ { if (t < 0.0)
+ { e = - t;
+ if (ae_max < e)
+ ae_max = re_max = e, ae_ind = re_ind = m+j;
+ }
+ }
+ /* check for negativity */
+#if 1 /* 08/III-2013 */
+ /* see comment above */
+ if (col->type == GLP_FR || col->type == GLP_UP)
+#else
+ if (col->stat == GLP_NF || col->stat == GLP_NU)
+#endif
+ { if (t > 0.0)
+ { e = + t;
+ if (ae_max < e)
+ ae_max = re_max = e, ae_ind = re_ind = m+j;
+ }
+ }
+ }
+ }
+ else
+ xassert(cond != cond);
+ if (_ae_max != NULL) *_ae_max = ae_max;
+ if (_ae_ind != NULL) *_ae_ind = ae_ind;
+ if (_re_max != NULL) *_re_max = re_max;
+ if (_re_ind != NULL) *_re_ind = re_ind;
+ return;
+}
+
+/* eof */
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