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<div class="headertitle"><div class="title">BlockHouseholder.h</div></div>
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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// Copyright (C) 2010 Vincent Lejeune</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">// Copyright (C) 2010 Gael Guennebaud <[email protected]></span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">//</span></div>
<div class="line"><a id="l00007" 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 id="l00008" 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 id="l00009" 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 id="l00010" name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#ifndef EIGEN_BLOCK_HOUSEHOLDER_H</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#define EIGEN_BLOCK_HOUSEHOLDER_H</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// This file contains some helper function to deal with block householder reflectors</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include "./InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// template<typename TriangularFactorType,typename VectorsType,typename CoeffsType></span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">// void make_block_householder_triangular_factor(TriangularFactorType& triFactor, const VectorsType& vectors, const CoeffsType& hCoeffs)</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">// {</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// typedef typename VectorsType::Scalar Scalar;</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// const Index nbVecs = vectors.cols();</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// </span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// for(Index i = 0; i < nbVecs; i++)</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// {</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// Index rs = vectors.rows() - i;</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">// // Warning, note that hCoeffs may alias with vectors.</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// // It is then necessary to copy it before modifying vectors(i,i). </span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// typename CoeffsType::Scalar h = hCoeffs(i);</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// // This hack permits to pass trough nested Block<> and Transpose<> expressions.</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// Scalar *Vii_ptr = const_cast<Scalar*>(vectors.data() + vectors.outerStride()*i + vectors.innerStride()*i);</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// Scalar Vii = *Vii_ptr;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// *Vii_ptr = Scalar(1);</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// triFactor.col(i).head(i).noalias() = -h * vectors.block(i, 0, rs, i).adjoint()</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// * vectors.col(i).tail(rs);</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// *Vii_ptr = Vii;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// // FIXME add .noalias() once the triangular product can work inplace</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// triFactor.col(i).head(i) = triFactor.block(0,0,i,i).template triangularView<Upper>()</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// * triFactor.col(i).head(i);</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// triFactor(i,i) = hCoeffs(i);</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// }</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// }</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// This variant avoid modifications in vectors</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="keyword">template</span><<span class="keyword">typename</span> TriangularFactorType,<span class="keyword">typename</span> VectorsType,<span class="keyword">typename</span> CoeffsType></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="keywordtype">void</span> make_block_householder_triangular_factor(TriangularFactorType& triFactor, <span class="keyword">const</span> VectorsType& vectors, <span class="keyword">const</span> CoeffsType& hCoeffs)</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span>{</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">const</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> nbVecs = vectors.cols();</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> eigen_assert(triFactor.rows() == nbVecs && triFactor.cols() == nbVecs && vectors.rows()>=nbVecs);</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordflow">for</span>(<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = nbVecs-1; i >=0 ; --i)</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rs = vectors.rows() - i - 1;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rt = nbVecs-i-1;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">if</span>(rt>0)</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> triFactor.row(i).tail(rt).noalias() = -hCoeffs(i) * vectors.col(i).tail(rs).adjoint()</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> * vectors.bottomRightCorner(rs, rt).template triangularView<UnitLower>();</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// FIXME use the following line with .noalias() once the triangular product can work inplace</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// triFactor.row(i).tail(rt) = triFactor.row(i).tail(rt) * triFactor.bottomRightCorner(rt,rt).template triangularView<Upper>();</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">for</span>(<a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j=nbVecs-1; j>i; --j)</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> {</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keyword">typename</span> TriangularFactorType::Scalar z = triFactor(i,j);</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> triFactor(i,j) = z * triFactor(j,j);</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">if</span>(nbVecs-j-1>0)</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> triFactor.row(i).tail(nbVecs-j-1) += z * triFactor.row(j).tail(nbVecs-j-1);</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> }</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> triFactor(i,i) = hCoeffs(i);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> }</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>}</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="keyword">template</span><<span class="keyword">typename</span> MatrixType,<span class="keyword">typename</span> VectorsType,<span class="keyword">typename</span> CoeffsType></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="keywordtype">void</span> apply_block_householder_on_the_left(MatrixType& mat, <span class="keyword">const</span> VectorsType& vectors, <span class="keyword">const</span> CoeffsType& hCoeffs, <span class="keywordtype">bool</span> forward)</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span>{</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keyword">enum</span> { TFactorSize = VectorsType::ColsAtCompileTime };</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> nbVecs = vectors.cols();</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> Matrix<typename MatrixType::Scalar, TFactorSize, TFactorSize, RowMajor> T(nbVecs,nbVecs);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">if</span>(forward) make_block_householder_triangular_factor(T, vectors, hCoeffs);</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">else</span> make_block_householder_triangular_factor(T, vectors, hCoeffs.conjugate()); </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keyword">const</span> TriangularView<const VectorsType, UnitLower> V(vectors);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// A -= V T V^* A</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> Matrix<<span class="keyword">typename</span> MatrixType::Scalar,VectorsType::ColsAtCompileTime,MatrixType::ColsAtCompileTime,</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> (VectorsType::MaxColsAtCompileTime==1 && MatrixType::MaxColsAtCompileTime!=1)?<a class="code hl_enumvalue" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>:<a class="code hl_enumvalue" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>,</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> VectorsType::MaxColsAtCompileTime,MatrixType::MaxColsAtCompileTime> tmp = V.adjoint() * mat;</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// FIXME add .noalias() once the triangular product can work inplace</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordflow">if</span>(forward) tmp = T.template triangularView<Upper>() * tmp;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">else</span> tmp = T.template triangularView<Upper>().adjoint() * tmp;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> mat.noalias() -= V * tmp;</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span>}</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span>} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="preprocessor">#endif </span><span class="comment">// EIGEN_BLOCK_HOUSEHOLDER_H</span></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">Eigen::ColMajor</a></div><div class="ttdeci">@ ColMajor</div><div class="ttdef"><b>Definition</b> Constants.h:321</div></div>
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<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition</b> Core:139</div></div>
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