1 | /* glpnet02.c (permutations to block triangular form) */ |
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2 | |
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3 | /*********************************************************************** |
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4 | * This code is part of GLPK (GNU Linear Programming Kit). |
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5 | * |
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6 | * This code is the result of translation of the Fortran subroutines |
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7 | * MC13D and MC13E associated with the following paper: |
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8 | * |
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9 | * I.S.Duff, J.K.Reid, Algorithm 529: Permutations to block triangular |
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10 | * form, ACM Trans. on Math. Softw. 4 (1978), 189-192. |
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11 | * |
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12 | * Use of ACM Algorithms is subject to the ACM Software Copyright and |
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13 | * License Agreement. See <http://www.acm.org/publications/policies>. |
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14 | * |
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15 | * The translation was made by Andrew Makhorin <mao@gnu.org>. |
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16 | * |
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17 | * GLPK is free software: you can redistribute it and/or modify it |
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18 | * under the terms of the GNU General Public License as published by |
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19 | * the Free Software Foundation, either version 3 of the License, or |
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20 | * (at your option) any later version. |
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21 | * |
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22 | * GLPK is distributed in the hope that it will be useful, but WITHOUT |
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23 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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24 | * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public |
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25 | * License for more details. |
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26 | * |
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27 | * You should have received a copy of the GNU General Public License |
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28 | * along with GLPK. If not, see <http://www.gnu.org/licenses/>. |
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29 | ***********************************************************************/ |
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30 | |
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31 | #include "glpnet.h" |
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32 | |
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33 | /*********************************************************************** |
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34 | * NAME |
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35 | * |
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36 | * mc13d - permutations to block triangular form |
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37 | * |
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38 | * SYNOPSIS |
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39 | * |
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40 | * #include "glpnet.h" |
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41 | * int mc13d(int n, const int icn[], const int ip[], const int lenr[], |
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42 | * int ior[], int ib[], int lowl[], int numb[], int prev[]); |
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43 | * |
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44 | * DESCRIPTION |
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45 | * |
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46 | * Given the column numbers of the nonzeros in each row of the sparse |
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47 | * matrix, the routine mc13d finds a symmetric permutation that makes |
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48 | * the matrix block lower triangular. |
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49 | * |
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50 | * INPUT PARAMETERS |
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51 | * |
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52 | * n order of the matrix. |
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53 | * |
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54 | * icn array containing the column indices of the non-zeros. Those |
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55 | * belonging to a single row must be contiguous but the ordering |
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56 | * of column indices within each row is unimportant and wasted |
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57 | * space between rows is permitted. |
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58 | * |
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59 | * ip ip[i], i = 1,2,...,n, is the position in array icn of the |
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60 | * first column index of a non-zero in row i. |
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61 | * |
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62 | * lenr lenr[i], i = 1,2,...,n, is the number of non-zeros in row i. |
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63 | * |
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64 | * OUTPUT PARAMETERS |
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65 | * |
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66 | * ior ior[i], i = 1,2,...,n, gives the position on the original |
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67 | * ordering of the row or column which is in position i in the |
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68 | * permuted form. |
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69 | * |
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70 | * ib ib[i], i = 1,2,...,num, is the row number in the permuted |
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71 | * matrix of the beginning of block i, 1 <= num <= n. |
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72 | * |
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73 | * WORKING ARRAYS |
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74 | * |
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75 | * arp working array of length [1+n], where arp[0] is not used. |
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76 | * arp[i] is one less than the number of unsearched edges leaving |
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77 | * node i. At the end of the algorithm it is set to a permutation |
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78 | * which puts the matrix in block lower triangular form. |
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79 | * |
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80 | * ib working array of length [1+n], where ib[0] is not used. |
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81 | * ib[i] is the position in the ordering of the start of the ith |
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82 | * block. ib[n+1-i] holds the node number of the ith node on the |
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83 | * stack. |
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84 | * |
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85 | * lowl working array of length [1+n], where lowl[0] is not used. |
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86 | * lowl[i] is the smallest stack position of any node to which a |
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87 | * path from node i has been found. It is set to n+1 when node i |
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88 | * is removed from the stack. |
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89 | * |
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90 | * numb working array of length [1+n], where numb[0] is not used. |
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91 | * numb[i] is the position of node i in the stack if it is on it, |
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92 | * is the permuted order of node i for those nodes whose final |
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93 | * position has been found and is otherwise zero. |
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94 | * |
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95 | * prev working array of length [1+n], where prev[0] is not used. |
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96 | * prev[i] is the node at the end of the path when node i was |
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97 | * placed on the stack. |
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98 | * |
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99 | * RETURNS |
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100 | * |
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101 | * The routine mc13d returns num, the number of blocks found. */ |
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102 | |
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103 | int mc13d(int n, const int icn[], const int ip[], const int lenr[], |
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104 | int ior[], int ib[], int lowl[], int numb[], int prev[]) |
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105 | { int *arp = ior; |
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106 | int dummy, i, i1, i2, icnt, ii, isn, ist, ist1, iv, iw, j, lcnt, |
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107 | nnm1, num, stp; |
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108 | /* icnt is the number of nodes whose positions in final ordering |
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109 | have been found. */ |
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110 | icnt = 0; |
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111 | /* num is the number of blocks that have been found. */ |
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112 | num = 0; |
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113 | nnm1 = n + n - 1; |
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114 | /* Initialization of arrays. */ |
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115 | for (j = 1; j <= n; j++) |
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116 | { numb[j] = 0; |
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117 | arp[j] = lenr[j] - 1; |
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118 | } |
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119 | for (isn = 1; isn <= n; isn++) |
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120 | { /* Look for a starting node. */ |
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121 | if (numb[isn] != 0) continue; |
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122 | iv = isn; |
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123 | /* ist is the number of nodes on the stack ... it is the stack |
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124 | pointer. */ |
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125 | ist = 1; |
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126 | /* Put node iv at beginning of stack. */ |
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127 | lowl[iv] = numb[iv] = 1; |
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128 | ib[n] = iv; |
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129 | /* The body of this loop puts a new node on the stack or |
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130 | backtracks. */ |
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131 | for (dummy = 1; dummy <= nnm1; dummy++) |
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132 | { i1 = arp[iv]; |
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133 | /* Have all edges leaving node iv been searched? */ |
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134 | if (i1 >= 0) |
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135 | { i2 = ip[iv] + lenr[iv] - 1; |
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136 | i1 = i2 - i1; |
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137 | /* Look at edges leaving node iv until one enters a new |
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138 | node or all edges are exhausted. */ |
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139 | for (ii = i1; ii <= i2; ii++) |
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140 | { iw = icn[ii]; |
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141 | /* Has node iw been on stack already? */ |
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142 | if (numb[iw] == 0) goto L70; |
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143 | /* Update value of lowl[iv] if necessary. */ |
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144 | if (lowl[iw] < lowl[iv]) lowl[iv] = lowl[iw]; |
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145 | } |
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146 | /* There are no more edges leaving node iv. */ |
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147 | arp[iv] = -1; |
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148 | } |
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149 | /* Is node iv the root of a block? */ |
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150 | if (lowl[iv] < numb[iv]) goto L60; |
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151 | /* Order nodes in a block. */ |
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152 | num++; |
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153 | ist1 = n + 1 - ist; |
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154 | lcnt = icnt + 1; |
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155 | /* Peel block off the top of the stack starting at the top |
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156 | and working down to the root of the block. */ |
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157 | for (stp = ist1; stp <= n; stp++) |
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158 | { iw = ib[stp]; |
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159 | lowl[iw] = n + 1; |
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160 | numb[iw] = ++icnt; |
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161 | if (iw == iv) break; |
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162 | } |
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163 | ist = n - stp; |
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164 | ib[num] = lcnt; |
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165 | /* Are there any nodes left on the stack? */ |
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166 | if (ist != 0) goto L60; |
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167 | /* Have all the nodes been ordered? */ |
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168 | if (icnt < n) break; |
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169 | goto L100; |
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170 | L60: /* Backtrack to previous node on path. */ |
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171 | iw = iv; |
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172 | iv = prev[iv]; |
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173 | /* Update value of lowl[iv] if necessary. */ |
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174 | if (lowl[iw] < lowl[iv]) lowl[iv] = lowl[iw]; |
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175 | continue; |
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176 | L70: /* Put new node on the stack. */ |
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177 | arp[iv] = i2 - ii - 1; |
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178 | prev[iw] = iv; |
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179 | iv = iw; |
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180 | lowl[iv] = numb[iv] = ++ist; |
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181 | ib[n+1-ist] = iv; |
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182 | } |
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183 | } |
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184 | L100: /* Put permutation in the required form. */ |
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185 | for (i = 1; i <= n; i++) |
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186 | arp[numb[i]] = i; |
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187 | return num; |
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188 | } |
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189 | |
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190 | /**********************************************************************/ |
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191 | |
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192 | #if 0 |
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193 | #include "glplib.h" |
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194 | |
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195 | void test(int n, int ipp); |
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196 | |
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197 | int main(void) |
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198 | { /* test program for routine mc13d */ |
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199 | test( 1, 0); |
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200 | test( 2, 1); |
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201 | test( 2, 2); |
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202 | test( 3, 3); |
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203 | test( 4, 4); |
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204 | test( 5, 10); |
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205 | test(10, 10); |
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206 | test(10, 20); |
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207 | test(20, 20); |
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208 | test(20, 50); |
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209 | test(50, 50); |
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210 | test(50, 200); |
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211 | return 0; |
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212 | } |
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213 | |
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214 | void fa01bs(int max, int *nrand); |
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215 | |
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216 | void setup(int n, char a[1+50][1+50], int ip[], int icn[], int lenr[]); |
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217 | |
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218 | void test(int n, int ipp) |
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219 | { int ip[1+50], icn[1+1000], ior[1+50], ib[1+51], iw[1+150], |
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220 | lenr[1+50]; |
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221 | char a[1+50][1+50], hold[1+100]; |
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222 | int i, ii, iblock, ij, index, j, jblock, jj, k9, num; |
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223 | xprintf("\n\n\nMatrix is of order %d and has %d off-diagonal non-" |
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224 | "zeros\n", n, ipp); |
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225 | for (j = 1; j <= n; j++) |
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226 | { for (i = 1; i <= n; i++) |
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227 | a[i][j] = 0; |
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228 | a[j][j] = 1; |
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229 | } |
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230 | for (k9 = 1; k9 <= ipp; k9++) |
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231 | { /* these statements should be replaced by calls to your |
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232 | favorite random number generator to place two pseudo-random |
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233 | numbers between 1 and n in the variables i and j */ |
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234 | for (;;) |
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235 | { fa01bs(n, &i); |
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236 | fa01bs(n, &j); |
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237 | if (!a[i][j]) break; |
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238 | } |
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239 | a[i][j] = 1; |
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240 | } |
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241 | /* setup converts matrix a[i,j] to required sparsity-oriented |
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242 | storage format */ |
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243 | setup(n, a, ip, icn, lenr); |
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244 | num = mc13d(n, icn, ip, lenr, ior, ib, &iw[0], &iw[n], &iw[n+n]); |
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245 | /* output reordered matrix with blocking to improve clarity */ |
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246 | xprintf("\nThe reordered matrix which has %d block%s is of the fo" |
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247 | "rm\n", num, num == 1 ? "" : "s"); |
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248 | ib[num+1] = n + 1; |
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249 | index = 100; |
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250 | iblock = 1; |
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251 | for (i = 1; i <= n; i++) |
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252 | { for (ij = 1; ij <= index; ij++) |
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253 | hold[ij] = ' '; |
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254 | if (i == ib[iblock]) |
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255 | { xprintf("\n"); |
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256 | iblock++; |
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257 | } |
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258 | jblock = 1; |
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259 | index = 0; |
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260 | for (j = 1; j <= n; j++) |
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261 | { if (j == ib[jblock]) |
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262 | { hold[++index] = ' '; |
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263 | jblock++; |
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264 | } |
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265 | ii = ior[i]; |
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266 | jj = ior[j]; |
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267 | hold[++index] = (char)(a[ii][jj] ? 'X' : '0'); |
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268 | } |
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269 | xprintf("%.*s\n", index, &hold[1]); |
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270 | } |
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271 | xprintf("\nThe starting point for each block is given by\n"); |
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272 | for (i = 1; i <= num; i++) |
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273 | { if ((i - 1) % 12 == 0) xprintf("\n"); |
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274 | xprintf(" %4d", ib[i]); |
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275 | } |
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276 | xprintf("\n"); |
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277 | return; |
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278 | } |
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279 | |
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280 | void setup(int n, char a[1+50][1+50], int ip[], int icn[], int lenr[]) |
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281 | { int i, j, ind; |
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282 | for (i = 1; i <= n; i++) |
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283 | lenr[i] = 0; |
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284 | ind = 1; |
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285 | for (i = 1; i <= n; i++) |
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286 | { ip[i] = ind; |
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287 | for (j = 1; j <= n; j++) |
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288 | { if (a[i][j]) |
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289 | { lenr[i]++; |
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290 | icn[ind++] = j; |
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291 | } |
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292 | } |
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293 | } |
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294 | return; |
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295 | } |
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296 | |
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297 | double g = 1431655765.0; |
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298 | |
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299 | double fa01as(int i) |
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300 | { /* random number generator */ |
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301 | g = fmod(g * 9228907.0, 4294967296.0); |
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302 | if (i >= 0) |
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303 | return g / 4294967296.0; |
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304 | else |
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305 | return 2.0 * g / 4294967296.0 - 1.0; |
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306 | } |
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307 | |
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308 | void fa01bs(int max, int *nrand) |
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309 | { *nrand = (int)(fa01as(1) * (double)max) + 1; |
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310 | return; |
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311 | } |
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312 | #endif |
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313 | |
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314 | /* eof */ |
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