lpsolve-sys 5.5.0

#include <string.h>
#include "commonlib.h"
#include "lp_lib.h"
#include "lp_report.h"
#include "lp_SOS.h"

#ifdef FORTIFY
# include "lp_fortify.h"
#endif


/*
    Specially Ordered Set (SOS) routines - w/interface for lp_solve v5.0+
   ----------------------------------------------------------------------------------
    Author:        Kjell Eikland
    Contact:       kjell.eikland@broadpark.no
    License terms: LGPL.

    Requires:      lp_lib.h

    Release notes:
    v1.0    1 September 2003    Complete package for SOS creation and use in a LP
                                setting.  Notable feature of this implementation
                                compared to those in other commercial systems is
                                the generalization to SOS'es of "unlimited" order.
    v1.1     8 December 2003    Added variable (index) deletion method.
    v1.2    17 December 2004    Added bound change tracking functionality.
    v1.3    18 September 2005   Added sparse SOS handling to speed up processing
                                of large number of SOS'es.

   ----------------------------------------------------------------------------------
*/

/* SOS group functions */
STATIC SOSgroup *create_SOSgroup(lprec *lp)
{
  SOSgroup *group;

  group = (SOSgroup *) calloc(1, sizeof(*group));
  group->lp = lp;
  group->sos_alloc = SOS_START_SIZE;
  group->sos_list = (SOSrec **) malloc((group->sos_alloc) * sizeof(*group->sos_list));
  return(group);
}

STATIC void resize_SOSgroup(SOSgroup *group)
{
  if(group->sos_count == group->sos_alloc) {
    group->sos_alloc = (int)((double) group->sos_alloc*RESIZEFACTOR);
    group->sos_list = (SOSrec **) realloc(group->sos_list,
                                          (group->sos_alloc) * sizeof(*group->sos_list));
  }
}

STATIC int append_SOSgroup(SOSgroup *group, SOSrec *SOS)
{
  int    i, k;
  SOSrec *SOSHold;

  /* Check if we should resize */
  resize_SOSgroup(group);

  /* First append to the end of the list */
  group->sos_list[group->sos_count] = SOS;
  group->sos_count++;
  i = abs(SOS->type);
  SETMAX(group->maxorder, i);
  if(i == 1)
    group->sos1_count++;
  k = group->sos_count;
  SOS->tagorder = k;

  /* Sort the SOS list by given priority */
  for(i = group->sos_count-1; i > 0; i--) {
    if(group->sos_list[i]->priority < group->sos_list[i-1]->priority) {
      SOSHold = group->sos_list[i];
      group->sos_list[i] = group->sos_list[i-1];
      group->sos_list[i-1] = SOSHold;
      if(SOSHold == SOS)
        k = i; /* This is the index in the [1..> range */
    }
    else
      break;
  }
  /* Return the list index of the new SOS */
  return( k );
}


STATIC int clean_SOSgroup(SOSgroup *group, MYBOOL forceupdatemap)
{
  int    i, n, k;
  SOSrec *SOS;

  if(group == NULL)
    return( 0 );

  /* Delete any SOS without members or trivial member count */
  n = 0;
  if(group->sos_alloc > 0) {
    group->maxorder = 0;
    for(i = group->sos_count; i > 0; i--) {
      SOS = group->sos_list[i-1];
      k = SOS->members[0];
      if((k == 0) ||                              /* Empty */
         ((k == abs(SOS->type)) && (k <= 2))) {   /* Trivial */
        delete_SOSrec(group, i);
        n++;
      }
      else {
        SETMAX(group->maxorder, abs(SOS->type));
      }
    }
    if((n > 0) || forceupdatemap)
      SOS_member_updatemap(group);
  }
  return( n );
}


STATIC void free_SOSgroup(SOSgroup **group)
{
  int i;

  if((group == NULL) || (*group == NULL))
    return;
  if((*group)->sos_alloc > 0) {
    for(i = 0; i < (*group)->sos_count; i++)
      free_SOSrec((*group)->sos_list[i]);
    FREE((*group)->sos_list);
    FREE((*group)->membership);
    FREE((*group)->memberpos);
  }
  FREE(*group);
}

/* SOS record functions */
STATIC SOSrec *create_SOSrec(SOSgroup *group, char *name, int type, int priority, int size, int *variables, REAL *weights)
{
  SOSrec *SOS;

  SOS = (SOSrec *) calloc(1 , sizeof(*SOS));
  SOS->parent = group;
  SOS->type = type;
  if(name == NULL)
    SOS->name = NULL;
  else
  {
    allocCHAR(group->lp, &SOS->name, (int) (strlen(name)+1), FALSE);
    strcpy(SOS->name, name);
  }
  if(type < 0)
    type = abs(type);
  SOS->tagorder = 0;
  SOS->size = 0;
  SOS->priority = priority;
  SOS->members = NULL;
  SOS->weights = NULL;
  SOS->membersSorted = NULL;
  SOS->membersMapped = NULL;

  if(size > 0)
    size = append_SOSrec(SOS, size, variables, weights);

  return(SOS);
}


STATIC int append_SOSrec(SOSrec *SOS, int size, int *variables, REAL *weights)
{
  int   i, oldsize, newsize, nn;
  lprec *lp = SOS->parent->lp;

  oldsize = SOS->size;
  newsize = oldsize + size;
  nn = abs(SOS->type);

 /* Shift existing active data right (normally zero) */
  if(SOS->members == NULL)
    allocINT(lp, &SOS->members, 1+newsize+1+nn, TRUE);
  else {
    allocINT(lp, &SOS->members, 1+newsize+1+nn, AUTOMATIC);
    for(i = newsize+1+nn; i > newsize+1; i--)
    SOS->members[i] = SOS->members[i-size];
  }
  SOS->members[0] = newsize;
  SOS->members[newsize+1] = nn;

 /* Copy the new data into the arrays */
  if(SOS->weights == NULL)
    allocREAL(lp, &SOS->weights, 1+newsize, TRUE);
  else
    allocREAL(lp, &SOS->weights, 1+newsize, AUTOMATIC);
  for(i = oldsize+1; i <= newsize; i++) {
    SOS->members[i] = variables[i-oldsize-1];
    if((SOS->members[i] < 1) || (SOS->members[i] > lp->columns))
      report(lp, IMPORTANT, "append_SOS_rec: Invalid SOS variable definition for index %d\n", SOS->members[i]);
    else {
      if(SOS->isGUB)
        lp->var_type[SOS->members[i]] |= ISGUB;
      else
        lp->var_type[SOS->members[i]] |= ISSOS;
    }
    if(weights == NULL)
      SOS->weights[i] = i;  /* Follow standard, which is sorted ascending */
    else
      SOS->weights[i] = weights[i-oldsize-1];
    SOS->weights[0] += SOS->weights[i];
  }

 /* Sort the new paired lists ascending by weight (simple bubble sort) */
  i = sortByREAL(SOS->members, SOS->weights, newsize, 1, TRUE);
  if(i > 0)
    report(lp, DETAILED, "append_SOS_rec: Non-unique SOS variable weight for index %d\n", i);

 /* Define mapping arrays to search large SOS's faster */
  allocINT(lp, &SOS->membersSorted, newsize, AUTOMATIC);
  allocINT(lp, &SOS->membersMapped, newsize, AUTOMATIC);
  for(i = oldsize+1; i <= newsize; i++) {
    SOS->membersSorted[i - 1] = SOS->members[i];
    SOS->membersMapped[i - 1] = i;
  }
  sortByINT(SOS->membersMapped, SOS->membersSorted, newsize, 0, TRUE);

 /* Confirm the new size */
  SOS->size = newsize;

  return(newsize);

}

STATIC int make_SOSchain(lprec *lp, MYBOOL forceresort)
{
  int      i, j, k, n;
  MYBOOL   *hold = NULL;
  REAL     *order, sum, weight;
  SOSgroup *group = lp->SOS;

  /* PART A: Resort individual SOS member lists, if specified */
  if(forceresort)
    SOS_member_sortlist(group, 0);

  /* PART B: Tally SOS variables and create master SOS variable list */
  n = 0;
  for(i = 0; i < group->sos_count; i++)
    n += group->sos_list[i]->size;
  lp->sos_vars = n;
  if(lp->sos_vars > 0) /* Prevent memory loss in case of multiple solves */
    FREE(lp->sos_priority);
  allocINT(lp, &lp->sos_priority, n, FALSE);
  allocREAL(lp, &order, n, FALSE);

  /* Move variable data to the master SOS list and sort by ascending weight */
  n = 0;
  sum = 0;
  for(i = 0; i < group->sos_count; i++) {
    for(j = 1; j <= group->sos_list[i]->size; j++) {
      lp->sos_priority[n] = group->sos_list[i]->members[j];
      weight = group->sos_list[i]->weights[j];
      sum += weight;
      order[n] = sum;
      n++;
    }
  }
  hpsortex(order, n, 0, sizeof(*order), FALSE, compareREAL, lp->sos_priority);
  FREE(order);

  /* Remove duplicate SOS variables */
  allocMYBOOL(lp, &hold, lp->columns+1, TRUE);
  k = 0;
  for(i = 0; i < n; i++) {
    j = lp->sos_priority[i];
    if(!hold[j]) {
      hold[j] = TRUE;
      if(k < i)
        lp->sos_priority[k] = j;
      k++;
    }
  }
  FREE(hold);

  /* Adjust the size of the master variable list, if necessary */
  if(k < lp->sos_vars) {
    allocINT(lp, &lp->sos_priority, k, AUTOMATIC);
    lp->sos_vars = k;
  }

  return( k );

}


STATIC MYBOOL delete_SOSrec(SOSgroup *group, int sosindex)
{
#ifdef Paranoia
  if((sosindex <= 0) || (sosindex > group->sos_count)) {
    report(group->lp, IMPORTANT, "delete_SOSrec: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  /* Delete and free the SOS record */
  if(abs(SOS_get_type(group, sosindex)) == 1)
    group->sos1_count--;
  free_SOSrec(group->sos_list[sosindex-1]);
  while(sosindex < group->sos_count) {
    group->sos_list[sosindex-1] = group->sos_list[sosindex];
    sosindex++;
  }
  group->sos_count--;

  /* Update maxorder */
  group->maxorder = 0;
  for(sosindex = 0; sosindex < group->sos_count; sosindex++) {
    SETMAX(group->maxorder, abs(group->sos_list[sosindex]->type));
  }

  return(TRUE);
}


STATIC void free_SOSrec(SOSrec *SOS)
{
  if(SOS->name != NULL)
    FREE(SOS->name);
  if(SOS->size > 0) {
    FREE(SOS->members);
    FREE(SOS->weights);
    FREE(SOS->membersSorted);
    FREE(SOS->membersMapped);
  }
  FREE(SOS);
}


STATIC MYBOOL SOS_member_sortlist(SOSgroup *group, int sosindex)
/* Routine to (re-)sort SOS member arrays for faster access to large SOSes */
{
  int    i, n;
  int    *list;
  lprec  *lp = group->lp;
  SOSrec *SOS;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_member_sortlist: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if((sosindex == 0) && (group->sos_count == 1))
    sosindex = 1;

  if(sosindex == 0) {
    for(i = 1; i <= group->sos_count; i++) {
      if(!SOS_member_sortlist(group, i))
        return(FALSE);
    }
  }
  else {
    SOS = group->sos_list[sosindex-1];
    list = SOS->members;
    n = list[0];
    /* Make sure that the arrays are properly allocated and sized */
    if(n != group->sos_list[sosindex-1]->size) {
      allocINT(lp, &SOS->membersSorted, n, AUTOMATIC);
      allocINT(lp, &SOS->membersMapped, n, AUTOMATIC);
      group->sos_list[sosindex-1]->size = n;
    }
    /* Reload the arrays and do the sorting */
    for(i = 1; i <= n; i++) {
      SOS->membersSorted[i - 1] = list[i];
      SOS->membersMapped[i - 1] = i;
    }
    sortByINT(SOS->membersMapped, SOS->membersSorted, n, 0, TRUE);
  }
  return( TRUE );
}

STATIC int SOS_member_updatemap(SOSgroup *group)
{
  int      i, j, k, n, nvars = 0,
           *list, *tally = NULL;
  SOSrec   *rec;
  lprec    *lp = group->lp;

  /* (Re)-initialize usage arrays */
  allocINT(lp, &group->memberpos, lp->columns+1, AUTOMATIC);
  allocINT(lp, &tally, lp->columns+1, TRUE);

  /* Get each variable's SOS membership count */
  for(i = 0; i < group->sos_count; i++) {
    rec = group->sos_list[i];
    n = rec->size;
    list = rec->members;
    for(j = 1; j <= n; j++) {
      k = list[j];
#ifdef Paranoia
      if((k < 1) || (k > lp->columns))
        report(lp, SEVERE, "SOS_member_updatemap: Member %j of SOS number %d is out of column range (%d)\n",
                            j, i+1, k);
#endif
      tally[k]++;
    }

  }

  /* Compute pointer into column-sorted array */
  group->memberpos[0] = 0;
  for(i = 1; i <= lp->columns; i++) {
    n = tally[i];
    if(n > 0)
      nvars++;
    group->memberpos[i] = group->memberpos[i-1] + n;
  }
  n = group->memberpos[lp->columns];
  MEMCOPY(tally+1, group->memberpos, lp->columns);

  /* Load the column-sorted SOS indeces / pointers */
  allocINT(lp, &group->membership, n+1, AUTOMATIC);
  for(i = 0; i < group->sos_count; i++) {
    rec = group->sos_list[i];
    n = rec->size;
    list = rec->members;
    for(j = 1; j <= n; j++) {
      k = tally[list[j]]++;
#ifdef Paranoia
      if(k > group->memberpos[lp->columns])
        report(lp, SEVERE, "SOS_member_updatemap: Member mapping for variable %j of SOS number %d is invalid\n",
                            list[j], i+1);
#endif
      group->membership[k] = i+1;
    }
  }
  FREE(tally);

  return( nvars );
}


STATIC MYBOOL SOS_shift_col(SOSgroup *group, int sosindex, int column, int delta, LLrec *usedmap, MYBOOL forceresort)
/* Routine to adjust SOS indeces for variable insertions or deletions;
   Note: SOS_shift_col must be called before make_SOSchain! */
{
  int    i, ii, n, nn, nr;
  int    changed;
  int    *list;
  REAL   *weights;

#ifdef Paranoia
  lprec  *lp = group->lp;

  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_shift_col: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
  else if((column < 1) || (delta == 0)) {
    report(lp, IMPORTANT, "SOS_shift_col: Invalid column %d specified with delta %d\n",
                          column, delta);
    return(FALSE);
  }
#endif

  if((sosindex == 0) && (group->sos_count == 1))
    sosindex = 1;

  if(sosindex == 0) {
    for(i = 1; i <= group->sos_count; i++) {
      if(!SOS_shift_col(group, i, column, delta, usedmap, forceresort))
        return(FALSE);
    }
  }
  else {
    list = group->sos_list[sosindex-1]->members;
    weights = group->sos_list[sosindex-1]->weights;
    n = list[0];
    nn = list[n+1];

    /* Case where variable indeces are to be incremented */
    if(delta > 0) {
      for(i = 1; i <= n; i++) {
        if(list[i] >= column)
          list[i] += delta;
      }
    }
    /* Case where variables are to be deleted/indeces decremented */
    else {
      changed = 0;
      if(usedmap != NULL) {
        int *newidx = NULL;
        /* Defer creation of index mapper until we are sure that a
           member of this SOS is actually targeted for deletion */
        if(newidx == NULL) {
          allocINT(group->lp, &newidx, group->lp->columns+1, TRUE);
          for(i = firstActiveLink(usedmap), ii = 1; i != 0;
              i = nextActiveLink(usedmap, i), ii++)
            newidx[i] = ii;
        }
        for(i = 1, ii = 0; i <= n; i++) {
          nr = list[i];
          /* Check if this SOS variable should be deleted */
          if(!isActiveLink(usedmap, nr))
            continue;

          /* If the index is "high" then make adjustment and shift */
          changed++;
          ii++;
          list[ii] = newidx[nr];
          weights[ii] = weights[i];
        }
        FREE(newidx);
      }
      else
        for(i = 1, ii = 0; i <= n; i++) {
          nr = list[i];
          /* Check if this SOS variable should be deleted */
          if((nr >= column) && (nr < column-delta))
            continue;
          /* If the index is "high" then decrement */
          if(nr > column) {
            changed++;
            nr += delta;
          }
          ii++;
          list[ii] = nr;
          weights[ii] = weights[i];
        }
      /* Update the SOS length / type indicators */
      if(ii < n) {
        list[0] = ii;
        list[ii+1] = nn;
      }

     /* Update mapping arrays to search large SOS's faster */
      if(forceresort && ((ii < n) || (changed > 0)))
        SOS_member_sortlist(group, sosindex);
    }

  }
  return(TRUE);

}

int SOS_member_count(SOSgroup *group, int sosindex)
{
  SOSrec *SOS;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(group->lp, IMPORTANT, "SOS_member_count: Invalid SOS index %d\n", sosindex);
    return( -1 );
  }
#endif
  SOS = group->sos_list[sosindex-1];
  return( SOS->members[0] );
}

int SOS_member_delete(SOSgroup *group, int sosindex, int member)
{
  int   *list, i, i2, k, n, nn = 0;
  SOSrec *SOS;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(group->lp, IMPORTANT, "SOS_member_delete: Invalid SOS index %d\n", sosindex);
    return( -1 );
  }
#endif

  if(sosindex == 0) {
    for(i = group->memberpos[member-1]; i < group->memberpos[member]; i++) {
      k = group->membership[i];
      n = SOS_member_delete(group, k, member);
      if(n >= 0)
        nn += n;
      else
        return( n );
    }
    /* We must update the mapper */
    k = group->memberpos[member];
    i = group->memberpos[member-1];
    n = group->memberpos[lp->columns] - k;
    if(n > 0)
      MEMCOPY(group->membership + i, group->membership + k, n);
    for(i = member; i <= lp->columns; i++)
      group->memberpos[i] = group->memberpos[i-1];
  }
  else {
    SOS = group->sos_list[sosindex-1];
    list = SOS->members;
    n = list[0];

    /* Find the offset of the member */
    i = 1;
    while((i <= n) && (abs(list[i]) != member))
      i++;
    if(i > n)
      return( -1 );
    nn++;

    /* Shift remaining members *and* the active count one position left */
    while(i <= n) {
      list[i] = list[i+1];
      i++;
    }
    list[0]--;
    SOS->size--;

    /* Do the same with the active list one position left */
    i = n + 1;
    i2 = i + list[n];
    k = i + 1;
    while(i < i2) {
      if(abs(list[k]) == member)
        k++;
      list[i] = list[k];
      i++;
      k++;
    }
  }

  return( nn );
}

int SOS_get_type(SOSgroup *group, int sosindex)
{
#ifdef Paranoia
  if((sosindex < 1) || (sosindex > group->sos_count)) {
    report(group->lp, IMPORTANT, "SOS_get_type: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  return(group->sos_list[sosindex-1]->type);
}


int SOS_infeasible(SOSgroup *group, int sosindex)
{
  int    i, n, nn, varnr, failindex, *list;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_infeasible: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if(sosindex == 0 && group->sos_count == 1)
    sosindex = 1;

  failindex = 0;
  if(sosindex == 0) {
    for(i = 1; i <= group->sos_count; i++) {
      failindex = SOS_infeasible(group, i);
      if(failindex > 0) break;
    }
  }
  else {
    list = group->sos_list[sosindex-1]->members;
    n = list[0];
    nn = list[n+1];
   /* Find index of next lower-bounded variable */
    for(i = 1; i <= n; i++) {
      varnr = abs(list[i]);
      if((lp->orig_lowbo[lp->rows + varnr] > 0) &&
         !((lp->sc_vars > 0) && is_semicont(lp, varnr)))
        break;
    }

   /* Find if there is another lower-bounded variable beyond the type window */
    i = i+nn;
    while(i <= n) {
      varnr = abs(list[i]);
      if((lp->orig_lowbo[lp->rows + varnr] > 0) &&
         !((lp->sc_vars > 0) && is_semicont(lp, varnr)))
        break;
      i++;
    }
    if(i <= n)
      failindex = abs(list[i]);
  }
  return(failindex);
}


int SOS_member_index(SOSgroup *group, int sosindex, int member)
{
  int    n;
  SOSrec *SOS;

  SOS = group->sos_list[sosindex-1];
  n = SOS->members[0];

  n = searchFor(member, SOS->membersSorted, n, 0, FALSE);
  if(n >= 0)
    n = SOS->membersMapped[n];

  return(n);
}


int SOS_memberships(SOSgroup *group, int varnr)
{
  int   i, n = 0;
  lprec *lp;

  /* Check if there is anything to do */
  if((group == NULL) || (SOS_count(lp = group->lp) == 0))
    return( n );

#ifdef Paranoia
  if((varnr < 0) || (varnr > lp->columns)) {
    report(lp, IMPORTANT, "SOS_memberships: Invalid variable index %d given\n", varnr);
    return( n );
  }
#endif

  if(varnr == 0) {
    for(i = 1; i <= lp->columns; i++)
      if(group->memberpos[i] > group->memberpos[i-1])
        n++;
  }
  else
    n = group->memberpos[varnr] - group->memberpos[varnr-1];

  return( n );
}


int SOS_is_member(SOSgroup *group, int sosindex, int column)
{
  int    i, n = FALSE, *list;
  lprec  *lp;

  if(group == NULL)
    return( FALSE );
  lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_is_member: Invalid SOS index %d\n", sosindex);
    return(n);
  }
#endif

  if(sosindex == 0) {
    if(lp->var_type[column] & (ISSOS | ISGUB))
      n = (MYBOOL) (SOS_memberships(group, column) > 0);
  }
  else if(lp->var_type[column] & (ISSOS | ISGUB)) {

   /* Search for the variable */
    i = SOS_member_index(group, sosindex, column);

   /* Signal active status if found, otherwise return FALSE */
    if(i > 0) {
      list = group->sos_list[sosindex-1]->members;
      if(list[i] < 0)
        n = -TRUE;
      else
      n = TRUE;
    }
  }
  return(n);
}


MYBOOL SOS_is_member_of_type(SOSgroup *group, int column, int sostype)
{
  int i, k, n;

  if(group != NULL)
  for(i = group->memberpos[column-1]; i < group->memberpos[column]; i++) {
    k = group->membership[i];
    n = SOS_get_type(group, k);
    if(((n == sostype) ||
        ((sostype == SOSn) && (n > 2))) && SOS_is_member(group, k, column))
      return(TRUE);
  }
  return(FALSE);
}


MYBOOL SOS_set_GUB(SOSgroup *group, int sosindex, MYBOOL state)
{
  int i;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(group->lp, IMPORTANT, "SOS_set_GUB: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif
  if((sosindex == 0) && (group->sos_count == 1))
    sosindex = 1;

  if(sosindex == 0) {
    for(i = 1; i <= group->sos_count; i++)
      SOS_set_GUB(group, i, state);
  }
  else
    group->sos_list[sosindex-1]->isGUB = state;
  return(TRUE);
}


MYBOOL SOS_is_GUB(SOSgroup *group, int sosindex)
{
  int    i;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(group->lp, IMPORTANT, "SOS_is_GUB: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if((sosindex == 0) && (group->sos_count == 1))
    sosindex = 1;

  if(sosindex == 0) {
    for(i = 1; i <= group->sos_count; i++) {
      if(SOS_is_GUB(group, i))
        return(TRUE);
    }
    return(FALSE);
  }
  else
    return( group->sos_list[sosindex-1]->isGUB );
}


MYBOOL SOS_is_marked(SOSgroup *group, int sosindex, int column)
{
  int    i, k, n, *list;
  lprec  *lp;

  if(group == NULL)
    return( FALSE );
  lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_is_marked: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if(!(lp->var_type[column] & (ISSOS | ISGUB)))
    return(FALSE);

  if(sosindex == 0) {
    for(i = group->memberpos[column-1]; i < group->memberpos[column]; i++) {
      k = group->membership[i];
      n = SOS_is_marked(group, k, column);
      if(n)
        return(TRUE);
    }
  }
  else  {
    list = group->sos_list[sosindex-1]->members;
    n = list[0];

   /* Search for the variable (normally always faster to do linear search here) */
    column = -column;
    for(i = 1; i <= n; i++)
      if(list[i] == column)
        return(TRUE);
  }
  return(FALSE);
}


MYBOOL SOS_is_active(SOSgroup *group, int sosindex, int column)
{
  int    i, n, nn, *list;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_is_active: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if(!(lp->var_type[column] & (ISSOS | ISGUB)))
    return(FALSE);

  if(sosindex == 0) {
    for(i = group->memberpos[column-1]; i < group->memberpos[column]; i++) {
      nn = group->membership[i];
      n = SOS_is_active(group, nn, column);
      if(n)
        return(TRUE);
    }
  }
  else {

    list = group->sos_list[sosindex-1]->members;
    n = list[0]+1;
    nn = list[n];

    /* Scan the active (non-zero) SOS index list */
    for(i = 1; (i <= nn) && (list[n+i] != 0); i++)
      if(list[n+i] == column)
        return(TRUE);
  }
  return(FALSE);
}


MYBOOL SOS_is_full(SOSgroup *group, int sosindex, int column, MYBOOL activeonly)
{
  int    i, nn, n, *list;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_is_full: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if(!(lp->var_type[column] & (ISSOS | ISGUB)))
    return(FALSE);

  if(sosindex == 0) {
    for(i = group->memberpos[column-1]; i < group->memberpos[column]; i++) {
      nn = group->membership[i];
      if(SOS_is_full(group, nn, column, activeonly))
        return(TRUE);
    }
  }
  else if(SOS_is_member(group, sosindex, column)) {

    list = group->sos_list[sosindex-1]->members;
    n = list[0]+1;
    nn = list[n];

   /* Info: Last item in the active list is non-zero if the current SOS is full */
    if(list[n+nn] != 0)
      return(TRUE);

    if(!activeonly) {
      /* Spool to last active variable */
      for(i = nn-1; (i > 0) && (list[n+i] == 0); i--);
      /* Having found it, check if subsequent variables are set (via bounds) as inactive */
      if(i > 0) {
        nn -= i;  /* Compute unused active slots */
        i = SOS_member_index(group, sosindex, list[n+i]);
        for(; (nn > 0) && (list[i] < 0); i++, nn--);
        if(nn == 0)
          return(TRUE);
      }
    }
  }

  return(FALSE);
}


MYBOOL SOS_can_activate(SOSgroup *group, int sosindex, int column)
{
  int    i, n, nn, nz, *list;
  lprec  *lp;

  if(group == NULL)
    return( FALSE );
  lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_can_activate: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if(!(lp->var_type[column] & (ISSOS | ISGUB)))
    return(FALSE);

  if(sosindex == 0) {
    for(i = group->memberpos[column-1]; i < group->memberpos[column]; i++) {
      nn = group->membership[i];
      n = SOS_can_activate(group, nn, column);
      if(n == FALSE)
        return(FALSE);
    }
  }
  else if(SOS_is_member(group, sosindex, column)) {

    list = group->sos_list[sosindex-1]->members;
    n = list[0]+1;
    nn = list[n];

#if 0
    /* Accept if the SOS is empty */
    if(list[n+1] == 0)
      return(TRUE);
#endif

    /* Cannot activate a variable if the SOS is full */
    if(list[n+nn] != 0)
      return(FALSE);

    /* Check if there are variables quasi-active via non-zero lower bounds */
    nz = 0;
    for(i = 1; i < n; i++)
      if(lp->bb_bounds->lowbo[lp->rows+abs(list[i])] > 0) {
        nz++;
        /* Reject outright if selected column has a non-zero lower bound */
        if(list[i] == column)
          return(FALSE);
      }
#ifdef Paranoia
    if(nz > nn)
      report(lp, SEVERE, "SOS_can_activate: Found too many non-zero member variables for SOS index %d\n", sosindex);
#endif
    for(i = 1; i <= nn; i++) {
      if(list[n+i] == 0)
        break;
      if(lp->bb_bounds->lowbo[lp->rows+list[n+i]] == 0)
        nz++;
    }
    if(nz == nn)
      return(FALSE);

    /* Accept if the SOS is empty */
    if(list[n+1] == 0)
      return(TRUE);

    /* Check if we can set variable active in SOS2..SOSn
      (must check left and right neighbours if one variable is already active) */
    if(nn > 1) {

     /* Find the variable that was last activated;
       Also check that the candidate variable is not already active */
      for(i = 1; i <= nn; i++) {
        if(list[n+i] == 0)
          break;
        if(list[n+i] == column)
          return(FALSE);
      }
      i--;
      nn = list[n+i];

      /* SOS accepts an additional variable; confirm neighbourness of candidate;
         Search for the SOS set index of the last activated variable */
      n = list[0];
      for(i = 1; i <= n; i++)
        if(abs(list[i]) == nn)
          break;
      if(i > n) {
        report(lp, CRITICAL, "SOS_can_activate: Internal index error at SOS %d\n", sosindex);
        return(FALSE);
      }

      /* SOS accepts an additional variable; confirm neighbourness of candidate */

      /* Check left neighbour */
      if((i > 1) && (list[i-1] == column))
        return(TRUE);
      /* Check right neighbour */
      if((i < n) && (list[i+1] == column))
        return(TRUE);

      /* It is not the right neighbour; return false */
      return(FALSE);
    }
  }
  return(TRUE);
}


MYBOOL SOS_set_marked(SOSgroup *group, int sosindex, int column, MYBOOL asactive)
{
  int    i, n, nn, *list;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_set_marked: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if(!(lp->var_type[column] & (ISSOS | ISGUB)))
    return(FALSE);

  if(sosindex == 0) {

   /* Define an IBM-"SOS3" member variable temporarily as integer, if it is
      not already a permanent integer; is reset in SOS_unmark */
    if(asactive && !is_int(lp, column) && SOS_is_member_of_type(group, column, SOS3)) {
      lp->var_type[column] |= ISSOSTEMPINT;
      set_int(lp, column, TRUE);
    }

    nn = 0;
    for(i = group->memberpos[column-1]; i < group->memberpos[column]; i++) {
      n = group->membership[i];
      if(SOS_set_marked(group, n, column, asactive))
        nn++;
    }
    return((MYBOOL) (nn == group->sos_count));
  }
  else {
    list = group->sos_list[sosindex-1]->members;
    n = list[0]+1;
    nn = list[n];

   /* Search for the variable */
    i = SOS_member_index(group, sosindex, column);

   /* First mark active in the set member list as used */
    if((i > 0) && (list[i] > 0))
      list[i] *= -1;
    else
      return(TRUE);

   /* Then move the variable to the live list */
    if(asactive) {
      for(i = 1; i <= nn; i++) {
        if(list[n+i] == column)
          return(FALSE);
        else if(list[n+i] == 0) {
          list[n+i] = column;
          return(FALSE);
        }
      }
    }
    return(TRUE);
  }
}


MYBOOL SOS_unmark(SOSgroup *group, int sosindex, int column)
{
  int    i, n, nn, *list;
  MYBOOL isactive;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_unmark: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if(!(lp->var_type[column] & (ISSOS | ISGUB)))
    return(FALSE);


  if(sosindex == 0) {

    /* Undefine a SOS3 member variable that has temporarily been set as integer */
    if(lp->var_type[column] & ISSOSTEMPINT) {
      lp->var_type[column] &= !ISSOSTEMPINT;
      set_int(lp, column, FALSE);
    }

    nn = 0;
    for(i = group->memberpos[column-1]; i < group->memberpos[column]; i++) {
      n = group->membership[i];
      if(SOS_unmark(group, n, column))
        nn++;
    }
    return((MYBOOL) (nn == group->sos_count));
  }
  else {
    list = group->sos_list[sosindex-1]->members;
    n = list[0]+1;
    nn = list[n];

   /* Search for the variable */
    i = SOS_member_index(group, sosindex, column);

   /* Restore sign in main list */
    if((i > 0) && (list[i] < 0))
      list[i] *= -1;
    else
      return(TRUE);

   /* Find the variable in the active list... */
    isactive = SOS_is_active(group, sosindex, column);
    if(isactive) {
      for(i = 1; i <= nn; i++)
        if(list[n+i] == column)
          break;
     /* ...shrink the list if found, otherwise return error */
      if(i <= nn) {
        for(; i<nn; i++)
        list[n+i] = list[n+i+1];
        list[n+nn] = 0;
        return(TRUE);
      }
      return(FALSE);
    }
    else
      return(TRUE);
  }
}


int SOS_fix_unmarked(SOSgroup *group, int sosindex, int variable, REAL *bound, REAL value, MYBOOL isupper,
                     int *diffcount, DeltaVrec *changelog)
{
  int    i, ii, count, n, nn, nLeft, nRight, *list;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_fix_unmarked: Invalid SOS index %d\n", sosindex);
    return(FALSE);
  }
#endif

  count = 0;
  if(sosindex == 0) {
    for(i = group->memberpos[variable-1]; i < group->memberpos[variable]; i++) {
      n = group->membership[i];
      count += SOS_fix_unmarked(group, n, variable, bound, value, isupper, diffcount, changelog);
    }
  }
  else {
    list = group->sos_list[sosindex-1]->members;
    n = list[0]+1;

   /* Count the number of active and free SOS variables */
    nn = list[n];
    for(i = 1; i <= nn; i++) {
      if(list[n+i] == 0)
      break;
    }
    i--;
    i = nn - i;  /* Establish the number of unused slots */

   /* Determine the free SOS variable window */
    if(i == nn) {
      nLeft = 0;
      nRight = SOS_member_index(group, sosindex, variable);
    }
    else {
      nLeft  = SOS_member_index(group, sosindex, list[n+1]);
      if(variable == list[n+1])
        nRight = nLeft;
      else
        nRight = SOS_member_index(group, sosindex, variable);
    }

    nRight += i;  /* Loop (nRight+1)..n */

   /* Fix variables outside of the free SOS variable window */
    for(i = 1; i < n; i++)  {
     /* Skip the SOS variable window */
      if((i >= nLeft) && (i <= nRight))
        continue;
     /* Otherwise proceed to set bound */
      ii = list[i];
      if(ii > 0) {
        ii += lp->rows;
        if(bound[ii] != value) {
         /* Verify that we don't violate original bounds */
          if(isupper && (value < lp->orig_lowbo[ii]))
            return(-ii);
          else if(!isupper && (value > lp->orig_upbo[ii]))
            return(-ii);
         /* OK, set the new bound */
          count++;
          if(changelog == NULL)
            bound[ii] = value;
          else
            modifyUndoLadder(changelog, ii, bound, value);

        }
        if((diffcount != NULL) && (lp->solution[ii] != value))
          (*diffcount)++;
      }
    }
  }
  return(count);
}

int *SOS_get_candidates(SOSgroup *group, int sosindex, int column, MYBOOL excludetarget,
                        REAL *upbound, REAL *lobound)
{
  int    i, ii, j, n, nn = 0, *list, *candidates = NULL;
  lprec  *lp = group->lp;

  if(group == NULL)
    return( candidates );

#ifdef Paranoia
  if(sosindex > group->sos_count) {
    report(lp, IMPORTANT, "SOS_get_candidates: Invalid index %d\n", sosindex);
    return( candidates );
  }
#endif

  /* Determine SOS target(s); note that if "sosindex" is negative, only
     the first non-empty SOS where "column" is a member is processed */
  if(sosindex <= 0) {
    i = 0;
    ii = group->sos_count;
  }
  else {
    i = sosindex - 1;
    ii = sosindex;
  }

  /* Tally candidate usage */
  allocINT(lp, &candidates, lp->columns+1, TRUE);
  for(; i < ii; i++) {
    if(!SOS_is_member(group, i+1, column))
      continue;
    list = group->sos_list[i]->members;
    n = list[0];
    while(n > 0) {
      j = list[n];
      if((j > 0) && (upbound[lp->rows+j] > 0)) {
        if(lobound[lp->rows+j] > 0) {
          report(lp, IMPORTANT, "SOS_get_candidates: Invalid non-zero lower bound setting\n");
          n = 0;
          goto Finish;
        }
        if(candidates[j] == 0)
          nn++;
        candidates[j]++;
      }
      n--;
    }
    if((sosindex < 0) && (nn > 1))
      break;
  }

  /* Condense the list into indeces */
  n = 0;
  for(i = 1; i <= lp->columns; i++) {
    if((candidates[i] > 0) && (!excludetarget || (i != column))) {
      n++;
      candidates[n] = i;
    }
  }

  /* Finalize */
Finish:
  candidates[0] = n;
  if(n == 0)
    FREE(candidates);

  return( candidates);

}

int SOS_fix_list(SOSgroup *group, int sosindex, int variable, REAL *bound,
                 int *varlist, MYBOOL isleft, DeltaVrec *changelog)
{
  int    i, ii, jj, count = 0;
  REAL   value = 0;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_fix_list: Invalid index %d\n", sosindex);
    return(FALSE);
  }
#endif

  if(sosindex == 0) {
    for(i = group->memberpos[variable-1]; i < group->memberpos[variable]; i++) {
      ii = group->membership[i];
      count += SOS_fix_list(group, ii, variable, bound, varlist, isleft, changelog);
    }
  }
  else {

    /* Establish the number of unmarked variables in the left window
       (note that "variable" should have been marked previously) */
    ii = varlist[0] / 2;
    if(isleft) {
      i = 1;
      if(isleft == AUTOMATIC)
        ii = varlist[0];
    }
    else {
      i = ii + 1;
      ii = varlist[0];
    }

    /* Loop over members to fix values at the new bound (zero) */
    while(i <= ii) {
      if(SOS_is_member(group, sosindex, varlist[i])) {
        jj = lp->rows + varlist[i];

        /* Verify that we don't violate original bounds */
        if(value < lp->orig_lowbo[jj])
          return( -jj );
        /* OK, set the new bound */
        count++;
        if(changelog == NULL)
          bound[jj] = value;
        else
          modifyUndoLadder(changelog, jj, bound, value);
      }
      i++;
    }

  }
  return( count );
}

int SOS_is_satisfied(SOSgroup *group, int sosindex, REAL *solution)
/* Determine if the SOS is satisfied for the current solution vector;
   The return code is in the range [-2..+2], depending on the type of
   satisfaction.  Positive return value means too many non-zero values,
   negative value means set incomplete:

              -2: Set member count not full (SOS3)
              -1: Set member count not full
               0: Set is full (also returned if the SOS index is invalid)
               1: Too many non-zero sequential variables
               2: Set consistency error

*/
{
  int    i, n, nn, count, *list;
  int    type, status = 0;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_is_satisfied: Invalid index %d\n", sosindex);
    return( SOS_COMPLETE );
  }
#endif

  if((sosindex == 0) && (group->sos_count == 1))
    sosindex = 1;

  if(sosindex == 0) {
    for(i = 1; i <= group->sos_count; i++) {
      status = SOS_is_satisfied(group, i, solution);
      if((status != SOS_COMPLETE) && (status != SOS_INCOMPLETE))
        break;
    }
  }
  else {
    type = SOS_get_type(group, sosindex);
    list = group->sos_list[sosindex-1]->members;
    n = list[0]+1;
    nn = list[n];

   /* Count the number of active SOS variables */
    for(i = 1; i <= nn; i++) {
      if(list[n+i] == 0)
        break;
    }
    count = i-1;
    if(count == nn)
      status = SOS_COMPLETE;    /* Set is full    */
    else
      status = SOS_INCOMPLETE;  /* Set is partial */

   /* Find index of the first active variable; fail if some are non-zero */
    if(count > 0) {
      nn = list[n+1];
      for(i = 1; i < n; i++) {
        if((abs(list[i]) == nn) || (solution[lp->rows + abs(list[i])] != 0))
          break;
      }
      if(abs(list[i]) != nn)
        status = SOS_INTERNALERROR;  /* Set consistency error (leading set variables are non-zero) */
      else {
       /* Scan active SOS variables until we find a non-zero value */
        while(count > 0) {
          if(solution[lp->rows + abs(list[i])] != 0)
            break;
          i++;
          count--;
        }
       /* Scan active non-zero SOS variables; break at first non-zero (rest required to be zero) */
        while(count > 0) {
          if(solution[lp->rows + abs(list[i])] == 0)
            break;
          i++;
          count--;
        }
        if(count > 0)
          status = SOS_INTERNALERROR; /* Set consistency error (active set variables are zero) */
      }
    }
    else {
      i = 1;
      /* There are no active variables; see if we have happened to find a valid header */
      while((i < n) && (solution[lp->rows + abs(list[i])] == 0))
        i++;
      count = 0;
      while((i < n) && (count <= nn) && (solution[lp->rows + abs(list[i])] != 0)) {
        count++;
        i++;
      }
      if(count > nn)
        status = SOS_INFEASIBLE;   /* Too-many sequential non-zero variables */
    }

    /* Scan the trailing set of SOS variables; fail if some are non-zero */
    if(status <= 0) {
      n--;
      while(i <= n) {
        if(solution[lp->rows + abs(list[i])] != 0)
          break;
        i++;
      }
      if(i <= n)
        status = SOS_INFEASIBLE;  /* Too-many sequential non-zero variables */

      /* Code member deficiency for SOS3 separately */
      else if((status == -1) && (type <= SOS3))
        status = SOS3_INCOMPLETE;
    }

  }
  return( status );
}

MYBOOL SOS_is_feasible(SOSgroup *group, int sosindex, REAL *solution)
/* Determine if the SOS is feasible up to the current SOS variable */
{
  int    i, n, nn, *list;
  MYBOOL status = TRUE;
  lprec  *lp = group->lp;

#ifdef Paranoia
  if((sosindex < 0) || (sosindex > group->sos_count)) {
    report(lp, IMPORTANT, "SOS_is_feasible: Invalid SOS index %d\n", sosindex);
    return( 0 );
  }
#endif

  if((sosindex == 0) && (group->sos_count == 1))
    sosindex = 1;

  if(sosindex == 0) {
    for(i = 1; status && (i <= group->sos_count); i++) {
      status = SOS_is_feasible(group, i, solution);
    }
  }
  else {
    list = group->sos_list[sosindex-1]->members;
    n = list[0]+1;
    nn = list[n];
    if(nn <= 2)
      return(status);

   /* Find if we have a gap in the non-zero solution values */
    i = 1;
    sosindex = 0;
    while((i <= nn) && (list[n+i] != 0)) {
      while((i <= nn) && (list[n+i] != 0) && (solution[lp->rows+list[n+i]] == 0))
        i++;
      if((i <= nn) && (list[n+i] != 0)) {
        i++;  /* Step to next */
        while((i <= nn) && (list[n+i] != 0) && (solution[lp->rows+list[n+i]] != 0))
          i++;
        sosindex++;
      }
      i++;    /* Step to next */
    }
    status = (MYBOOL) (sosindex <= 1);
  }
  return(status);
}