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<div class="title">Amd.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) 2010 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> </div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"></span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">NOTE: this routine has been adapted from the CSparse library:</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"></span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">Copyright (c) 2006, Timothy A. Davis.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">http://www.cise.ufl.edu/research/sparse/CSparse</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">CSparse is free software; you can redistribute it and/or</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">modify it under the terms of the GNU Lesser General Public</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">License as published by the Free Software Foundation; either</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">version 2.1 of the License, or (at your option) any later version.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">CSparse is distributed in the hope that it will be useful,</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">Lesser General Public License for more details.</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">You should have received a copy of the GNU Lesser General Public</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">License along with this Module; if not, write to the Free Software</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"></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> </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "../Core/util/NonMPL2.h"</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#ifndef EIGEN_SPARSE_AMD_H</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_SPARSE_AMD_H</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">template</span><<span class="keyword">typename</span> T> <span class="keyword">inline</span> T amd_flip(<span class="keyword">const</span> T& i) { <span class="keywordflow">return</span> -i-2; }</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="keyword">template</span><<span class="keyword">typename</span> T> <span class="keyword">inline</span> T amd_unflip(<span class="keyword">const</span> T& i) { <span class="keywordflow">return</span> i<0 ? amd_flip(i) : i; }</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="keyword">template</span><<span class="keyword">typename</span> T0, <span class="keyword">typename</span> T1> <span class="keyword">inline</span> <span class="keywordtype">bool</span> amd_marked(<span class="keyword">const</span> T0* w, <span class="keyword">const</span> T1& j) { <span class="keywordflow">return</span> w[j]<0; }</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">template</span><<span class="keyword">typename</span> T0, <span class="keyword">typename</span> T1> <span class="keyword">inline</span> <span class="keywordtype">void</span> amd_mark(<span class="keyword">const</span> T0* w, <span class="keyword">const</span> T1& j) { <span class="keywordflow">return</span> w[j] = amd_flip(w[j]); }</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> </div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">/* clear w */</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="keyword">template</span><<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">static</span> <span class="keywordtype">int</span> cs_wclear (Index mark, Index lemax, Index *w, Index n)</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  Index k;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">if</span>(mark < 2 || (mark + lemax < 0))</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">for</span>(k = 0; k < n; k++)</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">if</span>(w[k] != 0)</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  w[k] = 1;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  mark = 2;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">return</span> (mark); <span class="comment">/* at this point, w[0..n-1] < mark holds */</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> }</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment">/* depth-first search and postorder of a tree rooted at node j */</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="keyword">template</span><<span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> Index cs_tdfs(Index j, Index k, Index *head, <span class="keyword">const</span> Index *next, Index *post, Index *stack)</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordtype">int</span> i, p, top = 0;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">if</span>(!head || !next || !post || !stack) <span class="keywordflow">return</span> (-1); <span class="comment">/* check inputs */</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  stack[0] = j; <span class="comment">/* place j on the stack */</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">while</span> (top >= 0) <span class="comment">/* while (stack is not empty) */</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  p = stack[top]; <span class="comment">/* p = top of stack */</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  i = head[p]; <span class="comment">/* i = youngest child of p */</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">if</span>(i == -1)</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  {</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  top--; <span class="comment">/* p has no unordered children left */</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  post[k++] = p; <span class="comment">/* node p is the kth postordered node */</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  }</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  {</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  head[p] = next[i]; <span class="comment">/* remove i from children of p */</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  stack[++top] = i; <span class="comment">/* start dfs on child node i */</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  }</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">return</span> k;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> }</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar, <span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="keywordtype">void</span> minimum_degree_ordering(SparseMatrix<Scalar,ColMajor,Index>& C, PermutationMatrix<Dynamic,Dynamic,Index>& perm)</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> {</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">int</span> d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  ok, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, t;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> h;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  </div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  Index n = C.cols();</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  dense = std::max<Index> (16, Index(10 * sqrt(<span class="keywordtype">double</span>(n)))); <span class="comment">/* find dense threshold */</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  dense = std::min<Index> (n-2, dense);</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  </div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  Index cnz = C.nonZeros();</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  perm.resize(n+1);</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  t = cnz + cnz/5 + 2*n; <span class="comment">/* add elbow room to C */</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  C.resizeNonZeros(t);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  Index* W = <span class="keyword">new</span> Index[8*(n+1)]; <span class="comment">/* get workspace */</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  Index* len = W;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  Index* nv = W + (n+1);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  Index* next = W + 2*(n+1);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  Index* head = W + 3*(n+1);</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  Index* elen = W + 4*(n+1);</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  Index* degree = W + 5*(n+1);</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  Index* w = W + 6*(n+1);</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  Index* hhead = W + 7*(n+1);</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  Index* last = perm.indices().data(); <span class="comment">/* use P as workspace for last */</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">/* --- Initialize quotient graph ---------------------------------------- */</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  Index* Cp = C.outerIndexPtr();</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  Index* Ci = C.innerIndexPtr();</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">for</span>(k = 0; k < n; k++)</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  len[k] = Cp[k+1] - Cp[k];</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  len[n] = 0;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  nzmax = t;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  </div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">for</span>(i = 0; i <= n; i++)</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  {</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  head[i] = -1; <span class="comment">// degree list i is empty</span></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  last[i] = -1;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  next[i] = -1;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  hhead[i] = -1; <span class="comment">// hash list i is empty </span></div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  nv[i] = 1; <span class="comment">// node i is just one node</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  w[i] = 1; <span class="comment">// node i is alive</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  elen[i] = 0; <span class="comment">// Ek of node i is empty</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  degree[i] = len[i]; <span class="comment">// degree of node i</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  }</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  mark = internal::cs_wclear<Index>(0, 0, w, n); <span class="comment">/* clear w */</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  elen[n] = -2; <span class="comment">/* n is a dead element */</span></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  Cp[n] = -1; <span class="comment">/* n is a root of assembly tree */</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  w[n] = 0; <span class="comment">/* n is a dead element */</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  </div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="comment">/* --- Initialize degree lists ------------------------------------------ */</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">for</span>(i = 0; i < n; i++)</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  {</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  d = degree[i];</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">if</span>(d == 0) <span class="comment">/* node i is empty */</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  {</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  elen[i] = -2; <span class="comment">/* element i is dead */</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  nel++;</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  Cp[i] = -1; <span class="comment">/* i is a root of assembly tree */</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  w[i] = 0;</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  }</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(d > dense) <span class="comment">/* node i is dense */</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  {</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  nv[i] = 0; <span class="comment">/* absorb i into element n */</span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  elen[i] = -1; <span class="comment">/* node i is dead */</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  nel++;</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  Cp[i] = amd_flip (n);</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  nv[n]++;</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  }</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  {</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordflow">if</span>(head[d] != -1) last[head[d]] = i;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  next[i] = head[d]; <span class="comment">/* put node i in degree list d */</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  head[d] = i;</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  }</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>  <span class="keywordflow">while</span> (nel < n) <span class="comment">/* while (selecting pivots) do */</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  {</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="comment">/* --- Select node of minimum approximate degree -------------------- */</span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordflow">for</span>(k = -1; mindeg < n && (k = head[mindeg]) == -1; mindeg++) {}</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keywordflow">if</span>(next[k] != -1) last[next[k]] = -1;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  head[mindeg] = next[k]; <span class="comment">/* remove k from degree list */</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  elenk = elen[k]; <span class="comment">/* elenk = |Ek| */</span></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  nvk = nv[k]; <span class="comment">/* # of nodes k represents */</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  nel += nvk; <span class="comment">/* nv[k] nodes of A eliminated */</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  </div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="comment">/* --- Garbage collection ------------------------------------------- */</span></div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordflow">if</span>(elenk > 0 && cnz + mindeg >= nzmax)</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>  <span class="keywordflow">for</span>(j = 0; j < n; j++)</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  {</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordflow">if</span>((p = Cp[j]) >= 0) <span class="comment">/* j is a live node or element */</span></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>  Cp[j] = Ci[p]; <span class="comment">/* save first entry of object */</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  Ci[p] = amd_flip (j); <span class="comment">/* first entry is now amd_flip(j) */</span></div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  }</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keywordflow">for</span>(q = 0, p = 0; p < cnz; ) <span class="comment">/* scan all of memory */</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="keywordflow">if</span>((j = amd_flip (Ci[p++])) >= 0) <span class="comment">/* found object j */</span></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  {</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  Ci[q] = Cp[j]; <span class="comment">/* restore first entry of object */</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  Cp[j] = q++; <span class="comment">/* new pointer to object j */</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordflow">for</span>(k3 = 0; k3 < len[j]-1; k3++) Ci[q++] = Ci[p++];</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  }</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  }</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  cnz = q; <span class="comment">/* Ci[cnz...nzmax-1] now free */</span></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  }</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="comment">/* --- Construct new element ---------------------------------------- */</span></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  dk = 0;</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  nv[k] = -nvk; <span class="comment">/* flag k as in Lk */</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  p = Cp[k];</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  pk1 = (elenk == 0) ? p : cnz; <span class="comment">/* do in place if elen[k] == 0 */</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  pk2 = pk1;</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">for</span>(k1 = 1; k1 <= elenk + 1; k1++)</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="keywordflow">if</span>(k1 > elenk)</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  {</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  e = k; <span class="comment">/* search the nodes in k */</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  pj = p; <span class="comment">/* list of nodes starts at Ci[pj]*/</span></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  ln = len[k] - elenk; <span class="comment">/* length of list of nodes in k */</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  }</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">else</span></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>  e = Ci[p++]; <span class="comment">/* search the nodes in e */</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  pj = Cp[e];</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  ln = len[e]; <span class="comment">/* length of list of nodes in e */</span></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  }</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">for</span>(k2 = 1; k2 <= ln; k2++)</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>  i = Ci[pj++];</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">if</span>((nvi = nv[i]) <= 0) <span class="keywordflow">continue</span>; <span class="comment">/* node i dead, or seen */</span></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  dk += nvi; <span class="comment">/* degree[Lk] += size of node i */</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  nv[i] = -nvi; <span class="comment">/* negate nv[i] to denote i in Lk*/</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  Ci[pk2++] = i; <span class="comment">/* place i in Lk */</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keywordflow">if</span>(next[i] != -1) last[next[i]] = last[i];</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">if</span>(last[i] != -1) <span class="comment">/* remove i from degree list */</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  {</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  next[last[i]] = next[i];</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  }</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordflow">else</span></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>  head[degree[i]] = next[i];</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>  }</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">if</span>(e != k)</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  {</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  Cp[e] = amd_flip (k); <span class="comment">/* absorb e into k */</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  w[e] = 0; <span class="comment">/* e is now a dead element */</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  }</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  }</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keywordflow">if</span>(elenk != 0) cnz = pk2; <span class="comment">/* Ci[cnz...nzmax] is free */</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  degree[k] = dk; <span class="comment">/* external degree of k - |Lk\i| */</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  Cp[k] = pk1; <span class="comment">/* element k is in Ci[pk1..pk2-1] */</span></div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  len[k] = pk2 - pk1;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  elen[k] = -2; <span class="comment">/* k is now an element */</span></div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  </div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="comment">/* --- Find set differences ----------------------------------------- */</span></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  mark = internal::cs_wclear<Index>(mark, lemax, w, n); <span class="comment">/* clear w if necessary */</span></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keywordflow">for</span>(pk = pk1; pk < pk2; pk++) <span class="comment">/* scan 1: find |Le\Lk| */</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  {</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  i = Ci[pk];</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">if</span>((eln = elen[i]) <= 0) <span class="keywordflow">continue</span>;<span class="comment">/* skip if elen[i] empty */</span></div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  nvi = -nv[i]; <span class="comment">/* nv[i] was negated */</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  wnvi = mark - nvi;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordflow">for</span>(p = Cp[i]; p <= Cp[i] + eln - 1; p++) <span class="comment">/* scan Ei */</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  {</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  e = Ci[p];</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keywordflow">if</span>(w[e] >= mark)</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>  w[e] -= nvi; <span class="comment">/* decrement |Le\Lk| */</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  }</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(w[e] != 0) <span class="comment">/* ensure e is a live element */</span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  {</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  w[e] = degree[e] + wnvi; <span class="comment">/* 1st time e seen in scan 1 */</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  }</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  }</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  }</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="comment">/* --- Degree update ------------------------------------------------ */</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordflow">for</span>(pk = pk1; pk < pk2; pk++) <span class="comment">/* scan2: degree update */</span></div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  {</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  i = Ci[pk]; <span class="comment">/* consider node i in Lk */</span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  p1 = Cp[i];</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  p2 = p1 + elen[i] - 1;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  pn = p1;</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">for</span>(h = 0, d = 0, p = p1; p <= p2; p++) <span class="comment">/* scan Ei */</span></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  {</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  e = Ci[p];</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keywordflow">if</span>(w[e] != 0) <span class="comment">/* e is an unabsorbed element */</span></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  {</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  dext = w[e] - mark; <span class="comment">/* dext = |Le\Lk| */</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">if</span>(dext > 0)</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  {</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  d += dext; <span class="comment">/* sum up the set differences */</span></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  Ci[pn++] = e; <span class="comment">/* keep e in Ei */</span></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  h += e; <span class="comment">/* compute the hash of node i */</span></div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  }</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  {</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  Cp[e] = amd_flip (k); <span class="comment">/* aggressive absorb. e->k */</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  w[e] = 0; <span class="comment">/* e is a dead element */</span></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>  }</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>  elen[i] = pn - p1 + 1; <span class="comment">/* elen[i] = |Ei| */</span></div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  p3 = pn;</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  p4 = p1 + len[i];</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">for</span>(p = p2 + 1; p < p4; p++) <span class="comment">/* prune edges in Ai */</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  {</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  j = Ci[p];</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">if</span>((nvj = nv[j]) <= 0) <span class="keywordflow">continue</span>; <span class="comment">/* node j dead or in Lk */</span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  d += nvj; <span class="comment">/* degree(i) += |j| */</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  Ci[pn++] = j; <span class="comment">/* place j in node list of i */</span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  h += j; <span class="comment">/* compute hash for node i */</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  }</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">if</span>(d == 0) <span class="comment">/* check for mass elimination */</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  {</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  Cp[i] = amd_flip (k); <span class="comment">/* absorb i into k */</span></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  nvi = -nv[i];</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  dk -= nvi; <span class="comment">/* |Lk| -= |i| */</span></div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  nvk += nvi; <span class="comment">/* |k| += nv[i] */</span></div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  nel += nvi;</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  nv[i] = 0;</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  elen[i] = -1; <span class="comment">/* node i is dead */</span></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  }</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  {</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  degree[i] = std::min<Index> (degree[i], d); <span class="comment">/* update degree(i) */</span></div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  Ci[pn] = Ci[p3]; <span class="comment">/* move first node to end */</span></div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  Ci[p3] = Ci[p1]; <span class="comment">/* move 1st el. to end of Ei */</span></div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  Ci[p1] = k; <span class="comment">/* add k as 1st element in of Ei */</span></div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  len[i] = pn - p1 + 1; <span class="comment">/* new len of adj. list of node i */</span></div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  h %= n; <span class="comment">/* finalize hash of i */</span></div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  next[i] = hhead[h]; <span class="comment">/* place i in hash bucket */</span></div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  hhead[h] = i;</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  last[i] = h; <span class="comment">/* save hash of i in last[i] */</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  }</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  } <span class="comment">/* scan2 is done */</span></div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  degree[k] = dk; <span class="comment">/* finalize |Lk| */</span></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  lemax = std::max<Index>(lemax, dk);</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  mark = internal::cs_wclear<Index>(mark+lemax, lemax, w, n); <span class="comment">/* clear w */</span></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="comment">/* --- Supernode detection ------------------------------------------ */</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keywordflow">for</span>(pk = pk1; pk < pk2; pk++)</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  {</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  i = Ci[pk];</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keywordflow">if</span>(nv[i] >= 0) <span class="keywordflow">continue</span>; <span class="comment">/* skip if i is dead */</span></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  h = last[i]; <span class="comment">/* scan hash bucket of node i */</span></div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  i = hhead[h];</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  hhead[h] = -1; <span class="comment">/* hash bucket will be empty */</span></div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">for</span>(; i != -1 && next[i] != -1; i = next[i], mark++)</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>  ln = len[i];</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  eln = elen[i];</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keywordflow">for</span>(p = Cp[i]+1; p <= Cp[i] + ln-1; p++) w[Ci[p]] = mark;</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  jlast = i;</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="keywordflow">for</span>(j = next[i]; j != -1; ) <span class="comment">/* compare i with all j */</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  {</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  ok = (len[j] == ln) && (elen[j] == eln);</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keywordflow">for</span>(p = Cp[j] + 1; ok && p <= Cp[j] + ln - 1; p++)</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>  <span class="keywordflow">if</span>(w[Ci[p]] != mark) ok = 0; <span class="comment">/* compare i and j*/</span></div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  }</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keywordflow">if</span>(ok) <span class="comment">/* i and j are identical */</span></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>  Cp[j] = amd_flip (i); <span class="comment">/* absorb j into i */</span></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  nv[i] += nv[j];</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  nv[j] = 0;</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  elen[j] = -1; <span class="comment">/* node j is dead */</span></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  j = next[j]; <span class="comment">/* delete j from hash bucket */</span></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  next[jlast] = j;</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">else</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>  jlast = j; <span class="comment">/* j and i are different */</span></div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  j = next[j];</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</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>  }</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>  <span class="comment">/* --- Finalize new element------------------------------------------ */</span></div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="keywordflow">for</span>(p = pk1, pk = pk1; pk < pk2; pk++) <span class="comment">/* finalize Lk */</span></div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  {</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  i = Ci[pk];</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">if</span>((nvi = -nv[i]) <= 0) <span class="keywordflow">continue</span>;<span class="comment">/* skip if i is dead */</span></div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  nv[i] = nvi; <span class="comment">/* restore nv[i] */</span></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  d = degree[i] + dk - nvi; <span class="comment">/* compute external degree(i) */</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  d = std::min<Index> (d, n - nel - nvi);</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="keywordflow">if</span>(head[d] != -1) last[head[d]] = i;</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  next[i] = head[d]; <span class="comment">/* put i back in degree list */</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  last[i] = -1;</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  head[d] = i;</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  mindeg = std::min<Index> (mindeg, d); <span class="comment">/* find new minimum degree */</span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  degree[i] = d;</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  Ci[p++] = i; <span class="comment">/* place i in Lk */</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  }</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  nv[k] = nvk; <span class="comment">/* # nodes absorbed into k */</span></div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  <span class="keywordflow">if</span>((len[k] = p-pk1) == 0) <span class="comment">/* length of adj list of element k*/</span></div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  {</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  Cp[k] = -1; <span class="comment">/* k is a root of the tree */</span></div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  w[k] = 0; <span class="comment">/* k is now a dead element */</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>  <span class="keywordflow">if</span>(elenk != 0) cnz = p; <span class="comment">/* free unused space in Lk */</span></div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  }</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>  <span class="comment">/* --- Postordering ----------------------------------------------------- */</span></div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keywordflow">for</span>(i = 0; i < n; i++) Cp[i] = amd_flip (Cp[i]);<span class="comment">/* fix assembly tree */</span></div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="keywordflow">for</span>(j = 0; j <= n; j++) head[j] = -1;</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <span class="keywordflow">for</span>(j = n; j >= 0; j--) <span class="comment">/* place unordered nodes in lists */</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>  <span class="keywordflow">if</span>(nv[j] > 0) <span class="keywordflow">continue</span>; <span class="comment">/* skip if j is an element */</span></div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  next[j] = head[Cp[j]]; <span class="comment">/* place j in list of its parent */</span></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  head[Cp[j]] = j;</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  }</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">for</span>(e = n; e >= 0; e--) <span class="comment">/* place elements in lists */</span></div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  {</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keywordflow">if</span>(nv[e] <= 0) <span class="keywordflow">continue</span>; <span class="comment">/* skip unless e is an element */</span></div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <span class="keywordflow">if</span>(Cp[e] != -1)</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>  next[e] = head[Cp[e]]; <span class="comment">/* place e in list of its parent */</span></div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  head[Cp[e]] = e;</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  }</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  }</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">for</span>(k = 0, i = 0; i <= n; i++) <span class="comment">/* postorder the assembly tree */</span></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>(Cp[i] == -1) k = internal::cs_tdfs<Index>(i, k, head, next, perm.indices().data(), w);</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>  </div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  perm.indices().conservativeResize(n);</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> </div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keyword">delete</span>[] W;</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span> }</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span> </div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> } <span class="comment">// namespace internal</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> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> </div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="preprocessor">#endif // EIGEN_SPARSE_AMD_H</span></div>
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