<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.5"/>
<title>Eigen-unsupported: MatrixFunction.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<script type="text/javascript">
$(document).ready(initResizable);
$(window).load(resizeHeight);
</script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
$(document).ready(function() { searchBox.OnSelectItem(0); });
</script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="eigendoxy.css" rel="stylesheet" type="text/css">
<!-- -->
<script type="text/javascript" src="eigen_navtree_hacks.js"></script>
<!-- <script type="text/javascript"> -->
<!-- </script> -->
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<!-- <a name="top"></a> -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td id="projectlogo"><img alt="Logo" src="Eigen_Silly_Professor_64x64.png"/></td>
<td style="padding-left: 0.5em;">
<div id="projectname"><a href="http://eigen.tuxfamily.org">Eigen-unsupported</a>
 <span id="projectnumber">3.2.0</span>
</div>
</td>
<td> <div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<img id="MSearchSelect" src="search/mag_sel.png"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
alt=""/>
<input type="text" id="MSearchField" value="Search" accesskey="S"
onfocus="searchBox.OnSearchFieldFocus(true)"
onblur="searchBox.OnSearchFieldFocus(false)"
onkeyup="searchBox.OnSearchFieldChange(event)"/>
</span><span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.5 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "search",false,'Search');
</script>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
$(document).ready(function(){initNavTree('MatrixFunction_8h_source.html','');});
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
<a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(0)"><span class="SelectionMark"> </span>All</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(1)"><span class="SelectionMark"> </span>Classes</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(2)"><span class="SelectionMark"> </span>Namespaces</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(3)"><span class="SelectionMark"> </span>Functions</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(4)"><span class="SelectionMark"> </span>Variables</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(5)"><span class="SelectionMark"> </span>Typedefs</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(6)"><span class="SelectionMark"> </span>Enumerator</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(7)"><span class="SelectionMark"> </span>Groups</a><a class="SelectItem" href="javascript:void(0)" onclick="searchBox.OnSelectItem(8)"><span class="SelectionMark"> </span>Pages</a></div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0"
name="MSearchResults" id="MSearchResults">
</iframe>
</div>
<div class="header">
<div class="headertitle">
<div class="title">MatrixFunction.h</div> </div>
</div><!--header-->
<div class="contents">
<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) 2009-2011 Jitse Niesen <jitse@maths.leeds.ac.uk></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</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="l00008"></a><span class="lineno"> 8</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="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_MATRIX_FUNCTION</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MATRIX_FUNCTION</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#include "StemFunction.h"</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include "MatrixFunctionAtomic.h"</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </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="l00034"></a><span class="lineno"> 34</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">typename</span> AtomicType, </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keywordtype">int</span> IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex></div>
<div class="line"><a name="l00037"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixFunction.html"> 37</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixFunction.html">MatrixFunction</a></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> { </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <a class="code" href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">MatrixFunction</a>(<span class="keyword">const</span> MatrixType& A, AtomicType& atomic);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> </div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType> </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixFunction.html#a37407499d669c7dd9af708e7dd6f9217">compute</a>(ResultType &result); </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="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixFunction.html">MatrixFunction</a><MatrixType, AtomicType, 0></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> { </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">private</span>:</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>  <span class="keyword">typedef</span> internal::traits<MatrixType> Traits;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Traits::Scalar Scalar;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> Rows = Traits::RowsAtCompileTime;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> Cols = Traits::ColsAtCompileTime;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> Options = MatrixType::Options;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> MaxRows = Traits::MaxRowsAtCompileTime;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> MaxCols = Traits::MaxColsAtCompileTime;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keyword">typedef</span> std::complex<Scalar> ComplexScalar;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keyword">typedef</span> Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols> ComplexMatrix;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <a class="code" href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">MatrixFunction</a>(<span class="keyword">const</span> MatrixType& A, AtomicType& atomic) : m_A(A), m_atomic(atomic) { }</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixFunction.html#a37407499d669c7dd9af708e7dd6f9217">compute</a>(ResultType& result) </div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  {</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  ComplexMatrix CA = m_A.template cast<ComplexScalar>();</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  ComplexMatrix Cresult;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  MatrixFunction<ComplexMatrix, AtomicType> mf(CA, m_atomic);</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  mf.compute(Cresult);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  result = Cresult.real();</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  }</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> </div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keyword">typename</span> internal::nested<MatrixType>::type m_A; </div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  AtomicType& m_atomic; </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <a class="code" href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">MatrixFunction</a>& operator=(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">MatrixFunction</a>&);</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> };</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="keyword">class </span>MatrixFunction<MatrixType, AtomicType, 1></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> {</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> </div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keyword">typedef</span> internal::traits<MatrixType> Traits;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> RowsAtCompileTime = Traits::RowsAtCompileTime;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> ColsAtCompileTime = Traits::ColsAtCompileTime;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> Options = MatrixType::Options;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keyword">typedef</span> Matrix<Scalar, Traits::RowsAtCompileTime, 1> VectorType;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keyword">typedef</span> Matrix<Index, Traits::RowsAtCompileTime, 1> IntVectorType;</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="keyword">typedef</span> Matrix<Index, Dynamic, 1> DynamicIntVectorType;</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keyword">typedef</span> std::list<Scalar> Cluster;</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keyword">typedef</span> std::list<Cluster> ListOfClusters;</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keyword">typedef</span> Matrix<Scalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keyword">public</span>:</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>  <a class="code" href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">MatrixFunction</a>(<span class="keyword">const</span> MatrixType& A, AtomicType& atomic);</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixFunction.html#a37407499d669c7dd9af708e7dd6f9217">compute</a>(ResultType& result);</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordtype">void</span> computeSchurDecomposition();</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordtype">void</span> partitionEigenvalues();</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">typename</span> ListOfClusters::iterator findCluster(Scalar key);</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordtype">void</span> computeClusterSize();</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordtype">void</span> computeBlockStart();</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keywordtype">void</span> constructPermutation();</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keywordtype">void</span> permuteSchur();</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordtype">void</span> swapEntriesInSchur(Index index);</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordtype">void</span> computeBlockAtomic();</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  Block<MatrixType> block(MatrixType& A, Index i, Index j);</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordtype">void</span> computeOffDiagonal();</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  DynMatrixType solveTriangularSylvester(<span class="keyword">const</span> DynMatrixType& A, <span class="keyword">const</span> DynMatrixType& B, <span class="keyword">const</span> DynMatrixType& C);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keyword">typename</span> internal::nested<MatrixType>::type m_A; </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  AtomicType& m_atomic; </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  MatrixType m_T; </div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  MatrixType m_U; </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  MatrixType m_fT; </div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  ListOfClusters m_clusters; </div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  DynamicIntVectorType m_eivalToCluster; </div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  DynamicIntVectorType m_clusterSize; </div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  DynamicIntVectorType m_blockStart; </div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  IntVectorType m_permutation; </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keyword">static</span> <span class="keyword">const</span> RealScalar separation() { <span class="keywordflow">return</span> <span class="keyword">static_cast<</span>RealScalar<span class="keyword">></span>(0.1); }</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> </div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <a class="code" href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">MatrixFunction</a>& operator=(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">MatrixFunction</a>&);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> };</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <a class="code" href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">MatrixFunction<MatrixType,AtomicType,1>::MatrixFunction</a>(<span class="keyword">const</span> MatrixType& A, AtomicType& atomic)</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  : m_A(A), m_atomic(atomic)</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> {</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="comment">/* empty body */</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> }</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixFunction.html#a37407499d669c7dd9af708e7dd6f9217">MatrixFunction<MatrixType,AtomicType,1>::compute</a>(ResultType& result) </div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> {</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  computeSchurDecomposition();</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  partitionEigenvalues();</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  computeClusterSize();</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  computeBlockStart();</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  constructPermutation();</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  permuteSchur();</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  computeBlockAtomic();</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  computeOffDiagonal();</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  result = m_U * (m_fT.template triangularView<Upper>() * m_U.adjoint());</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> }</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::computeSchurDecomposition()</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> {</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keyword">const</span> ComplexSchur<MatrixType> schurOfA(m_A); </div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  m_T = schurOfA.matrixT();</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  m_U = schurOfA.matrixU();</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> }</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span> </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues()</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> {</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keyword">const</span> Index rows = m_T.rows();</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  VectorType diag = m_T.diagonal(); <span class="comment">// contains eigenvalues of A</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> </div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordflow">for</span> (Index i=0; i<rows; ++i) {</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="comment">// Find set containing diag(i), adding a new set if necessary</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keyword">typename</span> ListOfClusters::iterator qi = findCluster(diag(i));</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordflow">if</span> (qi == m_clusters.end()) {</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  Cluster l;</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  l.push_back(diag(i));</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  m_clusters.push_back(l);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  qi = m_clusters.end();</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  --qi;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  }</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="comment">// Look for other element to add to the set</span></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">for</span> (Index j=i+1; j<rows; ++j) {</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <span class="keywordflow">if</span> (abs(diag(j) - diag(i)) <= separation() && std::find(qi->begin(), qi->end(), diag(j)) == qi->end()) {</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keyword">typename</span> ListOfClusters::iterator qj = findCluster(diag(j));</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keywordflow">if</span> (qj == m_clusters.end()) {</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  qi->push_back(diag(j));</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  qi->insert(qi->end(), qj->begin(), qj->end());</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  m_clusters.erase(qj);</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  }</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  }</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  }</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  }</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> }</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span> </div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="keyword">typename</span> MatrixFunction<MatrixType,AtomicType,1>::ListOfClusters::iterator MatrixFunction<MatrixType,AtomicType,1>::findCluster(Scalar key)</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>  <span class="keyword">typename</span> Cluster::iterator j;</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> ListOfClusters::iterator i = m_clusters.begin(); i != m_clusters.end(); ++i) {</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  j = std::find(i->begin(), i->end(), key);</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordflow">if</span> (j != i->end())</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">return</span> i;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  }</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="keywordflow">return</span> m_clusters.end();</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> </div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::computeClusterSize()</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span> {</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keyword">const</span> Index rows = m_T.rows();</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  VectorType diag = m_T.diagonal(); </div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keyword">const</span> Index numClusters = <span class="keyword">static_cast<</span>Index<span class="keyword">></span>(m_clusters.size());</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> </div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  m_clusterSize.setZero(numClusters);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  m_eivalToCluster.resize(rows);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  Index clusterIndex = 0;</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> ListOfClusters::const_iterator cluster = m_clusters.begin(); cluster != m_clusters.end(); ++cluster) {</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">for</span> (Index i = 0; i < diag.rows(); ++i) {</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="keywordflow">if</span> (std::find(cluster->begin(), cluster->end(), diag(i)) != cluster->end()) {</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  ++m_clusterSize[clusterIndex];</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  m_eivalToCluster[i] = clusterIndex;</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  }</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  }</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  ++clusterIndex;</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  }</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> }</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::computeBlockStart()</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> {</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  m_blockStart.resize(m_clusterSize.rows());</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  m_blockStart(0) = 0;</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordflow">for</span> (Index i = 1; i < m_clusterSize.rows(); i++) {</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  m_blockStart(i) = m_blockStart(i-1) + m_clusterSize(i-1);</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  }</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span> }</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span> </div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::constructPermutation()</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> {</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  DynamicIntVectorType indexNextEntry = m_blockStart;</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  m_permutation.resize(m_T.rows());</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="keywordflow">for</span> (Index i = 0; i < m_T.rows(); i++) {</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  Index cluster = m_eivalToCluster[i];</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  m_permutation[i] = indexNextEntry[cluster];</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  ++indexNextEntry[cluster];</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  }</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> } </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> </div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::permuteSchur()</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>  IntVectorType p = m_permutation;</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">for</span> (Index i = 0; i < p.rows() - 1; i++) {</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  Index j;</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <span class="keywordflow">for</span> (j = i; j < p.rows(); j++) {</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keywordflow">if</span> (p(j) == i) <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  }</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  eigen_assert(p(j) == i);</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">for</span> (Index k = j-1; k >= i; k--) {</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  swapEntriesInSchur(k);</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  std::swap(p.coeffRef(k), p.coeffRef(k+1));</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>  }</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> </div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::swapEntriesInSchur(Index index)</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> {</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  JacobiRotation<Scalar> rotation;</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  rotation.makeGivens(m_T(index, index+1), m_T(index+1, index+1) - m_T(index, index));</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  m_T.applyOnTheLeft(index, index+1, rotation.adjoint());</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  m_T.applyOnTheRight(index, index+1, rotation);</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  m_U.applyOnTheRight(index, index+1, rotation);</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="l00366"></a><span class="lineno"> 366</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::computeBlockAtomic()</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> { </div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  m_fT.resize(m_T.rows(), m_T.cols());</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  m_fT.setZero();</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keywordflow">for</span> (Index i = 0; i < m_clusterSize.rows(); ++i) {</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  block(m_fT, i, i) = m_atomic.compute(block(m_T, i, i));</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  }</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> }</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> </div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> Block<MatrixType> MatrixFunction<MatrixType,AtomicType,1>::block(MatrixType& A, Index i, Index j)</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="keywordflow">return</span> A.block(m_blockStart(i), m_blockStart(j), m_clusterSize(i), m_clusterSize(j));</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> </div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span> <span class="keywordtype">void</span> MatrixFunction<MatrixType,AtomicType,1>::computeOffDiagonal()</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span> { </div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="keywordflow">for</span> (Index diagIndex = 1; diagIndex < m_clusterSize.rows(); diagIndex++) {</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordflow">for</span> (Index blockIndex = 0; blockIndex < m_clusterSize.rows() - diagIndex; blockIndex++) {</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  <span class="comment">// compute (blockIndex, blockIndex+diagIndex) block</span></div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  DynMatrixType A = block(m_T, blockIndex, blockIndex);</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  DynMatrixType B = -block(m_T, blockIndex+diagIndex, blockIndex+diagIndex);</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  DynMatrixType C = block(m_fT, blockIndex, blockIndex) * block(m_T, blockIndex, blockIndex+diagIndex);</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  C -= block(m_T, blockIndex, blockIndex+diagIndex) * block(m_fT, blockIndex+diagIndex, blockIndex+diagIndex);</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  <span class="keywordflow">for</span> (Index k = blockIndex + 1; k < blockIndex + diagIndex; k++) {</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  C += block(m_fT, blockIndex, k) * block(m_T, k, blockIndex+diagIndex);</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  C -= block(m_T, blockIndex, k) * block(m_fT, k, blockIndex+diagIndex);</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>  block(m_fT, blockIndex, blockIndex+diagIndex) = solveTriangularSylvester(A, B, C);</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  }</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  }</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="l00432"></a><span class="lineno"> 432</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> AtomicType></div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="keyword">typename</span> MatrixFunction<MatrixType,AtomicType,1>::DynMatrixType MatrixFunction<MatrixType,AtomicType,1>::solveTriangularSylvester(</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  <span class="keyword">const</span> DynMatrixType& A, </div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keyword">const</span> DynMatrixType& B, </div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keyword">const</span> DynMatrixType& C)</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> {</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  eigen_assert(A.rows() == A.cols());</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  eigen_assert(A.isUpperTriangular());</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  eigen_assert(B.rows() == B.cols());</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  eigen_assert(B.isUpperTriangular());</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  eigen_assert(C.rows() == A.rows());</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  eigen_assert(C.cols() == B.rows());</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>  Index m = A.rows();</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  Index n = B.rows();</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  DynMatrixType X(m, n);</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span> </div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">for</span> (Index i = m - 1; i >= 0; --i) {</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j) {</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> </div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="comment">// Compute AX = \sum_{k=i+1}^m A_{ik} X_{kj}</span></div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  Scalar AX;</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="keywordflow">if</span> (i == m - 1) {</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  AX = 0; </div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  Matrix<Scalar,1,1> AXmatrix = A.row(i).tail(m-1-i) * X.col(j).tail(m-1-i);</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  AX = AXmatrix(0,0);</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  }</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span> </div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <span class="comment">// Compute XB = \sum_{k=1}^{j-1} X_{ik} B_{kj}</span></div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  Scalar XB;</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="keywordflow">if</span> (j == 0) {</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  XB = 0; </div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  Matrix<Scalar,1,1> XBmatrix = X.row(i).head(j) * B.col(j).head(j);</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  XB = XBmatrix(0,0);</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  }</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span> </div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  X(i,j) = (C(i,j) - AX - XB) / (A(i,i) + B(j,j));</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  }</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  }</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="keywordflow">return</span> X;</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> }</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span> </div>
<div class="line"><a name="l00488"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixFunctionReturnValue.html"> 488</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixFunctionReturnValue.html">MatrixFunctionReturnValue</a></div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span> : <span class="keyword">public</span> ReturnByValue<MatrixFunctionReturnValue<Derived> ></div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span> {</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> </div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::Scalar Scalar;</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::Index Index;</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::stem_function<Scalar>::type StemFunction;</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> </div>
<div class="line"><a name="l00503"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixFunctionReturnValue.html#a43b73b3470694f1eb5a265a36fd730e0"> 503</a></span>  <a class="code" href="classEigen_1_1MatrixFunctionReturnValue.html#a43b73b3470694f1eb5a265a36fd730e0">MatrixFunctionReturnValue</a>(<span class="keyword">const</span> Derived& A, StemFunction f) : m_A(A), m_f(f) { }</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span> </div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00511"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixFunctionReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766"> 511</a></span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixFunctionReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766">evalTo</a>(ResultType& result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject PlainObject;</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keyword">typedef</span> internal::traits<PlainObject> Traits;</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> RowsAtCompileTime = Traits::RowsAtCompileTime;</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> ColsAtCompileTime = Traits::ColsAtCompileTime;</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> Options = PlainObject::Options;</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <span class="keyword">typedef</span> std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keyword">typedef</span> Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1MatrixFunctionAtomic.html">MatrixFunctionAtomic<DynMatrixType></a> AtomicType;</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  AtomicType atomic(m_f);</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> </div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="keyword">const</span> PlainObject Aevaluated = m_A.eval();</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <a class="code" href="classEigen_1_1MatrixFunction.html">MatrixFunction<PlainObject, AtomicType></a> mf(Aevaluated, atomic);</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  mf.compute(result);</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  }</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span> </div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.rows(); }</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.cols(); }</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span> </div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  <span class="keyword">typename</span> internal::nested<Derived>::type m_A;</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  StemFunction *m_f;</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> </div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <a class="code" href="classEigen_1_1MatrixFunctionReturnValue.html#a43b73b3470694f1eb5a265a36fd730e0">MatrixFunctionReturnValue</a>& operator=(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixFunctionReturnValue.html#a43b73b3470694f1eb5a265a36fd730e0">MatrixFunctionReturnValue</a>&);</div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span> };</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span> </div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span> <span class="keyword">struct </span>traits<MatrixFunctionReturnValue<Derived> ></div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> {</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject ReturnType;</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span> };</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span> }</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span> </div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span> </div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span> <span class="comment">/********** MatrixBase methods **********/</span></div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span> </div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span> </div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span> <span class="keyword">const</span> MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::matrixFunction(<span class="keyword">typename</span> internal::stem_function<<span class="keyword">typename</span> internal::traits<Derived>::Scalar>::type f)<span class="keyword"> const</span></div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  eigen_assert(rows() == cols());</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <span class="keywordflow">return</span> MatrixFunctionReturnValue<Derived>(derived(), f);</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span> }</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span> </div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="keyword">const</span> MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin()<span class="keyword"> const</span></div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  eigen_assert(rows() == cols());</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::stem_function<Scalar>::ComplexScalar ComplexScalar;</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="keywordflow">return</span> MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::sin);</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span> }</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span> </div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="keyword">const</span> MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos()<span class="keyword"> const</span></div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  eigen_assert(rows() == cols());</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::stem_function<Scalar>::ComplexScalar ComplexScalar;</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  <span class="keywordflow">return</span> MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::cos);</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span> }</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span> </div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span> <span class="keyword">const</span> MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sinh()<span class="keyword"> const</span></div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  eigen_assert(rows() == cols());</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::stem_function<Scalar>::ComplexScalar ComplexScalar;</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  <span class="keywordflow">return</span> MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::sinh);</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span> }</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span> </div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span> <span class="keyword">const</span> MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cosh()<span class="keyword"> const</span></div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  eigen_assert(rows() == cols());</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::stem_function<Scalar>::ComplexScalar ComplexScalar;</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="keywordflow">return</span> MatrixFunctionReturnValue<Derived>(derived(), StdStemFunctions<ComplexScalar>::cosh);</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span> }</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span> </div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span> </div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span> <span class="preprocessor">#endif // EIGEN_MATRIX_FUNCTION</span></div>
<div class="ttc" id="classEigen_1_1MatrixFunction_html_abf20da56863c164e96044d60b9b8d407"><div class="ttname"><a href="classEigen_1_1MatrixFunction.html#abf20da56863c164e96044d60b9b8d407">Eigen::MatrixFunction::MatrixFunction</a></div><div class="ttdeci">MatrixFunction(const MatrixType &A, AtomicType &atomic)</div><div class="ttdoc">Constructor. </div></div>
<div class="ttc" id="classEigen_1_1MatrixFunction_html"><div class="ttname"><a href="classEigen_1_1MatrixFunction.html">Eigen::MatrixFunction</a></div><div class="ttdoc">Class for computing matrix functions. </div><div class="ttdef"><b>Definition:</b> MatrixFunction.h:37</div></div>
<div class="ttc" id="classEigen_1_1MatrixFunctionReturnValue_html"><div class="ttname"><a href="classEigen_1_1MatrixFunctionReturnValue.html">Eigen::MatrixFunctionReturnValue</a></div><div class="ttdoc">Proxy for the matrix function of some matrix (expression). </div><div class="ttdef"><b>Definition:</b> MatrixFunction.h:488</div></div>
<div class="ttc" id="classEigen_1_1MatrixFunction_html_a37407499d669c7dd9af708e7dd6f9217"><div class="ttname"><a href="classEigen_1_1MatrixFunction.html#a37407499d669c7dd9af708e7dd6f9217">Eigen::MatrixFunction::compute</a></div><div class="ttdeci">void compute(ResultType &result)</div><div class="ttdoc">Compute the matrix function. </div></div>
<div class="ttc" id="classEigen_1_1MatrixFunctionAtomic_html"><div class="ttname"><a href="classEigen_1_1MatrixFunctionAtomic.html">Eigen::MatrixFunctionAtomic</a></div><div class="ttdoc">Helper class for computing matrix functions of atomic matrices. </div><div class="ttdef"><b>Definition:</b> MatrixFunctionAtomic.h:24</div></div>
<div class="ttc" id="classEigen_1_1MatrixFunctionReturnValue_html_a4f4ce27ebcf7fe1e0078d20d0393c766"><div class="ttname"><a href="classEigen_1_1MatrixFunctionReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766">Eigen::MatrixFunctionReturnValue::evalTo</a></div><div class="ttdeci">void evalTo(ResultType &result) const </div><div class="ttdoc">Compute the matrix function. </div><div class="ttdef"><b>Definition:</b> MatrixFunction.h:511</div></div>
<div class="ttc" id="classEigen_1_1MatrixFunctionReturnValue_html_a43b73b3470694f1eb5a265a36fd730e0"><div class="ttname"><a href="classEigen_1_1MatrixFunctionReturnValue.html#a43b73b3470694f1eb5a265a36fd730e0">Eigen::MatrixFunctionReturnValue::MatrixFunctionReturnValue</a></div><div class="ttdeci">MatrixFunctionReturnValue(const Derived &A, StemFunction f)</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> MatrixFunction.h:503</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="dir_70b2be79c95c9d5bfaa4c2dafa46bf10.html">unsupported</a></li><li class="navelem"><a class="el" href="dir_f12b092121fb86d54df52b635b2d8129.html">Eigen</a></li><li class="navelem"><a class="el" href="dir_756fd3610c3abb5994ea9c814224d188.html">src</a></li><li class="navelem"><a class="el" href="dir_65bfeaec144d3ee215f8be949603ee91.html">MatrixFunctions</a></li><li class="navelem"><b>MatrixFunction.h</b></li>
<li class="footer">Generated on Mon Oct 28 2013 11:05:27 for Eigen-unsupported by
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.5 </li>
</ul>
</div>
<!-- Piwik -->
<!--
<script type="text/javascript">
var pkBaseURL = (("https:" == document.location.protocol) ? "https://stats.sylphide-consulting.com/piwik/" : "http://stats.sylphide-consulting.com/piwik/");
document.write(unescape("%3Cscript src='" + pkBaseURL + "piwik.js' type='text/javascript'%3E%3C/script%3E"));
</script><script type="text/javascript">
try {
var piwikTracker = Piwik.getTracker(pkBaseURL + "piwik.php", 20);
piwikTracker.trackPageView();
piwikTracker.enableLinkTracking();
} catch( err ) {}
</script><noscript><p><img src="http://stats.sylphide-consulting.com/piwik/piwik.php?idsite=20" style="border:0" alt="" /></p></noscript>
-->
<!-- End Piwik Tracking Code -->
</body>
</html>
