alpar@1: /* glpios06.c (MIR cut generator) */
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  This code is part of GLPK (GNU Linear Programming Kit).
alpar@1: *
alpar@1: *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
alpar@1: *  2009, 2010 Andrew Makhorin, Department for Applied Informatics,
alpar@1: *  Moscow Aviation Institute, Moscow, Russia. All rights reserved.
alpar@1: *  E-mail: <mao@gnu.org>.
alpar@1: *
alpar@1: *  GLPK is free software: you can redistribute it and/or modify it
alpar@1: *  under the terms of the GNU General Public License as published by
alpar@1: *  the Free Software Foundation, either version 3 of the License, or
alpar@1: *  (at your option) any later version.
alpar@1: *
alpar@1: *  GLPK is distributed in the hope that it will be useful, but WITHOUT
alpar@1: *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
alpar@1: *  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
alpar@1: *  License for more details.
alpar@1: *
alpar@1: *  You should have received a copy of the GNU General Public License
alpar@1: *  along with GLPK. If not, see <http://www.gnu.org/licenses/>.
alpar@1: ***********************************************************************/
alpar@1: 
alpar@1: #include "glpios.h"
alpar@1: 
alpar@1: #define _MIR_DEBUG 0
alpar@1: 
alpar@1: #define MAXAGGR 5
alpar@1: /* maximal number of rows which can be aggregated */
alpar@1: 
alpar@1: struct MIR
alpar@1: {     /* MIR cut generator working area */
alpar@1:       /*--------------------------------------------------------------*/
alpar@1:       /* global information valid for the root subproblem */
alpar@1:       int m;
alpar@1:       /* number of rows (in the root subproblem) */
alpar@1:       int n;
alpar@1:       /* number of columns */
alpar@1:       char *skip; /* char skip[1+m]; */
alpar@1:       /* skip[i], 1 <= i <= m, is a flag that means that row i should
alpar@1:          not be used because (1) it is not suitable, or (2) because it
alpar@1:          has been used in the aggregated constraint */
alpar@1:       char *isint; /* char isint[1+m+n]; */
alpar@1:       /* isint[k], 1 <= k <= m+n, is a flag that means that variable
alpar@1:          x[k] is integer (otherwise, continuous) */
alpar@1:       double *lb; /* double lb[1+m+n]; */
alpar@1:       /* lb[k], 1 <= k <= m+n, is lower bound of x[k]; -DBL_MAX means
alpar@1:          that x[k] has no lower bound */
alpar@1:       int *vlb; /* int vlb[1+m+n]; */
alpar@1:       /* vlb[k] = k', 1 <= k <= m+n, is the number of integer variable,
alpar@1:          which defines variable lower bound x[k] >= lb[k] * x[k']; zero
alpar@1:          means that x[k] has simple lower bound */
alpar@1:       double *ub; /* double ub[1+m+n]; */
alpar@1:       /* ub[k], 1 <= k <= m+n, is upper bound of x[k]; +DBL_MAX means
alpar@1:          that x[k] has no upper bound */
alpar@1:       int *vub; /* int vub[1+m+n]; */
alpar@1:       /* vub[k] = k', 1 <= k <= m+n, is the number of integer variable,
alpar@1:          which defines variable upper bound x[k] <= ub[k] * x[k']; zero
alpar@1:          means that x[k] has simple upper bound */
alpar@1:       /*--------------------------------------------------------------*/
alpar@1:       /* current (fractional) point to be separated */
alpar@1:       double *x; /* double x[1+m+n]; */
alpar@1:       /* x[k] is current value of auxiliary (1 <= k <= m) or structural
alpar@1:          (m+1 <= k <= m+n) variable */
alpar@1:       /*--------------------------------------------------------------*/
alpar@1:       /* aggregated constraint sum a[k] * x[k] = b, which is a linear
alpar@1:          combination of original constraints transformed to equalities
alpar@1:          by introducing auxiliary variables */
alpar@1:       int agg_cnt;
alpar@1:       /* number of rows (original constraints) used to build aggregated
alpar@1:          constraint, 1 <= agg_cnt <= MAXAGGR */
alpar@1:       int *agg_row; /* int agg_row[1+MAXAGGR]; */
alpar@1:       /* agg_row[k], 1 <= k <= agg_cnt, is the row number used to build
alpar@1:          aggregated constraint */
alpar@1:       IOSVEC *agg_vec; /* IOSVEC agg_vec[1:m+n]; */
alpar@1:       /* sparse vector of aggregated constraint coefficients, a[k] */
alpar@1:       double agg_rhs;
alpar@1:       /* right-hand side of the aggregated constraint, b */
alpar@1:       /*--------------------------------------------------------------*/
alpar@1:       /* bound substitution flags for modified constraint */
alpar@1:       char *subst; /* char subst[1+m+n]; */
alpar@1:       /* subst[k], 1 <= k <= m+n, is a bound substitution flag used for
alpar@1:          variable x[k]:
alpar@1:          '?' - x[k] is missing in modified constraint
alpar@1:          'L' - x[k] = (lower bound) + x'[k]
alpar@1:          'U' - x[k] = (upper bound) - x'[k] */
alpar@1:       /*--------------------------------------------------------------*/
alpar@1:       /* modified constraint sum a'[k] * x'[k] = b', where x'[k] >= 0,
alpar@1:          derived from aggregated constraint by substituting bounds;
alpar@1:          note that due to substitution of variable bounds there may be
alpar@1:          additional terms in the modified constraint */
alpar@1:       IOSVEC *mod_vec; /* IOSVEC mod_vec[1:m+n]; */
alpar@1:       /* sparse vector of modified constraint coefficients, a'[k] */
alpar@1:       double mod_rhs;
alpar@1:       /* right-hand side of the modified constraint, b' */
alpar@1:       /*--------------------------------------------------------------*/
alpar@1:       /* cutting plane sum alpha[k] * x[k] <= beta */
alpar@1:       IOSVEC *cut_vec; /* IOSVEC cut_vec[1:m+n]; */
alpar@1:       /* sparse vector of cutting plane coefficients, alpha[k] */
alpar@1:       double cut_rhs;
alpar@1:       /* right-hand size of the cutting plane, beta */
alpar@1: };
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  ios_mir_init - initialize MIR cut generator
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  #include "glpios.h"
alpar@1: *  void *ios_mir_init(glp_tree *tree);
alpar@1: *
alpar@1: *  DESCRIPTION
alpar@1: *
alpar@1: *  The routine ios_mir_init initializes the MIR cut generator assuming
alpar@1: *  that the current subproblem is the root subproblem.
alpar@1: *
alpar@1: *  RETURNS
alpar@1: *
alpar@1: *  The routine ios_mir_init returns a pointer to the MIR cut generator
alpar@1: *  working area. */
alpar@1: 
alpar@1: static void set_row_attrib(glp_tree *tree, struct MIR *mir)
alpar@1: {     /* set global row attributes */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mir->m;
alpar@1:       int k;
alpar@1:       for (k = 1; k <= m; k++)
alpar@1:       {  GLPROW *row = mip->row[k];
alpar@1:          mir->skip[k] = 0;
alpar@1:          mir->isint[k] = 0;
alpar@1:          switch (row->type)
alpar@1:          {  case GLP_FR:
alpar@1:                mir->lb[k] = -DBL_MAX, mir->ub[k] = +DBL_MAX; break;
alpar@1:             case GLP_LO:
alpar@1:                mir->lb[k] = row->lb, mir->ub[k] = +DBL_MAX; break;
alpar@1:             case GLP_UP:
alpar@1:                mir->lb[k] = -DBL_MAX, mir->ub[k] = row->ub; break;
alpar@1:             case GLP_DB:
alpar@1:                mir->lb[k] = row->lb, mir->ub[k] = row->ub; break;
alpar@1:             case GLP_FX:
alpar@1:                mir->lb[k] = mir->ub[k] = row->lb; break;
alpar@1:             default:
alpar@1:                xassert(row != row);
alpar@1:          }
alpar@1:          mir->vlb[k] = mir->vub[k] = 0;
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static void set_col_attrib(glp_tree *tree, struct MIR *mir)
alpar@1: {     /* set global column attributes */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int k;
alpar@1:       for (k = m+1; k <= m+n; k++)
alpar@1:       {  GLPCOL *col = mip->col[k-m];
alpar@1:          switch (col->kind)
alpar@1:          {  case GLP_CV:
alpar@1:                mir->isint[k] = 0; break;
alpar@1:             case GLP_IV:
alpar@1:                mir->isint[k] = 1; break;
alpar@1:             default:
alpar@1:                xassert(col != col);
alpar@1:          }
alpar@1:          switch (col->type)
alpar@1:          {  case GLP_FR:
alpar@1:                mir->lb[k] = -DBL_MAX, mir->ub[k] = +DBL_MAX; break;
alpar@1:             case GLP_LO:
alpar@1:                mir->lb[k] = col->lb, mir->ub[k] = +DBL_MAX; break;
alpar@1:             case GLP_UP:
alpar@1:                mir->lb[k] = -DBL_MAX, mir->ub[k] = col->ub; break;
alpar@1:             case GLP_DB:
alpar@1:                mir->lb[k] = col->lb, mir->ub[k] = col->ub; break;
alpar@1:             case GLP_FX:
alpar@1:                mir->lb[k] = mir->ub[k] = col->lb; break;
alpar@1:             default:
alpar@1:                xassert(col != col);
alpar@1:          }
alpar@1:          mir->vlb[k] = mir->vub[k] = 0;
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static void set_var_bounds(glp_tree *tree, struct MIR *mir)
alpar@1: {     /* set variable bounds */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mir->m;
alpar@1:       GLPAIJ *aij;
alpar@1:       int i, k1, k2;
alpar@1:       double a1, a2;
alpar@1:       for (i = 1; i <= m; i++)
alpar@1:       {  /* we need the row to be '>= 0' or '<= 0' */
alpar@1:          if (!(mir->lb[i] == 0.0 && mir->ub[i] == +DBL_MAX ||
alpar@1:                mir->lb[i] == -DBL_MAX && mir->ub[i] == 0.0)) continue;
alpar@1:          /* take first term */
alpar@1:          aij = mip->row[i]->ptr;
alpar@1:          if (aij == NULL) continue;
alpar@1:          k1 = m + aij->col->j, a1 = aij->val;
alpar@1:          /* take second term */
alpar@1:          aij = aij->r_next;
alpar@1:          if (aij == NULL) continue;
alpar@1:          k2 = m + aij->col->j, a2 = aij->val;
alpar@1:          /* there must be only two terms */
alpar@1:          if (aij->r_next != NULL) continue;
alpar@1:          /* interchange terms, if needed */
alpar@1:          if (!mir->isint[k1] && mir->isint[k2])
alpar@1:             ;
alpar@1:          else if (mir->isint[k1] && !mir->isint[k2])
alpar@1:          {  k2 = k1, a2 = a1;
alpar@1:             k1 = m + aij->col->j, a1 = aij->val;
alpar@1:          }
alpar@1:          else
alpar@1:          {  /* both terms are either continuous or integer */
alpar@1:             continue;
alpar@1:          }
alpar@1:          /* x[k2] should be double-bounded */
alpar@1:          if (mir->lb[k2] == -DBL_MAX || mir->ub[k2] == +DBL_MAX ||
alpar@1:              mir->lb[k2] == mir->ub[k2]) continue;
alpar@1:          /* change signs, if necessary */
alpar@1:          if (mir->ub[i] == 0.0) a1 = - a1, a2 = - a2;
alpar@1:          /* now the row has the form a1 * x1 + a2 * x2 >= 0, where x1
alpar@1:             is continuous, x2 is integer */
alpar@1:          if (a1 > 0.0)
alpar@1:          {  /* x1 >= - (a2 / a1) * x2 */
alpar@1:             if (mir->vlb[k1] == 0)
alpar@1:             {  /* set variable lower bound for x1 */
alpar@1:                mir->lb[k1] = - a2 / a1;
alpar@1:                mir->vlb[k1] = k2;
alpar@1:                /* the row should not be used */
alpar@1:                mir->skip[i] = 1;
alpar@1:             }
alpar@1:          }
alpar@1:          else /* a1 < 0.0 */
alpar@1:          {  /* x1 <= - (a2 / a1) * x2 */
alpar@1:             if (mir->vub[k1] == 0)
alpar@1:             {  /* set variable upper bound for x1 */
alpar@1:                mir->ub[k1] = - a2 / a1;
alpar@1:                mir->vub[k1] = k2;
alpar@1:                /* the row should not be used */
alpar@1:                mir->skip[i] = 1;
alpar@1:             }
alpar@1:          }
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static void mark_useless_rows(glp_tree *tree, struct MIR *mir)
alpar@1: {     /* mark rows which should not be used */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mir->m;
alpar@1:       GLPAIJ *aij;
alpar@1:       int i, k, nv;
alpar@1:       for (i = 1; i <= m; i++)
alpar@1:       {  /* free rows should not be used */
alpar@1:          if (mir->lb[i] == -DBL_MAX && mir->ub[i] == +DBL_MAX)
alpar@1:          {  mir->skip[i] = 1;
alpar@1:             continue;
alpar@1:          }
alpar@1:          nv = 0;
alpar@1:          for (aij = mip->row[i]->ptr; aij != NULL; aij = aij->r_next)
alpar@1:          {  k = m + aij->col->j;
alpar@1:             /* rows with free variables should not be used */
alpar@1:             if (mir->lb[k] == -DBL_MAX && mir->ub[k] == +DBL_MAX)
alpar@1:             {  mir->skip[i] = 1;
alpar@1:                break;
alpar@1:             }
alpar@1:             /* rows with integer variables having infinite (lower or
alpar@1:                upper) bound should not be used */
alpar@1:             if (mir->isint[k] && mir->lb[k] == -DBL_MAX ||
alpar@1:                 mir->isint[k] && mir->ub[k] == +DBL_MAX)
alpar@1:             {  mir->skip[i] = 1;
alpar@1:                break;
alpar@1:             }
alpar@1:             /* count non-fixed variables */
alpar@1:             if (!(mir->vlb[k] == 0 && mir->vub[k] == 0 &&
alpar@1:                   mir->lb[k] == mir->ub[k])) nv++;
alpar@1:          }
alpar@1:          /* rows with all variables fixed should not be used */
alpar@1:          if (nv == 0)
alpar@1:          {  mir->skip[i] = 1;
alpar@1:             continue;
alpar@1:          }
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: void *ios_mir_init(glp_tree *tree)
alpar@1: {     /* initialize MIR cut generator */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mip->m;
alpar@1:       int n = mip->n;
alpar@1:       struct MIR *mir;
alpar@1: #if _MIR_DEBUG
alpar@1:       xprintf("ios_mir_init: warning: debug mode enabled\n");
alpar@1: #endif
alpar@1:       /* allocate working area */
alpar@1:       mir = xmalloc(sizeof(struct MIR));
alpar@1:       mir->m = m;
alpar@1:       mir->n = n;
alpar@1:       mir->skip = xcalloc(1+m, sizeof(char));
alpar@1:       mir->isint = xcalloc(1+m+n, sizeof(char));
alpar@1:       mir->lb = xcalloc(1+m+n, sizeof(double));
alpar@1:       mir->vlb = xcalloc(1+m+n, sizeof(int));
alpar@1:       mir->ub = xcalloc(1+m+n, sizeof(double));
alpar@1:       mir->vub = xcalloc(1+m+n, sizeof(int));
alpar@1:       mir->x = xcalloc(1+m+n, sizeof(double));
alpar@1:       mir->agg_row = xcalloc(1+MAXAGGR, sizeof(int));
alpar@1:       mir->agg_vec = ios_create_vec(m+n);
alpar@1:       mir->subst = xcalloc(1+m+n, sizeof(char));
alpar@1:       mir->mod_vec = ios_create_vec(m+n);
alpar@1:       mir->cut_vec = ios_create_vec(m+n);
alpar@1:       /* set global row attributes */
alpar@1:       set_row_attrib(tree, mir);
alpar@1:       /* set global column attributes */
alpar@1:       set_col_attrib(tree, mir);
alpar@1:       /* set variable bounds */
alpar@1:       set_var_bounds(tree, mir);
alpar@1:       /* mark rows which should not be used */
alpar@1:       mark_useless_rows(tree, mir);
alpar@1:       return mir;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  ios_mir_gen - generate MIR cuts
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  #include "glpios.h"
alpar@1: *  void ios_mir_gen(glp_tree *tree, void *gen, IOSPOOL *pool);
alpar@1: *
alpar@1: *  DESCRIPTION
alpar@1: *
alpar@1: *  The routine ios_mir_gen generates MIR cuts for the current point and
alpar@1: *  adds them to the cut pool. */
alpar@1: 
alpar@1: static void get_current_point(glp_tree *tree, struct MIR *mir)
alpar@1: {     /* obtain current point */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int k;
alpar@1:       for (k = 1; k <= m; k++)
alpar@1:          mir->x[k] = mip->row[k]->prim;
alpar@1:       for (k = m+1; k <= m+n; k++)
alpar@1:          mir->x[k] = mip->col[k-m]->prim;
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: #if _MIR_DEBUG
alpar@1: static void check_current_point(struct MIR *mir)
alpar@1: {     /* check current point */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int k, kk;
alpar@1:       double lb, ub, eps;
alpar@1:       for (k = 1; k <= m+n; k++)
alpar@1:       {  /* determine lower bound */
alpar@1:          lb = mir->lb[k];
alpar@1:          kk = mir->vlb[k];
alpar@1:          if (kk != 0)
alpar@1:          {  xassert(lb != -DBL_MAX);
alpar@1:             xassert(!mir->isint[k]);
alpar@1:             xassert(mir->isint[kk]);
alpar@1:             lb *= mir->x[kk];
alpar@1:          }
alpar@1:          /* check lower bound */
alpar@1:          if (lb != -DBL_MAX)
alpar@1:          {  eps = 1e-6 * (1.0 + fabs(lb));
alpar@1:             xassert(mir->x[k] >= lb - eps);
alpar@1:          }
alpar@1:          /* determine upper bound */
alpar@1:          ub = mir->ub[k];
alpar@1:          kk = mir->vub[k];
alpar@1:          if (kk != 0)
alpar@1:          {  xassert(ub != +DBL_MAX);
alpar@1:             xassert(!mir->isint[k]);
alpar@1:             xassert(mir->isint[kk]);
alpar@1:             ub *= mir->x[kk];
alpar@1:          }
alpar@1:          /* check upper bound */
alpar@1:          if (ub != +DBL_MAX)
alpar@1:          {  eps = 1e-6 * (1.0 + fabs(ub));
alpar@1:             xassert(mir->x[k] <= ub + eps);
alpar@1:          }
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: #endif
alpar@1: 
alpar@1: static void initial_agg_row(glp_tree *tree, struct MIR *mir, int i)
alpar@1: {     /* use original i-th row as initial aggregated constraint */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mir->m;
alpar@1:       GLPAIJ *aij;
alpar@1:       xassert(1 <= i && i <= m);
alpar@1:       xassert(!mir->skip[i]);
alpar@1:       /* mark i-th row in order not to use it in the same aggregated
alpar@1:          constraint */
alpar@1:       mir->skip[i] = 2;
alpar@1:       mir->agg_cnt = 1;
alpar@1:       mir->agg_row[1] = i;
alpar@1:       /* use x[i] - sum a[i,j] * x[m+j] = 0, where x[i] is auxiliary
alpar@1:          variable of row i, x[m+j] are structural variables */
alpar@1:       ios_clear_vec(mir->agg_vec);
alpar@1:       ios_set_vj(mir->agg_vec, i, 1.0);
alpar@1:       for (aij = mip->row[i]->ptr; aij != NULL; aij = aij->r_next)
alpar@1:          ios_set_vj(mir->agg_vec, m + aij->col->j, - aij->val);
alpar@1:       mir->agg_rhs = 0.0;
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->agg_vec);
alpar@1: #endif
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: #if _MIR_DEBUG
alpar@1: static void check_agg_row(struct MIR *mir)
alpar@1: {     /* check aggregated constraint */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, k;
alpar@1:       double r, big;
alpar@1:       /* compute the residual r = sum a[k] * x[k] - b and determine
alpar@1:          big = max(1, |a[k]|, |b|) */
alpar@1:       r = 0.0, big = 1.0;
alpar@1:       for (j = 1; j <= mir->agg_vec->nnz; j++)
alpar@1:       {  k = mir->agg_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          r += mir->agg_vec->val[j] * mir->x[k];
alpar@1:          if (big < fabs(mir->agg_vec->val[j]))
alpar@1:             big = fabs(mir->agg_vec->val[j]);
alpar@1:       }
alpar@1:       r -= mir->agg_rhs;
alpar@1:       if (big < fabs(mir->agg_rhs))
alpar@1:          big = fabs(mir->agg_rhs);
alpar@1:       /* the residual must be close to zero */
alpar@1:       xassert(fabs(r) <= 1e-6 * big);
alpar@1:       return;
alpar@1: }
alpar@1: #endif
alpar@1: 
alpar@1: static void subst_fixed_vars(struct MIR *mir)
alpar@1: {     /* substitute fixed variables into aggregated constraint */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, k;
alpar@1:       for (j = 1; j <= mir->agg_vec->nnz; j++)
alpar@1:       {  k = mir->agg_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (mir->vlb[k] == 0 && mir->vub[k] == 0 &&
alpar@1:              mir->lb[k] == mir->ub[k])
alpar@1:          {  /* x[k] is fixed */
alpar@1:             mir->agg_rhs -= mir->agg_vec->val[j] * mir->lb[k];
alpar@1:             mir->agg_vec->val[j] = 0.0;
alpar@1:          }
alpar@1:       }
alpar@1:       /* remove terms corresponding to fixed variables */
alpar@1:       ios_clean_vec(mir->agg_vec, DBL_EPSILON);
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->agg_vec);
alpar@1: #endif
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static void bound_subst_heur(struct MIR *mir)
alpar@1: {     /* bound substitution heuristic */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, k, kk;
alpar@1:       double d1, d2;
alpar@1:       for (j = 1; j <= mir->agg_vec->nnz; j++)
alpar@1:       {  k = mir->agg_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (mir->isint[k]) continue; /* skip integer variable */
alpar@1:          /* compute distance from x[k] to its lower bound */
alpar@1:          kk = mir->vlb[k];
alpar@1:          if (kk == 0)
alpar@1:          {  if (mir->lb[k] == -DBL_MAX)
alpar@1:                d1 = DBL_MAX;
alpar@1:             else
alpar@1:                d1 = mir->x[k] - mir->lb[k];
alpar@1:          }
alpar@1:          else
alpar@1:          {  xassert(1 <= kk && kk <= m+n);
alpar@1:             xassert(mir->isint[kk]);
alpar@1:             xassert(mir->lb[k] != -DBL_MAX);
alpar@1:             d1 = mir->x[k] - mir->lb[k] * mir->x[kk];
alpar@1:          }
alpar@1:          /* compute distance from x[k] to its upper bound */
alpar@1:          kk = mir->vub[k];
alpar@1:          if (kk == 0)
alpar@1:          {  if (mir->vub[k] == +DBL_MAX)
alpar@1:                d2 = DBL_MAX;
alpar@1:             else
alpar@1:                d2 = mir->ub[k] - mir->x[k];
alpar@1:          }
alpar@1:          else
alpar@1:          {  xassert(1 <= kk && kk <= m+n);
alpar@1:             xassert(mir->isint[kk]);
alpar@1:             xassert(mir->ub[k] != +DBL_MAX);
alpar@1:             d2 = mir->ub[k] * mir->x[kk] - mir->x[k];
alpar@1:          }
alpar@1:          /* x[k] cannot be free */
alpar@1:          xassert(d1 != DBL_MAX || d2 != DBL_MAX);
alpar@1:          /* choose the bound which is closer to x[k] */
alpar@1:          xassert(mir->subst[k] == '?');
alpar@1:          if (d1 <= d2)
alpar@1:             mir->subst[k] = 'L';
alpar@1:          else
alpar@1:             mir->subst[k] = 'U';
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static void build_mod_row(struct MIR *mir)
alpar@1: {     /* substitute bounds and build modified constraint */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, jj, k, kk;
alpar@1:       /* initially modified constraint is aggregated constraint */
alpar@1:       ios_copy_vec(mir->mod_vec, mir->agg_vec);
alpar@1:       mir->mod_rhs = mir->agg_rhs;
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->mod_vec);
alpar@1: #endif
alpar@1:       /* substitute bounds for continuous variables; note that due to
alpar@1:          substitution of variable bounds additional terms may appear in
alpar@1:          modified constraint */
alpar@1:       for (j = mir->mod_vec->nnz; j >= 1; j--)
alpar@1:       {  k = mir->mod_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (mir->isint[k]) continue; /* skip integer variable */
alpar@1:          if (mir->subst[k] == 'L')
alpar@1:          {  /* x[k] = (lower bound) + x'[k] */
alpar@1:             xassert(mir->lb[k] != -DBL_MAX);
alpar@1:             kk = mir->vlb[k];
alpar@1:             if (kk == 0)
alpar@1:             {  /* x[k] = lb[k] + x'[k] */
alpar@1:                mir->mod_rhs -= mir->mod_vec->val[j] * mir->lb[k];
alpar@1:             }
alpar@1:             else
alpar@1:             {  /* x[k] = lb[k] * x[kk] + x'[k] */
alpar@1:                xassert(mir->isint[kk]);
alpar@1:                jj = mir->mod_vec->pos[kk];
alpar@1:                if (jj == 0)
alpar@1:                {  ios_set_vj(mir->mod_vec, kk, 1.0);
alpar@1:                   jj = mir->mod_vec->pos[kk];
alpar@1:                   mir->mod_vec->val[jj] = 0.0;
alpar@1:                }
alpar@1:                mir->mod_vec->val[jj] +=
alpar@1:                   mir->mod_vec->val[j] * mir->lb[k];
alpar@1:             }
alpar@1:          }
alpar@1:          else if (mir->subst[k] == 'U')
alpar@1:          {  /* x[k] = (upper bound) - x'[k] */
alpar@1:             xassert(mir->ub[k] != +DBL_MAX);
alpar@1:             kk = mir->vub[k];
alpar@1:             if (kk == 0)
alpar@1:             {  /* x[k] = ub[k] - x'[k] */
alpar@1:                mir->mod_rhs -= mir->mod_vec->val[j] * mir->ub[k];
alpar@1:             }
alpar@1:             else
alpar@1:             {  /* x[k] = ub[k] * x[kk] - x'[k] */
alpar@1:                xassert(mir->isint[kk]);
alpar@1:                jj = mir->mod_vec->pos[kk];
alpar@1:                if (jj == 0)
alpar@1:                {  ios_set_vj(mir->mod_vec, kk, 1.0);
alpar@1:                   jj = mir->mod_vec->pos[kk];
alpar@1:                   mir->mod_vec->val[jj] = 0.0;
alpar@1:                }
alpar@1:                mir->mod_vec->val[jj] +=
alpar@1:                   mir->mod_vec->val[j] * mir->ub[k];
alpar@1:             }
alpar@1:             mir->mod_vec->val[j] = - mir->mod_vec->val[j];
alpar@1:          }
alpar@1:          else
alpar@1:             xassert(k != k);
alpar@1:       }
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->mod_vec);
alpar@1: #endif
alpar@1:       /* substitute bounds for integer variables */
alpar@1:       for (j = 1; j <= mir->mod_vec->nnz; j++)
alpar@1:       {  k = mir->mod_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (!mir->isint[k]) continue; /* skip continuous variable */
alpar@1:          xassert(mir->subst[k] == '?');
alpar@1:          xassert(mir->vlb[k] == 0 && mir->vub[k] == 0);
alpar@1:          xassert(mir->lb[k] != -DBL_MAX && mir->ub[k] != +DBL_MAX);
alpar@1:          if (fabs(mir->lb[k]) <= fabs(mir->ub[k]))
alpar@1:          {  /* x[k] = lb[k] + x'[k] */
alpar@1:             mir->subst[k] = 'L';
alpar@1:             mir->mod_rhs -= mir->mod_vec->val[j] * mir->lb[k];
alpar@1:          }
alpar@1:          else
alpar@1:          {  /* x[k] = ub[k] - x'[k] */
alpar@1:             mir->subst[k] = 'U';
alpar@1:             mir->mod_rhs -= mir->mod_vec->val[j] * mir->ub[k];
alpar@1:             mir->mod_vec->val[j] = - mir->mod_vec->val[j];
alpar@1:          }
alpar@1:       }
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->mod_vec);
alpar@1: #endif
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: #if _MIR_DEBUG
alpar@1: static void check_mod_row(struct MIR *mir)
alpar@1: {     /* check modified constraint */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, k, kk;
alpar@1:       double r, big, x;
alpar@1:       /* compute the residual r = sum a'[k] * x'[k] - b' and determine
alpar@1:          big = max(1, |a[k]|, |b|) */
alpar@1:       r = 0.0, big = 1.0;
alpar@1:       for (j = 1; j <= mir->mod_vec->nnz; j++)
alpar@1:       {  k = mir->mod_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (mir->subst[k] == 'L')
alpar@1:          {  /* x'[k] = x[k] - (lower bound) */
alpar@1:             xassert(mir->lb[k] != -DBL_MAX);
alpar@1:             kk = mir->vlb[k];
alpar@1:             if (kk == 0)
alpar@1:                x = mir->x[k] - mir->lb[k];
alpar@1:             else
alpar@1:                x = mir->x[k] - mir->lb[k] * mir->x[kk];
alpar@1:          }
alpar@1:          else if (mir->subst[k] == 'U')
alpar@1:          {  /* x'[k] = (upper bound) - x[k] */
alpar@1:             xassert(mir->ub[k] != +DBL_MAX);
alpar@1:             kk = mir->vub[k];
alpar@1:             if (kk == 0)
alpar@1:                x = mir->ub[k] - mir->x[k];
alpar@1:             else
alpar@1:                x = mir->ub[k] * mir->x[kk] - mir->x[k];
alpar@1:          }
alpar@1:          else
alpar@1:             xassert(k != k);
alpar@1:          r += mir->mod_vec->val[j] * x;
alpar@1:          if (big < fabs(mir->mod_vec->val[j]))
alpar@1:             big = fabs(mir->mod_vec->val[j]);
alpar@1:       }
alpar@1:       r -= mir->mod_rhs;
alpar@1:       if (big < fabs(mir->mod_rhs))
alpar@1:          big = fabs(mir->mod_rhs);
alpar@1:       /* the residual must be close to zero */
alpar@1:       xassert(fabs(r) <= 1e-6 * big);
alpar@1:       return;
alpar@1: }
alpar@1: #endif
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  mir_ineq - construct MIR inequality
alpar@1: *
alpar@1: *  Given the single constraint mixed integer set
alpar@1: *
alpar@1: *                    |N|
alpar@1: *     X = {(x,s) in Z    x R  : sum   a[j] * x[j] <= b + s},
alpar@1: *                    +      +  j in N
alpar@1: *
alpar@1: *  this routine constructs the mixed integer rounding (MIR) inequality
alpar@1: *
alpar@1: *     sum   alpha[j] * x[j] <= beta + gamma * s,
alpar@1: *    j in N
alpar@1: *
alpar@1: *  which is valid for X.
alpar@1: *
alpar@1: *  If the MIR inequality has been successfully constructed, the routine
alpar@1: *  returns zero. Otherwise, if b is close to nearest integer, there may
alpar@1: *  be numeric difficulties due to big coefficients; so in this case the
alpar@1: *  routine returns non-zero. */
alpar@1: 
alpar@1: static int mir_ineq(const int n, const double a[], const double b,
alpar@1:       double alpha[], double *beta, double *gamma)
alpar@1: {     int j;
alpar@1:       double f, t;
alpar@1:       if (fabs(b - floor(b + .5)) < 0.01)
alpar@1:          return 1;
alpar@1:       f = b - floor(b);
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  t = (a[j] - floor(a[j])) - f;
alpar@1:          if (t <= 0.0)
alpar@1:             alpha[j] = floor(a[j]);
alpar@1:          else
alpar@1:             alpha[j] = floor(a[j]) + t / (1.0 - f);
alpar@1:       }
alpar@1:       *beta = floor(b);
alpar@1:       *gamma = 1.0 / (1.0 - f);
alpar@1:       return 0;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  cmir_ineq - construct c-MIR inequality
alpar@1: *
alpar@1: *  Given the mixed knapsack set
alpar@1: *
alpar@1: *      MK              |N|
alpar@1: *     X   = {(x,s) in Z    x R  : sum   a[j] * x[j] <= b + s,
alpar@1: *                      +      +  j in N
alpar@1: *
alpar@1: *             x[j] <= u[j]},
alpar@1: *
alpar@1: *  a subset C of variables to be complemented, and a divisor delta > 0,
alpar@1: *  this routine constructs the complemented MIR (c-MIR) inequality
alpar@1: *
alpar@1: *     sum   alpha[j] * x[j] <= beta + gamma * s,
alpar@1: *    j in N
alpar@1: *                      MK
alpar@1: *  which is valid for X  .
alpar@1: *
alpar@1: *  If the c-MIR inequality has been successfully constructed, the
alpar@1: *  routine returns zero. Otherwise, if there is a risk of numerical
alpar@1: *  difficulties due to big coefficients (see comments to the routine
alpar@1: *  mir_ineq), the routine cmir_ineq returns non-zero. */
alpar@1: 
alpar@1: static int cmir_ineq(const int n, const double a[], const double b,
alpar@1:       const double u[], const char cset[], const double delta,
alpar@1:       double alpha[], double *beta, double *gamma)
alpar@1: {     int j;
alpar@1:       double *aa, bb;
alpar@1:       aa = alpha, bb = b;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  aa[j] = a[j] / delta;
alpar@1:          if (cset[j])
alpar@1:             aa[j] = - aa[j], bb -= a[j] * u[j];
alpar@1:       }
alpar@1:       bb /= delta;
alpar@1:       if (mir_ineq(n, aa, bb, alpha, beta, gamma)) return 1;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  if (cset[j])
alpar@1:             alpha[j] = - alpha[j], *beta += alpha[j] * u[j];
alpar@1:       }
alpar@1:       *gamma /= delta;
alpar@1:       return 0;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  cmir_sep - c-MIR separation heuristic
alpar@1: *
alpar@1: *  Given the mixed knapsack set
alpar@1: *
alpar@1: *      MK              |N|
alpar@1: *     X   = {(x,s) in Z    x R  : sum   a[j] * x[j] <= b + s,
alpar@1: *                      +      +  j in N
alpar@1: *
alpar@1: *             x[j] <= u[j]}
alpar@1: *
alpar@1: *                           *   *
alpar@1: *  and a fractional point (x , s ), this routine tries to construct
alpar@1: *  c-MIR inequality
alpar@1: *
alpar@1: *     sum   alpha[j] * x[j] <= beta + gamma * s,
alpar@1: *    j in N
alpar@1: *                      MK
alpar@1: *  which is valid for X   and has (desirably maximal) violation at the
alpar@1: *  fractional point given. This is attained by choosing an appropriate
alpar@1: *  set C of variables to be complemented and a divisor delta > 0, which
alpar@1: *  together define corresponding c-MIR inequality.
alpar@1: *
alpar@1: *  If a violated c-MIR inequality has been successfully constructed,
alpar@1: *  the routine returns its violation:
alpar@1: *
alpar@1: *                       *                      *
alpar@1: *     sum   alpha[j] * x [j] - beta - gamma * s ,
alpar@1: *    j in N
alpar@1: *
alpar@1: *  which is positive. In case of failure the routine returns zero. */
alpar@1: 
alpar@1: struct vset { int j; double v; };
alpar@1: 
alpar@1: static int cmir_cmp(const void *p1, const void *p2)
alpar@1: {     const struct vset *v1 = p1, *v2 = p2;
alpar@1:       if (v1->v < v2->v) return -1;
alpar@1:       if (v1->v > v2->v) return +1;
alpar@1:       return 0;
alpar@1: }
alpar@1: 
alpar@1: static double cmir_sep(const int n, const double a[], const double b,
alpar@1:       const double u[], const double x[], const double s,
alpar@1:       double alpha[], double *beta, double *gamma)
alpar@1: {     int fail, j, k, nv, v;
alpar@1:       double delta, eps, d_try[1+3], r, r_best;
alpar@1:       char *cset;
alpar@1:       struct vset *vset;
alpar@1:       /* allocate working arrays */
alpar@1:       cset = xcalloc(1+n, sizeof(char));
alpar@1:       vset = xcalloc(1+n, sizeof(struct vset));
alpar@1:       /* choose initial C */
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:          cset[j] = (char)(x[j] >= 0.5 * u[j]);
alpar@1:       /* choose initial delta */
alpar@1:       r_best = delta = 0.0;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  xassert(a[j] != 0.0);
alpar@1:          /* if x[j] is close to its bounds, skip it */
alpar@1:          eps = 1e-9 * (1.0 + fabs(u[j]));
alpar@1:          if (x[j] < eps || x[j] > u[j] - eps) continue;
alpar@1:          /* try delta = |a[j]| to construct c-MIR inequality */
alpar@1:          fail = cmir_ineq(n, a, b, u, cset, fabs(a[j]), alpha, beta,
alpar@1:             gamma);
alpar@1:          if (fail) continue;
alpar@1:          /* compute violation */
alpar@1:          r = - (*beta) - (*gamma) * s;
alpar@1:          for (k = 1; k <= n; k++) r += alpha[k] * x[k];
alpar@1:          if (r_best < r) r_best = r, delta = fabs(a[j]);
alpar@1:       }
alpar@1:       if (r_best < 0.001) r_best = 0.0;
alpar@1:       if (r_best == 0.0) goto done;
alpar@1:       xassert(delta > 0.0);
alpar@1:       /* try to increase violation by dividing delta by 2, 4, and 8,
alpar@1:          respectively */
alpar@1:       d_try[1] = delta / 2.0;
alpar@1:       d_try[2] = delta / 4.0;
alpar@1:       d_try[3] = delta / 8.0;
alpar@1:       for (j = 1; j <= 3; j++)
alpar@1:       {  /* construct c-MIR inequality */
alpar@1:          fail = cmir_ineq(n, a, b, u, cset, d_try[j], alpha, beta,
alpar@1:             gamma);
alpar@1:          if (fail) continue;
alpar@1:          /* compute violation */
alpar@1:          r = - (*beta) - (*gamma) * s;
alpar@1:          for (k = 1; k <= n; k++) r += alpha[k] * x[k];
alpar@1:          if (r_best < r) r_best = r, delta = d_try[j];
alpar@1:       }
alpar@1:       /* build subset of variables lying strictly between their bounds
alpar@1:          and order it by nondecreasing values of |x[j] - u[j]/2| */
alpar@1:       nv = 0;
alpar@1:       for (j = 1; j <= n; j++)
alpar@1:       {  /* if x[j] is close to its bounds, skip it */
alpar@1:          eps = 1e-9 * (1.0 + fabs(u[j]));
alpar@1:          if (x[j] < eps || x[j] > u[j] - eps) continue;
alpar@1:          /* add x[j] to the subset */
alpar@1:          nv++;
alpar@1:          vset[nv].j = j;
alpar@1:          vset[nv].v = fabs(x[j] - 0.5 * u[j]);
alpar@1:       }
alpar@1:       qsort(&vset[1], nv, sizeof(struct vset), cmir_cmp);
alpar@1:       /* try to increase violation by successively complementing each
alpar@1:          variable in the subset */
alpar@1:       for (v = 1; v <= nv; v++)
alpar@1:       {  j = vset[v].j;
alpar@1:          /* replace x[j] by its complement or vice versa */
alpar@1:          cset[j] = (char)!cset[j];
alpar@1:          /* construct c-MIR inequality */
alpar@1:          fail = cmir_ineq(n, a, b, u, cset, delta, alpha, beta, gamma);
alpar@1:          /* restore the variable */
alpar@1:          cset[j] = (char)!cset[j];
alpar@1:          /* do not replace the variable in case of failure */
alpar@1:          if (fail) continue;
alpar@1:          /* compute violation */
alpar@1:          r = - (*beta) - (*gamma) * s;
alpar@1:          for (k = 1; k <= n; k++) r += alpha[k] * x[k];
alpar@1:          if (r_best < r) r_best = r, cset[j] = (char)!cset[j];
alpar@1:       }
alpar@1:       /* construct the best c-MIR inequality chosen */
alpar@1:       fail = cmir_ineq(n, a, b, u, cset, delta, alpha, beta, gamma);
alpar@1:       xassert(!fail);
alpar@1: done: /* free working arrays */
alpar@1:       xfree(cset);
alpar@1:       xfree(vset);
alpar@1:       /* return to the calling routine */
alpar@1:       return r_best;
alpar@1: }
alpar@1: 
alpar@1: static double generate(struct MIR *mir)
alpar@1: {     /* try to generate violated c-MIR cut for modified constraint */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, k, kk, nint;
alpar@1:       double s, *u, *x, *alpha, r_best = 0.0, b, beta, gamma;
alpar@1:       ios_copy_vec(mir->cut_vec, mir->mod_vec);
alpar@1:       mir->cut_rhs = mir->mod_rhs;
alpar@1:       /* remove small terms, which can appear due to substitution of
alpar@1:          variable bounds */
alpar@1:       ios_clean_vec(mir->cut_vec, DBL_EPSILON);
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->cut_vec);
alpar@1: #endif
alpar@1:       /* remove positive continuous terms to obtain MK relaxation */
alpar@1:       for (j = 1; j <= mir->cut_vec->nnz; j++)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (!mir->isint[k] && mir->cut_vec->val[j] > 0.0)
alpar@1:             mir->cut_vec->val[j] = 0.0;
alpar@1:       }
alpar@1:       ios_clean_vec(mir->cut_vec, 0.0);
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->cut_vec);
alpar@1: #endif
alpar@1:       /* move integer terms to the beginning of the sparse vector and
alpar@1:          determine the number of integer variables */
alpar@1:       nint = 0;
alpar@1:       for (j = 1; j <= mir->cut_vec->nnz; j++)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (mir->isint[k])
alpar@1:          {  double temp;
alpar@1:             nint++;
alpar@1:             /* interchange elements [nint] and [j] */
alpar@1:             kk = mir->cut_vec->ind[nint];
alpar@1:             mir->cut_vec->pos[k] = nint;
alpar@1:             mir->cut_vec->pos[kk] = j;
alpar@1:             mir->cut_vec->ind[nint] = k;
alpar@1:             mir->cut_vec->ind[j] = kk;
alpar@1:             temp = mir->cut_vec->val[nint];
alpar@1:             mir->cut_vec->val[nint] = mir->cut_vec->val[j];
alpar@1:             mir->cut_vec->val[j] = temp;
alpar@1:          }
alpar@1:       }
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->cut_vec);
alpar@1: #endif
alpar@1:       /* if there is no integer variable, nothing to generate */
alpar@1:       if (nint == 0) goto done;
alpar@1:       /* allocate working arrays */
alpar@1:       u = xcalloc(1+nint, sizeof(double));
alpar@1:       x = xcalloc(1+nint, sizeof(double));
alpar@1:       alpha = xcalloc(1+nint, sizeof(double));
alpar@1:       /* determine u and x */
alpar@1:       for (j = 1; j <= nint; j++)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(m+1 <= k && k <= m+n);
alpar@1:          xassert(mir->isint[k]);
alpar@1:          u[j] = mir->ub[k] - mir->lb[k];
alpar@1:          xassert(u[j] >= 1.0);
alpar@1:          if (mir->subst[k] == 'L')
alpar@1:             x[j] = mir->x[k] - mir->lb[k];
alpar@1:          else if (mir->subst[k] == 'U')
alpar@1:             x[j] = mir->ub[k] - mir->x[k];
alpar@1:          else
alpar@1:             xassert(k != k);
alpar@1:          xassert(x[j] >= -0.001);
alpar@1:          if (x[j] < 0.0) x[j] = 0.0;
alpar@1:       }
alpar@1:       /* compute s = - sum of continuous terms */
alpar@1:       s = 0.0;
alpar@1:       for (j = nint+1; j <= mir->cut_vec->nnz; j++)
alpar@1:       {  double x;
alpar@1:          k = mir->cut_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          /* must be continuous */
alpar@1:          xassert(!mir->isint[k]);
alpar@1:          if (mir->subst[k] == 'L')
alpar@1:          {  xassert(mir->lb[k] != -DBL_MAX);
alpar@1:             kk = mir->vlb[k];
alpar@1:             if (kk == 0)
alpar@1:                x = mir->x[k] - mir->lb[k];
alpar@1:             else
alpar@1:                x = mir->x[k] - mir->lb[k] * mir->x[kk];
alpar@1:          }
alpar@1:          else if (mir->subst[k] == 'U')
alpar@1:          {  xassert(mir->ub[k] != +DBL_MAX);
alpar@1:             kk = mir->vub[k];
alpar@1:             if (kk == 0)
alpar@1:                x = mir->ub[k] - mir->x[k];
alpar@1:             else
alpar@1:                x = mir->ub[k] * mir->x[kk] - mir->x[k];
alpar@1:          }
alpar@1:          else
alpar@1:             xassert(k != k);
alpar@1:          xassert(x >= -0.001);
alpar@1:          if (x < 0.0) x = 0.0;
alpar@1:          s -= mir->cut_vec->val[j] * x;
alpar@1:       }
alpar@1:       xassert(s >= 0.0);
alpar@1:       /* apply heuristic to obtain most violated c-MIR inequality */
alpar@1:       b = mir->cut_rhs;
alpar@1:       r_best = cmir_sep(nint, mir->cut_vec->val, b, u, x, s, alpha,
alpar@1:          &beta, &gamma);
alpar@1:       if (r_best == 0.0) goto skip;
alpar@1:       xassert(r_best > 0.0);
alpar@1:       /* convert to raw cut */
alpar@1:       /* sum alpha[j] * x[j] <= beta + gamma * s */
alpar@1:       for (j = 1; j <= nint; j++)
alpar@1:          mir->cut_vec->val[j] = alpha[j];
alpar@1:       for (j = nint+1; j <= mir->cut_vec->nnz; j++)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          if (k <= m+n) mir->cut_vec->val[j] *= gamma;
alpar@1:       }
alpar@1:       mir->cut_rhs = beta;
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->cut_vec);
alpar@1: #endif
alpar@1: skip: /* free working arrays */
alpar@1:       xfree(u);
alpar@1:       xfree(x);
alpar@1:       xfree(alpha);
alpar@1: done: return r_best;
alpar@1: }
alpar@1: 
alpar@1: #if _MIR_DEBUG
alpar@1: static void check_raw_cut(struct MIR *mir, double r_best)
alpar@1: {     /* check raw cut before back bound substitution */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, k, kk;
alpar@1:       double r, big, x;
alpar@1:       /* compute the residual r = sum a[k] * x[k] - b and determine
alpar@1:          big = max(1, |a[k]|, |b|) */
alpar@1:       r = 0.0, big = 1.0;
alpar@1:       for (j = 1; j <= mir->cut_vec->nnz; j++)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (mir->subst[k] == 'L')
alpar@1:          {  xassert(mir->lb[k] != -DBL_MAX);
alpar@1:             kk = mir->vlb[k];
alpar@1:             if (kk == 0)
alpar@1:                x = mir->x[k] - mir->lb[k];
alpar@1:             else
alpar@1:                x = mir->x[k] - mir->lb[k] * mir->x[kk];
alpar@1:          }
alpar@1:          else if (mir->subst[k] == 'U')
alpar@1:          {  xassert(mir->ub[k] != +DBL_MAX);
alpar@1:             kk = mir->vub[k];
alpar@1:             if (kk == 0)
alpar@1:                x = mir->ub[k] - mir->x[k];
alpar@1:             else
alpar@1:                x = mir->ub[k] * mir->x[kk] - mir->x[k];
alpar@1:          }
alpar@1:          else
alpar@1:             xassert(k != k);
alpar@1:          r += mir->cut_vec->val[j] * x;
alpar@1:          if (big < fabs(mir->cut_vec->val[j]))
alpar@1:             big = fabs(mir->cut_vec->val[j]);
alpar@1:       }
alpar@1:       r -= mir->cut_rhs;
alpar@1:       if (big < fabs(mir->cut_rhs))
alpar@1:          big = fabs(mir->cut_rhs);
alpar@1:       /* the residual must be close to r_best */
alpar@1:       xassert(fabs(r - r_best) <= 1e-6 * big);
alpar@1:       return;
alpar@1: }
alpar@1: #endif
alpar@1: 
alpar@1: static void back_subst(struct MIR *mir)
alpar@1: {     /* back substitution of original bounds */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, jj, k, kk;
alpar@1:       /* at first, restore bounds of integer variables (because on
alpar@1:          restoring variable bounds of continuous variables we need
alpar@1:          original, not shifted, bounds of integer variables) */
alpar@1:       for (j = 1; j <= mir->cut_vec->nnz; j++)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (!mir->isint[k]) continue; /* skip continuous */
alpar@1:          if (mir->subst[k] == 'L')
alpar@1:          {  /* x'[k] = x[k] - lb[k] */
alpar@1:             xassert(mir->lb[k] != -DBL_MAX);
alpar@1:             xassert(mir->vlb[k] == 0);
alpar@1:             mir->cut_rhs += mir->cut_vec->val[j] * mir->lb[k];
alpar@1:          }
alpar@1:          else if (mir->subst[k] == 'U')
alpar@1:          {  /* x'[k] = ub[k] - x[k] */
alpar@1:             xassert(mir->ub[k] != +DBL_MAX);
alpar@1:             xassert(mir->vub[k] == 0);
alpar@1:             mir->cut_rhs -= mir->cut_vec->val[j] * mir->ub[k];
alpar@1:             mir->cut_vec->val[j] = - mir->cut_vec->val[j];
alpar@1:          }
alpar@1:          else
alpar@1:             xassert(k != k);
alpar@1:       }
alpar@1:       /* now restore bounds of continuous variables */
alpar@1:       for (j = 1; j <= mir->cut_vec->nnz; j++)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (mir->isint[k]) continue; /* skip integer */
alpar@1:          if (mir->subst[k] == 'L')
alpar@1:          {  /* x'[k] = x[k] - (lower bound) */
alpar@1:             xassert(mir->lb[k] != -DBL_MAX);
alpar@1:             kk = mir->vlb[k];
alpar@1:             if (kk == 0)
alpar@1:             {  /* x'[k] = x[k] - lb[k] */
alpar@1:                mir->cut_rhs += mir->cut_vec->val[j] * mir->lb[k];
alpar@1:             }
alpar@1:             else
alpar@1:             {  /* x'[k] = x[k] - lb[k] * x[kk] */
alpar@1:                jj = mir->cut_vec->pos[kk];
alpar@1: #if 0
alpar@1:                xassert(jj != 0);
alpar@1: #else
alpar@1:                if (jj == 0)
alpar@1:                {  ios_set_vj(mir->cut_vec, kk, 1.0);
alpar@1:                   jj = mir->cut_vec->pos[kk];
alpar@1:                   xassert(jj != 0);
alpar@1:                   mir->cut_vec->val[jj] = 0.0;
alpar@1:                }
alpar@1: #endif
alpar@1:                mir->cut_vec->val[jj] -= mir->cut_vec->val[j] *
alpar@1:                   mir->lb[k];
alpar@1:             }
alpar@1:          }
alpar@1:          else if (mir->subst[k] == 'U')
alpar@1:          {  /* x'[k] = (upper bound) - x[k] */
alpar@1:             xassert(mir->ub[k] != +DBL_MAX);
alpar@1:             kk = mir->vub[k];
alpar@1:             if (kk == 0)
alpar@1:             {  /* x'[k] = ub[k] - x[k] */
alpar@1:                mir->cut_rhs -= mir->cut_vec->val[j] * mir->ub[k];
alpar@1:             }
alpar@1:             else
alpar@1:             {  /* x'[k] = ub[k] * x[kk] - x[k] */
alpar@1:                jj = mir->cut_vec->pos[kk];
alpar@1:                if (jj == 0)
alpar@1:                {  ios_set_vj(mir->cut_vec, kk, 1.0);
alpar@1:                   jj = mir->cut_vec->pos[kk];
alpar@1:                   xassert(jj != 0);
alpar@1:                   mir->cut_vec->val[jj] = 0.0;
alpar@1:                }
alpar@1:                mir->cut_vec->val[jj] += mir->cut_vec->val[j] *
alpar@1:                   mir->ub[k];
alpar@1:             }
alpar@1:             mir->cut_vec->val[j] = - mir->cut_vec->val[j];
alpar@1:          }
alpar@1:          else
alpar@1:             xassert(k != k);
alpar@1:       }
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->cut_vec);
alpar@1: #endif
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: #if _MIR_DEBUG
alpar@1: static void check_cut_row(struct MIR *mir, double r_best)
alpar@1: {     /* check the cut after back bound substitution or elimination of
alpar@1:          auxiliary variables */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, k;
alpar@1:       double r, big;
alpar@1:       /* compute the residual r = sum a[k] * x[k] - b and determine
alpar@1:          big = max(1, |a[k]|, |b|) */
alpar@1:       r = 0.0, big = 1.0;
alpar@1:       for (j = 1; j <= mir->cut_vec->nnz; j++)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          r += mir->cut_vec->val[j] * mir->x[k];
alpar@1:          if (big < fabs(mir->cut_vec->val[j]))
alpar@1:             big = fabs(mir->cut_vec->val[j]);
alpar@1:       }
alpar@1:       r -= mir->cut_rhs;
alpar@1:       if (big < fabs(mir->cut_rhs))
alpar@1:          big = fabs(mir->cut_rhs);
alpar@1:       /* the residual must be close to r_best */
alpar@1:       xassert(fabs(r - r_best) <= 1e-6 * big);
alpar@1:       return;
alpar@1: }
alpar@1: #endif
alpar@1: 
alpar@1: static void subst_aux_vars(glp_tree *tree, struct MIR *mir)
alpar@1: {     /* final substitution to eliminate auxiliary variables */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       GLPAIJ *aij;
alpar@1:       int j, k, kk, jj;
alpar@1:       for (j = mir->cut_vec->nnz; j >= 1; j--)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (k > m) continue; /* skip structurals */
alpar@1:          for (aij = mip->row[k]->ptr; aij != NULL; aij = aij->r_next)
alpar@1:          {  kk = m + aij->col->j; /* structural */
alpar@1:             jj = mir->cut_vec->pos[kk];
alpar@1:             if (jj == 0)
alpar@1:             {  ios_set_vj(mir->cut_vec, kk, 1.0);
alpar@1:                jj = mir->cut_vec->pos[kk];
alpar@1:                mir->cut_vec->val[jj] = 0.0;
alpar@1:             }
alpar@1:             mir->cut_vec->val[jj] += mir->cut_vec->val[j] * aij->val;
alpar@1:          }
alpar@1:          mir->cut_vec->val[j] = 0.0;
alpar@1:       }
alpar@1:       ios_clean_vec(mir->cut_vec, 0.0);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static void add_cut(glp_tree *tree, struct MIR *mir)
alpar@1: {     /* add constructed cut inequality to the cut pool */
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int j, k, len;
alpar@1:       int *ind = xcalloc(1+n, sizeof(int));
alpar@1:       double *val = xcalloc(1+n, sizeof(double));
alpar@1:       len = 0;
alpar@1:       for (j = mir->cut_vec->nnz; j >= 1; j--)
alpar@1:       {  k = mir->cut_vec->ind[j];
alpar@1:          xassert(m+1 <= k && k <= m+n);
alpar@1:          len++, ind[len] = k - m, val[len] = mir->cut_vec->val[j];
alpar@1:       }
alpar@1: #if 0
alpar@1:       ios_add_cut_row(tree, pool, GLP_RF_MIR, len, ind, val, GLP_UP,
alpar@1:          mir->cut_rhs);
alpar@1: #else
alpar@1:       glp_ios_add_row(tree, NULL, GLP_RF_MIR, 0, len, ind, val, GLP_UP,
alpar@1:          mir->cut_rhs);
alpar@1: #endif
alpar@1:       xfree(ind);
alpar@1:       xfree(val);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: static int aggregate_row(glp_tree *tree, struct MIR *mir)
alpar@1: {     /* try to aggregate another row */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       GLPAIJ *aij;
alpar@1:       IOSVEC *v;
alpar@1:       int ii, j, jj, k, kk, kappa = 0, ret = 0;
alpar@1:       double d1, d2, d, d_max = 0.0;
alpar@1:       /* choose appropriate structural variable in the aggregated row
alpar@1:          to be substituted */
alpar@1:       for (j = 1; j <= mir->agg_vec->nnz; j++)
alpar@1:       {  k = mir->agg_vec->ind[j];
alpar@1:          xassert(1 <= k && k <= m+n);
alpar@1:          if (k <= m) continue; /* skip auxiliary var */
alpar@1:          if (mir->isint[k]) continue; /* skip integer var */
alpar@1:          if (fabs(mir->agg_vec->val[j]) < 0.001) continue;
alpar@1:          /* compute distance from x[k] to its lower bound */
alpar@1:          kk = mir->vlb[k];
alpar@1:          if (kk == 0)
alpar@1:          {  if (mir->lb[k] == -DBL_MAX)
alpar@1:                d1 = DBL_MAX;
alpar@1:             else
alpar@1:                d1 = mir->x[k] - mir->lb[k];
alpar@1:          }
alpar@1:          else
alpar@1:          {  xassert(1 <= kk && kk <= m+n);
alpar@1:             xassert(mir->isint[kk]);
alpar@1:             xassert(mir->lb[k] != -DBL_MAX);
alpar@1:             d1 = mir->x[k] - mir->lb[k] * mir->x[kk];
alpar@1:          }
alpar@1:          /* compute distance from x[k] to its upper bound */
alpar@1:          kk = mir->vub[k];
alpar@1:          if (kk == 0)
alpar@1:          {  if (mir->vub[k] == +DBL_MAX)
alpar@1:                d2 = DBL_MAX;
alpar@1:             else
alpar@1:                d2 = mir->ub[k] - mir->x[k];
alpar@1:          }
alpar@1:          else
alpar@1:          {  xassert(1 <= kk && kk <= m+n);
alpar@1:             xassert(mir->isint[kk]);
alpar@1:             xassert(mir->ub[k] != +DBL_MAX);
alpar@1:             d2 = mir->ub[k] * mir->x[kk] - mir->x[k];
alpar@1:          }
alpar@1:          /* x[k] cannot be free */
alpar@1:          xassert(d1 != DBL_MAX || d2 != DBL_MAX);
alpar@1:          /* d = min(d1, d2) */
alpar@1:          d = (d1 <= d2 ? d1 : d2);
alpar@1:          xassert(d != DBL_MAX);
alpar@1:          /* should not be close to corresponding bound */
alpar@1:          if (d < 0.001) continue;
alpar@1:          if (d_max < d) d_max = d, kappa = k;
alpar@1:       }
alpar@1:       if (kappa == 0)
alpar@1:       {  /* nothing chosen */
alpar@1:          ret = 1;
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* x[kappa] has been chosen */
alpar@1:       xassert(m+1 <= kappa && kappa <= m+n);
alpar@1:       xassert(!mir->isint[kappa]);
alpar@1:       /* find another row, which have not been used yet, to eliminate
alpar@1:          x[kappa] from the aggregated row */
alpar@1:       for (ii = 1; ii <= m; ii++)
alpar@1:       {  if (mir->skip[ii]) continue;
alpar@1:          for (aij = mip->row[ii]->ptr; aij != NULL; aij = aij->r_next)
alpar@1:             if (aij->col->j == kappa - m) break;
alpar@1:          if (aij != NULL && fabs(aij->val) >= 0.001) break;
alpar@1:       }
alpar@1:       if (ii > m)
alpar@1:       {  /* nothing found */
alpar@1:          ret = 2;
alpar@1:          goto done;
alpar@1:       }
alpar@1:       /* row ii has been found; include it in the aggregated list */
alpar@1:       mir->agg_cnt++;
alpar@1:       xassert(mir->agg_cnt <= MAXAGGR);
alpar@1:       mir->agg_row[mir->agg_cnt] = ii;
alpar@1:       mir->skip[ii] = 2;
alpar@1:       /* v := new row */
alpar@1:       v = ios_create_vec(m+n);
alpar@1:       ios_set_vj(v, ii, 1.0);
alpar@1:       for (aij = mip->row[ii]->ptr; aij != NULL; aij = aij->r_next)
alpar@1:          ios_set_vj(v, m + aij->col->j, - aij->val);
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(v);
alpar@1: #endif
alpar@1:       /* perform gaussian elimination to remove x[kappa] */
alpar@1:       j = mir->agg_vec->pos[kappa];
alpar@1:       xassert(j != 0);
alpar@1:       jj = v->pos[kappa];
alpar@1:       xassert(jj != 0);
alpar@1:       ios_linear_comb(mir->agg_vec,
alpar@1:          - mir->agg_vec->val[j] / v->val[jj], v);
alpar@1:       ios_delete_vec(v);
alpar@1:       ios_set_vj(mir->agg_vec, kappa, 0.0);
alpar@1: #if _MIR_DEBUG
alpar@1:       ios_check_vec(mir->agg_vec);
alpar@1: #endif
alpar@1: done: return ret;
alpar@1: }
alpar@1: 
alpar@1: void ios_mir_gen(glp_tree *tree, void *gen)
alpar@1: {     /* main routine to generate MIR cuts */
alpar@1:       glp_prob *mip = tree->mip;
alpar@1:       struct MIR *mir = gen;
alpar@1:       int m = mir->m;
alpar@1:       int n = mir->n;
alpar@1:       int i;
alpar@1:       double r_best;
alpar@1:       xassert(mip->m >= m);
alpar@1:       xassert(mip->n == n);
alpar@1:       /* obtain current point */
alpar@1:       get_current_point(tree, mir);
alpar@1: #if _MIR_DEBUG
alpar@1:       /* check current point */
alpar@1:       check_current_point(mir);
alpar@1: #endif
alpar@1:       /* reset bound substitution flags */
alpar@1:       memset(&mir->subst[1], '?', m+n);
alpar@1:       /* try to generate a set of violated MIR cuts */
alpar@1:       for (i = 1; i <= m; i++)
alpar@1:       {  if (mir->skip[i]) continue;
alpar@1:          /* use original i-th row as initial aggregated constraint */
alpar@1:          initial_agg_row(tree, mir, i);
alpar@1: loop:    ;
alpar@1: #if _MIR_DEBUG
alpar@1:          /* check aggregated row */
alpar@1:          check_agg_row(mir);
alpar@1: #endif
alpar@1:          /* substitute fixed variables into aggregated constraint */
alpar@1:          subst_fixed_vars(mir);
alpar@1: #if _MIR_DEBUG
alpar@1:          /* check aggregated row */
alpar@1:          check_agg_row(mir);
alpar@1: #endif
alpar@1: #if _MIR_DEBUG
alpar@1:          /* check bound substitution flags */
alpar@1:          {  int k;
alpar@1:             for (k = 1; k <= m+n; k++)
alpar@1:                xassert(mir->subst[k] == '?');
alpar@1:          }
alpar@1: #endif
alpar@1:          /* apply bound substitution heuristic */
alpar@1:          bound_subst_heur(mir);
alpar@1:          /* substitute bounds and build modified constraint */
alpar@1:          build_mod_row(mir);
alpar@1: #if _MIR_DEBUG
alpar@1:          /* check modified row */
alpar@1:          check_mod_row(mir);
alpar@1: #endif
alpar@1:          /* try to generate violated c-MIR cut for modified row */
alpar@1:          r_best = generate(mir);
alpar@1:          if (r_best > 0.0)
alpar@1:          {  /* success */
alpar@1: #if _MIR_DEBUG
alpar@1:             /* check raw cut before back bound substitution */
alpar@1:             check_raw_cut(mir, r_best);
alpar@1: #endif
alpar@1:             /* back substitution of original bounds */
alpar@1:             back_subst(mir);
alpar@1: #if _MIR_DEBUG
alpar@1:             /* check the cut after back bound substitution */
alpar@1:             check_cut_row(mir, r_best);
alpar@1: #endif
alpar@1:             /* final substitution to eliminate auxiliary variables */
alpar@1:             subst_aux_vars(tree, mir);
alpar@1: #if _MIR_DEBUG
alpar@1:             /* check the cut after elimination of auxiliaries */
alpar@1:             check_cut_row(mir, r_best);
alpar@1: #endif
alpar@1:             /* add constructed cut inequality to the cut pool */
alpar@1:             add_cut(tree, mir);
alpar@1:          }
alpar@1:          /* reset bound substitution flags */
alpar@1:          {  int j, k;
alpar@1:             for (j = 1; j <= mir->mod_vec->nnz; j++)
alpar@1:             {  k = mir->mod_vec->ind[j];
alpar@1:                xassert(1 <= k && k <= m+n);
alpar@1:                xassert(mir->subst[k] != '?');
alpar@1:                mir->subst[k] = '?';
alpar@1:             }
alpar@1:          }
alpar@1:          if (r_best == 0.0)
alpar@1:          {  /* failure */
alpar@1:             if (mir->agg_cnt < MAXAGGR)
alpar@1:             {  /* try to aggregate another row */
alpar@1:                if (aggregate_row(tree, mir) == 0) goto loop;
alpar@1:             }
alpar@1:          }
alpar@1:          /* unmark rows used in the aggregated constraint */
alpar@1:          {  int k, ii;
alpar@1:             for (k = 1; k <= mir->agg_cnt; k++)
alpar@1:             {  ii = mir->agg_row[k];
alpar@1:                xassert(1 <= ii && ii <= m);
alpar@1:                xassert(mir->skip[ii] == 2);
alpar@1:                mir->skip[ii] = 0;
alpar@1:             }
alpar@1:          }
alpar@1:       }
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: /***********************************************************************
alpar@1: *  NAME
alpar@1: *
alpar@1: *  ios_mir_term - terminate MIR cut generator
alpar@1: *
alpar@1: *  SYNOPSIS
alpar@1: *
alpar@1: *  #include "glpios.h"
alpar@1: *  void ios_mir_term(void *gen);
alpar@1: *
alpar@1: *  DESCRIPTION
alpar@1: *
alpar@1: *  The routine ios_mir_term deletes the MIR cut generator working area
alpar@1: *  freeing all the memory allocated to it. */
alpar@1: 
alpar@1: void ios_mir_term(void *gen)
alpar@1: {     struct MIR *mir = gen;
alpar@1:       xfree(mir->skip);
alpar@1:       xfree(mir->isint);
alpar@1:       xfree(mir->lb);
alpar@1:       xfree(mir->vlb);
alpar@1:       xfree(mir->ub);
alpar@1:       xfree(mir->vub);
alpar@1:       xfree(mir->x);
alpar@1:       xfree(mir->agg_row);
alpar@1:       ios_delete_vec(mir->agg_vec);
alpar@1:       xfree(mir->subst);
alpar@1:       ios_delete_vec(mir->mod_vec);
alpar@1:       ios_delete_vec(mir->cut_vec);
alpar@1:       xfree(mir);
alpar@1:       return;
alpar@1: }
alpar@1: 
alpar@1: /* eof */