1 | #include <stdio.h> |
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2 | #include <math.h> |
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3 | #include <strings.h> |
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4 | |
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5 | #include "PresolveMatrix.hpp" |
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6 | #include "PresolveSubst.hpp" |
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7 | #include "PresolveIsolated.hpp" |
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8 | #include "PresolveImpliedFree.hpp" |
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9 | #include "ClpMessage.hpp" |
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10 | |
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11 | |
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12 | |
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13 | // If there is a row with a singleton column such that no matter what |
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14 | // the values of the other variables are, the constraint forces the singleton |
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15 | // column to have a feasible value, then we can drop the column and row, |
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16 | // since we just compute the value of the column from the row in postsolve. |
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17 | // This seems vaguely similar to the case of a useless constraint, but it |
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18 | // is different. For example, if the singleton column is already free, |
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19 | // then this operation will eliminate it, but the constraint is not useless |
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20 | // (assuming the constraint is not trivial), since the variables do not imply an |
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21 | // upper or lower bound. |
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22 | // |
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23 | // If the column is not singleton, we can still do something similar if the |
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24 | // constraint is an equality constraint. In that case, we substitute away |
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25 | // the variable in the other constraints it appears in. This introduces |
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26 | // new coefficients, but the total number of coefficients never increases |
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27 | // if the column has only two constraints, and may not increase much even |
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28 | // if there are more. |
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29 | // |
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30 | // There is nothing to prevent us from substituting away a variable |
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31 | // in an equality from the other constraints it appears in, but since |
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32 | // that causes fill-in, it wouldn't make sense unless we could then |
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33 | // drop the equality itself. We can't do that if the bounds on the |
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34 | // variable in equation aren't implied by the equality. |
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35 | // Another way of thinking of this is that there is nothing special |
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36 | // about an equality; just like one can't always drop an inequality constraint |
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37 | // with a column singleton, one can't always drop an equality. |
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38 | // |
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39 | // It is possible for two singleton columns to be in the same row. |
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40 | // In that case, the other one will become empty. If it's bounds and |
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41 | // costs aren't just right, this signals an unbounded problem. |
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42 | // We don't need to check that specially here. |
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43 | // |
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44 | // invariant: loosely packed |
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45 | const PresolveAction *implied_free_action::presolve(PresolveMatrix *prob, |
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46 | const PresolveAction *next, |
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47 | int & fill_level) |
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48 | { |
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49 | double *colels = prob->colels_; |
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50 | int *hrow = prob->hrow_; |
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51 | const int *mcstrt = prob->mcstrt_; |
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52 | int *hincol = prob->hincol_; |
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53 | const int ncols = prob->ncols_; |
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54 | |
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55 | const double *clo = prob->clo_; |
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56 | const double *cup = prob->cup_; |
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57 | |
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58 | const double *rowels = prob->rowels_; |
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59 | const int *hcol = prob->hcol_; |
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60 | const int *mrstrt = prob->mrstrt_; |
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61 | int *hinrow = prob->hinrow_; |
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62 | const int nrows = prob->nrows_; |
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63 | |
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64 | /*const*/ double *rlo = prob->rlo_; |
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65 | /*const*/ double *rup = prob->rup_; |
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66 | |
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67 | double *cost = prob->cost_; |
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68 | |
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69 | presolvehlink *rlink = prob->rlink_; |
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70 | presolvehlink *clink = prob->clink_; |
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71 | |
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72 | const char *integerType = prob->integerType_; |
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73 | |
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74 | const double tol = ZTOLDP; |
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75 | |
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76 | int nbounds = 0; |
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77 | |
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78 | action *actions = new action [ncols]; |
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79 | int nactions = 0; |
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80 | |
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81 | char *implied_free = new char[ncols]; |
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82 | bzero(implied_free, ncols*sizeof(char)); |
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83 | |
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84 | double *ilbound = new double[ncols]; |
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85 | double *iubound = new double[ncols]; |
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86 | |
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87 | double *tclo = new double[ncols]; |
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88 | double *tcup = new double[ncols]; |
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89 | |
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90 | #if PRESOLVE_TRY_TIGHTEN |
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91 | for (int j=0; j<ncols; j++) { |
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92 | ilbound[j] = -PRESOLVE_INF; |
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93 | iubound[j] = PRESOLVE_INF; |
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94 | tclo[j] = clo[j]; |
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95 | tcup[j] = cup[j]; |
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96 | } |
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97 | |
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98 | { |
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99 | int ntightened; |
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100 | do { |
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101 | implied_bounds1(rowels, mrstrt, hrow, hinrow, clo, cup, hcol, ncols, |
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102 | rlo, rup, integerType, nrows, |
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103 | ilbound, iubound); |
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104 | |
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105 | ntightened = 0; |
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106 | for (int j=0; j<ncols; j++) { |
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107 | if (tclo[j] < ilbound[j]) { |
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108 | tclo[j] = ilbound[j]; |
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109 | ntightened++; |
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110 | } |
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111 | if (tcup[j] > iubound[j]) { |
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112 | tcup[j] = iubound[j]; |
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113 | ntightened++; |
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114 | } |
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115 | } |
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116 | printf("NTIGHT: %d\n", ntightened); |
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117 | } while (ntightened); |
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118 | } |
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119 | #endif |
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120 | |
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121 | int numberLook = prob->numberColsToDo_; |
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122 | int iLook; |
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123 | int * look = prob->colsToDo_; |
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124 | int * look2 = NULL; |
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125 | // if gone from 2 to 3 look at all |
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126 | if (fill_level<0) { |
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127 | look2 = new int[ncols]; |
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128 | look=look2; |
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129 | for (iLook=0;iLook<ncols;iLook++) |
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130 | look[iLook]=iLook; |
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131 | numberLook=ncols; |
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132 | } |
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133 | |
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134 | for (iLook=0;iLook<numberLook;iLook++) { |
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135 | int j=look[iLook]; |
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136 | if ((hincol[j] >= 1 && hincol[j] <= 3) && |
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137 | !integerType[j]) { |
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138 | int kcs = mcstrt[j]; |
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139 | int kce = kcs + hincol[j]; |
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140 | |
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141 | for (int k=kcs; k<kce; ++k) { |
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142 | int row = hrow[k]; |
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143 | double coeffj = colels[k]; |
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144 | |
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145 | // if its row is an equality constraint... |
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146 | if (hinrow[row] > 1 && // don't bother with singleton rows |
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147 | |
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148 | // either this is a singleton col, |
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149 | // or this particular row is an equality |
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150 | (hincol[j] == 1 || fabs(rlo[row] - rup[row]) < tol) && |
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151 | |
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152 | fabs(coeffj) > ZTOLDP) { |
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153 | |
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154 | int krs = mrstrt[row]; |
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155 | int kre = krs + hinrow[row]; |
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156 | |
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157 | double maxup, maxdown, ilow, iup; |
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158 | implied_bounds(rowels, clo, cup, hcol, |
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159 | krs, kre, |
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160 | &maxup, &maxdown, |
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161 | j, rlo[row], rup[row], &ilow, &iup); |
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162 | |
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163 | #if PRESOLVE_TRY_TIGHTEN |
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164 | if ((clo[j] <= ilbound[j] && iubound[j] <= cup[j]) && |
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165 | ! (clo[j] <= ilow && iup <= cup[j])) |
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166 | printf("TIGHTER: %6d %6d\n", row, j); |
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167 | #endif |
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168 | |
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169 | if (maxup < PRESOLVE_INF && maxup + tol < rlo[row]) { |
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170 | /* there is an upper bound and it can't be reached */ |
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171 | prob->status_|= 1; |
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172 | prob->originalModel_->messageHandler()->message(CLP_PRESOLVE_ROWINFEAS, |
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173 | prob->originalModel_->messages()) |
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174 | <<row |
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175 | <<rlo[row] |
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176 | <<rup[row] |
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177 | <<CoinMessageEol; |
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178 | break; |
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179 | } else if (-PRESOLVE_INF < maxdown && rup[row] < maxdown - tol) { |
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180 | /* there is a lower bound and it can't be reached */ |
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181 | prob->status_|= 1; |
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182 | prob->originalModel_->messageHandler()->message(CLP_PRESOLVE_ROWINFEAS, |
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183 | prob->originalModel_->messages()) |
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184 | <<row |
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185 | <<rlo[row] |
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186 | <<rup[row] |
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187 | <<CoinMessageEol; |
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188 | break; |
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189 | } else if (clo[j] <= ilow && iup <= cup[j]) { |
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190 | |
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191 | // both column bounds implied by the constraints of the problem |
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192 | implied_free[j] = hincol[j]; |
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193 | break; |
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194 | } |
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195 | } |
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196 | } |
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197 | } |
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198 | } |
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199 | // implied_free[j] == hincol[j] && hincol[j] > 0 ==> j is implied free |
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200 | |
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201 | #if 0 |
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202 | // DEBUG |
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203 | static int nfree = 0; |
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204 | static int maxfree = atoi(getenv("MAXFREE")); |
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205 | #endif |
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206 | |
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207 | int isolated_row = -1; |
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208 | |
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209 | // first pick off the easy ones |
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210 | // note that this will only deal with columns that were originally |
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211 | // singleton; it will not deal with doubleton columns that become |
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212 | // singletons as a result of dropping rows. |
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213 | for (iLook=0;iLook<numberLook;iLook++) { |
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214 | int j=look[iLook]; |
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215 | if (hincol[j] == 1 && implied_free[j] == 1) { |
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216 | int kcs = mcstrt[j]; |
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217 | int row = hrow[kcs]; |
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218 | double coeffj = colels[kcs]; |
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219 | |
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220 | int krs = mrstrt[row]; |
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221 | int kre = krs + hinrow[row]; |
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222 | |
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223 | #if 0 |
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224 | if (nfree >= maxfree) |
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225 | continue; |
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226 | nfree++; |
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227 | #endif |
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228 | |
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229 | // isolated rows are weird |
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230 | { |
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231 | int n = 0; |
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232 | for (int k=krs; k<kre; ++k) |
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233 | n += hincol[hcol[k]]; |
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234 | if (n==hinrow[row]) { |
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235 | isolated_row = row; |
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236 | break; |
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237 | } |
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238 | } |
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239 | |
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240 | const bool nonzero_cost = (cost[j] != 0.0); |
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241 | |
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242 | double *save_costs = nonzero_cost ? new double[hinrow[row]] : 0; |
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243 | |
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244 | { |
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245 | action *s = &actions[nactions++]; |
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246 | |
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247 | s->row = row; |
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248 | s->col = j; |
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249 | |
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250 | s->clo = clo[j]; |
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251 | s->cup = cup[j]; |
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252 | s->rlo = rlo[row]; |
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253 | s->rup = rup[row]; |
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254 | |
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255 | s->ninrow = hinrow[row]; |
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256 | s->rowels = presolve_duparray(&rowels[krs], hinrow[row]); |
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257 | s->rowcols = presolve_duparray(&hcol[krs], hinrow[row]); |
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258 | s->costs = save_costs; |
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259 | } |
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260 | |
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261 | if (nonzero_cost) { |
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262 | double rhs = rlo[row]; |
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263 | double costj = cost[j]; |
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264 | |
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265 | #if DEBUG_PRESOLVE |
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266 | printf("FREE COSTS: %g ", costj); |
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267 | #endif |
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268 | for (int k=krs; k<kre; k++) { |
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269 | int jcol = hcol[k]; |
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270 | save_costs[k-krs] = cost[jcol]; |
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271 | |
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272 | if (jcol != j) { |
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273 | double coeff = rowels[k]; |
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274 | |
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275 | #if DEBUG_PRESOLVE |
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276 | printf("%g %g ", cost[jcol], coeff/coeffj); |
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277 | #endif |
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278 | /* |
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279 | * Similar to eliminating doubleton: |
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280 | * cost1 x = cost1 (c - b y) / a = (c cost1)/a - (b cost1)/a |
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281 | * cost[icoly] += cost[icolx] * (-coeff2 / coeff1); |
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282 | */ |
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283 | cost[jcol] += costj * (-coeff / coeffj); |
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284 | } |
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285 | } |
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286 | #if DEBUG_PRESOLVE |
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287 | printf("\n"); |
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288 | |
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289 | /* similar to doubleton */ |
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290 | printf("BIAS??????? %g %g %g %g\n", |
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291 | costj * rhs / coeffj, |
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292 | costj, rhs, coeffj); |
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293 | #endif |
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294 | prob->change_bias(costj * rhs / coeffj); |
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295 | // ?? |
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296 | cost[j] = 0.0; |
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297 | } |
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298 | |
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299 | /* remove the row from the columns in the row */ |
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300 | for (int k=krs; k<kre; k++) { |
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301 | int jcol=hcol[k]; |
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302 | prob->addCol(jcol); |
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303 | presolve_delete_from_row(jcol, row, mcstrt, hincol, hrow, colels); |
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304 | } |
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305 | PRESOLVE_REMOVE_LINK(rlink, row); |
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306 | hinrow[row] = 0; |
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307 | |
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308 | // just to make things squeeky |
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309 | rlo[row] = 0.0; |
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310 | rup[row] = 0.0; |
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311 | |
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312 | PRESOLVE_REMOVE_LINK(clink, j); |
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313 | hincol[j] = 0; |
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314 | |
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315 | implied_free[j] = 0; // probably unnecessary |
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316 | } |
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317 | } |
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318 | |
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319 | delete [] look2; |
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320 | if (nactions) { |
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321 | #if PRESOLVE_SUMMARY |
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322 | printf("NIMPLIED FREE: %d\n", nactions); |
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323 | #endif |
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324 | next = new implied_free_action(nactions, copyOfArray(actions,nactions), next); |
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325 | } |
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326 | delete [] actions; |
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327 | |
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328 | delete[]ilbound; |
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329 | delete[]iubound; |
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330 | delete[]tclo; |
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331 | delete[]tcup; |
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332 | |
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333 | if (isolated_row != -1) |
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334 | next = isolated_constraint_action::presolve(prob, isolated_row, next); |
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335 | |
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336 | // try more complex ones |
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337 | if (fill_level) |
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338 | next = subst_constraint_action::presolve(prob, implied_free, next,fill_level); |
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339 | delete[]implied_free; |
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340 | |
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341 | return (next); |
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342 | } |
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343 | |
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344 | |
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345 | |
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346 | const char *implied_free_action::name() const |
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347 | { |
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348 | return ("implied_free_action"); |
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349 | } |
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350 | |
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351 | void implied_free_action::postsolve(PostsolveMatrix *prob) const |
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352 | { |
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353 | const action *const actions = actions_; |
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354 | const int nactions = nactions_; |
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355 | |
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356 | double *colels = prob->colels_; |
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357 | int *hrow = prob->hrow_; |
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358 | int *mcstrt = prob->mcstrt_; |
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359 | int *hincol = prob->hincol_; |
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360 | int *link = prob->link_; |
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361 | |
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362 | double *clo = prob->clo_; |
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363 | double *cup = prob->cup_; |
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364 | |
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365 | double *rlo = prob->rlo_; |
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366 | double *rup = prob->rup_; |
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367 | |
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368 | double *sol = prob->sol_; |
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369 | |
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370 | double *rcosts = prob->rcosts_; |
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371 | double *dcost = prob->cost_; |
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372 | |
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373 | double *acts = prob->acts_; |
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374 | double *rowduals = prob->rowduals_; |
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375 | |
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376 | const double ztoldj = prob->ztoldj_; |
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377 | const double ztolzb = prob->ztolzb_; |
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378 | |
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379 | const double maxmin = prob->maxmin_; |
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380 | |
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381 | char *cdone = prob->cdone_; |
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382 | char *rdone = prob->rdone_; |
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383 | int free_list = prob->free_list_; |
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384 | |
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385 | for (const action *f = &actions[nactions-1]; actions<=f; f--) { |
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386 | |
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387 | int irow = f->row; |
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388 | int icol = f->col; |
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389 | |
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390 | int ninrow = f->ninrow; |
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391 | const double *rowels = f->rowels; |
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392 | const int *rowcols = f->rowcols; |
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393 | const double *save_costs = f->costs; |
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394 | |
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395 | // put back coefficients in the row |
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396 | // this includes recreating the singleton column |
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397 | { |
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398 | for (int k = 0; k<ninrow; k++) { |
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399 | int jcol = rowcols[k]; |
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400 | double coeff = rowels[k]; |
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401 | |
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402 | if (save_costs) |
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403 | dcost[jcol] = save_costs[k]; |
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404 | |
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405 | { |
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406 | int kk = free_list; |
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407 | free_list = link[free_list]; |
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408 | |
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409 | check_free_list(free_list); |
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410 | |
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411 | link[kk] = mcstrt[jcol]; |
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412 | mcstrt[jcol] = kk; |
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413 | colels[kk] = coeff; |
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414 | hrow[kk] = irow; |
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415 | } |
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416 | |
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417 | if (jcol == icol) { |
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418 | // initialize the singleton column |
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419 | hincol[jcol] = 1; |
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420 | clo[icol] = f->clo; |
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421 | cup[icol] = f->cup; |
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422 | |
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423 | cdone[icol] = IMPLIED_FREE; |
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424 | } else { |
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425 | hincol[jcol]++; |
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426 | } |
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427 | } |
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428 | rdone[irow] = IMPLIED_FREE; |
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429 | |
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430 | rlo[irow] = f->rlo; |
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431 | rup[irow] = f->rup; |
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432 | } |
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433 | // coeff has now been initialized |
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434 | |
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435 | // compute solution |
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436 | { |
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437 | double act = 0.0; |
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438 | double coeff; |
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439 | |
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440 | for (int k = 0; k<ninrow; k++) |
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441 | if (rowcols[k] == icol) |
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442 | coeff = rowels[k]; |
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443 | else { |
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444 | int jcol = rowcols[k]; |
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445 | PRESOLVE_STMT(int kk = presolve_find_row2(irow, mcstrt[jcol], hincol[jcol], hrow, link)); |
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446 | PRESOLVEASSERT(colels[kk] == rowels[k]); |
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447 | act += rowels[k] * sol[jcol]; |
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448 | } |
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449 | |
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450 | PRESOLVEASSERT(fabs(coeff) > ZTOLDP); |
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451 | // choose rowdual to make this col basic |
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452 | rowduals[irow] = maxmin*dcost[icol] / coeff; |
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453 | rcosts[icol] = 0.0; |
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454 | if ((rlo[irow] < rup[irow] && rowduals[irow] < 0.0) |
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455 | || rlo[irow]< -1.0e20) { |
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456 | if (rlo[irow]<-1.0e20&&rowduals[irow]>=0.0) |
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457 | printf("IMP %g %g %g\n",rlo[irow],rup[irow],rowduals[irow]); |
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458 | sol[icol] = (rup[irow] - act) / coeff; |
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459 | acts[irow] = rup[irow]; |
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460 | } else { |
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461 | sol[icol] = (rlo[irow] - act) / coeff; |
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462 | acts[irow] = rlo[irow]; |
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463 | } |
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464 | |
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465 | |
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466 | prob->setRowStatus(irow,PrePostsolveMatrix::atLowerBound); |
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467 | prob->setColumnStatus(icol,PrePostsolveMatrix::basic); |
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468 | } |
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469 | } |
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470 | prob->free_list_ = free_list; |
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471 | } |
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