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<div class="title">MatrixLogarithm.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) 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">// Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net></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_MATRIX_LOGARITHM</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MATRIX_LOGARITHM</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="preprocessor">#ifndef M_PI</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor"></span><span class="preprocessor">#define M_PI 3.141592653589793238462643383279503L</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor"></span><span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00031"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixLogarithmAtomic.html"> 31</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html">MatrixLogarithmAtomic</a></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> {</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="comment">// typedef typename MatrixType::Index Index;</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="comment">// typedef typename internal::stem_function<Scalar>::type StemFunction;</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="comment">// typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixLogarithmAtomic.html#acf3a47acd2c12cdb22c718169a6d6c29"> 42</a></span>  <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html#acf3a47acd2c12cdb22c718169a6d6c29">MatrixLogarithmAtomic</a>() { }</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  MatrixType <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html#a64c0e596210ad59feb89cb2f061703fc">compute</a>(<span class="keyword">const</span> MatrixType& A);</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordtype">void</span> compute2x2(<span class="keyword">const</span> MatrixType& A, MatrixType& result);</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordtype">void</span> computeBig(<span class="keyword">const</span> MatrixType& A, MatrixType& result);</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordtype">int</span> getPadeDegree(<span class="keywordtype">float</span> normTminusI);</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordtype">int</span> getPadeDegree(<span class="keywordtype">double</span> normTminusI);</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordtype">int</span> getPadeDegree(<span class="keywordtype">long</span> <span class="keywordtype">double</span> normTminusI);</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordtype">void</span> computePade(MatrixType& result, <span class="keyword">const</span> MatrixType& T, <span class="keywordtype">int</span> degree);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordtype">void</span> computePade3(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordtype">void</span> computePade4(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordtype">void</span> computePade5(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordtype">void</span> computePade6(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keywordtype">void</span> computePade7(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordtype">void</span> computePade8(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordtype">void</span> computePade9(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordtype">void</span> computePade10(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordtype">void</span> computePade11(MatrixType& result, <span class="keyword">const</span> MatrixType& T);</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> minPadeDegree = 3;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> maxPadeDegree = std::numeric_limits<RealScalar>::digits<= 24? 5: <span class="comment">// single precision</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  std::numeric_limits<RealScalar>::digits<= 53? 7: <span class="comment">// double precision</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  std::numeric_limits<RealScalar>::digits<= 64? 8: <span class="comment">// extended precision</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  std::numeric_limits<RealScalar>::digits<=106? 10: <span class="comment">// double-double</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  11; <span class="comment">// quadruple precision</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// Prevent copying</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html#acf3a47acd2c12cdb22c718169a6d6c29">MatrixLogarithmAtomic</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html">MatrixLogarithmAtomic</a>&);</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html">MatrixLogarithmAtomic</a>& operator=(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html">MatrixLogarithmAtomic</a>&);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> };</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixLogarithmAtomic.html#a64c0e596210ad59feb89cb2f061703fc"> 82</a></span> MatrixType <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html#a64c0e596210ad59feb89cb2f061703fc">MatrixLogarithmAtomic<MatrixType>::compute</a>(<span class="keyword">const</span> MatrixType& A)</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keyword">using</span> std::log;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  MatrixType result(A.rows(), A.rows());</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">if</span> (A.rows() == 1)</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  result(0,0) = log(A(0,0));</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (A.rows() == 2)</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  compute2x2(A, result);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  computeBig(A, result);</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> }</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html">MatrixLogarithmAtomic<MatrixType>::compute2x2</a>(<span class="keyword">const</span> MatrixType& A, MatrixType& result)</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">using</span> std::ceil;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keyword">using</span> std::imag;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keyword">using</span> std::log;</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>  Scalar logA00 = log(A(0,0));</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  Scalar logA11 = log(A(1,1));</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> </div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  result(0,0) = logA00;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  result(1,0) = Scalar(0);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  result(1,1) = logA11;</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="keywordflow">if</span> (A(0,0) == A(1,1)) {</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  result(0,1) = A(0,1) / A(0,0);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> ((abs(A(0,0)) < 0.5*abs(A(1,1))) || (abs(A(0,0)) > 2*abs(A(1,1)))) {</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  result(0,1) = A(0,1) * (logA11 - logA00) / (A(1,1) - A(0,0));</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="comment">// computation in previous branch is inaccurate if A(1,1) \approx A(0,0)</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordtype">int</span> unwindingNumber = <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(ceil((imag(logA11 - logA00) - M_PI) / (2*M_PI)));</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  Scalar y = A(1,1) - A(0,0), x = A(1,1) + A(0,0);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  result(0,1) = A(0,1) * (Scalar(2) * numext::atanh2(y,x) + Scalar(0,2*M_PI*unwindingNumber)) / y;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</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="l00125"></a><span class="lineno"> 125</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computeBig(<span class="keyword">const</span> MatrixType& A, MatrixType& result)</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordtype">int</span> numberOfSquareRoots = 0;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">int</span> numberOfExtraSquareRoots = 0;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordtype">int</span> degree;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  MatrixType T = A, sqrtT;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">const</span> RealScalar maxNormForPade = maxPadeDegree<= 5? 5.3149729967117310e-1: <span class="comment">// single precision</span></div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  maxPadeDegree<= 7? 2.6429608311114350e-1: <span class="comment">// double precision</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  maxPadeDegree<= 8? 2.32777776523703892094e-1L: <span class="comment">// extended precision</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  maxPadeDegree<=10? 1.05026503471351080481093652651105e-1L: <span class="comment">// double-double</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  1.1880960220216759245467951592883642e-1L; <span class="comment">// quadruple precision</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  RealScalar normTminusI = (T - MatrixType::Identity(T.rows(), T.rows())).cwiseAbs().colwise().sum().maxCoeff();</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">if</span> (normTminusI < maxNormForPade) {</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  degree = getPadeDegree(normTminusI);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="keywordtype">int</span> degree2 = getPadeDegree(normTminusI / RealScalar(2));</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">if</span> ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1)) </div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  ++numberOfExtraSquareRoots;</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>  MatrixSquareRootTriangular<MatrixType>(T).compute(sqrtT);</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  T = sqrtT.template triangularView<Upper>();</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  ++numberOfSquareRoots;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> </div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  computePade(result, T, degree);</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  result *= pow(RealScalar(2), numberOfSquareRoots);</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> }</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> <span class="comment">/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = float) */</span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="keywordtype">int</span> MatrixLogarithmAtomic<MatrixType>::getPadeDegree(<span class="keywordtype">float</span> normTminusI)</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">const</span> <span class="keywordtype">float</span> maxNormForPade[] = { 2.5111573934555054e-1 <span class="comment">/* degree = 3 */</span> , 4.0535837411880493e-1,</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  5.3149729967117310e-1 };</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keywordtype">int</span> degree = 3;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">for</span> (; degree <= maxPadeDegree; ++degree) </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordflow">if</span> (normTminusI <= maxNormForPade[degree - minPadeDegree])</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keywordflow">return</span> degree;</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> }</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> </div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = double) */</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="keywordtype">int</span> MatrixLogarithmAtomic<MatrixType>::getPadeDegree(<span class="keywordtype">double</span> normTminusI)</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> {</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> maxNormForPade[] = { 1.6206284795015624e-2 <span class="comment">/* degree = 3 */</span> , 5.3873532631381171e-2,</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  1.1352802267628681e-1, 1.8662860613541288e-1, 2.642960831111435e-1 };</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keywordtype">int</span> degree = 3;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">for</span> (; degree <= maxPadeDegree; ++degree)</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">if</span> (normTminusI <= maxNormForPade[degree - minPadeDegree])</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordflow">return</span> degree;</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="l00183"></a><span class="lineno"> 183</span> <span class="comment">/* \brief Get suitable degree for Pade approximation. (specialized for RealScalar = long double) */</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="keywordtype">int</span> MatrixLogarithmAtomic<MatrixType>::getPadeDegree(<span class="keywordtype">long</span> <span class="keywordtype">double</span> normTminusI)</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> {</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="preprocessor">#if LDBL_MANT_DIG == 53 // double precision</span></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="preprocessor"></span> <span class="keyword">const</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> maxNormForPade[] = { 1.6206284795015624e-2L <span class="comment">/* degree = 3 */</span> , 5.3873532631381171e-2L,</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  1.1352802267628681e-1L, 1.8662860613541288e-1L, 2.642960831111435e-1L };</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="preprocessor">#elif LDBL_MANT_DIG <= 64 // extended precision</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="preprocessor"></span> <span class="keyword">const</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> maxNormForPade[] = { 5.48256690357782863103e-3L <span class="comment">/* degree = 3 */</span>, 2.34559162387971167321e-2L,</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  5.84603923897347449857e-2L, 1.08486423756725170223e-1L, 1.68385767881294446649e-1L,</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  2.32777776523703892094e-1L };</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="preprocessor">#elif LDBL_MANT_DIG <= 106 // double-double</span></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="preprocessor"></span> <span class="keyword">const</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> maxNormForPade[] = { 8.58970550342939562202529664318890e-5L <span class="comment">/* degree = 3 */</span>,</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  9.34074328446359654039446552677759e-4L, 4.26117194647672175773064114582860e-3L,</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  1.21546224740281848743149666560464e-2L, 2.61100544998339436713088248557444e-2L,</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  4.66170074627052749243018566390567e-2L, 7.32585144444135027565872014932387e-2L,</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  1.05026503471351080481093652651105e-1L };</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="preprocessor">#else // quadruple precision</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="preprocessor"></span> <span class="keyword">const</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> maxNormForPade[] = { 4.7419931187193005048501568167858103e-5L <span class="comment">/* degree = 3 */</span>,</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  5.8853168473544560470387769480192666e-4L, 2.9216120366601315391789493628113520e-3L,</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  8.8415758124319434347116734705174308e-3L, 1.9850836029449446668518049562565291e-2L,</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  3.6688019729653446926585242192447447e-2L, 5.9290962294020186998954055264528393e-2L,</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  8.6998436081634343903250580992127677e-2L, 1.1880960220216759245467951592883642e-1L };</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="preprocessor"></span> <span class="keywordtype">int</span> degree = 3;</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">for</span> (; degree <= maxPadeDegree; ++degree)</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="keywordflow">if</span> (normTminusI <= maxNormForPade[degree - minPadeDegree])</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keywordflow">return</span> degree;</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span> }</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> <span class="comment">/* \brief Compute Pade approximation to matrix logarithm */</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade(MatrixType& result, <span class="keyword">const</span> MatrixType& T, <span class="keywordtype">int</span> degree)</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> {</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">switch</span> (degree) {</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="keywordflow">case</span> 3: computePade3(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordflow">case</span> 4: computePade4(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordflow">case</span> 5: computePade5(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordflow">case</span> 6: computePade6(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">case</span> 7: computePade7(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">case</span> 8: computePade8(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keywordflow">case</span> 9: computePade9(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordflow">case</span> 10: computePade10(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">case</span> 11: computePade11(result, T); <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">default</span>: assert(<span class="keyword">false</span>); <span class="comment">// should never happen</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</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="l00232"></a><span class="lineno"> 232</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade3(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</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="keyword">const</span> <span class="keywordtype">int</span> degree = 3;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.1127016653792583114820734600217600L, 0.5000000000000000000000000000000000L,</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  0.8872983346207416885179265399782400L };</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.2777777777777777777777777777777778L, 0.4444444444444444444444444444444444L,</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  0.2777777777777777777777777777777778L };</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  .template triangularView<Upper>().solve(TminusI);</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> }</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> </div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade4(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> {</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> degree = 4;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.0694318442029737123880267555535953L, 0.3300094782075718675986671204483777L,</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  0.6699905217924281324013328795516223L, 0.9305681557970262876119732444464048L };</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.1739274225687269286865319746109997L, 0.3260725774312730713134680253890003L,</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  0.3260725774312730713134680253890003L, 0.1739274225687269286865319746109997L };</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  .template triangularView<Upper>().solve(TminusI);</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> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade5(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</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>  <span class="keyword">const</span> <span class="keywordtype">int</span> degree = 5;</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.0469100770306680036011865608503035L, 0.2307653449471584544818427896498956L,</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  0.5000000000000000000000000000000000L, 0.7692346550528415455181572103501044L,</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  0.9530899229693319963988134391496965L };</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.1184634425280945437571320203599587L, 0.2393143352496832340206457574178191L,</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  0.2844444444444444444444444444444444L, 0.2393143352496832340206457574178191L,</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  0.1184634425280945437571320203599587L };</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  .template triangularView<Upper>().solve(TminusI);</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> </div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade6(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> {</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> degree = 6;</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.0337652428984239860938492227530027L, 0.1693953067668677431693002024900473L,</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  0.3806904069584015456847491391596440L, 0.6193095930415984543152508608403560L,</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  0.8306046932331322568306997975099527L, 0.9662347571015760139061507772469973L };</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.0856622461895851725201480710863665L, 0.1803807865240693037849167569188581L,</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  0.2339569672863455236949351719947755L, 0.2339569672863455236949351719947755L,</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  0.1803807865240693037849167569188581L, 0.0856622461895851725201480710863665L };</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  .template triangularView<Upper>().solve(TminusI);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> }</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> </div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade7(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> {</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> degree = 7;</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.0254460438286207377369051579760744L, 0.1292344072003027800680676133596058L,</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  0.2970774243113014165466967939615193L, 0.5000000000000000000000000000000000L,</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  0.7029225756886985834533032060384807L, 0.8707655927996972199319323866403942L,</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  0.9745539561713792622630948420239256L };</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.0647424830844348466353057163395410L, 0.1398526957446383339507338857118898L,</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  0.1909150252525594724751848877444876L, 0.2089795918367346938775510204081633L,</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  0.1909150252525594724751848877444876L, 0.1398526957446383339507338857118898L,</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  0.0647424830844348466353057163395410L };</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  .template triangularView<Upper>().solve(TminusI);</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span> }</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade8(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</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>  <span class="keyword">const</span> <span class="keywordtype">int</span> degree = 8;</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.0198550717512318841582195657152635L, 0.1016667612931866302042230317620848L,</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  0.2372337950418355070911304754053768L, 0.4082826787521750975302619288199080L,</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  0.5917173212478249024697380711800920L, 0.7627662049581644929088695245946232L,</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  0.8983332387068133697957769682379152L, 0.9801449282487681158417804342847365L };</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.0506142681451881295762656771549811L, 0.1111905172266872352721779972131204L,</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  0.1568533229389436436689811009933007L, 0.1813418916891809914825752246385978L,</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  0.1813418916891809914825752246385978L, 0.1568533229389436436689811009933007L,</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  0.1111905172266872352721779972131204L, 0.0506142681451881295762656771549811L };</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  .template triangularView<Upper>().solve(TminusI);</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> }</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> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade9(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span> {</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> degree = 9;</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.0159198802461869550822118985481636L, 0.0819844463366821028502851059651326L,</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  0.1933142836497048013456489803292629L, 0.3378732882980955354807309926783317L,</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  0.5000000000000000000000000000000000L, 0.6621267117019044645192690073216683L,</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  0.8066857163502951986543510196707371L, 0.9180155536633178971497148940348674L,</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  0.9840801197538130449177881014518364L };</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.0406371941807872059859460790552618L, 0.0903240803474287020292360156214564L,</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  0.1303053482014677311593714347093164L, 0.1561735385200014200343152032922218L,</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  0.1651196775006298815822625346434870L, 0.1561735385200014200343152032922218L,</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  0.1303053482014677311593714347093164L, 0.0903240803474287020292360156214564L,</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  0.0406371941807872059859460790552618L };</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  .template triangularView<Upper>().solve(TminusI);</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> </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade10(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> {</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> degree = 10;</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.0130467357414141399610179939577740L, 0.0674683166555077446339516557882535L,</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  0.1602952158504877968828363174425632L, 0.2833023029353764046003670284171079L,</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  0.4255628305091843945575869994351400L, 0.5744371694908156054424130005648600L,</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  0.7166976970646235953996329715828921L, 0.8397047841495122031171636825574368L,</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  0.9325316833444922553660483442117465L, 0.9869532642585858600389820060422260L };</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.0333356721543440687967844049466659L, 0.0747256745752902965728881698288487L,</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  0.1095431812579910219977674671140816L, 0.1346333596549981775456134607847347L,</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  0.1477621123573764350869464973256692L, 0.1477621123573764350869464973256692L,</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  0.1346333596549981775456134607847347L, 0.1095431812579910219977674671140816L,</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  0.0747256745752902965728881698288487L, 0.0333356721543440687967844049466659L };</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  .template triangularView<Upper>().solve(TminusI);</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> }</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span> </div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="keywordtype">void</span> MatrixLogarithmAtomic<MatrixType>::computePade11(MatrixType& result, <span class="keyword">const</span> MatrixType& T)</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> {</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> degree = 11;</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keyword">const</span> RealScalar nodes[] = { 0.0108856709269715035980309994385713L, 0.0564687001159523504624211153480364L,</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  0.1349239972129753379532918739844233L, 0.2404519353965940920371371652706952L,</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  0.3652284220238275138342340072995692L, 0.5000000000000000000000000000000000L,</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  0.6347715779761724861657659927004308L, 0.7595480646034059079628628347293048L,</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  0.8650760027870246620467081260155767L, 0.9435312998840476495375788846519636L,</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  0.9891143290730284964019690005614287L };</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keyword">const</span> RealScalar weights[] = { 0.0278342835580868332413768602212743L, 0.0627901847324523123173471496119701L,</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  0.0931451054638671257130488207158280L, 0.1165968822959952399592618524215876L,</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  0.1314022722551233310903444349452546L, 0.1364625433889503153572417641681711L,</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  0.1314022722551233310903444349452546L, 0.1165968822959952399592618524215876L,</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  0.0931451054638671257130488207158280L, 0.0627901847324523123173471496119701L,</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  0.0278342835580868332413768602212743L };</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  eigen_assert(degree <= maxPadeDegree);</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  MatrixType TminusI = T - MatrixType::Identity(T.rows(), T.rows());</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  result.setZero(T.rows(), T.rows());</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < degree; ++k)</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  result += weights[k] * (MatrixType::Identity(T.rows(), T.rows()) + nodes[k] * TminusI)</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  .template triangularView<Upper>().solve(TminusI);</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="l00420"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixLogarithmReturnValue.html"> 420</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixLogarithmReturnValue.html">MatrixLogarithmReturnValue</a></div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span> : <span class="keyword">public</span> ReturnByValue<MatrixLogarithmReturnValue<Derived> ></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> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> </div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::Scalar Scalar;</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::Index Index;</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> </div>
<div class="line"><a name="l00432"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixLogarithmReturnValue.html#a5a3adc36be4386f3d03d0523b46f551f"> 432</a></span>  <a class="code" href="classEigen_1_1MatrixLogarithmReturnValue.html#a5a3adc36be4386f3d03d0523b46f551f">MatrixLogarithmReturnValue</a>(<span class="keyword">const</span> Derived& A) : m_A(A) { }</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  </div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00439"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixLogarithmReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766"> 439</a></span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixLogarithmReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766">evalTo</a>(ResultType& result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject PlainObject;</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keyword">typedef</span> internal::traits<PlainObject> Traits;</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</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="l00444"></a><span class="lineno"> 444</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="l00445"></a><span class="lineno"> 445</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="l00446"></a><span class="lineno"> 446</span>  <span class="keyword">typedef</span> std::complex<typename NumTraits<Scalar>::Real> ComplexScalar;</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="keyword">typedef</span> Matrix<ComplexScalar, Dynamic, Dynamic, Options, RowsAtCompileTime, ColsAtCompileTime> DynMatrixType;</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1MatrixLogarithmAtomic.html">MatrixLogarithmAtomic<DynMatrixType></a> AtomicType;</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  AtomicType atomic;</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  </div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="keyword">const</span> PlainObject Aevaluated = m_A.eval();</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <a class="code" href="classEigen_1_1MatrixFunction.html">MatrixFunction<PlainObject, AtomicType></a> mf(Aevaluated, atomic);</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  mf.<a class="code" href="classEigen_1_1MatrixFunction.html#a37407499d669c7dd9af708e7dd6f9217">compute</a>(result);</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</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>  Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.rows(); }</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_A.cols(); }</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  </div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="keyword">typename</span> internal::nested<Derived>::type m_A;</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  </div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <a class="code" href="classEigen_1_1MatrixLogarithmReturnValue.html#a5a3adc36be4386f3d03d0523b46f551f">MatrixLogarithmReturnValue</a>& operator=(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixLogarithmReturnValue.html#a5a3adc36be4386f3d03d0523b46f551f">MatrixLogarithmReturnValue</a>&);</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span> };</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span> </div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keyword">struct </span>traits<MatrixLogarithmReturnValue<Derived> ></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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject ReturnType;</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  };</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> </div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> <span class="comment">/********** MatrixBase method **********/</span></div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span> </div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span> </div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span> <span class="keyword">const</span> MatrixLogarithmReturnValue<Derived> MatrixBase<Derived>::log()<span class="keyword"> const</span></div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  eigen_assert(rows() == cols());</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">return</span> MatrixLogarithmReturnValue<Derived>(derived());</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span> }</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span> </div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> </div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span> <span class="preprocessor">#endif // EIGEN_MATRIX_LOGARITHM</span></div>
<div class="ttc" id="classEigen_1_1MatrixLogarithmReturnValue_html_a4f4ce27ebcf7fe1e0078d20d0393c766"><div class="ttname"><a href="classEigen_1_1MatrixLogarithmReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766">Eigen::MatrixLogarithmReturnValue::evalTo</a></div><div class="ttdeci">void evalTo(ResultType &result) const </div><div class="ttdoc">Compute the matrix logarithm. </div><div class="ttdef"><b>Definition:</b> MatrixLogarithm.h:439</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_1MatrixLogarithmAtomic_html_a64c0e596210ad59feb89cb2f061703fc"><div class="ttname"><a href="classEigen_1_1MatrixLogarithmAtomic.html#a64c0e596210ad59feb89cb2f061703fc">Eigen::MatrixLogarithmAtomic::compute</a></div><div class="ttdeci">MatrixType compute(const MatrixType &A)</div><div class="ttdoc">Compute matrix logarithm of atomic matrix. </div><div class="ttdef"><b>Definition:</b> MatrixLogarithm.h:82</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_1MatrixLogarithmAtomic_html"><div class="ttname"><a href="classEigen_1_1MatrixLogarithmAtomic.html">Eigen::MatrixLogarithmAtomic</a></div><div class="ttdoc">Helper class for computing matrix logarithm of atomic matrices. </div><div class="ttdef"><b>Definition:</b> MatrixLogarithm.h:31</div></div>
<div class="ttc" id="classEigen_1_1MatrixLogarithmReturnValue_html_a5a3adc36be4386f3d03d0523b46f551f"><div class="ttname"><a href="classEigen_1_1MatrixLogarithmReturnValue.html#a5a3adc36be4386f3d03d0523b46f551f">Eigen::MatrixLogarithmReturnValue::MatrixLogarithmReturnValue</a></div><div class="ttdeci">MatrixLogarithmReturnValue(const Derived &A)</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> MatrixLogarithm.h:432</div></div>
<div class="ttc" id="classEigen_1_1MatrixLogarithmReturnValue_html"><div class="ttname"><a href="classEigen_1_1MatrixLogarithmReturnValue.html">Eigen::MatrixLogarithmReturnValue</a></div><div class="ttdoc">Proxy for the matrix logarithm of some matrix (expression). </div><div class="ttdef"><b>Definition:</b> MatrixLogarithm.h:420</div></div>
<div class="ttc" id="classEigen_1_1MatrixLogarithmAtomic_html_acf3a47acd2c12cdb22c718169a6d6c29"><div class="ttname"><a href="classEigen_1_1MatrixLogarithmAtomic.html#acf3a47acd2c12cdb22c718169a6d6c29">Eigen::MatrixLogarithmAtomic::MatrixLogarithmAtomic</a></div><div class="ttdeci">MatrixLogarithmAtomic()</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> MatrixLogarithm.h:42</div></div>
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