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<div class="title">qr.hpp</div> </div>
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<a href="qr_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="preprocessor">#ifndef VIENNACL_LINALG_QR_HPP</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define VIENNACL_LINALG_QR_HPP</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> </div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">/* =========================================================================</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> Copyright (c) 2010-2016, Institute for Microelectronics,</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> Institute for Analysis and Scientific Computing,</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> TU Wien.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> Portions of this software are copyright by UChicago Argonne, LLC.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"></span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> -----------------</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> ViennaCL - The Vienna Computing Library</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> -----------------</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> Project Head: Karl Rupp rupp@iue.tuwien.ac.at</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"></span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> (A list of authors and contributors can be found in the manual)</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> License: MIT (X11), see file LICENSE in the base directory</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">============================================================================= */</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <utility></span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include <iostream></span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include <fstream></span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <string></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <algorithm></span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="preprocessor">#include <math.h></span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#include <cmath></span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#include "boost/numeric/ublas/vector.hpp"</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix.hpp"</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix_proxy.hpp"</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="preprocessor">#include "boost/numeric/ublas/vector_proxy.hpp"</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#include "boost/numeric/ublas/io.hpp"</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include "boost/numeric/ublas/matrix_expression.hpp"</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="preprocessor">#include "<a class="code" href="matrix__proxy_8hpp.html">viennacl/matrix_proxy.hpp</a>"</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="preprocessor">#include "<a class="code" href="range_8hpp.html">viennacl/range.hpp</a>"</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">namespace </span>viennacl</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>  <span class="keyword">namespace </span>linalg</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">namespace </span>detail</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00053"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a0f34407a1e24c1dee933cb03f978d139"> 53</a></span>  <span class="keyword">typename</span> MatrixType::value_type <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0f34407a1e24c1dee933cb03f978d139">setup_householder_vector_ublas</a>(MatrixType <span class="keyword">const</span> & A, VectorType & v, MatrixType & matrix_1x1, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j)</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>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::value_type <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">//compute norm of column below diagonal:</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  matrix_1x1 = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">boost::numeric::ublas::prod</a>( <a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, j+1))),</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, j+1))</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  );</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  ScalarType sigma = matrix_1x1(0,0);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  ScalarType beta = 0;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  ScalarType A_jj = A(j,j);</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>  assert( sigma >= 0.0 && <span class="keywordtype">bool</span>(<span class="stringliteral">"sigma must be non-negative!"</span>));</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">//get v from A:</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  v(j,0) = 1.0;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0,1)) = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j,j+1));</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="keywordflow">if</span> (sigma <= 0)</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  {</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  ScalarType mu = std::sqrt(sigma + A_jj*A_jj);</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>  ScalarType <a class="code" href="global__variables_8cpp.html#a1d3b09c2337808223ca760c55bdf5414">v1</a> = (A_jj <= 0) ? (A_jj - mu) : (-sigma / (A_jj + mu));</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  beta = <span class="keyword">static_cast<</span>ScalarType<span class="keyword">></span>(2.0) * v1 * v1 / (sigma + v1 * <a class="code" href="global__variables_8cpp.html#a1d3b09c2337808223ca760c55bdf5414">v1</a>);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">//divide v by its diagonal element v[j]</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0,1)) /= v1;</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> </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">return</span> beta;</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> </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>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type</a></div>
<div class="line"><a name="l00093"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#acfdf9d2d13f373340bf68cffd9586775"> 93</a></span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#acfdf9d2d13f373340bf68cffd9586775">setup_householder_vector_viennacl</a>(MatrixType <span class="keyword">const</span> & A, VectorType & v, MatrixType & matrix_1x1, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j)</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  {</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">viennacl::range</a>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a>;</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type</a> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</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="comment">//compute norm of column below diagonal:</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  matrix_1x1 = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>( <a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, j+1))),</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, j+1))</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  );</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  ScalarType sigma = matrix_1x1(0,0);</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  ScalarType beta = 0;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  ScalarType A_jj = A(j,j);</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  assert( sigma >= 0.0 && <span class="keywordtype">bool</span>(<span class="stringliteral">"sigma must be non-negative!"</span>));</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">//get v from A:</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  v(j,0) = 1.0;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0,1)) = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j,j+1));</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">if</span> (sigma == 0)</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  ScalarType mu = std::sqrt(sigma + A_jj*A_jj);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  ScalarType <a class="code" href="global__variables_8cpp.html#a1d3b09c2337808223ca760c55bdf5414">v1</a> = (A_jj <= 0) ? (A_jj - mu) : (-sigma / (A_jj + mu));</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  beta = 2.0 * v1 * v1 / (sigma + v1 * <a class="code" href="global__variables_8cpp.html#a1d3b09c2337808223ca760c55bdf5414">v1</a>);</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">//divide v by its diagonal element v[j]</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0,1)) /= v1;</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> </div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> beta;</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="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// Apply (I - beta v v^T) to the k-th column of A, where v is the reflector starting at j-th row/column</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType, <span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00134"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a08f92f37e68518e1e18dd6ef20b02947"> 134</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a08f92f37e68518e1e18dd6ef20b02947">householder_reflect</a>(MatrixType & A, VectorType & v, <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> beta, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k)</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  {</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> v_in_col = A(j,k);</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=j+1; i<A.size1(); ++i)</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  v_in_col += v[i] * A(i,k);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="comment">//assert(v[j] == 1.0);</span></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="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=j; i<A.size1(); ++i)</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  A(i,k) -= beta * v_in_col * v[i];</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  }</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType, <span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00147"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a48b9804b36f469aff716174b0dc0b573"> 147</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a48b9804b36f469aff716174b0dc0b573">householder_reflect_ublas</a>(MatrixType & A, VectorType & v, MatrixType & matrix_1x1, <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> beta, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k)</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  {</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> </div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> v_in_col = A(j,k);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  matrix_1x1 = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">boost::numeric::ublas::prod</a>(<a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1))),</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k,k+1)));</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  v_in_col += matrix_1x1(0,0);</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1)) -= (beta * v_in_col) * <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1));</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</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>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType, <span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00161"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#af17ac3429b78effc2d0c0238a9fcf7b1"> 161</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#af17ac3429b78effc2d0c0238a9fcf7b1">householder_reflect_viennacl</a>(MatrixType & A, VectorType & v, MatrixType & matrix_1x1, <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> beta, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k)</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="keyword">using</span> <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">viennacl::range</a>;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a>;</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> </div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> v_in_col = A(j,k);</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>  matrix_1x1 = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(<a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1))),</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k,k+1)));</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  v_in_col += matrix_1x1(0,0);</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keywordflow">if</span> ( beta * v_in_col != 0.0)</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>  VectorType temp = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1));</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1)) *= (beta * v_in_col);</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1)) -= <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1));</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1)) = temp;</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  }</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  }</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="comment">// Apply (I - beta v v^T) to A, where v is the reflector starting at j-th row/column</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType, <span class="keyword">typename</span> ScalarType></div>
<div class="line"><a name="l00184"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a26c2ded0fa31d617f56bad1c90b42374"> 184</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a08f92f37e68518e1e18dd6ef20b02947">householder_reflect</a>(MatrixType & A, VectorType & v, <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> beta, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j)</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>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> column_end = A.size2();</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> </div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k=j; k<column_end; ++k) <span class="comment">//over columns</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a08f92f37e68518e1e18dd6ef20b02947">householder_reflect</a>(A, v, beta, j, k);</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> </div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> </div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00194"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a0ff42f36e98db6c181b16c78f76f0fdb"> 194</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0ff42f36e98db6c181b16c78f76f0fdb">write_householder_to_A</a>(MatrixType & A, VectorType <span class="keyword">const</span> & v, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j)</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  {</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=j+1; i<A.size1(); ++i)</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  A(i,j) = v[i];</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  }</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> </div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00201"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a0481a094460753dd7fb519c9dda3bdc1"> 201</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0481a094460753dd7fb519c9dda3bdc1">write_householder_to_A_ublas</a>(MatrixType & A, VectorType <span class="keyword">const</span> & v, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j)</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  {</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>;</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>;</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="comment">//VectorType temp = project(v, range(j+1, A.size1()));</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>( A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, j+1) ) = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1) );;</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  }</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00211"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#ae04154f304cceaa81ae1fc24882fd7ba"> 211</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae04154f304cceaa81ae1fc24882fd7ba">write_householder_to_A_viennacl</a>(MatrixType & A, VectorType <span class="keyword">const</span> & v, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j)</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  {</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">viennacl::range</a>;</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a>;</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> </div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="comment">//VectorType temp = project(v, range(j+1, A.size1()));</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>( A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, j+1) ) = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1) );;</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> </div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00228"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a600f0692e7550cee41cc6382337cd8c5"> 228</a></span>  std::vector<typename MatrixType::value_type> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a600f0692e7550cee41cc6382337cd8c5">inplace_qr_ublas</a>(MatrixType & A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 32)</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>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::value_type <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keyword">typedef</span> boost::numeric::ublas::matrix_range<MatrixType> MatrixRange;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> </div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>;</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span> </div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  std::vector<ScalarType> betas(A.size2());</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  MatrixType v(A.size1(), 1);</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  MatrixType matrix_1x1(1,1);</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span> </div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  MatrixType Y(A.size1(), block_size); Y.clear(); Y.resize(A.size1(), block_size);</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  MatrixType W(A.size1(), block_size); W.clear(); W.resize(A.size1(), block_size);</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> </div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="comment">//run over A in a block-wise manner:</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j = 0; j < <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(A.size1(), A.size2()); j += block_size)</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  {</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> effective_block_size = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(A.size1(), A.size2()), j+block_size) - j;</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> </div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="comment">//determine Householder vectors:</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 0; k < effective_block_size; ++k)</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>  betas[j+k] = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0f34407a1e24c1dee933cb03f978d139">detail::setup_householder_vector_ublas</a>(A, v, matrix_1x1, j+k);</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> </div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> l = k; l < effective_block_size; ++l)</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a48b9804b36f469aff716174b0dc0b573">detail::householder_reflect_ublas</a>(A, v, matrix_1x1, betas[j+k], j+k, j+l);</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0481a094460753dd7fb519c9dda3bdc1">detail::write_householder_to_A_ublas</a>(A, v, j+k);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  }</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> </div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="comment">// Setup Y:</span></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  Y.clear(); Y.resize(A.size1(), block_size);</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 0; k < effective_block_size; ++k)</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  {</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="comment">//write Householder to Y:</span></div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  Y(j+k,k) = 1.0;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Y, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+k+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1)) = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+k+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+k, j+k+1));</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  }</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <span class="comment">// Setup W:</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="comment">//</span></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>  <span class="comment">//first vector:</span></div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  W.clear(); W.resize(A.size1(), block_size);</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  W(j, 0) = -betas[j];</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1)) = -betas[j] * <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, j+1));</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span> </div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span> </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="comment">//k-th column of W is given by -beta * (Id + W*Y^T) v_k, where W and Y have k-1 columns</span></div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 1; k < effective_block_size; ++k)</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  {</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  MatrixRange Y_old = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Y, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, k));</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  MatrixRange v_k = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Y, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1));</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  MatrixRange W_old = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, k));</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  MatrixRange z = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1));</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> </div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  MatrixType YT_prod_v = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">boost::numeric::ublas::prod</a>(<a class="code" href="blas3__solve_8cpp.html#ad8f94754a20a0c6dc74fd3cb5eb675b3">boost::numeric::ublas::trans</a>(Y_old), v_k);</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  z = - betas[j+k] * (v_k + <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">prod</a>(W_old, YT_prod_v));</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="l00292"></a><span class="lineno"> 292</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="comment">//apply (I+WY^T)^T = I + Y W^T to the remaining columns of A:</span></div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> </div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keywordflow">if</span> (A.size2() - j - effective_block_size > 0)</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  {</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> </div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  MatrixRange A_part(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+effective_block_size, A.size2()));</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  MatrixRange W_part(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, effective_block_size));</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  MatrixType temp = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">boost::numeric::ublas::prod</a>(<a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(W_part), A_part);</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> </div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  A_part += <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">prod</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Y, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, effective_block_size)),</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  temp);</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  }</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  }</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span> </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordflow">return</span> betas;</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  }</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> </div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> </div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  std::vector< typename viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type ></div>
<div class="line"><a name="l00322"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#ad5d436e9fd57a66afe69f56d78d22eeb"> 322</a></span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ad5d436e9fd57a66afe69f56d78d22eeb">inplace_qr_viennacl</a>(MatrixType & A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 16)</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="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type</a> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="keyword">typedef</span> <a class="code" href="classviennacl_1_1matrix__range.html">viennacl::matrix_range<MatrixType></a> MatrixRange;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span> </div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">viennacl::range</a>;</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keyword">using</span> <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a>;</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>  std::vector<ScalarType> betas(A.size2());</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  MatrixType v(A.size1(), 1);</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  MatrixType matrix_1x1(1,1);</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>  MatrixType Y(A.size1(), block_size); Y.clear();</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  MatrixType W(A.size1(), block_size); W.clear();</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span> </div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  MatrixType YT_prod_v(block_size, 1);</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  MatrixType z(A.size1(), 1);</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">//run over A in a block-wise manner:</span></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j = 0; j < <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(A.size1(), A.size2()); j += block_size)</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>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> effective_block_size = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(A.size1(), A.size2()), j+block_size) - j;</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <span class="comment">//determine Householder vectors:</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 0; k < effective_block_size; ++k)</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  {</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  betas[j+k] = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#acfdf9d2d13f373340bf68cffd9586775">detail::setup_householder_vector_viennacl</a>(A, v, matrix_1x1, j+k);</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> l = k; l < effective_block_size; ++l)</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#af17ac3429b78effc2d0c0238a9fcf7b1">detail::householder_reflect_viennacl</a>(A, v, matrix_1x1, betas[j+k], j+k, j+l);</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>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ae04154f304cceaa81ae1fc24882fd7ba">detail::write_householder_to_A_viennacl</a>(A, v, j+k);</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  }</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span> </div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="comment">// Setup Y:</span></div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  Y.clear();</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 0; k < effective_block_size; ++k)</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  {</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="comment">//write Householder to Y:</span></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  Y(j+k,k) = 1.0;</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Y, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+k+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1)) = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+k+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+k, j+k+1));</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  }</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> </div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="comment">// Setup W:</span></div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  <span class="comment">//</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>  <span class="comment">//first vector:</span></div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  W.clear();</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  W(j, 0) = -betas[j];</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="comment">//project(W, range(j+1, A.size1()), range(0, 1)) = -betas[j] * project(A, range(j+1, A.size1()), range(j, j+1));</span></div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1)) = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, j+1));</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+1, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, 1)) *= -betas[j];</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span> </div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span> </div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="comment">//k-th column of W is given by -beta * (Id + W*Y^T) v_k, where W and Y have k-1 columns</span></div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 1; k < effective_block_size; ++k)</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  {</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  MatrixRange Y_old = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Y, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, k));</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  MatrixRange v_k = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Y, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1));</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  MatrixRange W_old = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, k));</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> </div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(YT_prod_v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, k), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0,1)) = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">prod</a>(<a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(Y_old), v_k);</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(z, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0,1)) = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">prod</a>(W_old, <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(YT_prod_v, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, k), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0,1)));</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1)) = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(z, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0,1));</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1)) += v_k;</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(k, k+1)) *= - betas[j+k];</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> </div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="comment">//apply (I+WY^T)^T = I + Y W^T to the remaining columns of A:</span></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span> </div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">if</span> (A.size2() > j + effective_block_size)</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  {</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  MatrixRange A_part(A, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j+effective_block_size, A.size2()));</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  MatrixRange W_part(W, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, effective_block_size));</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  MatrixType temp = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">prod</a>(<a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(W_part), A_part);</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> </div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  A_part += <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">prod</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">project</a>(Y, <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(j, A.size1()), <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">range</a>(0, effective_block_size)),</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  temp);</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  }</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  }</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>  <span class="keywordflow">return</span> betas;</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> </div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> </div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span> </div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span> </div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span> </div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> </div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  <span class="comment">//MatrixType is ViennaCL-matrix</span></div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="comment"></span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  std::vector< typename viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type ></div>
<div class="line"><a name="l00426"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#aa3b53a769e6ce29affb7401b9118fde3"> 426</a></span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aa3b53a769e6ce29affb7401b9118fde3">inplace_qr_hybrid</a>(MatrixType & A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 16)</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="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type</a> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</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="keyword">typedef</span> <a class="code" href="classviennacl_1_1matrix__range.html">viennacl::matrix_range<MatrixType></a> VCLMatrixRange;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  <span class="keyword">typedef</span> boost::numeric::ublas::matrix<ScalarType> UblasMatrixType;</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  <span class="keyword">typedef</span> boost::numeric::ublas::matrix_range<UblasMatrixType> UblasMatrixRange;</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> </div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  std::vector<ScalarType> betas(A.size2());</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  UblasMatrixType v(A.size1(), 1);</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  UblasMatrixType matrix_1x1(1,1);</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> </div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  UblasMatrixType ublasW(A.size1(), block_size); ublasW.clear(); ublasW.resize(A.size1(), block_size);</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  UblasMatrixType ublasY(A.size1(), block_size); ublasY.clear(); ublasY.resize(A.size1(), block_size);</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span> </div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  UblasMatrixType ublasA(A.size1(), A.size1());</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span> </div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  MatrixType vclW(ublasW.size1(), ublasW.size2());</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  MatrixType vclY(ublasY.size1(), ublasY.size2());</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> </div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="comment">//run over A in a block-wise manner:</span></div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j = 0; j < <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(A.size1(), A.size2()); j += block_size)</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  {</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> effective_block_size = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(A.size1(), A.size2()), j+block_size) - j;</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  UblasMatrixRange ublasA_part = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasA,</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(0, A.size1()),</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j, j + effective_block_size));</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a>(A,</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(0, A.size1()),</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(j, j+effective_block_size)),</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  ublasA_part</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  );</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span> </div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="comment">//determine Householder vectors:</span></div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 0; k < effective_block_size; ++k)</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  {</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  betas[j+k] = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0f34407a1e24c1dee933cb03f978d139">detail::setup_householder_vector_ublas</a>(ublasA, v, matrix_1x1, j+k);</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span> </div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> l = k; l < effective_block_size; ++l)</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a48b9804b36f469aff716174b0dc0b573">detail::householder_reflect_ublas</a>(ublasA, v, matrix_1x1, betas[j+k], j+k, j+l);</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>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0481a094460753dd7fb519c9dda3bdc1">detail::write_householder_to_A_ublas</a>(ublasA, v, j+k);</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  }</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>  <span class="comment">//</span></div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="comment">// Setup Y:</span></div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  ublasY.clear(); ublasY.resize(A.size1(), block_size);</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 0; k < effective_block_size; ++k)</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  {</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <span class="comment">//write Householder to Y:</span></div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  ublasY(j+k,k) = 1.0;</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasY,</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j+k+1, A.size1()),</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(k, k+1))</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasA,</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j+k+1, A.size1()),</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j+k, j+k+1));</div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  }</div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span> </div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="comment">// Setup W:</span></div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span> </div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="comment">//first vector:</span></div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  ublasW.clear(); ublasW.resize(A.size1(), block_size);</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  ublasW(j, 0) = -betas[j];</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasW,</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j+1, A.size1()),</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(0, 1))</div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  = -betas[j] * <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasA,</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j+1, A.size1()),</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j, j+1));</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> </div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> </div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="comment">//k-th column of W is given by -beta * (Id + W*Y^T) v_k, where W and Y have k-1 columns</span></div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> k = 1; k < effective_block_size; ++k)</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  {</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  UblasMatrixRange Y_old = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasY,</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j, A.size1()),</div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(0, k));</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  UblasMatrixRange v_k = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasY,</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j, A.size1()),</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(k, k+1));</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  UblasMatrixRange W_old = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasW,</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j, A.size1()),</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(0, k));</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  UblasMatrixRange z = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasW,</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j, A.size1()),</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(k, k+1));</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>  UblasMatrixType YT_prod_v = <a class="code" href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">boost::numeric::ublas::prod</a>(<a class="code" href="blas3__solve_8cpp.html#ad8f94754a20a0c6dc74fd3cb5eb675b3">boost::numeric::ublas::trans</a>(Y_old), v_k);</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  z = - betas[j+k] * (v_k + <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">prod</a>(W_old, YT_prod_v));</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> </div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> </div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span> </div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <span class="comment">//apply (I+WY^T)^T = I + Y W^T to the remaining columns of A:</span></div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="comment">//</span></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>  VCLMatrixRange A_part = <a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a>(A,</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(0, A.size1()),</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(j, j+effective_block_size));</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>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">boost::numeric::ublas::project</a>(ublasA,</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(0, A.size1()),</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  <a class="code" href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">boost::numeric::ublas::range</a>(j, j+effective_block_size)),</div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  A_part);</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>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublasW, vclW);</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublasY, vclY);</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>  <span class="keywordflow">if</span> (A.size2() > j + effective_block_size)</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  {</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> </div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  VCLMatrixRange A_part2(A, <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(j, A.size1()), <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(j+effective_block_size, A.size2()));</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  VCLMatrixRange W_part(vclW, <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(j, A.size1()), <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(0, effective_block_size));</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  MatrixType temp = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(<a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(W_part), A_part2);</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>  A_part2 += <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(<a class="code" href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a>(vclY, <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(j, A.size1()), <a class="code" href="classviennacl_1_1basic__range.html">viennacl::range</a>(0, effective_block_size)),</div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  temp);</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>  }</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span> </div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <span class="keywordflow">return</span> betas;</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  }</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span> </div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span> </div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span> </div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  } <span class="comment">//namespace detail</span></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> </div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span> </div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span> </div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  <span class="comment">//takes an inplace QR matrix A and generates Q and R explicitly</span></div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00564"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d"> 564</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">recoverQ</a>(MatrixType <span class="keyword">const</span> & A, VectorType <span class="keyword">const</span> & betas, MatrixType & Q, MatrixType & R)</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  {</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::value_type <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span> </div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  std::vector<ScalarType> v(A.size1());</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span> </div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  Q.clear();</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  R.clear();</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span> </div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  <span class="comment">// Recover R from upper-triangular part of A:</span></div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i_max = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(R.size1(), R.size2());</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<i_max; ++i)</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=i; j<R.size2(); ++j)</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  R(i,j) = A(i,j);</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>  <span class="comment">//</span></div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="comment">// Recover Q by applying all the Householder reflectors to the identity matrix:</span></div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=0; i<Q.size1(); ++i)</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  Q(i,i) = 1.0;</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>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j_max = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(A.size1(), A.size2());</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> j=0; j<j_max; ++j)</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  {</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> col_index = j_max - j - 1;</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  v[col_index] = 1.0;</div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=col_index+1; i<A.size1(); ++i)</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  v[i] = A(i, col_index);</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>  <span class="keywordflow">if</span> (betas[col_index] > 0 || betas[col_index] < 0)</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a08f92f37e68518e1e18dd6ef20b02947">detail::householder_reflect</a>(Q, v, betas[col_index], col_index);</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  }</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  }</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="l00607"></a><span class="lineno"> 607</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> VectorType1, <span class="keyword">typename</span> VectorType2></div>
<div class="line"><a name="l00608"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#adf77bb0fe92ef09522d0458ee9df03db"> 608</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg.html#adf77bb0fe92ef09522d0458ee9df03db">inplace_qr_apply_trans_Q</a>(MatrixType <span class="keyword">const</span> & A, VectorType1 <span class="keyword">const</span> & betas, VectorType2 & b)</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  {</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type<typename MatrixType::value_type>::type</a> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span> </div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  <span class="comment">// Apply Q^T = (I - beta_m v_m v_m^T) \times ... \times (I - beta_0 v_0 v_0^T) by applying all the Householder reflectors to b:</span></div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> col_index=0; col_index<<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(A.size1(), A.size2()); ++col_index)</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>  ScalarType v_in_b = b[col_index];</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=col_index+1; i<A.size1(); ++i)</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  v_in_b += A(i, col_index) * b[i];</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span> </div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  b[col_index] -= betas[col_index] * v_in_b;</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i=col_index+1; i<A.size1(); ++i)</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  b[i] -= betas[col_index] * A(i, col_index) * v_in_b;</div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  }</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span>  }</div>
<div class="line"><a name="l00626"></a><span class="lineno"> 626</span> </div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T, <span class="keyword">typename</span> F, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ALIGNMENT, <span class="keyword">typename</span> VectorType1, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> A2></div>
<div class="line"><a name="l00628"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#aa926ae9008c3343c337f2aa5a90e8734"> 628</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg.html#adf77bb0fe92ef09522d0458ee9df03db">inplace_qr_apply_trans_Q</a>(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<T, F, ALIGNMENT></a> <span class="keyword">const</span> & A, VectorType1 <span class="keyword">const</span> & betas, <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<T, A2></a> & b)</div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  {</div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  boost::numeric::ublas::matrix<T> ublas_A(A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), A.<a class="code" href="classviennacl_1_1matrix__base.html#a4348766b3b9cb049f7acd6a795272dbe">size2</a>());</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(A, ublas_A);</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span> </div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  std::vector<T> stl_b(b.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>());</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(b, stl_b);</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>  <a class="code" href="namespaceviennacl_1_1linalg.html#adf77bb0fe92ef09522d0458ee9df03db">inplace_qr_apply_trans_Q</a>(ublas_A, betas, stl_b);</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span> </div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(stl_b, b);</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> </div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  <span class="keyword">template</span><<span class="keyword">typename</span> T, <span class="keyword">typename</span> F, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> ALIGNMENT></div>
<div class="line"><a name="l00647"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d"> 647</a></span>  std::vector<T> <a class="code" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">inplace_qr</a>(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<T, F, ALIGNMENT></a> & A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 16)</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="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aa3b53a769e6ce29affb7401b9118fde3">detail::inplace_qr_hybrid</a>(A, block_size);</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="l00657"></a><span class="lineno"> 657</span>  <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00658"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#a9728d85f4f7307ed9096524de8c77cdc"> 658</a></span>  std::vector<typename MatrixType::value_type> <a class="code" href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">inplace_qr</a>(MatrixType & A, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> block_size = 16)</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  {</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  <span class="keywordflow">return</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a600f0692e7550cee41cc6382337cd8c5">detail::inplace_qr_ublas</a>(A, block_size);</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  }</div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span> </div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span> </div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span> </div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  } <span class="comment">//linalg</span></div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span> } <span class="comment">//viennacl</span></div>
<div class="line"><a name="l00667"></a><span class="lineno"> 667</span> </div>
<div class="line"><a name="l00668"></a><span class="lineno"> 668</span> </div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a83f573386903bae3a5379ab4cbfc5e2d"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a83f573386903bae3a5379ab4cbfc5e2d">viennacl::linalg::inplace_qr</a></div><div class="ttdeci">std::vector< T > inplace_qr(viennacl::matrix< T, F, ALIGNMENT > &A, vcl_size_t block_size=16)</div><div class="ttdoc">Overload of inplace-QR factorization of a ViennaCL matrix A. </div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00647">qr.hpp:647</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_aa3b53a769e6ce29affb7401b9118fde3"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#aa3b53a769e6ce29affb7401b9118fde3">viennacl::linalg::detail::inplace_qr_hybrid</a></div><div class="ttdeci">std::vector< typename viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type > inplace_qr_hybrid(MatrixType &A, vcl_size_t block_size=16)</div><div class="ttdoc">Implementation of a hybrid QR factorization using uBLAS on the CPU and ViennaCL for GPUs (or multi-co...</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00426">qr.hpp:426</a></div></div>
<div class="ttc" id="blas3__solve_8cpp_html_ad8f94754a20a0c6dc74fd3cb5eb675b3"><div class="ttname"><a href="blas3__solve_8cpp.html#ad8f94754a20a0c6dc74fd3cb5eb675b3">trans</a></div><div class="ttdeci">std::vector< std::vector< NumericT > > trans(std::vector< std::vector< NumericT > > const &A)</div><div class="ttdef"><b>Definition:</b> <a href="blas3__solve_8cpp_source.html#l00195">blas3_solve.cpp:195</a></div></div>
<div class="ttc" id="prod_8hpp_html"><div class="ttname"><a href="prod_8hpp.html">prod.hpp</a></div><div class="ttdoc">Generic interface for matrix-vector and matrix-matrix products. See viennacl/linalg/vector_operations...</div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a600f0692e7550cee41cc6382337cd8c5"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a600f0692e7550cee41cc6382337cd8c5">viennacl::linalg::detail::inplace_qr_ublas</a></div><div class="ttdeci">std::vector< typename MatrixType::value_type > inplace_qr_ublas(MatrixType &A, vcl_size_t block_size=32)</div><div class="ttdoc">Implementation of inplace-QR factorization for a general Boost.uBLAS compatible matrix A...</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00228">qr.hpp:228</a></div></div>
<div class="ttc" id="matrix_8hpp_html"><div class="ttname"><a href="matrix_8hpp.html">matrix.hpp</a></div><div class="ttdoc">Implementation of the dense matrix class. </div></div>
<div class="ttc" id="classviennacl_1_1matrix_html"><div class="ttname"><a href="classviennacl_1_1matrix.html">viennacl::matrix</a></div><div class="ttdoc">A dense matrix class. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00375">forwards.h:375</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_ae04154f304cceaa81ae1fc24882fd7ba"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#ae04154f304cceaa81ae1fc24882fd7ba">viennacl::linalg::detail::write_householder_to_A_viennacl</a></div><div class="ttdeci">void write_householder_to_A_viennacl(MatrixType &A, VectorType const &v, vcl_size_t j)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00211">qr.hpp:211</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a0f34407a1e24c1dee933cb03f978d139"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a0f34407a1e24c1dee933cb03f978d139">viennacl::linalg::detail::setup_householder_vector_ublas</a></div><div class="ttdeci">MatrixType::value_type setup_householder_vector_ublas(MatrixType const &A, VectorType &v, MatrixType &matrix_1x1, vcl_size_t j)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00053">qr.hpp:53</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a0ff42f36e98db6c181b16c78f76f0fdb"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a0ff42f36e98db6c181b16c78f76f0fdb">viennacl::linalg::detail::write_householder_to_A</a></div><div class="ttdeci">void write_householder_to_A(MatrixType &A, VectorType const &v, vcl_size_t j)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00194">qr.hpp:194</a></div></div>
<div class="ttc" id="namespaceviennacl_html_ae92c62d9fd59870c1f6b881e391d32aa"><div class="ttname"><a href="namespaceviennacl.html#ae92c62d9fd59870c1f6b881e391d32aa">viennacl::range</a></div><div class="ttdeci">basic_range range</div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00424">forwards.h:424</a></div></div>
<div class="ttc" id="global__variables_8cpp_html_a1d3b09c2337808223ca760c55bdf5414"><div class="ttname"><a href="global__variables_8cpp.html#a1d3b09c2337808223ca760c55bdf5414">v1</a></div><div class="ttdeci">viennacl::vector< float > v1</div><div class="ttdef"><b>Definition:</b> <a href="global__variables_8cpp_source.html#l00060">global_variables.cpp:60</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_aa18d10f8a90e38bd9ff43c650fc670ef"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a></div><div class="ttdeci">VectorT prod(std::vector< std::vector< T, A1 >, A2 > const &matrix, VectorT const &vector)</div><div class="ttdef"><b>Definition:</b> <a href="prod_8hpp_source.html#l00102">prod.hpp:102</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a48b9804b36f469aff716174b0dc0b573"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a48b9804b36f469aff716174b0dc0b573">viennacl::linalg::detail::householder_reflect_ublas</a></div><div class="ttdeci">void householder_reflect_ublas(MatrixType &A, VectorType &v, MatrixType &matrix_1x1, ScalarType beta, vcl_size_t j, vcl_size_t k)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00147">qr.hpp:147</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_acfdf9d2d13f373340bf68cffd9586775"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#acfdf9d2d13f373340bf68cffd9586775">viennacl::linalg::detail::setup_householder_vector_viennacl</a></div><div class="ttdeci">viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type setup_householder_vector_viennacl(MatrixType const &A, VectorType &v, MatrixType &matrix_1x1, vcl_size_t j)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00093">qr.hpp:93</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a08f92f37e68518e1e18dd6ef20b02947"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a08f92f37e68518e1e18dd6ef20b02947">viennacl::linalg::detail::householder_reflect</a></div><div class="ttdeci">void householder_reflect(MatrixType &A, VectorType &v, ScalarType beta, vcl_size_t j, vcl_size_t k)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00134">qr.hpp:134</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_ad5d436e9fd57a66afe69f56d78d22eeb"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#ad5d436e9fd57a66afe69f56d78d22eeb">viennacl::linalg::detail::inplace_qr_viennacl</a></div><div class="ttdeci">std::vector< typename viennacl::result_of::cpu_value_type< typename MatrixType::value_type >::type > inplace_qr_viennacl(MatrixType &A, vcl_size_t block_size=16)</div><div class="ttdoc">Implementation of a OpenCL-only QR factorization for GPUs (or multi-core CPU). DEPRECATED! Use only i...</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00322">qr.hpp:322</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a76fc8bf8f5a20c576b7ddbad32d3e56d"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a76fc8bf8f5a20c576b7ddbad32d3e56d">viennacl::linalg::recoverQ</a></div><div class="ttdeci">void recoverQ(MatrixType const &A, VectorType const &betas, MatrixType &Q, MatrixType &R)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00564">qr.hpp:564</a></div></div>
<div class="ttc" id="namespaceviennacl_html_adc45a895937fe299100e2b235a442748"><div class="ttname"><a href="namespaceviennacl.html#adc45a895937fe299100e2b235a442748">viennacl::project</a></div><div class="ttdeci">matrix_range< MatrixType > project(MatrixType const &A, viennacl::range const &r1, viennacl::range const &r2)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__proxy_8hpp_source.html#l00326">matrix_proxy.hpp:326</a></div></div>
<div class="ttc" id="namespaceviennacl_html_a98a0afcc513111ffa0bd138f891930df"><div class="ttname"><a href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">viennacl::vcl_size_t</a></div><div class="ttdeci">std::size_t vcl_size_t</div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00075">forwards.h:75</a></div></div>
<div class="ttc" id="classviennacl_1_1matrix__base_html_a4348766b3b9cb049f7acd6a795272dbe"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a4348766b3b9cb049f7acd6a795272dbe">viennacl::matrix_base< NumericT >::size2</a></div><div class="ttdeci">size_type size2() const</div><div class="ttdoc">Returns the number of columns. </div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00226">matrix_def.hpp:226</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_ad88c948ebe30524e225cb523fe6f6cd7"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">viennacl::linalg::trans</a></div><div class="ttdeci">void trans(const matrix_expression< const matrix_base< NumericT, SizeT, DistanceT >, const matrix_base< NumericT, SizeT, DistanceT >, op_trans > &proxy, matrix_base< NumericT > &temp_trans)</div><div class="ttdef"><b>Definition:</b> <a href="matrix__operations_8hpp_source.html#l00083">matrix_operations.hpp:83</a></div></div>
<div class="ttc" id="classviennacl_1_1vector_html"><div class="ttname"><a href="classviennacl_1_1vector.html">viennacl::vector</a></div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00266">forwards.h:266</a></div></div>
<div class="ttc" id="structviennacl_1_1result__of_1_1cpu__value__type_html_aa015d93f419985879a7c13b09633c5c6"><div class="ttname"><a href="structviennacl_1_1result__of_1_1cpu__value__type.html#aa015d93f419985879a7c13b09633c5c6">viennacl::result_of::cpu_value_type::type</a></div><div class="ttdeci">T::ERROR_CANNOT_DEDUCE_CPU_SCALAR_TYPE_FOR_T type</div><div class="ttdef"><b>Definition:</b> <a href="result__of_8hpp_source.html#l00271">result_of.hpp:271</a></div></div>
<div class="ttc" id="classviennacl_1_1matrix__base_html_a24e4f5fa27a1af5ad47e52a97c065d68"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">viennacl::matrix_base< NumericT >::size1</a></div><div class="ttdeci">size_type size1() const</div><div class="ttdoc">Returns the number of rows. </div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00224">matrix_def.hpp:224</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a0481a094460753dd7fb519c9dda3bdc1"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a0481a094460753dd7fb519c9dda3bdc1">viennacl::linalg::detail::write_householder_to_A_ublas</a></div><div class="ttdeci">void write_householder_to_A_ublas(MatrixType &A, VectorType const &v, vcl_size_t j)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00201">qr.hpp:201</a></div></div>
<div class="ttc" id="matrix__proxy_8hpp_html"><div class="ttname"><a href="matrix__proxy_8hpp.html">matrix_proxy.hpp</a></div><div class="ttdoc">Proxy classes for matrices. </div></div>
<div class="ttc" id="sparse__prod_8cpp_html_a2c8637b3d6a972d1d8fd85fb3089c6da"><div class="ttname"><a href="sparse__prod_8cpp.html#a2c8637b3d6a972d1d8fd85fb3089c6da">prod</a></div><div class="ttdeci">void prod(std::vector< std::map< IndexT, NumericT > > const &stl_A, std::vector< std::map< IndexT, NumericT > > const &stl_B, std::vector< std::map< IndexT, NumericT > > &stl_C)</div><div class="ttdef"><b>Definition:</b> <a href="sparse__prod_8cpp_source.html#l00114">sparse_prod.cpp:114</a></div></div>
<div class="ttc" id="namespaceviennacl_html_a10b7f8cf6b8864a7aa196d670481a453"><div class="ttname"><a href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a></div><div class="ttdeci">void copy(std::vector< NumericT > &cpu_vec, circulant_matrix< NumericT, AlignmentV > &gpu_mat)</div><div class="ttdoc">Copies a circulant matrix from the std::vector to the OpenCL device (either GPU or multi-core CPU) ...</div><div class="ttdef"><b>Definition:</b> <a href="circulant__matrix_8hpp_source.html#l00150">circulant_matrix.hpp:150</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_af17ac3429b78effc2d0c0238a9fcf7b1"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#af17ac3429b78effc2d0c0238a9fcf7b1">viennacl::linalg::detail::householder_reflect_viennacl</a></div><div class="ttdeci">void householder_reflect_viennacl(MatrixType &A, VectorType &v, MatrixType &matrix_1x1, ScalarType beta, vcl_size_t j, vcl_size_t k)</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00161">qr.hpp:161</a></div></div>
<div class="ttc" id="classviennacl_1_1vector__base_html_a15c47ae4326098aeaa4ed6b91fc6df9b"><div class="ttname"><a href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">viennacl::vector_base< NumericT >::size</a></div><div class="ttdeci">size_type size() const</div><div class="ttdoc">Returns the length of the vector (cf. std::vector) </div><div class="ttdef"><b>Definition:</b> <a href="vector__def_8hpp_source.html#l00118">vector_def.hpp:118</a></div></div>
<div class="ttc" id="classviennacl_1_1basic__range_html"><div class="ttname"><a href="classviennacl_1_1basic__range.html">viennacl::basic_range</a></div><div class="ttdoc">A range class that refers to an interval [start, stop), where 'start' is included, and 'stop' is excluded. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00424">forwards.h:424</a></div></div>
<div class="ttc" id="fft__1d_8cpp_html_ad5c19ca4f47d3f8ec21232a5af2624e5"><div class="ttname"><a href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a></div><div class="ttdeci">float ScalarType</div><div class="ttdef"><b>Definition:</b> <a href="fft__1d_8cpp_source.html#l00042">fft_1d.cpp:42</a></div></div>
<div class="ttc" id="range_8hpp_html"><div class="ttname"><a href="range_8hpp.html">range.hpp</a></div><div class="ttdoc">Implementation of a range object for use with proxy objects. </div></div>
<div class="ttc" id="classviennacl_1_1matrix__range_html"><div class="ttname"><a href="classviennacl_1_1matrix__range.html">viennacl::matrix_range</a></div><div class="ttdoc">Class for representing non-strided submatrices of a bigger matrix A. </div><div class="ttdef"><b>Definition:</b> <a href="forwards_8h_source.html#l00440">forwards.h:440</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_aef015779a92be597e546c3491cebf6c1"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">viennacl::linalg::detail::min</a></div><div class="ttdeci">T min(const T &lhs, const T &rhs)</div><div class="ttdoc">Minimum. </div><div class="ttdef"><b>Definition:</b> <a href="linalg_2detail_2bisect_2util_8hpp_source.html#l00045">util.hpp:45</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_adf77bb0fe92ef09522d0458ee9df03db"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#adf77bb0fe92ef09522d0458ee9df03db">viennacl::linalg::inplace_qr_apply_trans_Q</a></div><div class="ttdeci">void inplace_qr_apply_trans_Q(MatrixType const &A, VectorType1 const &betas, VectorType2 &b)</div><div class="ttdoc">Computes Q^T b, where Q is an implicit orthogonal matrix defined via its Householder reflectors store...</div><div class="ttdef"><b>Definition:</b> <a href="qr_8hpp_source.html#l00608">qr.hpp:608</a></div></div>
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