1 | ////////////////////////////////////////////////////////////////////////////// |
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2 | version="version intprog.lib 4.0.0.0 Jun_2013 "; // $Id$ |
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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 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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99 | |
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100 | // read solution from created file |
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101 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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102 | string solution=read(SOLUTION); |
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103 | int pos; |
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104 | string s; |
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105 | if(alg=="ct" || alg=="pct") |
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106 | { |
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107 | pos=find(solution,"NO"); |
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108 | if(pos!=0) |
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109 | { |
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110 | "not solvable"; |
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111 | } |
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112 | else |
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113 | { |
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114 | pos=find(solution,"YES"); |
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115 | pos=find(solution,":",pos); |
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116 | pos++; |
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117 | for(j=1;j<=ncols(A);j++) |
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118 | { |
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119 | while(solution[pos]==" " || solution[pos]==newline) |
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120 | { |
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121 | pos++; |
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122 | } |
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123 | s=""; |
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124 | while(solution[pos]!=" " && solution[pos]!=newline) |
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125 | { |
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126 | s=s+solution[pos]; |
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127 | pos++; |
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128 | } |
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129 | execute("v[j]="+s+";"); |
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130 | } |
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131 | } |
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132 | } |
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133 | else |
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134 | { |
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135 | pos=find(solution,"optimal"); |
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136 | pos=find(solution,":",pos); |
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137 | pos++; |
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138 | for(j=1;j<=ncols(A);j++) |
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139 | { |
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140 | while(solution[pos]==" " || solution[pos]==newline) |
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141 | { |
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142 | pos++; |
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143 | } |
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144 | s=""; |
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145 | while(solution[pos]!=" " && solution[pos]!=newline) |
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146 | { |
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147 | s=s+solution[pos]; |
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148 | pos++; |
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149 | } |
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150 | execute("v[j]="+s+";"); |
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151 | } |
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152 | } |
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153 | |
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154 | // delete all created files |
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155 | dummy=system("sh","rm -f "+matrixfile); |
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156 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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157 | dummy=system("sh","rm -f "+problemfile); |
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158 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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159 | |
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160 | return(v); |
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161 | } |
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162 | /////////////////////////////////////////////////////////////////////////////// |
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163 | static proc solve_IP_2(intmat A, list bx, intvec c, string alg) |
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164 | { |
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165 | list l;; |
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166 | // to be returned |
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167 | |
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168 | // check arguments as far as necessary |
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169 | // other inconsistencies are detected by the external program |
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170 | if(size(c)!=ncols(A)) |
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171 | { |
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172 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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173 | return(l); |
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174 | } |
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175 | |
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176 | int k; |
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177 | for(k=2;k<=size(bx);k++) |
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178 | { |
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179 | if(size(bx[k])!=size(bx[1])) |
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180 | { |
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181 | "ERROR: The size of all right-hand vectors must be equal."; |
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182 | return(l); |
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183 | } |
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184 | } |
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185 | |
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186 | // create first temporary file with which the external program is |
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187 | // called |
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188 | |
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189 | int process=system("pid"); |
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190 | string matrixfile="temp_MATRIX"+string(process); |
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191 | link MATRIX=":w "+matrixfile; |
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192 | open(MATRIX); |
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193 | |
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194 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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195 | int i,j; |
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196 | for(j=1;j<=ncols(A);j++) |
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197 | { |
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198 | write(MATRIX,c[j]); |
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199 | } |
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200 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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201 | for(i=1;i<=nrows(A);i++) |
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202 | { |
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203 | for(j=1;j<=ncols(A);j++) |
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204 | { |
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205 | write(MATRIX,A[i,j]); |
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206 | } |
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207 | } |
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208 | |
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209 | // search for positive row space vector, if required by the |
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210 | // algorithm |
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211 | int found=0; |
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212 | if((alg=="blr") || (alg=="hs")) |
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213 | { |
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214 | for(i=1;i<=nrows(A);i++) |
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215 | { |
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216 | found=i; |
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217 | for(j=1;j<=ncols(A);j++) |
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218 | { |
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219 | if(A[i,j]<=0) |
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220 | { |
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221 | found=0; |
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222 | } |
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223 | } |
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224 | if(found>0) |
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225 | { |
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226 | break; |
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227 | } |
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228 | } |
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229 | if(found==0) |
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230 | { |
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231 | "ERROR: The chosen algorithm needs a positive vector in the row space of the matrix."; |
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232 | close(MATRIX); |
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233 | system("sh","rm -f "+matrixfile); |
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234 | return(l); |
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235 | } |
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236 | write(MATRIX,"positive row space vector:"); |
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237 | for(j=1;j<=ncols(A);j++) |
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238 | { |
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239 | write(MATRIX,A[found,j]); |
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240 | } |
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241 | } |
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242 | close(MATRIX); |
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243 | |
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244 | // create second temporary file for the external program |
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245 | |
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246 | string problemfile="temp_PROBLEM"+string(process); |
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247 | link PROBLEM=":w "+problemfile; |
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248 | open(PROBLEM); |
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249 | |
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250 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
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251 | for(k=1;k<=size(bx);k++) |
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252 | { |
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253 | for(i=1;i<=size(bx[1]);i++) |
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254 | { |
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255 | write(PROBLEM,bx[k][i]); |
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256 | } |
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257 | } |
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258 | close(PROBLEM); |
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259 | |
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260 | // call external program |
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261 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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262 | |
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263 | // read solution from created file |
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264 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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265 | string solution=read(SOLUTION); |
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266 | intvec v; |
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267 | int pos,pos1,pos2; |
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268 | string s; |
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269 | if(alg=="ct" || alg=="pct") |
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270 | { |
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271 | pos=1; |
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272 | for(k=1;k<=size(bx);k++) |
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273 | { |
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274 | pos1=find(solution,"NO",pos); |
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275 | pos2=find(solution,"YES",pos); |
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276 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
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277 | // first problem not solvable |
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278 | { |
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279 | pos=find(solution,":",pos1); |
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280 | l=insert(l,"not solvable",size(l)); |
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281 | } |
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282 | else |
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283 | // first problem solvable |
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284 | { |
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285 | pos=find(solution,":",pos2); |
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286 | pos++; |
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287 | for(j=1;j<=ncols(A);j++) |
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288 | { |
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289 | while(solution[pos]==" " || solution[pos]==newline) |
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290 | { |
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291 | pos++; |
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292 | } |
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293 | s=""; |
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294 | while(solution[pos]!=" " && solution[pos]!=newline) |
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295 | { |
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296 | s=s+solution[pos]; |
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297 | pos++; |
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298 | } |
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299 | execute("v[j]="+s+";"); |
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300 | } |
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301 | l=insert(l,v,size(l)); |
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302 | } |
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303 | } |
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304 | } |
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305 | else |
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306 | { |
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307 | pos=1; |
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308 | for(k=1;k<=size(bx);k++) |
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309 | { |
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310 | pos=find(solution,"optimal",pos); |
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311 | pos=find(solution,":",pos); |
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312 | pos++; |
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313 | for(j=1;j<=ncols(A);j++) |
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314 | { |
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315 | while(solution[pos]==" " || solution[pos]==newline) |
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316 | { |
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317 | pos++; |
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318 | } |
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319 | s=""; |
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320 | while(solution[pos]!=" " && solution[pos]!=newline) |
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321 | { |
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322 | s=s+solution[pos]; |
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323 | pos++; |
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324 | } |
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325 | execute("v[j]="+s+";"); |
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326 | } |
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327 | l=insert(l,v,size(l)); |
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328 | } |
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329 | } |
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330 | |
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331 | // delete all created files |
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332 | dummy=system("sh","rm -f "+matrixfile); |
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333 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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334 | dummy=system("sh","rm -f "+problemfile); |
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335 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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336 | |
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337 | return(l); |
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338 | } |
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339 | /////////////////////////////////////////////////////////////////////////////// |
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340 | |
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341 | static proc solve_IP_3(intmat A, intvec bx, intvec c, string alg, intvec prsv) |
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342 | { |
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343 | intvec v; |
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344 | // to be returned |
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345 | |
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346 | // check arguments as far as necessary |
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347 | // other inconsistencies are detected by the external program |
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348 | if(size(c)!=ncols(A)) |
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349 | { |
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350 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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351 | return(v); |
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352 | } |
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353 | |
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354 | if(size(prsv)!=ncols(A)) |
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355 | { |
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356 | "ERROR: The number of matrix columns does not equal the size of the positive row space vector."; |
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357 | return(v); |
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358 | } |
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359 | |
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360 | // create first temporary file with which the external program is |
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361 | // called |
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362 | |
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363 | int process=system("pid"); |
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364 | string matrixfile="temp_MATRIX"+string(process); |
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365 | link MATRIX=":w "+matrixfile; |
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366 | open(MATRIX); |
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367 | |
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368 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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369 | int i,j; |
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370 | for(j=1;j<=ncols(A);j++) |
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371 | { |
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372 | write(MATRIX,c[j]); |
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373 | } |
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374 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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375 | for(i=1;i<=nrows(A);i++) |
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376 | { |
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377 | for(j=1;j<=ncols(A);j++) |
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378 | { |
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379 | write(MATRIX,A[i,j]); |
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380 | } |
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381 | } |
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382 | |
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383 | // enter positive row space vector, if required by the algorithm |
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384 | if((alg=="blr") || (alg=="hs")) |
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385 | { |
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386 | write(MATRIX,"positive row space vector:"); |
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387 | for(j=1;j<=ncols(A);j++) |
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388 | { |
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389 | write(MATRIX,prsv[j]); |
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390 | } |
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391 | } |
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392 | close(MATRIX); |
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393 | |
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394 | // create second temporary file for the external program |
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395 | |
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396 | string problemfile="temp_PROBLEM"+string(process); |
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397 | link PROBLEM=":w "+problemfile; |
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398 | open(PROBLEM); |
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399 | |
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400 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
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401 | for(i=1;i<=size(bx);i++) |
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402 | { |
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403 | write(PROBLEM,bx[i]); |
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404 | } |
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405 | close(PROBLEM); |
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406 | |
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407 | // call external program |
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408 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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409 | |
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410 | // read solution from created file |
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411 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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412 | string solution=read(SOLUTION); |
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413 | int pos; |
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414 | string s; |
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415 | if(alg=="ct" || alg=="pct") |
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416 | { |
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417 | pos=find(solution,"NO"); |
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418 | if(pos!=0) |
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419 | { |
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420 | "not solvable"; |
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421 | } |
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422 | else |
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423 | { |
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424 | pos=find(solution,"YES"); |
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425 | pos=find(solution,":",pos); |
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426 | pos++; |
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427 | for(j=1;j<=ncols(A);j++) |
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428 | { |
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429 | while(solution[pos]==" " || solution[pos]==newline) |
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430 | { |
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431 | pos++; |
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432 | } |
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433 | s=""; |
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434 | while(solution[pos]!=" " && solution[pos]!=newline) |
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435 | { |
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436 | s=s+solution[pos]; |
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437 | pos++; |
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438 | } |
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439 | execute("v[j]="+s+";"); |
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440 | } |
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441 | } |
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442 | } |
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443 | else |
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444 | { |
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445 | pos=find(solution,"optimal"); |
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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 | // delete all created files |
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465 | dummy=system("sh","rm -f "+matrixfile); |
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466 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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467 | dummy=system("sh","rm -f "+problemfile); |
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468 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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469 | |
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470 | return(v); |
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471 | } |
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472 | /////////////////////////////////////////////////////////////////////////////// |
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473 | |
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474 | static proc solve_IP_4(intmat A, list bx, intvec c, string alg, intvec prsv) |
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475 | { |
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476 | list l; |
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477 | // to be returned |
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478 | |
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479 | // check arguments as far as necessary |
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480 | // other inconsistencies are detected by the external program |
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481 | if(size(c)!=ncols(A)) |
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482 | { |
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483 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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484 | return(l); |
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485 | } |
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486 | |
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487 | if(size(prsv)!=ncols(A)) |
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488 | { |
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489 | "ERROR: The number of matrix columns does not equal the size of the positive row space vector"; |
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490 | return(v); |
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491 | } |
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492 | |
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493 | int k; |
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494 | for(k=2;k<=size(bx);k++) |
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495 | { |
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496 | if(size(bx[k])!=size(bx[1])) |
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497 | { |
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498 | "ERROR: The size of all right-hand vectors must be equal."; |
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499 | return(l); |
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500 | } |
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501 | } |
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502 | |
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503 | // create first temporary file with which the external program is |
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504 | // called |
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505 | |
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506 | int process=system("pid"); |
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507 | string matrixfile="temp_MATRIX"+string(process); |
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508 | link MATRIX=":w "+matrixfile; |
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509 | open(MATRIX); |
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510 | |
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511 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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512 | int i,j; |
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513 | for(j=1;j<=ncols(A);j++) |
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514 | { |
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515 | write(MATRIX,c[j]); |
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516 | } |
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517 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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518 | for(i=1;i<=nrows(A);i++) |
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519 | { |
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520 | for(j=1;j<=ncols(A);j++) |
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521 | { |
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522 | write(MATRIX,A[i,j]); |
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523 | } |
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524 | } |
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525 | |
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526 | // enter positive row space vector if required by the algorithm |
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527 | if((alg=="blr") || (alg=="hs")) |
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528 | { |
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529 | write(MATRIX,"positive row space vector:"); |
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530 | for(j=1;j<=ncols(A);j++) |
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531 | { |
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532 | write(MATRIX,prsv[j]); |
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533 | } |
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534 | } |
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535 | close(MATRIX); |
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536 | |
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537 | // create second temporary file for the external program |
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538 | |
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539 | string problemfile="temp_PROBLEM"+string(process); |
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540 | link PROBLEM=":w "+problemfile; |
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541 | open(PROBLEM); |
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542 | |
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543 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
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544 | for(k=1;k<=size(bx);k++) |
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545 | { |
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546 | for(i=1;i<=size(bx[1]);i++) |
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547 | { |
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548 | write(PROBLEM,bx[k][i]); |
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549 | } |
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550 | } |
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551 | close(PROBLEM); |
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552 | |
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553 | // call external program |
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554 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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555 | |
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556 | // read solution from created file |
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557 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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558 | string solution=read(SOLUTION); |
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559 | intvec v; |
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560 | int pos,pos1,pos2; |
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561 | string s; |
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562 | if(alg=="ct" || alg=="pct") |
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563 | { |
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564 | pos=1; |
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565 | for(k=1;k<=size(bx);k++) |
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566 | { |
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567 | pos1=find(solution,"NO",pos); |
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568 | pos2=find(solution,"YES",pos); |
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569 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
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570 | // first problem not solvable |
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571 | { |
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572 | pos=find(solution,":",pos1); |
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573 | l=insert(l,"not solvable",size(l)); |
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574 | } |
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575 | else |
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576 | // first problem solvable |
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577 | { |
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578 | pos=find(solution,":",pos2); |
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579 | pos++; |
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580 | for(j=1;j<=ncols(A);j++) |
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581 | { |
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582 | while(solution[pos]==" " || solution[pos]==newline) |
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583 | { |
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584 | pos++; |
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585 | } |
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586 | s=""; |
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587 | while(solution[pos]!=" " && solution[pos]!=newline) |
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588 | { |
---|
589 | s=s+solution[pos]; |
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590 | pos++; |
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591 | } |
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592 | execute("v[j]="+s+";"); |
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593 | } |
---|
594 | l=insert(l,v,size(l)); |
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595 | } |
---|
596 | } |
---|
597 | } |
---|
598 | else |
---|
599 | { |
---|
600 | pos=1; |
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601 | for(k=1;k<=size(bx);k++) |
---|
602 | { |
---|
603 | pos=find(solution,"optimal",pos); |
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604 | pos=find(solution,":",pos); |
---|
605 | pos++; |
---|
606 | for(j=1;j<=ncols(A);j++) |
---|
607 | { |
---|
608 | while(solution[pos]==" " || solution[pos]==newline) |
---|
609 | { |
---|
610 | pos++; |
---|
611 | } |
---|
612 | s=""; |
---|
613 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
614 | { |
---|
615 | s=s+solution[pos]; |
---|
616 | pos++; |
---|
617 | } |
---|
618 | execute("v[j]="+s+";"); |
---|
619 | } |
---|
620 | l=insert(l,v,size(l)); |
---|
621 | } |
---|
622 | } |
---|
623 | |
---|
624 | // delete all created files |
---|
625 | dummy=system("sh","rm -f "+matrixfile); |
---|
626 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
---|
627 | dummy=system("sh","rm -f "+problemfile); |
---|
628 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
---|
629 | |
---|
630 | return(l); |
---|
631 | } |
---|
632 | /////////////////////////////////////////////////////////////////////////////// |
---|
633 | |
---|
634 | proc solve_IP |
---|
635 | "USAGE: solve_IP(A,bx,c,alg); A intmat, bx intvec, c intvec, alg string.@* |
---|
636 | solve_IP(A,bx,c,alg); A intmat, bx list of intvec, c intvec, |
---|
637 | alg string.@* |
---|
638 | solve_IP(A,bx,c,alg,prsv); A intmat, bx intvec, c intvec, |
---|
639 | alg string, prsv intvec.@* |
---|
640 | solve_IP(A,bx,c,alg,prsv); A intmat, bx list of intvec, c intvec, |
---|
641 | alg string, prsv intvec. |
---|
642 | RETURN: same type as bx: solution of the associated integer programming |
---|
643 | problem(s) as explained in |
---|
644 | @texinfo |
---|
645 | @ref{Toric ideals and integer programming}. |
---|
646 | @end texinfo |
---|
647 | NOTE: This procedure returns the solution(s) of the given IP-problem(s) |
---|
648 | or the message `not solvable'. |
---|
649 | One may call the procedure with several different algorithms: |
---|
650 | @*- the algorithm of Conti/Traverso (ct), |
---|
651 | @*- the positive variant of the algorithm of Conti/Traverso (pct), |
---|
652 | @*- the algorithm of Conti/Traverso using elimination (ect), |
---|
653 | @*- the algorithm of Pottier (pt), |
---|
654 | @*- an algorithm of Bigatti/La Scala/Robbiano (blr), |
---|
655 | @*- the algorithm of Hosten/Sturmfels (hs), |
---|
656 | @*- the algorithm of DiBiase/Urbanke (du). |
---|
657 | @*The argument `alg' should be the abbreviation for an algorithm as |
---|
658 | above: ct, pct, ect, pt, blr, hs or du. |
---|
659 | |
---|
660 | `ct' allows computation of an optimal solution of the IP-problem |
---|
661 | directly from the right-hand vector b. |
---|
662 | The same is true for its `positive' variant `pct' which may only be |
---|
663 | applied if A and b have nonnegative entries. |
---|
664 | All other algorithms need initial solutions of the IP-problem. |
---|
665 | |
---|
666 | If `alg' is chosen to be `ct' or `pct', bx is read as the right hand |
---|
667 | vector b of the system Ax=b. b should then be an intvec of size m |
---|
668 | where m is the number of rows of A. |
---|
669 | Furthermore, bx and A should be nonnegative if `pct' is used. |
---|
670 | If `alg' is chosen to be `ect',`pt',`blr',`hs' or `du', |
---|
671 | bx is read as an initial solution x of the system Ax=b. |
---|
672 | bx should then be a nonnegative intvec of size n where n is the |
---|
673 | number of columns of A. |
---|
674 | |
---|
675 | If `alg' is chosen to be `blr' or `hs', the algorithm needs a vector |
---|
676 | with positive coefficients in the row space of A. |
---|
677 | If no row of A contains only positive entries, one has to use the |
---|
678 | versions of solve_IP which take such a vector prsv as an argument. |
---|
679 | |
---|
680 | solve_IP may also be called with a list bx of intvecs instead of a |
---|
681 | single intvec. |
---|
682 | SEE ALSO: intprog_lib, toric_lib, Integer programming |
---|
683 | EXAMPLE: example solve_IP; shows an example |
---|
684 | " |
---|
685 | { |
---|
686 | if(size(#)==4) |
---|
687 | { |
---|
688 | if(typeof(#[2])=="intvec") |
---|
689 | { |
---|
690 | return(solve_IP_1(#[1],#[2],#[3],#[4])); |
---|
691 | } |
---|
692 | else |
---|
693 | { |
---|
694 | return(solve_IP_2(#[1],#[2],#[3],#[4])); |
---|
695 | } |
---|
696 | } |
---|
697 | else |
---|
698 | { |
---|
699 | if(typeof(#[2])=="intvec") |
---|
700 | { |
---|
701 | return(solve_IP_3(#[1],#[2],#[3],#[4],#[5])); |
---|
702 | } |
---|
703 | else |
---|
704 | { |
---|
705 | return(solve_IP_4(#[1],#[2],#[3],#[4],#[5])); |
---|
706 | } |
---|
707 | } |
---|
708 | } |
---|
709 | |
---|
710 | |
---|
711 | |
---|
712 | example |
---|
713 | { "EXAMPLE"; echo=2; |
---|
714 | // 1. call with single right-hand vector |
---|
715 | intmat A[2][3]=1,1,0,0,1,1; |
---|
716 | intvec b1=1,1; |
---|
717 | intvec c=2,2,1; |
---|
718 | intvec solution_vector=solve_IP(A,b1,c,"pct"); |
---|
719 | solution_vector;""; |
---|
720 | |
---|
721 | // 2. call with list of right-hand vectors |
---|
722 | intvec b2=-1,1; |
---|
723 | list l=b1,b2; |
---|
724 | l; |
---|
725 | list solution_list=solve_IP(A,l,c,"ct"); |
---|
726 | solution_list;""; |
---|
727 | |
---|
728 | // 3. call with single initial solution vector |
---|
729 | A=2,1,-1,-1,1,2; |
---|
730 | b1=3,4,5; |
---|
731 | solve_IP(A,b1,c,"du");""; |
---|
732 | |
---|
733 | // 4. call with single initial solution vector |
---|
734 | // and algorithm needing a positive row space vector |
---|
735 | solution_vector=solve_IP(A,b1,c,"hs");""; |
---|
736 | |
---|
737 | // 5. call with single initial solution vector |
---|
738 | // and positive row space vector |
---|
739 | intvec prsv=1,2,1; |
---|
740 | solution_vector=solve_IP(A,b1,c,"hs",prsv); |
---|
741 | solution_vector;""; |
---|
742 | |
---|
743 | // 6. call with list of initial solution vectors |
---|
744 | // and positive row space vector |
---|
745 | b2=7,8,0; |
---|
746 | l=b1,b2; |
---|
747 | l; |
---|
748 | solution_list=solve_IP(A,l,c,"blr",prsv); |
---|
749 | solution_list; |
---|
750 | } |
---|