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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<div class="fragment"><div class="line"><a id="l00001" 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 id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// We used the "A Divide-And-Conquer Algorithm for the Bidiagonal SVD"</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">// research report written by Ming Gu and Stanley C.Eisenstat</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// The code variable names correspond to the names they used in their</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">// report</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">//</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com></span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr></span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr></span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr></span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment">// Copyright (C) 2013 Jitse Niesen <jitse@maths.leeds.ac.uk></span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// Copyright (C) 2014-2017 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">//</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#ifndef EIGEN_BDCSVD_H</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#define EIGEN_BDCSVD_H</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// #define EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// #define EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#undef eigen_internal_assert</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#define eigen_internal_assert(X) assert(X);</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor">#include "./InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include <iostream></span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span>IOFormat bdcsvdfmt(8, 0, <span class="stringliteral">", "</span>, <span class="stringliteral">"\n"</span>, <span class="stringliteral">" ["</span>, <span class="stringliteral">"]"</span>);</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="keyword">class </span>BDCSVD;</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="keyword">struct </span>traits<BDCSVD<MatrixType_, Options> > : svd_traits<MatrixType_, Options> {</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span>};</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="keyword">struct </span>allocate_small_svd {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keyword">static</span> <span class="keywordtype">void</span> run(JacobiSVD<MatrixType, Options>& smallSvd, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> (void)computationOptions;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> smallSvd = JacobiSVD<MatrixType, Options>(rows, cols);</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>};</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span>EIGEN_DIAGNOSTICS(push)</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span>EIGEN_DISABLE_DEPRECATED_WARNING</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="keyword">struct </span>allocate_small_svd<MatrixType, 0> {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">static</span> <span class="keywordtype">void</span> run(JacobiSVD<MatrixType>& smallSvd, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> smallSvd = JacobiSVD<MatrixType>(rows, cols, computationOptions);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> }</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span>};</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span>EIGEN_DIAGNOSTICS(pop)</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> </div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> Options_></div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html"> 104</a></span><span class="keyword">class </span><a class="code hl_class" href="classEigen_1_1BDCSVD.html">BDCSVD</a> : <span class="keyword">public</span> <a class="code hl_class" href="classEigen_1_1SVDBase.html">SVDBase</a><BDCSVD<MatrixType_, Options_> > {</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1SVDBase.html">SVDBase<BDCSVD></a> <a class="code hl_class" href="classEigen_1_1SVDBase.html">Base</a>;</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keyword">using </span>Base::rows;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">using </span>Base::cols;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">using </span><a class="code hl_function" href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">Base::computeU</a>;</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">using </span><a class="code hl_function" href="classEigen_1_1SVDBase.html#a5f12efcb791eb007d4a4890ac5255ac4">Base::computeV</a>;</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::Scalar Scalar;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::RealScalar RealScalar;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_class" href="structEigen_1_1NumTraits.html">NumTraits<RealScalar>::Literal</a> Literal;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_typedef" href="classEigen_1_1SVDBase.html#a6229a37997eca1072b52cca5ee7a2bec">Base::Index</a> Index;</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keyword">enum</span> {</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> Options = Options_,</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> QRDecomposition = Options & internal::QRPreconditionerBits,</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> ComputationOptions = Options & internal::ComputationOptionsBits,</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> RowsAtCompileTime = Base::RowsAtCompileTime,</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> ColsAtCompileTime = Base::ColsAtCompileTime,</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> DiagSizeAtCompileTime = Base::DiagSizeAtCompileTime,</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> MaxRowsAtCompileTime = Base::MaxRowsAtCompileTime,</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> MaxColsAtCompileTime = Base::MaxColsAtCompileTime,</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> MaxDiagSizeAtCompileTime = Base::MaxDiagSizeAtCompileTime,</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> MatrixOptions = Base::MatrixOptions</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> };</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> </div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Base::MatrixUType</a> <a class="code hl_class" href="classEigen_1_1Matrix.html">MatrixUType</a>;</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Base::MatrixVType</a> <a class="code hl_class" href="classEigen_1_1Matrix.html">MatrixVType</a>;</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::SingularValuesType SingularValuesType;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Matrix<Scalar, Dynamic, Dynamic, ColMajor></a> <a class="code hl_class" href="classEigen_1_1Matrix.html">MatrixX</a>;</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Matrix<RealScalar, Dynamic, Dynamic, ColMajor></a> <a class="code hl_class" href="classEigen_1_1Matrix.html">MatrixXr</a>;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1Matrix.html">Matrix<RealScalar, Dynamic, 1></a> <a class="code hl_class" href="classEigen_1_1Matrix.html">VectorType</a>;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1Array.html">Array<RealScalar, Dynamic, 1></a> <a class="code hl_class" href="classEigen_1_1Array.html">ArrayXr</a>;</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1Array.html">Array<Index,1,Dynamic></a> <a class="code hl_class" href="classEigen_1_1Array.html">ArrayXi</a>;</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1Ref.html">Ref<ArrayXr></a> <a class="code hl_class" href="classEigen_1_1Ref.html">ArrayRef</a>;</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keyword">typedef</span> <a class="code hl_class" href="classEigen_1_1Ref.html">Ref<ArrayXi></a> <a class="code hl_class" href="classEigen_1_1Ref.html">IndicesRef</a>;</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a9c247985636005f4aef20bc92f713cd3"> 148</a></span> <a class="code hl_function" href="classEigen_1_1BDCSVD.html#a9c247985636005f4aef20bc92f713cd3">BDCSVD</a>() : m_algoswap(16), m_isTranspose(false), m_compU(false), m_compV(false), m_numIters(0)</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> {}</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> </div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#afa37310e3f27088f3e825f59ab822ef9"> 157</a></span> <a class="code hl_function" href="classEigen_1_1BDCSVD.html#afa37310e3f27088f3e825f59ab822ef9">BDCSVD</a>(Index rows, Index cols) : m_algoswap(16), m_numIters(0) {</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> allocate(rows, cols, internal::get_computation_options(Options));</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> }</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> EIGEN_DEPRECATED</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a7d9fac78e0c239b2e8e92cd189932f21"> 176</a></span> <a class="code hl_function" href="classEigen_1_1BDCSVD.html#a7d9fac78e0c239b2e8e92cd189932f21">BDCSVD</a>(Index rows, Index cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) : m_algoswap(16), m_numIters(0) {</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, rows, cols);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> allocate(rows, cols, computationOptions);</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> }</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a586d8a4d76bb40f315f8ae290419abf3"> 186</a></span> <a class="code hl_function" href="classEigen_1_1BDCSVD.html#a586d8a4d76bb40f315f8ae290419abf3">BDCSVD</a>(<span class="keyword">const</span> MatrixType& matrix) : m_algoswap(16), m_numIters(0) {</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> compute_impl(matrix, internal::get_computation_options(Options));</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> }</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> </div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> EIGEN_DEPRECATED</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a30778887eb456715a333ccf9cb75f14e"> 203</a></span> <a class="code hl_function" href="classEigen_1_1BDCSVD.html#a30778887eb456715a333ccf9cb75f14e">BDCSVD</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) : m_algoswap(16), m_numIters(0) {</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> compute_impl(matrix, computationOptions);</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> }</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> </div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <a class="code hl_class" href="classEigen_1_1BDCSVD.html">~BDCSVD</a>() {}</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#af18517139ba21f69036795cbce1bf542"> 215</a></span> <a class="code hl_class" href="classEigen_1_1BDCSVD.html">BDCSVD</a>& <a class="code hl_function" href="classEigen_1_1BDCSVD.html#af18517139ba21f69036795cbce1bf542">compute</a>(<span class="keyword">const</span> MatrixType& matrix) { <span class="keywordflow">return</span> compute_impl(matrix, m_computationOptions); }</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> </div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> EIGEN_DEPRECATED</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#ab68faab9299de41b7028818d37daffdc"> 227</a></span> <a class="code hl_class" href="classEigen_1_1BDCSVD.html">BDCSVD</a>& <a class="code hl_function" href="classEigen_1_1BDCSVD.html#ab68faab9299de41b7028818d37daffdc">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 id="l00228" name="l00228"></a><span class="lineno"> 228</span> internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">return</span> compute_impl(matrix, computationOptions);</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> }</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keywordtype">void</span> setSwitchSize(<span class="keywordtype">int</span> s)</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> {</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> eigen_assert(s>=3 && <span class="stringliteral">"BDCSVD the size of the algo switch has to be at least 3."</span>);</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> m_algoswap = s;</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> }</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> </div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <a class="code hl_function" href="classEigen_1_1BDCSVD.html#a9c247985636005f4aef20bc92f713cd3">BDCSVD</a>& compute_impl(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keywordtype">void</span> divide(Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift);</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordtype">void</span> computeSVDofM(Index firstCol, Index n, MatrixXr& U, VectorType& singVals, MatrixXr& V);</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="keywordtype">void</span> computeSingVals(<span class="keyword">const</span> ArrayRef& col0, <span class="keyword">const</span> ArrayRef& diag, <span class="keyword">const</span> IndicesRef& perm, VectorType& singVals, ArrayRef shifts, ArrayRef mus);</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keywordtype">void</span> perturbCol0(<span class="keyword">const</span> ArrayRef& col0, <span class="keyword">const</span> ArrayRef& diag, <span class="keyword">const</span> IndicesRef& perm, <span class="keyword">const</span> VectorType& singVals, <span class="keyword">const</span> ArrayRef& shifts, <span class="keyword">const</span> ArrayRef& mus, ArrayRef zhat);</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keywordtype">void</span> computeSingVecs(<span class="keyword">const</span> ArrayRef& zhat, <span class="keyword">const</span> ArrayRef& diag, <span class="keyword">const</span> IndicesRef& perm, <span class="keyword">const</span> VectorType& singVals, <span class="keyword">const</span> ArrayRef& shifts, <span class="keyword">const</span> ArrayRef& mus, MatrixXr& U, MatrixXr& V);</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keywordtype">void</span> deflation43(Index firstCol, Index shift, Index i, Index <a class="code hl_function" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>);</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keywordtype">void</span> deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index <a class="code hl_function" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>);</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keywordtype">void</span> deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift);</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="keyword">template</span><<span class="keyword">typename</span> HouseholderU, <span class="keyword">typename</span> HouseholderV, <span class="keyword">typename</span> NaiveU, <span class="keyword">typename</span> NaiveV></div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keywordtype">void</span> copyUV(<span class="keyword">const</span> HouseholderU &householderU, <span class="keyword">const</span> HouseholderV &householderV, <span class="keyword">const</span> NaiveU &naiveU, <span class="keyword">const</span> NaiveV &naivev);</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keywordtype">void</span> structured_update(Block<MatrixXr,Dynamic,Dynamic> A, <span class="keyword">const</span> MatrixXr &B, Index n1);</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keyword">static</span> RealScalar secularEq(RealScalar x, <span class="keyword">const</span> ArrayRef& col0, <span class="keyword">const</span> ArrayRef& diag, <span class="keyword">const</span> IndicesRef &perm, <span class="keyword">const</span> ArrayRef& diagShifted, RealScalar shift);</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SVDType></div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keywordtype">void</span> computeBaseCase(SVDType& svd, Index n, Index firstCol, Index firstRowW, Index firstColW, Index shift);</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keyword">protected</span>:</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</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 id="l00257" name="l00257"></a><span class="lineno"> 257</span> MatrixXr m_naiveU, m_naiveV;</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> MatrixXr m_computed;</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> Index m_nRec;</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> ArrayXr m_workspace;</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> ArrayXi m_workspaceI;</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="keywordtype">int</span> m_algoswap;</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="keywordtype">bool</span> m_isTranspose, m_compU, m_compV, m_useQrDecomp;</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> JacobiSVD<MatrixType, ComputationOptions> smallSvd;</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> HouseholderQR<MatrixX> qrDecomp;</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> internal::UpperBidiagonalization<MatrixX> bid;</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> MatrixX copyWorkspace;</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> MatrixX reducedTriangle;</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="keyword">using </span>Base::m_computationOptions;</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <span class="keyword">using </span>Base::m_computeThinU;</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <span class="keyword">using </span>Base::m_computeThinV;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keyword">using </span>Base::m_diagSize;</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="keyword">using </span>Base::m_info;</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">using </span>Base::m_isInitialized;</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keyword">using </span>Base::m_matrixU;</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keyword">using </span>Base::m_matrixV;</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> <span class="keyword">using </span>Base::m_nonzeroSingularValues;</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keyword">using </span>Base::m_singularValues;</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> </div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="keyword">public</span>:</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keywordtype">int</span> m_numIters;</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span>}; <span class="comment">// end class BDCSVD</span></div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> </div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span><span class="comment">// Method to allocate and initialize matrix and attributes</span></div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span><span class="keywordtype">void</span> BDCSVD<MatrixType, Options>::allocate(Index rows, Index cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordflow">if</span> (Base::allocate(rows, cols, computationOptions))</div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> </div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="keywordflow">if</span> (cols < m_algoswap)</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> internal::allocate_small_svd<MatrixType, ComputationOptions>::run(smallSvd, rows, cols, computationOptions);</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> </div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> m_computed = MatrixXr::Zero(m_diagSize + 1, m_diagSize );</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> m_compU = computeV();</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> m_compV = computeU();</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> m_isTranspose = (cols > rows);</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <span class="keywordflow">if</span> (m_isTranspose)</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> std::swap(m_compU, m_compV);</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> </div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <span class="comment">// kMinAspectRatio is the crossover point that determines if we perform R-Bidiagonalization</span></div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="comment">// or bidiagonalize the input matrix directly.</span></div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> <span class="comment">// It is based off of LAPACK's dgesdd routine, which uses 11.0/6.0</span></div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="comment">// we use a larger scalar to prevent a regression for relatively square matrices.</span></div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="keyword">constexpr</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> kMinAspectRatio = 4;</div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keyword">constexpr</span> <span class="keywordtype">bool</span> disableQrDecomp = <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(QRDecomposition) == <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(DisableQRDecomposition);</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> m_useQrDecomp = !disableQrDecomp && ((rows / kMinAspectRatio > cols) || (cols / kMinAspectRatio > rows));</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <span class="keywordflow">if</span> (m_useQrDecomp) {</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> qrDecomp = HouseholderQR<MatrixX>((std::max)(rows, cols), (std::min)(rows, cols));</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> reducedTriangle = <a class="code hl_typedef" href="group__matrixtypedefs.html#ga8a779d79defc9f822fa6ff5869c2ba6b">MatrixX</a>(m_diagSize, m_diagSize);</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> }</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> </div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> copyWorkspace = <a class="code hl_typedef" href="group__matrixtypedefs.html#ga8a779d79defc9f822fa6ff5869c2ba6b">MatrixX</a>(m_isTranspose ? cols : rows, m_isTranspose ? rows : cols);</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> bid = internal::UpperBidiagonalization<MatrixX>(m_useQrDecomp ? m_diagSize : copyWorkspace.rows(),</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> m_useQrDecomp ? m_diagSize : copyWorkspace.cols());</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> </div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> <span class="keywordflow">if</span> (m_compU) m_naiveU = MatrixXr::Zero(m_diagSize + 1, m_diagSize + 1 );</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> <span class="keywordflow">else</span> m_naiveU = MatrixXr::Zero(2, m_diagSize + 1 );</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> </div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <span class="keywordflow">if</span> (m_compV) m_naiveV = MatrixXr::Zero(m_diagSize, m_diagSize);</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> </div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> m_workspace.resize((m_diagSize+1)*(m_diagSize+1)*3);</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> m_workspaceI.resize(3*m_diagSize);</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span>} <span class="comment">// end allocate</span></div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> </div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span>BDCSVD<MatrixType, Options>& BDCSVD<MatrixType, Options>::compute_impl(<span class="keyword">const</span> MatrixType& matrix,</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> std::cout << <span class="stringliteral">"\n\n\n======================================================================================================================\n\n\n"</span>;</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> </div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> allocate(matrix.rows(), matrix.cols(), computationOptions);</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> </div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keyword">const</span> RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> </div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> <span class="comment">//**** step -1 - If the problem is too small, directly falls back to JacobiSVD and return</span></div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="keywordflow">if</span>(matrix.cols() < m_algoswap)</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> {</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> smallSvd.compute(matrix);</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> m_info = smallSvd.info();</div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> <span class="keywordflow">if</span> (m_info == Success || m_info == NoConvergence) {</div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="keywordflow">if</span> (computeU()) m_matrixU = smallSvd.matrixU();</div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> <span class="keywordflow">if</span> (computeV()) m_matrixV = smallSvd.matrixV();</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> m_singularValues = smallSvd.singularValues();</div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> m_nonzeroSingularValues = smallSvd.nonzeroSingularValues();</div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> }</div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> }</div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> </div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <span class="comment">//**** step 0 - Copy the input matrix and apply scaling to reduce over/under-flows</span></div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> RealScalar scale = matrix.cwiseAbs().template maxCoeff<PropagateNaN>();</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <span class="keywordflow">if</span> (!(numext::isfinite)(scale)) {</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> m_info = <a class="code hl_enumvalue" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf">InvalidInput</a>;</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> }</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> </div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="keywordflow">if</span>(numext::is_exactly_zero(scale)) scale = Literal(1);</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> </div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> <span class="keywordflow">if</span> (m_isTranspose) copyWorkspace = matrix.adjoint() / scale;</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> <span class="keywordflow">else</span> copyWorkspace = matrix / scale;</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> </div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> <span class="comment">//**** step 1 - Bidiagonalization.</span></div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> <span class="comment">// If the problem is sufficiently rectangular, we perform R-Bidiagonalization: compute A = Q(R/0)</span></div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> <span class="comment">// and then bidiagonalize R. Otherwise, if the problem is relatively square, we</span></div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> <span class="comment">// bidiagonalize the input matrix directly.</span></div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="keywordflow">if</span> (m_useQrDecomp) {</div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> qrDecomp.compute(copyWorkspace);</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> reducedTriangle = qrDecomp.matrixQR().topRows(m_diagSize);</div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> reducedTriangle.template triangularView<StrictlyLower>().setZero();</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> bid.compute(reducedTriangle);</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> bid.compute(copyWorkspace);</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> }</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> </div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> <span class="comment">//**** step 2 - Divide & Conquer</span></div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> m_naiveU.setZero();</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> m_naiveV.setZero();</div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span> <span class="comment">// FIXME this line involves a temporary matrix</span></div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> m_computed.topRows(m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();</div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span> m_computed.template bottomRows<1>().setZero();</div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> divide(0, m_diagSize - 1, 0, 0, 0);</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> <span class="keywordflow">if</span> (m_info != Success && m_info != NoConvergence) {</div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> }</div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> </div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="comment">//**** step 3 - Copy singular values and vectors</span></div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i<m_diagSize; i++)</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> {</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> RealScalar a = abs(m_computed.coeff(i, i));</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> m_singularValues.coeffRef(i) = a * scale;</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> <span class="keywordflow">if</span> (a<considerZero)</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> {</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> m_nonzeroSingularValues = i;</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> m_singularValues.tail(m_diagSize - i - 1).setZero();</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> }</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i == m_diagSize - 1)</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> {</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> m_nonzeroSingularValues = i + 1;</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> }</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> }</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> </div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> <span class="comment">//**** step 4 - Finalize unitaries U and V</span></div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <span class="keywordflow">if</span>(m_isTranspose) copyUV(bid.householderV(), bid.householderU(), m_naiveV, m_naiveU);</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <span class="keywordflow">else</span> copyUV(bid.householderU(), bid.householderV(), m_naiveU, m_naiveV);</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> </div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="keywordflow">if</span> (m_useQrDecomp) {</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <span class="keywordflow">if</span> (m_isTranspose && computeV()) m_matrixV.applyOnTheLeft(qrDecomp.householderQ());</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!m_isTranspose && computeU()) m_matrixU.applyOnTheLeft(qrDecomp.householderQ());</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> }</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> </div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span>} <span class="comment">// end compute</span></div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> </div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span><span class="keyword">template</span> <<span class="keyword">typename</span> HouseholderU, <span class="keyword">typename</span> HouseholderV, <span class="keyword">typename</span> NaiveU, <span class="keyword">typename</span> NaiveV></div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span><span class="keywordtype">void</span> BDCSVD<MatrixType, Options>::copyUV(<span class="keyword">const</span> HouseholderU& householderU, <span class="keyword">const</span> HouseholderV& householderV,</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <span class="keyword">const</span> NaiveU& naiveU, <span class="keyword">const</span> NaiveV& naiveV) {</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> <span class="comment">// Note exchange of U and V: m_matrixU is set from m_naiveV and vice versa</span></div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> <span class="keywordflow">if</span> (computeU())</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> {</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> Ucols = m_computeThinU ? m_diagSize : rows();</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> m_matrixU = MatrixX::Identity(rows(), Ucols);</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> m_matrixU.topLeftCorner(m_diagSize, m_diagSize) = naiveV.template cast<Scalar>().topLeftCorner(m_diagSize, m_diagSize);</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="comment">// FIXME the following conditionals involve temporary buffers</span></div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> <span class="keywordflow">if</span> (m_useQrDecomp) m_matrixU.topLeftCorner(householderU.cols(), m_diagSize).applyOnTheLeft(householderU);</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> <span class="keywordflow">else</span> m_matrixU.applyOnTheLeft(householderU);</div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> }</div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <span class="keywordflow">if</span> (computeV())</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> {</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> Vcols = m_computeThinV ? m_diagSize : cols();</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> m_matrixV = MatrixX::Identity(cols(), Vcols);</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> m_matrixV.topLeftCorner(m_diagSize, m_diagSize) = naiveU.template cast<Scalar>().topLeftCorner(m_diagSize, m_diagSize);</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> <span class="comment">// FIXME the following conditionals involve temporary buffers</span></div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> <span class="keywordflow">if</span> (m_useQrDecomp) m_matrixV.topLeftCorner(householderV.cols(), m_diagSize).applyOnTheLeft(householderV);</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> <span class="keywordflow">else</span> m_matrixV.applyOnTheLeft(householderV);</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> }</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span>}</div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> </div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span><span class="keywordtype">void</span> BDCSVD<MatrixType, Options>::structured_update(Block<MatrixXr, Dynamic, Dynamic> A, <span class="keyword">const</span> MatrixXr& B, Index n1) {</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = A.rows();</div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> <span class="keywordflow">if</span>(n>100)</div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> {</div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> <span class="comment">// If the matrices are large enough, let's exploit the sparse structure of A by</span></div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> <span class="comment">// splitting it in half (wrt n1), and packing the non-zero columns.</span></div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n2 = n - n1;</div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> Map<MatrixXr> A1(m_workspace.data() , n1, n);</div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> Map<MatrixXr> A2(m_workspace.data()+ n1*n, n2, n);</div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> Map<MatrixXr> B1(m_workspace.data()+ n*n, n, n);</div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> Map<MatrixXr> B2(m_workspace.data()+2*n*n, n, n);</div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k1=0, k2=0;</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> <span class="keywordflow">for</span>(Index j=0; j<n; ++j)</div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> {</div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="keywordflow">if</span>( (A.col(j).head(n1).array()!=Literal(0)).any() )</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> {</div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> A1.col(k1) = A.col(j).head(n1);</div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> B1.row(k1) = B.row(j);</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> ++k1;</div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> }</div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> <span class="keywordflow">if</span>( (A.col(j).tail(n2).array()!=Literal(0)).any() )</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> {</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> A2.col(k2) = A.col(j).tail(n2);</div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> B2.row(k2) = B.row(j);</div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> ++k2;</div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> }</div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> }</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> </div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> A.topRows(n1).noalias() = A1.leftCols(k1) * B1.topRows(k1);</div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> A.bottomRows(n2).noalias() = A2.leftCols(k2) * B2.topRows(k2);</div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> }</div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> {</div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> Map<MatrixXr,Aligned> tmp(m_workspace.data(),n,n);</div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> tmp.noalias() = A*B;</div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> A = tmp;</div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> }</div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span>}</div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> </div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span><span class="keyword">template</span> <<span class="keyword">typename</span> SVDType></div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span><span class="keywordtype">void</span> BDCSVD<MatrixType, Options>::computeBaseCase(SVDType& svd, Index n, Index firstCol, Index firstRowW,</div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> Index firstColW, Index shift) {</div>
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> svd.compute(m_computed.block(firstCol, firstCol, n + 1, n));</div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span> m_info = svd.info();</div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> <span class="keywordflow">if</span> (m_info != Success && m_info != NoConvergence) <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() = svd.matrixU();</div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> m_naiveU.row(0).segment(firstCol, n + 1).real() = svd.matrixU().row(0);</div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> m_naiveU.row(1).segment(firstCol, n + 1).real() = svd.matrixU().row(n);</div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> }</div>
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> <span class="keywordflow">if</span> (m_compV) m_naiveV.block(firstRowW, firstColW, n, n).real() = svd.matrixV();</div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> m_computed.block(firstCol + shift, firstCol + shift, n + 1, n).setZero();</div>
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span> m_computed.diagonal().segment(firstCol + shift, n) = svd.singularValues().head(n);</div>
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span>}</div>
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> </div>
<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span><span class="comment">// The divide algorithm is done "in place", we are always working on subsets of the same matrix. The divide methods</span></div>
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span><span class="comment">// takes as argument the place of the submatrix we are currently working on.</span></div>
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> </div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span><span class="comment">//@param firstCol : The Index of the first column of the submatrix of m_computed and for m_naiveU;</span></div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span><span class="comment">//@param lastCol : The Index of the last column of the submatrix of m_computed and for m_naiveU;</span></div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span><span class="comment">// lastCol + 1 - firstCol is the size of the submatrix.</span></div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span><span class="comment">//@param firstRowW : The Index of the first row of the matrix W that we are to change. (see the reference paper section 1 for more information on W)</span></div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span><span class="comment">//@param firstColW : Same as firstRowW with the column.</span></div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span><span class="comment">//@param shift : Each time one takes the left submatrix, one must add 1 to the shift. Why? Because! We actually want the last column of the U submatrix</span></div>
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span><span class="comment">// to become the first column (*coeff) and to shift all the other columns to the right. There are more details on the reference paper.</span></div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span><span class="keywordtype">void</span> BDCSVD<MatrixType, Options>::divide(Index firstCol, Index lastCol, Index firstRowW,</div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> Index firstColW, Index shift) {</div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> <span class="comment">// requires rows = cols + 1;</span></div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <span class="keyword">using </span>std::pow;</div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> <span class="keyword">using </span>std::sqrt;</div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = lastCol - firstCol + 1;</div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = n/2;</div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> <span class="keyword">const</span> RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();</div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> RealScalar alphaK;</div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> RealScalar betaK;</div>
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span> RealScalar r0;</div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> RealScalar lambda, phi, c0, s0;</div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> VectorType l, f;</div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> <span class="comment">// We use the other algorithm which is more efficient for small</span></div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> <span class="comment">// matrices.</span></div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> <span class="keywordflow">if</span> (n < m_algoswap)</div>
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span> {</div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> <span class="comment">// FIXME this block involves temporaries</span></div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> <span class="keywordflow">if</span> (m_compV) {</div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> JacobiSVD<MatrixXr, ComputeFullU | ComputeFullV> baseSvd;</div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span> computeBaseCase(baseSvd, n, firstCol, firstRowW, firstColW, shift);</div>
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span> JacobiSVD<MatrixXr, ComputeFullU> baseSvd;</div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> computeBaseCase(baseSvd, n, firstCol, firstRowW, firstColW, shift);</div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> }</div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span> }</div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> <span class="comment">// We use the divide and conquer algorithm</span></div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> alphaK = m_computed(firstCol + k, firstCol + k);</div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> betaK = m_computed(firstCol + k + 1, firstCol + k);</div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> <span class="comment">// The divide must be done in that order in order to have good results. Divide change the data inside the submatrices</span></div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> <span class="comment">// and the divide of the right submatrice reads one column of the left submatrice. That's why we need to treat the</span></div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> <span class="comment">// right submatrix before the left one.</span></div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift);</div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> <span class="keywordflow">if</span> (m_info != Success && m_info != NoConvergence) <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1);</div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> <span class="keywordflow">if</span> (m_info != Success && m_info != NoConvergence) <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> </div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span> {</div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> lambda = m_naiveU(firstCol + k, firstCol + k);</div>
<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span> phi = m_naiveU(firstCol + k + 1, lastCol + 1);</div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> }</div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> {</div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> lambda = m_naiveU(1, firstCol + k);</div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> phi = m_naiveU(0, lastCol + 1);</div>
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> }</div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda)) + abs(betaK * phi) * abs(betaK * phi));</div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span> <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> {</div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> l = m_naiveU.row(firstCol + k).segment(firstCol, k);</div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1);</div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> }</div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> {</div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> l = m_naiveU.row(1).segment(firstCol, k);</div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1);</div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> }</div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> <span class="keywordflow">if</span> (m_compV) m_naiveV(firstRowW+k, firstColW) = Literal(1);</div>
<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> <span class="keywordflow">if</span> (r0<considerZero)</div>
<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> {</div>
<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> c0 = Literal(1);</div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> s0 = Literal(0);</div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> }</div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> {</div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> c0 = alphaK * lambda / r0;</div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> s0 = betaK * phi / r0;</div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> }</div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> </div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> eigen_internal_assert(m_naiveU.allFinite());</div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> eigen_internal_assert(m_naiveV.allFinite());</div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> eigen_internal_assert(m_computed.allFinite());</div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> </div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> {</div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> MatrixXr q1 (m_naiveU.col(firstCol + k).segment(firstCol, k + 1));</div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> <span class="comment">// we shiftW Q1 to the right</span></div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> <span class="keywordflow">for</span> (Index i = firstCol + k - 1; i >= firstCol; i--)</div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> m_naiveU.col(i + 1).segment(firstCol, k + 1) = m_naiveU.col(i).segment(firstCol, k + 1);</div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span> <span class="comment">// we shift q1 at the left with a factor c0</span></div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span> m_naiveU.col(firstCol).segment( firstCol, k + 1) = (q1 * c0);</div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span> <span class="comment">// last column = q1 * - s0</span></div>
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> m_naiveU.col(lastCol + 1).segment(firstCol, k + 1) = (q1 * ( - s0));</div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span> <span class="comment">// first column = q2 * s0</span></div>
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span> m_naiveU.col(firstCol).segment(firstCol + k + 1, n - k) = m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) * s0;</div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span> <span class="comment">// q2 *= c0</span></div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *= c0;</div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span> }</div>
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> {</div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> RealScalar q1 = m_naiveU(0, firstCol + k);</div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> <span class="comment">// we shift Q1 to the right</span></div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> <span class="keywordflow">for</span> (Index i = firstCol + k - 1; i >= firstCol; i--)</div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> m_naiveU(0, i + 1) = m_naiveU(0, i);</div>
<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> <span class="comment">// we shift q1 at the left with a factor c0</span></div>
<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span> m_naiveU(0, firstCol) = (q1 * c0);</div>
<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> <span class="comment">// last column = q1 * - s0</span></div>
<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span> m_naiveU(0, lastCol + 1) = (q1 * ( - s0));</div>
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span> <span class="comment">// first column = q2 * s0</span></div>
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span> m_naiveU(1, firstCol) = m_naiveU(1, lastCol + 1) *s0;</div>
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> <span class="comment">// q2 *= c0</span></div>
<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span> m_naiveU(1, lastCol + 1) *= c0;</div>
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span> m_naiveU.row(1).segment(firstCol + 1, k).setZero();</div>
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span> m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1).setZero();</div>
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span> }</div>
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span> </div>
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span> eigen_internal_assert(m_naiveU.allFinite());</div>
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> eigen_internal_assert(m_naiveV.allFinite());</div>
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> eigen_internal_assert(m_computed.allFinite());</div>
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span> </div>
<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span> m_computed(firstCol + shift, firstCol + shift) = r0;</div>
<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"> 642</span> m_computed.col(firstCol + shift).segment(firstCol + shift + 1, k) = alphaK * l.transpose().real();</div>
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span> m_computed.col(firstCol + shift).segment(firstCol + shift + k + 1, n - k - 1) = betaK * f.transpose().real();</div>
<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span> </div>
<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> ArrayXr tmp1 = (m_computed.block(firstCol+shift, firstCol+shift, n, n)).jacobiSvd().singularValues();</div>
<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"> 648</span> <span class="comment">// Second part: try to deflate singular values in combined matrix</span></div>
<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span> deflation(firstCol, lastCol, k, firstRowW, firstColW, shift);</div>
<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00651" name="l00651"></a><span class="lineno"> 651</span> ArrayXr tmp2 = (m_computed.block(firstCol+shift, firstCol+shift, n, n)).jacobiSvd().singularValues();</div>
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"> 652</span> std::cout << <span class="stringliteral">"\n\nj1 = "</span> << tmp1.transpose().format(bdcsvdfmt) << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> std::cout << <span class="stringliteral">"j2 = "</span> << tmp2.transpose().format(bdcsvdfmt) << <span class="stringliteral">"\n\n"</span>;</div>
<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span> std::cout << <span class="stringliteral">"err: "</span> << ((tmp1-tmp2).abs()>1e-12*tmp2.abs()).transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span> <span class="keyword">static</span> <span class="keywordtype">int</span> count = 0;</div>
<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span> std::cout << <span class="stringliteral">"# "</span> << ++count << <span class="stringliteral">"\n\n"</span>;</div>
<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> eigen_internal_assert((tmp1-tmp2).matrix().norm() < 1e-14*tmp2.matrix().norm());</div>
<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span><span class="comment">// eigen_internal_assert(count<681);</span></div>
<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span><span class="comment">// eigen_internal_assert(((tmp1-tmp2).abs()<1e-13*tmp2.abs()).all());</span></div>
<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span> </div>
<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"> 662</span> <span class="comment">// Third part: compute SVD of combined matrix</span></div>
<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> MatrixXr UofSVD, VofSVD;</div>
<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> VectorType singVals;</div>
<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> computeSVDofM(firstCol + shift, n, UofSVD, singVals, VofSVD);</div>
<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> </div>
<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span> eigen_internal_assert(UofSVD.allFinite());</div>
<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> eigen_internal_assert(VofSVD.allFinite());</div>
<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> </div>
<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</span> <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> structured_update(m_naiveU.block(firstCol, firstCol, n + 1, n + 1), UofSVD, (n+2)/2);</div>
<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> {</div>
<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span> Map<Matrix<RealScalar,2,Dynamic>,<a class="code hl_enumvalue" href="group__enums.html#gga45fe06e29902b7a2773de05ba27b47a1ae12d0f8f869c40c76128260af2242bc8">Aligned</a>> tmp(m_workspace.data(),2,n+1);</div>
<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> tmp.noalias() = m_naiveU.middleCols(firstCol, n+1) * UofSVD;</div>
<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</span> m_naiveU.middleCols(firstCol, n + 1) = tmp;</div>
<div class="line"><a id="l00679" name="l00679"></a><span class="lineno"> 679</span> }</div>
<div class="line"><a id="l00680" name="l00680"></a><span class="lineno"> 680</span> </div>
<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</span> <span class="keywordflow">if</span> (m_compV) structured_update(m_naiveV.block(firstRowW, firstColW, n, n), VofSVD, (n+1)/2);</div>
<div class="line"><a id="l00682" name="l00682"></a><span class="lineno"> 682</span> </div>
<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> eigen_internal_assert(m_naiveU.allFinite());</div>
<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> eigen_internal_assert(m_naiveV.allFinite());</div>
<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> eigen_internal_assert(m_computed.allFinite());</div>
<div class="line"><a id="l00687" name="l00687"></a><span class="lineno"> 687</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> </div>
<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span> m_computed.block(firstCol + shift, firstCol + shift, n, n).setZero();</div>
<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span> m_computed.block(firstCol + shift, firstCol + shift, n, n).diagonal() = singVals;</div>
<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span>} <span class="comment">// end divide</span></div>
<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span> </div>
<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"> 693</span><span class="comment">// Compute SVD of m_computed.block(firstCol, firstCol, n + 1, n); this block only has non-zeros in</span></div>
<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span><span class="comment">// the first column and on the diagonal and has undergone deflation, so diagonal is in increasing</span></div>
<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span><span class="comment">// order except for possibly the (0,0) entry. The computed SVD is stored U, singVals and V, except</span></div>
<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span><span class="comment">// that if m_compV is false, then V is not computed. Singular values are sorted in decreasing order.</span></div>
<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span><span class="comment">//</span></div>
<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span><span class="comment">// TODO Opportunities for optimization: better root finding algo, better stopping criterion, better</span></div>
<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span><span class="comment">// handling of round-off errors, be consistent in ordering</span></div>
<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span><span class="comment">// For instance, to solve the secular equation using FMM, see http://www.stat.uchicago.edu/~lekheng/courses/302/classics/greengard-rokhlin.pdf</span></div>
<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"> 701</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span><span class="keywordtype">void</span> BDCSVD<MatrixType, Options>::computeSVDofM(Index firstCol, Index n, MatrixXr& U,</div>
<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span> VectorType& singVals, MatrixXr& V) {</div>
<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span> <span class="keyword">const</span> RealScalar considerZero = (std::numeric_limits<RealScalar>::min)();</div>
<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"> 706</span> ArrayRef col0 = m_computed.col(firstCol).segment(firstCol, n);</div>
<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> m_workspace.head(n) = m_computed.block(firstCol, firstCol, n, n).diagonal();</div>
<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> ArrayRef diag = m_workspace.head(n);</div>
<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"> 709</span> diag(0) = Literal(0);</div>
<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> </div>
<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> <span class="comment">// Allocate space for singular values and vectors</span></div>
<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> singVals.resize(n);</div>
<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span> U.resize(n+1, n+1);</div>
<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> <span class="keywordflow">if</span> (m_compV) V.resize(n, n);</div>
<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> </div>
<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> <span class="keywordflow">if</span> (col0.hasNaN() || diag.hasNaN())</div>
<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> std::cout << <span class="stringliteral">"\n\nHAS NAN\n\n"</span>;</div>
<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> </div>
<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span> <span class="comment">// Many singular values might have been deflated, the zero ones have been moved to the end,</span></div>
<div class="line"><a id="l00722" name="l00722"></a><span class="lineno"> 722</span> <span class="comment">// but others are interleaved and we must ignore them at this stage.</span></div>
<div class="line"><a id="l00723" name="l00723"></a><span class="lineno"> 723</span> <span class="comment">// To this end, let's compute a permutation skipping them:</span></div>
<div class="line"><a id="l00724" name="l00724"></a><span class="lineno"> 724</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> actual_n = n;</div>
<div class="line"><a id="l00725" name="l00725"></a><span class="lineno"> 725</span> <span class="keywordflow">while</span>(actual_n>1 && numext::is_exactly_zero(diag(actual_n - 1))) {</div>
<div class="line"><a id="l00726" name="l00726"></a><span class="lineno"> 726</span> --actual_n;</div>
<div class="line"><a id="l00727" name="l00727"></a><span class="lineno"> 727</span> eigen_internal_assert(numext::is_exactly_zero(col0(actual_n)));</div>
<div class="line"><a id="l00728" name="l00728"></a><span class="lineno"> 728</span> }</div>
<div class="line"><a id="l00729" name="l00729"></a><span class="lineno"> 729</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = 0; <span class="comment">// size of the deflated problem</span></div>
<div class="line"><a id="l00730" name="l00730"></a><span class="lineno"> 730</span> <span class="keywordflow">for</span>(Index k=0;k<actual_n;++k)</div>
<div class="line"><a id="l00731" name="l00731"></a><span class="lineno"> 731</span> <span class="keywordflow">if</span>(abs(col0(k))>considerZero)</div>
<div class="line"><a id="l00732" name="l00732"></a><span class="lineno"> 732</span> m_workspaceI(m++) = k;</div>
<div class="line"><a id="l00733" name="l00733"></a><span class="lineno"> 733</span> Map<ArrayXi> perm(m_workspaceI.data(),m);</div>
<div class="line"><a id="l00734" name="l00734"></a><span class="lineno"> 734</span> </div>
<div class="line"><a id="l00735" name="l00735"></a><span class="lineno"> 735</span> Map<ArrayXr> shifts(m_workspace.data()+1*n, n);</div>
<div class="line"><a id="l00736" name="l00736"></a><span class="lineno"> 736</span> Map<ArrayXr> mus(m_workspace.data()+2*n, n);</div>
<div class="line"><a id="l00737" name="l00737"></a><span class="lineno"> 737</span> Map<ArrayXr> zhat(m_workspace.data()+3*n, n);</div>
<div class="line"><a id="l00738" name="l00738"></a><span class="lineno"> 738</span> </div>
<div class="line"><a id="l00739" name="l00739"></a><span class="lineno"> 739</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00740" name="l00740"></a><span class="lineno"> 740</span> std::cout << <span class="stringliteral">"computeSVDofM using:\n"</span>;</div>
<div class="line"><a id="l00741" name="l00741"></a><span class="lineno"> 741</span> std::cout << <span class="stringliteral">" z: "</span> << col0.transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00742" name="l00742"></a><span class="lineno"> 742</span> std::cout << <span class="stringliteral">" d: "</span> << diag.transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00743" name="l00743"></a><span class="lineno"> 743</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00744" name="l00744"></a><span class="lineno"> 744</span> </div>
<div class="line"><a id="l00745" name="l00745"></a><span class="lineno"> 745</span> <span class="comment">// Compute singVals, shifts, and mus</span></div>
<div class="line"><a id="l00746" name="l00746"></a><span class="lineno"> 746</span> computeSingVals(col0, diag, perm, singVals, shifts, mus);</div>
<div class="line"><a id="l00747" name="l00747"></a><span class="lineno"> 747</span> </div>
<div class="line"><a id="l00748" name="l00748"></a><span class="lineno"> 748</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00749" name="l00749"></a><span class="lineno"> 749</span> std::cout << <span class="stringliteral">" j: "</span> << (m_computed.block(firstCol, firstCol, n, n)).jacobiSvd().singularValues().transpose().reverse() << <span class="stringliteral">"\n\n"</span>;</div>
<div class="line"><a id="l00750" name="l00750"></a><span class="lineno"> 750</span> std::cout << <span class="stringliteral">" sing-val: "</span> << singVals.transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00751" name="l00751"></a><span class="lineno"> 751</span> std::cout << <span class="stringliteral">" mu: "</span> << mus.transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00752" name="l00752"></a><span class="lineno"> 752</span> std::cout << <span class="stringliteral">" shift: "</span> << shifts.transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00753" name="l00753"></a><span class="lineno"> 753</span> </div>
<div class="line"><a id="l00754" name="l00754"></a><span class="lineno"> 754</span> {</div>
<div class="line"><a id="l00755" name="l00755"></a><span class="lineno"> 755</span> std::cout << <span class="stringliteral">"\n\n mus: "</span> << mus.head(actual_n).transpose() << <span class="stringliteral">"\n\n"</span>;</div>
<div class="line"><a id="l00756" name="l00756"></a><span class="lineno"> 756</span> std::cout << <span class="stringliteral">" check1 (expect0) : "</span> << ((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n).transpose() << <span class="stringliteral">"\n\n"</span>;</div>
<div class="line"><a id="l00757" name="l00757"></a><span class="lineno"> 757</span> eigen_internal_assert((((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n) >= 0).all());</div>
<div class="line"><a id="l00758" name="l00758"></a><span class="lineno"> 758</span> std::cout << <span class="stringliteral">" check2 (>0) : "</span> << ((singVals.array()-diag) / singVals.array()).head(actual_n).transpose() << <span class="stringliteral">"\n\n"</span>;</div>
<div class="line"><a id="l00759" name="l00759"></a><span class="lineno"> 759</span> eigen_internal_assert((((singVals.array()-diag) / singVals.array()).head(actual_n) >= 0).all());</div>
<div class="line"><a id="l00760" name="l00760"></a><span class="lineno"> 760</span> }</div>
<div class="line"><a id="l00761" name="l00761"></a><span class="lineno"> 761</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00762" name="l00762"></a><span class="lineno"> 762</span> </div>
<div class="line"><a id="l00763" name="l00763"></a><span class="lineno"> 763</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00764" name="l00764"></a><span class="lineno"> 764</span> eigen_internal_assert(singVals.allFinite());</div>
<div class="line"><a id="l00765" name="l00765"></a><span class="lineno"> 765</span> eigen_internal_assert(mus.allFinite());</div>
<div class="line"><a id="l00766" name="l00766"></a><span class="lineno"> 766</span> eigen_internal_assert(shifts.allFinite());</div>
<div class="line"><a id="l00767" name="l00767"></a><span class="lineno"> 767</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00768" name="l00768"></a><span class="lineno"> 768</span> </div>
<div class="line"><a id="l00769" name="l00769"></a><span class="lineno"> 769</span> <span class="comment">// Compute zhat</span></div>
<div class="line"><a id="l00770" name="l00770"></a><span class="lineno"> 770</span> perturbCol0(col0, diag, perm, singVals, shifts, mus, zhat);</div>
<div class="line"><a id="l00771" name="l00771"></a><span class="lineno"> 771</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00772" name="l00772"></a><span class="lineno"> 772</span> std::cout << <span class="stringliteral">" zhat: "</span> << zhat.transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00773" name="l00773"></a><span class="lineno"> 773</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00774" name="l00774"></a><span class="lineno"> 774</span> </div>
<div class="line"><a id="l00775" name="l00775"></a><span class="lineno"> 775</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00776" name="l00776"></a><span class="lineno"> 776</span> eigen_internal_assert(zhat.allFinite());</div>
<div class="line"><a id="l00777" name="l00777"></a><span class="lineno"> 777</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00778" name="l00778"></a><span class="lineno"> 778</span> </div>
<div class="line"><a id="l00779" name="l00779"></a><span class="lineno"> 779</span> computeSingVecs(zhat, diag, perm, singVals, shifts, mus, U, V);</div>
<div class="line"><a id="l00780" name="l00780"></a><span class="lineno"> 780</span> </div>
<div class="line"><a id="l00781" name="l00781"></a><span class="lineno"> 781</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00782" name="l00782"></a><span class="lineno"> 782</span> std::cout << <span class="stringliteral">"U^T U: "</span> << (U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00783" name="l00783"></a><span class="lineno"> 783</span> std::cout << <span class="stringliteral">"V^T V: "</span> << (V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00784" name="l00784"></a><span class="lineno"> 784</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00785" name="l00785"></a><span class="lineno"> 785</span> </div>
<div class="line"><a id="l00786" name="l00786"></a><span class="lineno"> 786</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00787" name="l00787"></a><span class="lineno"> 787</span> eigen_internal_assert(m_naiveU.allFinite());</div>
<div class="line"><a id="l00788" name="l00788"></a><span class="lineno"> 788</span> eigen_internal_assert(m_naiveV.allFinite());</div>
<div class="line"><a id="l00789" name="l00789"></a><span class="lineno"> 789</span> eigen_internal_assert(m_computed.allFinite());</div>
<div class="line"><a id="l00790" name="l00790"></a><span class="lineno"> 790</span> eigen_internal_assert(U.allFinite());</div>
<div class="line"><a id="l00791" name="l00791"></a><span class="lineno"> 791</span> eigen_internal_assert(V.allFinite());</div>
<div class="line"><a id="l00792" name="l00792"></a><span class="lineno"> 792</span><span class="comment">// eigen_internal_assert((U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() < 100*NumTraits<RealScalar>::epsilon() * n);</span></div>
<div class="line"><a id="l00793" name="l00793"></a><span class="lineno"> 793</span><span class="comment">// eigen_internal_assert((V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() < 100*NumTraits<RealScalar>::epsilon() * n);</span></div>
<div class="line"><a id="l00794" name="l00794"></a><span class="lineno"> 794</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00795" name="l00795"></a><span class="lineno"> 795</span> </div>
<div class="line"><a id="l00796" name="l00796"></a><span class="lineno"> 796</span> <span class="comment">// Because of deflation, the singular values might not be completely sorted.</span></div>
<div class="line"><a id="l00797" name="l00797"></a><span class="lineno"> 797</span> <span class="comment">// Fortunately, reordering them is a O(n) problem</span></div>
<div class="line"><a id="l00798" name="l00798"></a><span class="lineno"> 798</span> <span class="keywordflow">for</span>(Index i=0; i<actual_n-1; ++i)</div>
<div class="line"><a id="l00799" name="l00799"></a><span class="lineno"> 799</span> {</div>
<div class="line"><a id="l00800" name="l00800"></a><span class="lineno"> 800</span> <span class="keywordflow">if</span>(singVals(i)>singVals(i+1))</div>
<div class="line"><a id="l00801" name="l00801"></a><span class="lineno"> 801</span> {</div>
<div class="line"><a id="l00802" name="l00802"></a><span class="lineno"> 802</span> <span class="keyword">using </span>std::swap;</div>
<div class="line"><a id="l00803" name="l00803"></a><span class="lineno"> 803</span> swap(singVals(i),singVals(i+1));</div>
<div class="line"><a id="l00804" name="l00804"></a><span class="lineno"> 804</span> U.col(i).swap(U.col(i+1));</div>
<div class="line"><a id="l00805" name="l00805"></a><span class="lineno"> 805</span> <span class="keywordflow">if</span>(m_compV) V.col(i).swap(V.col(i+1));</div>
<div class="line"><a id="l00806" name="l00806"></a><span class="lineno"> 806</span> }</div>
<div class="line"><a id="l00807" name="l00807"></a><span class="lineno"> 807</span> }</div>
<div class="line"><a id="l00808" name="l00808"></a><span class="lineno"> 808</span> </div>
<div class="line"><a id="l00809" name="l00809"></a><span class="lineno"> 809</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00810" name="l00810"></a><span class="lineno"> 810</span> {</div>
<div class="line"><a id="l00811" name="l00811"></a><span class="lineno"> 811</span> <span class="keywordtype">bool</span> singular_values_sorted = (((singVals.segment(1,actual_n-1)-singVals.head(actual_n-1))).array() >= 0).all();</div>
<div class="line"><a id="l00812" name="l00812"></a><span class="lineno"> 812</span> <span class="keywordflow">if</span>(!singular_values_sorted)</div>
<div class="line"><a id="l00813" name="l00813"></a><span class="lineno"> 813</span> std::cout << <span class="stringliteral">"Singular values are not sorted: "</span> << singVals.segment(1,actual_n).transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00814" name="l00814"></a><span class="lineno"> 814</span> eigen_internal_assert(singular_values_sorted);</div>
<div class="line"><a id="l00815" name="l00815"></a><span class="lineno"> 815</span> }</div>
<div class="line"><a id="l00816" name="l00816"></a><span class="lineno"> 816</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00817" name="l00817"></a><span class="lineno"> 817</span> </div>
<div class="line"><a id="l00818" name="l00818"></a><span class="lineno"> 818</span> <span class="comment">// Reverse order so that singular values in increased order</span></div>
<div class="line"><a id="l00819" name="l00819"></a><span class="lineno"> 819</span> <span class="comment">// Because of deflation, the zeros singular-values are already at the end</span></div>
<div class="line"><a id="l00820" name="l00820"></a><span class="lineno"> 820</span> singVals.head(actual_n).reverseInPlace();</div>
<div class="line"><a id="l00821" name="l00821"></a><span class="lineno"> 821</span> U.leftCols(actual_n).rowwise().reverseInPlace();</div>
<div class="line"><a id="l00822" name="l00822"></a><span class="lineno"> 822</span> <span class="keywordflow">if</span> (m_compV) V.leftCols(actual_n).rowwise().reverseInPlace();</div>
<div class="line"><a id="l00823" name="l00823"></a><span class="lineno"> 823</span> </div>
<div class="line"><a id="l00824" name="l00824"></a><span class="lineno"> 824</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00825" name="l00825"></a><span class="lineno"> 825</span> JacobiSVD<MatrixXr> jsvd(m_computed.block(firstCol, firstCol, n, n) );</div>
<div class="line"><a id="l00826" name="l00826"></a><span class="lineno"> 826</span> std::cout << <span class="stringliteral">" * j: "</span> << jsvd.singularValues().transpose() << <span class="stringliteral">"\n\n"</span>;</div>
<div class="line"><a id="l00827" name="l00827"></a><span class="lineno"> 827</span> std::cout << <span class="stringliteral">" * sing-val: "</span> << singVals.transpose() << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00828" name="l00828"></a><span class="lineno"> 828</span><span class="comment">// std::cout << " * err: " << ((jsvd.singularValues()-singVals)>1e-13*singVals.norm()).transpose() << "\n";</span></div>
<div class="line"><a id="l00829" name="l00829"></a><span class="lineno"> 829</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00830" name="l00830"></a><span class="lineno"> 830</span>}</div>
<div class="line"><a id="l00831" name="l00831"></a><span class="lineno"> 831</span> </div>
<div class="line"><a id="l00832" name="l00832"></a><span class="lineno"> 832</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00833" name="l00833"></a><span class="lineno"> 833</span><span class="keyword">typename</span> BDCSVD<MatrixType, Options>::RealScalar BDCSVD<MatrixType, Options>::secularEq(</div>
<div class="line"><a id="l00834" name="l00834"></a><span class="lineno"> 834</span> RealScalar mu, <span class="keyword">const</span> ArrayRef& col0, <span class="keyword">const</span> ArrayRef& diag, <span class="keyword">const</span> IndicesRef& perm, <span class="keyword">const</span> ArrayRef& diagShifted,</div>
<div class="line"><a id="l00835" name="l00835"></a><span class="lineno"> 835</span> RealScalar shift) {</div>
<div class="line"><a id="l00836" name="l00836"></a><span class="lineno"> 836</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = perm.size();</div>
<div class="line"><a id="l00837" name="l00837"></a><span class="lineno"> 837</span> RealScalar res = Literal(1);</div>
<div class="line"><a id="l00838" name="l00838"></a><span class="lineno"> 838</span> <span class="keywordflow">for</span>(Index i=0; i<m; ++i)</div>
<div class="line"><a id="l00839" name="l00839"></a><span class="lineno"> 839</span> {</div>
<div class="line"><a id="l00840" name="l00840"></a><span class="lineno"> 840</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = perm(i);</div>
<div class="line"><a id="l00841" name="l00841"></a><span class="lineno"> 841</span> <span class="comment">// The following expression could be rewritten to involve only a single division,</span></div>
<div class="line"><a id="l00842" name="l00842"></a><span class="lineno"> 842</span> <span class="comment">// but this would make the expression more sensitive to overflow.</span></div>
<div class="line"><a id="l00843" name="l00843"></a><span class="lineno"> 843</span> res += (col0(j) / (diagShifted(j) - mu)) * (col0(j) / (diag(j) + shift + mu));</div>
<div class="line"><a id="l00844" name="l00844"></a><span class="lineno"> 844</span> }</div>
<div class="line"><a id="l00845" name="l00845"></a><span class="lineno"> 845</span> <span class="keywordflow">return</span> res;</div>
<div class="line"><a id="l00846" name="l00846"></a><span class="lineno"> 846</span>}</div>
<div class="line"><a id="l00847" name="l00847"></a><span class="lineno"> 847</span> </div>
<div class="line"><a id="l00848" name="l00848"></a><span class="lineno"> 848</span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options></div>
<div class="line"><a id="l00849" name="l00849"></a><span class="lineno"> 849</span><span class="keywordtype">void</span> BDCSVD<MatrixType, Options>::computeSingVals(<span class="keyword">const</span> ArrayRef& col0, <span class="keyword">const</span> ArrayRef& diag, <span class="keyword">const</span> IndicesRef& perm,</div>
<div class="line"><a id="l00850" name="l00850"></a><span class="lineno"> 850</span> VectorType& singVals, ArrayRef shifts, ArrayRef mus) {</div>
<div class="line"><a id="l00851" name="l00851"></a><span class="lineno"> 851</span> <span class="keyword">using </span>std::abs;</div>
<div class="line"><a id="l00852" name="l00852"></a><span class="lineno"> 852</span> <span class="keyword">using </span>std::swap;</div>
<div class="line"><a id="l00853" name="l00853"></a><span class="lineno"> 853</span> <span class="keyword">using </span>std::sqrt;</div>
<div class="line"><a id="l00854" name="l00854"></a><span class="lineno"> 854</span> </div>
<div class="line"><a id="l00855" name="l00855"></a><span class="lineno"> 855</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = col0.size();</div>
<div class="line"><a id="l00856" name="l00856"></a><span class="lineno"> 856</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> actual_n = n;</div>
<div class="line"><a id="l00857" name="l00857"></a><span class="lineno"> 857</span> <span class="comment">// Note that here actual_n is computed based on col0(i)==0 instead of diag(i)==0 as above</span></div>
<div class="line"><a id="l00858" name="l00858"></a><span class="lineno"> 858</span> <span class="comment">// because 1) we have diag(i)==0 => col0(i)==0 and 2) if col0(i)==0, then diag(i) is already a singular value.</span></div>
<div class="line"><a id="l00859" name="l00859"></a><span class="lineno"> 859</span> <span class="keywordflow">while</span>(actual_n>1 && numext::is_exactly_zero(col0(actual_n - 1))) --actual_n;</div>
<div class="line"><a id="l00860" name="l00860"></a><span class="lineno"> 860</span> </div>
<div class="line"><a id="l00861" name="l00861"></a><span class="lineno"> 861</span> <span class="keywordflow">for</span> (Index k = 0; k < n; ++k)</div>
<div class="line"><a id="l00862" name="l00862"></a><span class="lineno"> 862</span> {</div>
<div class="line"><a id="l00863" name="l00863"></a><span class="lineno"> 863</span> <span class="keywordflow">if</span> (numext::is_exactly_zero(col0(k)) || actual_n == 1)</div>
<div class="line"><a id="l00864" name="l00864"></a><span class="lineno"> 864</span> {</div>
<div class="line"><a id="l00865" name="l00865"></a><span class="lineno"> 865</span> <span class="comment">// if col0(k) == 0, then entry is deflated, so singular value is on diagonal</span></div>
<div class="line"><a id="l00866" name="l00866"></a><span class="lineno"> 866</span> <span class="comment">// if actual_n==1, then the deflated problem is already diagonalized</span></div>
<div class="line"><a id="l00867" name="l00867"></a><span class="lineno"> 867</span> singVals(k) = k==0 ? col0(0) : diag(k);</div>
<div class="line"><a id="l00868" name="l00868"></a><span class="lineno"> 868</span> mus(k) = Literal(0);</div>
<div class="line"><a id="l00869" name="l00869"></a><span class="lineno"> 869</span> shifts(k) = k==0 ? col0(0) : diag(k);</div>
<div class="line"><a id="l00870" name="l00870"></a><span class="lineno"> 870</span> <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00871" name="l00871"></a><span class="lineno"> 871</span> }</div>
<div class="line"><a id="l00872" name="l00872"></a><span class="lineno"> 872</span> </div>
<div class="line"><a id="l00873" name="l00873"></a><span class="lineno"> 873</span> <span class="comment">// otherwise, use secular equation to find singular value</span></div>
<div class="line"><a id="l00874" name="l00874"></a><span class="lineno"> 874</span> RealScalar left = diag(k);</div>
<div class="line"><a id="l00875" name="l00875"></a><span class="lineno"> 875</span> RealScalar right; <span class="comment">// was: = (k != actual_n-1) ? diag(k+1) : (diag(actual_n-1) + col0.matrix().norm());</span></div>
<div class="line"><a id="l00876" name="l00876"></a><span class="lineno"> 876</span> <span class="keywordflow">if</span>(k==actual_n-1)</div>
<div class="line"><a id="l00877" name="l00877"></a><span class="lineno"> 877</span> right = (diag(actual_n-1) + col0.matrix().norm());</div>
<div class="line"><a id="l00878" name="l00878"></a><span class="lineno"> 878</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00879" name="l00879"></a><span class="lineno"> 879</span> {</div>
<div class="line"><a id="l00880" name="l00880"></a><span class="lineno"> 880</span> <span class="comment">// Skip deflated singular values,</span></div>
<div class="line"><a id="l00881" name="l00881"></a><span class="lineno"> 881</span> <span class="comment">// recall that at this stage we assume that z[j]!=0 and all entries for which z[j]==0 have been put aside.</span></div>
<div class="line"><a id="l00882" name="l00882"></a><span class="lineno"> 882</span> <span class="comment">// This should be equivalent to using perm[]</span></div>
<div class="line"><a id="l00883" name="l00883"></a><span class="lineno"> 883</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> l = k+1;</div>
<div class="line"><a id="l00884" name="l00884"></a><span class="lineno"> 884</span> <span class="keywordflow">while</span>(numext::is_exactly_zero(col0(l))) { ++l; eigen_internal_assert(l < actual_n); }</div>
<div class="line"><a id="l00885" name="l00885"></a><span class="lineno"> 885</span> right = diag(l);</div>
<div class="line"><a id="l00886" name="l00886"></a><span class="lineno"> 886</span> }</div>
<div class="line"><a id="l00887" name="l00887"></a><span class="lineno"> 887</span> </div>
<div class="line"><a id="l00888" name="l00888"></a><span class="lineno"> 888</span> <span class="comment">// first decide whether it's closer to the left end or the right end</span></div>
<div class="line"><a id="l00889" name="l00889"></a><span class="lineno"> 889</span> RealScalar mid = left + (right-left) / Literal(2);</div>
<div class="line"><a id="l00890" name="l00890"></a><span class="lineno"> 890</span> RealScalar fMid = secularEq(mid, col0, diag, perm, diag, Literal(0));</div>
<div class="line"><a id="l00891" name="l00891"></a><span class="lineno"> 891</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a id="l00892" name="l00892"></a><span class="lineno"> 892</span> std::cout << <span class="stringliteral">"right-left = "</span> << right-left << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00893" name="l00893"></a><span class="lineno"> 893</span><span class="comment">// std::cout << "fMid = " << fMid << " " << secularEq(mid-left, col0, diag, perm, ArrayXr(diag-left), left)</span></div>
<div class="line"><a id="l00894" name="l00894"></a><span class="lineno"> 894</span><span class="comment">// << " " << secularEq(mid-right, col0, diag, perm, ArrayXr(diag-right), right) << "\n";</span></div>
<div class="line"><a id="l00895" name="l00895"></a><span class="lineno"> 895</span> std::cout << <span class="stringliteral">" = "</span> << secularEq(left+RealScalar(0.000001)*(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00896" name="l00896"></a><span class="lineno"> 896</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.1) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00897" name="l00897"></a><span class="lineno"> 897</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.2) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00898" name="l00898"></a><span class="lineno"> 898</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.3) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00899" name="l00899"></a><span class="lineno"> 899</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.4) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00900" name="l00900"></a><span class="lineno"> 900</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.49) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00901" name="l00901"></a><span class="lineno"> 901</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.5) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00902" name="l00902"></a><span class="lineno"> 902</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.51) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00903" name="l00903"></a><span class="lineno"> 903</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.6) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00904" name="l00904"></a><span class="lineno"> 904</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.7) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00905" name="l00905"></a><span class="lineno"> 905</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.8) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00906" name="l00906"></a><span class="lineno"> 906</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.9) *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a id="l00907" name="l00907"></a><span class="lineno"> 907</span> << <span class="stringliteral">" "</span> << secularEq(left+RealScalar(0.999999)*(right-left), col0, diag, perm, diag, 0) << <span class="stringliteral">"\n"</span>;</div>
<div class="line"><a id="l00908" name="l00908"></a><span class="lineno"> 908</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00909" name="l00909"></a><span class="lineno"> 909</span> RealScalar shift = (k == actual_n-1 || fMid > Literal(0)) ? left : right;</div>
<div class="line"><a id="l00910" name="l00910"></a><span class="lineno"> 910</span> </div>
<div class="line"><a id="l00911" name="l00911"></a><span class="lineno"> 911</span> <span class="comment">// measure everything relative to shift</span></div>
<div class="line"><a id="l00912" name="l00912"></a><span class="lineno"> 912</span> Map<ArrayXr> diagShifted(m_workspace.data()+4*n, n);</div>
<div class="line"><a id="l00913" name="l00913"></a><span class="lineno"> 913</span> diagShifted = diag - shift;</div>
<div class="line"><a id="l00914" name="l00914"></a><span class="lineno"> 914</span> </div>
<div class="line"><a id="l00915" name="l00915"></a><span class="lineno"> 915</span> <span class="keywordflow">if</span>(k!=actual_n-1)</div>
<div class="line"><a id="l00916" name="l00916"></a><span class="lineno"> 916</span> {</div>
<div class="line"><a id="l00917" name="l00917"></a><span class="lineno"> 917</span> <span class="comment">// check that after the shift, f(mid) is still negative:</span></div>
<div class="line"><a id="l00918" name="l00918"></a><span class="lineno"> 918</span> RealScalar midShifted = (right - left) / RealScalar(2);</div>
<div class="line"><a id="l00919" name="l00919"></a><span class="lineno"> 919</span> <span class="comment">// we can test exact equality here, because shift comes from `... ? left : right`</span></div>
<div class="line"><a id="l00920" name="l00920"></a><span class="lineno"> 920</span> <span class="keywordflow">if</span>(numext::equal_strict(shift, right))</div>
<div class="line"><a id="l00921" name="l00921"></a><span class="lineno"> 921</span> midShifted = -midShifted;</div>
<div class="line"><a id="l00922" name="l00922"></a><span class="lineno"> 922</span> RealScalar fMidShifted = secularEq(midShifted, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a id="l00923" name="l00923"></a><span class="lineno"> 923</span> <span class="keywordflow">if</span>(fMidShifted>0)</div>
<div class="line"><a id="l00924" name="l00924"></a><span class="lineno"> 924</span> {</div>
<div class="line"><a id="l00925" name="l00925"></a><span class="lineno"> 925</span> <span class="comment">// fMid was erroneous, fix it:</span></div>
<div class="line"><a id="l00926" name="l00926"></a><span class="lineno"> 926</span> shift = fMidShifted > Literal(0) ? left : right;</div>
<div class="line"><a id="l00927" name="l00927"></a><span class="lineno"> 927</span> diagShifted = diag - shift;</div>
<div class="line"><a id="l00928" name="l00928"></a><span class="lineno"> 928</span> }</div>
<div class="line"><a id="l00929" name="l00929"></a><span class="lineno"> 929</span> }</div>
<div class="line"><a id="l00930" name="l00930"></a><span class="lineno"> 930</span> </div>
<div class="line"><a id="l00931" name="l00931"></a><span class="lineno"> 931</span> <span class="comment">// initial guess</span></div>
<div class="line"><a id="l00932" name="l00932"></a><span class="lineno"> 932</span> RealScalar muPrev, muCur;</div>
<div class="line"><a id="l00933" name="l00933"></a><span class="lineno"> 933</span> <span class="comment">// we can test exact equality here, because shift comes from `... ? left : right`</span></div>
<div class="line"><a id="l00934" name="l00934"></a><span class="lineno"> 934</span> <span class="keywordflow">if</span> (numext::equal_strict(shift, left))</div>
<div class="line"><a id="l00935" name="l00935"></a><span class="lineno"> 935</span> {</div>
<div class="line"><a id="l00936" name="l00936"></a><span class="lineno"> 936</span> muPrev = (right - left) * RealScalar(0.1);</div>
<div class="line"><a id="l00937" name="l00937"></a><span class="lineno"> 937</span> <span class="keywordflow">if</span> (k == actual_n-1) muCur = right - left;</div>
<div class="line"><a id="l00938" name="l00938"></a><span class="lineno"> 938</span> <span class="keywordflow">else</span> muCur = (right - left) * RealScalar(0.5);</div>
<div class="line"><a id="l00939" name="l00939"></a><span class="lineno"> 939</span> }</div>
<div class="line"><a id="l00940" name="l00940"></a><span class="lineno"> 940</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00941" name="l00941"></a><span class="lineno"> 941</span> {</div>
<div class="line"><a id="l00942" name="l00942"></a><span class="lineno"> 942</span> muPrev = -(right - left) * RealScalar(0.1);</div>
<div class="line"><a id="l00943" name="l00943"></a><span class="lineno"> 943</span> muCur = -(right - left) * RealScalar(0.5);</div>
<div class="line"><a id="l00944" name="l00944"></a><span class="lineno"> 944</span> }</div>
<div class="line"><a id="l00945" name="l00945"></a><span class="lineno"> 945</span> </div>
<div class="line"><a id="l00946" name="l00946"></a><span class="lineno"> 946</span> RealScalar fPrev = secularEq(muPrev, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a id="l00947" name="l00947"></a><span class="lineno"> 947</span> RealScalar fCur = secularEq(muCur, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a id="l00948" name="l00948"></a><span class="lineno"> 948</span> <span class="keywordflow">if</span> (abs(fPrev) < abs(fCur))</div>
<div class="line"><a id="l00949" name="l00949"></a><span class="lineno"> 949</span> {</div>
<div class="line"><a id="l00950" name="l00950"></a><span class="lineno"> 950</span> swap(fPrev, fCur);</div>
<div class="line"><a id="l00951" name="l00951"></a><span class="lineno"> 951</span> swap(muPrev, muCur);</div>
<div class="line"><a id="l00952" name="l00952"></a><span class="lineno"> 952</span> }</div>
<div class="line"><a id="l00953" name="l00953"></a><span class="lineno"> 953</span> </div>
<div class="line"><a id="l00954" name="l00954"></a><span class="lineno"> 954</span> <span class="comment">// rational interpolation: fit a function of the form a / mu + b through the two previous</span></div>
<div class="line"><a id="l00955" name="l00955"></a><span class="lineno"> 955</span> <span class="comment">// iterates and use its zero to compute the next iterate</span></div>
<div class="line"><a id="l00956" name="l00956"></a><span class="lineno"> 956</span> <span class="keywordtype">bool</span> useBisection = fPrev*fCur>Literal(0);</div>
<div class="line"><a id="l00957" name="l00957"></a><span class="lineno"> 957</span> <span class="keywordflow">while</span> (!numext::is_exactly_zero(fCur) && abs(muCur - muPrev) > Literal(8) * NumTraits<RealScalar>::epsilon() * numext::maxi<RealScalar>(abs(muCur), abs(muPrev)) && abs(fCur - fPrev) > NumTraits<RealScalar>::epsilon() && !useBisection)</div>
<div class="line"><a id="l00958" name="l00958"></a><span class="lineno"> 958</span> {</div>
<div class="line"><a id="l00959" name="l00959"></a><span class="lineno"> 959</span> ++m_numIters;</div>
<div class="line"><a id="l00960" name="l00960"></a><span class="lineno"> 960</span> </div>
<div class="line"><a id="l00961" name="l00961"></a><span class="lineno"> 961</span> <span class="comment">// Find a and b such that the function f(mu) = a / mu + b matches the current and previous samples.</span></div>
<div class="line"><a id="l00962" name="l00962"></a><span class="lineno"> 962</span> RealScalar a = (fCur - fPrev) / (Literal(1)/muCur - Literal(1)/muPrev);</div>
<div class="line"><a id="l00963" name="l00963"></a><span class="lineno"> 963</span> RealScalar b = fCur - a / muCur;</div>
<div class="line"><a id="l00964" name="l00964"></a><span class="lineno"> 964</span> <span class="comment">// And find mu such that f(mu)==0:</span></div>
<div class="line"><a id="l00965" name="l00965"></a><span class="lineno"> 965</span> RealScalar muZero = -a/b;</div>
<div class="line"><a id="l00966" name="l00966"></a><span class="lineno"> 966</span> RealScalar fZero = secularEq(muZero, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a id="l00967" name="l00967"></a><span class="lineno"> 967</span> </div>
<div class="line"><a id="l00968" name="l00968"></a><span class="lineno"> 968</span><span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a id="l00969" name="l00969"></a><span class="lineno"> 969</span> eigen_internal_assert((numext::isfinite)(fZero));</div>
<div class="line"><a id="l00970" name="l00970"></a><span class="lineno"> 970</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00971" name="l00971"></a><span class="lineno"> 971</span> </div>
<div class="line"><a id="l00972" name="l00972"></a><span class="lineno"> 972</span> muPrev = muCur;</div>
<div class="line"><a id="l00973" name="l00973"></a><span class="lineno"> 973</span> fPrev = fCur;</div>
<div class="line"><a id="l00974" name="l00974"></a><span class="lineno"> 974</span> muCur = muZero;</div>
<div class="line"><a id="l00975" name="l00975"></a><span class="lineno"> 975</span> fCur = fZero;</div>
<div class="line"><a id="l00976" name="l00976"></a><span class="lineno"> 976</span> </div>
<div class="line"><a id="l00977" name="l00977"></a><span class="lineno"> 977</span> <span class="comment">// we can test exact equality here, because shift comes from `... ? left : right`</span></div>
<div class="line"><a id="l00978" name="l00978"></a><span class="lineno"> 978</span> <span class="keywordflow">if</span> (numext::equal_strict(shift, left) && (muCur < Literal(0) || muCur > right - left)) useBisection = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00979" name="l00979"></a><span class="lineno"> 979</span> <span class="keywordflow">if</span> (numext::equal_strict(shift, right) && (muCur < -(right - left) || muCur > Literal(0))) useBisection = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00980" name="l00980"></a><span class="lineno"> 980</span> <span class="keywordflow">if</span> (abs(fCur)>abs(fPrev)) useBisection = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00981" name="l00981"></a><span class="lineno"> 981</span> }</div>