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<div class="title">GeneralizedEigenSolver.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) 2012 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) 2010,2012 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_GENERALIZEDEIGENSOLVER_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_GENERALIZEDEIGENSOLVER_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="preprocessor">#include "./RealQZ.h"</span></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>Eigen { </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.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_1GeneralizedEigenSolver.html">GeneralizedEigenSolver</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_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf"> 62</a></span>  <span class="keyword">typedef</span> _MatrixType <a class="code" href="classEigen_1_1GeneralizedEigenSolver.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>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</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>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</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_1GeneralizedEigenSolver.html#a3f6fc00047c205ee590f676934aab28f"> 73</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar <a class="code" href="classEigen_1_1GeneralizedEigenSolver.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> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<Scalar>::Real</a> RealScalar;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#a1b9bc0a45616064df3a6168395e3cfcc"> 83</a></span>  <span class="keyword">typedef</span> std::complex<RealScalar> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#ae88654b9613217486067f07e394c88dc"> 90</a></span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1></a> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#ae88654b9613217486067f07e394c88dc">VectorType</a>;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a name="l00097"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#a12de5e55557c63e5efaa70c3d4e82060"> 97</a></span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<ComplexScalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1></a> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a12de5e55557c63e5efaa70c3d4e82060">ComplexVectorType</a>;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#a14f2d5bf9df5a70ea27bc1239aa30822"> 101</a></span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1CwiseBinaryOp.html">CwiseBinaryOp<internal::scalar_quotient_op<ComplexScalar,Scalar></a>,<a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a12de5e55557c63e5efaa70c3d4e82060">ComplexVectorType</a>,<a class="code" href="classEigen_1_1Matrix.html">VectorType</a>> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a14f2d5bf9df5a70ea27bc1239aa30822">EigenvalueType</a>;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#a50d070013a795db5621119f2b4a3d781"> 108</a></span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime></a> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a50d070013a795db5621119f2b4a3d781">EigenvectorsType</a>;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a name="l00117"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#a7289bdfc65bb36b51babcab21a1a9c14"> 117</a></span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a7289bdfc65bb36b51babcab21a1a9c14">GeneralizedEigenSolver</a>() : m_eivec(), m_alphas(), m_betas(), m_isInitialized(false), m_realQZ(), m_matS(), m_tmp() {}</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#ad454c37be646409992625586d2b21adb"> 125</a></span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#ad454c37be646409992625586d2b21adb">GeneralizedEigenSolver</a>(Index size)</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  : m_eivec(size, size),</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  m_alphas(size),</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  m_betas(size),</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  m_eigenvectorsOk(false),</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  m_realQZ(size),</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  m_matS(size, size),</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  m_tmp(size)</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  {}</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> </div>
<div class="line"><a name="l00148"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#aa0f561be93f959404ee232321b389468"> 148</a></span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aa0f561be93f959404ee232321b389468">GeneralizedEigenSolver</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& A, <span class="keyword">const</span> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& B, <span class="keywordtype">bool</span> computeEigenvectors = <span class="keyword">true</span>)</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  : m_eivec(A.rows(), A.cols()),</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  m_alphas(A.cols()),</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  m_betas(A.cols()),</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  m_eigenvectorsOk(false),</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  m_realQZ(A.cols()),</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  m_matS(A.rows(), A.cols()),</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  m_tmp(A.cols())</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>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a64e32bd0f28bb7b6e91775c3ac592e12">compute</a>(A, B, computeEigenvectors);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  }</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="comment">/* \brief Returns the computed generalized eigenvectors.</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment"> * \returns %Matrix whose columns are the (possibly complex) eigenvectors.</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment"> * \pre Either the constructor </span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment"> * GeneralizedEigenSolver(const MatrixType&,const MatrixType&, bool) or the member function</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment"> * compute(const MatrixType&, const MatrixType& bool) has been called before, and</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"> * \p computeEigenvectors was set to true (the default).</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment"> * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment"> * to eigenvalue number \f$ k \f$ as returned by eigenvalues(). The</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment"> * eigenvectors are normalized to have (Euclidean) norm equal to one. The</span></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"> * matrix returned by this function is the matrix \f$ V \f$ in the</span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment"> * generalized eigendecomposition \f$ A = B V D V^{-1} \f$, if it exists.</span></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment"> * \sa eigenvalues()</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// EigenvectorsType eigenvectors() const;</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a name="l00198"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#acffd08bee548eaa5c10414343a93529f"> 198</a></span>  <a class="code" href="classEigen_1_1CwiseBinaryOp.html">EigenvalueType</a> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#acffd08bee548eaa5c10414343a93529f">eigenvalues</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"GeneralizedEigenSolver is not initialized."</span>);</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a14f2d5bf9df5a70ea27bc1239aa30822">EigenvalueType</a>(m_alphas,m_betas);</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  }</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> </div>
<div class="line"><a name="l00209"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#ade79c282ebff0a23829fd9b9b18fe1c0"> 209</a></span>  <a class="code" href="classEigen_1_1Matrix.html">ComplexVectorType</a> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#ade79c282ebff0a23829fd9b9b18fe1c0">alphas</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"GeneralizedEigenSolver is not initialized."</span>);</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keywordflow">return</span> m_alphas;</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="l00220"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#a92c089793f883fd38cd2df4d7c6513e5"> 220</a></span>  <a class="code" href="classEigen_1_1Matrix.html">VectorType</a> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a92c089793f883fd38cd2df4d7c6513e5">betas</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"GeneralizedEigenSolver is not initialized."</span>);</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">return</span> m_betas;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  }</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> </div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html">GeneralizedEigenSolver</a>& <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a64e32bd0f28bb7b6e91775c3ac592e12">compute</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& A, <span class="keyword">const</span> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& B, <span class="keywordtype">bool</span> computeEigenvectors = <span class="keyword">true</span>);</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>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> info()<span class="keyword"> const</span></div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"EigenSolver is not initialized."</span>);</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">return</span> m_realQZ.<a class="code" href="classEigen_1_1RealQZ.html#a0c06d5c2034ebb329c54235369643ad2">info</a>();</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  }</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a name="l00259"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#af6db2eac907628bd50de67a4ede88a5a"> 259</a></span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html">GeneralizedEigenSolver</a>& <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#af6db2eac907628bd50de67a4ede88a5a">setMaxIterations</a>(Index maxIters)</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  {</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  m_realQZ.<a class="code" href="classEigen_1_1RealQZ.html#a1b369841b0e39a1ac80a6c32b721d242">setMaxIterations</a>(maxIters);</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  }</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> </div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a> m_eivec;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a12de5e55557c63e5efaa70c3d4e82060">ComplexVectorType</a> m_alphas;</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#ae88654b9613217486067f07e394c88dc">VectorType</a> m_betas;</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="keywordtype">bool</span> m_eigenvectorsOk;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <a class="code" href="classEigen_1_1RealQZ.html">RealQZ<MatrixType></a> m_realQZ;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a> m_matS;</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>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1></a> ColumnVectorType;</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  ColumnVectorType m_tmp;</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> </div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="comment">//template<typename MatrixType></span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="comment">//typename GeneralizedEigenSolver<MatrixType>::EigenvectorsType GeneralizedEigenSolver<MatrixType>::eigenvectors() const</span></div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="comment">//{</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment">// eigen_assert(m_isInitialized && "EigenSolver is not initialized.");</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment">// eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");</span></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment">// Index n = m_eivec.cols();</span></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="comment">// EigenvectorsType matV(n,n);</span></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> <span class="comment">// // TODO</span></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment">// return matV;</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment">//}</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span> </div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> GeneralizedEigenSolver<MatrixType>&</div>
<div class="line"><a name="l00291"></a><span class="lineno"><a class="line" href="classEigen_1_1GeneralizedEigenSolver.html#a64e32bd0f28bb7b6e91775c3ac592e12"> 291</a></span> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a64e32bd0f28bb7b6e91775c3ac592e12">GeneralizedEigenSolver<MatrixType>::compute</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& A, <span class="keyword">const</span> <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& B, <span class="keywordtype">bool</span> computeEigenvectors)</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> {</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  eigen_assert(A.cols() == A.rows() && B.cols() == A.rows() && B.cols() == B.rows());</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="comment">// Reduce to generalized real Schur form:</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">// A = Q S Z and B = Q T Z</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  m_realQZ.compute(A, B, computeEigenvectors);</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> </div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">if</span> (m_realQZ.info() == <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>)</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>  m_matS = m_realQZ.matrixS();</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">if</span> (computeEigenvectors)</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  m_eivec = m_realQZ.matrixZ().transpose();</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">// Compute eigenvalues from matS</span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  m_alphas.resize(A.cols());</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  m_betas.resize(A.cols());</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  Index i = 0;</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="keywordflow">while</span> (i < A.cols())</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  {</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordflow">if</span> (i == A.cols() - 1 || m_matS.coeff(i+1, i) == <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a>(0))</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  {</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  m_alphas.coeffRef(i) = m_matS.coeff(i, i);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  m_betas.coeffRef(i) = m_realQZ.matrixT().coeff(i,i);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  ++i;</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="keywordflow">else</span></div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  {</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a> p = <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a>(0.5) * (m_matS.coeff(i, i) - m_matS.coeff(i+1, i+1));</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a> z = sqrt(abs(p * p + m_matS.coeff(i+1, i) * m_matS.coeff(i, i+1)));</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  m_alphas.coeffRef(i) = <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>(m_matS.coeff(i+1, i+1) + p, z);</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  m_alphas.coeffRef(i+1) = <a class="code" href="classEigen_1_1GeneralizedEigenSolver.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>(m_matS.coeff(i+1, i+1) + p, -z);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span> </div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  m_betas.coeffRef(i) = m_realQZ.matrixT().coeff(i,i);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  m_betas.coeffRef(i+1) = m_realQZ.matrixT().coeff(i,i);</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  i += 2;</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>  }</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  }</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span> </div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  m_eigenvectorsOk = <span class="keyword">false</span>;<span class="comment">//computeEigenvectors;</span></div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> }</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span> </div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="preprocessor">#endif // EIGEN_GENERALIZEDEIGENSOLVER_H</span></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_ad454c37be646409992625586d2b21adb"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#ad454c37be646409992625586d2b21adb">Eigen::GeneralizedEigenSolver::GeneralizedEigenSolver</a></div><div class="ttdeci">GeneralizedEigenSolver(Index size)</div><div class="ttdoc">Default constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:125</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_1GeneralizedEigenSolver_html_a7289bdfc65bb36b51babcab21a1a9c14"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#a7289bdfc65bb36b51babcab21a1a9c14">Eigen::GeneralizedEigenSolver::GeneralizedEigenSolver</a></div><div class="ttdeci">GeneralizedEigenSolver()</div><div class="ttdoc">Default constructor. </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:117</div></div>
<div class="ttc" id="classEigen_1_1CwiseBinaryOp_html"><div class="ttname"><a href="classEigen_1_1CwiseBinaryOp.html">Eigen::CwiseBinaryOp</a></div><div class="ttdoc">Generic expression where a coefficient-wise binary operator is applied to two expressions. </div><div class="ttdef"><b>Definition:</b> CwiseBinaryOp.h:106</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_acffd08bee548eaa5c10414343a93529f"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#acffd08bee548eaa5c10414343a93529f">Eigen::GeneralizedEigenSolver::eigenvalues</a></div><div class="ttdeci">EigenvalueType eigenvalues() const </div><div class="ttdoc">Returns an expression of the computed generalized eigenvalues. </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:198</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_a92c089793f883fd38cd2df4d7c6513e5"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#a92c089793f883fd38cd2df4d7c6513e5">Eigen::GeneralizedEigenSolver::betas</a></div><div class="ttdeci">VectorType betas() const </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:220</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_aeb6c0eb89cc982629305f6c7e0791caf"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">Eigen::GeneralizedEigenSolver::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> GeneralizedEigenSolver.h:62</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_a14f2d5bf9df5a70ea27bc1239aa30822"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#a14f2d5bf9df5a70ea27bc1239aa30822">Eigen::GeneralizedEigenSolver::EigenvalueType</a></div><div class="ttdeci">CwiseBinaryOp< internal::scalar_quotient_op< ComplexScalar, Scalar >, ComplexVectorType, VectorType > EigenvalueType</div><div class="ttdoc">Expression type for the eigenvalues as returned by eigenvalues(). </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:101</div></div>
<div class="ttc" id="classEigen_1_1RealQZ_html_a1b369841b0e39a1ac80a6c32b721d242"><div class="ttname"><a href="classEigen_1_1RealQZ.html#a1b369841b0e39a1ac80a6c32b721d242">Eigen::RealQZ::setMaxIterations</a></div><div class="ttdeci">RealQZ & setMaxIterations(Index maxIters)</div><div class="ttdef"><b>Definition:</b> RealQZ.h:183</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_a64e32bd0f28bb7b6e91775c3ac592e12"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#a64e32bd0f28bb7b6e91775c3ac592e12">Eigen::GeneralizedEigenSolver::compute</a></div><div class="ttdeci">GeneralizedEigenSolver & compute(const MatrixType &A, const MatrixType &B, bool computeEigenvectors=true)</div><div class="ttdoc">Computes generalized eigendecomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:291</div></div>
<div class="ttc" id="classEigen_1_1RealQZ_html_a0c06d5c2034ebb329c54235369643ad2"><div class="ttname"><a href="classEigen_1_1RealQZ.html#a0c06d5c2034ebb329c54235369643ad2">Eigen::RealQZ::info</a></div><div class="ttdeci">ComputationInfo info() const </div><div class="ttdoc">Reports whether previous computation was successful. </div><div class="ttdef"><b>Definition:</b> RealQZ.h:166</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_a12de5e55557c63e5efaa70c3d4e82060"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#a12de5e55557c63e5efaa70c3d4e82060">Eigen::GeneralizedEigenSolver::ComplexVectorType</a></div><div class="ttdeci">Matrix< ComplexScalar, ColsAtCompileTime, 1, Options &~RowMajor, MaxColsAtCompileTime, 1 > ComplexVectorType</div><div class="ttdoc">Type for vector of complex scalar values eigenvalues as returned by betas(). </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:97</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_aa0f561be93f959404ee232321b389468"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#aa0f561be93f959404ee232321b389468">Eigen::GeneralizedEigenSolver::GeneralizedEigenSolver</a></div><div class="ttdeci">GeneralizedEigenSolver(const MatrixType &A, const MatrixType &B, bool computeEigenvectors=true)</div><div class="ttdoc">Constructor; computes the generalized eigendecomposition of given matrix pair. </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:148</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_af6db2eac907628bd50de67a4ede88a5a"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#af6db2eac907628bd50de67a4ede88a5a">Eigen::GeneralizedEigenSolver::setMaxIterations</a></div><div class="ttdeci">GeneralizedEigenSolver & setMaxIterations(Index maxIters)</div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:259</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_ae88654b9613217486067f07e394c88dc"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#ae88654b9613217486067f07e394c88dc">Eigen::GeneralizedEigenSolver::VectorType</a></div><div class="ttdeci">Matrix< Scalar, ColsAtCompileTime, 1, Options &~RowMajor, MaxColsAtCompileTime, 1 > VectorType</div><div class="ttdoc">Type for vector of real scalar values eigenvalues as returned by betas(). </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:90</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_a3f6fc00047c205ee590f676934aab28f"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#a3f6fc00047c205ee590f676934aab28f">Eigen::GeneralizedEigenSolver::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> GeneralizedEigenSolver.h:73</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_a50d070013a795db5621119f2b4a3d781"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#a50d070013a795db5621119f2b4a3d781">Eigen::GeneralizedEigenSolver::EigenvectorsType</a></div><div class="ttdeci">Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime > EigenvectorsType</div><div class="ttdoc">Type for matrix of eigenvectors as returned by eigenvectors(). </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:108</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Eigen::Success</a></div><div class="ttdef"><b>Definition:</b> Constants.h:376</div></div>
<div class="ttc" id="classEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix< Scalar, ColsAtCompileTime, 1, Options &~RowMajor, MaxColsAtCompileTime, 1 ></a></div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html">Eigen::GeneralizedEigenSolver</a></div><div class="ttdoc">Computes the generalized eigenvalues and eigenvectors of a pair of general matrices. </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:57</div></div>
<div class="ttc" id="group__enums_html_ga51bc1ac16f26ebe51eae1abb77bd037b"><div class="ttname"><a href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:374</div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_a1b9bc0a45616064df3a6168395e3cfcc"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#a1b9bc0a45616064df3a6168395e3cfcc">Eigen::GeneralizedEigenSolver::ComplexScalar</a></div><div class="ttdeci">std::complex< RealScalar > ComplexScalar</div><div class="ttdoc">Complex scalar type for MatrixType. </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:83</div></div>
<div class="ttc" id="classEigen_1_1RealQZ_html"><div class="ttname"><a href="classEigen_1_1RealQZ.html">Eigen::RealQZ< MatrixType ></a></div></div>
<div class="ttc" id="classEigen_1_1GeneralizedEigenSolver_html_ade79c282ebff0a23829fd9b9b18fe1c0"><div class="ttname"><a href="classEigen_1_1GeneralizedEigenSolver.html#ade79c282ebff0a23829fd9b9b18fe1c0">Eigen::GeneralizedEigenSolver::alphas</a></div><div class="ttdeci">ComplexVectorType alphas() const </div><div class="ttdef"><b>Definition:</b> GeneralizedEigenSolver.h:209</div></div>
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