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<div class="title">MatrixBaseEigenvalues.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#ifndef EIGEN_MATRIXBASEEIGENVALUES_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MATRIXBASEEIGENVALUES_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived, <span class="keywordtype">bool</span> IsComplex></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">struct </span>eigenvalues_selector</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> {</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  <span class="comment">// this is the implementation for the case IsComplex = true</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> MatrixBase<Derived>::EigenvaluesReturnType <span class="keyword">const</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  run(<span class="keyword">const</span> MatrixBase<Derived>& m)</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject PlainObject;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  PlainObject m_eval(m);</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keywordflow">return</span> ComplexEigenSolver<PlainObject>(m_eval, <span class="keyword">false</span>).eigenvalues();</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  }</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> };</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">struct </span>eigenvalues_selector<Derived, false></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> MatrixBase<Derived>::EigenvaluesReturnType <span class="keyword">const</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  run(<span class="keyword">const</span> MatrixBase<Derived>& m)</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject PlainObject;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  PlainObject m_eval(m);</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordflow">return</span> EigenSolver<PlainObject>(m_eval, <span class="keyword">false</span>).eigenvalues();</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  }</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> };</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> </div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">inline</span> <span class="keyword">typename</span> MatrixBase<Derived>::EigenvaluesReturnType</div>
<div class="line"><a name="l00067"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0ffa061371b1bd1b9f14ecef94b4502e"> 67</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#a0ffa061371b1bd1b9f14ecef94b4502e">MatrixBase<Derived>::eigenvalues</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::traits<Derived>::Scalar Scalar;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">return</span> internal::eigenvalues_selector<Derived, NumTraits<Scalar>::IsComplex>::run(derived());</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UpLo> </div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="keyword">inline</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">SelfAdjointView<MatrixType, UpLo>::EigenvaluesReturnType</a></div>
<div class="line"><a name="l00089"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointView.html#a847d0db612cd20e1b796c6a70d0f0d54"> 89</a></span> <a class="code" href="classEigen_1_1SelfAdjointView.html#a847d0db612cd20e1b796c6a70d0f0d54">SelfAdjointView<MatrixType, UpLo>::eigenvalues</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SelfAdjointView<MatrixType, UpLo>::PlainObject PlainObject;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  PlainObject thisAsMatrix(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1SelfAdjointEigenSolver.html">SelfAdjointEigenSolver<PlainObject></a>(thisAsMatrix, <span class="keyword">false</span>).eigenvalues();</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> }</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="keyword">inline</span> <span class="keyword">typename</span> MatrixBase<Derived>::RealScalar</div>
<div class="line"><a name="l00122"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0650a523c77a498a88b4998809d0bd14"> 122</a></span> <a class="code" href="classEigen_1_1MatrixBase.html#a0650a523c77a498a88b4998809d0bd14">MatrixBase<Derived>::operatorNorm</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keyword">typename</span> Derived::PlainObject m_eval(derived());</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">// FIXME if it is really guaranteed that the eigenvalues are already sorted,</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="comment">// then we don't need to compute a maxCoeff() here, comparing the 1st and last ones is enough.</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> sqrt((m_eval*m_eval.adjoint())</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  .eval()</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  .template selfadjointView<Lower>()</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  .eigenvalues()</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  .maxCoeff()</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  );</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> }</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> </div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UpLo></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="keyword">inline</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1SelfAdjointView.html#acb5c3dc237f99cf17167e8a629f01b43">SelfAdjointView<MatrixType, UpLo>::RealScalar</a></div>
<div class="line"><a name="l00153"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointView.html#a67279bc5b39fba3763acabf1d52ecad8"> 153</a></span> <a class="code" href="classEigen_1_1SelfAdjointView.html#a67279bc5b39fba3763acabf1d52ecad8">SelfAdjointView<MatrixType, UpLo>::operatorNorm</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">return</span> eigenvalues().cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> }</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a0650a523c77a498a88b4998809d0bd14"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a0650a523c77a498a88b4998809d0bd14">Eigen::MatrixBase::operatorNorm</a></div><div class="ttdeci">RealScalar operatorNorm() const </div><div class="ttdoc">Computes the L2 operator norm. </div><div class="ttdef"><b>Definition:</b> MatrixBaseEigenvalues.h:122</div></div>
<div class="ttc" id="classEigen_1_1SelfAdjointEigenSolver_html"><div class="ttname"><a href="classEigen_1_1SelfAdjointEigenSolver.html">Eigen::SelfAdjointEigenSolver</a></div><div class="ttdoc">Computes eigenvalues and eigenvectors of selfadjoint matrices. </div><div class="ttdef"><b>Definition:</b> SelfAdjointEigenSolver.h:68</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a0ffa061371b1bd1b9f14ecef94b4502e"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a0ffa061371b1bd1b9f14ecef94b4502e">Eigen::MatrixBase::eigenvalues</a></div><div class="ttdeci">EigenvaluesReturnType eigenvalues() const </div><div class="ttdoc">Computes the eigenvalues of a matrix. </div><div class="ttdef"><b>Definition:</b> MatrixBaseEigenvalues.h:67</div></div>
<div class="ttc" id="classEigen_1_1SelfAdjointView_html_acb5c3dc237f99cf17167e8a629f01b43"><div class="ttname"><a href="classEigen_1_1SelfAdjointView.html#acb5c3dc237f99cf17167e8a629f01b43">Eigen::SelfAdjointView::RealScalar</a></div><div class="ttdeci">NumTraits< Scalar >::Real RealScalar</div><div class="ttdef"><b>Definition:</b> SelfAdjointView.h:158</div></div>
<div class="ttc" id="classEigen_1_1SelfAdjointView_html_a847d0db612cd20e1b796c6a70d0f0d54"><div class="ttname"><a href="classEigen_1_1SelfAdjointView.html#a847d0db612cd20e1b796c6a70d0f0d54">Eigen::SelfAdjointView::eigenvalues</a></div><div class="ttdeci">EigenvaluesReturnType eigenvalues() const </div><div class="ttdoc">Computes the eigenvalues of a matrix. </div><div class="ttdef"><b>Definition:</b> MatrixBaseEigenvalues.h:89</div></div>
<div class="ttc" id="classEigen_1_1SelfAdjointView_html_a67279bc5b39fba3763acabf1d52ecad8"><div class="ttname"><a href="classEigen_1_1SelfAdjointView.html#a67279bc5b39fba3763acabf1d52ecad8">Eigen::SelfAdjointView::operatorNorm</a></div><div class="ttdeci">RealScalar operatorNorm() const </div><div class="ttdoc">Computes the L2 operator norm. </div><div class="ttdef"><b>Definition:</b> MatrixBaseEigenvalues.h:153</div></div>
<div class="ttc" id="classEigen_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:127</div></div>
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