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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_COLPIVOTINGHOUSEHOLDERQR_H</span></div> <div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_COLPIVOTINGHOUSEHOLDERQR_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="l00037"></a><span class="lineno"> 37</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span>ColPivHouseholderQR</div> <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> {</div> <div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keyword">public</span>:</div> <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> </div> <div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div> <div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">enum</span> {</div> <div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div> <div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div> <div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  Options = MatrixType::Options,</div> <div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div> <div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div> <div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  };</div> <div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div> <div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div> <div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div> <div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keyword">typedef</span> Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType;</div> <div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type<MatrixType>::type HCoeffsType;</div> <div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">typedef</span> PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> PermutationType;</div> <div class="line"><a name="l00055"></a><span class="lineno"> 55</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="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type<MatrixType>::type RowVectorType;</div> <div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type<MatrixType, RealScalar>::type RealRowVectorType;</div> <div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">typedef</span> HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;</div> <div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  </div> <div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">private</span>:</div> <div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  </div> <div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> PermutationType::Index PermIndexType;</div> <div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  </div> <div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">public</span>:</div> <div class="line"><a name="l00065"></a><span class="lineno"> 65</span> </div> <div class="line"><a name="l00072"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a72f7fb8c1359fa8d9743068e5699228e"> 72</a></span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a72f7fb8c1359fa8d9743068e5699228e">ColPivHouseholderQR</a>()</div> <div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  : m_qr(),</div> <div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  m_hCoeffs(),</div> <div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  m_colsPermutation(),</div> <div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  m_colsTranspositions(),</div> <div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  m_temp(),</div> <div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  m_colSqNorms(),</div> <div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  m_isInitialized(false) {}</div> <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> </div> <div class="line"><a name="l00087"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a4a15f3e5e33478b9969d8c71aabd09ea"> 87</a></span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a4a15f3e5e33478b9969d8c71aabd09ea">ColPivHouseholderQR</a>(Index rows, Index cols)</div> <div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  : m_qr(rows, cols),</div> <div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  m_hCoeffs((std::min)(rows,cols)),</div> <div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  m_colsPermutation(PermIndexType(cols)),</div> <div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  m_colsTranspositions(cols),</div> <div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  m_temp(cols),</div> <div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  m_colSqNorms(cols),</div> <div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  m_isInitialized(false),</div> <div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  m_usePrescribedThreshold(false) {}</div> <div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div> <div class="line"><a name="l00109"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#ac93cc6a4fd4247486c2c8eab79b4c0ad"> 109</a></span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#ac93cc6a4fd4247486c2c8eab79b4c0ad">ColPivHouseholderQR</a>(<span class="keyword">const</span> MatrixType& matrix)</div> <div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  : m_qr(matrix.rows(), matrix.cols()),</div> <div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),</div> <div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  m_colsPermutation(PermIndexType(matrix.cols())),</div> <div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  m_colsTranspositions(matrix.cols()),</div> <div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  m_temp(matrix.cols()),</div> <div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  m_colSqNorms(matrix.cols()),</div> <div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  m_isInitialized(false),</div> <div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  m_usePrescribedThreshold(false)</div> <div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  {</div> <div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">compute</a>(matrix);</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="l00139"></a><span class="lineno"> 139</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div> <div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<ColPivHouseholderQR, Rhs></div> <div class="line"><a name="l00141"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#afbe1cd1202964011ae7e7411577749a0"> 141</a></span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#afbe1cd1202964011ae7e7411577749a0">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="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">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">return</span> internal::solve_retval<ColPivHouseholderQR, Rhs>(*<span class="keyword">this</span>, b.derived());</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="l00147"></a><span class="lineno"> 147</span>  HouseholderSequenceType <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">householderQ</a>(<span class="keywordtype">void</span>) <span class="keyword">const</span>;</div> <div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  HouseholderSequenceType matrixQ(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div> <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">householderQ</a>(); </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"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1"> 155</a></span>  <span class="keyword">const</span> MatrixType& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">matrixQR</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">return</span> m_qr;</div> <div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  }</div> <div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  </div> <div class="line"><a name="l00170"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a84cd3aba44220008bdbd81506703de37"> 170</a></span>  <span class="keyword">const</span> MatrixType& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a84cd3aba44220008bdbd81506703de37">matrixR</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keywordflow">return</span> m_qr;</div> <div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  }</div> <div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  </div> <div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR</a>& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">compute</a>(<span class="keyword">const</span> MatrixType& matrix);</div> <div class="line"><a name="l00177"></a><span class="lineno"> 177</span> </div> <div class="line"><a name="l00179"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924"> 179</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924">colsPermutation</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordflow">return</span> m_colsPermutation;</div> <div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  }</div> <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> </div> <div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">absDeterminant</a>() <span class="keyword">const</span>;</div> <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> </div> <div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">logAbsDeterminant</a>() <span class="keyword">const</span>;</div> <div class="line"><a name="l00213"></a><span class="lineno"> 213</span> </div> <div class="line"><a name="l00220"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3"> 220</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keyword">using</span> std::abs;</div> <div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  RealScalar premultiplied_threshold = abs(m_maxpivot) * <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>();</div> <div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  Index result = 0;</div> <div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">for</span>(Index i = 0; i < m_nonzero_pivots; ++i)</div> <div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);</div> <div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">return</span> result;</div> <div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  }</div> <div class="line"><a name="l00230"></a><span class="lineno"> 230</span> </div> <div class="line"><a name="l00237"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc"> 237</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc">dimensionOfKernel</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">return</span> cols() - <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>();</div> <div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  }</div> <div class="line"><a name="l00242"></a><span class="lineno"> 242</span> </div> <div class="line"><a name="l00250"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40"> 250</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">isInjective</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>() == cols();</div> <div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  }</div> <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div> <div class="line"><a name="l00263"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6"> 263</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">isSurjective</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>() == rows();</div> <div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  }</div> <div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div> <div class="line"><a name="l00275"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094"> 275</a></span>  <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094">isInvertible</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">isInjective</a>() && <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">isSurjective</a>();</div> <div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  }</div> <div class="line"><a name="l00280"></a><span class="lineno"> 280</span> </div> <div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keyword">inline</span> <span class="keyword">const</span></div> <div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  internal::solve_retval<ColPivHouseholderQR, typename MatrixType::IdentityReturnType></div> <div class="line"><a name="l00288"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a3021b1285c868ef94b26f387766bdf92"> 288</a></span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a3021b1285c868ef94b26f387766bdf92">inverse</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keywordflow">return</span> internal::solve_retval<ColPivHouseholderQR,typename MatrixType::IdentityReturnType></div> <div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  (*<span class="keyword">this</span>, MatrixType::Identity(m_qr.rows(), m_qr.cols()));</div> <div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  }</div> <div class="line"><a name="l00294"></a><span class="lineno"> 294</span> </div> <div class="line"><a name="l00295"></a><span class="lineno"> 295</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="l00296"></a><span class="lineno"> 296</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="l00297"></a><span class="lineno"> 297</span>  </div> <div class="line"><a name="l00302"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9"> 302</a></span>  <span class="keyword">const</span> HCoeffsType& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9">hCoeffs</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hCoeffs; }</div> <div class="line"><a name="l00303"></a><span class="lineno"> 303</span> </div> <div class="line"><a name="l00321"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a5631914aef48f4f719789c823edacb2c"> 321</a></span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR</a>& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a5631914aef48f4f719789c823edacb2c">setThreshold</a>(<span class="keyword">const</span> RealScalar& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>)</div> <div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  {</div> <div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  m_usePrescribedThreshold = <span class="keyword">true</span>;</div> <div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  m_prescribedThreshold = <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>;</div> <div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div> <div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  }</div> <div class="line"><a name="l00327"></a><span class="lineno"> 327</span> </div> <div class="line"><a name="l00336"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a446f775405186b238f20bd092fd107a6"> 336</a></span>  <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR</a>& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a446f775405186b238f20bd092fd107a6">setThreshold</a>(Default_t)</div> <div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  {</div> <div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  m_usePrescribedThreshold = <span class="keyword">false</span>;</div> <div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div> <div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  }</div> <div class="line"><a name="l00341"></a><span class="lineno"> 341</span> </div> <div class="line"><a name="l00346"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0"> 346</a></span>  RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">threshold</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  eigen_assert(m_isInitialized || m_usePrescribedThreshold);</div> <div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">return</span> m_usePrescribedThreshold ? m_prescribedThreshold</div> <div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="comment">// this formula comes from experimenting (see "LU precision tuning" thread on the list)</span></div> <div class="line"><a name="l00351"></a><span class="lineno"> 351</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="l00352"></a><span class="lineno"> 352</span>  : <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::epsilon</a>() * m_qr.diagonalSize();</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_1ColPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988"> 362</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988">nonzeroPivots</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">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="keywordflow">return</span> m_nonzero_pivots;</div> <div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  }</div> <div class="line"><a name="l00367"></a><span class="lineno"> 367</span> </div> <div class="line"><a name="l00371"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed"> 371</a></span>  RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed">maxPivot</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_maxpivot; }</div> <div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  </div> <div class="line"><a name="l00379"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a0c06d5c2034ebb329c54235369643ad2"> 379</a></span>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a0c06d5c2034ebb329c54235369643ad2">info</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"Decomposition is not initialized."</span>);</div> <div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">return</span> <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>;</div> <div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  }</div> <div class="line"><a name="l00384"></a><span class="lineno"> 384</span> </div> <div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="keyword">protected</span>:</div> <div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  MatrixType m_qr;</div> <div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  HCoeffsType m_hCoeffs;</div> <div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  PermutationType m_colsPermutation;</div> <div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  IntRowVectorType m_colsTranspositions;</div> <div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  RowVectorType m_temp;</div> <div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  RealRowVectorType m_colSqNorms;</div> <div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keywordtype">bool</span> m_isInitialized, m_usePrescribedThreshold;</div> <div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  RealScalar m_prescribedThreshold, m_maxpivot;</div> <div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  Index m_nonzero_pivots;</div> <div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  Index m_det_pq;</div> <div class="line"><a name="l00396"></a><span class="lineno"> 396</span> };</div> <div class="line"><a name="l00397"></a><span class="lineno"> 397</span> </div> <div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div> <div class="line"><a name="l00399"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432"> 399</a></span> <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">ColPivHouseholderQR<MatrixType>::absDeterminant</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="keyword"></span>{</div> <div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="keyword">using</span> std::abs;</div> <div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00403"></a><span class="lineno"> 403</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="l00404"></a><span class="lineno"> 404</span>  <span class="keywordflow">return</span> abs(m_qr.diagonal().prod());</div> <div class="line"><a name="l00405"></a><span class="lineno"> 405</span> }</div> <div class="line"><a name="l00406"></a><span class="lineno"> 406</span> </div> <div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div> <div class="line"><a name="l00408"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9"> 408</a></span> <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">ColPivHouseholderQR<MatrixType>::logAbsDeterminant</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="keyword"></span>{</div> <div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00411"></a><span class="lineno"> 411</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="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">return</span> m_qr.diagonal().cwiseAbs().array().log().sum();</div> <div class="line"><a name="l00413"></a><span class="lineno"> 413</span> }</div> <div class="line"><a name="l00414"></a><span class="lineno"> 414</span> </div> <div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div> <div class="line"><a name="l00422"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b"> 422</a></span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR<MatrixType></a>& <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">ColPivHouseholderQR<MatrixType>::compute</a>(<span class="keyword">const</span> MatrixType& matrix)</div> <div class="line"><a name="l00423"></a><span class="lineno"> 423</span> {</div> <div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="keyword">using</span> std::abs;</div> <div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  Index rows = matrix.rows();</div> <div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  Index cols = matrix.cols();</div> <div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  Index size = matrix.diagonalSize();</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="comment">// the column permutation is stored as int indices, so just to be sure:</span></div> <div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  eigen_assert(cols<=<a class="code" href="structEigen_1_1NumTraits.html">NumTraits<int>::highest</a>());</div> <div class="line"><a name="l00431"></a><span class="lineno"> 431</span> </div> <div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  m_qr = matrix;</div> <div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  m_hCoeffs.resize(size);</div> <div class="line"><a name="l00434"></a><span class="lineno"> 434</span> </div> <div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  m_temp.resize(cols);</div> <div class="line"><a name="l00436"></a><span class="lineno"> 436</span> </div> <div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  m_colsTranspositions.resize(matrix.cols());</div> <div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  Index number_of_transpositions = 0;</div> <div class="line"><a name="l00439"></a><span class="lineno"> 439</span> </div> <div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  m_colSqNorms.resize(cols);</div> <div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="keywordflow">for</span>(Index k = 0; k < cols; ++k)</div> <div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  m_colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm();</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>  RealScalar threshold_helper = m_colSqNorms.maxCoeff() * numext::abs2(<a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::epsilon</a>()) / RealScalar(rows);</div> <div class="line"><a name="l00445"></a><span class="lineno"> 445</span> </div> <div class="line"><a name="l00446"></a><span class="lineno"> 446</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="l00447"></a><span class="lineno"> 447</span>  m_maxpivot = RealScalar(0);</div> <div class="line"><a name="l00448"></a><span class="lineno"> 448</span> </div> <div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">for</span>(Index k = 0; k < size; ++k)</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="comment">// first, we look up in our table m_colSqNorms which column has the biggest squared norm</span></div> <div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  Index biggest_col_index;</div> <div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  RealScalar biggest_col_sq_norm = m_colSqNorms.tail(cols-k).maxCoeff(&biggest_col_index);</div> <div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  biggest_col_index += k;</div> <div class="line"><a name="l00455"></a><span class="lineno"> 455</span> </div> <div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <span class="comment">// since our table m_colSqNorms accumulates imprecision at every step, we must now recompute</span></div> <div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="comment">// the actual squared norm of the selected column.</span></div> <div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="comment">// Note that not doing so does result in solve() sometimes returning inf/nan values</span></div> <div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="comment">// when running the unit test with 1000 repetitions.</span></div> <div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  biggest_col_sq_norm = m_qr.col(biggest_col_index).tail(rows-k).squaredNorm();</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="comment">// we store that back into our table: it can't hurt to correct our table.</span></div> <div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  m_colSqNorms.coeffRef(biggest_col_index) = biggest_col_sq_norm;</div> <div class="line"><a name="l00464"></a><span class="lineno"> 464</span> </div> <div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="comment">// if the current biggest column is smaller than epsilon times the initial biggest column,</span></div> <div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <span class="comment">// terminate to avoid generating nan/inf values.</span></div> <div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="comment">// Note that here, if we test instead for "biggest == 0", we get a failure every 1000 (or so)</span></div> <div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="comment">// repetitions of the unit test, with the result of solve() filled with large values of the order</span></div> <div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="comment">// of 1/(size*epsilon).</span></div> <div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <span class="keywordflow">if</span>(biggest_col_sq_norm < threshold_helper * RealScalar(rows-k))</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_nonzero_pivots = k;</div> <div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  m_hCoeffs.tail(size-k).setZero();</div> <div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  m_qr.bottomRightCorner(rows-k,cols-k)</div> <div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  .template triangularView<StrictlyLower>()</div> <div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  .setZero();</div> <div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <span class="keywordflow">break</span>;</div> <div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  }</div> <div class="line"><a name="l00479"></a><span class="lineno"> 479</span> </div> <div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  <span class="comment">// apply the transposition to the columns</span></div> <div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  m_colsTranspositions.coeffRef(k) = biggest_col_index;</div> <div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="keywordflow">if</span>(k != biggest_col_index) {</div> <div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  m_qr.col(k).swap(m_qr.col(biggest_col_index));</div> <div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  std::swap(m_colSqNorms.coeffRef(k), m_colSqNorms.coeffRef(biggest_col_index));</div> <div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  ++number_of_transpositions;</div> <div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  }</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="comment">// generate the householder vector, store it below the diagonal</span></div> <div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  RealScalar beta;</div> <div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  m_qr.col(k).tail(rows-k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);</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>  <span class="comment">// apply the householder transformation to the diagonal coefficient</span></div> <div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  m_qr.coeffRef(k,k) = beta;</div> <div class="line"><a name="l00494"></a><span class="lineno"> 494</span> </div> <div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <span class="comment">// remember the maximum absolute value of diagonal coefficients</span></div> <div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <span class="keywordflow">if</span>(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);</div> <div class="line"><a name="l00497"></a><span class="lineno"> 497</span> </div> <div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="comment">// apply the householder transformation</span></div> <div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  m_qr.bottomRightCorner(rows-k, cols-k-1)</div> <div class="line"><a name="l00500"></a><span class="lineno"> 500</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="l00501"></a><span class="lineno"> 501</span> </div> <div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="comment">// update our table of squared norms of the columns</span></div> <div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  m_colSqNorms.tail(cols-k-1) -= m_qr.row(k).tail(cols-k-1).cwiseAbs2();</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> </div> <div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  m_colsPermutation.setIdentity(PermIndexType(cols));</div> <div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keywordflow">for</span>(PermIndexType k = 0; k < m_nonzero_pivots; ++k)</div> <div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  m_colsPermutation.applyTranspositionOnTheRight(k, PermIndexType(m_colsTranspositions.coeff(k)));</div> <div class="line"><a name="l00509"></a><span class="lineno"> 509</span> </div> <div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  m_det_pq = (number_of_transpositions%2) ? -1 : 1;</div> <div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  m_isInitialized = <span class="keyword">true</span>;</div> <div class="line"><a name="l00512"></a><span class="lineno"> 512</span> </div> <div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div> <div class="line"><a name="l00514"></a><span class="lineno"> 514</span> }</div> <div class="line"><a name="l00515"></a><span class="lineno"> 515</span> </div> <div class="line"><a name="l00516"></a><span class="lineno"> 516</span> <span class="keyword">namespace </span>internal {</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> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> Rhs></div> <div class="line"><a name="l00519"></a><span class="lineno"> 519</span> <span class="keyword">struct </span>solve_retval<<a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR</a><_MatrixType>, Rhs></div> <div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  : solve_retval_base<ColPivHouseholderQR<_MatrixType>, Rhs></div> <div class="line"><a name="l00521"></a><span class="lineno"> 521</span> {</div> <div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  EIGEN_MAKE_SOLVE_HELPERS(<a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR<_MatrixType></a>,Rhs)</div> <div class="line"><a name="l00523"></a><span class="lineno"> 523</span> </div> <div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div> <div class="line"><a name="l00525"></a><span class="lineno"> 525</span> <span class="keyword"> </span>{</div> <div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  eigen_assert(rhs().rows() == dec().rows());</div> <div class="line"><a name="l00527"></a><span class="lineno"> 527</span> </div> <div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keyword">const</span> Index cols = dec().cols(),</div> <div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  nonzero_pivots = dec().nonzeroPivots();</div> <div class="line"><a name="l00530"></a><span class="lineno"> 530</span> </div> <div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="keywordflow">if</span>(nonzero_pivots == 0)</div> <div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  {</div> <div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  dst.setZero();</div> <div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <span class="keywordflow">return</span>;</div> <div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  }</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>  <span class="keyword">typename</span> Rhs::PlainObject c(rhs());</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>  <span class="comment">// Note that the matrix Q = H_0^* H_1^*... so its inverse is Q^* = (H_0 H_1 ...)^T</span></div> <div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  c.applyOnTheLeft(<a class="code" href="group__Householder__Module.html#ga5f2b3f80cdf7ae96609e4a8d2e55e371">householderSequence</a>(dec().matrixQR(), dec().hCoeffs())</div> <div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  .setLength(dec().nonzeroPivots())</div> <div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  .transpose()</div> <div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  );</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>  dec().matrixR()</div> <div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  .topLeftCorner(nonzero_pivots, nonzero_pivots)</div> <div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  .template triangularView<Upper>()</div> <div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  .solveInPlace(c.topRows(nonzero_pivots));</div> <div class="line"><a name="l00549"></a><span class="lineno"> 549</span> </div> <div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keywordflow">for</span>(Index i = 0; i < nonzero_pivots; ++i) dst.row(dec().colsPermutation().indices().coeff(i)) = c.row(i);</div> <div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="keywordflow">for</span>(Index i = nonzero_pivots; i < cols; ++i) dst.row(dec().colsPermutation().indices().coeff(i)).setZero();</div> <div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  }</div> <div class="line"><a name="l00553"></a><span class="lineno"> 553</span> };</div> <div class="line"><a name="l00554"></a><span class="lineno"> 554</span> </div> <div class="line"><a name="l00555"></a><span class="lineno"> 555</span> } <span class="comment">// end namespace internal</span></div> <div class="line"><a name="l00556"></a><span class="lineno"> 556</span> </div> <div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div> <div class="line"><a name="l00559"></a><span class="lineno"> 559</span> <span class="keyword">typename</span> ColPivHouseholderQR<MatrixType>::HouseholderSequenceType <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">ColPivHouseholderQR<MatrixType></a></div> <div class="line"><a name="l00560"></a><span class="lineno"><a class="line" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89"> 560</a></span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89"> ::householderQ</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00561"></a><span class="lineno"> 561</span> <span class="keyword"></span>{</div> <div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ColPivHouseholderQR is not initialized."</span>);</div> <div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a>(m_qr, m_hCoeffs.conjugate()).setLength(m_nonzero_pivots);</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> </div> <div class="line"><a name="l00570"></a><span class="lineno"> 570</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div> <div class="line"><a name="l00571"></a><span class="lineno"> 571</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR<typename MatrixBase<Derived>::PlainObject</a>></div> <div class="line"><a name="l00572"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a05afed751d3a7277951d1918468e0872"> 572</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#a05afed751d3a7277951d1918468e0872">MatrixBase<Derived>::colPivHouseholderQr</a>()<span class="keyword"> const</span></div> <div class="line"><a name="l00573"></a><span class="lineno"> 573</span> <span class="keyword"></span>{</div> <div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1ColPivHouseholderQR.html">ColPivHouseholderQR<PlainObject></a>(eval());</div> <div class="line"><a name="l00575"></a><span class="lineno"> 575</span> }</div> <div class="line"><a name="l00576"></a><span class="lineno"> 576</span> </div> <div class="line"><a name="l00577"></a><span class="lineno"> 577</span> } <span class="comment">// end namespace Eigen</span></div> <div class="line"><a name="l00578"></a><span class="lineno"> 578</span> </div> <div class="line"><a name="l00579"></a><span class="lineno"> 579</span> <span class="preprocessor">#endif // EIGEN_COLPIVOTINGHOUSEHOLDERQR_H</span></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a2bb8fa5593d2f447c16ba2e3cfb9c432"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">Eigen::ColPivHouseholderQR::absDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar absDeterminant() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:399</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a82a3f15f0cda1f4f874d50951344b5a9"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">Eigen::ColPivHouseholderQR::logAbsDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar logAbsDeterminant() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:408</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a067e9d4143ce0558fc684b736128a4ed"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a067e9d4143ce0558fc684b736128a4ed">Eigen::ColPivHouseholderQR::maxPivot</a></div><div class="ttdeci">RealScalar maxPivot() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:371</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_aa5a87faaa92a3081045d1f934e292ef0"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#aa5a87faaa92a3081045d1f934e292ef0">Eigen::ColPivHouseholderQR::threshold</a></div><div class="ttdeci">RealScalar threshold() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:346</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_1ColPivHouseholderQR_html_a321e96844544eacde2272c3a487048e9"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a321e96844544eacde2272c3a487048e9">Eigen::ColPivHouseholderQR::hCoeffs</a></div><div class="ttdeci">const HCoeffsType & hCoeffs() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:302</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a7b142db8924dd7fad99acbdd0ff4bdd1"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">Eigen::ColPivHouseholderQR::matrixQR</a></div><div class="ttdeci">const MatrixType & matrixQR() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:155</div></div> <div class="ttc" id="group__Householder__Module_html_ga5f2b3f80cdf7ae96609e4a8d2e55e371"><div class="ttname"><a href="group__Householder__Module.html#ga5f2b3f80cdf7ae96609e4a8d2e55e371">Eigen::householderSequence</a></div><div class="ttdeci">HouseholderSequence< VectorsType, CoeffsType > householderSequence(const VectorsType &v, const CoeffsType &h)</div><div class="ttdoc">Convenience function for constructing a Householder sequence. </div><div class="ttdef"><b>Definition:</b> HouseholderSequence.h:422</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a72f7fb8c1359fa8d9743068e5699228e"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a72f7fb8c1359fa8d9743068e5699228e">Eigen::ColPivHouseholderQR::ColPivHouseholderQR</a></div><div class="ttdeci">ColPivHouseholderQR()</div><div class="ttdoc">Default Constructor. </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:72</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a0c06d5c2034ebb329c54235369643ad2"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a0c06d5c2034ebb329c54235369643ad2">Eigen::ColPivHouseholderQR::info</a></div><div class="ttdeci">ComputationInfo info() const </div><div class="ttdoc">Reports whether the QR factorization was succesful. </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:379</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a97150efba7e2da32f48a7f823f047a89"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a97150efba7e2da32f48a7f823f047a89">Eigen::ColPivHouseholderQR::householderQ</a></div><div class="ttdeci">HouseholderSequenceType householderQ(void) const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:560</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_ac93cc6a4fd4247486c2c8eab79b4c0ad"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#ac93cc6a4fd4247486c2c8eab79b4c0ad">Eigen::ColPivHouseholderQR::ColPivHouseholderQR</a></div><div class="ttdeci">ColPivHouseholderQR(const MatrixType &matrix)</div><div class="ttdoc">Constructs a QR factorization from a given matrix. </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:109</div></div> <div class="ttc" id="classEigen_1_1HouseholderSequence_html"><div class="ttname"><a href="classEigen_1_1HouseholderSequence.html">Eigen::HouseholderSequence</a></div><div class="ttdoc">Sequence of Householder reflections acting on subspaces with decreasing size. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:227</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_1ColPivHouseholderQR_html_a812205d31cae2005b7779c7a3a442f1b"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a812205d31cae2005b7779c7a3a442f1b">Eigen::ColPivHouseholderQR::compute</a></div><div class="ttdeci">ColPivHouseholderQR & compute(const MatrixType &matrix)</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:422</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a1229744f4e8554ca6e96fe32ac359924"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a1229744f4e8554ca6e96fe32ac359924">Eigen::ColPivHouseholderQR::colsPermutation</a></div><div class="ttdeci">const PermutationType & colsPermutation() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:179</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a5968b9ca46303b3cc7250e7b120ab7e6"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a5968b9ca46303b3cc7250e7b120ab7e6">Eigen::ColPivHouseholderQR::isSurjective</a></div><div class="ttdeci">bool isSurjective() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:263</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html">Eigen::ColPivHouseholderQR</a></div><div class="ttdoc">Householder rank-revealing QR decomposition of a matrix with column-pivoting. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:222</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a1e119085e53eca65e9ba15451c102d40"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a1e119085e53eca65e9ba15451c102d40">Eigen::ColPivHouseholderQR::isInjective</a></div><div class="ttdeci">bool isInjective() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:250</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_ab60c7d993c9eba31668fb8886d621094"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#ab60c7d993c9eba31668fb8886d621094">Eigen::ColPivHouseholderQR::isInvertible</a></div><div class="ttdeci">bool isInvertible() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:275</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a446f775405186b238f20bd092fd107a6"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a446f775405186b238f20bd092fd107a6">Eigen::ColPivHouseholderQR::setThreshold</a></div><div class="ttdeci">ColPivHouseholderQR & setThreshold(Default_t)</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:336</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a5631914aef48f4f719789c823edacb2c"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a5631914aef48f4f719789c823edacb2c">Eigen::ColPivHouseholderQR::setThreshold</a></div><div class="ttdeci">ColPivHouseholderQR & setThreshold(const RealScalar &threshold)</div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:321</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_afbe1cd1202964011ae7e7411577749a0"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#afbe1cd1202964011ae7e7411577749a0">Eigen::ColPivHouseholderQR::solve</a></div><div class="ttdeci">const internal::solve_retval< ColPivHouseholderQR, Rhs > solve(const MatrixBase< Rhs > &b) const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:141</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a84cd3aba44220008bdbd81506703de37"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a84cd3aba44220008bdbd81506703de37">Eigen::ColPivHouseholderQR::matrixR</a></div><div class="ttdeci">const MatrixType & matrixR() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:170</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a6dda9285f13dec9f49e9c17229a89988"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a6dda9285f13dec9f49e9c17229a89988">Eigen::ColPivHouseholderQR::nonzeroPivots</a></div><div class="ttdeci">Index nonzeroPivots() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:362</div></div> <div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Eigen::Success</a></div><div class="ttdef"><b>Definition:</b> Constants.h:376</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a3021b1285c868ef94b26f387766bdf92"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a3021b1285c868ef94b26f387766bdf92">Eigen::ColPivHouseholderQR::inverse</a></div><div class="ttdeci">const internal::solve_retval< ColPivHouseholderQR, typename MatrixType::IdentityReturnType > inverse() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:288</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a7c6323871c4f080fc6e2d3ad7fc607fc"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a7c6323871c4f080fc6e2d3ad7fc607fc">Eigen::ColPivHouseholderQR::dimensionOfKernel</a></div><div class="ttdeci">Index dimensionOfKernel() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:237</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a4a15f3e5e33478b9969d8c71aabd09ea"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a4a15f3e5e33478b9969d8c71aabd09ea">Eigen::ColPivHouseholderQR::ColPivHouseholderQR</a></div><div class="ttdeci">ColPivHouseholderQR(Index rows, Index cols)</div><div class="ttdoc">Default Constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:87</div></div> <div class="ttc" id="group__enums_html_ga51bc1ac16f26ebe51eae1abb77bd037b"><div class="ttname"><a href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:374</div></div> <div class="ttc" id="classEigen_1_1ColPivHouseholderQR_html_a363d1c09d77f09d6ea2d2789776e7be3"><div class="ttname"><a href="classEigen_1_1ColPivHouseholderQR.html#a363d1c09d77f09d6ea2d2789776e7be3">Eigen::ColPivHouseholderQR::rank</a></div><div class="ttdeci">Index rank() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:220</div></div> <div class="ttc" id="classEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions. </div><div class="ttdef"><b>Definition:</b> MatrixBase.h:48</div></div> <div class="ttc" id="classEigen_1_1MatrixBase_html_a05afed751d3a7277951d1918468e0872"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a05afed751d3a7277951d1918468e0872">Eigen::MatrixBase::colPivHouseholderQr</a></div><div class="ttdeci">const ColPivHouseholderQR< PlainObject > colPivHouseholderQr() const </div><div class="ttdef"><b>Definition:</b> ColPivHouseholderQR.h:572</div></div> </div><!-- fragment --></div><!-- contents --> </div><!-- doc-content --> <!-- start footer part --> <div id="nav-path" class="navpath"><!-- id is needed for treeview function! --> <ul> <li class="navelem"><a class="el" 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