praat/external/glpk/glpios06.c

/* glpios06.c (MIR cut generator) */

/***********************************************************************
*  This code is part of GLPK (GNU Linear Programming Kit).
*
*  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
*  2009, 2010 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 "glpios.h"

#define _MIR_DEBUG 0

#define MAXAGGR 5
/* maximal number of rows which can be aggregated */

struct MIR
{     /* MIR cut generator working area */
      /*--------------------------------------------------------------*/
      /* global information valid for the root subproblem */
      int m;
      /* number of rows (in the root subproblem) */
      int n;
      /* number of columns */
      char *skip; /* char skip[1+m]; */
      /* skip[i], 1 <= i <= m, is a flag that means that row i should
         not be used because (1) it is not suitable, or (2) because it
         has been used in the aggregated constraint */
      char *isint; /* char isint[1+m+n]; */
      /* isint[k], 1 <= k <= m+n, is a flag that means that variable
         x[k] is integer (otherwise, continuous) */
      double *lb; /* double lb[1+m+n]; */
      /* lb[k], 1 <= k <= m+n, is lower bound of x[k]; -DBL_MAX means
         that x[k] has no lower bound */
      int *vlb; /* int vlb[1+m+n]; */
      /* vlb[k] = k', 1 <= k <= m+n, is the number of integer variable,
         which defines variable lower bound x[k] >= lb[k] * x[k']; zero
         means that x[k] has simple lower bound */
      double *ub; /* double ub[1+m+n]; */
      /* ub[k], 1 <= k <= m+n, is upper bound of x[k]; +DBL_MAX means
         that x[k] has no upper bound */
      int *vub; /* int vub[1+m+n]; */
      /* vub[k] = k', 1 <= k <= m+n, is the number of integer variable,
         which defines variable upper bound x[k] <= ub[k] * x[k']; zero
         means that x[k] has simple upper bound */
      /*--------------------------------------------------------------*/
      /* current (fractional) point to be separated */
      double *x; /* double x[1+m+n]; */
      /* x[k] is current value of auxiliary (1 <= k <= m) or structural
         (m+1 <= k <= m+n) variable */
      /*--------------------------------------------------------------*/
      /* aggregated constraint sum a[k] * x[k] = b, which is a linear
         combination of original constraints transformed to equalities
         by introducing auxiliary variables */
      int agg_cnt;
      /* number of rows (original constraints) used to build aggregated
         constraint, 1 <= agg_cnt <= MAXAGGR */
      int *agg_row; /* int agg_row[1+MAXAGGR]; */
      /* agg_row[k], 1 <= k <= agg_cnt, is the row number used to build
         aggregated constraint */
      IOSVEC *agg_vec; /* IOSVEC agg_vec[1:m+n]; */
      /* sparse vector of aggregated constraint coefficients, a[k] */
      double agg_rhs;
      /* right-hand side of the aggregated constraint, b */
      /*--------------------------------------------------------------*/
      /* bound substitution flags for modified constraint */
      char *subst; /* char subst[1+m+n]; */
      /* subst[k], 1 <= k <= m+n, is a bound substitution flag used for
         variable x[k]:
         '?' - x[k] is missing in modified constraint
         'L' - x[k] = (lower bound) + x'[k]
         'U' - x[k] = (upper bound) - x'[k] */
      /*--------------------------------------------------------------*/
      /* modified constraint sum a'[k] * x'[k] = b', where x'[k] >= 0,
         derived from aggregated constraint by substituting bounds;
         note that due to substitution of variable bounds there may be
         additional terms in the modified constraint */
      IOSVEC *mod_vec; /* IOSVEC mod_vec[1:m+n]; */
      /* sparse vector of modified constraint coefficients, a'[k] */
      double mod_rhs;
      /* right-hand side of the modified constraint, b' */
      /*--------------------------------------------------------------*/
      /* cutting plane sum alpha[k] * x[k] <= beta */
      IOSVEC *cut_vec; /* IOSVEC cut_vec[1:m+n]; */
      /* sparse vector of cutting plane coefficients, alpha[k] */
      double cut_rhs;
      /* right-hand size of the cutting plane, beta */
};

/***********************************************************************
*  NAME
*
*  ios_mir_init - initialize MIR cut generator
*
*  SYNOPSIS
*
*  #include "glpios.h"
*  void *ios_mir_init(glp_tree *tree);
*
*  DESCRIPTION
*
*  The routine ios_mir_init initializes the MIR cut generator assuming
*  that the current subproblem is the root subproblem.
*
*  RETURNS
*
*  The routine ios_mir_init returns a pointer to the MIR cut generator
*  working area. */

static void set_row_attrib(glp_tree *tree, struct MIR *mir)
{     /* set global row attributes */
      glp_prob *mip = tree->mip;
      int m = mir->m;
      int k;
      for (k = 1; k <= m; k++)
      {  GLPROW *row = mip->row[k];
         mir->skip[k] = 0;
         mir->isint[k] = 0;
         switch (row->type)
         {  case GLP_FR:
               mir->lb[k] = -DBL_MAX, mir->ub[k] = +DBL_MAX; break;
            case GLP_LO:
               mir->lb[k] = row->lb, mir->ub[k] = +DBL_MAX; break;
            case GLP_UP:
               mir->lb[k] = -DBL_MAX, mir->ub[k] = row->ub; break;
            case GLP_DB:
               mir->lb[k] = row->lb, mir->ub[k] = row->ub; break;
            case GLP_FX:
               mir->lb[k] = mir->ub[k] = row->lb; break;
            default:
               xassert(row != row);
         }
         mir->vlb[k] = mir->vub[k] = 0;
      }
      return;
}

static void set_col_attrib(glp_tree *tree, struct MIR *mir)
{     /* set global column attributes */
      glp_prob *mip = tree->mip;
      int m = mir->m;
      int n = mir->n;
      int k;
      for (k = m+1; k <= m+n; k++)
      {  GLPCOL *col = mip->col[k-m];
         switch (col->kind)
         {  case GLP_CV:
               mir->isint[k] = 0; break;
            case GLP_IV:
               mir->isint[k] = 1; break;
            default:
               xassert(col != col);
         }
         switch (col->type)
         {  case GLP_FR:
               mir->lb[k] = -DBL_MAX, mir->ub[k] = +DBL_MAX; break;
            case GLP_LO:
               mir->lb[k] = col->lb, mir->ub[k] = +DBL_MAX; break;
            case GLP_UP:
               mir->lb[k] = -DBL_MAX, mir->ub[k] = col->ub; break;
            case GLP_DB:
               mir->lb[k] = col->lb, mir->ub[k] = col->ub; break;
            case GLP_FX:
               mir->lb[k] = mir->ub[k] = col->lb; break;
            default:
               xassert(col != col);
         }
         mir->vlb[k] = mir->vub[k] = 0;
      }
      return;
}

static void set_var_bounds(glp_tree *tree, struct MIR *mir)
{     /* set variable bounds */
      glp_prob *mip = tree->mip;
      int m = mir->m;
      GLPAIJ *aij;
      int i, k1, k2;
      double a1, a2;
      for (i = 1; i <= m; i++)
      {  /* we need the row to be '>= 0' or '<= 0' */
         if (!(mir->lb[i] == 0.0 && mir->ub[i] == +DBL_MAX ||
               mir->lb[i] == -DBL_MAX && mir->ub[i] == 0.0)) continue;
         /* take first term */
         aij = mip->row[i]->ptr;
         if (aij == NULL) continue;
         k1 = m + aij->col->j, a1 = aij->val;
         /* take second term */
         aij = aij->r_next;
         if (aij == NULL) continue;
         k2 = m + aij->col->j, a2 = aij->val;
         /* there must be only two terms */
         if (aij->r_next != NULL) continue;
         /* interchange terms, if needed */
         if (!mir->isint[k1] && mir->isint[k2])
            ;
         else if (mir->isint[k1] && !mir->isint[k2])
         {  k2 = k1, a2 = a1;
            k1 = m + aij->col->j, a1 = aij->val;
         }
         else
         {  /* both terms are either continuous or integer */
            continue;
         }
         /* x[k2] should be double-bounded */
         if (mir->lb[k2] == -DBL_MAX || mir->ub[k2] == +DBL_MAX ||
             mir->lb[k2] == mir->ub[k2]) continue;
         /* change signs, if necessary */
         if (mir->ub[i] == 0.0) a1 = - a1, a2 = - a2;
         /* now the row has the form a1 * x1 + a2 * x2 >= 0, where x1
            is continuous, x2 is integer */
         if (a1 > 0.0)
         {  /* x1 >= - (a2 / a1) * x2 */
            if (mir->vlb[k1] == 0)
            {  /* set variable lower bound for x1 */
               mir->lb[k1] = - a2 / a1;
               mir->vlb[k1] = k2;
               /* the row should not be used */
               mir->skip[i] = 1;
            }
         }
         else /* a1 < 0.0 */
         {  /* x1 <= - (a2 / a1) * x2 */
            if (mir->vub[k1] == 0)
            {  /* set variable upper bound for x1 */
               mir->ub[k1] = - a2 / a1;
               mir->vub[k1] = k2;
               /* the row should not be used */
               mir->skip[i] = 1;
            }
         }
      }
      return;
}

static void mark_useless_rows(glp_tree *tree, struct MIR *mir)
{     /* mark rows which should not be used */
      glp_prob *mip = tree->mip;
      int m = mir->m;
      GLPAIJ *aij;
      int i, k, nv;
      for (i = 1; i <= m; i++)
      {  /* free rows should not be used */
         if (mir->lb[i] == -DBL_MAX && mir->ub[i] == +DBL_MAX)
         {  mir->skip[i] = 1;
            continue;
         }
         nv = 0;
         for (aij = mip->row[i]->ptr; aij != NULL; aij = aij->r_next)
         {  k = m + aij->col->j;
            /* rows with free variables should not be used */
            if (mir->lb[k] == -DBL_MAX && mir->ub[k] == +DBL_MAX)
            {  mir->skip[i] = 1;
               break;
            }
            /* rows with integer variables having infinite (lower or
               upper) bound should not be used */
            if (mir->isint[k] && mir->lb[k] == -DBL_MAX ||
                mir->isint[k] && mir->ub[k] == +DBL_MAX)
            {  mir->skip[i] = 1;
               break;
            }
            /* count non-fixed variables */
            if (!(mir->vlb[k] == 0 && mir->vub[k] == 0 &&
                  mir->lb[k] == mir->ub[k])) nv++;
         }
         /* rows with all variables fixed should not be used */
         if (nv == 0)
         {  mir->skip[i] = 1;
            continue;
         }
      }
      return;
}

void *ios_mir_init(glp_tree *tree)
{     /* initialize MIR cut generator */
      glp_prob *mip = tree->mip;
      int m = mip->m;
      int n = mip->n;
      struct MIR *mir;
#if _MIR_DEBUG
      xprintf("ios_mir_init: warning: debug mode enabled\n");
#endif
      /* allocate working area */
      mir = xmalloc(sizeof(struct MIR));
      mir->m = m;
      mir->n = n;
      mir->skip = xcalloc(1+m, sizeof(char));
      mir->isint = xcalloc(1+m+n, sizeof(char));
      mir->lb = xcalloc(1+m+n, sizeof(double));
      mir->vlb = xcalloc(1+m+n, sizeof(int));
      mir->ub = xcalloc(1+m+n, sizeof(double));
      mir->vub = xcalloc(1+m+n, sizeof(int));
      mir->x = xcalloc(1+m+n, sizeof(double));
      mir->agg_row = xcalloc(1+MAXAGGR, sizeof(int));
      mir->agg_vec = ios_create_vec(m+n);
      mir->subst = xcalloc(1+m+n, sizeof(char));
      mir->mod_vec = ios_create_vec(m+n);
      mir->cut_vec = ios_create_vec(m+n);
      /* set global row attributes */
      set_row_attrib(tree, mir);
      /* set global column attributes */
      set_col_attrib(tree, mir);
      /* set variable bounds */
      set_var_bounds(tree, mir);
      /* mark rows which should not be used */
      mark_useless_rows(tree, mir);
      return mir;
}

/***********************************************************************
*  NAME
*
*  ios_mir_gen - generate MIR cuts
*
*  SYNOPSIS
*
*  #include "glpios.h"
*  void ios_mir_gen(glp_tree *tree, void *gen, IOSPOOL *pool);
*
*  DESCRIPTION
*
*  The routine ios_mir_gen generates MIR cuts for the current point and
*  adds them to the cut pool. */

static void get_current_point(glp_tree *tree, struct MIR *mir)
{     /* obtain current point */
      glp_prob *mip = tree->mip;
      int m = mir->m;
      int n = mir->n;
      int k;
      for (k = 1; k <= m; k++)
         mir->x[k] = mip->row[k]->prim;
      for (k = m+1; k <= m+n; k++)
         mir->x[k] = mip->col[k-m]->prim;
      return;
}

#if _MIR_DEBUG
static void check_current_point(struct MIR *mir)
{     /* check current point */
      int m = mir->m;
      int n = mir->n;
      int k, kk;
      double lb, ub, eps;
      for (k = 1; k <= m+n; k++)
      {  /* determine lower bound */
         lb = mir->lb[k];
         kk = mir->vlb[k];
         if (kk != 0)
         {  xassert(lb != -DBL_MAX);
            xassert(!mir->isint[k]);
            xassert(mir->isint[kk]);
            lb *= mir->x[kk];
         }
         /* check lower bound */
         if (lb != -DBL_MAX)
         {  eps = 1e-6 * (1.0 + fabs(lb));
            xassert(mir->x[k] >= lb - eps);
         }
         /* determine upper bound */
         ub = mir->ub[k];
         kk = mir->vub[k];
         if (kk != 0)
         {  xassert(ub != +DBL_MAX);
            xassert(!mir->isint[k]);
            xassert(mir->isint[kk]);
            ub *= mir->x[kk];
         }
         /* check upper bound */
         if (ub != +DBL_MAX)
         {  eps = 1e-6 * (1.0 + fabs(ub));
            xassert(mir->x[k] <= ub + eps);
         }
      }
      return;
}
#endif

static void initial_agg_row(glp_tree *tree, struct MIR *mir, int i)
{     /* use original i-th row as initial aggregated constraint */
      glp_prob *mip = tree->mip;
      int m = mir->m;
      GLPAIJ *aij;
      xassert(1 <= i && i <= m);
      xassert(!mir->skip[i]);
      /* mark i-th row in order not to use it in the same aggregated
         constraint */
      mir->skip[i] = 2;
      mir->agg_cnt = 1;
      mir->agg_row[1] = i;
      /* use x[i] - sum a[i,j] * x[m+j] = 0, where x[i] is auxiliary
         variable of row i, x[m+j] are structural variables */
      ios_clear_vec(mir->agg_vec);
      ios_set_vj(mir->agg_vec, i, 1.0);
      for (aij = mip->row[i]->ptr; aij != NULL; aij = aij->r_next)
         ios_set_vj(mir->agg_vec, m + aij->col->j, - aij->val);
      mir->agg_rhs = 0.0;
#if _MIR_DEBUG
      ios_check_vec(mir->agg_vec);
#endif
      return;
}

#if _MIR_DEBUG
static void check_agg_row(struct MIR *mir)
{     /* check aggregated constraint */
      int m = mir->m;
      int n = mir->n;
      int j, k;
      double r, big;
      /* compute the residual r = sum a[k] * x[k] - b and determine
         big = max(1, |a[k]|, |b|) */
      r = 0.0, big = 1.0;
      for (j = 1; j <= mir->agg_vec->nnz; j++)
      {  k = mir->agg_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         r += mir->agg_vec->val[j] * mir->x[k];
         if (big < fabs(mir->agg_vec->val[j]))
            big = fabs(mir->agg_vec->val[j]);
      }
      r -= mir->agg_rhs;
      if (big < fabs(mir->agg_rhs))
         big = fabs(mir->agg_rhs);
      /* the residual must be close to zero */
      xassert(fabs(r) <= 1e-6 * big);
      return;
}
#endif

static void subst_fixed_vars(struct MIR *mir)
{     /* substitute fixed variables into aggregated constraint */
      int m = mir->m;
      int n = mir->n;
      int j, k;
      for (j = 1; j <= mir->agg_vec->nnz; j++)
      {  k = mir->agg_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (mir->vlb[k] == 0 && mir->vub[k] == 0 &&
             mir->lb[k] == mir->ub[k])
         {  /* x[k] is fixed */
            mir->agg_rhs -= mir->agg_vec->val[j] * mir->lb[k];
            mir->agg_vec->val[j] = 0.0;
         }
      }
      /* remove terms corresponding to fixed variables */
      ios_clean_vec(mir->agg_vec, DBL_EPSILON);
#if _MIR_DEBUG
      ios_check_vec(mir->agg_vec);
#endif
      return;
}

static void bound_subst_heur(struct MIR *mir)
{     /* bound substitution heuristic */
      int m = mir->m;
      int n = mir->n;
      int j, k, kk;
      double d1, d2;
      for (j = 1; j <= mir->agg_vec->nnz; j++)
      {  k = mir->agg_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (mir->isint[k]) continue; /* skip integer variable */
         /* compute distance from x[k] to its lower bound */
         kk = mir->vlb[k];
         if (kk == 0)
         {  if (mir->lb[k] == -DBL_MAX)
               d1 = DBL_MAX;
            else
               d1 = mir->x[k] - mir->lb[k];
         }
         else
         {  xassert(1 <= kk && kk <= m+n);
            xassert(mir->isint[kk]);
            xassert(mir->lb[k] != -DBL_MAX);
            d1 = mir->x[k] - mir->lb[k] * mir->x[kk];
         }
         /* compute distance from x[k] to its upper bound */
         kk = mir->vub[k];
         if (kk == 0)
         {  if (mir->vub[k] == +DBL_MAX)
               d2 = DBL_MAX;
            else
               d2 = mir->ub[k] - mir->x[k];
         }
         else
         {  xassert(1 <= kk && kk <= m+n);
            xassert(mir->isint[kk]);
            xassert(mir->ub[k] != +DBL_MAX);
            d2 = mir->ub[k] * mir->x[kk] - mir->x[k];
         }
         /* x[k] cannot be free */
         xassert(d1 != DBL_MAX || d2 != DBL_MAX);
         /* choose the bound which is closer to x[k] */
         xassert(mir->subst[k] == '?');
         if (d1 <= d2)
            mir->subst[k] = 'L';
         else
            mir->subst[k] = 'U';
      }
      return;
}

static void build_mod_row(struct MIR *mir)
{     /* substitute bounds and build modified constraint */
      int m = mir->m;
      int n = mir->n;
      int j, jj, k, kk;
      /* initially modified constraint is aggregated constraint */
      ios_copy_vec(mir->mod_vec, mir->agg_vec);
      mir->mod_rhs = mir->agg_rhs;
#if _MIR_DEBUG
      ios_check_vec(mir->mod_vec);
#endif
      /* substitute bounds for continuous variables; note that due to
         substitution of variable bounds additional terms may appear in
         modified constraint */
      for (j = mir->mod_vec->nnz; j >= 1; j--)
      {  k = mir->mod_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (mir->isint[k]) continue; /* skip integer variable */
         if (mir->subst[k] == 'L')
         {  /* x[k] = (lower bound) + x'[k] */
            xassert(mir->lb[k] != -DBL_MAX);
            kk = mir->vlb[k];
            if (kk == 0)
            {  /* x[k] = lb[k] + x'[k] */
               mir->mod_rhs -= mir->mod_vec->val[j] * mir->lb[k];
            }
            else
            {  /* x[k] = lb[k] * x[kk] + x'[k] */
               xassert(mir->isint[kk]);
               jj = mir->mod_vec->pos[kk];
               if (jj == 0)
               {  ios_set_vj(mir->mod_vec, kk, 1.0);
                  jj = mir->mod_vec->pos[kk];
                  mir->mod_vec->val[jj] = 0.0;
               }
               mir->mod_vec->val[jj] +=
                  mir->mod_vec->val[j] * mir->lb[k];
            }
         }
         else if (mir->subst[k] == 'U')
         {  /* x[k] = (upper bound) - x'[k] */
            xassert(mir->ub[k] != +DBL_MAX);
            kk = mir->vub[k];
            if (kk == 0)
            {  /* x[k] = ub[k] - x'[k] */
               mir->mod_rhs -= mir->mod_vec->val[j] * mir->ub[k];
            }
            else
            {  /* x[k] = ub[k] * x[kk] - x'[k] */
               xassert(mir->isint[kk]);
               jj = mir->mod_vec->pos[kk];
               if (jj == 0)
               {  ios_set_vj(mir->mod_vec, kk, 1.0);
                  jj = mir->mod_vec->pos[kk];
                  mir->mod_vec->val[jj] = 0.0;
               }
               mir->mod_vec->val[jj] +=
                  mir->mod_vec->val[j] * mir->ub[k];
            }
            mir->mod_vec->val[j] = - mir->mod_vec->val[j];
         }
         else
            xassert(k != k);
      }
#if _MIR_DEBUG
      ios_check_vec(mir->mod_vec);
#endif
      /* substitute bounds for integer variables */
      for (j = 1; j <= mir->mod_vec->nnz; j++)
      {  k = mir->mod_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (!mir->isint[k]) continue; /* skip continuous variable */
         xassert(mir->subst[k] == '?');
         xassert(mir->vlb[k] == 0 && mir->vub[k] == 0);
         xassert(mir->lb[k] != -DBL_MAX && mir->ub[k] != +DBL_MAX);
         if (fabs(mir->lb[k]) <= fabs(mir->ub[k]))
         {  /* x[k] = lb[k] + x'[k] */
            mir->subst[k] = 'L';
            mir->mod_rhs -= mir->mod_vec->val[j] * mir->lb[k];
         }
         else
         {  /* x[k] = ub[k] - x'[k] */
            mir->subst[k] = 'U';
            mir->mod_rhs -= mir->mod_vec->val[j] * mir->ub[k];
            mir->mod_vec->val[j] = - mir->mod_vec->val[j];
         }
      }
#if _MIR_DEBUG
      ios_check_vec(mir->mod_vec);
#endif
      return;
}

#if _MIR_DEBUG
static void check_mod_row(struct MIR *mir)
{     /* check modified constraint */
      int m = mir->m;
      int n = mir->n;
      int j, k, kk;
      double r, big, x;
      /* compute the residual r = sum a'[k] * x'[k] - b' and determine
         big = max(1, |a[k]|, |b|) */
      r = 0.0, big = 1.0;
      for (j = 1; j <= mir->mod_vec->nnz; j++)
      {  k = mir->mod_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (mir->subst[k] == 'L')
         {  /* x'[k] = x[k] - (lower bound) */
            xassert(mir->lb[k] != -DBL_MAX);
            kk = mir->vlb[k];
            if (kk == 0)
               x = mir->x[k] - mir->lb[k];
            else
               x = mir->x[k] - mir->lb[k] * mir->x[kk];
         }
         else if (mir->subst[k] == 'U')
         {  /* x'[k] = (upper bound) - x[k] */
            xassert(mir->ub[k] != +DBL_MAX);
            kk = mir->vub[k];
            if (kk == 0)
               x = mir->ub[k] - mir->x[k];
            else
               x = mir->ub[k] * mir->x[kk] - mir->x[k];
         }
         else
            xassert(k != k);
         r += mir->mod_vec->val[j] * x;
         if (big < fabs(mir->mod_vec->val[j]))
            big = fabs(mir->mod_vec->val[j]);
      }
      r -= mir->mod_rhs;
      if (big < fabs(mir->mod_rhs))
         big = fabs(mir->mod_rhs);
      /* the residual must be close to zero */
      xassert(fabs(r) <= 1e-6 * big);
      return;
}
#endif

/***********************************************************************
*  mir_ineq - construct MIR inequality
*
*  Given the single constraint mixed integer set
*
*                    |N|
*     X = {(x,s) in Z    x R  : sum   a[j] * x[j] <= b + s},
*                    +      +  j in N
*
*  this routine constructs the mixed integer rounding (MIR) inequality
*
*     sum   alpha[j] * x[j] <= beta + gamma * s,
*    j in N
*
*  which is valid for X.
*
*  If the MIR inequality has been successfully constructed, the routine
*  returns zero. Otherwise, if b is close to nearest integer, there may
*  be numeric difficulties due to big coefficients; so in this case the
*  routine returns non-zero. */

static int mir_ineq(const int n, const double a[], const double b,
      double alpha[], double *beta, double *gamma)
{     int j;
      double f, t;
      if (fabs(b - floor(b + .5)) < 0.01)
         return 1;
      f = b - floor(b);
      for (j = 1; j <= n; j++)
      {  t = (a[j] - floor(a[j])) - f;
         if (t <= 0.0)
            alpha[j] = floor(a[j]);
         else
            alpha[j] = floor(a[j]) + t / (1.0 - f);
      }
      *beta = floor(b);
      *gamma = 1.0 / (1.0 - f);
      return 0;
}

/***********************************************************************
*  cmir_ineq - construct c-MIR inequality
*
*  Given the mixed knapsack set
*
*      MK              |N|
*     X   = {(x,s) in Z    x R  : sum   a[j] * x[j] <= b + s,
*                      +      +  j in N
*
*             x[j] <= u[j]},
*
*  a subset C of variables to be complemented, and a divisor delta > 0,
*  this routine constructs the complemented MIR (c-MIR) inequality
*
*     sum   alpha[j] * x[j] <= beta + gamma * s,
*    j in N
*                      MK
*  which is valid for X  .
*
*  If the c-MIR inequality has been successfully constructed, the
*  routine returns zero. Otherwise, if there is a risk of numerical
*  difficulties due to big coefficients (see comments to the routine
*  mir_ineq), the routine cmir_ineq returns non-zero. */

static int cmir_ineq(const int n, const double a[], const double b,
      const double u[], const char cset[], const double delta,
      double alpha[], double *beta, double *gamma)
{     int j;
      double *aa, bb;
      aa = alpha, bb = b;
      for (j = 1; j <= n; j++)
      {  aa[j] = a[j] / delta;
         if (cset[j])
            aa[j] = - aa[j], bb -= a[j] * u[j];
      }
      bb /= delta;
      if (mir_ineq(n, aa, bb, alpha, beta, gamma)) return 1;
      for (j = 1; j <= n; j++)
      {  if (cset[j])
            alpha[j] = - alpha[j], *beta += alpha[j] * u[j];
      }
      *gamma /= delta;
      return 0;
}

/***********************************************************************
*  cmir_sep - c-MIR separation heuristic
*
*  Given the mixed knapsack set
*
*      MK              |N|
*     X   = {(x,s) in Z    x R  : sum   a[j] * x[j] <= b + s,
*                      +      +  j in N
*
*             x[j] <= u[j]}
*
*                           *   *
*  and a fractional point (x , s ), this routine tries to construct
*  c-MIR inequality
*
*     sum   alpha[j] * x[j] <= beta + gamma * s,
*    j in N
*                      MK
*  which is valid for X   and has (desirably maximal) violation at the
*  fractional point given. This is attained by choosing an appropriate
*  set C of variables to be complemented and a divisor delta > 0, which
*  together define corresponding c-MIR inequality.
*
*  If a violated c-MIR inequality has been successfully constructed,
*  the routine returns its violation:
*
*                       *                      *
*     sum   alpha[j] * x [j] - beta - gamma * s ,
*    j in N
*
*  which is positive. In case of failure the routine returns zero. */

struct vset { int j; double v; };

static int cmir_cmp(const void *p1, const void *p2)
{     const struct vset *v1 = p1, *v2 = p2;
      if (v1->v < v2->v) return -1;
      if (v1->v > v2->v) return +1;
      return 0;
}

static double cmir_sep(const int n, const double a[], const double b,
      const double u[], const double x[], const double s,
      double alpha[], double *beta, double *gamma)
{     int fail, j, k, nv, v;
      double delta, eps, d_try[1+3], r, r_best;
      char *cset;
      struct vset *vset;
      /* allocate working arrays */
      cset = xcalloc(1+n, sizeof(char));
      vset = xcalloc(1+n, sizeof(struct vset));
      /* choose initial C */
      for (j = 1; j <= n; j++)
         cset[j] = (char)(x[j] >= 0.5 * u[j]);
      /* choose initial delta */
      r_best = delta = 0.0;
      for (j = 1; j <= n; j++)
      {  xassert(a[j] != 0.0);
         /* if x[j] is close to its bounds, skip it */
         eps = 1e-9 * (1.0 + fabs(u[j]));
         if (x[j] < eps || x[j] > u[j] - eps) continue;
         /* try delta = |a[j]| to construct c-MIR inequality */
         fail = cmir_ineq(n, a, b, u, cset, fabs(a[j]), alpha, beta,
            gamma);
         if (fail) continue;
         /* compute violation */
         r = - (*beta) - (*gamma) * s;
         for (k = 1; k <= n; k++) r += alpha[k] * x[k];
         if (r_best < r) r_best = r, delta = fabs(a[j]);
      }
      if (r_best < 0.001) r_best = 0.0;
      if (r_best == 0.0) goto done;
      xassert(delta > 0.0);
      /* try to increase violation by dividing delta by 2, 4, and 8,
         respectively */
      d_try[1] = delta / 2.0;
      d_try[2] = delta / 4.0;
      d_try[3] = delta / 8.0;
      for (j = 1; j <= 3; j++)
      {  /* construct c-MIR inequality */
         fail = cmir_ineq(n, a, b, u, cset, d_try[j], alpha, beta,
            gamma);
         if (fail) continue;
         /* compute violation */
         r = - (*beta) - (*gamma) * s;
         for (k = 1; k <= n; k++) r += alpha[k] * x[k];
         if (r_best < r) r_best = r, delta = d_try[j];
      }
      /* build subset of variables lying strictly between their bounds
         and order it by nondecreasing values of |x[j] - u[j]/2| */
      nv = 0;
      for (j = 1; j <= n; j++)
      {  /* if x[j] is close to its bounds, skip it */
         eps = 1e-9 * (1.0 + fabs(u[j]));
         if (x[j] < eps || x[j] > u[j] - eps) continue;
         /* add x[j] to the subset */
         nv++;
         vset[nv].j = j;
         vset[nv].v = fabs(x[j] - 0.5 * u[j]);
      }
      qsort(&vset[1], nv, sizeof(struct vset), cmir_cmp);
      /* try to increase violation by successively complementing each
         variable in the subset */
      for (v = 1; v <= nv; v++)
      {  j = vset[v].j;
         /* replace x[j] by its complement or vice versa */
         cset[j] = (char)!cset[j];
         /* construct c-MIR inequality */
         fail = cmir_ineq(n, a, b, u, cset, delta, alpha, beta, gamma);
         /* restore the variable */
         cset[j] = (char)!cset[j];
         /* do not replace the variable in case of failure */
         if (fail) continue;
         /* compute violation */
         r = - (*beta) - (*gamma) * s;
         for (k = 1; k <= n; k++) r += alpha[k] * x[k];
         if (r_best < r) r_best = r, cset[j] = (char)!cset[j];
      }
      /* construct the best c-MIR inequality chosen */
      fail = cmir_ineq(n, a, b, u, cset, delta, alpha, beta, gamma);
      xassert(!fail);
done: /* free working arrays */
      xfree(cset);
      xfree(vset);
      /* return to the calling routine */
      return r_best;
}

static double generate(struct MIR *mir)
{     /* try to generate violated c-MIR cut for modified constraint */
      int m = mir->m;
      int n = mir->n;
      int j, k, kk, nint;
      double s, *u, *x, *alpha, r_best = 0.0, b, beta, gamma;
      ios_copy_vec(mir->cut_vec, mir->mod_vec);
      mir->cut_rhs = mir->mod_rhs;
      /* remove small terms, which can appear due to substitution of
         variable bounds */
      ios_clean_vec(mir->cut_vec, DBL_EPSILON);
#if _MIR_DEBUG
      ios_check_vec(mir->cut_vec);
#endif
      /* remove positive continuous terms to obtain MK relaxation */
      for (j = 1; j <= mir->cut_vec->nnz; j++)
      {  k = mir->cut_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (!mir->isint[k] && mir->cut_vec->val[j] > 0.0)
            mir->cut_vec->val[j] = 0.0;
      }
      ios_clean_vec(mir->cut_vec, 0.0);
#if _MIR_DEBUG
      ios_check_vec(mir->cut_vec);
#endif
      /* move integer terms to the beginning of the sparse vector and
         determine the number of integer variables */
      nint = 0;
      for (j = 1; j <= mir->cut_vec->nnz; j++)
      {  k = mir->cut_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (mir->isint[k])
         {  double temp;
            nint++;
            /* interchange elements [nint] and [j] */
            kk = mir->cut_vec->ind[nint];
            mir->cut_vec->pos[k] = nint;
            mir->cut_vec->pos[kk] = j;
            mir->cut_vec->ind[nint] = k;
            mir->cut_vec->ind[j] = kk;
            temp = mir->cut_vec->val[nint];
            mir->cut_vec->val[nint] = mir->cut_vec->val[j];
            mir->cut_vec->val[j] = temp;
         }
      }
#if _MIR_DEBUG
      ios_check_vec(mir->cut_vec);
#endif
      /* if there is no integer variable, nothing to generate */
      if (nint == 0) goto done;
      /* allocate working arrays */
      u = xcalloc(1+nint, sizeof(double));
      x = xcalloc(1+nint, sizeof(double));
      alpha = xcalloc(1+nint, sizeof(double));
      /* determine u and x */
      for (j = 1; j <= nint; j++)
      {  k = mir->cut_vec->ind[j];
         xassert(m+1 <= k && k <= m+n);
         xassert(mir->isint[k]);
         u[j] = mir->ub[k] - mir->lb[k];
         xassert(u[j] >= 1.0);
         if (mir->subst[k] == 'L')
            x[j] = mir->x[k] - mir->lb[k];
         else if (mir->subst[k] == 'U')
            x[j] = mir->ub[k] - mir->x[k];
         else
            xassert(k != k);
         xassert(x[j] >= -0.001);
         if (x[j] < 0.0) x[j] = 0.0;
      }
      /* compute s = - sum of continuous terms */
      s = 0.0;
      for (j = nint+1; j <= mir->cut_vec->nnz; j++)
      {  double x;
         k = mir->cut_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         /* must be continuous */
         xassert(!mir->isint[k]);
         if (mir->subst[k] == 'L')
         {  xassert(mir->lb[k] != -DBL_MAX);
            kk = mir->vlb[k];
            if (kk == 0)
               x = mir->x[k] - mir->lb[k];
            else
               x = mir->x[k] - mir->lb[k] * mir->x[kk];
         }
         else if (mir->subst[k] == 'U')
         {  xassert(mir->ub[k] != +DBL_MAX);
            kk = mir->vub[k];
            if (kk == 0)
               x = mir->ub[k] - mir->x[k];
            else
               x = mir->ub[k] * mir->x[kk] - mir->x[k];
         }
         else
            xassert(k != k);
         xassert(x >= -0.001);
         if (x < 0.0) x = 0.0;
         s -= mir->cut_vec->val[j] * x;
      }
      xassert(s >= 0.0);
      /* apply heuristic to obtain most violated c-MIR inequality */
      b = mir->cut_rhs;
      r_best = cmir_sep(nint, mir->cut_vec->val, b, u, x, s, alpha,
         &beta, &gamma);
      if (r_best == 0.0) goto skip;
      xassert(r_best > 0.0);
      /* convert to raw cut */
      /* sum alpha[j] * x[j] <= beta + gamma * s */
      for (j = 1; j <= nint; j++)
         mir->cut_vec->val[j] = alpha[j];
      for (j = nint+1; j <= mir->cut_vec->nnz; j++)
      {  k = mir->cut_vec->ind[j];
         if (k <= m+n) mir->cut_vec->val[j] *= gamma;
      }
      mir->cut_rhs = beta;
#if _MIR_DEBUG
      ios_check_vec(mir->cut_vec);
#endif
skip: /* free working arrays */
      xfree(u);
      xfree(x);
      xfree(alpha);
done: return r_best;
}

#if _MIR_DEBUG
static void check_raw_cut(struct MIR *mir, double r_best)
{     /* check raw cut before back bound substitution */
      int m = mir->m;
      int n = mir->n;
      int j, k, kk;
      double r, big, x;
      /* compute the residual r = sum a[k] * x[k] - b and determine
         big = max(1, |a[k]|, |b|) */
      r = 0.0, big = 1.0;
      for (j = 1; j <= mir->cut_vec->nnz; j++)
      {  k = mir->cut_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (mir->subst[k] == 'L')
         {  xassert(mir->lb[k] != -DBL_MAX);
            kk = mir->vlb[k];
            if (kk == 0)
               x = mir->x[k] - mir->lb[k];
            else
               x = mir->x[k] - mir->lb[k] * mir->x[kk];
         }
         else if (mir->subst[k] == 'U')
         {  xassert(mir->ub[k] != +DBL_MAX);
            kk = mir->vub[k];
            if (kk == 0)
               x = mir->ub[k] - mir->x[k];
            else
               x = mir->ub[k] * mir->x[kk] - mir->x[k];
         }
         else
            xassert(k != k);
         r += mir->cut_vec->val[j] * x;
         if (big < fabs(mir->cut_vec->val[j]))
            big = fabs(mir->cut_vec->val[j]);
      }
      r -= mir->cut_rhs;
      if (big < fabs(mir->cut_rhs))
         big = fabs(mir->cut_rhs);
      /* the residual must be close to r_best */
      xassert(fabs(r - r_best) <= 1e-6 * big);
      return;
}
#endif

static void back_subst(struct MIR *mir)
{     /* back substitution of original bounds */
      int m = mir->m;
      int n = mir->n;
      int j, jj, k, kk;
      /* at first, restore bounds of integer variables (because on
         restoring variable bounds of continuous variables we need
         original, not shifted, bounds of integer variables) */
      for (j = 1; j <= mir->cut_vec->nnz; j++)
      {  k = mir->cut_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (!mir->isint[k]) continue; /* skip continuous */
         if (mir->subst[k] == 'L')
         {  /* x'[k] = x[k] - lb[k] */
            xassert(mir->lb[k] != -DBL_MAX);
            xassert(mir->vlb[k] == 0);
            mir->cut_rhs += mir->cut_vec->val[j] * mir->lb[k];
         }
         else if (mir->subst[k] == 'U')
         {  /* x'[k] = ub[k] - x[k] */
            xassert(mir->ub[k] != +DBL_MAX);
            xassert(mir->vub[k] == 0);
            mir->cut_rhs -= mir->cut_vec->val[j] * mir->ub[k];
            mir->cut_vec->val[j] = - mir->cut_vec->val[j];
         }
         else
            xassert(k != k);
      }
      /* now restore bounds of continuous variables */
      for (j = 1; j <= mir->cut_vec->nnz; j++)
      {  k = mir->cut_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (mir->isint[k]) continue; /* skip integer */
         if (mir->subst[k] == 'L')
         {  /* x'[k] = x[k] - (lower bound) */
            xassert(mir->lb[k] != -DBL_MAX);
            kk = mir->vlb[k];
            if (kk == 0)
            {  /* x'[k] = x[k] - lb[k] */
               mir->cut_rhs += mir->cut_vec->val[j] * mir->lb[k];
            }
            else
            {  /* x'[k] = x[k] - lb[k] * x[kk] */
               jj = mir->cut_vec->pos[kk];
#if 0
               xassert(jj != 0);
#else
               if (jj == 0)
               {  ios_set_vj(mir->cut_vec, kk, 1.0);
                  jj = mir->cut_vec->pos[kk];
                  xassert(jj != 0);
                  mir->cut_vec->val[jj] = 0.0;
               }
#endif
               mir->cut_vec->val[jj] -= mir->cut_vec->val[j] *
                  mir->lb[k];
            }
         }
         else if (mir->subst[k] == 'U')
         {  /* x'[k] = (upper bound) - x[k] */
            xassert(mir->ub[k] != +DBL_MAX);
            kk = mir->vub[k];
            if (kk == 0)
            {  /* x'[k] = ub[k] - x[k] */
               mir->cut_rhs -= mir->cut_vec->val[j] * mir->ub[k];
            }
            else
            {  /* x'[k] = ub[k] * x[kk] - x[k] */
               jj = mir->cut_vec->pos[kk];
               if (jj == 0)
               {  ios_set_vj(mir->cut_vec, kk, 1.0);
                  jj = mir->cut_vec->pos[kk];
                  xassert(jj != 0);
                  mir->cut_vec->val[jj] = 0.0;
               }
               mir->cut_vec->val[jj] += mir->cut_vec->val[j] *
                  mir->ub[k];
            }
            mir->cut_vec->val[j] = - mir->cut_vec->val[j];
         }
         else
            xassert(k != k);
      }
#if _MIR_DEBUG
      ios_check_vec(mir->cut_vec);
#endif
      return;
}

#if _MIR_DEBUG
static void check_cut_row(struct MIR *mir, double r_best)
{     /* check the cut after back bound substitution or elimination of
         auxiliary variables */
      int m = mir->m;
      int n = mir->n;
      int j, k;
      double r, big;
      /* compute the residual r = sum a[k] * x[k] - b and determine
         big = max(1, |a[k]|, |b|) */
      r = 0.0, big = 1.0;
      for (j = 1; j <= mir->cut_vec->nnz; j++)
      {  k = mir->cut_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         r += mir->cut_vec->val[j] * mir->x[k];
         if (big < fabs(mir->cut_vec->val[j]))
            big = fabs(mir->cut_vec->val[j]);
      }
      r -= mir->cut_rhs;
      if (big < fabs(mir->cut_rhs))
         big = fabs(mir->cut_rhs);
      /* the residual must be close to r_best */
      xassert(fabs(r - r_best) <= 1e-6 * big);
      return;
}
#endif

static void subst_aux_vars(glp_tree *tree, struct MIR *mir)
{     /* final substitution to eliminate auxiliary variables */
      glp_prob *mip = tree->mip;
      int m = mir->m;
      int n = mir->n;
      GLPAIJ *aij;
      int j, k, kk, jj;
      for (j = mir->cut_vec->nnz; j >= 1; j--)
      {  k = mir->cut_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (k > m) continue; /* skip structurals */
         for (aij = mip->row[k]->ptr; aij != NULL; aij = aij->r_next)
         {  kk = m + aij->col->j; /* structural */
            jj = mir->cut_vec->pos[kk];
            if (jj == 0)
            {  ios_set_vj(mir->cut_vec, kk, 1.0);
               jj = mir->cut_vec->pos[kk];
               mir->cut_vec->val[jj] = 0.0;
            }
            mir->cut_vec->val[jj] += mir->cut_vec->val[j] * aij->val;
         }
         mir->cut_vec->val[j] = 0.0;
      }
      ios_clean_vec(mir->cut_vec, 0.0);
      return;
}

static void add_cut(glp_tree *tree, struct MIR *mir)
{     /* add constructed cut inequality to the cut pool */
      int m = mir->m;
      int n = mir->n;
      int j, k, len;
      int *ind = xcalloc(1+n, sizeof(int));
      double *val = xcalloc(1+n, sizeof(double));
      len = 0;
      for (j = mir->cut_vec->nnz; j >= 1; j--)
      {  k = mir->cut_vec->ind[j];
         xassert(m+1 <= k && k <= m+n);
         len++, ind[len] = k - m, val[len] = mir->cut_vec->val[j];
      }
#if 0
      ios_add_cut_row(tree, pool, GLP_RF_MIR, len, ind, val, GLP_UP,
         mir->cut_rhs);
#else
      glp_ios_add_row(tree, NULL, GLP_RF_MIR, 0, len, ind, val, GLP_UP,
         mir->cut_rhs);
#endif
      xfree(ind);
      xfree(val);
      return;
}

static int aggregate_row(glp_tree *tree, struct MIR *mir)
{     /* try to aggregate another row */
      glp_prob *mip = tree->mip;
      int m = mir->m;
      int n = mir->n;
      GLPAIJ *aij;
      IOSVEC *v;
      int ii, j, jj, k, kk, kappa = 0, ret = 0;
      double d1, d2, d, d_max = 0.0;
      /* choose appropriate structural variable in the aggregated row
         to be substituted */
      for (j = 1; j <= mir->agg_vec->nnz; j++)
      {  k = mir->agg_vec->ind[j];
         xassert(1 <= k && k <= m+n);
         if (k <= m) continue; /* skip auxiliary var */
         if (mir->isint[k]) continue; /* skip integer var */
         if (fabs(mir->agg_vec->val[j]) < 0.001) continue;
         /* compute distance from x[k] to its lower bound */
         kk = mir->vlb[k];
         if (kk == 0)
         {  if (mir->lb[k] == -DBL_MAX)
               d1 = DBL_MAX;
            else
               d1 = mir->x[k] - mir->lb[k];
         }
         else
         {  xassert(1 <= kk && kk <= m+n);
            xassert(mir->isint[kk]);
            xassert(mir->lb[k] != -DBL_MAX);
            d1 = mir->x[k] - mir->lb[k] * mir->x[kk];
         }
         /* compute distance from x[k] to its upper bound */
         kk = mir->vub[k];
         if (kk == 0)
         {  if (mir->vub[k] == +DBL_MAX)
               d2 = DBL_MAX;
            else
               d2 = mir->ub[k] - mir->x[k];
         }
         else
         {  xassert(1 <= kk && kk <= m+n);
            xassert(mir->isint[kk]);
            xassert(mir->ub[k] != +DBL_MAX);
            d2 = mir->ub[k] * mir->x[kk] - mir->x[k];
         }
         /* x[k] cannot be free */
         xassert(d1 != DBL_MAX || d2 != DBL_MAX);
         /* d = min(d1, d2) */
         d = (d1 <= d2 ? d1 : d2);
         xassert(d != DBL_MAX);
         /* should not be close to corresponding bound */
         if (d < 0.001) continue;
         if (d_max < d) d_max = d, kappa = k;
      }
      if (kappa == 0)
      {  /* nothing chosen */
         ret = 1;
         goto done;
      }
      /* x[kappa] has been chosen */
      xassert(m+1 <= kappa && kappa <= m+n);
      xassert(!mir->isint[kappa]);
      /* find another row, which have not been used yet, to eliminate
         x[kappa] from the aggregated row */
      for (ii = 1; ii <= m; ii++)
      {  if (mir->skip[ii]) continue;
         for (aij = mip->row[ii]->ptr; aij != NULL; aij = aij->r_next)
            if (aij->col->j == kappa - m) break;
         if (aij != NULL && fabs(aij->val) >= 0.001) break;
      }
      if (ii > m)
      {  /* nothing found */
         ret = 2;
         goto done;
      }
      /* row ii has been found; include it in the aggregated list */
      mir->agg_cnt++;
      xassert(mir->agg_cnt <= MAXAGGR);
      mir->agg_row[mir->agg_cnt] = ii;
      mir->skip[ii] = 2;
      /* v := new row */
      v = ios_create_vec(m+n);
      ios_set_vj(v, ii, 1.0);
      for (aij = mip->row[ii]->ptr; aij != NULL; aij = aij->r_next)
         ios_set_vj(v, m + aij->col->j, - aij->val);
#if _MIR_DEBUG
      ios_check_vec(v);
#endif
      /* perform gaussian elimination to remove x[kappa] */
      j = mir->agg_vec->pos[kappa];
      xassert(j != 0);
      jj = v->pos[kappa];
      xassert(jj != 0);
      ios_linear_comb(mir->agg_vec,
         - mir->agg_vec->val[j] / v->val[jj], v);
      ios_delete_vec(v);
      ios_set_vj(mir->agg_vec, kappa, 0.0);
#if _MIR_DEBUG
      ios_check_vec(mir->agg_vec);
#endif
done: return ret;
}

void ios_mir_gen(glp_tree *tree, void *gen)
{     /* main routine to generate MIR cuts */
      glp_prob *mip = tree->mip;
      struct MIR *mir = gen;
      int m = mir->m;
      int n = mir->n;
      int i;
      double r_best;
      xassert(mip->m >= m);
      xassert(mip->n == n);
      /* obtain current point */
      get_current_point(tree, mir);
#if _MIR_DEBUG
      /* check current point */
      check_current_point(mir);
#endif
      /* reset bound substitution flags */
      memset(&mir->subst[1], '?', m+n);
      /* try to generate a set of violated MIR cuts */
      for (i = 1; i <= m; i++)
      {  if (mir->skip[i]) continue;
         /* use original i-th row as initial aggregated constraint */
         initial_agg_row(tree, mir, i);
loop:    ;
#if _MIR_DEBUG
         /* check aggregated row */
         check_agg_row(mir);
#endif
         /* substitute fixed variables into aggregated constraint */
         subst_fixed_vars(mir);
#if _MIR_DEBUG
         /* check aggregated row */
         check_agg_row(mir);
#endif
#if _MIR_DEBUG
         /* check bound substitution flags */
         {  int k;
            for (k = 1; k <= m+n; k++)
               xassert(mir->subst[k] == '?');
         }
#endif
         /* apply bound substitution heuristic */
         bound_subst_heur(mir);
         /* substitute bounds and build modified constraint */
         build_mod_row(mir);
#if _MIR_DEBUG
         /* check modified row */
         check_mod_row(mir);
#endif
         /* try to generate violated c-MIR cut for modified row */
         r_best = generate(mir);
         if (r_best > 0.0)
         {  /* success */
#if _MIR_DEBUG
            /* check raw cut before back bound substitution */
            check_raw_cut(mir, r_best);
#endif
            /* back substitution of original bounds */
            back_subst(mir);
#if _MIR_DEBUG
            /* check the cut after back bound substitution */
            check_cut_row(mir, r_best);
#endif
            /* final substitution to eliminate auxiliary variables */
            subst_aux_vars(tree, mir);
#if _MIR_DEBUG
            /* check the cut after elimination of auxiliaries */
            check_cut_row(mir, r_best);
#endif
            /* add constructed cut inequality to the cut pool */
            add_cut(tree, mir);
         }
         /* reset bound substitution flags */
         {  int j, k;
            for (j = 1; j <= mir->mod_vec->nnz; j++)
            {  k = mir->mod_vec->ind[j];
               xassert(1 <= k && k <= m+n);
               xassert(mir->subst[k] != '?');
               mir->subst[k] = '?';
            }
         }
         if (r_best == 0.0)
         {  /* failure */
            if (mir->agg_cnt < MAXAGGR)
            {  /* try to aggregate another row */
               if (aggregate_row(tree, mir) == 0) goto loop;
            }
         }
         /* unmark rows used in the aggregated constraint */
         {  int k, ii;
            for (k = 1; k <= mir->agg_cnt; k++)
            {  ii = mir->agg_row[k];
               xassert(1 <= ii && ii <= m);
               xassert(mir->skip[ii] == 2);
               mir->skip[ii] = 0;
            }
         }
      }
      return;
}

/***********************************************************************
*  NAME
*
*  ios_mir_term - terminate MIR cut generator
*
*  SYNOPSIS
*
*  #include "glpios.h"
*  void ios_mir_term(void *gen);
*
*  DESCRIPTION
*
*  The routine ios_mir_term deletes the MIR cut generator working area
*  freeing all the memory allocated to it. */

void ios_mir_term(void *gen)
{     struct MIR *mir = gen;
      xfree(mir->skip);
      xfree(mir->isint);
      xfree(mir->lb);
      xfree(mir->vlb);
      xfree(mir->ub);
      xfree(mir->vub);
      xfree(mir->x);
      xfree(mir->agg_row);
      ios_delete_vec(mir->agg_vec);
      xfree(mir->subst);
      ios_delete_vec(mir->mod_vec);
      ios_delete_vec(mir->cut_vec);
      xfree(mir);
      return;
}

/* eof */