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<div class="title">HessenbergDecomposition.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#ifndef EIGEN_HESSENBERGDECOMPOSITION_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_HESSENBERGDECOMPOSITION_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType> <span class="keyword">struct </span>HessenbergDecompositionMatrixHReturnType;</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">struct </span>traits<HessenbergDecompositionMatrixHReturnType<MatrixType> ></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> {</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keyword">typedef</span> MatrixType ReturnType;</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> };</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> }</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html"> 57</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span><a class="code" href="classEigen_1_1HessenbergDecomposition.html">HessenbergDecomposition</a></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#aeb6c0eb89cc982629305f6c7e0791caf"> 62</a></span>  <span class="keyword">typedef</span> _MatrixType <a class="code" href="classEigen_1_1HessenbergDecomposition.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>;</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">enum</span> {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  Size = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  SizeMinusOne = Size == <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> : Size - 1,</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  Options = MatrixType::Options,</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  MaxSize = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  MaxSizeMinusOne = MaxSize == <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> : MaxSize - 1</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  };</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a name="l00073"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a3f6fc00047c205ee590f676934aab28f"> 73</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a>;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a1ed77f58452b7e53d18f2532e1763b29"> 82</a></span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1></a> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a1ed77f58452b7e53d18f2532e1763b29">CoeffVectorType</a>;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a name="l00085"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#aa96bdbc1b19c647e3372c31301ea4999"> 85</a></span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type</a>> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#aa96bdbc1b19c647e3372c31301ea4999">HouseholderSequenceType</a>;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">typedef</span> internal::HessenbergDecompositionMatrixHReturnType<MatrixType> MatrixHReturnType;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div>
<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a6a2313f1b3b5438f3ef622c5a6763390"> 100</a></span>  <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a6a2313f1b3b5438f3ef622c5a6763390">HessenbergDecomposition</a>(Index size = Size==<a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? 2 : Size)</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  : m_matrix(size,size),</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  m_temp(size),</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  m_isInitialized(false)</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  {</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">if</span>(size>1)</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  m_hCoeffs.<a class="code" href="classEigen_1_1PlainObjectBase.html#afbbb33d14fe7fb9683019a39ce1c659d">resize</a>(size-1);</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  }</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> </div>
<div class="line"><a name="l00118"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a5f1aa26a2c7a68fedb5f201912df9128"> 118</a></span>  <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a5f1aa26a2c7a68fedb5f201912df9128">HessenbergDecomposition</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& matrix)</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  : m_matrix(matrix),</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  m_temp(matrix.rows()),</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  m_isInitialized(false)</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  {</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">if</span>(matrix.rows()<2)</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  {</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  }</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  m_hCoeffs.<a class="code" href="classEigen_1_1PlainObjectBase.html#afbbb33d14fe7fb9683019a39ce1c659d">resize</a>(matrix.rows()-1,1);</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  _compute(m_matrix, m_hCoeffs, m_temp);</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  }</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> </div>
<div class="line"><a name="l00150"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a6e877604e408f4ca174fb489a329c03e"> 150</a></span>  <a class="code" href="classEigen_1_1HessenbergDecomposition.html">HessenbergDecomposition</a>& <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a6e877604e408f4ca174fb489a329c03e">compute</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& matrix)</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>  m_matrix = matrix;</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keywordflow">if</span>(matrix.rows()<2)</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  {</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  }</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  m_hCoeffs.<a class="code" href="classEigen_1_1PlainObjectBase.html#afbbb33d14fe7fb9683019a39ce1c659d">resize</a>(matrix.rows()-1,1);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  _compute(m_matrix, m_hCoeffs, m_temp);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  }</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> </div>
<div class="line"><a name="l00177"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a31170fe84e15e60baf72142b2b585fa9"> 177</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">CoeffVectorType</a>& <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a31170fe84e15e60baf72142b2b585fa9">householderCoefficients</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HessenbergDecomposition is not initialized."</span>);</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordflow">return</span> m_hCoeffs;</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> </div>
<div class="line"><a name="l00212"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a66adece364b64b26b3771662de70f2df"> 212</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a66adece364b64b26b3771662de70f2df">packedMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HessenbergDecomposition is not initialized."</span>);</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">return</span> m_matrix;</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  }</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> </div>
<div class="line"><a name="l00232"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#ad13845d7490115664924b3dc208ec369"> 232</a></span>  <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#ad13845d7490115664924b3dc208ec369">matrixQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HessenbergDecomposition is not initialized."</span>);</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#aa96bdbc1b19c647e3372c31301ea4999">HouseholderSequenceType</a>(m_matrix, m_hCoeffs.conjugate())</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  .setLength(m_matrix.rows() - 1)</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  .setShift(1);</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  }</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span> </div>
<div class="line"><a name="l00260"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#aea9518787b9570535e44a3f4ac7a66ff"> 260</a></span>  MatrixHReturnType <a class="code" href="classEigen_1_1HessenbergDecomposition.html#aea9518787b9570535e44a3f4ac7a66ff">matrixH</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"HessenbergDecomposition is not initialized."</span>);</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">return</span> MatrixHReturnType(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  }</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keyword">private</span>:</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>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize></a> VectorType;</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::Real</a> RealScalar;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> _compute(<a class="code" href="classEigen_1_1HessenbergDecomposition.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& matA, <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a1ed77f58452b7e53d18f2532e1763b29">CoeffVectorType</a>& hCoeffs, VectorType& temp);</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <a class="code" href="classEigen_1_1HessenbergDecomposition.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a> m_matrix;</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a1ed77f58452b7e53d18f2532e1763b29">CoeffVectorType</a> m_hCoeffs;</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  VectorType m_temp;</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span> };</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span> </div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="keywordtype">void</span> HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVectorType& hCoeffs, VectorType& temp)</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>  eigen_assert(matA.rows()==matA.cols());</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  Index n = matA.rows();</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  temp.resize(n);</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">for</span> (Index i = 0; i<n-1; ++i)</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>  <span class="comment">// let's consider the vector v = i-th column starting at position i+1</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  Index remainingSize = n-i-1;</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  RealScalar beta;</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  Scalar h;</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  matA.col(i).coeffRef(i+1) = beta;</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  hCoeffs.coeffRef(i) = h;</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> </div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="comment">// Apply similarity transformation to remaining columns,</span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="comment">// i.e., compute A = H A H'</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> </div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">// A = H A</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  matA.bottomRightCorner(remainingSize, remainingSize)</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  .applyHouseholderOnTheLeft(matA.col(i).tail(remainingSize-1), h, &temp.coeffRef(0));</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span> </div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="comment">// A = A H'</span></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  matA.rightCols(remainingSize)</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), numext::conj(h), &temp.coeffRef(0));</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  }</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span> }</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> </div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType> <span class="keyword">struct </span>HessenbergDecompositionMatrixHReturnType</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> : <span class="keyword">public</span> ReturnByValue<HessenbergDecompositionMatrixHReturnType<MatrixType> ></div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> {</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  HessenbergDecompositionMatrixHReturnType(<span class="keyword">const</span> HessenbergDecomposition<MatrixType>& hess) : m_hess(hess) { }</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> </div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> evalTo(ResultType& result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  result = m_hess.packedMatrix();</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  Index n = result.rows();</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keywordflow">if</span> (n>2)</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  result.bottomLeftCorner(n-2, n-2).template triangularView<Lower>().setZero();</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  }</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hess.packedMatrix().rows(); }</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hess.packedMatrix().cols(); }</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> </div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keyword">const</span> HessenbergDecomposition<MatrixType>& m_hess;</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> };</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> </div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> } <span class="comment">// end namespace internal</span></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> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> </div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> <span class="preprocessor">#endif // EIGEN_HESSENBERGDECOMPOSITION_H</span></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_a1ed77f58452b7e53d18f2532e1763b29"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a1ed77f58452b7e53d18f2532e1763b29">Eigen::HessenbergDecomposition::CoeffVectorType</a></div><div class="ttdeci">Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > CoeffVectorType</div><div class="ttdoc">Type for vector of Householder coefficients. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:82</div></div>
<div class="ttc" id="structEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...</div><div class="ttdef"><b>Definition:</b> NumTraits.h:88</div></div>
<div class="ttc" id="namespaceEigen_html_adc9da5be31bdce40c25a92c27999c0e3"><div class="ttname"><a href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:21</div></div>
<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_1HessenbergDecomposition_html_aeb6c0eb89cc982629305f6c7e0791caf"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#aeb6c0eb89cc982629305f6c7e0791caf">Eigen::HessenbergDecomposition::MatrixType</a></div><div class="ttdeci">_MatrixType MatrixType</div><div class="ttdoc">Synonym for the template parameter _MatrixType. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:62</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_aea9518787b9570535e44a3f4ac7a66ff"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#aea9518787b9570535e44a3f4ac7a66ff">Eigen::HessenbergDecomposition::matrixH</a></div><div class="ttdeci">MatrixHReturnType matrixH() const </div><div class="ttdoc">Constructs the Hessenberg matrix H in the decomposition. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:260</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_a5f1aa26a2c7a68fedb5f201912df9128"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a5f1aa26a2c7a68fedb5f201912df9128">Eigen::HessenbergDecomposition::HessenbergDecomposition</a></div><div class="ttdeci">HessenbergDecomposition(const MatrixType &matrix)</div><div class="ttdoc">Constructor; computes Hessenberg decomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:118</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_a3f6fc00047c205ee590f676934aab28f"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a3f6fc00047c205ee590f676934aab28f">Eigen::HessenbergDecomposition::Scalar</a></div><div class="ttdeci">MatrixType::Scalar Scalar</div><div class="ttdoc">Scalar type for matrices of type MatrixType. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:73</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_ad13845d7490115664924b3dc208ec369"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#ad13845d7490115664924b3dc208ec369">Eigen::HessenbergDecomposition::matrixQ</a></div><div class="ttdeci">HouseholderSequenceType matrixQ() const </div><div class="ttdoc">Reconstructs the orthogonal matrix Q in the decomposition. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:232</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_aa96bdbc1b19c647e3372c31301ea4999"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#aa96bdbc1b19c647e3372c31301ea4999">Eigen::HessenbergDecomposition::HouseholderSequenceType</a></div><div class="ttdeci">HouseholderSequence< MatrixType, typename internal::remove_all< typename CoeffVectorType::ConjugateReturnType >::type > HouseholderSequenceType</div><div class="ttdoc">Return type of matrixQ() </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:85</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_a6a2313f1b3b5438f3ef622c5a6763390"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a6a2313f1b3b5438f3ef622c5a6763390">Eigen::HessenbergDecomposition::HessenbergDecomposition</a></div><div class="ttdeci">HessenbergDecomposition(Index size=Size==Dynamic?2:Size)</div><div class="ttdoc">Default constructor; the decomposition will be computed later. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:100</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_a66adece364b64b26b3771662de70f2df"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a66adece364b64b26b3771662de70f2df">Eigen::HessenbergDecomposition::packedMatrix</a></div><div class="ttdeci">const MatrixType & packedMatrix() const </div><div class="ttdoc">Returns the internal representation of the decomposition. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:212</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html">Eigen::HessenbergDecomposition</a></div><div class="ttdoc">Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:57</div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_a31170fe84e15e60baf72142b2b585fa9"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a31170fe84e15e60baf72142b2b585fa9">Eigen::HessenbergDecomposition::householderCoefficients</a></div><div class="ttdeci">const CoeffVectorType & householderCoefficients() const </div><div class="ttdoc">Returns the Householder coefficients. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:177</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_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 ></a></div></div>
<div class="ttc" id="classEigen_1_1HessenbergDecomposition_html_a6e877604e408f4ca174fb489a329c03e"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a6e877604e408f4ca174fb489a329c03e">Eigen::HessenbergDecomposition::compute</a></div><div class="ttdeci">HessenbergDecomposition & compute(const MatrixType &matrix)</div><div class="ttdoc">Computes Hessenberg decomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:150</div></div>
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