1 | /* |
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2 | emd.c |
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3 | |
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4 | Last update: 3/14/98 |
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5 | |
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6 | An implementation of the Earth Movers Distance. |
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7 | Based of the solution for the Transportation problem as described in |
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8 | "Introduction to Mathematical Programming" by F. S. Hillier and |
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9 | G. J. Lieberman, McGraw-Hill, 1990. |
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10 | |
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11 | Copyright (C) 1998 Yossi Rubner |
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12 | Computer Science Department, Stanford University |
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13 | E-Mail: rubner@cs.stanford.edu URL: http://vision.stanford.edu/~rubner |
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14 | */ |
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15 | |
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16 | #include <stdio.h> |
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17 | #include <stdlib.h> |
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18 | #include <math.h> |
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19 | |
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20 | #include "emd.h" |
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21 | |
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22 | #define DEBUG_LEVEL 0 |
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23 | /* |
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24 | DEBUG_LEVEL: |
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25 | 0 = NO MESSAGES |
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26 | 1 = PRINT THE NUMBER OF ITERATIONS AND THE FINAL RESULT |
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27 | 2 = PRINT THE RESULT AFTER EVERY ITERATION |
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28 | 3 = PRINT ALSO THE FLOW AFTER EVERY ITERATION |
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29 | 4 = PRINT A LOT OF INFORMATION (PROBABLY USEFUL ONLY FOR THE AUTHOR) |
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30 | */ |
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31 | |
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32 | |
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33 | #define MAX_SIG_SIZE1 (MAX_SIG_SIZE+1) /* FOR THE POSIBLE DUMMY FEATURE */ |
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34 | |
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35 | /* NEW TYPES DEFINITION */ |
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36 | |
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37 | /* node1_t IS USED FOR SINGLE-LINKED LISTS */ |
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38 | typedef struct node1_t { |
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39 | int i; |
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40 | double val; |
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41 | struct node1_t *Next; |
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42 | } node1_t; |
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43 | |
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44 | /* node1_t IS USED FOR DOUBLE-LINKED LISTS */ |
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45 | typedef struct node2_t { |
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46 | int i, j; |
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47 | double val; |
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48 | struct node2_t *NextC; /* NEXT COLUMN */ |
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49 | struct node2_t *NextR; /* NEXT ROW */ |
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50 | } node2_t; |
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51 | |
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52 | |
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53 | |
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54 | /* GLOBAL VARIABLE DECLARATION */ |
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55 | static int _n1, _n2; /* SIGNATURES SIZES */ |
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56 | static float _C[MAX_SIG_SIZE1][MAX_SIG_SIZE1];/* THE COST MATRIX */ |
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57 | static node2_t _X[MAX_SIG_SIZE1*2]; /* THE BASIC VARIABLES VECTOR */ |
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58 | /* VARIABLES TO HANDLE _X EFFICIENTLY */ |
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59 | static node2_t *_EndX, *_EnterX; |
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60 | static char _IsX[MAX_SIG_SIZE1][MAX_SIG_SIZE1]; |
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61 | static node2_t *_RowsX[MAX_SIG_SIZE1], *_ColsX[MAX_SIG_SIZE1]; |
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62 | static double _maxW; |
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63 | static float _maxC; |
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64 | |
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65 | /* DECLARATION OF FUNCTIONS */ |
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66 | static float init(signature_t *Signature1, signature_t *Signature2, |
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67 | float (*Dist)(feature_t *, feature_t *)); |
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68 | static void findBasicVariables(node1_t *U, node1_t *V); |
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69 | static int isOptimal(node1_t *U, node1_t *V); |
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70 | static int findLoop(node2_t **Loop); |
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71 | static void newSol(); |
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72 | static void russel(double *S, double *D); |
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73 | static void addBasicVariable(int minI, int minJ, double *S, double *D, |
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74 | node1_t *PrevUMinI, node1_t *PrevVMinJ, |
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75 | node1_t *UHead); |
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76 | #if DEBUG_LEVEL > 0 |
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77 | static void printSolution(); |
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78 | #endif |
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79 | |
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80 | |
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81 | /****************************************************************************** |
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82 | float emd(signature_t *Signature1, signature_t *Signature2, |
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83 | float (*Dist)(feature_t *, feature_t *), flow_t *Flow, int *FlowSize) |
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84 | |
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85 | where |
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86 | |
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87 | Signature1, Signature2 Pointers to signatures that their distance we want |
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88 | to compute. |
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89 | Dist Pointer to the ground distance. i.e. the function that computes |
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90 | the distance between two features. |
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91 | Flow (Optional) Pointer to a vector of flow_t (defined in emd.h) |
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92 | where the resulting flow will be stored. Flow must have n1+n2-1 |
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93 | elements, where n1 and n2 are the sizes of the two signatures |
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94 | respectively. |
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95 | If NULL, the flow is not returned. |
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96 | FlowSize (Optional) Pointer to an integer where the number of elements in |
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97 | Flow will be stored |
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98 | |
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99 | ******************************************************************************/ |
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100 | |
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101 | float emd(signature_t *Signature1, signature_t *Signature2, |
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102 | float (*Dist)(feature_t *, feature_t *), |
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103 | flow_t *Flow, int *FlowSize) |
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104 | { |
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105 | int itr; |
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106 | double totalCost; |
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107 | float w; |
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108 | node2_t *XP; |
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109 | flow_t *FlowP; |
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110 | node1_t U[MAX_SIG_SIZE1], V[MAX_SIG_SIZE1]; |
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111 | |
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112 | w = init(Signature1, Signature2, Dist); |
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113 | |
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114 | #if DEBUG_LEVEL > 1 |
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115 | printf("\nINITIAL SOLUTION:\n"); |
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116 | printSolution(); |
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117 | #endif |
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118 | |
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119 | if (_n1 > 1 && _n2 > 1) /* IF _n1 = 1 OR _n2 = 1 THEN WE ARE DONE */ |
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120 | { |
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121 | for (itr = 1; itr < MAX_ITERATIONS; itr++) |
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122 | { |
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123 | /* FIND BASIC VARIABLES */ |
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124 | findBasicVariables(U, V); |
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125 | |
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126 | /* CHECK FOR OPTIMALITY */ |
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127 | if (isOptimal(U, V)) |
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128 | break; |
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129 | |
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130 | /* IMPROVE SOLUTION */ |
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131 | newSol(); |
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132 | |
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133 | #if DEBUG_LEVEL > 1 |
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134 | printf("\nITERATION # %d \n", itr); |
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135 | printSolution(); |
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136 | #endif |
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137 | } |
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138 | |
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139 | if (itr == MAX_ITERATIONS) |
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140 | fprintf(stderr, "emd: Maximum number of iterations has been reached (%d)\n", |
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141 | MAX_ITERATIONS); |
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142 | } |
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143 | |
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144 | /* COMPUTE THE TOTAL FLOW */ |
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145 | totalCost = 0; |
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146 | if (Flow != NULL) |
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147 | FlowP = Flow; |
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148 | for(XP=_X; XP < _EndX; XP++) |
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149 | { |
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150 | if (XP == _EnterX) /* _EnterX IS THE EMPTY SLOT */ |
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151 | continue; |
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152 | if (XP->i == Signature1->n || XP->j == Signature2->n) /* DUMMY FEATURE */ |
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153 | continue; |
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154 | |
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155 | if (XP->val == 0) /* ZERO FLOW */ |
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156 | continue; |
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157 | |
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158 | totalCost += (double)XP->val * _C[XP->i][XP->j]; |
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159 | if (Flow != NULL) |
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160 | { |
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161 | FlowP->from = XP->i; |
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162 | FlowP->to = XP->j; |
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163 | FlowP->amount = XP->val; |
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164 | FlowP++; |
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165 | } |
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166 | } |
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167 | if (Flow != NULL) |
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168 | *FlowSize = FlowP-Flow; |
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169 | |
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170 | #if DEBUG_LEVEL > 0 |
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171 | printf("\n*** OPTIMAL SOLUTION (%d ITERATIONS): %f ***\n", itr, totalCost); |
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172 | #endif |
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173 | |
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174 | /* RETURN THE NORMALIZED COST == EMD */ |
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175 | return (float)(totalCost / w); |
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176 | } |
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177 | |
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178 | |
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179 | |
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180 | |
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181 | |
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182 | /********************** |
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183 | init |
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184 | **********************/ |
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185 | static float init(signature_t *Signature1, signature_t *Signature2, |
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186 | float (*Dist)(feature_t *, feature_t *)) |
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187 | { |
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188 | int i, j; |
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189 | double sSum, dSum, diff; |
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190 | feature_t *P1, *P2; |
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191 | double S[MAX_SIG_SIZE1], D[MAX_SIG_SIZE1]; |
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192 | |
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193 | _n1 = Signature1->n; |
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194 | _n2 = Signature2->n; |
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195 | |
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196 | if (_n1 > MAX_SIG_SIZE || _n2 > MAX_SIG_SIZE) |
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197 | { |
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198 | fprintf(stderr, "emd: Signature size is limited to %d\n", MAX_SIG_SIZE); |
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199 | exit(1); |
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200 | } |
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201 | |
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202 | /* COMPUTE THE DISTANCE MATRIX */ |
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203 | _maxC = 0; |
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204 | for(i=0, P1=Signature1->Features; i < _n1; i++, P1++) |
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205 | for(j=0, P2=Signature2->Features; j < _n2; j++, P2++) |
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206 | { |
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207 | _C[i][j] = Dist(P1, P2); |
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208 | if (_C[i][j] > _maxC) |
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209 | _maxC = _C[i][j]; |
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210 | } |
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211 | |
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212 | /* SUM UP THE SUPPLY AND DEMAND */ |
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213 | sSum = 0.0; |
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214 | for(i=0; i < _n1; i++) |
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215 | { |
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216 | S[i] = Signature1->Weights[i]; |
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217 | sSum += Signature1->Weights[i]; |
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218 | _RowsX[i] = NULL; |
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219 | } |
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220 | dSum = 0.0; |
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221 | for(j=0; j < _n2; j++) |
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222 | { |
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223 | D[j] = Signature2->Weights[j]; |
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224 | dSum += Signature2->Weights[j]; |
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225 | _ColsX[j] = NULL; |
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226 | } |
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227 | |
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228 | /* IF SUPPLY DIFFERENT THAN THE DEMAND, ADD A ZERO-COST DUMMY CLUSTER */ |
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229 | diff = sSum - dSum; |
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230 | if (fabs(diff) >= EPSILON * sSum) |
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231 | { |
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232 | if (diff < 0.0) |
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233 | { |
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234 | for (j=0; j < _n2; j++) |
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235 | _C[_n1][j] = 0; |
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236 | S[_n1] = -diff; |
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237 | _RowsX[_n1] = NULL; |
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238 | _n1++; |
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239 | } |
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240 | else |
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241 | { |
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242 | for (i=0; i < _n1; i++) |
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243 | _C[i][_n2] = 0; |
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244 | D[_n2] = diff; |
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245 | _ColsX[_n2] = NULL; |
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246 | _n2++; |
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247 | } |
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248 | } |
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249 | |
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250 | /* INITIALIZE THE BASIC VARIABLE STRUCTURES */ |
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251 | for (i=0; i < _n1; i++) |
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252 | for (j=0; j < _n2; j++) |
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253 | _IsX[i][j] = 0; |
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254 | _EndX = _X; |
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255 | |
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256 | _maxW = sSum > dSum ? sSum : dSum; |
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257 | |
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258 | /* FIND INITIAL SOLUTION */ |
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259 | russel(S, D); |
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260 | |
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261 | _EnterX = _EndX++; /* AN EMPTY SLOT (ONLY _n1+_n2-1 BASIC VARIABLES) */ |
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262 | |
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263 | return sSum > dSum ? dSum : sSum; |
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264 | } |
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265 | |
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266 | |
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267 | /********************** |
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268 | findBasicVariables |
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269 | **********************/ |
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270 | static void findBasicVariables(node1_t *U, node1_t *V) |
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271 | { |
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272 | int i, j, found; |
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273 | int UfoundNum, VfoundNum; |
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274 | node1_t u0Head, u1Head, *CurU, *PrevU; |
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275 | node1_t v0Head, v1Head, *CurV, *PrevV; |
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276 | |
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277 | /* INITIALIZE THE ROWS LIST (U) AND THE COLUMNS LIST (V) */ |
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278 | u0Head.Next = CurU = U; |
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279 | for (i=0; i < _n1; i++) |
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280 | { |
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281 | CurU->i = i; |
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282 | CurU->Next = CurU+1; |
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283 | CurU++; |
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284 | } |
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285 | (--CurU)->Next = NULL; |
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286 | u1Head.Next = NULL; |
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287 | |
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288 | CurV = V+1; |
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289 | v0Head.Next = _n2 > 1 ? V+1 : NULL; |
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290 | for (j=1; j < _n2; j++) |
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291 | { |
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292 | CurV->i = j; |
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293 | CurV->Next = CurV+1; |
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294 | CurV++; |
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295 | } |
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296 | (--CurV)->Next = NULL; |
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297 | v1Head.Next = NULL; |
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298 | |
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299 | /* THERE ARE _n1+_n2 VARIABLES BUT ONLY _n1+_n2-1 INDEPENDENT EQUATIONS, |
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300 | SO SET V[0]=0 */ |
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301 | V[0].i = 0; |
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302 | V[0].val = 0; |
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303 | v1Head.Next = V; |
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304 | v1Head.Next->Next = NULL; |
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305 | |
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306 | /* LOOP UNTIL ALL VARIABLES ARE FOUND */ |
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307 | UfoundNum=VfoundNum=0; |
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308 | while (UfoundNum < _n1 || VfoundNum < _n2) |
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309 | { |
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310 | |
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311 | #if DEBUG_LEVEL > 3 |
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312 | printf("UfoundNum=%d/%d,VfoundNum=%d/%d\n",UfoundNum,_n1,VfoundNum,_n2); |
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313 | printf("U0="); |
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314 | for(CurU = u0Head.Next; CurU != NULL; CurU = CurU->Next) |
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315 | printf("[%d]",CurU-U); |
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316 | printf("\n"); |
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317 | printf("U1="); |
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318 | for(CurU = u1Head.Next; CurU != NULL; CurU = CurU->Next) |
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319 | printf("[%d]",CurU-U); |
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320 | printf("\n"); |
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321 | printf("V0="); |
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322 | for(CurV = v0Head.Next; CurV != NULL; CurV = CurV->Next) |
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323 | printf("[%d]",CurV-V); |
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324 | printf("\n"); |
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325 | printf("V1="); |
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326 | for(CurV = v1Head.Next; CurV != NULL; CurV = CurV->Next) |
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327 | printf("[%d]",CurV-V); |
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328 | printf("\n\n"); |
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329 | #endif |
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330 | |
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331 | found = 0; |
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332 | if (VfoundNum < _n2) |
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333 | { |
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334 | /* LOOP OVER ALL MARKED COLUMNS */ |
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335 | PrevV = &v1Head; |
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336 | for (CurV=v1Head.Next; CurV != NULL; CurV=CurV->Next) |
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337 | { |
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338 | j = CurV->i; |
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339 | /* FIND THE VARIABLES IN COLUMN j */ |
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340 | PrevU = &u0Head; |
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341 | for (CurU=u0Head.Next; CurU != NULL; CurU=CurU->Next) |
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342 | { |
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343 | i = CurU->i; |
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344 | if (_IsX[i][j]) |
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345 | { |
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346 | /* COMPUTE U[i] */ |
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347 | CurU->val = _C[i][j] - CurV->val; |
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348 | /* ...AND ADD IT TO THE MARKED LIST */ |
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349 | PrevU->Next = CurU->Next; |
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350 | CurU->Next = u1Head.Next != NULL ? u1Head.Next : NULL; |
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351 | u1Head.Next = CurU; |
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352 | CurU = PrevU; |
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353 | } |
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354 | else |
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355 | PrevU = CurU; |
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356 | } |
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357 | PrevV->Next = CurV->Next; |
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358 | VfoundNum++; |
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359 | found = 1; |
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360 | } |
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361 | } |
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362 | if (UfoundNum < _n1) |
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363 | { |
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364 | /* LOOP OVER ALL MARKED ROWS */ |
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365 | PrevU = &u1Head; |
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366 | for (CurU=u1Head.Next; CurU != NULL; CurU=CurU->Next) |
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367 | { |
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368 | i = CurU->i; |
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369 | /* FIND THE VARIABLES IN ROWS i */ |
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370 | PrevV = &v0Head; |
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371 | for (CurV=v0Head.Next; CurV != NULL; CurV=CurV->Next) |
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372 | { |
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373 | j = CurV->i; |
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374 | if (_IsX[i][j]) |
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375 | { |
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376 | /* COMPUTE V[j] */ |
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377 | CurV->val = _C[i][j] - CurU->val; |
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378 | /* ...AND ADD IT TO THE MARKED LIST */ |
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379 | PrevV->Next = CurV->Next; |
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380 | CurV->Next = v1Head.Next != NULL ? v1Head.Next: NULL; |
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381 | v1Head.Next = CurV; |
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382 | CurV = PrevV; |
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383 | } |
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384 | else |
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385 | PrevV = CurV; |
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386 | } |
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387 | PrevU->Next = CurU->Next; |
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388 | UfoundNum++; |
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389 | found = 1; |
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390 | } |
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391 | } |
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392 | if (! found) |
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393 | { |
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394 | fprintf(stderr, "emd: Unexpected error in findBasicVariables!\n"); |
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395 | fprintf(stderr, "This typically happens when the EPSILON defined in\n"); |
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396 | fprintf(stderr, "emd.h is not right for the scale of the problem.\n"); |
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397 | exit(1); |
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398 | } |
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399 | } |
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400 | } |
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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 | /********************** |
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406 | isOptimal |
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407 | **********************/ |
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408 | static int isOptimal(node1_t *U, node1_t *V) |
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409 | { |
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410 | double delta, deltaMin; |
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411 | int i, j, minI, minJ; |
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412 | |
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413 | /* FIND THE MINIMAL Cij-Ui-Vj OVER ALL i,j */ |
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414 | deltaMin = INFINITY; |
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415 | for(i=0; i < _n1; i++) |
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416 | for(j=0; j < _n2; j++) |
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417 | if (! _IsX[i][j]) |
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418 | { |
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419 | delta = _C[i][j] - U[i].val - V[j].val; |
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420 | if (deltaMin > delta) |
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421 | { |
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422 | deltaMin = delta; |
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423 | minI = i; |
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424 | minJ = j; |
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425 | } |
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426 | } |
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427 | |
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428 | #if DEBUG_LEVEL > 3 |
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429 | printf("deltaMin=%f\n", deltaMin); |
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430 | #endif |
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431 | |
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432 | if (deltaMin == INFINITY) |
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433 | { |
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434 | fprintf(stderr, "emd: Unexpected error in isOptimal.\n"); |
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435 | exit(0); |
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436 | } |
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437 | |
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438 | _EnterX->i = minI; |
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439 | _EnterX->j = minJ; |
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440 | |
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441 | /* IF NO NEGATIVE deltaMin, WE FOUND THE OPTIMAL SOLUTION */ |
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442 | return deltaMin >= -EPSILON * _maxC; |
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443 | |
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444 | /* |
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445 | return deltaMin >= -EPSILON; |
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446 | */ |
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447 | } |
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448 | |
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449 | |
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450 | /********************** |
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451 | newSol |
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452 | **********************/ |
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453 | static void newSol() |
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454 | { |
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455 | int i, j, k; |
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456 | double xMin; |
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457 | int steps; |
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458 | node2_t *Loop[2*MAX_SIG_SIZE1], *CurX, *LeaveX; |
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459 | |
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460 | #if DEBUG_LEVEL > 3 |
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461 | printf("EnterX = (%d,%d)\n", _EnterX->i, _EnterX->j); |
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462 | #endif |
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463 | |
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464 | /* ENTER THE NEW BASIC VARIABLE */ |
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465 | i = _EnterX->i; |
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466 | j = _EnterX->j; |
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467 | _IsX[i][j] = 1; |
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468 | _EnterX->NextC = _RowsX[i]; |
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469 | _EnterX->NextR = _ColsX[j]; |
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470 | _EnterX->val = 0; |
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471 | _RowsX[i] = _EnterX; |
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472 | _ColsX[j] = _EnterX; |
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473 | |
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474 | /* FIND A CHAIN REACTION */ |
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475 | steps = findLoop(Loop); |
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476 | |
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477 | /* FIND THE LARGEST VALUE IN THE LOOP */ |
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478 | xMin = INFINITY; |
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479 | for (k=1; k < steps; k+=2) |
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480 | { |
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481 | if (Loop[k]->val < xMin) |
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482 | { |
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483 | LeaveX = Loop[k]; |
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484 | xMin = Loop[k]->val; |
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485 | } |
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486 | } |
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487 | |
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488 | /* UPDATE THE LOOP */ |
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489 | for (k=0; k < steps; k+=2) |
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490 | { |
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491 | Loop[k]->val += xMin; |
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492 | Loop[k+1]->val -= xMin; |
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493 | } |
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494 | |
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495 | #if DEBUG_LEVEL > 3 |
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496 | printf("LeaveX = (%d,%d)\n", LeaveX->i, LeaveX->j); |
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497 | #endif |
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498 | |
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499 | /* REMOVE THE LEAVING BASIC VARIABLE */ |
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500 | i = LeaveX->i; |
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501 | j = LeaveX->j; |
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502 | _IsX[i][j] = 0; |
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503 | if (_RowsX[i] == LeaveX) |
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504 | _RowsX[i] = LeaveX->NextC; |
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505 | else |
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506 | for (CurX=_RowsX[i]; CurX != NULL; CurX = CurX->NextC) |
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507 | if (CurX->NextC == LeaveX) |
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508 | { |
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509 | CurX->NextC = CurX->NextC->NextC; |
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510 | break; |
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511 | } |
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512 | if (_ColsX[j] == LeaveX) |
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513 | _ColsX[j] = LeaveX->NextR; |
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514 | else |
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515 | for (CurX=_ColsX[j]; CurX != NULL; CurX = CurX->NextR) |
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516 | if (CurX->NextR == LeaveX) |
---|
517 | { |
---|
518 | CurX->NextR = CurX->NextR->NextR; |
---|
519 | break; |
---|
520 | } |
---|
521 | |
---|
522 | /* SET _EnterX TO BE THE NEW EMPTY SLOT */ |
---|
523 | _EnterX = LeaveX; |
---|
524 | } |
---|
525 | |
---|
526 | |
---|
527 | |
---|
528 | /********************** |
---|
529 | findLoop |
---|
530 | **********************/ |
---|
531 | static int findLoop(node2_t **Loop) |
---|
532 | { |
---|
533 | int i, steps; |
---|
534 | node2_t **CurX, *NewX; |
---|
535 | char IsUsed[2*MAX_SIG_SIZE1]; |
---|
536 | |
---|
537 | for (i=0; i < _n1+_n2; i++) |
---|
538 | IsUsed[i] = 0; |
---|
539 | |
---|
540 | CurX = Loop; |
---|
541 | NewX = *CurX = _EnterX; |
---|
542 | IsUsed[_EnterX-_X] = 1; |
---|
543 | steps = 1; |
---|
544 | |
---|
545 | do |
---|
546 | { |
---|
547 | if (steps%2 == 1) |
---|
548 | { |
---|
549 | /* FIND AN UNUSED X IN THE ROW */ |
---|
550 | NewX = _RowsX[NewX->i]; |
---|
551 | while (NewX != NULL && IsUsed[NewX-_X]) |
---|
552 | NewX = NewX->NextC; |
---|
553 | } |
---|
554 | else |
---|
555 | { |
---|
556 | /* FIND AN UNUSED X IN THE COLUMN, OR THE ENTERING X */ |
---|
557 | NewX = _ColsX[NewX->j]; |
---|
558 | while (NewX != NULL && IsUsed[NewX-_X] && NewX != _EnterX) |
---|
559 | NewX = NewX->NextR; |
---|
560 | if (NewX == _EnterX) |
---|
561 | break; |
---|
562 | } |
---|
563 | |
---|
564 | if (NewX != NULL) /* FOUND THE NEXT X */ |
---|
565 | { |
---|
566 | /* ADD X TO THE LOOP */ |
---|
567 | *++CurX = NewX; |
---|
568 | IsUsed[NewX-_X] = 1; |
---|
569 | steps++; |
---|
570 | #if DEBUG_LEVEL > 3 |
---|
571 | printf("steps=%d, NewX=(%d,%d)\n", steps, NewX->i, NewX->j); |
---|
572 | #endif |
---|
573 | } |
---|
574 | else /* DIDN'T FIND THE NEXT X */ |
---|
575 | { |
---|
576 | /* BACKTRACK */ |
---|
577 | do |
---|
578 | { |
---|
579 | NewX = *CurX; |
---|
580 | do |
---|
581 | { |
---|
582 | if (steps%2 == 1) |
---|
583 | NewX = NewX->NextR; |
---|
584 | else |
---|
585 | NewX = NewX->NextC; |
---|
586 | } while (NewX != NULL && IsUsed[NewX-_X]); |
---|
587 | |
---|
588 | if (NewX == NULL) |
---|
589 | { |
---|
590 | IsUsed[*CurX-_X] = 0; |
---|
591 | CurX--; |
---|
592 | steps--; |
---|
593 | } |
---|
594 | } while (NewX == NULL && CurX >= Loop); |
---|
595 | |
---|
596 | #if DEBUG_LEVEL > 3 |
---|
597 | printf("BACKTRACKING TO: steps=%d, NewX=(%d,%d)\n", |
---|
598 | steps, NewX->i, NewX->j); |
---|
599 | #endif |
---|
600 | IsUsed[*CurX-_X] = 0; |
---|
601 | *CurX = NewX; |
---|
602 | IsUsed[NewX-_X] = 1; |
---|
603 | } |
---|
604 | } while(CurX >= Loop); |
---|
605 | |
---|
606 | if (CurX == Loop) |
---|
607 | { |
---|
608 | fprintf(stderr, "emd: Unexpected error in findLoop!\n"); |
---|
609 | exit(1); |
---|
610 | } |
---|
611 | #if DEBUG_LEVEL > 3 |
---|
612 | printf("FOUND LOOP:\n"); |
---|
613 | for (i=0; i < steps; i++) |
---|
614 | printf("%d: (%d,%d)\n", i, Loop[i]->i, Loop[i]->j); |
---|
615 | #endif |
---|
616 | |
---|
617 | return steps; |
---|
618 | } |
---|
619 | |
---|
620 | |
---|
621 | |
---|
622 | /********************** |
---|
623 | russel |
---|
624 | **********************/ |
---|
625 | static void russel(double *S, double *D) |
---|
626 | { |
---|
627 | int i, j, found, minI, minJ; |
---|
628 | double deltaMin, oldVal, diff; |
---|
629 | double Delta[MAX_SIG_SIZE1][MAX_SIG_SIZE1]; |
---|
630 | node1_t Ur[MAX_SIG_SIZE1], Vr[MAX_SIG_SIZE1]; |
---|
631 | node1_t uHead, *CurU, *PrevU; |
---|
632 | node1_t vHead, *CurV, *PrevV; |
---|
633 | node1_t *PrevUMinI, *PrevVMinJ, *Remember; |
---|
634 | |
---|
635 | /* INITIALIZE THE ROWS LIST (Ur), AND THE COLUMNS LIST (Vr) */ |
---|
636 | uHead.Next = CurU = Ur; |
---|
637 | for (i=0; i < _n1; i++) |
---|
638 | { |
---|
639 | CurU->i = i; |
---|
640 | CurU->val = -INFINITY; |
---|
641 | CurU->Next = CurU+1; |
---|
642 | CurU++; |
---|
643 | } |
---|
644 | (--CurU)->Next = NULL; |
---|
645 | |
---|
646 | vHead.Next = CurV = Vr; |
---|
647 | for (j=0; j < _n2; j++) |
---|
648 | { |
---|
649 | CurV->i = j; |
---|
650 | CurV->val = -INFINITY; |
---|
651 | CurV->Next = CurV+1; |
---|
652 | CurV++; |
---|
653 | } |
---|
654 | (--CurV)->Next = NULL; |
---|
655 | |
---|
656 | /* FIND THE MAXIMUM ROW AND COLUMN VALUES (Ur[i] AND Vr[j]) */ |
---|
657 | for(i=0; i < _n1 ; i++) |
---|
658 | for(j=0; j < _n2 ; j++) |
---|
659 | { |
---|
660 | float v; |
---|
661 | v = _C[i][j]; |
---|
662 | if (Ur[i].val <= v) |
---|
663 | Ur[i].val = v; |
---|
664 | if (Vr[j].val <= v) |
---|
665 | Vr[j].val = v; |
---|
666 | } |
---|
667 | |
---|
668 | /* COMPUTE THE Delta MATRIX */ |
---|
669 | for(i=0; i < _n1 ; i++) |
---|
670 | for(j=0; j < _n2 ; j++) |
---|
671 | Delta[i][j] = _C[i][j] - Ur[i].val - Vr[j].val; |
---|
672 | |
---|
673 | /* FIND THE BASIC VARIABLES */ |
---|
674 | do |
---|
675 | { |
---|
676 | #if DEBUG_LEVEL > 3 |
---|
677 | printf("Ur="); |
---|
678 | for(CurU = uHead.Next; CurU != NULL; CurU = CurU->Next) |
---|
679 | printf("[%d]",CurU-Ur); |
---|
680 | printf("\n"); |
---|
681 | printf("Vr="); |
---|
682 | for(CurV = vHead.Next; CurV != NULL; CurV = CurV->Next) |
---|
683 | printf("[%d]",CurV-Vr); |
---|
684 | printf("\n"); |
---|
685 | printf("\n\n"); |
---|
686 | #endif |
---|
687 | |
---|
688 | /* FIND THE SMALLEST Delta[i][j] */ |
---|
689 | found = 0; |
---|
690 | deltaMin = INFINITY; |
---|
691 | PrevU = &uHead; |
---|
692 | for (CurU=uHead.Next; CurU != NULL; CurU=CurU->Next) |
---|
693 | { |
---|
694 | int i; |
---|
695 | i = CurU->i; |
---|
696 | PrevV = &vHead; |
---|
697 | for (CurV=vHead.Next; CurV != NULL; CurV=CurV->Next) |
---|
698 | { |
---|
699 | int j; |
---|
700 | j = CurV->i; |
---|
701 | if (deltaMin > Delta[i][j]) |
---|
702 | { |
---|
703 | deltaMin = Delta[i][j]; |
---|
704 | minI = i; |
---|
705 | minJ = j; |
---|
706 | PrevUMinI = PrevU; |
---|
707 | PrevVMinJ = PrevV; |
---|
708 | found = 1; |
---|
709 | } |
---|
710 | PrevV = CurV; |
---|
711 | } |
---|
712 | PrevU = CurU; |
---|
713 | } |
---|
714 | |
---|
715 | if (! found) |
---|
716 | break; |
---|
717 | |
---|
718 | /* ADD X[minI][minJ] TO THE BASIS, AND ADJUST SUPPLIES AND COST */ |
---|
719 | Remember = PrevUMinI->Next; |
---|
720 | addBasicVariable(minI, minJ, S, D, PrevUMinI, PrevVMinJ, &uHead); |
---|
721 | |
---|
722 | /* UPDATE THE NECESSARY Delta[][] */ |
---|
723 | if (Remember == PrevUMinI->Next) /* LINE minI WAS DELETED */ |
---|
724 | { |
---|
725 | for (CurV=vHead.Next; CurV != NULL; CurV=CurV->Next) |
---|
726 | { |
---|
727 | int j; |
---|
728 | j = CurV->i; |
---|
729 | if (CurV->val == _C[minI][j]) /* COLUMN j NEEDS UPDATING */ |
---|
730 | { |
---|
731 | /* FIND THE NEW MAXIMUM VALUE IN THE COLUMN */ |
---|
732 | oldVal = CurV->val; |
---|
733 | CurV->val = -INFINITY; |
---|
734 | for (CurU=uHead.Next; CurU != NULL; CurU=CurU->Next) |
---|
735 | { |
---|
736 | int i; |
---|
737 | i = CurU->i; |
---|
738 | if (CurV->val <= _C[i][j]) |
---|
739 | CurV->val = _C[i][j]; |
---|
740 | } |
---|
741 | |
---|
742 | /* IF NEEDED, ADJUST THE RELEVANT Delta[*][j] */ |
---|
743 | diff = oldVal - CurV->val; |
---|
744 | if (fabs(diff) < EPSILON * _maxC) |
---|
745 | for (CurU=uHead.Next; CurU != NULL; CurU=CurU->Next) |
---|
746 | Delta[CurU->i][j] += diff; |
---|
747 | } |
---|
748 | } |
---|
749 | } |
---|
750 | else /* COLUMN minJ WAS DELETED */ |
---|
751 | { |
---|
752 | for (CurU=uHead.Next; CurU != NULL; CurU=CurU->Next) |
---|
753 | { |
---|
754 | int i; |
---|
755 | i = CurU->i; |
---|
756 | if (CurU->val == _C[i][minJ]) /* ROW i NEEDS UPDATING */ |
---|
757 | { |
---|
758 | /* FIND THE NEW MAXIMUM VALUE IN THE ROW */ |
---|
759 | oldVal = CurU->val; |
---|
760 | CurU->val = -INFINITY; |
---|
761 | for (CurV=vHead.Next; CurV != NULL; CurV=CurV->Next) |
---|
762 | { |
---|
763 | int j; |
---|
764 | j = CurV->i; |
---|
765 | if(CurU->val <= _C[i][j]) |
---|
766 | CurU->val = _C[i][j]; |
---|
767 | } |
---|
768 | |
---|
769 | /* If NEEDED, ADJUST THE RELEVANT Delta[i][*] */ |
---|
770 | diff = oldVal - CurU->val; |
---|
771 | if (fabs(diff) < EPSILON * _maxC) |
---|
772 | for (CurV=vHead.Next; CurV != NULL; CurV=CurV->Next) |
---|
773 | Delta[i][CurV->i] += diff; |
---|
774 | } |
---|
775 | } |
---|
776 | } |
---|
777 | } while (uHead.Next != NULL || vHead.Next != NULL); |
---|
778 | } |
---|
779 | |
---|
780 | |
---|
781 | |
---|
782 | |
---|
783 | /********************** |
---|
784 | addBasicVariable |
---|
785 | **********************/ |
---|
786 | static void addBasicVariable(int minI, int minJ, double *S, double *D, |
---|
787 | node1_t *PrevUMinI, node1_t *PrevVMinJ, |
---|
788 | node1_t *UHead) |
---|
789 | { |
---|
790 | double T; |
---|
791 | |
---|
792 | if (fabs(S[minI]-D[minJ]) <= EPSILON * _maxW) /* DEGENERATE CASE */ |
---|
793 | { |
---|
794 | T = S[minI]; |
---|
795 | S[minI] = 0; |
---|
796 | D[minJ] -= T; |
---|
797 | } |
---|
798 | else if (S[minI] < D[minJ]) /* SUPPLY EXHAUSTED */ |
---|
799 | { |
---|
800 | T = S[minI]; |
---|
801 | S[minI] = 0; |
---|
802 | D[minJ] -= T; |
---|
803 | } |
---|
804 | else /* DEMAND EXHAUSTED */ |
---|
805 | { |
---|
806 | T = D[minJ]; |
---|
807 | D[minJ] = 0; |
---|
808 | S[minI] -= T; |
---|
809 | } |
---|
810 | |
---|
811 | /* X(minI,minJ) IS A BASIC VARIABLE */ |
---|
812 | _IsX[minI][minJ] = 1; |
---|
813 | |
---|
814 | _EndX->val = T; |
---|
815 | _EndX->i = minI; |
---|
816 | _EndX->j = minJ; |
---|
817 | _EndX->NextC = _RowsX[minI]; |
---|
818 | _EndX->NextR = _ColsX[minJ]; |
---|
819 | _RowsX[minI] = _EndX; |
---|
820 | _ColsX[minJ] = _EndX; |
---|
821 | _EndX++; |
---|
822 | |
---|
823 | /* DELETE SUPPLY ROW ONLY IF THE EMPTY, AND IF NOT LAST ROW */ |
---|
824 | if (S[minI] == 0 && UHead->Next->Next != NULL) |
---|
825 | PrevUMinI->Next = PrevUMinI->Next->Next; /* REMOVE ROW FROM LIST */ |
---|
826 | else |
---|
827 | PrevVMinJ->Next = PrevVMinJ->Next->Next; /* REMOVE COLUMN FROM LIST */ |
---|
828 | } |
---|