1 | /* |
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2 | * Copyright 1997, Regents of the University of Minnesota |
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3 | * |
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4 | * smbfactor.c |
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5 | * |
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6 | * This file performs the symbolic factorization of a matrix |
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7 | * |
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8 | * Started 8/1/97 |
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9 | * George |
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10 | * |
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11 | * $Id: smbfactor.c,v 1.1 1998/11/27 17:59:40 karypis Exp $ |
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12 | * |
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13 | */ |
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14 | |
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15 | #include <metis.h> |
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16 | |
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17 | |
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18 | /************************************************************************* |
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19 | * This function sets up data structures for fill-in computations |
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20 | **************************************************************************/ |
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21 | void ComputeFillIn(GraphType *graph, idxtype *iperm) |
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22 | { |
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23 | int i, j, k, nvtxs, maxlnz, maxsub; |
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24 | idxtype *xadj, *adjncy; |
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25 | idxtype *perm, *xlnz, *xnzsub, *nzsub; |
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26 | double opc; |
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27 | |
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28 | /* |
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29 | printf("\nSymbolic factorization... --------------------------------------------\n"); |
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30 | */ |
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31 | |
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32 | nvtxs = graph->nvtxs; |
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33 | xadj = graph->xadj; |
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34 | adjncy = graph->adjncy; |
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35 | |
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36 | maxsub = 4*xadj[nvtxs]; |
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37 | |
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38 | /* Relabel the vertices so that it starts from 1 */ |
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39 | k = xadj[nvtxs]; |
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40 | for (i=0; i<k; i++) |
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41 | adjncy[i]++; |
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42 | for (i=0; i<nvtxs+1; i++) |
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43 | xadj[i]++; |
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44 | |
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45 | /* Allocate the required memory */ |
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46 | perm = idxmalloc(nvtxs+1, "ComputeFillIn: perm"); |
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47 | xlnz = idxmalloc(nvtxs+1, "ComputeFillIn: xlnz"); |
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48 | xnzsub = idxmalloc(nvtxs+1, "ComputeFillIn: xnzsub"); |
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49 | nzsub = idxmalloc(maxsub, "ComputeFillIn: nzsub"); |
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50 | |
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51 | /* Construct perm from iperm and change the numbering of iperm */ |
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52 | for (i=0; i<nvtxs; i++) |
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53 | perm[iperm[i]] = i; |
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54 | for (i=0; i<nvtxs; i++) { |
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55 | iperm[i]++; |
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56 | perm[i]++; |
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57 | } |
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58 | |
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59 | /* |
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60 | * Call sparspak routine. |
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61 | */ |
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62 | if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) { |
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63 | free(nzsub); |
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64 | |
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65 | maxsub = 4*maxsub; |
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66 | nzsub = idxmalloc(maxsub, "ComputeFillIn: nzsub"); |
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67 | if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) |
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68 | errexit("MAXSUB is too small!"); |
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69 | } |
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70 | |
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71 | opc = 0; |
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72 | for (i=0; i<nvtxs; i++) |
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73 | xlnz[i]--; |
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74 | for (i=0; i<nvtxs; i++) |
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75 | opc += (xlnz[i+1]-xlnz[i])*(xlnz[i+1]-xlnz[i]) - (xlnz[i+1]-xlnz[i]); |
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76 | |
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77 | printf(" Nonzeros: %d, \tOperation Count: %6.4le\n", maxlnz, opc); |
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78 | |
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79 | |
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80 | GKfree(&perm, &xlnz, &xnzsub, &nzsub, LTERM); |
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81 | |
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82 | |
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83 | /* Relabel the vertices so that it starts from 0 */ |
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84 | for (i=0; i<nvtxs; i++) |
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85 | iperm[i]--; |
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86 | for (i=0; i<nvtxs+1; i++) |
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87 | xadj[i]--; |
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88 | k = xadj[nvtxs]; |
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89 | for (i=0; i<k; i++) |
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90 | adjncy[i]--; |
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91 | |
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92 | } |
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93 | |
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94 | |
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95 | |
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96 | /************************************************************************* |
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97 | * This function sets up data structures for fill-in computations |
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98 | **************************************************************************/ |
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99 | idxtype ComputeFillIn2(GraphType *graph, idxtype *iperm) |
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100 | { |
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101 | int i, j, k, nvtxs, maxlnz, maxsub; |
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102 | idxtype *xadj, *adjncy; |
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103 | idxtype *perm, *xlnz, *xnzsub, *nzsub; |
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104 | double opc; |
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105 | |
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106 | nvtxs = graph->nvtxs; |
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107 | xadj = graph->xadj; |
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108 | adjncy = graph->adjncy; |
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109 | |
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110 | maxsub = 4*xadj[nvtxs]; |
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111 | |
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112 | /* Relabel the vertices so that it starts from 1 */ |
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113 | k = xadj[nvtxs]; |
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114 | for (i=0; i<k; i++) |
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115 | adjncy[i]++; |
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116 | for (i=0; i<nvtxs+1; i++) |
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117 | xadj[i]++; |
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118 | |
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119 | /* Allocate the required memory */ |
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120 | perm = idxmalloc(nvtxs+1, "ComputeFillIn: perm"); |
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121 | xlnz = idxmalloc(nvtxs+1, "ComputeFillIn: xlnz"); |
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122 | xnzsub = idxmalloc(nvtxs+1, "ComputeFillIn: xnzsub"); |
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123 | nzsub = idxmalloc(maxsub, "ComputeFillIn: nzsub"); |
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124 | |
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125 | /* Construct perm from iperm and change the numbering of iperm */ |
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126 | for (i=0; i<nvtxs; i++) |
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127 | perm[iperm[i]] = i; |
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128 | for (i=0; i<nvtxs; i++) { |
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129 | iperm[i]++; |
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130 | perm[i]++; |
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131 | } |
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132 | |
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133 | /* |
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134 | * Call sparspak routine. |
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135 | */ |
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136 | if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) { |
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137 | free(nzsub); |
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138 | |
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139 | maxsub = 4*maxsub; |
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140 | nzsub = idxmalloc(maxsub, "ComputeFillIn: nzsub"); |
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141 | if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) |
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142 | errexit("MAXSUB is too small!"); |
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143 | } |
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144 | |
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145 | opc = 0; |
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146 | for (i=0; i<nvtxs; i++) |
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147 | xlnz[i]--; |
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148 | for (i=0; i<nvtxs; i++) |
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149 | opc += (xlnz[i+1]-xlnz[i])*(xlnz[i+1]-xlnz[i]) - (xlnz[i+1]-xlnz[i]); |
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150 | |
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151 | |
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152 | GKfree(&perm, &xlnz, &xnzsub, &nzsub, LTERM); |
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153 | |
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154 | |
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155 | /* Relabel the vertices so that it starts from 0 */ |
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156 | for (i=0; i<nvtxs; i++) |
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157 | iperm[i]--; |
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158 | for (i=0; i<nvtxs+1; i++) |
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159 | xadj[i]--; |
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160 | k = xadj[nvtxs]; |
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161 | for (i=0; i<k; i++) |
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162 | adjncy[i]--; |
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163 | |
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164 | return maxlnz; |
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165 | |
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166 | } |
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167 | |
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168 | |
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169 | /***************************************************************** |
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170 | ********** SMBFCT ..... SYMBOLIC FACTORIZATION ********* |
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171 | ****************************************************************** |
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172 | * PURPOSE - THIS ROUTINE PERFORMS SYMBOLIC FACTORIZATION |
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173 | * ON A PERMUTED LINEAR SYSTEM AND IT ALSO SETS UP THE |
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174 | * COMPRESSED DATA STRUCTURE FOR THE SYSTEM. |
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175 | * |
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176 | * INPUT PARAMETERS - |
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177 | * NEQNS - NUMBER OF EQUATIONS. |
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178 | * (XADJ, ADJNCY) - THE ADJACENCY STRUCTURE. |
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179 | * (PERM, INVP) - THE PERMUTATION VECTOR AND ITS INVERSE. |
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180 | * |
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181 | * UPDATED PARAMETERS - |
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182 | * MAXSUB - SIZE OF THE SUBSCRIPT ARRAY NZSUB. ON RETURN, |
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183 | * IT CONTAINS THE NUMBER OF SUBSCRIPTS USED |
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184 | * |
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185 | * OUTPUT PARAMETERS - |
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186 | * XLNZ - INDEX INTO THE NONZERO STORAGE VECTOR LNZ. |
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187 | * (XNZSUB, NZSUB) - THE COMPRESSED SUBSCRIPT VECTORS. |
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188 | * MAXLNZ - THE NUMBER OF NONZEROS FOUND. |
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189 | * |
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190 | *******************************************************************/ |
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191 | int smbfct(int neqns, idxtype *xadj, idxtype *adjncy, idxtype *perm, idxtype *invp, idxtype *xlnz, |
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192 | int *maxlnz, idxtype *xnzsub, idxtype *nzsub, int *maxsub) |
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193 | { |
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194 | /* Local variables */ |
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195 | int node, rchm, mrgk, lmax, i, j, k, m, nabor, nzbeg, nzend; |
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196 | int kxsub, jstop, jstrt, mrkflg, inz, knz, flag; |
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197 | idxtype *mrglnk, *marker, *rchlnk; |
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198 | |
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199 | rchlnk = idxmalloc(neqns+1, "smbfct: rchlnk"); |
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200 | marker = idxsmalloc(neqns+1, 0, "smbfct: marker"); |
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201 | mrglnk = idxsmalloc(neqns+1, 0, "smbfct: mgrlnk"); |
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202 | |
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203 | /* Parameter adjustments */ |
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204 | --marker; |
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205 | --mrglnk; |
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206 | --rchlnk; |
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207 | --nzsub; |
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208 | --xnzsub; |
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209 | --xlnz; |
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210 | --invp; |
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211 | --perm; |
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212 | --adjncy; |
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213 | --xadj; |
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214 | |
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215 | /* Function Body */ |
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216 | flag = 0; |
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217 | nzbeg = 1; |
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218 | nzend = 0; |
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219 | xlnz[1] = 1; |
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220 | |
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221 | /* FOR EACH COLUMN KNZ COUNTS THE NUMBER OF NONZEROS IN COLUMN K ACCUMULATED IN RCHLNK. */ |
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222 | for (k = 1; k <= neqns; ++k) { |
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223 | knz = 0; |
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224 | mrgk = mrglnk[k]; |
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225 | mrkflg = 0; |
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226 | marker[k] = k; |
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227 | if (mrgk != 0) |
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228 | marker[k] = marker[mrgk]; |
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229 | xnzsub[k] = nzend; |
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230 | node = perm[k]; |
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231 | |
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232 | if (xadj[node] >= xadj[node+1]) { |
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233 | xlnz[k+1] = xlnz[k]; |
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234 | continue; |
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235 | } |
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236 | |
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237 | /* USE RCHLNK TO LINK THROUGH THE STRUCTURE OF A(*,K) BELOW DIAGONAL */ |
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238 | rchlnk[k] = neqns+1; |
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239 | for (j=xadj[node]; j<xadj[node+1]; j++) { |
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240 | nabor = invp[adjncy[j]]; |
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241 | if (nabor <= k) |
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242 | continue; |
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243 | rchm = k; |
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244 | |
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245 | do { |
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246 | m = rchm; |
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247 | rchm = rchlnk[m]; |
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248 | } while (rchm <= nabor); |
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249 | |
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250 | knz++; |
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251 | rchlnk[m] = nabor; |
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252 | rchlnk[nabor] = rchm; |
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253 | if (marker[nabor] != marker[k]) |
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254 | mrkflg = 1; |
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255 | } |
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256 | |
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257 | /* TEST FOR MASS SYMBOLIC ELIMINATION */ |
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258 | lmax = 0; |
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259 | if (mrkflg != 0 || mrgk == 0 || mrglnk[mrgk] != 0) |
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260 | goto L350; |
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261 | xnzsub[k] = xnzsub[mrgk] + 1; |
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262 | knz = xlnz[mrgk + 1] - (xlnz[mrgk] + 1); |
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263 | goto L1400; |
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264 | |
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265 | |
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266 | /* LINK THROUGH EACH COLUMN I THAT AFFECTS L(*,K) */ |
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267 | L350: |
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268 | i = k; |
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269 | while ((i = mrglnk[i]) != 0) { |
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270 | inz = xlnz[i+1] - (xlnz[i]+1); |
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271 | jstrt = xnzsub[i] + 1; |
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272 | jstop = xnzsub[i] + inz; |
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273 | |
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274 | if (inz > lmax) { |
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275 | lmax = inz; |
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276 | xnzsub[k] = jstrt; |
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277 | } |
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278 | |
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279 | /* MERGE STRUCTURE OF L(*,I) IN NZSUB INTO RCHLNK. */ |
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280 | rchm = k; |
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281 | for (j = jstrt; j <= jstop; ++j) { |
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282 | nabor = nzsub[j]; |
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283 | do { |
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284 | m = rchm; |
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285 | rchm = rchlnk[m]; |
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286 | } while (rchm < nabor); |
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287 | |
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288 | if (rchm != nabor) { |
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289 | knz++; |
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290 | rchlnk[m] = nabor; |
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291 | rchlnk[nabor] = rchm; |
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292 | rchm = nabor; |
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293 | } |
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294 | } |
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295 | } |
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296 | |
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297 | /* CHECK IF SUBSCRIPTS DUPLICATE THOSE OF ANOTHER COLUMN */ |
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298 | if (knz == lmax) |
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299 | goto L1400; |
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300 | |
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301 | /* OR IF TAIL OF K-1ST COLUMN MATCHES HEAD OF KTH */ |
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302 | if (nzbeg > nzend) |
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303 | goto L1200; |
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304 | |
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305 | i = rchlnk[k]; |
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306 | for (jstrt = nzbeg; jstrt <= nzend; ++jstrt) { |
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307 | if (nzsub[jstrt] < i) |
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308 | continue; |
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309 | |
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310 | if (nzsub[jstrt] == i) |
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311 | goto L1000; |
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312 | else |
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313 | goto L1200; |
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314 | } |
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315 | goto L1200; |
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316 | |
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317 | L1000: |
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318 | xnzsub[k] = jstrt; |
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319 | for (j = jstrt; j <= nzend; ++j) { |
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320 | if (nzsub[j] != i) |
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321 | goto L1200; |
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322 | |
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323 | i = rchlnk[i]; |
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324 | if (i > neqns) |
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325 | goto L1400; |
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326 | } |
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327 | nzend = jstrt - 1; |
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328 | |
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329 | /* COPY THE STRUCTURE OF L(*,K) FROM RCHLNK TO THE DATA STRUCTURE (XNZSUB, NZSUB) */ |
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330 | L1200: |
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331 | nzbeg = nzend + 1; |
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332 | nzend += knz; |
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333 | |
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334 | if (nzend > *maxsub) { |
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335 | flag = 1; /* Out of memory */ |
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336 | break; |
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337 | } |
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338 | |
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339 | i = k; |
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340 | for (j=nzbeg; j<=nzend; ++j) { |
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341 | i = rchlnk[i]; |
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342 | nzsub[j] = i; |
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343 | marker[i] = k; |
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344 | } |
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345 | xnzsub[k] = nzbeg; |
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346 | marker[k] = k; |
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347 | |
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348 | /* |
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349 | * UPDATE THE VECTOR MRGLNK. NOTE COLUMN L(*,K) JUST FOUND |
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350 | * IS REQUIRED TO DETERMINE COLUMN L(*,J), WHERE |
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351 | * L(J,K) IS THE FIRST NONZERO IN L(*,K) BELOW DIAGONAL. |
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352 | */ |
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353 | L1400: |
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354 | if (knz > 1) { |
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355 | kxsub = xnzsub[k]; |
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356 | i = nzsub[kxsub]; |
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357 | mrglnk[k] = mrglnk[i]; |
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358 | mrglnk[i] = k; |
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359 | } |
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360 | |
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361 | xlnz[k + 1] = xlnz[k] + knz; |
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362 | } |
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363 | |
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364 | if (flag == 0) { |
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365 | *maxlnz = xlnz[neqns] - 1; |
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366 | *maxsub = xnzsub[neqns]; |
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367 | xnzsub[neqns + 1] = xnzsub[neqns]; |
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368 | } |
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369 | |
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370 | marker++; |
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371 | mrglnk++; |
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372 | rchlnk++; |
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373 | nzsub++; |
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374 | xnzsub++; |
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375 | xlnz++; |
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376 | invp++; |
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377 | perm++; |
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378 | adjncy++; |
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379 | xadj++; |
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380 | GKfree(&rchlnk, &mrglnk, &marker, LTERM); |
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381 | |
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382 | return flag; |
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383 | |
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384 | } |
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385 | |
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