/* 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 */