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<div class="title">LDLT.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) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2009 Keir Mierle <mierle@gmail.com></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Copyright (C) 2011 Timothy E. Holy <tim.holy@gmail.com ></span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">//</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</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="l00011"></a><span class="lineno"> 11</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="l00012"></a><span class="lineno"> 12</span> </div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#ifndef EIGEN_LDLT_H</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_LDLT_H</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00018"></a><span class="lineno"><a class="line" href="namespaceEigen_1_1internal.html"> 18</a></span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> UpLo> <span class="keyword">struct </span>LDLT_Traits;</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> }</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html"> 45</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keywordtype">int</span> _UpLo> <span class="keyword">class </span><a class="code" href="classEigen_1_1LDLT.html">LDLT</a></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>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  Options = MatrixType::Options & ~<a class="code" href="group__flags.html#ga7bd49e7b260e869e10fb9dc4fd081a85">RowMajorBit</a>, <span class="comment">// these are the options for the TmpMatrixType, we need a ColMajor matrix here!</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  UpLo = _UpLo</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<typename MatrixType::Scalar>::Real</a> RealScalar;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1></a> <a class="code" href="classEigen_1_1Matrix.html">TmpMatrixType</a>;</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="keyword">typedef</span> <a class="code" href="classEigen_1_1Transpositions.html">Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime></a> <a class="code" href="classEigen_1_1Transpositions.html">TranspositionType</a>;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime></a> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">typedef</span> internal::LDLT_Traits<MatrixType,UpLo> Traits;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> </div>
<div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#aec4c764dd032c14d861798976367e74d"> 72</a></span>  <a class="code" href="classEigen_1_1LDLT.html#aec4c764dd032c14d861798976367e74d">LDLT</a>() : m_matrix(), m_transpositions(), m_isInitialized(false) {}</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#ad329b592888d8f5db088dfa01504f6ad"> 80</a></span>  <a class="code" href="classEigen_1_1LDLT.html#ad329b592888d8f5db088dfa01504f6ad">LDLT</a>(Index size)</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  : m_matrix(size, size),</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  m_transpositions(size),</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  m_temporary(size),</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  m_isInitialized(false)</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  {}</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a4f9c1dcdc8070fb63772e3d940e41fb3"> 92</a></span>  <a class="code" href="classEigen_1_1LDLT.html#a4f9c1dcdc8070fb63772e3d940e41fb3">LDLT</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  : m_matrix(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  m_transpositions(matrix.rows()),</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  m_temporary(matrix.rows()),</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  m_isInitialized(false)</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>  <a class="code" href="classEigen_1_1LDLT.html#a46fcf31fdacf5205d1b6e6d64161a4b9">compute</a>(matrix);</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> </div>
<div class="line"><a name="l00104"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a47affd1a10b589811fc4828c1a2e0c6d"> 104</a></span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1LDLT.html#a47affd1a10b589811fc4828c1a2e0c6d">setZero</a>()</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  {</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  m_isInitialized = <span class="keyword">false</span>;</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> </div>
<div class="line"><a name="l00110"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#adc32fdba9f5b478afb2a96d53c6eacbb"> 110</a></span>  <span class="keyword">inline</span> <span class="keyword">typename</span> Traits::MatrixU <a class="code" href="classEigen_1_1LDLT.html#adc32fdba9f5b478afb2a96d53c6eacbb">matrixU</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">return</span> Traits::getU(m_matrix);</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  }</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a name="l00117"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a625f69b684b4434db1cf3cc434e86fe6"> 117</a></span>  <span class="keyword">inline</span> <span class="keyword">typename</span> Traits::MatrixL <a class="code" href="classEigen_1_1LDLT.html#a625f69b684b4434db1cf3cc434e86fe6">matrixL</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">return</span> Traits::getL(m_matrix);</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> </div>
<div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a9a07717c12ca93c79d792ae77f9767ae"> 125</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Transpositions.html">TranspositionType</a>& <a class="code" href="classEigen_1_1LDLT.html#a9a07717c12ca93c79d792ae77f9767ae">transpositionsP</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> m_transpositions;</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> </div>
<div class="line"><a name="l00132"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#adc5b1ae5b9cbc8a64912b8818cef9b9d"> 132</a></span>  <span class="keyword">inline</span> <a class="code" href="classEigen_1_1Diagonal.html">Diagonal<const MatrixType></a> <a class="code" href="classEigen_1_1LDLT.html#adc5b1ae5b9cbc8a64912b8818cef9b9d">vectorD</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">return</span> m_matrix.diagonal();</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> </div>
<div class="line"><a name="l00139"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a02588e810c938a215dfd59d933488ba3"> 139</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1LDLT.html#a02588e810c938a215dfd59d933488ba3">isPositive</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordflow">return</span> m_sign == 1;</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>  </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="preprocessor"> #ifdef EIGEN2_SUPPORT</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="preprocessor"></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> isPositiveDefinite()<span class="keyword"> const</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1LDLT.html#a02588e810c938a215dfd59d933488ba3">isPositive</a>();</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> <span class="preprocessor"> #endif</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00153"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a13ed609c8609698a470bb8dd0e43c09d"> 153</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1LDLT.html#a13ed609c8609698a470bb8dd0e43c09d">isNegative</a>(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">return</span> m_sign == -1;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  }</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<LDLT, Rhs></div>
<div class="line"><a name="l00176"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a71f78ede18adb53bdfe988161653e812"> 176</a></span>  <a class="code" href="classEigen_1_1LDLT.html#a71f78ede18adb53bdfe988161653e812">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Rhs></a>& b)<span class="keyword"> const</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  eigen_assert(m_matrix.rows()==b.rows()</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  && <span class="stringliteral">"LDLT::solve(): invalid number of rows of the right hand side matrix b"</span>);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordflow">return</span> internal::solve_retval<LDLT, Rhs>(*<span class="keyword">this</span>, b.derived());</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  }</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> </div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="preprocessor"> #ifdef EIGEN2_SUPPORT</span></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="preprocessor"></span> <span class="keyword">template</span><<span class="keyword">typename</span> OtherDerived, <span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1LDLT.html#a71f78ede18adb53bdfe988161653e812">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<OtherDerived></a>& b, ResultType *result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  *result = this-><a class="code" href="classEigen_1_1LDLT.html#a71f78ede18adb53bdfe988161653e812">solve</a>(b);</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="keywordflow">return</span> <span class="keyword">true</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> <span class="preprocessor"> #endif</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordtype">bool</span> solveInPlace(MatrixBase<Derived> &bAndX) <span class="keyword">const</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>  <a class="code" href="classEigen_1_1LDLT.html#aec4c764dd032c14d861798976367e74d">LDLT</a>& <a class="code" href="classEigen_1_1LDLT.html#a46fcf31fdacf5205d1b6e6d64161a4b9">compute</a>(<span class="keyword">const</span> MatrixType& matrix);</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <a class="code" href="classEigen_1_1LDLT.html#aec4c764dd032c14d861798976367e74d">LDLT</a>& rankUpdate(<span class="keyword">const</span> MatrixBase<Derived>& w, <span class="keyword">const</span> RealScalar& alpha=1);</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="line"><a name="l00205"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#abfb1a0b0f7ea94b420697055019a5b6a"> 205</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> MatrixType& <a class="code" href="classEigen_1_1LDLT.html#abfb1a0b0f7ea94b420697055019a5b6a">matrixLDLT</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">return</span> m_matrix;</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="l00211"></a><span class="lineno"> 211</span>  MatrixType <a class="code" href="classEigen_1_1LDLT.html#ac36925ac693435a090efee1cb5d6d16a">reconstructedMatrix</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">inline</span> Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_matrix.rows(); }</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">inline</span> Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_matrix.cols(); }</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> </div>
<div class="line"><a name="l00221"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a0c06d5c2034ebb329c54235369643ad2"> 221</a></span>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> <a class="code" href="classEigen_1_1LDLT.html#a0c06d5c2034ebb329c54235369643ad2">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">return</span> <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>;</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> </div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span> </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  MatrixType m_matrix;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  TranspositionType m_transpositions;</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  TmpMatrixType m_temporary;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keywordtype">int</span> m_sign;</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordtype">bool</span> m_isInitialized;</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> </div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> <span class="keyword">namespace </span>internal {</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">template</span><<span class="keywordtype">int</span> UpLo> <span class="keyword">struct </span>ldlt_inplace;</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> <span class="keyword">template</span><> <span class="keyword">struct </span>ldlt_inplace<<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>></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>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> TranspositionType, <span class="keyword">typename</span> Workspace></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keyword">static</span> <span class="keywordtype">bool</span> unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, <span class="keywordtype">int</span>* sign=0)</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  {</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  eigen_assert(mat.rows()==mat.cols());</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keyword">const</span> Index size = mat.rows();</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> </div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">if</span> (size <= 1)</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  {</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  transpositions.setIdentity();</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordflow">if</span>(sign)</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  *sign = numext::real(mat.coeff(0,0))>0 ? 1:-1;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  }</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>  RealScalar cutoff(0), biggest_in_corner;</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">for</span> (Index k = 0; k < size; ++k)</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">// Find largest diagonal element</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  Index index_of_biggest_in_corner;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  biggest_in_corner = mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&index_of_biggest_in_corner);</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  index_of_biggest_in_corner += k;</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="keywordflow">if</span>(k == 0)</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  {</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="comment">// The biggest overall is the point of reference to which further diagonals</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="comment">// are compared; if any diagonal is negligible compared</span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="comment">// to the largest overall, the algorithm bails.</span></div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  cutoff = abs(NumTraits<Scalar>::epsilon() * biggest_in_corner);</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  }</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> </div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="comment">// Finish early if the matrix is not full rank.</span></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordflow">if</span>(biggest_in_corner < cutoff)</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  {</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordflow">for</span>(Index i = k; i < size; i++) transpositions.coeffRef(i) = i;</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">if</span>(sign) *sign = 0;</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">break</span>;</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> </div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  transpositions.coeffRef(k) = index_of_biggest_in_corner;</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keywordflow">if</span>(k != index_of_biggest_in_corner)</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="comment">// apply the transposition while taking care to consider only</span></div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="comment">// the lower triangular part</span></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  Index s = size-index_of_biggest_in_corner-1; <span class="comment">// trailing size after the biggest element</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=k+1;i<index_of_biggest_in_corner;++i)</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  {</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  Scalar tmp = mat.coeffRef(i,k);</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);</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>  <span class="keywordflow">if</span>(NumTraits<Scalar>::IsComplex)</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  }</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> </div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// partition the matrix:</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="comment">// A00 | - | -</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="comment">// lu = A10 | A11 | -</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="comment">// A20 | A21 | A22</span></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  Index rs = size - k - 1;</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  Block<MatrixType,Dynamic,1> A21(mat,k+1,k,rs,1);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  Block<MatrixType,1,Dynamic> A10(mat,k,0,1,k);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  Block<MatrixType,Dynamic,Dynamic> A20(mat,k+1,0,rs,k);</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span> </div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keywordflow">if</span>(k>0)</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>  temp.head(k) = mat.diagonal().head(k).asDiagonal() * A10.adjoint();</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keywordflow">if</span>(rs>0)</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  A21.noalias() -= A20 * temp.head(k);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  }</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keywordflow">if</span>((rs>0) && (abs(mat.coeffRef(k,k)) > cutoff))</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  A21 /= mat.coeffRef(k,k);</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="keywordflow">if</span>(sign)</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  {</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="comment">// LDLT is not guaranteed to work for indefinite matrices, but let's try to get the sign right</span></div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="keywordtype">int</span> newSign = numext::real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0;</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keywordflow">if</span>(k == 0)</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  *sign = newSign;</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(*sign != newSign)</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  *sign = 0;</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</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> </div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</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> </div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="comment">// Reference for the algorithm: Davis and Hager, "Multiple Rank</span></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="comment">// Modifications of a Sparse Cholesky Factorization" (Algorithm 1)</span></div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">// Trivial rearrangements of their computations (Timothy E. Holy)</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="comment">// allow their algorithm to work for rank-1 updates even if the</span></div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="comment">// original matrix is not of full rank.</span></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="comment">// Here only rank-1 updates are implemented, to reduce the</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="comment">// requirement for intermediate storage and improve accuracy</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> WDerived></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keyword">static</span> <span class="keywordtype">bool</span> updateInPlace(MatrixType& mat, MatrixBase<WDerived>& w, <span class="keyword">const</span> <span class="keyword">typename</span> MatrixType::RealScalar& sigma=1)</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  {</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="keyword">using</span> numext::isfinite;</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</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="keyword">const</span> Index size = mat.rows();</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  eigen_assert(mat.cols() == size && w.size()==size);</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> </div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  RealScalar alpha = 1;</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> </div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="comment">// Apply the update</span></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="keywordflow">for</span> (Index j = 0; j < size; j++)</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  {</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="comment">// Check for termination due to an original decomposition of low-rank</span></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="keywordflow">if</span> (!(isfinite)(alpha))</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keywordflow">break</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>  <span class="comment">// Update the diagonal terms</span></div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  RealScalar dj = numext::real(mat.coeff(j,j));</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  Scalar wj = w.coeff(j);</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  RealScalar swj2 = sigma*numext::abs2(wj);</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  RealScalar gamma = dj*alpha + swj2;</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>  mat.coeffRef(j,j) += swj2/alpha;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  alpha += swj2/dj;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> </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>  <span class="comment">// Update the terms of L</span></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  Index rs = size-j-1;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  w.tail(rs) -= wj * mat.col(j).tail(rs);</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keywordflow">if</span>(gamma != 0)</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  }</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  }</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> </div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> TranspositionType, <span class="keyword">typename</span> Workspace, <span class="keyword">typename</span> WType></div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="keyword">static</span> <span class="keywordtype">bool</span> update(MatrixType& mat, <span class="keyword">const</span> TranspositionType& transpositions, Workspace& tmp, <span class="keyword">const</span> WType& w, <span class="keyword">const</span> <span class="keyword">typename</span> MatrixType::RealScalar& sigma=1)</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>  <span class="comment">// Apply the permutation to the input w</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  tmp = transpositions * w;</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="keywordflow">return</span> ldlt_inplace<Lower>::updateInPlace(mat,tmp,sigma);</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> };</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="keyword">template</span><> <span class="keyword">struct </span>ldlt_inplace<<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910bae70afef0d3ff7aca74e17e85ff6c9f2e">Upper</a>></div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> {</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> TranspositionType, <span class="keyword">typename</span> Workspace></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="keyword">static</span> EIGEN_STRONG_INLINE <span class="keywordtype">bool</span> unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, <span class="keywordtype">int</span>* sign=0)</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  {</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  Transpose<MatrixType> matt(mat);</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="keywordflow">return</span> ldlt_inplace<Lower>::unblocked(matt, transpositions, temp, sign);</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> </div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> TranspositionType, <span class="keyword">typename</span> Workspace, <span class="keyword">typename</span> WType></div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="keyword">static</span> EIGEN_STRONG_INLINE <span class="keywordtype">bool</span> update(MatrixType& mat, TranspositionType& transpositions, Workspace& tmp, WType& w, <span class="keyword">const</span> <span class="keyword">typename</span> MatrixType::RealScalar& sigma=1)</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  {</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  Transpose<MatrixType> matt(mat);</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">return</span> ldlt_inplace<Lower>::update(matt, transpositions, tmp, w.conjugate(), sigma);</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> };</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> </div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType> <span class="keyword">struct </span>LDLT_Traits<MatrixType,<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Lower</a>></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="keyword">typedef</span> <span class="keyword">const</span> TriangularView<const MatrixType, UnitLower> MatrixL;</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <span class="keyword">typedef</span> <span class="keyword">const</span> TriangularView<const typename MatrixType::AdjointReturnType, UnitUpper> MatrixU;</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <span class="keyword">static</span> <span class="keyword">inline</span> MatrixL getL(<span class="keyword">const</span> MatrixType& m) { <span class="keywordflow">return</span> m; }</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keyword">static</span> <span class="keyword">inline</span> MatrixU getU(<span class="keyword">const</span> MatrixType& m) { <span class="keywordflow">return</span> m.adjoint(); }</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> </div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType> <span class="keyword">struct </span>LDLT_Traits<MatrixType,<a class="code" href="group__enums.html#ggab59c1bec446b10af208f977a871d910bae70afef0d3ff7aca74e17e85ff6c9f2e">Upper</a>></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>  <span class="keyword">typedef</span> <span class="keyword">const</span> TriangularView<const typename MatrixType::AdjointReturnType, UnitLower> MatrixL;</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <span class="keyword">typedef</span> <span class="keyword">const</span> TriangularView<const MatrixType, UnitUpper> MatrixU;</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keyword">static</span> <span class="keyword">inline</span> MatrixL getL(<span class="keyword">const</span> MatrixType& m) { <span class="keywordflow">return</span> m.adjoint(); }</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="keyword">static</span> <span class="keyword">inline</span> MatrixU getU(<span class="keyword">const</span> MatrixType& m) { <span class="keywordflow">return</span> m; }</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> </div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> </div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> _UpLo></div>
<div class="line"><a name="l00437"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a46fcf31fdacf5205d1b6e6d64161a4b9"> 437</a></span> <a class="code" href="classEigen_1_1LDLT.html">LDLT<MatrixType,_UpLo></a>& <a class="code" href="classEigen_1_1LDLT.html#a46fcf31fdacf5205d1b6e6d64161a4b9">LDLT<MatrixType,_UpLo>::compute</a>(<span class="keyword">const</span> MatrixType& a)</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span> {</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  eigen_assert(a.rows()==a.cols());</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="keyword">const</span> Index size = a.rows();</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span> </div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  m_matrix = a;</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_transpositions.resize(size);</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  m_isInitialized = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  m_temporary.resize(size);</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>  internal::ldlt_inplace<UpLo>::unblocked(m_matrix, m_transpositions, m_temporary, &m_sign);</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>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span> }</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span> </div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> _UpLo></div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00461"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a910d592df729f6d1cee0ae2abf5f9612"> 461</a></span> <a class="code" href="classEigen_1_1LDLT.html">LDLT<MatrixType,_UpLo></a>& <a class="code" href="classEigen_1_1LDLT.html">LDLT<MatrixType,_UpLo>::rankUpdate</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived></a>& w, <span class="keyword">const</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<typename MatrixType::Scalar>::Real</a>& sigma)</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="keyword">const</span> Index size = w.rows();</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="keywordflow">if</span> (m_isInitialized)</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  {</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  eigen_assert(m_matrix.rows()==size);</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  }</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  { </div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  m_matrix.resize(size,size);</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  m_matrix.setZero();</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  m_transpositions.resize(size);</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="keywordflow">for</span> (Index i = 0; i < size; i++)</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  m_transpositions.coeffRef(i) = i;</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  m_temporary.resize(size);</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  m_sign = sigma>=0 ? 1 : -1;</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  }</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span> </div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  internal::ldlt_inplace<UpLo>::update(m_matrix, m_transpositions, m_temporary, w, sigma);</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span> </div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span> }</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> </div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keywordtype">int</span> _UpLo, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span> <span class="keyword">struct </span>solve_retval<<a class="code" href="classEigen_1_1LDLT.html">LDLT</a><_MatrixType,_UpLo>, Rhs></div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  : solve_retval_base<LDLT<_MatrixType,_UpLo>, Rhs></div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span> {</div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT<_MatrixType,_UpLo></a> LDLTType;</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  EIGEN_MAKE_SOLVE_HELPERS(LDLTType,Rhs)</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> </div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  eigen_assert(rhs().rows() == dec().matrixLDLT().rows());</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <span class="comment">// dst = P b</span></div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  dst = dec().transpositionsP() * rhs();</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span> </div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="comment">// dst = L^-1 (P b)</span></div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  dec().matrixL().solveInPlace(dst);</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> </div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="comment">// dst = D^-1 (L^-1 P b)</span></div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="comment">// more precisely, use pseudo-inverse of D (see bug 241)</span></div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <span class="keyword">using</span> std::max;</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> LDLTType::MatrixType MatrixType;</div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> LDLTType::Scalar Scalar;</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> LDLTType::RealScalar RealScalar;</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Diagonal.html">Diagonal<const MatrixType></a> vectorD = dec().vectorD();</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  RealScalar tolerance = (max)(vectorD.array().abs().maxCoeff() * <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::epsilon</a>(),</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  RealScalar(1) / <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<RealScalar>::highest</a>()); <span class="comment">// motivated by LAPACK's xGELSS</span></div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="keywordflow">for</span> (Index i = 0; i < vectorD.size(); ++i) {</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="keywordflow">if</span>(abs(vectorD(i)) > tolerance)</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  dst.row(i) /= vectorD(i);</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  dst.row(i).setZero();</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  }</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> </div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="comment">// dst = L^-T (D^-1 L^-1 P b)</span></div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  dec().matrixU().solveInPlace(dst);</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span> </div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="comment">// dst = P^-1 (L^-T D^-1 L^-1 P b) = A^-1 b</span></div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  dst = dec().transpositionsP().transpose() * dst;</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  }</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span> };</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span> }</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span> </div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType,<span class="keywordtype">int</span> _UpLo></div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span> <span class="keywordtype">bool</span> LDLT<MatrixType,_UpLo>::solveInPlace(MatrixBase<Derived> &bAndX)<span class="keyword"> const</span></div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  eigen_assert(m_matrix.rows() == bAndX.rows());</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span> </div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  bAndX = this->solve(bAndX);</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span> </div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span> }</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span> </div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> _UpLo></div>
<div class="line"><a name="l00557"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#ac36925ac693435a090efee1cb5d6d16a"> 557</a></span> MatrixType <a class="code" href="classEigen_1_1LDLT.html#ac36925ac693435a090efee1cb5d6d16a">LDLT<MatrixType,_UpLo>::reconstructedMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LDLT is not initialized."</span>);</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <span class="keyword">const</span> Index size = m_matrix.rows();</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  MatrixType res(size,size);</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span> </div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="comment">// P</span></div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  res.setIdentity();</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  res = transpositionsP() * res;</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <span class="comment">// L^* P</span></div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  res = matrixU() * res;</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="comment">// D(L^*P)</span></div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  res = vectorD().asDiagonal() * res;</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  <span class="comment">// L(DL^*P)</span></div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  res = matrixL() * res;</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <span class="comment">// P^T (LDL^*P)</span></div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  res = transpositionsP().transpose() * res;</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span> </div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span> }</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span> </div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UpLo></div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span> <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT<typename SelfAdjointView<MatrixType, UpLo>::PlainObject</a>, UpLo></div>
<div class="line"><a name="l00583"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointView.html#a245df21a519cd34f5eb6f724cf5bf8e7"> 583</a></span> <a class="code" href="classEigen_1_1SelfAdjointView.html#a245df21a519cd34f5eb6f724cf5bf8e7">SelfAdjointView<MatrixType, UpLo>::ldlt</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT<PlainObject,UpLo></a>(m_matrix);</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span> }</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span> </div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span> <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT<typename MatrixBase<Derived>::PlainObject</a>></div>
<div class="line"><a name="l00593"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a197a04cda6b4606ec2416fd3f950371f"> 593</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#a197a04cda6b4606ec2416fd3f950371f">MatrixBase<Derived>::ldlt</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT<PlainObject></a>(derived());</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span> }</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span> </div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span> </div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span> <span class="preprocessor">#endif // EIGEN_LDLT_H</span></div>
<div class="ttc" id="classEigen_1_1LDLT_html"><div class="ttname"><a href="classEigen_1_1LDLT.html">Eigen::LDLT</a></div><div class="ttdoc">Robust Cholesky decomposition of a matrix with pivoting. </div><div class="ttdef"><b>Definition:</b> LDLT.h:45</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a0c06d5c2034ebb329c54235369643ad2"><div class="ttname"><a href="classEigen_1_1LDLT.html#a0c06d5c2034ebb329c54235369643ad2">Eigen::LDLT::info</a></div><div class="ttdeci">ComputationInfo info() const </div><div class="ttdoc">Reports whether previous computation was successful. </div><div class="ttdef"><b>Definition:</b> LDLT.h:221</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a4f9c1dcdc8070fb63772e3d940e41fb3"><div class="ttname"><a href="classEigen_1_1LDLT.html#a4f9c1dcdc8070fb63772e3d940e41fb3">Eigen::LDLT::LDLT</a></div><div class="ttdeci">LDLT(const MatrixType &matrix)</div><div class="ttdoc">Constructor with decomposition. </div><div class="ttdef"><b>Definition:</b> LDLT.h:92</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_ac36925ac693435a090efee1cb5d6d16a"><div class="ttname"><a href="classEigen_1_1LDLT.html#ac36925ac693435a090efee1cb5d6d16a">Eigen::LDLT::reconstructedMatrix</a></div><div class="ttdeci">MatrixType reconstructedMatrix() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:557</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a9a07717c12ca93c79d792ae77f9767ae"><div class="ttname"><a href="classEigen_1_1LDLT.html#a9a07717c12ca93c79d792ae77f9767ae">Eigen::LDLT::transpositionsP</a></div><div class="ttdeci">const TranspositionType & transpositionsP() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:125</div></div>
<div class="ttc" id="structEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...</div><div class="ttdef"><b>Definition:</b> NumTraits.h:88</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a625f69b684b4434db1cf3cc434e86fe6"><div class="ttname"><a href="classEigen_1_1LDLT.html#a625f69b684b4434db1cf3cc434e86fe6">Eigen::LDLT::matrixL</a></div><div class="ttdeci">Traits::MatrixL matrixL() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:117</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a71f78ede18adb53bdfe988161653e812"><div class="ttname"><a href="classEigen_1_1LDLT.html#a71f78ede18adb53bdfe988161653e812">Eigen::LDLT::solve</a></div><div class="ttdeci">const internal::solve_retval< LDLT, Rhs > solve(const MatrixBase< Rhs > &b) const </div><div class="ttdef"><b>Definition:</b> LDLT.h:176</div></div>
<div class="ttc" id="classEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime ></a></div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a02588e810c938a215dfd59d933488ba3"><div class="ttname"><a href="classEigen_1_1LDLT.html#a02588e810c938a215dfd59d933488ba3">Eigen::LDLT::isPositive</a></div><div class="ttdeci">bool isPositive() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:139</div></div>
<div class="ttc" id="classEigen_1_1SelfAdjointView_html_a245df21a519cd34f5eb6f724cf5bf8e7"><div class="ttname"><a href="classEigen_1_1SelfAdjointView.html#a245df21a519cd34f5eb6f724cf5bf8e7">Eigen::SelfAdjointView::ldlt</a></div><div class="ttdeci">const LDLT< PlainObject, UpLo > ldlt() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:583</div></div>
<div class="ttc" id="group__enums_html_ggab59c1bec446b10af208f977a871d910bae70afef0d3ff7aca74e17e85ff6c9f2e"><div class="ttname"><a href="group__enums.html#ggab59c1bec446b10af208f977a871d910bae70afef0d3ff7aca74e17e85ff6c9f2e">Eigen::Upper</a></div><div class="ttdef"><b>Definition:</b> Constants.h:169</div></div>
<div class="ttc" id="group__enums_html_ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc"><div class="ttname"><a href="group__enums.html#ggab59c1bec446b10af208f977a871d910baf886b397626076218462d53d50eb96bc">Eigen::Lower</a></div><div class="ttdef"><b>Definition:</b> Constants.h:167</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a46fcf31fdacf5205d1b6e6d64161a4b9"><div class="ttname"><a href="classEigen_1_1LDLT.html#a46fcf31fdacf5205d1b6e6d64161a4b9">Eigen::LDLT::compute</a></div><div class="ttdeci">LDLT & compute(const MatrixType &matrix)</div><div class="ttdef"><b>Definition:</b> LDLT.h:437</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_ad329b592888d8f5db088dfa01504f6ad"><div class="ttname"><a href="classEigen_1_1LDLT.html#ad329b592888d8f5db088dfa01504f6ad">Eigen::LDLT::LDLT</a></div><div class="ttdeci">LDLT(Index size)</div><div class="ttdoc">Default Constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> LDLT.h:80</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a47affd1a10b589811fc4828c1a2e0c6d"><div class="ttname"><a href="classEigen_1_1LDLT.html#a47affd1a10b589811fc4828c1a2e0c6d">Eigen::LDLT::setZero</a></div><div class="ttdeci">void setZero()</div><div class="ttdef"><b>Definition:</b> LDLT.h:104</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_adc5b1ae5b9cbc8a64912b8818cef9b9d"><div class="ttname"><a href="classEigen_1_1LDLT.html#adc5b1ae5b9cbc8a64912b8818cef9b9d">Eigen::LDLT::vectorD</a></div><div class="ttdeci">Diagonal< const MatrixType > vectorD() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:132</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_aec4c764dd032c14d861798976367e74d"><div class="ttname"><a href="classEigen_1_1LDLT.html#aec4c764dd032c14d861798976367e74d">Eigen::LDLT::LDLT</a></div><div class="ttdeci">LDLT()</div><div class="ttdoc">Default Constructor. </div><div class="ttdef"><b>Definition:</b> LDLT.h:72</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Eigen::Success</a></div><div class="ttdef"><b>Definition:</b> Constants.h:376</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_a13ed609c8609698a470bb8dd0e43c09d"><div class="ttname"><a href="classEigen_1_1LDLT.html#a13ed609c8609698a470bb8dd0e43c09d">Eigen::LDLT::isNegative</a></div><div class="ttdeci">bool isNegative(void) const </div><div class="ttdef"><b>Definition:</b> LDLT.h:153</div></div>
<div class="ttc" id="group__flags_html_ga7bd49e7b260e869e10fb9dc4fd081a85"><div class="ttname"><a href="group__flags.html#ga7bd49e7b260e869e10fb9dc4fd081a85">Eigen::RowMajorBit</a></div><div class="ttdeci">const unsigned int RowMajorBit</div><div class="ttdef"><b>Definition:</b> Constants.h:53</div></div>
<div class="ttc" id="classEigen_1_1Diagonal_html"><div class="ttname"><a href="classEigen_1_1Diagonal.html">Eigen::Diagonal</a></div><div class="ttdoc">Expression of a diagonal/subdiagonal/superdiagonal in a matrix. </div><div class="ttdef"><b>Definition:</b> Diagonal.h:64</div></div>
<div class="ttc" id="classEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix< Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1 ></a></div></div>
<div class="ttc" id="group__enums_html_ga51bc1ac16f26ebe51eae1abb77bd037b"><div class="ttname"><a href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:374</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions. </div><div class="ttdef"><b>Definition:</b> MatrixBase.h:48</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a197a04cda6b4606ec2416fd3f950371f"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a197a04cda6b4606ec2416fd3f950371f">Eigen::MatrixBase::ldlt</a></div><div class="ttdeci">const LDLT< PlainObject > ldlt() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:593</div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_adc32fdba9f5b478afb2a96d53c6eacbb"><div class="ttname"><a href="classEigen_1_1LDLT.html#adc32fdba9f5b478afb2a96d53c6eacbb">Eigen::LDLT::matrixU</a></div><div class="ttdeci">Traits::MatrixU matrixU() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:110</div></div>
<div class="ttc" id="classEigen_1_1Transpositions_html"><div class="ttname"><a href="classEigen_1_1Transpositions.html">Eigen::Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime ></a></div></div>
<div class="ttc" id="classEigen_1_1LDLT_html_abfb1a0b0f7ea94b420697055019a5b6a"><div class="ttname"><a href="classEigen_1_1LDLT.html#abfb1a0b0f7ea94b420697055019a5b6a">Eigen::LDLT::matrixLDLT</a></div><div class="ttdeci">const MatrixType & matrixLDLT() const </div><div class="ttdef"><b>Definition:</b> LDLT.h:205</div></div>
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