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<div class="title">SparseQR.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2012-2013 Desire Nuentsa <desire.nuentsa_wakam@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2012-2013 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#ifndef EIGEN_SPARSE_QR_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_SPARSE_QR_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="keyword">namespace </span>Eigen {</div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html"> 16</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> OrderingType> <span class="keyword">class </span><a class="code" href="classEigen_1_1SparseQR.html">SparseQR</a>;</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">template</span><<span class="keyword">typename</span> SparseQRType> <span class="keyword">struct </span>SparseQRMatrixQReturnType;</div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="keyword">template</span><<span class="keyword">typename</span> SparseQRType> <span class="keyword">struct </span>SparseQRMatrixQTransposeReturnType;</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">template</span><<span class="keyword">typename</span> SparseQRType, <span class="keyword">typename</span> Derived> <span class="keyword">struct </span>SparseQR_QProduct;</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SparseQRType> <span class="keyword">struct </span>traits<SparseQRMatrixQReturnType<SparseQRType> ></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  {</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::MatrixType ReturnType;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> ReturnType::Index Index;</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> ReturnType::StorageKind StorageKind;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  };</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SparseQRType> <span class="keyword">struct </span>traits<SparseQRMatrixQTransposeReturnType<SparseQRType> ></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  {</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::MatrixType ReturnType;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  };</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SparseQRType, <span class="keyword">typename</span> Derived> <span class="keyword">struct </span>traits<SparseQR_QProduct<SparseQRType, Derived> ></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  {</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject ReturnType;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  };</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> } <span class="comment">// End namespace internal</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _OrderingType></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="keyword">class </span>SparseQR</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">typedef</span> _OrderingType OrderingType;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keyword">typedef</span> SparseMatrix<Scalar,ColMajor,Index> QRMatrixType;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keyword">typedef</span> Matrix<Index, Dynamic, 1> IndexVector;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">typedef</span> Matrix<Scalar, Dynamic, 1> ScalarVector;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keyword">typedef</span> PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  SparseQR () : m_isInitialized(false), m_analysisIsok(false), m_lastError(<span class="stringliteral">""</span>), m_useDefaultThreshold(true),m_isQSorted(false)</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  { }</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  SparseQR(<span class="keyword">const</span> MatrixType& mat) : m_isInitialized(false), m_analysisIsok(false), m_lastError(<span class="stringliteral">""</span>), m_useDefaultThreshold(true),m_isQSorted(false)</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>  compute(mat);</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  }</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordtype">void</span> compute(<span class="keyword">const</span> MatrixType& mat)</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <a class="code" href="classEigen_1_1SparseQR.html#a5907227f29f3911de653273efef11b45">analyzePattern</a>(mat);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <a class="code" href="classEigen_1_1SparseQR.html#aca041ec6ace60e0e597f40706e9c894d">factorize</a>(mat);</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#a5907227f29f3911de653273efef11b45">analyzePattern</a>(<span class="keyword">const</span> MatrixType& mat);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#aca041ec6ace60e0e597f40706e9c894d">factorize</a>(<span class="keyword">const</span> MatrixType& mat);</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  </div>
<div class="line"><a name="l00094"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a5552abd83dbd03c85cea6d61fd8875a5"> 94</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1SparseQR.html#a5552abd83dbd03c85cea6d61fd8875a5">rows</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_pmat.<a class="code" href="classEigen_1_1SparseMatrix.html#a5552abd83dbd03c85cea6d61fd8875a5">rows</a>(); }</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  </div>
<div class="line"><a name="l00098"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#aaca1908a5ec508a25ff0a8bca803e5f3"> 98</a></span>  <span class="keyword">inline</span> Index <a class="code" href="classEigen_1_1SparseQR.html#aaca1908a5ec508a25ff0a8bca803e5f3">cols</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_pmat.<a class="code" href="classEigen_1_1SparseMatrix.html#aaca1908a5ec508a25ff0a8bca803e5f3">cols</a>();}</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  </div>
<div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a934752a840893040688fc788848a1e06"> 102</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1SparseMatrix.html">QRMatrixType</a>& <a class="code" href="classEigen_1_1SparseQR.html#a934752a840893040688fc788848a1e06">matrixR</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_R; }</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  </div>
<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a363d1c09d77f09d6ea2d2789776e7be3"> 108</a></span>  Index <a class="code" href="classEigen_1_1SparseQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>()<span class="keyword"> const </span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"The factorization should be called first, use compute()"</span>);</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordflow">return</span> m_nonzeropivots; </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="l00132"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#ac27067ab301641fe6cc35c216a9b18a2"> 132</a></span>  SparseQRMatrixQReturnType<SparseQR> <a class="code" href="classEigen_1_1SparseQR.html#ac27067ab301641fe6cc35c216a9b18a2">matrixQ</a>()<span class="keyword"> const </span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="keyword"> </span>{ <span class="keywordflow">return</span> SparseQRMatrixQReturnType<SparseQR>(*this); }</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  </div>
<div class="line"><a name="l00138"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a1229744f4e8554ca6e96fe32ac359924"> 138</a></span>  <span class="keyword">const</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>& <a class="code" href="classEigen_1_1SparseQR.html#a1229744f4e8554ca6e96fe32ac359924">colsPermutation</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="keyword"> </span>{ </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"Decomposition is not initialized."</span>);</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keywordflow">return</span> m_outputPerm_c;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  }</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  </div>
<div class="line"><a name="l00147"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a040b16815cde46c7f2f6d26a2298ca4b"> 147</a></span>  std::string <a class="code" href="classEigen_1_1SparseQR.html#a040b16815cde46c7f2f6d26a2298ca4b">lastErrorMessage</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_lastError; }</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  </div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordtype">bool</span> _solve(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Rhs></a> &B, <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Dest></a> &dest)<span class="keyword"> const</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"The factorization should be called first, use compute()"</span>);</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  eigen_assert(this-><a class="code" href="classEigen_1_1SparseQR.html#a5552abd83dbd03c85cea6d61fd8875a5">rows</a>() == B.rows() && <span class="stringliteral">"SparseQR::solve() : invalid number of rows in the right hand side matrix"</span>);</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  Index <a class="code" href="classEigen_1_1SparseQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a> = this-><a class="code" href="classEigen_1_1SparseQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>();</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  </div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="comment">// Compute Q^T * b;</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keyword">typename</span> Dest::PlainObject y, b;</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  y = this-><a class="code" href="classEigen_1_1SparseQR.html#ac27067ab301641fe6cc35c216a9b18a2">matrixQ</a>().transpose() * B; </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  b = y;</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  </div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="comment">// Solve with the triangular matrix R</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  y.<a class="code" href="classEigen_1_1DenseBase.html#afdfced3e157f74b3bc68892aad178424">topRows</a>(rank) = this-><a class="code" href="classEigen_1_1SparseQR.html#a934752a840893040688fc788848a1e06">matrixR</a>().<a class="code" href="classEigen_1_1SparseMatrixBase.html#a6f5fc5fe9d3fb70e62d4a9b1795704a8">topLeftCorner</a>(rank, rank).template triangularView<Upper>().<a class="code" href="classEigen_1_1SparseQR.html#a2faae287189af711e5f8ac62c140c71f">solve</a>(b.topRows(rank));</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  y.bottomRows(y.size()-<a class="code" href="classEigen_1_1SparseQR.html#a363d1c09d77f09d6ea2d2789776e7be3">rank</a>).setZero();</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="comment">// Apply the column permutation</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">if</span> (m_perm_c.<a class="code" href="classEigen_1_1PermutationBase.html#a76f5bc8a03ec105ab4be1f2b91b7b5d5">size</a>()) dest.<a class="code" href="classEigen_1_1DenseBase.html#afdfced3e157f74b3bc68892aad178424">topRows</a>(<a class="code" href="classEigen_1_1SparseQR.html#aaca1908a5ec508a25ff0a8bca803e5f3">cols</a>()) = <a class="code" href="classEigen_1_1SparseQR.html#a1229744f4e8554ca6e96fe32ac359924">colsPermutation</a>() * y.topRows(<a class="code" href="classEigen_1_1SparseQR.html#aaca1908a5ec508a25ff0a8bca803e5f3">cols</a>());</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordflow">else</span> dest = y.<a class="code" href="classEigen_1_1DenseBase.html#afdfced3e157f74b3bc68892aad178424">topRows</a>(<a class="code" href="classEigen_1_1SparseQR.html#aaca1908a5ec508a25ff0a8bca803e5f3">cols</a>());</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  </div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  m_info = <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>;</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</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>  </div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div>
<div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#ad00a1dda3c45b53e1f91219824773b1c"> 181</a></span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#ad00a1dda3c45b53e1f91219824773b1c">setPivotThreshold</a>(<span class="keyword">const</span> RealScalar& threshold)</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>  m_useDefaultThreshold = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  m_threshold = threshold;</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  }</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  </div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00192"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a2faae287189af711e5f8ac62c140c71f"> 192</a></span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval<SparseQR, Rhs> <a class="code" href="classEigen_1_1SparseQR.html#a2faae287189af711e5f8ac62c140c71f">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Rhs></a>& B)<span class="keyword"> const </span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"The factorization should be called first, use compute()"</span>);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  eigen_assert(this-><a class="code" href="classEigen_1_1SparseQR.html#a5552abd83dbd03c85cea6d61fd8875a5">rows</a>() == B.rows() && <span class="stringliteral">"SparseQR::solve() : invalid number of rows in the right hand side matrix"</span>);</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">return</span> internal::solve_retval<SparseQR, Rhs>(*<span class="keyword">this</span>, B.derived());</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  }</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::sparse_solve_retval<SparseQR, Rhs> <a class="code" href="classEigen_1_1SparseQR.html#a2faae287189af711e5f8ac62c140c71f">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1SparseMatrixBase.html">SparseMatrixBase<Rhs></a>& B)<span class="keyword"> const</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"The factorization should be called first, use compute()"</span>);</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  eigen_assert(this-><a class="code" href="classEigen_1_1SparseQR.html#a5552abd83dbd03c85cea6d61fd8875a5">rows</a>() == B.<a class="code" href="classEigen_1_1SparseMatrixBase.html#a5552abd83dbd03c85cea6d61fd8875a5">rows</a>() && <span class="stringliteral">"SparseQR::solve() : invalid number of rows in the right hand side matrix"</span>);</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordflow">return</span> internal::sparse_solve_retval<SparseQR, Rhs>(*<span class="keyword">this</span>, B.<a class="code" href="structEigen_1_1EigenBase.html#aa84222add803ad7c9db07dd4dd91d5d9">derived</a>());</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  }</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  </div>
<div class="line"><a name="l00214"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a0c06d5c2034ebb329c54235369643ad2"> 214</a></span>  <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> <a class="code" href="classEigen_1_1SparseQR.html#a0c06d5c2034ebb329c54235369643ad2">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"Decomposition is not initialized."</span>);</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  }</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> </div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> sort_matrix_Q()</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  {</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">if</span>(this->m_isQSorted) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="comment">// The matrix Q is sorted during the transposition</span></div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <a class="code" href="classEigen_1_1SparseMatrix.html">SparseMatrix<Scalar, RowMajor, Index></a> mQrm(this->m_Q);</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  this->m_Q = mQrm;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  this->m_isQSorted = <span class="keyword">true</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> </div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  </div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordtype">bool</span> m_analysisIsok;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keywordtype">bool</span> m_factorizationIsok;</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keyword">mutable</span> <a class="code" href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  std::string m_lastError;</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  QRMatrixType m_pmat; <span class="comment">// Temporary matrix</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  QRMatrixType m_R; <span class="comment">// The triangular factor matrix</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  QRMatrixType m_Q; <span class="comment">// The orthogonal reflectors</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  ScalarVector m_hcoeffs; <span class="comment">// The Householder coefficients</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  PermutationType m_perm_c; <span class="comment">// Fill-reducing Column permutation</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  PermutationType m_pivotperm; <span class="comment">// The permutation for rank revealing</span></div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  PermutationType m_outputPerm_c; <span class="comment">// The final column permutation</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  RealScalar m_threshold; <span class="comment">// Threshold to determine null Householder reflections</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordtype">bool</span> m_useDefaultThreshold; <span class="comment">// Use default threshold</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  Index m_nonzeropivots; <span class="comment">// Number of non zero pivots found </span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  IndexVector m_etree; <span class="comment">// Column elimination tree</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  IndexVector m_firstRowElt; <span class="comment">// First element in each row</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordtype">bool</span> m_isQSorted; <span class="comment">// whether Q is sorted or not</span></div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  </div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keyword">template</span> <<span class="keyword">typename</span>, <span class="keyword">typename</span> > <span class="keyword">friend</span> <span class="keyword">struct </span>SparseQR_QProduct;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> > <span class="keyword">friend</span> <span class="keyword">struct </span>SparseQRMatrixQReturnType;</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> };</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> OrderingType></div>
<div class="line"><a name="l00264"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#a5907227f29f3911de653273efef11b45"> 264</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#a5907227f29f3911de653273efef11b45">SparseQR<MatrixType,OrderingType>::analyzePattern</a>(<span class="keyword">const</span> MatrixType& mat)</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> {</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="comment">// Compute the column fill reducing ordering</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  OrderingType ord; </div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  ord(mat, m_perm_c); </div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  Index n = mat.cols();</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  Index m = mat.rows();</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">if</span> (!m_perm_c.size())</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>  m_perm_c.resize(n);</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  m_perm_c.indices().setLinSpaced(n, 0,n-1);</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>  </div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="comment">// Compute the column elimination tree of the permuted matrix</span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  m_outputPerm_c = m_perm_c.inverse();</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <a class="code" href="namespaceEigen_1_1internal.html#a22b184331e5fb270a37d1305e95cb064">internal::coletree</a>(mat, m_etree, m_firstRowElt, m_outputPerm_c.indices().data());</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>  m_R.resize(n, n);</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  m_Q.resize(m, n);</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  </div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="comment">// Allocate space for nonzero elements : rough estimation</span></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  m_R.reserve(2*mat.nonZeros()); <span class="comment">//FIXME Get a more accurate estimation through symbolic factorization with the etree</span></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  m_Q.reserve(2*mat.nonZeros());</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  m_hcoeffs.resize(n);</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  m_analysisIsok = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> }</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> </div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> OrderingType></div>
<div class="line"><a name="l00300"></a><span class="lineno"><a class="line" href="classEigen_1_1SparseQR.html#aca041ec6ace60e0e597f40706e9c894d"> 300</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1SparseQR.html#aca041ec6ace60e0e597f40706e9c894d">SparseQR<MatrixType,OrderingType>::factorize</a>(<span class="keyword">const</span> MatrixType& mat)</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span> {</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keyword">using</span> std::max;</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  eigen_assert(m_analysisIsok && <span class="stringliteral">"analyzePattern() should be called before this step"</span>);</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  Index m = mat.rows();</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  Index n = mat.cols();</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <a class="code" href="classEigen_1_1Matrix.html">IndexVector</a> mark(m); mark.<a class="code" href="classEigen_1_1PlainObjectBase.html#aabcf7b6f4543f6255253b9ccee3309b8">setConstant</a>(-1); <span class="comment">// Record the visited nodes</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <a class="code" href="classEigen_1_1Matrix.html">IndexVector</a> Ridx(n), Qidx(m); <span class="comment">// Store temporarily the row indexes for the current column of R and Q</span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  Index nzcolR, nzcolQ; <span class="comment">// Number of nonzero for the current column of R and Q</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <a class="code" href="classEigen_1_1Matrix.html">ScalarVector</a> tval(m); <span class="comment">// The dense vector used to compute the current column</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordtype">bool</span> found_diag;</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  </div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  m_pmat = mat;</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  m_pmat.uncompress(); <span class="comment">// To have the innerNonZeroPtr allocated</span></div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="comment">// Apply the fill-in reducing permutation lazily:</span></div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; i++)</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  {</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  Index p = m_perm_c.size() ? m_perm_c.indices()(i) : i;</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  m_pmat.outerIndexPtr()[p] = mat.outerIndexPtr()[i]; </div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  m_pmat.innerNonZeroPtr()[p] = mat.outerIndexPtr()[i+1] - mat.outerIndexPtr()[i]; </div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  }</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  </div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="comment">/* Compute the default threshold, see : </span></div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span> <span class="comment"> * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing</span></div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span> <span class="comment"> * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3 </span></div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keywordflow">if</span>(m_useDefaultThreshold) </div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  {</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  RealScalar max2Norm = 0.0;</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < n; j++) max2Norm = (max)(max2Norm, m_pmat.col(j).norm());</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  m_threshold = 20 * (m + n) * max2Norm * <a class="code" href="structEigen_1_1NumTraits.html">NumTraits<RealScalar>::epsilon</a>();</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>  </div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="comment">// Initialize the numerical permutation</span></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  m_pivotperm.setIdentity(n);</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  </div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  Index nonzeroCol = 0; <span class="comment">// Record the number of valid pivots</span></div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  </div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="comment">// Left looking rank-revealing QR factorization: compute a column of R and Q at a time</span></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordflow">for</span> (Index col = 0; col < n; ++col)</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>  mark.<a class="code" href="classEigen_1_1PlainObjectBase.html#aabcf7b6f4543f6255253b9ccee3309b8">setConstant</a>(-1);</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  m_R.startVec(col);</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  m_Q.startVec(col);</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  mark(nonzeroCol) = col;</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  Qidx(0) = nonzeroCol;</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  nzcolR = 0; nzcolQ = 1;</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  found_diag = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  tval.<a class="code" href="classEigen_1_1PlainObjectBase.html#a04abe84a9a894de335a232681d9a0722">setZero</a>(); </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">// Symbolic factorization: find the nonzero locations of the column k of the factors R and Q, i.e.,</span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="comment">// all the nodes (with indexes lower than rank) reachable through the column elimination tree (etree) rooted at node k.</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="comment">// Note: if the diagonal entry does not exist, then its contribution must be explicitly added,</span></div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="comment">// thus the trick with found_diag that permits to do one more iteration on the diagonal element if this one has not been found.</span></div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> MatrixType::InnerIterator itp(m_pmat, col); itp || !found_diag; ++itp)</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  {</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  Index curIdx = nonzeroCol ;</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keywordflow">if</span>(itp) curIdx = itp.row();</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keywordflow">if</span>(curIdx == nonzeroCol) found_diag = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="comment">// Get the nonzeros indexes of the current column of R</span></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  Index st = m_firstRowElt(curIdx); <span class="comment">// The traversal of the etree starts here </span></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="keywordflow">if</span> (st < 0 )</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>  m_lastError = <span class="stringliteral">"Empty row found during numerical factorization"</span>;</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  m_info = <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bae1252631a63be5890a1e78ff417d378f">InvalidInput</a>;</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  }</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> </div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="comment">// Traverse the etree </span></div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  Index bi = nzcolR;</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="keywordflow">for</span> (; mark(st) != col; st = m_etree(st))</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  {</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  Ridx(nzcolR) = st; <span class="comment">// Add this row to the list,</span></div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  mark(st) = col; <span class="comment">// and mark this row as visited</span></div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  nzcolR++;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  }</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> </div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="comment">// Reverse the list to get the topological ordering</span></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  Index nt = nzcolR-bi;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <span class="keywordflow">for</span>(Index i = 0; i < nt/2; i++) std::swap(Ridx(bi+i), Ridx(nzcolR-i-1));</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  </div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="comment">// Copy the current (curIdx,pcol) value of the input matrix</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="keywordflow">if</span>(itp) tval(curIdx) = itp.value();</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="keywordflow">else</span> tval(curIdx) = Scalar(0);</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="comment">// Compute the pattern of Q(:,k)</span></div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="keywordflow">if</span>(curIdx > nonzeroCol && mark(curIdx) != col ) </div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  {</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  Qidx(nzcolQ) = curIdx; <span class="comment">// Add this row to the pattern of Q,</span></div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  mark(curIdx) = col; <span class="comment">// and mark it as visited</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  nzcolQ++;</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  }</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  }</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span> </div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="comment">// Browse all the indexes of R(:,col) in reverse order</span></div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <span class="keywordflow">for</span> (Index i = nzcolR-1; i >= 0; i--)</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  {</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  Index curIdx = m_pivotperm.indices()(Ridx(i));</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  </div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="comment">// Apply the curIdx-th householder vector to the current column (temporarily stored into tval)</span></div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  Scalar tdot(0);</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  </div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="comment">// First compute q' * tval</span></div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  tdot = m_Q.col(curIdx).dot(tval);</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> </div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  tdot *= m_hcoeffs(curIdx);</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  </div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <span class="comment">// Then update tval = tval - q * tau</span></div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="comment">// FIXME: tval -= tdot * m_Q.col(curIdx) should amount to the same (need to check/add support for efficient "dense ?= sparse")</span></div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  tval(itq.row()) -= itq.value() * tdot;</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span> </div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <span class="comment">// Detect fill-in for the current column of Q</span></div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="keywordflow">if</span>(m_etree(Ridx(i)) == nonzeroCol)</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>  <span class="keywordflow">for</span> (<span class="keyword">typename</span> QRMatrixType::InnerIterator itq(m_Q, curIdx); itq; ++itq)</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  {</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  Index iQ = itq.row();</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">if</span> (mark(iQ) != col)</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>  Qidx(nzcolQ++) = iQ; <span class="comment">// Add this row to the pattern of Q,</span></div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  mark(iQ) = col; <span class="comment">// and mark it as visited</span></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>  }</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  }</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  } <span class="comment">// End update current column</span></div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  </div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="comment">// Compute the Householder reflection that eliminate the current column</span></div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  <span class="comment">// FIXME this step should call the Householder module.</span></div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  Scalar tau;</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  RealScalar beta;</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  Scalar c0 = nzcolQ ? tval(Qidx(0)) : Scalar(0);</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  </div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="comment">// First, the squared norm of Q((col+1):m, col)</span></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  RealScalar sqrNorm = 0.;</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keywordflow">for</span> (Index itq = 1; itq < nzcolQ; ++itq) sqrNorm += numext::abs2(tval(Qidx(itq)));</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  </div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="keywordflow">if</span>(sqrNorm == RealScalar(0) && numext::imag(c0) == RealScalar(0))</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  {</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  tau = RealScalar(0);</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  beta = numext::real(c0);</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  tval(Qidx(0)) = 1;</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  }</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  {</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  beta = std::sqrt(numext::abs2(c0) + sqrNorm);</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">if</span>(numext::real(c0) >= RealScalar(0))</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  beta = -beta;</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  tval(Qidx(0)) = 1;</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="keywordflow">for</span> (Index itq = 1; itq < nzcolQ; ++itq)</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  tval(Qidx(itq)) /= (c0 - beta);</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  tau = numext::conj((beta-c0) / beta);</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  </div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  }</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span> </div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="comment">// Insert values in R</span></div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="keywordflow">for</span> (Index i = nzcolR-1; i >= 0; 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>  Index curIdx = Ridx(i);</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="keywordflow">if</span>(curIdx < nonzeroCol) </div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  {</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  m_R.insertBackByOuterInnerUnordered(col, curIdx) = tval(curIdx);</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  tval(curIdx) = Scalar(0.);</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  }</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  }</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span> </div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="keywordflow">if</span>(abs(beta) >= m_threshold)</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  {</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  m_R.insertBackByOuterInner(col, nonzeroCol) = beta;</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  nonzeroCol++;</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="comment">// The householder coefficient</span></div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  m_hcoeffs(col) = tau;</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="comment">// Record the householder reflections</span></div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="keywordflow">for</span> (Index itq = 0; itq < nzcolQ; ++itq)</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>  Index iQ = Qidx(itq);</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  m_Q.insertBackByOuterInnerUnordered(col,iQ) = tval(iQ);</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  tval(iQ) = Scalar(0.);</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</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>  <span class="keywordflow">else</span></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">// Zero pivot found: move implicitly this column to the end</span></div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  m_hcoeffs(col) = Scalar(0);</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="keywordflow">for</span> (Index j = nonzeroCol; j < n-1; j++) </div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  std::swap(m_pivotperm.indices()(j), m_pivotperm.indices()[j+1]);</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  </div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <span class="comment">// Recompute the column elimination tree</span></div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <a class="code" href="namespaceEigen_1_1internal.html#a22b184331e5fb270a37d1305e95cb064">internal::coletree</a>(m_pmat, m_etree, m_firstRowElt, m_pivotperm.indices().data());</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  }</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  }</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  </div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <span class="comment">// Finalize the column pointers of the sparse matrices R and Q</span></div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  m_Q.finalize();</div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  m_Q.makeCompressed();</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  m_R.finalize();</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  m_R.makeCompressed();</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  m_isQSorted = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  </div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  m_nonzeropivots = nonzeroCol;</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  </div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  <span class="keywordflow">if</span>(nonzeroCol<n)</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  {</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="comment">// Permute the triangular factor to put the 'dead' columns to the end</span></div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  MatrixType tempR(m_R);</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  m_R = tempR * m_pivotperm;</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  </div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <span class="comment">// Update the column permutation</span></div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  m_outputPerm_c = m_outputPerm_c * m_pivotperm;</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  }</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  </div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  m_isInitialized = <span class="keyword">true</span>; </div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  m_factorizationIsok = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  m_info = <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a>;</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span> }</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> </div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  </div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> OrderingType, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> <span class="keyword">struct </span>solve_retval<<a class="code" href="classEigen_1_1SparseQR.html">SparseQR</a><_MatrixType,OrderingType>, Rhs></div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  : solve_retval_base<SparseQR<_MatrixType,OrderingType>, Rhs></div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span> {</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SparseQR.html">SparseQR<_MatrixType,OrderingType></a> Dec;</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span> </div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  dec()._solve(rhs(),dst);</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="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> OrderingType, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> <span class="keyword">struct </span>sparse_solve_retval<SparseQR<_MatrixType, OrderingType>, Rhs></div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  : sparse_solve_retval_base<SparseQR<_MatrixType, OrderingType>, Rhs></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span> {</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="keyword">typedef</span> SparseQR<_MatrixType, OrderingType> Dec;</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec, Rhs)</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span> </div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  this->defaultEvalTo(dst);</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  }</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span> };</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span> </div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SparseQRType, <span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span> <span class="keyword">struct </span>SparseQR_QProduct : ReturnByValue<SparseQR_QProduct<SparseQRType, Derived> ></div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span> {</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::QRMatrixType MatrixType;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::Scalar Scalar;</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::Index Index;</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  <span class="comment">// Get the references </span></div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  SparseQR_QProduct(<span class="keyword">const</span> SparseQRType& qr, <span class="keyword">const</span> Derived& other, <span class="keywordtype">bool</span> transpose) : </div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  m_qr(qr),m_other(other),m_transpose(transpose) {}</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="keyword">inline</span> Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_transpose ? m_qr.rows() : m_qr.cols(); }</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="keyword">inline</span> Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_other.cols(); }</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>  <span class="comment">// Assign to a vector</span></div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <span class="keyword">template</span><<span class="keyword">typename</span> DesType></div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="keywordtype">void</span> evalTo(DesType& res)<span class="keyword"> const</span></div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  Index n = m_qr.cols();</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  res = m_other;</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="keywordflow">if</span> (m_transpose)</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  {</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  eigen_assert(m_qr.m_Q.rows() == m_other.rows() && <span class="stringliteral">"Non conforming object sizes"</span>);</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="comment">//Compute res = Q' * other column by column</span></div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <span class="keywordflow">for</span>(Index j = 0; j < res.cols(); j++){</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  <span class="keywordflow">for</span> (Index k = 0; k < n; k++)</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>  Scalar tau = Scalar(0);</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  tau = m_qr.m_Q.col(k).dot(res.col(j));</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  tau = tau * m_qr.m_hcoeffs(k);</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  res.col(j) -= tau * m_qr.m_Q.col(k);</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  }</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  }</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  }</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  {</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  eigen_assert(m_qr.m_Q.cols() == m_other.rows() && <span class="stringliteral">"Non conforming object sizes"</span>);</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="comment">// Compute res = Q' * other column by column</span></div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  <span class="keywordflow">for</span>(Index j = 0; j < res.cols(); j++)</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  {</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  <span class="keywordflow">for</span> (Index k = n-1; k >=0; k--)</div>
<div class="line"><a name="l00586"></a><span class="lineno"> 586</span>  {</div>
<div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  Scalar tau = Scalar(0);</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  tau = m_qr.m_Q.col(k).dot(res.col(j));</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  tau = tau * m_qr.m_hcoeffs(k);</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  res.col(j) -= tau * m_qr.m_Q.col(k);</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  }</div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  }</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  }</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  }</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>  <span class="keyword">const</span> SparseQRType& m_qr;</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  <span class="keyword">const</span> Derived& m_other;</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  <span class="keywordtype">bool</span> m_transpose;</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> </div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span> <span class="keyword">template</span><<span class="keyword">typename</span> SparseQRType></div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span> <span class="keyword">struct </span>SparseQRMatrixQReturnType : <span class="keyword">public</span> EigenBase<SparseQRMatrixQReturnType<SparseQRType> ></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="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::Index Index;</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> SparseQRType::Scalar Scalar;</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  SparseQRMatrixQReturnType(<span class="keyword">const</span> SparseQRType& qr) : m_qr(qr) {}</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  SparseQR_QProduct<SparseQRType, Derived> <a class="code" href="namespaceEigen.html#a81fb70d0dc1c6deb42e9816647607247">operator*</a>(<span class="keyword">const</span> MatrixBase<Derived>& other)</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  {</div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  <span class="keywordflow">return</span> SparseQR_QProduct<SparseQRType,Derived>(m_qr,other.derived(),<span class="keyword">false</span>);</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>  SparseQRMatrixQTransposeReturnType<SparseQRType> adjoint()<span class="keyword"> const</span></div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <span class="keywordflow">return</span> SparseQRMatrixQTransposeReturnType<SparseQRType>(m_qr);</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  }</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  <span class="keyword">inline</span> Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.rows(); }</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="keyword">inline</span> Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.cols(); }</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  <span class="comment">// To use for operations with the transpose of Q</span></div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  SparseQRMatrixQTransposeReturnType<SparseQRType> transpose()<span class="keyword"> const</span></div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  <span class="keywordflow">return</span> SparseQRMatrixQTransposeReturnType<SparseQRType>(m_qr);</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>  <span class="keyword">template</span><<span class="keyword">typename</span> Dest> <span class="keywordtype">void</span> evalTo(MatrixBase<Dest>& dest)<span class="keyword"> const</span></div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span>  dest.derived() = m_qr.matrixQ() * Dest::Identity(m_qr.rows(), m_qr.rows());</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  }</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Dest> <span class="keywordtype">void</span> evalTo(SparseMatrixBase<Dest>& dest)<span class="keyword"> const</span></div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  Dest idMat(m_qr.rows(), m_qr.rows());</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  idMat.setIdentity();</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  <span class="comment">// Sort the sparse householder reflectors if needed</span></div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  <span class="keyword">const_cast<</span>SparseQRType *<span class="keyword">></span>(&m_qr)->sort_matrix_Q();</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  dest.derived() = SparseQR_QProduct<SparseQRType, Dest>(m_qr, idMat, <span class="keyword">false</span>);</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> </div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  <span class="keyword">const</span> SparseQRType& m_qr;</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span> };</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span> </div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span> <span class="keyword">template</span><<span class="keyword">typename</span> SparseQRType></div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span> <span class="keyword">struct </span>SparseQRMatrixQTransposeReturnType</div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span> {</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  SparseQRMatrixQTransposeReturnType(<span class="keyword">const</span> SparseQRType& qr) : m_qr(qr) {}</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  SparseQR_QProduct<SparseQRType,Derived> <a class="code" href="namespaceEigen.html#a81fb70d0dc1c6deb42e9816647607247">operator*</a>(<span class="keyword">const</span> MatrixBase<Derived>& other)</div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  {</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  <span class="keywordflow">return</span> SparseQR_QProduct<SparseQRType,Derived>(m_qr,other.derived(), <span class="keyword">true</span>);</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="keyword">const</span> SparseQRType& m_qr;</div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span> };</div>
<div class="line"><a name="l00651"></a><span class="lineno"> 651</span> </div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span> </div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="classEigen_1_1SparseMatrix_html_a5552abd83dbd03c85cea6d61fd8875a5"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html#a5552abd83dbd03c85cea6d61fd8875a5">Eigen::SparseMatrix::rows</a></div><div class="ttdeci">Index rows() const </div><div class="ttdef"><b>Definition:</b> SparseMatrix.h:119</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_a040b16815cde46c7f2f6d26a2298ca4b"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a040b16815cde46c7f2f6d26a2298ca4b">Eigen::SparseQR::lastErrorMessage</a></div><div class="ttdeci">std::string lastErrorMessage() const </div><div class="ttdef"><b>Definition:</b> SparseQR.h:147</div></div>
<div class="ttc" id="classEigen_1_1SparseMatrix_html_aaca1908a5ec508a25ff0a8bca803e5f3"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html#aaca1908a5ec508a25ff0a8bca803e5f3">Eigen::SparseMatrix::cols</a></div><div class="ttdeci">Index cols() const </div><div class="ttdef"><b>Definition:</b> SparseMatrix.h:121</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_a363d1c09d77f09d6ea2d2789776e7be3"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a363d1c09d77f09d6ea2d2789776e7be3">Eigen::SparseQR::rank</a></div><div class="ttdeci">Index rank() const </div><div class="ttdef"><b>Definition:</b> SparseQR.h:108</div></div>
<div class="ttc" id="classEigen_1_1SparseMatrix_html"><div class="ttname"><a href="classEigen_1_1SparseMatrix.html">Eigen::SparseMatrix< Scalar, ColMajor, Index ></a></div></div>
<div class="ttc" id="structEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...</div><div class="ttdef"><b>Definition:</b> NumTraits.h:88</div></div>
<div class="ttc" id="namespaceEigen_html_a81fb70d0dc1c6deb42e9816647607247"><div class="ttname"><a href="namespaceEigen.html#a81fb70d0dc1c6deb42e9816647607247">Eigen::operator*</a></div><div class="ttdeci">const internal::permut_matrix_product_retval< PermutationDerived, Derived, OnTheRight > operator*(const MatrixBase< Derived > &matrix, const PermutationBase< PermutationDerived > &permutation)</div><div class="ttdef"><b>Definition:</b> PermutationMatrix.h:510</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_aca041ec6ace60e0e597f40706e9c894d"><div class="ttname"><a href="classEigen_1_1SparseQR.html#aca041ec6ace60e0e597f40706e9c894d">Eigen::SparseQR::factorize</a></div><div class="ttdeci">void factorize(const MatrixType &mat)</div><div class="ttdoc">Performs the numerical QR factorization of the input matrix. </div><div class="ttdef"><b>Definition:</b> SparseQR.h:300</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_ac27067ab301641fe6cc35c216a9b18a2"><div class="ttname"><a href="classEigen_1_1SparseQR.html#ac27067ab301641fe6cc35c216a9b18a2">Eigen::SparseQR::matrixQ</a></div><div class="ttdeci">SparseQRMatrixQReturnType< SparseQR > matrixQ() const </div><div class="ttdef"><b>Definition:</b> SparseQR.h:132</div></div>
<div class="ttc" id="namespaceEigen_1_1internal_html_a22b184331e5fb270a37d1305e95cb064"><div class="ttname"><a href="namespaceEigen_1_1internal.html#a22b184331e5fb270a37d1305e95cb064">Eigen::internal::coletree</a></div><div class="ttdeci">int coletree(const MatrixType &mat, IndexVector &parent, IndexVector &firstRowElt, typename MatrixType::Index *perm=0)</div><div class="ttdef"><b>Definition:</b> SparseColEtree.h:61</div></div>
<div class="ttc" id="classEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix< Dynamic, Dynamic, Index ></a></div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html"><div class="ttname"><a href="classEigen_1_1SparseQR.html">Eigen::SparseQR</a></div><div class="ttdoc">Sparse left-looking rank-revealing QR factorization. </div><div class="ttdef"><b>Definition:</b> SparseQR.h:16</div></div>
<div class="ttc" id="classEigen_1_1PermutationBase_html_a76f5bc8a03ec105ab4be1f2b91b7b5d5"><div class="ttname"><a href="classEigen_1_1PermutationBase.html#a76f5bc8a03ec105ab4be1f2b91b7b5d5">Eigen::PermutationBase::size</a></div><div class="ttdeci">Index size() const </div><div class="ttdef"><b>Definition:</b> PermutationMatrix.h:114</div></div>
<div class="ttc" id="classEigen_1_1SparseMatrixBase_html"><div class="ttname"><a href="classEigen_1_1SparseMatrixBase.html">Eigen::SparseMatrixBase</a></div><div class="ttdoc">Base class of any sparse matrices or sparse expressions. </div><div class="ttdef"><b>Definition:</b> SparseMatrixBase.h:26</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_a5552abd83dbd03c85cea6d61fd8875a5"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a5552abd83dbd03c85cea6d61fd8875a5">Eigen::SparseQR::rows</a></div><div class="ttdeci">Index rows() const </div><div class="ttdef"><b>Definition:</b> SparseQR.h:94</div></div>
<div class="ttc" id="structEigen_1_1EigenBase_html_aa84222add803ad7c9db07dd4dd91d5d9"><div class="ttname"><a href="structEigen_1_1EigenBase.html#aa84222add803ad7c9db07dd4dd91d5d9">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived & derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:34</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_a0c06d5c2034ebb329c54235369643ad2"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a0c06d5c2034ebb329c54235369643ad2">Eigen::SparseQR::info</a></div><div class="ttdeci">ComputationInfo info() const </div><div class="ttdoc">Reports whether previous computation was successful. </div><div class="ttdef"><b>Definition:</b> SparseQR.h:214</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_aaca1908a5ec508a25ff0a8bca803e5f3"><div class="ttname"><a href="classEigen_1_1SparseQR.html#aaca1908a5ec508a25ff0a8bca803e5f3">Eigen::SparseQR::cols</a></div><div class="ttdeci">Index cols() const </div><div class="ttdef"><b>Definition:</b> SparseQR.h:98</div></div>
<div class="ttc" id="classEigen_1_1PlainObjectBase_html_aabcf7b6f4543f6255253b9ccee3309b8"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#aabcf7b6f4543f6255253b9ccee3309b8">Eigen::PlainObjectBase::setConstant</a></div><div class="ttdeci">Derived & setConstant(Index size, const Scalar &value)</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:348</div></div>
<div class="ttc" id="classEigen_1_1DenseBase_html_afdfced3e157f74b3bc68892aad178424"><div class="ttname"><a href="classEigen_1_1DenseBase.html#afdfced3e157f74b3bc68892aad178424">Eigen::DenseBase::topRows</a></div><div class="ttdeci">RowsBlockXpr topRows(Index n)</div><div class="ttdef"><b>Definition:</b> DenseBase.h:381</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037bae1252631a63be5890a1e78ff417d378f"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bae1252631a63be5890a1e78ff417d378f">Eigen::InvalidInput</a></div><div class="ttdef"><b>Definition:</b> Constants.h:383</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_ad00a1dda3c45b53e1f91219824773b1c"><div class="ttname"><a href="classEigen_1_1SparseQR.html#ad00a1dda3c45b53e1f91219824773b1c">Eigen::SparseQR::setPivotThreshold</a></div><div class="ttdeci">void setPivotThreshold(const RealScalar &threshold)</div><div class="ttdef"><b>Definition:</b> SparseQR.h:181</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_a1229744f4e8554ca6e96fe32ac359924"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a1229744f4e8554ca6e96fe32ac359924">Eigen::SparseQR::colsPermutation</a></div><div class="ttdeci">const PermutationType & colsPermutation() const </div><div class="ttdef"><b>Definition:</b> SparseQR.h:138</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_a2faae287189af711e5f8ac62c140c71f"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a2faae287189af711e5f8ac62c140c71f">Eigen::SparseQR::solve</a></div><div class="ttdeci">const internal::solve_retval< SparseQR, Rhs > solve(const MatrixBase< Rhs > &B) const </div><div class="ttdef"><b>Definition:</b> SparseQR.h:192</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_a934752a840893040688fc788848a1e06"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a934752a840893040688fc788848a1e06">Eigen::SparseQR::matrixR</a></div><div class="ttdeci">const QRMatrixType & matrixR() const </div><div class="ttdef"><b>Definition:</b> SparseQR.h:102</div></div>
<div class="ttc" id="classEigen_1_1SparseQR_html_a5907227f29f3911de653273efef11b45"><div class="ttname"><a href="classEigen_1_1SparseQR.html#a5907227f29f3911de653273efef11b45">Eigen::SparseQR::analyzePattern</a></div><div class="ttdeci">void analyzePattern(const MatrixType &mat)</div><div class="ttdoc">Preprocessing step of a QR factorization. </div><div class="ttdef"><b>Definition:</b> SparseQR.h:264</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Eigen::Success</a></div><div class="ttdef"><b>Definition:</b> Constants.h:376</div></div>
<div class="ttc" id="classEigen_1_1SparseMatrixBase_html_a6f5fc5fe9d3fb70e62d4a9b1795704a8"><div class="ttname"><a href="classEigen_1_1SparseMatrixBase.html#a6f5fc5fe9d3fb70e62d4a9b1795704a8">Eigen::SparseMatrixBase::topLeftCorner</a></div><div class="ttdeci">Block< Derived > topLeftCorner(Index cRows, Index cCols)</div><div class="ttdef"><b>Definition:</b> SparseMatrixBase.h:157</div></div>
<div class="ttc" id="classEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix< Index, Dynamic, 1 ></a></div></div>
<div class="ttc" id="classEigen_1_1SparseMatrixBase_html_a5552abd83dbd03c85cea6d61fd8875a5"><div class="ttname"><a href="classEigen_1_1SparseMatrixBase.html#a5552abd83dbd03c85cea6d61fd8875a5">Eigen::SparseMatrixBase::rows</a></div><div class="ttdeci">Index rows() const </div><div class="ttdef"><b>Definition:</b> SparseMatrixBase.h:150</div></div>
<div class="ttc" id="group__enums_html_ga51bc1ac16f26ebe51eae1abb77bd037b"><div class="ttname"><a href="group__enums.html#ga51bc1ac16f26ebe51eae1abb77bd037b">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:374</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions. </div><div class="ttdef"><b>Definition:</b> MatrixBase.h:48</div></div>
<div class="ttc" id="classEigen_1_1PlainObjectBase_html_a04abe84a9a894de335a232681d9a0722"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#a04abe84a9a894de335a232681d9a0722">Eigen::PlainObjectBase::setZero</a></div><div class="ttdeci">Derived & setZero(Index size)</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:515</div></div>
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