1 | // // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | // This file is modified from the colamd/symamd library. The copyright is below
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11 |
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12 | // The authors of the code itself are Stefan I. Larimore and Timothy A.
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13 | // Davis (davis@cise.ufl.edu), University of Florida. The algorithm was
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14 | // developed in collaboration with John Gilbert, Xerox PARC, and Esmond
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15 | // Ng, Oak Ridge National Laboratory.
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16 | //
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17 | // Date:
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18 | //
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19 | // September 8, 2003. Version 2.3.
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20 | //
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21 | // Acknowledgements:
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22 | //
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23 | // This work was supported by the National Science Foundation, under
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24 | // grants DMS-9504974 and DMS-9803599.
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25 | //
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26 | // Notice:
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27 | //
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28 | // Copyright (c) 1998-2003 by the University of Florida.
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29 | // All Rights Reserved.
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30 | //
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31 | // THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
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32 | // EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
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33 | //
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34 | // Permission is hereby granted to use, copy, modify, and/or distribute
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35 | // this program, provided that the Copyright, this License, and the
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36 | // Availability of the original version is retained on all copies and made
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37 | // accessible to the end-user of any code or package that includes COLAMD
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38 | // or any modified version of COLAMD.
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39 | //
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40 | // Availability:
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41 | //
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42 | // The colamd/symamd library is available at
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43 | //
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44 | // http://www.suitesparse.com
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45 |
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46 |
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47 | #ifndef EIGEN_COLAMD_H
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48 | #define EIGEN_COLAMD_H
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49 |
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50 | namespace internal {
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51 | /* Ensure that debugging is turned off: */
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52 | #ifndef COLAMD_NDEBUG
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53 | #define COLAMD_NDEBUG
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54 | #endif /* NDEBUG */
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55 | /* ========================================================================== */
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56 | /* === Knob and statistics definitions ====================================== */
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57 | /* ========================================================================== */
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58 |
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59 | /* size of the knobs [ ] array. Only knobs [0..1] are currently used. */
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60 | #define COLAMD_KNOBS 20
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61 |
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62 | /* number of output statistics. Only stats [0..6] are currently used. */
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63 | #define COLAMD_STATS 20
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64 |
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65 | /* knobs [0] and stats [0]: dense row knob and output statistic. */
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66 | #define COLAMD_DENSE_ROW 0
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67 |
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68 | /* knobs [1] and stats [1]: dense column knob and output statistic. */
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69 | #define COLAMD_DENSE_COL 1
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70 |
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71 | /* stats [2]: memory defragmentation count output statistic */
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72 | #define COLAMD_DEFRAG_COUNT 2
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73 |
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74 | /* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */
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75 | #define COLAMD_STATUS 3
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76 |
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77 | /* stats [4..6]: error info, or info on jumbled columns */
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78 | #define COLAMD_INFO1 4
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79 | #define COLAMD_INFO2 5
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80 | #define COLAMD_INFO3 6
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81 |
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82 | /* error codes returned in stats [3]: */
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83 | #define COLAMD_OK (0)
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84 | #define COLAMD_OK_BUT_JUMBLED (1)
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85 | #define COLAMD_ERROR_A_not_present (-1)
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86 | #define COLAMD_ERROR_p_not_present (-2)
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87 | #define COLAMD_ERROR_nrow_negative (-3)
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88 | #define COLAMD_ERROR_ncol_negative (-4)
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89 | #define COLAMD_ERROR_nnz_negative (-5)
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90 | #define COLAMD_ERROR_p0_nonzero (-6)
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91 | #define COLAMD_ERROR_A_too_small (-7)
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92 | #define COLAMD_ERROR_col_length_negative (-8)
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93 | #define COLAMD_ERROR_row_index_out_of_bounds (-9)
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94 | #define COLAMD_ERROR_out_of_memory (-10)
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95 | #define COLAMD_ERROR_internal_error (-999)
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96 |
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97 | /* ========================================================================== */
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98 | /* === Definitions ========================================================== */
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99 | /* ========================================================================== */
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100 |
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101 | #define ONES_COMPLEMENT(r) (-(r)-1)
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102 |
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103 | /* -------------------------------------------------------------------------- */
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104 |
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105 | #define COLAMD_EMPTY (-1)
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106 |
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107 | /* Row and column status */
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108 | #define ALIVE (0)
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109 | #define DEAD (-1)
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110 |
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111 | /* Column status */
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112 | #define DEAD_PRINCIPAL (-1)
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113 | #define DEAD_NON_PRINCIPAL (-2)
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114 |
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115 | /* Macros for row and column status update and checking. */
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116 | #define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
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117 | #define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
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118 | #define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
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119 | #define COL_IS_DEAD(c) (Col [c].start < ALIVE)
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120 | #define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
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121 | #define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
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122 | #define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
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123 | #define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }
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124 | #define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
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125 |
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126 | /* ========================================================================== */
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127 | /* === Colamd reporting mechanism =========================================== */
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128 | /* ========================================================================== */
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129 |
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130 | // == Row and Column structures ==
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131 | template <typename Index>
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132 | struct colamd_col
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133 | {
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134 | Index start ; /* index for A of first row in this column, or DEAD */
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135 | /* if column is dead */
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136 | Index length ; /* number of rows in this column */
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137 | union
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138 | {
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139 | Index thickness ; /* number of original columns represented by this */
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140 | /* col, if the column is alive */
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141 | Index parent ; /* parent in parent tree super-column structure, if */
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142 | /* the column is dead */
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143 | } shared1 ;
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144 | union
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145 | {
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146 | Index score ; /* the score used to maintain heap, if col is alive */
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147 | Index order ; /* pivot ordering of this column, if col is dead */
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148 | } shared2 ;
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149 | union
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150 | {
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151 | Index headhash ; /* head of a hash bucket, if col is at the head of */
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152 | /* a degree list */
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153 | Index hash ; /* hash value, if col is not in a degree list */
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154 | Index prev ; /* previous column in degree list, if col is in a */
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155 | /* degree list (but not at the head of a degree list) */
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156 | } shared3 ;
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157 | union
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158 | {
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159 | Index degree_next ; /* next column, if col is in a degree list */
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160 | Index hash_next ; /* next column, if col is in a hash list */
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161 | } shared4 ;
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162 |
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163 | };
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164 |
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165 | template <typename Index>
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166 | struct Colamd_Row
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167 | {
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168 | Index start ; /* index for A of first col in this row */
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169 | Index length ; /* number of principal columns in this row */
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170 | union
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171 | {
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172 | Index degree ; /* number of principal & non-principal columns in row */
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173 | Index p ; /* used as a row pointer in init_rows_cols () */
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174 | } shared1 ;
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175 | union
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176 | {
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177 | Index mark ; /* for computing set differences and marking dead rows*/
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178 | Index first_column ;/* first column in row (used in garbage collection) */
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179 | } shared2 ;
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180 |
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181 | };
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182 |
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183 | /* ========================================================================== */
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184 | /* === Colamd recommended memory size ======================================= */
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185 | /* ========================================================================== */
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186 |
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187 | /*
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188 | The recommended length Alen of the array A passed to colamd is given by
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189 | the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any
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190 | argument is negative. 2*nnz space is required for the row and column
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191 | indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is
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192 | required for the Col and Row arrays, respectively, which are internal to
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193 | colamd. An additional n_col space is the minimal amount of "elbow room",
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194 | and nnz/5 more space is recommended for run time efficiency.
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195 |
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196 | This macro is not needed when using symamd.
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197 |
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198 | Explicit typecast to Index added Sept. 23, 2002, COLAMD version 2.2, to avoid
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199 | gcc -pedantic warning messages.
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200 | */
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201 | template <typename Index>
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202 | inline Index colamd_c(Index n_col)
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203 | { return Index( ((n_col) + 1) * sizeof (colamd_col<Index>) / sizeof (Index) ) ; }
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204 |
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205 | template <typename Index>
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206 | inline Index colamd_r(Index n_row)
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207 | { return Index(((n_row) + 1) * sizeof (Colamd_Row<Index>) / sizeof (Index)); }
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208 |
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209 | // Prototypes of non-user callable routines
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210 | template <typename Index>
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211 | static Index init_rows_cols (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> col [], Index A [], Index p [], Index stats[COLAMD_STATS] );
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212 |
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213 | template <typename Index>
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214 | static void init_scoring (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index head [], double knobs[COLAMD_KNOBS], Index *p_n_row2, Index *p_n_col2, Index *p_max_deg);
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215 |
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216 | template <typename Index>
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217 | static Index find_ordering (Index n_row, Index n_col, Index Alen, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index head [], Index n_col2, Index max_deg, Index pfree);
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218 |
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219 | template <typename Index>
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220 | static void order_children (Index n_col, colamd_col<Index> Col [], Index p []);
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221 |
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222 | template <typename Index>
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223 | static void detect_super_cols (colamd_col<Index> Col [], Index A [], Index head [], Index row_start, Index row_length ) ;
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224 |
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225 | template <typename Index>
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226 | static Index garbage_collection (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index *pfree) ;
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227 |
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228 | template <typename Index>
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229 | static inline Index clear_mark (Index n_row, Colamd_Row<Index> Row [] ) ;
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230 |
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231 | /* === No debugging ========================================================= */
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232 |
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233 | #define COLAMD_DEBUG0(params) ;
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234 | #define COLAMD_DEBUG1(params) ;
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235 | #define COLAMD_DEBUG2(params) ;
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236 | #define COLAMD_DEBUG3(params) ;
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237 | #define COLAMD_DEBUG4(params) ;
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238 |
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239 | #define COLAMD_ASSERT(expression) ((void) 0)
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240 |
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241 |
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242 | /**
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243 | * \brief Returns the recommended value of Alen
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244 | *
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245 | * Returns recommended value of Alen for use by colamd.
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246 | * Returns -1 if any input argument is negative.
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247 | * The use of this routine or macro is optional.
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248 | * Note that the macro uses its arguments more than once,
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249 | * so be careful for side effects, if you pass expressions as arguments to COLAMD_RECOMMENDED.
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250 | *
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251 | * \param nnz nonzeros in A
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252 | * \param n_row number of rows in A
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253 | * \param n_col number of columns in A
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254 | * \return recommended value of Alen for use by colamd
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255 | */
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256 | template <typename Index>
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257 | inline Index colamd_recommended ( Index nnz, Index n_row, Index n_col)
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258 | {
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259 | if ((nnz) < 0 || (n_row) < 0 || (n_col) < 0)
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260 | return (-1);
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261 | else
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262 | return (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5));
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263 | }
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264 |
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265 | /**
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266 | * \brief set default parameters The use of this routine is optional.
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267 | *
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268 | * Colamd: rows with more than (knobs [COLAMD_DENSE_ROW] * n_col)
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269 | * entries are removed prior to ordering. Columns with more than
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270 | * (knobs [COLAMD_DENSE_COL] * n_row) entries are removed prior to
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271 | * ordering, and placed last in the output column ordering.
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272 | *
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273 | * COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,
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274 | * respectively, in colamd.h. Default values of these two knobs
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275 | * are both 0.5. Currently, only knobs [0] and knobs [1] are
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276 | * used, but future versions may use more knobs. If so, they will
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277 | * be properly set to their defaults by the future version of
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278 | * colamd_set_defaults, so that the code that calls colamd will
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279 | * not need to change, assuming that you either use
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280 | * colamd_set_defaults, or pass a (double *) NULL pointer as the
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281 | * knobs array to colamd or symamd.
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282 | *
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283 | * \param knobs parameter settings for colamd
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284 | */
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285 |
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286 | static inline void colamd_set_defaults(double knobs[COLAMD_KNOBS])
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287 | {
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288 | /* === Local variables ================================================== */
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289 |
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290 | int i ;
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291 |
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292 | if (!knobs)
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293 | {
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294 | return ; /* no knobs to initialize */
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295 | }
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296 | for (i = 0 ; i < COLAMD_KNOBS ; i++)
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297 | {
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298 | knobs [i] = 0 ;
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299 | }
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300 | knobs [COLAMD_DENSE_ROW] = 0.5 ; /* ignore rows over 50% dense */
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301 | knobs [COLAMD_DENSE_COL] = 0.5 ; /* ignore columns over 50% dense */
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302 | }
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303 |
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304 | /**
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305 | * \brief Computes a column ordering using the column approximate minimum degree ordering
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306 | *
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307 | * Computes a column ordering (Q) of A such that P(AQ)=LU or
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308 | * (AQ)'AQ=LL' have less fill-in and require fewer floating point
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309 | * operations than factorizing the unpermuted matrix A or A'A,
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310 | * respectively.
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311 | *
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312 | *
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313 | * \param n_row number of rows in A
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314 | * \param n_col number of columns in A
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315 | * \param Alen, size of the array A
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316 | * \param A row indices of the matrix, of size ALen
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317 | * \param p column pointers of A, of size n_col+1
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318 | * \param knobs parameter settings for colamd
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319 | * \param stats colamd output statistics and error codes
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320 | */
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321 | template <typename Index>
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322 | static bool colamd(Index n_row, Index n_col, Index Alen, Index *A, Index *p, double knobs[COLAMD_KNOBS], Index stats[COLAMD_STATS])
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323 | {
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324 | /* === Local variables ================================================== */
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325 |
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326 | Index i ; /* loop index */
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327 | Index nnz ; /* nonzeros in A */
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328 | Index Row_size ; /* size of Row [], in integers */
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329 | Index Col_size ; /* size of Col [], in integers */
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330 | Index need ; /* minimum required length of A */
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331 | Colamd_Row<Index> *Row ; /* pointer into A of Row [0..n_row] array */
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332 | colamd_col<Index> *Col ; /* pointer into A of Col [0..n_col] array */
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333 | Index n_col2 ; /* number of non-dense, non-empty columns */
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334 | Index n_row2 ; /* number of non-dense, non-empty rows */
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335 | Index ngarbage ; /* number of garbage collections performed */
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336 | Index max_deg ; /* maximum row degree */
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337 | double default_knobs [COLAMD_KNOBS] ; /* default knobs array */
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338 |
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339 |
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340 | /* === Check the input arguments ======================================== */
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341 |
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342 | if (!stats)
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343 | {
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344 | COLAMD_DEBUG0 (("colamd: stats not present\n")) ;
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345 | return (false) ;
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346 | }
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347 | for (i = 0 ; i < COLAMD_STATS ; i++)
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348 | {
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349 | stats [i] = 0 ;
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350 | }
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351 | stats [COLAMD_STATUS] = COLAMD_OK ;
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352 | stats [COLAMD_INFO1] = -1 ;
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353 | stats [COLAMD_INFO2] = -1 ;
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354 |
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355 | if (!A) /* A is not present */
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356 | {
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357 | stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;
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358 | COLAMD_DEBUG0 (("colamd: A not present\n")) ;
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359 | return (false) ;
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360 | }
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361 |
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362 | if (!p) /* p is not present */
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363 | {
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364 | stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;
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365 | COLAMD_DEBUG0 (("colamd: p not present\n")) ;
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366 | return (false) ;
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367 | }
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368 |
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369 | if (n_row < 0) /* n_row must be >= 0 */
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370 | {
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371 | stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;
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372 | stats [COLAMD_INFO1] = n_row ;
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373 | COLAMD_DEBUG0 (("colamd: nrow negative %d\n", n_row)) ;
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374 | return (false) ;
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375 | }
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376 |
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377 | if (n_col < 0) /* n_col must be >= 0 */
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378 | {
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379 | stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;
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380 | stats [COLAMD_INFO1] = n_col ;
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381 | COLAMD_DEBUG0 (("colamd: ncol negative %d\n", n_col)) ;
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382 | return (false) ;
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383 | }
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384 |
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385 | nnz = p [n_col] ;
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386 | if (nnz < 0) /* nnz must be >= 0 */
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387 | {
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388 | stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;
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389 | stats [COLAMD_INFO1] = nnz ;
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390 | COLAMD_DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ;
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391 | return (false) ;
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392 | }
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393 |
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394 | if (p [0] != 0)
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395 | {
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396 | stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;
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397 | stats [COLAMD_INFO1] = p [0] ;
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398 | COLAMD_DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ;
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399 | return (false) ;
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400 | }
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401 |
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402 | /* === If no knobs, set default knobs =================================== */
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403 |
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404 | if (!knobs)
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405 | {
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406 | colamd_set_defaults (default_knobs) ;
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407 | knobs = default_knobs ;
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408 | }
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409 |
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410 | /* === Allocate the Row and Col arrays from array A ===================== */
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411 |
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412 | Col_size = colamd_c (n_col) ;
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413 | Row_size = colamd_r (n_row) ;
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414 | need = 2*nnz + n_col + Col_size + Row_size ;
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415 |
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416 | if (need > Alen)
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417 | {
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418 | /* not enough space in array A to perform the ordering */
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---|
419 | stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;
|
---|
420 | stats [COLAMD_INFO1] = need ;
|
---|
421 | stats [COLAMD_INFO2] = Alen ;
|
---|
422 | COLAMD_DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen));
|
---|
423 | return (false) ;
|
---|
424 | }
|
---|
425 |
|
---|
426 | Alen -= Col_size + Row_size ;
|
---|
427 | Col = (colamd_col<Index> *) &A [Alen] ;
|
---|
428 | Row = (Colamd_Row<Index> *) &A [Alen + Col_size] ;
|
---|
429 |
|
---|
430 | /* === Construct the row and column data structures ===================== */
|
---|
431 |
|
---|
432 | if (!Eigen::internal::init_rows_cols (n_row, n_col, Row, Col, A, p, stats))
|
---|
433 | {
|
---|
434 | /* input matrix is invalid */
|
---|
435 | COLAMD_DEBUG0 (("colamd: Matrix invalid\n")) ;
|
---|
436 | return (false) ;
|
---|
437 | }
|
---|
438 |
|
---|
439 | /* === Initialize scores, kill dense rows/columns ======================= */
|
---|
440 |
|
---|
441 | Eigen::internal::init_scoring (n_row, n_col, Row, Col, A, p, knobs,
|
---|
442 | &n_row2, &n_col2, &max_deg) ;
|
---|
443 |
|
---|
444 | /* === Order the supercolumns =========================================== */
|
---|
445 |
|
---|
446 | ngarbage = Eigen::internal::find_ordering (n_row, n_col, Alen, Row, Col, A, p,
|
---|
447 | n_col2, max_deg, 2*nnz) ;
|
---|
448 |
|
---|
449 | /* === Order the non-principal columns ================================== */
|
---|
450 |
|
---|
451 | Eigen::internal::order_children (n_col, Col, p) ;
|
---|
452 |
|
---|
453 | /* === Return statistics in stats ======================================= */
|
---|
454 |
|
---|
455 | stats [COLAMD_DENSE_ROW] = n_row - n_row2 ;
|
---|
456 | stats [COLAMD_DENSE_COL] = n_col - n_col2 ;
|
---|
457 | stats [COLAMD_DEFRAG_COUNT] = ngarbage ;
|
---|
458 | COLAMD_DEBUG0 (("colamd: done.\n")) ;
|
---|
459 | return (true) ;
|
---|
460 | }
|
---|
461 |
|
---|
462 | /* ========================================================================== */
|
---|
463 | /* === NON-USER-CALLABLE ROUTINES: ========================================== */
|
---|
464 | /* ========================================================================== */
|
---|
465 |
|
---|
466 | /* There are no user-callable routines beyond this point in the file */
|
---|
467 |
|
---|
468 |
|
---|
469 | /* ========================================================================== */
|
---|
470 | /* === init_rows_cols ======================================================= */
|
---|
471 | /* ========================================================================== */
|
---|
472 |
|
---|
473 | /*
|
---|
474 | Takes the column form of the matrix in A and creates the row form of the
|
---|
475 | matrix. Also, row and column attributes are stored in the Col and Row
|
---|
476 | structs. If the columns are un-sorted or contain duplicate row indices,
|
---|
477 | this routine will also sort and remove duplicate row indices from the
|
---|
478 | column form of the matrix. Returns false if the matrix is invalid,
|
---|
479 | true otherwise. Not user-callable.
|
---|
480 | */
|
---|
481 | template <typename Index>
|
---|
482 | static Index init_rows_cols /* returns true if OK, or false otherwise */
|
---|
483 | (
|
---|
484 | /* === Parameters ======================================================= */
|
---|
485 |
|
---|
486 | Index n_row, /* number of rows of A */
|
---|
487 | Index n_col, /* number of columns of A */
|
---|
488 | Colamd_Row<Index> Row [], /* of size n_row+1 */
|
---|
489 | colamd_col<Index> Col [], /* of size n_col+1 */
|
---|
490 | Index A [], /* row indices of A, of size Alen */
|
---|
491 | Index p [], /* pointers to columns in A, of size n_col+1 */
|
---|
492 | Index stats [COLAMD_STATS] /* colamd statistics */
|
---|
493 | )
|
---|
494 | {
|
---|
495 | /* === Local variables ================================================== */
|
---|
496 |
|
---|
497 | Index col ; /* a column index */
|
---|
498 | Index row ; /* a row index */
|
---|
499 | Index *cp ; /* a column pointer */
|
---|
500 | Index *cp_end ; /* a pointer to the end of a column */
|
---|
501 | Index *rp ; /* a row pointer */
|
---|
502 | Index *rp_end ; /* a pointer to the end of a row */
|
---|
503 | Index last_row ; /* previous row */
|
---|
504 |
|
---|
505 | /* === Initialize columns, and check column pointers ==================== */
|
---|
506 |
|
---|
507 | for (col = 0 ; col < n_col ; col++)
|
---|
508 | {
|
---|
509 | Col [col].start = p [col] ;
|
---|
510 | Col [col].length = p [col+1] - p [col] ;
|
---|
511 |
|
---|
512 | if ((Col [col].length) < 0) // extra parentheses to work-around gcc bug 10200
|
---|
513 | {
|
---|
514 | /* column pointers must be non-decreasing */
|
---|
515 | stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;
|
---|
516 | stats [COLAMD_INFO1] = col ;
|
---|
517 | stats [COLAMD_INFO2] = Col [col].length ;
|
---|
518 | COLAMD_DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ;
|
---|
519 | return (false) ;
|
---|
520 | }
|
---|
521 |
|
---|
522 | Col [col].shared1.thickness = 1 ;
|
---|
523 | Col [col].shared2.score = 0 ;
|
---|
524 | Col [col].shared3.prev = COLAMD_EMPTY ;
|
---|
525 | Col [col].shared4.degree_next = COLAMD_EMPTY ;
|
---|
526 | }
|
---|
527 |
|
---|
528 | /* p [0..n_col] no longer needed, used as "head" in subsequent routines */
|
---|
529 |
|
---|
530 | /* === Scan columns, compute row degrees, and check row indices ========= */
|
---|
531 |
|
---|
532 | stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
|
---|
533 |
|
---|
534 | for (row = 0 ; row < n_row ; row++)
|
---|
535 | {
|
---|
536 | Row [row].length = 0 ;
|
---|
537 | Row [row].shared2.mark = -1 ;
|
---|
538 | }
|
---|
539 |
|
---|
540 | for (col = 0 ; col < n_col ; col++)
|
---|
541 | {
|
---|
542 | last_row = -1 ;
|
---|
543 |
|
---|
544 | cp = &A [p [col]] ;
|
---|
545 | cp_end = &A [p [col+1]] ;
|
---|
546 |
|
---|
547 | while (cp < cp_end)
|
---|
548 | {
|
---|
549 | row = *cp++ ;
|
---|
550 |
|
---|
551 | /* make sure row indices within range */
|
---|
552 | if (row < 0 || row >= n_row)
|
---|
553 | {
|
---|
554 | stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;
|
---|
555 | stats [COLAMD_INFO1] = col ;
|
---|
556 | stats [COLAMD_INFO2] = row ;
|
---|
557 | stats [COLAMD_INFO3] = n_row ;
|
---|
558 | COLAMD_DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ;
|
---|
559 | return (false) ;
|
---|
560 | }
|
---|
561 |
|
---|
562 | if (row <= last_row || Row [row].shared2.mark == col)
|
---|
563 | {
|
---|
564 | /* row index are unsorted or repeated (or both), thus col */
|
---|
565 | /* is jumbled. This is a notice, not an error condition. */
|
---|
566 | stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;
|
---|
567 | stats [COLAMD_INFO1] = col ;
|
---|
568 | stats [COLAMD_INFO2] = row ;
|
---|
569 | (stats [COLAMD_INFO3]) ++ ;
|
---|
570 | COLAMD_DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col));
|
---|
571 | }
|
---|
572 |
|
---|
573 | if (Row [row].shared2.mark != col)
|
---|
574 | {
|
---|
575 | Row [row].length++ ;
|
---|
576 | }
|
---|
577 | else
|
---|
578 | {
|
---|
579 | /* this is a repeated entry in the column, */
|
---|
580 | /* it will be removed */
|
---|
581 | Col [col].length-- ;
|
---|
582 | }
|
---|
583 |
|
---|
584 | /* mark the row as having been seen in this column */
|
---|
585 | Row [row].shared2.mark = col ;
|
---|
586 |
|
---|
587 | last_row = row ;
|
---|
588 | }
|
---|
589 | }
|
---|
590 |
|
---|
591 | /* === Compute row pointers ============================================= */
|
---|
592 |
|
---|
593 | /* row form of the matrix starts directly after the column */
|
---|
594 | /* form of matrix in A */
|
---|
595 | Row [0].start = p [n_col] ;
|
---|
596 | Row [0].shared1.p = Row [0].start ;
|
---|
597 | Row [0].shared2.mark = -1 ;
|
---|
598 | for (row = 1 ; row < n_row ; row++)
|
---|
599 | {
|
---|
600 | Row [row].start = Row [row-1].start + Row [row-1].length ;
|
---|
601 | Row [row].shared1.p = Row [row].start ;
|
---|
602 | Row [row].shared2.mark = -1 ;
|
---|
603 | }
|
---|
604 |
|
---|
605 | /* === Create row form ================================================== */
|
---|
606 |
|
---|
607 | if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
|
---|
608 | {
|
---|
609 | /* if cols jumbled, watch for repeated row indices */
|
---|
610 | for (col = 0 ; col < n_col ; col++)
|
---|
611 | {
|
---|
612 | cp = &A [p [col]] ;
|
---|
613 | cp_end = &A [p [col+1]] ;
|
---|
614 | while (cp < cp_end)
|
---|
615 | {
|
---|
616 | row = *cp++ ;
|
---|
617 | if (Row [row].shared2.mark != col)
|
---|
618 | {
|
---|
619 | A [(Row [row].shared1.p)++] = col ;
|
---|
620 | Row [row].shared2.mark = col ;
|
---|
621 | }
|
---|
622 | }
|
---|
623 | }
|
---|
624 | }
|
---|
625 | else
|
---|
626 | {
|
---|
627 | /* if cols not jumbled, we don't need the mark (this is faster) */
|
---|
628 | for (col = 0 ; col < n_col ; col++)
|
---|
629 | {
|
---|
630 | cp = &A [p [col]] ;
|
---|
631 | cp_end = &A [p [col+1]] ;
|
---|
632 | while (cp < cp_end)
|
---|
633 | {
|
---|
634 | A [(Row [*cp++].shared1.p)++] = col ;
|
---|
635 | }
|
---|
636 | }
|
---|
637 | }
|
---|
638 |
|
---|
639 | /* === Clear the row marks and set row degrees ========================== */
|
---|
640 |
|
---|
641 | for (row = 0 ; row < n_row ; row++)
|
---|
642 | {
|
---|
643 | Row [row].shared2.mark = 0 ;
|
---|
644 | Row [row].shared1.degree = Row [row].length ;
|
---|
645 | }
|
---|
646 |
|
---|
647 | /* === See if we need to re-create columns ============================== */
|
---|
648 |
|
---|
649 | if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)
|
---|
650 | {
|
---|
651 | COLAMD_DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ;
|
---|
652 |
|
---|
653 |
|
---|
654 | /* === Compute col pointers ========================================= */
|
---|
655 |
|
---|
656 | /* col form of the matrix starts at A [0]. */
|
---|
657 | /* Note, we may have a gap between the col form and the row */
|
---|
658 | /* form if there were duplicate entries, if so, it will be */
|
---|
659 | /* removed upon the first garbage collection */
|
---|
660 | Col [0].start = 0 ;
|
---|
661 | p [0] = Col [0].start ;
|
---|
662 | for (col = 1 ; col < n_col ; col++)
|
---|
663 | {
|
---|
664 | /* note that the lengths here are for pruned columns, i.e. */
|
---|
665 | /* no duplicate row indices will exist for these columns */
|
---|
666 | Col [col].start = Col [col-1].start + Col [col-1].length ;
|
---|
667 | p [col] = Col [col].start ;
|
---|
668 | }
|
---|
669 |
|
---|
670 | /* === Re-create col form =========================================== */
|
---|
671 |
|
---|
672 | for (row = 0 ; row < n_row ; row++)
|
---|
673 | {
|
---|
674 | rp = &A [Row [row].start] ;
|
---|
675 | rp_end = rp + Row [row].length ;
|
---|
676 | while (rp < rp_end)
|
---|
677 | {
|
---|
678 | A [(p [*rp++])++] = row ;
|
---|
679 | }
|
---|
680 | }
|
---|
681 | }
|
---|
682 |
|
---|
683 | /* === Done. Matrix is not (or no longer) jumbled ====================== */
|
---|
684 |
|
---|
685 | return (true) ;
|
---|
686 | }
|
---|
687 |
|
---|
688 |
|
---|
689 | /* ========================================================================== */
|
---|
690 | /* === init_scoring ========================================================= */
|
---|
691 | /* ========================================================================== */
|
---|
692 |
|
---|
693 | /*
|
---|
694 | Kills dense or empty columns and rows, calculates an initial score for
|
---|
695 | each column, and places all columns in the degree lists. Not user-callable.
|
---|
696 | */
|
---|
697 | template <typename Index>
|
---|
698 | static void init_scoring
|
---|
699 | (
|
---|
700 | /* === Parameters ======================================================= */
|
---|
701 |
|
---|
702 | Index n_row, /* number of rows of A */
|
---|
703 | Index n_col, /* number of columns of A */
|
---|
704 | Colamd_Row<Index> Row [], /* of size n_row+1 */
|
---|
705 | colamd_col<Index> Col [], /* of size n_col+1 */
|
---|
706 | Index A [], /* column form and row form of A */
|
---|
707 | Index head [], /* of size n_col+1 */
|
---|
708 | double knobs [COLAMD_KNOBS],/* parameters */
|
---|
709 | Index *p_n_row2, /* number of non-dense, non-empty rows */
|
---|
710 | Index *p_n_col2, /* number of non-dense, non-empty columns */
|
---|
711 | Index *p_max_deg /* maximum row degree */
|
---|
712 | )
|
---|
713 | {
|
---|
714 | /* === Local variables ================================================== */
|
---|
715 |
|
---|
716 | Index c ; /* a column index */
|
---|
717 | Index r, row ; /* a row index */
|
---|
718 | Index *cp ; /* a column pointer */
|
---|
719 | Index deg ; /* degree of a row or column */
|
---|
720 | Index *cp_end ; /* a pointer to the end of a column */
|
---|
721 | Index *new_cp ; /* new column pointer */
|
---|
722 | Index col_length ; /* length of pruned column */
|
---|
723 | Index score ; /* current column score */
|
---|
724 | Index n_col2 ; /* number of non-dense, non-empty columns */
|
---|
725 | Index n_row2 ; /* number of non-dense, non-empty rows */
|
---|
726 | Index dense_row_count ; /* remove rows with more entries than this */
|
---|
727 | Index dense_col_count ; /* remove cols with more entries than this */
|
---|
728 | Index min_score ; /* smallest column score */
|
---|
729 | Index max_deg ; /* maximum row degree */
|
---|
730 | Index next_col ; /* Used to add to degree list.*/
|
---|
731 |
|
---|
732 |
|
---|
733 | /* === Extract knobs ==================================================== */
|
---|
734 |
|
---|
735 | dense_row_count = std::max<Index>(0, (std::min)(Index(knobs [COLAMD_DENSE_ROW] * n_col), n_col)) ;
|
---|
736 | dense_col_count = std::max<Index>(0, (std::min)(Index(knobs [COLAMD_DENSE_COL] * n_row), n_row)) ;
|
---|
737 | COLAMD_DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ;
|
---|
738 | max_deg = 0 ;
|
---|
739 | n_col2 = n_col ;
|
---|
740 | n_row2 = n_row ;
|
---|
741 |
|
---|
742 | /* === Kill empty columns =============================================== */
|
---|
743 |
|
---|
744 | /* Put the empty columns at the end in their natural order, so that LU */
|
---|
745 | /* factorization can proceed as far as possible. */
|
---|
746 | for (c = n_col-1 ; c >= 0 ; c--)
|
---|
747 | {
|
---|
748 | deg = Col [c].length ;
|
---|
749 | if (deg == 0)
|
---|
750 | {
|
---|
751 | /* this is a empty column, kill and order it last */
|
---|
752 | Col [c].shared2.order = --n_col2 ;
|
---|
753 | KILL_PRINCIPAL_COL (c) ;
|
---|
754 | }
|
---|
755 | }
|
---|
756 | COLAMD_DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ;
|
---|
757 |
|
---|
758 | /* === Kill dense columns =============================================== */
|
---|
759 |
|
---|
760 | /* Put the dense columns at the end, in their natural order */
|
---|
761 | for (c = n_col-1 ; c >= 0 ; c--)
|
---|
762 | {
|
---|
763 | /* skip any dead columns */
|
---|
764 | if (COL_IS_DEAD (c))
|
---|
765 | {
|
---|
766 | continue ;
|
---|
767 | }
|
---|
768 | deg = Col [c].length ;
|
---|
769 | if (deg > dense_col_count)
|
---|
770 | {
|
---|
771 | /* this is a dense column, kill and order it last */
|
---|
772 | Col [c].shared2.order = --n_col2 ;
|
---|
773 | /* decrement the row degrees */
|
---|
774 | cp = &A [Col [c].start] ;
|
---|
775 | cp_end = cp + Col [c].length ;
|
---|
776 | while (cp < cp_end)
|
---|
777 | {
|
---|
778 | Row [*cp++].shared1.degree-- ;
|
---|
779 | }
|
---|
780 | KILL_PRINCIPAL_COL (c) ;
|
---|
781 | }
|
---|
782 | }
|
---|
783 | COLAMD_DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ;
|
---|
784 |
|
---|
785 | /* === Kill dense and empty rows ======================================== */
|
---|
786 |
|
---|
787 | for (r = 0 ; r < n_row ; r++)
|
---|
788 | {
|
---|
789 | deg = Row [r].shared1.degree ;
|
---|
790 | COLAMD_ASSERT (deg >= 0 && deg <= n_col) ;
|
---|
791 | if (deg > dense_row_count || deg == 0)
|
---|
792 | {
|
---|
793 | /* kill a dense or empty row */
|
---|
794 | KILL_ROW (r) ;
|
---|
795 | --n_row2 ;
|
---|
796 | }
|
---|
797 | else
|
---|
798 | {
|
---|
799 | /* keep track of max degree of remaining rows */
|
---|
800 | max_deg = (std::max)(max_deg, deg) ;
|
---|
801 | }
|
---|
802 | }
|
---|
803 | COLAMD_DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ;
|
---|
804 |
|
---|
805 | /* === Compute initial column scores ==================================== */
|
---|
806 |
|
---|
807 | /* At this point the row degrees are accurate. They reflect the number */
|
---|
808 | /* of "live" (non-dense) columns in each row. No empty rows exist. */
|
---|
809 | /* Some "live" columns may contain only dead rows, however. These are */
|
---|
810 | /* pruned in the code below. */
|
---|
811 |
|
---|
812 | /* now find the initial matlab score for each column */
|
---|
813 | for (c = n_col-1 ; c >= 0 ; c--)
|
---|
814 | {
|
---|
815 | /* skip dead column */
|
---|
816 | if (COL_IS_DEAD (c))
|
---|
817 | {
|
---|
818 | continue ;
|
---|
819 | }
|
---|
820 | score = 0 ;
|
---|
821 | cp = &A [Col [c].start] ;
|
---|
822 | new_cp = cp ;
|
---|
823 | cp_end = cp + Col [c].length ;
|
---|
824 | while (cp < cp_end)
|
---|
825 | {
|
---|
826 | /* get a row */
|
---|
827 | row = *cp++ ;
|
---|
828 | /* skip if dead */
|
---|
829 | if (ROW_IS_DEAD (row))
|
---|
830 | {
|
---|
831 | continue ;
|
---|
832 | }
|
---|
833 | /* compact the column */
|
---|
834 | *new_cp++ = row ;
|
---|
835 | /* add row's external degree */
|
---|
836 | score += Row [row].shared1.degree - 1 ;
|
---|
837 | /* guard against integer overflow */
|
---|
838 | score = (std::min)(score, n_col) ;
|
---|
839 | }
|
---|
840 | /* determine pruned column length */
|
---|
841 | col_length = (Index) (new_cp - &A [Col [c].start]) ;
|
---|
842 | if (col_length == 0)
|
---|
843 | {
|
---|
844 | /* a newly-made null column (all rows in this col are "dense" */
|
---|
845 | /* and have already been killed) */
|
---|
846 | COLAMD_DEBUG2 (("Newly null killed: %d\n", c)) ;
|
---|
847 | Col [c].shared2.order = --n_col2 ;
|
---|
848 | KILL_PRINCIPAL_COL (c) ;
|
---|
849 | }
|
---|
850 | else
|
---|
851 | {
|
---|
852 | /* set column length and set score */
|
---|
853 | COLAMD_ASSERT (score >= 0) ;
|
---|
854 | COLAMD_ASSERT (score <= n_col) ;
|
---|
855 | Col [c].length = col_length ;
|
---|
856 | Col [c].shared2.score = score ;
|
---|
857 | }
|
---|
858 | }
|
---|
859 | COLAMD_DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n",
|
---|
860 | n_col-n_col2)) ;
|
---|
861 |
|
---|
862 | /* At this point, all empty rows and columns are dead. All live columns */
|
---|
863 | /* are "clean" (containing no dead rows) and simplicial (no supercolumns */
|
---|
864 | /* yet). Rows may contain dead columns, but all live rows contain at */
|
---|
865 | /* least one live column. */
|
---|
866 |
|
---|
867 | /* === Initialize degree lists ========================================== */
|
---|
868 |
|
---|
869 |
|
---|
870 | /* clear the hash buckets */
|
---|
871 | for (c = 0 ; c <= n_col ; c++)
|
---|
872 | {
|
---|
873 | head [c] = COLAMD_EMPTY ;
|
---|
874 | }
|
---|
875 | min_score = n_col ;
|
---|
876 | /* place in reverse order, so low column indices are at the front */
|
---|
877 | /* of the lists. This is to encourage natural tie-breaking */
|
---|
878 | for (c = n_col-1 ; c >= 0 ; c--)
|
---|
879 | {
|
---|
880 | /* only add principal columns to degree lists */
|
---|
881 | if (COL_IS_ALIVE (c))
|
---|
882 | {
|
---|
883 | COLAMD_DEBUG4 (("place %d score %d minscore %d ncol %d\n",
|
---|
884 | c, Col [c].shared2.score, min_score, n_col)) ;
|
---|
885 |
|
---|
886 | /* === Add columns score to DList =============================== */
|
---|
887 |
|
---|
888 | score = Col [c].shared2.score ;
|
---|
889 |
|
---|
890 | COLAMD_ASSERT (min_score >= 0) ;
|
---|
891 | COLAMD_ASSERT (min_score <= n_col) ;
|
---|
892 | COLAMD_ASSERT (score >= 0) ;
|
---|
893 | COLAMD_ASSERT (score <= n_col) ;
|
---|
894 | COLAMD_ASSERT (head [score] >= COLAMD_EMPTY) ;
|
---|
895 |
|
---|
896 | /* now add this column to dList at proper score location */
|
---|
897 | next_col = head [score] ;
|
---|
898 | Col [c].shared3.prev = COLAMD_EMPTY ;
|
---|
899 | Col [c].shared4.degree_next = next_col ;
|
---|
900 |
|
---|
901 | /* if there already was a column with the same score, set its */
|
---|
902 | /* previous pointer to this new column */
|
---|
903 | if (next_col != COLAMD_EMPTY)
|
---|
904 | {
|
---|
905 | Col [next_col].shared3.prev = c ;
|
---|
906 | }
|
---|
907 | head [score] = c ;
|
---|
908 |
|
---|
909 | /* see if this score is less than current min */
|
---|
910 | min_score = (std::min)(min_score, score) ;
|
---|
911 |
|
---|
912 |
|
---|
913 | }
|
---|
914 | }
|
---|
915 |
|
---|
916 |
|
---|
917 | /* === Return number of remaining columns, and max row degree =========== */
|
---|
918 |
|
---|
919 | *p_n_col2 = n_col2 ;
|
---|
920 | *p_n_row2 = n_row2 ;
|
---|
921 | *p_max_deg = max_deg ;
|
---|
922 | }
|
---|
923 |
|
---|
924 |
|
---|
925 | /* ========================================================================== */
|
---|
926 | /* === find_ordering ======================================================== */
|
---|
927 | /* ========================================================================== */
|
---|
928 |
|
---|
929 | /*
|
---|
930 | Order the principal columns of the supercolumn form of the matrix
|
---|
931 | (no supercolumns on input). Uses a minimum approximate column minimum
|
---|
932 | degree ordering method. Not user-callable.
|
---|
933 | */
|
---|
934 | template <typename Index>
|
---|
935 | static Index find_ordering /* return the number of garbage collections */
|
---|
936 | (
|
---|
937 | /* === Parameters ======================================================= */
|
---|
938 |
|
---|
939 | Index n_row, /* number of rows of A */
|
---|
940 | Index n_col, /* number of columns of A */
|
---|
941 | Index Alen, /* size of A, 2*nnz + n_col or larger */
|
---|
942 | Colamd_Row<Index> Row [], /* of size n_row+1 */
|
---|
943 | colamd_col<Index> Col [], /* of size n_col+1 */
|
---|
944 | Index A [], /* column form and row form of A */
|
---|
945 | Index head [], /* of size n_col+1 */
|
---|
946 | Index n_col2, /* Remaining columns to order */
|
---|
947 | Index max_deg, /* Maximum row degree */
|
---|
948 | Index pfree /* index of first free slot (2*nnz on entry) */
|
---|
949 | )
|
---|
950 | {
|
---|
951 | /* === Local variables ================================================== */
|
---|
952 |
|
---|
953 | Index k ; /* current pivot ordering step */
|
---|
954 | Index pivot_col ; /* current pivot column */
|
---|
955 | Index *cp ; /* a column pointer */
|
---|
956 | Index *rp ; /* a row pointer */
|
---|
957 | Index pivot_row ; /* current pivot row */
|
---|
958 | Index *new_cp ; /* modified column pointer */
|
---|
959 | Index *new_rp ; /* modified row pointer */
|
---|
960 | Index pivot_row_start ; /* pointer to start of pivot row */
|
---|
961 | Index pivot_row_degree ; /* number of columns in pivot row */
|
---|
962 | Index pivot_row_length ; /* number of supercolumns in pivot row */
|
---|
963 | Index pivot_col_score ; /* score of pivot column */
|
---|
964 | Index needed_memory ; /* free space needed for pivot row */
|
---|
965 | Index *cp_end ; /* pointer to the end of a column */
|
---|
966 | Index *rp_end ; /* pointer to the end of a row */
|
---|
967 | Index row ; /* a row index */
|
---|
968 | Index col ; /* a column index */
|
---|
969 | Index max_score ; /* maximum possible score */
|
---|
970 | Index cur_score ; /* score of current column */
|
---|
971 | unsigned int hash ; /* hash value for supernode detection */
|
---|
972 | Index head_column ; /* head of hash bucket */
|
---|
973 | Index first_col ; /* first column in hash bucket */
|
---|
974 | Index tag_mark ; /* marker value for mark array */
|
---|
975 | Index row_mark ; /* Row [row].shared2.mark */
|
---|
976 | Index set_difference ; /* set difference size of row with pivot row */
|
---|
977 | Index min_score ; /* smallest column score */
|
---|
978 | Index col_thickness ; /* "thickness" (no. of columns in a supercol) */
|
---|
979 | Index max_mark ; /* maximum value of tag_mark */
|
---|
980 | Index pivot_col_thickness ; /* number of columns represented by pivot col */
|
---|
981 | Index prev_col ; /* Used by Dlist operations. */
|
---|
982 | Index next_col ; /* Used by Dlist operations. */
|
---|
983 | Index ngarbage ; /* number of garbage collections performed */
|
---|
984 |
|
---|
985 |
|
---|
986 | /* === Initialization and clear mark ==================================== */
|
---|
987 |
|
---|
988 | max_mark = INT_MAX - n_col ; /* INT_MAX defined in <limits.h> */
|
---|
989 | tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
|
---|
990 | min_score = 0 ;
|
---|
991 | ngarbage = 0 ;
|
---|
992 | COLAMD_DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ;
|
---|
993 |
|
---|
994 | /* === Order the columns ================================================ */
|
---|
995 |
|
---|
996 | for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */)
|
---|
997 | {
|
---|
998 |
|
---|
999 | /* === Select pivot column, and order it ============================ */
|
---|
1000 |
|
---|
1001 | /* make sure degree list isn't empty */
|
---|
1002 | COLAMD_ASSERT (min_score >= 0) ;
|
---|
1003 | COLAMD_ASSERT (min_score <= n_col) ;
|
---|
1004 | COLAMD_ASSERT (head [min_score] >= COLAMD_EMPTY) ;
|
---|
1005 |
|
---|
1006 | /* get pivot column from head of minimum degree list */
|
---|
1007 | while (head [min_score] == COLAMD_EMPTY && min_score < n_col)
|
---|
1008 | {
|
---|
1009 | min_score++ ;
|
---|
1010 | }
|
---|
1011 | pivot_col = head [min_score] ;
|
---|
1012 | COLAMD_ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;
|
---|
1013 | next_col = Col [pivot_col].shared4.degree_next ;
|
---|
1014 | head [min_score] = next_col ;
|
---|
1015 | if (next_col != COLAMD_EMPTY)
|
---|
1016 | {
|
---|
1017 | Col [next_col].shared3.prev = COLAMD_EMPTY ;
|
---|
1018 | }
|
---|
1019 |
|
---|
1020 | COLAMD_ASSERT (COL_IS_ALIVE (pivot_col)) ;
|
---|
1021 | COLAMD_DEBUG3 (("Pivot col: %d\n", pivot_col)) ;
|
---|
1022 |
|
---|
1023 | /* remember score for defrag check */
|
---|
1024 | pivot_col_score = Col [pivot_col].shared2.score ;
|
---|
1025 |
|
---|
1026 | /* the pivot column is the kth column in the pivot order */
|
---|
1027 | Col [pivot_col].shared2.order = k ;
|
---|
1028 |
|
---|
1029 | /* increment order count by column thickness */
|
---|
1030 | pivot_col_thickness = Col [pivot_col].shared1.thickness ;
|
---|
1031 | k += pivot_col_thickness ;
|
---|
1032 | COLAMD_ASSERT (pivot_col_thickness > 0) ;
|
---|
1033 |
|
---|
1034 | /* === Garbage_collection, if necessary ============================= */
|
---|
1035 |
|
---|
1036 | needed_memory = (std::min)(pivot_col_score, n_col - k) ;
|
---|
1037 | if (pfree + needed_memory >= Alen)
|
---|
1038 | {
|
---|
1039 | pfree = Eigen::internal::garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;
|
---|
1040 | ngarbage++ ;
|
---|
1041 | /* after garbage collection we will have enough */
|
---|
1042 | COLAMD_ASSERT (pfree + needed_memory < Alen) ;
|
---|
1043 | /* garbage collection has wiped out the Row[].shared2.mark array */
|
---|
1044 | tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
|
---|
1045 |
|
---|
1046 | }
|
---|
1047 |
|
---|
1048 | /* === Compute pivot row pattern ==================================== */
|
---|
1049 |
|
---|
1050 | /* get starting location for this new merged row */
|
---|
1051 | pivot_row_start = pfree ;
|
---|
1052 |
|
---|
1053 | /* initialize new row counts to zero */
|
---|
1054 | pivot_row_degree = 0 ;
|
---|
1055 |
|
---|
1056 | /* tag pivot column as having been visited so it isn't included */
|
---|
1057 | /* in merged pivot row */
|
---|
1058 | Col [pivot_col].shared1.thickness = -pivot_col_thickness ;
|
---|
1059 |
|
---|
1060 | /* pivot row is the union of all rows in the pivot column pattern */
|
---|
1061 | cp = &A [Col [pivot_col].start] ;
|
---|
1062 | cp_end = cp + Col [pivot_col].length ;
|
---|
1063 | while (cp < cp_end)
|
---|
1064 | {
|
---|
1065 | /* get a row */
|
---|
1066 | row = *cp++ ;
|
---|
1067 | COLAMD_DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ;
|
---|
1068 | /* skip if row is dead */
|
---|
1069 | if (ROW_IS_DEAD (row))
|
---|
1070 | {
|
---|
1071 | continue ;
|
---|
1072 | }
|
---|
1073 | rp = &A [Row [row].start] ;
|
---|
1074 | rp_end = rp + Row [row].length ;
|
---|
1075 | while (rp < rp_end)
|
---|
1076 | {
|
---|
1077 | /* get a column */
|
---|
1078 | col = *rp++ ;
|
---|
1079 | /* add the column, if alive and untagged */
|
---|
1080 | col_thickness = Col [col].shared1.thickness ;
|
---|
1081 | if (col_thickness > 0 && COL_IS_ALIVE (col))
|
---|
1082 | {
|
---|
1083 | /* tag column in pivot row */
|
---|
1084 | Col [col].shared1.thickness = -col_thickness ;
|
---|
1085 | COLAMD_ASSERT (pfree < Alen) ;
|
---|
1086 | /* place column in pivot row */
|
---|
1087 | A [pfree++] = col ;
|
---|
1088 | pivot_row_degree += col_thickness ;
|
---|
1089 | }
|
---|
1090 | }
|
---|
1091 | }
|
---|
1092 |
|
---|
1093 | /* clear tag on pivot column */
|
---|
1094 | Col [pivot_col].shared1.thickness = pivot_col_thickness ;
|
---|
1095 | max_deg = (std::max)(max_deg, pivot_row_degree) ;
|
---|
1096 |
|
---|
1097 |
|
---|
1098 | /* === Kill all rows used to construct pivot row ==================== */
|
---|
1099 |
|
---|
1100 | /* also kill pivot row, temporarily */
|
---|
1101 | cp = &A [Col [pivot_col].start] ;
|
---|
1102 | cp_end = cp + Col [pivot_col].length ;
|
---|
1103 | while (cp < cp_end)
|
---|
1104 | {
|
---|
1105 | /* may be killing an already dead row */
|
---|
1106 | row = *cp++ ;
|
---|
1107 | COLAMD_DEBUG3 (("Kill row in pivot col: %d\n", row)) ;
|
---|
1108 | KILL_ROW (row) ;
|
---|
1109 | }
|
---|
1110 |
|
---|
1111 | /* === Select a row index to use as the new pivot row =============== */
|
---|
1112 |
|
---|
1113 | pivot_row_length = pfree - pivot_row_start ;
|
---|
1114 | if (pivot_row_length > 0)
|
---|
1115 | {
|
---|
1116 | /* pick the "pivot" row arbitrarily (first row in col) */
|
---|
1117 | pivot_row = A [Col [pivot_col].start] ;
|
---|
1118 | COLAMD_DEBUG3 (("Pivotal row is %d\n", pivot_row)) ;
|
---|
1119 | }
|
---|
1120 | else
|
---|
1121 | {
|
---|
1122 | /* there is no pivot row, since it is of zero length */
|
---|
1123 | pivot_row = COLAMD_EMPTY ;
|
---|
1124 | COLAMD_ASSERT (pivot_row_length == 0) ;
|
---|
1125 | }
|
---|
1126 | COLAMD_ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;
|
---|
1127 |
|
---|
1128 | /* === Approximate degree computation =============================== */
|
---|
1129 |
|
---|
1130 | /* Here begins the computation of the approximate degree. The column */
|
---|
1131 | /* score is the sum of the pivot row "length", plus the size of the */
|
---|
1132 | /* set differences of each row in the column minus the pattern of the */
|
---|
1133 | /* pivot row itself. The column ("thickness") itself is also */
|
---|
1134 | /* excluded from the column score (we thus use an approximate */
|
---|
1135 | /* external degree). */
|
---|
1136 |
|
---|
1137 | /* The time taken by the following code (compute set differences, and */
|
---|
1138 | /* add them up) is proportional to the size of the data structure */
|
---|
1139 | /* being scanned - that is, the sum of the sizes of each column in */
|
---|
1140 | /* the pivot row. Thus, the amortized time to compute a column score */
|
---|
1141 | /* is proportional to the size of that column (where size, in this */
|
---|
1142 | /* context, is the column "length", or the number of row indices */
|
---|
1143 | /* in that column). The number of row indices in a column is */
|
---|
1144 | /* monotonically non-decreasing, from the length of the original */
|
---|
1145 | /* column on input to colamd. */
|
---|
1146 |
|
---|
1147 | /* === Compute set differences ====================================== */
|
---|
1148 |
|
---|
1149 | COLAMD_DEBUG3 (("** Computing set differences phase. **\n")) ;
|
---|
1150 |
|
---|
1151 | /* pivot row is currently dead - it will be revived later. */
|
---|
1152 |
|
---|
1153 | COLAMD_DEBUG3 (("Pivot row: ")) ;
|
---|
1154 | /* for each column in pivot row */
|
---|
1155 | rp = &A [pivot_row_start] ;
|
---|
1156 | rp_end = rp + pivot_row_length ;
|
---|
1157 | while (rp < rp_end)
|
---|
1158 | {
|
---|
1159 | col = *rp++ ;
|
---|
1160 | COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
|
---|
1161 | COLAMD_DEBUG3 (("Col: %d\n", col)) ;
|
---|
1162 |
|
---|
1163 | /* clear tags used to construct pivot row pattern */
|
---|
1164 | col_thickness = -Col [col].shared1.thickness ;
|
---|
1165 | COLAMD_ASSERT (col_thickness > 0) ;
|
---|
1166 | Col [col].shared1.thickness = col_thickness ;
|
---|
1167 |
|
---|
1168 | /* === Remove column from degree list =========================== */
|
---|
1169 |
|
---|
1170 | cur_score = Col [col].shared2.score ;
|
---|
1171 | prev_col = Col [col].shared3.prev ;
|
---|
1172 | next_col = Col [col].shared4.degree_next ;
|
---|
1173 | COLAMD_ASSERT (cur_score >= 0) ;
|
---|
1174 | COLAMD_ASSERT (cur_score <= n_col) ;
|
---|
1175 | COLAMD_ASSERT (cur_score >= COLAMD_EMPTY) ;
|
---|
1176 | if (prev_col == COLAMD_EMPTY)
|
---|
1177 | {
|
---|
1178 | head [cur_score] = next_col ;
|
---|
1179 | }
|
---|
1180 | else
|
---|
1181 | {
|
---|
1182 | Col [prev_col].shared4.degree_next = next_col ;
|
---|
1183 | }
|
---|
1184 | if (next_col != COLAMD_EMPTY)
|
---|
1185 | {
|
---|
1186 | Col [next_col].shared3.prev = prev_col ;
|
---|
1187 | }
|
---|
1188 |
|
---|
1189 | /* === Scan the column ========================================== */
|
---|
1190 |
|
---|
1191 | cp = &A [Col [col].start] ;
|
---|
1192 | cp_end = cp + Col [col].length ;
|
---|
1193 | while (cp < cp_end)
|
---|
1194 | {
|
---|
1195 | /* get a row */
|
---|
1196 | row = *cp++ ;
|
---|
1197 | row_mark = Row [row].shared2.mark ;
|
---|
1198 | /* skip if dead */
|
---|
1199 | if (ROW_IS_MARKED_DEAD (row_mark))
|
---|
1200 | {
|
---|
1201 | continue ;
|
---|
1202 | }
|
---|
1203 | COLAMD_ASSERT (row != pivot_row) ;
|
---|
1204 | set_difference = row_mark - tag_mark ;
|
---|
1205 | /* check if the row has been seen yet */
|
---|
1206 | if (set_difference < 0)
|
---|
1207 | {
|
---|
1208 | COLAMD_ASSERT (Row [row].shared1.degree <= max_deg) ;
|
---|
1209 | set_difference = Row [row].shared1.degree ;
|
---|
1210 | }
|
---|
1211 | /* subtract column thickness from this row's set difference */
|
---|
1212 | set_difference -= col_thickness ;
|
---|
1213 | COLAMD_ASSERT (set_difference >= 0) ;
|
---|
1214 | /* absorb this row if the set difference becomes zero */
|
---|
1215 | if (set_difference == 0)
|
---|
1216 | {
|
---|
1217 | COLAMD_DEBUG3 (("aggressive absorption. Row: %d\n", row)) ;
|
---|
1218 | KILL_ROW (row) ;
|
---|
1219 | }
|
---|
1220 | else
|
---|
1221 | {
|
---|
1222 | /* save the new mark */
|
---|
1223 | Row [row].shared2.mark = set_difference + tag_mark ;
|
---|
1224 | }
|
---|
1225 | }
|
---|
1226 | }
|
---|
1227 |
|
---|
1228 |
|
---|
1229 | /* === Add up set differences for each column ======================= */
|
---|
1230 |
|
---|
1231 | COLAMD_DEBUG3 (("** Adding set differences phase. **\n")) ;
|
---|
1232 |
|
---|
1233 | /* for each column in pivot row */
|
---|
1234 | rp = &A [pivot_row_start] ;
|
---|
1235 | rp_end = rp + pivot_row_length ;
|
---|
1236 | while (rp < rp_end)
|
---|
1237 | {
|
---|
1238 | /* get a column */
|
---|
1239 | col = *rp++ ;
|
---|
1240 | COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;
|
---|
1241 | hash = 0 ;
|
---|
1242 | cur_score = 0 ;
|
---|
1243 | cp = &A [Col [col].start] ;
|
---|
1244 | /* compact the column */
|
---|
1245 | new_cp = cp ;
|
---|
1246 | cp_end = cp + Col [col].length ;
|
---|
1247 |
|
---|
1248 | COLAMD_DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ;
|
---|
1249 |
|
---|
1250 | while (cp < cp_end)
|
---|
1251 | {
|
---|
1252 | /* get a row */
|
---|
1253 | row = *cp++ ;
|
---|
1254 | COLAMD_ASSERT(row >= 0 && row < n_row) ;
|
---|
1255 | row_mark = Row [row].shared2.mark ;
|
---|
1256 | /* skip if dead */
|
---|
1257 | if (ROW_IS_MARKED_DEAD (row_mark))
|
---|
1258 | {
|
---|
1259 | continue ;
|
---|
1260 | }
|
---|
1261 | COLAMD_ASSERT (row_mark > tag_mark) ;
|
---|
1262 | /* compact the column */
|
---|
1263 | *new_cp++ = row ;
|
---|
1264 | /* compute hash function */
|
---|
1265 | hash += row ;
|
---|
1266 | /* add set difference */
|
---|
1267 | cur_score += row_mark - tag_mark ;
|
---|
1268 | /* integer overflow... */
|
---|
1269 | cur_score = (std::min)(cur_score, n_col) ;
|
---|
1270 | }
|
---|
1271 |
|
---|
1272 | /* recompute the column's length */
|
---|
1273 | Col [col].length = (Index) (new_cp - &A [Col [col].start]) ;
|
---|
1274 |
|
---|
1275 | /* === Further mass elimination ================================= */
|
---|
1276 |
|
---|
1277 | if (Col [col].length == 0)
|
---|
1278 | {
|
---|
1279 | COLAMD_DEBUG4 (("further mass elimination. Col: %d\n", col)) ;
|
---|
1280 | /* nothing left but the pivot row in this column */
|
---|
1281 | KILL_PRINCIPAL_COL (col) ;
|
---|
1282 | pivot_row_degree -= Col [col].shared1.thickness ;
|
---|
1283 | COLAMD_ASSERT (pivot_row_degree >= 0) ;
|
---|
1284 | /* order it */
|
---|
1285 | Col [col].shared2.order = k ;
|
---|
1286 | /* increment order count by column thickness */
|
---|
1287 | k += Col [col].shared1.thickness ;
|
---|
1288 | }
|
---|
1289 | else
|
---|
1290 | {
|
---|
1291 | /* === Prepare for supercolumn detection ==================== */
|
---|
1292 |
|
---|
1293 | COLAMD_DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ;
|
---|
1294 |
|
---|
1295 | /* save score so far */
|
---|
1296 | Col [col].shared2.score = cur_score ;
|
---|
1297 |
|
---|
1298 | /* add column to hash table, for supercolumn detection */
|
---|
1299 | hash %= n_col + 1 ;
|
---|
1300 |
|
---|
1301 | COLAMD_DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ;
|
---|
1302 | COLAMD_ASSERT (hash <= n_col) ;
|
---|
1303 |
|
---|
1304 | head_column = head [hash] ;
|
---|
1305 | if (head_column > COLAMD_EMPTY)
|
---|
1306 | {
|
---|
1307 | /* degree list "hash" is non-empty, use prev (shared3) of */
|
---|
1308 | /* first column in degree list as head of hash bucket */
|
---|
1309 | first_col = Col [head_column].shared3.headhash ;
|
---|
1310 | Col [head_column].shared3.headhash = col ;
|
---|
1311 | }
|
---|
1312 | else
|
---|
1313 | {
|
---|
1314 | /* degree list "hash" is empty, use head as hash bucket */
|
---|
1315 | first_col = - (head_column + 2) ;
|
---|
1316 | head [hash] = - (col + 2) ;
|
---|
1317 | }
|
---|
1318 | Col [col].shared4.hash_next = first_col ;
|
---|
1319 |
|
---|
1320 | /* save hash function in Col [col].shared3.hash */
|
---|
1321 | Col [col].shared3.hash = (Index) hash ;
|
---|
1322 | COLAMD_ASSERT (COL_IS_ALIVE (col)) ;
|
---|
1323 | }
|
---|
1324 | }
|
---|
1325 |
|
---|
1326 | /* The approximate external column degree is now computed. */
|
---|
1327 |
|
---|
1328 | /* === Supercolumn detection ======================================== */
|
---|
1329 |
|
---|
1330 | COLAMD_DEBUG3 (("** Supercolumn detection phase. **\n")) ;
|
---|
1331 |
|
---|
1332 | Eigen::internal::detect_super_cols (Col, A, head, pivot_row_start, pivot_row_length) ;
|
---|
1333 |
|
---|
1334 | /* === Kill the pivotal column ====================================== */
|
---|
1335 |
|
---|
1336 | KILL_PRINCIPAL_COL (pivot_col) ;
|
---|
1337 |
|
---|
1338 | /* === Clear mark =================================================== */
|
---|
1339 |
|
---|
1340 | tag_mark += (max_deg + 1) ;
|
---|
1341 | if (tag_mark >= max_mark)
|
---|
1342 | {
|
---|
1343 | COLAMD_DEBUG2 (("clearing tag_mark\n")) ;
|
---|
1344 | tag_mark = Eigen::internal::clear_mark (n_row, Row) ;
|
---|
1345 | }
|
---|
1346 |
|
---|
1347 | /* === Finalize the new pivot row, and column scores ================ */
|
---|
1348 |
|
---|
1349 | COLAMD_DEBUG3 (("** Finalize scores phase. **\n")) ;
|
---|
1350 |
|
---|
1351 | /* for each column in pivot row */
|
---|
1352 | rp = &A [pivot_row_start] ;
|
---|
1353 | /* compact the pivot row */
|
---|
1354 | new_rp = rp ;
|
---|
1355 | rp_end = rp + pivot_row_length ;
|
---|
1356 | while (rp < rp_end)
|
---|
1357 | {
|
---|
1358 | col = *rp++ ;
|
---|
1359 | /* skip dead columns */
|
---|
1360 | if (COL_IS_DEAD (col))
|
---|
1361 | {
|
---|
1362 | continue ;
|
---|
1363 | }
|
---|
1364 | *new_rp++ = col ;
|
---|
1365 | /* add new pivot row to column */
|
---|
1366 | A [Col [col].start + (Col [col].length++)] = pivot_row ;
|
---|
1367 |
|
---|
1368 | /* retrieve score so far and add on pivot row's degree. */
|
---|
1369 | /* (we wait until here for this in case the pivot */
|
---|
1370 | /* row's degree was reduced due to mass elimination). */
|
---|
1371 | cur_score = Col [col].shared2.score + pivot_row_degree ;
|
---|
1372 |
|
---|
1373 | /* calculate the max possible score as the number of */
|
---|
1374 | /* external columns minus the 'k' value minus the */
|
---|
1375 | /* columns thickness */
|
---|
1376 | max_score = n_col - k - Col [col].shared1.thickness ;
|
---|
1377 |
|
---|
1378 | /* make the score the external degree of the union-of-rows */
|
---|
1379 | cur_score -= Col [col].shared1.thickness ;
|
---|
1380 |
|
---|
1381 | /* make sure score is less or equal than the max score */
|
---|
1382 | cur_score = (std::min)(cur_score, max_score) ;
|
---|
1383 | COLAMD_ASSERT (cur_score >= 0) ;
|
---|
1384 |
|
---|
1385 | /* store updated score */
|
---|
1386 | Col [col].shared2.score = cur_score ;
|
---|
1387 |
|
---|
1388 | /* === Place column back in degree list ========================= */
|
---|
1389 |
|
---|
1390 | COLAMD_ASSERT (min_score >= 0) ;
|
---|
1391 | COLAMD_ASSERT (min_score <= n_col) ;
|
---|
1392 | COLAMD_ASSERT (cur_score >= 0) ;
|
---|
1393 | COLAMD_ASSERT (cur_score <= n_col) ;
|
---|
1394 | COLAMD_ASSERT (head [cur_score] >= COLAMD_EMPTY) ;
|
---|
1395 | next_col = head [cur_score] ;
|
---|
1396 | Col [col].shared4.degree_next = next_col ;
|
---|
1397 | Col [col].shared3.prev = COLAMD_EMPTY ;
|
---|
1398 | if (next_col != COLAMD_EMPTY)
|
---|
1399 | {
|
---|
1400 | Col [next_col].shared3.prev = col ;
|
---|
1401 | }
|
---|
1402 | head [cur_score] = col ;
|
---|
1403 |
|
---|
1404 | /* see if this score is less than current min */
|
---|
1405 | min_score = (std::min)(min_score, cur_score) ;
|
---|
1406 |
|
---|
1407 | }
|
---|
1408 |
|
---|
1409 | /* === Resurrect the new pivot row ================================== */
|
---|
1410 |
|
---|
1411 | if (pivot_row_degree > 0)
|
---|
1412 | {
|
---|
1413 | /* update pivot row length to reflect any cols that were killed */
|
---|
1414 | /* during super-col detection and mass elimination */
|
---|
1415 | Row [pivot_row].start = pivot_row_start ;
|
---|
1416 | Row [pivot_row].length = (Index) (new_rp - &A[pivot_row_start]) ;
|
---|
1417 | Row [pivot_row].shared1.degree = pivot_row_degree ;
|
---|
1418 | Row [pivot_row].shared2.mark = 0 ;
|
---|
1419 | /* pivot row is no longer dead */
|
---|
1420 | }
|
---|
1421 | }
|
---|
1422 |
|
---|
1423 | /* === All principal columns have now been ordered ====================== */
|
---|
1424 |
|
---|
1425 | return (ngarbage) ;
|
---|
1426 | }
|
---|
1427 |
|
---|
1428 |
|
---|
1429 | /* ========================================================================== */
|
---|
1430 | /* === order_children ======================================================= */
|
---|
1431 | /* ========================================================================== */
|
---|
1432 |
|
---|
1433 | /*
|
---|
1434 | The find_ordering routine has ordered all of the principal columns (the
|
---|
1435 | representatives of the supercolumns). The non-principal columns have not
|
---|
1436 | yet been ordered. This routine orders those columns by walking up the
|
---|
1437 | parent tree (a column is a child of the column which absorbed it). The
|
---|
1438 | final permutation vector is then placed in p [0 ... n_col-1], with p [0]
|
---|
1439 | being the first column, and p [n_col-1] being the last. It doesn't look
|
---|
1440 | like it at first glance, but be assured that this routine takes time linear
|
---|
1441 | in the number of columns. Although not immediately obvious, the time
|
---|
1442 | taken by this routine is O (n_col), that is, linear in the number of
|
---|
1443 | columns. Not user-callable.
|
---|
1444 | */
|
---|
1445 | template <typename Index>
|
---|
1446 | static inline void order_children
|
---|
1447 | (
|
---|
1448 | /* === Parameters ======================================================= */
|
---|
1449 |
|
---|
1450 | Index n_col, /* number of columns of A */
|
---|
1451 | colamd_col<Index> Col [], /* of size n_col+1 */
|
---|
1452 | Index p [] /* p [0 ... n_col-1] is the column permutation*/
|
---|
1453 | )
|
---|
1454 | {
|
---|
1455 | /* === Local variables ================================================== */
|
---|
1456 |
|
---|
1457 | Index i ; /* loop counter for all columns */
|
---|
1458 | Index c ; /* column index */
|
---|
1459 | Index parent ; /* index of column's parent */
|
---|
1460 | Index order ; /* column's order */
|
---|
1461 |
|
---|
1462 | /* === Order each non-principal column ================================== */
|
---|
1463 |
|
---|
1464 | for (i = 0 ; i < n_col ; i++)
|
---|
1465 | {
|
---|
1466 | /* find an un-ordered non-principal column */
|
---|
1467 | COLAMD_ASSERT (COL_IS_DEAD (i)) ;
|
---|
1468 | if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == COLAMD_EMPTY)
|
---|
1469 | {
|
---|
1470 | parent = i ;
|
---|
1471 | /* once found, find its principal parent */
|
---|
1472 | do
|
---|
1473 | {
|
---|
1474 | parent = Col [parent].shared1.parent ;
|
---|
1475 | } while (!COL_IS_DEAD_PRINCIPAL (parent)) ;
|
---|
1476 |
|
---|
1477 | /* now, order all un-ordered non-principal columns along path */
|
---|
1478 | /* to this parent. collapse tree at the same time */
|
---|
1479 | c = i ;
|
---|
1480 | /* get order of parent */
|
---|
1481 | order = Col [parent].shared2.order ;
|
---|
1482 |
|
---|
1483 | do
|
---|
1484 | {
|
---|
1485 | COLAMD_ASSERT (Col [c].shared2.order == COLAMD_EMPTY) ;
|
---|
1486 |
|
---|
1487 | /* order this column */
|
---|
1488 | Col [c].shared2.order = order++ ;
|
---|
1489 | /* collaps tree */
|
---|
1490 | Col [c].shared1.parent = parent ;
|
---|
1491 |
|
---|
1492 | /* get immediate parent of this column */
|
---|
1493 | c = Col [c].shared1.parent ;
|
---|
1494 |
|
---|
1495 | /* continue until we hit an ordered column. There are */
|
---|
1496 | /* guarranteed not to be anymore unordered columns */
|
---|
1497 | /* above an ordered column */
|
---|
1498 | } while (Col [c].shared2.order == COLAMD_EMPTY) ;
|
---|
1499 |
|
---|
1500 | /* re-order the super_col parent to largest order for this group */
|
---|
1501 | Col [parent].shared2.order = order ;
|
---|
1502 | }
|
---|
1503 | }
|
---|
1504 |
|
---|
1505 | /* === Generate the permutation ========================================= */
|
---|
1506 |
|
---|
1507 | for (c = 0 ; c < n_col ; c++)
|
---|
1508 | {
|
---|
1509 | p [Col [c].shared2.order] = c ;
|
---|
1510 | }
|
---|
1511 | }
|
---|
1512 |
|
---|
1513 |
|
---|
1514 | /* ========================================================================== */
|
---|
1515 | /* === detect_super_cols ==================================================== */
|
---|
1516 | /* ========================================================================== */
|
---|
1517 |
|
---|
1518 | /*
|
---|
1519 | Detects supercolumns by finding matches between columns in the hash buckets.
|
---|
1520 | Check amongst columns in the set A [row_start ... row_start + row_length-1].
|
---|
1521 | The columns under consideration are currently *not* in the degree lists,
|
---|
1522 | and have already been placed in the hash buckets.
|
---|
1523 |
|
---|
1524 | The hash bucket for columns whose hash function is equal to h is stored
|
---|
1525 | as follows:
|
---|
1526 |
|
---|
1527 | if head [h] is >= 0, then head [h] contains a degree list, so:
|
---|
1528 |
|
---|
1529 | head [h] is the first column in degree bucket h.
|
---|
1530 | Col [head [h]].headhash gives the first column in hash bucket h.
|
---|
1531 |
|
---|
1532 | otherwise, the degree list is empty, and:
|
---|
1533 |
|
---|
1534 | -(head [h] + 2) is the first column in hash bucket h.
|
---|
1535 |
|
---|
1536 | For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous
|
---|
1537 | column" pointer. Col [c].shared3.hash is used instead as the hash number
|
---|
1538 | for that column. The value of Col [c].shared4.hash_next is the next column
|
---|
1539 | in the same hash bucket.
|
---|
1540 |
|
---|
1541 | Assuming no, or "few" hash collisions, the time taken by this routine is
|
---|
1542 | linear in the sum of the sizes (lengths) of each column whose score has
|
---|
1543 | just been computed in the approximate degree computation.
|
---|
1544 | Not user-callable.
|
---|
1545 | */
|
---|
1546 | template <typename Index>
|
---|
1547 | static void detect_super_cols
|
---|
1548 | (
|
---|
1549 | /* === Parameters ======================================================= */
|
---|
1550 |
|
---|
1551 | colamd_col<Index> Col [], /* of size n_col+1 */
|
---|
1552 | Index A [], /* row indices of A */
|
---|
1553 | Index head [], /* head of degree lists and hash buckets */
|
---|
1554 | Index row_start, /* pointer to set of columns to check */
|
---|
1555 | Index row_length /* number of columns to check */
|
---|
1556 | )
|
---|
1557 | {
|
---|
1558 | /* === Local variables ================================================== */
|
---|
1559 |
|
---|
1560 | Index hash ; /* hash value for a column */
|
---|
1561 | Index *rp ; /* pointer to a row */
|
---|
1562 | Index c ; /* a column index */
|
---|
1563 | Index super_c ; /* column index of the column to absorb into */
|
---|
1564 | Index *cp1 ; /* column pointer for column super_c */
|
---|
1565 | Index *cp2 ; /* column pointer for column c */
|
---|
1566 | Index length ; /* length of column super_c */
|
---|
1567 | Index prev_c ; /* column preceding c in hash bucket */
|
---|
1568 | Index i ; /* loop counter */
|
---|
1569 | Index *rp_end ; /* pointer to the end of the row */
|
---|
1570 | Index col ; /* a column index in the row to check */
|
---|
1571 | Index head_column ; /* first column in hash bucket or degree list */
|
---|
1572 | Index first_col ; /* first column in hash bucket */
|
---|
1573 |
|
---|
1574 | /* === Consider each column in the row ================================== */
|
---|
1575 |
|
---|
1576 | rp = &A [row_start] ;
|
---|
1577 | rp_end = rp + row_length ;
|
---|
1578 | while (rp < rp_end)
|
---|
1579 | {
|
---|
1580 | col = *rp++ ;
|
---|
1581 | if (COL_IS_DEAD (col))
|
---|
1582 | {
|
---|
1583 | continue ;
|
---|
1584 | }
|
---|
1585 |
|
---|
1586 | /* get hash number for this column */
|
---|
1587 | hash = Col [col].shared3.hash ;
|
---|
1588 | COLAMD_ASSERT (hash <= n_col) ;
|
---|
1589 |
|
---|
1590 | /* === Get the first column in this hash bucket ===================== */
|
---|
1591 |
|
---|
1592 | head_column = head [hash] ;
|
---|
1593 | if (head_column > COLAMD_EMPTY)
|
---|
1594 | {
|
---|
1595 | first_col = Col [head_column].shared3.headhash ;
|
---|
1596 | }
|
---|
1597 | else
|
---|
1598 | {
|
---|
1599 | first_col = - (head_column + 2) ;
|
---|
1600 | }
|
---|
1601 |
|
---|
1602 | /* === Consider each column in the hash bucket ====================== */
|
---|
1603 |
|
---|
1604 | for (super_c = first_col ; super_c != COLAMD_EMPTY ;
|
---|
1605 | super_c = Col [super_c].shared4.hash_next)
|
---|
1606 | {
|
---|
1607 | COLAMD_ASSERT (COL_IS_ALIVE (super_c)) ;
|
---|
1608 | COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ;
|
---|
1609 | length = Col [super_c].length ;
|
---|
1610 |
|
---|
1611 | /* prev_c is the column preceding column c in the hash bucket */
|
---|
1612 | prev_c = super_c ;
|
---|
1613 |
|
---|
1614 | /* === Compare super_c with all columns after it ================ */
|
---|
1615 |
|
---|
1616 | for (c = Col [super_c].shared4.hash_next ;
|
---|
1617 | c != COLAMD_EMPTY ; c = Col [c].shared4.hash_next)
|
---|
1618 | {
|
---|
1619 | COLAMD_ASSERT (c != super_c) ;
|
---|
1620 | COLAMD_ASSERT (COL_IS_ALIVE (c)) ;
|
---|
1621 | COLAMD_ASSERT (Col [c].shared3.hash == hash) ;
|
---|
1622 |
|
---|
1623 | /* not identical if lengths or scores are different */
|
---|
1624 | if (Col [c].length != length ||
|
---|
1625 | Col [c].shared2.score != Col [super_c].shared2.score)
|
---|
1626 | {
|
---|
1627 | prev_c = c ;
|
---|
1628 | continue ;
|
---|
1629 | }
|
---|
1630 |
|
---|
1631 | /* compare the two columns */
|
---|
1632 | cp1 = &A [Col [super_c].start] ;
|
---|
1633 | cp2 = &A [Col [c].start] ;
|
---|
1634 |
|
---|
1635 | for (i = 0 ; i < length ; i++)
|
---|
1636 | {
|
---|
1637 | /* the columns are "clean" (no dead rows) */
|
---|
1638 | COLAMD_ASSERT (ROW_IS_ALIVE (*cp1)) ;
|
---|
1639 | COLAMD_ASSERT (ROW_IS_ALIVE (*cp2)) ;
|
---|
1640 | /* row indices will same order for both supercols, */
|
---|
1641 | /* no gather scatter nessasary */
|
---|
1642 | if (*cp1++ != *cp2++)
|
---|
1643 | {
|
---|
1644 | break ;
|
---|
1645 | }
|
---|
1646 | }
|
---|
1647 |
|
---|
1648 | /* the two columns are different if the for-loop "broke" */
|
---|
1649 | if (i != length)
|
---|
1650 | {
|
---|
1651 | prev_c = c ;
|
---|
1652 | continue ;
|
---|
1653 | }
|
---|
1654 |
|
---|
1655 | /* === Got it! two columns are identical =================== */
|
---|
1656 |
|
---|
1657 | COLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;
|
---|
1658 |
|
---|
1659 | Col [super_c].shared1.thickness += Col [c].shared1.thickness ;
|
---|
1660 | Col [c].shared1.parent = super_c ;
|
---|
1661 | KILL_NON_PRINCIPAL_COL (c) ;
|
---|
1662 | /* order c later, in order_children() */
|
---|
1663 | Col [c].shared2.order = COLAMD_EMPTY ;
|
---|
1664 | /* remove c from hash bucket */
|
---|
1665 | Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;
|
---|
1666 | }
|
---|
1667 | }
|
---|
1668 |
|
---|
1669 | /* === Empty this hash bucket ======================================= */
|
---|
1670 |
|
---|
1671 | if (head_column > COLAMD_EMPTY)
|
---|
1672 | {
|
---|
1673 | /* corresponding degree list "hash" is not empty */
|
---|
1674 | Col [head_column].shared3.headhash = COLAMD_EMPTY ;
|
---|
1675 | }
|
---|
1676 | else
|
---|
1677 | {
|
---|
1678 | /* corresponding degree list "hash" is empty */
|
---|
1679 | head [hash] = COLAMD_EMPTY ;
|
---|
1680 | }
|
---|
1681 | }
|
---|
1682 | }
|
---|
1683 |
|
---|
1684 |
|
---|
1685 | /* ========================================================================== */
|
---|
1686 | /* === garbage_collection =================================================== */
|
---|
1687 | /* ========================================================================== */
|
---|
1688 |
|
---|
1689 | /*
|
---|
1690 | Defragments and compacts columns and rows in the workspace A. Used when
|
---|
1691 | all avaliable memory has been used while performing row merging. Returns
|
---|
1692 | the index of the first free position in A, after garbage collection. The
|
---|
1693 | time taken by this routine is linear is the size of the array A, which is
|
---|
1694 | itself linear in the number of nonzeros in the input matrix.
|
---|
1695 | Not user-callable.
|
---|
1696 | */
|
---|
1697 | template <typename Index>
|
---|
1698 | static Index garbage_collection /* returns the new value of pfree */
|
---|
1699 | (
|
---|
1700 | /* === Parameters ======================================================= */
|
---|
1701 |
|
---|
1702 | Index n_row, /* number of rows */
|
---|
1703 | Index n_col, /* number of columns */
|
---|
1704 | Colamd_Row<Index> Row [], /* row info */
|
---|
1705 | colamd_col<Index> Col [], /* column info */
|
---|
1706 | Index A [], /* A [0 ... Alen-1] holds the matrix */
|
---|
1707 | Index *pfree /* &A [0] ... pfree is in use */
|
---|
1708 | )
|
---|
1709 | {
|
---|
1710 | /* === Local variables ================================================== */
|
---|
1711 |
|
---|
1712 | Index *psrc ; /* source pointer */
|
---|
1713 | Index *pdest ; /* destination pointer */
|
---|
1714 | Index j ; /* counter */
|
---|
1715 | Index r ; /* a row index */
|
---|
1716 | Index c ; /* a column index */
|
---|
1717 | Index length ; /* length of a row or column */
|
---|
1718 |
|
---|
1719 | /* === Defragment the columns =========================================== */
|
---|
1720 |
|
---|
1721 | pdest = &A[0] ;
|
---|
1722 | for (c = 0 ; c < n_col ; c++)
|
---|
1723 | {
|
---|
1724 | if (COL_IS_ALIVE (c))
|
---|
1725 | {
|
---|
1726 | psrc = &A [Col [c].start] ;
|
---|
1727 |
|
---|
1728 | /* move and compact the column */
|
---|
1729 | COLAMD_ASSERT (pdest <= psrc) ;
|
---|
1730 | Col [c].start = (Index) (pdest - &A [0]) ;
|
---|
1731 | length = Col [c].length ;
|
---|
1732 | for (j = 0 ; j < length ; j++)
|
---|
1733 | {
|
---|
1734 | r = *psrc++ ;
|
---|
1735 | if (ROW_IS_ALIVE (r))
|
---|
1736 | {
|
---|
1737 | *pdest++ = r ;
|
---|
1738 | }
|
---|
1739 | }
|
---|
1740 | Col [c].length = (Index) (pdest - &A [Col [c].start]) ;
|
---|
1741 | }
|
---|
1742 | }
|
---|
1743 |
|
---|
1744 | /* === Prepare to defragment the rows =================================== */
|
---|
1745 |
|
---|
1746 | for (r = 0 ; r < n_row ; r++)
|
---|
1747 | {
|
---|
1748 | if (ROW_IS_ALIVE (r))
|
---|
1749 | {
|
---|
1750 | if (Row [r].length == 0)
|
---|
1751 | {
|
---|
1752 | /* this row is of zero length. cannot compact it, so kill it */
|
---|
1753 | COLAMD_DEBUG3 (("Defrag row kill\n")) ;
|
---|
1754 | KILL_ROW (r) ;
|
---|
1755 | }
|
---|
1756 | else
|
---|
1757 | {
|
---|
1758 | /* save first column index in Row [r].shared2.first_column */
|
---|
1759 | psrc = &A [Row [r].start] ;
|
---|
1760 | Row [r].shared2.first_column = *psrc ;
|
---|
1761 | COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;
|
---|
1762 | /* flag the start of the row with the one's complement of row */
|
---|
1763 | *psrc = ONES_COMPLEMENT (r) ;
|
---|
1764 |
|
---|
1765 | }
|
---|
1766 | }
|
---|
1767 | }
|
---|
1768 |
|
---|
1769 | /* === Defragment the rows ============================================== */
|
---|
1770 |
|
---|
1771 | psrc = pdest ;
|
---|
1772 | while (psrc < pfree)
|
---|
1773 | {
|
---|
1774 | /* find a negative number ... the start of a row */
|
---|
1775 | if (*psrc++ < 0)
|
---|
1776 | {
|
---|
1777 | psrc-- ;
|
---|
1778 | /* get the row index */
|
---|
1779 | r = ONES_COMPLEMENT (*psrc) ;
|
---|
1780 | COLAMD_ASSERT (r >= 0 && r < n_row) ;
|
---|
1781 | /* restore first column index */
|
---|
1782 | *psrc = Row [r].shared2.first_column ;
|
---|
1783 | COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;
|
---|
1784 |
|
---|
1785 | /* move and compact the row */
|
---|
1786 | COLAMD_ASSERT (pdest <= psrc) ;
|
---|
1787 | Row [r].start = (Index) (pdest - &A [0]) ;
|
---|
1788 | length = Row [r].length ;
|
---|
1789 | for (j = 0 ; j < length ; j++)
|
---|
1790 | {
|
---|
1791 | c = *psrc++ ;
|
---|
1792 | if (COL_IS_ALIVE (c))
|
---|
1793 | {
|
---|
1794 | *pdest++ = c ;
|
---|
1795 | }
|
---|
1796 | }
|
---|
1797 | Row [r].length = (Index) (pdest - &A [Row [r].start]) ;
|
---|
1798 |
|
---|
1799 | }
|
---|
1800 | }
|
---|
1801 | /* ensure we found all the rows */
|
---|
1802 | COLAMD_ASSERT (debug_rows == 0) ;
|
---|
1803 |
|
---|
1804 | /* === Return the new value of pfree ==================================== */
|
---|
1805 |
|
---|
1806 | return ((Index) (pdest - &A [0])) ;
|
---|
1807 | }
|
---|
1808 |
|
---|
1809 |
|
---|
1810 | /* ========================================================================== */
|
---|
1811 | /* === clear_mark =========================================================== */
|
---|
1812 | /* ========================================================================== */
|
---|
1813 |
|
---|
1814 | /*
|
---|
1815 | Clears the Row [].shared2.mark array, and returns the new tag_mark.
|
---|
1816 | Return value is the new tag_mark. Not user-callable.
|
---|
1817 | */
|
---|
1818 | template <typename Index>
|
---|
1819 | static inline Index clear_mark /* return the new value for tag_mark */
|
---|
1820 | (
|
---|
1821 | /* === Parameters ======================================================= */
|
---|
1822 |
|
---|
1823 | Index n_row, /* number of rows in A */
|
---|
1824 | Colamd_Row<Index> Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */
|
---|
1825 | )
|
---|
1826 | {
|
---|
1827 | /* === Local variables ================================================== */
|
---|
1828 |
|
---|
1829 | Index r ;
|
---|
1830 |
|
---|
1831 | for (r = 0 ; r < n_row ; r++)
|
---|
1832 | {
|
---|
1833 | if (ROW_IS_ALIVE (r))
|
---|
1834 | {
|
---|
1835 | Row [r].shared2.mark = 0 ;
|
---|
1836 | }
|
---|
1837 | }
|
---|
1838 | return (1) ;
|
---|
1839 | }
|
---|
1840 |
|
---|
1841 |
|
---|
1842 | } // namespace internal
|
---|
1843 | #endif
|
---|