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839 lines
27 KiB
839 lines
27 KiB
/* glpssx01.c (simplex method, rational arithmetic) */
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/***********************************************************************
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* This code is part of GLPK (GNU Linear Programming Kit).
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*
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* Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
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* 2009, 2010, 2011, 2013 Andrew Makhorin, Department for Applied
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* Informatics, Moscow Aviation Institute, Moscow, Russia. All rights
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* reserved. E-mail: <mao@gnu.org>.
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*
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* GLPK is free software: you can redistribute it and/or modify it
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* under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* GLPK is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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* License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
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***********************************************************************/
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#include "env.h"
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#include "glpssx.h"
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#define xfault xerror
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/*----------------------------------------------------------------------
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// ssx_create - create simplex solver workspace.
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//
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// This routine creates the workspace used by simplex solver routines,
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// and returns a pointer to it.
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//
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// Parameters m, n, and nnz specify, respectively, the number of rows,
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// columns, and non-zero constraint coefficients.
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//
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// This routine only allocates the memory for the workspace components,
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// so the workspace needs to be saturated by data. */
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SSX *ssx_create(int m, int n, int nnz)
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{ SSX *ssx;
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int i, j, k;
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if (m < 1)
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xfault("ssx_create: m = %d; invalid number of rows\n", m);
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if (n < 1)
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xfault("ssx_create: n = %d; invalid number of columns\n", n);
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if (nnz < 0)
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xfault("ssx_create: nnz = %d; invalid number of non-zero const"
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"raint coefficients\n", nnz);
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ssx = xmalloc(sizeof(SSX));
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ssx->m = m;
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ssx->n = n;
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ssx->type = xcalloc(1+m+n, sizeof(int));
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ssx->lb = xcalloc(1+m+n, sizeof(mpq_t));
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for (k = 1; k <= m+n; k++) mpq_init(ssx->lb[k]);
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ssx->ub = xcalloc(1+m+n, sizeof(mpq_t));
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for (k = 1; k <= m+n; k++) mpq_init(ssx->ub[k]);
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ssx->coef = xcalloc(1+m+n, sizeof(mpq_t));
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for (k = 0; k <= m+n; k++) mpq_init(ssx->coef[k]);
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ssx->A_ptr = xcalloc(1+n+1, sizeof(int));
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ssx->A_ptr[n+1] = nnz+1;
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ssx->A_ind = xcalloc(1+nnz, sizeof(int));
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ssx->A_val = xcalloc(1+nnz, sizeof(mpq_t));
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for (k = 1; k <= nnz; k++) mpq_init(ssx->A_val[k]);
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ssx->stat = xcalloc(1+m+n, sizeof(int));
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ssx->Q_row = xcalloc(1+m+n, sizeof(int));
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ssx->Q_col = xcalloc(1+m+n, sizeof(int));
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ssx->binv = bfx_create_binv();
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ssx->bbar = xcalloc(1+m, sizeof(mpq_t));
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for (i = 0; i <= m; i++) mpq_init(ssx->bbar[i]);
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ssx->pi = xcalloc(1+m, sizeof(mpq_t));
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for (i = 1; i <= m; i++) mpq_init(ssx->pi[i]);
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ssx->cbar = xcalloc(1+n, sizeof(mpq_t));
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for (j = 1; j <= n; j++) mpq_init(ssx->cbar[j]);
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ssx->rho = xcalloc(1+m, sizeof(mpq_t));
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for (i = 1; i <= m; i++) mpq_init(ssx->rho[i]);
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ssx->ap = xcalloc(1+n, sizeof(mpq_t));
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for (j = 1; j <= n; j++) mpq_init(ssx->ap[j]);
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ssx->aq = xcalloc(1+m, sizeof(mpq_t));
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for (i = 1; i <= m; i++) mpq_init(ssx->aq[i]);
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mpq_init(ssx->delta);
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return ssx;
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}
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/*----------------------------------------------------------------------
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// ssx_factorize - factorize the current basis matrix.
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//
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// This routine computes factorization of the current basis matrix B
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// and returns the singularity flag. If the matrix B is non-singular,
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// the flag is zero, otherwise non-zero. */
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static int basis_col(void *info, int j, int ind[], mpq_t val[])
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{ /* this auxiliary routine provides row indices and numeric values
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of non-zero elements in j-th column of the matrix B */
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SSX *ssx = info;
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int m = ssx->m;
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int n = ssx->n;
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int *A_ptr = ssx->A_ptr;
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int *A_ind = ssx->A_ind;
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mpq_t *A_val = ssx->A_val;
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int *Q_col = ssx->Q_col;
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int k, len, ptr;
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xassert(1 <= j && j <= m);
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k = Q_col[j]; /* x[k] = xB[j] */
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xassert(1 <= k && k <= m+n);
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/* j-th column of the matrix B is k-th column of the augmented
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constraint matrix (I | -A) */
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if (k <= m)
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{ /* it is a column of the unity matrix I */
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len = 1, ind[1] = k, mpq_set_si(val[1], 1, 1);
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}
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else
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{ /* it is a column of the original constraint matrix -A */
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len = 0;
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for (ptr = A_ptr[k-m]; ptr < A_ptr[k-m+1]; ptr++)
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{ len++;
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ind[len] = A_ind[ptr];
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mpq_neg(val[len], A_val[ptr]);
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}
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}
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return len;
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}
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int ssx_factorize(SSX *ssx)
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{ int ret;
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ret = bfx_factorize(ssx->binv, ssx->m, basis_col, ssx);
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return ret;
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}
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/*----------------------------------------------------------------------
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// ssx_get_xNj - determine value of non-basic variable.
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//
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// This routine determines the value of non-basic variable xN[j] in the
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// current basic solution defined as follows:
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//
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// 0, if xN[j] is free variable
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// lN[j], if xN[j] is on its lower bound
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// uN[j], if xN[j] is on its upper bound
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// lN[j] = uN[j], if xN[j] is fixed variable
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//
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// where lN[j] and uN[j] are lower and upper bounds of xN[j]. */
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void ssx_get_xNj(SSX *ssx, int j, mpq_t x)
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{ int m = ssx->m;
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int n = ssx->n;
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mpq_t *lb = ssx->lb;
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mpq_t *ub = ssx->ub;
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int *stat = ssx->stat;
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int *Q_col = ssx->Q_col;
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int k;
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xassert(1 <= j && j <= n);
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k = Q_col[m+j]; /* x[k] = xN[j] */
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xassert(1 <= k && k <= m+n);
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switch (stat[k])
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{ case SSX_NL:
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/* xN[j] is on its lower bound */
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mpq_set(x, lb[k]); break;
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case SSX_NU:
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/* xN[j] is on its upper bound */
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mpq_set(x, ub[k]); break;
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case SSX_NF:
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/* xN[j] is free variable */
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mpq_set_si(x, 0, 1); break;
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case SSX_NS:
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/* xN[j] is fixed variable */
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mpq_set(x, lb[k]); break;
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default:
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xassert(stat != stat);
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}
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return;
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}
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/*----------------------------------------------------------------------
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// ssx_eval_bbar - compute values of basic variables.
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//
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// This routine computes values of basic variables xB in the current
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// basic solution as follows:
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//
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// beta = - inv(B) * N * xN,
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//
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// where B is the basis matrix, N is the matrix of non-basic columns,
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// xN is a vector of current values of non-basic variables. */
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void ssx_eval_bbar(SSX *ssx)
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{ int m = ssx->m;
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int n = ssx->n;
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mpq_t *coef = ssx->coef;
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int *A_ptr = ssx->A_ptr;
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int *A_ind = ssx->A_ind;
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mpq_t *A_val = ssx->A_val;
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int *Q_col = ssx->Q_col;
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mpq_t *bbar = ssx->bbar;
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int i, j, k, ptr;
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mpq_t x, temp;
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mpq_init(x);
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mpq_init(temp);
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/* bbar := 0 */
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for (i = 1; i <= m; i++)
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mpq_set_si(bbar[i], 0, 1);
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/* bbar := - N * xN = - N[1] * xN[1] - ... - N[n] * xN[n] */
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for (j = 1; j <= n; j++)
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{ ssx_get_xNj(ssx, j, x);
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if (mpq_sgn(x) == 0) continue;
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k = Q_col[m+j]; /* x[k] = xN[j] */
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if (k <= m)
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{ /* N[j] is a column of the unity matrix I */
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mpq_sub(bbar[k], bbar[k], x);
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}
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else
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{ /* N[j] is a column of the original constraint matrix -A */
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for (ptr = A_ptr[k-m]; ptr < A_ptr[k-m+1]; ptr++)
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{ mpq_mul(temp, A_val[ptr], x);
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mpq_add(bbar[A_ind[ptr]], bbar[A_ind[ptr]], temp);
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}
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}
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}
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/* bbar := inv(B) * bbar */
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bfx_ftran(ssx->binv, bbar, 0);
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#if 1
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/* compute value of the objective function */
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/* bbar[0] := c[0] */
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mpq_set(bbar[0], coef[0]);
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/* bbar[0] := bbar[0] + sum{i in B} cB[i] * xB[i] */
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for (i = 1; i <= m; i++)
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{ k = Q_col[i]; /* x[k] = xB[i] */
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if (mpq_sgn(coef[k]) == 0) continue;
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mpq_mul(temp, coef[k], bbar[i]);
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mpq_add(bbar[0], bbar[0], temp);
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}
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/* bbar[0] := bbar[0] + sum{j in N} cN[j] * xN[j] */
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for (j = 1; j <= n; j++)
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{ k = Q_col[m+j]; /* x[k] = xN[j] */
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if (mpq_sgn(coef[k]) == 0) continue;
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ssx_get_xNj(ssx, j, x);
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mpq_mul(temp, coef[k], x);
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mpq_add(bbar[0], bbar[0], temp);
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}
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#endif
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mpq_clear(x);
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mpq_clear(temp);
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return;
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}
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/*----------------------------------------------------------------------
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// ssx_eval_pi - compute values of simplex multipliers.
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//
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// This routine computes values of simplex multipliers (shadow prices)
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// pi in the current basic solution as follows:
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//
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// pi = inv(B') * cB,
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//
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// where B' is a matrix transposed to the basis matrix B, cB is a vector
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// of objective coefficients at basic variables xB. */
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void ssx_eval_pi(SSX *ssx)
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{ int m = ssx->m;
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mpq_t *coef = ssx->coef;
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int *Q_col = ssx->Q_col;
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mpq_t *pi = ssx->pi;
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int i;
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/* pi := cB */
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for (i = 1; i <= m; i++) mpq_set(pi[i], coef[Q_col[i]]);
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/* pi := inv(B') * cB */
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bfx_btran(ssx->binv, pi);
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return;
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}
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/*----------------------------------------------------------------------
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// ssx_eval_dj - compute reduced cost of non-basic variable.
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//
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// This routine computes reduced cost d[j] of non-basic variable xN[j]
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// in the current basic solution as follows:
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//
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// d[j] = cN[j] - N[j] * pi,
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//
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// where cN[j] is an objective coefficient at xN[j], N[j] is a column
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// of the augmented constraint matrix (I | -A) corresponding to xN[j],
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// pi is the vector of simplex multipliers (shadow prices). */
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void ssx_eval_dj(SSX *ssx, int j, mpq_t dj)
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{ int m = ssx->m;
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int n = ssx->n;
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mpq_t *coef = ssx->coef;
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int *A_ptr = ssx->A_ptr;
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int *A_ind = ssx->A_ind;
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mpq_t *A_val = ssx->A_val;
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int *Q_col = ssx->Q_col;
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mpq_t *pi = ssx->pi;
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int k, ptr, end;
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mpq_t temp;
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mpq_init(temp);
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xassert(1 <= j && j <= n);
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k = Q_col[m+j]; /* x[k] = xN[j] */
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xassert(1 <= k && k <= m+n);
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/* j-th column of the matrix N is k-th column of the augmented
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constraint matrix (I | -A) */
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if (k <= m)
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{ /* it is a column of the unity matrix I */
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mpq_sub(dj, coef[k], pi[k]);
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}
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else
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{ /* it is a column of the original constraint matrix -A */
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mpq_set(dj, coef[k]);
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for (ptr = A_ptr[k-m], end = A_ptr[k-m+1]; ptr < end; ptr++)
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{ mpq_mul(temp, A_val[ptr], pi[A_ind[ptr]]);
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mpq_add(dj, dj, temp);
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}
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}
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mpq_clear(temp);
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return;
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}
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/*----------------------------------------------------------------------
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// ssx_eval_cbar - compute reduced costs of all non-basic variables.
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//
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// This routine computes the vector of reduced costs pi in the current
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// basic solution for all non-basic variables, including fixed ones. */
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void ssx_eval_cbar(SSX *ssx)
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{ int n = ssx->n;
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mpq_t *cbar = ssx->cbar;
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int j;
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for (j = 1; j <= n; j++)
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ssx_eval_dj(ssx, j, cbar[j]);
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return;
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}
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/*----------------------------------------------------------------------
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// ssx_eval_rho - compute p-th row of the inverse.
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//
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// This routine computes p-th row of the matrix inv(B), where B is the
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// current basis matrix.
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//
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// p-th row of the inverse is computed using the following formula:
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//
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// rho = inv(B') * e[p],
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//
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// where B' is a matrix transposed to B, e[p] is a unity vector, which
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// contains one in p-th position. */
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void ssx_eval_rho(SSX *ssx)
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{ int m = ssx->m;
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int p = ssx->p;
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mpq_t *rho = ssx->rho;
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int i;
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xassert(1 <= p && p <= m);
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/* rho := 0 */
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for (i = 1; i <= m; i++) mpq_set_si(rho[i], 0, 1);
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/* rho := e[p] */
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mpq_set_si(rho[p], 1, 1);
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/* rho := inv(B') * rho */
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bfx_btran(ssx->binv, rho);
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return;
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}
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/*----------------------------------------------------------------------
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// ssx_eval_row - compute pivot row of the simplex table.
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//
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// This routine computes p-th (pivot) row of the current simplex table
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// A~ = - inv(B) * N using the following formula:
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//
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// A~[p] = - N' * inv(B') * e[p] = - N' * rho[p],
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//
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// where N' is a matrix transposed to the matrix N, rho[p] is p-th row
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// of the inverse inv(B). */
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void ssx_eval_row(SSX *ssx)
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{ int m = ssx->m;
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int n = ssx->n;
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int *A_ptr = ssx->A_ptr;
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int *A_ind = ssx->A_ind;
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mpq_t *A_val = ssx->A_val;
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int *Q_col = ssx->Q_col;
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mpq_t *rho = ssx->rho;
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mpq_t *ap = ssx->ap;
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int j, k, ptr;
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mpq_t temp;
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mpq_init(temp);
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for (j = 1; j <= n; j++)
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{ /* ap[j] := - N'[j] * rho (inner product) */
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k = Q_col[m+j]; /* x[k] = xN[j] */
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if (k <= m)
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mpq_neg(ap[j], rho[k]);
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else
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{ mpq_set_si(ap[j], 0, 1);
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for (ptr = A_ptr[k-m]; ptr < A_ptr[k-m+1]; ptr++)
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{ mpq_mul(temp, A_val[ptr], rho[A_ind[ptr]]);
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mpq_add(ap[j], ap[j], temp);
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}
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}
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}
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mpq_clear(temp);
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return;
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}
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/*----------------------------------------------------------------------
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// ssx_eval_col - compute pivot column of the simplex table.
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//
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// This routine computes q-th (pivot) column of the current simplex
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// table A~ = - inv(B) * N using the following formula:
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//
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// A~[q] = - inv(B) * N[q],
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//
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// where N[q] is q-th column of the matrix N corresponding to chosen
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// non-basic variable xN[q]. */
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void ssx_eval_col(SSX *ssx)
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{ int m = ssx->m;
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int n = ssx->n;
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int *A_ptr = ssx->A_ptr;
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int *A_ind = ssx->A_ind;
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mpq_t *A_val = ssx->A_val;
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int *Q_col = ssx->Q_col;
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int q = ssx->q;
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mpq_t *aq = ssx->aq;
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int i, k, ptr;
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xassert(1 <= q && q <= n);
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/* aq := 0 */
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for (i = 1; i <= m; i++) mpq_set_si(aq[i], 0, 1);
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/* aq := N[q] */
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k = Q_col[m+q]; /* x[k] = xN[q] */
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if (k <= m)
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{ /* N[q] is a column of the unity matrix I */
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mpq_set_si(aq[k], 1, 1);
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}
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else
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{ /* N[q] is a column of the original constraint matrix -A */
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for (ptr = A_ptr[k-m]; ptr < A_ptr[k-m+1]; ptr++)
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mpq_neg(aq[A_ind[ptr]], A_val[ptr]);
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}
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/* 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 */
|