1 | version="$Id: intprog.lib,v 1.1 2000-09-14 12:37:09 Singular Exp $"; |
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2 | |
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3 | /////////////////////////////////////////////////////////////////////////////// |
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4 | |
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5 | info=" |
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6 | LIBRARY: intprog.lib INTEGER PROGRAMMING WITH GROEBNER BASIS METHODS |
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7 | |
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8 | AUTHOR: Christine Theis, email: ctheis@math.uni-sb.de |
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9 | |
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10 | PROCEDURES: |
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11 | |
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12 | solve_IP(intmat A, [intvec|list] bx, intvec c, string alg [, intvec prsv]); |
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13 | procedures for solving IP-problems |
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14 | "; |
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15 | |
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16 | /////////////////////////////////////////////////////////////////////////////// |
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17 | |
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18 | |
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19 | |
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20 | static proc solve_IP_1(intmat A, intvec bx, intvec c, string alg) |
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21 | { |
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22 | intvec v; |
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23 | // to be returned |
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24 | |
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25 | // check arguments as far as necessary |
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26 | // other inconsistencies are detected by the external program |
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27 | if(size(c)!=ncols(A)) |
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28 | { |
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29 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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30 | return(v); |
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31 | } |
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32 | |
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33 | // create first temporary file with which the external program is |
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34 | // called |
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35 | |
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36 | int process=system("pid"); |
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37 | string matrixfile="temp_MATRIX"+string(process); |
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38 | link MATRIX=":w "+matrixfile; |
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39 | open(MATRIX); |
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40 | |
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41 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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42 | int i,j; |
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43 | for(j=1;j<=ncols(A);j++) |
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44 | { |
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45 | write(MATRIX,c[j]); |
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46 | } |
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47 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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48 | for(i=1;i<=nrows(A);i++) |
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49 | { |
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50 | for(j=1;j<=ncols(A);j++) |
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51 | { |
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52 | write(MATRIX,A[i,j]); |
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53 | } |
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54 | } |
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55 | |
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56 | // search for positive row space vector, if required by the |
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57 | // algorithm |
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58 | int found=0; |
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59 | if((alg=="blr") || (alg=="hs")) |
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60 | { |
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61 | for(i=1;i<=nrows(A);i++) |
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62 | { |
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63 | found=i; |
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64 | for(j=1;j<=ncols(A);j++) |
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65 | { |
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66 | if(A[i,j]<=0) |
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67 | { |
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68 | found=0; |
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69 | } |
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70 | } |
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71 | if(found>0) |
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72 | { |
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73 | break; |
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74 | } |
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75 | } |
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76 | if(found==0) |
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77 | { |
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78 | "ERROR: The chosen algorithm needs a positive vector in the row space of the matrix."; |
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79 | close(MATRIX); |
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80 | system("sh","rm -f "+matrixfile); |
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81 | return(v); |
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82 | } |
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83 | write(MATRIX,"positive row space vector:"); |
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84 | for(j=1;j<=ncols(A);j++) |
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85 | { |
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86 | write(MATRIX,A[found,j]); |
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87 | } |
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88 | } |
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89 | close(MATRIX); |
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90 | |
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91 | // create second temporary file for the external program |
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92 | |
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93 | string problemfile="temp_PROBLEM"+string(process); |
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94 | link PROBLEM=":w "+problemfile; |
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95 | open(PROBLEM); |
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96 | |
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97 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
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98 | for(i=1;i<=size(bx);i++) |
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99 | { |
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100 | write(PROBLEM,bx[i]); |
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101 | } |
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102 | close(PROBLEM); |
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103 | |
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104 | // call external program |
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105 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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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 | |
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171 | |
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172 | static proc solve_IP_2(intmat A, list bx, intvec c, string alg) |
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173 | { |
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174 | list l;; |
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175 | // to be returned |
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176 | |
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177 | // check arguments as far as necessary |
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178 | // other inconsistencies are detected by the external program |
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179 | if(size(c)!=ncols(A)) |
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180 | { |
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181 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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182 | return(l); |
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183 | } |
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184 | |
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185 | int k; |
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186 | for(k=2;k<=size(bx);k++) |
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187 | { |
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188 | if(size(bx[k])!=size(bx[1])) |
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189 | { |
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190 | "ERROR: The size of all right-hand vectors must be equal."; |
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191 | return(l); |
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192 | } |
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193 | } |
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194 | |
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195 | // create first temporary file with which the external program is |
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196 | // called |
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197 | |
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198 | int process=system("pid"); |
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199 | string matrixfile="temp_MATRIX"+string(process); |
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200 | link MATRIX=":w "+matrixfile; |
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201 | open(MATRIX); |
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202 | |
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203 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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204 | int i,j; |
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205 | for(j=1;j<=ncols(A);j++) |
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206 | { |
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207 | write(MATRIX,c[j]); |
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208 | } |
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209 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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210 | for(i=1;i<=nrows(A);i++) |
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211 | { |
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212 | for(j=1;j<=ncols(A);j++) |
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213 | { |
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214 | write(MATRIX,A[i,j]); |
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215 | } |
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216 | } |
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217 | |
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218 | // search for positive row space vector, if required by the |
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219 | // algorithm |
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220 | int found=0; |
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221 | if((alg=="blr") || (alg=="hs")) |
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222 | { |
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223 | for(i=1;i<=nrows(A);i++) |
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224 | { |
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225 | found=i; |
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226 | for(j=1;j<=ncols(A);j++) |
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227 | { |
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228 | if(A[i,j]<=0) |
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229 | { |
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230 | found=0; |
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231 | } |
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232 | } |
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233 | if(found>0) |
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234 | { |
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235 | break; |
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236 | } |
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237 | } |
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238 | if(found==0) |
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239 | { |
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240 | "ERROR: The chosen algorithm needs a positive vector in the row space of the matrix."; |
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241 | close(MATRIX); |
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242 | system("sh","rm -f "+matrixfile); |
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243 | return(l); |
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244 | } |
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245 | write(MATRIX,"positive row space vector:"); |
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246 | for(j=1;j<=ncols(A);j++) |
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247 | { |
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248 | write(MATRIX,A[found,j]); |
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249 | } |
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250 | } |
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251 | close(MATRIX); |
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252 | |
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253 | // create second temporary file for the external program |
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254 | |
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255 | string problemfile="temp_PROBLEM"+string(process); |
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256 | link PROBLEM=":w "+problemfile; |
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257 | open(PROBLEM); |
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258 | |
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259 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
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260 | for(k=1;k<=size(bx);k++) |
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261 | { |
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262 | for(i=1;i<=size(bx[1]);i++) |
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263 | { |
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264 | write(PROBLEM,bx[k][i]); |
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265 | } |
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266 | } |
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267 | close(PROBLEM); |
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268 | |
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269 | // call external program |
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270 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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271 | |
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272 | // read solution from created file |
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273 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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274 | string solution=read(SOLUTION); |
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275 | intvec v; |
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276 | int pos,pos1,pos2; |
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277 | string s; |
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278 | if(alg=="ct" || alg=="pct") |
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279 | { |
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280 | pos=1; |
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281 | for(k=1;k<=size(bx);k++) |
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282 | { |
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283 | pos1=find(solution,"NO",pos); |
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284 | pos2=find(solution,"YES",pos); |
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285 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
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286 | // first problem not solvable |
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287 | { |
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288 | pos=find(solution,":",pos1); |
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289 | l=insert(l,"not solvable",size(l)); |
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290 | } |
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291 | else |
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292 | // first problem solvable |
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293 | { |
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294 | pos=find(solution,":",pos2); |
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295 | pos++; |
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296 | for(j=1;j<=ncols(A);j++) |
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297 | { |
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298 | while(solution[pos]==" " || solution[pos]==newline) |
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299 | { |
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300 | pos++; |
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301 | } |
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302 | s=""; |
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303 | while(solution[pos]!=" " && solution[pos]!=newline) |
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304 | { |
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305 | s=s+solution[pos]; |
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306 | pos++; |
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307 | } |
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308 | execute("v[j]="+s+";"); |
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309 | } |
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310 | l=insert(l,v,size(l)); |
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311 | } |
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312 | } |
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313 | } |
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314 | else |
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315 | { |
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316 | pos=1; |
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317 | for(k=1;k<=size(bx);k++) |
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318 | { |
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319 | pos=find(solution,"optimal",pos); |
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320 | pos=find(solution,":",pos); |
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321 | pos++; |
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322 | for(j=1;j<=ncols(A);j++) |
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323 | { |
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324 | while(solution[pos]==" " || solution[pos]==newline) |
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325 | { |
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326 | pos++; |
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327 | } |
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328 | s=""; |
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329 | while(solution[pos]!=" " && solution[pos]!=newline) |
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330 | { |
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331 | s=s+solution[pos]; |
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332 | pos++; |
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333 | } |
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334 | execute("v[j]="+s+";"); |
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335 | } |
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336 | l=insert(l,v,size(l)); |
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337 | } |
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338 | } |
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339 | |
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340 | // delete all created files |
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341 | dummy=system("sh","rm -f "+matrixfile); |
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342 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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343 | dummy=system("sh","rm -f "+problemfile); |
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344 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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345 | |
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346 | return(l); |
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347 | } |
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348 | |
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349 | |
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350 | |
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351 | static proc solve_IP_3(intmat A, intvec bx, intvec c, string alg, intvec prsv) |
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352 | { |
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353 | intvec v; |
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354 | // to be returned |
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355 | |
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356 | // check arguments as far as necessary |
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357 | // other inconsistencies are detected by the external program |
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358 | if(size(c)!=ncols(A)) |
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359 | { |
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360 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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361 | return(v); |
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362 | } |
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363 | |
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364 | if(size(prsv)!=ncols(A)) |
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365 | { |
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366 | "ERROR: The number of matrix columns does not equal the size of the positive row space vector."; |
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367 | return(v); |
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368 | } |
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369 | |
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370 | // create first temporary file with which the external program is |
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371 | // called |
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372 | |
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373 | int process=system("pid"); |
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374 | string matrixfile="temp_MATRIX"+string(process); |
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375 | link MATRIX=":w "+matrixfile; |
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376 | open(MATRIX); |
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377 | |
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378 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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379 | int i,j; |
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380 | for(j=1;j<=ncols(A);j++) |
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381 | { |
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382 | write(MATRIX,c[j]); |
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383 | } |
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384 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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385 | for(i=1;i<=nrows(A);i++) |
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386 | { |
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387 | for(j=1;j<=ncols(A);j++) |
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388 | { |
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389 | write(MATRIX,A[i,j]); |
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390 | } |
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391 | } |
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392 | |
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393 | // enter positive row space vector, if required by the algorithm |
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394 | if((alg=="blr") || (alg=="hs")) |
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395 | { |
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396 | write(MATRIX,"positive row space vector:"); |
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397 | for(j=1;j<=ncols(A);j++) |
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398 | { |
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399 | write(MATRIX,prsv[j]); |
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400 | } |
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401 | } |
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402 | close(MATRIX); |
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403 | |
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404 | // create second temporary file for the external program |
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405 | |
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406 | string problemfile="temp_PROBLEM"+string(process); |
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407 | link PROBLEM=":w "+problemfile; |
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408 | open(PROBLEM); |
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409 | |
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410 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
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411 | for(i=1;i<=size(bx);i++) |
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412 | { |
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413 | write(PROBLEM,bx[i]); |
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414 | } |
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415 | close(PROBLEM); |
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416 | |
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417 | // call external program |
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418 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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419 | |
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420 | // read solution from created file |
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421 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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422 | string solution=read(SOLUTION); |
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423 | int pos; |
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424 | string s; |
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425 | if(alg=="ct" || alg=="pct") |
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426 | { |
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427 | pos=find(solution,"NO"); |
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428 | if(pos!=0) |
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429 | { |
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430 | "not solvable"; |
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431 | } |
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432 | else |
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433 | { |
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434 | pos=find(solution,"YES"); |
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435 | pos=find(solution,":",pos); |
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436 | pos++; |
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437 | for(j=1;j<=ncols(A);j++) |
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438 | { |
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439 | while(solution[pos]==" " || solution[pos]==newline) |
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440 | { |
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441 | pos++; |
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442 | } |
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443 | s=""; |
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444 | while(solution[pos]!=" " && solution[pos]!=newline) |
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445 | { |
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446 | s=s+solution[pos]; |
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447 | pos++; |
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448 | } |
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449 | execute("v[j]="+s+";"); |
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450 | } |
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451 | } |
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452 | } |
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453 | else |
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454 | { |
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455 | pos=find(solution,"optimal"); |
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456 | pos=find(solution,":",pos); |
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457 | pos++; |
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458 | for(j=1;j<=ncols(A);j++) |
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459 | { |
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460 | while(solution[pos]==" " || solution[pos]==newline) |
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461 | { |
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462 | pos++; |
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463 | } |
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464 | s=""; |
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465 | while(solution[pos]!=" " && solution[pos]!=newline) |
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466 | { |
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467 | s=s+solution[pos]; |
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468 | pos++; |
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469 | } |
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470 | execute("v[j]="+s+";"); |
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471 | } |
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472 | } |
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473 | |
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474 | // delete all created files |
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475 | dummy=system("sh","rm -f "+matrixfile); |
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476 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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477 | dummy=system("sh","rm -f "+problemfile); |
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478 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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479 | |
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480 | return(v); |
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481 | } |
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482 | |
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483 | |
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484 | |
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485 | static proc solve_IP_4(intmat A, list bx, intvec c, string alg, intvec prsv) |
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486 | { |
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487 | list l; |
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488 | // to be returned |
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489 | |
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490 | // check arguments as far as necessary |
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491 | // other inconsistencies are detected by the external program |
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492 | if(size(c)!=ncols(A)) |
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493 | { |
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494 | "ERROR: The number of matrix columns does not equal the size of the cost vector."; |
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495 | return(l); |
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496 | } |
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497 | |
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498 | if(size(prsv)!=ncols(A)) |
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499 | { |
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500 | "ERROR: The number of matrix columns does not equal the size of the positive row space vector"; |
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501 | return(v); |
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502 | } |
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503 | |
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504 | int k; |
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505 | for(k=2;k<=size(bx);k++) |
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506 | { |
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507 | if(size(bx[k])!=size(bx[1])) |
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508 | { |
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509 | "ERROR: The size of all right-hand vectors must be equal."; |
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510 | return(l); |
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511 | } |
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512 | } |
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513 | |
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514 | // create first temporary file with which the external program is |
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515 | // called |
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516 | |
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517 | int process=system("pid"); |
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518 | string matrixfile="temp_MATRIX"+string(process); |
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519 | link MATRIX=":w "+matrixfile; |
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520 | open(MATRIX); |
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521 | |
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522 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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523 | int i,j; |
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524 | for(j=1;j<=ncols(A);j++) |
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525 | { |
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526 | write(MATRIX,c[j]); |
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527 | } |
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528 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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529 | for(i=1;i<=nrows(A);i++) |
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530 | { |
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531 | for(j=1;j<=ncols(A);j++) |
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532 | { |
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533 | write(MATRIX,A[i,j]); |
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534 | } |
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535 | } |
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536 | |
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537 | // enter positive row space vector if required by the algorithm |
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538 | if((alg=="blr") || (alg=="hs")) |
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539 | { |
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540 | write(MATRIX,"positive row space vector:"); |
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541 | for(j=1;j<=ncols(A);j++) |
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542 | { |
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543 | write(MATRIX,prsv[j]); |
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544 | } |
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545 | } |
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546 | close(MATRIX); |
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547 | |
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548 | // create second temporary file for the external program |
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549 | |
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550 | string problemfile="temp_PROBLEM"+string(process); |
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551 | link PROBLEM=":w "+problemfile; |
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552 | open(PROBLEM); |
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553 | |
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554 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
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555 | for(k=1;k<=size(bx);k++) |
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556 | { |
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557 | for(i=1;i<=size(bx[1]);i++) |
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558 | { |
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559 | write(PROBLEM,bx[k][i]); |
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560 | } |
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561 | } |
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562 | close(PROBLEM); |
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563 | |
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564 | // call external program |
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565 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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566 | |
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567 | // read solution from created file |
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568 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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569 | string solution=read(SOLUTION); |
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570 | intvec v; |
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571 | int pos,pos1,pos2; |
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572 | string s; |
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573 | if(alg=="ct" || alg=="pct") |
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574 | { |
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575 | pos=1; |
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576 | for(k=1;k<=size(bx);k++) |
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577 | { |
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578 | pos1=find(solution,"NO",pos); |
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579 | pos2=find(solution,"YES",pos); |
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580 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
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581 | // first problem not solvable |
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582 | { |
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583 | pos=find(solution,":",pos1); |
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584 | l=insert(l,"not solvable",size(l)); |
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585 | } |
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586 | else |
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587 | // first problem solvable |
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588 | { |
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589 | pos=find(solution,":",pos2); |
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590 | pos++; |
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591 | for(j=1;j<=ncols(A);j++) |
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592 | { |
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593 | while(solution[pos]==" " || solution[pos]==newline) |
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594 | { |
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595 | pos++; |
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596 | } |
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597 | s=""; |
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598 | while(solution[pos]!=" " && solution[pos]!=newline) |
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599 | { |
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600 | s=s+solution[pos]; |
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601 | pos++; |
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602 | } |
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603 | execute("v[j]="+s+";"); |
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604 | } |
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605 | l=insert(l,v,size(l)); |
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606 | } |
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607 | } |
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608 | } |
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609 | else |
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610 | { |
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611 | pos=1; |
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612 | for(k=1;k<=size(bx);k++) |
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613 | { |
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614 | pos=find(solution,"optimal",pos); |
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615 | pos=find(solution,":",pos); |
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616 | pos++; |
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617 | for(j=1;j<=ncols(A);j++) |
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618 | { |
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619 | while(solution[pos]==" " || solution[pos]==newline) |
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620 | { |
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621 | pos++; |
---|
622 | } |
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623 | s=""; |
---|
624 | while(solution[pos]!=" " && solution[pos]!=newline) |
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625 | { |
---|
626 | s=s+solution[pos]; |
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627 | pos++; |
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628 | } |
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629 | execute("v[j]="+s+";"); |
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630 | } |
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631 | l=insert(l,v,size(l)); |
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632 | } |
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633 | } |
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634 | |
---|
635 | // delete all created files |
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636 | dummy=system("sh","rm -f "+matrixfile); |
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637 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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638 | dummy=system("sh","rm -f "+problemfile); |
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639 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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640 | |
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641 | return(l); |
---|
642 | } |
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643 | |
---|
644 | |
---|
645 | |
---|
646 | |
---|
647 | |
---|
648 | |
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649 | proc solve_IP |
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650 | "USAGE: solve_IP(A,bx,c,alg); A intmat, bx intvec, c intvec, alg string |
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651 | |
---|
652 | solve_IP(A,bx,c,alg); A intmat, bx list of intvec, c intvec, alg string |
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653 | |
---|
654 | solve_IP(A,bx,c,alg,prsv); A intmat, bx intvec, c intvec, alg string, prsv intvec |
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655 | |
---|
656 | solve_IP(A,bx,c,alg,prsv); A intmat, bx list of intvec, c intvec, alg string, prsv intvec |
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657 | RETURN: type of bx: solution of the associated integer programming problem(s) as explained in |
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658 | @texinfo |
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659 | @ref{Toric ideals and integer programming}. |
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660 | @end texinfo |
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661 | NOTE: This procedure returns the solution(s) of the given IP-problem(s) or the message `not solvable'. |
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662 | |
---|
663 | One may call the procedure with several different algorithms: |
---|
664 | |
---|
665 | - the algorithm of Conti/Traverso using elimination (ect), |
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666 | |
---|
667 | - the algorithm of Pottier (pt), |
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668 | |
---|
669 | - an algorithm of Bigatti/La Scala/Robbiano (blr), |
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670 | |
---|
671 | - the algorithm of Hosten/Sturmfels (hs), |
---|
672 | |
---|
673 | - the algorithm of DiBiase/Urbanke (du). |
---|
674 | |
---|
675 | The argument `alg' should be the abbreviation for an algorithm as above: ect, pt, blr, hs or du. |
---|
676 | |
---|
677 | `ct' allows to compute an optimal solution of the IP-problem directly from the right-hand vector b. The same is true for its `positive' variant `pct' which may only be applied if A and b have nonnegative entries. All other algorithms need initial solutions of the IP-problem. |
---|
678 | |
---|
679 | If `alg' is chosen to be `ct' or `pct', bx is read as the right hand vector b of the system Ax=b. b should then be an intvec of size m where m is the number of rows of A. Furthermore, bx and A should be nonnegative if `pct' is used. If `alg' is chosen to be `ect',`pt',`blr',`hs' or `du', bx is read as an initial solution x of the system Ax=b. bx should then be a nonnegative intvec of size n where n is the number of columns of A. |
---|
680 | |
---|
681 | If `alg' is chosen to be `blr' or `hs', the algorithm needs a vector with positive coefficients in the row space of A. If no row of A contains only positive entries, one has to use the versions of solve_IP which take such a vector prsv as an argument. |
---|
682 | |
---|
683 | solve_IP may also be called with a list bx of intvecs instead of a single intvec. |
---|
684 | EXAMPLE: example solve_IP; shows an example |
---|
685 | SEE ALSO: intprog_lib, toric_lib, Integer programming |
---|
686 | " |
---|
687 | { |
---|
688 | if(size(#)==4) |
---|
689 | { |
---|
690 | if(typeof(#[2])=="intvec") |
---|
691 | { |
---|
692 | return(solve_IP_1(#[1],#[2],#[3],#[4])); |
---|
693 | } |
---|
694 | else |
---|
695 | { |
---|
696 | return(solve_IP_2(#[1],#[2],#[3],#[4])); |
---|
697 | } |
---|
698 | } |
---|
699 | else |
---|
700 | { |
---|
701 | if(typeof(#[2])=="intvec") |
---|
702 | { |
---|
703 | return(solve_IP_3(#[1],#[2],#[3],#[4],#[5])); |
---|
704 | } |
---|
705 | else |
---|
706 | { |
---|
707 | return(solve_IP_4(#[1],#[2],#[3],#[4],#[5])); |
---|
708 | } |
---|
709 | } |
---|
710 | } |
---|
711 | |
---|
712 | |
---|
713 | |
---|
714 | example |
---|
715 | { |
---|
716 | "EXAMPLE"; echo=2; |
---|
717 | |
---|
718 | // call with single right-hand vector |
---|
719 | intmat A[2][3]=1,1,0,0,1,1; |
---|
720 | A; |
---|
721 | intvec b1=1,1; |
---|
722 | b1; |
---|
723 | intvec c=2,2,1; |
---|
724 | c; |
---|
725 | intvec solution_vector=solve_IP(A,b1,c,"pct"); |
---|
726 | solution_vector; |
---|
727 | |
---|
728 | // call with list of right-hand vectors |
---|
729 | intvec b2=-1,1; |
---|
730 | list l=b1,b2; |
---|
731 | l; |
---|
732 | list solution_list=solve_IP(A,l,c,"ct"); |
---|
733 | solution_list; |
---|
734 | |
---|
735 | // call with single initial solution vector |
---|
736 | A=2,1,-1,-1,1,2; |
---|
737 | A; |
---|
738 | b1=3,4,5; |
---|
739 | solution_vector=solve_IP(A,b1,c,"du"); |
---|
740 | |
---|
741 | // call with single initial solution vector |
---|
742 | // and algorithm needing a positive row space vector |
---|
743 | solution_vector=solve_IP(A,b1,c,"hs"); |
---|
744 | |
---|
745 | // call with single initial solution vector |
---|
746 | // and positive row space vector |
---|
747 | intvec prsv=1,2,1; |
---|
748 | prsv; |
---|
749 | solution_vector=solve_IP(A,b1,c,"hs",prsv); |
---|
750 | solution_vector; |
---|
751 | |
---|
752 | // call with list of initial solution vectors |
---|
753 | // and positive row space vector |
---|
754 | b2=7,8,0; |
---|
755 | l=b1,b2; |
---|
756 | l; |
---|
757 | solution_list=solve_IP(A,l,c,"blr",prsv); |
---|
758 | solution_list; |
---|
759 | } |
---|