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<div class="title">ComplexSchur.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_SCHUR_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_SCHUR_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 "./HessenbergDecomposition.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="l00019"></a><span class="lineno"> 19</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</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 name="l00021"></a><span class="lineno"> 21</span> }</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> </div>
<div class="line"><a name="l00051"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html"> 51</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span><a class="code" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  Options = MatrixType::Options,</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  };</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a3f6fc00047c205ee590f676934aab28f"> 64</a></span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar <a class="code" href="classEigen_1_1ComplexSchur.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a>;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</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="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc"> 74</a></span>  <span class="keyword">typedef</span> std::complex<RealScalar> <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a name="l00081"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5"> 81</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_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5">ComplexMatrixType</a>;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00094"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a9ba3a59c1e385a4a5a80c08bf40f8fd1"> 94</a></span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a9ba3a59c1e385a4a5a80c08bf40f8fd1">ComplexSchur</a>(Index size = RowsAtCompileTime==<a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? 1 : RowsAtCompileTime)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  : m_matT(size,size),</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  m_matU(size,size),</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  m_hess(size),</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  m_matUisUptodate(false),</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  m_maxIters(-1)</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  {}</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a797849e56b60a3cb8f80ac23e3eb73f9"> 112</a></span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a797849e56b60a3cb8f80ac23e3eb73f9">ComplexSchur</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">bool</span> computeU = <span class="keyword">true</span>)</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  : m_matT(matrix.rows(),matrix.cols()),</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  m_matU(matrix.rows(),matrix.cols()),</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  m_hess(matrix.rows()),</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  m_isInitialized(false),</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  m_matUisUptodate(false),</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  m_maxIters(-1)</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  {</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21">compute</a>(matrix, computeU);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  }</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a name="l00137"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a6a4f89228ca0a093f34029706fd13aeb"> 137</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">ComplexMatrixType</a>& <a class="code" href="classEigen_1_1ComplexSchur.html#a6a4f89228ca0a093f34029706fd13aeb">matrixU</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ComplexSchur is not initialized."</span>);</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</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 name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">return</span> m_matU;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  }</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> </div>
<div class="line"><a name="l00161"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a868f6394b0c189a3ee3be039d9108095"> 161</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">ComplexMatrixType</a>& <a class="code" href="classEigen_1_1ComplexSchur.html#a868f6394b0c189a3ee3be039d9108095">matrixT</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ComplexSchur is not initialized."</span>);</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">return</span> m_matT;</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  }</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <a class="code" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>& <a class="code" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21">compute</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">bool</span> computeU = <span class="keyword">true</span>);</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  </div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keyword">template</span><<span class="keyword">typename</span> HessMatrixType, <span class="keyword">typename</span> OrthMatrixType></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <a class="code" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>& <a class="code" href="classEigen_1_1ComplexSchur.html#afd453e43385a3b38cb2ddd32d97c5eb7">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 name="l00210"></a><span class="lineno"> 210</span> </div>
<div class="line"><a name="l00215"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a0c06d5c2034ebb329c54235369643ad2"> 215</a></span>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> <a class="code" href="classEigen_1_1ComplexSchur.html#a0c06d5c2034ebb329c54235369643ad2">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"ComplexSchur is not initialized."</span>);</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  }</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span> </div>
<div class="line"><a name="l00226"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#a8178c4999e63b2bfbdc424ff84a91b10"> 226</a></span>  <a class="code" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a>& <a class="code" href="classEigen_1_1ComplexSchur.html#a8178c4999e63b2bfbdc424ff84a91b10">setMaxIterations</a>(Index maxIters)</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  {</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  m_maxIters = maxIters;</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  }</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a name="l00233"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#ab6f0a63ea1d26cef5e748207043eb43e"> 233</a></span>  Index <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>  <span class="keywordflow">return</span> m_maxIters;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  }</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> </div>
<div class="line"><a name="l00243"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#afdafb24d67af7529bb903a4c9bff3ea4"> 243</a></span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="classEigen_1_1ComplexSchur.html#afdafb24d67af7529bb903a4c9bff3ea4">m_maxIterationsPerRow</a> = 30;</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> </div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <a class="code" href="classEigen_1_1Matrix.html">ComplexMatrixType</a> m_matT, m_matU;</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <a class="code" href="classEigen_1_1HessenbergDecomposition.html">HessenbergDecomposition<MatrixType></a> m_hess;</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keywordtype">bool</span> m_matUisUptodate;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  Index m_maxIters;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> </div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keyword">private</span>: </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordtype">bool</span> subdiagonalEntryIsNeglegible(Index i);</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a> computeShift(Index iu, Index iter);</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordtype">void</span> reduceToTriangularForm(<span class="keywordtype">bool</span> computeU);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keyword">friend</span> <span class="keyword">struct </span>internal::complex_schur_reduce_to_hessenberg<MatrixType, <a class="code" href="structEigen_1_1NumTraits.html">NumTraits</a><<a class="code" href="classEigen_1_1ComplexSchur.html#a3f6fc00047c205ee590f676934aab28f">Scalar</a>>::IsComplex>;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> };</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> template<typename MatrixType></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> inline bool <a class="code" href="classEigen_1_1ComplexSchur.html">ComplexSchur</a><MatrixType>::subdiagonalEntryIsNeglegible(Index i)</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> {</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordflow">if</span> (internal::isMuchSmallerThan(sd, d, <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<RealScalar>::epsilon</a>()))</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  {</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  m_matT.coeffRef(i+1,i) = <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>(0);</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="keywordflow">return</span> <span class="keyword">true</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>  <span class="keywordflow">return</span> <span class="keyword">false</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> </div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> </div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexSchur<MatrixType>::ComplexScalar</a> ComplexSchur<MatrixType>::computeShift(Index iu, Index iter)</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span> {</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">if</span> (iter == 10 || iter == 20) </div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  {</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="comment">// exceptional shift, taken from http://www.netlib.org/eispack/comqr.f</span></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keywordflow">return</span> abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  }</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> </div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">// compute the shift as one of the eigenvalues of t, the 2x2</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">// diagonal block on the bottom of the active submatrix</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  Matrix<ComplexScalar,2,2> t = m_matT.template block<2,2>(iu-1,iu-1);</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  RealScalar normt = t.cwiseAbs().sum();</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  t /= normt; <span class="comment">// the normalization by sf is to avoid under/overflow</span></div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> </div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a> b = t.coeff(0,1) * t.coeff(1,0);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a> c = t.coeff(0,0) - t.coeff(1,1);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a> disc = sqrt(c*c + RealScalar(4)*b);</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a> det = t.coeff(0,0) * t.coeff(1,1) - b;</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a> trace = t.coeff(0,0) + t.coeff(1,1);</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a> eival1 = (trace + disc) / RealScalar(2);</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a> eival2 = (trace - disc) / RealScalar(2);</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>  <span class="keywordflow">if</span>(numext::norm1(eival1) > numext::norm1(eival2))</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  eival2 = det / eival1;</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  eival1 = det / eival2;</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> </div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="comment">// choose the eigenvalue closest to the bottom entry of the diagonal</span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</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 name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">return</span> normt * eival1;</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="keywordflow">return</span> normt * eival2;</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> </div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> </div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00316"></a><span class="lineno"><a class="line" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21"> 316</a></span> <a class="code" href="classEigen_1_1ComplexSchur.html">ComplexSchur<MatrixType></a>& <a class="code" href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21">ComplexSchur<MatrixType>::compute</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">bool</span> computeU)</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span> {</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  m_matUisUptodate = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  eigen_assert(matrix.cols() == matrix.rows());</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> </div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">if</span>(matrix.cols() == 1)</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>  m_matT = matrix.template cast<ComplexScalar>();</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="keywordflow">if</span>(computeU) m_matU = ComplexMatrixType::Identity(1,1);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  m_info = <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  m_matUisUptodate = computeU;</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keywordflow">return</span> *<span class="keyword">this</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>  internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*<span class="keyword">this</span>, matrix, computeU);</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <a class="code" href="classEigen_1_1ComplexSchur.html#afd453e43385a3b38cb2ddd32d97c5eb7">computeFromHessenberg</a>(m_matT, m_matU, computeU);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span> }</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="keyword">template</span><<span class="keyword">typename</span> HessMatrixType, <span class="keyword">typename</span> OrthMatrixType></div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <a class="code" href="classEigen_1_1ComplexSchur.html">ComplexSchur<MatrixType></a>& <a class="code" href="classEigen_1_1ComplexSchur.html#afd453e43385a3b38cb2ddd32d97c5eb7">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 name="l00339"></a><span class="lineno"> 339</span> {</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  m_matT = matrixH;</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordflow">if</span>(computeU)</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  m_matU = matrixQ;</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  reduceToTriangularForm(computeU);</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> }</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> </div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment">/* Reduce given matrix to Hessenberg form */</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">bool</span> IsComplex></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="keyword">struct </span>complex_schur_reduce_to_hessenberg</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span> {</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <span class="comment">// this is the implementation for the case IsComplex = true</span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</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 name="l00354"></a><span class="lineno"> 354</span>  {</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  _this.m_hess.compute(matrix);</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  _this.m_matT = _this.m_hess.matrixH();</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="keywordflow">if</span>(computeU) _this.m_matU = _this.m_hess.matrixQ();</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  }</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span> };</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> </div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="keyword">struct </span>complex_schur_reduce_to_hessenberg<MatrixType, false></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> {</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</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 name="l00365"></a><span class="lineno"> 365</span>  {</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexSchur<MatrixType>::ComplexScalar</a> <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>;</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> </div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="comment">// Note: m_hess is over RealScalar; m_matT and m_matU is over ComplexScalar</span></div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  _this.m_hess.compute(matrix);</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  _this.m_matT = _this.m_hess.matrixH().template cast<ComplexScalar>();</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keywordflow">if</span>(computeU) </div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  {</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="comment">// This may cause an allocation which seems to be avoidable</span></div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  MatrixType Q = _this.m_hess.matrixQ(); </div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  _this.m_matU = Q.template cast<ComplexScalar>();</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  }</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  }</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> };</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> </div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> </div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="comment">// Reduce the Hessenberg matrix m_matT to triangular form by QR iteration.</span></div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="keywordtype">void</span> ComplexSchur<MatrixType>::reduceToTriangularForm(<span class="keywordtype">bool</span> computeU)</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> { </div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  Index maxIters = m_maxIters;</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <span class="keywordflow">if</span> (maxIters == -1)</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  maxIters = <a class="code" href="classEigen_1_1ComplexSchur.html#afdafb24d67af7529bb903a4c9bff3ea4">m_maxIterationsPerRow</a> * m_matT.rows();</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span> </div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="comment">// The matrix m_matT is divided in three parts. </span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</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 name="l00392"></a><span class="lineno"> 392</span>  <span class="comment">// Rows il,...,iu is the part we are working on (the active submatrix).</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="comment">// Rows iu+1,...,end are already brought in triangular form.</span></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  Index iu = m_matT.cols() - 1;</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  Index il;</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  Index iter = 0; <span class="comment">// number of iterations we are working on the (iu,iu) element</span></div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  Index totalIter = 0; <span class="comment">// number of iterations for whole matrix</span></div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="keywordflow">while</span>(<span class="keyword">true</span>)</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  {</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="comment">// find iu, the bottom row of the active submatrix</span></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="keywordflow">while</span>(iu > 0)</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  {</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keywordflow">if</span>(!subdiagonalEntryIsNeglegible(iu-1)) <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  iter = 0;</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  --iu;</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  }</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span> </div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="comment">// if iu is zero then we are done; the whole matrix is triangularized</span></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <span class="keywordflow">if</span>(iu==0) <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> </div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="comment">// if we spent too many iterations, we give up</span></div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  iter++;</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  totalIter++;</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <span class="keywordflow">if</span>(totalIter > maxIters) <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> </div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="comment">// find il, the top row of the active submatrix</span></div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  il = iu-1;</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <span class="keywordflow">while</span>(il > 0 && !subdiagonalEntryIsNeglegible(il-1))</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  {</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  --il;</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  }</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span> </div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <span class="comment">/* perform the QR step using Givens rotations. The first rotation</span></div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment"> creates a bulge; the (il+2,il) element becomes nonzero. This</span></div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment"> bulge is chased down to the bottom of the active submatrix. */</span></div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> </div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  ComplexScalar shift = computeShift(iu, iter);</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  JacobiRotation<ComplexScalar> rot;</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  rot.makeGivens(m_matT.coeff(il,il) - shift, m_matT.coeff(il+1,il));</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  m_matT.topRows((std::min)(il+2,iu)+1).applyOnTheRight(il, il+1, rot);</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <span class="keywordflow">if</span>(computeU) m_matU.applyOnTheRight(il, il+1, rot);</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> </div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keywordflow">for</span>(Index i=il+1 ; i<iu ; i++)</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  {</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  rot.makeGivens(m_matT.coeffRef(i,i-1), m_matT.coeffRef(i+1,i-1), &m_matT.coeffRef(i,i-1));</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  m_matT.coeffRef(i+1,i-1) = <a class="code" href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">ComplexScalar</a>(0);</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  m_matT.topRows((std::min)(i+2,iu)+1).applyOnTheRight(i, i+1, rot);</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="keywordflow">if</span>(computeU) m_matU.applyOnTheRight(i, i+1, rot);</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  }</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  }</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span> </div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="keywordflow">if</span>(totalIter <= maxIters)</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  m_info = <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>;</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  m_info = <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037ba4ff235bd185f3c5fceeec8d6540eb847">NoConvergence</a>;</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span> </div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  m_matUisUptodate = computeU;</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span> }</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span> </div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span> </div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span> <span class="preprocessor">#endif // EIGEN_COMPLEX_SCHUR_H</span></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_a797849e56b60a3cb8f80ac23e3eb73f9"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a797849e56b60a3cb8f80ac23e3eb73f9">Eigen::ComplexSchur::ComplexSchur</a></div><div class="ttdeci">ComplexSchur(const MatrixType &matrix, bool computeU=true)</div><div class="ttdoc">Constructor; computes Schur decomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> ComplexSchur.h:112</div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_afdafb24d67af7529bb903a4c9bff3ea4"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#afdafb24d67af7529bb903a4c9bff3ea4">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:243</div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_a1333fc417f8ad137effb6a7f751337e5"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a1333fc417f8ad137effb6a7f751337e5">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:81</div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_af6c75391a881ca5e56d9aac55f838e21"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#af6c75391a881ca5e56d9aac55f838e21">Eigen::ComplexSchur::compute</a></div><div class="ttdeci">ComplexSchur & compute(const MatrixType &matrix, bool computeU=true)</div><div class="ttdoc">Computes Schur decomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> ComplexSchur.h:316</div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_a9ba3a59c1e385a4a5a80c08bf40f8fd1"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a9ba3a59c1e385a4a5a80c08bf40f8fd1">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:94</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_1ComplexSchur_html_afd453e43385a3b38cb2ddd32d97c5eb7"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#afd453e43385a3b38cb2ddd32d97c5eb7">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="namespaceEigen_html_adc9da5be31bdce40c25a92c27999c0e3"><div class="ttname"><a href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:21</div></div>
<div class="ttc" id="classEigen_1_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_1ComplexSchur_html_a3f6fc00047c205ee590f676934aab28f"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a3f6fc00047c205ee590f676934aab28f">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:64</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_1HessenbergDecomposition_html"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html">Eigen::HessenbergDecomposition< MatrixType ></a></div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_a6a4f89228ca0a093f34029706fd13aeb"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a6a4f89228ca0a093f34029706fd13aeb">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:137</div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_a868f6394b0c189a3ee3be039d9108095"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a868f6394b0c189a3ee3be039d9108095">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:161</div></div>
<div class="ttc" id="classEigen_1_1ComplexSchur_html_a1b9bc0a45616064df3a6168395e3cfcc"><div class="ttname"><a href="classEigen_1_1ComplexSchur.html#a1b9bc0a45616064df3a6168395e3cfcc">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:74</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037ba4ff235bd185f3c5fceeec8d6540eb847"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037ba4ff235bd185f3c5fceeec8d6540eb847">Eigen::NoConvergence</a></div><div class="ttdef"><b>Definition:</b> Constants.h:380</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_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix< ComplexScalar, RowsAtCompileTime, ColsAtCompileTime, Options, MaxRowsAtCompileTime, MaxColsAtCompileTime ></a></div></div>
<div class="ttc" id="classEigen_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:51</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>
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