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<div class="title">HouseholderQR.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) 2008-2010 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">// Copyright (C) 2010 Vincent Lejeune</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</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="l00010"></a><span class="lineno"> 10</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="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#ifndef EIGEN_QR_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_QR_H</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span>HouseholderQR</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  Options = MatrixType::Options,</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  };</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">typedef</span> Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixQType;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type<MatrixType>::type HCoeffsType;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type<MatrixType>::type RowVectorType;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">typedef</span> HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> HouseholderSequenceType;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#ab7e9b80266fe7d1592e4c9de652d9f50"> 68</a></span>  <a class="code" href="classEigen_1_1HouseholderQR.html#ab7e9b80266fe7d1592e4c9de652d9f50">HouseholderQR</a>() : m_qr(), m_hCoeffs(), m_temp(), m_isInitialized(false) {}</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#abf25ea0833fe1e846c20968103f69141"> 76</a></span>  <a class="code" href="classEigen_1_1HouseholderQR.html#abf25ea0833fe1e846c20968103f69141">HouseholderQR</a>(Index rows, Index cols)</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  : m_qr(rows, cols),</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  m_hCoeffs((std::min)(rows,cols)),</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  m_temp(cols),</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  m_isInitialized(false) {}</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> </div>
<div class="line"><a name="l00094"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#ab592f6a05d7ba94c0108382baa8c993e"> 94</a></span>  <a class="code" href="classEigen_1_1HouseholderQR.html#ab592f6a05d7ba94c0108382baa8c993e">HouseholderQR</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  : m_qr(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  m_temp(matrix.cols()),</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  m_isInitialized(false)</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  {</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <a class="code" href="classEigen_1_1HouseholderQR.html#a5851b8e7d2a7f91592e7fa69f8b7684c">compute</a>(matrix);</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  }</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<HouseholderQR, Rhs></div>
<div class="line"><a name="l00122"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a3912046746c14d7b4e9dba999da46a68"> 122</a></span>  <a class="code" href="classEigen_1_1HouseholderQR.html#a3912046746c14d7b4e9dba999da46a68">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="l00123"></a><span class="lineno"> 123</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">return</span> internal::solve_retval<HouseholderQR, Rhs>(*<span class="keyword">this</span>, b.derived());</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="l00136"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a520fc76215d7722387a76e7b7a484ee0"> 136</a></span>  <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a> <a class="code" href="classEigen_1_1HouseholderQR.html#a520fc76215d7722387a76e7b7a484ee0">householderQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a>(m_qr, m_hCoeffs.conjugate());</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  }</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> </div>
<div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1"> 145</a></span>  <span class="keyword">const</span> MatrixType& <a class="code" href="classEigen_1_1HouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">matrixQR</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">return</span> m_qr;</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  }</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR</a>& <a class="code" href="classEigen_1_1HouseholderQR.html#a5851b8e7d2a7f91592e7fa69f8b7684c">compute</a>(<span class="keyword">const</span> MatrixType& matrix);</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1HouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">absDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1HouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">logAbsDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</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="l00183"></a><span class="lineno"> 183</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="l00184"></a><span class="lineno"> 184</span>  </div>
<div class="line"><a name="l00189"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a321e96844544eacde2272c3a487048e9"> 189</a></span>  <span class="keyword">const</span> HCoeffsType& <a class="code" href="classEigen_1_1HouseholderQR.html#a321e96844544eacde2272c3a487048e9">hCoeffs</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hCoeffs; }</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  MatrixType m_qr;</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  HCoeffsType m_hCoeffs;</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  RowVectorType m_temp;</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> };</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00199"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432"> 199</a></span> <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1HouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">HouseholderQR<MatrixType>::absDeterminant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</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="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">return</span> abs(m_qr.diagonal().prod());</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> }</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> </div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00208"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9"> 208</a></span> <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1HouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">HouseholderQR<MatrixType>::logAbsDeterminant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HouseholderQR is not initialized."</span>);</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</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="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">return</span> m_qr.diagonal().cwiseAbs().array().log().sum();</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> }</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> </div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixQR, <span class="keyword">typename</span> HCoeffs></div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="keywordtype">void</span> householder_qr_inplace_unblocked(MatrixQR& mat, HCoeffs& hCoeffs, <span class="keyword">typename</span> MatrixQR::Scalar* tempData = 0)</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span> {</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::Index Index;</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::Scalar Scalar;</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::RealScalar RealScalar;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  Index rows = mat.rows();</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  Index cols = mat.cols();</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  Index size = (std::min)(rows,cols);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> </div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  eigen_assert(hCoeffs.size() == size);</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>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar,MatrixQR::ColsAtCompileTime,1></a> TempType;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  TempType tempVector;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">if</span>(tempData==0)</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  {</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  tempVector.<a class="code" href="classEigen_1_1PlainObjectBase.html#afbbb33d14fe7fb9683019a39ce1c659d">resize</a>(cols);</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  tempData = tempVector.data();</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  }</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>  <span class="keywordflow">for</span>(Index k = 0; k < size; ++k)</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  {</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  Index remainingRows = rows - k;</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  Index remainingCols = cols - k - 1;</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> </div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  RealScalar beta;</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  mat.col(k).tail(remainingRows).makeHouseholderInPlace(hCoeffs.coeffRef(k), beta);</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  mat.coeffRef(k,k) = beta;</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> </div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="comment">// apply H to remaining part of m_qr from the left</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  mat.bottomRightCorner(remainingRows, remainingCols)</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  .applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows-1), hCoeffs.coeffRef(k), tempData+k+1);</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="l00252"></a><span class="lineno"> 252</span> </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixQR, <span class="keyword">typename</span> HCoeffs></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="keywordtype">void</span> householder_qr_inplace_blocked(MatrixQR& mat, HCoeffs& hCoeffs,</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keyword">typename</span> MatrixQR::Index maxBlockSize=32,</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keyword">typename</span> MatrixQR::Scalar* tempData = 0)</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> {</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::Index Index;</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::Scalar Scalar;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keyword">typedef</span> Block<MatrixQR,Dynamic,Dynamic> BlockType;</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  Index rows = mat.rows();</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  Index cols = mat.cols();</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  Index size = (std::min)(rows, cols);</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> </div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,1,ColMajor,MatrixQR::MaxColsAtCompileTime,1> TempType;</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  TempType tempVector;</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keywordflow">if</span>(tempData==0)</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  {</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  tempVector.resize(cols);</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  tempData = tempVector.data();</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  }</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  Index blockSize = (std::min)(maxBlockSize,size);</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> </div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  Index k = 0;</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keywordflow">for</span> (k = 0; k < size; k += blockSize)</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>  Index bs = (std::min)(size-k,blockSize); <span class="comment">// actual size of the block</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  Index tcols = cols - k - bs; <span class="comment">// trailing columns</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  Index brows = rows-k; <span class="comment">// rows of the block</span></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="comment">// partition the matrix:</span></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="comment">// A00 | A01 | A02</span></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">// mat = A10 | A11 | A12</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="comment">// A20 | A21 | A22</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">// and performs the qr dec of [A11^T A12^T]^T</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">// and update [A21^T A22^T]^T using level 3 operations.</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="comment">// Finally, the algorithm continue on A22</span></div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> </div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  BlockType A11_21 = mat.block(k,k,brows,bs);</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  Block<HCoeffs,Dynamic,1> hCoeffsSegment = hCoeffs.segment(k,bs);</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>  householder_qr_inplace_unblocked(A11_21, hCoeffsSegment, tempData);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> </div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">if</span>(tcols)</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  {</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  BlockType A21_22 = mat.block(k,k+bs,brows,tcols);</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment.adjoint());</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  }</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  }</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span> }</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span> </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="keyword">struct </span>solve_retval<HouseholderQR<_MatrixType>, Rhs></div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  : solve_retval_base<HouseholderQR<_MatrixType>, Rhs></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span> {</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  EIGEN_MAKE_SOLVE_HELPERS(HouseholderQR<_MatrixType>,Rhs)</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> </div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keyword">const</span> Index rows = dec().rows(), cols = dec().cols();</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keyword">const</span> Index rank = (std::min)(rows, cols);</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  eigen_assert(rhs().rows() == rows);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span> </div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keyword">typename</span> Rhs::PlainObject c(rhs());</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span> </div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="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="l00320"></a><span class="lineno"> 320</span>  c.applyOnTheLeft(<a class="code" href="group__Householder__Module.html#ga5f2b3f80cdf7ae96609e4a8d2e55e371">householderSequence</a>(</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  dec().matrixQR().leftCols(rank),</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  dec().hCoeffs().head(rank)).transpose()</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  );</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span> </div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  dec().matrixQR()</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  .topLeftCorner(rank, rank)</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  .template triangularView<Upper>()</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  .solveInPlace(c.topRows(rank));</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  dst.topRows(rank) = c.topRows(rank);</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  dst.bottomRows(cols-rank).setZero();</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> };</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span> </div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span> </div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00344"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a5851b8e7d2a7f91592e7fa69f8b7684c"> 344</a></span> <a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR<MatrixType></a>& <a class="code" href="classEigen_1_1HouseholderQR.html#a5851b8e7d2a7f91592e7fa69f8b7684c">HouseholderQR<MatrixType>::compute</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> {</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  Index rows = matrix.rows();</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  Index cols = matrix.cols();</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  Index size = (std::min)(rows,cols);</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span> </div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  m_qr = matrix;</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  m_hCoeffs.resize(size);</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> </div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  m_temp.resize(cols);</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span> </div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  internal::householder_qr_inplace_blocked(m_qr, m_hCoeffs, 48, m_temp.data());</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span> }</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> </div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR<typename MatrixBase<Derived>::PlainObject</a>></div>
<div class="line"><a name="l00367"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#abafaafa2e7eb9f485b282041833034bf"> 367</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#abafaafa2e7eb9f485b282041833034bf">MatrixBase<Derived>::householderQr</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR<PlainObject></a>(eval());</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> }</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> </div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> </div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> <span class="preprocessor">#endif // EIGEN_QR_H</span></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_ab592f6a05d7ba94c0108382baa8c993e"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#ab592f6a05d7ba94c0108382baa8c993e">Eigen::HouseholderQR::HouseholderQR</a></div><div class="ttdeci">HouseholderQR(const MatrixType &matrix)</div><div class="ttdoc">Constructs a QR factorization from a given matrix. </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:94</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_a82a3f15f0cda1f4f874d50951344b5a9"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a82a3f15f0cda1f4f874d50951344b5a9">Eigen::HouseholderQR::logAbsDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar logAbsDeterminant() const </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:208</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_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_1HouseholderQR_html_a520fc76215d7722387a76e7b7a484ee0"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a520fc76215d7722387a76e7b7a484ee0">Eigen::HouseholderQR::householderQ</a></div><div class="ttdeci">HouseholderSequenceType householderQ() const </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:136</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_abafaafa2e7eb9f485b282041833034bf"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#abafaafa2e7eb9f485b282041833034bf">Eigen::MatrixBase::householderQr</a></div><div class="ttdeci">const HouseholderQR< PlainObject > householderQr() const </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:367</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_a3912046746c14d7b4e9dba999da46a68"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a3912046746c14d7b4e9dba999da46a68">Eigen::HouseholderQR::solve</a></div><div class="ttdeci">const internal::solve_retval< HouseholderQR, Rhs > solve(const MatrixBase< Rhs > &b) const </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:122</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_ab7e9b80266fe7d1592e4c9de652d9f50"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#ab7e9b80266fe7d1592e4c9de652d9f50">Eigen::HouseholderQR::HouseholderQR</a></div><div class="ttdeci">HouseholderQR()</div><div class="ttdoc">Default Constructor. </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:68</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_a2bb8fa5593d2f447c16ba2e3cfb9c432"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a2bb8fa5593d2f447c16ba2e3cfb9c432">Eigen::HouseholderQR::absDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar absDeterminant() const </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:199</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_a321e96844544eacde2272c3a487048e9"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a321e96844544eacde2272c3a487048e9">Eigen::HouseholderQR::hCoeffs</a></div><div class="ttdeci">const HCoeffsType & hCoeffs() const </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:189</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_a5851b8e7d2a7f91592e7fa69f8b7684c"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a5851b8e7d2a7f91592e7fa69f8b7684c">Eigen::HouseholderQR::compute</a></div><div class="ttdeci">HouseholderQR & compute(const MatrixType &matrix)</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:344</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html">Eigen::HouseholderQR</a></div><div class="ttdoc">Householder QR decomposition of a matrix. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:221</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_abf25ea0833fe1e846c20968103f69141"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#abf25ea0833fe1e846c20968103f69141">Eigen::HouseholderQR::HouseholderQR</a></div><div class="ttdeci">HouseholderQR(Index rows, Index cols)</div><div class="ttdoc">Default Constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:76</div></div>
<div class="ttc" id="classEigen_1_1PlainObjectBase_html_afbbb33d14fe7fb9683019a39ce1c659d"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#afbbb33d14fe7fb9683019a39ce1c659d">Eigen::PlainObjectBase::resize</a></div><div class="ttdeci">void resize(Index nbRows, Index nbCols)</div><div class="ttdef"><b>Definition:</b> PlainObjectBase.h:232</div></div>
<div class="ttc" id="classEigen_1_1HouseholderQR_html_a7b142db8924dd7fad99acbdd0ff4bdd1"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a7b142db8924dd7fad99acbdd0ff4bdd1">Eigen::HouseholderQR::matrixQR</a></div><div class="ttdeci">const MatrixType & matrixQR() const </div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:145</div></div>
<div class="ttc" id="classEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors. </div><div class="ttdef"><b>Definition:</b> Matrix.h:127</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>
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