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<div class="title">qr-method.hpp</div> </div>
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<a href="qr-method_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_METHOD_HPP_</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="preprocessor">#define VIENNACL_LINALG_QR_METHOD_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="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "<a class="code" href="vector_8hpp.html">viennacl/vector.hpp</a>"</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include "<a class="code" href="qr-method-common_8hpp.html">viennacl/linalg/qr-method-common.hpp</a>"</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include "<a class="code" href="tql2_8hpp.html">viennacl/linalg/tql2.hpp</a>"</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <boost/numeric/ublas/vector.hpp></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include <boost/numeric/ublas/matrix.hpp></span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">namespace </span>viennacl</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">namespace </span>linalg</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="keyword">namespace </span>detail</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE></div>
<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a6308577bb366f4b0698dc43ff75ad4a5"> 42</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a6308577bb366f4b0698dc43ff75ad4a5">final_iter_update_gpu</a>(<a class="code" href="classviennacl_1_1matrix__base.html">matrix_base<SCALARTYPE></a> & A,</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordtype">int</span> n,</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordtype">int</span> last_n,</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  SCALARTYPE q,</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  SCALARTYPE p</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  )</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>  (void)A; (void)n; (void)last_n; (void)q; (void)p;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="preprocessor">#ifdef VIENNACL_WITH_OPENCL</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> & ctx = <span class="keyword">const_cast<</span><a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> &<span class="keyword">></span>(viennacl::traits::opencl_handle(A).context());</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">if</span>(A.<a class="code" href="classviennacl_1_1matrix__base.html#a15ec879f9e85a6fc209454b0bf137084">row_major</a>())</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>  <a class="code" href="classviennacl_1_1ocl_1_1kernel.html">viennacl::ocl::kernel</a>& kernel = ctx.<a class="code" href="classviennacl_1_1ocl_1_1context.html#afe68ad8c2df449f40f45db6605038946">get_kernel</a>(<a class="code" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1svd.html">viennacl::linalg::opencl::kernels::svd<SCALARTYPE, row_major>::program_name</a>(), <a class="code" href="namespaceviennacl_1_1linalg.html#a8477d884683dafc7e6ca04f2e02a1d1f">SVD_FINAL_ITER_UPDATE_KERNEL</a>);</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <a class="code" href="namespaceviennacl_1_1ocl.html#a5f2022f653ea1cf364d20e3ff84dcada">viennacl::ocl::enqueue</a>(kernel(</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  A,</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  static_cast<cl_uint>(A.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>()),</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  static_cast<cl_uint>(n),</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keyword">static_cast<</span>cl_uint<span class="keyword">></span>(last_n),</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  q,</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  p</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  ));</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  }</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordflow">else</span></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>  <a class="code" href="classviennacl_1_1ocl_1_1kernel.html">viennacl::ocl::kernel</a>& kernel = ctx.<a class="code" href="classviennacl_1_1ocl_1_1context.html#afe68ad8c2df449f40f45db6605038946">get_kernel</a>(<a class="code" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1svd.html">viennacl::linalg::opencl::kernels::svd<SCALARTYPE, column_major>::program_name</a>(), <a class="code" href="namespaceviennacl_1_1linalg.html#a8477d884683dafc7e6ca04f2e02a1d1f">SVD_FINAL_ITER_UPDATE_KERNEL</a>);</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>  <a class="code" href="namespaceviennacl_1_1ocl.html#a5f2022f653ea1cf364d20e3ff84dcada">viennacl::ocl::enqueue</a>(kernel(</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  A,</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  static_cast<cl_uint>(A.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>()),</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  static_cast<cl_uint>(n),</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">static_cast<</span>cl_uint<span class="keyword">></span>(last_n),</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  q,</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  p</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>  }</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> }</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a0ce6438b322e096df65112ac6536b0b1"> 82</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0ce6438b322e096df65112ac6536b0b1">update_float_QR_column_gpu</a>(<a class="code" href="classviennacl_1_1matrix__base.html">matrix_base<SCALARTYPE></a> & A,</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keyword">const</span> VectorType& buf,</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<SCALARTYPE></a>& buf_vcl,</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">int</span> m,</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordtype">int</span> n,</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordtype">int</span> last_n,</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordtype">bool</span> <span class="comment">//is_triangular</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>  (void)A; (void)buf; (void)buf_vcl; (void)m; (void)n; (void)last_n;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="preprocessor">#ifdef VIENNACL_WITH_OPENCL</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> & ctx = <span class="keyword">const_cast<</span><a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> &<span class="keyword">></span>(viennacl::traits::opencl_handle(A).context());</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>  <a class="code" href="namespaceviennacl.html#aaa5c8726b45bc89a523ca2fa8c42107a">viennacl::fast_copy</a>(buf, buf_vcl);</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">if</span>(A.<a class="code" href="classviennacl_1_1matrix__base.html#a15ec879f9e85a6fc209454b0bf137084">row_major</a>())</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <a class="code" href="classviennacl_1_1ocl_1_1kernel.html">viennacl::ocl::kernel</a>& kernel = ctx.<a class="code" href="classviennacl_1_1ocl_1_1context.html#afe68ad8c2df449f40f45db6605038946">get_kernel</a>(<a class="code" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1svd.html">viennacl::linalg::opencl::kernels::svd<SCALARTYPE, row_major>::program_name</a>(), <a class="code" href="namespaceviennacl_1_1linalg.html#a3a439370108ddfa59c2fcb4136b13c8d">SVD_UPDATE_QR_COLUMN_KERNEL</a>);</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <a class="code" href="namespaceviennacl_1_1ocl.html#a5f2022f653ea1cf364d20e3ff84dcada">viennacl::ocl::enqueue</a>(kernel(</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  A,</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  static_cast<cl_uint>(A.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>()),</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  buf_vcl,</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  static_cast<cl_uint>(m),</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">static_cast<</span>cl_uint<span class="keyword">></span>(n),</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  static_cast<cl_uint>(last_n)</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</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="keywordflow">else</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  {</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <a class="code" href="classviennacl_1_1ocl_1_1kernel.html">viennacl::ocl::kernel</a>& kernel = ctx.<a class="code" href="classviennacl_1_1ocl_1_1context.html#afe68ad8c2df449f40f45db6605038946">get_kernel</a>(<a class="code" href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1svd.html">viennacl::linalg::opencl::kernels::svd<SCALARTYPE, column_major>::program_name</a>(), <a class="code" href="namespaceviennacl_1_1linalg.html#a3a439370108ddfa59c2fcb4136b13c8d">SVD_UPDATE_QR_COLUMN_KERNEL</a>);</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>  <a class="code" href="namespaceviennacl_1_1ocl.html#a5f2022f653ea1cf364d20e3ff84dcada">viennacl::ocl::enqueue</a>(kernel(</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  A,</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  static_cast<cl_uint>(A.<a class="code" href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">internal_size1</a>()),</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  buf_vcl,</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  static_cast<cl_uint>(m),</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">static_cast<</span>cl_uint<span class="keyword">></span>(n),</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  static_cast<cl_uint>(last_n)</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>  }</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="preprocessor">#endif</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> }</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>  <span class="keyword">template</span><<span class="keyword">typename</span> SCALARTYPE, <span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00128"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#abe90cd38a99c15edfb19d57c524dd2d5"> 128</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#abe90cd38a99c15edfb19d57c524dd2d5">final_iter_update</a>(MatrixT& A,</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordtype">int</span> n,</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">int</span> last_n,</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  SCALARTYPE q,</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  SCALARTYPE p</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  )</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  {</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < last_n; i++)</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  {</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  SCALARTYPE v_in = A(i, n);</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  SCALARTYPE z = A(i, n - 1);</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  A(i, n - 1) = q * z + p * v_in;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  A(i, n) = q * v_in - p * z;</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>  }</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> </div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keyword">template</span><<span class="keyword">typename</span> SCALARTYPE, <span class="keyword">typename</span> MatrixT></div>
<div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a4d6d704d39ec27eb15a604580eb1df5b"> 145</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a4d6d704d39ec27eb15a604580eb1df5b">update_float_QR_column</a>(MatrixT& A,</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keyword">const</span> std::vector<SCALARTYPE>& buf,</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keywordtype">int</span> m,</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordtype">int</span> n,</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordtype">int</span> last_i,</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordtype">bool</span> is_triangular</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>  {</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < last_i; i++)</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  {</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordtype">int</span> start_k = is_triangular?<a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a5d46fe9558b0e462f10fd44942ad4fc6">std::max</a>(i + 1, m):m;</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>  SCALARTYPE* a_row = A.row(i);</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>  SCALARTYPE a_ik = a_row[start_k];</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  SCALARTYPE a_ik_1 = 0;</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  SCALARTYPE a_ik_2 = 0;</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="keywordflow">if</span> (start_k < n)</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  a_ik_1 = a_row[start_k + 1];</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>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = start_k; k < n; 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>  <span class="keywordtype">bool</span> notlast = (k != n - 1);</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> </div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  SCALARTYPE p = buf[5 * <span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(k)] * a_ik + buf[5 * static_cast<vcl_size_t>(k) + 1] * a_ik_1;</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> (notlast)</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>  a_ik_2 = a_row[k + 2];</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  p = p + buf[5 * <span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(k) + 2] * a_ik_2;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  a_ik_2 = a_ik_2 - p * buf[5 * <span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(k) + 4];</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  }</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>  a_row[k] = a_ik - p;</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  a_ik_1 = a_ik_1 - p * buf[5 * <span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(k) + 3];</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>  a_ik = a_ik_1;</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  a_ik_1 = a_ik_2;</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  }</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>  <span class="keywordflow">if</span> (start_k < n)</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  a_row[n] = a_ik;</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  }</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  }</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> </div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="keyword">template</span><<span class="keyword">typename</span> SCALARTYPE></div>
<div class="line"><a name="l00193"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html"> 193</a></span>  <span class="keyword">class </span><a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html">FastMatrix</a></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  {</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00196"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a08da5e21bebae44672a6324dbfb8db75"> 196</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a08da5e21bebae44672a6324dbfb8db75">FastMatrix</a>()</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  {</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  size_ = 0;</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> </div>
<div class="line"><a name="l00201"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a0c734d3daf535e0d567c2fd5f59cc451"> 201</a></span>  <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a0c734d3daf535e0d567c2fd5f59cc451">FastMatrix</a>(<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> sz, <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1traits.html#a0cd530f8a76a5fb3d60a9230bea30bca">internal_size</a>) : size_(sz), internal_size_(internal_size)</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>  <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb">data</a>.resize(internal_size * internal_size);</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  }</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a name="l00206"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a46b6503e572003d0fd4e9b30ca51572d"> 206</a></span>  SCALARTYPE& <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a46b6503e572003d0fd4e9b30ca51572d">operator()</a>(<span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j)</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  {</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">return</span> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb">data</a>[<span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(i) * internal_size_ + static_cast<vcl_size_t>(j)];</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> </div>
<div class="line"><a name="l00211"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a8302dc145b6238b4a8859b775192da6e"> 211</a></span>  SCALARTYPE* <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a8302dc145b6238b4a8859b775192da6e">row</a>(<span class="keywordtype">int</span> i)</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="keywordflow">return</span> &<a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb">data</a>[<span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(i) * internal_size_];</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  }</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> </div>
<div class="line"><a name="l00216"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a98acf809bbc8cb44eef44d87e83a4a05"> 216</a></span>  SCALARTYPE* <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a98acf809bbc8cb44eef44d87e83a4a05">begin</a>()</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  {</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">return</span> &<a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb">data</a>[0];</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"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ae44eed79eed4c1f5ce358963e48fd459"> 221</a></span>  SCALARTYPE* <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ae44eed79eed4c1f5ce358963e48fd459">end</a>()</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  {</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordflow">return</span> &<a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb">data</a>[0] + <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb">data</a>.size();</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  }</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> </div>
<div class="line"><a name="l00226"></a><span class="lineno"><a class="line" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb"> 226</a></span>  std::vector<SCALARTYPE> <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb">data</a>;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> size_;</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> internal_size_;</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  };</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="comment">// Nonsymmetric reduction from Hessenberg to real Schur form.</span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="comment">// This is derived from the Algol procedure hqr2, by Martin and Wilkinson, Handbook for Auto. Comp.,</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="comment">// Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00236"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#afb7f93e8826f0e5c8f0c83a825a28cc8"> 236</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#afb7f93e8826f0e5c8f0c83a825a28cc8">hqr2</a>(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a>& vcl_H,</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a>& V,</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  VectorType & d,</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  VectorType & e)</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  {</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aad4cd2951549618c93f74ff26444675f">transpose</a>(V);</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="keywordtype">int</span> nn = <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(vcl_H.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>());</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span> </div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html">FastMatrix<SCALARTYPE></a> H(<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(nn), vcl_H.<a class="code" href="classviennacl_1_1matrix__base.html#a00e30fdc61081a73995b54175a91d220">internal_size2</a>());<span class="comment">//, V(nn);</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> </div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  std::vector<SCALARTYPE> buf(5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(nn));</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="comment">//boost::numeric::ublas::vector<float> buf(5 * nn);</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<SCALARTYPE></a> buf_vcl(5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(nn));</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>  <a class="code" href="namespaceviennacl.html#aaa5c8726b45bc89a523ca2fa8c42107a">viennacl::fast_copy</a>(vcl_H, H.begin());</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> </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordtype">int</span> n = nn - 1;</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>  SCALARTYPE eps = 2 * <span class="keyword">static_cast<</span>SCALARTYPE<span class="keyword">></span>(<a class="code" href="tests_2src_2bisect_8cpp.html#a6ebf6899d6c1c8b7b9d09be872c05aae">EPS</a>);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  SCALARTYPE exshift = 0;</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  SCALARTYPE p = 0;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  SCALARTYPE q = 0;</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  SCALARTYPE r = 0;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  SCALARTYPE s = 0;</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  SCALARTYPE z = 0;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  SCALARTYPE t;</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  SCALARTYPE w;</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  SCALARTYPE x;</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  SCALARTYPE y;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span> </div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  SCALARTYPE out1, out2;</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">// compute matrix norm</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  SCALARTYPE norm = 0;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < nn; i++)</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="keywordflow">for</span> (<span class="keywordtype">int</span> j = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a5d46fe9558b0e462f10fd44942ad4fc6">std::max</a>(i - 1, 0); j < nn; j++)</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  norm = norm + std::fabs(H(i, j));</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  }</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span> </div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="comment">// Outer loop over eigenvalue index</span></div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordtype">int</span> iter = 0;</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">while</span> (n >= 0)</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  {</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="comment">// Look for single small sub-diagonal element</span></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keywordtype">int</span> l = n;</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keywordflow">while</span> (l > 0)</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  {</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  s = std::fabs(H(l - 1, l - 1)) + std::fabs(H(l, l));</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">if</span> (s <= 0)</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  s = norm;</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keywordflow">if</span> (std::fabs(H(l, l - 1)) < eps * s)</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <span class="keywordflow">break</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>  l--;</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  }</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> </div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="comment">// Check for convergence</span></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  <span class="keywordflow">if</span> (l == n)</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>  <span class="comment">// One root found</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  H(n, n) = H(n, n) + exshift;</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)] = H(n, n);</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)] = 0;</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  n--;</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  iter = 0;</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  }</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (l == n - 1)</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>  <span class="comment">// Two roots found</span></div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  w = H(n, n - 1) * H(n - 1, n);</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  p = (H(n - 1, n - 1) - H(n, n)) / 2;</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  q = p * p + w;</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  z = <span class="keyword">static_cast<</span>SCALARTYPE<span class="keyword">></span>(std::sqrt(std::fabs(q)));</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  H(n, n) = H(n, n) + exshift;</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  H(n - 1, n - 1) = H(n - 1, n - 1) + exshift;</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  x = H(n, n);</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> </div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordflow">if</span> (q >= 0)</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  {</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="comment">// Real pair</span></div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  z = (p >= 0) ? (p + z) : (p - z);</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n) - 1] = x + z;</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)] = d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n) - 1];</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordflow">if</span> (z <= 0 && z >= 0) <span class="comment">// z == 0 without compiler complaints</span></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)] = x - w / z;</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n) - 1] = 0;</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)] = 0;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  x = H(n, n - 1);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  s = std::fabs(x) + std::fabs(z);</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  p = x / s;</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  q = z / s;</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  r = <span class="keyword">static_cast<</span>SCALARTYPE<span class="keyword">></span>(std::sqrt(p * p + q * q));</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  p = p / r;</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  q = q / r;</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>  <span class="comment">// Row modification</span></div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = n - 1; j < nn; j++)</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>  SCALARTYPE h_nj = H(n, j);</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  z = H(n - 1, j);</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  H(n - 1, j) = q * z + p * h_nj;</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  H(n, j) = q * h_nj - p * z;</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  }</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_1_1linalg_1_1detail.html#abe90cd38a99c15edfb19d57c524dd2d5">final_iter_update</a>(H, n, n + 1, q, p);</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a6308577bb366f4b0698dc43ff75ad4a5">final_iter_update_gpu</a>(V, n, nn, q, p);</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  }</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  <span class="keywordflow">else</span></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>  <span class="comment">// Complex pair</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n) - 1] = x + p;</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)] = x + p;</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n) - 1] = z;</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)] = -z;</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>  n = n - 2;</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  iter = 0;</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  }</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  {</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="comment">// No convergence yet</span></div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="comment">// Form shift</span></div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  x = H(n, n);</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  y = 0;</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  w = 0;</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">if</span> (l < n)</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  {</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  y = H(n - 1, n - 1);</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  w = H(n, n - 1) * H(n - 1, n);</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  }</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> </div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="comment">// Wilkinson's original ad hoc shift</span></div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="keywordflow">if</span> (iter == 10)</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  {</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  exshift += x;</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i <= n; i++)</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  H(i, i) -= x;</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> </div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  s = std::fabs(H(n, n - 1)) + std::fabs(H(n - 1, n - 2));</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  x = y = SCALARTYPE(0.75) * s;</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  w = SCALARTYPE(-0.4375) * s * s;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  }</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span> </div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="comment">// MATLAB's new ad hoc shift</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="keywordflow">if</span> (iter == 30)</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  {</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  s = (y - x) / 2;</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  s = s * s + w;</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <span class="keywordflow">if</span> (s > 0)</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>  s = <span class="keyword">static_cast<</span>SCALARTYPE<span class="keyword">></span>(std::sqrt(s));</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keywordflow">if</span> (y < x) s = -s;</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  s = x - w / ((y - x) / 2 + s);</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i <= n; i++)</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  H(i, i) -= s;</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  exshift += s;</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  x = y = w = SCALARTYPE(0.964);</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>  }</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> </div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  iter = iter + 1;</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>  <span class="comment">// Look for two consecutive small sub-diagonal elements</span></div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keywordtype">int</span> m = n - 2;</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="keywordflow">while</span> (m >= l)</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>  SCALARTYPE h_m1_m1 = H(m + 1, m + 1);</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  z = H(m, m);</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  r = x - z;</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  s = y - z;</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  p = (r * s - w) / H(m + 1, m) + H(m, m + 1);</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  q = h_m1_m1 - z - r - s;</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  r = H(m + 2, m + 1);</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  s = std::fabs(p) + std::fabs(q) + std::fabs(r);</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  p = p / s;</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  q = q / s;</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  r = r / s;</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  <span class="keywordflow">if</span> (m == l)</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <span class="keywordflow">if</span> (std::fabs(H(m, m - 1)) * (std::fabs(q) + std::fabs(r)) < eps * (std::fabs(p) * (std::fabs(H(m - 1, m - 1)) + std::fabs(z) + std::fabs(h_m1_m1))))</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  m--;</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  }</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> </div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = m + 2; i <= n; i++)</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  {</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  H(i, i - 2) = 0;</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keywordflow">if</span> (i > m + 2)</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  H(i, i - 3) = 0;</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  }</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> </div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  <span class="comment">// float QR step involving rows l:n and columns m:n</span></div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = m; k < n; k++)</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  {</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="keywordtype">bool</span> notlast = (k != n - 1);</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keywordflow">if</span> (k != m)</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>  p = H(k, k - 1);</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  q = H(k + 1, k - 1);</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  r = (notlast ? H(k + 2, k - 1) : 0);</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  x = std::fabs(p) + std::fabs(q) + std::fabs(r);</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keywordflow">if</span> (x > 0)</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  {</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  p = p / x;</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  q = q / x;</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  r = r / x;</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  }</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  }</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>  <span class="keywordflow">if</span> (x <= 0 && x >= 0) <span class="keywordflow">break</span>; <span class="comment">// x == 0 without compiler complaints</span></div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> </div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  s = <span class="keyword">static_cast<</span>SCALARTYPE<span class="keyword">></span>(std::sqrt(p * p + q * q + r * r));</div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  <span class="keywordflow">if</span> (p < 0) s = -s;</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span> </div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="keywordflow">if</span> (s < 0 || s > 0)</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  {</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="keywordflow">if</span> (k != m)</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  H(k, k - 1) = -s * x;</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="keywordflow">if</span> (l != m)</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  H(k, k - 1) = -H(k, k - 1);</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>  p = p + s;</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  y = q / s;</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  z = r / s;</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  x = p / s;</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  q = q / p;</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  r = r / p;</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>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k)] = x;</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k) + 1] = y;</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k) + 2] = z;</div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k) + 3] = q;</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k) + 4] = r;</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span> </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>  SCALARTYPE* a_row_k = H.<a class="code" href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a8302dc145b6238b4a8859b775192da6e">row</a>(k);</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  SCALARTYPE* a_row_k_1 = H.row(k + 1);</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  SCALARTYPE* a_row_k_2 = H.row(k + 2);</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  <span class="comment">// Row modification</span></div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = k; j < nn; j++)</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  {</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  SCALARTYPE h_kj = a_row_k[j];</div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  SCALARTYPE h_k1_j = a_row_k_1[j];</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>  p = h_kj + q * h_k1_j;</div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="keywordflow">if</span> (notlast)</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  {</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  SCALARTYPE h_k2_j = a_row_k_2[j];</div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  p = p + r * h_k2_j;</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  a_row_k_2[j] = h_k2_j - p * z;</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  }</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span> </div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  a_row_k[j] = h_kj - p * x;</div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  a_row_k_1[j] = h_k1_j - p * y;</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  }</div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span> </div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="comment">//H(k + 1, nn - 1) = h_kj;</span></div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span> </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>  <span class="comment">// Column modification</span></div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = k; i < <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#aef015779a92be597e546c3491cebf6c1">std::min</a>(nn, k + 4); i++)</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  {</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  p = x * H(i, k) + y * H(i, k + 1);</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <span class="keywordflow">if</span> (notlast)</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  {</div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  p = p + z * H(i, k + 2);</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  H(i, k + 2) = H(i, k + 2) - p * r;</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  }</div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span> </div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  H(i, k) = H(i, k) - p;</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  H(i, k + 1) = H(i, k + 1) - p * q;</div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  }</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  }</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  {</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k)] = 0;</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k) + 1] = 0;</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k) + 2] = 0;</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k) + 3] = 0;</div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  buf[5 * <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(k) + 4] = 0;</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> </div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <span class="comment">// Timer timer;</span></div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="comment">// timer.start();</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>  update_float_QR_column<SCALARTYPE>(H, buf, m, n, n, <span class="keyword">true</span>);</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a0ce6438b322e096df65112ac6536b0b1">update_float_QR_column_gpu</a>(V, buf, buf_vcl, m, n, nn, <span class="keyword">false</span>);</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span> </div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="comment">// std::cout << timer.get() << "\n";</span></div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  }</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  }</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> </div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="comment">// Backsubstitute to find vectors of upper triangular form</span></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  <span class="keywordflow">if</span> (norm <= 0)</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  {</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <span class="keywordflow">return</span>;</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> </div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  <span class="keywordflow">for</span> (n = nn - 1; n >= 0; n--)</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>  p = d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)];</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  q = e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(n)];</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span> </div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <span class="comment">// Real vector</span></div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  <span class="keywordflow">if</span> (q <= 0 && q >= 0)</div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span>  {</div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="keywordtype">int</span> l = n;</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  H(n, n) = 1;</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i >= 0; i--)</div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  {</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  w = H(i, i) - p;</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  r = 0;</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = l; j <= n; j++)</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  r = r + H(i, j) * H(j, n);</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span> </div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="keywordflow">if</span> (e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] < 0)</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>  z = w;</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  s = r;</div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span>  }</div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  {</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  l = i;</div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <span class="keywordflow">if</span> (e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] <= 0) <span class="comment">// e[i] == 0 with previous if</span></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>  H(i, n) = (w > 0 || w < 0) ? (-r / w) : (-r / (eps * norm));</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>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  {</div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <span class="comment">// Solve real equations</span></div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  x = H(i, i + 1);</div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span>  y = H(i + 1, i);</div>
<div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  q = (d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] - p) * (d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] - p) + e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] * e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)];</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  t = (x * s - z * r) / q;</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  H(i, n) = t;</div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  H(i + 1, n) = (std::fabs(x) > std::fabs(z)) ? ((-r - w * t) / x) : ((-s - y * t) / z);</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  }</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span> </div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <span class="comment">// Overflow control</span></div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  t = std::fabs(H(i, n));</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  <span class="keywordflow">if</span> ((eps * t) * t > 1)</div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i; j <= n; j++)</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span>  H(j, n) /= t;</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>  }</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  }</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (q < 0)</div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  {</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="comment">// Complex vector</span></div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="keywordtype">int</span> l = n - 1;</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span> </div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  <span class="comment">// Last vector component imaginary so matrix is triangular</span></div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <span class="keywordflow">if</span> (std::fabs(H(n, n - 1)) > std::fabs(H(n - 1, n)))</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  {</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  H(n - 1, n - 1) = q / H(n, n - 1);</div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  H(n - 1, n) = -(H(n, n) - p) / H(n, n - 1);</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>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  {</div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  cdiv<SCALARTYPE>(0, -H(n - 1, n), H(n - 1, n - 1) - p, q, out1, out2);</div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span> </div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  H(n - 1, n - 1) = out1;</div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  H(n - 1, n) = out2;</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  }</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span> </div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  H(n, n - 1) = 0;</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  H(n, n) = 1;</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 2; i >= 0; i--)</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>  SCALARTYPE ra, sa, vr, vi;</div>
<div class="line"><a name="l00613"></a><span class="lineno"> 613</span>  ra = 0;</div>
<div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  sa = 0;</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = l; j <= n; j++)</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 h_ij = H(i, j);</div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  ra = ra + h_ij * H(j, n - 1);</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  sa = sa + h_ij * H(j, n);</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> </div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  w = H(i, i) - p;</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span> </div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <span class="keywordflow">if</span> (e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] < 0)</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>  z = w;</div>
<div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  r = ra;</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  s = sa;</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>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  {</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  l = i;</div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  <span class="keywordflow">if</span> (e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] <= 0) <span class="comment">// e[i] == 0 with previous if</span></div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  {</div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  cdiv<SCALARTYPE>(-ra, -sa, w, q, out1, out2);</div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  H(i, n - 1) = out1;</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span>  H(i, n) = out2;</div>
<div class="line"><a name="l00638"></a><span class="lineno"> 638</span>  }</div>
<div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  {</div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <span class="comment">// Solve complex equations</span></div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  x = H(i, i + 1);</div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  y = H(i + 1, i);</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  vr = (d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] - p) * (d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] - p) + e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] * e[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] - q * q;</div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  vi = (d[<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a>(i)] - p) * 2 * q;</div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  <span class="keywordflow">if</span> ( (vr <= 0 && vr >= 0) && (vi <= 0 && vi >= 0) )</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  vr = eps * norm * (std::fabs(w) + std::fabs(q) + std::fabs(x) + std::fabs(y) + std::fabs(z));</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>  cdiv<SCALARTYPE>(x * r - z * ra + q * sa, x * s - z * sa - q * ra, vr, vi, out1, out2);</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>  H(i, n - 1) = out1;</div>
<div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  H(i, n) = out2;</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span> </div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span> </div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  <span class="keywordflow">if</span> (std::fabs(x) > (std::fabs(z) + std::fabs(q)))</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  {</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  H(i + 1, n - 1) = (-ra - w * H(i, n - 1) + q * H(i, n)) / x;</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  H(i + 1, n) = (-sa - w * H(i, n) - q * H(i, n - 1)) / x;</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">else</span></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>  cdiv<SCALARTYPE>(-r - y * H(i, n - 1), -s - y * H(i, n), z, q, out1, out2);</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>  H(i + 1, n - 1) = out1;</div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  H(i + 1, n) = out2;</div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</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="comment">// Overflow control</span></div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  t = <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a5d46fe9558b0e462f10fd44942ad4fc6">std::max</a>(std::fabs(H(i, n - 1)), std::fabs(H(i, n)));</div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  <span class="keywordflow">if</span> ((eps * t) * t > 1)</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  {</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i; j <= n; j++)</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  {</div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  H(j, n - 1) /= t;</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  H(j, n) /= t;</div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  }</div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  }</div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  }</div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  }</div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  }</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  }</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span> </div>
<div class="line"><a name="l00684"></a><span class="lineno"> 684</span>  <a class="code" href="namespaceviennacl.html#aaa5c8726b45bc89a523ca2fa8c42107a">viennacl::fast_copy</a>(H.begin(), H.end(), vcl_H);</div>
<div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  <span class="comment">// viennacl::fast_copy(V.begin(), V.end(), vcl_V);</span></div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span> </div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a> tmp = V;</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span> </div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  V = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(<a class="code" href="namespaceviennacl_1_1linalg.html#ad88c948ebe30524e225cb523fe6f6cd7">trans</a>(tmp), vcl_H);</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  }</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span> </div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span> </div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE></div>
<div class="line"><a name="l00694"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#ac4a1dce18e411cc95eb72efd802f50d8"> 694</a></span>  <span class="keywordtype">bool</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ac4a1dce18e411cc95eb72efd802f50d8">householder_twoside</a>(</div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  <a class="code" href="classviennacl_1_1matrix__base.html">matrix_base<SCALARTYPE></a>& A,</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  <a class="code" href="classviennacl_1_1matrix__base.html">matrix_base<SCALARTYPE></a>& Q,</div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  <a class="code" href="classviennacl_1_1vector__base.html">vector_base<SCALARTYPE></a>& D,</div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> <a class="code" href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">start</a>)</div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  {</div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> A_size1 = <span class="keyword">static_cast<</span><a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a><span class="keyword">></span>(<a class="code" href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2">viennacl::traits::size1</a>(A));</div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  <span class="keywordflow">if</span>(start + 2 >= A_size1)</div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span> </div>
<div class="line"><a name="l00704"></a><span class="lineno"> 704</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a5852aa7527c0599681f1b0fbc753d357">prepare_householder_vector</a>(A, D, A_size1, start + 1, start, start + 1, <span class="keyword">true</span>);</div>
<div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a706c4d0b456ec669c3a8c2eea8cc3fc4">viennacl::linalg::house_update_A_left</a>(A, D, start);</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a34c93371a5e45fe498bf1dc4dd475497">viennacl::linalg::house_update_A_right</a>(A, D);</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#ab58751eae7fc9a4af532b447728880ab">viennacl::linalg::house_update_QL</a>(Q, D, A_size1);</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span> </div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  }</div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span> </div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE></div>
<div class="line"><a name="l00713"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#acba51b008828151aabb684d1bb9b350f"> 713</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#acba51b008828151aabb684d1bb9b350f">tridiagonal_reduction</a>(<a class="code" href="classviennacl_1_1matrix__base.html">matrix_base<SCALARTYPE></a>& A,</div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  <a class="code" href="classviennacl_1_1matrix__base.html">matrix_base<SCALARTYPE></a>& Q)</div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  {</div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> sz = A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>();</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span> </div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<SCALARTYPE></a> hh_vector(sz);</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span> </div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  <span class="keywordflow">for</span>(<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i = 0; i < sz; i++)</div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  {</div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#ac4a1dce18e411cc95eb72efd802f50d8">householder_twoside</a>(A, Q, hh_vector, i);</div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  }</div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span> </div>
<div class="line"><a name="l00725"></a><span class="lineno"> 725</span>  }</div>
<div class="line"><a name="l00726"></a><span class="lineno"> 726</span> </div>
<div class="line"><a name="l00727"></a><span class="lineno"> 727</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE></div>
<div class="line"><a name="l00728"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg_1_1detail.html#a4983f4960a80f96d1dc3ff5ff23a0ffa"> 728</a></span>  <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a4983f4960a80f96d1dc3ff5ff23a0ffa">qr_method</a>(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a> & A,</div>
<div class="line"><a name="l00729"></a><span class="lineno"> 729</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a> & Q,</div>
<div class="line"><a name="l00730"></a><span class="lineno"> 730</span>  std::vector<SCALARTYPE> & D,</div>
<div class="line"><a name="l00731"></a><span class="lineno"> 731</span>  std::vector<SCALARTYPE> & E,</div>
<div class="line"><a name="l00732"></a><span class="lineno"> 732</span>  <span class="keywordtype">bool</span> is_symmetric = <span class="keyword">true</span>)</div>
<div class="line"><a name="l00733"></a><span class="lineno"> 733</span>  {</div>
<div class="line"><a name="l00734"></a><span class="lineno"> 734</span> </div>
<div class="line"><a name="l00735"></a><span class="lineno"> 735</span>  assert(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>() && bool(<span class="stringliteral">"Input matrix must be square for QR method!"</span>));</div>
<div class="line"><a name="l00736"></a><span class="lineno"> 736</span>  <span class="comment">/* if (!viennacl::is_row_major<F>::value && !is_symmetric)</span></div>
<div class="line"><a name="l00737"></a><span class="lineno"> 737</span> <span class="comment"> {</span></div>
<div class="line"><a name="l00738"></a><span class="lineno"> 738</span> <span class="comment"> std::cout << "qr_method for non-symmetric column-major matrices not implemented yet!" << std::endl;</span></div>
<div class="line"><a name="l00739"></a><span class="lineno"> 739</span> <span class="comment"> exit(EXIT_FAILURE);</span></div>
<div class="line"><a name="l00740"></a><span class="lineno"> 740</span> <span class="comment"> }</span></div>
<div class="line"><a name="l00741"></a><span class="lineno"> 741</span> <span class="comment"></span></div>
<div class="line"><a name="l00742"></a><span class="lineno"> 742</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00743"></a><span class="lineno"> 743</span>  <a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> mat_size = A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>();</div>
<div class="line"><a name="l00744"></a><span class="lineno"> 744</span>  D.resize(A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>());</div>
<div class="line"><a name="l00745"></a><span class="lineno"> 745</span>  E.resize(A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>());</div>
<div class="line"><a name="l00746"></a><span class="lineno"> 746</span> </div>
<div class="line"><a name="l00747"></a><span class="lineno"> 747</span>  <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<SCALARTYPE></a> vcl_D(mat_size), vcl_E(mat_size);</div>
<div class="line"><a name="l00748"></a><span class="lineno"> 748</span>  <span class="comment">//std::vector<SCALARTYPE> std_D(mat_size), std_E(mat_size);</span></div>
<div class="line"><a name="l00749"></a><span class="lineno"> 749</span> </div>
<div class="line"><a name="l00750"></a><span class="lineno"> 750</span>  Q = <a class="code" href="classviennacl_1_1identity__matrix.html">viennacl::identity_matrix<SCALARTYPE></a>(Q.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>());</div>
<div class="line"><a name="l00751"></a><span class="lineno"> 751</span> </div>
<div class="line"><a name="l00752"></a><span class="lineno"> 752</span>  <span class="comment">// reduce to tridiagonal form</span></div>
<div class="line"><a name="l00753"></a><span class="lineno"> 753</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#acba51b008828151aabb684d1bb9b350f">detail::tridiagonal_reduction</a>(A, Q);</div>
<div class="line"><a name="l00754"></a><span class="lineno"> 754</span> </div>
<div class="line"><a name="l00755"></a><span class="lineno"> 755</span>  <span class="comment">// pack diagonal and super-diagonal</span></div>
<div class="line"><a name="l00756"></a><span class="lineno"> 756</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a9bb0d10b3784c0eec40296cd94f1bd38">viennacl::linalg::bidiag_pack</a>(A, vcl_D, vcl_E);</div>
<div class="line"><a name="l00757"></a><span class="lineno"> 757</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">copy</a>(vcl_D, D);</div>
<div class="line"><a name="l00758"></a><span class="lineno"> 758</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">copy</a>(vcl_E, E);</div>
<div class="line"><a name="l00759"></a><span class="lineno"> 759</span> </div>
<div class="line"><a name="l00760"></a><span class="lineno"> 760</span>  <span class="comment">// find eigenvalues of symmetric tridiagonal matrix</span></div>
<div class="line"><a name="l00761"></a><span class="lineno"> 761</span>  <span class="keywordflow">if</span>(is_symmetric)</div>
<div class="line"><a name="l00762"></a><span class="lineno"> 762</span>  {</div>
<div class="line"><a name="l00763"></a><span class="lineno"> 763</span>  <a class="code" href="namespaceviennacl_1_1linalg.html#a3fe3eb20d4dcda794259fd6a6d30afb6">viennacl::linalg::tql2</a>(Q, D, E);</div>
<div class="line"><a name="l00764"></a><span class="lineno"> 764</span> </div>
<div class="line"><a name="l00765"></a><span class="lineno"> 765</span>  }</div>
<div class="line"><a name="l00766"></a><span class="lineno"> 766</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00767"></a><span class="lineno"> 767</span>  {</div>
<div class="line"><a name="l00768"></a><span class="lineno"> 768</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#afb7f93e8826f0e5c8f0c83a825a28cc8">detail::hqr2</a>(A, Q, D, E);</div>
<div class="line"><a name="l00769"></a><span class="lineno"> 769</span>  }</div>
<div class="line"><a name="l00770"></a><span class="lineno"> 770</span> </div>
<div class="line"><a name="l00771"></a><span class="lineno"> 771</span> </div>
<div class="line"><a name="l00772"></a><span class="lineno"> 772</span>  boost::numeric::ublas::matrix<SCALARTYPE> eigen_values(A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(), A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>());</div>
<div class="line"><a name="l00773"></a><span class="lineno"> 773</span>  eigen_values.clear();</div>
<div class="line"><a name="l00774"></a><span class="lineno"> 774</span> </div>
<div class="line"><a name="l00775"></a><span class="lineno"> 775</span>  <span class="keywordflow">for</span> (<a class="code" href="namespaceviennacl.html#a98a0afcc513111ffa0bd138f891930df">vcl_size_t</a> i = 0; i < A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>(); i++)</div>
<div class="line"><a name="l00776"></a><span class="lineno"> 776</span>  {</div>
<div class="line"><a name="l00777"></a><span class="lineno"> 777</span>  <span class="keywordflow">if</span>(std::fabs(E[i]) < <a class="code" href="tests_2src_2bisect_8cpp.html#a6ebf6899d6c1c8b7b9d09be872c05aae">EPS</a>)</div>
<div class="line"><a name="l00778"></a><span class="lineno"> 778</span>  {</div>
<div class="line"><a name="l00779"></a><span class="lineno"> 779</span>  eigen_values(i, i) = D[i];</div>
<div class="line"><a name="l00780"></a><span class="lineno"> 780</span>  }</div>
<div class="line"><a name="l00781"></a><span class="lineno"> 781</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00782"></a><span class="lineno"> 782</span>  {</div>
<div class="line"><a name="l00783"></a><span class="lineno"> 783</span>  eigen_values(i, i) = D[i];</div>
<div class="line"><a name="l00784"></a><span class="lineno"> 784</span>  eigen_values(i, i + 1) = E[i];</div>
<div class="line"><a name="l00785"></a><span class="lineno"> 785</span>  eigen_values(i + 1, i) = -E[i];</div>
<div class="line"><a name="l00786"></a><span class="lineno"> 786</span>  eigen_values(i + 1, i + 1) = D[i];</div>
<div class="line"><a name="l00787"></a><span class="lineno"> 787</span>  i++;</div>
<div class="line"><a name="l00788"></a><span class="lineno"> 788</span>  }</div>
<div class="line"><a name="l00789"></a><span class="lineno"> 789</span>  }</div>
<div class="line"><a name="l00790"></a><span class="lineno"> 790</span> </div>
<div class="line"><a name="l00791"></a><span class="lineno"> 791</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">copy</a>(eigen_values, A);</div>
<div class="line"><a name="l00792"></a><span class="lineno"> 792</span>  }</div>
<div class="line"><a name="l00793"></a><span class="lineno"> 793</span> }</div>
<div class="line"><a name="l00794"></a><span class="lineno"> 794</span> </div>
<div class="line"><a name="l00795"></a><span class="lineno"> 795</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE></div>
<div class="line"><a name="l00796"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#abe64190e92ee58ad753947142204d0f9"> 796</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg.html#abe64190e92ee58ad753947142204d0f9">qr_method_nsm</a>(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a>& A,</div>
<div class="line"><a name="l00797"></a><span class="lineno"> 797</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a>& Q,</div>
<div class="line"><a name="l00798"></a><span class="lineno"> 798</span>  std::vector<SCALARTYPE>& D,</div>
<div class="line"><a name="l00799"></a><span class="lineno"> 799</span>  std::vector<SCALARTYPE>& E</div>
<div class="line"><a name="l00800"></a><span class="lineno"> 800</span>  )</div>
<div class="line"><a name="l00801"></a><span class="lineno"> 801</span> {</div>
<div class="line"><a name="l00802"></a><span class="lineno"> 802</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a4983f4960a80f96d1dc3ff5ff23a0ffa">detail::qr_method</a>(A, Q, D, E, <span class="keyword">false</span>);</div>
<div class="line"><a name="l00803"></a><span class="lineno"> 803</span> }</div>
<div class="line"><a name="l00804"></a><span class="lineno"> 804</span> </div>
<div class="line"><a name="l00805"></a><span class="lineno"> 805</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE></div>
<div class="line"><a name="l00806"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71"> 806</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71">qr_method_sym</a>(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a>& A,</div>
<div class="line"><a name="l00807"></a><span class="lineno"> 807</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a>& Q,</div>
<div class="line"><a name="l00808"></a><span class="lineno"> 808</span>  std::vector<SCALARTYPE>& D</div>
<div class="line"><a name="l00809"></a><span class="lineno"> 809</span>  )</div>
<div class="line"><a name="l00810"></a><span class="lineno"> 810</span> {</div>
<div class="line"><a name="l00811"></a><span class="lineno"> 811</span>  std::vector<SCALARTYPE> E(A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>());</div>
<div class="line"><a name="l00812"></a><span class="lineno"> 812</span> </div>
<div class="line"><a name="l00813"></a><span class="lineno"> 813</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a4983f4960a80f96d1dc3ff5ff23a0ffa">detail::qr_method</a>(A, Q, D, E, <span class="keyword">true</span>);</div>
<div class="line"><a name="l00814"></a><span class="lineno"> 814</span> }</div>
<div class="line"><a name="l00815"></a><span class="lineno"> 815</span> </div>
<div class="line"><a name="l00816"></a><span class="lineno"> 816</span> <span class="keyword">template</span> <<span class="keyword">typename</span> SCALARTYPE></div>
<div class="line"><a name="l00817"></a><span class="lineno"><a class="line" href="namespaceviennacl_1_1linalg.html#aec312fb569dcc41351adb8aeacbea571"> 817</a></span> <span class="keywordtype">void</span> <a class="code" href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71">qr_method_sym</a>(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a>& A,</div>
<div class="line"><a name="l00818"></a><span class="lineno"> 818</span>  <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<SCALARTYPE></a>& Q,</div>
<div class="line"><a name="l00819"></a><span class="lineno"> 819</span>  <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<SCALARTYPE></a>& D</div>
<div class="line"><a name="l00820"></a><span class="lineno"> 820</span>  )</div>
<div class="line"><a name="l00821"></a><span class="lineno"> 821</span> {</div>
<div class="line"><a name="l00822"></a><span class="lineno"> 822</span>  std::vector<SCALARTYPE> std_D(D.<a class="code" href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">size</a>());</div>
<div class="line"><a name="l00823"></a><span class="lineno"> 823</span>  std::vector<SCALARTYPE> E(A.<a class="code" href="classviennacl_1_1matrix__base.html#a24e4f5fa27a1af5ad47e52a97c065d68">size1</a>());</div>
<div class="line"><a name="l00824"></a><span class="lineno"> 824</span> </div>
<div class="line"><a name="l00825"></a><span class="lineno"> 825</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(D, std_D);</div>
<div class="line"><a name="l00826"></a><span class="lineno"> 826</span>  <a class="code" href="namespaceviennacl_1_1linalg_1_1detail.html#a4983f4960a80f96d1dc3ff5ff23a0ffa">detail::qr_method</a>(A, Q, std_D, E, <span class="keyword">true</span>);</div>
<div class="line"><a name="l00827"></a><span class="lineno"> 827</span>  <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(std_D, D);</div>
<div class="line"><a name="l00828"></a><span class="lineno"> 828</span> }</div>
<div class="line"><a name="l00829"></a><span class="lineno"> 829</span> </div>
<div class="line"><a name="l00830"></a><span class="lineno"> 830</span> }</div>
<div class="line"><a name="l00831"></a><span class="lineno"> 831</span> }</div>
<div class="line"><a name="l00832"></a><span class="lineno"> 832</span> </div>
<div class="line"><a name="l00833"></a><span class="lineno"> 833</span> <span class="preprocessor">#endif</span></div>
<div class="ttc" id="tests_2src_2bisect_8cpp_html_a6ebf6899d6c1c8b7b9d09be872c05aae"><div class="ttname"><a href="tests_2src_2bisect_8cpp.html#a6ebf6899d6c1c8b7b9d09be872c05aae">EPS</a></div><div class="ttdeci">#define EPS</div><div class="ttdef"><b>Definition:</b> <a href="tests_2src_2bisect_8cpp_source.html#l00038">bisect.cpp:38</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_abe90cd38a99c15edfb19d57c524dd2d5"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#abe90cd38a99c15edfb19d57c524dd2d5">viennacl::linalg::detail::final_iter_update</a></div><div class="ttdeci">void final_iter_update(MatrixT &A, int n, int last_n, SCALARTYPE q, SCALARTYPE p)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00128">qr-method.hpp:128</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix_html_a8302dc145b6238b4a8859b775192da6e"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a8302dc145b6238b4a8859b775192da6e">viennacl::linalg::detail::FastMatrix::row</a></div><div class="ttdeci">SCALARTYPE * row(int i)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00211">qr-method.hpp:211</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix_html"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html">viennacl::linalg::detail::FastMatrix</a></div><div class="ttdoc">Internal helper class representing a row-major dense matrix used for the QR method for the purpose of...</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00193">qr-method.hpp:193</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="classviennacl_1_1ocl_1_1kernel_html"><div class="ttname"><a href="classviennacl_1_1ocl_1_1kernel.html">viennacl::ocl::kernel</a></div><div class="ttdoc">Represents an OpenCL kernel within ViennaCL. </div><div class="ttdef"><b>Definition:</b> <a href="kernel_8hpp_source.html#l00058">kernel.hpp:58</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="namespaceviennacl_1_1linalg_html_a34c93371a5e45fe498bf1dc4dd475497"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a34c93371a5e45fe498bf1dc4dd475497">viennacl::linalg::house_update_A_right</a></div><div class="ttdeci">void house_update_A_right(matrix_base< NumericT > &A, vector_base< NumericT > &D)</div><div class="ttdoc">This function applies a householder transformation to a matrix: A <- A * P with a householder reflect...</div><div class="ttdef"><b>Definition:</b> <a href="matrix__operations_8hpp_source.html#l01018">matrix_operations.hpp:1018</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_aa756f5d6820722094cae0d8b9bb6d5e2"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2">viennacl::traits::size1</a></div><div class="ttdeci">vcl_size_t size1(MatrixType const &mat)</div><div class="ttdoc">Generic routine for obtaining the number of rows of a matrix (ViennaCL, uBLAS, etc.) </div><div class="ttdef"><b>Definition:</b> <a href="size_8hpp_source.html#l00163">size.hpp:163</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a3fe3eb20d4dcda794259fd6a6d30afb6"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a3fe3eb20d4dcda794259fd6a6d30afb6">viennacl::linalg::tql2</a></div><div class="ttdeci">void tql2(matrix_base< SCALARTYPE, F > &Q, VectorType &d, VectorType &e)</div><div class="ttdef"><b>Definition:</b> <a href="tql2_8hpp_source.html#l00131">tql2.hpp:131</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_ab58751eae7fc9a4af532b447728880ab"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#ab58751eae7fc9a4af532b447728880ab">viennacl::linalg::house_update_QL</a></div><div class="ttdeci">void house_update_QL(matrix_base< NumericT > &Q, vector_base< NumericT > &D, vcl_size_t A_size1)</div><div class="ttdoc">This function updates the matrix Q, which is needed for the computation of the eigenvectors. </div><div class="ttdef"><b>Definition:</b> <a href="matrix__operations_8hpp_source.html#l01053">matrix_operations.hpp:1053</a></div></div>
<div class="ttc" id="classviennacl_1_1ocl_1_1context_html"><div class="ttname"><a href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a></div><div class="ttdoc">Manages an OpenCL context and provides the respective convenience functions for creating buffers...</div><div class="ttdef"><b>Definition:</b> <a href="ocl_2context_8hpp_source.html#l00055">context.hpp:55</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a6308577bb366f4b0698dc43ff75ad4a5"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a6308577bb366f4b0698dc43ff75ad4a5">viennacl::linalg::detail::final_iter_update_gpu</a></div><div class="ttdeci">void final_iter_update_gpu(matrix_base< SCALARTYPE > &A, int n, int last_n, SCALARTYPE q, SCALARTYPE p)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00042">qr-method.hpp:42</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a3a439370108ddfa59c2fcb4136b13c8d"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a3a439370108ddfa59c2fcb4136b13c8d">viennacl::linalg::SVD_UPDATE_QR_COLUMN_KERNEL</a></div><div class="ttdeci">const std::string SVD_UPDATE_QR_COLUMN_KERNEL</div><div class="ttdef"><b>Definition:</b> <a href="qr-method-common_8hpp_source.html#l00054">qr-method-common.hpp:54</a></div></div>
<div class="ttc" id="tql2_8hpp_html"><div class="ttname"><a href="tql2_8hpp.html">tql2.hpp</a></div><div class="ttdoc">Implementation of the tql2-algorithm for eigenvalue computations. </div></div>
<div class="ttc" id="classviennacl_1_1matrix__base_html"><div class="ttname"><a href="classviennacl_1_1matrix__base.html">viennacl::matrix_base</a></div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00103">matrix_def.hpp:103</a></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_aad4cd2951549618c93f74ff26444675f"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#aad4cd2951549618c93f74ff26444675f">viennacl::linalg::detail::transpose</a></div><div class="ttdeci">void transpose(matrix_base< SCALARTYPE > &A)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method-common_8hpp_source.html#l00107">qr-method-common.hpp:107</a></div></div>
<div class="ttc" id="classviennacl_1_1identity__matrix_html"><div class="ttname"><a href="classviennacl_1_1identity__matrix.html">viennacl::identity_matrix</a></div><div class="ttdoc">Represents a vector consisting of 1 at a given index and zeros otherwise. To be used as an initialize...</div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00069">matrix_def.hpp:69</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_a0cd530f8a76a5fb3d60a9230bea30bca"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#a0cd530f8a76a5fb3d60a9230bea30bca">viennacl::traits::internal_size</a></div><div class="ttdeci">vcl_size_t internal_size(vector_base< NumericT > const &vec)</div><div class="ttdoc">Helper routine for obtaining the buffer length of a ViennaCL vector. </div><div class="ttdef"><b>Definition:</b> <a href="size_8hpp_source.html#l00375">size.hpp:375</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a5d46fe9558b0e462f10fd44942ad4fc6"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a5d46fe9558b0e462f10fd44942ad4fc6">viennacl::linalg::detail::max</a></div><div class="ttdeci">T max(const T &lhs, const T &rhs)</div><div class="ttdoc">Maximum. </div><div class="ttdef"><b>Definition:</b> <a href="linalg_2detail_2bisect_2util_8hpp_source.html#l00059">util.hpp:59</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a5852aa7527c0599681f1b0fbc753d357"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a5852aa7527c0599681f1b0fbc753d357">viennacl::linalg::detail::prepare_householder_vector</a></div><div class="ttdeci">void prepare_householder_vector(matrix_base< SCALARTYPE > &A, vector_base< SCALARTYPE > &D, vcl_size_t size, vcl_size_t row_start, vcl_size_t col_start, vcl_size_t start, bool is_column)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method-common_8hpp_source.html#l00165">qr-method-common.hpp:165</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a0ce6438b322e096df65112ac6536b0b1"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a0ce6438b322e096df65112ac6536b0b1">viennacl::linalg::detail::update_float_QR_column_gpu</a></div><div class="ttdeci">void update_float_QR_column_gpu(matrix_base< SCALARTYPE > &A, const VectorType &buf, viennacl::vector< SCALARTYPE > &buf_vcl, int m, int n, int last_n, bool)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00082">qr-method.hpp:82</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="qr-method-common_8hpp_html"><div class="ttname"><a href="qr-method-common_8hpp.html">qr-method-common.hpp</a></div><div class="ttdoc">Common routines used for the QR method and SVD. Experimental. </div></div>
<div class="ttc" id="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1svd_html"><div class="ttname"><a href="structviennacl_1_1linalg_1_1opencl_1_1kernels_1_1svd.html">viennacl::linalg::opencl::kernels::svd</a></div><div class="ttdoc">Main kernel class for generating OpenCL kernels for singular value decomposition of dense matrices...</div><div class="ttdef"><b>Definition:</b> <a href="opencl_2kernels_2svd_8hpp_source.html#l00644">svd.hpp:644</a></div></div>
<div class="ttc" id="classviennacl_1_1ocl_1_1context_html_afe68ad8c2df449f40f45db6605038946"><div class="ttname"><a href="classviennacl_1_1ocl_1_1context.html#afe68ad8c2df449f40f45db6605038946">viennacl::ocl::context::get_kernel</a></div><div class="ttdeci">viennacl::ocl::kernel & get_kernel(std::string const &program_name, std::string const &kernel_name)</div><div class="ttdoc">Convenience function for retrieving the kernel of a program directly from the context. </div><div class="ttdef"><b>Definition:</b> <a href="ocl_2context_8hpp_source.html#l00605">context.hpp:605</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a9bb0d10b3784c0eec40296cd94f1bd38"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a9bb0d10b3784c0eec40296cd94f1bd38">viennacl::linalg::bidiag_pack</a></div><div class="ttdeci">void bidiag_pack(matrix_base< NumericT > &A, VectorType &dh, VectorType &sh)</div><div class="ttdoc">This function stores the diagonal and the superdiagonal of a matrix in two vectors. </div><div class="ttdef"><b>Definition:</b> <a href="matrix__operations_8hpp_source.html#l00901">matrix_operations.hpp:901</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1traits_html_a68603a1e1ca1bfb6d107831ba5096786"><div class="ttname"><a href="namespaceviennacl_1_1traits.html#a68603a1e1ca1bfb6d107831ba5096786">viennacl::traits::start</a></div><div class="ttdeci">result_of::size_type< T >::type start(T const &obj)</div><div class="ttdef"><b>Definition:</b> <a href="start_8hpp_source.html#l00044">start.hpp:44</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_abe64190e92ee58ad753947142204d0f9"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#abe64190e92ee58ad753947142204d0f9">viennacl::linalg::qr_method_nsm</a></div><div class="ttdeci">void qr_method_nsm(viennacl::matrix< SCALARTYPE > &A, viennacl::matrix< SCALARTYPE > &Q, std::vector< SCALARTYPE > &D, std::vector< SCALARTYPE > &E)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00796">qr-method.hpp:796</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix_html_a98acf809bbc8cb44eef44d87e83a4a05"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a98acf809bbc8cb44eef44d87e83a4a05">viennacl::linalg::detail::FastMatrix::begin</a></div><div class="ttdeci">SCALARTYPE * begin()</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00216">qr-method.hpp:216</a></div></div>
<div class="ttc" id="classviennacl_1_1vector__base_html"><div class="ttname"><a href="classviennacl_1_1vector__base.html">viennacl::vector_base</a></div><div class="ttdoc">Common base class for dense vectors, vector ranges, and vector slices. </div><div class="ttdef"><b>Definition:</b> <a href="vector__def_8hpp_source.html#l00104">vector_def.hpp:104</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a706c4d0b456ec669c3a8c2eea8cc3fc4"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a706c4d0b456ec669c3a8c2eea8cc3fc4">viennacl::linalg::house_update_A_left</a></div><div class="ttdeci">void house_update_A_left(matrix_base< NumericT > &A, vector_base< NumericT > &D, vcl_size_t start)</div><div class="ttdoc">This function applies a householder transformation to a matrix. A <- P * A with a householder reflect...</div><div class="ttdef"><b>Definition:</b> <a href="matrix__operations_8hpp_source.html#l00981">matrix_operations.hpp:981</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="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix_html_ae44eed79eed4c1f5ce358963e48fd459"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ae44eed79eed4c1f5ce358963e48fd459">viennacl::linalg::detail::FastMatrix::end</a></div><div class="ttdeci">SCALARTYPE * end()</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00221">qr-method.hpp:221</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="namespaceviennacl_1_1linalg_1_1detail_html_acba51b008828151aabb684d1bb9b350f"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#acba51b008828151aabb684d1bb9b350f">viennacl::linalg::detail::tridiagonal_reduction</a></div><div class="ttdeci">void tridiagonal_reduction(matrix_base< SCALARTYPE > &A, matrix_base< SCALARTYPE > &Q)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00713">qr-method.hpp:713</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="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix_html_ab677d20b12fe7b71e76252077fec4abb"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#ab677d20b12fe7b71e76252077fec4abb">viennacl::linalg::detail::FastMatrix::data</a></div><div class="ttdeci">std::vector< SCALARTYPE > data</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00226">qr-method.hpp:226</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a4983f4960a80f96d1dc3ff5ff23a0ffa"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a4983f4960a80f96d1dc3ff5ff23a0ffa">viennacl::linalg::detail::qr_method</a></div><div class="ttdeci">void qr_method(viennacl::matrix< SCALARTYPE > &A, viennacl::matrix< SCALARTYPE > &Q, std::vector< SCALARTYPE > &D, std::vector< SCALARTYPE > &E, bool is_symmetric=true)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00728">qr-method.hpp:728</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix_html_a46b6503e572003d0fd4e9b30ca51572d"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a46b6503e572003d0fd4e9b30ca51572d">viennacl::linalg::detail::FastMatrix::operator()</a></div><div class="ttdeci">SCALARTYPE & operator()(int i, int j)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00206">qr-method.hpp:206</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_a4d6d704d39ec27eb15a604580eb1df5b"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#a4d6d704d39ec27eb15a604580eb1df5b">viennacl::linalg::detail::update_float_QR_column</a></div><div class="ttdeci">void update_float_QR_column(MatrixT &A, const std::vector< SCALARTYPE > &buf, int m, int n, int last_i, bool is_triangular)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00145">qr-method.hpp:145</a></div></div>
<div class="ttc" id="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix_html_a0c734d3daf535e0d567c2fd5f59cc451"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a0c734d3daf535e0d567c2fd5f59cc451">viennacl::linalg::detail::FastMatrix::FastMatrix</a></div><div class="ttdeci">FastMatrix(vcl_size_t sz, vcl_size_t internal_size)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00201">qr-method.hpp:201</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1ocl_html_a5f2022f653ea1cf364d20e3ff84dcada"><div class="ttname"><a href="namespaceviennacl_1_1ocl.html#a5f2022f653ea1cf364d20e3ff84dcada">viennacl::ocl::enqueue</a></div><div class="ttdeci">void enqueue(KernelType &k, viennacl::ocl::command_queue const &queue)</div><div class="ttdoc">Enqueues a kernel in the provided queue. </div><div class="ttdef"><b>Definition:</b> <a href="enqueue_8hpp_source.html#l00050">enqueue.hpp:50</a></div></div>
<div class="ttc" id="vector_8hpp_html"><div class="ttname"><a href="vector_8hpp.html">vector.hpp</a></div><div class="ttdoc">The vector type with operator-overloads and proxy classes is defined here. Linear algebra operations ...</div></div>
<div class="ttc" id="classviennacl_1_1matrix__base_html_a15ec879f9e85a6fc209454b0bf137084"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a15ec879f9e85a6fc209454b0bf137084">viennacl::matrix_base::row_major</a></div><div class="ttdeci">bool row_major() const </div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00248">matrix_def.hpp:248</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="classviennacl_1_1vector__base_html_a15c47ae4326098aeaa4ed6b91fc6df9b"><div class="ttname"><a href="classviennacl_1_1vector__base.html#a15c47ae4326098aeaa4ed6b91fc6df9b">viennacl::vector_base::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="namespaceviennacl_1_1linalg_html_a8477d884683dafc7e6ca04f2e02a1d1f"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a8477d884683dafc7e6ca04f2e02a1d1f">viennacl::linalg::SVD_FINAL_ITER_UPDATE_KERNEL</a></div><div class="ttdeci">const std::string SVD_FINAL_ITER_UPDATE_KERNEL</div><div class="ttdef"><b>Definition:</b> <a href="qr-method-common_8hpp_source.html#l00053">qr-method-common.hpp:53</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_afb7f93e8826f0e5c8f0c83a825a28cc8"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#afb7f93e8826f0e5c8f0c83a825a28cc8">viennacl::linalg::detail::hqr2</a></div><div class="ttdeci">void hqr2(viennacl::matrix< SCALARTYPE > &vcl_H, viennacl::matrix< SCALARTYPE > &V, VectorType &d, VectorType &e)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00236">qr-method.hpp:236</a></div></div>
<div class="ttc" id="classviennacl_1_1matrix__base_html_a00e30fdc61081a73995b54175a91d220"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a00e30fdc61081a73995b54175a91d220">viennacl::matrix_base< NumericT >::internal_size2</a></div><div class="ttdeci">size_type internal_size2() const</div><div class="ttdoc">Returns the internal number of columns. Usually required for launching OpenCL kernels only...</div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00240">matrix_def.hpp:240</a></div></div>
<div class="ttc" id="classviennacl_1_1matrix__base_html_a82018b4e169973bdfb9d3be68ceb5be0"><div class="ttname"><a href="classviennacl_1_1matrix__base.html#a82018b4e169973bdfb9d3be68ceb5be0">viennacl::matrix_base::internal_size1</a></div><div class="ttdeci">size_type internal_size1() const </div><div class="ttdoc">Returns the internal number of rows. Usually required for launching OpenCL kernels only...</div><div class="ttdef"><b>Definition:</b> <a href="matrix__def_8hpp_source.html#l00238">matrix_def.hpp:238</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="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix_html_a08da5e21bebae44672a6324dbfb8db75"><div class="ttname"><a href="classviennacl_1_1linalg_1_1detail_1_1_fast_matrix.html#a08da5e21bebae44672a6324dbfb8db75">viennacl::linalg::detail::FastMatrix::FastMatrix</a></div><div class="ttdeci">FastMatrix()</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00196">qr-method.hpp:196</a></div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_1_1detail_html_ac4a1dce18e411cc95eb72efd802f50d8"><div class="ttname"><a href="namespaceviennacl_1_1linalg_1_1detail.html#ac4a1dce18e411cc95eb72efd802f50d8">viennacl::linalg::detail::householder_twoside</a></div><div class="ttdeci">bool householder_twoside(matrix_base< SCALARTYPE > &A, matrix_base< SCALARTYPE > &Q, vector_base< SCALARTYPE > &D, vcl_size_t start)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00694">qr-method.hpp:694</a></div></div>
<div class="ttc" id="namespaceviennacl_html_aaa5c8726b45bc89a523ca2fa8c42107a"><div class="ttname"><a href="namespaceviennacl.html#aaa5c8726b45bc89a523ca2fa8c42107a">viennacl::fast_copy</a></div><div class="ttdeci">void fast_copy(const const_vector_iterator< SCALARTYPE, ALIGNMENT > &gpu_begin, const const_vector_iterator< SCALARTYPE, ALIGNMENT > &gpu_end, CPU_ITERATOR cpu_begin)</div></div>
<div class="ttc" id="namespaceviennacl_1_1linalg_html_a51cbe06645207f9b3054e8725269cc71"><div class="ttname"><a href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71">viennacl::linalg::qr_method_sym</a></div><div class="ttdeci">void qr_method_sym(viennacl::matrix< SCALARTYPE > &A, viennacl::matrix< SCALARTYPE > &Q, std::vector< SCALARTYPE > &D)</div><div class="ttdef"><b>Definition:</b> <a href="qr-method_8hpp_source.html#l00806">qr-method.hpp:806</a></div></div>
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