/* glpssx01.c */

/***********************************************************************

*  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 "glpenv.h"

#include "glpssx.h"

#define xfault xerror

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

// ssx_create - create simplex solver workspace.

//

// This routine creates the workspace used by simplex solver routines,

// and returns a pointer to it.

//

// Parameters m, n, and nnz specify, respectively, the number of rows,

// columns, and non-zero constraint coefficients.

//

// This routine only allocates the memory for the workspace components,

// so the workspace needs to be saturated by data. */

SSX *ssx_create(int m, int n, int nnz)

{     SSX *ssx;

      int i, j, k;

      if (m < 1)

         xfault("ssx_create: m = %d; invalid number of rows\n", m);

      if (n < 1)

         xfault("ssx_create: n = %d; invalid number of columns\n", n);

      if (nnz < 0)

         xfault("ssx_create: nnz = %d; invalid number of non-zero const"

            "raint coefficients\n", nnz);

      ssx = xmalloc(sizeof(SSX));

      ssx->m = m;

      ssx->n = n;

      ssx->type = xcalloc(1+m+n, sizeof(int));

      ssx->lb = xcalloc(1+m+n, sizeof(mpq_t));

      for (k = 1; k <= m+n; k++) mpq_init(ssx->lb[k]);

      ssx->ub = xcalloc(1+m+n, sizeof(mpq_t));

      for (k = 1; k <= m+n; k++) mpq_init(ssx->ub[k]);

      ssx->coef = xcalloc(1+m+n, sizeof(mpq_t));

      for (k = 0; k <= m+n; k++) mpq_init(ssx->coef[k]);

      ssx->A_ptr = xcalloc(1+n+1, sizeof(int));

      ssx->A_ptr[n+1] = nnz+1;

      ssx->A_ind = xcalloc(1+nnz, sizeof(int));

      ssx->A_val = xcalloc(1+nnz, sizeof(mpq_t));

      for (k = 1; k <= nnz; k++) mpq_init(ssx->A_val[k]);

      ssx->stat = xcalloc(1+m+n, sizeof(int));

      ssx->Q_row = xcalloc(1+m+n, sizeof(int));

      ssx->Q_col = xcalloc(1+m+n, sizeof(int));

      ssx->binv = bfx_create_binv();

      ssx->bbar = xcalloc(1+m, sizeof(mpq_t));

      for (i = 0; i <= m; i++) mpq_init(ssx->bbar[i]);

      ssx->pi = xcalloc(1+m, sizeof(mpq_t));

      for (i = 1; i <= m; i++) mpq_init(ssx->pi[i]);

      ssx->cbar = xcalloc(1+n, sizeof(mpq_t));

      for (j = 1; j <= n; j++) mpq_init(ssx->cbar[j]);

      ssx->rho = xcalloc(1+m, sizeof(mpq_t));

      for (i = 1; i <= m; i++) mpq_init(ssx->rho[i]);

      ssx->ap = xcalloc(1+n, sizeof(mpq_t));

      for (j = 1; j <= n; j++) mpq_init(ssx->ap[j]);

      ssx->aq = xcalloc(1+m, sizeof(mpq_t));

      for (i = 1; i <= m; i++) mpq_init(ssx->aq[i]);

      mpq_init(ssx->delta);

      return ssx;

}

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

// ssx_factorize - factorize the current basis matrix.

//

// This routine computes factorization of the current basis matrix B

// and returns the singularity flag. If the matrix B is non-singular,

// the flag is zero, otherwise non-zero. */

static int basis_col(void *info, int j, int ind[], mpq_t val[])

{     /* this auxiliary routine provides row indices and numeric values

         of non-zero elements in j-th column of the matrix B */

      SSX *ssx = info;

      int m = ssx->m;

      int n = ssx->n;

      int *A_ptr = ssx->A_ptr;

      int *A_ind = ssx->A_ind;

      mpq_t *A_val = ssx->A_val;

      int *Q_col = ssx->Q_col;

      int k, len, ptr;

      xassert(1 <= j && j <= m);

      k = Q_col[j]; /* x[k] = xB[j] */

      xassert(1 <= k && k <= m+n);

      /* j-th column of the matrix B is k-th column of the augmented

         constraint matrix (I | -A) */

      if (k <= m)

      {  /* it is a column of the unity matrix I */

         len = 1, ind[1] = k, mpq_set_si(val[1], 1, 1);

      }

      else

      {  /* it is a column of the original constraint matrix -A */

         len = 0;

         for (ptr = A_ptr[k-m]; ptr < A_ptr[k-m+1]; ptr++)

         {  len++;

            ind[len] = A_ind[ptr];

            mpq_neg(val[len], A_val[ptr]);

         }

      }

      return len;

}

int ssx_factorize(SSX *ssx)

{     int ret;

      ret = bfx_factorize(ssx->binv, ssx->m, basis_col, ssx);

      return ret;

}

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

// ssx_get_xNj - determine value of non-basic variable.

//

// This routine determines the value of non-basic variable xN[j] in the

// current basic solution defined as follows:

//

//    0,             if xN[j] is free variable

//    lN[j],         if xN[j] is on its lower bound

//    uN[j],         if xN[j] is on its upper bound

//    lN[j] = uN[j], if xN[j] is fixed variable

//

// where lN[j] and uN[j] are lower and upper bounds of xN[j]. */

void ssx_get_xNj(SSX *ssx, int j, mpq_t x)

{     int m = ssx->m;

      int n = ssx->n;

      mpq_t *lb = ssx->lb;

      mpq_t *ub = ssx->ub;

      int *stat = ssx->stat;

      int *Q_col = ssx->Q_col;

      int k;

      xassert(1 <= j && j <= n);

      k = Q_col[m+j]; /* x[k] = xN[j] */

      xassert(1 <= k && k <= m+n);

      switch (stat[k])

      {  case SSX_NL:

            /* xN[j] is on its lower bound */

            mpq_set(x, lb[k]); break;

         case SSX_NU:

            /* xN[j] is on its upper bound */

            mpq_set(x, ub[k]); break;

         case SSX_NF:

            /* xN[j] is free variable */

            mpq_set_si(x, 0, 1); break;

         case SSX_NS:

            /* xN[j] is fixed variable */

            mpq_set(x, lb[k]); break;

         default:

            xassert(stat != stat);

      }

      return;

}

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

// ssx_eval_bbar - compute values of basic variables.

//

// This routine computes values of basic variables xB in the current

// basic solution as follows:

//

//    beta = - inv(B) * N * xN,

//

// where B is the basis matrix, N is the matrix of non-basic columns,

// xN is a vector of current values of non-basic variables. */

void ssx_eval_bbar(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      mpq_t *coef = ssx->coef;

      int *A_ptr = ssx->A_ptr;

      int *A_ind = ssx->A_ind;

      mpq_t *A_val = ssx->A_val;

      int *Q_col = ssx->Q_col;

      mpq_t *bbar = ssx->bbar;

      int i, j, k, ptr;

      mpq_t x, temp;

      mpq_init(x);

      mpq_init(temp);

      /* bbar := 0 */

      for (i = 1; i <= m; i++)

         mpq_set_si(bbar[i], 0, 1);

      /* bbar := - N * xN = - N[1] * xN[1] - ... - N[n] * xN[n] */

      for (j = 1; j <= n; j++)

      {  ssx_get_xNj(ssx, j, x);

         if (mpq_sgn(x) == 0) continue;

         k = Q_col[m+j]; /* x[k] = xN[j] */

         if (k <= m)

         {  /* N[j] is a column of the unity matrix I */

            mpq_sub(bbar[k], bbar[k], x);

         }

         else

         {  /* N[j] is a column of the original constraint matrix -A */

            for (ptr = A_ptr[k-m]; ptr < A_ptr[k-m+1]; ptr++)

            {  mpq_mul(temp, A_val[ptr], x);

               mpq_add(bbar[A_ind[ptr]], bbar[A_ind[ptr]], temp);

            }

         }

      }

      /* bbar := inv(B) * bbar */

      bfx_ftran(ssx->binv, bbar, 0);

#if 1

      /* compute value of the objective function */

      /* bbar[0] := c[0] */

      mpq_set(bbar[0], coef[0]);

      /* bbar[0] := bbar[0] + sum{i in B} cB[i] * xB[i] */

      for (i = 1; i <= m; i++)

      {  k = Q_col[i]; /* x[k] = xB[i] */

         if (mpq_sgn(coef[k]) == 0) continue;

         mpq_mul(temp, coef[k], bbar[i]);

         mpq_add(bbar[0], bbar[0], temp);

      }

      /* bbar[0] := bbar[0] + sum{j in N} cN[j] * xN[j] */

      for (j = 1; j <= n; j++)

      {  k = Q_col[m+j]; /* x[k] = xN[j] */

         if (mpq_sgn(coef[k]) == 0) continue;

         ssx_get_xNj(ssx, j, x);

         mpq_mul(temp, coef[k], x);

         mpq_add(bbar[0], bbar[0], temp);

      }

#endif

      mpq_clear(x);

      mpq_clear(temp);

      return;

}

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

// ssx_eval_pi - compute values of simplex multipliers.

//

// This routine computes values of simplex multipliers (shadow prices)

// pi in the current basic solution as follows:

//

//    pi = inv(B') * cB,

//

// where B' is a matrix transposed to the basis matrix B, cB is a vector

// of objective coefficients at basic variables xB. */

void ssx_eval_pi(SSX *ssx)

{     int m = ssx->m;

      mpq_t *coef = ssx->coef;

      int *Q_col = ssx->Q_col;

      mpq_t *pi = ssx->pi;

      int i;

      /* pi := cB */

      for (i = 1; i <= m; i++) mpq_set(pi[i], coef[Q_col[i]]);

      /* pi := inv(B') * cB */

      bfx_btran(ssx->binv, pi);

      return;

}

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

// ssx_eval_dj - compute reduced cost of non-basic variable.

//

// This routine computes reduced cost d[j] of non-basic variable xN[j]

// in the current basic solution as follows:

//

//    d[j] = cN[j] - N[j] * pi,

//

// where cN[j] is an objective coefficient at xN[j], N[j] is a column

// of the augmented constraint matrix (I | -A) corresponding to xN[j],

// pi is the vector of simplex multipliers (shadow prices). */

void ssx_eval_dj(SSX *ssx, int j, mpq_t dj)

{     int m = ssx->m;

      int n = ssx->n;

      mpq_t *coef = ssx->coef;

      int *A_ptr = ssx->A_ptr;

      int *A_ind = ssx->A_ind;

      mpq_t *A_val = ssx->A_val;

      int *Q_col = ssx->Q_col;

      mpq_t *pi = ssx->pi;

      int k, ptr, end;

      mpq_t temp;

      mpq_init(temp);

      xassert(1 <= j && j <= n);

      k = Q_col[m+j]; /* x[k] = xN[j] */

      xassert(1 <= k && k <= m+n);

      /* j-th column of the matrix N is k-th column of the augmented

         constraint matrix (I | -A) */

      if (k <= m)

      {  /* it is a column of the unity matrix I */

         mpq_sub(dj, coef[k], pi[k]);

      }

      else

      {  /* it is a column of the original constraint matrix -A */

         mpq_set(dj, coef[k]);

         for (ptr = A_ptr[k-m], end = A_ptr[k-m+1]; ptr < end; ptr++)

         {  mpq_mul(temp, A_val[ptr], pi[A_ind[ptr]]);

            mpq_add(dj, dj, temp);

         }

      }

      mpq_clear(temp);

      return;

}

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

// ssx_eval_cbar - compute reduced costs of all non-basic variables.

//

// This routine computes the vector of reduced costs pi in the current

// basic solution for all non-basic variables, including fixed ones. */

void ssx_eval_cbar(SSX *ssx)

{     int n = ssx->n;

      mpq_t *cbar = ssx->cbar;

      int j;

      for (j = 1; j <= n; j++)

         ssx_eval_dj(ssx, j, cbar[j]);

      return;

}

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

// ssx_eval_rho - compute p-th row of the inverse.

//

// This routine computes p-th row of the matrix inv(B), where B is the

// current basis matrix.

//

// p-th row of the inverse is computed using the following formula:

//

//    rho = inv(B') * e[p],

//

// where B' is a matrix transposed to B, e[p] is a unity vector, which

// contains one in p-th position. */

void ssx_eval_rho(SSX *ssx)

{     int m = ssx->m;

      int p = ssx->p;

      mpq_t *rho = ssx->rho;

      int i;

      xassert(1 <= p && p <= m);

      /* rho := 0 */

      for (i = 1; i <= m; i++) mpq_set_si(rho[i], 0, 1);

      /* rho := e[p] */

      mpq_set_si(rho[p], 1, 1);

      /* rho := inv(B') * rho */

      bfx_btran(ssx->binv, rho);

      return;

}

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

// ssx_eval_row - compute pivot row of the simplex table.

//

// This routine computes p-th (pivot) row of the current simplex table

// A~ = - inv(B) * N using the following formula:

//

//    A~[p] = - N' * inv(B') * e[p] = - N' * rho[p],

//

// where N' is a matrix transposed to the matrix N, rho[p] is p-th row

// of the inverse inv(B). */

void ssx_eval_row(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      int *A_ptr = ssx->A_ptr;

      int *A_ind = ssx->A_ind;

      mpq_t *A_val = ssx->A_val;

      int *Q_col = ssx->Q_col;

      mpq_t *rho = ssx->rho;

      mpq_t *ap = ssx->ap;

      int j, k, ptr;

      mpq_t temp;

      mpq_init(temp);

      for (j = 1; j <= n; j++)

      {  /* ap[j] := - N'[j] * rho (inner product) */

         k = Q_col[m+j]; /* x[k] = xN[j] */

         if (k <= m)

            mpq_neg(ap[j], rho[k]);

         else

         {  mpq_set_si(ap[j], 0, 1);

            for (ptr = A_ptr[k-m]; ptr < A_ptr[k-m+1]; ptr++)

            {  mpq_mul(temp, A_val[ptr], rho[A_ind[ptr]]);

               mpq_add(ap[j], ap[j], temp);

            }

         }

      }

      mpq_clear(temp);

      return;

}

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

// ssx_eval_col - compute pivot column of the simplex table.

//

// This routine computes q-th (pivot) column of the current simplex

// table A~ = - inv(B) * N using the following formula:

//

//    A~[q] = - inv(B) * N[q],

//

// where N[q] is q-th column of the matrix N corresponding to chosen

// non-basic variable xN[q]. */

void ssx_eval_col(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      int *A_ptr = ssx->A_ptr;

      int *A_ind = ssx->A_ind;

      mpq_t *A_val = ssx->A_val;

      int *Q_col = ssx->Q_col;

      int q = ssx->q;

      mpq_t *aq = ssx->aq;

      int i, k, ptr;

      xassert(1 <= q && q <= n);

      /* aq := 0 */

      for (i = 1; i <= m; i++) mpq_set_si(aq[i], 0, 1);

      /* aq := N[q] */

      k = Q_col[m+q]; /* x[k] = xN[q] */

      if (k <= m)

      {  /* N[q] is a column of the unity matrix I */

         mpq_set_si(aq[k], 1, 1);

      }

      else

      {  /* N[q] is a column of the original constraint matrix -A */

         for (ptr = A_ptr[k-m]; ptr < A_ptr[k-m+1]; ptr++)

            mpq_neg(aq[A_ind[ptr]], A_val[ptr]);

      }

      /* aq := inv(B) * aq */

      bfx_ftran(ssx->binv, aq, 1);

      /* aq := - aq */

      for (i = 1; i <= m; i++) mpq_neg(aq[i], aq[i]);

      return;

}

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

// ssx_chuzc - choose pivot column.

//

// This routine chooses non-basic variable xN[q] whose reduced cost

// indicates possible improving of the objective function to enter it

// in the basis.

//

// Currently the standard (textbook) pricing is used, i.e. that

// non-basic variable is preferred which has greatest reduced cost (in

// magnitude).

//

// If xN[q] has been chosen, the routine stores its number q and also

// sets the flag q_dir that indicates direction in which xN[q] has to

// change (+1 means increasing, -1 means decreasing).

//

// If the choice cannot be made, because the current basic solution is

// dual feasible, the routine sets the number q to 0. */

void ssx_chuzc(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      int dir = (ssx->dir == SSX_MIN ? +1 : -1);

      int *Q_col = ssx->Q_col;

      int *stat = ssx->stat;

      mpq_t *cbar = ssx->cbar;

      int j, k, s, q, q_dir;

      double best, temp;

      /* nothing is chosen so far */

      q = 0, q_dir = 0, best = 0.0;

      /* look through the list of non-basic variables */

      for (j = 1; j <= n; j++)

      {  k = Q_col[m+j]; /* x[k] = xN[j] */

         s = dir * mpq_sgn(cbar[j]);

         if ((stat[k] == SSX_NF || stat[k] == SSX_NL) && s < 0 ||

             (stat[k] == SSX_NF || stat[k] == SSX_NU) && s > 0)

         {  /* reduced cost of xN[j] indicates possible improving of

               the objective function */

            temp = fabs(mpq_get_d(cbar[j]));

            xassert(temp != 0.0);

            if (q == 0 || best < temp)

               q = j, q_dir = - s, best = temp;

         }

      }

      ssx->q = q, ssx->q_dir = q_dir;

      return;

}

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

// ssx_chuzr - choose pivot row.

//

// This routine looks through elements of q-th column of the simplex

// table and chooses basic variable xB[p] which should leave the basis.

//

// The choice is based on the standard (textbook) ratio test.

//

// If xB[p] has been chosen, the routine stores its number p and also

// sets its non-basic status p_stat which should be assigned to xB[p]

// when it has left the basis and become xN[q].

//

// Special case p < 0 means that xN[q] is double-bounded variable and

// it reaches its opposite bound before any basic variable does that,

// so the current basis remains unchanged.

//

// If the choice cannot be made, because xN[q] can infinitely change in

// the feasible direction, the routine sets the number p to 0. */

void ssx_chuzr(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      int *type = ssx->type;

      mpq_t *lb = ssx->lb;

      mpq_t *ub = ssx->ub;

      int *Q_col = ssx->Q_col;

      mpq_t *bbar = ssx->bbar;

      int q = ssx->q;

      mpq_t *aq = ssx->aq;

      int q_dir = ssx->q_dir;

      int i, k, s, t, p, p_stat;

      mpq_t teta, temp;

      mpq_init(teta);

      mpq_init(temp);

      xassert(1 <= q && q <= n);

      xassert(q_dir == +1 || q_dir == -1);

      /* nothing is chosen so far */

      p = 0, p_stat = 0;

      /* look through the list of basic variables */

      for (i = 1; i <= m; i++)

      {  s = q_dir * mpq_sgn(aq[i]);

         if (s < 0)

         {  /* xB[i] decreases */

            k = Q_col[i]; /* x[k] = xB[i] */

            t = type[k];

            if (t == SSX_LO || t == SSX_DB || t == SSX_FX)

            {  /* xB[i] has finite lower bound */

               mpq_sub(temp, bbar[i], lb[k]);

               mpq_div(temp, temp, aq[i]);

               mpq_abs(temp, temp);

               if (p == 0 || mpq_cmp(teta, temp) > 0)

               {  p = i;

                  p_stat = (t == SSX_FX ? SSX_NS : SSX_NL);

                  mpq_set(teta, temp);

               }

            }

         }

         else if (s > 0)

         {  /* xB[i] increases */

            k = Q_col[i]; /* x[k] = xB[i] */

            t = type[k];

            if (t == SSX_UP || t == SSX_DB || t == SSX_FX)

            {  /* xB[i] has finite upper bound */

               mpq_sub(temp, bbar[i], ub[k]);

               mpq_div(temp, temp, aq[i]);

               mpq_abs(temp, temp);

               if (p == 0 || mpq_cmp(teta, temp) > 0)

               {  p = i;

                  p_stat = (t == SSX_FX ? SSX_NS : SSX_NU);

                  mpq_set(teta, temp);

               }

            }

         }

         /* if something has been chosen and the ratio test indicates

            exact degeneracy, the search can be finished */

         if (p != 0 && mpq_sgn(teta) == 0) break;

      }

      /* if xN[q] is double-bounded, check if it can reach its opposite

         bound before any basic variable */

      k = Q_col[m+q]; /* x[k] = xN[q] */

      if (type[k] == SSX_DB)

      {  mpq_sub(temp, ub[k], lb[k]);

         if (p == 0 || mpq_cmp(teta, temp) > 0)

         {  p = -1;

            p_stat = -1;

            mpq_set(teta, temp);

         }

      }

      ssx->p = p;

      ssx->p_stat = p_stat;

      /* if xB[p] has been chosen, determine its actual change in the

         adjacent basis (it has the same sign as q_dir) */

      if (p != 0)

      {  xassert(mpq_sgn(teta) >= 0);

         if (q_dir > 0)

            mpq_set(ssx->delta, teta);

         else

            mpq_neg(ssx->delta, teta);

      }

      mpq_clear(teta);

      mpq_clear(temp);

      return;

}

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

// ssx_update_bbar - update values of basic variables.

//

// This routine recomputes the current values of basic variables for

// the adjacent basis.

//

// The simplex table for the current basis is the following:

//

//    xB[i] = sum{j in 1..n} alfa[i,j] * xN[q],  i = 1,...,m

//

// therefore

//

//    delta xB[i] = alfa[i,q] * delta xN[q],  i = 1,...,m

//

// where delta xN[q] = xN.new[q] - xN[q] is the change of xN[q] in the

// adjacent basis, and delta xB[i] = xB.new[i] - xB[i] is the change of

// xB[i]. This gives formulae for recomputing values of xB[i]:

//

//    xB.new[p] = xN[q] + delta xN[q]

//

// (because xN[q] becomes xB[p] in the adjacent basis), and

//

//    xB.new[i] = xB[i] + alfa[i,q] * delta xN[q],  i != p

//

// for other basic variables. */

void ssx_update_bbar(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      mpq_t *bbar = ssx->bbar;

      mpq_t *cbar = ssx->cbar;

      int p = ssx->p;

      int q = ssx->q;

      mpq_t *aq = ssx->aq;

      int i;

      mpq_t temp;

      mpq_init(temp);

      xassert(1 <= q && q <= n);

      if (p < 0)

      {  /* xN[q] is double-bounded and goes to its opposite bound */

         /* nop */;

      }

      else

      {  /* xN[q] becomes xB[p] in the adjacent basis */

         /* xB.new[p] = xN[q] + delta xN[q] */

         xassert(1 <= p && p <= m);

         ssx_get_xNj(ssx, q, temp);

         mpq_add(bbar[p], temp, ssx->delta);

      }

      /* update values of other basic variables depending on xN[q] */

      for (i = 1; i <= m; i++)

      {  if (i == p) continue;

         /* xB.new[i] = xB[i] + alfa[i,q] * delta xN[q] */

         if (mpq_sgn(aq[i]) == 0) continue;

         mpq_mul(temp, aq[i], ssx->delta);

         mpq_add(bbar[i], bbar[i], temp);

      }

#if 1

      /* update value of the objective function */

      /* z.new = z + d[q] * delta xN[q] */

      mpq_mul(temp, cbar[q], ssx->delta);

      mpq_add(bbar[0], bbar[0], temp);

#endif

      mpq_clear(temp);

      return;

}

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

-- ssx_update_pi - update simplex multipliers.

--

-- This routine recomputes the vector of simplex multipliers for the

-- adjacent basis. */

void ssx_update_pi(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      mpq_t *pi = ssx->pi;

      mpq_t *cbar = ssx->cbar;

      int p = ssx->p;

      int q = ssx->q;

      mpq_t *aq = ssx->aq;

      mpq_t *rho = ssx->rho;

      int i;

      mpq_t new_dq, temp;

      mpq_init(new_dq);

      mpq_init(temp);

      xassert(1 <= p && p <= m);

      xassert(1 <= q && q <= n);

      /* compute d[q] in the adjacent basis */

      mpq_div(new_dq, cbar[q], aq[p]);

      /* update the vector of simplex multipliers */

      for (i = 1; i <= m; i++)

      {  if (mpq_sgn(rho[i]) == 0) continue;

         mpq_mul(temp, new_dq, rho[i]);

         mpq_sub(pi[i], pi[i], temp);

      }

      mpq_clear(new_dq);

      mpq_clear(temp);

      return;

}

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

// ssx_update_cbar - update reduced costs of non-basic variables.

//

// This routine recomputes the vector of reduced costs of non-basic

// variables for the adjacent basis. */

void ssx_update_cbar(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      mpq_t *cbar = ssx->cbar;

      int p = ssx->p;

      int q = ssx->q;

      mpq_t *ap = ssx->ap;

      int j;

      mpq_t temp;

      mpq_init(temp);

      xassert(1 <= p && p <= m);

      xassert(1 <= q && q <= n);

      /* compute d[q] in the adjacent basis */

      /* d.new[q] = d[q] / alfa[p,q] */

      mpq_div(cbar[q], cbar[q], ap[q]);

      /* update reduced costs of other non-basic variables */

      for (j = 1; j <= n; j++)

      {  if (j == q) continue;

         /* d.new[j] = d[j] - (alfa[p,j] / alfa[p,q]) * d[q] */

         if (mpq_sgn(ap[j]) == 0) continue;

         mpq_mul(temp, ap[j], cbar[q]);

         mpq_sub(cbar[j], cbar[j], temp);

      }

      mpq_clear(temp);

      return;

}

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

// ssx_change_basis - change current basis to adjacent one.

//

// This routine changes the current basis to the adjacent one swapping

// basic variable xB[p] and non-basic variable xN[q]. */

void ssx_change_basis(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      int *type = ssx->type;

      int *stat = ssx->stat;

      int *Q_row = ssx->Q_row;

      int *Q_col = ssx->Q_col;

      int p = ssx->p;

      int q = ssx->q;

      int p_stat = ssx->p_stat;

      int k, kp, kq;

      if (p < 0)

      {  /* special case: xN[q] goes to its opposite bound */

         xassert(1 <= q && q <= n);

         k = Q_col[m+q]; /* x[k] = xN[q] */

         xassert(type[k] == SSX_DB);

         switch (stat[k])

         {  case SSX_NL:

               stat[k] = SSX_NU;

               break;

            case SSX_NU:

               stat[k] = SSX_NL;

               break;

            default:

               xassert(stat != stat);

         }

      }

      else

      {  /* xB[p] leaves the basis, xN[q] enters the basis */

         xassert(1 <= p && p <= m);

         xassert(1 <= q && q <= n);

         kp = Q_col[p];   /* x[kp] = xB[p] */

         kq = Q_col[m+q]; /* x[kq] = xN[q] */

         /* check non-basic status of xB[p] which becomes xN[q] */

         switch (type[kp])

         {  case SSX_FR:

               xassert(p_stat == SSX_NF);

               break;

            case SSX_LO:

               xassert(p_stat == SSX_NL);

               break;

            case SSX_UP:

               xassert(p_stat == SSX_NU);

               break;

            case SSX_DB:

               xassert(p_stat == SSX_NL || p_stat == SSX_NU);

               break;

            case SSX_FX:

               xassert(p_stat == SSX_NS);

               break;

            default:

               xassert(type != type);

         }

         /* swap xB[p] and xN[q] */

         stat[kp] = (char)p_stat, stat[kq] = SSX_BS;

         Q_row[kp] = m+q, Q_row[kq] = p;

         Q_col[p] = kq, Q_col[m+q] = kp;

         /* update factorization of the basis matrix */

         if (bfx_update(ssx->binv, p))

         {  if (ssx_factorize(ssx))

               xassert(("Internal error: basis matrix is singular", 0));

         }

      }

      return;

}

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

// ssx_delete - delete simplex solver workspace.

//

// This routine deletes the simplex solver workspace freeing all the

// memory allocated to this object. */

void ssx_delete(SSX *ssx)

{     int m = ssx->m;

      int n = ssx->n;

      int nnz = ssx->A_ptr[n+1]-1;

      int i, j, k;

      xfree(ssx->type);

      for (k = 1; k <= m+n; k++) mpq_clear(ssx->lb[k]);

      xfree(ssx->lb);

      for (k = 1; k <= m+n; k++) mpq_clear(ssx->ub[k]);

      xfree(ssx->ub);

      for (k = 0; k <= m+n; k++) mpq_clear(ssx->coef[k]);

      xfree(ssx->coef);

      xfree(ssx->A_ptr);

      xfree(ssx->A_ind);

      for (k = 1; k <= nnz; k++) mpq_clear(ssx->A_val[k]);

      xfree(ssx->A_val);

      xfree(ssx->stat);

      xfree(ssx->Q_row);

      xfree(ssx->Q_col);

      bfx_delete_binv(ssx->binv);

      for (i = 0; i <= m; i++) mpq_clear(ssx->bbar[i]);

      xfree(ssx->bbar);

      for (i = 1; i <= m; i++) mpq_clear(ssx->pi[i]);

      xfree(ssx->pi);

      for (j = 1; j <= n; j++) mpq_clear(ssx->cbar[j]);

      xfree(ssx->cbar);

      for (i = 1; i <= m; i++) mpq_clear(ssx->rho[i]);

      xfree(ssx->rho);

      for (j = 1; j <= n; j++) mpq_clear(ssx->ap[j]);

      xfree(ssx->ap);

      for (i = 1; i <= m; i++) mpq_clear(ssx->aq[i]);

      xfree(ssx->aq);

      mpq_clear(ssx->delta);

      xfree(ssx);

      return;

}

/* eof */