[9] | 1 | /* glpapi12.c (basis factorization and simplex tableau routines) */ |
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| 2 | |
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| 3 | /*********************************************************************** |
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| 4 | * This code is part of GLPK (GNU Linear Programming Kit). |
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| 5 | * |
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| 6 | * Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, |
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| 7 | * 2009, 2010, 2011 Andrew Makhorin, Department for Applied Informatics, |
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| 8 | * Moscow Aviation Institute, Moscow, Russia. All rights reserved. |
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| 9 | * E-mail: <mao@gnu.org>. |
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| 10 | * |
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| 11 | * GLPK is free software: you can redistribute it and/or modify it |
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| 12 | * under the terms of the GNU General Public License as published by |
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| 13 | * the Free Software Foundation, either version 3 of the License, or |
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| 14 | * (at your option) any later version. |
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| 15 | * |
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| 16 | * GLPK is distributed in the hope that it will be useful, but WITHOUT |
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| 17 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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| 18 | * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public |
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| 19 | * License for more details. |
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| 20 | * |
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| 21 | * You should have received a copy of the GNU General Public License |
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| 22 | * along with GLPK. If not, see <http://www.gnu.org/licenses/>. |
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| 23 | ***********************************************************************/ |
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| 24 | |
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| 25 | #include "glpapi.h" |
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| 26 | |
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| 27 | /*********************************************************************** |
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| 28 | * NAME |
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| 29 | * |
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| 30 | * glp_bf_exists - check if the basis factorization exists |
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| 31 | * |
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| 32 | * SYNOPSIS |
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| 33 | * |
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| 34 | * int glp_bf_exists(glp_prob *lp); |
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| 35 | * |
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| 36 | * RETURNS |
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| 37 | * |
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| 38 | * If the basis factorization for the current basis associated with |
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| 39 | * the specified problem object exists and therefore is available for |
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| 40 | * computations, the routine glp_bf_exists returns non-zero. Otherwise |
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| 41 | * the routine returns zero. */ |
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| 42 | |
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| 43 | int glp_bf_exists(glp_prob *lp) |
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| 44 | { int ret; |
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| 45 | ret = (lp->m == 0 || lp->valid); |
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| 46 | return ret; |
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| 47 | } |
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| 48 | |
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| 49 | /*********************************************************************** |
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| 50 | * NAME |
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| 51 | * |
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| 52 | * glp_factorize - compute the basis factorization |
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| 53 | * |
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| 54 | * SYNOPSIS |
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| 55 | * |
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| 56 | * int glp_factorize(glp_prob *lp); |
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| 57 | * |
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| 58 | * DESCRIPTION |
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| 59 | * |
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| 60 | * The routine glp_factorize computes the basis factorization for the |
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| 61 | * current basis associated with the specified problem object. |
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| 62 | * |
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| 63 | * RETURNS |
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| 64 | * |
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| 65 | * 0 The basis factorization has been successfully computed. |
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| 66 | * |
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| 67 | * GLP_EBADB |
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| 68 | * The basis matrix is invalid, i.e. the number of basic (auxiliary |
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| 69 | * and structural) variables differs from the number of rows in the |
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| 70 | * problem object. |
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| 71 | * |
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| 72 | * GLP_ESING |
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| 73 | * The basis matrix is singular within the working precision. |
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| 74 | * |
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| 75 | * GLP_ECOND |
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| 76 | * The basis matrix is ill-conditioned. */ |
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| 77 | |
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| 78 | static int b_col(void *info, int j, int ind[], double val[]) |
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| 79 | { glp_prob *lp = info; |
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| 80 | int m = lp->m; |
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| 81 | GLPAIJ *aij; |
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| 82 | int k, len; |
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| 83 | xassert(1 <= j && j <= m); |
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| 84 | /* determine the ordinal number of basic auxiliary or structural |
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| 85 | variable x[k] corresponding to basic variable xB[j] */ |
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| 86 | k = lp->head[j]; |
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| 87 | /* build j-th column of the basic matrix, which is k-th column of |
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| 88 | the scaled augmented matrix (I | -R*A*S) */ |
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| 89 | if (k <= m) |
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| 90 | { /* x[k] is auxiliary variable */ |
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| 91 | len = 1; |
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| 92 | ind[1] = k; |
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| 93 | val[1] = 1.0; |
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| 94 | } |
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| 95 | else |
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| 96 | { /* x[k] is structural variable */ |
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| 97 | len = 0; |
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| 98 | for (aij = lp->col[k-m]->ptr; aij != NULL; aij = aij->c_next) |
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| 99 | { len++; |
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| 100 | ind[len] = aij->row->i; |
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| 101 | val[len] = - aij->row->rii * aij->val * aij->col->sjj; |
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| 102 | } |
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| 103 | } |
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| 104 | return len; |
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| 105 | } |
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| 106 | |
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| 107 | static void copy_bfcp(glp_prob *lp); |
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| 108 | |
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| 109 | int glp_factorize(glp_prob *lp) |
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| 110 | { int m = lp->m; |
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| 111 | int n = lp->n; |
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| 112 | GLPROW **row = lp->row; |
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| 113 | GLPCOL **col = lp->col; |
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| 114 | int *head = lp->head; |
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| 115 | int j, k, stat, ret; |
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| 116 | /* invalidate the basis factorization */ |
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| 117 | lp->valid = 0; |
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| 118 | /* build the basis header */ |
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| 119 | j = 0; |
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| 120 | for (k = 1; k <= m+n; k++) |
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| 121 | { if (k <= m) |
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| 122 | { stat = row[k]->stat; |
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| 123 | row[k]->bind = 0; |
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| 124 | } |
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| 125 | else |
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| 126 | { stat = col[k-m]->stat; |
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| 127 | col[k-m]->bind = 0; |
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| 128 | } |
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| 129 | if (stat == GLP_BS) |
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| 130 | { j++; |
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| 131 | if (j > m) |
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| 132 | { /* too many basic variables */ |
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| 133 | ret = GLP_EBADB; |
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| 134 | goto fini; |
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| 135 | } |
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| 136 | head[j] = k; |
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| 137 | if (k <= m) |
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| 138 | row[k]->bind = j; |
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| 139 | else |
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| 140 | col[k-m]->bind = j; |
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| 141 | } |
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| 142 | } |
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| 143 | if (j < m) |
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| 144 | { /* too few basic variables */ |
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| 145 | ret = GLP_EBADB; |
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| 146 | goto fini; |
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| 147 | } |
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| 148 | /* try to factorize the basis matrix */ |
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| 149 | if (m > 0) |
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| 150 | { if (lp->bfd == NULL) |
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| 151 | { lp->bfd = bfd_create_it(); |
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| 152 | copy_bfcp(lp); |
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| 153 | } |
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| 154 | switch (bfd_factorize(lp->bfd, m, lp->head, b_col, lp)) |
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| 155 | { case 0: |
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| 156 | /* ok */ |
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| 157 | break; |
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| 158 | case BFD_ESING: |
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| 159 | /* singular matrix */ |
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| 160 | ret = GLP_ESING; |
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| 161 | goto fini; |
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| 162 | case BFD_ECOND: |
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| 163 | /* ill-conditioned matrix */ |
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| 164 | ret = GLP_ECOND; |
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| 165 | goto fini; |
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| 166 | default: |
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| 167 | xassert(lp != lp); |
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| 168 | } |
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| 169 | lp->valid = 1; |
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| 170 | } |
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| 171 | /* factorization successful */ |
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| 172 | ret = 0; |
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| 173 | fini: /* bring the return code to the calling program */ |
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| 174 | return ret; |
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| 175 | } |
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| 176 | |
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| 177 | /*********************************************************************** |
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| 178 | * NAME |
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| 179 | * |
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| 180 | * glp_bf_updated - check if the basis factorization has been updated |
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| 181 | * |
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| 182 | * SYNOPSIS |
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| 183 | * |
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| 184 | * int glp_bf_updated(glp_prob *lp); |
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| 185 | * |
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| 186 | * RETURNS |
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| 187 | * |
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| 188 | * If the basis factorization has been just computed from scratch, the |
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| 189 | * routine glp_bf_updated returns zero. Otherwise, if the factorization |
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| 190 | * has been updated one or more times, the routine returns non-zero. */ |
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| 191 | |
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| 192 | int glp_bf_updated(glp_prob *lp) |
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| 193 | { int cnt; |
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| 194 | if (!(lp->m == 0 || lp->valid)) |
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| 195 | xerror("glp_bf_update: basis factorization does not exist\n"); |
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| 196 | #if 0 /* 15/XI-2009 */ |
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| 197 | cnt = (lp->m == 0 ? 0 : lp->bfd->upd_cnt); |
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| 198 | #else |
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| 199 | cnt = (lp->m == 0 ? 0 : bfd_get_count(lp->bfd)); |
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| 200 | #endif |
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| 201 | return cnt; |
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| 202 | } |
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| 203 | |
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| 204 | /*********************************************************************** |
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| 205 | * NAME |
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| 206 | * |
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| 207 | * glp_get_bfcp - retrieve basis factorization control parameters |
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| 208 | * |
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| 209 | * SYNOPSIS |
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| 210 | * |
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| 211 | * void glp_get_bfcp(glp_prob *lp, glp_bfcp *parm); |
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| 212 | * |
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| 213 | * DESCRIPTION |
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| 214 | * |
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| 215 | * The routine glp_get_bfcp retrieves control parameters, which are |
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| 216 | * used on computing and updating the basis factorization associated |
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| 217 | * with the specified problem object. |
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| 218 | * |
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| 219 | * Current values of control parameters are stored by the routine in |
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| 220 | * a glp_bfcp structure, which the parameter parm points to. */ |
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| 221 | |
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| 222 | void glp_get_bfcp(glp_prob *lp, glp_bfcp *parm) |
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| 223 | { glp_bfcp *bfcp = lp->bfcp; |
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| 224 | if (bfcp == NULL) |
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| 225 | { parm->type = GLP_BF_FT; |
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| 226 | parm->lu_size = 0; |
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| 227 | parm->piv_tol = 0.10; |
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| 228 | parm->piv_lim = 4; |
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| 229 | parm->suhl = GLP_ON; |
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| 230 | parm->eps_tol = 1e-15; |
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| 231 | parm->max_gro = 1e+10; |
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| 232 | parm->nfs_max = 100; |
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| 233 | parm->upd_tol = 1e-6; |
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| 234 | parm->nrs_max = 100; |
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| 235 | parm->rs_size = 0; |
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| 236 | } |
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| 237 | else |
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| 238 | memcpy(parm, bfcp, sizeof(glp_bfcp)); |
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| 239 | return; |
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| 240 | } |
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| 241 | |
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| 242 | /*********************************************************************** |
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| 243 | * NAME |
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| 244 | * |
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| 245 | * glp_set_bfcp - change basis factorization control parameters |
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| 246 | * |
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| 247 | * SYNOPSIS |
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| 248 | * |
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| 249 | * void glp_set_bfcp(glp_prob *lp, const glp_bfcp *parm); |
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| 250 | * |
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| 251 | * DESCRIPTION |
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| 252 | * |
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| 253 | * The routine glp_set_bfcp changes control parameters, which are used |
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| 254 | * by internal GLPK routines in computing and updating the basis |
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| 255 | * factorization associated with the specified problem object. |
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| 256 | * |
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| 257 | * New values of the control parameters should be passed in a structure |
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| 258 | * glp_bfcp, which the parameter parm points to. |
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| 259 | * |
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| 260 | * The parameter parm can be specified as NULL, in which case all |
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| 261 | * control parameters are reset to their default values. */ |
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| 262 | |
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| 263 | #if 0 /* 15/XI-2009 */ |
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| 264 | static void copy_bfcp(glp_prob *lp) |
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| 265 | { glp_bfcp _parm, *parm = &_parm; |
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| 266 | BFD *bfd = lp->bfd; |
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| 267 | glp_get_bfcp(lp, parm); |
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| 268 | xassert(bfd != NULL); |
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| 269 | bfd->type = parm->type; |
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| 270 | bfd->lu_size = parm->lu_size; |
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| 271 | bfd->piv_tol = parm->piv_tol; |
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| 272 | bfd->piv_lim = parm->piv_lim; |
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| 273 | bfd->suhl = parm->suhl; |
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| 274 | bfd->eps_tol = parm->eps_tol; |
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| 275 | bfd->max_gro = parm->max_gro; |
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| 276 | bfd->nfs_max = parm->nfs_max; |
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| 277 | bfd->upd_tol = parm->upd_tol; |
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| 278 | bfd->nrs_max = parm->nrs_max; |
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| 279 | bfd->rs_size = parm->rs_size; |
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| 280 | return; |
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| 281 | } |
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| 282 | #else |
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| 283 | static void copy_bfcp(glp_prob *lp) |
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| 284 | { glp_bfcp _parm, *parm = &_parm; |
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| 285 | glp_get_bfcp(lp, parm); |
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| 286 | bfd_set_parm(lp->bfd, parm); |
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| 287 | return; |
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| 288 | } |
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| 289 | #endif |
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| 290 | |
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| 291 | void glp_set_bfcp(glp_prob *lp, const glp_bfcp *parm) |
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| 292 | { glp_bfcp *bfcp = lp->bfcp; |
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| 293 | if (parm == NULL) |
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| 294 | { /* reset to default values */ |
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| 295 | if (bfcp != NULL) |
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| 296 | xfree(bfcp), lp->bfcp = NULL; |
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| 297 | } |
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| 298 | else |
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| 299 | { /* set to specified values */ |
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| 300 | if (bfcp == NULL) |
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| 301 | bfcp = lp->bfcp = xmalloc(sizeof(glp_bfcp)); |
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| 302 | memcpy(bfcp, parm, sizeof(glp_bfcp)); |
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| 303 | if (!(bfcp->type == GLP_BF_FT || bfcp->type == GLP_BF_BG || |
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| 304 | bfcp->type == GLP_BF_GR)) |
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| 305 | xerror("glp_set_bfcp: type = %d; invalid parameter\n", |
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| 306 | bfcp->type); |
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| 307 | if (bfcp->lu_size < 0) |
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| 308 | xerror("glp_set_bfcp: lu_size = %d; invalid parameter\n", |
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| 309 | bfcp->lu_size); |
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| 310 | if (!(0.0 < bfcp->piv_tol && bfcp->piv_tol < 1.0)) |
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| 311 | xerror("glp_set_bfcp: piv_tol = %g; invalid parameter\n", |
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| 312 | bfcp->piv_tol); |
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| 313 | if (bfcp->piv_lim < 1) |
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| 314 | xerror("glp_set_bfcp: piv_lim = %d; invalid parameter\n", |
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| 315 | bfcp->piv_lim); |
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| 316 | if (!(bfcp->suhl == GLP_ON || bfcp->suhl == GLP_OFF)) |
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| 317 | xerror("glp_set_bfcp: suhl = %d; invalid parameter\n", |
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| 318 | bfcp->suhl); |
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| 319 | if (!(0.0 <= bfcp->eps_tol && bfcp->eps_tol <= 1e-6)) |
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| 320 | xerror("glp_set_bfcp: eps_tol = %g; invalid parameter\n", |
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| 321 | bfcp->eps_tol); |
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| 322 | if (bfcp->max_gro < 1.0) |
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| 323 | xerror("glp_set_bfcp: max_gro = %g; invalid parameter\n", |
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| 324 | bfcp->max_gro); |
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| 325 | if (!(1 <= bfcp->nfs_max && bfcp->nfs_max <= 32767)) |
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| 326 | xerror("glp_set_bfcp: nfs_max = %d; invalid parameter\n", |
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| 327 | bfcp->nfs_max); |
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| 328 | if (!(0.0 < bfcp->upd_tol && bfcp->upd_tol < 1.0)) |
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| 329 | xerror("glp_set_bfcp: upd_tol = %g; invalid parameter\n", |
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| 330 | bfcp->upd_tol); |
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| 331 | if (!(1 <= bfcp->nrs_max && bfcp->nrs_max <= 32767)) |
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| 332 | xerror("glp_set_bfcp: nrs_max = %d; invalid parameter\n", |
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| 333 | bfcp->nrs_max); |
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| 334 | if (bfcp->rs_size < 0) |
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| 335 | xerror("glp_set_bfcp: rs_size = %d; invalid parameter\n", |
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| 336 | bfcp->nrs_max); |
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| 337 | if (bfcp->rs_size == 0) |
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| 338 | bfcp->rs_size = 20 * bfcp->nrs_max; |
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| 339 | } |
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| 340 | if (lp->bfd != NULL) copy_bfcp(lp); |
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| 341 | return; |
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| 342 | } |
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| 343 | |
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| 344 | /*********************************************************************** |
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| 345 | * NAME |
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| 346 | * |
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| 347 | * glp_get_bhead - retrieve the basis header information |
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| 348 | * |
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| 349 | * SYNOPSIS |
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| 350 | * |
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| 351 | * int glp_get_bhead(glp_prob *lp, int k); |
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| 352 | * |
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| 353 | * DESCRIPTION |
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| 354 | * |
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| 355 | * The routine glp_get_bhead returns the basis header information for |
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| 356 | * the current basis associated with the specified problem object. |
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| 357 | * |
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| 358 | * RETURNS |
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| 359 | * |
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| 360 | * If xB[k], 1 <= k <= m, is i-th auxiliary variable (1 <= i <= m), the |
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| 361 | * routine returns i. Otherwise, if xB[k] is j-th structural variable |
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| 362 | * (1 <= j <= n), the routine returns m+j. Here m is the number of rows |
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| 363 | * and n is the number of columns in the problem object. */ |
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| 364 | |
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| 365 | int glp_get_bhead(glp_prob *lp, int k) |
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| 366 | { if (!(lp->m == 0 || lp->valid)) |
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| 367 | xerror("glp_get_bhead: basis factorization does not exist\n"); |
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| 368 | if (!(1 <= k && k <= lp->m)) |
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| 369 | xerror("glp_get_bhead: k = %d; index out of range\n", k); |
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| 370 | return lp->head[k]; |
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| 371 | } |
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| 372 | |
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| 373 | /*********************************************************************** |
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| 374 | * NAME |
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| 375 | * |
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| 376 | * glp_get_row_bind - retrieve row index in the basis header |
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| 377 | * |
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| 378 | * SYNOPSIS |
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| 379 | * |
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| 380 | * int glp_get_row_bind(glp_prob *lp, int i); |
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| 381 | * |
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| 382 | * RETURNS |
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| 383 | * |
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| 384 | * The routine glp_get_row_bind returns the index k of basic variable |
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| 385 | * xB[k], 1 <= k <= m, which is i-th auxiliary variable, 1 <= i <= m, |
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| 386 | * in the current basis associated with the specified problem object, |
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| 387 | * where m is the number of rows. However, if i-th auxiliary variable |
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| 388 | * is non-basic, the routine returns zero. */ |
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| 389 | |
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| 390 | int glp_get_row_bind(glp_prob *lp, int i) |
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| 391 | { if (!(lp->m == 0 || lp->valid)) |
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| 392 | xerror("glp_get_row_bind: basis factorization does not exist\n" |
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| 393 | ); |
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| 394 | if (!(1 <= i && i <= lp->m)) |
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| 395 | xerror("glp_get_row_bind: i = %d; row number out of range\n", |
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| 396 | i); |
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| 397 | return lp->row[i]->bind; |
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| 398 | } |
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| 399 | |
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| 400 | /*********************************************************************** |
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| 401 | * NAME |
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| 402 | * |
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| 403 | * glp_get_col_bind - retrieve column index in the basis header |
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| 404 | * |
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| 405 | * SYNOPSIS |
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| 406 | * |
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| 407 | * int glp_get_col_bind(glp_prob *lp, int j); |
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| 408 | * |
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| 409 | * RETURNS |
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| 410 | * |
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| 411 | * The routine glp_get_col_bind returns the index k of basic variable |
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| 412 | * xB[k], 1 <= k <= m, which is j-th structural variable, 1 <= j <= n, |
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| 413 | * in the current basis associated with the specified problem object, |
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| 414 | * where m is the number of rows, n is the number of columns. However, |
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| 415 | * if j-th structural variable is non-basic, the routine returns zero.*/ |
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| 416 | |
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| 417 | int glp_get_col_bind(glp_prob *lp, int j) |
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| 418 | { if (!(lp->m == 0 || lp->valid)) |
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| 419 | xerror("glp_get_col_bind: basis factorization does not exist\n" |
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| 420 | ); |
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| 421 | if (!(1 <= j && j <= lp->n)) |
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| 422 | xerror("glp_get_col_bind: j = %d; column number out of range\n" |
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| 423 | , j); |
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| 424 | return lp->col[j]->bind; |
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| 425 | } |
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| 426 | |
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| 427 | /*********************************************************************** |
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| 428 | * NAME |
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| 429 | * |
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| 430 | * glp_ftran - perform forward transformation (solve system B*x = b) |
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| 431 | * |
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| 432 | * SYNOPSIS |
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| 433 | * |
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| 434 | * void glp_ftran(glp_prob *lp, double x[]); |
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| 435 | * |
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| 436 | * DESCRIPTION |
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| 437 | * |
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| 438 | * The routine glp_ftran performs forward transformation, i.e. solves |
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| 439 | * the system B*x = b, where B is the basis matrix corresponding to the |
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| 440 | * current basis for the specified problem object, x is the vector of |
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| 441 | * unknowns to be computed, b is the vector of right-hand sides. |
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| 442 | * |
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| 443 | * On entry elements of the vector b should be stored in dense format |
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| 444 | * in locations x[1], ..., x[m], where m is the number of rows. On exit |
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| 445 | * the routine stores elements of the vector x in the same locations. |
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| 446 | * |
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| 447 | * SCALING/UNSCALING |
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| 448 | * |
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| 449 | * Let A~ = (I | -A) is the augmented constraint matrix of the original |
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| 450 | * (unscaled) problem. In the scaled LP problem instead the matrix A the |
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| 451 | * scaled matrix A" = R*A*S is actually used, so |
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| 452 | * |
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| 453 | * A~" = (I | A") = (I | R*A*S) = (R*I*inv(R) | R*A*S) = |
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| 454 | * (1) |
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| 455 | * = R*(I | A)*S~ = R*A~*S~, |
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| 456 | * |
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| 457 | * is the scaled augmented constraint matrix, where R and S are diagonal |
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| 458 | * scaling matrices used to scale rows and columns of the matrix A, and |
---|
| 459 | * |
---|
| 460 | * S~ = diag(inv(R) | S) (2) |
---|
| 461 | * |
---|
| 462 | * is an augmented diagonal scaling matrix. |
---|
| 463 | * |
---|
| 464 | * By definition: |
---|
| 465 | * |
---|
| 466 | * A~ = (B | N), (3) |
---|
| 467 | * |
---|
| 468 | * where B is the basic matrix, which consists of basic columns of the |
---|
| 469 | * augmented constraint matrix A~, and N is a matrix, which consists of |
---|
| 470 | * non-basic columns of A~. From (1) it follows that: |
---|
| 471 | * |
---|
| 472 | * A~" = (B" | N") = (R*B*SB | R*N*SN), (4) |
---|
| 473 | * |
---|
| 474 | * where SB and SN are parts of the augmented scaling matrix S~, which |
---|
| 475 | * correspond to basic and non-basic variables, respectively. Therefore |
---|
| 476 | * |
---|
| 477 | * B" = R*B*SB, (5) |
---|
| 478 | * |
---|
| 479 | * which is the scaled basis matrix. */ |
---|
| 480 | |
---|
| 481 | void glp_ftran(glp_prob *lp, double x[]) |
---|
| 482 | { int m = lp->m; |
---|
| 483 | GLPROW **row = lp->row; |
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| 484 | GLPCOL **col = lp->col; |
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| 485 | int i, k; |
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| 486 | /* B*x = b ===> (R*B*SB)*(inv(SB)*x) = R*b ===> |
---|
| 487 | B"*x" = b", where b" = R*b, x = SB*x" */ |
---|
| 488 | if (!(m == 0 || lp->valid)) |
---|
| 489 | xerror("glp_ftran: basis factorization does not exist\n"); |
---|
| 490 | /* b" := R*b */ |
---|
| 491 | for (i = 1; i <= m; i++) |
---|
| 492 | x[i] *= row[i]->rii; |
---|
| 493 | /* x" := inv(B")*b" */ |
---|
| 494 | if (m > 0) bfd_ftran(lp->bfd, x); |
---|
| 495 | /* x := SB*x" */ |
---|
| 496 | for (i = 1; i <= m; i++) |
---|
| 497 | { k = lp->head[i]; |
---|
| 498 | if (k <= m) |
---|
| 499 | x[i] /= row[k]->rii; |
---|
| 500 | else |
---|
| 501 | x[i] *= col[k-m]->sjj; |
---|
| 502 | } |
---|
| 503 | return; |
---|
| 504 | } |
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| 505 | |
---|
| 506 | /*********************************************************************** |
---|
| 507 | * NAME |
---|
| 508 | * |
---|
| 509 | * glp_btran - perform backward transformation (solve system B'*x = b) |
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| 510 | * |
---|
| 511 | * SYNOPSIS |
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| 512 | * |
---|
| 513 | * void glp_btran(glp_prob *lp, double x[]); |
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| 514 | * |
---|
| 515 | * DESCRIPTION |
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| 516 | * |
---|
| 517 | * The routine glp_btran performs backward transformation, i.e. solves |
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| 518 | * the system B'*x = b, where B' is a matrix transposed to the basis |
---|
| 519 | * matrix corresponding to the current basis for the specified problem |
---|
| 520 | * problem object, x is the vector of unknowns to be computed, b is the |
---|
| 521 | * vector of right-hand sides. |
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| 522 | * |
---|
| 523 | * On entry elements of the vector b should be stored in dense format |
---|
| 524 | * in locations x[1], ..., x[m], where m is the number of rows. On exit |
---|
| 525 | * the routine stores elements of the vector x in the same locations. |
---|
| 526 | * |
---|
| 527 | * SCALING/UNSCALING |
---|
| 528 | * |
---|
| 529 | * See comments to the routine glp_ftran. */ |
---|
| 530 | |
---|
| 531 | void glp_btran(glp_prob *lp, double x[]) |
---|
| 532 | { int m = lp->m; |
---|
| 533 | GLPROW **row = lp->row; |
---|
| 534 | GLPCOL **col = lp->col; |
---|
| 535 | int i, k; |
---|
| 536 | /* B'*x = b ===> (SB*B'*R)*(inv(R)*x) = SB*b ===> |
---|
| 537 | (B")'*x" = b", where b" = SB*b, x = R*x" */ |
---|
| 538 | if (!(m == 0 || lp->valid)) |
---|
| 539 | xerror("glp_btran: basis factorization does not exist\n"); |
---|
| 540 | /* b" := SB*b */ |
---|
| 541 | for (i = 1; i <= m; i++) |
---|
| 542 | { k = lp->head[i]; |
---|
| 543 | if (k <= m) |
---|
| 544 | x[i] /= row[k]->rii; |
---|
| 545 | else |
---|
| 546 | x[i] *= col[k-m]->sjj; |
---|
| 547 | } |
---|
| 548 | /* x" := inv[(B")']*b" */ |
---|
| 549 | if (m > 0) bfd_btran(lp->bfd, x); |
---|
| 550 | /* x := R*x" */ |
---|
| 551 | for (i = 1; i <= m; i++) |
---|
| 552 | x[i] *= row[i]->rii; |
---|
| 553 | return; |
---|
| 554 | } |
---|
| 555 | |
---|
| 556 | /*********************************************************************** |
---|
| 557 | * NAME |
---|
| 558 | * |
---|
| 559 | * glp_warm_up - "warm up" LP basis |
---|
| 560 | * |
---|
| 561 | * SYNOPSIS |
---|
| 562 | * |
---|
| 563 | * int glp_warm_up(glp_prob *P); |
---|
| 564 | * |
---|
| 565 | * DESCRIPTION |
---|
| 566 | * |
---|
| 567 | * The routine glp_warm_up "warms up" the LP basis for the specified |
---|
| 568 | * problem object using current statuses assigned to rows and columns |
---|
| 569 | * (that is, to auxiliary and structural variables). |
---|
| 570 | * |
---|
| 571 | * This operation includes computing factorization of the basis matrix |
---|
| 572 | * (if it does not exist), computing primal and dual components of basic |
---|
| 573 | * solution, and determining the solution status. |
---|
| 574 | * |
---|
| 575 | * RETURNS |
---|
| 576 | * |
---|
| 577 | * 0 The operation has been successfully performed. |
---|
| 578 | * |
---|
| 579 | * GLP_EBADB |
---|
| 580 | * The basis matrix is invalid, i.e. the number of basic (auxiliary |
---|
| 581 | * and structural) variables differs from the number of rows in the |
---|
| 582 | * problem object. |
---|
| 583 | * |
---|
| 584 | * GLP_ESING |
---|
| 585 | * The basis matrix is singular within the working precision. |
---|
| 586 | * |
---|
| 587 | * GLP_ECOND |
---|
| 588 | * The basis matrix is ill-conditioned. */ |
---|
| 589 | |
---|
| 590 | int glp_warm_up(glp_prob *P) |
---|
| 591 | { GLPROW *row; |
---|
| 592 | GLPCOL *col; |
---|
| 593 | GLPAIJ *aij; |
---|
| 594 | int i, j, type, ret; |
---|
| 595 | double eps, temp, *work; |
---|
| 596 | /* invalidate basic solution */ |
---|
| 597 | P->pbs_stat = P->dbs_stat = GLP_UNDEF; |
---|
| 598 | P->obj_val = 0.0; |
---|
| 599 | P->some = 0; |
---|
| 600 | for (i = 1; i <= P->m; i++) |
---|
| 601 | { row = P->row[i]; |
---|
| 602 | row->prim = row->dual = 0.0; |
---|
| 603 | } |
---|
| 604 | for (j = 1; j <= P->n; j++) |
---|
| 605 | { col = P->col[j]; |
---|
| 606 | col->prim = col->dual = 0.0; |
---|
| 607 | } |
---|
| 608 | /* compute the basis factorization, if necessary */ |
---|
| 609 | if (!glp_bf_exists(P)) |
---|
| 610 | { ret = glp_factorize(P); |
---|
| 611 | if (ret != 0) goto done; |
---|
| 612 | } |
---|
| 613 | /* allocate working array */ |
---|
| 614 | work = xcalloc(1+P->m, sizeof(double)); |
---|
| 615 | /* determine and store values of non-basic variables, compute |
---|
| 616 | vector (- N * xN) */ |
---|
| 617 | for (i = 1; i <= P->m; i++) |
---|
| 618 | work[i] = 0.0; |
---|
| 619 | for (i = 1; i <= P->m; i++) |
---|
| 620 | { row = P->row[i]; |
---|
| 621 | if (row->stat == GLP_BS) |
---|
| 622 | continue; |
---|
| 623 | else if (row->stat == GLP_NL) |
---|
| 624 | row->prim = row->lb; |
---|
| 625 | else if (row->stat == GLP_NU) |
---|
| 626 | row->prim = row->ub; |
---|
| 627 | else if (row->stat == GLP_NF) |
---|
| 628 | row->prim = 0.0; |
---|
| 629 | else if (row->stat == GLP_NS) |
---|
| 630 | row->prim = row->lb; |
---|
| 631 | else |
---|
| 632 | xassert(row != row); |
---|
| 633 | /* N[j] is i-th column of matrix (I|-A) */ |
---|
| 634 | work[i] -= row->prim; |
---|
| 635 | } |
---|
| 636 | for (j = 1; j <= P->n; j++) |
---|
| 637 | { col = P->col[j]; |
---|
| 638 | if (col->stat == GLP_BS) |
---|
| 639 | continue; |
---|
| 640 | else if (col->stat == GLP_NL) |
---|
| 641 | col->prim = col->lb; |
---|
| 642 | else if (col->stat == GLP_NU) |
---|
| 643 | col->prim = col->ub; |
---|
| 644 | else if (col->stat == GLP_NF) |
---|
| 645 | col->prim = 0.0; |
---|
| 646 | else if (col->stat == GLP_NS) |
---|
| 647 | col->prim = col->lb; |
---|
| 648 | else |
---|
| 649 | xassert(col != col); |
---|
| 650 | /* N[j] is (m+j)-th column of matrix (I|-A) */ |
---|
| 651 | if (col->prim != 0.0) |
---|
| 652 | { for (aij = col->ptr; aij != NULL; aij = aij->c_next) |
---|
| 653 | work[aij->row->i] += aij->val * col->prim; |
---|
| 654 | } |
---|
| 655 | } |
---|
| 656 | /* compute vector of basic variables xB = - inv(B) * N * xN */ |
---|
| 657 | glp_ftran(P, work); |
---|
| 658 | /* store values of basic variables, check primal feasibility */ |
---|
| 659 | P->pbs_stat = GLP_FEAS; |
---|
| 660 | for (i = 1; i <= P->m; i++) |
---|
| 661 | { row = P->row[i]; |
---|
| 662 | if (row->stat != GLP_BS) |
---|
| 663 | continue; |
---|
| 664 | row->prim = work[row->bind]; |
---|
| 665 | type = row->type; |
---|
| 666 | if (type == GLP_LO || type == GLP_DB || type == GLP_FX) |
---|
| 667 | { eps = 1e-6 + 1e-9 * fabs(row->lb); |
---|
| 668 | if (row->prim < row->lb - eps) |
---|
| 669 | P->pbs_stat = GLP_INFEAS; |
---|
| 670 | } |
---|
| 671 | if (type == GLP_UP || type == GLP_DB || type == GLP_FX) |
---|
| 672 | { eps = 1e-6 + 1e-9 * fabs(row->ub); |
---|
| 673 | if (row->prim > row->ub + eps) |
---|
| 674 | P->pbs_stat = GLP_INFEAS; |
---|
| 675 | } |
---|
| 676 | } |
---|
| 677 | for (j = 1; j <= P->n; j++) |
---|
| 678 | { col = P->col[j]; |
---|
| 679 | if (col->stat != GLP_BS) |
---|
| 680 | continue; |
---|
| 681 | col->prim = work[col->bind]; |
---|
| 682 | type = col->type; |
---|
| 683 | if (type == GLP_LO || type == GLP_DB || type == GLP_FX) |
---|
| 684 | { eps = 1e-6 + 1e-9 * fabs(col->lb); |
---|
| 685 | if (col->prim < col->lb - eps) |
---|
| 686 | P->pbs_stat = GLP_INFEAS; |
---|
| 687 | } |
---|
| 688 | if (type == GLP_UP || type == GLP_DB || type == GLP_FX) |
---|
| 689 | { eps = 1e-6 + 1e-9 * fabs(col->ub); |
---|
| 690 | if (col->prim > col->ub + eps) |
---|
| 691 | P->pbs_stat = GLP_INFEAS; |
---|
| 692 | } |
---|
| 693 | } |
---|
| 694 | /* compute value of the objective function */ |
---|
| 695 | P->obj_val = P->c0; |
---|
| 696 | for (j = 1; j <= P->n; j++) |
---|
| 697 | { col = P->col[j]; |
---|
| 698 | P->obj_val += col->coef * col->prim; |
---|
| 699 | } |
---|
| 700 | /* build vector cB of objective coefficients at basic variables */ |
---|
| 701 | for (i = 1; i <= P->m; i++) |
---|
| 702 | work[i] = 0.0; |
---|
| 703 | for (j = 1; j <= P->n; j++) |
---|
| 704 | { col = P->col[j]; |
---|
| 705 | if (col->stat == GLP_BS) |
---|
| 706 | work[col->bind] = col->coef; |
---|
| 707 | } |
---|
| 708 | /* compute vector of simplex multipliers pi = inv(B') * cB */ |
---|
| 709 | glp_btran(P, work); |
---|
| 710 | /* compute and store reduced costs of non-basic variables d[j] = |
---|
| 711 | c[j] - N'[j] * pi, check dual feasibility */ |
---|
| 712 | P->dbs_stat = GLP_FEAS; |
---|
| 713 | for (i = 1; i <= P->m; i++) |
---|
| 714 | { row = P->row[i]; |
---|
| 715 | if (row->stat == GLP_BS) |
---|
| 716 | { row->dual = 0.0; |
---|
| 717 | continue; |
---|
| 718 | } |
---|
| 719 | /* N[j] is i-th column of matrix (I|-A) */ |
---|
| 720 | row->dual = - work[i]; |
---|
| 721 | type = row->type; |
---|
| 722 | temp = (P->dir == GLP_MIN ? + row->dual : - row->dual); |
---|
| 723 | if ((type == GLP_FR || type == GLP_LO) && temp < -1e-5 || |
---|
| 724 | (type == GLP_FR || type == GLP_UP) && temp > +1e-5) |
---|
| 725 | P->dbs_stat = GLP_INFEAS; |
---|
| 726 | } |
---|
| 727 | for (j = 1; j <= P->n; j++) |
---|
| 728 | { col = P->col[j]; |
---|
| 729 | if (col->stat == GLP_BS) |
---|
| 730 | { col->dual = 0.0; |
---|
| 731 | continue; |
---|
| 732 | } |
---|
| 733 | /* N[j] is (m+j)-th column of matrix (I|-A) */ |
---|
| 734 | col->dual = col->coef; |
---|
| 735 | for (aij = col->ptr; aij != NULL; aij = aij->c_next) |
---|
| 736 | col->dual += aij->val * work[aij->row->i]; |
---|
| 737 | type = col->type; |
---|
| 738 | temp = (P->dir == GLP_MIN ? + col->dual : - col->dual); |
---|
| 739 | if ((type == GLP_FR || type == GLP_LO) && temp < -1e-5 || |
---|
| 740 | (type == GLP_FR || type == GLP_UP) && temp > +1e-5) |
---|
| 741 | P->dbs_stat = GLP_INFEAS; |
---|
| 742 | } |
---|
| 743 | /* free working array */ |
---|
| 744 | xfree(work); |
---|
| 745 | ret = 0; |
---|
| 746 | done: return ret; |
---|
| 747 | } |
---|
| 748 | |
---|
| 749 | /*********************************************************************** |
---|
| 750 | * NAME |
---|
| 751 | * |
---|
| 752 | * glp_eval_tab_row - compute row of the simplex tableau |
---|
| 753 | * |
---|
| 754 | * SYNOPSIS |
---|
| 755 | * |
---|
| 756 | * int glp_eval_tab_row(glp_prob *lp, int k, int ind[], double val[]); |
---|
| 757 | * |
---|
| 758 | * DESCRIPTION |
---|
| 759 | * |
---|
| 760 | * The routine glp_eval_tab_row computes a row of the current simplex |
---|
| 761 | * tableau for the basic variable, which is specified by the number k: |
---|
| 762 | * if 1 <= k <= m, x[k] is k-th auxiliary variable; if m+1 <= k <= m+n, |
---|
| 763 | * x[k] is (k-m)-th structural variable, where m is number of rows, and |
---|
| 764 | * n is number of columns. The current basis must be available. |
---|
| 765 | * |
---|
| 766 | * The routine stores column indices and numerical values of non-zero |
---|
| 767 | * elements of the computed row using sparse format to the locations |
---|
| 768 | * ind[1], ..., ind[len] and val[1], ..., val[len], respectively, where |
---|
| 769 | * 0 <= len <= n is number of non-zeros returned on exit. |
---|
| 770 | * |
---|
| 771 | * Element indices stored in the array ind have the same sense as the |
---|
| 772 | * index k, i.e. indices 1 to m denote auxiliary variables and indices |
---|
| 773 | * m+1 to m+n denote structural ones (all these variables are obviously |
---|
| 774 | * non-basic by definition). |
---|
| 775 | * |
---|
| 776 | * The computed row shows how the specified basic variable x[k] = xB[i] |
---|
| 777 | * depends on non-basic variables: |
---|
| 778 | * |
---|
| 779 | * xB[i] = alfa[i,1]*xN[1] + alfa[i,2]*xN[2] + ... + alfa[i,n]*xN[n], |
---|
| 780 | * |
---|
| 781 | * where alfa[i,j] are elements of the simplex table row, xN[j] are |
---|
| 782 | * non-basic (auxiliary and structural) variables. |
---|
| 783 | * |
---|
| 784 | * RETURNS |
---|
| 785 | * |
---|
| 786 | * The routine returns number of non-zero elements in the simplex table |
---|
| 787 | * row stored in the arrays ind and val. |
---|
| 788 | * |
---|
| 789 | * BACKGROUND |
---|
| 790 | * |
---|
| 791 | * The system of equality constraints of the LP problem is: |
---|
| 792 | * |
---|
| 793 | * xR = A * xS, (1) |
---|
| 794 | * |
---|
| 795 | * where xR is the vector of auxliary variables, xS is the vector of |
---|
| 796 | * structural variables, A is the matrix of constraint coefficients. |
---|
| 797 | * |
---|
| 798 | * The system (1) can be written in homogenous form as follows: |
---|
| 799 | * |
---|
| 800 | * A~ * x = 0, (2) |
---|
| 801 | * |
---|
| 802 | * where A~ = (I | -A) is the augmented constraint matrix (has m rows |
---|
| 803 | * and m+n columns), x = (xR | xS) is the vector of all (auxiliary and |
---|
| 804 | * structural) variables. |
---|
| 805 | * |
---|
| 806 | * By definition for the current basis we have: |
---|
| 807 | * |
---|
| 808 | * A~ = (B | N), (3) |
---|
| 809 | * |
---|
| 810 | * where B is the basis matrix. Thus, the system (2) can be written as: |
---|
| 811 | * |
---|
| 812 | * B * xB + N * xN = 0. (4) |
---|
| 813 | * |
---|
| 814 | * From (4) it follows that: |
---|
| 815 | * |
---|
| 816 | * xB = A^ * xN, (5) |
---|
| 817 | * |
---|
| 818 | * where the matrix |
---|
| 819 | * |
---|
| 820 | * A^ = - inv(B) * N (6) |
---|
| 821 | * |
---|
| 822 | * is called the simplex table. |
---|
| 823 | * |
---|
| 824 | * It is understood that i-th row of the simplex table is: |
---|
| 825 | * |
---|
| 826 | * e * A^ = - e * inv(B) * N, (7) |
---|
| 827 | * |
---|
| 828 | * where e is a unity vector with e[i] = 1. |
---|
| 829 | * |
---|
| 830 | * To compute i-th row of the simplex table the routine first computes |
---|
| 831 | * i-th row of the inverse: |
---|
| 832 | * |
---|
| 833 | * rho = inv(B') * e, (8) |
---|
| 834 | * |
---|
| 835 | * where B' is a matrix transposed to B, and then computes elements of |
---|
| 836 | * i-th row of the simplex table as scalar products: |
---|
| 837 | * |
---|
| 838 | * alfa[i,j] = - rho * N[j] for all j, (9) |
---|
| 839 | * |
---|
| 840 | * where N[j] is a column of the augmented constraint matrix A~, which |
---|
| 841 | * corresponds to some non-basic auxiliary or structural variable. */ |
---|
| 842 | |
---|
| 843 | int glp_eval_tab_row(glp_prob *lp, int k, int ind[], double val[]) |
---|
| 844 | { int m = lp->m; |
---|
| 845 | int n = lp->n; |
---|
| 846 | int i, t, len, lll, *iii; |
---|
| 847 | double alfa, *rho, *vvv; |
---|
| 848 | if (!(m == 0 || lp->valid)) |
---|
| 849 | xerror("glp_eval_tab_row: basis factorization does not exist\n" |
---|
| 850 | ); |
---|
| 851 | if (!(1 <= k && k <= m+n)) |
---|
| 852 | xerror("glp_eval_tab_row: k = %d; variable number out of range" |
---|
| 853 | , k); |
---|
| 854 | /* determine xB[i] which corresponds to x[k] */ |
---|
| 855 | if (k <= m) |
---|
| 856 | i = glp_get_row_bind(lp, k); |
---|
| 857 | else |
---|
| 858 | i = glp_get_col_bind(lp, k-m); |
---|
| 859 | if (i == 0) |
---|
| 860 | xerror("glp_eval_tab_row: k = %d; variable must be basic", k); |
---|
| 861 | xassert(1 <= i && i <= m); |
---|
| 862 | /* allocate working arrays */ |
---|
| 863 | rho = xcalloc(1+m, sizeof(double)); |
---|
| 864 | iii = xcalloc(1+m, sizeof(int)); |
---|
| 865 | vvv = xcalloc(1+m, sizeof(double)); |
---|
| 866 | /* compute i-th row of the inverse; see (8) */ |
---|
| 867 | for (t = 1; t <= m; t++) rho[t] = 0.0; |
---|
| 868 | rho[i] = 1.0; |
---|
| 869 | glp_btran(lp, rho); |
---|
| 870 | /* compute i-th row of the simplex table */ |
---|
| 871 | len = 0; |
---|
| 872 | for (k = 1; k <= m+n; k++) |
---|
| 873 | { if (k <= m) |
---|
| 874 | { /* x[k] is auxiliary variable, so N[k] is a unity column */ |
---|
| 875 | if (glp_get_row_stat(lp, k) == GLP_BS) continue; |
---|
| 876 | /* compute alfa[i,j]; see (9) */ |
---|
| 877 | alfa = - rho[k]; |
---|
| 878 | } |
---|
| 879 | else |
---|
| 880 | { /* x[k] is structural variable, so N[k] is a column of the |
---|
| 881 | original constraint matrix A with negative sign */ |
---|
| 882 | if (glp_get_col_stat(lp, k-m) == GLP_BS) continue; |
---|
| 883 | /* compute alfa[i,j]; see (9) */ |
---|
| 884 | lll = glp_get_mat_col(lp, k-m, iii, vvv); |
---|
| 885 | alfa = 0.0; |
---|
| 886 | for (t = 1; t <= lll; t++) alfa += rho[iii[t]] * vvv[t]; |
---|
| 887 | } |
---|
| 888 | /* store alfa[i,j] */ |
---|
| 889 | if (alfa != 0.0) len++, ind[len] = k, val[len] = alfa; |
---|
| 890 | } |
---|
| 891 | xassert(len <= n); |
---|
| 892 | /* free working arrays */ |
---|
| 893 | xfree(rho); |
---|
| 894 | xfree(iii); |
---|
| 895 | xfree(vvv); |
---|
| 896 | /* return to the calling program */ |
---|
| 897 | return len; |
---|
| 898 | } |
---|
| 899 | |
---|
| 900 | /*********************************************************************** |
---|
| 901 | * NAME |
---|
| 902 | * |
---|
| 903 | * glp_eval_tab_col - compute column of the simplex tableau |
---|
| 904 | * |
---|
| 905 | * SYNOPSIS |
---|
| 906 | * |
---|
| 907 | * int glp_eval_tab_col(glp_prob *lp, int k, int ind[], double val[]); |
---|
| 908 | * |
---|
| 909 | * DESCRIPTION |
---|
| 910 | * |
---|
| 911 | * The routine glp_eval_tab_col computes a column of the current simplex |
---|
| 912 | * table for the non-basic variable, which is specified by the number k: |
---|
| 913 | * if 1 <= k <= m, x[k] is k-th auxiliary variable; if m+1 <= k <= m+n, |
---|
| 914 | * x[k] is (k-m)-th structural variable, where m is number of rows, and |
---|
| 915 | * n is number of columns. The current basis must be available. |
---|
| 916 | * |
---|
| 917 | * The routine stores row indices and numerical values of non-zero |
---|
| 918 | * elements of the computed column using sparse format to the locations |
---|
| 919 | * ind[1], ..., ind[len] and val[1], ..., val[len] respectively, where |
---|
| 920 | * 0 <= len <= m is number of non-zeros returned on exit. |
---|
| 921 | * |
---|
| 922 | * Element indices stored in the array ind have the same sense as the |
---|
| 923 | * index k, i.e. indices 1 to m denote auxiliary variables and indices |
---|
| 924 | * m+1 to m+n denote structural ones (all these variables are obviously |
---|
| 925 | * basic by the definition). |
---|
| 926 | * |
---|
| 927 | * The computed column shows how basic variables depend on the specified |
---|
| 928 | * non-basic variable x[k] = xN[j]: |
---|
| 929 | * |
---|
| 930 | * xB[1] = ... + alfa[1,j]*xN[j] + ... |
---|
| 931 | * xB[2] = ... + alfa[2,j]*xN[j] + ... |
---|
| 932 | * . . . . . . |
---|
| 933 | * xB[m] = ... + alfa[m,j]*xN[j] + ... |
---|
| 934 | * |
---|
| 935 | * where alfa[i,j] are elements of the simplex table column, xB[i] are |
---|
| 936 | * basic (auxiliary and structural) variables. |
---|
| 937 | * |
---|
| 938 | * RETURNS |
---|
| 939 | * |
---|
| 940 | * The routine returns number of non-zero elements in the simplex table |
---|
| 941 | * column stored in the arrays ind and val. |
---|
| 942 | * |
---|
| 943 | * BACKGROUND |
---|
| 944 | * |
---|
| 945 | * As it was explained in comments to the routine glp_eval_tab_row (see |
---|
| 946 | * above) the simplex table is the following matrix: |
---|
| 947 | * |
---|
| 948 | * A^ = - inv(B) * N. (1) |
---|
| 949 | * |
---|
| 950 | * Therefore j-th column of the simplex table is: |
---|
| 951 | * |
---|
| 952 | * A^ * e = - inv(B) * N * e = - inv(B) * N[j], (2) |
---|
| 953 | * |
---|
| 954 | * where e is a unity vector with e[j] = 1, B is the basis matrix, N[j] |
---|
| 955 | * is a column of the augmented constraint matrix A~, which corresponds |
---|
| 956 | * to the given non-basic auxiliary or structural variable. */ |
---|
| 957 | |
---|
| 958 | int glp_eval_tab_col(glp_prob *lp, int k, int ind[], double val[]) |
---|
| 959 | { int m = lp->m; |
---|
| 960 | int n = lp->n; |
---|
| 961 | int t, len, stat; |
---|
| 962 | double *col; |
---|
| 963 | if (!(m == 0 || lp->valid)) |
---|
| 964 | xerror("glp_eval_tab_col: basis factorization does not exist\n" |
---|
| 965 | ); |
---|
| 966 | if (!(1 <= k && k <= m+n)) |
---|
| 967 | xerror("glp_eval_tab_col: k = %d; variable number out of range" |
---|
| 968 | , k); |
---|
| 969 | if (k <= m) |
---|
| 970 | stat = glp_get_row_stat(lp, k); |
---|
| 971 | else |
---|
| 972 | stat = glp_get_col_stat(lp, k-m); |
---|
| 973 | if (stat == GLP_BS) |
---|
| 974 | xerror("glp_eval_tab_col: k = %d; variable must be non-basic", |
---|
| 975 | k); |
---|
| 976 | /* obtain column N[k] with negative sign */ |
---|
| 977 | col = xcalloc(1+m, sizeof(double)); |
---|
| 978 | for (t = 1; t <= m; t++) col[t] = 0.0; |
---|
| 979 | if (k <= m) |
---|
| 980 | { /* x[k] is auxiliary variable, so N[k] is a unity column */ |
---|
| 981 | col[k] = -1.0; |
---|
| 982 | } |
---|
| 983 | else |
---|
| 984 | { /* x[k] is structural variable, so N[k] is a column of the |
---|
| 985 | original constraint matrix A with negative sign */ |
---|
| 986 | len = glp_get_mat_col(lp, k-m, ind, val); |
---|
| 987 | for (t = 1; t <= len; t++) col[ind[t]] = val[t]; |
---|
| 988 | } |
---|
| 989 | /* compute column of the simplex table, which corresponds to the |
---|
| 990 | specified non-basic variable x[k] */ |
---|
| 991 | glp_ftran(lp, col); |
---|
| 992 | len = 0; |
---|
| 993 | for (t = 1; t <= m; t++) |
---|
| 994 | { if (col[t] != 0.0) |
---|
| 995 | { len++; |
---|
| 996 | ind[len] = glp_get_bhead(lp, t); |
---|
| 997 | val[len] = col[t]; |
---|
| 998 | } |
---|
| 999 | } |
---|
| 1000 | xfree(col); |
---|
| 1001 | /* return to the calling program */ |
---|
| 1002 | return len; |
---|
| 1003 | } |
---|
| 1004 | |
---|
| 1005 | /*********************************************************************** |
---|
| 1006 | * NAME |
---|
| 1007 | * |
---|
| 1008 | * glp_transform_row - transform explicitly specified row |
---|
| 1009 | * |
---|
| 1010 | * SYNOPSIS |
---|
| 1011 | * |
---|
| 1012 | * int glp_transform_row(glp_prob *P, int len, int ind[], double val[]); |
---|
| 1013 | * |
---|
| 1014 | * DESCRIPTION |
---|
| 1015 | * |
---|
| 1016 | * The routine glp_transform_row performs the same operation as the |
---|
| 1017 | * routine glp_eval_tab_row with exception that the row to be |
---|
| 1018 | * transformed is specified explicitly as a sparse vector. |
---|
| 1019 | * |
---|
| 1020 | * The explicitly specified row may be thought as a linear form: |
---|
| 1021 | * |
---|
| 1022 | * x = a[1]*x[m+1] + a[2]*x[m+2] + ... + a[n]*x[m+n], (1) |
---|
| 1023 | * |
---|
| 1024 | * where x is an auxiliary variable for this row, a[j] are coefficients |
---|
| 1025 | * of the linear form, x[m+j] are structural variables. |
---|
| 1026 | * |
---|
| 1027 | * On entry column indices and numerical values of non-zero elements of |
---|
| 1028 | * the row should be stored in locations ind[1], ..., ind[len] and |
---|
| 1029 | * val[1], ..., val[len], where len is the number of non-zero elements. |
---|
| 1030 | * |
---|
| 1031 | * This routine uses the system of equality constraints and the current |
---|
| 1032 | * basis in order to express the auxiliary variable x in (1) through the |
---|
| 1033 | * current non-basic variables (as if the transformed row were added to |
---|
| 1034 | * the problem object and its auxiliary variable were basic), i.e. the |
---|
| 1035 | * resultant row has the form: |
---|
| 1036 | * |
---|
| 1037 | * x = alfa[1]*xN[1] + alfa[2]*xN[2] + ... + alfa[n]*xN[n], (2) |
---|
| 1038 | * |
---|
| 1039 | * where xN[j] are non-basic (auxiliary or structural) variables, n is |
---|
| 1040 | * the number of columns in the LP problem object. |
---|
| 1041 | * |
---|
| 1042 | * On exit the routine stores indices and numerical values of non-zero |
---|
| 1043 | * elements of the resultant row (2) in locations ind[1], ..., ind[len'] |
---|
| 1044 | * and val[1], ..., val[len'], where 0 <= len' <= n is the number of |
---|
| 1045 | * non-zero elements in the resultant row returned by the routine. Note |
---|
| 1046 | * that indices (numbers) of non-basic variables stored in the array ind |
---|
| 1047 | * correspond to original ordinal numbers of variables: indices 1 to m |
---|
| 1048 | * mean auxiliary variables and indices m+1 to m+n mean structural ones. |
---|
| 1049 | * |
---|
| 1050 | * RETURNS |
---|
| 1051 | * |
---|
| 1052 | * The routine returns len', which is the number of non-zero elements in |
---|
| 1053 | * the resultant row stored in the arrays ind and val. |
---|
| 1054 | * |
---|
| 1055 | * BACKGROUND |
---|
| 1056 | * |
---|
| 1057 | * The explicitly specified row (1) is transformed in the same way as it |
---|
| 1058 | * were the objective function row. |
---|
| 1059 | * |
---|
| 1060 | * From (1) it follows that: |
---|
| 1061 | * |
---|
| 1062 | * x = aB * xB + aN * xN, (3) |
---|
| 1063 | * |
---|
| 1064 | * where xB is the vector of basic variables, xN is the vector of |
---|
| 1065 | * non-basic variables. |
---|
| 1066 | * |
---|
| 1067 | * The simplex table, which corresponds to the current basis, is: |
---|
| 1068 | * |
---|
| 1069 | * xB = [-inv(B) * N] * xN. (4) |
---|
| 1070 | * |
---|
| 1071 | * Therefore substituting xB from (4) to (3) we have: |
---|
| 1072 | * |
---|
| 1073 | * x = aB * [-inv(B) * N] * xN + aN * xN = |
---|
| 1074 | * (5) |
---|
| 1075 | * = rho * (-N) * xN + aN * xN = alfa * xN, |
---|
| 1076 | * |
---|
| 1077 | * where: |
---|
| 1078 | * |
---|
| 1079 | * rho = inv(B') * aB, (6) |
---|
| 1080 | * |
---|
| 1081 | * and |
---|
| 1082 | * |
---|
| 1083 | * alfa = aN + rho * (-N) (7) |
---|
| 1084 | * |
---|
| 1085 | * is the resultant row computed by the routine. */ |
---|
| 1086 | |
---|
| 1087 | int glp_transform_row(glp_prob *P, int len, int ind[], double val[]) |
---|
| 1088 | { int i, j, k, m, n, t, lll, *iii; |
---|
| 1089 | double alfa, *a, *aB, *rho, *vvv; |
---|
| 1090 | if (!glp_bf_exists(P)) |
---|
| 1091 | xerror("glp_transform_row: basis factorization does not exist " |
---|
| 1092 | "\n"); |
---|
| 1093 | m = glp_get_num_rows(P); |
---|
| 1094 | n = glp_get_num_cols(P); |
---|
| 1095 | /* unpack the row to be transformed to the array a */ |
---|
| 1096 | a = xcalloc(1+n, sizeof(double)); |
---|
| 1097 | for (j = 1; j <= n; j++) a[j] = 0.0; |
---|
| 1098 | if (!(0 <= len && len <= n)) |
---|
| 1099 | xerror("glp_transform_row: len = %d; invalid row length\n", |
---|
| 1100 | len); |
---|
| 1101 | for (t = 1; t <= len; t++) |
---|
| 1102 | { j = ind[t]; |
---|
| 1103 | if (!(1 <= j && j <= n)) |
---|
| 1104 | xerror("glp_transform_row: ind[%d] = %d; column index out o" |
---|
| 1105 | "f range\n", t, j); |
---|
| 1106 | if (val[t] == 0.0) |
---|
| 1107 | xerror("glp_transform_row: val[%d] = 0; zero coefficient no" |
---|
| 1108 | "t allowed\n", t); |
---|
| 1109 | if (a[j] != 0.0) |
---|
| 1110 | xerror("glp_transform_row: ind[%d] = %d; duplicate column i" |
---|
| 1111 | "ndices not allowed\n", t, j); |
---|
| 1112 | a[j] = val[t]; |
---|
| 1113 | } |
---|
| 1114 | /* construct the vector aB */ |
---|
| 1115 | aB = xcalloc(1+m, sizeof(double)); |
---|
| 1116 | for (i = 1; i <= m; i++) |
---|
| 1117 | { k = glp_get_bhead(P, i); |
---|
| 1118 | /* xB[i] is k-th original variable */ |
---|
| 1119 | xassert(1 <= k && k <= m+n); |
---|
| 1120 | aB[i] = (k <= m ? 0.0 : a[k-m]); |
---|
| 1121 | } |
---|
| 1122 | /* solve the system B'*rho = aB to compute the vector rho */ |
---|
| 1123 | rho = aB, glp_btran(P, rho); |
---|
| 1124 | /* compute coefficients at non-basic auxiliary variables */ |
---|
| 1125 | len = 0; |
---|
| 1126 | for (i = 1; i <= m; i++) |
---|
| 1127 | { if (glp_get_row_stat(P, i) != GLP_BS) |
---|
| 1128 | { alfa = - rho[i]; |
---|
| 1129 | if (alfa != 0.0) |
---|
| 1130 | { len++; |
---|
| 1131 | ind[len] = i; |
---|
| 1132 | val[len] = alfa; |
---|
| 1133 | } |
---|
| 1134 | } |
---|
| 1135 | } |
---|
| 1136 | /* compute coefficients at non-basic structural variables */ |
---|
| 1137 | iii = xcalloc(1+m, sizeof(int)); |
---|
| 1138 | vvv = xcalloc(1+m, sizeof(double)); |
---|
| 1139 | for (j = 1; j <= n; j++) |
---|
| 1140 | { if (glp_get_col_stat(P, j) != GLP_BS) |
---|
| 1141 | { alfa = a[j]; |
---|
| 1142 | lll = glp_get_mat_col(P, j, iii, vvv); |
---|
| 1143 | for (t = 1; t <= lll; t++) alfa += vvv[t] * rho[iii[t]]; |
---|
| 1144 | if (alfa != 0.0) |
---|
| 1145 | { len++; |
---|
| 1146 | ind[len] = m+j; |
---|
| 1147 | val[len] = alfa; |
---|
| 1148 | } |
---|
| 1149 | } |
---|
| 1150 | } |
---|
| 1151 | xassert(len <= n); |
---|
| 1152 | xfree(iii); |
---|
| 1153 | xfree(vvv); |
---|
| 1154 | xfree(aB); |
---|
| 1155 | xfree(a); |
---|
| 1156 | return len; |
---|
| 1157 | } |
---|
| 1158 | |
---|
| 1159 | /*********************************************************************** |
---|
| 1160 | * NAME |
---|
| 1161 | * |
---|
| 1162 | * glp_transform_col - transform explicitly specified column |
---|
| 1163 | * |
---|
| 1164 | * SYNOPSIS |
---|
| 1165 | * |
---|
| 1166 | * int glp_transform_col(glp_prob *P, int len, int ind[], double val[]); |
---|
| 1167 | * |
---|
| 1168 | * DESCRIPTION |
---|
| 1169 | * |
---|
| 1170 | * The routine glp_transform_col performs the same operation as the |
---|
| 1171 | * routine glp_eval_tab_col with exception that the column to be |
---|
| 1172 | * transformed is specified explicitly as a sparse vector. |
---|
| 1173 | * |
---|
| 1174 | * The explicitly specified column may be thought as if it were added |
---|
| 1175 | * to the original system of equality constraints: |
---|
| 1176 | * |
---|
| 1177 | * x[1] = a[1,1]*x[m+1] + ... + a[1,n]*x[m+n] + a[1]*x |
---|
| 1178 | * x[2] = a[2,1]*x[m+1] + ... + a[2,n]*x[m+n] + a[2]*x (1) |
---|
| 1179 | * . . . . . . . . . . . . . . . |
---|
| 1180 | * x[m] = a[m,1]*x[m+1] + ... + a[m,n]*x[m+n] + a[m]*x |
---|
| 1181 | * |
---|
| 1182 | * where x[i] are auxiliary variables, x[m+j] are structural variables, |
---|
| 1183 | * x is a structural variable for the explicitly specified column, a[i] |
---|
| 1184 | * are constraint coefficients for x. |
---|
| 1185 | * |
---|
| 1186 | * On entry row indices and numerical values of non-zero elements of |
---|
| 1187 | * the column should be stored in locations ind[1], ..., ind[len] and |
---|
| 1188 | * val[1], ..., val[len], where len is the number of non-zero elements. |
---|
| 1189 | * |
---|
| 1190 | * This routine uses the system of equality constraints and the current |
---|
| 1191 | * basis in order to express the current basic variables through the |
---|
| 1192 | * structural variable x in (1) (as if the transformed column were added |
---|
| 1193 | * to the problem object and the variable x were non-basic), i.e. the |
---|
| 1194 | * resultant column has the form: |
---|
| 1195 | * |
---|
| 1196 | * xB[1] = ... + alfa[1]*x |
---|
| 1197 | * xB[2] = ... + alfa[2]*x (2) |
---|
| 1198 | * . . . . . . |
---|
| 1199 | * xB[m] = ... + alfa[m]*x |
---|
| 1200 | * |
---|
| 1201 | * where xB are basic (auxiliary and structural) variables, m is the |
---|
| 1202 | * number of rows in the problem object. |
---|
| 1203 | * |
---|
| 1204 | * On exit the routine stores indices and numerical values of non-zero |
---|
| 1205 | * elements of the resultant column (2) in locations ind[1], ..., |
---|
| 1206 | * ind[len'] and val[1], ..., val[len'], where 0 <= len' <= m is the |
---|
| 1207 | * number of non-zero element in the resultant column returned by the |
---|
| 1208 | * routine. Note that indices (numbers) of basic variables stored in |
---|
| 1209 | * the array ind correspond to original ordinal numbers of variables: |
---|
| 1210 | * indices 1 to m mean auxiliary variables and indices m+1 to m+n mean |
---|
| 1211 | * structural ones. |
---|
| 1212 | * |
---|
| 1213 | * RETURNS |
---|
| 1214 | * |
---|
| 1215 | * The routine returns len', which is the number of non-zero elements |
---|
| 1216 | * in the resultant column stored in the arrays ind and val. |
---|
| 1217 | * |
---|
| 1218 | * BACKGROUND |
---|
| 1219 | * |
---|
| 1220 | * The explicitly specified column (1) is transformed in the same way |
---|
| 1221 | * as any other column of the constraint matrix using the formula: |
---|
| 1222 | * |
---|
| 1223 | * alfa = inv(B) * a, (3) |
---|
| 1224 | * |
---|
| 1225 | * where alfa is the resultant column computed by the routine. */ |
---|
| 1226 | |
---|
| 1227 | int glp_transform_col(glp_prob *P, int len, int ind[], double val[]) |
---|
| 1228 | { int i, m, t; |
---|
| 1229 | double *a, *alfa; |
---|
| 1230 | if (!glp_bf_exists(P)) |
---|
| 1231 | xerror("glp_transform_col: basis factorization does not exist " |
---|
| 1232 | "\n"); |
---|
| 1233 | m = glp_get_num_rows(P); |
---|
| 1234 | /* unpack the column to be transformed to the array a */ |
---|
| 1235 | a = xcalloc(1+m, sizeof(double)); |
---|
| 1236 | for (i = 1; i <= m; i++) a[i] = 0.0; |
---|
| 1237 | if (!(0 <= len && len <= m)) |
---|
| 1238 | xerror("glp_transform_col: len = %d; invalid column length\n", |
---|
| 1239 | len); |
---|
| 1240 | for (t = 1; t <= len; t++) |
---|
| 1241 | { i = ind[t]; |
---|
| 1242 | if (!(1 <= i && i <= m)) |
---|
| 1243 | xerror("glp_transform_col: ind[%d] = %d; row index out of r" |
---|
| 1244 | "ange\n", t, i); |
---|
| 1245 | if (val[t] == 0.0) |
---|
| 1246 | xerror("glp_transform_col: val[%d] = 0; zero coefficient no" |
---|
| 1247 | "t allowed\n", t); |
---|
| 1248 | if (a[i] != 0.0) |
---|
| 1249 | xerror("glp_transform_col: ind[%d] = %d; duplicate row indi" |
---|
| 1250 | "ces not allowed\n", t, i); |
---|
| 1251 | a[i] = val[t]; |
---|
| 1252 | } |
---|
| 1253 | /* solve the system B*a = alfa to compute the vector alfa */ |
---|
| 1254 | alfa = a, glp_ftran(P, alfa); |
---|
| 1255 | /* store resultant coefficients */ |
---|
| 1256 | len = 0; |
---|
| 1257 | for (i = 1; i <= m; i++) |
---|
| 1258 | { if (alfa[i] != 0.0) |
---|
| 1259 | { len++; |
---|
| 1260 | ind[len] = glp_get_bhead(P, i); |
---|
| 1261 | val[len] = alfa[i]; |
---|
| 1262 | } |
---|
| 1263 | } |
---|
| 1264 | xfree(a); |
---|
| 1265 | return len; |
---|
| 1266 | } |
---|
| 1267 | |
---|
| 1268 | /*********************************************************************** |
---|
| 1269 | * NAME |
---|
| 1270 | * |
---|
| 1271 | * glp_prim_rtest - perform primal ratio test |
---|
| 1272 | * |
---|
| 1273 | * SYNOPSIS |
---|
| 1274 | * |
---|
| 1275 | * int glp_prim_rtest(glp_prob *P, int len, const int ind[], |
---|
| 1276 | * const double val[], int dir, double eps); |
---|
| 1277 | * |
---|
| 1278 | * DESCRIPTION |
---|
| 1279 | * |
---|
| 1280 | * The routine glp_prim_rtest performs the primal ratio test using an |
---|
| 1281 | * explicitly specified column of the simplex table. |
---|
| 1282 | * |
---|
| 1283 | * The current basic solution associated with the LP problem object |
---|
| 1284 | * must be primal feasible. |
---|
| 1285 | * |
---|
| 1286 | * The explicitly specified column of the simplex table shows how the |
---|
| 1287 | * basic variables xB depend on some non-basic variable x (which is not |
---|
| 1288 | * necessarily presented in the problem object): |
---|
| 1289 | * |
---|
| 1290 | * xB[1] = ... + alfa[1] * x + ... |
---|
| 1291 | * xB[2] = ... + alfa[2] * x + ... (*) |
---|
| 1292 | * . . . . . . . . |
---|
| 1293 | * xB[m] = ... + alfa[m] * x + ... |
---|
| 1294 | * |
---|
| 1295 | * The column (*) is specifed on entry to the routine using the sparse |
---|
| 1296 | * format. Ordinal numbers of basic variables xB[i] should be placed in |
---|
| 1297 | * locations ind[1], ..., ind[len], where ordinal number 1 to m denote |
---|
| 1298 | * auxiliary variables, and ordinal numbers m+1 to m+n denote structural |
---|
| 1299 | * variables. The corresponding non-zero coefficients alfa[i] should be |
---|
| 1300 | * placed in locations val[1], ..., val[len]. The arrays ind and val are |
---|
| 1301 | * not changed on exit. |
---|
| 1302 | * |
---|
| 1303 | * The parameter dir specifies direction in which the variable x changes |
---|
| 1304 | * on entering the basis: +1 means increasing, -1 means decreasing. |
---|
| 1305 | * |
---|
| 1306 | * The parameter eps is an absolute tolerance (small positive number) |
---|
| 1307 | * used by the routine to skip small alfa[j] of the row (*). |
---|
| 1308 | * |
---|
| 1309 | * The routine determines which basic variable (among specified in |
---|
| 1310 | * ind[1], ..., ind[len]) should leave the basis in order to keep primal |
---|
| 1311 | * feasibility. |
---|
| 1312 | * |
---|
| 1313 | * RETURNS |
---|
| 1314 | * |
---|
| 1315 | * The routine glp_prim_rtest returns the index piv in the arrays ind |
---|
| 1316 | * and val corresponding to the pivot element chosen, 1 <= piv <= len. |
---|
| 1317 | * If the adjacent basic solution is primal unbounded and therefore the |
---|
| 1318 | * choice cannot be made, the routine returns zero. |
---|
| 1319 | * |
---|
| 1320 | * COMMENTS |
---|
| 1321 | * |
---|
| 1322 | * If the non-basic variable x is presented in the LP problem object, |
---|
| 1323 | * the column (*) can be computed with the routine glp_eval_tab_col; |
---|
| 1324 | * otherwise it can be computed with the routine glp_transform_col. */ |
---|
| 1325 | |
---|
| 1326 | int glp_prim_rtest(glp_prob *P, int len, const int ind[], |
---|
| 1327 | const double val[], int dir, double eps) |
---|
| 1328 | { int k, m, n, piv, t, type, stat; |
---|
| 1329 | double alfa, big, beta, lb, ub, temp, teta; |
---|
| 1330 | if (glp_get_prim_stat(P) != GLP_FEAS) |
---|
| 1331 | xerror("glp_prim_rtest: basic solution is not primal feasible " |
---|
| 1332 | "\n"); |
---|
| 1333 | if (!(dir == +1 || dir == -1)) |
---|
| 1334 | xerror("glp_prim_rtest: dir = %d; invalid parameter\n", dir); |
---|
| 1335 | if (!(0.0 < eps && eps < 1.0)) |
---|
| 1336 | xerror("glp_prim_rtest: eps = %g; invalid parameter\n", eps); |
---|
| 1337 | m = glp_get_num_rows(P); |
---|
| 1338 | n = glp_get_num_cols(P); |
---|
| 1339 | /* initial settings */ |
---|
| 1340 | piv = 0, teta = DBL_MAX, big = 0.0; |
---|
| 1341 | /* walk through the entries of the specified column */ |
---|
| 1342 | for (t = 1; t <= len; t++) |
---|
| 1343 | { /* get the ordinal number of basic variable */ |
---|
| 1344 | k = ind[t]; |
---|
| 1345 | if (!(1 <= k && k <= m+n)) |
---|
| 1346 | xerror("glp_prim_rtest: ind[%d] = %d; variable number out o" |
---|
| 1347 | "f range\n", t, k); |
---|
| 1348 | /* determine type, bounds, status and primal value of basic |
---|
| 1349 | variable xB[i] = x[k] in the current basic solution */ |
---|
| 1350 | if (k <= m) |
---|
| 1351 | { type = glp_get_row_type(P, k); |
---|
| 1352 | lb = glp_get_row_lb(P, k); |
---|
| 1353 | ub = glp_get_row_ub(P, k); |
---|
| 1354 | stat = glp_get_row_stat(P, k); |
---|
| 1355 | beta = glp_get_row_prim(P, k); |
---|
| 1356 | } |
---|
| 1357 | else |
---|
| 1358 | { type = glp_get_col_type(P, k-m); |
---|
| 1359 | lb = glp_get_col_lb(P, k-m); |
---|
| 1360 | ub = glp_get_col_ub(P, k-m); |
---|
| 1361 | stat = glp_get_col_stat(P, k-m); |
---|
| 1362 | beta = glp_get_col_prim(P, k-m); |
---|
| 1363 | } |
---|
| 1364 | if (stat != GLP_BS) |
---|
| 1365 | xerror("glp_prim_rtest: ind[%d] = %d; non-basic variable no" |
---|
| 1366 | "t allowed\n", t, k); |
---|
| 1367 | /* determine influence coefficient at basic variable xB[i] |
---|
| 1368 | in the explicitly specified column and turn to the case of |
---|
| 1369 | increasing the variable x in order to simplify the program |
---|
| 1370 | logic */ |
---|
| 1371 | alfa = (dir > 0 ? + val[t] : - val[t]); |
---|
| 1372 | /* analyze main cases */ |
---|
| 1373 | if (type == GLP_FR) |
---|
| 1374 | { /* xB[i] is free variable */ |
---|
| 1375 | continue; |
---|
| 1376 | } |
---|
| 1377 | else if (type == GLP_LO) |
---|
| 1378 | lo: { /* xB[i] has an lower bound */ |
---|
| 1379 | if (alfa > - eps) continue; |
---|
| 1380 | temp = (lb - beta) / alfa; |
---|
| 1381 | } |
---|
| 1382 | else if (type == GLP_UP) |
---|
| 1383 | up: { /* xB[i] has an upper bound */ |
---|
| 1384 | if (alfa < + eps) continue; |
---|
| 1385 | temp = (ub - beta) / alfa; |
---|
| 1386 | } |
---|
| 1387 | else if (type == GLP_DB) |
---|
| 1388 | { /* xB[i] has both lower and upper bounds */ |
---|
| 1389 | if (alfa < 0.0) goto lo; else goto up; |
---|
| 1390 | } |
---|
| 1391 | else if (type == GLP_FX) |
---|
| 1392 | { /* xB[i] is fixed variable */ |
---|
| 1393 | if (- eps < alfa && alfa < + eps) continue; |
---|
| 1394 | temp = 0.0; |
---|
| 1395 | } |
---|
| 1396 | else |
---|
| 1397 | xassert(type != type); |
---|
| 1398 | /* if the value of the variable xB[i] violates its lower or |
---|
| 1399 | upper bound (slightly, because the current basis is assumed |
---|
| 1400 | to be primal feasible), temp is negative; we can think this |
---|
| 1401 | happens due to round-off errors and the value is exactly on |
---|
| 1402 | the bound; this allows replacing temp by zero */ |
---|
| 1403 | if (temp < 0.0) temp = 0.0; |
---|
| 1404 | /* apply the minimal ratio test */ |
---|
| 1405 | if (teta > temp || teta == temp && big < fabs(alfa)) |
---|
| 1406 | piv = t, teta = temp, big = fabs(alfa); |
---|
| 1407 | } |
---|
| 1408 | /* return index of the pivot element chosen */ |
---|
| 1409 | return piv; |
---|
| 1410 | } |
---|
| 1411 | |
---|
| 1412 | /*********************************************************************** |
---|
| 1413 | * NAME |
---|
| 1414 | * |
---|
| 1415 | * glp_dual_rtest - perform dual ratio test |
---|
| 1416 | * |
---|
| 1417 | * SYNOPSIS |
---|
| 1418 | * |
---|
| 1419 | * int glp_dual_rtest(glp_prob *P, int len, const int ind[], |
---|
| 1420 | * const double val[], int dir, double eps); |
---|
| 1421 | * |
---|
| 1422 | * DESCRIPTION |
---|
| 1423 | * |
---|
| 1424 | * The routine glp_dual_rtest performs the dual ratio test using an |
---|
| 1425 | * explicitly specified row of the simplex table. |
---|
| 1426 | * |
---|
| 1427 | * The current basic solution associated with the LP problem object |
---|
| 1428 | * must be dual feasible. |
---|
| 1429 | * |
---|
| 1430 | * The explicitly specified row of the simplex table is a linear form |
---|
| 1431 | * that shows how some basic variable x (which is not necessarily |
---|
| 1432 | * presented in the problem object) depends on non-basic variables xN: |
---|
| 1433 | * |
---|
| 1434 | * x = alfa[1] * xN[1] + alfa[2] * xN[2] + ... + alfa[n] * xN[n]. (*) |
---|
| 1435 | * |
---|
| 1436 | * The row (*) is specified on entry to the routine using the sparse |
---|
| 1437 | * format. Ordinal numbers of non-basic variables xN[j] should be placed |
---|
| 1438 | * in locations ind[1], ..., ind[len], where ordinal numbers 1 to m |
---|
| 1439 | * denote auxiliary variables, and ordinal numbers m+1 to m+n denote |
---|
| 1440 | * structural variables. The corresponding non-zero coefficients alfa[j] |
---|
| 1441 | * should be placed in locations val[1], ..., val[len]. The arrays ind |
---|
| 1442 | * and val are not changed on exit. |
---|
| 1443 | * |
---|
| 1444 | * The parameter dir specifies direction in which the variable x changes |
---|
| 1445 | * on leaving the basis: +1 means that x goes to its lower bound, and -1 |
---|
| 1446 | * means that x goes to its upper bound. |
---|
| 1447 | * |
---|
| 1448 | * The parameter eps is an absolute tolerance (small positive number) |
---|
| 1449 | * used by the routine to skip small alfa[j] of the row (*). |
---|
| 1450 | * |
---|
| 1451 | * The routine determines which non-basic variable (among specified in |
---|
| 1452 | * ind[1], ..., ind[len]) should enter the basis in order to keep dual |
---|
| 1453 | * feasibility. |
---|
| 1454 | * |
---|
| 1455 | * RETURNS |
---|
| 1456 | * |
---|
| 1457 | * The routine glp_dual_rtest returns the index piv in the arrays ind |
---|
| 1458 | * and val corresponding to the pivot element chosen, 1 <= piv <= len. |
---|
| 1459 | * If the adjacent basic solution is dual unbounded and therefore the |
---|
| 1460 | * choice cannot be made, the routine returns zero. |
---|
| 1461 | * |
---|
| 1462 | * COMMENTS |
---|
| 1463 | * |
---|
| 1464 | * If the basic variable x is presented in the LP problem object, the |
---|
| 1465 | * row (*) can be computed with the routine glp_eval_tab_row; otherwise |
---|
| 1466 | * it can be computed with the routine glp_transform_row. */ |
---|
| 1467 | |
---|
| 1468 | int glp_dual_rtest(glp_prob *P, int len, const int ind[], |
---|
| 1469 | const double val[], int dir, double eps) |
---|
| 1470 | { int k, m, n, piv, t, stat; |
---|
| 1471 | double alfa, big, cost, obj, temp, teta; |
---|
| 1472 | if (glp_get_dual_stat(P) != GLP_FEAS) |
---|
| 1473 | xerror("glp_dual_rtest: basic solution is not dual feasible\n") |
---|
| 1474 | ; |
---|
| 1475 | if (!(dir == +1 || dir == -1)) |
---|
| 1476 | xerror("glp_dual_rtest: dir = %d; invalid parameter\n", dir); |
---|
| 1477 | if (!(0.0 < eps && eps < 1.0)) |
---|
| 1478 | xerror("glp_dual_rtest: eps = %g; invalid parameter\n", eps); |
---|
| 1479 | m = glp_get_num_rows(P); |
---|
| 1480 | n = glp_get_num_cols(P); |
---|
| 1481 | /* take into account optimization direction */ |
---|
| 1482 | obj = (glp_get_obj_dir(P) == GLP_MIN ? +1.0 : -1.0); |
---|
| 1483 | /* initial settings */ |
---|
| 1484 | piv = 0, teta = DBL_MAX, big = 0.0; |
---|
| 1485 | /* walk through the entries of the specified row */ |
---|
| 1486 | for (t = 1; t <= len; t++) |
---|
| 1487 | { /* get ordinal number of non-basic variable */ |
---|
| 1488 | k = ind[t]; |
---|
| 1489 | if (!(1 <= k && k <= m+n)) |
---|
| 1490 | xerror("glp_dual_rtest: ind[%d] = %d; variable number out o" |
---|
| 1491 | "f range\n", t, k); |
---|
| 1492 | /* determine status and reduced cost of non-basic variable |
---|
| 1493 | x[k] = xN[j] in the current basic solution */ |
---|
| 1494 | if (k <= m) |
---|
| 1495 | { stat = glp_get_row_stat(P, k); |
---|
| 1496 | cost = glp_get_row_dual(P, k); |
---|
| 1497 | } |
---|
| 1498 | else |
---|
| 1499 | { stat = glp_get_col_stat(P, k-m); |
---|
| 1500 | cost = glp_get_col_dual(P, k-m); |
---|
| 1501 | } |
---|
| 1502 | if (stat == GLP_BS) |
---|
| 1503 | xerror("glp_dual_rtest: ind[%d] = %d; basic variable not al" |
---|
| 1504 | "lowed\n", t, k); |
---|
| 1505 | /* determine influence coefficient at non-basic variable xN[j] |
---|
| 1506 | in the explicitly specified row and turn to the case of |
---|
| 1507 | increasing the variable x in order to simplify the program |
---|
| 1508 | logic */ |
---|
| 1509 | alfa = (dir > 0 ? + val[t] : - val[t]); |
---|
| 1510 | /* analyze main cases */ |
---|
| 1511 | if (stat == GLP_NL) |
---|
| 1512 | { /* xN[j] is on its lower bound */ |
---|
| 1513 | if (alfa < + eps) continue; |
---|
| 1514 | temp = (obj * cost) / alfa; |
---|
| 1515 | } |
---|
| 1516 | else if (stat == GLP_NU) |
---|
| 1517 | { /* xN[j] is on its upper bound */ |
---|
| 1518 | if (alfa > - eps) continue; |
---|
| 1519 | temp = (obj * cost) / alfa; |
---|
| 1520 | } |
---|
| 1521 | else if (stat == GLP_NF) |
---|
| 1522 | { /* xN[j] is non-basic free variable */ |
---|
| 1523 | if (- eps < alfa && alfa < + eps) continue; |
---|
| 1524 | temp = 0.0; |
---|
| 1525 | } |
---|
| 1526 | else if (stat == GLP_NS) |
---|
| 1527 | { /* xN[j] is non-basic fixed variable */ |
---|
| 1528 | continue; |
---|
| 1529 | } |
---|
| 1530 | else |
---|
| 1531 | xassert(stat != stat); |
---|
| 1532 | /* if the reduced cost of the variable xN[j] violates its zero |
---|
| 1533 | bound (slightly, because the current basis is assumed to be |
---|
| 1534 | dual feasible), temp is negative; we can think this happens |
---|
| 1535 | due to round-off errors and the reduced cost is exact zero; |
---|
| 1536 | this allows replacing temp by zero */ |
---|
| 1537 | if (temp < 0.0) temp = 0.0; |
---|
| 1538 | /* apply the minimal ratio test */ |
---|
| 1539 | if (teta > temp || teta == temp && big < fabs(alfa)) |
---|
| 1540 | piv = t, teta = temp, big = fabs(alfa); |
---|
| 1541 | } |
---|
| 1542 | /* return index of the pivot element chosen */ |
---|
| 1543 | return piv; |
---|
| 1544 | } |
---|
| 1545 | |
---|
| 1546 | /*********************************************************************** |
---|
| 1547 | * NAME |
---|
| 1548 | * |
---|
| 1549 | * glp_analyze_row - simulate one iteration of dual simplex method |
---|
| 1550 | * |
---|
| 1551 | * SYNOPSIS |
---|
| 1552 | * |
---|
| 1553 | * int glp_analyze_row(glp_prob *P, int len, const int ind[], |
---|
| 1554 | * const double val[], int type, double rhs, double eps, int *piv, |
---|
| 1555 | * double *x, double *dx, double *y, double *dy, double *dz); |
---|
| 1556 | * |
---|
| 1557 | * DESCRIPTION |
---|
| 1558 | * |
---|
| 1559 | * Let the current basis be optimal or dual feasible, and there be |
---|
| 1560 | * specified a row (constraint), which is violated by the current basic |
---|
| 1561 | * solution. The routine glp_analyze_row simulates one iteration of the |
---|
| 1562 | * dual simplex method to determine some information on the adjacent |
---|
| 1563 | * basis (see below), where the specified row becomes active constraint |
---|
| 1564 | * (i.e. its auxiliary variable becomes non-basic). |
---|
| 1565 | * |
---|
| 1566 | * The current basic solution associated with the problem object passed |
---|
| 1567 | * to the routine must be dual feasible, and its primal components must |
---|
| 1568 | * be defined. |
---|
| 1569 | * |
---|
| 1570 | * The row to be analyzed must be previously transformed either with |
---|
| 1571 | * the routine glp_eval_tab_row (if the row is in the problem object) |
---|
| 1572 | * or with the routine glp_transform_row (if the row is external, i.e. |
---|
| 1573 | * not in the problem object). This is needed to express the row only |
---|
| 1574 | * through (auxiliary and structural) variables, which are non-basic in |
---|
| 1575 | * the current basis: |
---|
| 1576 | * |
---|
| 1577 | * y = alfa[1] * xN[1] + alfa[2] * xN[2] + ... + alfa[n] * xN[n], |
---|
| 1578 | * |
---|
| 1579 | * where y is an auxiliary variable of the row, alfa[j] is an influence |
---|
| 1580 | * coefficient, xN[j] is a non-basic variable. |
---|
| 1581 | * |
---|
| 1582 | * The row is passed to the routine in sparse format. Ordinal numbers |
---|
| 1583 | * of non-basic variables are stored in locations ind[1], ..., ind[len], |
---|
| 1584 | * where numbers 1 to m denote auxiliary variables while numbers m+1 to |
---|
| 1585 | * m+n denote structural variables. Corresponding non-zero coefficients |
---|
| 1586 | * alfa[j] are stored in locations val[1], ..., val[len]. The arrays |
---|
| 1587 | * ind and val are ot changed on exit. |
---|
| 1588 | * |
---|
| 1589 | * The parameters type and rhs specify the row type and its right-hand |
---|
| 1590 | * side as follows: |
---|
| 1591 | * |
---|
| 1592 | * type = GLP_LO: y = sum alfa[j] * xN[j] >= rhs |
---|
| 1593 | * |
---|
| 1594 | * type = GLP_UP: y = sum alfa[j] * xN[j] <= rhs |
---|
| 1595 | * |
---|
| 1596 | * The parameter eps is an absolute tolerance (small positive number) |
---|
| 1597 | * used by the routine to skip small coefficients alfa[j] on performing |
---|
| 1598 | * the dual ratio test. |
---|
| 1599 | * |
---|
| 1600 | * If the operation was successful, the routine stores the following |
---|
| 1601 | * information to corresponding location (if some parameter is NULL, |
---|
| 1602 | * its value is not stored): |
---|
| 1603 | * |
---|
| 1604 | * piv index in the array ind and val, 1 <= piv <= len, determining |
---|
| 1605 | * the non-basic variable, which would enter the adjacent basis; |
---|
| 1606 | * |
---|
| 1607 | * x value of the non-basic variable in the current basis; |
---|
| 1608 | * |
---|
| 1609 | * dx difference between values of the non-basic variable in the |
---|
| 1610 | * adjacent and current bases, dx = x.new - x.old; |
---|
| 1611 | * |
---|
| 1612 | * y value of the row (i.e. of its auxiliary variable) in the |
---|
| 1613 | * current basis; |
---|
| 1614 | * |
---|
| 1615 | * dy difference between values of the row in the adjacent and |
---|
| 1616 | * current bases, dy = y.new - y.old; |
---|
| 1617 | * |
---|
| 1618 | * dz difference between values of the objective function in the |
---|
| 1619 | * adjacent and current bases, dz = z.new - z.old. Note that in |
---|
| 1620 | * case of minimization dz >= 0, and in case of maximization |
---|
| 1621 | * dz <= 0, i.e. in the adjacent basis the objective function |
---|
| 1622 | * always gets worse (degrades). */ |
---|
| 1623 | |
---|
| 1624 | int _glp_analyze_row(glp_prob *P, int len, const int ind[], |
---|
| 1625 | const double val[], int type, double rhs, double eps, int *_piv, |
---|
| 1626 | double *_x, double *_dx, double *_y, double *_dy, double *_dz) |
---|
| 1627 | { int t, k, dir, piv, ret = 0; |
---|
| 1628 | double x, dx, y, dy, dz; |
---|
| 1629 | if (P->pbs_stat == GLP_UNDEF) |
---|
| 1630 | xerror("glp_analyze_row: primal basic solution components are " |
---|
| 1631 | "undefined\n"); |
---|
| 1632 | if (P->dbs_stat != GLP_FEAS) |
---|
| 1633 | xerror("glp_analyze_row: basic solution is not dual feasible\n" |
---|
| 1634 | ); |
---|
| 1635 | /* compute the row value y = sum alfa[j] * xN[j] in the current |
---|
| 1636 | basis */ |
---|
| 1637 | if (!(0 <= len && len <= P->n)) |
---|
| 1638 | xerror("glp_analyze_row: len = %d; invalid row length\n", len); |
---|
| 1639 | y = 0.0; |
---|
| 1640 | for (t = 1; t <= len; t++) |
---|
| 1641 | { /* determine value of x[k] = xN[j] in the current basis */ |
---|
| 1642 | k = ind[t]; |
---|
| 1643 | if (!(1 <= k && k <= P->m+P->n)) |
---|
| 1644 | xerror("glp_analyze_row: ind[%d] = %d; row/column index out" |
---|
| 1645 | " of range\n", t, k); |
---|
| 1646 | if (k <= P->m) |
---|
| 1647 | { /* x[k] is auxiliary variable */ |
---|
| 1648 | if (P->row[k]->stat == GLP_BS) |
---|
| 1649 | xerror("glp_analyze_row: ind[%d] = %d; basic auxiliary v" |
---|
| 1650 | "ariable is not allowed\n", t, k); |
---|
| 1651 | x = P->row[k]->prim; |
---|
| 1652 | } |
---|
| 1653 | else |
---|
| 1654 | { /* x[k] is structural variable */ |
---|
| 1655 | if (P->col[k-P->m]->stat == GLP_BS) |
---|
| 1656 | xerror("glp_analyze_row: ind[%d] = %d; basic structural " |
---|
| 1657 | "variable is not allowed\n", t, k); |
---|
| 1658 | x = P->col[k-P->m]->prim; |
---|
| 1659 | } |
---|
| 1660 | y += val[t] * x; |
---|
| 1661 | } |
---|
| 1662 | /* check if the row is primal infeasible in the current basis, |
---|
| 1663 | i.e. the constraint is violated at the current point */ |
---|
| 1664 | if (type == GLP_LO) |
---|
| 1665 | { if (y >= rhs) |
---|
| 1666 | { /* the constraint is not violated */ |
---|
| 1667 | ret = 1; |
---|
| 1668 | goto done; |
---|
| 1669 | } |
---|
| 1670 | /* in the adjacent basis y goes to its lower bound */ |
---|
| 1671 | dir = +1; |
---|
| 1672 | } |
---|
| 1673 | else if (type == GLP_UP) |
---|
| 1674 | { if (y <= rhs) |
---|
| 1675 | { /* the constraint is not violated */ |
---|
| 1676 | ret = 1; |
---|
| 1677 | goto done; |
---|
| 1678 | } |
---|
| 1679 | /* in the adjacent basis y goes to its upper bound */ |
---|
| 1680 | dir = -1; |
---|
| 1681 | } |
---|
| 1682 | else |
---|
| 1683 | xerror("glp_analyze_row: type = %d; invalid parameter\n", |
---|
| 1684 | type); |
---|
| 1685 | /* compute dy = y.new - y.old */ |
---|
| 1686 | dy = rhs - y; |
---|
| 1687 | /* perform dual ratio test to determine which non-basic variable |
---|
| 1688 | should enter the adjacent basis to keep it dual feasible */ |
---|
| 1689 | piv = glp_dual_rtest(P, len, ind, val, dir, eps); |
---|
| 1690 | if (piv == 0) |
---|
| 1691 | { /* no dual feasible adjacent basis exists */ |
---|
| 1692 | ret = 2; |
---|
| 1693 | goto done; |
---|
| 1694 | } |
---|
| 1695 | /* non-basic variable x[k] = xN[j] should enter the basis */ |
---|
| 1696 | k = ind[piv]; |
---|
| 1697 | xassert(1 <= k && k <= P->m+P->n); |
---|
| 1698 | /* determine its value in the current basis */ |
---|
| 1699 | if (k <= P->m) |
---|
| 1700 | x = P->row[k]->prim; |
---|
| 1701 | else |
---|
| 1702 | x = P->col[k-P->m]->prim; |
---|
| 1703 | /* compute dx = x.new - x.old = dy / alfa[j] */ |
---|
| 1704 | xassert(val[piv] != 0.0); |
---|
| 1705 | dx = dy / val[piv]; |
---|
| 1706 | /* compute dz = z.new - z.old = d[j] * dx, where d[j] is reduced |
---|
| 1707 | cost of xN[j] in the current basis */ |
---|
| 1708 | if (k <= P->m) |
---|
| 1709 | dz = P->row[k]->dual * dx; |
---|
| 1710 | else |
---|
| 1711 | dz = P->col[k-P->m]->dual * dx; |
---|
| 1712 | /* store the analysis results */ |
---|
| 1713 | if (_piv != NULL) *_piv = piv; |
---|
| 1714 | if (_x != NULL) *_x = x; |
---|
| 1715 | if (_dx != NULL) *_dx = dx; |
---|
| 1716 | if (_y != NULL) *_y = y; |
---|
| 1717 | if (_dy != NULL) *_dy = dy; |
---|
| 1718 | if (_dz != NULL) *_dz = dz; |
---|
| 1719 | done: return ret; |
---|
| 1720 | } |
---|
| 1721 | |
---|
| 1722 | #if 0 |
---|
| 1723 | int main(void) |
---|
| 1724 | { /* example program for the routine glp_analyze_row */ |
---|
| 1725 | glp_prob *P; |
---|
| 1726 | glp_smcp parm; |
---|
| 1727 | int i, k, len, piv, ret, ind[1+100]; |
---|
| 1728 | double rhs, x, dx, y, dy, dz, val[1+100]; |
---|
| 1729 | P = glp_create_prob(); |
---|
| 1730 | /* read plan.mps (see glpk/examples) */ |
---|
| 1731 | ret = glp_read_mps(P, GLP_MPS_DECK, NULL, "plan.mps"); |
---|
| 1732 | glp_assert(ret == 0); |
---|
| 1733 | /* and solve it to optimality */ |
---|
| 1734 | ret = glp_simplex(P, NULL); |
---|
| 1735 | glp_assert(ret == 0); |
---|
| 1736 | glp_assert(glp_get_status(P) == GLP_OPT); |
---|
| 1737 | /* the optimal objective value is 296.217 */ |
---|
| 1738 | /* we would like to know what happens if we would add a new row |
---|
| 1739 | (constraint) to plan.mps: |
---|
| 1740 | .01 * bin1 + .01 * bin2 + .02 * bin4 + .02 * bin5 <= 12 */ |
---|
| 1741 | /* first, we specify this new row */ |
---|
| 1742 | glp_create_index(P); |
---|
| 1743 | len = 0; |
---|
| 1744 | ind[++len] = glp_find_col(P, "BIN1"), val[len] = .01; |
---|
| 1745 | ind[++len] = glp_find_col(P, "BIN2"), val[len] = .01; |
---|
| 1746 | ind[++len] = glp_find_col(P, "BIN4"), val[len] = .02; |
---|
| 1747 | ind[++len] = glp_find_col(P, "BIN5"), val[len] = .02; |
---|
| 1748 | rhs = 12; |
---|
| 1749 | /* then we can compute value of the row (i.e. of its auxiliary |
---|
| 1750 | variable) in the current basis to see if the constraint is |
---|
| 1751 | violated */ |
---|
| 1752 | y = 0.0; |
---|
| 1753 | for (k = 1; k <= len; k++) |
---|
| 1754 | y += val[k] * glp_get_col_prim(P, ind[k]); |
---|
| 1755 | glp_printf("y = %g\n", y); |
---|
| 1756 | /* this prints y = 15.1372, so the constraint is violated, since |
---|
| 1757 | we require that y <= rhs = 12 */ |
---|
| 1758 | /* now we transform the row to express it only through non-basic |
---|
| 1759 | (auxiliary and artificial) variables */ |
---|
| 1760 | len = glp_transform_row(P, len, ind, val); |
---|
| 1761 | /* finally, we simulate one step of the dual simplex method to |
---|
| 1762 | obtain necessary information for the adjacent basis */ |
---|
| 1763 | ret = _glp_analyze_row(P, len, ind, val, GLP_UP, rhs, 1e-9, &piv, |
---|
| 1764 | &x, &dx, &y, &dy, &dz); |
---|
| 1765 | glp_assert(ret == 0); |
---|
| 1766 | glp_printf("k = %d, x = %g; dx = %g; y = %g; dy = %g; dz = %g\n", |
---|
| 1767 | ind[piv], x, dx, y, dy, dz); |
---|
| 1768 | /* this prints dz = 5.64418 and means that in the adjacent basis |
---|
| 1769 | the objective function would be 296.217 + 5.64418 = 301.861 */ |
---|
| 1770 | /* now we actually include the row into the problem object; note |
---|
| 1771 | that the arrays ind and val are clobbered, so we need to build |
---|
| 1772 | them once again */ |
---|
| 1773 | len = 0; |
---|
| 1774 | ind[++len] = glp_find_col(P, "BIN1"), val[len] = .01; |
---|
| 1775 | ind[++len] = glp_find_col(P, "BIN2"), val[len] = .01; |
---|
| 1776 | ind[++len] = glp_find_col(P, "BIN4"), val[len] = .02; |
---|
| 1777 | ind[++len] = glp_find_col(P, "BIN5"), val[len] = .02; |
---|
| 1778 | rhs = 12; |
---|
| 1779 | i = glp_add_rows(P, 1); |
---|
| 1780 | glp_set_row_bnds(P, i, GLP_UP, 0, rhs); |
---|
| 1781 | glp_set_mat_row(P, i, len, ind, val); |
---|
| 1782 | /* and perform one dual simplex iteration */ |
---|
| 1783 | glp_init_smcp(&parm); |
---|
| 1784 | parm.meth = GLP_DUAL; |
---|
| 1785 | parm.it_lim = 1; |
---|
| 1786 | glp_simplex(P, &parm); |
---|
| 1787 | /* the current objective value is 301.861 */ |
---|
| 1788 | return 0; |
---|
| 1789 | } |
---|
| 1790 | #endif |
---|
| 1791 | |
---|
| 1792 | /*********************************************************************** |
---|
| 1793 | * NAME |
---|
| 1794 | * |
---|
| 1795 | * glp_analyze_bound - analyze active bound of non-basic variable |
---|
| 1796 | * |
---|
| 1797 | * SYNOPSIS |
---|
| 1798 | * |
---|
| 1799 | * void glp_analyze_bound(glp_prob *P, int k, double *limit1, int *var1, |
---|
| 1800 | * double *limit2, int *var2); |
---|
| 1801 | * |
---|
| 1802 | * DESCRIPTION |
---|
| 1803 | * |
---|
| 1804 | * The routine glp_analyze_bound analyzes the effect of varying the |
---|
| 1805 | * active bound of specified non-basic variable. |
---|
| 1806 | * |
---|
| 1807 | * The non-basic variable is specified by the parameter k, where |
---|
| 1808 | * 1 <= k <= m means auxiliary variable of corresponding row while |
---|
| 1809 | * m+1 <= k <= m+n means structural variable (column). |
---|
| 1810 | * |
---|
| 1811 | * Note that the current basic solution must be optimal, and the basis |
---|
| 1812 | * factorization must exist. |
---|
| 1813 | * |
---|
| 1814 | * Results of the analysis have the following meaning. |
---|
| 1815 | * |
---|
| 1816 | * value1 is the minimal value of the active bound, at which the basis |
---|
| 1817 | * still remains primal feasible and thus optimal. -DBL_MAX means that |
---|
| 1818 | * the active bound has no lower limit. |
---|
| 1819 | * |
---|
| 1820 | * var1 is the ordinal number of an auxiliary (1 to m) or structural |
---|
| 1821 | * (m+1 to n) basic variable, which reaches its bound first and thereby |
---|
| 1822 | * limits further decreasing the active bound being analyzed. |
---|
| 1823 | * if value1 = -DBL_MAX, var1 is set to 0. |
---|
| 1824 | * |
---|
| 1825 | * value2 is the maximal value of the active bound, at which the basis |
---|
| 1826 | * still remains primal feasible and thus optimal. +DBL_MAX means that |
---|
| 1827 | * the active bound has no upper limit. |
---|
| 1828 | * |
---|
| 1829 | * var2 is the ordinal number of an auxiliary (1 to m) or structural |
---|
| 1830 | * (m+1 to n) basic variable, which reaches its bound first and thereby |
---|
| 1831 | * limits further increasing the active bound being analyzed. |
---|
| 1832 | * if value2 = +DBL_MAX, var2 is set to 0. */ |
---|
| 1833 | |
---|
| 1834 | void glp_analyze_bound(glp_prob *P, int k, double *value1, int *var1, |
---|
| 1835 | double *value2, int *var2) |
---|
| 1836 | { GLPROW *row; |
---|
| 1837 | GLPCOL *col; |
---|
| 1838 | int m, n, stat, kase, p, len, piv, *ind; |
---|
| 1839 | double x, new_x, ll, uu, xx, delta, *val; |
---|
| 1840 | /* sanity checks */ |
---|
| 1841 | if (P == NULL || P->magic != GLP_PROB_MAGIC) |
---|
| 1842 | xerror("glp_analyze_bound: P = %p; invalid problem object\n", |
---|
| 1843 | P); |
---|
| 1844 | m = P->m, n = P->n; |
---|
| 1845 | if (!(P->pbs_stat == GLP_FEAS && P->dbs_stat == GLP_FEAS)) |
---|
| 1846 | xerror("glp_analyze_bound: optimal basic solution required\n"); |
---|
| 1847 | if (!(m == 0 || P->valid)) |
---|
| 1848 | xerror("glp_analyze_bound: basis factorization required\n"); |
---|
| 1849 | if (!(1 <= k && k <= m+n)) |
---|
| 1850 | xerror("glp_analyze_bound: k = %d; variable number out of rang" |
---|
| 1851 | "e\n", k); |
---|
| 1852 | /* retrieve information about the specified non-basic variable |
---|
| 1853 | x[k] whose active bound is to be analyzed */ |
---|
| 1854 | if (k <= m) |
---|
| 1855 | { row = P->row[k]; |
---|
| 1856 | stat = row->stat; |
---|
| 1857 | x = row->prim; |
---|
| 1858 | } |
---|
| 1859 | else |
---|
| 1860 | { col = P->col[k-m]; |
---|
| 1861 | stat = col->stat; |
---|
| 1862 | x = col->prim; |
---|
| 1863 | } |
---|
| 1864 | if (stat == GLP_BS) |
---|
| 1865 | xerror("glp_analyze_bound: k = %d; basic variable not allowed " |
---|
| 1866 | "\n", k); |
---|
| 1867 | /* allocate working arrays */ |
---|
| 1868 | ind = xcalloc(1+m, sizeof(int)); |
---|
| 1869 | val = xcalloc(1+m, sizeof(double)); |
---|
| 1870 | /* compute column of the simplex table corresponding to the |
---|
| 1871 | non-basic variable x[k] */ |
---|
| 1872 | len = glp_eval_tab_col(P, k, ind, val); |
---|
| 1873 | xassert(0 <= len && len <= m); |
---|
| 1874 | /* perform analysis */ |
---|
| 1875 | for (kase = -1; kase <= +1; kase += 2) |
---|
| 1876 | { /* kase < 0 means active bound of x[k] is decreasing; |
---|
| 1877 | kase > 0 means active bound of x[k] is increasing */ |
---|
| 1878 | /* use the primal ratio test to determine some basic variable |
---|
| 1879 | x[p] which reaches its bound first */ |
---|
| 1880 | piv = glp_prim_rtest(P, len, ind, val, kase, 1e-9); |
---|
| 1881 | if (piv == 0) |
---|
| 1882 | { /* nothing limits changing the active bound of x[k] */ |
---|
| 1883 | p = 0; |
---|
| 1884 | new_x = (kase < 0 ? -DBL_MAX : +DBL_MAX); |
---|
| 1885 | goto store; |
---|
| 1886 | } |
---|
| 1887 | /* basic variable x[p] limits changing the active bound of |
---|
| 1888 | x[k]; determine its value in the current basis */ |
---|
| 1889 | xassert(1 <= piv && piv <= len); |
---|
| 1890 | p = ind[piv]; |
---|
| 1891 | if (p <= m) |
---|
| 1892 | { row = P->row[p]; |
---|
| 1893 | ll = glp_get_row_lb(P, row->i); |
---|
| 1894 | uu = glp_get_row_ub(P, row->i); |
---|
| 1895 | stat = row->stat; |
---|
| 1896 | xx = row->prim; |
---|
| 1897 | } |
---|
| 1898 | else |
---|
| 1899 | { col = P->col[p-m]; |
---|
| 1900 | ll = glp_get_col_lb(P, col->j); |
---|
| 1901 | uu = glp_get_col_ub(P, col->j); |
---|
| 1902 | stat = col->stat; |
---|
| 1903 | xx = col->prim; |
---|
| 1904 | } |
---|
| 1905 | xassert(stat == GLP_BS); |
---|
| 1906 | /* determine delta x[p] = bound of x[p] - value of x[p] */ |
---|
| 1907 | if (kase < 0 && val[piv] > 0.0 || |
---|
| 1908 | kase > 0 && val[piv] < 0.0) |
---|
| 1909 | { /* delta x[p] < 0, so x[p] goes toward its lower bound */ |
---|
| 1910 | xassert(ll != -DBL_MAX); |
---|
| 1911 | delta = ll - xx; |
---|
| 1912 | } |
---|
| 1913 | else |
---|
| 1914 | { /* delta x[p] > 0, so x[p] goes toward its upper bound */ |
---|
| 1915 | xassert(uu != +DBL_MAX); |
---|
| 1916 | delta = uu - xx; |
---|
| 1917 | } |
---|
| 1918 | /* delta x[p] = alfa[p,k] * delta x[k], so new x[k] = x[k] + |
---|
| 1919 | delta x[k] = x[k] + delta x[p] / alfa[p,k] is the value of |
---|
| 1920 | x[k] in the adjacent basis */ |
---|
| 1921 | xassert(val[piv] != 0.0); |
---|
| 1922 | new_x = x + delta / val[piv]; |
---|
| 1923 | store: /* store analysis results */ |
---|
| 1924 | if (kase < 0) |
---|
| 1925 | { if (value1 != NULL) *value1 = new_x; |
---|
| 1926 | if (var1 != NULL) *var1 = p; |
---|
| 1927 | } |
---|
| 1928 | else |
---|
| 1929 | { if (value2 != NULL) *value2 = new_x; |
---|
| 1930 | if (var2 != NULL) *var2 = p; |
---|
| 1931 | } |
---|
| 1932 | } |
---|
| 1933 | /* free working arrays */ |
---|
| 1934 | xfree(ind); |
---|
| 1935 | xfree(val); |
---|
| 1936 | return; |
---|
| 1937 | } |
---|
| 1938 | |
---|
| 1939 | /*********************************************************************** |
---|
| 1940 | * NAME |
---|
| 1941 | * |
---|
| 1942 | * glp_analyze_coef - analyze objective coefficient at basic variable |
---|
| 1943 | * |
---|
| 1944 | * SYNOPSIS |
---|
| 1945 | * |
---|
| 1946 | * void glp_analyze_coef(glp_prob *P, int k, double *coef1, int *var1, |
---|
| 1947 | * double *value1, double *coef2, int *var2, double *value2); |
---|
| 1948 | * |
---|
| 1949 | * DESCRIPTION |
---|
| 1950 | * |
---|
| 1951 | * The routine glp_analyze_coef analyzes the effect of varying the |
---|
| 1952 | * objective coefficient at specified basic variable. |
---|
| 1953 | * |
---|
| 1954 | * The basic variable is specified by the parameter k, where |
---|
| 1955 | * 1 <= k <= m means auxiliary variable of corresponding row while |
---|
| 1956 | * m+1 <= k <= m+n means structural variable (column). |
---|
| 1957 | * |
---|
| 1958 | * Note that the current basic solution must be optimal, and the basis |
---|
| 1959 | * factorization must exist. |
---|
| 1960 | * |
---|
| 1961 | * Results of the analysis have the following meaning. |
---|
| 1962 | * |
---|
| 1963 | * coef1 is the minimal value of the objective coefficient, at which |
---|
| 1964 | * the basis still remains dual feasible and thus optimal. -DBL_MAX |
---|
| 1965 | * means that the objective coefficient has no lower limit. |
---|
| 1966 | * |
---|
| 1967 | * var1 is the ordinal number of an auxiliary (1 to m) or structural |
---|
| 1968 | * (m+1 to n) non-basic variable, whose reduced cost reaches its zero |
---|
| 1969 | * bound first and thereby limits further decreasing the objective |
---|
| 1970 | * coefficient being analyzed. If coef1 = -DBL_MAX, var1 is set to 0. |
---|
| 1971 | * |
---|
| 1972 | * value1 is value of the basic variable being analyzed in an adjacent |
---|
| 1973 | * basis, which is defined as follows. Let the objective coefficient |
---|
| 1974 | * reaches its minimal value (coef1) and continues decreasing. Then the |
---|
| 1975 | * reduced cost of the limiting non-basic variable (var1) becomes dual |
---|
| 1976 | * infeasible and the current basis becomes non-optimal that forces the |
---|
| 1977 | * limiting non-basic variable to enter the basis replacing there some |
---|
| 1978 | * basic variable that leaves the basis to keep primal feasibility. |
---|
| 1979 | * Should note that on determining the adjacent basis current bounds |
---|
| 1980 | * of the basic variable being analyzed are ignored as if it were free |
---|
| 1981 | * (unbounded) variable, so it cannot leave the basis. It may happen |
---|
| 1982 | * that no dual feasible adjacent basis exists, in which case value1 is |
---|
| 1983 | * set to -DBL_MAX or +DBL_MAX. |
---|
| 1984 | * |
---|
| 1985 | * coef2 is the maximal value of the objective coefficient, at which |
---|
| 1986 | * the basis still remains dual feasible and thus optimal. +DBL_MAX |
---|
| 1987 | * means that the objective coefficient has no upper limit. |
---|
| 1988 | * |
---|
| 1989 | * var2 is the ordinal number of an auxiliary (1 to m) or structural |
---|
| 1990 | * (m+1 to n) non-basic variable, whose reduced cost reaches its zero |
---|
| 1991 | * bound first and thereby limits further increasing the objective |
---|
| 1992 | * coefficient being analyzed. If coef2 = +DBL_MAX, var2 is set to 0. |
---|
| 1993 | * |
---|
| 1994 | * value2 is value of the basic variable being analyzed in an adjacent |
---|
| 1995 | * basis, which is defined exactly in the same way as value1 above with |
---|
| 1996 | * exception that now the objective coefficient is increasing. */ |
---|
| 1997 | |
---|
| 1998 | void glp_analyze_coef(glp_prob *P, int k, double *coef1, int *var1, |
---|
| 1999 | double *value1, double *coef2, int *var2, double *value2) |
---|
| 2000 | { GLPROW *row; GLPCOL *col; |
---|
| 2001 | int m, n, type, stat, kase, p, q, dir, clen, cpiv, rlen, rpiv, |
---|
| 2002 | *cind, *rind; |
---|
| 2003 | double lb, ub, coef, x, lim_coef, new_x, d, delta, ll, uu, xx, |
---|
| 2004 | *rval, *cval; |
---|
| 2005 | /* sanity checks */ |
---|
| 2006 | if (P == NULL || P->magic != GLP_PROB_MAGIC) |
---|
| 2007 | xerror("glp_analyze_coef: P = %p; invalid problem object\n", |
---|
| 2008 | P); |
---|
| 2009 | m = P->m, n = P->n; |
---|
| 2010 | if (!(P->pbs_stat == GLP_FEAS && P->dbs_stat == GLP_FEAS)) |
---|
| 2011 | xerror("glp_analyze_coef: optimal basic solution required\n"); |
---|
| 2012 | if (!(m == 0 || P->valid)) |
---|
| 2013 | xerror("glp_analyze_coef: basis factorization required\n"); |
---|
| 2014 | if (!(1 <= k && k <= m+n)) |
---|
| 2015 | xerror("glp_analyze_coef: k = %d; variable number out of range" |
---|
| 2016 | "\n", k); |
---|
| 2017 | /* retrieve information about the specified basic variable x[k] |
---|
| 2018 | whose objective coefficient c[k] is to be analyzed */ |
---|
| 2019 | if (k <= m) |
---|
| 2020 | { row = P->row[k]; |
---|
| 2021 | type = row->type; |
---|
| 2022 | lb = row->lb; |
---|
| 2023 | ub = row->ub; |
---|
| 2024 | coef = 0.0; |
---|
| 2025 | stat = row->stat; |
---|
| 2026 | x = row->prim; |
---|
| 2027 | } |
---|
| 2028 | else |
---|
| 2029 | { col = P->col[k-m]; |
---|
| 2030 | type = col->type; |
---|
| 2031 | lb = col->lb; |
---|
| 2032 | ub = col->ub; |
---|
| 2033 | coef = col->coef; |
---|
| 2034 | stat = col->stat; |
---|
| 2035 | x = col->prim; |
---|
| 2036 | } |
---|
| 2037 | if (stat != GLP_BS) |
---|
| 2038 | xerror("glp_analyze_coef: k = %d; non-basic variable not allow" |
---|
| 2039 | "ed\n", k); |
---|
| 2040 | /* allocate working arrays */ |
---|
| 2041 | cind = xcalloc(1+m, sizeof(int)); |
---|
| 2042 | cval = xcalloc(1+m, sizeof(double)); |
---|
| 2043 | rind = xcalloc(1+n, sizeof(int)); |
---|
| 2044 | rval = xcalloc(1+n, sizeof(double)); |
---|
| 2045 | /* compute row of the simplex table corresponding to the basic |
---|
| 2046 | variable x[k] */ |
---|
| 2047 | rlen = glp_eval_tab_row(P, k, rind, rval); |
---|
| 2048 | xassert(0 <= rlen && rlen <= n); |
---|
| 2049 | /* perform analysis */ |
---|
| 2050 | for (kase = -1; kase <= +1; kase += 2) |
---|
| 2051 | { /* kase < 0 means objective coefficient c[k] is decreasing; |
---|
| 2052 | kase > 0 means objective coefficient c[k] is increasing */ |
---|
| 2053 | /* note that decreasing c[k] is equivalent to increasing dual |
---|
| 2054 | variable lambda[k] and vice versa; we need to correctly set |
---|
| 2055 | the dir flag as required by the routine glp_dual_rtest */ |
---|
| 2056 | if (P->dir == GLP_MIN) |
---|
| 2057 | dir = - kase; |
---|
| 2058 | else if (P->dir == GLP_MAX) |
---|
| 2059 | dir = + kase; |
---|
| 2060 | else |
---|
| 2061 | xassert(P != P); |
---|
| 2062 | /* use the dual ratio test to determine non-basic variable |
---|
| 2063 | x[q] whose reduced cost d[q] reaches zero bound first */ |
---|
| 2064 | rpiv = glp_dual_rtest(P, rlen, rind, rval, dir, 1e-9); |
---|
| 2065 | if (rpiv == 0) |
---|
| 2066 | { /* nothing limits changing c[k] */ |
---|
| 2067 | lim_coef = (kase < 0 ? -DBL_MAX : +DBL_MAX); |
---|
| 2068 | q = 0; |
---|
| 2069 | /* x[k] keeps its current value */ |
---|
| 2070 | new_x = x; |
---|
| 2071 | goto store; |
---|
| 2072 | } |
---|
| 2073 | /* non-basic variable x[q] limits changing coefficient c[k]; |
---|
| 2074 | determine its status and reduced cost d[k] in the current |
---|
| 2075 | basis */ |
---|
| 2076 | xassert(1 <= rpiv && rpiv <= rlen); |
---|
| 2077 | q = rind[rpiv]; |
---|
| 2078 | xassert(1 <= q && q <= m+n); |
---|
| 2079 | if (q <= m) |
---|
| 2080 | { row = P->row[q]; |
---|
| 2081 | stat = row->stat; |
---|
| 2082 | d = row->dual; |
---|
| 2083 | } |
---|
| 2084 | else |
---|
| 2085 | { col = P->col[q-m]; |
---|
| 2086 | stat = col->stat; |
---|
| 2087 | d = col->dual; |
---|
| 2088 | } |
---|
| 2089 | /* note that delta d[q] = new d[q] - d[q] = - d[q], because |
---|
| 2090 | new d[q] = 0; delta d[q] = alfa[k,q] * delta c[k], so |
---|
| 2091 | delta c[k] = delta d[q] / alfa[k,q] = - d[q] / alfa[k,q] */ |
---|
| 2092 | xassert(rval[rpiv] != 0.0); |
---|
| 2093 | delta = - d / rval[rpiv]; |
---|
| 2094 | /* compute new c[k] = c[k] + delta c[k], which is the limiting |
---|
| 2095 | value of the objective coefficient c[k] */ |
---|
| 2096 | lim_coef = coef + delta; |
---|
| 2097 | /* let c[k] continue decreasing/increasing that makes d[q] |
---|
| 2098 | dual infeasible and forces x[q] to enter the basis; |
---|
| 2099 | to perform the primal ratio test we need to know in which |
---|
| 2100 | direction x[q] changes on entering the basis; we determine |
---|
| 2101 | that analyzing the sign of delta d[q] (see above), since |
---|
| 2102 | d[q] may be close to zero having wrong sign */ |
---|
| 2103 | /* let, for simplicity, the problem is minimization */ |
---|
| 2104 | if (kase < 0 && rval[rpiv] > 0.0 || |
---|
| 2105 | kase > 0 && rval[rpiv] < 0.0) |
---|
| 2106 | { /* delta d[q] < 0, so d[q] being non-negative will become |
---|
| 2107 | negative, so x[q] will increase */ |
---|
| 2108 | dir = +1; |
---|
| 2109 | } |
---|
| 2110 | else |
---|
| 2111 | { /* delta d[q] > 0, so d[q] being non-positive will become |
---|
| 2112 | positive, so x[q] will decrease */ |
---|
| 2113 | dir = -1; |
---|
| 2114 | } |
---|
| 2115 | /* if the problem is maximization, correct the direction */ |
---|
| 2116 | if (P->dir == GLP_MAX) dir = - dir; |
---|
| 2117 | /* check that we didn't make a silly mistake */ |
---|
| 2118 | if (dir > 0) |
---|
| 2119 | xassert(stat == GLP_NL || stat == GLP_NF); |
---|
| 2120 | else |
---|
| 2121 | xassert(stat == GLP_NU || stat == GLP_NF); |
---|
| 2122 | /* compute column of the simplex table corresponding to the |
---|
| 2123 | non-basic variable x[q] */ |
---|
| 2124 | clen = glp_eval_tab_col(P, q, cind, cval); |
---|
| 2125 | /* make x[k] temporarily free (unbounded) */ |
---|
| 2126 | if (k <= m) |
---|
| 2127 | { row = P->row[k]; |
---|
| 2128 | row->type = GLP_FR; |
---|
| 2129 | row->lb = row->ub = 0.0; |
---|
| 2130 | } |
---|
| 2131 | else |
---|
| 2132 | { col = P->col[k-m]; |
---|
| 2133 | col->type = GLP_FR; |
---|
| 2134 | col->lb = col->ub = 0.0; |
---|
| 2135 | } |
---|
| 2136 | /* use the primal ratio test to determine some basic variable |
---|
| 2137 | which leaves the basis */ |
---|
| 2138 | cpiv = glp_prim_rtest(P, clen, cind, cval, dir, 1e-9); |
---|
| 2139 | /* restore original bounds of the basic variable x[k] */ |
---|
| 2140 | if (k <= m) |
---|
| 2141 | { row = P->row[k]; |
---|
| 2142 | row->type = type; |
---|
| 2143 | row->lb = lb, row->ub = ub; |
---|
| 2144 | } |
---|
| 2145 | else |
---|
| 2146 | { col = P->col[k-m]; |
---|
| 2147 | col->type = type; |
---|
| 2148 | col->lb = lb, col->ub = ub; |
---|
| 2149 | } |
---|
| 2150 | if (cpiv == 0) |
---|
| 2151 | { /* non-basic variable x[q] can change unlimitedly */ |
---|
| 2152 | if (dir < 0 && rval[rpiv] > 0.0 || |
---|
| 2153 | dir > 0 && rval[rpiv] < 0.0) |
---|
| 2154 | { /* delta x[k] = alfa[k,q] * delta x[q] < 0 */ |
---|
| 2155 | new_x = -DBL_MAX; |
---|
| 2156 | } |
---|
| 2157 | else |
---|
| 2158 | { /* delta x[k] = alfa[k,q] * delta x[q] > 0 */ |
---|
| 2159 | new_x = +DBL_MAX; |
---|
| 2160 | } |
---|
| 2161 | goto store; |
---|
| 2162 | } |
---|
| 2163 | /* some basic variable x[p] limits changing non-basic variable |
---|
| 2164 | x[q] in the adjacent basis */ |
---|
| 2165 | xassert(1 <= cpiv && cpiv <= clen); |
---|
| 2166 | p = cind[cpiv]; |
---|
| 2167 | xassert(1 <= p && p <= m+n); |
---|
| 2168 | xassert(p != k); |
---|
| 2169 | if (p <= m) |
---|
| 2170 | { row = P->row[p]; |
---|
| 2171 | xassert(row->stat == GLP_BS); |
---|
| 2172 | ll = glp_get_row_lb(P, row->i); |
---|
| 2173 | uu = glp_get_row_ub(P, row->i); |
---|
| 2174 | xx = row->prim; |
---|
| 2175 | } |
---|
| 2176 | else |
---|
| 2177 | { col = P->col[p-m]; |
---|
| 2178 | xassert(col->stat == GLP_BS); |
---|
| 2179 | ll = glp_get_col_lb(P, col->j); |
---|
| 2180 | uu = glp_get_col_ub(P, col->j); |
---|
| 2181 | xx = col->prim; |
---|
| 2182 | } |
---|
| 2183 | /* determine delta x[p] = new x[p] - x[p] */ |
---|
| 2184 | if (dir < 0 && cval[cpiv] > 0.0 || |
---|
| 2185 | dir > 0 && cval[cpiv] < 0.0) |
---|
| 2186 | { /* delta x[p] < 0, so x[p] goes toward its lower bound */ |
---|
| 2187 | xassert(ll != -DBL_MAX); |
---|
| 2188 | delta = ll - xx; |
---|
| 2189 | } |
---|
| 2190 | else |
---|
| 2191 | { /* delta x[p] > 0, so x[p] goes toward its upper bound */ |
---|
| 2192 | xassert(uu != +DBL_MAX); |
---|
| 2193 | delta = uu - xx; |
---|
| 2194 | } |
---|
| 2195 | /* compute new x[k] = x[k] + alfa[k,q] * delta x[q], where |
---|
| 2196 | delta x[q] = delta x[p] / alfa[p,q] */ |
---|
| 2197 | xassert(cval[cpiv] != 0.0); |
---|
| 2198 | new_x = x + (rval[rpiv] / cval[cpiv]) * delta; |
---|
| 2199 | store: /* store analysis results */ |
---|
| 2200 | if (kase < 0) |
---|
| 2201 | { if (coef1 != NULL) *coef1 = lim_coef; |
---|
| 2202 | if (var1 != NULL) *var1 = q; |
---|
| 2203 | if (value1 != NULL) *value1 = new_x; |
---|
| 2204 | } |
---|
| 2205 | else |
---|
| 2206 | { if (coef2 != NULL) *coef2 = lim_coef; |
---|
| 2207 | if (var2 != NULL) *var2 = q; |
---|
| 2208 | if (value2 != NULL) *value2 = new_x; |
---|
| 2209 | } |
---|
| 2210 | } |
---|
| 2211 | /* free working arrays */ |
---|
| 2212 | xfree(cind); |
---|
| 2213 | xfree(cval); |
---|
| 2214 | xfree(rind); |
---|
| 2215 | xfree(rval); |
---|
| 2216 | return; |
---|
| 2217 | } |
---|
| 2218 | |
---|
| 2219 | /* eof */ |
---|