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<div class="title">Tridiagonalization.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 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_TRIDIAGONALIZATION_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_TRIDIAGONALIZATION_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>TridiagonalizationMatrixTReturnType;</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<TridiagonalizationMatrixTReturnType<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> <span class="keyword">typename</span> MatrixType::PlainObject 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> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> CoeffVectorType></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keywordtype">void</span> tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs);</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> }</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html"> 61</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span><a class="code" href="classEigen_1_1Tridiagonalization.html">Tridiagonalization</a></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#aeb6c0eb89cc982629305f6c7e0791caf"> 66</a></span>  <span class="keyword">typedef</span> _MatrixType <a class="code" href="classEigen_1_1Tridiagonalization.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</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="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  Size = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  SizeMinusOne = Size == <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> : (Size > 1 ? Size - 1 : 1),</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  Options = MatrixType::Options,</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  MaxSize = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  MaxSizeMinusOne = MaxSize == <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? <a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> : (MaxSize > 1 ? MaxSize - 1 : 1)</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  };</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1></a> CoeffVectorType;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type<MatrixType, RealScalar>::type DiagonalType;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1></a> SubDiagonalType;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::remove_all<typename MatrixType::RealReturnType>::type MatrixTypeRealView;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keyword">typedef</span> internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> MatrixTReturnType;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::conditional<NumTraits<Scalar>::IsComplex,</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keyword">typename</span> internal::add_const_on_value_type<typename Diagonal<const MatrixType>::RealReturnType>::type,</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Diagonal.html">Diagonal<const MatrixType></a></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  >::type DiagonalReturnType;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::conditional<NumTraits<Scalar>::IsComplex,</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keyword">typename</span> internal::add_const_on_value_type<<span class="keyword">typename</span> <a class="code" href="classEigen_1_1Diagonal.html">Diagonal</a><</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <a class="code" href="classEigen_1_1Block.html">Block<const MatrixType,SizeMinusOne,SizeMinusOne></a> >::RealReturnType>::type,</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Diagonal.html">Diagonal</a><</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <a class="code" href="classEigen_1_1Block.html">Block<const MatrixType,SizeMinusOne,SizeMinusOne></a> ></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  >::type SubDiagonalReturnType;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00099"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#aa96bdbc1b19c647e3372c31301ea4999"> 99</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_1Tridiagonalization.html#aa96bdbc1b19c647e3372c31301ea4999">HouseholderSequenceType</a>;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#a0698ae78b0ab6f239c475b73b9c6bbee"> 113</a></span>  <a class="code" href="classEigen_1_1Tridiagonalization.html#a0698ae78b0ab6f239c475b73b9c6bbee">Tridiagonalization</a>(Index size = Size==<a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? 2 : Size)</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  : m_matrix(size,size),</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  m_hCoeffs(size > 1 ? size-1 : 1),</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>  {}</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a name="l00129"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#aa9f9722d2cef9425e2c0da3553dfbac7"> 129</a></span>  <a class="code" href="classEigen_1_1Tridiagonalization.html#aa9f9722d2cef9425e2c0da3553dfbac7">Tridiagonalization</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1Tridiagonalization.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& matrix)</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  : m_matrix(matrix),</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1),</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  m_isInitialized(false)</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  {</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  }</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> </div>
<div class="line"><a name="l00155"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#aa69e607a4aab4fb6321ca6acbf074fc2"> 155</a></span>  <a class="code" href="classEigen_1_1Tridiagonalization.html">Tridiagonalization</a>& <a class="code" href="classEigen_1_1Tridiagonalization.html#aa69e607a4aab4fb6321ca6acbf074fc2">compute</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1Tridiagonalization.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& matrix)</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  {</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  m_matrix = matrix;</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>  internal::tridiagonalization_inplace(m_matrix, m_hCoeffs);</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="l00180"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#a2ab889c75460c178d941ee24e371b206"> 180</a></span>  <span class="keyword">inline</span> <a class="code" href="classEigen_1_1Matrix.html">CoeffVectorType</a> <a class="code" href="classEigen_1_1Tridiagonalization.html#a2ab889c75460c178d941ee24e371b206">householderCoefficients</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"Tridiagonalization is not initialized."</span>);</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keywordflow">return</span> m_hCoeffs;</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  }</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> </div>
<div class="line"><a name="l00217"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#a66adece364b64b26b3771662de70f2df"> 217</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Tridiagonalization.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& <a class="code" href="classEigen_1_1Tridiagonalization.html#a66adece364b64b26b3771662de70f2df">packedMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"Tridiagonalization is not initialized."</span>);</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordflow">return</span> m_matrix;</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  }</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> </div>
<div class="line"><a name="l00238"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#ad13845d7490115664924b3dc208ec369"> 238</a></span>  <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a> <a class="code" href="classEigen_1_1Tridiagonalization.html#ad13845d7490115664924b3dc208ec369">matrixQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"Tridiagonalization is not initialized."</span>);</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Tridiagonalization.html#aa96bdbc1b19c647e3372c31301ea4999">HouseholderSequenceType</a>(m_matrix, m_hCoeffs.conjugate())</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  .setLength(m_matrix.rows() - 1)</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  .setShift(1);</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  }</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span> </div>
<div class="line"><a name="l00263"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#aceb0f16a166f4c236a1b536b7424d292"> 263</a></span>  MatrixTReturnType <a class="code" href="classEigen_1_1Tridiagonalization.html#aceb0f16a166f4c236a1b536b7424d292">matrixT</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">"Tridiagonalization is not initialized."</span>);</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">return</span> MatrixTReturnType(m_matrix.real());</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="l00282"></a><span class="lineno"> 282</span>  DiagonalReturnType <a class="code" href="classEigen_1_1Tridiagonalization.html#ac109eefddd733d8e82841da5bb2dd8d3">diagonal</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  SubDiagonalReturnType <a class="code" href="classEigen_1_1Tridiagonalization.html#a8fa49216273ab7579b7bea06debb1e51">subDiagonal</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> </div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> </div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <a class="code" href="classEigen_1_1Tridiagonalization.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a> m_matrix;</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  CoeffVectorType m_hCoeffs;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordtype">bool</span> m_isInitialized;</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> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="keyword">typename</span> Tridiagonalization<MatrixType>::DiagonalReturnType</div>
<div class="line"><a name="l00305"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#ac109eefddd733d8e82841da5bb2dd8d3"> 305</a></span> <a class="code" href="classEigen_1_1Tridiagonalization.html#ac109eefddd733d8e82841da5bb2dd8d3">Tridiagonalization<MatrixType>::diagonal</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"Tridiagonalization is not initialized."</span>);</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordflow">return</span> m_matrix.diagonal();</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> </div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="keyword">typename</span> Tridiagonalization<MatrixType>::SubDiagonalReturnType</div>
<div class="line"><a name="l00313"></a><span class="lineno"><a class="line" href="classEigen_1_1Tridiagonalization.html#a8fa49216273ab7579b7bea06debb1e51"> 313</a></span> <a class="code" href="classEigen_1_1Tridiagonalization.html#a8fa49216273ab7579b7bea06debb1e51">Tridiagonalization<MatrixType>::subDiagonal</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"Tridiagonalization is not initialized."</span>);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  Index n = m_matrix.rows();</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1Block.html">Block<const MatrixType,SizeMinusOne,SizeMinusOne></a>(m_matrix, 1, 0, n-1,n-1).diagonal();</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="l00345"></a><span class="lineno"> 345</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> CoeffVectorType></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="keywordtype">void</span> tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> {</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="keyword">using</span> numext::conj;</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  Index n = matA.rows();</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  eigen_assert(n==matA.cols());</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  eigen_assert(n==hCoeffs.size()+1 || n==1);</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  </div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keywordflow">for</span> (Index i = 0; i<n-1; ++i)</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  {</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  Index remainingSize = n-i-1;</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  RealScalar beta;</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  Scalar h;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> </div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="comment">// Apply similarity transformation to remaining columns,</span></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="comment">// i.e., A = H A H' where H = I - h v v' and v = matA.col(i).tail(n-i-1)</span></div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  matA.col(i).coeffRef(i+1) = 1;</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>  hCoeffs.tail(n-i-1).noalias() = (matA.bottomRightCorner(remainingSize,remainingSize).template selfadjointView<Lower>()</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  * (conj(h) * matA.col(i).tail(remainingSize)));</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  hCoeffs.tail(n-i-1) += (conj(h)*Scalar(-0.5)*(hCoeffs.tail(remainingSize).dot(matA.col(i).tail(remainingSize)))) * matA.col(i).tail(n-i-1);</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>  matA.bottomRightCorner(remainingSize, remainingSize).template selfadjointView<Lower>()</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  .rankUpdate(matA.col(i).tail(remainingSize), hCoeffs.tail(remainingSize), -1);</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> </div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  matA.col(i).coeffRef(i+1) = beta;</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  hCoeffs.coeffRef(i) = h;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  }</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> }</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> </div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="comment">// forward declaration, implementation at the end of this file</span></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType,</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordtype">int</span> Size=MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keywordtype">bool</span> IsComplex=NumTraits<typename MatrixType::Scalar>::IsComplex></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="keyword">struct </span>tridiagonalization_inplace_selector;</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> </div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> DiagonalType, <span class="keyword">typename</span> SubDiagonalType></div>
<div class="line"><a name="l00427"></a><span class="lineno"><a class="line" href="namespaceEigen_1_1internal.html#aa53570cf2e676b41631f08397658ca0f"> 427</a></span> <span class="keywordtype">void</span> tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, <span class="keywordtype">bool</span> extractQ)</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>  eigen_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1);</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ);</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> </div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Size, <span class="keywordtype">bool</span> IsComplex></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="keyword">struct </span>tridiagonalization_inplace_selector</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span> {</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">Tridiagonalization<MatrixType>::CoeffVectorType</a> CoeffVectorType;</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">Tridiagonalization<MatrixType>::HouseholderSequenceType</a> HouseholderSequenceType;</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keyword">template</span><<span class="keyword">typename</span> DiagonalType, <span class="keyword">typename</span> SubDiagonalType></div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, <span class="keywordtype">bool</span> extractQ)</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  {</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  CoeffVectorType hCoeffs(mat.cols()-1);</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  tridiagonalization_inplace(mat,hCoeffs);</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  diag = mat.diagonal().real();</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  subdiag = mat.template diagonal<-1>().real();</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">if</span>(extractQ)</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  mat = HouseholderSequenceType(mat, hCoeffs.conjugate())</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  .setLength(mat.rows() - 1)</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  .setShift(1);</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  }</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span> };</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span> </div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span> <span class="keyword">struct </span>tridiagonalization_inplace_selector<MatrixType,3,false></div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span> {</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span> </div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <span class="keyword">template</span><<span class="keyword">typename</span> DiagonalType, <span class="keyword">typename</span> SubDiagonalType></div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, <span class="keywordtype">bool</span> extractQ)</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  {</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  diag[0] = mat(0,0);</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  RealScalar v1norm2 = numext::abs2(mat(2,0));</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="keywordflow">if</span>(v1norm2 == RealScalar(0))</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  {</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  diag[1] = mat(1,1);</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  diag[2] = mat(2,2);</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  subdiag[0] = mat(1,0);</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  subdiag[1] = mat(2,1);</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  <span class="keywordflow">if</span> (extractQ)</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  mat.setIdentity();</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  }</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  {</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  RealScalar invBeta = RealScalar(1)/beta;</div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  Scalar m01 = mat(1,0) * invBeta;</div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  Scalar m02 = mat(2,0) * invBeta;</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  Scalar q = RealScalar(2)*m01*mat(2,1) + m02*(mat(2,2) - mat(1,1));</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  diag[1] = mat(1,1) + m02*q;</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  diag[2] = mat(2,2) - m02*q;</div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  subdiag[0] = beta;</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  subdiag[1] = mat(2,1) - m01 * q;</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  <span class="keywordflow">if</span> (extractQ)</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  {</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  mat << 1, 0, 0,</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  0, m01, m02,</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  0, m02, -m01;</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>  }</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  }</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> };</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> </div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">bool</span> IsComplex></div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span> <span class="keyword">struct </span>tridiagonalization_inplace_selector<MatrixType,1,IsComplex></div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span> {</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</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>  <span class="keyword">template</span><<span class="keyword">typename</span> DiagonalType, <span class="keyword">typename</span> SubDiagonalType></div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, <span class="keywordtype">bool</span> extractQ)</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>  diag(0,0) = numext::real(mat(0,0));</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordflow">if</span>(extractQ)</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  mat(0,0) = Scalar(1);</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  }</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span> };</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> </div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType> <span class="keyword">struct </span>TridiagonalizationMatrixTReturnType</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span> : <span class="keyword">public</span> ReturnByValue<TridiagonalizationMatrixTReturnType<MatrixType> ></div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span> {</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  TridiagonalizationMatrixTReturnType(<span class="keyword">const</span> MatrixType& mat) : m_matrix(mat) { }</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">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</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="l00539"></a><span class="lineno"> 539</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  result.setZero();</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  result.template diagonal<1>() = m_matrix.template diagonal<-1>().conjugate();</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  result.diagonal() = m_matrix.diagonal();</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  result.template diagonal<-1>() = m_matrix.template diagonal<-1>();</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> </div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_matrix.rows(); }</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_matrix.cols(); }</div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span> </div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keyword">typename</span> MatrixType::Nested m_matrix;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span> };</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span> </div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span> } <span class="comment">// end namespace internal</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 Eigen</span></div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span> </div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span> <span class="preprocessor">#endif // EIGEN_TRIDIAGONALIZATION_H</span></div>
<div class="ttc" id="classEigen_1_1Tridiagonalization_html_a8fa49216273ab7579b7bea06debb1e51"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#a8fa49216273ab7579b7bea06debb1e51">Eigen::Tridiagonalization::subDiagonal</a></div><div class="ttdeci">SubDiagonalReturnType subDiagonal() const </div><div class="ttdoc">Returns the subdiagonal of the tridiagonal matrix T in the decomposition. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:313</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_1Tridiagonalization_html"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html">Eigen::Tridiagonalization</a></div><div class="ttdoc">Tridiagonal decomposition of a selfadjoint matrix. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:61</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_1Tridiagonalization_html_aa96bdbc1b19c647e3372c31301ea4999"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#aa96bdbc1b19c647e3372c31301ea4999">Eigen::Tridiagonalization::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> Tridiagonalization.h:99</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_1Tridiagonalization_html_aa9f9722d2cef9425e2c0da3553dfbac7"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#aa9f9722d2cef9425e2c0da3553dfbac7">Eigen::Tridiagonalization::Tridiagonalization</a></div><div class="ttdeci">Tridiagonalization(const MatrixType &matrix)</div><div class="ttdoc">Constructor; computes tridiagonal decomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:129</div></div>
<div class="ttc" id="classEigen_1_1Tridiagonalization_html_aceb0f16a166f4c236a1b536b7424d292"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#aceb0f16a166f4c236a1b536b7424d292">Eigen::Tridiagonalization::matrixT</a></div><div class="ttdeci">MatrixTReturnType matrixT() const </div><div class="ttdoc">Returns an expression of the tridiagonal matrix T in the decomposition. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:263</div></div>
<div class="ttc" id="classEigen_1_1Tridiagonalization_html_aa69e607a4aab4fb6321ca6acbf074fc2"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#aa69e607a4aab4fb6321ca6acbf074fc2">Eigen::Tridiagonalization::compute</a></div><div class="ttdeci">Tridiagonalization & compute(const MatrixType &matrix)</div><div class="ttdoc">Computes tridiagonal decomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:155</div></div>
<div class="ttc" id="classEigen_1_1Tridiagonalization_html_a0698ae78b0ab6f239c475b73b9c6bbee"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#a0698ae78b0ab6f239c475b73b9c6bbee">Eigen::Tridiagonalization::Tridiagonalization</a></div><div class="ttdeci">Tridiagonalization(Index size=Size==Dynamic?2:Size)</div><div class="ttdoc">Default constructor. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:113</div></div>
<div class="ttc" id="classEigen_1_1Tridiagonalization_html_a66adece364b64b26b3771662de70f2df"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#a66adece364b64b26b3771662de70f2df">Eigen::Tridiagonalization::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> Tridiagonalization.h:217</div></div>
<div class="ttc" id="classEigen_1_1Block_html"><div class="ttname"><a href="classEigen_1_1Block.html">Eigen::Block</a></div><div class="ttdoc">Expression of a fixed-size or dynamic-size block. </div><div class="ttdef"><b>Definition:</b> Block.h:102</div></div>
<div class="ttc" id="classEigen_1_1Tridiagonalization_html_a2ab889c75460c178d941ee24e371b206"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#a2ab889c75460c178d941ee24e371b206">Eigen::Tridiagonalization::householderCoefficients</a></div><div class="ttdeci">CoeffVectorType householderCoefficients() const </div><div class="ttdoc">Returns the Householder coefficients. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:180</div></div>
<div class="ttc" id="classEigen_1_1Tridiagonalization_html_ad13845d7490115664924b3dc208ec369"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#ad13845d7490115664924b3dc208ec369">Eigen::Tridiagonalization::matrixQ</a></div><div class="ttdeci">HouseholderSequenceType matrixQ() const </div><div class="ttdoc">Returns the unitary matrix Q in the decomposition. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:238</div></div>
<div class="ttc" id="classEigen_1_1Diagonal_html"><div class="ttname"><a href="classEigen_1_1Diagonal.html">Eigen::Diagonal</a></div><div class="ttdoc">Expression of a diagonal/subdiagonal/superdiagonal in a matrix. </div><div class="ttdef"><b>Definition:</b> Diagonal.h:64</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_1Tridiagonalization_html_ac109eefddd733d8e82841da5bb2dd8d3"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#ac109eefddd733d8e82841da5bb2dd8d3">Eigen::Tridiagonalization::diagonal</a></div><div class="ttdeci">DiagonalReturnType diagonal() const </div><div class="ttdoc">Returns the diagonal of the tridiagonal matrix T in the decomposition. </div><div class="ttdef"><b>Definition:</b> Tridiagonalization.h:305</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_1Tridiagonalization_html_aeb6c0eb89cc982629305f6c7e0791caf"><div class="ttname"><a href="classEigen_1_1Tridiagonalization.html#aeb6c0eb89cc982629305f6c7e0791caf">Eigen::Tridiagonalization::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> Tridiagonalization.h:66</div></div>
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