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<div class="title">ComplexEigenSolver.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) 2009 Claire Maurice</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk></span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#ifndef EIGEN_COMPLEX_EIGEN_SOLVER_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_COMPLEX_EIGEN_SOLVER_H</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#include "./ComplexSchur.h"</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html"> 45</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span><a class="code" href="classEigen_1_1ComplexEigenSolver.html">ComplexEigenSolver</a></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a name="l00050"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf"> 50</a></span>  <span class="keyword">typedef</span> _MatrixType <a class="code" href="classEigen_1_1ComplexEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  Options = MatrixType::Options,</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</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> </div>
<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a3f6fc00047c205ee590f676934aab28f"> 61</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a>;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</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="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a name="l00071"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a1b9bc0a45616064df3a6168395e3cfcc"> 71</a></span>  <span class="keyword">typedef</span> std::complex<RealScalar> <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a1bacc53058a77ef90a61b1f24eac57ea"> 78</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_1ComplexEigenSolver.html#a1bacc53058a77ef90a61b1f24eac57ea">EigenvalueType</a>;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a name="l00085"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#ab56d974ddc62e97452c463987159c040"> 85</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_1ComplexEigenSolver.html#ab56d974ddc62e97452c463987159c040">EigenvectorType</a>;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a6df2ea6989cb34f6febf45c6a961560f"> 92</a></span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a6df2ea6989cb34f6febf45c6a961560f">ComplexEigenSolver</a>()</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  : m_eivec(),</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  m_eivalues(),</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  m_schur(),</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  m_eigenvectorsOk(false),</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  m_matX()</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  {}</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00107"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a24a667e12f56defc879c90eee4ba1971"> 107</a></span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a24a667e12f56defc879c90eee4ba1971">ComplexEigenSolver</a>(Index size)</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  : m_eivec(size, size),</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  m_eivalues(size),</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  m_schur(size),</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  m_eigenvectorsOk(false),</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  m_matX(size, size)</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  {}</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#af7c9eab1a5d3a2b3a6acdf599b917953"> 125</a></span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html#af7c9eab1a5d3a2b3a6acdf599b917953">ComplexEigenSolver</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1ComplexEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& matrix, <span class="keywordtype">bool</span> computeEigenvectors = <span class="keyword">true</span>)</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  : m_eivec(matrix.rows(),matrix.cols()),</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  m_eivalues(matrix.cols()),</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  m_schur(matrix.rows()),</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_matX(matrix.rows(),matrix.cols())</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  {</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a5c53421aa899f6214349c62bad5f36f8">compute</a>(matrix, computeEigenvectors);</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="l00156"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a810ff7d8ff9ee9bfc5641d4f3f904eb6"> 156</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">EigenvectorType</a>& <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a810ff7d8ff9ee9bfc5641d4f3f904eb6">eigenvectors</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ComplexEigenSolver is not initialized."</span>);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  eigen_assert(m_eigenvectorsOk && <span class="stringliteral">"The eigenvectors have not been computed together with the eigenvalues."</span>);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordflow">return</span> m_eivec;</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  }</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> </div>
<div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a1165fd63a951c6afaf239174d22e9945"> 181</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">EigenvalueType</a>& <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a1165fd63a951c6afaf239174d22e9945">eigenvalues</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ComplexEigenSolver is not initialized."</span>);</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">return</span> m_eivalues;</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  }</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> </div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html">ComplexEigenSolver</a>& <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a5c53421aa899f6214349c62bad5f36f8">compute</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1ComplexEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& matrix, <span class="keywordtype">bool</span> computeEigenvectors = <span class="keyword">true</span>);</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a name="l00217"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a0c06d5c2034ebb329c54235369643ad2"> 217</a></span>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a0c06d5c2034ebb329c54235369643ad2">info</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">"ComplexEigenSolver is not initialized."</span>);</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordflow">return</span> m_schur.<a class="code" href="classEigen_1_1ComplexSchur.html#a0c06d5c2034ebb329c54235369643ad2">info</a>();</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="l00224"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a3b1b6c1fccb22b96c7ecc6d8c0a11a1e"> 224</a></span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html">ComplexEigenSolver</a>& <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a3b1b6c1fccb22b96c7ecc6d8c0a11a1e">setMaxIterations</a>(Index maxIters)</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  {</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  m_schur.<a class="code" href="classEigen_1_1ComplexSchur.html#a8178c4999e63b2bfbdc424ff84a91b10">setMaxIterations</a>(maxIters);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  }</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> </div>
<div class="line"><a name="l00231"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#ab6f0a63ea1d26cef5e748207043eb43e"> 231</a></span>  Index <a class="code" href="classEigen_1_1ComplexEigenSolver.html#ab6f0a63ea1d26cef5e748207043eb43e">getMaxIterations</a>()</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  {</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">return</span> m_schur.<a class="code" href="classEigen_1_1ComplexSchur.html#ab6f0a63ea1d26cef5e748207043eb43e">getMaxIterations</a>();</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  }</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> </div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html#ab56d974ddc62e97452c463987159c040">EigenvectorType</a> m_eivec;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a1bacc53058a77ef90a61b1f24eac57ea">EigenvalueType</a> m_eivalues;</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <a class="code" href="classEigen_1_1ComplexSchur.html">ComplexSchur<MatrixType></a> m_schur;</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordtype">bool</span> m_eigenvectorsOk;</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <a class="code" href="classEigen_1_1ComplexEigenSolver.html#ab56d974ddc62e97452c463987159c040">EigenvectorType</a> m_matX;</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordtype">void</span> doComputeEigenvectors(<span class="keyword">const</span> RealScalar& matrixnorm);</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordtype">void</span> sortEigenvalues(<span class="keywordtype">bool</span> computeEigenvectors);</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> };</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> </div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span> </div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> ComplexEigenSolver<MatrixType>& </div>
<div class="line"><a name="l00252"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexEigenSolver.html#a5c53421aa899f6214349c62bad5f36f8"> 252</a></span> <a class="code" href="classEigen_1_1ComplexEigenSolver.html#a5c53421aa899f6214349c62bad5f36f8">ComplexEigenSolver<MatrixType>::compute</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1ComplexEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">MatrixType</a>& matrix, <span class="keywordtype">bool</span> computeEigenvectors)</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span> {</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="comment">// this code is inspired from Jampack</span></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  eigen_assert(matrix.cols() == matrix.rows());</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="comment">// Do a complex Schur decomposition, A = U T U^*</span></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="comment">// The eigenvalues are on the diagonal of T.</span></div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  m_schur.compute(matrix, computeEigenvectors);</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>  <span class="keywordflow">if</span>(m_schur.info() == <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>)</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  {</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  m_eivalues = m_schur.matrixT().diagonal();</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="keywordflow">if</span>(computeEigenvectors)</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  doComputeEigenvectors(matrix.norm());</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  sortEigenvalues(computeEigenvectors);</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="l00269"></a><span class="lineno"> 269</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  m_eigenvectorsOk = computeEigenvectors;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> }</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> </div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1ComplexEigenSolver.html">ComplexEigenSolver<MatrixType>::doComputeEigenvectors</a>(<span class="keyword">const</span> RealScalar& matrixnorm)</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="keyword">const</span> Index n = m_eivalues.size();</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="comment">// Compute X such that T = X D X^(-1), where D is the diagonal of T.</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="comment">// The matrix X is unit triangular.</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  m_matX = EigenvectorType::Zero(n, n);</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keywordflow">for</span>(Index k=n-1 ; k>=0 ; k--)</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  {</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  m_matX.coeffRef(k,k) = ComplexScalar(1.0,0.0);</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">// Compute X(i,k) using the (i,k) entry of the equation X T = D X</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">for</span>(Index i=k-1 ; i>=0 ; i--)</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>  m_matX.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keywordflow">if</span>(k-i-1>0)</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  m_matX.coeffRef(i,k) -= (m_schur.matrixT().row(i).segment(i+1,k-i-1) * m_matX.col(k).segment(i+1,k-i-1)).value();</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  ComplexScalar z = m_schur.matrixT().coeff(i,i) - m_schur.matrixT().coeff(k,k);</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keywordflow">if</span>(z==ComplexScalar(0))</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  {</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="comment">// If the i-th and k-th eigenvalue are equal, then z equals 0.</span></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="comment">// Use a small value instead, to prevent division by zero.</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  numext::real_ref(z) = <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<RealScalar>::epsilon</a>() * matrixnorm;</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  }</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;</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>  }</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="comment">// Compute V as V = U X; now A = U T U^* = U X D X^(-1) U^* = V D V^(-1)</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  m_eivec.noalias() = m_schur.matrixU() * m_matX;</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="comment">// .. and normalize the eigenvectors</span></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="keywordflow">for</span>(Index k=0 ; k<n ; k++)</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  {</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  m_eivec.col(k).normalize();</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> </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="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="keywordtype">void</span> ComplexEigenSolver<MatrixType>::sortEigenvalues(<span class="keywordtype">bool</span> computeEigenvectors)</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> {</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keyword">const</span> Index n = m_eivalues.size();</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">for</span> (Index i=0; i<n; 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>  Index k;</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  m_eivalues.cwiseAbs().tail(n-i).minCoeff(&k);</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">if</span> (k != 0)</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  {</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  k += i;</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  std::swap(m_eivalues[k],m_eivalues[i]);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordflow">if</span>(computeEigenvectors)</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  m_eivec.col(i).swap(m_eivec.col(k));</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  }</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  }</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> } <span class="comment">// end namespace Eigen</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> <span class="preprocessor">#endif // EIGEN_COMPLEX_EIGEN_SOLVER_H</span></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_aeb6c0eb89cc982629305f6c7e0791caf"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#aeb6c0eb89cc982629305f6c7e0791caf">Eigen::ComplexEigenSolver::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> ComplexEigenSolver.h:50</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a1165fd63a951c6afaf239174d22e9945"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a1165fd63a951c6afaf239174d22e9945">Eigen::ComplexEigenSolver::eigenvalues</a></div><div class="ttdeci">const EigenvalueType & eigenvalues() const </div><div class="ttdoc">Returns the eigenvalues of given matrix. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:181</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_1ComplexEigenSolver_html_a0c06d5c2034ebb329c54235369643ad2"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a0c06d5c2034ebb329c54235369643ad2">Eigen::ComplexEigenSolver::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> ComplexEigenSolver.h:217</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_ab6f0a63ea1d26cef5e748207043eb43e"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#ab6f0a63ea1d26cef5e748207043eb43e">Eigen::ComplexEigenSolver::getMaxIterations</a></div><div class="ttdeci">Index getMaxIterations()</div><div class="ttdoc">Returns the maximum number of iterations. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:231</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a810ff7d8ff9ee9bfc5641d4f3f904eb6"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a810ff7d8ff9ee9bfc5641d4f3f904eb6">Eigen::ComplexEigenSolver::eigenvectors</a></div><div class="ttdeci">const EigenvectorType & eigenvectors() const </div><div class="ttdoc">Returns the eigenvectors of given matrix. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:156</div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_a8178c4999e63b2bfbdc424ff84a91b10"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a8178c4999e63b2bfbdc424ff84a91b10">Eigen::ComplexSchur::setMaxIterations</a></div><div class="ttdeci">ComplexSchur & setMaxIterations(Index maxIters)</div><div class="ttdoc">Sets the maximum number of iterations allowed. </div><div class="ttdef"><b>Definition:</b> ComplexSchur.h:226</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a1bacc53058a77ef90a61b1f24eac57ea"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a1bacc53058a77ef90a61b1f24eac57ea">Eigen::ComplexEigenSolver::EigenvalueType</a></div><div class="ttdeci">Matrix< ComplexScalar, ColsAtCompileTime, 1, Options &(~RowMajor), MaxColsAtCompileTime, 1 > EigenvalueType</div><div class="ttdoc">Type for vector of eigenvalues as returned by eigenvalues(). </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:78</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a3f6fc00047c205ee590f676934aab28f"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a3f6fc00047c205ee590f676934aab28f">Eigen::ComplexEigenSolver::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> ComplexEigenSolver.h:61</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_ab56d974ddc62e97452c463987159c040"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#ab56d974ddc62e97452c463987159c040">Eigen::ComplexEigenSolver::EigenvectorType</a></div><div class="ttdeci">Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime > EigenvectorType</div><div class="ttdoc">Type for matrix of eigenvectors as returned by eigenvectors(). </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:85</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a5c53421aa899f6214349c62bad5f36f8"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a5c53421aa899f6214349c62bad5f36f8">Eigen::ComplexEigenSolver::compute</a></div><div class="ttdeci">ComplexEigenSolver & compute(const MatrixType &matrix, bool computeEigenvectors=true)</div><div class="ttdoc">Computes eigendecomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:252</div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_ab6f0a63ea1d26cef5e748207043eb43e"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#ab6f0a63ea1d26cef5e748207043eb43e">Eigen::ComplexSchur::getMaxIterations</a></div><div class="ttdeci">Index getMaxIterations()</div><div class="ttdoc">Returns the maximum number of iterations. </div><div class="ttdef"><b>Definition:</b> ComplexSchur.h:233</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a6df2ea6989cb34f6febf45c6a961560f"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a6df2ea6989cb34f6febf45c6a961560f">Eigen::ComplexEigenSolver::ComplexEigenSolver</a></div><div class="ttdeci">ComplexEigenSolver()</div><div class="ttdoc">Default constructor. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:92</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_af7c9eab1a5d3a2b3a6acdf599b917953"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#af7c9eab1a5d3a2b3a6acdf599b917953">Eigen::ComplexEigenSolver::ComplexEigenSolver</a></div><div class="ttdeci">ComplexEigenSolver(const MatrixType &matrix, bool computeEigenvectors=true)</div><div class="ttdoc">Constructor; computes eigendecomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:125</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a24a667e12f56defc879c90eee4ba1971"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a24a667e12f56defc879c90eee4ba1971">Eigen::ComplexEigenSolver::ComplexEigenSolver</a></div><div class="ttdeci">ComplexEigenSolver(Index size)</div><div class="ttdoc">Default Constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:107</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_1ComplexSchur_html_a0c06d5c2034ebb329c54235369643ad2"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a0c06d5c2034ebb329c54235369643ad2">Eigen::ComplexSchur::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> ComplexSchur.h:215</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a1b9bc0a45616064df3a6168395e3cfcc"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a1b9bc0a45616064df3a6168395e3cfcc">Eigen::ComplexEigenSolver::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> ComplexEigenSolver.h:71</div></div>
<div class="ttc" id="classEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix< ComplexScalar, ColsAtCompileTime, 1, Options &(~RowMajor), MaxColsAtCompileTime, 1 ></a></div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html">Eigen::ComplexSchur< MatrixType ></a></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_1ComplexEigenSolver_html"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html">Eigen::ComplexEigenSolver</a></div><div class="ttdoc">Computes eigenvalues and eigenvectors of general complex matrices. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:45</div></div>
<div class="ttc" id="classEigen_1_1ComplexEigenSolver_html_a3b1b6c1fccb22b96c7ecc6d8c0a11a1e"><div class="ttname"><a href="classEigen_1_1ComplexEigenSolver.html#a3b1b6c1fccb22b96c7ecc6d8c0a11a1e">Eigen::ComplexEigenSolver::setMaxIterations</a></div><div class="ttdeci">ComplexEigenSolver & setMaxIterations(Index maxIters)</div><div class="ttdoc">Sets the maximum number of iterations allowed. </div><div class="ttdef"><b>Definition:</b> ComplexEigenSolver.h:224</div></div>
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