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+/* glpssx01.c (simplex method, rational arithmetic) */
+
+/***********************************************************************
+* This code is part of GLPK (GNU Linear Programming Kit).
+*
+* Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
+* 2009, 2010, 2011, 2013 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 "env.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 */