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<div class="fragment"><div class="line"><a id="l00001" 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 id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// Copyright (C) 2009 Claire Maurice</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">// Copyright (C) 2009 Gael Guennebaud <[email protected]></span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// Copyright (C) 2010,2012 Jitse Niesen <[email protected]></span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
<div class="line"><a id="l00008" 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 id="l00009" 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 id="l00010" 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 id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#ifndef EIGEN_COMPLEX_SCHUR_H</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#define EIGEN_COMPLEX_SCHUR_H</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include "./HessenbergDecomposition.h"</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include "./InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">bool</span> IsComplex> <span class="keyword">struct </span>complex_schur_reduce_to_hessenberg;</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span>}</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html"> 53</a></span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType_> <span class="keyword">class </span><a class="code hl_class" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span>{</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keyword">enum</span> {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> Options = MatrixType::Options,</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> };</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a3121a90f56446ec9a68f53f9b79bef9c"> 66</a></span> <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a3121a90f56446ec9a68f53f9b79bef9c">Scalar</a>;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf"> 68</a></span> <span class="keyword">typedef</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a>; </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4"> 76</a></span> <span class="keyword">typedef</span> std::complex<RealScalar> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a>;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#abed305877f8fec28d44a4e46fec72cb6"> 83</a></span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Matrix<ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime></a> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#abed305877f8fec28d44a4e46fec72cb6">ComplexMatrixType</a>;</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a49e78b336c89147fdc80589444884b1b"> 96</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#a49e78b336c89147fdc80589444884b1b">ComplexSchur</a>(<a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> size = RowsAtCompileTime==<a class="code hl_variable" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? 1 : RowsAtCompileTime)</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> : m_matT(size,size),</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> m_matU(size,size),</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> m_hess(size),</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> m_isInitialized(false),</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> m_matUisUptodate(false),</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> m_maxIters(-1)</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> {}</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">template</span><<span class="keyword">typename</span> InputType></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#ab5745362c6c27d259188a06b7ba74733"> 115</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#ab5745362c6c27d259188a06b7ba74733">ComplexSchur</a>(<span class="keyword">const</span> <a class="code hl_class" href="structEigen_1_1EigenBase.html">EigenBase<InputType></a>& matrix, <span class="keywordtype">bool</span> computeU = <span class="keyword">true</span>)</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> : m_matT(matrix.rows(),matrix.cols()),</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> m_matU(matrix.rows(),matrix.cols()),</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> m_hess(matrix.rows()),</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> m_isInitialized(false),</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> m_matUisUptodate(false),</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> m_maxIters(-1)</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> {</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#aca1195e9326f381dbabc047f2dbcc24d">compute</a>(matrix.<a class="code hl_function" href="structEigen_1_1EigenBase.html#a749b057c52245e486a101868d2578a24">derived</a>(), computeU);</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> }</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#afea5892af4e61a14898813082c86c6c5"> 140</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">ComplexMatrixType</a>& <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#afea5892af4e61a14898813082c86c6c5">matrixU</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> eigen_assert(m_isInitialized && <span class="stringliteral">"ComplexSchur is not initialized."</span>);</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> eigen_assert(m_matUisUptodate && <span class="stringliteral">"The matrix U has not been computed during the ComplexSchur decomposition."</span>);</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordflow">return</span> m_matU;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> }</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a508cd5453a15a3e543dc66ad1f54aec2"> 164</a></span> <span class="keyword">const</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">ComplexMatrixType</a>& <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#a508cd5453a15a3e543dc66ad1f54aec2">matrixT</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> eigen_assert(m_isInitialized && <span class="stringliteral">"ComplexSchur is not initialized."</span>);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">return</span> m_matT;</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> }</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> </div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keyword">template</span><<span class="keyword">typename</span> InputType></div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#aca1195e9326f381dbabc047f2dbcc24d"> 193</a></span> <a class="code hl_class" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>& <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#aca1195e9326f381dbabc047f2dbcc24d">compute</a>(<span class="keyword">const</span> <a class="code hl_class" href="structEigen_1_1EigenBase.html">EigenBase<InputType></a>& matrix, <span class="keywordtype">bool</span> computeU = <span class="keyword">true</span>);</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keyword">template</span><<span class="keyword">typename</span> HessMatrixType, <span class="keyword">typename</span> OrthMatrixType></div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a68de44741d2c4985a4ce78464295b80b"> 213</a></span> <a class="code hl_class" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>& <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#a68de44741d2c4985a4ce78464295b80b">computeFromHessenberg</a>(<span class="keyword">const</span> HessMatrixType& matrixH, <span class="keyword">const</span> OrthMatrixType& matrixQ, <span class="keywordtype">bool</span> computeU=<span class="keyword">true</span>);</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a13adef2a54e61bb5789eb7821a3b7b46"> 219</a></span> <a class="code hl_enumeration" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#a13adef2a54e61bb5789eb7821a3b7b46">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> eigen_assert(m_isInitialized && <span class="stringliteral">"ComplexSchur is not initialized."</span>);</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> }</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#af87b9cdada99e8a6f3b0e0406d7fda86"> 230</a></span> <a class="code hl_class" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>& <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#af87b9cdada99e8a6f3b0e0406d7fda86">setMaxIterations</a>(<a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> maxIters)</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> {</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> m_maxIters = maxIters;</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> }</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> </div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a6f35999b87c247bb24b2ad6ba1abee69"> 237</a></span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#a6f35999b87c247bb24b2ad6ba1abee69">getMaxIterations</a>()</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> {</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keywordflow">return</span> m_maxIters;</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> }</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> </div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a79450087274edce80ee268e2f42e64f1"> 247</a></span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="classEigen_1_1ComplexSchur.html#a79450087274edce80ee268e2f42e64f1">m_maxIterationsPerRow</a> = 30;</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> </div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keyword">protected</span>:</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">ComplexMatrixType</a> m_matT, m_matU;</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <a class="code hl_class" href="classEigen_1_1HessenbergDecomposition.html">HessenbergDecomposition<MatrixType></a> m_hess;</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <a class="code hl_enumeration" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> m_info;</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <span class="keywordtype">bool</span> m_matUisUptodate;</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> m_maxIters;</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> </div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="keyword">private</span>: </div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> <span class="keywordtype">bool</span> subdiagonalEntryIsNeglegible(<a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> i);</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> computeShift(<a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> iu, <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> iter);</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="keywordtype">void</span> reduceToTriangularForm(<span class="keywordtype">bool</span> computeU);</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="keyword">friend</span> <span class="keyword">struct </span>internal::complex_schur_reduce_to_hessenberg<MatrixType, <a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits</a><<a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a3121a90f56446ec9a68f53f9b79bef9c">Scalar</a>>::IsComplex>;</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span>};</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> </div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span>template<typename MatrixType></div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span>inline bool <a class="code hl_class" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a><MatrixType>::subdiagonalEntryIsNeglegible(Index i)</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span>{</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> RealScalar d = numext::norm1(m_matT.<a class="code hl_function" href="classEigen_1_1PlainObjectBase.html#a5f8bb3d199528bd3ea4055a887ea7f0f">coeff</a>(i,i)) + numext::norm1(m_matT.<a class="code hl_function" href="classEigen_1_1PlainObjectBase.html#a5f8bb3d199528bd3ea4055a887ea7f0f">coeff</a>(i+1,i+1));</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> RealScalar sd = numext::norm1(m_matT.<a class="code hl_function" href="classEigen_1_1PlainObjectBase.html#a5f8bb3d199528bd3ea4055a887ea7f0f">coeff</a>(i+1,i));</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keywordflow">if</span> (internal::isMuchSmallerThan(sd, d, <a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits<RealScalar>::epsilon</a>()))</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> {</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> m_matT.<a class="code hl_function" href="classEigen_1_1Matrix.html#ae85597963bd263f97437a7f0581b63fb">coeffRef</a>(i+1,i) = <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a>(0);</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> }</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span>}</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> </div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> </div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span><span class="keyword">typename</span> ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::computeShift(<a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> iu, <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> iter)</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span>{</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="keywordflow">if</span> (iter == 10 || iter == 20) </div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> {</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="comment">// exceptional shift, taken from http://www.netlib.org/eispack/comqr.f</span></div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="keywordflow">return</span> abs(numext::real(m_matT.<a class="code hl_function" href="classEigen_1_1PlainObjectBase.html#a5f8bb3d199528bd3ea4055a887ea7f0f">coeff</a>(iu,iu-1))) + abs(numext::real(m_matT.<a class="code hl_function" href="classEigen_1_1PlainObjectBase.html#a5f8bb3d199528bd3ea4055a887ea7f0f">coeff</a>(iu-1,iu-2)));</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> }</div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> </div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="comment">// compute the shift as one of the eigenvalues of t, the 2x2</span></div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <span class="comment">// diagonal block on the bottom of the active submatrix</span></div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> Matrix<ComplexScalar,2,2> t = m_matT.template block<2,2>(iu-1,iu-1);</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> RealScalar normt = t.cwiseAbs().sum();</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> t /= normt; <span class="comment">// the normalization by sf is to avoid under/overflow</span></div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> </div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> b = t.coeff(0,1) * t.coeff(1,0);</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> c = t.coeff(0,0) - t.coeff(1,1);</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> disc = sqrt(c*c + RealScalar(4)*b);</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> det = t.coeff(0,0) * t.coeff(1,1) - b;</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> trace = t.coeff(0,0) + t.coeff(1,1);</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> eival1 = (trace + disc) / RealScalar(2);</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> eival2 = (trace - disc) / RealScalar(2);</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> RealScalar eival1_norm = numext::norm1(eival1);</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> RealScalar eival2_norm = numext::norm1(eival2);</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> <span class="comment">// A division by zero can only occur if eival1==eival2==0.</span></div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <span class="comment">// In this case, det==0, and all we have to do is checking that eival2_norm!=0</span></div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> <span class="keywordflow">if</span>(eival1_norm > eival2_norm)</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> eival2 = det / eival1;</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span>(!numext::is_exactly_zero(eival2_norm))</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> eival1 = det / eival2;</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> </div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> <span class="comment">// choose the eigenvalue closest to the bottom entry of the diagonal</span></div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> <span class="keywordflow">if</span>(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> <span class="keywordflow">return</span> normt * eival1;</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> <span class="keywordflow">return</span> normt * eival2;</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span>}</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> </div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> </div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span><span class="keyword">template</span><<span class="keyword">typename</span> InputType></div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span>ComplexSchur<MatrixType>& <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#aca1195e9326f381dbabc047f2dbcc24d">ComplexSchur<MatrixType>::compute</a>(<span class="keyword">const</span> EigenBase<InputType>& matrix, <span class="keywordtype">bool</span> computeU)</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span>{</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> m_matUisUptodate = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> eigen_assert(matrix.cols() == matrix.rows());</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> <span class="keywordflow">if</span>(matrix.cols() == 1)</div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> {</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> m_matT = matrix.derived().template cast<ComplexScalar>();</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="keywordflow">if</span>(computeU) m_matU = ComplexMatrixType::Identity(1,1);</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> m_info = <a class="code hl_enumvalue" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> m_matUisUptodate = computeU;</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> }</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> </div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*<span class="keyword">this</span>, matrix.derived(), computeU);</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#a68de44741d2c4985a4ce78464295b80b">computeFromHessenberg</a>(m_matT, m_matU, computeU);</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span>}</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> </div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span><span class="keyword">template</span><<span class="keyword">typename</span> HessMatrixType, <span class="keyword">typename</span> OrthMatrixType></div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span>ComplexSchur<MatrixType>& <a class="code hl_function" href="classEigen_1_1ComplexSchur.html#a68de44741d2c4985a4ce78464295b80b">ComplexSchur<MatrixType>::computeFromHessenberg</a>(<span class="keyword">const</span> HessMatrixType& matrixH, <span class="keyword">const</span> OrthMatrixType& matrixQ, <span class="keywordtype">bool</span> computeU)</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span>{</div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> m_matT = matrixH;</div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> <span class="keywordflow">if</span>(computeU)</div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> m_matU = matrixQ;</div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> reduceToTriangularForm(computeU);</div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span>}</div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> </div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span><span class="comment">/* Reduce given matrix to Hessenberg form */</span></div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">bool</span> IsComplex></div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span><span class="keyword">struct </span>complex_schur_reduce_to_hessenberg</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span>{</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> <span class="comment">// this is the implementation for the case IsComplex = true</span></div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="keyword">static</span> <span class="keywordtype">void</span> run(ComplexSchur<MatrixType>& _this, <span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">bool</span> computeU)</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> {</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> _this.m_hess.compute(matrix);</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> _this.m_matT = _this.m_hess.matrixH();</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> <span class="keywordflow">if</span>(computeU) _this.m_matU = _this.m_hess.matrixQ();</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> }</div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span>};</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> </div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span><span class="keyword">struct </span>complex_schur_reduce_to_hessenberg<MatrixType, false></div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span>{</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> <span class="keyword">static</span> <span class="keywordtype">void</span> run(ComplexSchur<MatrixType>& _this, <span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">bool</span> computeU)</div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> {</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> </div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="comment">// Note: m_hess is over RealScalar; m_matT and m_matU is over ComplexScalar</span></div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> _this.m_hess.compute(matrix);</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> _this.m_matT = _this.m_hess.matrixH().template cast<ComplexScalar>();</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="keywordflow">if</span>(computeU) </div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> {</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> <span class="comment">// This may cause an allocation which seems to be avoidable</span></div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> MatrixType Q = _this.m_hess.matrixQ(); </div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> _this.m_matU = Q.template cast<ComplexScalar>();</div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> }</div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> }</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span>};</div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> </div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> </div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span><span class="comment">// Reduce the Hessenberg matrix m_matT to triangular form by QR iteration.</span></div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span><span class="keywordtype">void</span> ComplexSchur<MatrixType>::reduceToTriangularForm(<span class="keywordtype">bool</span> computeU)</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span>{ </div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> maxIters = m_maxIters;</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> <span class="keywordflow">if</span> (maxIters == -1)</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> maxIters = <a class="code hl_variable" href="classEigen_1_1ComplexSchur.html#a79450087274edce80ee268e2f42e64f1">m_maxIterationsPerRow</a> * m_matT.rows();</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> </div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> <span class="comment">// The matrix m_matT is divided in three parts. </span></div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> <span class="comment">// Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero. </span></div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> <span class="comment">// Rows il,...,iu is the part we are working on (the active submatrix).</span></div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <span class="comment">// Rows iu+1,...,end are already brought in triangular form.</span></div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> iu = m_matT.cols() - 1;</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> il;</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> iter = 0; <span class="comment">// number of iterations we are working on the (iu,iu) element</span></div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> totalIter = 0; <span class="comment">// number of iterations for whole matrix</span></div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> </div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> <span class="keywordflow">while</span>(<span class="keyword">true</span>)</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> {</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> <span class="comment">// find iu, the bottom row of the active submatrix</span></div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <span class="keywordflow">while</span>(iu > 0)</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> {</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> <span class="keywordflow">if</span>(!subdiagonalEntryIsNeglegible(iu-1)) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> iter = 0;</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> --iu;</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> }</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> </div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> <span class="comment">// if iu is zero then we are done; the whole matrix is triangularized</span></div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> <span class="keywordflow">if</span>(iu==0) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> </div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <span class="comment">// if we spent too many iterations, we give up</span></div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> iter++;</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> totalIter++;</div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> <span class="keywordflow">if</span>(totalIter > maxIters) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> </div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <span class="comment">// find il, the top row of the active submatrix</span></div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> il = iu-1;</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> <span class="keywordflow">while</span>(il > 0 && !subdiagonalEntryIsNeglegible(il-1))</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> {</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> --il;</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> }</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> </div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="comment">/* perform the QR step using Givens rotations. The first rotation</span></div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span><span class="comment"> creates a bulge; the (il+2,il) element becomes nonzero. This</span></div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span><span class="comment"> bulge is chased down to the bottom of the active submatrix. */</span></div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> </div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a> shift = computeShift(iu, iter);</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> JacobiRotation<ComplexScalar> rot;</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> rot.makeGivens(m_matT.<a class="code hl_function" href="classEigen_1_1PlainObjectBase.html#a5f8bb3d199528bd3ea4055a887ea7f0f">coeff</a>(il,il) - shift, m_matT.<a class="code hl_function" href="classEigen_1_1PlainObjectBase.html#a5f8bb3d199528bd3ea4055a887ea7f0f">coeff</a>(il+1,il));</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> m_matT.topRows((std::min)(il+2,iu)+1).applyOnTheRight(il, il+1, rot);</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> <span class="keywordflow">if</span>(computeU) m_matU.applyOnTheRight(il, il+1, rot);</div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> </div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> <span class="keywordflow">for</span>(<a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Index</a> i=il+1 ; i<iu ; i++)</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> {</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> rot.makeGivens(m_matT.<a class="code hl_function" href="classEigen_1_1Matrix.html#ae85597963bd263f97437a7f0581b63fb">coeffRef</a>(i,i-1), m_matT.<a class="code hl_function" href="classEigen_1_1Matrix.html#ae85597963bd263f97437a7f0581b63fb">coeffRef</a>(i+1,i-1), &m_matT.<a class="code hl_function" href="classEigen_1_1Matrix.html#ae85597963bd263f97437a7f0581b63fb">coeffRef</a>(i,i-1));</div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> m_matT.<a class="code hl_function" href="classEigen_1_1Matrix.html#ae85597963bd263f97437a7f0581b63fb">coeffRef</a>(i+1,i-1) = <a class="code hl_typedef" href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">ComplexScalar</a>(0);</div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());</div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> m_matT.topRows((std::min)(i+2,iu)+1).applyOnTheRight(i, i+1, rot);</div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> <span class="keywordflow">if</span>(computeU) m_matU.applyOnTheRight(i, i+1, rot);</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> }</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> }</div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> </div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> <span class="keywordflow">if</span>(totalIter <= maxIters)</div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> m_info = <a class="code hl_enumvalue" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a>;</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> m_info = <a class="code hl_enumvalue" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>;</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> </div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> m_matUisUptodate = computeU;</div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span>}</div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> </div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span>} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> </div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span><span class="preprocessor">#endif </span><span class="comment">// EIGEN_COMPLEX_SCHUR_H</span></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html">Eigen::ComplexSchur</a></div><div class="ttdoc">Performs a complex Schur decomposition of a real or complex square matrix.</div><div class="ttdef"><b>Definition</b> ComplexSchur.h:54</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a13adef2a54e61bb5789eb7821a3b7b46"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a13adef2a54e61bb5789eb7821a3b7b46">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:219</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a3121a90f56446ec9a68f53f9b79bef9c"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a3121a90f56446ec9a68f53f9b79bef9c">Eigen::ComplexSchur::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> ComplexSchur.h:66</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a49e78b336c89147fdc80589444884b1b"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a49e78b336c89147fdc80589444884b1b">Eigen::ComplexSchur::ComplexSchur</a></div><div class="ttdeci">ComplexSchur(Index size=RowsAtCompileTime==Dynamic ? 1 :RowsAtCompileTime)</div><div class="ttdoc">Default constructor.</div><div class="ttdef"><b>Definition</b> ComplexSchur.h:96</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a508cd5453a15a3e543dc66ad1f54aec2"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a508cd5453a15a3e543dc66ad1f54aec2">Eigen::ComplexSchur::matrixT</a></div><div class="ttdeci">const ComplexMatrixType & matrixT() const</div><div class="ttdoc">Returns the triangular matrix in the Schur decomposition.</div><div class="ttdef"><b>Definition</b> ComplexSchur.h:164</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a68de44741d2c4985a4ce78464295b80b"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a68de44741d2c4985a4ce78464295b80b">Eigen::ComplexSchur::computeFromHessenberg</a></div><div class="ttdeci">ComplexSchur & computeFromHessenberg(const HessMatrixType &matrixH, const OrthMatrixType &matrixQ, bool computeU=true)</div><div class="ttdoc">Compute Schur decomposition from a given Hessenberg matrix.</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a6f35999b87c247bb24b2ad6ba1abee69"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a6f35999b87c247bb24b2ad6ba1abee69">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:237</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a79450087274edce80ee268e2f42e64f1"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a79450087274edce80ee268e2f42e64f1">Eigen::ComplexSchur::m_maxIterationsPerRow</a></div><div class="ttdeci">static const int m_maxIterationsPerRow</div><div class="ttdoc">Maximum number of iterations per row.</div><div class="ttdef"><b>Definition</b> ComplexSchur.h:247</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a8e273074f2cafe49725fcc774b93d6bf"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a8e273074f2cafe49725fcc774b93d6bf">Eigen::ComplexSchur::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdef"><b>Definition</b> ComplexSchur.h:68</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_a9cfc7d20234dd51933b0cb6ef427c8b4"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a9cfc7d20234dd51933b0cb6ef427c8b4">Eigen::ComplexSchur::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> ComplexSchur.h:76</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_ab5745362c6c27d259188a06b7ba74733"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#ab5745362c6c27d259188a06b7ba74733">Eigen::ComplexSchur::ComplexSchur</a></div><div class="ttdeci">ComplexSchur(const EigenBase< InputType > &matrix, bool computeU=true)</div><div class="ttdoc">Constructor; computes Schur decomposition of given matrix.</div><div class="ttdef"><b>Definition</b> ComplexSchur.h:115</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_abed305877f8fec28d44a4e46fec72cb6"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#abed305877f8fec28d44a4e46fec72cb6">Eigen::ComplexSchur::ComplexMatrixType</a></div><div class="ttdeci">Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime > ComplexMatrixType</div><div class="ttdoc">Type for the matrices in the Schur decomposition.</div><div class="ttdef"><b>Definition</b> ComplexSchur.h:83</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_aca1195e9326f381dbabc047f2dbcc24d"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#aca1195e9326f381dbabc047f2dbcc24d">Eigen::ComplexSchur::compute</a></div><div class="ttdeci">ComplexSchur & compute(const EigenBase< InputType > &matrix, bool computeU=true)</div><div class="ttdoc">Computes Schur decomposition of given matrix.</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_af87b9cdada99e8a6f3b0e0406d7fda86"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#af87b9cdada99e8a6f3b0e0406d7fda86">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:230</div></div>
<div class="ttc" id="aclassEigen_1_1ComplexSchur_html_afea5892af4e61a14898813082c86c6c5"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#afea5892af4e61a14898813082c86c6c5">Eigen::ComplexSchur::matrixU</a></div><div class="ttdeci">const ComplexMatrixType & matrixU() const</div><div class="ttdoc">Returns the unitary matrix in the Schur decomposition.</div><div class="ttdef"><b>Definition</b> ComplexSchur.h:140</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html">Eigen::HessenbergDecomposition</a></div><div class="ttdoc">Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation.</div><div class="ttdef"><b>Definition</b> HessenbergDecomposition.h:60</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition</b> Matrix.h:182</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html_ae85597963bd263f97437a7f0581b63fb"><div class="ttname"><a href="classEigen_1_1Matrix.html#ae85597963bd263f97437a7f0581b63fb">Eigen::Matrix::coeffRef</a></div><div class="ttdeci">constexpr Scalar & coeffRef(Index rowId, Index colId)</div><div class="ttdef"><b>Definition</b> PlainObjectBase.h:198</div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_a5f8bb3d199528bd3ea4055a887ea7f0f"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#a5f8bb3d199528bd3ea4055a887ea7f0f">Eigen::PlainObjectBase::coeff</a></div><div class="ttdeci">constexpr const Scalar & coeff(Index rowId, Index colId) const</div><div class="ttdef"><b>Definition</b> PlainObjectBase.h:177</div></div>
<div class="ttc" id="agroup__enums_html_ga85fad7b87587764e5cf6b513a9e0ee5e"><div class="ttname"><a href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition</b> Constants.h:444</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition</b> Constants.h:446</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">Eigen::NoConvergence</a></div><div class="ttdeci">@ NoConvergence</div><div class="ttdef"><b>Definition</b> Constants.h:450</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition</b> Meta.h:82</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition</b> Constants.h:24</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a749b057c52245e486a101868d2578a24"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a749b057c52245e486a101868d2578a24">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived & derived()</div><div class="ttdef"><b>Definition</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_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:231</div></div>
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