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<div class="title">FullPivLU.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2006-2009 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_LU_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_LU_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span>FullPivLU</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  Options = MatrixType::Options,</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  };</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<typename MatrixType::Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::traits<MatrixType>::StorageKind StorageKind;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type<MatrixType, Index>::type IntRowVectorType;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type<MatrixType, Index>::type IntColVectorType;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keyword">typedef</span> PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationQType;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">typedef</span> PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> PermutationPType;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <a class="code" href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046">FullPivLU</a>();</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <a class="code" href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046">FullPivLU</a>(Index rows, Index cols);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <a class="code" href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046">FullPivLU</a>(<span class="keyword">const</span> MatrixType& matrix);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <a class="code" href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046">FullPivLU</a>& <a class="code" href="classEigen_1_1FullPivLU.html#ac1c60e27ca149bb599662fb554a0949a">compute</a>(<span class="keyword">const</span> MatrixType& matrix);</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a name="l00103"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ad69664a62ab4d3026566d0d4a261b187"> 103</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> MatrixType& <a class="code" href="classEigen_1_1FullPivLU.html#ad69664a62ab4d3026566d0d4a261b187">matrixLU</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">return</span> m_lu;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  }</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a6dda9285f13dec9f49e9c17229a89988"> 116</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1FullPivLU.html#a6dda9285f13dec9f49e9c17229a89988">nonzeroPivots</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordflow">return</span> m_nonzero_pivots;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a067e9d4143ce0558fc684b736128a4ed"> 125</a></span>  RealScalar <a class="code" href="classEigen_1_1FullPivLU.html#a067e9d4143ce0558fc684b736128a4ed">maxPivot</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_maxpivot; }</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a38416f9985b9c7ad9dc3bd355479dd67"> 131</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationPType</a>& <a class="code" href="classEigen_1_1FullPivLU.html#a38416f9985b9c7ad9dc3bd355479dd67">permutationP</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">return</span> m_p;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  }</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a name="l00141"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ae85e85c3d1488b5882a6ccd63678a4d1"> 141</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationQType</a>& <a class="code" href="classEigen_1_1FullPivLU.html#ae85e85c3d1488b5882a6ccd63678a4d1">permutationQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">return</span> m_q;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  }</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="line"><a name="l00161"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a6e8f1d2fcbd86d3dc5a8a013b6e7200a"> 161</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::kernel_retval<FullPivLU> <a class="code" href="classEigen_1_1FullPivLU.html#a6e8f1d2fcbd86d3dc5a8a013b6e7200a">kernel</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">return</span> internal::kernel_retval<FullPivLU>(*this);</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  }</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::image_retval<FullPivLU></div>
<div class="line"><a name="l00187"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ad854843c6dc601252dc107e7b29133e9"> 187</a></span>  <a class="code" href="classEigen_1_1FullPivLU.html#ad854843c6dc601252dc107e7b29133e9">image</a>(<span class="keyword">const</span> MatrixType& originalMatrix)<span class="keyword"> const</span></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordflow">return</span> internal::image_retval<FullPivLU>(*<span class="keyword">this</span>, originalMatrix);</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  }</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> </div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<FullPivLU, Rhs></div>
<div class="line"><a name="l00214"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ac1a642d728c059c7625863f126e2e718"> 214</a></span>  <a class="code" href="classEigen_1_1FullPivLU.html#ac1a642d728c059c7625863f126e2e718">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Rhs></a>& b)<span class="keyword"> const</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">return</span> internal::solve_retval<FullPivLU, Rhs>(*<span class="keyword">this</span>, b.derived());</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  }</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keyword">typename</span> internal::traits<MatrixType>::Scalar <a class="code" href="classEigen_1_1FullPivLU.html#aa47f041dae554fe1f135e2794ae914a7">determinant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> </div>
<div class="line"><a name="l00254"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ae47399e3cf7943075ce18ef89fe17f21"> 254</a></span>  <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a>& <a class="code" href="classEigen_1_1FullPivLU.html#ae47399e3cf7943075ce18ef89fe17f21">setThreshold</a>(<span class="keyword">const</span> RealScalar& <a class="code" href="classEigen_1_1FullPivLU.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>)</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  {</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  m_usePrescribedThreshold = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  m_prescribedThreshold = <a class="code" href="classEigen_1_1FullPivLU.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  }</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a name="l00269"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a02b74b9b823e060825443fd82cd25fd4"> 269</a></span>  <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a>& <a class="code" href="classEigen_1_1FullPivLU.html#a02b74b9b823e060825443fd82cd25fd4">setThreshold</a>(Default_t)</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  {</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  m_usePrescribedThreshold = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  }</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> </div>
<div class="line"><a name="l00279"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aa5a87faaa92a3081045d1f934e292ef0"> 279</a></span>  RealScalar <a class="code" href="classEigen_1_1FullPivLU.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  eigen_assert(m_isInitialized || m_usePrescribedThreshold);</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">return</span> m_usePrescribedThreshold ? m_prescribedThreshold</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="comment">// this formula comes from experimenting (see "LU precision tuning" thread on the list)</span></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="comment">// and turns out to be identical to Higham's formula used already in LDLt.</span></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  : <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::epsilon</a>() * m_lu.diagonalSize();</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  }</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> </div>
<div class="line"><a name="l00294"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a363d1c09d77f09d6ea2d2789776e7be3"> 294</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1FullPivLU.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  RealScalar premultiplied_threshold = abs(m_maxpivot) * <a class="code" href="classEigen_1_1FullPivLU.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>();</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  Index result = 0;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordflow">for</span>(Index i = 0; i < m_nonzero_pivots; ++i)</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  result += (abs(m_lu.coeff(i,i)) > premultiplied_threshold);</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  }</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span> </div>
<div class="line"><a name="l00311"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a7c6323871c4f080fc6e2d3ad7fc607fc"> 311</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1FullPivLU.html#a7c6323871c4f080fc6e2d3ad7fc607fc">dimensionOfKernel</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keywordflow">return</span> cols() - <a class="code" href="classEigen_1_1FullPivLU.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>();</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  }</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span> </div>
<div class="line"><a name="l00324"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a1e119085e53eca65e9ba15451c102d40"> 324</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivLU.html#a1e119085e53eca65e9ba15451c102d40">isInjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivLU.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>() == cols();</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  }</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> </div>
<div class="line"><a name="l00337"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a5968b9ca46303b3cc7250e7b120ab7e6"> 337</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivLU.html#a5968b9ca46303b3cc7250e7b120ab7e6">isSurjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivLU.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>() == rows();</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  }</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span> </div>
<div class="line"><a name="l00349"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ab60c7d993c9eba31668fb8886d621094"> 349</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivLU.html#ab60c7d993c9eba31668fb8886d621094">isInvertible</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivLU.html#a1e119085e53eca65e9ba15451c102d40">isInjective</a>() && (m_lu.rows() == m_lu.cols());</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  }</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span> </div>
<div class="line"><a name="l00362"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a5ca20e3802e96fb14c2be37039afcae9"> 362</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<FullPivLU,typename MatrixType::IdentityReturnType> <a class="code" href="classEigen_1_1FullPivLU.html#a5ca20e3802e96fb14c2be37039afcae9">inverse</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</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 name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">return</span> internal::solve_retval<FullPivLU,typename MatrixType::IdentityReturnType></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  (*<span class="keyword">this</span>, MatrixType::Identity(m_lu.rows(), m_lu.cols()));</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  }</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  MatrixType <a class="code" href="classEigen_1_1FullPivLU.html#ac36925ac693435a090efee1cb5d6d16a">reconstructedMatrix</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> </div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keyword">inline</span> Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_lu.rows(); }</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="keyword">inline</span> Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_lu.cols(); }</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> </div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  MatrixType m_lu;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  PermutationPType m_p;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  PermutationQType m_q;</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  IntColVectorType m_rowsTranspositions;</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  IntRowVectorType m_colsTranspositions;</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  Index m_det_pq, m_nonzero_pivots;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  RealScalar m_maxpivot, m_prescribedThreshold;</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keywordtype">bool</span> m_isInitialized, m_usePrescribedThreshold;</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> };</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> </div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00387"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046"> 387</a></span> <a class="code" href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046">FullPivLU<MatrixType>::FullPivLU</a>()</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  : m_isInitialized(false), m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span> {</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span> }</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span> </div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00393"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ab6c78ecd953ba165ef421fa67c05753a"> 393</a></span> <a class="code" href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046">FullPivLU<MatrixType>::FullPivLU</a>(Index rows, Index cols)</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  : m_lu(rows, cols),</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  m_p(rows),</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  m_q(cols),</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  m_rowsTranspositions(rows),</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  m_colsTranspositions(cols),</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span> {</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> }</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span> </div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00405"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ab66f95f8f6b6455a0a38d95486330808"> 405</a></span> <a class="code" href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046">FullPivLU<MatrixType>::FullPivLU</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  : m_lu(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  m_p(matrix.rows()),</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  m_q(matrix.cols()),</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  m_rowsTranspositions(matrix.rows()),</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  m_colsTranspositions(matrix.cols()),</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span> {</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <a class="code" href="classEigen_1_1FullPivLU.html#ac1c60e27ca149bb599662fb554a0949a">compute</a>(matrix);</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> }</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> </div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00418"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ac1c60e27ca149bb599662fb554a0949a"> 418</a></span> <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU<MatrixType></a>& <a class="code" href="classEigen_1_1FullPivLU.html#ac1c60e27ca149bb599662fb554a0949a">FullPivLU<MatrixType>::compute</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span> {</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <span class="comment">// the permutations are stored as int indices, so just to be sure:</span></div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  eigen_assert(matrix.rows()<=<a class="code" href="structEigen_1_1NumTraits.html">NumTraits<int>::highest</a>() && matrix.cols()<=<a class="code" href="structEigen_1_1NumTraits.html">NumTraits<int>::highest</a>());</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  </div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  m_lu = matrix;</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span> </div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  <span class="keyword">const</span> Index size = matrix.diagonalSize();</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <span class="keyword">const</span> Index rows = matrix.rows();</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keyword">const</span> Index cols = matrix.cols();</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span> </div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="comment">// will store the transpositions, before we accumulate them at the end.</span></div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</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 name="l00432"></a><span class="lineno"> 432</span>  m_rowsTranspositions.resize(matrix.rows());</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  m_colsTranspositions.resize(matrix.cols());</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  Index number_of_transpositions = 0; <span class="comment">// number of NONTRIVIAL transpositions, i.e. m_rowsTranspositions[i]!=i</span></div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> </div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  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 name="l00437"></a><span class="lineno"> 437</span>  m_maxpivot = RealScalar(0);</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span> </div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keywordflow">for</span>(Index k = 0; k < size; ++k)</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  {</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="comment">// First, we need to find the pivot.</span></div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span> </div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  <span class="comment">// biggest coefficient in the remaining bottom-right corner (starting at row k, col k)</span></div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  Index row_of_biggest_in_corner, col_of_biggest_in_corner;</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  RealScalar biggest_in_corner;</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  biggest_in_corner = m_lu.bottomRightCorner(rows-k, cols-k)</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  .cwiseAbs()</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</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 name="l00450"></a><span class="lineno"> 450</span>  col_of_biggest_in_corner += k; <span class="comment">// need to add k to them.</span></div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> </div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="keywordflow">if</span>(biggest_in_corner==RealScalar(0))</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  {</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="comment">// before exiting, make sure to initialize the still uninitialized transpositions</span></div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="comment">// in a sane state without destroying what we already have.</span></div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  m_nonzero_pivots = k;</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="keywordflow">for</span>(Index i = k; i < size; ++i)</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  {</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  m_rowsTranspositions.coeffRef(i) = i;</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  m_colsTranspositions.coeffRef(i) = i;</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  }</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  }</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span> </div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordflow">if</span>(biggest_in_corner > m_maxpivot) m_maxpivot = biggest_in_corner;</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span> </div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="comment">// Now that we've found the pivot, we need to apply the row/col swaps to</span></div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="comment">// bring it to the location (k,k).</span></div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span> </div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  m_rowsTranspositions.coeffRef(k) = row_of_biggest_in_corner;</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  m_colsTranspositions.coeffRef(k) = col_of_biggest_in_corner;</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="keywordflow">if</span>(k != row_of_biggest_in_corner) {</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  m_lu.row(k).swap(m_lu.row(row_of_biggest_in_corner));</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  ++number_of_transpositions;</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  }</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="keywordflow">if</span>(k != col_of_biggest_in_corner) {</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  m_lu.col(k).swap(m_lu.col(col_of_biggest_in_corner));</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  ++number_of_transpositions;</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  }</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span> </div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="comment">// Now that the pivot is at the right location, we update the remaining</span></div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="comment">// bottom-right corner by Gaussian elimination.</span></div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span> </div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  <span class="keywordflow">if</span>(k<rows-1)</div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  m_lu.col(k).tail(rows-k-1) /= m_lu.coeff(k,k);</div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  <span class="keywordflow">if</span>(k<size-1)</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</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 name="l00488"></a><span class="lineno"> 488</span>  }</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span> </div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <span class="comment">// the main loop is over, we still have to accumulate the transpositions to find the</span></div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="comment">// permutations P and Q</span></div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> </div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  m_p.setIdentity(rows);</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  <span class="keywordflow">for</span>(Index k = size-1; k >= 0; --k)</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  m_p.applyTranspositionOnTheRight(k, m_rowsTranspositions.coeff(k));</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> </div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  m_q.setIdentity(cols);</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="keywordflow">for</span>(Index k = 0; k < size; ++k)</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  m_q.applyTranspositionOnTheRight(k, m_colsTranspositions.coeff(k));</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> </div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  m_det_pq = (number_of_transpositions%2) ? -1 : 1;</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span> }</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span> </div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00506"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#aa47f041dae554fe1f135e2794ae914a7"> 506</a></span> <span class="keyword">typename</span> internal::traits<MatrixType>::Scalar <a class="code" href="classEigen_1_1FullPivLU.html#aa47f041dae554fe1f135e2794ae914a7">FullPivLU<MatrixType>::determinant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</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 name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordflow">return</span> Scalar(m_det_pq) * Scalar(m_lu.diagonal().prod());</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span> }</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00517"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivLU.html#ac36925ac693435a090efee1cb5d6d16a"> 517</a></span> MatrixType <a class="code" href="classEigen_1_1FullPivLU.html#ac36925ac693435a090efee1cb5d6d16a">FullPivLU<MatrixType>::reconstructedMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="keyword">const</span> Index smalldim = (std::min)(m_lu.rows(), m_lu.cols());</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="comment">// LU</span></div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  MatrixType res(m_lu.rows(),m_lu.cols());</div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="comment">// FIXME the .toDenseMatrix() should not be needed...</span></div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  res = m_lu.leftCols(smalldim)</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  .template triangularView<UnitLower>().toDenseMatrix()</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  * m_lu.topRows(smalldim)</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  .template triangularView<Upper>().toDenseMatrix();</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span> </div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="comment">// P^{-1}(LU)</span></div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  res = m_p.inverse() * res;</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span> </div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <span class="comment">// (P^{-1}LU)Q^{-1}</span></div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  res = res * m_q.inverse();</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> </div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span> }</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span> </div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span> <span class="comment">/********* Implementation of kernel() **************************************************/</span></div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span> </div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType></div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="keyword">struct </span>kernel_retval<<a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU</a><_MatrixType> ></div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  : kernel_retval_base<FullPivLU<_MatrixType> ></div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span> {</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  EIGEN_MAKE_KERNEL_HELPERS(<a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU<_MatrixType></a>)</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span> </div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  enum { MaxSmallDimAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(</div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  MatrixType::MaxRowsAtCompileTime)</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  };</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span> </div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</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 name="l00553"></a><span class="lineno"> 553</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="keyword">const</span> Index cols = dec().matrixLU().cols(), dimker = cols - rank();</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="keywordflow">if</span>(dimker == 0)</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  {</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="comment">// The Kernel is just {0}, so it doesn't have a basis properly speaking, but let's</span></div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="comment">// avoid crashing/asserting as that depends on floating point calculations. Let's</span></div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <span class="comment">// just return a single column vector filled with zeros.</span></div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  dst.setZero();</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  }</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span> </div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="comment">/* Let us use the following lemma:</span></div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span> <span class="comment"> * Lemma: If the matrix A has the LU decomposition PAQ = LU,</span></div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span> <span class="comment"> * then Ker A = Q(Ker U).</span></div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span> <span class="comment"> * Proof: trivial: just keep in mind that P, Q, L are invertible.</span></div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span> </div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</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 name="l00574"></a><span class="lineno"> 574</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</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 name="l00576"></a><span class="lineno"> 576</span> <span class="comment"> * Thus, the diagonal of U ends with exactly</span></div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span> <span class="comment"> * dimKer zero's. Let us use that to construct dimKer linearly</span></div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span> <span class="comment"> * independent vectors in Ker U.</span></div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span> </div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  Index p = 0;</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="keywordflow">for</span>(Index i = 0; i < dec().nonzeroPivots(); ++i)</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <span class="keywordflow">if</span>(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  pivots.coeffRef(p++) = i;</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  eigen_internal_assert(p == rank());</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span> </div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  <span class="comment">// we construct a temporaty trapezoid matrix m, by taking the U matrix and</span></div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <span class="comment">// permuting the rows and cols to bring the nonnegligible pivots to the top of</span></div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="comment">// the main diagonal. We need that to be able to apply our triangular solvers.</span></div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="comment">// FIXME when we get triangularView-for-rectangular-matrices, this can be simplified</span></div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  Matrix<<span class="keyword">typename</span> MatrixType::Scalar, <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a>, <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a>, MatrixType::Options,</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  MaxSmallDimAtCompileTime, MatrixType::MaxColsAtCompileTime></div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  m(dec().matrixLU().block(0, 0, rank(), cols));</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  <span class="keywordflow">for</span>(Index i = 0; i < rank(); ++i)</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  {</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  <span class="keywordflow">if</span>(i) m.row(i).head(i).setZero();</div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  m.row(i).tail(cols-i) = dec().matrixLU().row(pivots.coeff(i)).tail(cols-i);</div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  }</div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  m.block(0, 0, rank(), rank());</div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  m.block(0, 0, rank(), rank()).template triangularView<StrictlyLower>().setZero();</div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  <span class="keywordflow">for</span>(Index i = 0; i < rank(); ++i)</div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  m.col(i).swap(m.col(pivots.coeff(i)));</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span> </div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="comment">// ok, we have our trapezoid matrix, we can apply the triangular solver.</span></div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  <span class="comment">// notice that the math behind this suggests that we should apply this to the</span></div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</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 name="l00609"></a><span class="lineno"> 609</span>  m.topLeftCorner(rank(), rank())</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  .template triangularView<Upper>().solveInPlace(</div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  m.topRightCorner(rank(), dimker)</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  );</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span> </div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  <span class="comment">// now we must undo the column permutation that we had applied!</span></div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <span class="keywordflow">for</span>(Index i = rank()-1; i >= 0; --i)</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  m.col(i).swap(m.col(pivots.coeff(i)));</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span> </div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</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 name="l00619"></a><span class="lineno"> 619</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 name="l00620"></a><span class="lineno"> 620</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 name="l00621"></a><span class="lineno"> 621</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 name="l00622"></a><span class="lineno"> 622</span>  }</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span> };</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span> </div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span> <span class="comment">/***** Implementation of image() *****************************************************/</span></div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span> </div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType></div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span> <span class="keyword">struct </span>image_retval<FullPivLU<_MatrixType> ></div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  : image_retval_base<FullPivLU<_MatrixType> ></div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span> {</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  EIGEN_MAKE_IMAGE_HELPERS(FullPivLU<_MatrixType>)</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span> </div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  enum { MaxSmallDimAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  MatrixType::MaxRowsAtCompileTime)</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  };</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span> </div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</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 name="l00639"></a><span class="lineno"> 639</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <span class="keywordflow">if</span>(rank() == 0)</div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  {</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  <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 name="l00644"></a><span class="lineno"> 644</span>  <span class="comment">// avoid crashing/asserting as that depends on floating point calculations. Let's</span></div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  <span class="comment">// just return a single column vector filled with zeros.</span></div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  dst.setZero();</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  }</div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span> </div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  Matrix<Index, Dynamic, 1, 0, MaxSmallDimAtCompileTime, 1> pivots(rank());</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  RealScalar premultiplied_threshold = dec().maxPivot() * dec().threshold();</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  Index p = 0;</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  <span class="keywordflow">for</span>(Index i = 0; i < dec().nonzeroPivots(); ++i)</div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  <span class="keywordflow">if</span>(abs(dec().matrixLU().coeff(i,i)) > premultiplied_threshold)</div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  pivots.coeffRef(p++) = i;</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  eigen_internal_assert(p == rank());</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span> </div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <span class="keywordflow">for</span>(Index i = 0; i < rank(); ++i)</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  dst.col(i) = originalMatrix().col(dec().permutationQ().indices().coeff(pivots.coeff(i)));</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  }</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span> };</div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span> </div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span> <span class="comment">/***** Implementation of solve() *****************************************************/</span></div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span> </div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span> <span class="keyword">struct </span>solve_retval<FullPivLU<_MatrixType>, Rhs></div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  : solve_retval_base<FullPivLU<_MatrixType>, Rhs></div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span> {</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  EIGEN_MAKE_SOLVE_HELPERS(FullPivLU<_MatrixType>,Rhs)</div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span> </div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</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 name="l00674"></a><span class="lineno"> 674</span> <span class="comment"> * So we proceed as follows:</span></div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span> <span class="comment"> * Step 1: compute c = P * rhs.</span></div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</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 name="l00677"></a><span class="lineno"> 677</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 name="l00678"></a><span class="lineno"> 678</span> <span class="comment"> * Step 4: result = Q * c;</span></div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span> </div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  <span class="keyword">const</span> Index rows = dec().rows(), cols = dec().cols(),</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  nonzero_pivots = dec().nonzeroPivots();</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  eigen_assert(rhs().rows() == rows);</div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  <span class="keyword">const</span> Index smalldim = (std::min)(rows, cols);</div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span> </div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  <span class="keywordflow">if</span>(nonzero_pivots == 0)</div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  {</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  dst.setZero();</div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  }</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span> </div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  <span class="keyword">typename</span> Rhs::PlainObject c(rhs().rows(), rhs().cols());</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span> </div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  <span class="comment">// Step 1</span></div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  c = dec().permutationP() * rhs();</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span> </div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  <span class="comment">// Step 2</span></div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  dec().matrixLU()</div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  .topLeftCorner(smalldim,smalldim)</div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  .template triangularView<UnitLower>()</div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  .solveInPlace(c.topRows(smalldim));</div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  <span class="keywordflow">if</span>(rows>cols)</div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span>  {</div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  c.bottomRows(rows-cols)</div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  -= dec().matrixLU().bottomRows(rows-cols)</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  * c.topRows(cols);</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  }</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span> </div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  <span class="comment">// Step 3</span></div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  dec().matrixLU()</div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  .topLeftCorner(nonzero_pivots, nonzero_pivots)</div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  .template triangularView<Upper>()</div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  .solveInPlace(c.topRows(nonzero_pivots));</div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span> </div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  <span class="comment">// Step 4</span></div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  <span class="keywordflow">for</span>(Index i = 0; i < nonzero_pivots; ++i)</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  dst.row(dec().permutationQ().indices().coeff(i)) = c.row(i);</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  <span class="keywordflow">for</span>(Index i = nonzero_pivots; i < dec().matrixLU().cols(); ++i)</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  dst.row(dec().permutationQ().indices().coeff(i)).setZero();</div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  }</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span> };</div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span> </div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span> </div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span> <span class="comment">/******* MatrixBase methods *****************************************************************/</span></div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span> </div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span> <span class="keyword">inline</span> <span class="keyword">const</span> FullPivLU<typename MatrixBase<Derived>::PlainObject></div>
<div class="line"><a name="l00735"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0844e94f8f95ae01a2cd88dbbf5cbf91"> 735</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#a0844e94f8f95ae01a2cd88dbbf5cbf91">MatrixBase<Derived>::fullPivLu</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivLU.html">FullPivLU<PlainObject></a>(eval());</div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span> }</div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span> </div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span> </div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span> <span class="preprocessor">#endif // EIGEN_LU_H</span></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_ab60c7d993c9eba31668fb8886d621094"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ab60c7d993c9eba31668fb8886d621094">Eigen::FullPivLU::isInvertible</a></div><div class="ttdeci">bool isInvertible() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:349</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_aa5a87faaa92a3081045d1f934e292ef0"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aa5a87faaa92a3081045d1f934e292ef0">Eigen::FullPivLU::threshold</a></div><div class="ttdeci">RealScalar threshold() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:279</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_ad69664a62ab4d3026566d0d4a261b187"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ad69664a62ab4d3026566d0d4a261b187">Eigen::FullPivLU::matrixLU</a></div><div class="ttdeci">const MatrixType & matrixLU() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:103</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a0844e94f8f95ae01a2cd88dbbf5cbf91"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a0844e94f8f95ae01a2cd88dbbf5cbf91">Eigen::MatrixBase::fullPivLu</a></div><div class="ttdeci">const FullPivLU< PlainObject > fullPivLu() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:735</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_aa47f041dae554fe1f135e2794ae914a7"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#aa47f041dae554fe1f135e2794ae914a7">Eigen::FullPivLU::determinant</a></div><div class="ttdeci">internal::traits< MatrixType >::Scalar determinant() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:506</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_ac36925ac693435a090efee1cb5d6d16a"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ac36925ac693435a090efee1cb5d6d16a">Eigen::FullPivLU::reconstructedMatrix</a></div><div class="ttdeci">MatrixType reconstructedMatrix() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:517</div></div>
<div class="ttc" id="structEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...</div><div class="ttdef"><b>Definition:</b> NumTraits.h:88</div></div>
<div class="ttc" id="namespaceEigen_html_adc9da5be31bdce40c25a92c27999c0e3"><div class="ttname"><a href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:21</div></div>
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<div class="ttc" id="classEigen_1_1FullPivLU_html_a10dec2fa1767ac0712af1efa732b2046"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a10dec2fa1767ac0712af1efa732b2046">Eigen::FullPivLU::FullPivLU</a></div><div class="ttdeci">FullPivLU()</div><div class="ttdoc">Default Constructor. </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:387</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_ac1c60e27ca149bb599662fb554a0949a"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ac1c60e27ca149bb599662fb554a0949a">Eigen::FullPivLU::compute</a></div><div class="ttdeci">FullPivLU & compute(const MatrixType &matrix)</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:418</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a38416f9985b9c7ad9dc3bd355479dd67"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a38416f9985b9c7ad9dc3bd355479dd67">Eigen::FullPivLU::permutationP</a></div><div class="ttdeci">const PermutationPType & permutationP() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:131</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a363d1c09d77f09d6ea2d2789776e7be3"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a363d1c09d77f09d6ea2d2789776e7be3">Eigen::FullPivLU::rank</a></div><div class="ttdeci">Index rank() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:294</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_ad854843c6dc601252dc107e7b29133e9"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ad854843c6dc601252dc107e7b29133e9">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:187</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a02b74b9b823e060825443fd82cd25fd4"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a02b74b9b823e060825443fd82cd25fd4">Eigen::FullPivLU::setThreshold</a></div><div class="ttdeci">FullPivLU & setThreshold(Default_t)</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:269</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a6dda9285f13dec9f49e9c17229a89988"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a6dda9285f13dec9f49e9c17229a89988">Eigen::FullPivLU::nonzeroPivots</a></div><div class="ttdeci">Index nonzeroPivots() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:116</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a7c6323871c4f080fc6e2d3ad7fc607fc"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a7c6323871c4f080fc6e2d3ad7fc607fc">Eigen::FullPivLU::dimensionOfKernel</a></div><div class="ttdeci">Index dimensionOfKernel() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:311</div></div>
<div class="ttc" id="classEigen_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> ForwardDeclarations.h:216</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_ae47399e3cf7943075ce18ef89fe17f21"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ae47399e3cf7943075ce18ef89fe17f21">Eigen::FullPivLU::setThreshold</a></div><div class="ttdeci">FullPivLU & setThreshold(const RealScalar &threshold)</div><div class="ttdef"><b>Definition:</b> FullPivLU.h:254</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a6e8f1d2fcbd86d3dc5a8a013b6e7200a"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a6e8f1d2fcbd86d3dc5a8a013b6e7200a">Eigen::FullPivLU::kernel</a></div><div class="ttdeci">const internal::kernel_retval< FullPivLU > kernel() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:161</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a067e9d4143ce0558fc684b736128a4ed"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a067e9d4143ce0558fc684b736128a4ed">Eigen::FullPivLU::maxPivot</a></div><div class="ttdeci">RealScalar maxPivot() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:125</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions. </div><div class="ttdef"><b>Definition:</b> MatrixBase.h:48</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_ac1a642d728c059c7625863f126e2e718"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ac1a642d728c059c7625863f126e2e718">Eigen::FullPivLU::solve</a></div><div class="ttdeci">const internal::solve_retval< FullPivLU, Rhs > solve(const MatrixBase< Rhs > &b) const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:214</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a5968b9ca46303b3cc7250e7b120ab7e6"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a5968b9ca46303b3cc7250e7b120ab7e6">Eigen::FullPivLU::isSurjective</a></div><div class="ttdeci">bool isSurjective() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:337</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_a5ca20e3802e96fb14c2be37039afcae9"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#a5ca20e3802e96fb14c2be37039afcae9">Eigen::FullPivLU::inverse</a></div><div class="ttdeci">const internal::solve_retval< FullPivLU, typename MatrixType::IdentityReturnType > inverse() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:362</div></div>
<div class="ttc" id="classEigen_1_1FullPivLU_html_ae85e85c3d1488b5882a6ccd63678a4d1"><div class="ttname"><a href="classEigen_1_1FullPivLU.html#ae85e85c3d1488b5882a6ccd63678a4d1">Eigen::FullPivLU::permutationQ</a></div><div class="ttdeci">const PermutationQType & permutationQ() const </div><div class="ttdef"><b>Definition:</b> FullPivLU.h:141</div></div>
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