1 | ////////////////////////////////////////////////////////////////////////////// |
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2 | version="version intprog.lib 4.2.1.3 Dec_2021 "; // $Id$ |
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3 | category="Commutative Algebra"; |
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4 | info=" |
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5 | LIBRARY: intprog.lib Integer Programming with Groebner Basis Methods |
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6 | AUTHOR: Christine Theis, email: ctheis@math.uni-sb.de |
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7 | |
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8 | PROCEDURES: |
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9 | solve_IP(..); procedures for solving Integer Programming problems |
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10 | "; |
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11 | |
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12 | /////////////////////////////////////////////////////////////////////////////// |
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13 | static proc solve_IP_1(intmat A, intvec bx, intvec c, string alg) |
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14 | { |
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15 | intvec v; |
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16 | // to be returned |
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17 | |
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18 | // check arguments as far as necessary |
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19 | // other inconsistencies are detected by the external program |
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20 | if(size(c)!=ncols(A)) |
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21 | { |
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22 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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23 | return(v); |
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24 | } |
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25 | |
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26 | // create first temporary file with which the external program is |
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27 | // called |
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28 | |
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29 | int process=system("pid"); |
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30 | string matrixfile="temp_MATRIX"+string(process); |
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31 | link MATRIX=":w "+matrixfile; |
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32 | open(MATRIX); |
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33 | |
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34 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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35 | int i,j; |
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36 | for(j=1;j<=ncols(A);j++) |
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37 | { |
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38 | write(MATRIX,c[j]); |
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39 | } |
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40 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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41 | for(i=1;i<=nrows(A);i++) |
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42 | { |
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43 | for(j=1;j<=ncols(A);j++) |
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44 | { |
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45 | write(MATRIX,A[i,j]); |
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46 | } |
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47 | } |
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48 | |
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49 | // search for positive row space vector, if required by the |
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50 | // algorithm |
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51 | int found=0; |
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52 | if((alg=="blr") || (alg=="hs")) |
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53 | { |
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54 | for(i=1;i<=nrows(A);i++) |
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55 | { |
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56 | found=i; |
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57 | for(j=1;j<=ncols(A);j++) |
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58 | { |
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59 | if(A[i,j]<=0) |
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60 | { |
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61 | found=0; |
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62 | } |
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63 | } |
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64 | if(found>0) |
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65 | { |
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66 | break; |
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67 | } |
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68 | } |
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69 | if(found==0) |
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70 | { |
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71 | "ERROR: The chosen algorithm needs a positive vector in the row space of the matrix."; |
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72 | close(MATRIX); |
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73 | system("sh","rm -f "+matrixfile); |
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74 | return(v); |
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75 | } |
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76 | write(MATRIX,"positive row space vector:"); |
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77 | for(j=1;j<=ncols(A);j++) |
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78 | { |
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79 | write(MATRIX,A[found,j]); |
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80 | } |
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81 | } |
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82 | close(MATRIX); |
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83 | |
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84 | // create second temporary file for the external program |
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85 | |
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86 | string problemfile="temp_PROBLEM"+string(process); |
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87 | link PROBLEM=":w "+problemfile; |
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88 | open(PROBLEM); |
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89 | |
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90 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
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91 | for(i=1;i<=size(bx);i++) |
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92 | { |
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93 | write(PROBLEM,bx[i]); |
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94 | } |
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95 | close(PROBLEM); |
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96 | |
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97 | // call external program |
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98 | if (status(system("SingularBin")+"solve_IP","exists")=="yes") |
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99 | { |
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100 | int dummy=system("sh",system("SingularBin")+"solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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101 | } |
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102 | else |
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103 | { |
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104 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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105 | } |
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106 | |
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107 | // read solution from created file |
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108 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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109 | string solution=read(SOLUTION); |
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110 | int pos; |
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111 | string s; |
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112 | if(alg=="ct" || alg=="pct") |
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113 | { |
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114 | pos=find(solution,"NO"); |
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115 | if(pos!=0) |
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116 | { |
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117 | "not solvable"; |
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118 | } |
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119 | else |
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120 | { |
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121 | pos=find(solution,"YES"); |
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122 | pos=find(solution,":",pos); |
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123 | pos++; |
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124 | for(j=1;j<=ncols(A);j++) |
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125 | { |
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126 | while(solution[pos]==" " || solution[pos]==newline) |
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127 | { |
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128 | pos++; |
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129 | } |
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130 | s=""; |
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131 | while(solution[pos]!=" " && solution[pos]!=newline) |
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132 | { |
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133 | s=s+solution[pos]; |
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134 | pos++; |
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135 | } |
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136 | execute("v[j]="+s+";"); |
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137 | } |
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138 | } |
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139 | } |
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140 | else |
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141 | { |
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142 | pos=find(solution,"optimal"); |
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143 | pos=find(solution,":",pos); |
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144 | pos++; |
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145 | for(j=1;j<=ncols(A);j++) |
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146 | { |
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147 | while(solution[pos]==" " || solution[pos]==newline) |
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148 | { |
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149 | pos++; |
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150 | } |
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151 | s=""; |
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152 | while(solution[pos]!=" " && solution[pos]!=newline) |
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153 | { |
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154 | s=s+solution[pos]; |
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155 | pos++; |
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156 | } |
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157 | execute("v[j]="+s+";"); |
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158 | } |
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159 | } |
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160 | |
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161 | // delete all created files |
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162 | dummy=system("sh","rm -f "+matrixfile); |
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163 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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164 | dummy=system("sh","rm -f "+problemfile); |
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165 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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166 | |
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167 | return(v); |
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168 | } |
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169 | /////////////////////////////////////////////////////////////////////////////// |
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170 | static proc solve_IP_2(intmat A, list bx, intvec c, string alg) |
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171 | { |
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172 | list l;; |
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173 | // to be returned |
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174 | |
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175 | // check arguments as far as necessary |
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176 | // other inconsistencies are detected by the external program |
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177 | if(size(c)!=ncols(A)) |
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178 | { |
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179 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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180 | return(l); |
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181 | } |
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182 | |
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183 | int k; |
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184 | for(k=2;k<=size(bx);k++) |
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185 | { |
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186 | if(size(bx[k])!=size(bx[1])) |
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187 | { |
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188 | "ERROR: The size of all right-hand vectors must be equal."; |
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189 | return(l); |
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190 | } |
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191 | } |
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192 | |
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193 | // create first temporary file with which the external program is |
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194 | // called |
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195 | |
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196 | int process=system("pid"); |
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197 | string matrixfile="temp_MATRIX"+string(process); |
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198 | link MATRIX=":w "+matrixfile; |
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199 | open(MATRIX); |
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200 | |
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201 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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202 | int i,j; |
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203 | for(j=1;j<=ncols(A);j++) |
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204 | { |
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205 | write(MATRIX,c[j]); |
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206 | } |
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207 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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208 | for(i=1;i<=nrows(A);i++) |
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209 | { |
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210 | for(j=1;j<=ncols(A);j++) |
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211 | { |
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212 | write(MATRIX,A[i,j]); |
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213 | } |
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214 | } |
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215 | |
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216 | // search for positive row space vector, if required by the |
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217 | // algorithm |
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218 | int found=0; |
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219 | if((alg=="blr") || (alg=="hs")) |
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220 | { |
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221 | for(i=1;i<=nrows(A);i++) |
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222 | { |
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223 | found=i; |
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224 | for(j=1;j<=ncols(A);j++) |
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225 | { |
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226 | if(A[i,j]<=0) |
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227 | { |
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228 | found=0; |
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229 | } |
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230 | } |
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231 | if(found>0) |
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232 | { |
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233 | break; |
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234 | } |
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235 | } |
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236 | if(found==0) |
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237 | { |
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238 | "ERROR: The chosen algorithm needs a positive vector in the row space of the matrix."; |
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239 | close(MATRIX); |
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240 | system("sh","rm -f "+matrixfile); |
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241 | return(l); |
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242 | } |
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243 | write(MATRIX,"positive row space vector:"); |
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244 | for(j=1;j<=ncols(A);j++) |
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245 | { |
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246 | write(MATRIX,A[found,j]); |
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247 | } |
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248 | } |
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249 | close(MATRIX); |
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250 | |
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251 | // create second temporary file for the external program |
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252 | |
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253 | string problemfile="temp_PROBLEM"+string(process); |
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254 | link PROBLEM=":w "+problemfile; |
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255 | open(PROBLEM); |
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256 | |
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257 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
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258 | for(k=1;k<=size(bx);k++) |
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259 | { |
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260 | for(i=1;i<=size(bx[1]);i++) |
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261 | { |
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262 | write(PROBLEM,bx[k][i]); |
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263 | } |
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264 | } |
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265 | close(PROBLEM); |
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266 | |
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267 | // call external program |
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268 | if (status(system("SingularBin")+"solve_IP","exists")=="yes") |
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269 | { |
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270 | int dummy=system("sh",system("SingularBin")+"solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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271 | } |
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272 | else |
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273 | { |
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274 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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275 | } |
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276 | |
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277 | // read solution from created file |
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278 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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279 | string solution=read(SOLUTION); |
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280 | intvec v; |
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281 | int pos,pos1,pos2; |
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282 | string s; |
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283 | if(alg=="ct" || alg=="pct") |
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284 | { |
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285 | pos=1; |
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286 | for(k=1;k<=size(bx);k++) |
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287 | { |
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288 | pos1=find(solution,"NO",pos); |
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289 | pos2=find(solution,"YES",pos); |
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290 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
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291 | // first problem not solvable |
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292 | { |
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293 | pos=find(solution,":",pos1); |
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294 | l=insert(l,"not solvable",size(l)); |
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295 | } |
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296 | else |
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297 | // first problem solvable |
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298 | { |
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299 | pos=find(solution,":",pos2); |
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300 | pos++; |
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301 | for(j=1;j<=ncols(A);j++) |
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302 | { |
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303 | while(solution[pos]==" " || solution[pos]==newline) |
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304 | { |
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305 | pos++; |
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306 | } |
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307 | s=""; |
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308 | while(solution[pos]!=" " && solution[pos]!=newline) |
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309 | { |
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310 | s=s+solution[pos]; |
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311 | pos++; |
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312 | } |
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313 | execute("v[j]="+s+";"); |
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314 | } |
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315 | l=insert(l,v,size(l)); |
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316 | } |
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317 | } |
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318 | } |
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319 | else |
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320 | { |
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321 | pos=1; |
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322 | for(k=1;k<=size(bx);k++) |
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323 | { |
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324 | pos=find(solution,"optimal",pos); |
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325 | pos=find(solution,":",pos); |
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326 | pos++; |
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327 | for(j=1;j<=ncols(A);j++) |
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328 | { |
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329 | while(solution[pos]==" " || solution[pos]==newline) |
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330 | { |
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331 | pos++; |
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332 | } |
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333 | s=""; |
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334 | while(solution[pos]!=" " && solution[pos]!=newline) |
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335 | { |
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336 | s=s+solution[pos]; |
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337 | pos++; |
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338 | } |
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339 | execute("v[j]="+s+";"); |
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340 | } |
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341 | l=insert(l,v,size(l)); |
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342 | } |
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343 | } |
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344 | |
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345 | // delete all created files |
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346 | dummy=system("sh","rm -f "+matrixfile); |
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347 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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348 | dummy=system("sh","rm -f "+problemfile); |
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349 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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350 | |
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351 | return(l); |
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352 | } |
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353 | /////////////////////////////////////////////////////////////////////////////// |
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354 | |
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355 | static proc solve_IP_3(intmat A, intvec bx, intvec c, string alg, intvec prsv) |
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356 | { |
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357 | intvec v; |
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358 | // to be returned |
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359 | |
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360 | // check arguments as far as necessary |
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361 | // other inconsistencies are detected by the external program |
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362 | if(size(c)!=ncols(A)) |
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363 | { |
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364 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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365 | return(v); |
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366 | } |
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367 | |
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368 | if(size(prsv)!=ncols(A)) |
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369 | { |
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370 | "ERROR: The number of matrix columns does not equal the size of the positive row space vector."; |
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371 | return(v); |
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372 | } |
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373 | |
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374 | // create first temporary file with which the external program is |
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375 | // called |
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376 | |
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377 | int process=system("pid"); |
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378 | string matrixfile="temp_MATRIX"+string(process); |
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379 | link MATRIX=":w "+matrixfile; |
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380 | open(MATRIX); |
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381 | |
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382 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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383 | int i,j; |
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384 | for(j=1;j<=ncols(A);j++) |
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385 | { |
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386 | write(MATRIX,c[j]); |
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387 | } |
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388 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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389 | for(i=1;i<=nrows(A);i++) |
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390 | { |
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391 | for(j=1;j<=ncols(A);j++) |
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392 | { |
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393 | write(MATRIX,A[i,j]); |
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394 | } |
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395 | } |
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396 | |
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397 | // enter positive row space vector, if required by the algorithm |
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398 | if((alg=="blr") || (alg=="hs")) |
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399 | { |
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400 | write(MATRIX,"positive row space vector:"); |
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401 | for(j=1;j<=ncols(A);j++) |
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402 | { |
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403 | write(MATRIX,prsv[j]); |
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404 | } |
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405 | } |
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406 | close(MATRIX); |
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407 | |
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408 | // create second temporary file for the external program |
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409 | |
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410 | string problemfile="temp_PROBLEM"+string(process); |
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411 | link PROBLEM=":w "+problemfile; |
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412 | open(PROBLEM); |
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413 | |
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414 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
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415 | for(i=1;i<=size(bx);i++) |
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416 | { |
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417 | write(PROBLEM,bx[i]); |
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418 | } |
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419 | close(PROBLEM); |
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420 | |
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421 | // call external program |
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422 | if (status(system("SingularBin")+"solve_IP","exists")=="yes") |
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423 | { |
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424 | int dummy=system("sh",system("SingularBin")+"solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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425 | } |
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426 | else |
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427 | { |
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428 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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429 | } |
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430 | |
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431 | // read solution from created file |
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432 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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433 | string solution=read(SOLUTION); |
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434 | int pos; |
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435 | string s; |
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436 | if(alg=="ct" || alg=="pct") |
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437 | { |
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438 | pos=find(solution,"NO"); |
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439 | if(pos!=0) |
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440 | { |
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441 | "not solvable"; |
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442 | } |
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443 | else |
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444 | { |
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445 | pos=find(solution,"YES"); |
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446 | pos=find(solution,":",pos); |
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447 | pos++; |
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448 | for(j=1;j<=ncols(A);j++) |
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449 | { |
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450 | while(solution[pos]==" " || solution[pos]==newline) |
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451 | { |
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452 | pos++; |
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453 | } |
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454 | s=""; |
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455 | while(solution[pos]!=" " && solution[pos]!=newline) |
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456 | { |
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457 | s=s+solution[pos]; |
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458 | pos++; |
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459 | } |
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460 | execute("v[j]="+s+";"); |
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461 | } |
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462 | } |
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463 | } |
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464 | else |
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465 | { |
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466 | pos=find(solution,"optimal"); |
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467 | pos=find(solution,":",pos); |
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468 | pos++; |
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469 | for(j=1;j<=ncols(A);j++) |
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470 | { |
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471 | while(solution[pos]==" " || solution[pos]==newline) |
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472 | { |
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473 | pos++; |
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474 | } |
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475 | s=""; |
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476 | while(solution[pos]!=" " && solution[pos]!=newline) |
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477 | { |
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478 | s=s+solution[pos]; |
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479 | pos++; |
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480 | } |
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481 | execute("v[j]="+s+";"); |
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482 | } |
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483 | } |
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484 | |
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485 | // delete all created files |
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486 | dummy=system("sh","rm -f "+matrixfile); |
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487 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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488 | dummy=system("sh","rm -f "+problemfile); |
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489 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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490 | |
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491 | return(v); |
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492 | } |
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493 | /////////////////////////////////////////////////////////////////////////////// |
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494 | |
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495 | static proc solve_IP_4(intmat A, list bx, intvec c, string alg, intvec prsv) |
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496 | { |
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497 | list l; |
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498 | // to be returned |
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499 | |
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500 | // check arguments as far as necessary |
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501 | // other inconsistencies are detected by the external program |
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502 | if(size(c)!=ncols(A)) |
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503 | { |
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504 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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505 | return(l); |
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506 | } |
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507 | |
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508 | if(size(prsv)!=ncols(A)) |
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509 | { |
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510 | "ERROR: The number of matrix columns does not equal the size of the positive row space vector"; |
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511 | return(v); |
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512 | } |
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513 | |
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514 | int k; |
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515 | for(k=2;k<=size(bx);k++) |
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516 | { |
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517 | if(size(bx[k])!=size(bx[1])) |
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518 | { |
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519 | "ERROR: The size of all right-hand vectors must be equal."; |
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520 | return(l); |
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521 | } |
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522 | } |
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523 | |
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524 | // create first temporary file with which the external program is |
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525 | // called |
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526 | |
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527 | int process=system("pid"); |
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528 | string matrixfile="temp_MATRIX"+string(process); |
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529 | link MATRIX=":w "+matrixfile; |
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530 | open(MATRIX); |
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531 | |
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532 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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533 | int i,j; |
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534 | for(j=1;j<=ncols(A);j++) |
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535 | { |
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536 | write(MATRIX,c[j]); |
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537 | } |
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538 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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539 | for(i=1;i<=nrows(A);i++) |
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540 | { |
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541 | for(j=1;j<=ncols(A);j++) |
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542 | { |
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543 | write(MATRIX,A[i,j]); |
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544 | } |
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545 | } |
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546 | |
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547 | // enter positive row space vector if required by the algorithm |
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548 | if((alg=="blr") || (alg=="hs")) |
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549 | { |
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550 | write(MATRIX,"positive row space vector:"); |
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551 | for(j=1;j<=ncols(A);j++) |
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552 | { |
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553 | write(MATRIX,prsv[j]); |
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554 | } |
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555 | } |
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556 | close(MATRIX); |
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557 | |
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558 | // create second temporary file for the external program |
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559 | |
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560 | string problemfile="temp_PROBLEM"+string(process); |
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561 | link PROBLEM=":w "+problemfile; |
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562 | open(PROBLEM); |
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563 | |
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564 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
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565 | for(k=1;k<=size(bx);k++) |
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566 | { |
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567 | for(i=1;i<=size(bx[1]);i++) |
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568 | { |
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569 | write(PROBLEM,bx[k][i]); |
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570 | } |
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571 | } |
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572 | close(PROBLEM); |
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573 | |
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574 | // call external program |
---|
575 | if (status(system("SingularBin")+"solve_IP","exists")=="yes") |
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576 | { |
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577 | int dummy=system("sh",system("SingularBin")+"solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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578 | } |
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579 | else |
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580 | { |
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581 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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582 | } |
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583 | |
---|
584 | // read solution from created file |
---|
585 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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586 | string solution=read(SOLUTION); |
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587 | intvec v; |
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588 | int pos,pos1,pos2; |
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589 | string s; |
---|
590 | if(alg=="ct" || alg=="pct") |
---|
591 | { |
---|
592 | pos=1; |
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593 | for(k=1;k<=size(bx);k++) |
---|
594 | { |
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595 | pos1=find(solution,"NO",pos); |
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596 | pos2=find(solution,"YES",pos); |
---|
597 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
---|
598 | // first problem not solvable |
---|
599 | { |
---|
600 | pos=find(solution,":",pos1); |
---|
601 | l=insert(l,"not solvable",size(l)); |
---|
602 | } |
---|
603 | else |
---|
604 | // first problem solvable |
---|
605 | { |
---|
606 | pos=find(solution,":",pos2); |
---|
607 | pos++; |
---|
608 | for(j=1;j<=ncols(A);j++) |
---|
609 | { |
---|
610 | while(solution[pos]==" " || solution[pos]==newline) |
---|
611 | { |
---|
612 | pos++; |
---|
613 | } |
---|
614 | s=""; |
---|
615 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
616 | { |
---|
617 | s=s+solution[pos]; |
---|
618 | pos++; |
---|
619 | } |
---|
620 | execute("v[j]="+s+";"); |
---|
621 | } |
---|
622 | l=insert(l,v,size(l)); |
---|
623 | } |
---|
624 | } |
---|
625 | } |
---|
626 | else |
---|
627 | { |
---|
628 | pos=1; |
---|
629 | for(k=1;k<=size(bx);k++) |
---|
630 | { |
---|
631 | pos=find(solution,"optimal",pos); |
---|
632 | pos=find(solution,":",pos); |
---|
633 | pos++; |
---|
634 | for(j=1;j<=ncols(A);j++) |
---|
635 | { |
---|
636 | while(solution[pos]==" " || solution[pos]==newline) |
---|
637 | { |
---|
638 | pos++; |
---|
639 | } |
---|
640 | s=""; |
---|
641 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
642 | { |
---|
643 | s=s+solution[pos]; |
---|
644 | pos++; |
---|
645 | } |
---|
646 | execute("v[j]="+s+";"); |
---|
647 | } |
---|
648 | l=insert(l,v,size(l)); |
---|
649 | } |
---|
650 | } |
---|
651 | |
---|
652 | // delete all created files |
---|
653 | dummy=system("sh","rm -f "+matrixfile); |
---|
654 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
---|
655 | dummy=system("sh","rm -f "+problemfile); |
---|
656 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
---|
657 | |
---|
658 | return(l); |
---|
659 | } |
---|
660 | /////////////////////////////////////////////////////////////////////////////// |
---|
661 | |
---|
662 | proc solve_IP |
---|
663 | "USAGE: solve_IP(A,bx,c,alg); A intmat, bx intvec, c intvec, alg string.@* |
---|
664 | solve_IP(A,bx,c,alg); A intmat, bx list of intvec, c intvec, |
---|
665 | alg string.@* |
---|
666 | solve_IP(A,bx,c,alg,prsv); A intmat, bx intvec, c intvec, |
---|
667 | alg string, prsv intvec.@* |
---|
668 | solve_IP(A,bx,c,alg,prsv); A intmat, bx list of intvec, c intvec, |
---|
669 | alg string, prsv intvec. |
---|
670 | RETURN: same type as bx: solution of the associated integer programming |
---|
671 | problem(s) as explained in |
---|
672 | @texinfo |
---|
673 | @ref{Toric ideals and integer programming}. |
---|
674 | @end texinfo |
---|
675 | NOTE: This procedure returns the solution(s) of the given IP-problem(s) |
---|
676 | or the message `not solvable'. |
---|
677 | One may call the procedure with several different algorithms: |
---|
678 | @*- the algorithm of Conti/Traverso (ct), |
---|
679 | @*- the positive variant of the algorithm of Conti/Traverso (pct), |
---|
680 | @*- the algorithm of Conti/Traverso using elimination (ect), |
---|
681 | @*- the algorithm of Pottier (pt), |
---|
682 | @*- an algorithm of Bigatti/La Scala/Robbiano (blr), |
---|
683 | @*- the algorithm of Hosten/Sturmfels (hs), |
---|
684 | @*- the algorithm of DiBiase/Urbanke (du). |
---|
685 | @*The argument `alg' should be the abbreviation for an algorithm as |
---|
686 | above: ct, pct, ect, pt, blr, hs or du. |
---|
687 | |
---|
688 | `ct' allows computation of an optimal solution of the IP-problem |
---|
689 | directly from the right-hand vector b. |
---|
690 | The same is true for its `positive' variant `pct' which may only be |
---|
691 | applied if A and b have nonnegative entries. |
---|
692 | All other algorithms need initial solutions of the IP-problem. |
---|
693 | |
---|
694 | If `alg' is chosen to be `ct' or `pct', bx is read as the right hand |
---|
695 | vector b of the system Ax=b. b should then be an intvec of size m |
---|
696 | where m is the number of rows of A. |
---|
697 | Furthermore, bx and A should be nonnegative if `pct' is used. |
---|
698 | If `alg' is chosen to be `ect',`pt',`blr',`hs' or `du', |
---|
699 | bx is read as an initial solution x of the system Ax=b. |
---|
700 | bx should then be a nonnegative intvec of size n where n is the |
---|
701 | number of columns of A. |
---|
702 | |
---|
703 | If `alg' is chosen to be `blr' or `hs', the algorithm needs a vector |
---|
704 | with positive coefficients in the row space of A. |
---|
705 | If no row of A contains only positive entries, one has to use the |
---|
706 | versions of solve_IP which take such a vector prsv as an argument. |
---|
707 | |
---|
708 | solve_IP may also be called with a list bx of intvecs instead of a |
---|
709 | single intvec. |
---|
710 | SEE ALSO: intprog_lib, toric_lib, Integer programming |
---|
711 | EXAMPLE: example solve_IP; shows an example |
---|
712 | " |
---|
713 | { |
---|
714 | if(size(#)==4) |
---|
715 | { |
---|
716 | if(typeof(#[2])=="intvec") |
---|
717 | { |
---|
718 | return(solve_IP_1(#[1],#[2],#[3],#[4])); |
---|
719 | } |
---|
720 | else |
---|
721 | { |
---|
722 | return(solve_IP_2(#[1],#[2],#[3],#[4])); |
---|
723 | } |
---|
724 | } |
---|
725 | else |
---|
726 | { |
---|
727 | if(typeof(#[2])=="intvec") |
---|
728 | { |
---|
729 | return(solve_IP_3(#[1],#[2],#[3],#[4],#[5])); |
---|
730 | } |
---|
731 | else |
---|
732 | { |
---|
733 | return(solve_IP_4(#[1],#[2],#[3],#[4],#[5])); |
---|
734 | } |
---|
735 | } |
---|
736 | } |
---|
737 | |
---|
738 | |
---|
739 | |
---|
740 | example |
---|
741 | { "EXAMPLE"; echo=2; |
---|
742 | // 1. call with single right-hand vector |
---|
743 | intmat A[2][3]=1,1,0,0,1,1; |
---|
744 | intvec b1=1,1; |
---|
745 | intvec c=2,2,1; |
---|
746 | intvec solution_vector=solve_IP(A,b1,c,"pct"); |
---|
747 | solution_vector;""; |
---|
748 | |
---|
749 | // 2. call with list of right-hand vectors |
---|
750 | intvec b2=-1,1; |
---|
751 | list l=b1,b2; |
---|
752 | l; |
---|
753 | list solution_list=solve_IP(A,l,c,"ct"); |
---|
754 | solution_list;""; |
---|
755 | |
---|
756 | // 3. call with single initial solution vector |
---|
757 | A=2,1,-1,-1,1,2; |
---|
758 | b1=3,4,5; |
---|
759 | solve_IP(A,b1,c,"du");""; |
---|
760 | |
---|
761 | // 4. call with single initial solution vector |
---|
762 | // and algorithm needing a positive row space vector |
---|
763 | solution_vector=solve_IP(A,b1,c,"hs");""; |
---|
764 | |
---|
765 | // 5. call with single initial solution vector |
---|
766 | // and positive row space vector |
---|
767 | intvec prsv=1,2,1; |
---|
768 | solution_vector=solve_IP(A,b1,c,"hs",prsv); |
---|
769 | solution_vector;""; |
---|
770 | |
---|
771 | // 6. call with list of initial solution vectors |
---|
772 | // and positive row space vector |
---|
773 | b2=7,8,0; |
---|
774 | l=b1,b2; |
---|
775 | l; |
---|
776 | solution_list=solve_IP(A,l,c,"blr",prsv); |
---|
777 | solution_list; |
---|
778 | } |
---|