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<div class="title">UpperBidiagonalization.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">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</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="l00008"></a><span class="lineno"> 8</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="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_BIDIAGONALIZATION_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_BIDIAGONALIZATION_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// UpperBidiagonalization will probably be replaced by a Bidiagonalization class, don't want to make it stable API.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">// At the same time, it's useful to keep for now as it's about the only thing that is testing the BandMatrix class.</span></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">template</span><<span class="keyword">typename</span> _MatrixType> <span class="keyword">class </span>UpperBidiagonalization</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> {</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  <span class="keyword">public</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>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  RowsAtCompileTime = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  ColsAtCompileTime = MatrixType::ColsAtCompileTime,</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  ColsAtCompileTimeMinusOne = internal::decrement_size<ColsAtCompileTime>::ret</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> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">typedef</span> Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">typedef</span> Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">typedef</span> BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0> BidiagonalType;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">typedef</span> Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keyword">typedef</span> Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">typedef</span> HouseholderSequence<</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keyword">const</span> MatrixType,</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, <span class="keyword">const</span> Diagonal<const MatrixType,0> ></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  > HouseholderUSequenceType;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">typedef</span> HouseholderSequence<</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">const</span> <span class="keyword">typename</span> internal::remove_all<typename MatrixType::ConjugateReturnType>::type,</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  Diagonal<const MatrixType,1>,</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <a class="code" href="group__enums.html#gga3f4a95405348aa63ef907e692901011faeda0d7b1859ec757de18ee3b7c6c541c">OnTheRight</a></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  > HouseholderVSequenceType;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  UpperBidiagonalization() : m_householder(), m_bidiagonal(), m_isInitialized(false) {}</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  UpperBidiagonalization(<span class="keyword">const</span> MatrixType& matrix)</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  : m_householder(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  m_bidiagonal(matrix.cols(), matrix.cols()),</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  m_isInitialized(false)</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  {</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  compute(matrix);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  }</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  UpperBidiagonalization& compute(<span class="keyword">const</span> MatrixType& matrix);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  </div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">const</span> MatrixType& householder()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_householder; }</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">const</span> BidiagonalType& bidiagonal()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_bidiagonal; }</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">const</span> HouseholderUSequenceType householderU()<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>  eigen_assert(m_isInitialized && <span class="stringliteral">"UpperBidiagonalization is not initialized."</span>);</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">return</span> HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());</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> </div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">const</span> HouseholderVSequenceType householderV() <span class="comment">// const here gives nasty errors and i'm lazy</span></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>  eigen_assert(m_isInitialized && <span class="stringliteral">"UpperBidiagonalization is not initialized."</span>);</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">return</span> HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  .setLength(m_householder.cols()-1)</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  .setShift(1);</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>  </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  MatrixType m_householder;</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  BidiagonalType m_bidiagonal;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">bool</span> m_isInitialized;</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> </div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> UpperBidiagonalization<_MatrixType>& UpperBidiagonalization<_MatrixType>::compute(<span class="keyword">const</span> _MatrixType& matrix)</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> {</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  Index rows = matrix.rows();</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  Index cols = matrix.cols();</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>  eigen_assert(rows >= cols && <span class="stringliteral">"UpperBidiagonalization is only for matrices satisfying rows>=cols."</span>);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  m_householder = matrix;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  ColVectorType temp(rows);</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> </div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordflow">for</span> (Index k = 0; <span class="comment">/* breaks at k==cols-1 below */</span> ; ++k)</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  {</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  Index remainingRows = rows - k;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  Index remainingCols = cols - k - 1;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="comment">// construct left householder transform in-place in m_householder</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  m_householder.col(k).tail(remainingRows)</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  .makeHouseholderInPlace(m_householder.coeffRef(k,k),</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  m_bidiagonal.template diagonal<0>().coeffRef(k));</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="comment">// apply householder transform to remaining part of m_householder on the left</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  m_householder.bottomRightCorner(remainingRows, remainingCols)</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  .applyHouseholderOnTheLeft(m_householder.col(k).tail(remainingRows-1),</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  m_householder.coeff(k,k),</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  temp.data());</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">if</span>(k == cols-1) <span class="keywordflow">break</span>;</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="comment">// construct right householder transform in-place in m_householder</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  m_householder.row(k).tail(remainingCols)</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  .makeHouseholderInPlace(m_householder.coeffRef(k,k+1),</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  m_bidiagonal.template diagonal<1>().coeffRef(k));</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <span class="comment">// apply householder transform to remaining part of m_householder on the left</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  m_householder.bottomRightCorner(remainingRows-1, remainingCols)</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  .applyHouseholderOnTheRight(m_householder.row(k).tail(remainingCols-1).transpose(),</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  m_householder.coeff(k,k+1),</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  temp.data());</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  }</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</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> <span class="preprocessor">#if 0</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="keyword">const</span> UpperBidiagonalization<typename MatrixBase<Derived>::PlainObject></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> MatrixBase<Derived>::bidiagonalization()<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>  <span class="keywordflow">return</span> UpperBidiagonalization<PlainObject>(eval());</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> }</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="preprocessor">#endif // EIGEN_BIDIAGONALIZATION_H</span></div>
<div class="ttc" id="group__enums_html_gga3f4a95405348aa63ef907e692901011faeda0d7b1859ec757de18ee3b7c6c541c"><div class="ttname"><a href="group__enums.html#gga3f4a95405348aa63ef907e692901011faeda0d7b1859ec757de18ee3b7c6c541c">Eigen::OnTheRight</a></div><div class="ttdef"><b>Definition:</b> Constants.h:279</div></div>
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