1 | /* -*- C++ -*- |
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2 | * lemon/lp_base.h - Part of LEMON, a generic C++ optimization library |
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3 | * |
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4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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6 | * |
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7 | * Permission to use, modify and distribute this software is granted |
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8 | * provided that this copyright notice appears in all copies. For |
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9 | * precise terms see the accompanying LICENSE file. |
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10 | * |
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11 | * This software is provided "AS IS" with no warranty of any kind, |
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12 | * express or implied, and with no claim as to its suitability for any |
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13 | * purpose. |
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14 | * |
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15 | */ |
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16 | |
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17 | #ifndef LEMON_LP_BASE_H |
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18 | #define LEMON_LP_BASE_H |
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19 | |
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20 | #include<vector> |
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21 | #include<map> |
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22 | #include<limits> |
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23 | #include<cmath> |
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24 | |
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25 | #include<lemon/utility.h> |
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26 | #include<lemon/error.h> |
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27 | #include<lemon/invalid.h> |
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28 | |
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29 | //#include"lin_expr.h" |
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30 | |
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31 | ///\file |
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32 | ///\brief The interface of the LP solver interface. |
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33 | ///\ingroup gen_opt_group |
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34 | namespace lemon { |
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35 | |
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36 | ///Internal data structure to convert floating id's to fix one's |
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37 | |
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38 | ///\todo This might be implemented to be also usable in other places. |
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39 | class _FixId |
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40 | { |
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41 | std::vector<int> index; |
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42 | std::vector<int> cross; |
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43 | int first_free; |
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44 | public: |
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45 | _FixId() : first_free(-1) {}; |
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46 | ///Convert a floating id to a fix one |
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47 | |
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48 | ///\param n is a floating id |
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49 | ///\return the corresponding fix id |
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50 | int fixId(int n) {return cross[n];} |
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51 | ///Convert a fix id to a floating one |
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52 | |
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53 | ///\param n is a fix id |
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54 | ///\return the corresponding floating id |
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55 | int floatingId(int n) { return index[n];} |
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56 | ///Add a new floating id. |
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57 | |
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58 | ///\param n is a floating id |
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59 | ///\return the fix id of the new value |
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60 | ///\todo Multiple additions should also be handled. |
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61 | int insert(int n) |
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62 | { |
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63 | if(n>=int(cross.size())) { |
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64 | cross.resize(n+1); |
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65 | if(first_free==-1) { |
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66 | cross[n]=index.size(); |
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67 | index.push_back(n); |
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68 | } |
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69 | else { |
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70 | cross[n]=first_free; |
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71 | int next=index[first_free]; |
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72 | index[first_free]=n; |
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73 | first_free=next; |
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74 | } |
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75 | return cross[n]; |
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76 | } |
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77 | ///\todo Create an own exception type. |
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78 | else throw LogicError(); //floatingId-s must form a continuous range; |
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79 | } |
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80 | ///Remove a fix id. |
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81 | |
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82 | ///\param n is a fix id |
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83 | /// |
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84 | void erase(int n) |
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85 | { |
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86 | int fl=index[n]; |
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87 | index[n]=first_free; |
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88 | first_free=n; |
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89 | for(int i=fl+1;i<int(cross.size());++i) { |
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90 | cross[i-1]=cross[i]; |
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91 | index[cross[i]]--; |
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92 | } |
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93 | cross.pop_back(); |
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94 | } |
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95 | ///An upper bound on the largest fix id. |
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96 | |
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97 | ///\todo Do we need this? |
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98 | /// |
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99 | std::size_t maxFixId() { return cross.size()-1; } |
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100 | |
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101 | }; |
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102 | |
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103 | ///Common base class for LP solvers |
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104 | |
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105 | ///\todo Much more docs |
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106 | ///\ingroup gen_opt_group |
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107 | class LpSolverBase { |
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108 | |
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109 | public: |
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110 | |
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111 | ///\e |
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112 | enum SolveExitStatus { |
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113 | ///\e |
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114 | SOLVED = 0, |
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115 | ///\e |
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116 | UNSOLVED = 1 |
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117 | }; |
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118 | |
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119 | ///\e |
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120 | enum SolutionStatus { |
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121 | ///Feasible solution has'n been found (but may exist). |
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122 | |
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123 | ///\todo NOTFOUND might be a better name. |
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124 | /// |
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125 | UNDEFINED = 0, |
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126 | ///The problem has no feasible solution |
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127 | INFEASIBLE = 1, |
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128 | ///Feasible solution found |
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129 | FEASIBLE = 2, |
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130 | ///Optimal solution exists and found |
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131 | OPTIMAL = 3, |
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132 | ///The cost function is unbounded |
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133 | |
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134 | ///\todo Give a feasible solution and an infinite ray (and the |
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135 | ///corresponding bases) |
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136 | INFINITE = 4 |
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137 | }; |
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138 | |
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139 | ///The floating point type used by the solver |
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140 | typedef double Value; |
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141 | ///The infinity constant |
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142 | static const Value INF; |
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143 | ///The not a number constant |
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144 | static const Value NaN; |
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145 | |
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146 | ///Refer to a column of the LP. |
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147 | |
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148 | ///This type is used to refer to a column of the LP. |
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149 | /// |
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150 | ///Its value remains valid and correct even after the addition or erase of |
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151 | ///other columns. |
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152 | /// |
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153 | ///\todo Document what can one do with a Col (INVALID, comparing, |
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154 | ///it is similar to Node/Edge) |
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155 | class Col { |
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156 | protected: |
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157 | int id; |
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158 | friend class LpSolverBase; |
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159 | public: |
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160 | typedef Value ExprValue; |
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161 | typedef True LpSolverCol; |
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162 | Col() {} |
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163 | Col(const Invalid&) : id(-1) {} |
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164 | bool operator<(Col c) const {return id<c.id;} |
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165 | bool operator==(Col c) const {return id==c.id;} |
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166 | bool operator!=(Col c) const {return id==c.id;} |
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167 | }; |
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168 | |
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169 | ///Refer to a row of the LP. |
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170 | |
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171 | ///This type is used to refer to a row of the LP. |
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172 | /// |
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173 | ///Its value remains valid and correct even after the addition or erase of |
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174 | ///other rows. |
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175 | /// |
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176 | ///\todo Document what can one do with a Row (INVALID, comparing, |
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177 | ///it is similar to Node/Edge) |
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178 | class Row { |
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179 | protected: |
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180 | int id; |
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181 | friend class LpSolverBase; |
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182 | public: |
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183 | typedef Value ExprValue; |
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184 | typedef True LpSolverRow; |
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185 | Row() {} |
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186 | Row(const Invalid&) : id(-1) {} |
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187 | |
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188 | bool operator<(Row c) const {return id<c.id;} |
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189 | bool operator==(Row c) const {return id==c.id;} |
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190 | bool operator!=(Row c) const {return id==c.id;} |
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191 | }; |
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192 | |
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193 | ///Linear expression of variables and a constant component |
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194 | |
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195 | ///This data structure strores a linear expression of the variables |
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196 | ///(\ref Col "Col"s) and also has a constant component. |
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197 | /// |
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198 | ///There are several ways to access and modify the contents of this |
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199 | ///container. |
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200 | ///- Its it fully compatible with \c std::map<Col,double>, so for expamle |
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201 | ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can |
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202 | ///read and modify the coefficients like |
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203 | ///these. |
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204 | ///\code |
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205 | ///e[v]=5; |
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206 | ///e[v]+=12; |
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207 | ///e.erase(v); |
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208 | ///\endcode |
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209 | ///or you can also iterate through its elements. |
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210 | ///\code |
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211 | ///double s=0; |
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212 | ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i) |
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213 | /// s+=i->second; |
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214 | ///\endcode |
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215 | ///(This code computes the sum of all coefficients). |
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216 | ///- Numbers (<tt>double</tt>'s) |
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217 | ///and variables (\ref Col "Col"s) directly convert to an |
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218 | ///\ref Expr and the usual linear operations are defined so |
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219 | ///\code |
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220 | ///v+w |
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221 | ///2*v-3.12*(v-w/2)+2 |
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222 | ///v*2.1+(3*v+(v*12+w+6)*3)/2 |
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223 | ///\endcode |
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224 | ///are valid \ref Expr "Expr"essions. |
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225 | ///The usual assignment operations are also defined. |
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226 | ///\code |
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227 | ///e=v+w; |
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228 | ///e+=2*v-3.12*(v-w/2)+2; |
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229 | ///e*=3.4; |
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230 | ///e/=5; |
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231 | ///\endcode |
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232 | ///- The constant member can be set and read by \ref constComp() |
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233 | ///\code |
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234 | ///e.constComp()=12; |
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235 | ///double c=e.constComp(); |
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236 | ///\endcode |
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237 | /// |
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238 | ///\note \ref clear() not only sets all coefficients to 0 but also |
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239 | ///clears the constant components. |
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240 | /// |
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241 | ///\sa Constr |
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242 | /// |
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243 | class Expr : public std::map<Col,Value> |
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244 | { |
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245 | public: |
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246 | typedef LpSolverBase::Col Key; |
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247 | typedef LpSolverBase::Value Value; |
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248 | |
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249 | protected: |
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250 | typedef std::map<Col,Value> Base; |
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251 | |
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252 | Value const_comp; |
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253 | public: |
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254 | typedef True IsLinExpression; |
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255 | ///\e |
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256 | Expr() : Base(), const_comp(0) { } |
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257 | ///\e |
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258 | Expr(const Key &v) : const_comp(0) { |
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259 | Base::insert(std::make_pair(v, 1)); |
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260 | } |
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261 | ///\e |
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262 | Expr(const Value &v) : const_comp(v) {} |
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263 | ///\e |
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264 | void set(const Key &v,const Value &c) { |
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265 | Base::insert(std::make_pair(v, c)); |
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266 | } |
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267 | ///\e |
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268 | Value &constComp() { return const_comp; } |
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269 | ///\e |
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270 | const Value &constComp() const { return const_comp; } |
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271 | |
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272 | ///Removes the components with zero coefficient. |
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273 | void simplify() { |
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274 | for (Base::iterator i=Base::begin(); i!=Base::end();) { |
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275 | Base::iterator j=i; |
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276 | ++j; |
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277 | if ((*i).second==0) Base::erase(i); |
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278 | j=i; |
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279 | } |
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280 | } |
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281 | |
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282 | ///Sets all coefficients and the constant component to 0. |
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283 | void clear() { |
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284 | Base::clear(); |
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285 | const_comp=0; |
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286 | } |
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287 | |
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288 | ///\e |
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289 | Expr &operator+=(const Expr &e) { |
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290 | for (Base::const_iterator j=e.begin(); j!=e.end(); ++j) |
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291 | (*this)[j->first]+=j->second; |
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292 | ///\todo it might be speeded up using "hints" |
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293 | const_comp+=e.const_comp; |
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294 | return *this; |
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295 | } |
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296 | ///\e |
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297 | Expr &operator-=(const Expr &e) { |
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298 | for (Base::const_iterator j=e.begin(); j!=e.end(); ++j) |
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299 | (*this)[j->first]-=j->second; |
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300 | const_comp-=e.const_comp; |
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301 | return *this; |
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302 | } |
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303 | ///\e |
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304 | Expr &operator*=(const Value &c) { |
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305 | for (Base::iterator j=Base::begin(); j!=Base::end(); ++j) |
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306 | j->second*=c; |
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307 | const_comp*=c; |
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308 | return *this; |
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309 | } |
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310 | ///\e |
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311 | Expr &operator/=(const Value &c) { |
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312 | for (Base::iterator j=Base::begin(); j!=Base::end(); ++j) |
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313 | j->second/=c; |
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314 | const_comp/=c; |
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315 | return *this; |
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316 | } |
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317 | }; |
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318 | |
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319 | ///Linear constraint |
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320 | |
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321 | ///This data stucture represents a linear constraint in the LP. |
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322 | ///Basically it is a linear expression with a lower or an upper bound |
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323 | ///(or both). These parts of the constraint can be obtained by the member |
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324 | ///functions \ref expr(), \ref lowerBound() and \ref upperBound(), |
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325 | ///respectively. |
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326 | ///There are two ways to construct a constraint. |
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327 | ///- You can set the linear expression and the bounds directly |
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328 | /// by the functions above. |
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329 | ///- The operators <tt>\<=</tt>, <tt>==</tt> and <tt>\>=</tt> |
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330 | /// are defined between expressions, or even between constraints whenever |
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331 | /// it makes sense. Therefore if \c e and \c f are linear expressions and |
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332 | /// \c s and \c t are numbers, then the followings are valid expressions |
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333 | /// and thus they can be used directly e.g. in \ref addRow() whenever |
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334 | /// it makes sense. |
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335 | /// \code |
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336 | /// e<=s |
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337 | /// e<=f |
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338 | /// s<=e<=t |
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339 | /// e>=t |
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340 | /// \endcode |
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341 | ///\warning The validity of a constraint is checked only at run time, so |
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342 | ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a |
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343 | ///\ref LogicError exception. |
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344 | class Constr |
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345 | { |
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346 | public: |
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347 | typedef LpSolverBase::Expr Expr; |
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348 | typedef Expr::Key Key; |
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349 | typedef Expr::Value Value; |
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350 | |
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351 | // static const Value INF; |
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352 | // static const Value NaN; |
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353 | |
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354 | protected: |
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355 | Expr _expr; |
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356 | Value _lb,_ub; |
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357 | public: |
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358 | ///\e |
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359 | Constr() : _expr(), _lb(NaN), _ub(NaN) {} |
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360 | ///\e |
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361 | Constr(Value lb,const Expr &e,Value ub) : |
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362 | _expr(e), _lb(lb), _ub(ub) {} |
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363 | ///\e |
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364 | Constr(const Expr &e,Value ub) : |
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365 | _expr(e), _lb(NaN), _ub(ub) {} |
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366 | ///\e |
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367 | Constr(Value lb,const Expr &e) : |
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368 | _expr(e), _lb(lb), _ub(NaN) {} |
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369 | ///\e |
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370 | Constr(const Expr &e) : |
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371 | _expr(e), _lb(NaN), _ub(NaN) {} |
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372 | ///\e |
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373 | void clear() |
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374 | { |
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375 | _expr.clear(); |
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376 | _lb=_ub=NaN; |
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377 | } |
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378 | |
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379 | ///Reference to the linear expression |
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380 | Expr &expr() { return _expr; } |
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381 | ///Cont reference to the linear expression |
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382 | const Expr &expr() const { return _expr; } |
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383 | ///Reference to the lower bound. |
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384 | |
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385 | ///\return |
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386 | ///- -\ref INF: the constraint is lower unbounded. |
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387 | ///- -\ref NaN: lower bound has not been set. |
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388 | ///- finite number: the lower bound |
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389 | Value &lowerBound() { return _lb; } |
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390 | ///The const version of \ref lowerBound() |
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391 | const Value &lowerBound() const { return _lb; } |
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392 | ///Reference to the upper bound. |
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393 | |
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394 | ///\return |
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395 | ///- -\ref INF: the constraint is upper unbounded. |
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396 | ///- -\ref NaN: upper bound has not been set. |
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397 | ///- finite number: the upper bound |
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398 | Value &upperBound() { return _ub; } |
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399 | ///The const version of \ref upperBound() |
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400 | const Value &upperBound() const { return _ub; } |
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401 | ///Is the constraint lower bounded? |
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402 | bool lowerBounded() const { |
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403 | using namespace std; |
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404 | return finite(_lb); |
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405 | } |
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406 | ///Is the constraint upper bounded? |
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407 | bool upperBounded() const { |
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408 | using namespace std; |
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409 | return finite(_ub); |
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410 | } |
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411 | }; |
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412 | |
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413 | ///Linear expression of rows |
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414 | |
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415 | ///This data structure represents a column of the matrix, |
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416 | ///thas is it strores a linear expression of the dual variables |
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417 | ///(\ref Row "Row"s). |
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418 | /// |
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419 | ///There are several ways to access and modify the contents of this |
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420 | ///container. |
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421 | ///- Its it fully compatible with \c std::map<Row,double>, so for expamle |
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422 | ///if \c e is an DualExpr and \c v |
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423 | ///and \c w are of type \ref Row, then you can |
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424 | ///read and modify the coefficients like |
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425 | ///these. |
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426 | ///\code |
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427 | ///e[v]=5; |
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428 | ///e[v]+=12; |
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429 | ///e.erase(v); |
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430 | ///\endcode |
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431 | ///or you can also iterate through its elements. |
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432 | ///\code |
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433 | ///double s=0; |
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434 | ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i) |
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435 | /// s+=i->second; |
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436 | ///\endcode |
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437 | ///(This code computes the sum of all coefficients). |
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438 | ///- Numbers (<tt>double</tt>'s) |
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439 | ///and variables (\ref Row "Row"s) directly convert to an |
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440 | ///\ref DualExpr and the usual linear operations are defined so |
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441 | ///\code |
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442 | ///v+w |
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443 | ///2*v-3.12*(v-w/2) |
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444 | ///v*2.1+(3*v+(v*12+w)*3)/2 |
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445 | ///\endcode |
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446 | ///are valid \ref DualExpr "DualExpr"essions. |
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447 | ///The usual assignment operations are also defined. |
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448 | ///\code |
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449 | ///e=v+w; |
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450 | ///e+=2*v-3.12*(v-w/2); |
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451 | ///e*=3.4; |
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452 | ///e/=5; |
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453 | ///\endcode |
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454 | /// |
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455 | ///\sa Expr |
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456 | /// |
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457 | class DualExpr : public std::map<Row,Value> |
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458 | { |
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459 | public: |
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460 | typedef LpSolverBase::Row Key; |
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461 | typedef LpSolverBase::Value Value; |
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462 | |
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463 | protected: |
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464 | typedef std::map<Row,Value> Base; |
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465 | |
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466 | public: |
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467 | typedef True IsLinExpression; |
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468 | ///\e |
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469 | DualExpr() : Base() { } |
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470 | ///\e |
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471 | DualExpr(const Key &v) { |
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472 | Base::insert(std::make_pair(v, 1)); |
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473 | } |
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474 | ///\e |
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475 | DualExpr(const Value &v) {} |
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476 | ///\e |
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477 | void set(const Key &v,const Value &c) { |
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478 | Base::insert(std::make_pair(v, c)); |
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479 | } |
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480 | |
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481 | ///Removes the components with zero coefficient. |
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482 | void simplify() { |
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483 | for (Base::iterator i=Base::begin(); i!=Base::end();) { |
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484 | Base::iterator j=i; |
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485 | ++j; |
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486 | if ((*i).second==0) Base::erase(i); |
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487 | j=i; |
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488 | } |
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489 | } |
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490 | |
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491 | ///Sets all coefficients to 0. |
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492 | void clear() { |
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493 | Base::clear(); |
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494 | } |
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495 | |
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496 | ///\e |
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497 | DualExpr &operator+=(const DualExpr &e) { |
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498 | for (Base::const_iterator j=e.begin(); j!=e.end(); ++j) |
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499 | (*this)[j->first]+=j->second; |
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500 | ///\todo it might be speeded up using "hints" |
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501 | return *this; |
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502 | } |
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503 | ///\e |
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504 | DualExpr &operator-=(const DualExpr &e) { |
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505 | for (Base::const_iterator j=e.begin(); j!=e.end(); ++j) |
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506 | (*this)[j->first]-=j->second; |
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507 | return *this; |
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508 | } |
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509 | ///\e |
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510 | DualExpr &operator*=(const Value &c) { |
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511 | for (Base::iterator j=Base::begin(); j!=Base::end(); ++j) |
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512 | j->second*=c; |
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513 | return *this; |
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514 | } |
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515 | ///\e |
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516 | DualExpr &operator/=(const Value &c) { |
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517 | for (Base::iterator j=Base::begin(); j!=Base::end(); ++j) |
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518 | j->second/=c; |
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519 | return *this; |
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520 | } |
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521 | }; |
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522 | |
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523 | |
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524 | protected: |
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525 | _FixId rows; |
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526 | _FixId cols; |
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527 | |
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528 | //Abstract virtual functions |
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529 | virtual LpSolverBase &_newLp() = 0; |
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530 | virtual LpSolverBase &_copyLp(){ |
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531 | ///\todo This should be implemented here, too, when we have problem retrieving routines. It can be overriden. |
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532 | |
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533 | //Starting: |
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534 | LpSolverBase & newlp(_newLp()); |
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535 | return newlp; |
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536 | //return *(LpSolverBase*)0; |
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537 | }; |
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538 | |
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539 | virtual int _addCol() = 0; |
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540 | virtual int _addRow() = 0; |
---|
541 | virtual void _setRowCoeffs(int i, |
---|
542 | int length, |
---|
543 | int const * indices, |
---|
544 | Value const * values ) = 0; |
---|
545 | virtual void _setColCoeffs(int i, |
---|
546 | int length, |
---|
547 | int const * indices, |
---|
548 | Value const * values ) = 0; |
---|
549 | virtual void _setCoeff(int row, int col, Value value) = 0; |
---|
550 | virtual void _setColLowerBound(int i, Value value) = 0; |
---|
551 | virtual void _setColUpperBound(int i, Value value) = 0; |
---|
552 | // virtual void _setRowLowerBound(int i, Value value) = 0; |
---|
553 | // virtual void _setRowUpperBound(int i, Value value) = 0; |
---|
554 | virtual void _setRowBounds(int i, Value lower, Value upper) = 0; |
---|
555 | virtual void _setObjCoeff(int i, Value obj_coef) = 0; |
---|
556 | virtual void _clearObj()=0; |
---|
557 | // virtual void _setObj(int length, |
---|
558 | // int const * indices, |
---|
559 | // Value const * values ) = 0; |
---|
560 | virtual SolveExitStatus _solve() = 0; |
---|
561 | virtual Value _getPrimal(int i) = 0; |
---|
562 | virtual Value _getPrimalValue() = 0; |
---|
563 | virtual SolutionStatus _getPrimalStatus() = 0; |
---|
564 | virtual void _setMax() = 0; |
---|
565 | virtual void _setMin() = 0; |
---|
566 | |
---|
567 | //Own protected stuff |
---|
568 | |
---|
569 | //Constant component of the objective function |
---|
570 | Value obj_const_comp; |
---|
571 | |
---|
572 | |
---|
573 | |
---|
574 | |
---|
575 | public: |
---|
576 | |
---|
577 | ///\e |
---|
578 | LpSolverBase() : obj_const_comp(0) {} |
---|
579 | |
---|
580 | ///\e |
---|
581 | virtual ~LpSolverBase() {} |
---|
582 | |
---|
583 | ///Creates a new LP problem |
---|
584 | LpSolverBase &newLp() {return _newLp();} |
---|
585 | ///Makes a copy of the LP problem |
---|
586 | LpSolverBase ©Lp() {return _copyLp();} |
---|
587 | |
---|
588 | ///\name Build up and modify of the LP |
---|
589 | |
---|
590 | ///@{ |
---|
591 | |
---|
592 | ///Add a new empty column (i.e a new variable) to the LP |
---|
593 | Col addCol() { Col c; c.id=cols.insert(_addCol()); return c;} |
---|
594 | |
---|
595 | ///\brief Adds several new columns |
---|
596 | ///(i.e a variables) at once |
---|
597 | /// |
---|
598 | ///This magic function takes a container as its argument |
---|
599 | ///and fills its elements |
---|
600 | ///with new columns (i.e. variables) |
---|
601 | ///\param t can be |
---|
602 | ///- a standard STL compatible iterable container with |
---|
603 | ///\ref Col as its \c values_type |
---|
604 | ///like |
---|
605 | ///\code |
---|
606 | ///std::vector<LpSolverBase::Col> |
---|
607 | ///std::list<LpSolverBase::Col> |
---|
608 | ///\endcode |
---|
609 | ///- a standard STL compatible iterable container with |
---|
610 | ///\ref Col as its \c mapped_type |
---|
611 | ///like |
---|
612 | ///\code |
---|
613 | ///std::map<AnyType,LpSolverBase::Col> |
---|
614 | ///\endcode |
---|
615 | ///- an iterable lemon \ref concept::WriteMap "write map" like |
---|
616 | ///\code |
---|
617 | ///ListGraph::NodeMap<LpSolverBase::Col> |
---|
618 | ///ListGraph::EdgeMap<LpSolverBase::Col> |
---|
619 | ///\endcode |
---|
620 | ///\return The number of the created column. |
---|
621 | #ifdef DOXYGEN |
---|
622 | template<class T> |
---|
623 | int addColSet(T &t) { return 0;} |
---|
624 | #else |
---|
625 | template<class T> |
---|
626 | typename enable_if<typename T::value_type::LpSolverCol,int>::type |
---|
627 | addColSet(T &t,dummy<0> = 0) { |
---|
628 | int s=0; |
---|
629 | for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;} |
---|
630 | return s; |
---|
631 | } |
---|
632 | template<class T> |
---|
633 | typename enable_if<typename T::value_type::second_type::LpSolverCol, |
---|
634 | int>::type |
---|
635 | addColSet(T &t,dummy<1> = 1) { |
---|
636 | int s=0; |
---|
637 | for(typename T::iterator i=t.begin();i!=t.end();++i) { |
---|
638 | i->second=addCol(); |
---|
639 | s++; |
---|
640 | } |
---|
641 | return s; |
---|
642 | } |
---|
643 | template<class T> |
---|
644 | typename enable_if<typename T::ValueSet::value_type::LpSolverCol, |
---|
645 | int>::type |
---|
646 | addColSet(T &t,dummy<2> = 2) { |
---|
647 | ///\bug <tt>return addColSet(t.valueSet());</tt> should also work. |
---|
648 | int s=0; |
---|
649 | for(typename T::ValueSet::iterator i=t.valueSet().begin(); |
---|
650 | i!=t.valueSet().end(); |
---|
651 | ++i) |
---|
652 | { |
---|
653 | *i=addCol(); |
---|
654 | s++; |
---|
655 | } |
---|
656 | return s; |
---|
657 | } |
---|
658 | #endif |
---|
659 | |
---|
660 | ///Set a column (i.e a dual constraint) of the LP |
---|
661 | |
---|
662 | ///\param c is the column to be modified |
---|
663 | ///\param e is a dual linear expression (see \ref DualExpr) |
---|
664 | ///\bug This is a temportary function. The interface will change to |
---|
665 | ///a better one. |
---|
666 | void setCol(Col c,const DualExpr &e) { |
---|
667 | std::vector<int> indices; |
---|
668 | std::vector<Value> values; |
---|
669 | indices.push_back(0); |
---|
670 | values.push_back(0); |
---|
671 | for(DualExpr::const_iterator i=e.begin(); i!=e.end(); ++i) |
---|
672 | if((*i).second!=0) { ///\bug EPSILON would be necessary here!!! |
---|
673 | indices.push_back(cols.floatingId((*i).first.id)); |
---|
674 | values.push_back((*i).second); |
---|
675 | } |
---|
676 | _setColCoeffs(cols.floatingId(c.id),indices.size()-1, |
---|
677 | &indices[0],&values[0]); |
---|
678 | } |
---|
679 | |
---|
680 | ///Add a new column to the LP |
---|
681 | |
---|
682 | ///\param e is a dual linear expression (see \ref DualExpr) |
---|
683 | ///\param obj is the corresponding component of the objective |
---|
684 | ///function. It is 0 by default. |
---|
685 | ///\return The created column. |
---|
686 | ///\bug This is a temportary function. The interface will change to |
---|
687 | ///a better one. |
---|
688 | Col addCol(Value l,const DualExpr &e, Value obj=0) { |
---|
689 | Col c=addCol(); |
---|
690 | setCol(c,e); |
---|
691 | objCoeff(c,0); |
---|
692 | return c; |
---|
693 | } |
---|
694 | |
---|
695 | ///Add a new empty row (i.e a new constraint) to the LP |
---|
696 | |
---|
697 | ///This function adds a new empty row (i.e a new constraint) to the LP. |
---|
698 | ///\return The created row |
---|
699 | Row addRow() { Row r; r.id=rows.insert(_addRow()); return r;} |
---|
700 | |
---|
701 | ///\brief Adds several new row |
---|
702 | ///(i.e a variables) at once |
---|
703 | /// |
---|
704 | ///This magic function takes a container as its argument |
---|
705 | ///and fills its elements |
---|
706 | ///with new row (i.e. variables) |
---|
707 | ///\param t can be |
---|
708 | ///- a standard STL compatible iterable container with |
---|
709 | ///\ref Row as its \c values_type |
---|
710 | ///like |
---|
711 | ///\code |
---|
712 | ///std::vector<LpSolverBase::Row> |
---|
713 | ///std::list<LpSolverBase::Row> |
---|
714 | ///\endcode |
---|
715 | ///- a standard STL compatible iterable container with |
---|
716 | ///\ref Row as its \c mapped_type |
---|
717 | ///like |
---|
718 | ///\code |
---|
719 | ///std::map<AnyType,LpSolverBase::Row> |
---|
720 | ///\endcode |
---|
721 | ///- an iterable lemon \ref concept::WriteMap "write map" like |
---|
722 | ///\code |
---|
723 | ///ListGraph::NodeMap<LpSolverBase::Row> |
---|
724 | ///ListGraph::EdgeMap<LpSolverBase::Row> |
---|
725 | ///\endcode |
---|
726 | ///\return The number of rows created. |
---|
727 | #ifdef DOXYGEN |
---|
728 | template<class T> |
---|
729 | int addRowSet(T &t) { return 0;} |
---|
730 | #else |
---|
731 | template<class T> |
---|
732 | typename enable_if<typename T::value_type::LpSolverRow,int>::type |
---|
733 | addRowSet(T &t,dummy<0> = 0) { |
---|
734 | int s=0; |
---|
735 | for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;} |
---|
736 | return s; |
---|
737 | } |
---|
738 | template<class T> |
---|
739 | typename enable_if<typename T::value_type::second_type::LpSolverRow, |
---|
740 | int>::type |
---|
741 | addRowSet(T &t,dummy<1> = 1) { |
---|
742 | int s=0; |
---|
743 | for(typename T::iterator i=t.begin();i!=t.end();++i) { |
---|
744 | i->second=addRow(); |
---|
745 | s++; |
---|
746 | } |
---|
747 | return s; |
---|
748 | } |
---|
749 | template<class T> |
---|
750 | typename enable_if<typename T::ValueSet::value_type::LpSolverRow, |
---|
751 | int>::type |
---|
752 | addRowSet(T &t,dummy<2> = 2) { |
---|
753 | ///\bug <tt>return addRowSet(t.valueSet());</tt> should also work. |
---|
754 | int s=0; |
---|
755 | for(typename T::ValueSet::iterator i=t.valueSet().begin(); |
---|
756 | i!=t.valueSet().end(); |
---|
757 | ++i) |
---|
758 | { |
---|
759 | *i=addRow(); |
---|
760 | s++; |
---|
761 | } |
---|
762 | return s; |
---|
763 | } |
---|
764 | #endif |
---|
765 | |
---|
766 | ///Set a row (i.e a constraint) of the LP |
---|
767 | |
---|
768 | ///\param r is the row to be modified |
---|
769 | ///\param l is lower bound (-\ref INF means no bound) |
---|
770 | ///\param e is a linear expression (see \ref Expr) |
---|
771 | ///\param u is the upper bound (\ref INF means no bound) |
---|
772 | ///\bug This is a temportary function. The interface will change to |
---|
773 | ///a better one. |
---|
774 | ///\todo Option to control whether a constraint with a single variable is |
---|
775 | ///added or not. |
---|
776 | void setRow(Row r, Value l,const Expr &e, Value u) { |
---|
777 | std::vector<int> indices; |
---|
778 | std::vector<Value> values; |
---|
779 | indices.push_back(0); |
---|
780 | values.push_back(0); |
---|
781 | for(Expr::const_iterator i=e.begin(); i!=e.end(); ++i) |
---|
782 | if((*i).second!=0) { ///\bug EPSILON would be necessary here!!! |
---|
783 | indices.push_back(cols.floatingId((*i).first.id)); |
---|
784 | values.push_back((*i).second); |
---|
785 | } |
---|
786 | _setRowCoeffs(rows.floatingId(r.id),indices.size()-1, |
---|
787 | &indices[0],&values[0]); |
---|
788 | // _setRowLowerBound(rows.floatingId(r.id),l-e.constComp()); |
---|
789 | // _setRowUpperBound(rows.floatingId(r.id),u-e.constComp()); |
---|
790 | _setRowBounds(rows.floatingId(r.id),l-e.constComp(),u-e.constComp()); |
---|
791 | } |
---|
792 | |
---|
793 | ///Set a row (i.e a constraint) of the LP |
---|
794 | |
---|
795 | ///\param r is the row to be modified |
---|
796 | ///\param c is a linear expression (see \ref Constr) |
---|
797 | void setRow(Row r, const Constr &c) { |
---|
798 | setRow(r, |
---|
799 | c.lowerBounded()?c.lowerBound():-INF, |
---|
800 | c.expr(), |
---|
801 | c.upperBounded()?c.upperBound():INF); |
---|
802 | } |
---|
803 | |
---|
804 | ///Add a new row (i.e a new constraint) to the LP |
---|
805 | |
---|
806 | ///\param l is the lower bound (-\ref INF means no bound) |
---|
807 | ///\param e is a linear expression (see \ref Expr) |
---|
808 | ///\param u is the upper bound (\ref INF means no bound) |
---|
809 | ///\return The created row. |
---|
810 | ///\bug This is a temportary function. The interface will change to |
---|
811 | ///a better one. |
---|
812 | Row addRow(Value l,const Expr &e, Value u) { |
---|
813 | Row r=addRow(); |
---|
814 | setRow(r,l,e,u); |
---|
815 | return r; |
---|
816 | } |
---|
817 | |
---|
818 | ///Add a new row (i.e a new constraint) to the LP |
---|
819 | |
---|
820 | ///\param c is a linear expression (see \ref Constr) |
---|
821 | ///\return The created row. |
---|
822 | Row addRow(const Constr &c) { |
---|
823 | Row r=addRow(); |
---|
824 | setRow(r,c); |
---|
825 | return r; |
---|
826 | } |
---|
827 | |
---|
828 | ///Set an element of the coefficient matrix of the LP |
---|
829 | |
---|
830 | ///\param r is the row of the element to be modified |
---|
831 | ///\param c is the coloumn of the element to be modified |
---|
832 | ///\param val is the new value of the coefficient |
---|
833 | void setCoeff(Row r, Col c, Value val){ |
---|
834 | _setCoeff(rows.floatingId(r.id),cols.floatingId(c.id), val); |
---|
835 | } |
---|
836 | |
---|
837 | /// Set the lower bound of a column (i.e a variable) |
---|
838 | |
---|
839 | /// The upper bound of a variable (column) has to be given by an |
---|
840 | /// extended number of type Value, i.e. a finite number of type |
---|
841 | /// Value or -\ref INF. |
---|
842 | void colLowerBound(Col c, Value value) { |
---|
843 | _setColLowerBound(cols.floatingId(c.id),value); |
---|
844 | } |
---|
845 | /// Set the upper bound of a column (i.e a variable) |
---|
846 | |
---|
847 | /// The upper bound of a variable (column) has to be given by an |
---|
848 | /// extended number of type Value, i.e. a finite number of type |
---|
849 | /// Value or \ref INF. |
---|
850 | void colUpperBound(Col c, Value value) { |
---|
851 | _setColUpperBound(cols.floatingId(c.id),value); |
---|
852 | }; |
---|
853 | /// Set the lower and the upper bounds of a column (i.e a variable) |
---|
854 | |
---|
855 | /// The lower and the upper bounds of |
---|
856 | /// a variable (column) have to be given by an |
---|
857 | /// extended number of type Value, i.e. a finite number of type |
---|
858 | /// Value, -\ref INF or \ref INF. |
---|
859 | void colBounds(Col c, Value lower, Value upper) { |
---|
860 | _setColLowerBound(cols.floatingId(c.id),lower); |
---|
861 | _setColUpperBound(cols.floatingId(c.id),upper); |
---|
862 | } |
---|
863 | |
---|
864 | // /// Set the lower bound of a row (i.e a constraint) |
---|
865 | |
---|
866 | // /// The lower bound of a linear expression (row) has to be given by an |
---|
867 | // /// extended number of type Value, i.e. a finite number of type |
---|
868 | // /// Value or -\ref INF. |
---|
869 | // void rowLowerBound(Row r, Value value) { |
---|
870 | // _setRowLowerBound(rows.floatingId(r.id),value); |
---|
871 | // }; |
---|
872 | // /// Set the upper bound of a row (i.e a constraint) |
---|
873 | |
---|
874 | // /// The upper bound of a linear expression (row) has to be given by an |
---|
875 | // /// extended number of type Value, i.e. a finite number of type |
---|
876 | // /// Value or \ref INF. |
---|
877 | // void rowUpperBound(Row r, Value value) { |
---|
878 | // _setRowUpperBound(rows.floatingId(r.id),value); |
---|
879 | // }; |
---|
880 | |
---|
881 | /// Set the lower and the upper bounds of a row (i.e a constraint) |
---|
882 | |
---|
883 | /// The lower and the upper bounds of |
---|
884 | /// a constraint (row) have to be given by an |
---|
885 | /// extended number of type Value, i.e. a finite number of type |
---|
886 | /// Value, -\ref INF or \ref INF. |
---|
887 | void rowBounds(Row c, Value lower, Value upper) { |
---|
888 | _setRowBounds(rows.floatingId(c.id),lower, upper); |
---|
889 | // _setRowUpperBound(rows.floatingId(c.id),upper); |
---|
890 | } |
---|
891 | |
---|
892 | ///Set an element of the objective function |
---|
893 | void objCoeff(Col c, Value v) {_setObjCoeff(cols.floatingId(c.id),v); }; |
---|
894 | ///Set the objective function |
---|
895 | |
---|
896 | ///\param e is a linear expression of type \ref Expr. |
---|
897 | ///\bug The previous objective function is not cleared! |
---|
898 | void setObj(Expr e) { |
---|
899 | _clearObj(); |
---|
900 | for (Expr::iterator i=e.begin(); i!=e.end(); ++i) |
---|
901 | objCoeff((*i).first,(*i).second); |
---|
902 | obj_const_comp=e.constComp(); |
---|
903 | } |
---|
904 | |
---|
905 | ///Maximize |
---|
906 | void max() { _setMax(); } |
---|
907 | ///Minimize |
---|
908 | void min() { _setMin(); } |
---|
909 | |
---|
910 | |
---|
911 | ///@} |
---|
912 | |
---|
913 | |
---|
914 | ///\name Solve the LP |
---|
915 | |
---|
916 | ///@{ |
---|
917 | |
---|
918 | ///\e |
---|
919 | SolveExitStatus solve() { return _solve(); } |
---|
920 | |
---|
921 | ///@} |
---|
922 | |
---|
923 | ///\name Obtain the solution |
---|
924 | |
---|
925 | ///@{ |
---|
926 | |
---|
927 | ///\e |
---|
928 | SolutionStatus primalStatus() { |
---|
929 | return _getPrimalStatus(); |
---|
930 | } |
---|
931 | |
---|
932 | ///\e |
---|
933 | Value primal(Col c) { return _getPrimal(cols.floatingId(c.id)); } |
---|
934 | |
---|
935 | ///\e |
---|
936 | |
---|
937 | ///\return |
---|
938 | ///- \ref INF or -\ref INF means either infeasibility or unboundedness |
---|
939 | /// of the primal problem, depending on whether we minimize or maximize. |
---|
940 | ///- \ref NaN if no primal solution is found. |
---|
941 | ///- The (finite) objective value if an optimal solution is found. |
---|
942 | Value primalValue() { return _getPrimalValue()+obj_const_comp;} |
---|
943 | ///@} |
---|
944 | |
---|
945 | }; |
---|
946 | |
---|
947 | ///\e |
---|
948 | |
---|
949 | ///\relates LpSolverBase::Expr |
---|
950 | /// |
---|
951 | inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a, |
---|
952 | const LpSolverBase::Expr &b) |
---|
953 | { |
---|
954 | LpSolverBase::Expr tmp(a); |
---|
955 | tmp+=b; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
956 | return tmp; |
---|
957 | } |
---|
958 | ///\e |
---|
959 | |
---|
960 | ///\relates LpSolverBase::Expr |
---|
961 | /// |
---|
962 | inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a, |
---|
963 | const LpSolverBase::Expr &b) |
---|
964 | { |
---|
965 | LpSolverBase::Expr tmp(a); |
---|
966 | tmp-=b; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
967 | return tmp; |
---|
968 | } |
---|
969 | ///\e |
---|
970 | |
---|
971 | ///\relates LpSolverBase::Expr |
---|
972 | /// |
---|
973 | inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a, |
---|
974 | const LpSolverBase::Value &b) |
---|
975 | { |
---|
976 | LpSolverBase::Expr tmp(a); |
---|
977 | tmp*=b; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
978 | return tmp; |
---|
979 | } |
---|
980 | |
---|
981 | ///\e |
---|
982 | |
---|
983 | ///\relates LpSolverBase::Expr |
---|
984 | /// |
---|
985 | inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a, |
---|
986 | const LpSolverBase::Expr &b) |
---|
987 | { |
---|
988 | LpSolverBase::Expr tmp(b); |
---|
989 | tmp*=a; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
990 | return tmp; |
---|
991 | } |
---|
992 | ///\e |
---|
993 | |
---|
994 | ///\relates LpSolverBase::Expr |
---|
995 | /// |
---|
996 | inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a, |
---|
997 | const LpSolverBase::Value &b) |
---|
998 | { |
---|
999 | LpSolverBase::Expr tmp(a); |
---|
1000 | tmp/=b; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
1001 | return tmp; |
---|
1002 | } |
---|
1003 | |
---|
1004 | ///\e |
---|
1005 | |
---|
1006 | ///\relates LpSolverBase::Constr |
---|
1007 | /// |
---|
1008 | inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e, |
---|
1009 | const LpSolverBase::Expr &f) |
---|
1010 | { |
---|
1011 | return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0); |
---|
1012 | } |
---|
1013 | |
---|
1014 | ///\e |
---|
1015 | |
---|
1016 | ///\relates LpSolverBase::Constr |
---|
1017 | /// |
---|
1018 | inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e, |
---|
1019 | const LpSolverBase::Expr &f) |
---|
1020 | { |
---|
1021 | return LpSolverBase::Constr(e,f); |
---|
1022 | } |
---|
1023 | |
---|
1024 | ///\e |
---|
1025 | |
---|
1026 | ///\relates LpSolverBase::Constr |
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1027 | /// |
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1028 | inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e, |
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1029 | const LpSolverBase::Value &f) |
---|
1030 | { |
---|
1031 | return LpSolverBase::Constr(e,f); |
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1032 | } |
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1033 | |
---|
1034 | ///\e |
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1035 | |
---|
1036 | ///\relates LpSolverBase::Constr |
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1037 | /// |
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1038 | inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e, |
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1039 | const LpSolverBase::Expr &f) |
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1040 | { |
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1041 | return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0); |
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1042 | } |
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1043 | |
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1044 | |
---|
1045 | ///\e |
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1046 | |
---|
1047 | ///\relates LpSolverBase::Constr |
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1048 | /// |
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1049 | inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e, |
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1050 | const LpSolverBase::Expr &f) |
---|
1051 | { |
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1052 | return LpSolverBase::Constr(f,e); |
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1053 | } |
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1054 | |
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1055 | |
---|
1056 | ///\e |
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1057 | |
---|
1058 | ///\relates LpSolverBase::Constr |
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1059 | /// |
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1060 | inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e, |
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1061 | const LpSolverBase::Value &f) |
---|
1062 | { |
---|
1063 | return LpSolverBase::Constr(f,e); |
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1064 | } |
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1065 | |
---|
1066 | ///\e |
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1067 | |
---|
1068 | ///\relates LpSolverBase::Constr |
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1069 | /// |
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1070 | inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e, |
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1071 | const LpSolverBase::Expr &f) |
---|
1072 | { |
---|
1073 | return LpSolverBase::Constr(0,e-f,0); |
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1074 | } |
---|
1075 | |
---|
1076 | ///\e |
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1077 | |
---|
1078 | ///\relates LpSolverBase::Constr |
---|
1079 | /// |
---|
1080 | inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n, |
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1081 | const LpSolverBase::Constr&c) |
---|
1082 | { |
---|
1083 | LpSolverBase::Constr tmp(c); |
---|
1084 | ///\todo Create an own exception type. |
---|
1085 | if(!isnan(tmp.lowerBound())) throw LogicError(); |
---|
1086 | else tmp.lowerBound()=n; |
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1087 | return tmp; |
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1088 | } |
---|
1089 | ///\e |
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1090 | |
---|
1091 | ///\relates LpSolverBase::Constr |
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1092 | /// |
---|
1093 | inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c, |
---|
1094 | const LpSolverBase::Value &n) |
---|
1095 | { |
---|
1096 | LpSolverBase::Constr tmp(c); |
---|
1097 | ///\todo Create an own exception type. |
---|
1098 | if(!isnan(tmp.upperBound())) throw LogicError(); |
---|
1099 | else tmp.upperBound()=n; |
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1100 | return tmp; |
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1101 | } |
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1102 | |
---|
1103 | ///\e |
---|
1104 | |
---|
1105 | ///\relates LpSolverBase::Constr |
---|
1106 | /// |
---|
1107 | inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n, |
---|
1108 | const LpSolverBase::Constr&c) |
---|
1109 | { |
---|
1110 | LpSolverBase::Constr tmp(c); |
---|
1111 | ///\todo Create an own exception type. |
---|
1112 | if(!isnan(tmp.upperBound())) throw LogicError(); |
---|
1113 | else tmp.upperBound()=n; |
---|
1114 | return tmp; |
---|
1115 | } |
---|
1116 | ///\e |
---|
1117 | |
---|
1118 | ///\relates LpSolverBase::Constr |
---|
1119 | /// |
---|
1120 | inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c, |
---|
1121 | const LpSolverBase::Value &n) |
---|
1122 | { |
---|
1123 | LpSolverBase::Constr tmp(c); |
---|
1124 | ///\todo Create an own exception type. |
---|
1125 | if(!isnan(tmp.lowerBound())) throw LogicError(); |
---|
1126 | else tmp.lowerBound()=n; |
---|
1127 | return tmp; |
---|
1128 | } |
---|
1129 | |
---|
1130 | ///\e |
---|
1131 | |
---|
1132 | ///\relates LpSolverBase::DualExpr |
---|
1133 | /// |
---|
1134 | inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a, |
---|
1135 | const LpSolverBase::DualExpr &b) |
---|
1136 | { |
---|
1137 | LpSolverBase::DualExpr tmp(a); |
---|
1138 | tmp+=b; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
1139 | return tmp; |
---|
1140 | } |
---|
1141 | ///\e |
---|
1142 | |
---|
1143 | ///\relates LpSolverBase::DualExpr |
---|
1144 | /// |
---|
1145 | inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a, |
---|
1146 | const LpSolverBase::DualExpr &b) |
---|
1147 | { |
---|
1148 | LpSolverBase::DualExpr tmp(a); |
---|
1149 | tmp-=b; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
1150 | return tmp; |
---|
1151 | } |
---|
1152 | ///\e |
---|
1153 | |
---|
1154 | ///\relates LpSolverBase::DualExpr |
---|
1155 | /// |
---|
1156 | inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a, |
---|
1157 | const LpSolverBase::Value &b) |
---|
1158 | { |
---|
1159 | LpSolverBase::DualExpr tmp(a); |
---|
1160 | tmp*=b; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
1161 | return tmp; |
---|
1162 | } |
---|
1163 | |
---|
1164 | ///\e |
---|
1165 | |
---|
1166 | ///\relates LpSolverBase::DualExpr |
---|
1167 | /// |
---|
1168 | inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a, |
---|
1169 | const LpSolverBase::DualExpr &b) |
---|
1170 | { |
---|
1171 | LpSolverBase::DualExpr tmp(b); |
---|
1172 | tmp*=a; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
1173 | return tmp; |
---|
1174 | } |
---|
1175 | ///\e |
---|
1176 | |
---|
1177 | ///\relates LpSolverBase::DualExpr |
---|
1178 | /// |
---|
1179 | inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a, |
---|
1180 | const LpSolverBase::Value &b) |
---|
1181 | { |
---|
1182 | LpSolverBase::DualExpr tmp(a); |
---|
1183 | tmp/=b; ///\todo Doesn't STL have some special 'merge' algorithm? |
---|
1184 | return tmp; |
---|
1185 | } |
---|
1186 | |
---|
1187 | |
---|
1188 | } //namespace lemon |
---|
1189 | |
---|
1190 | #endif //LEMON_LP_BASE_H |
---|