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<div class="title">IncompleteLUT.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 Désiré 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="preprocessor">#ifndef EIGEN_INCOMPLETE_LUT_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_INCOMPLETE_LUT_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  </div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">template</span> <<span class="keyword">typename</span> VectorV, <span class="keyword">typename</span> VectorI, <span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> Index QuickSplit(VectorV &row, VectorI &ind, Index ncut)</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> VectorV::RealScalar RealScalar;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">using</span> std::swap;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  Index mid;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  Index n = row.size(); <span class="comment">/* length of the vector */</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  Index first, last ;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  ncut--; <span class="comment">/* to fit the zero-based indices */</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  first = 0; </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  last = n-1; </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">if</span> (ncut < first || ncut > last ) <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  mid = first; </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  RealScalar abskey = abs(row(mid)); </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">for</span> (Index j = first + 1; j <= last; j++) {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordflow">if</span> ( abs(row(j)) > abskey) {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  ++mid;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  swap(row(mid), row(j));</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  swap(ind(mid), ind(j));</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>  }</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">/* Interchange for the pivot element */</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  swap(row(mid), row(first));</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  swap(ind(mid), ind(first));</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">if</span> (mid > ncut) last = mid - 1;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (mid < ncut ) first = mid + 1; </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  } <span class="keywordflow">while</span> (mid != ncut );</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordflow">return</span> 0; <span class="comment">/* mid is equal to ncut */</span> </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> </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> }<span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="keyword">template</span> <<span class="keyword">typename</span> _Scalar></div>
<div class="line"><a name="l00096"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteLUT.html"> 96</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1IncompleteLUT.html">IncompleteLUT</a> : internal::noncopyable</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> {</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keyword">typedef</span> _Scalar Scalar;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::Real</a> RealScalar;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar,Dynamic,1></a> <a class="code" href="classEigen_1_1Matrix.html">Vector</a>;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix<Scalar,RowMajor></a> <a class="code" href="classEigen_1_1SparseMatrix.html">FactorType</a>;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix<Scalar,ColMajor></a> <a class="code" href="classEigen_1_1SparseMatrix.html">PermutType</a>;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> FactorType::Index Index;</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="keyword">public</span>:</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar,Dynamic,Dynamic></a> <a class="code" href="classEigen_1_1Matrix.html">MatrixType</a>;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <a class="code" href="classEigen_1_1IncompleteLUT.html">IncompleteLUT</a>()</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  : m_droptol(<a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::dummy_precision</a>()), m_fillfactor(10),</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  m_analysisIsOk(<span class="keyword">false</span>), m_factorizationIsOk(<span class="keyword">false</span>), m_isInitialized(<span class="keyword">false</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>  </div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <a class="code" href="classEigen_1_1IncompleteLUT.html">IncompleteLUT</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">MatrixType</a>& mat, <span class="keyword">const</span> RealScalar& droptol=<a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::dummy_precision</a>(), <span class="keywordtype">int</span> fillfactor = 10)</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  : m_droptol(droptol),m_fillfactor(fillfactor),</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  m_analysisIsOk(<span class="keyword">false</span>),m_factorizationIsOk(<span class="keyword">false</span>),m_isInitialized(<span class="keyword">false</span>)</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  eigen_assert(fillfactor != 0);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <a class="code" href="classEigen_1_1IncompleteLUT.html#acb5eacde7eef2117f27460a93890894d">compute</a>(mat); </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_lu.<a class="code" href="classEigen_1_1SparseMatrix.html#a5552abd83dbd03c85cea6d61fd8875a5">rows</a>(); }</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_lu.<a class="code" href="classEigen_1_1SparseMatrix.html#aaca1908a5ec508a25ff0a8bca803e5f3">cols</a>(); }</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteLUT.html#a0c06d5c2034ebb329c54235369643ad2"> 131</a></span>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> <a class="code" href="classEigen_1_1IncompleteLUT.html#a0c06d5c2034ebb329c54235369643ad2">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"IncompleteLUT is not initialized."</span>);</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</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="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordtype">void</span> analyzePattern(<span class="keyword">const</span> MatrixType& amat);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordtype">void</span> factorize(<span class="keyword">const</span> MatrixType& amat);</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00149"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteLUT.html#acb5eacde7eef2117f27460a93890894d"> 149</a></span>  <a class="code" href="classEigen_1_1IncompleteLUT.html">IncompleteLUT<Scalar></a>& <a class="code" href="classEigen_1_1IncompleteLUT.html#acb5eacde7eef2117f27460a93890894d">compute</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">MatrixType</a>& amat)</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  {</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  analyzePattern(amat); </div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  factorize(amat);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  m_isInitialized = m_factorizationIsOk;</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</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>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteLUT.html#a14211b3c36a5e783813d41524e0309e6">setDroptol</a>(<span class="keyword">const</span> RealScalar& droptol); </div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteLUT.html#a8d520cb344dd5c3944c811b357fea77f">setFillfactor</a>(<span class="keywordtype">int</span> fillfactor); </div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  </div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordtype">void</span> _solve(<span class="keyword">const</span> Rhs& b, Dest& x)<span class="keyword"> const</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  x = m_Pinv * b; </div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  x = m_lu.template triangularView<UnitLower>().solve(x);</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  x = m_lu.template triangularView<Upper>().solve(x);</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  x = m_P * x; </div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  }</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>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs> <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<IncompleteLUT, Rhs></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  solve(<span class="keyword">const</span> MatrixBase<Rhs>& b)<span class="keyword"> const</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"IncompleteLUT is not initialized."</span>);</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  eigen_assert(cols()==b.rows()</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  && <span class="stringliteral">"IncompleteLUT::solve(): invalid number of rows of the right hand side matrix b"</span>);</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keywordflow">return</span> internal::solve_retval<IncompleteLUT, Rhs>(*<span class="keyword">this</span>, b.derived());</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  }</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="structEigen_1_1IncompleteLUT_1_1keep__diag.html"> 181</a></span>  <span class="keyword">struct </span><a class="code" href="structEigen_1_1IncompleteLUT_1_1keep__diag.html">keep_diag</a> {</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> operator() (<span class="keyword">const</span> Index& row, <span class="keyword">const</span> Index& col, <span class="keyword">const</span> Scalar&)<span class="keyword"> const</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">return</span> row!=col;</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>  };</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> <span class="keyword">protected</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>  <a class="code" href="classEigen_1_1SparseMatrix.html">FactorType</a> m_lu;</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  RealScalar m_droptol;</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keywordtype">int</span> m_fillfactor;</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordtype">bool</span> m_analysisIsOk;</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordtype">bool</span> m_factorizationIsOk;</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix<Dynamic,Dynamic,Index></a> m_P; <span class="comment">// Fill-reducing permutation</span></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix<Dynamic,Dynamic,Index></a> m_Pinv; <span class="comment">// Inverse permutation</span></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="l00205"></a><span class="lineno"> 205</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00206"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteLUT.html#a14211b3c36a5e783813d41524e0309e6"> 206</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteLUT.html#a14211b3c36a5e783813d41524e0309e6">IncompleteLUT<Scalar>::setDroptol</a>(<span class="keyword">const</span> RealScalar& droptol)</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> {</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  this->m_droptol = droptol; </div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> }</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">template</span><<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00216"></a><span class="lineno"><a class="line" href="classEigen_1_1IncompleteLUT.html#a8d520cb344dd5c3944c811b357fea77f"> 216</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteLUT.html#a8d520cb344dd5c3944c811b357fea77f">IncompleteLUT<Scalar>::setFillfactor</a>(<span class="keywordtype">int</span> fillfactor)</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>  this->m_fillfactor = fillfactor; </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> </div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1IncompleteLUT.html">IncompleteLUT<Scalar>::analyzePattern</a>(<span class="keyword">const</span> _MatrixType& amat)</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span> {</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="comment">// Compute the Fill-reducing permutation</span></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix<Scalar,ColMajor, Index></a> mat1 = amat;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix<Scalar,ColMajor, Index></a> mat2 = amat.transpose();</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="comment">// Symmetrize the pattern</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="comment">// FIXME for a matrix with nearly symmetric pattern, mat2+mat1 is the appropriate choice.</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="comment">// on the other hand for a really non-symmetric pattern, mat2*mat1 should be prefered...</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix<Scalar,ColMajor, Index></a> AtA = mat2 + mat1;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  AtA.<a class="code" href="classEigen_1_1SparseMatrix.html#aa4592d803de19800d8fb3cb07a5036b6">prune</a>(keep_diag());</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  internal::minimum_degree_ordering<Scalar, Index>(AtA, m_P); <span class="comment">// Then compute the AMD ordering...</span></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>  m_Pinv = m_P.inverse(); <span class="comment">// ... and the inverse permutation</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> </div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  m_analysisIsOk = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</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="keyword">template</span> <<span class="keyword">typename</span> Scalar></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="keywordtype">void</span> IncompleteLUT<Scalar>::factorize(<span class="keyword">const</span> _MatrixType& amat)</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> {</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keyword">using</span> std::swap;</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> </div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  eigen_assert((amat.rows() == amat.cols()) && <span class="stringliteral">"The factorization should be done on a square matrix"</span>);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  Index n = amat.cols(); <span class="comment">// Size of the matrix</span></div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  m_lu.resize(n,n);</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="comment">// Declare Working vectors and variables</span></div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  Vector u(n) ; <span class="comment">// real values of the row -- maximum size is n --</span></div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <a class="code" href="group__matrixtypedefs.html#ga0312eb421909d32007ae4a55b9f22abb">VectorXi</a> ju(n); <span class="comment">// column position of the values in u -- maximum size is n</span></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <a class="code" href="group__matrixtypedefs.html#ga0312eb421909d32007ae4a55b9f22abb">VectorXi</a> jr(n); <span class="comment">// Indicate the position of the nonzero elements in the vector u -- A zero location is indicated by -1</span></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="comment">// Apply the fill-reducing permutation</span></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  eigen_assert(m_analysisIsOk && <span class="stringliteral">"You must first call analyzePattern()"</span>);</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  SparseMatrix<Scalar,RowMajor, Index> mat;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  mat = amat.twistedBy(m_Pinv);</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="comment">// Initialization</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  jr.<a class="code" href="classEigen_1_1DenseBase.html#a98692bec8f3d859f1e7a60eab87ac571">fill</a>(-1);</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  ju.fill(0);</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  u.fill(0);</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="comment">// number of largest elements to keep in each row:</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  Index fill_in = <span class="keyword">static_cast<</span>Index<span class="keyword">></span> (amat.nonZeros()*m_fillfactor)/n+1;</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordflow">if</span> (fill_in > n) fill_in = n;</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>  <span class="comment">// number of largest nonzero elements to keep in the L and the U part of the current row:</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  Index nnzL = fill_in/2;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  Index nnzU = nnzL;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  m_lu.reserve(n * (nnzL + nnzU + 1));</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">// global loop over the rows of the sparse matrix</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordflow">for</span> (Index ii = 0; ii < n; ii++)</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>  <span class="comment">// 1 - copy the lower and the upper part of the row i of mat in the working vector u</span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  Index sizeu = 1; <span class="comment">// number of nonzero elements in the upper part of the current row</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  Index sizel = 0; <span class="comment">// number of nonzero elements in the lower part of the current row</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  ju(ii) = ii;</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  u(ii) = 0;</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  jr(ii) = ii;</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  RealScalar rownorm = 0;</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>  <span class="keyword">typename</span> FactorType::InnerIterator j_it(mat, ii); <span class="comment">// Iterate through the current row ii</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">for</span> (; j_it; ++j_it)</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>  Index k = j_it.index();</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keywordflow">if</span> (k < ii)</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  {</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="comment">// copy the lower part</span></div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  ju(sizel) = k;</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  u(sizel) = j_it.value();</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  jr(k) = sizel;</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  ++sizel;</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">else</span> <span class="keywordflow">if</span> (k == ii)</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>  u(ii) = j_it.value();</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">else</span></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>  <span class="comment">// copy the upper part</span></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  Index jpos = ii + sizeu;</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  ju(jpos) = k;</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  u(jpos) = j_it.value();</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  jr(k) = jpos;</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  ++sizeu;</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>  rownorm += numext::abs2(j_it.value());</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> </div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="comment">// 2 - detect possible zero row</span></div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordflow">if</span>(rownorm==0)</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  {</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  m_info = <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037ba710fff14e8fc77846d4b75d8f4cc2d5c">NumericalIssue</a>;</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  }</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="comment">// Take the 2-norm of the current row as a relative tolerance</span></div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  rownorm = sqrt(rownorm);</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>  <span class="comment">// 3 - eliminate the previous nonzero rows</span></div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  Index jj = 0;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  Index len = 0;</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keywordflow">while</span> (jj < sizel)</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  {</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="comment">// In order to eliminate in the correct order,</span></div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="comment">// we must select first the smallest column index among ju(jj:sizel)</span></div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  Index k;</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  Index minrow = ju.segment(jj,sizel-jj).minCoeff(&k); <span class="comment">// k is relative to the segment</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  k += jj;</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">if</span> (minrow != ju(jj))</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  {</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="comment">// swap the two locations</span></div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  Index j = ju(jj);</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  swap(ju(jj), ju(k));</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  jr(minrow) = jj; jr(j) = k;</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  swap(u(jj), u(k));</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>  <span class="comment">// Reset this location</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  jr(minrow) = -1;</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">// Start elimination</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keyword">typename</span> FactorType::InnerIterator ki_it(m_lu, minrow);</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">while</span> (ki_it && ki_it.index() < minrow) ++ki_it;</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  eigen_internal_assert(ki_it && ki_it.col()==minrow);</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  Scalar fact = u(jj) / ki_it.value();</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>  <span class="comment">// drop too small elements</span></div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="keywordflow">if</span>(abs(fact) <= m_droptol)</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>  jj++;</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  }</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="comment">// linear combination of the current row ii and the row minrow</span></div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  ++ki_it;</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keywordflow">for</span> (; ki_it; ++ki_it)</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>  Scalar prod = fact * ki_it.value();</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  Index j = ki_it.index();</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  Index jpos = jr(j);</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="keywordflow">if</span> (jpos == -1) <span class="comment">// fill-in element</span></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  {</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  Index newpos;</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keywordflow">if</span> (j >= ii) <span class="comment">// dealing with the upper part</span></div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  {</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  newpos = ii + sizeu;</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  sizeu++;</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  eigen_internal_assert(sizeu<=n);</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>  <span class="keywordflow">else</span> <span class="comment">// dealing with the lower part</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>  newpos = sizel;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  sizel++;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  eigen_internal_assert(sizel<=ii);</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  }</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  ju(newpos) = j;</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  u(newpos) = -prod;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  jr(j) = newpos;</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">else</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  u(jpos) -= prod;</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  }</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <span class="comment">// store the pivot element</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  u(len) = fact;</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  ju(len) = minrow;</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  ++len;</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>  jj++;</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  } <span class="comment">// end of the elimination on the row ii</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>  <span class="comment">// reset the upper part of the pointer jr to zero</span></div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">for</span>(Index k = 0; k <sizeu; k++) jr(ju(ii+k)) = -1;</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span> </div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="comment">// 4 - partially sort and insert the elements in the m_lu matrix</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="comment">// sort the L-part of the row</span></div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  sizel = len;</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  len = (std::min)(sizel, nnzL);</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keyword">typename</span> Vector::SegmentReturnType ul(u.segment(0, sizel));</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keyword">typename</span> VectorXi::SegmentReturnType jul(ju.segment(0, sizel));</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  internal::QuickSplit(ul, jul, len);</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> </div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  <span class="comment">// store the largest m_fill elements of the L part</span></div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  m_lu.startVec(ii);</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="keywordflow">for</span>(Index k = 0; k < len; k++)</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k);</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="comment">// store the diagonal element</span></div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  <span class="comment">// apply a shifting rule to avoid zero pivots (we are doing an incomplete factorization)</span></div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keywordflow">if</span> (u(ii) == Scalar(0))</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  u(ii) = sqrt(m_droptol) * rownorm;</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  m_lu.insertBackByOuterInnerUnordered(ii, ii) = u(ii);</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span> </div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  <span class="comment">// sort the U-part of the row</span></div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <span class="comment">// apply the dropping rule first</span></div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  len = 0;</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">for</span>(Index k = 1; k < sizeu; k++)</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>(abs(u(ii+k)) > m_droptol * rownorm )</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>  ++len;</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  u(ii + len) = u(ii + k);</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  ju(ii + len) = ju(ii + k);</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  }</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>  sizeu = len + 1; <span class="comment">// +1 to take into account the diagonal element</span></div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  len = (std::min)(sizeu, nnzU);</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  <span class="keyword">typename</span> Vector::SegmentReturnType uu(u.segment(ii+1, sizeu-1));</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <span class="keyword">typename</span> VectorXi::SegmentReturnType juu(ju.segment(ii+1, sizeu-1));</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  internal::QuickSplit(uu, juu, len);</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> </div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="comment">// store the largest elements of the U part</span></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="keywordflow">for</span>(Index k = ii + 1; k < ii + len; k++)</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k);</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  }</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>  m_lu.finalize();</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  m_lu.makeCompressed();</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span> </div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  m_factorizationIsOk = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  m_info = <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>;</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</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> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span> </div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="keyword">struct </span>solve_retval<IncompleteLUT<_MatrixType>, Rhs></div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  : solve_retval_base<IncompleteLUT<_MatrixType>, Rhs></div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span> {</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keyword">typedef</span> IncompleteLUT<_MatrixType> Dec;</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span> </div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  dec()._solve(rhs(),dst);</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</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> </div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span> </div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span> </div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span> <span class="preprocessor">#endif // EIGEN_INCOMPLETE_LUT_H</span></div>
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<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037ba710fff14e8fc77846d4b75d8f4cc2d5c"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037ba710fff14e8fc77846d4b75d8f4cc2d5c">Eigen::NumericalIssue</a></div><div class="ttdef"><b>Definition:</b> Constants.h:378</div></div>
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