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<div class="title">FullPivHouseholderQR.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</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="l00009"></a><span class="lineno"> 9</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="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#ifndef EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType> <span class="keyword">struct </span>FullPivHouseholderQRMatrixQReturnType;</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">struct </span>traits<FullPivHouseholderQRMatrixQReturnType<MatrixType> ></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> {</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::PlainObject ReturnType;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> };</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> }</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span>FullPivHouseholderQR</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  Options = MatrixType::Options,</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  };</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">typedef</span> internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> MatrixQReturnType;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type<MatrixType>::type HCoeffsType;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">typedef</span> Matrix<Index, 1, ColsAtCompileTime, RowMajor, 1, MaxColsAtCompileTime> IntRowVectorType;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keyword">typedef</span> PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</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="l00069"></a><span class="lineno"> 69</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type<MatrixType>::type RowVectorType;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type<MatrixType>::type ColVectorType;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a name="l00077"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#acc93f6afaf0d058c8c1e242b3276977a"> 77</a></span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#acc93f6afaf0d058c8c1e242b3276977a">FullPivHouseholderQR</a>()</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  : m_qr(),</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  m_hCoeffs(),</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  m_rows_transpositions(),</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  m_cols_transpositions(),</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  m_cols_permutation(),</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  m_temp(),</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  m_usePrescribedThreshold(false) {}</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00093"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a8a9705034ce6895c61fe9d0b026837b1"> 93</a></span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a8a9705034ce6895c61fe9d0b026837b1">FullPivHouseholderQR</a>(Index rows, Index cols)</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  : m_qr(rows, cols),</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  m_hCoeffs((std::min)(rows,cols)),</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  m_rows_transpositions(rows),</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  m_cols_transpositions(cols),</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  m_cols_permutation(cols),</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  m_temp((std::min)(rows,cols)),</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  m_usePrescribedThreshold(false) {}</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a8df275c9896e2585fe5748512fca8e8f"> 115</a></span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a8df275c9896e2585fe5748512fca8e8f">FullPivHouseholderQR</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  : m_qr(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  m_rows_transpositions(matrix.rows()),</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  m_cols_transpositions(matrix.cols()),</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  m_cols_permutation(matrix.cols()),</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  m_temp((std::min)(matrix.rows(), matrix.cols())),</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  m_usePrescribedThreshold(false)</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  {</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#aa414ed474b31fecd794cb33003da65d5">compute</a>(matrix);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  }</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<FullPivHouseholderQR, Rhs></div>
<div class="line"><a name="l00147"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a56ecc85ee98ff3625d222fdee1774b73"> 147</a></span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a56ecc85ee98ff3625d222fdee1774b73">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="l00148"></a><span class="lineno"> 148</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">return</span> internal::solve_retval<FullPivHouseholderQR, Rhs>(*<span class="keyword">this</span>, b.derived());</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  MatrixQReturnType <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a455514157d49695dadaf7dc534fe9ced">matrixQ</a>(<span class="keywordtype">void</span>) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a name="l00159"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1"> 159</a></span>  <span class="keyword">const</span> MatrixType& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">matrixQR</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordflow">return</span> m_qr;</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  }</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a>& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#aa414ed474b31fecd794cb33003da65d5">compute</a>(<span class="keyword">const</span> MatrixType& matrix);</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a name="l00168"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924"> 168</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924">colsPermutation</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordflow">return</span> m_cols_permutation;</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  }</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> </div>
<div class="line"><a name="l00175"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a58a5850e4bac88c002035f337424f0bc"> 175</a></span>  <span class="keyword">const</span> IntColVectorType& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a58a5850e4bac88c002035f337424f0bc">rowsTranspositions</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">return</span> m_rows_transpositions;</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  }</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">absDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">logAbsDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a name="l00216"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3"> 216</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  RealScalar premultiplied_threshold = abs(m_maxpivot) * <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>();</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  Index result = 0;</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordflow">for</span>(Index i = 0; i < m_nonzero_pivots; ++i)</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  }</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span> </div>
<div class="line"><a name="l00233"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc"> 233</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc">dimensionOfKernel</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordflow">return</span> cols() - <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>();</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  }</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> </div>
<div class="line"><a name="l00246"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40"> 246</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">isInjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>() == cols();</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  }</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> </div>
<div class="line"><a name="l00259"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6"> 259</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">isSurjective</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>() == rows();</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  }</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div>
<div class="line"><a name="l00271"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094"> 271</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094">isInvertible</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">isInjective</a>() && <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">isSurjective</a>();</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  }</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keyword">inline</span> <span class="keyword">const</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  internal::solve_retval<FullPivHouseholderQR, typename MatrixType::IdentityReturnType></div>
<div class="line"><a name="l00283"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a6c4acc52d7014703cc351dcdc3538b9d"> 283</a></span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a6c4acc52d7014703cc351dcdc3538b9d">inverse</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordflow">return</span> internal::solve_retval<FullPivHouseholderQR,typename MatrixType::IdentityReturnType></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  (*<span class="keyword">this</span>, MatrixType::Identity(m_qr.rows(), m_qr.cols()));</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  }</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span> </div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keyword">inline</span> Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.rows(); }</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keyword">inline</span> Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.cols(); }</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  </div>
<div class="line"><a name="l00297"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9"> 297</a></span>  <span class="keyword">const</span> HCoeffsType& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9">hCoeffs</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hCoeffs; }</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> </div>
<div class="line"><a name="l00316"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a559f82325764bd1e204fc6f56ba1a145"> 316</a></span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a>& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a559f82325764bd1e204fc6f56ba1a145">setThreshold</a>(<span class="keyword">const</span> RealScalar& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>)</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  {</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  m_usePrescribedThreshold = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  m_prescribedThreshold = <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>;</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  }</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span> </div>
<div class="line"><a name="l00331"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#acbb58557944348658f9a88afa60b6b2b"> 331</a></span>  <a class="code" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a>& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#acbb58557944348658f9a88afa60b6b2b">setThreshold</a>(Default_t)</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  {</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  m_usePrescribedThreshold = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  }</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span> </div>
<div class="line"><a name="l00341"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0"> 341</a></span>  RealScalar <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  eigen_assert(m_isInitialized || m_usePrescribedThreshold);</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keywordflow">return</span> m_usePrescribedThreshold ? m_prescribedThreshold</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">// this formula comes from experimenting (see "LU precision tuning" thread on the list)</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</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="l00347"></a><span class="lineno"> 347</span>  : <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::epsilon</a>() * m_qr.diagonalSize();</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  }</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span> </div>
<div class="line"><a name="l00357"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988"> 357</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988">nonzeroPivots</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"LU is not initialized."</span>);</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keywordflow">return</span> m_nonzero_pivots;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  }</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> </div>
<div class="line"><a name="l00366"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed"> 366</a></span>  RealScalar <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed">maxPivot</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_maxpivot; }</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> </div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  MatrixType m_qr;</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  HCoeffsType m_hCoeffs;</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  IntColVectorType m_rows_transpositions;</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  IntRowVectorType m_cols_transpositions;</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  PermutationType m_cols_permutation;</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  RowVectorType m_temp;</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="keywordtype">bool</span> m_isInitialized, m_usePrescribedThreshold;</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  RealScalar m_prescribedThreshold, m_maxpivot;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  Index m_nonzero_pivots;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  RealScalar m_precision;</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  Index m_det_pq;</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> };</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> </div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00383"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432"> 383</a></span> <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">FullPivHouseholderQR<MatrixType>::absDeterminant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  eigen_assert(m_qr.rows() == m_qr.cols() && <span class="stringliteral">"You can't take the determinant of a non-square matrix!"</span>);</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keywordflow">return</span> abs(m_qr.diagonal().prod());</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> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00392"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9"> 392</a></span> <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">FullPivHouseholderQR<MatrixType>::logAbsDeterminant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  eigen_assert(m_qr.rows() == m_qr.cols() && <span class="stringliteral">"You can't take the determinant of a non-square matrix!"</span>);</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">return</span> m_qr.diagonal().cwiseAbs().array().log().sum();</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span> }</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00406"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#aa414ed474b31fecd794cb33003da65d5"> 406</a></span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR<MatrixType></a>& <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#aa414ed474b31fecd794cb33003da65d5">FullPivHouseholderQR<MatrixType>::compute</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> {</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  Index rows = matrix.rows();</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  Index cols = matrix.cols();</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  Index size = (std::min)(rows,cols);</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span> </div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  m_qr = matrix;</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  m_hCoeffs.resize(size);</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>  m_temp.resize(cols);</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span> </div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  m_precision = <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::epsilon</a>() * size;</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>  m_rows_transpositions.resize(matrix.rows());</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  m_cols_transpositions.resize(matrix.cols());</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  Index number_of_transpositions = 0;</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span> </div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  RealScalar biggest(0);</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>  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="l00427"></a><span class="lineno"> 427</span>  m_maxpivot = RealScalar(0);</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> </div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="keywordflow">for</span> (Index k = 0; k < size; ++k)</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  {</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  Index row_of_biggest_in_corner, col_of_biggest_in_corner;</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  RealScalar biggest_in_corner;</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> </div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  biggest_in_corner = m_qr.bottomRightCorner(rows-k, cols-k)</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  .cwiseAbs()</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  row_of_biggest_in_corner += k;</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  col_of_biggest_in_corner += k;</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keywordflow">if</span>(k==0) biggest = biggest_in_corner;</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">// if the corner is negligible, then we have less than full rank, and we can finish early</span></div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keywordflow">if</span>(internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision))</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  {</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  m_nonzero_pivots = k;</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="keywordflow">for</span>(Index i = k; i < size; i++)</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  {</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  m_rows_transpositions.coeffRef(i) = i;</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  m_cols_transpositions.coeffRef(i) = i;</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  m_hCoeffs.coeffRef(i) = Scalar(0);</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  }</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  }</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span> </div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  m_rows_transpositions.coeffRef(k) = row_of_biggest_in_corner;</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  m_cols_transpositions.coeffRef(k) = col_of_biggest_in_corner;</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <span class="keywordflow">if</span>(k != row_of_biggest_in_corner) {</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  m_qr.row(k).tail(cols-k).swap(m_qr.row(row_of_biggest_in_corner).tail(cols-k));</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  ++number_of_transpositions;</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  }</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="keywordflow">if</span>(k != col_of_biggest_in_corner) {</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner));</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  ++number_of_transpositions;</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>  RealScalar beta;</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  m_qr.coeffRef(k,k) = beta;</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span> </div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="comment">// remember the maximum absolute value of diagonal coefficients</span></div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <span class="keywordflow">if</span>(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span> </div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  m_qr.bottomRightCorner(rows-k, cols-k-1)</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  }</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>  m_cols_permutation.setIdentity(cols);</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <span class="keywordflow">for</span>(Index k = 0; k < size; ++k)</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  m_cols_permutation.applyTranspositionOnTheRight(k, m_cols_transpositions.coeff(k));</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>  m_det_pq = (number_of_transpositions%2) ? -1 : 1;</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span> </div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> }</div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> </div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span> </div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span> <span class="keyword">struct </span>solve_retval<<a class="code" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR</a><_MatrixType>, Rhs></div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  : solve_retval_base<FullPivHouseholderQR<_MatrixType>, Rhs></div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span> {</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  EIGEN_MAKE_SOLVE_HELPERS(<a class="code" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR<_MatrixType></a>,Rhs)</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span> </div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <span class="keyword">const</span> Index rows = dec().rows(), cols = dec().cols();</div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  eigen_assert(rhs().rows() == rows);</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span> </div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="comment">// FIXME introduce nonzeroPivots() and use it here. and more generally,</span></div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  <span class="comment">// make the same improvements in this dec as in FullPivLU.</span></div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  <span class="keywordflow">if</span>(dec().rank()==0)</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  {</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  dst.setZero();</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  }</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span> </div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keyword">typename</span> Rhs::PlainObject c(rhs());</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span> </div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  Matrix<Scalar,1,Rhs::ColsAtCompileTime> temp(rhs().cols());</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keywordflow">for</span> (Index k = 0; k < dec().rank(); ++k)</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>  Index remainingSize = rows-k;</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  c.row(k).swap(c.row(dec().rowsTranspositions().coeff(k)));</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  c.bottomRightCorner(remainingSize, rhs().cols())</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  .applyHouseholderOnTheLeft(dec().matrixQR().col(k).tail(remainingSize-1),</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  dec().hCoeffs().coeff(k), &temp.coeffRef(0));</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  }</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> </div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keywordflow">if</span>(!dec().isSurjective())</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  {</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="comment">// is c is in the image of R ?</span></div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  RealScalar biggest_in_upper_part_of_c = c.topRows( dec().rank() ).cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  RealScalar biggest_in_lower_part_of_c = c.bottomRows(rows-dec().rank()).cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="comment">// FIXME brain dead</span></div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <span class="keyword">const</span> RealScalar m_precision = NumTraits<Scalar>::epsilon() * (std::min)(rows,cols);</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="comment">// this internal:: prefix is needed by at least gcc 3.4 and ICC</span></div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <span class="keywordflow">if</span>(!internal::isMuchSmallerThan(biggest_in_lower_part_of_c, biggest_in_upper_part_of_c, m_precision))</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  }</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  dec().matrixQR()</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  .topLeftCorner(dec().rank(), dec().rank())</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  .template triangularView<Upper>()</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  .solveInPlace(c.topRows(dec().rank()));</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">for</span>(Index i = 0; i < dec().rank(); ++i) dst.row(dec().colsPermutation().indices().coeff(i)) = c.row(i);</div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="keywordflow">for</span>(Index i = dec().rank(); i < cols; ++i) dst.row(dec().colsPermutation().indices().coeff(i)).setZero();</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> };</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span> </div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType> <span class="keyword">struct </span>FullPivHouseholderQRMatrixQReturnType</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  : <span class="keyword">public</span> ReturnByValue<FullPivHouseholderQRMatrixQReturnType<MatrixType> ></div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span> {</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</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="l00552"></a><span class="lineno"> 552</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type<MatrixType>::type HCoeffsType;</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  <span class="keyword">typedef</span> Matrix<<span class="keyword">typename</span> MatrixType::Scalar, 1, MatrixType::RowsAtCompileTime, <a class="code" href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044">RowMajor</a>, 1,</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  MatrixType::MaxRowsAtCompileTime> WorkVectorType;</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span> </div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  FullPivHouseholderQRMatrixQReturnType(<span class="keyword">const</span> MatrixType& qr,</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="keyword">const</span> HCoeffsType& hCoeffs,</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="keyword">const</span> IntColVectorType& rowsTranspositions)</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  : m_qr(qr),</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  m_hCoeffs(hCoeffs),</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  m_rowsTranspositions(rowsTranspositions)</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  {}</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span> </div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="keywordtype">void</span> evalTo(ResultType& result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  <span class="keyword">const</span> Index rows = m_qr.rows();</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  WorkVectorType workspace(rows);</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  evalTo(result, workspace);</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  }</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span> </div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  <span class="keywordtype">void</span> evalTo(ResultType& result, WorkVectorType& workspace)<span class="keyword"> const</span></div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  <span class="keyword">using</span> numext::conj;</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  <span class="comment">// compute the product H'_0 H'_1 ... H'_n-1,</span></div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  <span class="comment">// where H_k is the k-th Householder transformation I - h_k v_k v_k'</span></div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  <span class="comment">// and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]</span></div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  <span class="keyword">const</span> Index rows = m_qr.rows();</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  <span class="keyword">const</span> Index cols = m_qr.cols();</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="keyword">const</span> Index size = (std::min)(rows, cols);</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  workspace.resize(rows);</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  result.setIdentity(rows, rows);</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="keywordflow">for</span> (Index k = size-1; k >= 0; k--)</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  {</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  result.block(k, k, rows-k, rows-k)</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), conj(m_hCoeffs.coeff(k)), &workspace.coeffRef(k));</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  result.row(k).swap(result.row(m_rowsTranspositions.coeff(k)));</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  }</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  }</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span> </div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.rows(); }</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.rows(); }</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span> </div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span> <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  <span class="keyword">typename</span> MatrixType::Nested m_qr;</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  <span class="keyword">typename</span> HCoeffsType::Nested m_hCoeffs;</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  <span class="keyword">typename</span> IntColVectorType::Nested m_rowsTranspositions;</div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span> };</div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span> </div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span> </div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00604"></a><span class="lineno"><a class="line" href="classEigen_1_1FullPivHouseholderQR.html#a455514157d49695dadaf7dc534fe9ced"> 604</a></span> <span class="keyword">inline</span> <span class="keyword">typename</span> FullPivHouseholderQR<MatrixType>::MatrixQReturnType <a class="code" href="classEigen_1_1FullPivHouseholderQR.html#a455514157d49695dadaf7dc534fe9ced">FullPivHouseholderQR<MatrixType>::matrixQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"FullPivHouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  <span class="keywordflow">return</span> MatrixQReturnType(m_qr, m_hCoeffs, m_rows_transpositions);</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span> }</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span> </div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR<typename MatrixBase<Derived>::PlainObject</a>></div>
<div class="line"><a name="l00616"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#aae22be8c5d589a13a872d2b43614d3a7"> 616</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#aae22be8c5d589a13a872d2b43614d3a7">MatrixBase<Derived>::fullPivHouseholderQr</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1FullPivHouseholderQR.html">FullPivHouseholderQR<PlainObject></a>(eval());</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span> }</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span> </div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span> } <span class="comment">// end namespace Eigen</span></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> <span class="preprocessor">#endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H</span></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a2bb8fa5593d2f447c16ba2e3cfb9c432"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">Eigen::FullPivHouseholderQR::absDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar absDeterminant() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:383</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a56ecc85ee98ff3625d222fdee1774b73"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a56ecc85ee98ff3625d222fdee1774b73">Eigen::FullPivHouseholderQR::solve</a></div><div class="ttdeci">const internal::solve_retval< FullPivHouseholderQR, Rhs > solve(const MatrixBase< Rhs > &b) const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:147</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a1e119085e53eca65e9ba15451c102d40"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">Eigen::FullPivHouseholderQR::isInjective</a></div><div class="ttdeci">bool isInjective() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:246</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html">Eigen::FullPivHouseholderQR</a></div><div class="ttdoc">Householder rank-revealing QR decomposition of a matrix with full pivoting. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:223</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a1229744f4e8554ca6e96fe32ac359924"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924">Eigen::FullPivHouseholderQR::colsPermutation</a></div><div class="ttdeci">const PermutationType & colsPermutation() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:168</div></div>
<div class="ttc" id="group__enums_html_gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044"><div class="ttname"><a href="group__enums.html#gga0c5bde183ecefe103f70b49ad9740bcda1e16fa1b92ed7a058cd4ce7a9a0db044">Eigen::RowMajor</a></div><div class="ttdef"><b>Definition:</b> Constants.h:266</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a7c6323871c4f080fc6e2d3ad7fc607fc"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc">Eigen::FullPivHouseholderQR::dimensionOfKernel</a></div><div class="ttdeci">Index dimensionOfKernel() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:233</div></div>
<div class="ttc" id="structEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...</div><div class="ttdef"><b>Definition:</b> NumTraits.h:88</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a321e96844544eacde2272c3a487048e9"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9">Eigen::FullPivHouseholderQR::hCoeffs</a></div><div class="ttdeci">const HCoeffsType & hCoeffs() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:297</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a8a9705034ce6895c61fe9d0b026837b1"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a8a9705034ce6895c61fe9d0b026837b1">Eigen::FullPivHouseholderQR::FullPivHouseholderQR</a></div><div class="ttdeci">FullPivHouseholderQR(Index rows, Index cols)</div><div class="ttdoc">Default Constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:93</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_ab60c7d993c9eba31668fb8886d621094"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094">Eigen::FullPivHouseholderQR::isInvertible</a></div><div class="ttdeci">bool isInvertible() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:271</div></div>
<div class="ttc" id="classEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime ></a></div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a5968b9ca46303b3cc7250e7b120ab7e6"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">Eigen::FullPivHouseholderQR::isSurjective</a></div><div class="ttdeci">bool isSurjective() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:259</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_aa414ed474b31fecd794cb33003da65d5"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#aa414ed474b31fecd794cb33003da65d5">Eigen::FullPivHouseholderQR::compute</a></div><div class="ttdeci">FullPivHouseholderQR & compute(const MatrixType &matrix)</div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:406</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a067e9d4143ce0558fc684b736128a4ed"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed">Eigen::FullPivHouseholderQR::maxPivot</a></div><div class="ttdeci">RealScalar maxPivot() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:366</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_aae22be8c5d589a13a872d2b43614d3a7"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#aae22be8c5d589a13a872d2b43614d3a7">Eigen::MatrixBase::fullPivHouseholderQr</a></div><div class="ttdeci">const FullPivHouseholderQR< PlainObject > fullPivHouseholderQr() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:616</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_acc93f6afaf0d058c8c1e242b3276977a"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#acc93f6afaf0d058c8c1e242b3276977a">Eigen::FullPivHouseholderQR::FullPivHouseholderQR</a></div><div class="ttdeci">FullPivHouseholderQR()</div><div class="ttdoc">Default Constructor. </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:77</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a363d1c09d77f09d6ea2d2789776e7be3"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">Eigen::FullPivHouseholderQR::rank</a></div><div class="ttdeci">Index rank() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:216</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a58a5850e4bac88c002035f337424f0bc"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a58a5850e4bac88c002035f337424f0bc">Eigen::FullPivHouseholderQR::rowsTranspositions</a></div><div class="ttdeci">const IntColVectorType & rowsTranspositions() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:175</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_aa5a87faaa92a3081045d1f934e292ef0"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">Eigen::FullPivHouseholderQR::threshold</a></div><div class="ttdeci">RealScalar threshold() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:341</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a7b142db8924dd7fad99acbdd0ff4bdd1"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">Eigen::FullPivHouseholderQR::matrixQR</a></div><div class="ttdeci">const MatrixType & matrixQR() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:159</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_acbb58557944348658f9a88afa60b6b2b"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#acbb58557944348658f9a88afa60b6b2b">Eigen::FullPivHouseholderQR::setThreshold</a></div><div class="ttdeci">FullPivHouseholderQR & setThreshold(Default_t)</div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:331</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a8df275c9896e2585fe5748512fca8e8f"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a8df275c9896e2585fe5748512fca8e8f">Eigen::FullPivHouseholderQR::FullPivHouseholderQR</a></div><div class="ttdeci">FullPivHouseholderQR(const MatrixType &matrix)</div><div class="ttdoc">Constructs a QR factorization from a given matrix. </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:115</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a6dda9285f13dec9f49e9c17229a89988"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988">Eigen::FullPivHouseholderQR::nonzeroPivots</a></div><div class="ttdeci">Index nonzeroPivots() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:357</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a6c4acc52d7014703cc351dcdc3538b9d"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a6c4acc52d7014703cc351dcdc3538b9d">Eigen::FullPivHouseholderQR::inverse</a></div><div class="ttdeci">const internal::solve_retval< FullPivHouseholderQR, typename MatrixType::IdentityReturnType > inverse() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:283</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a82a3f15f0cda1f4f874d50951344b5a9"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">Eigen::FullPivHouseholderQR::logAbsDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar logAbsDeterminant() const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:392</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_1FullPivHouseholderQR_html_a455514157d49695dadaf7dc534fe9ced"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a455514157d49695dadaf7dc534fe9ced">Eigen::FullPivHouseholderQR::matrixQ</a></div><div class="ttdeci">MatrixQReturnType matrixQ(void) const </div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:604</div></div>
<div class="ttc" id="classEigen_1_1FullPivHouseholderQR_html_a559f82325764bd1e204fc6f56ba1a145"><div class="ttname"><a href="classEigen_1_1FullPivHouseholderQR.html#a559f82325764bd1e204fc6f56ba1a145">Eigen::FullPivHouseholderQR::setThreshold</a></div><div class="ttdeci">FullPivHouseholderQR & setThreshold(const RealScalar &threshold)</div><div class="ttdef"><b>Definition:</b> FullPivHouseholderQR.h:316</div></div>
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