[6ba162] | 1 | // $Id: IP.lib,v 1.1.1.1 2000-05-02 12:58:31 Singular Exp $ |
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| 2 | // |
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| 3 | // author : Christine Theis |
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| 4 | // |
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| 5 | |
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| 6 | //version="$Id: IP.lib,v 1.1.1.1 2000-05-02 12:58:31 Singular Exp $"; |
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| 7 | |
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| 8 | /////////////////////////////////////////////////////////////////////////////// |
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| 9 | |
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| 10 | info=" |
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| 11 | LIBRARY: IP.lib PROCEDURES FOR INTEGER PROGRAMMING USING GROEBNER BASIS METHODS |
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| 12 | |
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| 13 | |
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| 14 | Let A an integral (mxn)-matrix, b a vector with m integral |
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| 15 | coefficients and c a vector with n nonnegative integral coefficients. The |
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| 16 | solution of the IP-problem |
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| 17 | |
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| 18 | (*) minimize{ cx | Ax=b, all components of x are nonnegative integers } |
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| 19 | |
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| 20 | proceeds in two steps: |
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| 21 | |
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| 22 | 1. We compute the toric ideal of A and its Groebner basis with respect |
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| 23 | to a term ordering refining the cost function c (such an ordering |
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| 24 | exists because c is nonnegative). |
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| 25 | |
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| 26 | 2. We reduce the right hand vector b or an initial solution of the problem |
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| 27 | modulo this ideal. |
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| 28 | |
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| 29 | For these purposes, we can use seven different algorithms: |
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| 30 | The algorithm of Conti/Traverso (ct) can compute an optimal solution |
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| 31 | of the IP-problem directly from the right hand vector b. The same is |
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| 32 | true for its `positive' variant (pct) which can only be applied if A |
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| 33 | and b have nonnegative entries, but should be faster in that case. |
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| 34 | All other algorithms need initial solutions of the IP-problem. Except |
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| 35 | from the Conti-Traverso algorithm with elimination (ect), |
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| 36 | they should be more efficient than the algorithm mentionned before. |
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| 37 | These are the algorithms of Pottier (pt), Bigatti/La Scala/Robbiano |
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| 38 | (blr), Hosten/Sturmfels (hs) and Di Biase/Urbanke (du). The last two |
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| 39 | seem to be the fastest in the actual implementation. |
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| 40 | |
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| 41 | |
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| 42 | solve_IP(intmat A, intvec bx, intvec c, string alg); |
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| 43 | solve_IP(intmat A, list bx, intvec c, string alg); |
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| 44 | solve_IP(intmat A, intvec bx, intvec c, string alg, intvec prsv); |
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| 45 | solve_IP(intmat A, list bx, intvec c, string alg, intvec prsv); |
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| 46 | |
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| 47 | procedures for solving the IP-problem (*) |
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| 48 | They return the solution(s) of the given problem(s) or the |
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| 49 | message `not solvable'. |
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| 50 | `alg' may be one of the algorithm abbreviations as above. |
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| 51 | If `alg' is chosen to be `ct' or `pct', bx is read as the right |
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| 52 | hand vector b of the system Ax=b. b should then be an intvec of |
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| 53 | size m where m is the number of rows of A. Furthermore, bx and |
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| 54 | A should be nonnegative if `pct' is used. |
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| 55 | If `alg' is chosen to be `ect',`pt',`blr',`hs' or `du', bx is |
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| 56 | read as an initial solution x of the system Ax=b. bx should |
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| 57 | then be a nonnegative intvec of size n where n is the number |
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| 58 | of columns of A. |
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| 59 | If `alg' is chosen to be `blr' or `hs', the algorithm needs a |
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| 60 | vector with positive coefficcients in the row space of A. If |
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| 61 | no row of A contains only positive entries, one must use the |
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| 62 | versions of solve_IP which take such a vector prsv as |
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| 63 | argument. |
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| 64 | solve_IP may also be called with a list bx of intvecs instead |
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| 65 | of a single intvec. |
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| 66 | |
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| 67 | |
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| 68 | "; |
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| 69 | |
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| 70 | /////////////////////////////////////////////////////////////////////////////// |
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| 71 | |
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| 72 | |
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| 73 | |
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| 74 | static proc solve_IP_1(intmat A, intvec bx, intvec c, string alg) |
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| 75 | { |
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| 76 | intvec v; |
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| 77 | // to be returned |
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| 78 | |
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| 79 | // check arguments as far as necessary |
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| 80 | // other inconsistencies are detected by the external program |
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| 81 | if(size(c)!=ncols(A)) |
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| 82 | { |
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| 83 | "ERROR: number of matrix columns must equal size of cost vector"; |
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| 84 | return(v); |
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| 85 | } |
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| 86 | |
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| 87 | // create first temporary file with that the external program is |
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| 88 | // called |
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| 89 | |
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| 90 | int process=system("pid"); |
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| 91 | string matrixfile="temp_MATRIX"+string(process); |
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| 92 | link MATRIX=":w "+matrixfile; |
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| 93 | open(MATRIX); |
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| 94 | |
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| 95 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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| 96 | int i,j; |
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| 97 | for(j=1;j<=ncols(A);j++) |
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| 98 | { |
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| 99 | write(MATRIX,c[j]); |
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| 100 | } |
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| 101 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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| 102 | for(i=1;i<=nrows(A);i++) |
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| 103 | { |
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| 104 | for(j=1;j<=ncols(A);j++) |
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| 105 | { |
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| 106 | write(MATRIX,A[i,j]); |
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| 107 | } |
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| 108 | } |
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| 109 | |
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| 110 | // search for positive row space vector, if required by the |
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| 111 | // algorithm |
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| 112 | int found=0; |
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| 113 | if((alg=="blr") || (alg=="hs")) |
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| 114 | { |
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| 115 | for(i=1;i<=nrows(A);i++) |
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| 116 | { |
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| 117 | found=i; |
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| 118 | for(j=1;j<=ncols(A);j++) |
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| 119 | { |
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| 120 | if(A[i,j]<=0) |
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| 121 | { |
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| 122 | found=0; |
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| 123 | } |
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| 124 | } |
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| 125 | if(found>0) |
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| 126 | { |
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| 127 | break; |
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| 128 | } |
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| 129 | } |
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| 130 | if(found==0) |
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| 131 | { |
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| 132 | "ERROR: algorithm needs positive vector in the row space of the matrix"; |
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| 133 | close(MATRIX); |
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| 134 | system("sh","rm -f "+matrixfile); |
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| 135 | return(v); |
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| 136 | } |
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| 137 | write(MATRIX,"positive row space vector:"); |
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| 138 | for(j=1;j<=ncols(A);j++) |
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| 139 | { |
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| 140 | write(MATRIX,A[found,j]); |
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| 141 | } |
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| 142 | } |
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| 143 | close(MATRIX); |
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| 144 | |
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| 145 | // create second temporary file for the external program |
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| 146 | |
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| 147 | string problemfile="temp_PROBLEM"+string(process); |
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| 148 | link PROBLEM=":w "+problemfile; |
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| 149 | open(PROBLEM); |
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| 150 | |
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| 151 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
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| 152 | for(i=1;i<=size(bx);i++) |
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| 153 | { |
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| 154 | write(PROBLEM,bx[i]); |
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| 155 | } |
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| 156 | close(PROBLEM); |
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| 157 | |
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| 158 | // call external program |
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| 159 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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| 160 | |
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| 161 | // read solution from created file |
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| 162 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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| 163 | string solution=read(SOLUTION); |
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| 164 | int pos; |
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| 165 | string s; |
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| 166 | if(alg=="ct" || alg=="pct") |
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| 167 | { |
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| 168 | pos=find(solution,"NO"); |
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| 169 | if(pos!=0) |
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| 170 | { |
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| 171 | "not solvable"; |
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| 172 | } |
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| 173 | else |
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| 174 | { |
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| 175 | pos=find(solution,"YES"); |
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| 176 | pos=find(solution,":",pos); |
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| 177 | pos++; |
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| 178 | for(j=1;j<=ncols(A);j++) |
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| 179 | { |
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| 180 | while(solution[pos]==" " || solution[pos]==newline) |
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| 181 | { |
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| 182 | pos++; |
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| 183 | } |
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| 184 | s=""; |
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| 185 | while(solution[pos]!=" " && solution[pos]!=newline) |
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| 186 | { |
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| 187 | s=s+solution[pos]; |
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| 188 | pos++; |
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| 189 | } |
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| 190 | execute("v[j]="+s+";"); |
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| 191 | } |
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| 192 | } |
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| 193 | } |
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| 194 | else |
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| 195 | { |
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| 196 | pos=find(solution,"optimal"); |
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| 197 | pos=find(solution,":",pos); |
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| 198 | pos++; |
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| 199 | for(j=1;j<=ncols(A);j++) |
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| 200 | { |
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| 201 | while(solution[pos]==" " || solution[pos]==newline) |
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| 202 | { |
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| 203 | pos++; |
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| 204 | } |
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| 205 | s=""; |
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| 206 | while(solution[pos]!=" " && solution[pos]!=newline) |
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| 207 | { |
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| 208 | s=s+solution[pos]; |
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| 209 | pos++; |
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| 210 | } |
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| 211 | execute("v[j]="+s+";"); |
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| 212 | } |
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| 213 | } |
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| 214 | |
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| 215 | // delete all created files |
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| 216 | dummy=system("sh","rm -f "+matrixfile); |
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| 217 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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| 218 | dummy=system("sh","rm -f "+problemfile); |
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| 219 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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| 220 | |
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| 221 | return(v); |
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| 222 | } |
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| 223 | |
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| 224 | |
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| 225 | |
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| 226 | static proc solve_IP_2(intmat A, list bx, intvec c, string alg) |
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| 227 | { |
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| 228 | list l;; |
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| 229 | // to be returned |
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| 230 | |
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| 231 | // check arguments as far as necessary |
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| 232 | // other inconsistencies are detected by the external program |
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| 233 | if(size(c)!=ncols(A)) |
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| 234 | { |
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| 235 | "ERROR: number of matrix columns must equal size of cost vector"; |
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| 236 | return(l); |
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| 237 | } |
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| 238 | |
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| 239 | int k; |
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| 240 | for(k=2;k<=size(bx);k++) |
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| 241 | { |
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| 242 | if(size(bx[k])!=size(bx[1])) |
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| 243 | { |
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| 244 | "ERROR: size of all right hand vectors must be equal"; |
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| 245 | return(l); |
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| 246 | } |
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| 247 | } |
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| 248 | |
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| 249 | // create first temporary file with that the external program is |
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| 250 | // called |
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| 251 | |
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| 252 | int process=system("pid"); |
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| 253 | string matrixfile="temp_MATRIX"+string(process); |
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| 254 | link MATRIX=":w "+matrixfile; |
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| 255 | open(MATRIX); |
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| 256 | |
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| 257 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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| 258 | int i,j; |
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| 259 | for(j=1;j<=ncols(A);j++) |
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| 260 | { |
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| 261 | write(MATRIX,c[j]); |
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| 262 | } |
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| 263 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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| 264 | for(i=1;i<=nrows(A);i++) |
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| 265 | { |
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| 266 | for(j=1;j<=ncols(A);j++) |
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| 267 | { |
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| 268 | write(MATRIX,A[i,j]); |
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| 269 | } |
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| 270 | } |
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| 271 | |
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| 272 | // search for positive row space vector, if required by the |
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| 273 | // algorithm |
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| 274 | int found=0; |
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| 275 | if((alg=="blr") || (alg=="hs")) |
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| 276 | { |
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| 277 | for(i=1;i<=nrows(A);i++) |
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| 278 | { |
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| 279 | found=i; |
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| 280 | for(j=1;j<=ncols(A);j++) |
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| 281 | { |
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| 282 | if(A[i,j]<=0) |
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| 283 | { |
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| 284 | found=0; |
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| 285 | } |
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| 286 | } |
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| 287 | if(found>0) |
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| 288 | { |
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| 289 | break; |
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| 290 | } |
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| 291 | } |
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| 292 | if(found==0) |
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| 293 | { |
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| 294 | "ERROR: algorithm needs positive vector in the row space of the matrix"; |
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| 295 | close(MATRIX); |
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| 296 | system("sh","rm -f "+matrixfile); |
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| 297 | return(l); |
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| 298 | } |
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| 299 | write(MATRIX,"positive row space vector:"); |
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| 300 | for(j=1;j<=ncols(A);j++) |
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| 301 | { |
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| 302 | write(MATRIX,A[found,j]); |
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| 303 | } |
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| 304 | } |
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| 305 | close(MATRIX); |
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| 306 | |
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| 307 | // create second temporary file for the external program |
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| 308 | |
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| 309 | string problemfile="temp_PROBLEM"+string(process); |
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| 310 | link PROBLEM=":w "+problemfile; |
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| 311 | open(PROBLEM); |
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| 312 | |
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| 313 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
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| 314 | for(k=1;k<=size(bx);k++) |
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| 315 | { |
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| 316 | for(i=1;i<=size(bx[1]);i++) |
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| 317 | { |
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| 318 | write(PROBLEM,bx[k][i]); |
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| 319 | } |
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| 320 | } |
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| 321 | close(PROBLEM); |
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| 322 | |
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| 323 | // call external program |
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| 324 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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| 325 | |
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| 326 | // read solution from created file |
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| 327 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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| 328 | string solution=read(SOLUTION); |
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| 329 | intvec v; |
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| 330 | int pos,pos1,pos2; |
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| 331 | string s; |
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| 332 | if(alg=="ct" || alg=="pct") |
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| 333 | { |
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| 334 | pos=1; |
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| 335 | for(k=1;k<=size(bx);k++) |
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| 336 | { |
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| 337 | pos1=find(solution,"NO",pos); |
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| 338 | pos2=find(solution,"YES",pos); |
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| 339 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
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| 340 | // first problem not solvable |
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| 341 | { |
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| 342 | pos=find(solution,":",pos1); |
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| 343 | l=insert(l,"not solvable",size(l)); |
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| 344 | } |
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| 345 | else |
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| 346 | // first problem solvable |
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| 347 | { |
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| 348 | pos=find(solution,":",pos2); |
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| 349 | pos++; |
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| 350 | for(j=1;j<=ncols(A);j++) |
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| 351 | { |
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| 352 | while(solution[pos]==" " || solution[pos]==newline) |
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| 353 | { |
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| 354 | pos++; |
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| 355 | } |
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| 356 | s=""; |
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| 357 | while(solution[pos]!=" " && solution[pos]!=newline) |
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| 358 | { |
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| 359 | s=s+solution[pos]; |
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| 360 | pos++; |
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| 361 | } |
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| 362 | execute("v[j]="+s+";"); |
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| 363 | } |
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| 364 | l=insert(l,v,size(l)); |
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| 365 | } |
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| 366 | } |
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| 367 | } |
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| 368 | else |
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| 369 | { |
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| 370 | pos=1; |
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| 371 | for(k=1;k<=size(bx);k++) |
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| 372 | { |
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| 373 | pos=find(solution,"optimal",pos); |
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| 374 | pos=find(solution,":",pos); |
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| 375 | pos++; |
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| 376 | for(j=1;j<=ncols(A);j++) |
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| 377 | { |
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| 378 | while(solution[pos]==" " || solution[pos]==newline) |
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| 379 | { |
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| 380 | pos++; |
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| 381 | } |
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| 382 | s=""; |
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| 383 | while(solution[pos]!=" " && solution[pos]!=newline) |
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| 384 | { |
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| 385 | s=s+solution[pos]; |
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| 386 | pos++; |
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| 387 | } |
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| 388 | execute("v[j]="+s+";"); |
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| 389 | } |
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| 390 | l=insert(l,v,size(l)); |
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| 391 | } |
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| 392 | } |
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| 393 | |
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| 394 | // delete all created files |
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| 395 | dummy=system("sh","rm -f "+matrixfile); |
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| 396 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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| 397 | dummy=system("sh","rm -f "+problemfile); |
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| 398 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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| 399 | |
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| 400 | return(l); |
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| 401 | } |
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| 402 | |
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| 403 | |
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| 404 | |
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| 405 | static proc solve_IP_3(intmat A, intvec bx, intvec c, string alg, intvec prsv) |
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| 406 | { |
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| 407 | intvec v; |
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| 408 | // to be returned |
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| 409 | |
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| 410 | // check arguments as far as necessary |
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| 411 | // other inconsistencies are detected by the external program |
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| 412 | if(size(c)!=ncols(A)) |
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| 413 | { |
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| 414 | "ERROR: number of matrix columns must equal size of cost vector"; |
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| 415 | return(v); |
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| 416 | } |
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| 417 | |
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| 418 | if(size(prsv)!=ncols(A)) |
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| 419 | { |
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| 420 | "ERROR: number of matrix columns must equal size of positive row space vector"; |
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| 421 | return(v); |
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| 422 | } |
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| 423 | |
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| 424 | // create first temporary file with that the external program is |
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| 425 | // called |
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| 426 | |
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| 427 | int process=system("pid"); |
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| 428 | string matrixfile="temp_MATRIX"+string(process); |
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| 429 | link MATRIX=":w "+matrixfile; |
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| 430 | open(MATRIX); |
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| 431 | |
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| 432 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
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| 433 | int i,j; |
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| 434 | for(j=1;j<=ncols(A);j++) |
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| 435 | { |
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| 436 | write(MATRIX,c[j]); |
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| 437 | } |
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| 438 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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| 439 | for(i=1;i<=nrows(A);i++) |
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| 440 | { |
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| 441 | for(j=1;j<=ncols(A);j++) |
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| 442 | { |
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| 443 | write(MATRIX,A[i,j]); |
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| 444 | } |
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| 445 | } |
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| 446 | |
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| 447 | // enter positive row space vector, if required by the algorithm |
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| 448 | if((alg=="blr") || (alg=="hs")) |
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| 449 | { |
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| 450 | write(MATRIX,"positive row space vector:"); |
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| 451 | for(j=1;j<=ncols(A);j++) |
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| 452 | { |
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| 453 | write(MATRIX,prsv[j]); |
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| 454 | } |
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| 455 | } |
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| 456 | close(MATRIX); |
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| 457 | |
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| 458 | // create second temporary file for the external program |
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| 459 | |
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| 460 | string problemfile="temp_PROBLEM"+string(process); |
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| 461 | link PROBLEM=":w "+problemfile; |
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| 462 | open(PROBLEM); |
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| 463 | |
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| 464 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
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| 465 | for(i=1;i<=size(bx);i++) |
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| 466 | { |
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| 467 | write(PROBLEM,bx[i]); |
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| 468 | } |
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| 469 | close(PROBLEM); |
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| 470 | |
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| 471 | // call external program |
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| 472 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
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| 473 | |
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| 474 | // read solution from created file |
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| 475 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
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| 476 | string solution=read(SOLUTION); |
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| 477 | int pos; |
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| 478 | string s; |
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| 479 | if(alg=="ct" || alg=="pct") |
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| 480 | { |
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| 481 | pos=find(solution,"NO"); |
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| 482 | if(pos!=0) |
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| 483 | { |
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| 484 | "not solvable"; |
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| 485 | } |
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| 486 | else |
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| 487 | { |
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| 488 | pos=find(solution,"YES"); |
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| 489 | pos=find(solution,":",pos); |
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| 490 | pos++; |
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| 491 | for(j=1;j<=ncols(A);j++) |
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| 492 | { |
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| 493 | while(solution[pos]==" " || solution[pos]==newline) |
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| 494 | { |
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| 495 | pos++; |
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| 496 | } |
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| 497 | s=""; |
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| 498 | while(solution[pos]!=" " && solution[pos]!=newline) |
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| 499 | { |
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| 500 | s=s+solution[pos]; |
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| 501 | pos++; |
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| 502 | } |
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| 503 | execute("v[j]="+s+";"); |
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| 504 | } |
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| 505 | } |
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| 506 | } |
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| 507 | else |
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| 508 | { |
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| 509 | pos=find(solution,"optimal"); |
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| 510 | pos=find(solution,":",pos); |
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| 511 | pos++; |
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| 512 | for(j=1;j<=ncols(A);j++) |
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| 513 | { |
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| 514 | while(solution[pos]==" " || solution[pos]==newline) |
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| 515 | { |
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| 516 | pos++; |
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| 517 | } |
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| 518 | s=""; |
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| 519 | while(solution[pos]!=" " && solution[pos]!=newline) |
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| 520 | { |
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| 521 | s=s+solution[pos]; |
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| 522 | pos++; |
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| 523 | } |
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| 524 | execute("v[j]="+s+";"); |
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| 525 | } |
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| 526 | } |
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| 527 | |
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| 528 | // delete all created files |
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| 529 | dummy=system("sh","rm -f "+matrixfile); |
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| 530 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
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| 531 | dummy=system("sh","rm -f "+problemfile); |
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| 532 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
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| 533 | |
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| 534 | return(v); |
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| 535 | } |
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| 536 | |
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| 537 | |
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| 538 | |
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| 539 | static proc solve_IP_4(intmat A, list bx, intvec c, string alg, intvec prsv) |
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| 540 | { |
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| 541 | list l; |
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| 542 | // to be returned |
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| 543 | |
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| 544 | // check arguments as far as necessary |
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| 545 | // other inconsistencies are detected by the external program |
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| 546 | if(size(c)!=ncols(A)) |
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| 547 | { |
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| 548 | "ERROR: number of matrix columns must equal size of cost vector"; |
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| 549 | return(l); |
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| 550 | } |
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| 551 | |
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| 552 | if(size(prsv)!=ncols(A)) |
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| 553 | { |
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| 554 | "ERROR: number of matrix columns must equal size of positive row space vector"; |
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| 555 | return(v); |
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| 556 | } |
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| 557 | |
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| 558 | int k; |
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| 559 | for(k=2;k<=size(bx);k++) |
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| 560 | { |
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| 561 | if(size(bx[k])!=size(bx[1])) |
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| 562 | { |
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| 563 | "ERROR: size of all right hand vectors must be equal"; |
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| 564 | return(l); |
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| 565 | } |
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| 566 | } |
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| 567 | |
---|
| 568 | // create first temporary file with that the external program is |
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| 569 | // called |
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| 570 | |
---|
| 571 | int process=system("pid"); |
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| 572 | string matrixfile="temp_MATRIX"+string(process); |
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| 573 | link MATRIX=":w "+matrixfile; |
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| 574 | open(MATRIX); |
---|
| 575 | |
---|
| 576 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
---|
| 577 | int i,j; |
---|
| 578 | for(j=1;j<=ncols(A);j++) |
---|
| 579 | { |
---|
| 580 | write(MATRIX,c[j]); |
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| 581 | } |
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| 582 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
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| 583 | for(i=1;i<=nrows(A);i++) |
---|
| 584 | { |
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| 585 | for(j=1;j<=ncols(A);j++) |
---|
| 586 | { |
---|
| 587 | write(MATRIX,A[i,j]); |
---|
| 588 | } |
---|
| 589 | } |
---|
| 590 | |
---|
| 591 | // enter positive row space vector if required by the algorithm |
---|
| 592 | if((alg=="blr") || (alg=="hs")) |
---|
| 593 | { |
---|
| 594 | write(MATRIX,"positive row space vector:"); |
---|
| 595 | for(j=1;j<=ncols(A);j++) |
---|
| 596 | { |
---|
| 597 | write(MATRIX,prsv[j]); |
---|
| 598 | } |
---|
| 599 | } |
---|
| 600 | close(MATRIX); |
---|
| 601 | |
---|
| 602 | // create second temporary file for the external program |
---|
| 603 | |
---|
| 604 | string problemfile="temp_PROBLEM"+string(process); |
---|
| 605 | link PROBLEM=":w "+problemfile; |
---|
| 606 | open(PROBLEM); |
---|
| 607 | |
---|
| 608 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
---|
| 609 | for(k=1;k<=size(bx);k++) |
---|
| 610 | { |
---|
| 611 | for(i=1;i<=size(bx[1]);i++) |
---|
| 612 | { |
---|
| 613 | write(PROBLEM,bx[k][i]); |
---|
| 614 | } |
---|
| 615 | } |
---|
| 616 | close(PROBLEM); |
---|
| 617 | |
---|
| 618 | // call external program |
---|
| 619 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
---|
| 620 | |
---|
| 621 | // read solution from created file |
---|
| 622 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
---|
| 623 | string solution=read(SOLUTION); |
---|
| 624 | intvec v; |
---|
| 625 | int pos,pos1,pos2; |
---|
| 626 | string s; |
---|
| 627 | if(alg=="ct" || alg=="pct") |
---|
| 628 | { |
---|
| 629 | pos=1; |
---|
| 630 | for(k=1;k<=size(bx);k++) |
---|
| 631 | { |
---|
| 632 | pos1=find(solution,"NO",pos); |
---|
| 633 | pos2=find(solution,"YES",pos); |
---|
| 634 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
---|
| 635 | // first problem not solvable |
---|
| 636 | { |
---|
| 637 | pos=find(solution,":",pos1); |
---|
| 638 | l=insert(l,"not solvable",size(l)); |
---|
| 639 | } |
---|
| 640 | else |
---|
| 641 | // first problem solvable |
---|
| 642 | { |
---|
| 643 | pos=find(solution,":",pos2); |
---|
| 644 | pos++; |
---|
| 645 | for(j=1;j<=ncols(A);j++) |
---|
| 646 | { |
---|
| 647 | while(solution[pos]==" " || solution[pos]==newline) |
---|
| 648 | { |
---|
| 649 | pos++; |
---|
| 650 | } |
---|
| 651 | s=""; |
---|
| 652 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
| 653 | { |
---|
| 654 | s=s+solution[pos]; |
---|
| 655 | pos++; |
---|
| 656 | } |
---|
| 657 | execute("v[j]="+s+";"); |
---|
| 658 | } |
---|
| 659 | l=insert(l,v,size(l)); |
---|
| 660 | } |
---|
| 661 | } |
---|
| 662 | } |
---|
| 663 | else |
---|
| 664 | { |
---|
| 665 | pos=1; |
---|
| 666 | for(k=1;k<=size(bx);k++) |
---|
| 667 | { |
---|
| 668 | pos=find(solution,"optimal",pos); |
---|
| 669 | pos=find(solution,":",pos); |
---|
| 670 | pos++; |
---|
| 671 | for(j=1;j<=ncols(A);j++) |
---|
| 672 | { |
---|
| 673 | while(solution[pos]==" " || solution[pos]==newline) |
---|
| 674 | { |
---|
| 675 | pos++; |
---|
| 676 | } |
---|
| 677 | s=""; |
---|
| 678 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
| 679 | { |
---|
| 680 | s=s+solution[pos]; |
---|
| 681 | pos++; |
---|
| 682 | } |
---|
| 683 | execute("v[j]="+s+";"); |
---|
| 684 | } |
---|
| 685 | l=insert(l,v,size(l)); |
---|
| 686 | } |
---|
| 687 | } |
---|
| 688 | |
---|
| 689 | // delete all created files |
---|
| 690 | dummy=system("sh","rm -f "+matrixfile); |
---|
| 691 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
---|
| 692 | dummy=system("sh","rm -f "+problemfile); |
---|
| 693 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
---|
| 694 | |
---|
| 695 | return(l); |
---|
| 696 | } |
---|
| 697 | |
---|
| 698 | |
---|
| 699 | |
---|
| 700 | |
---|
| 701 | |
---|
| 702 | |
---|
| 703 | proc solve_IP |
---|
| 704 | "USAGE: |
---|
| 705 | solve_IP(A,bx,c,alg); A intmat, bx intvec, c intvec, alg string |
---|
| 706 | solve_IP(A,bx,c,alg); A intmat, bx list of intvec, c intvec, alg string |
---|
| 707 | solve_IP(A,bx,c,alg,prsv); A intmat, bx intvec, c intvec, alg string, |
---|
| 708 | prsv intvec |
---|
| 709 | solve_IP(A,bx,c,alg,prsv); A intmat, bx list of intvec, c intvec, alg string, |
---|
| 710 | prsv intvec |
---|
| 711 | RETURN: solution of the associated integer programming problem as explained |
---|
| 712 | in IP.lib |
---|
| 713 | return type = type of bx |
---|
| 714 | EXAMPLE: example solve_IP; shows an example" |
---|
| 715 | { |
---|
| 716 | if(size(#)==4) |
---|
| 717 | { |
---|
| 718 | if(typeof(#[2])=="intvec") |
---|
| 719 | { |
---|
| 720 | return(solve_IP_1(#[1],#[2],#[3],#[4])); |
---|
| 721 | } |
---|
| 722 | else |
---|
| 723 | { |
---|
| 724 | return(solve_IP_2(#[1],#[2],#[3],#[4])); |
---|
| 725 | } |
---|
| 726 | } |
---|
| 727 | else |
---|
| 728 | { |
---|
| 729 | if(typeof(#[2])=="intvec") |
---|
| 730 | { |
---|
| 731 | return(solve_IP_3(#[1],#[2],#[3],#[4],#[5])); |
---|
| 732 | } |
---|
| 733 | else |
---|
| 734 | { |
---|
| 735 | return(solve_IP_4(#[1],#[2],#[3],#[4],#[5])); |
---|
| 736 | } |
---|
| 737 | } |
---|
| 738 | } |
---|
| 739 | |
---|
| 740 | |
---|
| 741 | |
---|
| 742 | example |
---|
| 743 | { |
---|
| 744 | "EXAMPLE"; echo=2; |
---|
| 745 | |
---|
| 746 | // call with single right hand vector |
---|
| 747 | intmat A[2][3]=1,1,0,0,1,1; |
---|
| 748 | A; |
---|
| 749 | intvec b1=1,1; |
---|
| 750 | b1; |
---|
| 751 | intvec c=2,2,1; |
---|
| 752 | c; |
---|
| 753 | intvec solution_vector=solve_IP(A,b1,c,"pct"); |
---|
| 754 | solution_vector; |
---|
| 755 | |
---|
| 756 | // call with list of right hand vectors |
---|
| 757 | intvec b2=-1,1; |
---|
| 758 | list l=b1,b2; |
---|
| 759 | l; |
---|
| 760 | list solution_list=solve_IP(A,l,c,"ct"); |
---|
| 761 | solution_list; |
---|
| 762 | |
---|
| 763 | // call with single initial solution vector |
---|
| 764 | A=2,1,-1,-1,1,2; |
---|
| 765 | A; |
---|
| 766 | b1=3,4,5; |
---|
| 767 | solution_vector=solve_IP(A,b1,c,"du"); |
---|
| 768 | |
---|
| 769 | // call with single initial solution vector and algorithm needing a positive |
---|
| 770 | // row space vector |
---|
| 771 | solution_vector=solve_IP(A,b1,c,"hs"); |
---|
| 772 | |
---|
| 773 | // call with single initial solution vector and positive row space vector |
---|
| 774 | intvec prsv=1,2,1; |
---|
| 775 | prsv; |
---|
| 776 | solution_vector=solve_IP(A,b1,c,"hs",prsv); |
---|
| 777 | solution_vector; |
---|
| 778 | |
---|
| 779 | // call with list of initial solution vectors and positive row space vector |
---|
| 780 | b2=7,8,0; |
---|
| 781 | l=b1,b2; |
---|
| 782 | l; |
---|
| 783 | solution_list=solve_IP(A,l,c,"blr",prsv); |
---|
| 784 | solution_list; |
---|
| 785 | } |
---|
| 786 | |
---|
| 787 | |
---|
| 788 | |
---|