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<div class="title">JacobiSVD.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com></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_JACOBISVD_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_JACOBISVD_H</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="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// forward declaration (needed by ICC)</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// the empty body is required by MSVC</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner,</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  <span class="keywordtype">bool</span> IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">struct </span>svd_precondition_2x2_block_to_be_real {};</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">/*** QR preconditioners (R-SVD)</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment"> ***</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment"> *** Their role is to reduce the problem of computing the SVD to the case of a square matrix.</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment"> *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment"> *** JacobiSVD which by itself is only able to work on square matrices.</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment"> ***/</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">enum</span> { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner, <span class="keywordtype">int</span> Case></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">struct </span>qr_preconditioner_should_do_anything</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">enum</span> { a = MatrixType::RowsAtCompileTime != Dynamic &&</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  MatrixType::ColsAtCompileTime != Dynamic &&</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  b = MatrixType::RowsAtCompileTime != Dynamic &&</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  MatrixType::ColsAtCompileTime != Dynamic &&</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  ret = !( (QRPreconditioner == NoQRPreconditioner) ||</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  (Case == PreconditionIfMoreColsThanRows && <span class="keywordtype">bool</span>(a)) ||</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  (Case == PreconditionIfMoreRowsThanCols && <span class="keywordtype">bool</span>(b)) )</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  };</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> };</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner, <span class="keywordtype">int</span> Case,</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordtype">bool</span> DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> > <span class="keyword">struct </span>qr_preconditioner_impl {};</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">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner, <span class="keywordtype">int</span> Case></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">class </span>qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> JacobiSVD<MatrixType, QRPreconditioner>&) {}</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordtype">bool</span> run(JacobiSVD<MatrixType, QRPreconditioner>&, <span class="keyword">const</span> MatrixType&)</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  {</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  }</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> };</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> <span class="comment">/*** preconditioner using FullPivHouseholderQR ***/</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">class </span>qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">enum</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>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime</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="keyword">typedef</span> Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)</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>  <span class="keywordflow">if</span> (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  {</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  m_qr.~QRType();</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  ::new (&m_qr) QRType(svd.rows(), svd.cols());</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>  if (svd.m_computeFullU) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordtype">bool</span> run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  {</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordflow">if</span>(matrix.rows() > matrix.cols())</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  {</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  m_qr.compute(matrix);</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).<span class="keyword">template</span> triangularView<Upper>();</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">if</span>(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">if</span>(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  }</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</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">private</span>:</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">typedef</span> FullPivHouseholderQR<MatrixType> QRType;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  QRType m_qr;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  WorkspaceType m_workspace;</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> </div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">class </span>qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> {</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">enum</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  {</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  Options = MatrixType::Options</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  };</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">typedef</span> Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  TransposeTypeWithSameStorageOrder;</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>  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  {</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keywordflow">if</span> (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  {</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  m_qr.~QRType();</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  ::new (&m_qr) QRType(svd.cols(), svd.rows());</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  }</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  m_adjoint.resize(svd.cols(), svd.rows());</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  if (svd.m_computeFullV) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  }</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> </div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordtype">bool</span> run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  {</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">if</span>(matrix.cols() > matrix.rows())</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  {</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  m_adjoint = matrix.adjoint();</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  m_qr.compute(m_adjoint);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).<span class="keyword">template</span> triangularView<Upper>().adjoint();</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordflow">if</span>(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">else</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</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>  <span class="keyword">typedef</span> FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  QRType m_qr;</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  TransposeTypeWithSameStorageOrder m_adjoint;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">typename</span> internal::plain_row_type<MatrixType>::type m_workspace;</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> <span class="comment">/*** preconditioner using ColPivHouseholderQR ***/</span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">class </span>qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</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="keywordtype">void</span> allocate(<span class="keyword">const</span> JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  {</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keywordflow">if</span> (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  {</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  m_qr.~QRType();</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  ::new (&m_qr) QRType(svd.rows(), svd.cols());</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  }</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  if (svd.m_computeFullU) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  else if (svd.m_computeThinU) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  }</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordtype">bool</span> run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)</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="keywordflow">if</span>(matrix.rows() > matrix.cols())</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  {</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  m_qr.compute(matrix);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).<span class="keyword">template</span> triangularView<Upper>();</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">if</span>(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(svd.m_computeThinU)</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  {</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  }</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keywordflow">if</span>(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</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="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  }</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">typedef</span> ColPivHouseholderQR<MatrixType> QRType;</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  QRType m_qr;</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keyword">typename</span> internal::plain_col_type<MatrixType>::type m_workspace;</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> };</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="keyword">class </span>qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true></div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> {</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">enum</span></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>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  Options = MatrixType::Options</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  };</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> </div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keyword">typedef</span> Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  TransposeTypeWithSameStorageOrder;</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="keywordtype">void</span> allocate(<span class="keyword">const</span> JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  {</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keywordflow">if</span> (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())</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>  m_qr.~QRType();</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  ::new (&m_qr) QRType(svd.cols(), svd.rows());</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  }</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  if (svd.m_computeFullV) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  else if (svd.m_computeThinV) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  m_adjoint.resize(svd.cols(), svd.rows());</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  }</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> </div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordtype">bool</span> run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  {</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">if</span>(matrix.cols() > matrix.rows())</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>  m_adjoint = matrix.adjoint();</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  m_qr.compute(m_adjoint);</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> </div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).<span class="keyword">template</span> triangularView<Upper>().adjoint();</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordflow">if</span>(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(svd.m_computeThinV)</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  {</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  }</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  }</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">else</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  }</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span> </div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keyword">typedef</span> ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  QRType m_qr;</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  TransposeTypeWithSameStorageOrder m_adjoint;</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keyword">typename</span> internal::plain_row_type<MatrixType>::type m_workspace;</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">/*** preconditioner using HouseholderQR ***/</span></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="keyword">class </span>qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> {</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)</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>  <span class="keywordflow">if</span> (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())</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>  m_qr.~QRType();</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  ::new (&m_qr) QRType(svd.rows(), svd.cols());</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  }</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  if (svd.m_computeFullU) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  else if (svd.m_computeThinU) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  }</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordtype">bool</span> run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  {</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keywordflow">if</span>(matrix.rows() > matrix.cols())</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>  m_qr.compute(matrix);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).<span class="keyword">template</span> triangularView<Upper>();</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keywordflow">if</span>(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(svd.m_computeThinU)</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>  svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  }</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordflow">if</span>(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  }</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</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">private</span>:</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keyword">typedef</span> HouseholderQR<MatrixType> QRType;</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  QRType m_qr;</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  <span class="keyword">typename</span> internal::plain_col_type<MatrixType>::type m_workspace;</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> };</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> </div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="keyword">class </span>qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> {</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keyword">enum</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>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  Options = MatrixType::Options</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  };</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> </div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keyword">typedef</span> Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  TransposeTypeWithSameStorageOrder;</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> </div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordtype">void</span> allocate(<span class="keyword">const</span> JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  {</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keywordflow">if</span> (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())</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>  m_qr.~QRType();</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  ::new (&m_qr) QRType(svd.cols(), svd.rows());</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>  if (svd.m_computeFullV) m_workspace.resize(svd.cols());</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  else if (svd.m_computeThinV) m_workspace.resize(svd.rows());</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  m_adjoint.resize(svd.cols(), svd.rows());</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  }</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span> </div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keywordtype">bool</span> run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  {</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keywordflow">if</span>(matrix.cols() > matrix.rows())</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>  m_adjoint = matrix.adjoint();</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  m_qr.compute(m_adjoint);</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).<span class="keyword">template</span> triangularView<Upper>().adjoint();</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  <span class="keywordflow">if</span>(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(svd.m_computeThinV)</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  {</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);</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>  <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  }</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">else</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  }</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keyword">typedef</span> HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  QRType m_qr;</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  TransposeTypeWithSameStorageOrder m_adjoint;</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keyword">typename</span> internal::plain_row_type<MatrixType>::type m_workspace;</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> };</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span> </div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment">/*** 2x2 SVD implementation</span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="comment"> ***</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span> <span class="comment"> *** JacobiSVD consists in performing a series of 2x2 SVD subproblems</span></div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="comment"> ***/</span></div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="keyword">struct </span>svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false></div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span> {</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keyword">typedef</span> JacobiSVD<MatrixType, QRPreconditioner> SVD;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SVD::Index Index;</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(<span class="keyword">typename</span> SVD::WorkMatrixType&, SVD&, Index, Index) {}</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> };</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> </div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="keyword">struct </span>svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> {</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keyword">typedef</span> JacobiSVD<MatrixType, QRPreconditioner> SVD;</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SVD::Index Index;</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> run(<span class="keyword">typename</span> SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q)</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>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  Scalar z;</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  JacobiRotation<Scalar> rot;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="keywordflow">if</span>(n==0)</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>  z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  work_matrix.row(p) *= z;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  work_matrix.row(q) *= z;</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);</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="keywordflow">else</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  {</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  rot.c() = conj(work_matrix.coeff(p,p)) / n;</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  rot.s() = work_matrix.coeff(q,p) / n;</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  work_matrix.applyOnTheLeft(p,q,rot);</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="keywordflow">if</span>(work_matrix.coeff(p,q) != Scalar(0))</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  {</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  Scalar z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  work_matrix.col(q) *= z;</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keywordflow">if</span>(svd.computeV()) svd.m_matrixV.col(q) *= z;</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  }</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="keywordflow">if</span>(work_matrix.coeff(q,q) != Scalar(0))</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  {</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  work_matrix.row(q) *= z;</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keywordflow">if</span>(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  }</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="l00409"></a><span class="lineno"> 409</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> RealScalar, <span class="keyword">typename</span> Index></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="keywordtype">void</span> real_2x2_jacobi_svd(<span class="keyword">const</span> MatrixType& matrix, Index p, Index q,</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  JacobiRotation<RealScalar> *j_left,</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  JacobiRotation<RealScalar> *j_right)</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span> {</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  Matrix<RealScalar,2,2> m;</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  JacobiRotation<RealScalar> rot1;</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  RealScalar t = m.coeff(0,0) + m.coeff(1,1);</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  RealScalar d = m.coeff(1,0) - m.coeff(0,1);</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">if</span>(t == RealScalar(0))</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>  rot1.c() = RealScalar(0);</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  }</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  {</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  RealScalar u = d / t;</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  rot1.s() = rot1.c() * u;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  }</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  m.applyOnTheLeft(0,1,rot1);</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  j_right->makeJacobi(m,0,1);</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  *j_left = rot1 * j_right->transpose();</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> }</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> </div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span> </div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keywordtype">int</span> QRPreconditioner> </div>
<div class="line"><a name="l00493"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html"> 493</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a><_MatrixType></div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span> {</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> </div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<typename MatrixType::Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  MatrixOptions = MatrixType::Options</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  };</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span> </div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  <span class="keyword">typedef</span> Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime></div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  MatrixUType;</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keyword">typedef</span> Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime></div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  MatrixVType;</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type<MatrixType>::type RowType;</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type<MatrixType>::type ColType;</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  <span class="keyword">typedef</span> Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime></div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  WorkMatrixType;</div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span> </div>
<div class="line"><a name="l00529"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a0e963136a69da877ff06f27e7b746351"> 529</a></span>  <a class="code" href="classEigen_1_1JacobiSVD.html#a0e963136a69da877ff06f27e7b746351">JacobiSVD</a>()</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  : <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a><_MatrixType>::<a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a>()</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  {}</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span> </div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span> </div>
<div class="line"><a name="l00540"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a18cfaad45164fc79a0b5e65c194d049d"> 540</a></span>  <a class="code" href="classEigen_1_1JacobiSVD.html#a18cfaad45164fc79a0b5e65c194d049d">JacobiSVD</a>(Index rows, Index cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions = 0)</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  : <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a><_MatrixType>::<a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a>() </div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  {</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  allocate(rows, cols, computationOptions);</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="l00556"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#af7d98465f0e886d96423857591a34b26"> 556</a></span>  <a class="code" href="classEigen_1_1JacobiSVD.html#af7d98465f0e886d96423857591a34b26">JacobiSVD</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions = 0)</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  : <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a><_MatrixType>::<a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a>()</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  {</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  compute(matrix, computationOptions);</div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  }</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span> </div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType></a>& compute(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span> </div>
<div class="line"><a name="l00580"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a26e02670d0a94c92ab41c2bc7f70e781"> 580</a></span>  <a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType></a>& <a class="code" href="classEigen_1_1JacobiSVD.html#a26e02670d0a94c92ab41c2bc7f70e781">compute</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  {</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="keywordflow">return</span> compute(matrix, this->m_computationOptions);</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  }</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  </div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<JacobiSVD, Rhs></div>
<div class="line"><a name="l00596"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#ae86e342cd51b067b08f8de8bae77537f"> 596</a></span>  <a class="code" href="classEigen_1_1JacobiSVD.html#ae86e342cd51b067b08f8de8bae77537f">solve</a>(<span class="keyword">const</span> MatrixBase<Rhs>& b)<span class="keyword"> const</span></div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  eigen_assert(this->m_isInitialized && <span class="stringliteral">"JacobiSVD is not initialized."</span>);</div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  eigen_assert(<a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType>::computeU</a>() && <a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType>::computeV</a>() && <span class="stringliteral">"JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice)."</span>);</div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  <span class="keywordflow">return</span> internal::solve_retval<JacobiSVD, Rhs>(*<span class="keyword">this</span>, b.derived());</div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  }</div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span> </div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  </div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span> </div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="keywordtype">void</span> allocate(Index rows, Index cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span> </div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  WorkMatrixType m_workMatrix;</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  </div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  <span class="keyword">template</span><<span class="keyword">typename</span> __MatrixType, <span class="keywordtype">int</span> _QRPreconditioner, <span class="keywordtype">bool</span> _IsComplex></div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  <span class="keyword">friend</span> <span class="keyword">struct </span>internal::svd_precondition_2x2_block_to_be_real;</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <span class="keyword">template</span><<span class="keyword">typename</span> __MatrixType, <span class="keywordtype">int</span> _QRPreconditioner, <span class="keywordtype">int</span> _Case, <span class="keywordtype">bool</span> _DoAnything></div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  <span class="keyword">friend</span> <span class="keyword">struct </span>internal::qr_preconditioner_impl;</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span> </div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols;</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows;</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span> };</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span> </div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner></div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span> <span class="keywordtype">void</span> JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions)</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span> {</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  <span class="keywordflow">if</span> (SVDBase<MatrixType>::allocate(rows, cols, computationOptions)) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span> </div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  <span class="keywordflow">if</span> (QRPreconditioner == FullPivHouseholderQRPreconditioner)</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  {</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  eigen_assert(!(this->m_computeThinU || this->m_computeThinV) &&</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="stringliteral">"JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "</span></div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  <span class="stringliteral">"Use the ColPivHouseholderQR preconditioner instead."</span>);</div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  }</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span> </div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  m_workMatrix.resize(this->m_diagSize, this->m_diagSize);</div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  </div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  <span class="keywordflow">if</span>(this->m_cols>this->m_rows) m_qr_precond_morecols.allocate(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  <span class="keywordflow">if</span>(this->m_rows>this->m_cols) m_qr_precond_morerows.allocate(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span> }</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span> </div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> QRPreconditioner></div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span> SVDBase<MatrixType>&</div>
<div class="line"><a name="l00640"></a><span class="lineno"><a class="line" href="classEigen_1_1JacobiSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434"> 640</a></span> <a class="code" href="classEigen_1_1JacobiSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434">JacobiSVD<MatrixType, QRPreconditioner>::compute</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions)</div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span> {</div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  allocate(matrix.rows(), matrix.cols(), computationOptions);</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span> </div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  <span class="comment">// currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,</span></div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  <span class="comment">// only worsening the precision of U and V as we accumulate more rotations</span></div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  <span class="keyword">const</span> RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span> </div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  <span class="comment">// limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)</span></div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  <span class="keyword">const</span> RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min();</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span> </div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  <span class="comment">/*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */</span></div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span> </div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  <span class="keywordflow">if</span>(!m_qr_precond_morecols.run(*<span class="keyword">this</span>, matrix) && !m_qr_precond_morerows.run(*<span class="keyword">this</span>, matrix))</div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  {</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  m_workMatrix = matrix.block(0,0,this->m_diagSize,this->m_diagSize);</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  <span class="keywordflow">if</span>(this->m_computeFullU) this->m_matrixU.setIdentity(this->m_rows,this->m_rows);</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <span class="keywordflow">if</span>(this->m_computeThinU) this->m_matrixU.setIdentity(this->m_rows,this->m_diagSize);</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  <span class="keywordflow">if</span>(this->m_computeFullV) this->m_matrixV.setIdentity(this->m_cols,this->m_cols);</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  <span class="keywordflow">if</span>(this->m_computeThinV) this->m_matrixV.setIdentity(this->m_cols, this->m_diagSize);</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  }</div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span> </div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  <span class="comment">/*** step 2. The main Jacobi SVD iteration. ***/</span></div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span> </div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  <span class="keywordtype">bool</span> finished = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  <span class="keywordflow">while</span>(!finished)</div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  {</div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  finished = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span> </div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  <span class="comment">// do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix</span></div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span> </div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  <span class="keywordflow">for</span>(Index p = 1; p < this->m_diagSize; ++p)</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  {</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keywordflow">for</span>(Index q = 0; q < p; ++q)</div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  {</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  <span class="comment">// if this 2x2 sub-matrix is not diagonal already...</span></div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  <span class="comment">// notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't</span></div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  <span class="comment">// keep us iterating forever. Similarly, small denormal numbers are considered zero.</span></div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  <span class="keyword">using</span> std::max;</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),</div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  abs(m_workMatrix.coeff(q,q))));</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  <span class="keywordflow">if</span>((max)(abs(m_workMatrix.coeff(p,q)),abs(m_workMatrix.coeff(q,p))) > threshold)</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  {</div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  finished = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span> </div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  <span class="comment">// perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal</span></div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *<span class="keyword">this</span>, p, q);</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  JacobiRotation<RealScalar> j_left, j_right;</div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span> </div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  <span class="comment">// accumulate resulting Jacobi rotations</span></div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  m_workMatrix.applyOnTheLeft(p,q,j_left);</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType>::computeU</a>()) this->m_matrixU.applyOnTheRight(p,q,j_left.transpose());</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span> </div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  m_workMatrix.applyOnTheRight(p,q,j_right);</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType>::computeV</a>()) this->m_matrixV.applyOnTheRight(p,q,j_right);</div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  }</div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  }</div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  }</div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  }</div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span> </div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  <span class="comment">/*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/</span></div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span> </div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  <span class="keywordflow">for</span>(Index i = 0; i < this->m_diagSize; ++i)</div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  {</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  RealScalar a = abs(m_workMatrix.coeff(i,i));</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  this->m_singularValues.coeffRef(i) = a;</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType>::computeU</a>() && (a!=RealScalar(0))) this->m_matrixU.col(i) *= this->m_workMatrix.coeff(i,i)/a;</div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  }</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span> </div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  <span class="comment">/*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/</span></div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span> </div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  this->m_nonzeroSingularValues = this->m_diagSize;</div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  <span class="keywordflow">for</span>(Index i = 0; i < this->m_diagSize; i++)</div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  {</div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  Index pos;</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  RealScalar maxRemainingSingularValue = this->m_singularValues.tail(this->m_diagSize-i).maxCoeff(&pos);</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  <span class="keywordflow">if</span>(maxRemainingSingularValue == RealScalar(0))</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  {</div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  this->m_nonzeroSingularValues = i;</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  }</div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  <span class="keywordflow">if</span>(pos)</div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  {</div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  pos += i;</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span>  std::swap(this->m_singularValues.coeffRef(i), this->m_singularValues.coeffRef(pos));</div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType>::computeU</a>()) this->m_matrixU.col(pos).swap(this->m_matrixU.col(i));</div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span>  <span class="keywordflow">if</span>(<a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType>::computeV</a>()) this->m_matrixV.col(pos).swap(this->m_matrixV.col(i));</div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  }</div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  }</div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span> </div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  this->m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span> }</div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span> </div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keywordtype">int</span> QRPreconditioner, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span> <span class="keyword">struct </span>solve_retval<<a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD</a><_MatrixType, QRPreconditioner>, Rhs></div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span>  : solve_retval_base<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs></div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span> {</div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD<_MatrixType, QRPreconditioner></a> JacobiSVDType;</div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span>  EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs)</div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span> </div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span>  eigen_assert(rhs().rows() == dec().rows());</div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span> </div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  <span class="comment">// A = U S V^*</span></div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span>  <span class="comment">// So A^{-1} = V S^{-1} U^*</span></div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span> </div>
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span>  Index diagSize = (std::min)(dec().rows(), dec().cols());</div>
<div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  <span class="keyword">typename</span> JacobiSVDType::SingularValuesType invertedSingVals(diagSize);</div>
<div class="line"><a name="l00753"></a><span class="lineno"> 753</span> </div>
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span>  Index nonzeroSingVals = dec().nonzeroSingularValues();</div>
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span>  invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse();</div>
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  invertedSingVals.tail(diagSize - nonzeroSingVals).setZero();</div>
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span> </div>
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  dst = dec().matrixV().leftCols(diagSize)</div>
<div class="line"><a name="l00759"></a><span class="lineno"> 759</span>  * invertedSingVals.asDiagonal()</div>
<div class="line"><a name="l00760"></a><span class="lineno"> 760</span>  * dec().matrixU().leftCols(diagSize).adjoint()</div>
<div class="line"><a name="l00761"></a><span class="lineno"> 761</span>  * rhs();</div>
<div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  }</div>
<div class="line"><a name="l00763"></a><span class="lineno"> 763</span> };</div>
<div class="line"><a name="l00764"></a><span class="lineno"> 764</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00765"></a><span class="lineno"> 765</span> </div>
<div class="line"><a name="l00773"></a><span class="lineno"> 773</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00774"></a><span class="lineno"> 774</span> JacobiSVD<typename MatrixBase<Derived>::PlainObject></div>
<div class="line"><a name="l00775"></a><span class="lineno"> 775</span> MatrixBase<Derived>::jacobiSvd(<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions)<span class="keyword"> const</span></div>
<div class="line"><a name="l00776"></a><span class="lineno"> 776</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  <span class="keywordflow">return</span> JacobiSVD<PlainObject>(*<span class="keyword">this</span>, computationOptions);</div>
<div class="line"><a name="l00778"></a><span class="lineno"> 778</span> }</div>
<div class="line"><a name="l00779"></a><span class="lineno"> 779</span> </div>
<div class="line"><a name="l00780"></a><span class="lineno"> 780</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00781"></a><span class="lineno"> 781</span> </div>
<div class="line"><a name="l00782"></a><span class="lineno"> 782</span> <span class="preprocessor">#endif // EIGEN_JACOBISVD_H</span></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_ae86e342cd51b067b08f8de8bae77537f"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#ae86e342cd51b067b08f8de8bae77537f">Eigen::JacobiSVD::solve</a></div><div class="ttdeci">const internal::solve_retval< JacobiSVD, Rhs > solve(const MatrixBase< Rhs > &b) const </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:596</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_a26e02670d0a94c92ab41c2bc7f70e781"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a26e02670d0a94c92ab41c2bc7f70e781">Eigen::JacobiSVD::compute</a></div><div class="ttdeci">SVDBase< MatrixType > & compute(const MatrixType &matrix)</div><div class="ttdoc">Method performing the decomposition of given matrix using current options. </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:580</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_a3b2bfdc0a8dd672390fb4ba22f4ef434"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434">Eigen::JacobiSVD::compute</a></div><div class="ttdeci">SVDBase< MatrixType > & compute(const MatrixType &matrix, unsigned int computationOptions)</div><div class="ttdoc">Method performing the decomposition of given matrix using custom options. </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:640</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_a0e963136a69da877ff06f27e7b746351"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a0e963136a69da877ff06f27e7b746351">Eigen::JacobiSVD::JacobiSVD</a></div><div class="ttdeci">JacobiSVD()</div><div class="ttdoc">Default Constructor. </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:529</div></div>
<div class="ttc" id="classEigen_1_1SVDBase_html"><div class="ttname"><a href="classEigen_1_1SVDBase.html">Eigen::SVDBase</a></div><div class="ttdoc">Mother class of SVD classes algorithms. </div><div class="ttdef"><b>Definition:</b> SVDBase.h:46</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_a18cfaad45164fc79a0b5e65c194d049d"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#a18cfaad45164fc79a0b5e65c194d049d">Eigen::JacobiSVD::JacobiSVD</a></div><div class="ttdeci">JacobiSVD(Index rows, Index cols, unsigned int computationOptions=0)</div><div class="ttdoc">Default Constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:540</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html">Eigen::JacobiSVD</a></div><div class="ttdoc">Two-sided Jacobi SVD decomposition of a rectangular matrix. </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:493</div></div>
<div class="ttc" id="classEigen_1_1JacobiSVD_html_af7d98465f0e886d96423857591a34b26"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html#af7d98465f0e886d96423857591a34b26">Eigen::JacobiSVD::JacobiSVD</a></div><div class="ttdeci">JacobiSVD(const MatrixType &matrix, unsigned int computationOptions=0)</div><div class="ttdoc">Constructor performing the decomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:556</div></div>
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