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<div class="title">Eigen_Colamd.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// // This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// This file is modified from the colamd/symamd library. The copyright is below</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// The authors of the code itself are Stefan I. Larimore and Timothy A.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">// Davis (davis@cise.ufl.edu), University of Florida. The algorithm was</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// developed in collaboration with John Gilbert, Xerox PARC, and Esmond</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// Ng, Oak Ridge National Laboratory.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// </span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// Date:</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">// </span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">// September 8, 2003. Version 2.3.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">// </span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">// Acknowledgements:</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">// </span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">// This work was supported by the National Science Foundation, under</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">// grants DMS-9504974 and DMS-9803599.</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">// </span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">// Notice:</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">// </span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">// Copyright (c) 1998-2003 by the University of Florida.</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">// All Rights Reserved.</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">// </span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">// THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// </span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// Permission is hereby granted to use, copy, modify, and/or distribute</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// this program, provided that the Copyright, this License, and the</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// Availability of the original version is retained on all copies and made</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// accessible to the end-user of any code or package that includes COLAMD</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// or any modified version of COLAMD. </span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// </span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// Availability:</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// </span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// The colamd/symamd library is available at</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// </span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">// http://www.cise.ufl.edu/research/sparse/colamd/</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.h</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// file. It is required by the colamd.c, colamdmex.c, and symamdmex.c</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// files, and by any C code that calls the routines whose prototypes are</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// listed below, or that uses the colamd/symamd definitions listed below.</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="preprocessor">#ifndef EIGEN_COLAMD_H</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_COLAMD_H</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">/* Ensure that debugging is turned off: */</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="preprocessor">#ifndef COLAMD_NDEBUG</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_NDEBUG</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="preprocessor"></span><span class="preprocessor">#endif </span><span class="comment">/* NDEBUG */</span><span class="preprocessor"></span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="preprocessor"></span><span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment">/* === Knob and statistics definitions ====================================== */</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">/* size of the knobs [ ] array. Only knobs [0..1] are currently used. */</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="preprocessor">#define COLAMD_KNOBS 20</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">/* number of output statistics. Only stats [0..6] are currently used. */</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="preprocessor">#define COLAMD_STATS 20 </span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">/* knobs [0] and stats [0]: dense row knob and output statistic. */</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="preprocessor">#define COLAMD_DENSE_ROW 0</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment">/* knobs [1] and stats [1]: dense column knob and output statistic. */</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="preprocessor">#define COLAMD_DENSE_COL 1</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">/* stats [2]: memory defragmentation count output statistic */</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="preprocessor">#define COLAMD_DEFRAG_COUNT 2</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment">/* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="preprocessor">#define COLAMD_STATUS 3</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">/* stats [4..6]: error info, or info on jumbled columns */</span> </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="preprocessor">#define COLAMD_INFO1 4</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_INFO2 5</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_INFO3 6</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment">/* error codes returned in stats [3]: */</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="preprocessor">#define COLAMD_OK (0)</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_OK_BUT_JUMBLED (1)</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_A_not_present (-1)</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_p_not_present (-2)</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_nrow_negative (-3)</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_ncol_negative (-4)</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_nnz_negative (-5)</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_p0_nonzero (-6)</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_A_too_small (-7)</span></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_col_length_negative (-8)</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_row_index_out_of_bounds (-9)</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_out_of_memory (-10)</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_ERROR_internal_error (-999)</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment">/* === Definitions ========================================================== */</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="preprocessor">#define COLAMD_MAX(a,b) (((a) > (b)) ? (a) : (b))</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_MIN(a,b) (((a) < (b)) ? (a) : (b))</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="preprocessor">#define ONES_COMPLEMENT(r) (-(r)-1)</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment">/* -------------------------------------------------------------------------- */</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="preprocessor">#define COLAMD_EMPTY (-1)</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment">/* Row and column status */</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="preprocessor">#define ALIVE (0)</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="preprocessor"></span><span class="preprocessor">#define DEAD (-1)</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment">/* Column status */</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="preprocessor">#define DEAD_PRINCIPAL (-1)</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="preprocessor"></span><span class="preprocessor">#define DEAD_NON_PRINCIPAL (-2)</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment">/* Macros for row and column status update and checking. */</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="preprocessor">#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="preprocessor"></span><span class="preprocessor">#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="preprocessor"></span><span class="preprocessor">#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="preprocessor"></span><span class="preprocessor">#define COL_IS_DEAD(c) (Col [c].start < ALIVE)</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="preprocessor"></span><span class="preprocessor">#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="preprocessor"></span><span class="preprocessor">#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)</span></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="preprocessor"></span><span class="preprocessor">#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="preprocessor"></span><span class="preprocessor">#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }</span></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="preprocessor"></span><span class="preprocessor">#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment">/* === Colamd reporting mechanism =========================================== */</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment">// == Row and Column structures ==</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="keyword">struct </span>colamd_col</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> {</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  Index start ; <span class="comment">/* index for A of first row in this column, or DEAD */</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="comment">/* if column is dead */</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  Index length ; <span class="comment">/* number of rows in this column */</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keyword">union</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  {</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  Index thickness ; <span class="comment">/* number of original columns represented by this */</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="comment">/* col, if the column is alive */</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  Index parent ; <span class="comment">/* parent in parent tree super-column structure, if */</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">/* the column is dead */</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  } shared1 ;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keyword">union</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  {</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  Index score ; <span class="comment">/* the score used to maintain heap, if col is alive */</span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  Index order ; <span class="comment">/* pivot ordering of this column, if col is dead */</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  } shared2 ;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keyword">union</span></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  Index headhash ; <span class="comment">/* head of a hash bucket, if col is at the head of */</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="comment">/* a degree list */</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  Index hash ; <span class="comment">/* hash value, if col is not in a degree list */</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  Index prev ; <span class="comment">/* previous column in degree list, if col is in a */</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">/* degree list (but not at the head of a degree list) */</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  } shared3 ;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keyword">union</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  {</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  Index degree_next ; <span class="comment">/* next column, if col is in a degree list */</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  Index hash_next ; <span class="comment">/* next column, if col is in a hash list */</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  } shared4 ;</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  </div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> };</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="keyword">struct </span>Colamd_Row</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> {</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  Index start ; <span class="comment">/* index for A of first col in this row */</span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  Index length ; <span class="comment">/* number of principal columns in this row */</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keyword">union</span></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  {</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  Index degree ; <span class="comment">/* number of principal & non-principal columns in row */</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  Index p ; <span class="comment">/* used as a row pointer in init_rows_cols () */</span></div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  } shared1 ;</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keyword">union</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  {</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  Index mark ; <span class="comment">/* for computing set differences and marking dead rows*/</span></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  Index first_column ;<span class="comment">/* first column in row (used in garbage collection) */</span></div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  } shared2 ;</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  </div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> };</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  </div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment">/* === Colamd recommended memory size ======================================= */</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment"> The recommended length Alen of the array A passed to colamd is given by</span></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment"> the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment"> argument is negative. 2*nnz space is required for the row and column</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment"> indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment"> required for the Col and Row arrays, respectively, which are internal to</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment"> colamd. An additional n_col space is the minimal amount of "elbow room",</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment"> and nnz/5 more space is recommended for run time efficiency.</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment"> </span></div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment"> This macro is not needed when using symamd.</span></div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment"> </span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"> Explicit typecast to Index added Sept. 23, 2002, COLAMD version 2.2, to avoid</span></div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> gcc -pedantic warning messages.</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="keyword">inline</span> Index colamd_c(Index n_col) </div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> { <span class="keywordflow">return</span> Index( ((n_col) + 1) * <span class="keyword">sizeof</span> (colamd_col<Index>) / <span class="keyword">sizeof</span> (Index) ) ; }</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> </div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="keyword">inline</span> Index colamd_r(Index n_row)</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> { <span class="keywordflow">return</span> Index(((n_row) + 1) * <span class="keyword">sizeof</span> (Colamd_Row<Index>) / <span class="keyword">sizeof</span> (Index)); }</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> </div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// Prototypes of non-user callable routines</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">static</span> 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] ); </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="keyword">static</span> <span class="keywordtype">void</span> init_scoring (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index head [], <span class="keywordtype">double</span> knobs[COLAMD_KNOBS], Index *p_n_row2, Index *p_n_col2, Index *p_max_deg);</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> </div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="keyword">static</span> 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);</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> </div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="keyword">static</span> <span class="keywordtype">void</span> order_children (Index n_col, colamd_col<Index> Col [], Index p []);</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span> </div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="keyword">static</span> <span class="keywordtype">void</span> detect_super_cols (colamd_col<Index> Col [], Index A [], Index head [], Index row_start, Index row_length ) ;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="keyword">static</span> Index garbage_collection (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index *pfree) ;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="keyword">static</span> <span class="keyword">inline</span> Index clear_mark (Index n_row, Colamd_Row<Index> Row [] ) ;</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> </div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="comment">/* === No debugging ========================================================= */</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span> </div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="preprocessor">#define COLAMD_DEBUG0(params) ;</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_DEBUG1(params) ;</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_DEBUG2(params) ;</span></div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_DEBUG3(params) ;</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> <span class="preprocessor"></span><span class="preprocessor">#define COLAMD_DEBUG4(params) ;</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="preprocessor">#define COLAMD_ASSERT(expression) ((void) 0)</span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="keyword">inline</span> Index colamd_recommended ( Index nnz, Index n_row, Index n_col)</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> {</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">if</span> ((nnz) < 0 || (n_row) < 0 || (n_col) < 0)</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">return</span> (-1);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keywordflow">return</span> (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5)); </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span> }</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> </div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> colamd_set_defaults(<span class="keywordtype">double</span> knobs[COLAMD_KNOBS])</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> {</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  </div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordtype">int</span> i ;</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> </div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordflow">if</span> (!knobs)</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  {</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  return ; <span class="comment">/* no knobs to initialize */</span></div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  }</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keywordflow">for</span> (i = 0 ; i < COLAMD_KNOBS ; i++)</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  {</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  knobs [i] = 0 ;</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  }</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  knobs [COLAMD_DENSE_ROW] = 0.5 ; <span class="comment">/* ignore rows over 50% dense */</span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  knobs [COLAMD_DENSE_COL] = 0.5 ; <span class="comment">/* ignore columns over 50% dense */</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> }</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> </div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> <span class="keyword">static</span> <span class="keywordtype">bool</span> colamd(Index n_row, Index n_col, Index Alen, Index *A, Index *p, <span class="keywordtype">double</span> knobs[COLAMD_KNOBS], Index stats[COLAMD_STATS])</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> {</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  </div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  Index i ; <span class="comment">/* loop index */</span></div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  Index nnz ; <span class="comment">/* nonzeros in A */</span></div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  Index Row_size ; <span class="comment">/* size of Row [], in integers */</span></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  Index Col_size ; <span class="comment">/* size of Col [], in integers */</span></div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  Index need ; <span class="comment">/* minimum required length of A */</span></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  Colamd_Row<Index> *Row ; <span class="comment">/* pointer into A of Row [0..n_row] array */</span></div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  colamd_col<Index> *Col ; <span class="comment">/* pointer into A of Col [0..n_col] array */</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  Index n_col2 ; <span class="comment">/* number of non-dense, non-empty columns */</span></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  Index n_row2 ; <span class="comment">/* number of non-dense, non-empty rows */</span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  Index ngarbage ; <span class="comment">/* number of garbage collections performed */</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  Index max_deg ; <span class="comment">/* maximum row degree */</span></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keywordtype">double</span> default_knobs [COLAMD_KNOBS] ; <span class="comment">/* default knobs array */</span></div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  </div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  </div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="comment">/* === Check the input arguments ======================================== */</span></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  </div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">if</span> (!stats)</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  {</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: stats not present\n"</span>)) ;</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  }</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keywordflow">for</span> (i = 0 ; i < COLAMD_STATS ; i++)</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  {</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  stats [i] = 0 ;</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  }</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  stats [COLAMD_STATUS] = COLAMD_OK ;</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  stats [COLAMD_INFO1] = -1 ;</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  stats [COLAMD_INFO2] = -1 ;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keywordflow">if</span> (!A) <span class="comment">/* A is not present */</span></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  {</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ;</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: A not present\n"</span>)) ;</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  }</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  </div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keywordflow">if</span> (!p) <span class="comment">/* p is not present */</span></div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  {</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ;</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: p not present\n"</span>)) ;</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  }</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  </div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="keywordflow">if</span> (n_row < 0) <span class="comment">/* n_row must be >= 0 */</span></div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  {</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ;</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  stats [COLAMD_INFO1] = n_row ;</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: nrow negative %d\n"</span>, n_row)) ;</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  }</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  </div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordflow">if</span> (n_col < 0) <span class="comment">/* n_col must be >= 0 */</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  {</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ;</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  stats [COLAMD_INFO1] = n_col ;</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: ncol negative %d\n"</span>, n_col)) ;</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  }</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  </div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  nnz = p [n_col] ;</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="keywordflow">if</span> (nnz < 0) <span class="comment">/* nnz must be >= 0 */</span></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  {</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ;</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  stats [COLAMD_INFO1] = nnz ;</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: number of entries negative %d\n"</span>, nnz)) ;</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  }</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  </div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="keywordflow">if</span> (p [0] != 0)</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  {</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ;</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  stats [COLAMD_INFO1] = p [0] ;</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: p[0] not zero %d\n"</span>, p [0])) ;</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  }</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  </div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="comment">/* === If no knobs, set default knobs =================================== */</span></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  </div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keywordflow">if</span> (!knobs)</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  {</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  colamd_set_defaults (default_knobs) ;</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  knobs = default_knobs ;</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  }</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  </div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="comment">/* === Allocate the Row and Col arrays from array A ===================== */</span></div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  </div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  Col_size = colamd_c (n_col) ;</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  Row_size = colamd_r (n_row) ;</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  need = 2*nnz + n_col + Col_size + Row_size ;</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  </div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <span class="keywordflow">if</span> (need > Alen)</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  {</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="comment">/* not enough space in array A to perform the ordering */</span></div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ;</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  stats [COLAMD_INFO1] = need ;</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  stats [COLAMD_INFO2] = Alen ;</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: Need Alen >= %d, given only Alen = %d\n"</span>, need,Alen));</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  }</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  </div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  Alen -= Col_size + Row_size ;</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  Col = (colamd_col<Index> *) &A [Alen] ;</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  Row = (Colamd_Row<Index> *) &A [Alen + Col_size] ;</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> </div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="comment">/* === Construct the row and column data structures ===================== */</span></div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  </div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keywordflow">if</span> (!Eigen::internal::init_rows_cols (n_row, n_col, Row, Col, A, p, stats))</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  {</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="comment">/* input matrix is invalid */</span></div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: Matrix invalid\n"</span>)) ;</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  }</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  </div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <span class="comment">/* === Initialize scores, kill dense rows/columns ======================= */</span></div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span> </div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  Eigen::internal::init_scoring (n_row, n_col, Row, Col, A, p, knobs,</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  &n_row2, &n_col2, &max_deg) ;</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  </div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="comment">/* === Order the supercolumns =========================================== */</span></div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  </div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  ngarbage = Eigen::internal::find_ordering (n_row, n_col, Alen, Row, Col, A, p,</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  n_col2, max_deg, 2*nnz) ;</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  </div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <span class="comment">/* === Order the non-principal columns ================================== */</span></div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  </div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  Eigen::internal::order_children (n_col, Col, p) ;</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  </div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="comment">/* === Return statistics in stats ======================================= */</span></div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  </div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  stats [COLAMD_DENSE_ROW] = n_row - n_row2 ;</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  stats [COLAMD_DENSE_COL] = n_col - n_col2 ;</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  stats [COLAMD_DEFRAG_COUNT] = ngarbage ;</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: done.\n"</span>)) ; </div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <span class="keywordflow">return</span> (<span class="keyword">true</span>) ;</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span> }</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span> </div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span> <span class="comment">/* === NON-USER-CALLABLE ROUTINES: ========================================== */</span></div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span> </div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span> <span class="comment">/* There are no user-callable routines beyond this point in the file */</span></div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> </div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span> </div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> <span class="comment">/* === init_rows_cols ======================================================= */</span></div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span> </div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span> <span class="comment"> Takes the column form of the matrix in A and creates the row form of the</span></div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span> <span class="comment"> matrix. Also, row and column attributes are stored in the Col and Row</span></div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span> <span class="comment"> structs. If the columns are un-sorted or contain duplicate row indices,</span></div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> <span class="comment"> this routine will also sort and remove duplicate row indices from the</span></div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> <span class="comment"> column form of the matrix. Returns false if the matrix is invalid,</span></div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span> <span class="comment"> true otherwise. Not user-callable.</span></div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span> <span class="keyword">static</span> Index init_rows_cols <span class="comment">/* returns true if OK, or false otherwise */</span></div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  (</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> </div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  Index n_row, <span class="comment">/* number of rows of A */</span></div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  Index n_col, <span class="comment">/* number of columns of A */</span></div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  Colamd_Row<Index> Row [], <span class="comment">/* of size n_row+1 */</span></div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  colamd_col<Index> Col [], <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  Index A [], <span class="comment">/* row indices of A, of size Alen */</span></div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  Index p [], <span class="comment">/* pointers to columns in A, of size n_col+1 */</span></div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  Index stats [COLAMD_STATS] <span class="comment">/* colamd statistics */</span> </div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  )</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> {</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span> </div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  Index col ; <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  Index row ; <span class="comment">/* a row index */</span></div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  Index *cp ; <span class="comment">/* a column pointer */</span></div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  Index *cp_end ; <span class="comment">/* a pointer to the end of a column */</span></div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  Index *rp ; <span class="comment">/* a row pointer */</span></div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  Index *rp_end ; <span class="comment">/* a pointer to the end of a row */</span></div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  Index last_row ; <span class="comment">/* previous row */</span></div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span> </div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="comment">/* === Initialize columns, and check column pointers ==================== */</span></div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span> </div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordflow">for</span> (col = 0 ; col < n_col ; col++)</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  {</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  Col [col].start = p [col] ;</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  Col [col].length = p [col+1] - p [col] ;</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> </div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keywordflow">if</span> (Col [col].length < 0)</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  {</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="comment">/* column pointers must be non-decreasing */</span></div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ;</div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  stats [COLAMD_INFO1] = col ;</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  stats [COLAMD_INFO2] = Col [col].length ;</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: col %d length %d < 0\n"</span>, col, Col [col].length)) ;</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  }</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span> </div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  Col [col].shared1.thickness = 1 ;</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  Col [col].shared2.score = 0 ;</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  Col [col].shared3.prev = COLAMD_EMPTY ;</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  Col [col].shared4.degree_next = COLAMD_EMPTY ;</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  }</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> </div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="comment">/* p [0..n_col] no longer needed, used as "head" in subsequent routines */</span></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span> </div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="comment">/* === Scan columns, compute row degrees, and check row indices ========= */</span></div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span> </div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  stats [COLAMD_INFO3] = 0 ; <span class="comment">/* number of duplicate or unsorted row indices*/</span></div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span> </div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  <span class="keywordflow">for</span> (row = 0 ; row < n_row ; row++)</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  {</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  Row [row].length = 0 ;</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  Row [row].shared2.mark = -1 ;</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  }</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span> </div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  <span class="keywordflow">for</span> (col = 0 ; col < n_col ; col++)</div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  {</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  last_row = -1 ;</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span> </div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  cp = &A [p [col]] ;</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  cp_end = &A [p [col+1]] ;</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span> </div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  {</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  row = *cp++ ;</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span> </div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="comment">/* make sure row indices within range */</span></div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="keywordflow">if</span> (row < 0 || row >= n_row)</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  {</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ;</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  stats [COLAMD_INFO1] = col ;</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  stats [COLAMD_INFO2] = row ;</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  stats [COLAMD_INFO3] = n_row ;</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: row %d col %d out of bounds\n"</span>, row, col)) ;</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <span class="keywordflow">return</span> (<span class="keyword">false</span>) ;</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  }</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span> </div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <span class="keywordflow">if</span> (row <= last_row || Row [row].shared2.mark == col)</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  {</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  <span class="comment">/* row index are unsorted or repeated (or both), thus col */</span></div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <span class="comment">/* is jumbled. This is a notice, not an error condition. */</span></div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ;</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  stats [COLAMD_INFO1] = col ;</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  stats [COLAMD_INFO2] = row ;</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  (stats [COLAMD_INFO3]) ++ ;</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  COLAMD_DEBUG1 ((<span class="stringliteral">"colamd: row %d col %d unsorted/duplicate\n"</span>,row,col));</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  }</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span> </div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  <span class="keywordflow">if</span> (Row [row].shared2.mark != col)</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  {</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  Row [row].length++ ;</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  }</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  {</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="comment">/* this is a repeated entry in the column, */</span></div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  <span class="comment">/* it will be removed */</span></div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  Col [col].length-- ;</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  }</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span> </div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="comment">/* mark the row as having been seen in this column */</span></div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  Row [row].shared2.mark = col ;</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span> </div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  last_row = row ;</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  }</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  }</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span> </div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  <span class="comment">/* === Compute row pointers ============================================= */</span></div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span> </div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  <span class="comment">/* row form of the matrix starts directly after the column */</span></div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  <span class="comment">/* form of matrix in A */</span></div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  Row [0].start = p [n_col] ;</div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  Row [0].shared1.p = Row [0].start ;</div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  Row [0].shared2.mark = -1 ;</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  <span class="keywordflow">for</span> (row = 1 ; row < n_row ; row++)</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  {</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  Row [row].start = Row [row-1].start + Row [row-1].length ;</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  Row [row].shared1.p = Row [row].start ;</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  Row [row].shared2.mark = -1 ;</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  }</div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span> </div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  <span class="comment">/* === Create row form ================================================== */</span></div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span> </div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  <span class="keywordflow">if</span> (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  {</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  <span class="comment">/* if cols jumbled, watch for repeated row indices */</span></div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  <span class="keywordflow">for</span> (col = 0 ; col < n_col ; col++)</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  {</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  cp = &A [p [col]] ;</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  cp_end = &A [p [col+1]] ;</div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  {</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  row = *cp++ ;</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <span class="keywordflow">if</span> (Row [row].shared2.mark != col)</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  {</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  A [(Row [row].shared1.p)++] = col ;</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  Row [row].shared2.mark = col ;</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  }</div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  }</div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  }</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  }</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  {</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  <span class="comment">/* if cols not jumbled, we don't need the mark (this is faster) */</span></div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  <span class="keywordflow">for</span> (col = 0 ; col < n_col ; col++)</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  {</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  cp = &A [p [col]] ;</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  cp_end = &A [p [col+1]] ;</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  {</div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  A [(Row [*cp++].shared1.p)++] = col ;</div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  }</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  }</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  }</div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span> </div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  <span class="comment">/* === Clear the row marks and set row degrees ========================== */</span></div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span> </div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  <span class="keywordflow">for</span> (row = 0 ; row < n_row ; row++)</div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  {</div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  Row [row].shared2.mark = 0 ;</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  Row [row].shared1.degree = Row [row].length ;</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  }</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span> </div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  <span class="comment">/* === See if we need to re-create columns ============================== */</span></div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span> </div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  <span class="keywordflow">if</span> (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED)</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  {</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  COLAMD_DEBUG0 ((<span class="stringliteral">"colamd: reconstructing column form, matrix jumbled\n"</span>)) ;</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span> </div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span> </div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  <span class="comment">/* === Compute col pointers ========================================= */</span></div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span> </div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  <span class="comment">/* col form of the matrix starts at A [0]. */</span></div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  <span class="comment">/* Note, we may have a gap between the col form and the row */</span></div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  <span class="comment">/* form if there were duplicate entries, if so, it will be */</span></div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  <span class="comment">/* removed upon the first garbage collection */</span></div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  Col [0].start = 0 ;</div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  p [0] = Col [0].start ;</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  <span class="keywordflow">for</span> (col = 1 ; col < n_col ; col++)</div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  {</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  <span class="comment">/* note that the lengths here are for pruned columns, i.e. */</span></div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  <span class="comment">/* no duplicate row indices will exist for these columns */</span></div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  Col [col].start = Col [col-1].start + Col [col-1].length ;</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  p [col] = Col [col].start ;</div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  }</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span> </div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  <span class="comment">/* === Re-create col form =========================================== */</span></div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span> </div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  <span class="keywordflow">for</span> (row = 0 ; row < n_row ; row++)</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  {</div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  rp = &A [Row [row].start] ;</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  rp_end = rp + Row [row].length ;</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  <span class="keywordflow">while</span> (rp < rp_end)</div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  {</div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  A [(p [*rp++])++] = row ;</div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  }</div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  }</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  }</div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span> </div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  <span class="comment">/* === Done. Matrix is not (or no longer) jumbled ====================== */</span></div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span> </div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  <span class="keywordflow">return</span> (<span class="keyword">true</span>) ;</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span> }</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span> </div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span> </div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span> <span class="comment">/* === init_scoring ========================================================= */</span></div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span> </div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span> <span class="comment"> Kills dense or empty columns and rows, calculates an initial score for</span></div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span> <span class="comment"> each column, and places all columns in the degree lists. Not user-callable.</span></div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span> <span class="keyword">static</span> <span class="keywordtype">void</span> init_scoring</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  (</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span> </div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  Index n_row, <span class="comment">/* number of rows of A */</span></div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  Index n_col, <span class="comment">/* number of columns of A */</span></div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  Colamd_Row<Index> Row [], <span class="comment">/* of size n_row+1 */</span></div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  colamd_col<Index> Col [], <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  Index A [], <span class="comment">/* column form and row form of A */</span></div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  Index head [], <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  <span class="keywordtype">double</span> knobs [COLAMD_KNOBS],<span class="comment">/* parameters */</span></div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  Index *p_n_row2, <span class="comment">/* number of non-dense, non-empty rows */</span></div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  Index *p_n_col2, <span class="comment">/* number of non-dense, non-empty columns */</span></div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  Index *p_max_deg <span class="comment">/* maximum row degree */</span></div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  )</div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span> {</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span> </div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  Index c ; <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  Index r, row ; <span class="comment">/* a row index */</span></div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  Index *cp ; <span class="comment">/* a column pointer */</span></div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  Index deg ; <span class="comment">/* degree of a row or column */</span></div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  Index *cp_end ; <span class="comment">/* a pointer to the end of a column */</span></div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  Index *new_cp ; <span class="comment">/* new column pointer */</span></div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  Index col_length ; <span class="comment">/* length of pruned column */</span></div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  Index score ; <span class="comment">/* current column score */</span></div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  Index n_col2 ; <span class="comment">/* number of non-dense, non-empty columns */</span></div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  Index n_row2 ; <span class="comment">/* number of non-dense, non-empty rows */</span></div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span>  Index dense_row_count ; <span class="comment">/* remove rows with more entries than this */</span></div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span>  Index dense_col_count ; <span class="comment">/* remove cols with more entries than this */</span></div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  Index min_score ; <span class="comment">/* smallest column score */</span></div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  Index max_deg ; <span class="comment">/* maximum row degree */</span></div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  Index next_col ; <span class="comment">/* Used to add to degree list.*/</span></div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span> </div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span> </div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span>  <span class="comment">/* === Extract knobs ==================================================== */</span></div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span> </div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  dense_row_count = COLAMD_MAX (0, COLAMD_MIN (knobs [COLAMD_DENSE_ROW] * n_col, n_col)) ;</div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  dense_col_count = COLAMD_MAX (0, COLAMD_MIN (knobs [COLAMD_DENSE_COL] * n_row, n_row)) ;</div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  COLAMD_DEBUG1 ((<span class="stringliteral">"colamd: densecount: %d %d\n"</span>, dense_row_count, dense_col_count)) ;</div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  max_deg = 0 ;</div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  n_col2 = n_col ;</div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  n_row2 = n_row ;</div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span> </div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  <span class="comment">/* === Kill empty columns =============================================== */</span></div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span> </div>
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  <span class="comment">/* Put the empty columns at the end in their natural order, so that LU */</span></div>
<div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  <span class="comment">/* factorization can proceed as far as possible. */</span></div>
<div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  <span class="keywordflow">for</span> (c = n_col-1 ; c >= 0 ; c--)</div>
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  {</div>
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span>  deg = Col [c].length ;</div>
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  <span class="keywordflow">if</span> (deg == 0)</div>
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  {</div>
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  <span class="comment">/* this is a empty column, kill and order it last */</span></div>
<div class="line"><a name="l00759"></a><span class="lineno"> 759</span>  Col [c].shared2.order = --n_col2 ;</div>
<div class="line"><a name="l00760"></a><span class="lineno"> 760</span>  KILL_PRINCIPAL_COL (c) ;</div>
<div class="line"><a name="l00761"></a><span class="lineno"> 761</span>  }</div>
<div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  }</div>
<div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  COLAMD_DEBUG1 ((<span class="stringliteral">"colamd: null columns killed: %d\n"</span>, n_col - n_col2)) ;</div>
<div class="line"><a name="l00764"></a><span class="lineno"> 764</span> </div>
<div class="line"><a name="l00765"></a><span class="lineno"> 765</span>  <span class="comment">/* === Kill dense columns =============================================== */</span></div>
<div class="line"><a name="l00766"></a><span class="lineno"> 766</span> </div>
<div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  <span class="comment">/* Put the dense columns at the end, in their natural order */</span></div>
<div class="line"><a name="l00768"></a><span class="lineno"> 768</span>  <span class="keywordflow">for</span> (c = n_col-1 ; c >= 0 ; c--)</div>
<div class="line"><a name="l00769"></a><span class="lineno"> 769</span>  {</div>
<div class="line"><a name="l00770"></a><span class="lineno"> 770</span>  <span class="comment">/* skip any dead columns */</span></div>
<div class="line"><a name="l00771"></a><span class="lineno"> 771</span>  <span class="keywordflow">if</span> (COL_IS_DEAD (c))</div>
<div class="line"><a name="l00772"></a><span class="lineno"> 772</span>  {</div>
<div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  continue ;</div>
<div class="line"><a name="l00774"></a><span class="lineno"> 774</span>  }</div>
<div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  deg = Col [c].length ;</div>
<div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  <span class="keywordflow">if</span> (deg > dense_col_count)</div>
<div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  {</div>
<div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  <span class="comment">/* this is a dense column, kill and order it last */</span></div>
<div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  Col [c].shared2.order = --n_col2 ;</div>
<div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  <span class="comment">/* decrement the row degrees */</span></div>
<div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  cp = &A [Col [c].start] ;</div>
<div class="line"><a name="l00782"></a><span class="lineno"> 782</span>  cp_end = cp + Col [c].length ;</div>
<div class="line"><a name="l00783"></a><span class="lineno"> 783</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l00784"></a><span class="lineno"> 784</span>  {</div>
<div class="line"><a name="l00785"></a><span class="lineno"> 785</span>  Row [*cp++].shared1.degree-- ;</div>
<div class="line"><a name="l00786"></a><span class="lineno"> 786</span>  }</div>
<div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  KILL_PRINCIPAL_COL (c) ;</div>
<div class="line"><a name="l00788"></a><span class="lineno"> 788</span>  }</div>
<div class="line"><a name="l00789"></a><span class="lineno"> 789</span>  }</div>
<div class="line"><a name="l00790"></a><span class="lineno"> 790</span>  COLAMD_DEBUG1 ((<span class="stringliteral">"colamd: Dense and null columns killed: %d\n"</span>, n_col - n_col2)) ;</div>
<div class="line"><a name="l00791"></a><span class="lineno"> 791</span> </div>
<div class="line"><a name="l00792"></a><span class="lineno"> 792</span>  <span class="comment">/* === Kill dense and empty rows ======================================== */</span></div>
<div class="line"><a name="l00793"></a><span class="lineno"> 793</span> </div>
<div class="line"><a name="l00794"></a><span class="lineno"> 794</span>  <span class="keywordflow">for</span> (r = 0 ; r < n_row ; r++)</div>
<div class="line"><a name="l00795"></a><span class="lineno"> 795</span>  {</div>
<div class="line"><a name="l00796"></a><span class="lineno"> 796</span>  deg = Row [r].shared1.degree ;</div>
<div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  COLAMD_ASSERT (deg >= 0 && deg <= n_col) ;</div>
<div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  <span class="keywordflow">if</span> (deg > dense_row_count || deg == 0)</div>
<div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  {</div>
<div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  <span class="comment">/* kill a dense or empty row */</span></div>
<div class="line"><a name="l00801"></a><span class="lineno"> 801</span>  KILL_ROW (r) ;</div>
<div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  --n_row2 ;</div>
<div class="line"><a name="l00803"></a><span class="lineno"> 803</span>  }</div>
<div class="line"><a name="l00804"></a><span class="lineno"> 804</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00805"></a><span class="lineno"> 805</span>  {</div>
<div class="line"><a name="l00806"></a><span class="lineno"> 806</span>  <span class="comment">/* keep track of max degree of remaining rows */</span></div>
<div class="line"><a name="l00807"></a><span class="lineno"> 807</span>  max_deg = COLAMD_MAX (max_deg, deg) ;</div>
<div class="line"><a name="l00808"></a><span class="lineno"> 808</span>  }</div>
<div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  }</div>
<div class="line"><a name="l00810"></a><span class="lineno"> 810</span>  COLAMD_DEBUG1 ((<span class="stringliteral">"colamd: Dense and null rows killed: %d\n"</span>, n_row - n_row2)) ;</div>
<div class="line"><a name="l00811"></a><span class="lineno"> 811</span> </div>
<div class="line"><a name="l00812"></a><span class="lineno"> 812</span>  <span class="comment">/* === Compute initial column scores ==================================== */</span></div>
<div class="line"><a name="l00813"></a><span class="lineno"> 813</span> </div>
<div class="line"><a name="l00814"></a><span class="lineno"> 814</span>  <span class="comment">/* At this point the row degrees are accurate. They reflect the number */</span></div>
<div class="line"><a name="l00815"></a><span class="lineno"> 815</span>  <span class="comment">/* of "live" (non-dense) columns in each row. No empty rows exist. */</span></div>
<div class="line"><a name="l00816"></a><span class="lineno"> 816</span>  <span class="comment">/* Some "live" columns may contain only dead rows, however. These are */</span></div>
<div class="line"><a name="l00817"></a><span class="lineno"> 817</span>  <span class="comment">/* pruned in the code below. */</span></div>
<div class="line"><a name="l00818"></a><span class="lineno"> 818</span> </div>
<div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  <span class="comment">/* now find the initial matlab score for each column */</span></div>
<div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  <span class="keywordflow">for</span> (c = n_col-1 ; c >= 0 ; c--)</div>
<div class="line"><a name="l00821"></a><span class="lineno"> 821</span>  {</div>
<div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  <span class="comment">/* skip dead column */</span></div>
<div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  <span class="keywordflow">if</span> (COL_IS_DEAD (c))</div>
<div class="line"><a name="l00824"></a><span class="lineno"> 824</span>  {</div>
<div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  continue ;</div>
<div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  }</div>
<div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  score = 0 ;</div>
<div class="line"><a name="l00828"></a><span class="lineno"> 828</span>  cp = &A [Col [c].start] ;</div>
<div class="line"><a name="l00829"></a><span class="lineno"> 829</span>  new_cp = cp ;</div>
<div class="line"><a name="l00830"></a><span class="lineno"> 830</span>  cp_end = cp + Col [c].length ;</div>
<div class="line"><a name="l00831"></a><span class="lineno"> 831</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l00832"></a><span class="lineno"> 832</span>  {</div>
<div class="line"><a name="l00833"></a><span class="lineno"> 833</span>  <span class="comment">/* get a row */</span></div>
<div class="line"><a name="l00834"></a><span class="lineno"> 834</span>  row = *cp++ ;</div>
<div class="line"><a name="l00835"></a><span class="lineno"> 835</span>  <span class="comment">/* skip if dead */</span></div>
<div class="line"><a name="l00836"></a><span class="lineno"> 836</span>  <span class="keywordflow">if</span> (ROW_IS_DEAD (row))</div>
<div class="line"><a name="l00837"></a><span class="lineno"> 837</span>  {</div>
<div class="line"><a name="l00838"></a><span class="lineno"> 838</span>  continue ;</div>
<div class="line"><a name="l00839"></a><span class="lineno"> 839</span>  }</div>
<div class="line"><a name="l00840"></a><span class="lineno"> 840</span>  <span class="comment">/* compact the column */</span></div>
<div class="line"><a name="l00841"></a><span class="lineno"> 841</span>  *new_cp++ = row ;</div>
<div class="line"><a name="l00842"></a><span class="lineno"> 842</span>  <span class="comment">/* add row's external degree */</span></div>
<div class="line"><a name="l00843"></a><span class="lineno"> 843</span>  score += Row [row].shared1.degree - 1 ;</div>
<div class="line"><a name="l00844"></a><span class="lineno"> 844</span>  <span class="comment">/* guard against integer overflow */</span></div>
<div class="line"><a name="l00845"></a><span class="lineno"> 845</span>  score = COLAMD_MIN (score, n_col) ;</div>
<div class="line"><a name="l00846"></a><span class="lineno"> 846</span>  }</div>
<div class="line"><a name="l00847"></a><span class="lineno"> 847</span>  <span class="comment">/* determine pruned column length */</span></div>
<div class="line"><a name="l00848"></a><span class="lineno"> 848</span>  col_length = (Index) (new_cp - &A [Col [c].start]) ;</div>
<div class="line"><a name="l00849"></a><span class="lineno"> 849</span>  <span class="keywordflow">if</span> (col_length == 0)</div>
<div class="line"><a name="l00850"></a><span class="lineno"> 850</span>  {</div>
<div class="line"><a name="l00851"></a><span class="lineno"> 851</span>  <span class="comment">/* a newly-made null column (all rows in this col are "dense" */</span></div>
<div class="line"><a name="l00852"></a><span class="lineno"> 852</span>  <span class="comment">/* and have already been killed) */</span></div>
<div class="line"><a name="l00853"></a><span class="lineno"> 853</span>  COLAMD_DEBUG2 ((<span class="stringliteral">"Newly null killed: %d\n"</span>, c)) ;</div>
<div class="line"><a name="l00854"></a><span class="lineno"> 854</span>  Col [c].shared2.order = --n_col2 ;</div>
<div class="line"><a name="l00855"></a><span class="lineno"> 855</span>  KILL_PRINCIPAL_COL (c) ;</div>
<div class="line"><a name="l00856"></a><span class="lineno"> 856</span>  }</div>
<div class="line"><a name="l00857"></a><span class="lineno"> 857</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00858"></a><span class="lineno"> 858</span>  {</div>
<div class="line"><a name="l00859"></a><span class="lineno"> 859</span>  <span class="comment">/* set column length and set score */</span></div>
<div class="line"><a name="l00860"></a><span class="lineno"> 860</span>  COLAMD_ASSERT (score >= 0) ;</div>
<div class="line"><a name="l00861"></a><span class="lineno"> 861</span>  COLAMD_ASSERT (score <= n_col) ;</div>
<div class="line"><a name="l00862"></a><span class="lineno"> 862</span>  Col [c].length = col_length ;</div>
<div class="line"><a name="l00863"></a><span class="lineno"> 863</span>  Col [c].shared2.score = score ;</div>
<div class="line"><a name="l00864"></a><span class="lineno"> 864</span>  }</div>
<div class="line"><a name="l00865"></a><span class="lineno"> 865</span>  }</div>
<div class="line"><a name="l00866"></a><span class="lineno"> 866</span>  COLAMD_DEBUG1 ((<span class="stringliteral">"colamd: Dense, null, and newly-null columns killed: %d\n"</span>,</div>
<div class="line"><a name="l00867"></a><span class="lineno"> 867</span>  n_col-n_col2)) ;</div>
<div class="line"><a name="l00868"></a><span class="lineno"> 868</span> </div>
<div class="line"><a name="l00869"></a><span class="lineno"> 869</span>  <span class="comment">/* At this point, all empty rows and columns are dead. All live columns */</span></div>
<div class="line"><a name="l00870"></a><span class="lineno"> 870</span>  <span class="comment">/* are "clean" (containing no dead rows) and simplicial (no supercolumns */</span></div>
<div class="line"><a name="l00871"></a><span class="lineno"> 871</span>  <span class="comment">/* yet). Rows may contain dead columns, but all live rows contain at */</span></div>
<div class="line"><a name="l00872"></a><span class="lineno"> 872</span>  <span class="comment">/* least one live column. */</span></div>
<div class="line"><a name="l00873"></a><span class="lineno"> 873</span> </div>
<div class="line"><a name="l00874"></a><span class="lineno"> 874</span>  <span class="comment">/* === Initialize degree lists ========================================== */</span></div>
<div class="line"><a name="l00875"></a><span class="lineno"> 875</span> </div>
<div class="line"><a name="l00876"></a><span class="lineno"> 876</span> </div>
<div class="line"><a name="l00877"></a><span class="lineno"> 877</span>  <span class="comment">/* clear the hash buckets */</span></div>
<div class="line"><a name="l00878"></a><span class="lineno"> 878</span>  <span class="keywordflow">for</span> (c = 0 ; c <= n_col ; c++)</div>
<div class="line"><a name="l00879"></a><span class="lineno"> 879</span>  {</div>
<div class="line"><a name="l00880"></a><span class="lineno"> 880</span>  head [c] = COLAMD_EMPTY ;</div>
<div class="line"><a name="l00881"></a><span class="lineno"> 881</span>  }</div>
<div class="line"><a name="l00882"></a><span class="lineno"> 882</span>  min_score = n_col ;</div>
<div class="line"><a name="l00883"></a><span class="lineno"> 883</span>  <span class="comment">/* place in reverse order, so low column indices are at the front */</span></div>
<div class="line"><a name="l00884"></a><span class="lineno"> 884</span>  <span class="comment">/* of the lists. This is to encourage natural tie-breaking */</span></div>
<div class="line"><a name="l00885"></a><span class="lineno"> 885</span>  <span class="keywordflow">for</span> (c = n_col-1 ; c >= 0 ; c--)</div>
<div class="line"><a name="l00886"></a><span class="lineno"> 886</span>  {</div>
<div class="line"><a name="l00887"></a><span class="lineno"> 887</span>  <span class="comment">/* only add principal columns to degree lists */</span></div>
<div class="line"><a name="l00888"></a><span class="lineno"> 888</span>  <span class="keywordflow">if</span> (COL_IS_ALIVE (c))</div>
<div class="line"><a name="l00889"></a><span class="lineno"> 889</span>  {</div>
<div class="line"><a name="l00890"></a><span class="lineno"> 890</span>  COLAMD_DEBUG4 ((<span class="stringliteral">"place %d score %d minscore %d ncol %d\n"</span>,</div>
<div class="line"><a name="l00891"></a><span class="lineno"> 891</span>  c, Col [c].shared2.score, min_score, n_col)) ;</div>
<div class="line"><a name="l00892"></a><span class="lineno"> 892</span> </div>
<div class="line"><a name="l00893"></a><span class="lineno"> 893</span>  <span class="comment">/* === Add columns score to DList =============================== */</span></div>
<div class="line"><a name="l00894"></a><span class="lineno"> 894</span> </div>
<div class="line"><a name="l00895"></a><span class="lineno"> 895</span>  score = Col [c].shared2.score ;</div>
<div class="line"><a name="l00896"></a><span class="lineno"> 896</span> </div>
<div class="line"><a name="l00897"></a><span class="lineno"> 897</span>  COLAMD_ASSERT (min_score >= 0) ;</div>
<div class="line"><a name="l00898"></a><span class="lineno"> 898</span>  COLAMD_ASSERT (min_score <= n_col) ;</div>
<div class="line"><a name="l00899"></a><span class="lineno"> 899</span>  COLAMD_ASSERT (score >= 0) ;</div>
<div class="line"><a name="l00900"></a><span class="lineno"> 900</span>  COLAMD_ASSERT (score <= n_col) ;</div>
<div class="line"><a name="l00901"></a><span class="lineno"> 901</span>  COLAMD_ASSERT (head [score] >= COLAMD_EMPTY) ;</div>
<div class="line"><a name="l00902"></a><span class="lineno"> 902</span> </div>
<div class="line"><a name="l00903"></a><span class="lineno"> 903</span>  <span class="comment">/* now add this column to dList at proper score location */</span></div>
<div class="line"><a name="l00904"></a><span class="lineno"> 904</span>  next_col = head [score] ;</div>
<div class="line"><a name="l00905"></a><span class="lineno"> 905</span>  Col [c].shared3.prev = COLAMD_EMPTY ;</div>
<div class="line"><a name="l00906"></a><span class="lineno"> 906</span>  Col [c].shared4.degree_next = next_col ;</div>
<div class="line"><a name="l00907"></a><span class="lineno"> 907</span> </div>
<div class="line"><a name="l00908"></a><span class="lineno"> 908</span>  <span class="comment">/* if there already was a column with the same score, set its */</span></div>
<div class="line"><a name="l00909"></a><span class="lineno"> 909</span>  <span class="comment">/* previous pointer to this new column */</span></div>
<div class="line"><a name="l00910"></a><span class="lineno"> 910</span>  <span class="keywordflow">if</span> (next_col != COLAMD_EMPTY)</div>
<div class="line"><a name="l00911"></a><span class="lineno"> 911</span>  {</div>
<div class="line"><a name="l00912"></a><span class="lineno"> 912</span>  Col [next_col].shared3.prev = c ;</div>
<div class="line"><a name="l00913"></a><span class="lineno"> 913</span>  }</div>
<div class="line"><a name="l00914"></a><span class="lineno"> 914</span>  head [score] = c ;</div>
<div class="line"><a name="l00915"></a><span class="lineno"> 915</span> </div>
<div class="line"><a name="l00916"></a><span class="lineno"> 916</span>  <span class="comment">/* see if this score is less than current min */</span></div>
<div class="line"><a name="l00917"></a><span class="lineno"> 917</span>  min_score = COLAMD_MIN (min_score, score) ;</div>
<div class="line"><a name="l00918"></a><span class="lineno"> 918</span> </div>
<div class="line"><a name="l00919"></a><span class="lineno"> 919</span> </div>
<div class="line"><a name="l00920"></a><span class="lineno"> 920</span>  }</div>
<div class="line"><a name="l00921"></a><span class="lineno"> 921</span>  }</div>
<div class="line"><a name="l00922"></a><span class="lineno"> 922</span> </div>
<div class="line"><a name="l00923"></a><span class="lineno"> 923</span> </div>
<div class="line"><a name="l00924"></a><span class="lineno"> 924</span>  <span class="comment">/* === Return number of remaining columns, and max row degree =========== */</span></div>
<div class="line"><a name="l00925"></a><span class="lineno"> 925</span> </div>
<div class="line"><a name="l00926"></a><span class="lineno"> 926</span>  *p_n_col2 = n_col2 ;</div>
<div class="line"><a name="l00927"></a><span class="lineno"> 927</span>  *p_n_row2 = n_row2 ;</div>
<div class="line"><a name="l00928"></a><span class="lineno"> 928</span>  *p_max_deg = max_deg ;</div>
<div class="line"><a name="l00929"></a><span class="lineno"> 929</span> }</div>
<div class="line"><a name="l00930"></a><span class="lineno"> 930</span> </div>
<div class="line"><a name="l00931"></a><span class="lineno"> 931</span> </div>
<div class="line"><a name="l00932"></a><span class="lineno"> 932</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00933"></a><span class="lineno"> 933</span> <span class="comment">/* === find_ordering ======================================================== */</span></div>
<div class="line"><a name="l00934"></a><span class="lineno"> 934</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l00935"></a><span class="lineno"> 935</span> </div>
<div class="line"><a name="l00936"></a><span class="lineno"> 936</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00937"></a><span class="lineno"> 937</span> <span class="comment"> Order the principal columns of the supercolumn form of the matrix</span></div>
<div class="line"><a name="l00938"></a><span class="lineno"> 938</span> <span class="comment"> (no supercolumns on input). Uses a minimum approximate column minimum</span></div>
<div class="line"><a name="l00939"></a><span class="lineno"> 939</span> <span class="comment"> degree ordering method. Not user-callable.</span></div>
<div class="line"><a name="l00940"></a><span class="lineno"> 940</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00941"></a><span class="lineno"> 941</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00942"></a><span class="lineno"> 942</span> <span class="keyword">static</span> Index find_ordering <span class="comment">/* return the number of garbage collections */</span></div>
<div class="line"><a name="l00943"></a><span class="lineno"> 943</span>  (</div>
<div class="line"><a name="l00944"></a><span class="lineno"> 944</span>  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l00945"></a><span class="lineno"> 945</span> </div>
<div class="line"><a name="l00946"></a><span class="lineno"> 946</span>  Index n_row, <span class="comment">/* number of rows of A */</span></div>
<div class="line"><a name="l00947"></a><span class="lineno"> 947</span>  Index n_col, <span class="comment">/* number of columns of A */</span></div>
<div class="line"><a name="l00948"></a><span class="lineno"> 948</span>  Index Alen, <span class="comment">/* size of A, 2*nnz + n_col or larger */</span></div>
<div class="line"><a name="l00949"></a><span class="lineno"> 949</span>  Colamd_Row<Index> Row [], <span class="comment">/* of size n_row+1 */</span></div>
<div class="line"><a name="l00950"></a><span class="lineno"> 950</span>  colamd_col<Index> Col [], <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00951"></a><span class="lineno"> 951</span>  Index A [], <span class="comment">/* column form and row form of A */</span></div>
<div class="line"><a name="l00952"></a><span class="lineno"> 952</span>  Index head [], <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l00953"></a><span class="lineno"> 953</span>  Index n_col2, <span class="comment">/* Remaining columns to order */</span></div>
<div class="line"><a name="l00954"></a><span class="lineno"> 954</span>  Index max_deg, <span class="comment">/* Maximum row degree */</span></div>
<div class="line"><a name="l00955"></a><span class="lineno"> 955</span>  Index pfree <span class="comment">/* index of first free slot (2*nnz on entry) */</span></div>
<div class="line"><a name="l00956"></a><span class="lineno"> 956</span>  )</div>
<div class="line"><a name="l00957"></a><span class="lineno"> 957</span> {</div>
<div class="line"><a name="l00958"></a><span class="lineno"> 958</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l00959"></a><span class="lineno"> 959</span> </div>
<div class="line"><a name="l00960"></a><span class="lineno"> 960</span>  Index k ; <span class="comment">/* current pivot ordering step */</span></div>
<div class="line"><a name="l00961"></a><span class="lineno"> 961</span>  Index pivot_col ; <span class="comment">/* current pivot column */</span></div>
<div class="line"><a name="l00962"></a><span class="lineno"> 962</span>  Index *cp ; <span class="comment">/* a column pointer */</span></div>
<div class="line"><a name="l00963"></a><span class="lineno"> 963</span>  Index *rp ; <span class="comment">/* a row pointer */</span></div>
<div class="line"><a name="l00964"></a><span class="lineno"> 964</span>  Index pivot_row ; <span class="comment">/* current pivot row */</span></div>
<div class="line"><a name="l00965"></a><span class="lineno"> 965</span>  Index *new_cp ; <span class="comment">/* modified column pointer */</span></div>
<div class="line"><a name="l00966"></a><span class="lineno"> 966</span>  Index *new_rp ; <span class="comment">/* modified row pointer */</span></div>
<div class="line"><a name="l00967"></a><span class="lineno"> 967</span>  Index pivot_row_start ; <span class="comment">/* pointer to start of pivot row */</span></div>
<div class="line"><a name="l00968"></a><span class="lineno"> 968</span>  Index pivot_row_degree ; <span class="comment">/* number of columns in pivot row */</span></div>
<div class="line"><a name="l00969"></a><span class="lineno"> 969</span>  Index pivot_row_length ; <span class="comment">/* number of supercolumns in pivot row */</span></div>
<div class="line"><a name="l00970"></a><span class="lineno"> 970</span>  Index pivot_col_score ; <span class="comment">/* score of pivot column */</span></div>
<div class="line"><a name="l00971"></a><span class="lineno"> 971</span>  Index needed_memory ; <span class="comment">/* free space needed for pivot row */</span></div>
<div class="line"><a name="l00972"></a><span class="lineno"> 972</span>  Index *cp_end ; <span class="comment">/* pointer to the end of a column */</span></div>
<div class="line"><a name="l00973"></a><span class="lineno"> 973</span>  Index *rp_end ; <span class="comment">/* pointer to the end of a row */</span></div>
<div class="line"><a name="l00974"></a><span class="lineno"> 974</span>  Index row ; <span class="comment">/* a row index */</span></div>
<div class="line"><a name="l00975"></a><span class="lineno"> 975</span>  Index col ; <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l00976"></a><span class="lineno"> 976</span>  Index max_score ; <span class="comment">/* maximum possible score */</span></div>
<div class="line"><a name="l00977"></a><span class="lineno"> 977</span>  Index cur_score ; <span class="comment">/* score of current column */</span></div>
<div class="line"><a name="l00978"></a><span class="lineno"> 978</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> hash ; <span class="comment">/* hash value for supernode detection */</span></div>
<div class="line"><a name="l00979"></a><span class="lineno"> 979</span>  Index head_column ; <span class="comment">/* head of hash bucket */</span></div>
<div class="line"><a name="l00980"></a><span class="lineno"> 980</span>  Index first_col ; <span class="comment">/* first column in hash bucket */</span></div>
<div class="line"><a name="l00981"></a><span class="lineno"> 981</span>  Index tag_mark ; <span class="comment">/* marker value for mark array */</span></div>
<div class="line"><a name="l00982"></a><span class="lineno"> 982</span>  Index row_mark ; <span class="comment">/* Row [row].shared2.mark */</span></div>
<div class="line"><a name="l00983"></a><span class="lineno"> 983</span>  Index set_difference ; <span class="comment">/* set difference size of row with pivot row */</span></div>
<div class="line"><a name="l00984"></a><span class="lineno"> 984</span>  Index min_score ; <span class="comment">/* smallest column score */</span></div>
<div class="line"><a name="l00985"></a><span class="lineno"> 985</span>  Index col_thickness ; <span class="comment">/* "thickness" (no. of columns in a supercol) */</span></div>
<div class="line"><a name="l00986"></a><span class="lineno"> 986</span>  Index max_mark ; <span class="comment">/* maximum value of tag_mark */</span></div>
<div class="line"><a name="l00987"></a><span class="lineno"> 987</span>  Index pivot_col_thickness ; <span class="comment">/* number of columns represented by pivot col */</span></div>
<div class="line"><a name="l00988"></a><span class="lineno"> 988</span>  Index prev_col ; <span class="comment">/* Used by Dlist operations. */</span></div>
<div class="line"><a name="l00989"></a><span class="lineno"> 989</span>  Index next_col ; <span class="comment">/* Used by Dlist operations. */</span></div>
<div class="line"><a name="l00990"></a><span class="lineno"> 990</span>  Index ngarbage ; <span class="comment">/* number of garbage collections performed */</span></div>
<div class="line"><a name="l00991"></a><span class="lineno"> 991</span> </div>
<div class="line"><a name="l00992"></a><span class="lineno"> 992</span> </div>
<div class="line"><a name="l00993"></a><span class="lineno"> 993</span>  <span class="comment">/* === Initialization and clear mark ==================================== */</span></div>
<div class="line"><a name="l00994"></a><span class="lineno"> 994</span> </div>
<div class="line"><a name="l00995"></a><span class="lineno"> 995</span>  max_mark = INT_MAX - n_col ; <span class="comment">/* INT_MAX defined in <limits.h> */</span></div>
<div class="line"><a name="l00996"></a><span class="lineno"> 996</span>  tag_mark = Eigen::internal::clear_mark (n_row, Row) ;</div>
<div class="line"><a name="l00997"></a><span class="lineno"> 997</span>  min_score = 0 ;</div>
<div class="line"><a name="l00998"></a><span class="lineno"> 998</span>  ngarbage = 0 ;</div>
<div class="line"><a name="l00999"></a><span class="lineno"> 999</span>  COLAMD_DEBUG1 ((<span class="stringliteral">"colamd: Ordering, n_col2=%d\n"</span>, n_col2)) ;</div>
<div class="line"><a name="l01000"></a><span class="lineno"> 1000</span> </div>
<div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>  <span class="comment">/* === Order the columns ================================================ */</span></div>
<div class="line"><a name="l01002"></a><span class="lineno"> 1002</span> </div>
<div class="line"><a name="l01003"></a><span class="lineno"> 1003</span>  <span class="keywordflow">for</span> (k = 0 ; k < n_col2 ; <span class="comment">/* 'k' is incremented below */</span>)</div>
<div class="line"><a name="l01004"></a><span class="lineno"> 1004</span>  {</div>
<div class="line"><a name="l01005"></a><span class="lineno"> 1005</span> </div>
<div class="line"><a name="l01006"></a><span class="lineno"> 1006</span>  <span class="comment">/* === Select pivot column, and order it ============================ */</span></div>
<div class="line"><a name="l01007"></a><span class="lineno"> 1007</span> </div>
<div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>  <span class="comment">/* make sure degree list isn't empty */</span></div>
<div class="line"><a name="l01009"></a><span class="lineno"> 1009</span>  COLAMD_ASSERT (min_score >= 0) ;</div>
<div class="line"><a name="l01010"></a><span class="lineno"> 1010</span>  COLAMD_ASSERT (min_score <= n_col) ;</div>
<div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>  COLAMD_ASSERT (head [min_score] >= COLAMD_EMPTY) ;</div>
<div class="line"><a name="l01012"></a><span class="lineno"> 1012</span> </div>
<div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>  <span class="comment">/* get pivot column from head of minimum degree list */</span></div>
<div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>  <span class="keywordflow">while</span> (head [min_score] == COLAMD_EMPTY && min_score < n_col)</div>
<div class="line"><a name="l01015"></a><span class="lineno"> 1015</span>  {</div>
<div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>  min_score++ ;</div>
<div class="line"><a name="l01017"></a><span class="lineno"> 1017</span>  }</div>
<div class="line"><a name="l01018"></a><span class="lineno"> 1018</span>  pivot_col = head [min_score] ;</div>
<div class="line"><a name="l01019"></a><span class="lineno"> 1019</span>  COLAMD_ASSERT (pivot_col >= 0 && pivot_col <= n_col) ;</div>
<div class="line"><a name="l01020"></a><span class="lineno"> 1020</span>  next_col = Col [pivot_col].shared4.degree_next ;</div>
<div class="line"><a name="l01021"></a><span class="lineno"> 1021</span>  head [min_score] = next_col ;</div>
<div class="line"><a name="l01022"></a><span class="lineno"> 1022</span>  <span class="keywordflow">if</span> (next_col != COLAMD_EMPTY)</div>
<div class="line"><a name="l01023"></a><span class="lineno"> 1023</span>  {</div>
<div class="line"><a name="l01024"></a><span class="lineno"> 1024</span>  Col [next_col].shared3.prev = COLAMD_EMPTY ;</div>
<div class="line"><a name="l01025"></a><span class="lineno"> 1025</span>  }</div>
<div class="line"><a name="l01026"></a><span class="lineno"> 1026</span> </div>
<div class="line"><a name="l01027"></a><span class="lineno"> 1027</span>  COLAMD_ASSERT (COL_IS_ALIVE (pivot_col)) ;</div>
<div class="line"><a name="l01028"></a><span class="lineno"> 1028</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"Pivot col: %d\n"</span>, pivot_col)) ;</div>
<div class="line"><a name="l01029"></a><span class="lineno"> 1029</span> </div>
<div class="line"><a name="l01030"></a><span class="lineno"> 1030</span>  <span class="comment">/* remember score for defrag check */</span></div>
<div class="line"><a name="l01031"></a><span class="lineno"> 1031</span>  pivot_col_score = Col [pivot_col].shared2.score ;</div>
<div class="line"><a name="l01032"></a><span class="lineno"> 1032</span> </div>
<div class="line"><a name="l01033"></a><span class="lineno"> 1033</span>  <span class="comment">/* the pivot column is the kth column in the pivot order */</span></div>
<div class="line"><a name="l01034"></a><span class="lineno"> 1034</span>  Col [pivot_col].shared2.order = k ;</div>
<div class="line"><a name="l01035"></a><span class="lineno"> 1035</span> </div>
<div class="line"><a name="l01036"></a><span class="lineno"> 1036</span>  <span class="comment">/* increment order count by column thickness */</span></div>
<div class="line"><a name="l01037"></a><span class="lineno"> 1037</span>  pivot_col_thickness = Col [pivot_col].shared1.thickness ;</div>
<div class="line"><a name="l01038"></a><span class="lineno"> 1038</span>  k += pivot_col_thickness ;</div>
<div class="line"><a name="l01039"></a><span class="lineno"> 1039</span>  COLAMD_ASSERT (pivot_col_thickness > 0) ;</div>
<div class="line"><a name="l01040"></a><span class="lineno"> 1040</span> </div>
<div class="line"><a name="l01041"></a><span class="lineno"> 1041</span>  <span class="comment">/* === Garbage_collection, if necessary ============================= */</span></div>
<div class="line"><a name="l01042"></a><span class="lineno"> 1042</span> </div>
<div class="line"><a name="l01043"></a><span class="lineno"> 1043</span>  needed_memory = COLAMD_MIN (pivot_col_score, n_col - k) ;</div>
<div class="line"><a name="l01044"></a><span class="lineno"> 1044</span>  <span class="keywordflow">if</span> (pfree + needed_memory >= Alen)</div>
<div class="line"><a name="l01045"></a><span class="lineno"> 1045</span>  {</div>
<div class="line"><a name="l01046"></a><span class="lineno"> 1046</span>  pfree = Eigen::internal::garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ;</div>
<div class="line"><a name="l01047"></a><span class="lineno"> 1047</span>  ngarbage++ ;</div>
<div class="line"><a name="l01048"></a><span class="lineno"> 1048</span>  <span class="comment">/* after garbage collection we will have enough */</span></div>
<div class="line"><a name="l01049"></a><span class="lineno"> 1049</span>  COLAMD_ASSERT (pfree + needed_memory < Alen) ;</div>
<div class="line"><a name="l01050"></a><span class="lineno"> 1050</span>  <span class="comment">/* garbage collection has wiped out the Row[].shared2.mark array */</span></div>
<div class="line"><a name="l01051"></a><span class="lineno"> 1051</span>  tag_mark = Eigen::internal::clear_mark (n_row, Row) ;</div>
<div class="line"><a name="l01052"></a><span class="lineno"> 1052</span> </div>
<div class="line"><a name="l01053"></a><span class="lineno"> 1053</span>  }</div>
<div class="line"><a name="l01054"></a><span class="lineno"> 1054</span> </div>
<div class="line"><a name="l01055"></a><span class="lineno"> 1055</span>  <span class="comment">/* === Compute pivot row pattern ==================================== */</span></div>
<div class="line"><a name="l01056"></a><span class="lineno"> 1056</span> </div>
<div class="line"><a name="l01057"></a><span class="lineno"> 1057</span>  <span class="comment">/* get starting location for this new merged row */</span></div>
<div class="line"><a name="l01058"></a><span class="lineno"> 1058</span>  pivot_row_start = pfree ;</div>
<div class="line"><a name="l01059"></a><span class="lineno"> 1059</span> </div>
<div class="line"><a name="l01060"></a><span class="lineno"> 1060</span>  <span class="comment">/* initialize new row counts to zero */</span></div>
<div class="line"><a name="l01061"></a><span class="lineno"> 1061</span>  pivot_row_degree = 0 ;</div>
<div class="line"><a name="l01062"></a><span class="lineno"> 1062</span> </div>
<div class="line"><a name="l01063"></a><span class="lineno"> 1063</span>  <span class="comment">/* tag pivot column as having been visited so it isn't included */</span></div>
<div class="line"><a name="l01064"></a><span class="lineno"> 1064</span>  <span class="comment">/* in merged pivot row */</span></div>
<div class="line"><a name="l01065"></a><span class="lineno"> 1065</span>  Col [pivot_col].shared1.thickness = -pivot_col_thickness ;</div>
<div class="line"><a name="l01066"></a><span class="lineno"> 1066</span> </div>
<div class="line"><a name="l01067"></a><span class="lineno"> 1067</span>  <span class="comment">/* pivot row is the union of all rows in the pivot column pattern */</span></div>
<div class="line"><a name="l01068"></a><span class="lineno"> 1068</span>  cp = &A [Col [pivot_col].start] ;</div>
<div class="line"><a name="l01069"></a><span class="lineno"> 1069</span>  cp_end = cp + Col [pivot_col].length ;</div>
<div class="line"><a name="l01070"></a><span class="lineno"> 1070</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l01071"></a><span class="lineno"> 1071</span>  {</div>
<div class="line"><a name="l01072"></a><span class="lineno"> 1072</span>  <span class="comment">/* get a row */</span></div>
<div class="line"><a name="l01073"></a><span class="lineno"> 1073</span>  row = *cp++ ;</div>
<div class="line"><a name="l01074"></a><span class="lineno"> 1074</span>  COLAMD_DEBUG4 ((<span class="stringliteral">"Pivot col pattern %d %d\n"</span>, ROW_IS_ALIVE (row), row)) ;</div>
<div class="line"><a name="l01075"></a><span class="lineno"> 1075</span>  <span class="comment">/* skip if row is dead */</span></div>
<div class="line"><a name="l01076"></a><span class="lineno"> 1076</span>  <span class="keywordflow">if</span> (ROW_IS_DEAD (row))</div>
<div class="line"><a name="l01077"></a><span class="lineno"> 1077</span>  {</div>
<div class="line"><a name="l01078"></a><span class="lineno"> 1078</span>  continue ;</div>
<div class="line"><a name="l01079"></a><span class="lineno"> 1079</span>  }</div>
<div class="line"><a name="l01080"></a><span class="lineno"> 1080</span>  rp = &A [Row [row].start] ;</div>
<div class="line"><a name="l01081"></a><span class="lineno"> 1081</span>  rp_end = rp + Row [row].length ;</div>
<div class="line"><a name="l01082"></a><span class="lineno"> 1082</span>  <span class="keywordflow">while</span> (rp < rp_end)</div>
<div class="line"><a name="l01083"></a><span class="lineno"> 1083</span>  {</div>
<div class="line"><a name="l01084"></a><span class="lineno"> 1084</span>  <span class="comment">/* get a column */</span></div>
<div class="line"><a name="l01085"></a><span class="lineno"> 1085</span>  col = *rp++ ;</div>
<div class="line"><a name="l01086"></a><span class="lineno"> 1086</span>  <span class="comment">/* add the column, if alive and untagged */</span></div>
<div class="line"><a name="l01087"></a><span class="lineno"> 1087</span>  col_thickness = Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01088"></a><span class="lineno"> 1088</span>  <span class="keywordflow">if</span> (col_thickness > 0 && COL_IS_ALIVE (col))</div>
<div class="line"><a name="l01089"></a><span class="lineno"> 1089</span>  {</div>
<div class="line"><a name="l01090"></a><span class="lineno"> 1090</span>  <span class="comment">/* tag column in pivot row */</span></div>
<div class="line"><a name="l01091"></a><span class="lineno"> 1091</span>  Col [col].shared1.thickness = -col_thickness ;</div>
<div class="line"><a name="l01092"></a><span class="lineno"> 1092</span>  COLAMD_ASSERT (pfree < Alen) ;</div>
<div class="line"><a name="l01093"></a><span class="lineno"> 1093</span>  <span class="comment">/* place column in pivot row */</span></div>
<div class="line"><a name="l01094"></a><span class="lineno"> 1094</span>  A [pfree++] = col ;</div>
<div class="line"><a name="l01095"></a><span class="lineno"> 1095</span>  pivot_row_degree += col_thickness ;</div>
<div class="line"><a name="l01096"></a><span class="lineno"> 1096</span>  }</div>
<div class="line"><a name="l01097"></a><span class="lineno"> 1097</span>  }</div>
<div class="line"><a name="l01098"></a><span class="lineno"> 1098</span>  }</div>
<div class="line"><a name="l01099"></a><span class="lineno"> 1099</span> </div>
<div class="line"><a name="l01100"></a><span class="lineno"> 1100</span>  <span class="comment">/* clear tag on pivot column */</span></div>
<div class="line"><a name="l01101"></a><span class="lineno"> 1101</span>  Col [pivot_col].shared1.thickness = pivot_col_thickness ;</div>
<div class="line"><a name="l01102"></a><span class="lineno"> 1102</span>  max_deg = COLAMD_MAX (max_deg, pivot_row_degree) ;</div>
<div class="line"><a name="l01103"></a><span class="lineno"> 1103</span> </div>
<div class="line"><a name="l01104"></a><span class="lineno"> 1104</span> </div>
<div class="line"><a name="l01105"></a><span class="lineno"> 1105</span>  <span class="comment">/* === Kill all rows used to construct pivot row ==================== */</span></div>
<div class="line"><a name="l01106"></a><span class="lineno"> 1106</span> </div>
<div class="line"><a name="l01107"></a><span class="lineno"> 1107</span>  <span class="comment">/* also kill pivot row, temporarily */</span></div>
<div class="line"><a name="l01108"></a><span class="lineno"> 1108</span>  cp = &A [Col [pivot_col].start] ;</div>
<div class="line"><a name="l01109"></a><span class="lineno"> 1109</span>  cp_end = cp + Col [pivot_col].length ;</div>
<div class="line"><a name="l01110"></a><span class="lineno"> 1110</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l01111"></a><span class="lineno"> 1111</span>  {</div>
<div class="line"><a name="l01112"></a><span class="lineno"> 1112</span>  <span class="comment">/* may be killing an already dead row */</span></div>
<div class="line"><a name="l01113"></a><span class="lineno"> 1113</span>  row = *cp++ ;</div>
<div class="line"><a name="l01114"></a><span class="lineno"> 1114</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"Kill row in pivot col: %d\n"</span>, row)) ;</div>
<div class="line"><a name="l01115"></a><span class="lineno"> 1115</span>  KILL_ROW (row) ;</div>
<div class="line"><a name="l01116"></a><span class="lineno"> 1116</span>  }</div>
<div class="line"><a name="l01117"></a><span class="lineno"> 1117</span> </div>
<div class="line"><a name="l01118"></a><span class="lineno"> 1118</span>  <span class="comment">/* === Select a row index to use as the new pivot row =============== */</span></div>
<div class="line"><a name="l01119"></a><span class="lineno"> 1119</span> </div>
<div class="line"><a name="l01120"></a><span class="lineno"> 1120</span>  pivot_row_length = pfree - pivot_row_start ;</div>
<div class="line"><a name="l01121"></a><span class="lineno"> 1121</span>  <span class="keywordflow">if</span> (pivot_row_length > 0)</div>
<div class="line"><a name="l01122"></a><span class="lineno"> 1122</span>  {</div>
<div class="line"><a name="l01123"></a><span class="lineno"> 1123</span>  <span class="comment">/* pick the "pivot" row arbitrarily (first row in col) */</span></div>
<div class="line"><a name="l01124"></a><span class="lineno"> 1124</span>  pivot_row = A [Col [pivot_col].start] ;</div>
<div class="line"><a name="l01125"></a><span class="lineno"> 1125</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"Pivotal row is %d\n"</span>, pivot_row)) ;</div>
<div class="line"><a name="l01126"></a><span class="lineno"> 1126</span>  }</div>
<div class="line"><a name="l01127"></a><span class="lineno"> 1127</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l01128"></a><span class="lineno"> 1128</span>  {</div>
<div class="line"><a name="l01129"></a><span class="lineno"> 1129</span>  <span class="comment">/* there is no pivot row, since it is of zero length */</span></div>
<div class="line"><a name="l01130"></a><span class="lineno"> 1130</span>  pivot_row = COLAMD_EMPTY ;</div>
<div class="line"><a name="l01131"></a><span class="lineno"> 1131</span>  COLAMD_ASSERT (pivot_row_length == 0) ;</div>
<div class="line"><a name="l01132"></a><span class="lineno"> 1132</span>  }</div>
<div class="line"><a name="l01133"></a><span class="lineno"> 1133</span>  COLAMD_ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ;</div>
<div class="line"><a name="l01134"></a><span class="lineno"> 1134</span> </div>
<div class="line"><a name="l01135"></a><span class="lineno"> 1135</span>  <span class="comment">/* === Approximate degree computation =============================== */</span></div>
<div class="line"><a name="l01136"></a><span class="lineno"> 1136</span> </div>
<div class="line"><a name="l01137"></a><span class="lineno"> 1137</span>  <span class="comment">/* Here begins the computation of the approximate degree. The column */</span></div>
<div class="line"><a name="l01138"></a><span class="lineno"> 1138</span>  <span class="comment">/* score is the sum of the pivot row "length", plus the size of the */</span></div>
<div class="line"><a name="l01139"></a><span class="lineno"> 1139</span>  <span class="comment">/* set differences of each row in the column minus the pattern of the */</span></div>
<div class="line"><a name="l01140"></a><span class="lineno"> 1140</span>  <span class="comment">/* pivot row itself. The column ("thickness") itself is also */</span></div>
<div class="line"><a name="l01141"></a><span class="lineno"> 1141</span>  <span class="comment">/* excluded from the column score (we thus use an approximate */</span></div>
<div class="line"><a name="l01142"></a><span class="lineno"> 1142</span>  <span class="comment">/* external degree). */</span></div>
<div class="line"><a name="l01143"></a><span class="lineno"> 1143</span> </div>
<div class="line"><a name="l01144"></a><span class="lineno"> 1144</span>  <span class="comment">/* The time taken by the following code (compute set differences, and */</span></div>
<div class="line"><a name="l01145"></a><span class="lineno"> 1145</span>  <span class="comment">/* add them up) is proportional to the size of the data structure */</span></div>
<div class="line"><a name="l01146"></a><span class="lineno"> 1146</span>  <span class="comment">/* being scanned - that is, the sum of the sizes of each column in */</span></div>
<div class="line"><a name="l01147"></a><span class="lineno"> 1147</span>  <span class="comment">/* the pivot row. Thus, the amortized time to compute a column score */</span></div>
<div class="line"><a name="l01148"></a><span class="lineno"> 1148</span>  <span class="comment">/* is proportional to the size of that column (where size, in this */</span></div>
<div class="line"><a name="l01149"></a><span class="lineno"> 1149</span>  <span class="comment">/* context, is the column "length", or the number of row indices */</span></div>
<div class="line"><a name="l01150"></a><span class="lineno"> 1150</span>  <span class="comment">/* in that column). The number of row indices in a column is */</span></div>
<div class="line"><a name="l01151"></a><span class="lineno"> 1151</span>  <span class="comment">/* monotonically non-decreasing, from the length of the original */</span></div>
<div class="line"><a name="l01152"></a><span class="lineno"> 1152</span>  <span class="comment">/* column on input to colamd. */</span></div>
<div class="line"><a name="l01153"></a><span class="lineno"> 1153</span> </div>
<div class="line"><a name="l01154"></a><span class="lineno"> 1154</span>  <span class="comment">/* === Compute set differences ====================================== */</span></div>
<div class="line"><a name="l01155"></a><span class="lineno"> 1155</span> </div>
<div class="line"><a name="l01156"></a><span class="lineno"> 1156</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"** Computing set differences phase. **\n"</span>)) ;</div>
<div class="line"><a name="l01157"></a><span class="lineno"> 1157</span> </div>
<div class="line"><a name="l01158"></a><span class="lineno"> 1158</span>  <span class="comment">/* pivot row is currently dead - it will be revived later. */</span></div>
<div class="line"><a name="l01159"></a><span class="lineno"> 1159</span> </div>
<div class="line"><a name="l01160"></a><span class="lineno"> 1160</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"Pivot row: "</span>)) ;</div>
<div class="line"><a name="l01161"></a><span class="lineno"> 1161</span>  <span class="comment">/* for each column in pivot row */</span></div>
<div class="line"><a name="l01162"></a><span class="lineno"> 1162</span>  rp = &A [pivot_row_start] ;</div>
<div class="line"><a name="l01163"></a><span class="lineno"> 1163</span>  rp_end = rp + pivot_row_length ;</div>
<div class="line"><a name="l01164"></a><span class="lineno"> 1164</span>  <span class="keywordflow">while</span> (rp < rp_end)</div>
<div class="line"><a name="l01165"></a><span class="lineno"> 1165</span>  {</div>
<div class="line"><a name="l01166"></a><span class="lineno"> 1166</span>  col = *rp++ ;</div>
<div class="line"><a name="l01167"></a><span class="lineno"> 1167</span>  COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;</div>
<div class="line"><a name="l01168"></a><span class="lineno"> 1168</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"Col: %d\n"</span>, col)) ;</div>
<div class="line"><a name="l01169"></a><span class="lineno"> 1169</span> </div>
<div class="line"><a name="l01170"></a><span class="lineno"> 1170</span>  <span class="comment">/* clear tags used to construct pivot row pattern */</span></div>
<div class="line"><a name="l01171"></a><span class="lineno"> 1171</span>  col_thickness = -Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01172"></a><span class="lineno"> 1172</span>  COLAMD_ASSERT (col_thickness > 0) ;</div>
<div class="line"><a name="l01173"></a><span class="lineno"> 1173</span>  Col [col].shared1.thickness = col_thickness ;</div>
<div class="line"><a name="l01174"></a><span class="lineno"> 1174</span> </div>
<div class="line"><a name="l01175"></a><span class="lineno"> 1175</span>  <span class="comment">/* === Remove column from degree list =========================== */</span></div>
<div class="line"><a name="l01176"></a><span class="lineno"> 1176</span> </div>
<div class="line"><a name="l01177"></a><span class="lineno"> 1177</span>  cur_score = Col [col].shared2.score ;</div>
<div class="line"><a name="l01178"></a><span class="lineno"> 1178</span>  prev_col = Col [col].shared3.prev ;</div>
<div class="line"><a name="l01179"></a><span class="lineno"> 1179</span>  next_col = Col [col].shared4.degree_next ;</div>
<div class="line"><a name="l01180"></a><span class="lineno"> 1180</span>  COLAMD_ASSERT (cur_score >= 0) ;</div>
<div class="line"><a name="l01181"></a><span class="lineno"> 1181</span>  COLAMD_ASSERT (cur_score <= n_col) ;</div>
<div class="line"><a name="l01182"></a><span class="lineno"> 1182</span>  COLAMD_ASSERT (cur_score >= COLAMD_EMPTY) ;</div>
<div class="line"><a name="l01183"></a><span class="lineno"> 1183</span>  <span class="keywordflow">if</span> (prev_col == COLAMD_EMPTY)</div>
<div class="line"><a name="l01184"></a><span class="lineno"> 1184</span>  {</div>
<div class="line"><a name="l01185"></a><span class="lineno"> 1185</span>  head [cur_score] = next_col ;</div>
<div class="line"><a name="l01186"></a><span class="lineno"> 1186</span>  }</div>
<div class="line"><a name="l01187"></a><span class="lineno"> 1187</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l01188"></a><span class="lineno"> 1188</span>  {</div>
<div class="line"><a name="l01189"></a><span class="lineno"> 1189</span>  Col [prev_col].shared4.degree_next = next_col ;</div>
<div class="line"><a name="l01190"></a><span class="lineno"> 1190</span>  }</div>
<div class="line"><a name="l01191"></a><span class="lineno"> 1191</span>  <span class="keywordflow">if</span> (next_col != COLAMD_EMPTY)</div>
<div class="line"><a name="l01192"></a><span class="lineno"> 1192</span>  {</div>
<div class="line"><a name="l01193"></a><span class="lineno"> 1193</span>  Col [next_col].shared3.prev = prev_col ;</div>
<div class="line"><a name="l01194"></a><span class="lineno"> 1194</span>  }</div>
<div class="line"><a name="l01195"></a><span class="lineno"> 1195</span> </div>
<div class="line"><a name="l01196"></a><span class="lineno"> 1196</span>  <span class="comment">/* === Scan the column ========================================== */</span></div>
<div class="line"><a name="l01197"></a><span class="lineno"> 1197</span> </div>
<div class="line"><a name="l01198"></a><span class="lineno"> 1198</span>  cp = &A [Col [col].start] ;</div>
<div class="line"><a name="l01199"></a><span class="lineno"> 1199</span>  cp_end = cp + Col [col].length ;</div>
<div class="line"><a name="l01200"></a><span class="lineno"> 1200</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l01201"></a><span class="lineno"> 1201</span>  {</div>
<div class="line"><a name="l01202"></a><span class="lineno"> 1202</span>  <span class="comment">/* get a row */</span></div>
<div class="line"><a name="l01203"></a><span class="lineno"> 1203</span>  row = *cp++ ;</div>
<div class="line"><a name="l01204"></a><span class="lineno"> 1204</span>  row_mark = Row [row].shared2.mark ;</div>
<div class="line"><a name="l01205"></a><span class="lineno"> 1205</span>  <span class="comment">/* skip if dead */</span></div>
<div class="line"><a name="l01206"></a><span class="lineno"> 1206</span>  <span class="keywordflow">if</span> (ROW_IS_MARKED_DEAD (row_mark))</div>
<div class="line"><a name="l01207"></a><span class="lineno"> 1207</span>  {</div>
<div class="line"><a name="l01208"></a><span class="lineno"> 1208</span>  continue ;</div>
<div class="line"><a name="l01209"></a><span class="lineno"> 1209</span>  }</div>
<div class="line"><a name="l01210"></a><span class="lineno"> 1210</span>  COLAMD_ASSERT (row != pivot_row) ;</div>
<div class="line"><a name="l01211"></a><span class="lineno"> 1211</span>  set_difference = row_mark - tag_mark ;</div>
<div class="line"><a name="l01212"></a><span class="lineno"> 1212</span>  <span class="comment">/* check if the row has been seen yet */</span></div>
<div class="line"><a name="l01213"></a><span class="lineno"> 1213</span>  <span class="keywordflow">if</span> (set_difference < 0)</div>
<div class="line"><a name="l01214"></a><span class="lineno"> 1214</span>  {</div>
<div class="line"><a name="l01215"></a><span class="lineno"> 1215</span>  COLAMD_ASSERT (Row [row].shared1.degree <= max_deg) ;</div>
<div class="line"><a name="l01216"></a><span class="lineno"> 1216</span>  set_difference = Row [row].shared1.degree ;</div>
<div class="line"><a name="l01217"></a><span class="lineno"> 1217</span>  }</div>
<div class="line"><a name="l01218"></a><span class="lineno"> 1218</span>  <span class="comment">/* subtract column thickness from this row's set difference */</span></div>
<div class="line"><a name="l01219"></a><span class="lineno"> 1219</span>  set_difference -= col_thickness ;</div>
<div class="line"><a name="l01220"></a><span class="lineno"> 1220</span>  COLAMD_ASSERT (set_difference >= 0) ;</div>
<div class="line"><a name="l01221"></a><span class="lineno"> 1221</span>  <span class="comment">/* absorb this row if the set difference becomes zero */</span></div>
<div class="line"><a name="l01222"></a><span class="lineno"> 1222</span>  <span class="keywordflow">if</span> (set_difference == 0)</div>
<div class="line"><a name="l01223"></a><span class="lineno"> 1223</span>  {</div>
<div class="line"><a name="l01224"></a><span class="lineno"> 1224</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"aggressive absorption. Row: %d\n"</span>, row)) ;</div>
<div class="line"><a name="l01225"></a><span class="lineno"> 1225</span>  KILL_ROW (row) ;</div>
<div class="line"><a name="l01226"></a><span class="lineno"> 1226</span>  }</div>
<div class="line"><a name="l01227"></a><span class="lineno"> 1227</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l01228"></a><span class="lineno"> 1228</span>  {</div>
<div class="line"><a name="l01229"></a><span class="lineno"> 1229</span>  <span class="comment">/* save the new mark */</span></div>
<div class="line"><a name="l01230"></a><span class="lineno"> 1230</span>  Row [row].shared2.mark = set_difference + tag_mark ;</div>
<div class="line"><a name="l01231"></a><span class="lineno"> 1231</span>  }</div>
<div class="line"><a name="l01232"></a><span class="lineno"> 1232</span>  }</div>
<div class="line"><a name="l01233"></a><span class="lineno"> 1233</span>  }</div>
<div class="line"><a name="l01234"></a><span class="lineno"> 1234</span> </div>
<div class="line"><a name="l01235"></a><span class="lineno"> 1235</span> </div>
<div class="line"><a name="l01236"></a><span class="lineno"> 1236</span>  <span class="comment">/* === Add up set differences for each column ======================= */</span></div>
<div class="line"><a name="l01237"></a><span class="lineno"> 1237</span> </div>
<div class="line"><a name="l01238"></a><span class="lineno"> 1238</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"** Adding set differences phase. **\n"</span>)) ;</div>
<div class="line"><a name="l01239"></a><span class="lineno"> 1239</span> </div>
<div class="line"><a name="l01240"></a><span class="lineno"> 1240</span>  <span class="comment">/* for each column in pivot row */</span></div>
<div class="line"><a name="l01241"></a><span class="lineno"> 1241</span>  rp = &A [pivot_row_start] ;</div>
<div class="line"><a name="l01242"></a><span class="lineno"> 1242</span>  rp_end = rp + pivot_row_length ;</div>
<div class="line"><a name="l01243"></a><span class="lineno"> 1243</span>  <span class="keywordflow">while</span> (rp < rp_end)</div>
<div class="line"><a name="l01244"></a><span class="lineno"> 1244</span>  {</div>
<div class="line"><a name="l01245"></a><span class="lineno"> 1245</span>  <span class="comment">/* get a column */</span></div>
<div class="line"><a name="l01246"></a><span class="lineno"> 1246</span>  col = *rp++ ;</div>
<div class="line"><a name="l01247"></a><span class="lineno"> 1247</span>  COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ;</div>
<div class="line"><a name="l01248"></a><span class="lineno"> 1248</span>  hash = 0 ;</div>
<div class="line"><a name="l01249"></a><span class="lineno"> 1249</span>  cur_score = 0 ;</div>
<div class="line"><a name="l01250"></a><span class="lineno"> 1250</span>  cp = &A [Col [col].start] ;</div>
<div class="line"><a name="l01251"></a><span class="lineno"> 1251</span>  <span class="comment">/* compact the column */</span></div>
<div class="line"><a name="l01252"></a><span class="lineno"> 1252</span>  new_cp = cp ;</div>
<div class="line"><a name="l01253"></a><span class="lineno"> 1253</span>  cp_end = cp + Col [col].length ;</div>
<div class="line"><a name="l01254"></a><span class="lineno"> 1254</span> </div>
<div class="line"><a name="l01255"></a><span class="lineno"> 1255</span>  COLAMD_DEBUG4 ((<span class="stringliteral">"Adding set diffs for Col: %d.\n"</span>, col)) ;</div>
<div class="line"><a name="l01256"></a><span class="lineno"> 1256</span> </div>
<div class="line"><a name="l01257"></a><span class="lineno"> 1257</span>  <span class="keywordflow">while</span> (cp < cp_end)</div>
<div class="line"><a name="l01258"></a><span class="lineno"> 1258</span>  {</div>
<div class="line"><a name="l01259"></a><span class="lineno"> 1259</span>  <span class="comment">/* get a row */</span></div>
<div class="line"><a name="l01260"></a><span class="lineno"> 1260</span>  row = *cp++ ;</div>
<div class="line"><a name="l01261"></a><span class="lineno"> 1261</span>  COLAMD_ASSERT(row >= 0 && row < n_row) ;</div>
<div class="line"><a name="l01262"></a><span class="lineno"> 1262</span>  row_mark = Row [row].shared2.mark ;</div>
<div class="line"><a name="l01263"></a><span class="lineno"> 1263</span>  <span class="comment">/* skip if dead */</span></div>
<div class="line"><a name="l01264"></a><span class="lineno"> 1264</span>  <span class="keywordflow">if</span> (ROW_IS_MARKED_DEAD (row_mark))</div>
<div class="line"><a name="l01265"></a><span class="lineno"> 1265</span>  {</div>
<div class="line"><a name="l01266"></a><span class="lineno"> 1266</span>  continue ;</div>
<div class="line"><a name="l01267"></a><span class="lineno"> 1267</span>  }</div>
<div class="line"><a name="l01268"></a><span class="lineno"> 1268</span>  COLAMD_ASSERT (row_mark > tag_mark) ;</div>
<div class="line"><a name="l01269"></a><span class="lineno"> 1269</span>  <span class="comment">/* compact the column */</span></div>
<div class="line"><a name="l01270"></a><span class="lineno"> 1270</span>  *new_cp++ = row ;</div>
<div class="line"><a name="l01271"></a><span class="lineno"> 1271</span>  <span class="comment">/* compute hash function */</span></div>
<div class="line"><a name="l01272"></a><span class="lineno"> 1272</span>  hash += row ;</div>
<div class="line"><a name="l01273"></a><span class="lineno"> 1273</span>  <span class="comment">/* add set difference */</span></div>
<div class="line"><a name="l01274"></a><span class="lineno"> 1274</span>  cur_score += row_mark - tag_mark ;</div>
<div class="line"><a name="l01275"></a><span class="lineno"> 1275</span>  <span class="comment">/* integer overflow... */</span></div>
<div class="line"><a name="l01276"></a><span class="lineno"> 1276</span>  cur_score = COLAMD_MIN (cur_score, n_col) ;</div>
<div class="line"><a name="l01277"></a><span class="lineno"> 1277</span>  }</div>
<div class="line"><a name="l01278"></a><span class="lineno"> 1278</span> </div>
<div class="line"><a name="l01279"></a><span class="lineno"> 1279</span>  <span class="comment">/* recompute the column's length */</span></div>
<div class="line"><a name="l01280"></a><span class="lineno"> 1280</span>  Col [col].length = (Index) (new_cp - &A [Col [col].start]) ;</div>
<div class="line"><a name="l01281"></a><span class="lineno"> 1281</span> </div>
<div class="line"><a name="l01282"></a><span class="lineno"> 1282</span>  <span class="comment">/* === Further mass elimination ================================= */</span></div>
<div class="line"><a name="l01283"></a><span class="lineno"> 1283</span> </div>
<div class="line"><a name="l01284"></a><span class="lineno"> 1284</span>  <span class="keywordflow">if</span> (Col [col].length == 0)</div>
<div class="line"><a name="l01285"></a><span class="lineno"> 1285</span>  {</div>
<div class="line"><a name="l01286"></a><span class="lineno"> 1286</span>  COLAMD_DEBUG4 ((<span class="stringliteral">"further mass elimination. Col: %d\n"</span>, col)) ;</div>
<div class="line"><a name="l01287"></a><span class="lineno"> 1287</span>  <span class="comment">/* nothing left but the pivot row in this column */</span></div>
<div class="line"><a name="l01288"></a><span class="lineno"> 1288</span>  KILL_PRINCIPAL_COL (col) ;</div>
<div class="line"><a name="l01289"></a><span class="lineno"> 1289</span>  pivot_row_degree -= Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01290"></a><span class="lineno"> 1290</span>  COLAMD_ASSERT (pivot_row_degree >= 0) ;</div>
<div class="line"><a name="l01291"></a><span class="lineno"> 1291</span>  <span class="comment">/* order it */</span></div>
<div class="line"><a name="l01292"></a><span class="lineno"> 1292</span>  Col [col].shared2.order = k ;</div>
<div class="line"><a name="l01293"></a><span class="lineno"> 1293</span>  <span class="comment">/* increment order count by column thickness */</span></div>
<div class="line"><a name="l01294"></a><span class="lineno"> 1294</span>  k += Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01295"></a><span class="lineno"> 1295</span>  }</div>
<div class="line"><a name="l01296"></a><span class="lineno"> 1296</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l01297"></a><span class="lineno"> 1297</span>  {</div>
<div class="line"><a name="l01298"></a><span class="lineno"> 1298</span>  <span class="comment">/* === Prepare for supercolumn detection ==================== */</span></div>
<div class="line"><a name="l01299"></a><span class="lineno"> 1299</span> </div>
<div class="line"><a name="l01300"></a><span class="lineno"> 1300</span>  COLAMD_DEBUG4 ((<span class="stringliteral">"Preparing supercol detection for Col: %d.\n"</span>, col)) ;</div>
<div class="line"><a name="l01301"></a><span class="lineno"> 1301</span> </div>
<div class="line"><a name="l01302"></a><span class="lineno"> 1302</span>  <span class="comment">/* save score so far */</span></div>
<div class="line"><a name="l01303"></a><span class="lineno"> 1303</span>  Col [col].shared2.score = cur_score ;</div>
<div class="line"><a name="l01304"></a><span class="lineno"> 1304</span> </div>
<div class="line"><a name="l01305"></a><span class="lineno"> 1305</span>  <span class="comment">/* add column to hash table, for supercolumn detection */</span></div>
<div class="line"><a name="l01306"></a><span class="lineno"> 1306</span>  hash %= n_col + 1 ;</div>
<div class="line"><a name="l01307"></a><span class="lineno"> 1307</span> </div>
<div class="line"><a name="l01308"></a><span class="lineno"> 1308</span>  COLAMD_DEBUG4 ((<span class="stringliteral">" Hash = %d, n_col = %d.\n"</span>, hash, n_col)) ;</div>
<div class="line"><a name="l01309"></a><span class="lineno"> 1309</span>  COLAMD_ASSERT (hash <= n_col) ;</div>
<div class="line"><a name="l01310"></a><span class="lineno"> 1310</span> </div>
<div class="line"><a name="l01311"></a><span class="lineno"> 1311</span>  head_column = head [hash] ;</div>
<div class="line"><a name="l01312"></a><span class="lineno"> 1312</span>  <span class="keywordflow">if</span> (head_column > COLAMD_EMPTY)</div>
<div class="line"><a name="l01313"></a><span class="lineno"> 1313</span>  {</div>
<div class="line"><a name="l01314"></a><span class="lineno"> 1314</span>  <span class="comment">/* degree list "hash" is non-empty, use prev (shared3) of */</span></div>
<div class="line"><a name="l01315"></a><span class="lineno"> 1315</span>  <span class="comment">/* first column in degree list as head of hash bucket */</span></div>
<div class="line"><a name="l01316"></a><span class="lineno"> 1316</span>  first_col = Col [head_column].shared3.headhash ;</div>
<div class="line"><a name="l01317"></a><span class="lineno"> 1317</span>  Col [head_column].shared3.headhash = col ;</div>
<div class="line"><a name="l01318"></a><span class="lineno"> 1318</span>  }</div>
<div class="line"><a name="l01319"></a><span class="lineno"> 1319</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l01320"></a><span class="lineno"> 1320</span>  {</div>
<div class="line"><a name="l01321"></a><span class="lineno"> 1321</span>  <span class="comment">/* degree list "hash" is empty, use head as hash bucket */</span></div>
<div class="line"><a name="l01322"></a><span class="lineno"> 1322</span>  first_col = - (head_column + 2) ;</div>
<div class="line"><a name="l01323"></a><span class="lineno"> 1323</span>  head [hash] = - (col + 2) ;</div>
<div class="line"><a name="l01324"></a><span class="lineno"> 1324</span>  }</div>
<div class="line"><a name="l01325"></a><span class="lineno"> 1325</span>  Col [col].shared4.hash_next = first_col ;</div>
<div class="line"><a name="l01326"></a><span class="lineno"> 1326</span> </div>
<div class="line"><a name="l01327"></a><span class="lineno"> 1327</span>  <span class="comment">/* save hash function in Col [col].shared3.hash */</span></div>
<div class="line"><a name="l01328"></a><span class="lineno"> 1328</span>  Col [col].shared3.hash = (Index) hash ;</div>
<div class="line"><a name="l01329"></a><span class="lineno"> 1329</span>  COLAMD_ASSERT (COL_IS_ALIVE (col)) ;</div>
<div class="line"><a name="l01330"></a><span class="lineno"> 1330</span>  }</div>
<div class="line"><a name="l01331"></a><span class="lineno"> 1331</span>  }</div>
<div class="line"><a name="l01332"></a><span class="lineno"> 1332</span> </div>
<div class="line"><a name="l01333"></a><span class="lineno"> 1333</span>  <span class="comment">/* The approximate external column degree is now computed. */</span></div>
<div class="line"><a name="l01334"></a><span class="lineno"> 1334</span> </div>
<div class="line"><a name="l01335"></a><span class="lineno"> 1335</span>  <span class="comment">/* === Supercolumn detection ======================================== */</span></div>
<div class="line"><a name="l01336"></a><span class="lineno"> 1336</span> </div>
<div class="line"><a name="l01337"></a><span class="lineno"> 1337</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"** Supercolumn detection phase. **\n"</span>)) ;</div>
<div class="line"><a name="l01338"></a><span class="lineno"> 1338</span> </div>
<div class="line"><a name="l01339"></a><span class="lineno"> 1339</span>  Eigen::internal::detect_super_cols (Col, A, head, pivot_row_start, pivot_row_length) ;</div>
<div class="line"><a name="l01340"></a><span class="lineno"> 1340</span> </div>
<div class="line"><a name="l01341"></a><span class="lineno"> 1341</span>  <span class="comment">/* === Kill the pivotal column ====================================== */</span></div>
<div class="line"><a name="l01342"></a><span class="lineno"> 1342</span> </div>
<div class="line"><a name="l01343"></a><span class="lineno"> 1343</span>  KILL_PRINCIPAL_COL (pivot_col) ;</div>
<div class="line"><a name="l01344"></a><span class="lineno"> 1344</span> </div>
<div class="line"><a name="l01345"></a><span class="lineno"> 1345</span>  <span class="comment">/* === Clear mark =================================================== */</span></div>
<div class="line"><a name="l01346"></a><span class="lineno"> 1346</span> </div>
<div class="line"><a name="l01347"></a><span class="lineno"> 1347</span>  tag_mark += (max_deg + 1) ;</div>
<div class="line"><a name="l01348"></a><span class="lineno"> 1348</span>  <span class="keywordflow">if</span> (tag_mark >= max_mark)</div>
<div class="line"><a name="l01349"></a><span class="lineno"> 1349</span>  {</div>
<div class="line"><a name="l01350"></a><span class="lineno"> 1350</span>  COLAMD_DEBUG2 ((<span class="stringliteral">"clearing tag_mark\n"</span>)) ;</div>
<div class="line"><a name="l01351"></a><span class="lineno"> 1351</span>  tag_mark = Eigen::internal::clear_mark (n_row, Row) ;</div>
<div class="line"><a name="l01352"></a><span class="lineno"> 1352</span>  }</div>
<div class="line"><a name="l01353"></a><span class="lineno"> 1353</span> </div>
<div class="line"><a name="l01354"></a><span class="lineno"> 1354</span>  <span class="comment">/* === Finalize the new pivot row, and column scores ================ */</span></div>
<div class="line"><a name="l01355"></a><span class="lineno"> 1355</span> </div>
<div class="line"><a name="l01356"></a><span class="lineno"> 1356</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"** Finalize scores phase. **\n"</span>)) ;</div>
<div class="line"><a name="l01357"></a><span class="lineno"> 1357</span> </div>
<div class="line"><a name="l01358"></a><span class="lineno"> 1358</span>  <span class="comment">/* for each column in pivot row */</span></div>
<div class="line"><a name="l01359"></a><span class="lineno"> 1359</span>  rp = &A [pivot_row_start] ;</div>
<div class="line"><a name="l01360"></a><span class="lineno"> 1360</span>  <span class="comment">/* compact the pivot row */</span></div>
<div class="line"><a name="l01361"></a><span class="lineno"> 1361</span>  new_rp = rp ;</div>
<div class="line"><a name="l01362"></a><span class="lineno"> 1362</span>  rp_end = rp + pivot_row_length ;</div>
<div class="line"><a name="l01363"></a><span class="lineno"> 1363</span>  <span class="keywordflow">while</span> (rp < rp_end)</div>
<div class="line"><a name="l01364"></a><span class="lineno"> 1364</span>  {</div>
<div class="line"><a name="l01365"></a><span class="lineno"> 1365</span>  col = *rp++ ;</div>
<div class="line"><a name="l01366"></a><span class="lineno"> 1366</span>  <span class="comment">/* skip dead columns */</span></div>
<div class="line"><a name="l01367"></a><span class="lineno"> 1367</span>  <span class="keywordflow">if</span> (COL_IS_DEAD (col))</div>
<div class="line"><a name="l01368"></a><span class="lineno"> 1368</span>  {</div>
<div class="line"><a name="l01369"></a><span class="lineno"> 1369</span>  continue ;</div>
<div class="line"><a name="l01370"></a><span class="lineno"> 1370</span>  }</div>
<div class="line"><a name="l01371"></a><span class="lineno"> 1371</span>  *new_rp++ = col ;</div>
<div class="line"><a name="l01372"></a><span class="lineno"> 1372</span>  <span class="comment">/* add new pivot row to column */</span></div>
<div class="line"><a name="l01373"></a><span class="lineno"> 1373</span>  A [Col [col].start + (Col [col].length++)] = pivot_row ;</div>
<div class="line"><a name="l01374"></a><span class="lineno"> 1374</span> </div>
<div class="line"><a name="l01375"></a><span class="lineno"> 1375</span>  <span class="comment">/* retrieve score so far and add on pivot row's degree. */</span></div>
<div class="line"><a name="l01376"></a><span class="lineno"> 1376</span>  <span class="comment">/* (we wait until here for this in case the pivot */</span></div>
<div class="line"><a name="l01377"></a><span class="lineno"> 1377</span>  <span class="comment">/* row's degree was reduced due to mass elimination). */</span></div>
<div class="line"><a name="l01378"></a><span class="lineno"> 1378</span>  cur_score = Col [col].shared2.score + pivot_row_degree ;</div>
<div class="line"><a name="l01379"></a><span class="lineno"> 1379</span> </div>
<div class="line"><a name="l01380"></a><span class="lineno"> 1380</span>  <span class="comment">/* calculate the max possible score as the number of */</span></div>
<div class="line"><a name="l01381"></a><span class="lineno"> 1381</span>  <span class="comment">/* external columns minus the 'k' value minus the */</span></div>
<div class="line"><a name="l01382"></a><span class="lineno"> 1382</span>  <span class="comment">/* columns thickness */</span></div>
<div class="line"><a name="l01383"></a><span class="lineno"> 1383</span>  max_score = n_col - k - Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01384"></a><span class="lineno"> 1384</span> </div>
<div class="line"><a name="l01385"></a><span class="lineno"> 1385</span>  <span class="comment">/* make the score the external degree of the union-of-rows */</span></div>
<div class="line"><a name="l01386"></a><span class="lineno"> 1386</span>  cur_score -= Col [col].shared1.thickness ;</div>
<div class="line"><a name="l01387"></a><span class="lineno"> 1387</span> </div>
<div class="line"><a name="l01388"></a><span class="lineno"> 1388</span>  <span class="comment">/* make sure score is less or equal than the max score */</span></div>
<div class="line"><a name="l01389"></a><span class="lineno"> 1389</span>  cur_score = COLAMD_MIN (cur_score, max_score) ;</div>
<div class="line"><a name="l01390"></a><span class="lineno"> 1390</span>  COLAMD_ASSERT (cur_score >= 0) ;</div>
<div class="line"><a name="l01391"></a><span class="lineno"> 1391</span> </div>
<div class="line"><a name="l01392"></a><span class="lineno"> 1392</span>  <span class="comment">/* store updated score */</span></div>
<div class="line"><a name="l01393"></a><span class="lineno"> 1393</span>  Col [col].shared2.score = cur_score ;</div>
<div class="line"><a name="l01394"></a><span class="lineno"> 1394</span> </div>
<div class="line"><a name="l01395"></a><span class="lineno"> 1395</span>  <span class="comment">/* === Place column back in degree list ========================= */</span></div>
<div class="line"><a name="l01396"></a><span class="lineno"> 1396</span> </div>
<div class="line"><a name="l01397"></a><span class="lineno"> 1397</span>  COLAMD_ASSERT (min_score >= 0) ;</div>
<div class="line"><a name="l01398"></a><span class="lineno"> 1398</span>  COLAMD_ASSERT (min_score <= n_col) ;</div>
<div class="line"><a name="l01399"></a><span class="lineno"> 1399</span>  COLAMD_ASSERT (cur_score >= 0) ;</div>
<div class="line"><a name="l01400"></a><span class="lineno"> 1400</span>  COLAMD_ASSERT (cur_score <= n_col) ;</div>
<div class="line"><a name="l01401"></a><span class="lineno"> 1401</span>  COLAMD_ASSERT (head [cur_score] >= COLAMD_EMPTY) ;</div>
<div class="line"><a name="l01402"></a><span class="lineno"> 1402</span>  next_col = head [cur_score] ;</div>
<div class="line"><a name="l01403"></a><span class="lineno"> 1403</span>  Col [col].shared4.degree_next = next_col ;</div>
<div class="line"><a name="l01404"></a><span class="lineno"> 1404</span>  Col [col].shared3.prev = COLAMD_EMPTY ;</div>
<div class="line"><a name="l01405"></a><span class="lineno"> 1405</span>  <span class="keywordflow">if</span> (next_col != COLAMD_EMPTY)</div>
<div class="line"><a name="l01406"></a><span class="lineno"> 1406</span>  {</div>
<div class="line"><a name="l01407"></a><span class="lineno"> 1407</span>  Col [next_col].shared3.prev = col ;</div>
<div class="line"><a name="l01408"></a><span class="lineno"> 1408</span>  }</div>
<div class="line"><a name="l01409"></a><span class="lineno"> 1409</span>  head [cur_score] = col ;</div>
<div class="line"><a name="l01410"></a><span class="lineno"> 1410</span> </div>
<div class="line"><a name="l01411"></a><span class="lineno"> 1411</span>  <span class="comment">/* see if this score is less than current min */</span></div>
<div class="line"><a name="l01412"></a><span class="lineno"> 1412</span>  min_score = COLAMD_MIN (min_score, cur_score) ;</div>
<div class="line"><a name="l01413"></a><span class="lineno"> 1413</span> </div>
<div class="line"><a name="l01414"></a><span class="lineno"> 1414</span>  }</div>
<div class="line"><a name="l01415"></a><span class="lineno"> 1415</span> </div>
<div class="line"><a name="l01416"></a><span class="lineno"> 1416</span>  <span class="comment">/* === Resurrect the new pivot row ================================== */</span></div>
<div class="line"><a name="l01417"></a><span class="lineno"> 1417</span> </div>
<div class="line"><a name="l01418"></a><span class="lineno"> 1418</span>  <span class="keywordflow">if</span> (pivot_row_degree > 0)</div>
<div class="line"><a name="l01419"></a><span class="lineno"> 1419</span>  {</div>
<div class="line"><a name="l01420"></a><span class="lineno"> 1420</span>  <span class="comment">/* update pivot row length to reflect any cols that were killed */</span></div>
<div class="line"><a name="l01421"></a><span class="lineno"> 1421</span>  <span class="comment">/* during super-col detection and mass elimination */</span></div>
<div class="line"><a name="l01422"></a><span class="lineno"> 1422</span>  Row [pivot_row].start = pivot_row_start ;</div>
<div class="line"><a name="l01423"></a><span class="lineno"> 1423</span>  Row [pivot_row].length = (Index) (new_rp - &A[pivot_row_start]) ;</div>
<div class="line"><a name="l01424"></a><span class="lineno"> 1424</span>  Row [pivot_row].shared1.degree = pivot_row_degree ;</div>
<div class="line"><a name="l01425"></a><span class="lineno"> 1425</span>  Row [pivot_row].shared2.mark = 0 ;</div>
<div class="line"><a name="l01426"></a><span class="lineno"> 1426</span>  <span class="comment">/* pivot row is no longer dead */</span></div>
<div class="line"><a name="l01427"></a><span class="lineno"> 1427</span>  }</div>
<div class="line"><a name="l01428"></a><span class="lineno"> 1428</span>  }</div>
<div class="line"><a name="l01429"></a><span class="lineno"> 1429</span> </div>
<div class="line"><a name="l01430"></a><span class="lineno"> 1430</span>  <span class="comment">/* === All principal columns have now been ordered ====================== */</span></div>
<div class="line"><a name="l01431"></a><span class="lineno"> 1431</span> </div>
<div class="line"><a name="l01432"></a><span class="lineno"> 1432</span>  <span class="keywordflow">return</span> (ngarbage) ;</div>
<div class="line"><a name="l01433"></a><span class="lineno"> 1433</span> }</div>
<div class="line"><a name="l01434"></a><span class="lineno"> 1434</span> </div>
<div class="line"><a name="l01435"></a><span class="lineno"> 1435</span> </div>
<div class="line"><a name="l01436"></a><span class="lineno"> 1436</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01437"></a><span class="lineno"> 1437</span> <span class="comment">/* === order_children ======================================================= */</span></div>
<div class="line"><a name="l01438"></a><span class="lineno"> 1438</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01439"></a><span class="lineno"> 1439</span> </div>
<div class="line"><a name="l01440"></a><span class="lineno"> 1440</span> <span class="comment">/*</span></div>
<div class="line"><a name="l01441"></a><span class="lineno"> 1441</span> <span class="comment"> The find_ordering routine has ordered all of the principal columns (the</span></div>
<div class="line"><a name="l01442"></a><span class="lineno"> 1442</span> <span class="comment"> representatives of the supercolumns). The non-principal columns have not</span></div>
<div class="line"><a name="l01443"></a><span class="lineno"> 1443</span> <span class="comment"> yet been ordered. This routine orders those columns by walking up the</span></div>
<div class="line"><a name="l01444"></a><span class="lineno"> 1444</span> <span class="comment"> parent tree (a column is a child of the column which absorbed it). The</span></div>
<div class="line"><a name="l01445"></a><span class="lineno"> 1445</span> <span class="comment"> final permutation vector is then placed in p [0 ... n_col-1], with p [0]</span></div>
<div class="line"><a name="l01446"></a><span class="lineno"> 1446</span> <span class="comment"> being the first column, and p [n_col-1] being the last. It doesn't look</span></div>
<div class="line"><a name="l01447"></a><span class="lineno"> 1447</span> <span class="comment"> like it at first glance, but be assured that this routine takes time linear</span></div>
<div class="line"><a name="l01448"></a><span class="lineno"> 1448</span> <span class="comment"> in the number of columns. Although not immediately obvious, the time</span></div>
<div class="line"><a name="l01449"></a><span class="lineno"> 1449</span> <span class="comment"> taken by this routine is O (n_col), that is, linear in the number of</span></div>
<div class="line"><a name="l01450"></a><span class="lineno"> 1450</span> <span class="comment"> columns. Not user-callable.</span></div>
<div class="line"><a name="l01451"></a><span class="lineno"> 1451</span> <span class="comment">*/</span></div>
<div class="line"><a name="l01452"></a><span class="lineno"> 1452</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l01453"></a><span class="lineno"> 1453</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">void</span> order_children</div>
<div class="line"><a name="l01454"></a><span class="lineno"> 1454</span> (</div>
<div class="line"><a name="l01455"></a><span class="lineno"> 1455</span>  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l01456"></a><span class="lineno"> 1456</span> </div>
<div class="line"><a name="l01457"></a><span class="lineno"> 1457</span>  Index n_col, <span class="comment">/* number of columns of A */</span></div>
<div class="line"><a name="l01458"></a><span class="lineno"> 1458</span>  colamd_col<Index> Col [], <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l01459"></a><span class="lineno"> 1459</span>  Index p [] <span class="comment">/* p [0 ... n_col-1] is the column permutation*/</span></div>
<div class="line"><a name="l01460"></a><span class="lineno"> 1460</span>  )</div>
<div class="line"><a name="l01461"></a><span class="lineno"> 1461</span> {</div>
<div class="line"><a name="l01462"></a><span class="lineno"> 1462</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l01463"></a><span class="lineno"> 1463</span> </div>
<div class="line"><a name="l01464"></a><span class="lineno"> 1464</span>  Index i ; <span class="comment">/* loop counter for all columns */</span></div>
<div class="line"><a name="l01465"></a><span class="lineno"> 1465</span>  Index c ; <span class="comment">/* column index */</span></div>
<div class="line"><a name="l01466"></a><span class="lineno"> 1466</span>  Index parent ; <span class="comment">/* index of column's parent */</span></div>
<div class="line"><a name="l01467"></a><span class="lineno"> 1467</span>  Index order ; <span class="comment">/* column's order */</span></div>
<div class="line"><a name="l01468"></a><span class="lineno"> 1468</span> </div>
<div class="line"><a name="l01469"></a><span class="lineno"> 1469</span>  <span class="comment">/* === Order each non-principal column ================================== */</span></div>
<div class="line"><a name="l01470"></a><span class="lineno"> 1470</span> </div>
<div class="line"><a name="l01471"></a><span class="lineno"> 1471</span>  <span class="keywordflow">for</span> (i = 0 ; i < n_col ; i++)</div>
<div class="line"><a name="l01472"></a><span class="lineno"> 1472</span>  {</div>
<div class="line"><a name="l01473"></a><span class="lineno"> 1473</span>  <span class="comment">/* find an un-ordered non-principal column */</span></div>
<div class="line"><a name="l01474"></a><span class="lineno"> 1474</span>  COLAMD_ASSERT (COL_IS_DEAD (i)) ;</div>
<div class="line"><a name="l01475"></a><span class="lineno"> 1475</span>  <span class="keywordflow">if</span> (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == COLAMD_EMPTY)</div>
<div class="line"><a name="l01476"></a><span class="lineno"> 1476</span>  {</div>
<div class="line"><a name="l01477"></a><span class="lineno"> 1477</span>  parent = i ;</div>
<div class="line"><a name="l01478"></a><span class="lineno"> 1478</span>  <span class="comment">/* once found, find its principal parent */</span></div>
<div class="line"><a name="l01479"></a><span class="lineno"> 1479</span>  <span class="keywordflow">do</span></div>
<div class="line"><a name="l01480"></a><span class="lineno"> 1480</span>  {</div>
<div class="line"><a name="l01481"></a><span class="lineno"> 1481</span>  parent = Col [parent].shared1.parent ;</div>
<div class="line"><a name="l01482"></a><span class="lineno"> 1482</span>  } <span class="keywordflow">while</span> (!COL_IS_DEAD_PRINCIPAL (parent)) ;</div>
<div class="line"><a name="l01483"></a><span class="lineno"> 1483</span> </div>
<div class="line"><a name="l01484"></a><span class="lineno"> 1484</span>  <span class="comment">/* now, order all un-ordered non-principal columns along path */</span></div>
<div class="line"><a name="l01485"></a><span class="lineno"> 1485</span>  <span class="comment">/* to this parent. collapse tree at the same time */</span></div>
<div class="line"><a name="l01486"></a><span class="lineno"> 1486</span>  c = i ;</div>
<div class="line"><a name="l01487"></a><span class="lineno"> 1487</span>  <span class="comment">/* get order of parent */</span></div>
<div class="line"><a name="l01488"></a><span class="lineno"> 1488</span>  order = Col [parent].shared2.order ;</div>
<div class="line"><a name="l01489"></a><span class="lineno"> 1489</span> </div>
<div class="line"><a name="l01490"></a><span class="lineno"> 1490</span>  <span class="keywordflow">do</span></div>
<div class="line"><a name="l01491"></a><span class="lineno"> 1491</span>  {</div>
<div class="line"><a name="l01492"></a><span class="lineno"> 1492</span>  COLAMD_ASSERT (Col [c].shared2.order == COLAMD_EMPTY) ;</div>
<div class="line"><a name="l01493"></a><span class="lineno"> 1493</span> </div>
<div class="line"><a name="l01494"></a><span class="lineno"> 1494</span>  <span class="comment">/* order this column */</span></div>
<div class="line"><a name="l01495"></a><span class="lineno"> 1495</span>  Col [c].shared2.order = order++ ;</div>
<div class="line"><a name="l01496"></a><span class="lineno"> 1496</span>  <span class="comment">/* collaps tree */</span></div>
<div class="line"><a name="l01497"></a><span class="lineno"> 1497</span>  Col [c].shared1.parent = parent ;</div>
<div class="line"><a name="l01498"></a><span class="lineno"> 1498</span> </div>
<div class="line"><a name="l01499"></a><span class="lineno"> 1499</span>  <span class="comment">/* get immediate parent of this column */</span></div>
<div class="line"><a name="l01500"></a><span class="lineno"> 1500</span>  c = Col [c].shared1.parent ;</div>
<div class="line"><a name="l01501"></a><span class="lineno"> 1501</span> </div>
<div class="line"><a name="l01502"></a><span class="lineno"> 1502</span>  <span class="comment">/* continue until we hit an ordered column. There are */</span></div>
<div class="line"><a name="l01503"></a><span class="lineno"> 1503</span>  <span class="comment">/* guarranteed not to be anymore unordered columns */</span></div>
<div class="line"><a name="l01504"></a><span class="lineno"> 1504</span>  <span class="comment">/* above an ordered column */</span></div>
<div class="line"><a name="l01505"></a><span class="lineno"> 1505</span>  } <span class="keywordflow">while</span> (Col [c].shared2.order == COLAMD_EMPTY) ;</div>
<div class="line"><a name="l01506"></a><span class="lineno"> 1506</span> </div>
<div class="line"><a name="l01507"></a><span class="lineno"> 1507</span>  <span class="comment">/* re-order the super_col parent to largest order for this group */</span></div>
<div class="line"><a name="l01508"></a><span class="lineno"> 1508</span>  Col [parent].shared2.order = order ;</div>
<div class="line"><a name="l01509"></a><span class="lineno"> 1509</span>  }</div>
<div class="line"><a name="l01510"></a><span class="lineno"> 1510</span>  }</div>
<div class="line"><a name="l01511"></a><span class="lineno"> 1511</span> </div>
<div class="line"><a name="l01512"></a><span class="lineno"> 1512</span>  <span class="comment">/* === Generate the permutation ========================================= */</span></div>
<div class="line"><a name="l01513"></a><span class="lineno"> 1513</span> </div>
<div class="line"><a name="l01514"></a><span class="lineno"> 1514</span>  <span class="keywordflow">for</span> (c = 0 ; c < n_col ; c++)</div>
<div class="line"><a name="l01515"></a><span class="lineno"> 1515</span>  {</div>
<div class="line"><a name="l01516"></a><span class="lineno"> 1516</span>  p [Col [c].shared2.order] = c ;</div>
<div class="line"><a name="l01517"></a><span class="lineno"> 1517</span>  }</div>
<div class="line"><a name="l01518"></a><span class="lineno"> 1518</span> }</div>
<div class="line"><a name="l01519"></a><span class="lineno"> 1519</span> </div>
<div class="line"><a name="l01520"></a><span class="lineno"> 1520</span> </div>
<div class="line"><a name="l01521"></a><span class="lineno"> 1521</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01522"></a><span class="lineno"> 1522</span> <span class="comment">/* === detect_super_cols ==================================================== */</span></div>
<div class="line"><a name="l01523"></a><span class="lineno"> 1523</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01524"></a><span class="lineno"> 1524</span> </div>
<div class="line"><a name="l01525"></a><span class="lineno"> 1525</span> <span class="comment">/*</span></div>
<div class="line"><a name="l01526"></a><span class="lineno"> 1526</span> <span class="comment"> Detects supercolumns by finding matches between columns in the hash buckets.</span></div>
<div class="line"><a name="l01527"></a><span class="lineno"> 1527</span> <span class="comment"> Check amongst columns in the set A [row_start ... row_start + row_length-1].</span></div>
<div class="line"><a name="l01528"></a><span class="lineno"> 1528</span> <span class="comment"> The columns under consideration are currently *not* in the degree lists,</span></div>
<div class="line"><a name="l01529"></a><span class="lineno"> 1529</span> <span class="comment"> and have already been placed in the hash buckets.</span></div>
<div class="line"><a name="l01530"></a><span class="lineno"> 1530</span> <span class="comment"></span></div>
<div class="line"><a name="l01531"></a><span class="lineno"> 1531</span> <span class="comment"> The hash bucket for columns whose hash function is equal to h is stored</span></div>
<div class="line"><a name="l01532"></a><span class="lineno"> 1532</span> <span class="comment"> as follows:</span></div>
<div class="line"><a name="l01533"></a><span class="lineno"> 1533</span> <span class="comment"></span></div>
<div class="line"><a name="l01534"></a><span class="lineno"> 1534</span> <span class="comment"> if head [h] is >= 0, then head [h] contains a degree list, so:</span></div>
<div class="line"><a name="l01535"></a><span class="lineno"> 1535</span> <span class="comment"></span></div>
<div class="line"><a name="l01536"></a><span class="lineno"> 1536</span> <span class="comment"> head [h] is the first column in degree bucket h.</span></div>
<div class="line"><a name="l01537"></a><span class="lineno"> 1537</span> <span class="comment"> Col [head [h]].headhash gives the first column in hash bucket h.</span></div>
<div class="line"><a name="l01538"></a><span class="lineno"> 1538</span> <span class="comment"></span></div>
<div class="line"><a name="l01539"></a><span class="lineno"> 1539</span> <span class="comment"> otherwise, the degree list is empty, and:</span></div>
<div class="line"><a name="l01540"></a><span class="lineno"> 1540</span> <span class="comment"></span></div>
<div class="line"><a name="l01541"></a><span class="lineno"> 1541</span> <span class="comment"> -(head [h] + 2) is the first column in hash bucket h.</span></div>
<div class="line"><a name="l01542"></a><span class="lineno"> 1542</span> <span class="comment"></span></div>
<div class="line"><a name="l01543"></a><span class="lineno"> 1543</span> <span class="comment"> For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous</span></div>
<div class="line"><a name="l01544"></a><span class="lineno"> 1544</span> <span class="comment"> column" pointer. Col [c].shared3.hash is used instead as the hash number</span></div>
<div class="line"><a name="l01545"></a><span class="lineno"> 1545</span> <span class="comment"> for that column. The value of Col [c].shared4.hash_next is the next column</span></div>
<div class="line"><a name="l01546"></a><span class="lineno"> 1546</span> <span class="comment"> in the same hash bucket.</span></div>
<div class="line"><a name="l01547"></a><span class="lineno"> 1547</span> <span class="comment"></span></div>
<div class="line"><a name="l01548"></a><span class="lineno"> 1548</span> <span class="comment"> Assuming no, or "few" hash collisions, the time taken by this routine is</span></div>
<div class="line"><a name="l01549"></a><span class="lineno"> 1549</span> <span class="comment"> linear in the sum of the sizes (lengths) of each column whose score has</span></div>
<div class="line"><a name="l01550"></a><span class="lineno"> 1550</span> <span class="comment"> just been computed in the approximate degree computation.</span></div>
<div class="line"><a name="l01551"></a><span class="lineno"> 1551</span> <span class="comment"> Not user-callable.</span></div>
<div class="line"><a name="l01552"></a><span class="lineno"> 1552</span> <span class="comment">*/</span></div>
<div class="line"><a name="l01553"></a><span class="lineno"> 1553</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l01554"></a><span class="lineno"> 1554</span> <span class="keyword">static</span> <span class="keywordtype">void</span> detect_super_cols</div>
<div class="line"><a name="l01555"></a><span class="lineno"> 1555</span> (</div>
<div class="line"><a name="l01556"></a><span class="lineno"> 1556</span>  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l01557"></a><span class="lineno"> 1557</span>  </div>
<div class="line"><a name="l01558"></a><span class="lineno"> 1558</span>  colamd_col<Index> Col [], <span class="comment">/* of size n_col+1 */</span></div>
<div class="line"><a name="l01559"></a><span class="lineno"> 1559</span>  Index A [], <span class="comment">/* row indices of A */</span></div>
<div class="line"><a name="l01560"></a><span class="lineno"> 1560</span>  Index head [], <span class="comment">/* head of degree lists and hash buckets */</span></div>
<div class="line"><a name="l01561"></a><span class="lineno"> 1561</span>  Index row_start, <span class="comment">/* pointer to set of columns to check */</span></div>
<div class="line"><a name="l01562"></a><span class="lineno"> 1562</span>  Index row_length <span class="comment">/* number of columns to check */</span></div>
<div class="line"><a name="l01563"></a><span class="lineno"> 1563</span> )</div>
<div class="line"><a name="l01564"></a><span class="lineno"> 1564</span> {</div>
<div class="line"><a name="l01565"></a><span class="lineno"> 1565</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l01566"></a><span class="lineno"> 1566</span> </div>
<div class="line"><a name="l01567"></a><span class="lineno"> 1567</span>  Index hash ; <span class="comment">/* hash value for a column */</span></div>
<div class="line"><a name="l01568"></a><span class="lineno"> 1568</span>  Index *rp ; <span class="comment">/* pointer to a row */</span></div>
<div class="line"><a name="l01569"></a><span class="lineno"> 1569</span>  Index c ; <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l01570"></a><span class="lineno"> 1570</span>  Index super_c ; <span class="comment">/* column index of the column to absorb into */</span></div>
<div class="line"><a name="l01571"></a><span class="lineno"> 1571</span>  Index *cp1 ; <span class="comment">/* column pointer for column super_c */</span></div>
<div class="line"><a name="l01572"></a><span class="lineno"> 1572</span>  Index *cp2 ; <span class="comment">/* column pointer for column c */</span></div>
<div class="line"><a name="l01573"></a><span class="lineno"> 1573</span>  Index length ; <span class="comment">/* length of column super_c */</span></div>
<div class="line"><a name="l01574"></a><span class="lineno"> 1574</span>  Index prev_c ; <span class="comment">/* column preceding c in hash bucket */</span></div>
<div class="line"><a name="l01575"></a><span class="lineno"> 1575</span>  Index i ; <span class="comment">/* loop counter */</span></div>
<div class="line"><a name="l01576"></a><span class="lineno"> 1576</span>  Index *rp_end ; <span class="comment">/* pointer to the end of the row */</span></div>
<div class="line"><a name="l01577"></a><span class="lineno"> 1577</span>  Index col ; <span class="comment">/* a column index in the row to check */</span></div>
<div class="line"><a name="l01578"></a><span class="lineno"> 1578</span>  Index head_column ; <span class="comment">/* first column in hash bucket or degree list */</span></div>
<div class="line"><a name="l01579"></a><span class="lineno"> 1579</span>  Index first_col ; <span class="comment">/* first column in hash bucket */</span></div>
<div class="line"><a name="l01580"></a><span class="lineno"> 1580</span> </div>
<div class="line"><a name="l01581"></a><span class="lineno"> 1581</span>  <span class="comment">/* === Consider each column in the row ================================== */</span></div>
<div class="line"><a name="l01582"></a><span class="lineno"> 1582</span> </div>
<div class="line"><a name="l01583"></a><span class="lineno"> 1583</span>  rp = &A [row_start] ;</div>
<div class="line"><a name="l01584"></a><span class="lineno"> 1584</span>  rp_end = rp + row_length ;</div>
<div class="line"><a name="l01585"></a><span class="lineno"> 1585</span>  <span class="keywordflow">while</span> (rp < rp_end)</div>
<div class="line"><a name="l01586"></a><span class="lineno"> 1586</span>  {</div>
<div class="line"><a name="l01587"></a><span class="lineno"> 1587</span>  col = *rp++ ;</div>
<div class="line"><a name="l01588"></a><span class="lineno"> 1588</span>  <span class="keywordflow">if</span> (COL_IS_DEAD (col))</div>
<div class="line"><a name="l01589"></a><span class="lineno"> 1589</span>  {</div>
<div class="line"><a name="l01590"></a><span class="lineno"> 1590</span>  continue ;</div>
<div class="line"><a name="l01591"></a><span class="lineno"> 1591</span>  }</div>
<div class="line"><a name="l01592"></a><span class="lineno"> 1592</span> </div>
<div class="line"><a name="l01593"></a><span class="lineno"> 1593</span>  <span class="comment">/* get hash number for this column */</span></div>
<div class="line"><a name="l01594"></a><span class="lineno"> 1594</span>  hash = Col [col].shared3.hash ;</div>
<div class="line"><a name="l01595"></a><span class="lineno"> 1595</span>  COLAMD_ASSERT (hash <= n_col) ;</div>
<div class="line"><a name="l01596"></a><span class="lineno"> 1596</span> </div>
<div class="line"><a name="l01597"></a><span class="lineno"> 1597</span>  <span class="comment">/* === Get the first column in this hash bucket ===================== */</span></div>
<div class="line"><a name="l01598"></a><span class="lineno"> 1598</span> </div>
<div class="line"><a name="l01599"></a><span class="lineno"> 1599</span>  head_column = head [hash] ;</div>
<div class="line"><a name="l01600"></a><span class="lineno"> 1600</span>  <span class="keywordflow">if</span> (head_column > COLAMD_EMPTY)</div>
<div class="line"><a name="l01601"></a><span class="lineno"> 1601</span>  {</div>
<div class="line"><a name="l01602"></a><span class="lineno"> 1602</span>  first_col = Col [head_column].shared3.headhash ;</div>
<div class="line"><a name="l01603"></a><span class="lineno"> 1603</span>  }</div>
<div class="line"><a name="l01604"></a><span class="lineno"> 1604</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l01605"></a><span class="lineno"> 1605</span>  {</div>
<div class="line"><a name="l01606"></a><span class="lineno"> 1606</span>  first_col = - (head_column + 2) ;</div>
<div class="line"><a name="l01607"></a><span class="lineno"> 1607</span>  }</div>
<div class="line"><a name="l01608"></a><span class="lineno"> 1608</span> </div>
<div class="line"><a name="l01609"></a><span class="lineno"> 1609</span>  <span class="comment">/* === Consider each column in the hash bucket ====================== */</span></div>
<div class="line"><a name="l01610"></a><span class="lineno"> 1610</span> </div>
<div class="line"><a name="l01611"></a><span class="lineno"> 1611</span>  <span class="keywordflow">for</span> (super_c = first_col ; super_c != COLAMD_EMPTY ;</div>
<div class="line"><a name="l01612"></a><span class="lineno"> 1612</span>  super_c = Col [super_c].shared4.hash_next)</div>
<div class="line"><a name="l01613"></a><span class="lineno"> 1613</span>  {</div>
<div class="line"><a name="l01614"></a><span class="lineno"> 1614</span>  COLAMD_ASSERT (COL_IS_ALIVE (super_c)) ;</div>
<div class="line"><a name="l01615"></a><span class="lineno"> 1615</span>  COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ;</div>
<div class="line"><a name="l01616"></a><span class="lineno"> 1616</span>  length = Col [super_c].length ;</div>
<div class="line"><a name="l01617"></a><span class="lineno"> 1617</span> </div>
<div class="line"><a name="l01618"></a><span class="lineno"> 1618</span>  <span class="comment">/* prev_c is the column preceding column c in the hash bucket */</span></div>
<div class="line"><a name="l01619"></a><span class="lineno"> 1619</span>  prev_c = super_c ;</div>
<div class="line"><a name="l01620"></a><span class="lineno"> 1620</span> </div>
<div class="line"><a name="l01621"></a><span class="lineno"> 1621</span>  <span class="comment">/* === Compare super_c with all columns after it ================ */</span></div>
<div class="line"><a name="l01622"></a><span class="lineno"> 1622</span> </div>
<div class="line"><a name="l01623"></a><span class="lineno"> 1623</span>  <span class="keywordflow">for</span> (c = Col [super_c].shared4.hash_next ;</div>
<div class="line"><a name="l01624"></a><span class="lineno"> 1624</span>  c != COLAMD_EMPTY ; c = Col [c].shared4.hash_next)</div>
<div class="line"><a name="l01625"></a><span class="lineno"> 1625</span>  {</div>
<div class="line"><a name="l01626"></a><span class="lineno"> 1626</span>  COLAMD_ASSERT (c != super_c) ;</div>
<div class="line"><a name="l01627"></a><span class="lineno"> 1627</span>  COLAMD_ASSERT (COL_IS_ALIVE (c)) ;</div>
<div class="line"><a name="l01628"></a><span class="lineno"> 1628</span>  COLAMD_ASSERT (Col [c].shared3.hash == hash) ;</div>
<div class="line"><a name="l01629"></a><span class="lineno"> 1629</span> </div>
<div class="line"><a name="l01630"></a><span class="lineno"> 1630</span>  <span class="comment">/* not identical if lengths or scores are different */</span></div>
<div class="line"><a name="l01631"></a><span class="lineno"> 1631</span>  <span class="keywordflow">if</span> (Col [c].length != length ||</div>
<div class="line"><a name="l01632"></a><span class="lineno"> 1632</span>  Col [c].shared2.score != Col [super_c].shared2.score)</div>
<div class="line"><a name="l01633"></a><span class="lineno"> 1633</span>  {</div>
<div class="line"><a name="l01634"></a><span class="lineno"> 1634</span>  prev_c = c ;</div>
<div class="line"><a name="l01635"></a><span class="lineno"> 1635</span>  continue ;</div>
<div class="line"><a name="l01636"></a><span class="lineno"> 1636</span>  }</div>
<div class="line"><a name="l01637"></a><span class="lineno"> 1637</span> </div>
<div class="line"><a name="l01638"></a><span class="lineno"> 1638</span>  <span class="comment">/* compare the two columns */</span></div>
<div class="line"><a name="l01639"></a><span class="lineno"> 1639</span>  cp1 = &A [Col [super_c].start] ;</div>
<div class="line"><a name="l01640"></a><span class="lineno"> 1640</span>  cp2 = &A [Col [c].start] ;</div>
<div class="line"><a name="l01641"></a><span class="lineno"> 1641</span> </div>
<div class="line"><a name="l01642"></a><span class="lineno"> 1642</span>  <span class="keywordflow">for</span> (i = 0 ; i < length ; i++)</div>
<div class="line"><a name="l01643"></a><span class="lineno"> 1643</span>  {</div>
<div class="line"><a name="l01644"></a><span class="lineno"> 1644</span>  <span class="comment">/* the columns are "clean" (no dead rows) */</span></div>
<div class="line"><a name="l01645"></a><span class="lineno"> 1645</span>  COLAMD_ASSERT (ROW_IS_ALIVE (*cp1)) ;</div>
<div class="line"><a name="l01646"></a><span class="lineno"> 1646</span>  COLAMD_ASSERT (ROW_IS_ALIVE (*cp2)) ;</div>
<div class="line"><a name="l01647"></a><span class="lineno"> 1647</span>  <span class="comment">/* row indices will same order for both supercols, */</span></div>
<div class="line"><a name="l01648"></a><span class="lineno"> 1648</span>  <span class="comment">/* no gather scatter nessasary */</span></div>
<div class="line"><a name="l01649"></a><span class="lineno"> 1649</span>  <span class="keywordflow">if</span> (*cp1++ != *cp2++)</div>
<div class="line"><a name="l01650"></a><span class="lineno"> 1650</span>  {</div>
<div class="line"><a name="l01651"></a><span class="lineno"> 1651</span>  break ;</div>
<div class="line"><a name="l01652"></a><span class="lineno"> 1652</span>  }</div>
<div class="line"><a name="l01653"></a><span class="lineno"> 1653</span>  }</div>
<div class="line"><a name="l01654"></a><span class="lineno"> 1654</span> </div>
<div class="line"><a name="l01655"></a><span class="lineno"> 1655</span>  <span class="comment">/* the two columns are different if the for-loop "broke" */</span></div>
<div class="line"><a name="l01656"></a><span class="lineno"> 1656</span>  <span class="keywordflow">if</span> (i != length)</div>
<div class="line"><a name="l01657"></a><span class="lineno"> 1657</span>  {</div>
<div class="line"><a name="l01658"></a><span class="lineno"> 1658</span>  prev_c = c ;</div>
<div class="line"><a name="l01659"></a><span class="lineno"> 1659</span>  continue ;</div>
<div class="line"><a name="l01660"></a><span class="lineno"> 1660</span>  }</div>
<div class="line"><a name="l01661"></a><span class="lineno"> 1661</span> </div>
<div class="line"><a name="l01662"></a><span class="lineno"> 1662</span>  <span class="comment">/* === Got it! two columns are identical =================== */</span></div>
<div class="line"><a name="l01663"></a><span class="lineno"> 1663</span> </div>
<div class="line"><a name="l01664"></a><span class="lineno"> 1664</span>  COLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ;</div>
<div class="line"><a name="l01665"></a><span class="lineno"> 1665</span> </div>
<div class="line"><a name="l01666"></a><span class="lineno"> 1666</span>  Col [super_c].shared1.thickness += Col [c].shared1.thickness ;</div>
<div class="line"><a name="l01667"></a><span class="lineno"> 1667</span>  Col [c].shared1.parent = super_c ;</div>
<div class="line"><a name="l01668"></a><span class="lineno"> 1668</span>  KILL_NON_PRINCIPAL_COL (c) ;</div>
<div class="line"><a name="l01669"></a><span class="lineno"> 1669</span>  <span class="comment">/* order c later, in order_children() */</span></div>
<div class="line"><a name="l01670"></a><span class="lineno"> 1670</span>  Col [c].shared2.order = COLAMD_EMPTY ;</div>
<div class="line"><a name="l01671"></a><span class="lineno"> 1671</span>  <span class="comment">/* remove c from hash bucket */</span></div>
<div class="line"><a name="l01672"></a><span class="lineno"> 1672</span>  Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ;</div>
<div class="line"><a name="l01673"></a><span class="lineno"> 1673</span>  }</div>
<div class="line"><a name="l01674"></a><span class="lineno"> 1674</span>  }</div>
<div class="line"><a name="l01675"></a><span class="lineno"> 1675</span> </div>
<div class="line"><a name="l01676"></a><span class="lineno"> 1676</span>  <span class="comment">/* === Empty this hash bucket ======================================= */</span></div>
<div class="line"><a name="l01677"></a><span class="lineno"> 1677</span> </div>
<div class="line"><a name="l01678"></a><span class="lineno"> 1678</span>  <span class="keywordflow">if</span> (head_column > COLAMD_EMPTY)</div>
<div class="line"><a name="l01679"></a><span class="lineno"> 1679</span>  {</div>
<div class="line"><a name="l01680"></a><span class="lineno"> 1680</span>  <span class="comment">/* corresponding degree list "hash" is not empty */</span></div>
<div class="line"><a name="l01681"></a><span class="lineno"> 1681</span>  Col [head_column].shared3.headhash = COLAMD_EMPTY ;</div>
<div class="line"><a name="l01682"></a><span class="lineno"> 1682</span>  }</div>
<div class="line"><a name="l01683"></a><span class="lineno"> 1683</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l01684"></a><span class="lineno"> 1684</span>  {</div>
<div class="line"><a name="l01685"></a><span class="lineno"> 1685</span>  <span class="comment">/* corresponding degree list "hash" is empty */</span></div>
<div class="line"><a name="l01686"></a><span class="lineno"> 1686</span>  head [hash] = COLAMD_EMPTY ;</div>
<div class="line"><a name="l01687"></a><span class="lineno"> 1687</span>  }</div>
<div class="line"><a name="l01688"></a><span class="lineno"> 1688</span>  }</div>
<div class="line"><a name="l01689"></a><span class="lineno"> 1689</span> }</div>
<div class="line"><a name="l01690"></a><span class="lineno"> 1690</span> </div>
<div class="line"><a name="l01691"></a><span class="lineno"> 1691</span> </div>
<div class="line"><a name="l01692"></a><span class="lineno"> 1692</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01693"></a><span class="lineno"> 1693</span> <span class="comment">/* === garbage_collection =================================================== */</span></div>
<div class="line"><a name="l01694"></a><span class="lineno"> 1694</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01695"></a><span class="lineno"> 1695</span> </div>
<div class="line"><a name="l01696"></a><span class="lineno"> 1696</span> <span class="comment">/*</span></div>
<div class="line"><a name="l01697"></a><span class="lineno"> 1697</span> <span class="comment"> Defragments and compacts columns and rows in the workspace A. Used when</span></div>
<div class="line"><a name="l01698"></a><span class="lineno"> 1698</span> <span class="comment"> all avaliable memory has been used while performing row merging. Returns</span></div>
<div class="line"><a name="l01699"></a><span class="lineno"> 1699</span> <span class="comment"> the index of the first free position in A, after garbage collection. The</span></div>
<div class="line"><a name="l01700"></a><span class="lineno"> 1700</span> <span class="comment"> time taken by this routine is linear is the size of the array A, which is</span></div>
<div class="line"><a name="l01701"></a><span class="lineno"> 1701</span> <span class="comment"> itself linear in the number of nonzeros in the input matrix.</span></div>
<div class="line"><a name="l01702"></a><span class="lineno"> 1702</span> <span class="comment"> Not user-callable.</span></div>
<div class="line"><a name="l01703"></a><span class="lineno"> 1703</span> <span class="comment">*/</span></div>
<div class="line"><a name="l01704"></a><span class="lineno"> 1704</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l01705"></a><span class="lineno"> 1705</span> <span class="keyword">static</span> Index garbage_collection <span class="comment">/* returns the new value of pfree */</span></div>
<div class="line"><a name="l01706"></a><span class="lineno"> 1706</span>  (</div>
<div class="line"><a name="l01707"></a><span class="lineno"> 1707</span>  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l01708"></a><span class="lineno"> 1708</span>  </div>
<div class="line"><a name="l01709"></a><span class="lineno"> 1709</span>  Index n_row, <span class="comment">/* number of rows */</span></div>
<div class="line"><a name="l01710"></a><span class="lineno"> 1710</span>  Index n_col, <span class="comment">/* number of columns */</span></div>
<div class="line"><a name="l01711"></a><span class="lineno"> 1711</span>  Colamd_Row<Index> Row [], <span class="comment">/* row info */</span></div>
<div class="line"><a name="l01712"></a><span class="lineno"> 1712</span>  colamd_col<Index> Col [], <span class="comment">/* column info */</span></div>
<div class="line"><a name="l01713"></a><span class="lineno"> 1713</span>  Index A [], <span class="comment">/* A [0 ... Alen-1] holds the matrix */</span></div>
<div class="line"><a name="l01714"></a><span class="lineno"> 1714</span>  Index *pfree <span class="comment">/* &A [0] ... pfree is in use */</span></div>
<div class="line"><a name="l01715"></a><span class="lineno"> 1715</span>  )</div>
<div class="line"><a name="l01716"></a><span class="lineno"> 1716</span> {</div>
<div class="line"><a name="l01717"></a><span class="lineno"> 1717</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l01718"></a><span class="lineno"> 1718</span> </div>
<div class="line"><a name="l01719"></a><span class="lineno"> 1719</span>  Index *psrc ; <span class="comment">/* source pointer */</span></div>
<div class="line"><a name="l01720"></a><span class="lineno"> 1720</span>  Index *pdest ; <span class="comment">/* destination pointer */</span></div>
<div class="line"><a name="l01721"></a><span class="lineno"> 1721</span>  Index j ; <span class="comment">/* counter */</span></div>
<div class="line"><a name="l01722"></a><span class="lineno"> 1722</span>  Index r ; <span class="comment">/* a row index */</span></div>
<div class="line"><a name="l01723"></a><span class="lineno"> 1723</span>  Index c ; <span class="comment">/* a column index */</span></div>
<div class="line"><a name="l01724"></a><span class="lineno"> 1724</span>  Index length ; <span class="comment">/* length of a row or column */</span></div>
<div class="line"><a name="l01725"></a><span class="lineno"> 1725</span> </div>
<div class="line"><a name="l01726"></a><span class="lineno"> 1726</span>  <span class="comment">/* === Defragment the columns =========================================== */</span></div>
<div class="line"><a name="l01727"></a><span class="lineno"> 1727</span> </div>
<div class="line"><a name="l01728"></a><span class="lineno"> 1728</span>  pdest = &A[0] ;</div>
<div class="line"><a name="l01729"></a><span class="lineno"> 1729</span>  <span class="keywordflow">for</span> (c = 0 ; c < n_col ; c++)</div>
<div class="line"><a name="l01730"></a><span class="lineno"> 1730</span>  {</div>
<div class="line"><a name="l01731"></a><span class="lineno"> 1731</span>  <span class="keywordflow">if</span> (COL_IS_ALIVE (c))</div>
<div class="line"><a name="l01732"></a><span class="lineno"> 1732</span>  {</div>
<div class="line"><a name="l01733"></a><span class="lineno"> 1733</span>  psrc = &A [Col [c].start] ;</div>
<div class="line"><a name="l01734"></a><span class="lineno"> 1734</span> </div>
<div class="line"><a name="l01735"></a><span class="lineno"> 1735</span>  <span class="comment">/* move and compact the column */</span></div>
<div class="line"><a name="l01736"></a><span class="lineno"> 1736</span>  COLAMD_ASSERT (pdest <= psrc) ;</div>
<div class="line"><a name="l01737"></a><span class="lineno"> 1737</span>  Col [c].start = (Index) (pdest - &A [0]) ;</div>
<div class="line"><a name="l01738"></a><span class="lineno"> 1738</span>  length = Col [c].length ;</div>
<div class="line"><a name="l01739"></a><span class="lineno"> 1739</span>  <span class="keywordflow">for</span> (j = 0 ; j < length ; j++)</div>
<div class="line"><a name="l01740"></a><span class="lineno"> 1740</span>  {</div>
<div class="line"><a name="l01741"></a><span class="lineno"> 1741</span>  r = *psrc++ ;</div>
<div class="line"><a name="l01742"></a><span class="lineno"> 1742</span>  <span class="keywordflow">if</span> (ROW_IS_ALIVE (r))</div>
<div class="line"><a name="l01743"></a><span class="lineno"> 1743</span>  {</div>
<div class="line"><a name="l01744"></a><span class="lineno"> 1744</span>  *pdest++ = r ;</div>
<div class="line"><a name="l01745"></a><span class="lineno"> 1745</span>  }</div>
<div class="line"><a name="l01746"></a><span class="lineno"> 1746</span>  }</div>
<div class="line"><a name="l01747"></a><span class="lineno"> 1747</span>  Col [c].length = (Index) (pdest - &A [Col [c].start]) ;</div>
<div class="line"><a name="l01748"></a><span class="lineno"> 1748</span>  }</div>
<div class="line"><a name="l01749"></a><span class="lineno"> 1749</span>  }</div>
<div class="line"><a name="l01750"></a><span class="lineno"> 1750</span> </div>
<div class="line"><a name="l01751"></a><span class="lineno"> 1751</span>  <span class="comment">/* === Prepare to defragment the rows =================================== */</span></div>
<div class="line"><a name="l01752"></a><span class="lineno"> 1752</span> </div>
<div class="line"><a name="l01753"></a><span class="lineno"> 1753</span>  <span class="keywordflow">for</span> (r = 0 ; r < n_row ; r++)</div>
<div class="line"><a name="l01754"></a><span class="lineno"> 1754</span>  {</div>
<div class="line"><a name="l01755"></a><span class="lineno"> 1755</span>  <span class="keywordflow">if</span> (ROW_IS_ALIVE (r))</div>
<div class="line"><a name="l01756"></a><span class="lineno"> 1756</span>  {</div>
<div class="line"><a name="l01757"></a><span class="lineno"> 1757</span>  <span class="keywordflow">if</span> (Row [r].length == 0)</div>
<div class="line"><a name="l01758"></a><span class="lineno"> 1758</span>  {</div>
<div class="line"><a name="l01759"></a><span class="lineno"> 1759</span>  <span class="comment">/* this row is of zero length. cannot compact it, so kill it */</span></div>
<div class="line"><a name="l01760"></a><span class="lineno"> 1760</span>  COLAMD_DEBUG3 ((<span class="stringliteral">"Defrag row kill\n"</span>)) ;</div>
<div class="line"><a name="l01761"></a><span class="lineno"> 1761</span>  KILL_ROW (r) ;</div>
<div class="line"><a name="l01762"></a><span class="lineno"> 1762</span>  }</div>
<div class="line"><a name="l01763"></a><span class="lineno"> 1763</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l01764"></a><span class="lineno"> 1764</span>  {</div>
<div class="line"><a name="l01765"></a><span class="lineno"> 1765</span>  <span class="comment">/* save first column index in Row [r].shared2.first_column */</span></div>
<div class="line"><a name="l01766"></a><span class="lineno"> 1766</span>  psrc = &A [Row [r].start] ;</div>
<div class="line"><a name="l01767"></a><span class="lineno"> 1767</span>  Row [r].shared2.first_column = *psrc ;</div>
<div class="line"><a name="l01768"></a><span class="lineno"> 1768</span>  COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;</div>
<div class="line"><a name="l01769"></a><span class="lineno"> 1769</span>  <span class="comment">/* flag the start of the row with the one's complement of row */</span></div>
<div class="line"><a name="l01770"></a><span class="lineno"> 1770</span>  *psrc = ONES_COMPLEMENT (r) ;</div>
<div class="line"><a name="l01771"></a><span class="lineno"> 1771</span> </div>
<div class="line"><a name="l01772"></a><span class="lineno"> 1772</span>  }</div>
<div class="line"><a name="l01773"></a><span class="lineno"> 1773</span>  }</div>
<div class="line"><a name="l01774"></a><span class="lineno"> 1774</span>  }</div>
<div class="line"><a name="l01775"></a><span class="lineno"> 1775</span> </div>
<div class="line"><a name="l01776"></a><span class="lineno"> 1776</span>  <span class="comment">/* === Defragment the rows ============================================== */</span></div>
<div class="line"><a name="l01777"></a><span class="lineno"> 1777</span> </div>
<div class="line"><a name="l01778"></a><span class="lineno"> 1778</span>  psrc = pdest ;</div>
<div class="line"><a name="l01779"></a><span class="lineno"> 1779</span>  <span class="keywordflow">while</span> (psrc < pfree)</div>
<div class="line"><a name="l01780"></a><span class="lineno"> 1780</span>  {</div>
<div class="line"><a name="l01781"></a><span class="lineno"> 1781</span>  <span class="comment">/* find a negative number ... the start of a row */</span></div>
<div class="line"><a name="l01782"></a><span class="lineno"> 1782</span>  <span class="keywordflow">if</span> (*psrc++ < 0)</div>
<div class="line"><a name="l01783"></a><span class="lineno"> 1783</span>  {</div>
<div class="line"><a name="l01784"></a><span class="lineno"> 1784</span>  psrc-- ;</div>
<div class="line"><a name="l01785"></a><span class="lineno"> 1785</span>  <span class="comment">/* get the row index */</span></div>
<div class="line"><a name="l01786"></a><span class="lineno"> 1786</span>  r = ONES_COMPLEMENT (*psrc) ;</div>
<div class="line"><a name="l01787"></a><span class="lineno"> 1787</span>  COLAMD_ASSERT (r >= 0 && r < n_row) ;</div>
<div class="line"><a name="l01788"></a><span class="lineno"> 1788</span>  <span class="comment">/* restore first column index */</span></div>
<div class="line"><a name="l01789"></a><span class="lineno"> 1789</span>  *psrc = Row [r].shared2.first_column ;</div>
<div class="line"><a name="l01790"></a><span class="lineno"> 1790</span>  COLAMD_ASSERT (ROW_IS_ALIVE (r)) ;</div>
<div class="line"><a name="l01791"></a><span class="lineno"> 1791</span> </div>
<div class="line"><a name="l01792"></a><span class="lineno"> 1792</span>  <span class="comment">/* move and compact the row */</span></div>
<div class="line"><a name="l01793"></a><span class="lineno"> 1793</span>  COLAMD_ASSERT (pdest <= psrc) ;</div>
<div class="line"><a name="l01794"></a><span class="lineno"> 1794</span>  Row [r].start = (Index) (pdest - &A [0]) ;</div>
<div class="line"><a name="l01795"></a><span class="lineno"> 1795</span>  length = Row [r].length ;</div>
<div class="line"><a name="l01796"></a><span class="lineno"> 1796</span>  <span class="keywordflow">for</span> (j = 0 ; j < length ; j++)</div>
<div class="line"><a name="l01797"></a><span class="lineno"> 1797</span>  {</div>
<div class="line"><a name="l01798"></a><span class="lineno"> 1798</span>  c = *psrc++ ;</div>
<div class="line"><a name="l01799"></a><span class="lineno"> 1799</span>  <span class="keywordflow">if</span> (COL_IS_ALIVE (c))</div>
<div class="line"><a name="l01800"></a><span class="lineno"> 1800</span>  {</div>
<div class="line"><a name="l01801"></a><span class="lineno"> 1801</span>  *pdest++ = c ;</div>
<div class="line"><a name="l01802"></a><span class="lineno"> 1802</span>  }</div>
<div class="line"><a name="l01803"></a><span class="lineno"> 1803</span>  }</div>
<div class="line"><a name="l01804"></a><span class="lineno"> 1804</span>  Row [r].length = (Index) (pdest - &A [Row [r].start]) ;</div>
<div class="line"><a name="l01805"></a><span class="lineno"> 1805</span> </div>
<div class="line"><a name="l01806"></a><span class="lineno"> 1806</span>  }</div>
<div class="line"><a name="l01807"></a><span class="lineno"> 1807</span>  }</div>
<div class="line"><a name="l01808"></a><span class="lineno"> 1808</span>  <span class="comment">/* ensure we found all the rows */</span></div>
<div class="line"><a name="l01809"></a><span class="lineno"> 1809</span>  COLAMD_ASSERT (debug_rows == 0) ;</div>
<div class="line"><a name="l01810"></a><span class="lineno"> 1810</span> </div>
<div class="line"><a name="l01811"></a><span class="lineno"> 1811</span>  <span class="comment">/* === Return the new value of pfree ==================================== */</span></div>
<div class="line"><a name="l01812"></a><span class="lineno"> 1812</span> </div>
<div class="line"><a name="l01813"></a><span class="lineno"> 1813</span>  <span class="keywordflow">return</span> ((Index) (pdest - &A [0])) ;</div>
<div class="line"><a name="l01814"></a><span class="lineno"> 1814</span> }</div>
<div class="line"><a name="l01815"></a><span class="lineno"> 1815</span> </div>
<div class="line"><a name="l01816"></a><span class="lineno"> 1816</span> </div>
<div class="line"><a name="l01817"></a><span class="lineno"> 1817</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01818"></a><span class="lineno"> 1818</span> <span class="comment">/* === clear_mark =========================================================== */</span></div>
<div class="line"><a name="l01819"></a><span class="lineno"> 1819</span> <span class="comment">/* ========================================================================== */</span></div>
<div class="line"><a name="l01820"></a><span class="lineno"> 1820</span> </div>
<div class="line"><a name="l01821"></a><span class="lineno"> 1821</span> <span class="comment">/*</span></div>
<div class="line"><a name="l01822"></a><span class="lineno"> 1822</span> <span class="comment"> Clears the Row [].shared2.mark array, and returns the new tag_mark.</span></div>
<div class="line"><a name="l01823"></a><span class="lineno"> 1823</span> <span class="comment"> Return value is the new tag_mark. Not user-callable.</span></div>
<div class="line"><a name="l01824"></a><span class="lineno"> 1824</span> <span class="comment">*/</span></div>
<div class="line"><a name="l01825"></a><span class="lineno"> 1825</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l01826"></a><span class="lineno"> 1826</span> <span class="keyword">static</span> <span class="keyword">inline</span> Index clear_mark <span class="comment">/* return the new value for tag_mark */</span></div>
<div class="line"><a name="l01827"></a><span class="lineno"> 1827</span>  (</div>
<div class="line"><a name="l01828"></a><span class="lineno"> 1828</span>  <span class="comment">/* === Parameters ======================================================= */</span></div>
<div class="line"><a name="l01829"></a><span class="lineno"> 1829</span> </div>
<div class="line"><a name="l01830"></a><span class="lineno"> 1830</span>  Index n_row, <span class="comment">/* number of rows in A */</span></div>
<div class="line"><a name="l01831"></a><span class="lineno"> 1831</span>  Colamd_Row<Index> Row [] <span class="comment">/* Row [0 ... n_row-1].shared2.mark is set to zero */</span></div>
<div class="line"><a name="l01832"></a><span class="lineno"> 1832</span>  )</div>
<div class="line"><a name="l01833"></a><span class="lineno"> 1833</span> {</div>
<div class="line"><a name="l01834"></a><span class="lineno"> 1834</span>  <span class="comment">/* === Local variables ================================================== */</span></div>
<div class="line"><a name="l01835"></a><span class="lineno"> 1835</span> </div>
<div class="line"><a name="l01836"></a><span class="lineno"> 1836</span>  Index r ;</div>
<div class="line"><a name="l01837"></a><span class="lineno"> 1837</span> </div>
<div class="line"><a name="l01838"></a><span class="lineno"> 1838</span>  <span class="keywordflow">for</span> (r = 0 ; r < n_row ; r++)</div>
<div class="line"><a name="l01839"></a><span class="lineno"> 1839</span>  {</div>
<div class="line"><a name="l01840"></a><span class="lineno"> 1840</span>  <span class="keywordflow">if</span> (ROW_IS_ALIVE (r))</div>
<div class="line"><a name="l01841"></a><span class="lineno"> 1841</span>  {</div>
<div class="line"><a name="l01842"></a><span class="lineno"> 1842</span>  Row [r].shared2.mark = 0 ;</div>
<div class="line"><a name="l01843"></a><span class="lineno"> 1843</span>  }</div>
<div class="line"><a name="l01844"></a><span class="lineno"> 1844</span>  }</div>
<div class="line"><a name="l01845"></a><span class="lineno"> 1845</span>  <span class="keywordflow">return</span> (1) ;</div>
<div class="line"><a name="l01846"></a><span class="lineno"> 1846</span> }</div>
<div class="line"><a name="l01847"></a><span class="lineno"> 1847</span> </div>
<div class="line"><a name="l01848"></a><span class="lineno"> 1848</span> </div>
<div class="line"><a name="l01849"></a><span class="lineno"> 1849</span> } <span class="comment">// namespace internal </span></div>
<div class="line"><a name="l01850"></a><span class="lineno"> 1850</span> <span class="preprocessor">#endif</span></div>
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