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<div class="title">Householder.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) 2010 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2009 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_HOUSEHOLDER_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_HOUSEHOLDER_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"> 16</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">template</span><<span class="keywordtype">int</span> n> <span class="keyword">struct </span>decrement_size</div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> {</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  ret = n==<a class="code" href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Dynamic</a> ? n : n-1</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  };</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> };</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> }</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#ab04e8cc14dd5445607ab15a0d27745a5"> 42</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixBase.html#ab04e8cc14dd5445607ab15a0d27745a5">MatrixBase<Derived>::makeHouseholderInPlace</a>(Scalar& tau, RealScalar& beta)</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> {</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <a class="code" href="classEigen_1_1VectorBlock.html">VectorBlock<Derived, internal::decrement_size<Base::SizeAtCompileTime>::ret</a>> essentialPart(derived(), 1, size()-1);</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  makeHouseholder(essentialPart, tau, beta);</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> }</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="keyword">template</span><<span class="keyword">typename</span> EssentialPart></div>
<div class="line"><a name="l00065"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a306f9da1f2385c4a6e33e1d0e09173f2"> 65</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixBase.html#a306f9da1f2385c4a6e33e1d0e09173f2">MatrixBase<Derived>::makeHouseholder</a>(</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  EssentialPart& essential,</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  Scalar& tau,</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  RealScalar& beta)<span class="keyword"> const</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keyword">using</span> numext::conj;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <a class="code" href="classEigen_1_1VectorBlock.html">VectorBlock<const Derived, EssentialPart::SizeAtCompileTime></a> tail(derived(), 1, size()-1);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  Scalar c0 = coeff(0);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">if</span>(tailSqNorm == RealScalar(0) && numext::imag(c0)==RealScalar(0))</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  {</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  tau = RealScalar(0);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  beta = numext::real(c0);</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  essential.setZero();</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  }</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  {</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  beta = sqrt(numext::abs2(c0) + tailSqNorm);</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordflow">if</span> (numext::real(c0)>=RealScalar(0))</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  beta = -beta;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  essential = tail / (c0 - beta);</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  tau = conj((beta - c0) / beta);</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  }</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> }</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">template</span><<span class="keyword">typename</span> EssentialPart></div>
<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a627d53362b0753eb710d8132e84fa490"> 112</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixBase.html#a627d53362b0753eb710d8132e84fa490">MatrixBase<Derived>::applyHouseholderOnTheLeft</a>(</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">const</span> EssentialPart& essential,</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keyword">const</span> Scalar& tau,</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  Scalar* workspace)</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> {</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">if</span>(rows() == 1)</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  {</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  *<span class="keyword">this</span> *= Scalar(1)-tau;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  {</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <a class="code" href="classEigen_1_1Map.html">Map<typename internal::plain_row_type<PlainObject>::type</a>> tmp(workspace,cols());</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <a class="code" href="classEigen_1_1Block.html">Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime></a> bottom(derived(), 1, 0, rows()-1, cols());</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  tmp.noalias() = essential.adjoint() * bottom;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  tmp += this->row(0);</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  this->row(0) -= tau * tmp;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  bottom.noalias() -= tau * essential * tmp;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  }</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> }</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> </div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="keyword">template</span><<span class="keyword">typename</span> EssentialPart></div>
<div class="line"><a name="l00149"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a146f355a8e78e220a49a0344d56b28e9"> 149</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixBase.html#a146f355a8e78e220a49a0344d56b28e9">MatrixBase<Derived>::applyHouseholderOnTheRight</a>(</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">const</span> EssentialPart& essential,</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keyword">const</span> Scalar& tau,</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  Scalar* workspace)</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> {</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keywordflow">if</span>(cols() == 1)</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>  *<span class="keyword">this</span> *= Scalar(1)-tau;</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="keywordflow">else</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  {</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <a class="code" href="classEigen_1_1Map.html">Map<typename internal::plain_col_type<PlainObject>::type</a>> tmp(workspace,rows());</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <a class="code" href="classEigen_1_1Block.html">Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime></a> right(derived(), 0, 1, rows(), cols()-1);</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  tmp.noalias() = right * essential.conjugate();</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  tmp += this->col(0);</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  this->col(0) -= tau * tmp;</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  right.noalias() -= tau * tmp * essential.transpose();</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> }</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> </div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> } <span class="comment">// end namespace Eigen</span></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> <span class="preprocessor">#endif // EIGEN_HOUSEHOLDER_H</span></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a146f355a8e78e220a49a0344d56b28e9"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a146f355a8e78e220a49a0344d56b28e9">Eigen::MatrixBase::applyHouseholderOnTheRight</a></div><div class="ttdeci">void applyHouseholderOnTheRight(const EssentialPart &essential, const Scalar &tau, Scalar *workspace)</div><div class="ttdef"><b>Definition:</b> Householder.h:149</div></div>
<div class="ttc" id="classEigen_1_1Map_html"><div class="ttname"><a href="classEigen_1_1Map.html">Eigen::Map</a></div><div class="ttdoc">A matrix or vector expression mapping an existing array of data. </div><div class="ttdef"><b>Definition:</b> Map.h:104</div></div>
<div class="ttc" id="namespaceEigen_html_adc9da5be31bdce40c25a92c27999c0e3"><div class="ttname"><a href="namespaceEigen.html#adc9da5be31bdce40c25a92c27999c0e3">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:21</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a306f9da1f2385c4a6e33e1d0e09173f2"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a306f9da1f2385c4a6e33e1d0e09173f2">Eigen::MatrixBase::makeHouseholder</a></div><div class="ttdeci">void makeHouseholder(EssentialPart &essential, Scalar &tau, RealScalar &beta) const </div><div class="ttdef"><b>Definition:</b> Householder.h:65</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_a627d53362b0753eb710d8132e84fa490"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a627d53362b0753eb710d8132e84fa490">Eigen::MatrixBase::applyHouseholderOnTheLeft</a></div><div class="ttdeci">void applyHouseholderOnTheLeft(const EssentialPart &essential, const Scalar &tau, Scalar *workspace)</div><div class="ttdef"><b>Definition:</b> Householder.h:112</div></div>
<div class="ttc" id="classEigen_1_1VectorBlock_html"><div class="ttname"><a href="classEigen_1_1VectorBlock.html">Eigen::VectorBlock</a></div><div class="ttdoc">Expression of a fixed-size or dynamic-size sub-vector. </div><div class="ttdef"><b>Definition:</b> ForwardDeclarations.h:83</div></div>
<div class="ttc" id="classEigen_1_1Block_html"><div class="ttname"><a href="classEigen_1_1Block.html">Eigen::Block</a></div><div class="ttdoc">Expression of a fixed-size or dynamic-size block. </div><div class="ttdef"><b>Definition:</b> Block.h:102</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html_ab04e8cc14dd5445607ab15a0d27745a5"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#ab04e8cc14dd5445607ab15a0d27745a5">Eigen::MatrixBase::makeHouseholderInPlace</a></div><div class="ttdeci">void makeHouseholderInPlace(Scalar &tau, RealScalar &beta)</div><div class="ttdef"><b>Definition:</b> Householder.h:42</div></div>
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