1 | /* glpini02.c */ |
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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 | struct var |
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28 | { /* structural variable */ |
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29 | int j; |
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30 | /* ordinal number */ |
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31 | double q; |
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32 | /* penalty value */ |
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33 | }; |
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34 | |
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35 | static int fcmp(const void *ptr1, const void *ptr2) |
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36 | { /* this routine is passed to the qsort() function */ |
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37 | struct var *col1 = (void *)ptr1, *col2 = (void *)ptr2; |
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38 | if (col1->q < col2->q) return -1; |
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39 | if (col1->q > col2->q) return +1; |
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40 | return 0; |
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41 | } |
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42 | |
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43 | static int get_column(glp_prob *lp, int j, int ind[], double val[]) |
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44 | { /* Bixby's algorithm assumes that the constraint matrix is scaled |
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45 | such that the maximum absolute value in every non-zero row and |
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46 | column is 1 */ |
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47 | int k, len; |
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48 | double big; |
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49 | len = glp_get_mat_col(lp, j, ind, val); |
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50 | big = 0.0; |
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51 | for (k = 1; k <= len; k++) |
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52 | if (big < fabs(val[k])) big = fabs(val[k]); |
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53 | if (big == 0.0) big = 1.0; |
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54 | for (k = 1; k <= len; k++) val[k] /= big; |
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55 | return len; |
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56 | } |
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57 | |
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58 | static void cpx_basis(glp_prob *lp) |
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59 | { /* main routine */ |
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60 | struct var *C, *C2, *C3, *C4; |
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61 | int m, n, i, j, jk, k, l, ll, t, n2, n3, n4, type, len, *I, *r, |
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62 | *ind; |
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63 | double alpha, gamma, cmax, temp, *v, *val; |
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64 | xprintf("Constructing initial basis...\n"); |
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65 | /* determine the number of rows and columns */ |
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66 | m = glp_get_num_rows(lp); |
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67 | n = glp_get_num_cols(lp); |
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68 | /* allocate working arrays */ |
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69 | C = xcalloc(1+n, sizeof(struct var)); |
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70 | I = xcalloc(1+m, sizeof(int)); |
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71 | r = xcalloc(1+m, sizeof(int)); |
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72 | v = xcalloc(1+m, sizeof(double)); |
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73 | ind = xcalloc(1+m, sizeof(int)); |
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74 | val = xcalloc(1+m, sizeof(double)); |
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75 | /* make all auxiliary variables non-basic */ |
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76 | for (i = 1; i <= m; i++) |
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77 | { if (glp_get_row_type(lp, i) != GLP_DB) |
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78 | glp_set_row_stat(lp, i, GLP_NS); |
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79 | else if (fabs(glp_get_row_lb(lp, i)) <= |
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80 | fabs(glp_get_row_ub(lp, i))) |
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81 | glp_set_row_stat(lp, i, GLP_NL); |
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82 | else |
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83 | glp_set_row_stat(lp, i, GLP_NU); |
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84 | } |
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85 | /* make all structural variables non-basic */ |
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86 | for (j = 1; j <= n; j++) |
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87 | { if (glp_get_col_type(lp, j) != GLP_DB) |
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88 | glp_set_col_stat(lp, j, GLP_NS); |
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89 | else if (fabs(glp_get_col_lb(lp, j)) <= |
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90 | fabs(glp_get_col_ub(lp, j))) |
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91 | glp_set_col_stat(lp, j, GLP_NL); |
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92 | else |
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93 | glp_set_col_stat(lp, j, GLP_NU); |
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94 | } |
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95 | /* C2 is a set of free structural variables */ |
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96 | n2 = 0, C2 = C + 0; |
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97 | for (j = 1; j <= n; j++) |
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98 | { type = glp_get_col_type(lp, j); |
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99 | if (type == GLP_FR) |
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100 | { n2++; |
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101 | C2[n2].j = j; |
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102 | C2[n2].q = 0.0; |
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103 | } |
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104 | } |
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105 | /* C3 is a set of structural variables having excatly one (lower |
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106 | or upper) bound */ |
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107 | n3 = 0, C3 = C2 + n2; |
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108 | for (j = 1; j <= n; j++) |
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109 | { type = glp_get_col_type(lp, j); |
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110 | if (type == GLP_LO) |
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111 | { n3++; |
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112 | C3[n3].j = j; |
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113 | C3[n3].q = + glp_get_col_lb(lp, j); |
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114 | } |
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115 | else if (type == GLP_UP) |
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116 | { n3++; |
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117 | C3[n3].j = j; |
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118 | C3[n3].q = - glp_get_col_ub(lp, j); |
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119 | } |
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120 | } |
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121 | /* C4 is a set of structural variables having both (lower and |
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122 | upper) bounds */ |
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123 | n4 = 0, C4 = C3 + n3; |
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124 | for (j = 1; j <= n; j++) |
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125 | { type = glp_get_col_type(lp, j); |
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126 | if (type == GLP_DB) |
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127 | { n4++; |
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128 | C4[n4].j = j; |
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129 | C4[n4].q = glp_get_col_lb(lp, j) - glp_get_col_ub(lp, j); |
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130 | } |
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131 | } |
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132 | /* compute gamma = max{|c[j]|: 1 <= j <= n} */ |
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133 | gamma = 0.0; |
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134 | for (j = 1; j <= n; j++) |
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135 | { temp = fabs(glp_get_obj_coef(lp, j)); |
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136 | if (gamma < temp) gamma = temp; |
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137 | } |
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138 | /* compute cmax */ |
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139 | cmax = (gamma == 0.0 ? 1.0 : 1000.0 * gamma); |
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140 | /* compute final penalty for all structural variables within sets |
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141 | C2, C3, and C4 */ |
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142 | switch (glp_get_obj_dir(lp)) |
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143 | { case GLP_MIN: temp = +1.0; break; |
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144 | case GLP_MAX: temp = -1.0; break; |
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145 | default: xassert(lp != lp); |
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146 | } |
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147 | for (k = 1; k <= n2+n3+n4; k++) |
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148 | { j = C[k].j; |
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149 | C[k].q += (temp * glp_get_obj_coef(lp, j)) / cmax; |
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150 | } |
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151 | /* sort structural variables within C2, C3, and C4 in ascending |
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152 | order of penalty value */ |
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153 | qsort(C2+1, n2, sizeof(struct var), fcmp); |
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154 | for (k = 1; k < n2; k++) xassert(C2[k].q <= C2[k+1].q); |
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155 | qsort(C3+1, n3, sizeof(struct var), fcmp); |
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156 | for (k = 1; k < n3; k++) xassert(C3[k].q <= C3[k+1].q); |
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157 | qsort(C4+1, n4, sizeof(struct var), fcmp); |
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158 | for (k = 1; k < n4; k++) xassert(C4[k].q <= C4[k+1].q); |
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159 | /*** STEP 1 ***/ |
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160 | for (i = 1; i <= m; i++) |
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161 | { type = glp_get_row_type(lp, i); |
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162 | if (type != GLP_FX) |
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163 | { /* row i is either free or inequality constraint */ |
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164 | glp_set_row_stat(lp, i, GLP_BS); |
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165 | I[i] = 1; |
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166 | r[i] = 1; |
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167 | } |
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168 | else |
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169 | { /* row i is equality constraint */ |
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170 | I[i] = 0; |
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171 | r[i] = 0; |
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172 | } |
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173 | v[i] = +DBL_MAX; |
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174 | } |
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175 | /*** STEP 2 ***/ |
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176 | for (k = 1; k <= n2+n3+n4; k++) |
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177 | { jk = C[k].j; |
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178 | len = get_column(lp, jk, ind, val); |
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179 | /* let alpha = max{|A[l,jk]|: r[l] = 0} and let l' be such |
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180 | that alpha = |A[l',jk]| */ |
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181 | alpha = 0.0, ll = 0; |
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182 | for (t = 1; t <= len; t++) |
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183 | { l = ind[t]; |
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184 | if (r[l] == 0 && alpha < fabs(val[t])) |
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185 | alpha = fabs(val[t]), ll = l; |
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186 | } |
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187 | if (alpha >= 0.99) |
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188 | { /* B := B union {jk} */ |
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189 | glp_set_col_stat(lp, jk, GLP_BS); |
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190 | I[ll] = 1; |
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191 | v[ll] = alpha; |
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192 | /* r[l] := r[l] + 1 for all l such that |A[l,jk]| != 0 */ |
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193 | for (t = 1; t <= len; t++) |
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194 | { l = ind[t]; |
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195 | if (val[t] != 0.0) r[l]++; |
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196 | } |
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197 | /* continue to the next k */ |
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198 | continue; |
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199 | } |
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200 | /* if |A[l,jk]| > 0.01 * v[l] for some l, continue to the |
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201 | next k */ |
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202 | for (t = 1; t <= len; t++) |
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203 | { l = ind[t]; |
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204 | if (fabs(val[t]) > 0.01 * v[l]) break; |
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205 | } |
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206 | if (t <= len) continue; |
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207 | /* otherwise, let alpha = max{|A[l,jk]|: I[l] = 0} and let l' |
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208 | be such that alpha = |A[l',jk]| */ |
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209 | alpha = 0.0, ll = 0; |
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210 | for (t = 1; t <= len; t++) |
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211 | { l = ind[t]; |
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212 | if (I[l] == 0 && alpha < fabs(val[t])) |
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213 | alpha = fabs(val[t]), ll = l; |
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214 | } |
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215 | /* if alpha = 0, continue to the next k */ |
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216 | if (alpha == 0.0) continue; |
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217 | /* B := B union {jk} */ |
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218 | glp_set_col_stat(lp, jk, GLP_BS); |
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219 | I[ll] = 1; |
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220 | v[ll] = alpha; |
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221 | /* r[l] := r[l] + 1 for all l such that |A[l,jk]| != 0 */ |
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222 | for (t = 1; t <= len; t++) |
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223 | { l = ind[t]; |
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224 | if (val[t] != 0.0) r[l]++; |
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225 | } |
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226 | } |
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227 | /*** STEP 3 ***/ |
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228 | /* add an artificial variable (auxiliary variable for equality |
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229 | constraint) to cover each remaining uncovered row */ |
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230 | for (i = 1; i <= m; i++) |
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231 | if (I[i] == 0) glp_set_row_stat(lp, i, GLP_BS); |
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232 | /* free working arrays */ |
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233 | xfree(C); |
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234 | xfree(I); |
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235 | xfree(r); |
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236 | xfree(v); |
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237 | xfree(ind); |
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238 | xfree(val); |
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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_cpx_basis - construct Bixby's initial LP basis |
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246 | * |
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247 | * SYNOPSIS |
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248 | * |
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249 | * void glp_cpx_basis(glp_prob *lp); |
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250 | * |
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251 | * DESCRIPTION |
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252 | * |
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253 | * The routine glp_cpx_basis constructs an advanced initial basis for |
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254 | * the specified problem object. |
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255 | * |
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256 | * The routine is based on Bixby's algorithm described in the paper: |
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257 | * |
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258 | * Robert E. Bixby. Implementing the Simplex Method: The Initial Basis. |
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259 | * ORSA Journal on Computing, Vol. 4, No. 3, 1992, pp. 267-84. */ |
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260 | |
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261 | void glp_cpx_basis(glp_prob *lp) |
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262 | { if (lp->m == 0 || lp->n == 0) |
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263 | glp_std_basis(lp); |
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264 | else |
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265 | cpx_basis(lp); |
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266 | return; |
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267 | } |
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268 | |
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269 | /* eof */ |
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