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<div class="fragment"><div class="line"><a id="l00001" 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 id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// Copyright (C) 2006-2009 Benoit Jacob <[email protected]></span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<div class="line"><a id="l00006" 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 id="l00007" 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 id="l00008" 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 id="l00009" name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#ifndef EIGEN_LU_H</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#define EIGEN_LU_H</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include "./InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType_, <span class="keyword">typename</span> PermutationIndex_> <span class="keyword">struct </span>traits<FullPivLU<MatrixType_, PermutationIndex_> ></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> : traits<MatrixType_></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span>{</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">typedef</span> MatrixXpr XprKind;</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <span class="keyword">typedef</span> SolverStorage StorageKind;</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">typedef</span> PermutationIndex_ StorageIndex;</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keyword">enum</span> { Flags = 0 };</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span>};</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html"> 62</a></span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType_, <span class="keyword">typename</span> PermutationIndex_> <span class="keyword">class </span><a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU</a></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> : <span class="keyword">public</span> <a class="code hl_class" href="classEigen_1_1SolverBase.html">SolverBase</a><FullPivLU<MatrixType_, PermutationIndex_> ></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span>{</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1SolverBase.html">SolverBase<FullPivLU></a> <a class="code hl_class" href="classEigen_1_1SolverBase.html">Base</a>;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keyword">friend</span> <span class="keyword">class </span><a class="code hl_class" href="classEigen_1_1SolverBase.html">SolverBase</a><<a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU</a>>;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> EIGEN_GENERIC_PUBLIC_INTERFACE(<a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU</a>)</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keyword">enum</span> {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> };</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keyword">using </span>PermutationIndex = PermutationIndex_;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type<MatrixType, PermutationIndex>::type IntRowVectorType;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type<MatrixType, PermutationIndex>::type IntColVectorType;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime, PermutationIndex></a> <a class="code hl_class" href="classEigen_1_1PermutationMatrix.html">PermutationQType</a>;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime, PermutationIndex></a> <a class="code hl_class" href="classEigen_1_1PermutationMatrix.html">PermutationPType</a>;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::PlainObject PlainObject;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#aff435f4b563a5ac72620d3ed9a94535a">FullPivLU</a>();</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#aff435f4b563a5ac72620d3ed9a94535a">FullPivLU</a>(<a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keyword">template</span><<span class="keyword">typename</span> InputType></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keyword">explicit</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#aff435f4b563a5ac72620d3ed9a94535a">FullPivLU</a>(<span class="keyword">const</span> <a class="code hl_class" href="structEigen_1_1EigenBase.html">EigenBase<InputType></a>& matrix);</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keyword">template</span><<span class="keyword">typename</span> InputType></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">explicit</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#aff435f4b563a5ac72620d3ed9a94535a">FullPivLU</a>(<a class="code hl_class" href="structEigen_1_1EigenBase.html">EigenBase<InputType></a>& matrix);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keyword">template</span><<span class="keyword">typename</span> InputType></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#af266621b5d114229566caff0de1aa44b"> 123</a></span> <a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU</a>& <a class="code hl_function" href="classEigen_1_1FullPivLU.html#af266621b5d114229566caff0de1aa44b">compute</a>(<span class="keyword">const</span> <a class="code hl_class" href="structEigen_1_1EigenBase.html">EigenBase<InputType></a>& matrix) {</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> m_lu = matrix.<a class="code hl_function" href="structEigen_1_1EigenBase.html#a749b057c52245e486a101868d2578a24">derived</a>();</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> computeInPlace();</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ad32738c9a0c08e5f6e7ada743c8b3a77"> 135</a></span> <span class="keyword">inline</span> <span class="keyword">const</span> MatrixType& <a class="code hl_function" href="classEigen_1_1FullPivLU.html#ad32738c9a0c08e5f6e7ada743c8b3a77">matrixLU</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordflow">return</span> m_lu;</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> }</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a4c56727da24405610cb3091b2d617968"> 148</a></span> <span class="keyword">inline</span> <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a4c56727da24405610cb3091b2d617968">nonzeroPivots</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordflow">return</span> m_nonzero_pivots;</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> }</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a7e6b69595a7290385bb8fe7f1e3e33cc"> 157</a></span> RealScalar <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a7e6b69595a7290385bb8fe7f1e3e33cc">maxPivot</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_maxpivot; }</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a14a2f6000a53705373a53592b0f4085d"> 163</a></span> EIGEN_DEVICE_FUNC <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1PermutationMatrix.html">PermutationPType</a>& <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a14a2f6000a53705373a53592b0f4085d">permutationP</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">return</span> m_p;</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> }</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aea8ad7d1c2d653b83cd3e044e2b51ff6"> 173</a></span> <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1PermutationMatrix.html">PermutationQType</a>& <a class="code hl_function" href="classEigen_1_1FullPivLU.html#aea8ad7d1c2d653b83cd3e044e2b51ff6">permutationQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keywordflow">return</span> m_q;</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> }</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> </div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aa27f4b6be627987145705644de7b9d69"> 193</a></span> <span class="keyword">inline</span> <span class="keyword">const</span> internal::kernel_retval<FullPivLU> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#aa27f4b6be627987145705644de7b9d69">kernel</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordflow">return</span> internal::kernel_retval<FullPivLU>(*<span class="keyword">this</span>);</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> }</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">inline</span> <span class="keyword">const</span> internal::image_retval<FullPivLU></div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a051c752c78b34cda7b485f1610e6a5f5"> 219</a></span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a051c752c78b34cda7b485f1610e6a5f5">image</a>(<span class="keyword">const</span> MatrixType& originalMatrix)<span class="keyword"> const</span></div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keywordflow">return</span> internal::image_retval<FullPivLU>(*<span class="keyword">this</span>, originalMatrix);</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> }</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span><span class="preprocessor"> #ifdef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1Solve.html">Solve<FullPivLU, Rhs></a></div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a600413f31d66142f3fdd4677c2661062"> 247</a></span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a600413f31d66142f3fdd4677c2661062">solve</a>(<span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Rhs></a>& b) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span><span class="preprocessor"> #endif</span></div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> </div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a3bc84ae31abe29028abddf9366c61530"> 253</a></span> <span class="keyword">inline</span> RealScalar <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a3bc84ae31abe29028abddf9366c61530">rcond</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> eigen_assert(m_isInitialized && <span class="stringliteral">"PartialPivLU is not initialized."</span>);</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keywordflow">return</span> internal::rcond_estimate_helper(m_l1_norm, *<span class="keyword">this</span>);</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> }</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> </div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="keyword">typename</span> internal::traits<MatrixType>::Scalar <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a276fd43d9ebf467638c1a4ddbd0dc2e3">determinant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> </div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aadc831f7ad5c448f087b3af54056e377"> 293</a></span> <a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU</a>& <a class="code hl_function" href="classEigen_1_1FullPivLU.html#aadc831f7ad5c448f087b3af54056e377">setThreshold</a>(<span class="keyword">const</span> RealScalar& <a class="code hl_function" href="classEigen_1_1FullPivLU.html#abdffac048d2d5e6f120012b6353b7811">threshold</a>)</div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> {</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> m_usePrescribedThreshold = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> m_prescribedThreshold = <a class="code hl_function" href="classEigen_1_1FullPivLU.html#abdffac048d2d5e6f120012b6353b7811">threshold</a>;</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> }</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> </div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a5d39f901a6a75995a2117f6f10118a06"> 308</a></span> <a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU</a>& <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a5d39f901a6a75995a2117f6f10118a06">setThreshold</a>(Default_t)</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> {</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> m_usePrescribedThreshold = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> }</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> </div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#abdffac048d2d5e6f120012b6353b7811"> 318</a></span> RealScalar <a class="code hl_function" href="classEigen_1_1FullPivLU.html#abdffac048d2d5e6f120012b6353b7811">threshold</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> eigen_assert(m_isInitialized || m_usePrescribedThreshold);</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> <span class="keywordflow">return</span> m_usePrescribedThreshold ? m_prescribedThreshold</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <span class="comment">// this formula comes from experimenting (see "LU precision tuning" thread on the list)</span></div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> <span class="comment">// and turns out to be identical to Higham's formula used already in LDLt.</span></div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> : <a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::epsilon</a>() * RealScalar(m_lu.diagonalSize());</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> }</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> </div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a820cc4babd876453801cea257243ee12"> 333</a></span> <span class="keyword">inline</span> <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a820cc4babd876453801cea257243ee12">rank</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> RealScalar premultiplied_threshold = abs(m_maxpivot) * <a class="code hl_function" href="classEigen_1_1FullPivLU.html#abdffac048d2d5e6f120012b6353b7811">threshold</a>();</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> result = 0;</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="keywordflow">for</span>(<a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> i = 0; i < m_nonzero_pivots; ++i)</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> result += (abs(m_lu.coeff(i,i)) > premultiplied_threshold);</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> <span class="keywordflow">return</span> result;</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> }</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#af6839a14a4003e001de5dbedc0274dd2"> 350</a></span> <span class="keyword">inline</span> <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#af6839a14a4003e001de5dbedc0274dd2">dimensionOfKernel</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <span class="keywordflow">return</span> cols() - <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a820cc4babd876453801cea257243ee12">rank</a>();</div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> }</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> </div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a1c502e81eae9cc22066090a6443c96f2"> 363</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a1c502e81eae9cc22066090a6443c96f2">isInjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a820cc4babd876453801cea257243ee12">rank</a>() == cols();</div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> }</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> </div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aae89d4edbe5dca9ac1d97e87699ce1cf"> 376</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#aae89d4edbe5dca9ac1d97e87699ce1cf">isSurjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a820cc4babd876453801cea257243ee12">rank</a>() == rows();</div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> }</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> </div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a213884b919c477067987fe5b68c064d4"> 388</a></span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a213884b919c477067987fe5b68c064d4">isInvertible</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="keywordflow">return</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a1c502e81eae9cc22066090a6443c96f2">isInjective</a>() && (m_lu.rows() == m_lu.cols());</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> }</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> </div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a9f54eba7ac4d22abe1f4867517ece4e9"> 401</a></span> <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1Inverse.html">Inverse<FullPivLU></a> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a9f54eba7ac4d22abe1f4867517ece4e9">inverse</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> eigen_assert(m_lu.rows() == m_lu.cols() && <span class="stringliteral">"You can't take the inverse of a non-square matrix!"</span>);</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> <span class="keywordflow">return</span> <a class="code hl_class" href="classEigen_1_1Inverse.html">Inverse<FullPivLU></a>(*<span class="keyword">this</span>);</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> }</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> </div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> MatrixType <a class="code hl_function" href="classEigen_1_1FullPivLU.html#a636b6d21732dc04f3d2155f7932d4521">reconstructedMatrix</a>() <span class="keyword">const</span>;</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> </div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <span class="keyword">inline</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows() const EIGEN_NOEXCEPT { <span class="keywordflow">return</span> m_lu.rows(); }</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="keyword">inline</span> <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols() const EIGEN_NOEXCEPT { <span class="keywordflow">return</span> m_lu.cols(); }</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> </div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span><span class="preprocessor"> #ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> <span class="keyword">template</span><<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType></div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> <span class="keywordtype">void</span> _solve_impl(<span class="keyword">const</span> RhsType &rhs, DstType &dst) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> </div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <span class="keyword">template</span><<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType></div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <span class="keywordtype">void</span> _solve_impl_transposed(<span class="keyword">const</span> RhsType &rhs, DstType &dst) <span class="keyword">const</span>;</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span><span class="preprocessor"> #endif</span></div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> </div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> <span class="keyword">protected</span>:</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> </div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> </div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> <span class="keywordtype">void</span> computeInPlace();</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> </div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> MatrixType m_lu;</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> PermutationPType m_p;</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> PermutationQType m_q;</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> IntColVectorType m_rowsTranspositions;</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> IntRowVectorType m_colsTranspositions;</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> m_nonzero_pivots;</div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> RealScalar m_l1_norm;</div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> RealScalar m_maxpivot, m_prescribedThreshold;</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="keywordtype">signed</span> <span class="keywordtype">char</span> m_det_pq;</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <span class="keywordtype">bool</span> m_isInitialized, m_usePrescribedThreshold;</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span>};</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> </div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aff435f4b563a5ac72620d3ed9a94535a"> 442</a></span><a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType, PermutationIndex>::FullPivLU</a>()</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> : m_isInitialized(false), m_usePrescribedThreshold(false)</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span>{</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span>}</div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> </div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ae98eda37867362efadc3079715e4164e"> 448</a></span><a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType, PermutationIndex>::FullPivLU</a>(<a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols)</div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> : m_lu(rows, cols),</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> m_p(rows),</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> m_q(cols),</div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> m_rowsTranspositions(rows),</div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> m_colsTranspositions(cols),</div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> m_isInitialized(false),</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> m_usePrescribedThreshold(false)</div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span>{</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span>}</div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> </div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span><span class="keyword">template</span><<span class="keyword">typename</span> InputType></div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#abb2984ad1b29636c402037d4b55f0926"> 461</a></span><a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType, PermutationIndex>::FullPivLU</a>(<span class="keyword">const</span> <a class="code hl_class" href="structEigen_1_1EigenBase.html">EigenBase<InputType></a>& matrix)</div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> : m_lu(matrix.rows(), matrix.cols()),</div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> m_p(matrix.rows()),</div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> m_q(matrix.cols()),</div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> m_rowsTranspositions(matrix.rows()),</div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> m_colsTranspositions(matrix.cols()),</div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> m_isInitialized(false),</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> m_usePrescribedThreshold(false)</div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span>{</div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <a class="code hl_function" href="classEigen_1_1FullPivLU.html#af266621b5d114229566caff0de1aa44b">compute</a>(matrix.<a class="code hl_function" href="structEigen_1_1EigenBase.html#a749b057c52245e486a101868d2578a24">derived</a>());</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span>}</div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> </div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span><span class="keyword">template</span><<span class="keyword">typename</span> InputType></div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a042bfb48570e7f2b360fb4aa9b0c3749"> 475</a></span><a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType, PermutationIndex>::FullPivLU</a>(<a class="code hl_class" href="structEigen_1_1EigenBase.html">EigenBase<InputType></a>& matrix)</div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> : m_lu(matrix.derived()),</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> m_p(matrix.rows()),</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> m_q(matrix.cols()),</div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> m_rowsTranspositions(matrix.rows()),</div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> m_colsTranspositions(matrix.cols()),</div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> m_isInitialized(false),</div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> m_usePrescribedThreshold(false)</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span>{</div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> computeInPlace();</div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span>}</div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> </div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span><span class="keywordtype">void</span> <a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType, PermutationIndex>::computeInPlace</a>()</div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span>{</div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> eigen_assert(m_lu.rows()<=<a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits<PermutationIndex>::highest</a>() && m_lu.cols()<=<a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits<PermutationIndex>::highest</a>());</div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> </div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();</div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> </div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size = m_lu.diagonalSize();</div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = m_lu.rows();</div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols = m_lu.cols();</div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> </div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> <span class="comment">// will store the transpositions, before we accumulate them at the end.</span></div>
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> <span class="comment">// can't accumulate on-the-fly because that will be done in reverse order for the rows.</span></div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span> m_rowsTranspositions.resize(m_lu.rows());</div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> m_colsTranspositions.resize(m_lu.cols());</div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> number_of_transpositions = 0; <span class="comment">// number of NONTRIVIAL transpositions, i.e. m_rowsTranspositions[i]!=i</span></div>
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> </div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> m_nonzero_pivots = size; <span class="comment">// the generic case is that in which all pivots are nonzero (invertible case)</span></div>
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> m_maxpivot = RealScalar(0);</div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> </div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> <span class="keywordflow">for</span>(<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k < size; ++k)</div>
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> {</div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> <span class="comment">// First, we need to find the pivot.</span></div>
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span> </div>
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> <span class="comment">// biggest coefficient in the remaining bottom-right corner (starting at row k, col k)</span></div>
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> row_of_biggest_in_corner, col_of_biggest_in_corner;</div>
<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> <span class="keyword">typedef</span> internal::scalar_score_coeff_op<Scalar> Scoring;</div>
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Scoring::result_type Score;</div>
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> Score biggest_in_corner;</div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span> biggest_in_corner = m_lu.bottomRightCorner(rows-k, cols-k)</div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> .unaryExpr(Scoring())</div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);</div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> row_of_biggest_in_corner += k; <span class="comment">// correct the values! since they were computed in the corner,</span></div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> col_of_biggest_in_corner += k; <span class="comment">// need to add k to them.</span></div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span> </div>
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> <span class="keywordflow">if</span>(numext::is_exactly_zero(biggest_in_corner))</div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span> {</div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> <span class="comment">// before exiting, make sure to initialize the still uninitialized transpositions</span></div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> <span class="comment">// in a sane state without destroying what we already have.</span></div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> m_nonzero_pivots = k;</div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <span class="keywordflow">for</span>(<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = k; i < size; ++i)</div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> {</div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> m_rowsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);</div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> m_colsTranspositions.coeffRef(i) = internal::convert_index<StorageIndex>(i);</div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> }</div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> }</div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> </div>
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span> RealScalar abs_pivot = internal::abs_knowing_score<Scalar>()(m_lu(row_of_biggest_in_corner, col_of_biggest_in_corner), biggest_in_corner);</div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> <span class="keywordflow">if</span>(abs_pivot > m_maxpivot) m_maxpivot = abs_pivot;</div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> </div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> <span class="comment">// Now that we've found the pivot, we need to apply the row/col swaps to</span></div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> <span class="comment">// bring it to the location (k,k).</span></div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> </div>
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span> m_rowsTranspositions.coeffRef(k) = internal::convert_index<StorageIndex>(row_of_biggest_in_corner);</div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> m_colsTranspositions.coeffRef(k) = internal::convert_index<StorageIndex>(col_of_biggest_in_corner);</div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> <span class="keywordflow">if</span>(k != row_of_biggest_in_corner) {</div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> m_lu.row(k).swap(m_lu.row(row_of_biggest_in_corner));</div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span> ++number_of_transpositions;</div>
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> }</div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span> <span class="keywordflow">if</span>(k != col_of_biggest_in_corner) {</div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> m_lu.col(k).swap(m_lu.col(col_of_biggest_in_corner));</div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> ++number_of_transpositions;</div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> }</div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span> </div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> <span class="comment">// Now that the pivot is at the right location, we update the remaining</span></div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> <span class="comment">// bottom-right corner by Gaussian elimination.</span></div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> </div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> <span class="keywordflow">if</span>(k<rows-1)</div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> m_lu.col(k).tail(rows-k-1) /= m_lu.coeff(k,k);</div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> <span class="keywordflow">if</span>(k<size-1)</div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> m_lu.block(k+1,k+1,rows-k-1,cols-k-1).noalias() -= m_lu.col(k).tail(rows-k-1) * m_lu.row(k).tail(cols-k-1);</div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> }</div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> </div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> <span class="comment">// the main loop is over, we still have to accumulate the transpositions to find the</span></div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> <span class="comment">// permutations P and Q</span></div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> </div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span> m_p.setIdentity(rows);</div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> <span class="keywordflow">for</span>(Index k = size-1; k >= 0; --k)</div>
<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span> m_p.applyTranspositionOnTheRight(k, m_rowsTranspositions.coeff(k));</div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> </div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> m_q.setIdentity(cols);</div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> <span class="keywordflow">for</span>(Index k = 0; k < size; ++k)</div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> m_q.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k));</div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> </div>
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> m_det_pq = (number_of_transpositions%2) ? -1 : 1;</div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> </div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span> m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span>}</div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> </div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a276fd43d9ebf467638c1a4ddbd0dc2e3"> 578</a></span><span class="keyword">typename</span> internal::traits<MatrixType>::Scalar <a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType, PermutationIndex>::determinant</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> eigen_assert(m_lu.rows() == m_lu.cols() && <span class="stringliteral">"You can't take the determinant of a non-square matrix!"</span>);</div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> <span class="keywordflow">return</span> Scalar(m_det_pq) * Scalar(m_lu.diagonal().prod());</div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span>}</div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> </div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a636b6d21732dc04f3d2155f7932d4521"> 589</a></span>MatrixType <a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType, PermutationIndex>::reconstructedMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> <span class="keyword">const</span> <a class="code hl_typedef" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> smalldim = (std::min)(m_lu.rows(), m_lu.cols());</div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> <span class="comment">// LU</span></div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> MatrixType res(m_lu.rows(),m_lu.cols());</div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> <span class="comment">// FIXME the .toDenseMatrix() should not be needed...</span></div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> res = m_lu.leftCols(smalldim)</div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> .template triangularView<UnitLower>().toDenseMatrix()</div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> * m_lu.topRows(smalldim)</div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> .template triangularView<Upper>().toDenseMatrix();</div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> </div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> <span class="comment">// P^{-1}(LU)</span></div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> res = m_p.inverse() * res;</div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> </div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> <span class="comment">// (P^{-1}LU)Q^{-1}</span></div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> res = res * m_q.inverse();</div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> </div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span>}</div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span> </div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span><span class="comment">/********* Implementation of kernel() **************************************************/</span></div>
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> </div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType_, <span class="keyword">typename</span> PermutationIndex_></div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span><span class="keyword">struct </span>kernel_retval<<a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU</a><MatrixType_, PermutationIndex_> ></div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> : kernel_retval_base<FullPivLU<MatrixType_, PermutationIndex_> ></div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span>{</div>
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> <span class="keyword">using </span>DecompositionType = <a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType_, PermutationIndex_></a>;</div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> EIGEN_MAKE_KERNEL_HELPERS(DecompositionType)</div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> </div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> <span class="keyword">enum</span> { MaxSmallDimAtCompileTime = min_size_prefer_fixed(</div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> MatrixType::MaxRowsAtCompileTime)</div>
<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> };</div>
<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span> </div>
<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> <span class="keyword">template</span><<span class="keyword">typename</span> Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span> <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span> <span class="keyword">const</span> Index cols = dec().matrixLU().cols(), dimker = cols - rank();</div>
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> <span class="keywordflow">if</span>(dimker == 0)</div>
<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span> {</div>
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span> <span class="comment">// The Kernel is just {0}, so it doesn't have a basis properly speaking, but let's</span></div>
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span> <span class="comment">// avoid crashing/asserting as that depends on floating point calculations. Let's</span></div>
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span> <span class="comment">// just return a single column vector filled with zeros.</span></div>
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span> dst.setZero();</div>
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span> }</div>
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> </div>
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> <span class="comment">/* Let us use the following lemma:</span></div>
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span><span class="comment"> *</span></div>
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span><span class="comment"> * Lemma: If the matrix A has the LU decomposition PAQ = LU,</span></div>
<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span><span class="comment"> * then Ker A = Q(Ker U).</span></div>
<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"> 642</span><span class="comment"> *</span></div>
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span><span class="comment"> * Proof: trivial: just keep in mind that P, Q, L are invertible.</span></div>
<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span><span class="comment"> */</span></div>
<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span> </div>
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> <span class="comment">/* Thus, all we need to do is to compute Ker U, and then apply Q.</span></div>
<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span><span class="comment"> *</span></div>
<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"> 648</span><span class="comment"> * U is upper triangular, with eigenvalues sorted so that any zeros appear at the end.</span></div>
<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span><span class="comment"> * Thus, the diagonal of U ends with exactly</span></div>
<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span><span class="comment"> * dimKer zero's. Let us use that to construct dimKer linearly</span></div>
<div class="line"><a id="l00651" name="l00651"></a><span class="lineno"> 651</span><span class="comment"> * independent vectors in Ker U.</span></div>
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"> 652</span><span class="comment"> */</span></div>
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> </div>
<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span> Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());</div>
<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span> RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();</div>
<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p = 0;</div>
<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> <span class="keywordflow">for</span>(Index i = 0; i < dec().nonzeroPivots(); ++i)</div>
<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span> <span class="keywordflow">if</span>(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)</div>
<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span> pivots.coeffRef(p++) = i;</div>
<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span> eigen_internal_assert(p == rank());</div>
<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span> </div>
<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"> 662</span> <span class="comment">// we construct a temporaty trapezoid matrix m, by taking the U matrix and</span></div>
<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> <span class="comment">// permuting the rows and cols to bring the nonnegligible pivots to the top of</span></div>
<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> <span class="comment">// the main diagonal. We need that to be able to apply our triangular solvers.</span></div>
<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> <span class="comment">// FIXME when we get triangularView-for-rectangular-matrices, this can be simplified</span></div>
<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> Matrix<<span class="keyword">typename</span> MatrixType::Scalar, <a class="code hl_variable" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>, <a class="code hl_variable" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>, MatrixType::Options,</div>
<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span> MaxSmallDimAtCompileTime, MatrixType::MaxColsAtCompileTime></div>
<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span> m(dec().matrixLU().block(0, 0, rank(), cols));</div>
<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> <span class="keywordflow">for</span>(Index i = 0; i < rank(); ++i)</div>
<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span> {</div>
<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> <span class="keywordflow">if</span>(i) m.row(i).head(i).setZero();</div>
<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</span> m.row(i).tail(cols-i) = dec().matrixLU().row(pivots.coeff(i)).tail(cols-i);</div>
<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> }</div>
<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span> m.block(0, 0, rank(), rank());</div>
<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> m.block(0, 0, rank(), rank()).template triangularView<StrictlyLower>().setZero();</div>
<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span> <span class="keywordflow">for</span>(Index i = 0; i < rank(); ++i)</div>
<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> m.col(i).swap(m.col(pivots.coeff(i)));</div>
<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</span> </div>
<div class="line"><a id="l00679" name="l00679"></a><span class="lineno"> 679</span> <span class="comment">// ok, we have our trapezoid matrix, we can apply the triangular solver.</span></div>
<div class="line"><a id="l00680" name="l00680"></a><span class="lineno"> 680</span> <span class="comment">// notice that the math behind this suggests that we should apply this to the</span></div>
<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</span> <span class="comment">// negative of the RHS, but for performance we just put the negative sign elsewhere, see below.</span></div>
<div class="line"><a id="l00682" name="l00682"></a><span class="lineno"> 682</span> m.topLeftCorner(rank(), rank())</div>
<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span> .<span class="keyword">template</span> triangularView<Upper>().solveInPlace(</div>
<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> m.topRightCorner(rank(), dimker)</div>
<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> );</div>
<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> </div>
<div class="line"><a id="l00687" name="l00687"></a><span class="lineno"> 687</span> <span class="comment">// now we must undo the column permutation that we had applied!</span></div>
<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> <span class="keywordflow">for</span>(Index i = rank()-1; i >= 0; --i)</div>
<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span> m.col(i).swap(m.col(pivots.coeff(i)));</div>
<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span> </div>
<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span> <span class="comment">// see the negative sign in the next line, that's what we were talking about above.</span></div>
<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span> <span class="keywordflow">for</span>(Index i = 0; i < rank(); ++i) dst.row(dec().permutationQ().indices().coeff(i)) = -m.row(i).tail(dimker);</div>
<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"> 693</span> <span class="keywordflow">for</span>(Index i = rank(); i < cols; ++i) dst.row(dec().permutationQ().indices().coeff(i)).setZero();</div>
<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span> <span class="keywordflow">for</span>(Index k = 0; k < dimker; ++k) dst.coeffRef(dec().permutationQ().indices().coeff(rank()+k), k) = Scalar(1);</div>
<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span> }</div>
<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span>};</div>
<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span> </div>
<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span><span class="comment">/***** Implementation of image() *****************************************************/</span></div>
<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span> </div>
<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType_, <span class="keyword">typename</span> PermutationIndex_></div>
<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"> 701</span><span class="keyword">struct </span>image_retval<FullPivLU<MatrixType_, PermutationIndex_> ></div>
<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span> : image_retval_base<FullPivLU<MatrixType_, PermutationIndex_> ></div>
<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span>{</div>
<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span> <span class="keyword">using </span>DecompositionType = FullPivLU<MatrixType_, PermutationIndex_>;</div>
<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> EIGEN_MAKE_IMAGE_HELPERS(DecompositionType)</div>
<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"> 706</span> </div>
<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> <span class="keyword">enum</span> { MaxSmallDimAtCompileTime = min_size_prefer_fixed(</div>
<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"> 709</span> MatrixType::MaxRowsAtCompileTime)</div>
<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> };</div>
<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> </div>
<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> <span class="keyword">template</span><<span class="keyword">typename</span> Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> <span class="keywordflow">if</span>(rank() == 0)</div>
<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span> {</div>
<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> <span class="comment">// The Image is just {0}, so it doesn't have a basis properly speaking, but let's</span></div>
<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> <span class="comment">// avoid crashing/asserting as that depends on floating point calculations. Let's</span></div>
<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span> <span class="comment">// just return a single column vector filled with zeros.</span></div>
<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> dst.setZero();</div>
<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00722" name="l00722"></a><span class="lineno"> 722</span> }</div>
<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"> 723</span> </div>
<div class="line"><a id="l00724" name="l00724"></a><span class="lineno"> 724</span> Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());</div>
<div class="line"><a id="l00725" name="l00725"></a><span class="lineno"> 725</span> RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();</div>
<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"> 726</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p = 0;</div>
<div class="line"><a id="l00727" name="l00727"></a><span class="lineno"> 727</span> <span class="keywordflow">for</span>(Index i = 0; i < dec().nonzeroPivots(); ++i)</div>
<div class="line"><a id="l00728" name="l00728"></a><span class="lineno"> 728</span> <span class="keywordflow">if</span>(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)</div>
<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"> 729</span> pivots.coeffRef(p++) = i;</div>
<div class="line"><a id="l00730" name="l00730"></a><span class="lineno"> 730</span> eigen_internal_assert(p == rank());</div>
<div class="line"><a id="l00731" name="l00731"></a><span class="lineno"> 731</span> </div>
<div class="line"><a id="l00732" name="l00732"></a><span class="lineno"> 732</span> <span class="keywordflow">for</span>(Index i = 0; i < rank(); ++i)</div>
<div class="line"><a id="l00733" name="l00733"></a><span class="lineno"> 733</span> dst.col(i) = originalMatrix().col(dec().permutationQ().indices().coeff(pivots.coeff(i)));</div>
<div class="line"><a id="l00734" name="l00734"></a><span class="lineno"> 734</span> }</div>
<div class="line"><a id="l00735" name="l00735"></a><span class="lineno"> 735</span>};</div>
<div class="line"><a id="l00736" name="l00736"></a><span class="lineno"> 736</span> </div>
<div class="line"><a id="l00737" name="l00737"></a><span class="lineno"> 737</span><span class="comment">/***** Implementation of solve() *****************************************************/</span></div>
<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"> 738</span> </div>
<div class="line"><a id="l00739" name="l00739"></a><span class="lineno"> 739</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00740" name="l00740"></a><span class="lineno"> 740</span> </div>
<div class="line"><a id="l00741" name="l00741"></a><span class="lineno"> 741</span><span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a id="l00742" name="l00742"></a><span class="lineno"> 742</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType_, <span class="keyword">typename</span> PermutationIndex_></div>
<div class="line"><a id="l00743" name="l00743"></a><span class="lineno"> 743</span><span class="keyword">template</span><<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType></div>
<div class="line"><a id="l00744" name="l00744"></a><span class="lineno"> 744</span><span class="keywordtype">void</span> FullPivLU<MatrixType_, PermutationIndex_>::_solve_impl(<span class="keyword">const</span> RhsType &rhs, DstType &dst)<span class="keyword"> const</span></div>
<div class="line"><a id="l00745" name="l00745"></a><span class="lineno"> 745</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00746" name="l00746"></a><span class="lineno"> 746</span> <span class="comment">/* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1}.</span></div>
<div class="line"><a id="l00747" name="l00747"></a><span class="lineno"> 747</span><span class="comment"> * So we proceed as follows:</span></div>
<div class="line"><a id="l00748" name="l00748"></a><span class="lineno"> 748</span><span class="comment"> * Step 1: compute c = P * rhs.</span></div>
<div class="line"><a id="l00749" name="l00749"></a><span class="lineno"> 749</span><span class="comment"> * Step 2: replace c by the solution x to Lx = c. Exists because L is invertible.</span></div>
<div class="line"><a id="l00750" name="l00750"></a><span class="lineno"> 750</span><span class="comment"> * Step 3: replace c by the solution x to Ux = c. May or may not exist.</span></div>
<div class="line"><a id="l00751" name="l00751"></a><span class="lineno"> 751</span><span class="comment"> * Step 4: result = Q * c;</span></div>
<div class="line"><a id="l00752" name="l00752"></a><span class="lineno"> 752</span><span class="comment"> */</span></div>
<div class="line"><a id="l00753" name="l00753"></a><span class="lineno"> 753</span> </div>
<div class="line"><a id="l00754" name="l00754"></a><span class="lineno"> 754</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = this->rows(),</div>
<div class="line"><a id="l00755" name="l00755"></a><span class="lineno"> 755</span> cols = this->cols(),</div>
<div class="line"><a id="l00756" name="l00756"></a><span class="lineno"> 756</span> nonzero_pivots = this->rank();</div>
<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"> 757</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> smalldim = (std::min)(rows, cols);</div>
<div class="line"><a id="l00758" name="l00758"></a><span class="lineno"> 758</span> </div>
<div class="line"><a id="l00759" name="l00759"></a><span class="lineno"> 759</span> <span class="keywordflow">if</span>(nonzero_pivots == 0)</div>
<div class="line"><a id="l00760" name="l00760"></a><span class="lineno"> 760</span> {</div>
<div class="line"><a id="l00761" name="l00761"></a><span class="lineno"> 761</span> dst.setZero();</div>
<div class="line"><a id="l00762" name="l00762"></a><span class="lineno"> 762</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00763" name="l00763"></a><span class="lineno"> 763</span> }</div>
<div class="line"><a id="l00764" name="l00764"></a><span class="lineno"> 764</span> </div>
<div class="line"><a id="l00765" name="l00765"></a><span class="lineno"> 765</span> <span class="keyword">typename</span> RhsType::PlainObject c(rhs.rows(), rhs.cols());</div>
<div class="line"><a id="l00766" name="l00766"></a><span class="lineno"> 766</span> </div>
<div class="line"><a id="l00767" name="l00767"></a><span class="lineno"> 767</span> <span class="comment">// Step 1</span></div>
<div class="line"><a id="l00768" name="l00768"></a><span class="lineno"> 768</span> c = permutationP() * rhs;</div>
<div class="line"><a id="l00769" name="l00769"></a><span class="lineno"> 769</span> </div>
<div class="line"><a id="l00770" name="l00770"></a><span class="lineno"> 770</span> <span class="comment">// Step 2</span></div>
<div class="line"><a id="l00771" name="l00771"></a><span class="lineno"> 771</span> m_lu.topLeftCorner(smalldim,smalldim)</div>
<div class="line"><a id="l00772" name="l00772"></a><span class="lineno"> 772</span> .template triangularView<UnitLower>()</div>
<div class="line"><a id="l00773" name="l00773"></a><span class="lineno"> 773</span> .solveInPlace(c.topRows(smalldim));</div>
<div class="line"><a id="l00774" name="l00774"></a><span class="lineno"> 774</span> <span class="keywordflow">if</span>(rows>cols)</div>
<div class="line"><a id="l00775" name="l00775"></a><span class="lineno"> 775</span> c.bottomRows(rows-cols) -= m_lu.bottomRows(rows-cols) * c.topRows(cols);</div>
<div class="line"><a id="l00776" name="l00776"></a><span class="lineno"> 776</span> </div>
<div class="line"><a id="l00777" name="l00777"></a><span class="lineno"> 777</span> <span class="comment">// Step 3</span></div>
<div class="line"><a id="l00778" name="l00778"></a><span class="lineno"> 778</span> m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)</div>
<div class="line"><a id="l00779" name="l00779"></a><span class="lineno"> 779</span> .template triangularView<Upper>()</div>
<div class="line"><a id="l00780" name="l00780"></a><span class="lineno"> 780</span> .solveInPlace(c.topRows(nonzero_pivots));</div>
<div class="line"><a id="l00781" name="l00781"></a><span class="lineno"> 781</span> </div>
<div class="line"><a id="l00782" name="l00782"></a><span class="lineno"> 782</span> <span class="comment">// Step 4</span></div>
<div class="line"><a id="l00783" name="l00783"></a><span class="lineno"> 783</span> <span class="keywordflow">for</span>(Index i = 0; i < nonzero_pivots; ++i)</div>
<div class="line"><a id="l00784" name="l00784"></a><span class="lineno"> 784</span> dst.row(permutationQ().indices().coeff(i)) = c.row(i);</div>
<div class="line"><a id="l00785" name="l00785"></a><span class="lineno"> 785</span> <span class="keywordflow">for</span>(Index i = nonzero_pivots; i < m_lu.cols(); ++i)</div>
<div class="line"><a id="l00786" name="l00786"></a><span class="lineno"> 786</span> dst.row(permutationQ().indices().coeff(i)).setZero();</div>
<div class="line"><a id="l00787" name="l00787"></a><span class="lineno"> 787</span>}</div>
<div class="line"><a id="l00788" name="l00788"></a><span class="lineno"> 788</span> </div>
<div class="line"><a id="l00789" name="l00789"></a><span class="lineno"> 789</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType_, <span class="keyword">typename</span> PermutationIndex_></div>
<div class="line"><a id="l00790" name="l00790"></a><span class="lineno"> 790</span><span class="keyword">template</span><<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType></div>
<div class="line"><a id="l00791" name="l00791"></a><span class="lineno"> 791</span><span class="keywordtype">void</span> FullPivLU<MatrixType_, PermutationIndex_>::_solve_impl_transposed(<span class="keyword">const</span> RhsType &rhs, DstType &dst)<span class="keyword"> const</span></div>
<div class="line"><a id="l00792" name="l00792"></a><span class="lineno"> 792</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00793" name="l00793"></a><span class="lineno"> 793</span> <span class="comment">/* The decomposition PAQ = LU can be rewritten as A = P^{-1} L U Q^{-1},</span></div>
<div class="line"><a id="l00794" name="l00794"></a><span class="lineno"> 794</span><span class="comment"> * and since permutations are real and unitary, we can write this</span></div>
<div class="line"><a id="l00795" name="l00795"></a><span class="lineno"> 795</span><span class="comment"> * as A^T = Q U^T L^T P,</span></div>
<div class="line"><a id="l00796" name="l00796"></a><span class="lineno"> 796</span><span class="comment"> * So we proceed as follows:</span></div>
<div class="line"><a id="l00797" name="l00797"></a><span class="lineno"> 797</span><span class="comment"> * Step 1: compute c = Q^T rhs.</span></div>
<div class="line"><a id="l00798" name="l00798"></a><span class="lineno"> 798</span><span class="comment"> * Step 2: replace c by the solution x to U^T x = c. May or may not exist.</span></div>
<div class="line"><a id="l00799" name="l00799"></a><span class="lineno"> 799</span><span class="comment"> * Step 3: replace c by the solution x to L^T x = c.</span></div>
<div class="line"><a id="l00800" name="l00800"></a><span class="lineno"> 800</span><span class="comment"> * Step 4: result = P^T c.</span></div>
<div class="line"><a id="l00801" name="l00801"></a><span class="lineno"> 801</span><span class="comment"> * If Conjugate is true, replace "^T" by "^*" above.</span></div>
<div class="line"><a id="l00802" name="l00802"></a><span class="lineno"> 802</span><span class="comment"> */</span></div>
<div class="line"><a id="l00803" name="l00803"></a><span class="lineno"> 803</span> </div>
<div class="line"><a id="l00804" name="l00804"></a><span class="lineno"> 804</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = this->rows(), cols = this->cols(),</div>
<div class="line"><a id="l00805" name="l00805"></a><span class="lineno"> 805</span> nonzero_pivots = this->rank();</div>
<div class="line"><a id="l00806" name="l00806"></a><span class="lineno"> 806</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> smalldim = (std::min)(rows, cols);</div>
<div class="line"><a id="l00807" name="l00807"></a><span class="lineno"> 807</span> </div>
<div class="line"><a id="l00808" name="l00808"></a><span class="lineno"> 808</span> <span class="keywordflow">if</span>(nonzero_pivots == 0)</div>
<div class="line"><a id="l00809" name="l00809"></a><span class="lineno"> 809</span> {</div>
<div class="line"><a id="l00810" name="l00810"></a><span class="lineno"> 810</span> dst.setZero();</div>
<div class="line"><a id="l00811" name="l00811"></a><span class="lineno"> 811</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00812" name="l00812"></a><span class="lineno"> 812</span> }</div>
<div class="line"><a id="l00813" name="l00813"></a><span class="lineno"> 813</span> </div>
<div class="line"><a id="l00814" name="l00814"></a><span class="lineno"> 814</span> <span class="keyword">typename</span> RhsType::PlainObject c(rhs.rows(), rhs.cols());</div>
<div class="line"><a id="l00815" name="l00815"></a><span class="lineno"> 815</span> </div>
<div class="line"><a id="l00816" name="l00816"></a><span class="lineno"> 816</span> <span class="comment">// Step 1</span></div>
<div class="line"><a id="l00817" name="l00817"></a><span class="lineno"> 817</span> c = permutationQ().inverse() * rhs;</div>
<div class="line"><a id="l00818" name="l00818"></a><span class="lineno"> 818</span> </div>
<div class="line"><a id="l00819" name="l00819"></a><span class="lineno"> 819</span> <span class="comment">// Step 2</span></div>
<div class="line"><a id="l00820" name="l00820"></a><span class="lineno"> 820</span> m_lu.topLeftCorner(nonzero_pivots, nonzero_pivots)</div>
<div class="line"><a id="l00821" name="l00821"></a><span class="lineno"> 821</span> .template triangularView<Upper>()</div>
<div class="line"><a id="l00822" name="l00822"></a><span class="lineno"> 822</span> .transpose()</div>
<div class="line"><a id="l00823" name="l00823"></a><span class="lineno"> 823</span> .template conjugateIf<Conjugate>()</div>
<div class="line"><a id="l00824" name="l00824"></a><span class="lineno"> 824</span> .solveInPlace(c.topRows(nonzero_pivots));</div>
<div class="line"><a id="l00825" name="l00825"></a><span class="lineno"> 825</span> </div>
<div class="line"><a id="l00826" name="l00826"></a><span class="lineno"> 826</span> <span class="comment">// Step 3</span></div>
<div class="line"><a id="l00827" name="l00827"></a><span class="lineno"> 827</span> m_lu.topLeftCorner(smalldim, smalldim)</div>
<div class="line"><a id="l00828" name="l00828"></a><span class="lineno"> 828</span> .template triangularView<UnitLower>()</div>
<div class="line"><a id="l00829" name="l00829"></a><span class="lineno"> 829</span> .transpose()</div>
<div class="line"><a id="l00830" name="l00830"></a><span class="lineno"> 830</span> .template conjugateIf<Conjugate>()</div>
<div class="line"><a id="l00831" name="l00831"></a><span class="lineno"> 831</span> .solveInPlace(c.topRows(smalldim));</div>
<div class="line"><a id="l00832" name="l00832"></a><span class="lineno"> 832</span> </div>
<div class="line"><a id="l00833" name="l00833"></a><span class="lineno"> 833</span> <span class="comment">// Step 4</span></div>
<div class="line"><a id="l00834" name="l00834"></a><span class="lineno"> 834</span> PermutationPType invp = permutationP().inverse().eval();</div>
<div class="line"><a id="l00835" name="l00835"></a><span class="lineno"> 835</span> <span class="keywordflow">for</span>(Index i = 0; i < smalldim; ++i)</div>
<div class="line"><a id="l00836" name="l00836"></a><span class="lineno"> 836</span> dst.row(invp.indices().coeff(i)) = c.row(i);</div>
<div class="line"><a id="l00837" name="l00837"></a><span class="lineno"> 837</span> <span class="keywordflow">for</span>(Index i = smalldim; i < rows; ++i)</div>
<div class="line"><a id="l00838" name="l00838"></a><span class="lineno"> 838</span> dst.row(invp.indices().coeff(i)).setZero();</div>
<div class="line"><a id="l00839" name="l00839"></a><span class="lineno"> 839</span>}</div>
<div class="line"><a id="l00840" name="l00840"></a><span class="lineno"> 840</span> </div>
<div class="line"><a id="l00841" name="l00841"></a><span class="lineno"> 841</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00842" name="l00842"></a><span class="lineno"> 842</span> </div>
<div class="line"><a id="l00843" name="l00843"></a><span class="lineno"> 843</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00844" name="l00844"></a><span class="lineno"> 844</span> </div>
<div class="line"><a id="l00845" name="l00845"></a><span class="lineno"> 845</span> </div>
<div class="line"><a id="l00846" name="l00846"></a><span class="lineno"> 846</span><span class="comment">/***** Implementation of inverse() *****************************************************/</span></div>
<div class="line"><a id="l00847" name="l00847"></a><span class="lineno"> 847</span><span class="keyword">template</span><<span class="keyword">typename</span> DstXprType, <span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00848" name="l00848"></a><span class="lineno"> 848</span><span class="keyword">struct </span>Assignment<DstXprType, Inverse<FullPivLU<MatrixType, PermutationIndex> >, internal::assign_op<typename DstXprType::Scalar,typename FullPivLU<MatrixType, PermutationIndex>::Scalar>, Dense2Dense></div>
<div class="line"><a id="l00849" name="l00849"></a><span class="lineno"> 849</span>{</div>
<div class="line"><a id="l00850" name="l00850"></a><span class="lineno"> 850</span> <span class="keyword">typedef</span> FullPivLU<MatrixType, PermutationIndex> LuType;</div>
<div class="line"><a id="l00851" name="l00851"></a><span class="lineno"> 851</span> <span class="keyword">typedef</span> Inverse<LuType> SrcXprType;</div>
<div class="line"><a id="l00852" name="l00852"></a><span class="lineno"> 852</span> <span class="keyword">static</span> <span class="keywordtype">void</span> run(DstXprType &dst, <span class="keyword">const</span> SrcXprType &src, <span class="keyword">const</span> internal::assign_op<typename DstXprType::Scalar,typename MatrixType::Scalar> &)</div>
<div class="line"><a id="l00853" name="l00853"></a><span class="lineno"> 853</span> {</div>
<div class="line"><a id="l00854" name="l00854"></a><span class="lineno"> 854</span> dst = src.nestedExpression().<a class="code hl_function" href="classEigen_1_1SolverBase.html#a943c352b597e3cd4744d5c11bfd77520">solve</a>(MatrixType::Identity(src.rows(), src.cols()));</div>
<div class="line"><a id="l00855" name="l00855"></a><span class="lineno"> 855</span> }</div>
<div class="line"><a id="l00856" name="l00856"></a><span class="lineno"> 856</span>};</div>
<div class="line"><a id="l00857" name="l00857"></a><span class="lineno"> 857</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00858" name="l00858"></a><span class="lineno"> 858</span> </div>
<div class="line"><a id="l00859" name="l00859"></a><span class="lineno"> 859</span><span class="comment">/******* MatrixBase methods *****************************************************************/</span></div>
<div class="line"><a id="l00860" name="l00860"></a><span class="lineno"> 860</span> </div>
<div class="line"><a id="l00867" name="l00867"></a><span class="lineno"> 867</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00868" name="l00868"></a><span class="lineno"> 868</span><span class="keyword">template</span><<span class="keyword">typename</span> PermutationIndex></div>
<div class="line"><a id="l00869" name="l00869"></a><span class="lineno"> 869</span><span class="keyword">inline</span> <span class="keyword">const</span> FullPivLU<typename MatrixBase<Derived>::PlainObject, PermutationIndex></div>
<div class="line"><a id="l00870" name="l00870"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a7c3bebf2e777a9df0778d8a96ef3b500"> 870</a></span><a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::fullPivLu</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00871" name="l00871"></a><span class="lineno"> 871</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00872" name="l00872"></a><span class="lineno"> 872</span> <span class="keywordflow">return</span> <a class="code hl_class" href="classEigen_1_1FullPivLU.html">FullPivLU<PlainObject, PermutationIndex></a>(eval());</div>
<div class="line"><a id="l00873" name="l00873"></a><span class="lineno"> 873</span>}</div>
<div class="line"><a id="l00874" name="l00874"></a><span class="lineno"> 874</span> </div>
<div class="line"><a id="l00875" name="l00875"></a><span class="lineno"> 875</span>} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a id="l00876" name="l00876"></a><span class="lineno"> 876</span> </div>
<div class="line"><a id="l00877" name="l00877"></a><span class="lineno"> 877</span><span class="preprocessor">#endif </span><span class="comment">// EIGEN_LU_H</span></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html"><div class="ttname"><a href="classEigen_1_1FullPivLU.html">Eigen::FullPivLU</a></div><div class="ttdoc">LU decomposition of a matrix with complete pivoting, and related features.</div><div class="ttdef"><b>Definition</b> FullPivLU.h:64</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a051c752c78b34cda7b485f1610e6a5f5"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a051c752c78b34cda7b485f1610e6a5f5">Eigen::FullPivLU::image</a></div><div class="ttdeci">const internal::image_retval< FullPivLU > image(const MatrixType &originalMatrix) const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:219</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a14a2f6000a53705373a53592b0f4085d"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a14a2f6000a53705373a53592b0f4085d">Eigen::FullPivLU::permutationP</a></div><div class="ttdeci">const PermutationPType & permutationP() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:163</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a1c502e81eae9cc22066090a6443c96f2"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a1c502e81eae9cc22066090a6443c96f2">Eigen::FullPivLU::isInjective</a></div><div class="ttdeci">bool isInjective() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:363</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a213884b919c477067987fe5b68c064d4"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a213884b919c477067987fe5b68c064d4">Eigen::FullPivLU::isInvertible</a></div><div class="ttdeci">bool isInvertible() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:388</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a276fd43d9ebf467638c1a4ddbd0dc2e3"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a276fd43d9ebf467638c1a4ddbd0dc2e3">Eigen::FullPivLU::determinant</a></div><div class="ttdeci">internal::traits< MatrixType >::Scalar determinant() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:578</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a3bc84ae31abe29028abddf9366c61530"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a3bc84ae31abe29028abddf9366c61530">Eigen::FullPivLU::rcond</a></div><div class="ttdeci">RealScalar rcond() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:253</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a4c56727da24405610cb3091b2d617968"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a4c56727da24405610cb3091b2d617968">Eigen::FullPivLU::nonzeroPivots</a></div><div class="ttdeci">Index nonzeroPivots() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:148</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a5d39f901a6a75995a2117f6f10118a06"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a5d39f901a6a75995a2117f6f10118a06">Eigen::FullPivLU::setThreshold</a></div><div class="ttdeci">FullPivLU & setThreshold(Default_t)</div><div class="ttdef"><b>Definition</b> FullPivLU.h:308</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a600413f31d66142f3fdd4677c2661062"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a600413f31d66142f3fdd4677c2661062">Eigen::FullPivLU::solve</a></div><div class="ttdeci">const Solve< FullPivLU, Rhs > solve(const MatrixBase< Rhs > &b) const</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a636b6d21732dc04f3d2155f7932d4521"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a636b6d21732dc04f3d2155f7932d4521">Eigen::FullPivLU::reconstructedMatrix</a></div><div class="ttdeci">MatrixType reconstructedMatrix() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:589</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a7e6b69595a7290385bb8fe7f1e3e33cc"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a7e6b69595a7290385bb8fe7f1e3e33cc">Eigen::FullPivLU::maxPivot</a></div><div class="ttdeci">RealScalar maxPivot() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:157</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a820cc4babd876453801cea257243ee12"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a820cc4babd876453801cea257243ee12">Eigen::FullPivLU::rank</a></div><div class="ttdeci">Index rank() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:333</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_a9f54eba7ac4d22abe1f4867517ece4e9"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a9f54eba7ac4d22abe1f4867517ece4e9">Eigen::FullPivLU::inverse</a></div><div class="ttdeci">const Inverse< FullPivLU > inverse() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:401</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_aa27f4b6be627987145705644de7b9d69"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aa27f4b6be627987145705644de7b9d69">Eigen::FullPivLU::kernel</a></div><div class="ttdeci">const internal::kernel_retval< FullPivLU > kernel() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:193</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_aadc831f7ad5c448f087b3af54056e377"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aadc831f7ad5c448f087b3af54056e377">Eigen::FullPivLU::setThreshold</a></div><div class="ttdeci">FullPivLU & setThreshold(const RealScalar &threshold)</div><div class="ttdef"><b>Definition</b> FullPivLU.h:293</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_aae89d4edbe5dca9ac1d97e87699ce1cf"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aae89d4edbe5dca9ac1d97e87699ce1cf">Eigen::FullPivLU::isSurjective</a></div><div class="ttdeci">bool isSurjective() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:376</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_abdffac048d2d5e6f120012b6353b7811"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#abdffac048d2d5e6f120012b6353b7811">Eigen::FullPivLU::threshold</a></div><div class="ttdeci">RealScalar threshold() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:318</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_ad32738c9a0c08e5f6e7ada743c8b3a77"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ad32738c9a0c08e5f6e7ada743c8b3a77">Eigen::FullPivLU::matrixLU</a></div><div class="ttdeci">const MatrixType & matrixLU() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:135</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_aea8ad7d1c2d653b83cd3e044e2b51ff6"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aea8ad7d1c2d653b83cd3e044e2b51ff6">Eigen::FullPivLU::permutationQ</a></div><div class="ttdeci">const PermutationQType & permutationQ() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:173</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_af266621b5d114229566caff0de1aa44b"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#af266621b5d114229566caff0de1aa44b">Eigen::FullPivLU::compute</a></div><div class="ttdeci">FullPivLU & compute(const EigenBase< InputType > &matrix)</div><div class="ttdef"><b>Definition</b> FullPivLU.h:123</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_af6839a14a4003e001de5dbedc0274dd2"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#af6839a14a4003e001de5dbedc0274dd2">Eigen::FullPivLU::dimensionOfKernel</a></div><div class="ttdeci">Index dimensionOfKernel() const</div><div class="ttdef"><b>Definition</b> FullPivLU.h:350</div></div>
<div class="ttc" id="aclassEigen_1_1FullPivLU_html_aff435f4b563a5ac72620d3ed9a94535a"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aff435f4b563a5ac72620d3ed9a94535a">Eigen::FullPivLU::FullPivLU</a></div><div class="ttdeci">FullPivLU()</div><div class="ttdoc">Default Constructor.</div><div class="ttdef"><b>Definition</b> FullPivLU.h:442</div></div>
<div class="ttc" id="aclassEigen_1_1Inverse_html"><div class="ttname"><a href="classEigen_1_1Inverse.html">Eigen::Inverse</a></div><div class="ttdoc">Expression of the inverse of another expression.</div><div class="ttdef"><b>Definition</b> Inverse.h:46</div></div>
<div class="ttc" id="aclassEigen_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:52</div></div>
<div class="ttc" id="aclassEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix</a></div><div class="ttdoc">Permutation matrix.</div><div class="ttdef"><b>Definition</b> PermutationMatrix.h:300</div></div>
<div class="ttc" id="aclassEigen_1_1Solve_html"><div class="ttname"><a href="classEigen_1_1Solve.html">Eigen::Solve</a></div><div class="ttdoc">Pseudo expression representing a solving operation.</div><div class="ttdef"><b>Definition</b> Solve.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html"><div class="ttname"><a href="classEigen_1_1SolverBase.html">Eigen::SolverBase</a></div><div class="ttdoc">A base class for matrix decomposition and solvers.</div><div class="ttdef"><b>Definition</b> SolverBase.h:71</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html_a943c352b597e3cd4744d5c11bfd77520"><div class="ttname"><a href="classEigen_1_1SolverBase.html#a943c352b597e3cd4744d5c11bfd77520">Eigen::SolverBase::solve</a></div><div class="ttdeci">const Solve< Derived, Rhs > solve(const MatrixBase< Rhs > &b) const</div><div class="ttdef"><b>Definition</b> SolverBase.h:107</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition</b> Meta.h:82</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition</b> Constants.h:24</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a554f30542cc2316add4b1ea0a492ff02"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Eigen::EigenBase::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdoc">The interface type of indices.</div><div class="ttdef"><b>Definition</b> EigenBase.h:41</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a749b057c52245e486a101868d2578a24"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a749b057c52245e486a101868d2578a24">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived & derived()</div><div class="ttdef"><b>Definition</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_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:231</div></div>
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