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<div class="title">BDCSVD.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// </span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// We used the "A Divide-And-Conquer Algorithm for the Bidiagonal SVD"</span></div>
<div class="line"><a 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 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 name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// report</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">//</span></div>
<div class="line"><a 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 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 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 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 name="l00013"></a><span class="lineno"> 13</span> <span class="comment">//</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#ifndef EIGEN_BDCSVD_H</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_BDCSVD_H</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#define EPSILON 0.0000000000000001</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#define ALGOSWAP 32</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="keyword">namespace </span>Eigen {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType> </div>
<div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html"> 38</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a><_MatrixType></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SVDBase.html">SVDBase<_MatrixType></a> <a class="code" href="classEigen_1_1SVDBase.html">Base</a>;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">using</span> Base::rows;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">using</span> Base::cols;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<typename MatrixType::Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime, </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime, </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime), </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime, MaxColsAtCompileTime), </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  MatrixOptions = MatrixType::Options</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  };</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">typedef</span> Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  MatrixUType;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">typedef</span> Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, </div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  MatrixVType;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type<MatrixType>::type RowType;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_col_type<MatrixType>::type ColType;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keyword">typedef</span> Matrix<Scalar, Dynamic, Dynamic> MatrixX;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">typedef</span> Matrix<RealScalar, Dynamic, Dynamic> MatrixXr;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keyword">typedef</span> Matrix<RealScalar, Dynamic, 1> VectorType;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a15bb6fe0bfbcf6ac5bad8ddcafd34387"> 78</a></span>  <a class="code" href="classEigen_1_1BDCSVD.html#a15bb6fe0bfbcf6ac5bad8ddcafd34387">BDCSVD</a>()</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  : <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a><_MatrixType>::<a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a>(), </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  algoswap(ALGOSWAP)</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  {}</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> </div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a0b1282c48b843773424d97e65ee21060"> 90</a></span>  <a class="code" href="classEigen_1_1BDCSVD.html#a0b1282c48b843773424d97e65ee21060">BDCSVD</a>(Index rows, Index cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions = 0)</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  : <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a><_MatrixType>::<a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a>(), </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  algoswap(ALGOSWAP)</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  {</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  allocate(rows, cols, computationOptions);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  }</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a name="l00107"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a3c9182989cf14fd0111ad6c2bc0eb8b3"> 107</a></span>  <a class="code" href="classEigen_1_1BDCSVD.html#a3c9182989cf14fd0111ad6c2bc0eb8b3">BDCSVD</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions = 0)</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  : <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a><_MatrixType>::<a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a>(), </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  algoswap(ALGOSWAP)</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  {</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <a class="code" href="classEigen_1_1BDCSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434">compute</a>(matrix, computationOptions);</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  }</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  ~<a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD</a>() </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  {</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  }</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  SVDBase<MatrixType>& <a class="code" href="classEigen_1_1BDCSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434">compute</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="line"><a name="l00135"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a26e02670d0a94c92ab41c2bc7f70e781"> 135</a></span>  <a class="code" href="classEigen_1_1SVDBase.html">SVDBase<MatrixType></a>& <a class="code" href="classEigen_1_1BDCSVD.html#a26e02670d0a94c92ab41c2bc7f70e781">compute</a>(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  {</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1BDCSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434">compute</a>(matrix, this->m_computationOptions);</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  }</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordtype">void</span> setSwitchSize(<span class="keywordtype">int</span> s) </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  {</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  eigen_assert(s>3 && <span class="stringliteral">"BDCSVD the size of the algo switch has to be greater than 4"</span>);</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  algoswap = s;</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  }</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<BDCSVD, Rhs></div>
<div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#ac872405f6364be4078b367ac4c6c0c01"> 158</a></span>  <a class="code" href="classEigen_1_1BDCSVD.html#ac872405f6364be4078b367ac4c6c0c01">solve</a>(<span class="keyword">const</span> MatrixBase<Rhs>& b)<span class="keyword"> const</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  eigen_assert(this->m_isInitialized && <span class="stringliteral">"BDCSVD is not initialized."</span>);</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  eigen_assert(<a class="code" href="classEigen_1_1SVDBase.html">SVDBase<_MatrixType>::computeU</a>() && <a class="code" href="classEigen_1_1SVDBase.html">SVDBase<_MatrixType>::computeV</a>() && </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="stringliteral">"BDCSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice)."</span>);</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keywordflow">return</span> internal::solve_retval<BDCSVD, Rhs>(*<span class="keyword">this</span>, b.derived());</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  }</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> </div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  </div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keyword">const</span> MatrixUType& matrixU()<span class="keyword"> const</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  eigen_assert(this->m_isInitialized && <span class="stringliteral">"SVD is not initialized."</span>);</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordflow">if</span> (isTranspose){</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  eigen_assert(this-><a class="code" href="classEigen_1_1SVDBase.html#a92e99646eefbeb071ef220841555a703">computeV</a>() && <span class="stringliteral">"This SVD decomposition didn't compute U. Did you ask for it?"</span>);</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">return</span> this->m_matrixV;</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  }</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keywordflow">else</span> </div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  {</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  eigen_assert(this-><a class="code" href="classEigen_1_1SVDBase.html#a1ffab6aab715fe0918a841611a95e9aa">computeU</a>() && <span class="stringliteral">"This SVD decomposition didn't compute U. Did you ask for it?"</span>);</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">return</span> this->m_matrixU;</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  }</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  </div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  }</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keyword">const</span> MatrixVType& matrixV()<span class="keyword"> const</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  eigen_assert(this->m_isInitialized && <span class="stringliteral">"SVD is not initialized."</span>);</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordflow">if</span> (isTranspose){</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  eigen_assert(this-><a class="code" href="classEigen_1_1SVDBase.html#a1ffab6aab715fe0918a841611a95e9aa">computeU</a>() && <span class="stringliteral">"This SVD decomposition didn't compute V. Did you ask for it?"</span>);</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">return</span> this->m_matrixU;</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  }</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  {</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  eigen_assert(this-><a class="code" href="classEigen_1_1SVDBase.html#a92e99646eefbeb071ef220841555a703">computeV</a>() && <span class="stringliteral">"This SVD decomposition didn't compute V. Did you ask for it?"</span>);</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">return</span> this->m_matrixV;</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  }</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  }</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  </div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordtype">void</span> allocate(Index rows, Index cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordtype">void</span> divide (Index firstCol, Index lastCol, Index firstRowW, </div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  Index firstColW, Index shift);</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordtype">void</span> deflation43(Index firstCol, Index shift, Index i, Index size);</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordtype">void</span> deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size);</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordtype">void</span> deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift);</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordtype">void</span> copyUV(MatrixXr naiveU, MatrixXr naiveV, MatrixX householderU, MatrixX houseHolderV);</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  MatrixXr m_naiveU, m_naiveV;</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  MatrixXr m_computed;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  Index nRec;</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordtype">int</span> algoswap;</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keywordtype">bool</span> isTranspose, compU, compV;</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  </div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> }; <span class="comment">//end class BDCSVD</span></div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> </div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment">// Methode to allocate ans initialize matrix and attributs</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="keywordtype">void</span> BDCSVD<MatrixType>::allocate(Index rows, Index cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions)</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> {</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  isTranspose = (cols > rows);</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordflow">if</span> (SVDBase<MatrixType>::allocate(rows, cols, computationOptions)) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  m_computed = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize );</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">if</span> (isTranspose){</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  compU = this->computeU();</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  compV = this->computeV(); </div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  } </div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  {</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  compV = this->computeU();</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  compU = this->computeV(); </div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  }</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">if</span> (compU) m_naiveU = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize + 1 );</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">else</span> m_naiveU = MatrixXr::Zero(2, this->m_diagSize + 1 );</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">if</span> (compV) m_naiveV = MatrixXr::Zero(this->m_diagSize, this->m_diagSize);</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  </div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span> </div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">//should be changed for a cleaner implementation</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keywordflow">if</span> (isTranspose){</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keywordtype">bool</span> aux;</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">if</span> (this->computeU()||this->computeV()){</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  aux = this->m_computeFullU;</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  this->m_computeFullU = this->m_computeFullV;</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  this->m_computeFullV = aux;</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  aux = this->m_computeThinU;</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  this->m_computeThinU = this->m_computeThinV;</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  this->m_computeThinV = aux;</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  } </div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  }</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> }<span class="comment">// end allocate</span></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> </div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment">// Methode which compute the BDCSVD for the int</span></div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="keyword">template</span><></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> SVDBase<Matrix<int, Dynamic, Dynamic> >&</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  allocate(matrix.rows(), matrix.cols(), computationOptions);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  this->m_nonzeroSingularValues = 0;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  m_computed = Matrix<int, Dynamic, Dynamic>::Zero(rows(), cols());</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i<this->m_diagSize; i++) {</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  this->m_singularValues.coeffRef(i) = 0;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  }</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordflow">if</span> (this->m_computeFullU) this->m_matrixU = Matrix<int, Dynamic, Dynamic>::Zero(rows(), rows());</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">if</span> (this->m_computeFullV) this->m_matrixV = Matrix<int, Dynamic, Dynamic>::Zero(cols(), cols()); </div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  this->m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> }</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span> </div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment">// Methode which compute the BDCSVD</span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> SVDBase<MatrixType>&</div>
<div class="line"><a name="l00272"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434"> 272</a></span> <a class="code" href="classEigen_1_1BDCSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434">BDCSVD<MatrixType>::compute</a>(<span class="keyword">const</span> MatrixType& matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) </div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> {</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  allocate(matrix.rows(), matrix.cols(), computationOptions);</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span> </div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="comment">//**** step 1 Bidiagonalization isTranspose = (matrix.cols()>matrix.rows()) ;</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  MatrixType copy;</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordflow">if</span> (isTranspose) copy = matrix.adjoint();</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">else</span> copy = matrix;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  </div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  internal::UpperBidiagonalization<MatrixX > bid(copy);</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="comment">//**** step 2 Divide</span></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="comment">// this is ugly and has to be redone (care of complex cast)</span></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  MatrixXr temp;</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  temp = bid.bidiagonal().toDenseMatrix().transpose();</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  m_computed.setZero();</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i<this->m_diagSize - 1; i++) {</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  m_computed(i, i) = temp(i, i);</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  m_computed(i + 1, i) = temp(i + 1, i);</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  }</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  m_computed(this->m_diagSize - 1, this->m_diagSize - 1) = temp(this->m_diagSize - 1, this->m_diagSize - 1);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  divide(0, this->m_diagSize - 1, 0, 0, 0);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> </div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="comment">//**** step 3 copy</span></div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i<this->m_diagSize; i++) {</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  RealScalar a = abs(m_computed.coeff(i, i));</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  this->m_singularValues.coeffRef(i) = a;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keywordflow">if</span> (a == 0){</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  this->m_nonzeroSingularValues = i;</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  }</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i == this->m_diagSize - 1)</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  {</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  this->m_nonzeroSingularValues = i + 1;</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  }</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  }</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  copyUV(m_naiveV, m_naiveU, bid.householderU(), bid.householderV());</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  this->m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span> }<span class="comment">// end compute</span></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> </div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> </div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD<MatrixType>::copyUV</a>(MatrixXr naiveU, MatrixXr naiveV, MatrixX householderU, MatrixX householderV){</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keywordflow">if</span> (this->computeU()){</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  MatrixX temp = MatrixX::Zero(naiveU.rows(), naiveU.cols());</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  temp.real() = naiveU;</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">if</span> (this->m_computeThinU){</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  this->m_matrixU = MatrixX::Identity(householderU.cols(), this->m_nonzeroSingularValues );</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  this->m_matrixU.block(0, 0, this->m_diagSize, this->m_nonzeroSingularValues) = </div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  temp.block(0, 0, this->m_diagSize, this->m_nonzeroSingularValues);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  this->m_matrixU = householderU * this->m_matrixU ;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  }</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  {</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  this->m_matrixU = MatrixX::Identity(householderU.cols(), householderU.cols());</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  this->m_matrixU.block(0, 0, this->m_diagSize, this->m_diagSize) = temp.block(0, 0, this->m_diagSize, this->m_diagSize);</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  this->m_matrixU = householderU * this->m_matrixU ;</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  }</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  }</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordflow">if</span> (this->computeV()){</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  MatrixX temp = MatrixX::Zero(naiveV.rows(), naiveV.cols());</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  temp.real() = naiveV;</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordflow">if</span> (this->m_computeThinV){</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  this->m_matrixV = MatrixX::Identity(householderV.cols(),this->m_nonzeroSingularValues );</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  this->m_matrixV.block(0, 0, this->m_nonzeroSingularValues, this->m_nonzeroSingularValues) = </div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  temp.block(0, 0, this->m_nonzeroSingularValues, this->m_nonzeroSingularValues);</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  this->m_matrixV = householderV * this->m_matrixV ;</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  }</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="keywordflow">else</span> </div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  {</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  this->m_matrixV = MatrixX::Identity(householderV.cols(), householderV.cols());</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  this->m_matrixV.block(0, 0, this->m_diagSize, this->m_diagSize) = temp.block(0, 0, this->m_diagSize, this->m_diagSize);</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  this->m_matrixV = householderV * this->m_matrixV;</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  }</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  }</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> }</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span> </div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment">// The divide algorithm is done "in place", we are always working on subsets of the same matrix. The divide methods takes as argument the </span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="comment">// place of the submatrix we are currently working on.</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span> </div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</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 name="l00356"></a><span class="lineno"> 356</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 name="l00357"></a><span class="lineno"> 357</span> <span class="comment">// lastCol + 1 - firstCol is the size of the submatrix.</span></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</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 name="l00359"></a><span class="lineno"> 359</span> <span class="comment">//@param firstRowW : Same as firstRowW with the column.</span></div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</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 name="l00361"></a><span class="lineno"> 361</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 name="l00362"></a><span class="lineno"> 362</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="keywordtype">void</span> BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW, </div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  Index firstColW, Index shift)</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> {</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="comment">// requires nbRows = nbCols + 1;</span></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <span class="keyword">const</span> Index n = lastCol - firstCol + 1;</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keyword">const</span> Index k = n/2;</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  RealScalar alphaK;</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  RealScalar betaK; </div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  RealScalar r0; </div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  RealScalar lambda, phi, c0, s0;</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  MatrixXr l, f;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="comment">// We use the other algorithm which is more efficient for small </span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="comment">// matrices.</span></div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="keywordflow">if</span> (n < algoswap){</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  JacobiSVD<MatrixXr> b(m_computed.block(firstCol, firstCol, n + 1, n), </div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  ComputeFullU | (ComputeFullV * compV)) ;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">if</span> (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() << b.matrixU();</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="keywordflow">else</span> </div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  {</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  m_naiveU.row(0).segment(firstCol, n + 1).real() << b.matrixU().row(0);</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  m_naiveU.row(1).segment(firstCol, n + 1).real() << b.matrixU().row(n);</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  }</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <span class="keywordflow">if</span> (compV) m_naiveV.block(firstRowW, firstColW, n, n).real() << b.matrixV();</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  m_computed.block(firstCol + shift, firstCol + shift, n + 1, n).setZero();</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i<n; i++)</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  {</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  m_computed(firstCol + shift + i, firstCol + shift +i) = b.singularValues().coeffRef(i);</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  }</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  }</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="comment">// We use the divide and conquer algorithm</span></div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  alphaK = m_computed(firstCol + k, firstCol + k);</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  betaK = m_computed(firstCol + k + 1, firstCol + k);</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</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 name="l00400"></a><span class="lineno"> 400</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 name="l00401"></a><span class="lineno"> 401</span>  <span class="comment">// right submatrix before the left one. </span></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift);</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1);</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keywordflow">if</span> (compU)</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  {</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  lambda = m_naiveU(firstCol + k, firstCol + k);</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  phi = m_naiveU(firstCol + k + 1, lastCol + 1);</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  } </div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="keywordflow">else</span> </div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  {</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  lambda = m_naiveU(1, firstCol + k);</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  phi = m_naiveU(0, lastCol + 1);</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  }</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda))</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  + abs(betaK * phi) * abs(betaK * phi));</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="keywordflow">if</span> (compU)</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  {</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  l = m_naiveU.row(firstCol + k).segment(firstCol, k);</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1);</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  } </div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">else</span> </div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  {</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  l = m_naiveU.row(1).segment(firstCol, k);</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1);</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  }</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  <span class="keywordflow">if</span> (compV) m_naiveV(firstRowW+k, firstColW) = 1;</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  <span class="keywordflow">if</span> (r0 == 0)</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  {</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  c0 = 1;</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  s0 = 0;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  }</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  {</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  c0 = alphaK * lambda / r0;</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  s0 = betaK * phi / r0;</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  }</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="keywordflow">if</span> (compU)</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  {</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  MatrixXr q1 (m_naiveU.col(firstCol + k).segment(firstCol, k + 1)); </div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="comment">// we shiftW Q1 to the right</span></div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="keywordflow">for</span> (Index i = firstCol + k - 1; i >= firstCol; i--) </div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  {</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  m_naiveU.col(i + 1).segment(firstCol, k + 1) << m_naiveU.col(i).segment(firstCol, k + 1);</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  }</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  <span class="comment">// we shift q1 at the left with a factor c0</span></div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  m_naiveU.col(firstCol).segment( firstCol, k + 1) << (q1 * c0);</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="comment">// last column = q1 * - s0</span></div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  m_naiveU.col(lastCol + 1).segment(firstCol, k + 1) << (q1 * ( - s0));</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="comment">// first column = q2 * s0</span></div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  m_naiveU.col(firstCol).segment(firstCol + k + 1, n - k) << </div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *s0; </div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="comment">// q2 *= c0</span></div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *= c0; </div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  } </div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="keywordflow">else</span> </div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  {</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  RealScalar q1 = (m_naiveU(0, firstCol + k));</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="comment">// we shift Q1 to the right</span></div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="keywordflow">for</span> (Index i = firstCol + k - 1; i >= firstCol; i--) </div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  {</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  m_naiveU(0, i + 1) = m_naiveU(0, i);</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  }</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="comment">// we shift q1 at the left with a factor c0</span></div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  m_naiveU(0, firstCol) = (q1 * c0);</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="comment">// last column = q1 * - s0</span></div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  m_naiveU(0, lastCol + 1) = (q1 * ( - s0));</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="comment">// first column = q2 * s0</span></div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  m_naiveU(1, firstCol) = m_naiveU(1, lastCol + 1) *s0; </div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="comment">// q2 *= c0</span></div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  m_naiveU(1, lastCol + 1) *= c0;</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  m_naiveU.row(1).segment(firstCol + 1, k).setZero();</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1).setZero();</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  }</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  m_computed(firstCol + shift, firstCol + shift) = r0;</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  m_computed.col(firstCol + shift).segment(firstCol + shift + 1, k) << alphaK * l.transpose().real();</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  m_computed.col(firstCol + shift).segment(firstCol + shift + k + 1, n - k - 1) << betaK * f.transpose().real();</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> </div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span> </div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <span class="comment">// the line below do the deflation of the matrix for the third part of the algorithm</span></div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  <span class="comment">// Here the deflation is commented because the third part of the algorithm is not implemented</span></div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="comment">// the third part of the algorithm is a fast SVD on the matrix m_computed which works thanks to the deflation</span></div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span> </div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  deflation(firstCol, lastCol, k, firstRowW, firstColW, shift);</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> </div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  <span class="comment">// Third part of the algorithm, since the real third part of the algorithm is not implemeted we use a JacobiSVD</span></div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  JacobiSVD<MatrixXr> res= JacobiSVD<MatrixXr>(m_computed.block(firstCol + shift, firstCol +shift, n + 1, n), </div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  ComputeFullU | (ComputeFullV * compV)) ;</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keywordflow">if</span> (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1) *= res.matrixU();</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="keywordflow">else</span> m_naiveU.block(0, firstCol, 2, n + 1) *= res.matrixU();</div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  </div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="keywordflow">if</span> (compV) m_naiveV.block(firstRowW, firstColW, n, n) *= res.matrixV();</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  m_computed.block(firstCol + shift, firstCol + shift, n, n) << MatrixXr::Zero(n, n);</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i<n; i++)</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  m_computed(firstCol + shift + i, firstCol + shift +i) = res.singularValues().coeffRef(i);</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <span class="comment">// end of the third part</span></div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> </div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span> </div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span> }<span class="comment">// end divide</span></div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span> </div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> </div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> <span class="comment">// page 12_13</span></div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span> <span class="comment">// i >= 1, di almost null and zi non null.</span></div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span> <span class="comment">// We use a rotation to zero out zi applied to the left of M</span></div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span> <span class="keywordtype">void</span> BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index size){</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  RealScalar c = m_computed(firstCol + shift, firstCol + shift);</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  RealScalar s = m_computed(i, firstCol + shift);</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  RealScalar r = sqrt(pow(abs(c), 2) + pow(abs(s), 2));</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="keywordflow">if</span> (r == 0){</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  m_computed(i, i)=0;</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  }</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  c/=r;</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  s/=r;</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  m_computed(firstCol + shift, firstCol + shift) = r; </div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  m_computed(i, firstCol + shift) = 0;</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  m_computed(i, i) = 0;</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <span class="keywordflow">if</span> (compU){</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  m_naiveU.col(firstCol).segment(firstCol,size) = </div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  c * m_naiveU.col(firstCol).segment(firstCol, size) - </div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  s * m_naiveU.col(i).segment(firstCol, size) ;</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span> </div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  m_naiveU.col(i).segment(firstCol, size) = </div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  (c + s*s/c) * m_naiveU.col(i).segment(firstCol, size) + </div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  (s/c) * m_naiveU.col(firstCol).segment(firstCol,size);</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  }</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span> }<span class="comment">// end deflation 43</span></div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span> </div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span> </div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span> <span class="comment">// page 13</span></div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> <span class="comment">// i,j >= 1, i != j and |di - dj| < epsilon * norm2(M)</span></div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span> <span class="comment">// We apply two rotations to have zj = 0;</span></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span> <span class="keywordtype">void</span> BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size){</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <span class="keyword">using</span> std::conj;</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  RealScalar c = m_computed(firstColm, firstColm + j - 1);</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  RealScalar s = m_computed(firstColm, firstColm + i - 1);</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  RealScalar r = sqrt(pow(abs(c), 2) + pow(abs(s), 2));</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  <span class="keywordflow">if</span> (r==0){</div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  }</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  c/=r;</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  s/=r;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  m_computed(firstColm + i, firstColm) = r; </div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  m_computed(firstColm + j, firstColm) = 0;</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <span class="keywordflow">if</span> (compU){</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  m_naiveU.col(firstColu + i).segment(firstColu, size) = </div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  c * m_naiveU.col(firstColu + i).segment(firstColu, size) - </div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  s * m_naiveU.col(firstColu + j).segment(firstColu, size) ;</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span> </div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  m_naiveU.col(firstColu + j).segment(firstColu, size) = </div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  (c + s*s/c) * m_naiveU.col(firstColu + j).segment(firstColu, size) + </div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  (s/c) * m_naiveU.col(firstColu + i).segment(firstColu, size);</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  } </div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="keywordflow">if</span> (compV){</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  m_naiveV.col(firstColW + i).segment(firstRowW, size - 1) = </div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  c * m_naiveV.col(firstColW + i).segment(firstRowW, size - 1) + </div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  s * m_naiveV.col(firstColW + j).segment(firstRowW, size - 1) ;</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span> </div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  m_naiveV.col(firstColW + j).segment(firstRowW, size - 1) = </div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  (c + s*s/c) * m_naiveV.col(firstColW + j).segment(firstRowW, size - 1) - </div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  (s/c) * m_naiveV.col(firstColW + i).segment(firstRowW, size - 1);</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  }</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span> }<span class="comment">// end deflation 44</span></div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span> </div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span> </div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span> </div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span> <span class="keywordtype">void</span> BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift){</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  <span class="comment">//condition 4.1</span></div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  RealScalar EPS = EPSILON * (std::max<RealScalar>(m_computed(firstCol + shift + 1, firstCol + shift + 1), m_computed(firstCol + k, firstCol + k)));</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  <span class="keyword">const</span> Index length = lastCol + 1 - firstCol;</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="keywordflow">if</span> (m_computed(firstCol + shift, firstCol + shift) < EPS){</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  m_computed(firstCol + shift, firstCol + shift) = EPS;</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  }</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="comment">//condition 4.2</span></div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <span class="keywordflow">for</span> (Index i=firstCol + shift + 1;i<=lastCol + shift;i++){</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  <span class="keywordflow">if</span> (std::abs(m_computed(i, firstCol + shift)) < EPS){</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  m_computed(i, firstCol + shift) = 0;</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  }</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  }</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span> </div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="comment">//condition 4.3</span></div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="keywordflow">for</span> (Index i=firstCol + shift + 1;i<=lastCol + shift; i++){</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  <span class="keywordflow">if</span> (m_computed(i, i) < EPS){</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  deflation43(firstCol, shift, i, length);</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  }</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  }</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span> </div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  <span class="comment">//condition 4.4</span></div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span>  </div>
<div class="line"><a name="l00600"></a><span class="lineno"> 600</span>  Index i=firstCol + shift + 1, j=firstCol + shift + k + 1;</div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  <span class="comment">//we stock the final place of each line</span></div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  Index *permutation = <span class="keyword">new</span> Index[length];</div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span> </div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  <span class="keywordflow">for</span> (Index p =1; p < length; p++) {</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  <span class="keywordflow">if</span> (i> firstCol + shift + k){</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  permutation[p] = j;</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  j++;</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j> lastCol + shift) </div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  {</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  permutation[p] = i;</div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  i++;</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  }</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <span class="keywordflow">else</span> </div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  {</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <span class="keywordflow">if</span> (m_computed(i, i) < m_computed(j, j)){</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  permutation[p] = j;</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  j++;</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  } </div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  {</div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  permutation[p] = i;</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  i++;</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  }</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  }</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  }</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  <span class="comment">//we do the permutation</span></div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  RealScalar aux;</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="comment">//we stock the current index of each col</span></div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  <span class="comment">//and the column of each index</span></div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  Index *realInd = <span class="keyword">new</span> Index[length];</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  Index *realCol = <span class="keyword">new</span> Index[length];</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> pos = 0; pos< length; pos++){</div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  realCol[pos] = pos + firstCol + shift;</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  realInd[pos] = pos;</div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  }</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  <span class="keyword">const</span> Index Zero = firstCol + shift;</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  VectorType temp;</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i < length - 1; i++){</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  <span class="keyword">const</span> Index I = i + Zero;</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  <span class="keyword">const</span> Index realI = realInd[i];</div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <span class="keyword">const</span> Index j = permutation[length - i] - Zero;</div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  <span class="keyword">const</span> Index J = realCol[j];</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  </div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  <span class="comment">//diag displace</span></div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  aux = m_computed(I, I); </div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  m_computed(I, I) = m_computed(J, J);</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  m_computed(J, J) = aux;</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  </div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  <span class="comment">//firstrow displace</span></div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span>  aux = m_computed(I, Zero); </div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span>  m_computed(I, Zero) = m_computed(J, Zero);</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  m_computed(J, Zero) = aux;</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span> </div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  <span class="comment">// change columns</span></div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  <span class="keywordflow">if</span> (compU) {</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  temp = m_naiveU.col(I - shift).segment(firstCol, length + 1);</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  m_naiveU.col(I - shift).segment(firstCol, length + 1) << </div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  m_naiveU.col(J - shift).segment(firstCol, length + 1);</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  m_naiveU.col(J - shift).segment(firstCol, length + 1) << temp;</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  } </div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  {</div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  temp = m_naiveU.col(I - shift).segment(0, 2);</div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  m_naiveU.col(I - shift).segment(0, 2) << </div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  m_naiveU.col(J - shift).segment(0, 2);</div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span>  m_naiveU.col(J - shift).segment(0, 2) << temp; </div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span>  }</div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  <span class="keywordflow">if</span> (compV) {</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  <span class="keyword">const</span> Index CWI = I + firstColW - Zero;</div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  <span class="keyword">const</span> Index CWJ = J + firstColW - Zero;</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  temp = m_naiveV.col(CWI).segment(firstRowW, length);</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  m_naiveV.col(CWI).segment(firstRowW, length) << m_naiveV.col(CWJ).segment(firstRowW, length);</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  m_naiveV.col(CWJ).segment(firstRowW, length) << temp;</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  }</div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span> </div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  <span class="comment">//update real pos</span></div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  realCol[realI] = J;</div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  realCol[j] = I;</div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  realInd[J - Zero] = realI;</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  realInd[I - Zero] = j;</div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  }</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  <span class="keywordflow">for</span> (Index i = firstCol + shift + 1; i<lastCol + shift;i++){</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span>  <span class="keywordflow">if</span> ((m_computed(i + 1, i + 1) - m_computed(i, i)) < EPS){</div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  deflation44(firstCol , </div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  firstCol + shift, </div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  firstRowW, </div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  firstColW, </div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  i - Zero, </div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  i + 1 - Zero, </div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  length);</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  }</div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  }</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keyword">delete</span> [] permutation;</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  <span class="keyword">delete</span> [] realInd;</div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  <span class="keyword">delete</span> [] realCol;</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span> </div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span> }<span class="comment">//end deflation</span></div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span> </div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span> </div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span> <span class="keyword">namespace </span>internal{</div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span> </div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span> <span class="keyword">struct </span>solve_retval<BDCSVD<_MatrixType>, Rhs></div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  : solve_retval_base<BDCSVD<_MatrixType>, Rhs></div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span> {</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  <span class="keyword">typedef</span> BDCSVD<_MatrixType> BDCSVDType;</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  EIGEN_MAKE_SOLVE_HELPERS(BDCSVDType, Rhs)</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span> </div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  eigen_assert(rhs().rows() == dec().rows());</div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  <span class="comment">// A = U S V^*</span></div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  <span class="comment">// So A^{ - 1} = V S^{ - 1} U^* </span></div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  Index diagSize = (std::min)(dec().rows(), dec().cols());</div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  <span class="keyword">typename</span> BDCSVDType::SingularValuesType invertedSingVals(diagSize);</div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  Index nonzeroSingVals = dec().nonzeroSingularValues();</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse();</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  invertedSingVals.tail(diagSize - nonzeroSingVals).setZero();</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  </div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  dst = dec().matrixV().leftCols(diagSize)</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  * invertedSingVals.asDiagonal()</div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  * dec().matrixU().leftCols(diagSize).adjoint()</div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  * rhs(); </div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  }</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span> };</div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span> </div>
<div class="line"><a name="l00728"></a><span class="lineno"> 728</span> } <span class="comment">//end namespace internal</span></div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span> </div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span> <span class="comment">template<typename Derived></span></div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span> <span class="comment">BDCSVD<typename MatrixBase<Derived>::PlainObject></span></div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span> <span class="comment">MatrixBase<Derived>::bdcSvd(unsigned int computationOptions) const</span></div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span> <span class="comment">{</span></div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span> <span class="comment"> return BDCSVD<PlainObject>(*this, computationOptions);</span></div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span> <span class="comment">}</span></div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span> <span class="comment">*/</span></div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span> </div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span> </div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="classEigen_1_1SVDBase_html_a1ffab6aab715fe0918a841611a95e9aa"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a1ffab6aab715fe0918a841611a95e9aa">Eigen::SVDBase::computeU</a></div><div class="ttdeci">bool computeU() const </div><div class="ttdef"><b>Definition:</b> SVDBase.h:155</div></div>
<div class="ttc" id="classEigen_1_1BDCSVD_html_ac872405f6364be4078b367ac4c6c0c01"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#ac872405f6364be4078b367ac4c6c0c01">Eigen::BDCSVD::solve</a></div><div class="ttdeci">const internal::solve_retval< BDCSVD, Rhs > solve(const MatrixBase< Rhs > &b) const </div><div class="ttdef"><b>Definition:</b> BDCSVD.h:158</div></div>
<div class="ttc" id="classEigen_1_1BDCSVD_html_a3b2bfdc0a8dd672390fb4ba22f4ef434"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a3b2bfdc0a8dd672390fb4ba22f4ef434">Eigen::BDCSVD::compute</a></div><div class="ttdeci">SVDBase< MatrixType > & compute(const MatrixType &matrix, unsigned int computationOptions)</div><div class="ttdoc">Method performing the decomposition of given matrix using custom options. </div><div class="ttdef"><b>Definition:</b> BDCSVD.h:272</div></div>
<div class="ttc" id="classEigen_1_1BDCSVD_html_a3c9182989cf14fd0111ad6c2bc0eb8b3"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a3c9182989cf14fd0111ad6c2bc0eb8b3">Eigen::BDCSVD::BDCSVD</a></div><div class="ttdeci">BDCSVD(const MatrixType &matrix, unsigned int computationOptions=0)</div><div class="ttdoc">Constructor performing the decomposition of given matrix. </div><div class="ttdef"><b>Definition:</b> BDCSVD.h:107</div></div>
<div class="ttc" id="classEigen_1_1SVDBase_html"><div class="ttname"><a href="classEigen_1_1SVDBase.html">Eigen::SVDBase</a></div><div class="ttdoc">Mother class of SVD classes algorithms. </div><div class="ttdef"><b>Definition:</b> SVDBase.h:46</div></div>
<div class="ttc" id="classEigen_1_1BDCSVD_html"><div class="ttname"><a href="classEigen_1_1BDCSVD.html">Eigen::BDCSVD</a></div><div class="ttdoc">class Bidiagonal Divide and Conquer SVD </div><div class="ttdef"><b>Definition:</b> BDCSVD.h:38</div></div>
<div class="ttc" id="classEigen_1_1BDCSVD_html_a15bb6fe0bfbcf6ac5bad8ddcafd34387"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a15bb6fe0bfbcf6ac5bad8ddcafd34387">Eigen::BDCSVD::BDCSVD</a></div><div class="ttdeci">BDCSVD()</div><div class="ttdoc">Default Constructor. </div><div class="ttdef"><b>Definition:</b> BDCSVD.h:78</div></div>
<div class="ttc" id="classEigen_1_1SVDBase_html_a92e99646eefbeb071ef220841555a703"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a92e99646eefbeb071ef220841555a703">Eigen::SVDBase::computeV</a></div><div class="ttdeci">bool computeV() const </div><div class="ttdef"><b>Definition:</b> SVDBase.h:157</div></div>
<div class="ttc" id="classEigen_1_1BDCSVD_html_a0b1282c48b843773424d97e65ee21060"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a0b1282c48b843773424d97e65ee21060">Eigen::BDCSVD::BDCSVD</a></div><div class="ttdeci">BDCSVD(Index rows, Index cols, unsigned int computationOptions=0)</div><div class="ttdoc">Default Constructor with memory preallocation. </div><div class="ttdef"><b>Definition:</b> BDCSVD.h:90</div></div>
<div class="ttc" id="classEigen_1_1BDCSVD_html_a26e02670d0a94c92ab41c2bc7f70e781"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a26e02670d0a94c92ab41c2bc7f70e781">Eigen::BDCSVD::compute</a></div><div class="ttdeci">SVDBase< MatrixType > & compute(const MatrixType &matrix)</div><div class="ttdoc">Method performing the decomposition of given matrix using current options. </div><div class="ttdef"><b>Definition:</b> BDCSVD.h:135</div></div>
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