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 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 |
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459 | * |
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460 | * S~ = diag(inv(R) | S) (2) |
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461 | * |
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462 | * is an augmented diagonal scaling matrix. |
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463 | * |
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464 | * By definition: |
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465 | * |
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466 | * A~ = (B | N), (3) |
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467 | * |
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468 | * where B is the basic matrix, which consists of basic columns of the |
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469 | * augmented constraint matrix A~, and N is a matrix, which consists of |
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470 | * non-basic columns of A~. From (1) it follows that: |
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471 | * |
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472 | * A~" = (B" | N") = (R*B*SB | R*N*SN), (4) |
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473 | * |
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474 | * where SB and SN are parts of the augmented scaling matrix S~, which |
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475 | * correspond to basic and non-basic variables, respectively. Therefore |
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476 | * |
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477 | * B" = R*B*SB, (5) |
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478 | * |
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479 | * which is the scaled basis matrix. */ |
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480 | |
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481 | void glp_ftran(glp_prob *lp, double x[]) |
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482 | { int m = lp->m; |
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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 | } |
---|
505 | |
---|
506 | /*********************************************************************** |
---|
507 | * NAME |
---|
508 | * |
---|
509 | * glp_btran - perform backward transformation (solve system B'*x = b) |
---|
510 | * |
---|
511 | * SYNOPSIS |
---|
512 | * |
---|
513 | * void glp_btran(glp_prob *lp, double x[]); |
---|
514 | * |
---|
515 | * DESCRIPTION |
---|
516 | * |
---|
517 | * The routine glp_btran performs backward transformation, i.e. solves |
---|
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. |
---|
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 */ |
---|